European Symposium on Computer Aided Process Engineering - 13, Volume 14: 36th European Symposium of the Working Party on Computer Aided Process Engineering (Computer Aided Chemical Engineering)

EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING -13

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:

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 (I. PallaiandZ. Fonyo, Editors) Part B: Systems (I. 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) European Symposium on Computer Aided Process Engineering-10 (S. Pierucci, Editor) European Symposium 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 Toolsfor 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)

COMPUTER-AIDED CHEMICAL ENGINEERING, 14

EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING -13 36th European Symposium of the Working Party on Computer Aided Process Engineering ESCAPE-13,1-4 June, 2003, Lappeenranta, Finland

Edited by

Andrzej Kraslawski Ilkka Turunen Lappeenranta University of Technology Lappeenranta Finland

2003 ELSEVIER Amsterdam - Boston - London - New York - Oxford - Paris San Diego - San Francisco - Singapore - Sydney -Toiiyo

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Preface

This book contains papers presented at the 13th European Symposium on Computer Aided Process Engineering (ESCAPE-13) held in Lappeenranta, Finland from the V^ to 4* June 2003. The symposia on Computer Aided Process Engineering (CAPE) have been promoted by the Working Party on CAPE of the European Federation of Chemical Engineering (EFCE) since 1968. The most recent symposia were organised in The Hague, The Netherlands 2002, (ESCAPE-12), Kolding, Denmark, 2001 (ESCAPE-U), and Florence, Italy, 2000 (ESCAPE-10) The series of ESCAPE symposia assist in bringing together scientists, students and engineers from academia and industry, which are active in research and application of CAPE. The objective of ESCAPE-13 is to highlight the use of computers and information technology tools on five specific themes: 7. Process Design, 2. Process Control and Dynamics, 3. Modelling, Simulation and Optimisation, 4. Applications in Pulp and Paper Industry, 5. Applications in Biotechnology. The main theme for ESCAPE-13 is Expanding Application Field of CAPE Methods and Tools. It means extending CAPE approach, mainly used in chemical industry, into different sectors of process industry and promoting CAPE applications aiming at generation of new businesses and technologies. This book includes 190 papers selected from 391 submitted abstracts. All papers have been reviewed by 33 members of the international scientific committee. The selection process involved review of abstracts, manuscripts and final acceptance of the revised manuscripts. We are very grateful to the members of international scientific committee for their comments and recommendations. This book is the fourth ESCAPE Symposium Proceedings included in the series on Computer Aided Chemical Engineering. We hope that, as the previous Proceedings, it will contribute to the progress in computer aided process and product engineering.

Andrzej Kraslawski Ilkka Turunen

VI

International Scientific Committee Andrzej Kraslawski Ilkka Turunen

J. Aittamaa A. Barbosa-Povoa L. T. Biegler D. Bogle B. Braunschweig K. Edelmann Z. Fonyo R. Gani U.Gren P. Glavie J. Grievink I. E. Grossmann L. Hammarstrom G. Heyen A. Isakson S. B. J0rgensen B. Kalitventzeff

(Finland) (Portugal) (USA) (United Kingdom) (France) (Finland) (Hungary) (Denmark) (Sweden) (Slovenia) (The Netherlands) (USA) (Finland) (Belgium) (Sweden) (Denmark) (Belgium)

(Finland, co-chairman) (Finland, co-chairman)

S. Karrila J-M. Le Lann K. Leiviska W. Marquardt J. Paloschi C. Pantelides T. Perris S. Pierucci H. Pingen L. Puigjaner Y. Qian H. Schmidt-Traub S. Skogestad P. Taskinen S. de Wolf T. Westerlund

(USA) (France) (Finland) (Germany) (United Kingdom) (United Kingdom) (United Kingdom) (Italy) (The Netherlands) (Spain) (P. R. China) (Germany) (Norway) (Finland) (The Netherlands) (Finland)

National Organising Committee Andrzej Kraslawski Ilkka Turunen

(Finland, co-chairman) (Finland, co-chairman)

J. Aittamaa M. Hurme M. Karlsson K. Leiviska P. Piiroinen R. Ritala P. Taskinen A. Vuori T. Westerlund

Helsinki University of Technology Helsinki University of Technology Metso Corporation Oulu University Danisco Sugar Oy Keskuslaboratorio Oy Outokumpu Research Oy Kemira Oyj Abo Akademi University

vu

Contents Keynote Paper Bogle, I.D.L. Computer A ided Biochemical Process Engineering

1

Contributed Papers Process Design Abebe, S., Shang, Z., Kokossis, A. A Two-stage Optimisation Approach to the Design of Water-using Systems in Process Plants 11 Andersen, N.K., Coll, N., Jensen, N., Gani, R., Uerdingen, E., Fischer, U., Hungerbiihler, K. Generation and Screening of Retrofit Alternatives Using a Systematic IndicatorBased Retrofit Analysis Method 17 Balendra, S., Bogle, I.D.L. A Comparison of Flowsheet Solving Strategies Using Interval Global Optimisation Methods 23 Bayer, B., von Wedel, L., Marquardt, W. An Integration of Design Data and Mathematical Models in Chemical Process Design 29 Berard, F., Azzaro-Pantel, C , Pibouleau, L., Domenech, S. A Production Planning Strategic Framework for Batch Plants 35 Bonfill, A., Canton, J., Bagajewicz, M., Espuna, A., Puigjaner, L. Managing Financial Risk in Scheduling of Batch Plants 41 Borissova, A., Fairweather, M., Goltz, G.E. A Network Model for the Design of Agile Plants 47 Borissova, A., Fairweather, M., Goltz, G.E. A Vision of Computer Aids for the Design of Agile Production Plants 53 Caballero, J.A., Reyes-Labarta, J.A., Grossmann, I.E. Synthesis of Integrated Distillation Systems 59 Cafaro, D.C., Cerda, J. A Continuous-Time Approach to Multiproduct Pipeline Scheduling 65 Chatzidoukas, C , Kiparissides, C , Perkins, J.D., Pistikopoulos, E.N. Optimal Grade Transition Campaign Scheduling in a Gas-Phase Polyolefin FBR Using Mixed Integer Dynamic Optimization 11 Chavali, S., Huismann, T., Lin, B., Miller, D.C., Camarda, K.V. Environmentally-Benign Transition Metal Catalyst Design using Optimization Techniques 11 Cisternas, L.A., Cueto, J.Y., Swaney, R.E. Complete Separation System Synthesis of Fractional Crystallization Processes 83

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Dumont, M.-N., Heyen, G. Mathematical Modelling and Design of an Advanced Once-Through Heat Recovery Steam Generator Duque, J., Barbosa-Povoa, A.P.F.D., Novais, A.Q. Synthesis and Optimisation of the Recovery Route for Residual Products Eden, M.R., J0rgensen, S.B., Gani, R. A New Modeling Approach for Future Challenges in Process and Product Design Emet, S., Westerlund, T. Solving an MINLP Problem Including Partial Differential Algebraic Constraints Using Branch and Bound and Cutting Plane Techniques Farkas, T., Avramenko, Y., Kraslawski, A., Lelkes, Z., Nystrom, L. Selection of MINLP Model of Distillation Column Synthesis by Case-Based Reasoning Fraga, E.S., Papageorgiou L.G., Sharma, R. Discrete Model and Visualization Interface for Water Distribution Network Design Galvez, E.D., Zavala, M.F., Magna, J.A., Cisternas, L.A. Optimal Design of Mineral Flotation Circuits Gerogiorgis, D.I., Ydstie, B.E. An MINLP Model for the Conceptual Design of a Carbothermic Aluminium Reactor Giovanoglou, A., Adjiman, C.S., Galindo, A., Jackson, G. Towards the Identification of Optimal Solvents for Long Chain Alkanes with the SAFT Equation of State Godat, J., Marechal, F. Combined Optimisation and Process Integration Techniques for the Synthesis of Fuel Cells Systems Guadix, A., S0rensen, E., Papageorgiou, L.G., Guadix, E.M. Optimal Design and Operation of Batch Ultrafiltration Systems Heimann, F. Process Intensification through the Combined Use of Process Simulation and Miniplant Technology Huang, W., Chung, P.W.H. A Constraint Approach for Rescheduling Batch Processing Plants Including Pipeless Plants Irsic Bedenik, N., Pahor, B., Kravanja, Z. Integrated MINLP Synthesis of Overall Process Flowsheets by a Combined Synthesis / Analysis Approach Kotoulas, C., Pladis, P., Papadopoulos, E., Kiparissides, C. Computer Aided Design ofStyrene Batch Suspension Polymerization Reactors Kovae Kralj, A., Glavic, P. Waste Heat Integration Between Processes III: Mixed Integer Nonlinear Programming Model Kulay, L., Jimenez, L., Castells, F., Bafiares-Alcantara, R., Silva, G.A. Integration of Process Modelling and Life Cycle Inventory. Case Study: iPentane Purification Process from Naphtha

89 95

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119 125

131

137

143 149

155

161

167 173

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IX

Lee, S., Logsdon, J.S., Foral, M.J., Grossmann, I.E. Superstructure Optimization of the Olefin Separation Process Lelkes, Z., Rev, E., Steger, C , Varga, V., Fonyo, Z., Horvath, L. Batch Extractive Distillation with Intermediate Boiling Entrainer Lelkes, Z., Szitkai, Z., Farkas, T., Rev, E., Fonyo, Z. Short-cut Design of Batch Extractive Distillation using MINLP Li, X.-N., Rong, B.-G., Kjaslawski, A., Nystrom, L. A Conflict-Based Approach for Process Synthesis with Wastes Minimization Maravelias, C.T., Grossmann, LE. A New Continuous-Time State Task Network Formulation for Short Term Scheduling of Multipurpose Batch Plants Masruroh, N.A., Li, B., Klemes, J. Life Cycle Analysis of a Solar Thermal System with Thermochemical Storage Process Msiza, A.K., Eraser, D.M. Hybrid Synthesis Method For Mass Exchange Networks Oliveira Francisco, A.P., Matos, H.A. Multiperiod Synthesis and Operational Planning of Utility Systems with Environmental Concerns Orban-Mihalyko, E., Lakatos, B.G. Sizing Intermediate Storage with Stochastic Equipment Failures under General Operation Conditions Papaeconomou, I., J0rgensen, S.B., Gani, R., Cordiner, J. Synthesis, Design and Operational Modelling of Batch Processes: An Integrated Approach Pierucci, S., Bombardi, D., Concu, A., Lugli, G. Modelling, Design and Commissioning of a Sustainable Process for VOCs Recovery from Spray Paint Booths Pinto, T., Barbosa-Povoa, A.P.F.D., Novais, A.Q. Comparison Between STN, m-STN and RTNfor the Design of Multipurpose Batch Plants Proios, P., Pistikopoulos, E.N. Generalized Modular Framework for the Representation ofPetlyuk Distillation Columns Rodriguez-Martinez, A., Lopez-Arevalo, I., Banares-Alcantara, R., Aldea, A. A Multi-Modelling Approach for the Retrofit of Processes Rong, B.-G., Kraslawski, A., Turunen, I. Synthesis of Partially Thermally Coupled Column Configurations for Multicomponent Distillations Shang, Z., Kokossis, A. A Multicriteria Process Synthesis Approach to the Design of Sustainable and Economic Utility Systems Srinivasan, R., Chia, K.C., Heikkila, A.-M., Schabel, J. A Decision Support Database for Inherently Safer Design Stalker, I.D., Fraga, E.S., von Wedel, L., Yang, A. Using Design Prototypes to Build an Ontology for Automated Process Design Stalker, I.D., Stalker Firth, R.A., Fraga, E.S. Engineer Computer Interaction for Automated Process Design in COGents

191 197 203 209

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281 287 293 299

Stikkelman, R.M., Herder, P.M., van der Wal, R., Schor, D. Developing a Methanol-Based Industrial Cluster Sundqvist, S., Pajula, E., Ritala, R. Risk Premium and Robustness in Design Optimization of a simplified TMP plant Syrjanen, T.L. Process Design as Part of a Concurrent Plant Design Project Szitkai, Z., Farkas, T., Kravanja, Z., Lelkes, Z., Rev, E., Fonyo, Z. A New MINLP Model for Mass Exchange Network Synthesis Weiten, M., Wozny, G. A Knowledge Based System for the Documentation of Research Concerning Physical and Chemical Processes - System Design and Case Studies for Application Yuceer, M., Atasoy, I., Berber, R. A Semi Heuristic MINLP Algorithm for Production Scheduling Zhao, Ch., Bhushan, M., Venkatasubramanian, V. Roles of Ontology in Automated Process Safety Analysis

305 311 317 323

329 335 341

Process Control and Dynamics Abonyi, J., Arva, P., Nemeth, S., Vincze, Cs., Bodolai, B., Dobosne Horvath, Zs., Nagy, G., Nemeth, M. Operator Support System for Multi Product Processes - Application to Polyethylene Production Alstad, v., Skogestad, S. Combination of Measurements as Controlled Variables for Self-Optimizing Control Badell, M., Romero, J., Puigjaner, L. Integrating Budgeting Models into APS Systems in Batch Chemical Industries Batzias, A.F., Batzias, F.A. A System for Support and Training of Personnel Working in the Electrochemical Treatment of Metallic Surfaces BenqUlou, C , Bagajewicz, M.J., Espufia, A., Puigjaner, L. Sensor-Placement for Dynamic Processes Berezowski, M., Dubaj, D. Chaotic Oscillations in a System of Two Parallel Reactors with Recirculation of Mass Cao, Y., Saha, P. Control Structure Selection for Unstable Processes Using Hankel Singular Value Cristea, M.V., Roman, R., Agachi, S.P. Neural Networks Based Model Predictive Control of the Drying Process Cubillos, F.A., Lima, E.L. Real-Time Optimization Systems Based On Grey-Box Neural Models Duarte, B.P.M., Saraiva, P.M. Change Point Detection for Quality Monitoring of Chemical Processes Engelien, H.K., Skogestad, S. Selecting Appropriate Control Variables for a Heat Integrated Distillation System with Prefractionator Espufia, A., Rodrigues, M.T., Gimeno, L., Puigjaner, L. A Holistic Framework for Supply Chain Management

347

353 359

365 371

377 383 389 395 401

407 413

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Guillen, G., Mele, F.D., Bagajewicz, M., Espuna, A., Puigjaner, L. Management of Financial and Consumer Satisfaction Risks in Supply Chain Design 419 Hyllseth, M., Cameron, D., Havre, K. Operator Training and Operator Support using Multiphase Pipeline Models and Dynamic Process Simulation: Sub-Sea Production and On-Shore Processing 425 Kiss, A.A., Bildea, C.S., Dimian, A.C., ledema, P.D. Unstable Behaviour of Plants with Recycle 431 Kwon, S.P., Kim, Y.H., Cho, J., Yoon, E.S. Development of an Intelligent Multivariable Filtering System based on the RuleBased Method ^2>1 Lee, G., Yoon, E.S. Multiple-Fault Diagnosis Using Dynamic PLS Built on Qualitative Relations 443 Li, H., Gani, R., J0rgensen, S.B. Integration of Design and Control for Energy Integrated Distillation 449 Li, X.X., Qian, Y., Wang, J. Process Monitoring Based on Wavelet Packet Principal Component Analysis 455 Li, X.X., Qian, Y., Wang, J., Qin, S.J. Information Criterion for Determination Time Window Length of Dynamic PCA for Process Monitoring 461 Madar, J., Szeifert, P., Nagy, L., Chovan, T., Abonyi, J. Tendency Model-based Improvement of the Slave Loop in Cascade Temperature Control of Batch Process Units 467 Maurya, M.R., Rengaswamy, R., Venkatasubramanian, V. Consistent Malfunction Diagnosis Inside Control Loops Using Signed Directed Graphs 473 Mele, F.D., Bagajewicz, M., Espuna, A., Puigjaner, L. Financial Risk Control in a Discrete Event Supply Chain 479 Meng, Q.F., Nougues, J.M., Bagajewicz, M.J., Puigjaner, L. Control Application Study Based on PROCEL 485 Mizsey, P., Emtir, M., Racz, L., Lengyel, A., Kraslawski, A., Fonyo, Z. Challenges in Controllability Investigations of Chemical Processes 491 Reinikainen, S.-P., Hoskuldsson, A. Analysis of Linear Dynamic Systems of Low Rank 497 Saxen, B., Nyberg, J. Data Based Classification of Roaster Bed Stability 503 Seferlis, P., Giannelos, N.F. A Two-Layered Optimisation-Based Control Strategy for Multi-Echelon Supply Chain Networks 509 Segovia-Hernandez, J.G., Hernandez, S., Femat, R., Jimenez, A. Dynamic Control of a Petlyuk Column via Proportional-Integral Action with Dynamic Estimation of Uncertainties 515 Segovia-Hernandez, J.G., Hernandez, S., Rico-Ramirez, V., Jimenez, A. Dynamic Study of Thermally Coupled Distillation Sequences Using Proportional - Integral Controllers 521 Vu, T.T.L., Hourigan, J.A., Sleigh, R.W., Ang, M.H., Tade, M.O. Metastable Control of Cooling Crystallisation 527

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Yen, Ch.H., Tsai, P.-F., Jang, S.S. Regional Knowledge Analysis of Artificial Neural Network Models and a Robust Model Predictive Control Architecture

533

Modelling, Simulation and Optimisation Ahola, J., Kangas, j ! , Maunula, T., Tanskanen, J. Optimisation of Automotive Catalytic Converter Warm-Up: Tackling by Guidance of Reactor Modelling Alopaeus, V., Keskinen, K.I., Koskinen, J., Majander, J. Gas-Liquid and Liquid-Liquid System Modeling Using Population Balances for Local Mass Transfer Arellano-Garcia, H., Martini, W., Wendt, M., Li, P., Wozny, G. Robust Optimization of a Reactive Semibatch Distillation Process under Uncertainty Attarakih, M.M., Bart, H.-J., Faqir, N.M. Solution of the Population Balance Equation for Liquid-Liquid Extraction Columns using a Generalized Fixed-Pivot and Central Difference Schemes Bardow, A., Marquardt, W. Identification of Multicomponent Mass Transfer by Means of an Incremental Approach Barrett, W., Harten, P. Development of the US EPA's Metal Finishing Facility Pollution Prevention Tool Bozga, G., Bumbac, G., Plesu, V., Muja, I., Popescu, CD. Modelling and Simulation of Kinetics and Operation for the TAME Synthesis by Catalytic Distillation Brad, R.B., Fairweather, M., Griffiths, J.F., Tomlin, A.S. Reduction of a Chemical Kinetic Scheme for Carbon Monoxide-Hydrogen Oxidation Brauner, N., Shacham, M. A Procedure for Constructing Optimal Regression Models in Conjunction with a Web-based Stepwise Regression Library Chatzidoukas, C., Perkins, J.D., Pistikopoulos, E.N., Kiparissides, C. Dynamic Simulation of the Borstar® Multistage Olefin Polymerization Process Cheng, H.N., Qian, Y., Li, X.X., Li, H. Agent-Oriented Modelling and Integration of Process Operation Systems Citir, C., Aktas, Z., Berber, R. Off-line Image Analysis for Froth Flotation of Coal Coimbra, M.d.C., Sereno, C , Rodrigues, A. Moving Finite Element Method: Applications to Science and Engineering Problems Dalai, N.M., Malik, R.K. Solution Multiplicity in Multicomponent Distillation. A Computational Study Dave, DJ., Zhang, N. Multiobjective Optimisation of Fluid Catalytic Cracker Unit Using Genetic Algorithms

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587 593 599 605

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Demicoli, D., Stichlmair, J. Novel Operational Strategy for the Separation of Ternary Mixtures via Cyclic Operation of a Batch Distillation Column with Side Withdrawal Dietzsch, L., Fischer, I., Machefer, S., Ladwig, H.-J. Modelling and Optimisation of a Semihatch Polymerisation Process Elgue, S., Cabassud, M., Prat, L., Le Lann, J.M., Cezerac, J. A Global Approach for the Optimisation of Batch Reaction-Separation Processes Gopinathan, N., Fairweather, M., Jia, X. Computational Modelling of Packed Bed Systems Hadj-Kali, M., Gerbaud, V., Joulia, X., Boutin, A., Ungerer, P., Mijoule, C , Roques, J. Application of molecular simulation in the Gibbs Ensemble to Predict LiquidVapor Equilibrium Curves of Acetonitrile Hallas, I.e., S0rensen, E. Simulation of Supported Liquid Membranes in Hollow Fibre Configuration Haug-Warberg, T. On the Principles of Thermodynamic Modeling Heinonen, J., Pettersson, F. Short-Term Scheduling in Batch Plants: A generic Approach with Evolutionary Computation Hinnela, J., Saxen, H. Model of Burden Distribution in Operating Blast Furnaces Hugo, A., Ciumei, C , Buxton, A., Pistikopoulos, E.N. Environmental Impact Minimisation through Material Substitution: A MultiObjective Optimisation Approach Inglez de Souza, E.T., Maciel Filho, R., Victorino, I.R.S. Genetic Algorithms as an Optimisation Toll for Rotary Kiln Incineration Process Kasiri, N., Hosseini, A.R., Moghadam, M. Dynamic Simulation of an Ammonia Synthesis Reactor Katare, S., Caruthers, J., Delgass, W.N., Venkatasubramanian, V. Reaction Modeling Suite: A Rational, Intelligent and Automated Framework for Modeling Surface Reactions and Catalyst Design Kim, Y.H., Ryu, M.J., Han, E., Kwon, S.-P., Yoon, E.S. Computer Aided Prediction of Thermal Hazard for Decomposition Processes Kloker, M., Kenig, E., Gorak, A., Fraczek, K., Salacki, W., Orlikowski, W. Experimental and Theoretical Studies of the TAME Synthesis by Reactive Distillation Ko5i, P., Marek, M., Kubicek, M. Oscillatory Behaviour in Mathematical Model ofTWC with Microkinetics and Internal Diffusion Kohout, M., Vanickova, T., Schreiber, I., Kubicek, M. Methods of Analysis of Complex Dynamics in Reaction-Diffusion-Convection Models Korpi, M., Toivonen, H., Saxen B. Modelling and Identification of the Feed Preparation Process of a Copper Flash Smelter

629 635 641 647

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Koskinen, J., Pattikangas, T., Manninen, M., Alopaeus, V., Keskinen, K.L, Koskinen, K., Majander, J. CFD Modelling of Drag Reduction Effects in Pipe Flows Kreis, P., Gorak, A. Modelling and Simulation of a Combined Membrane/Distillation Process Lacks, DJ. Consequences ofOn-Line Optimization in Highly Nonlinear Chemical Processes Lakner, R., Hangos, K.M., Cameron, I.T. Construction of Minimal Models for Control Purposes Lievo, P., Almark, M., Purola, V.-M., Pyhalahti, A., Aittamaa, J. Miniplant - Effective Tool in Process Development and Design Lim, Y.-L, Christensen, S., J0rgensen, S.B. A Generalized Adsorption Rate Model Based on the Limiting-Component Constraint in Ion-Exchange Chromatographic Separation for Multicomponent Systems Miettinen, T., Laakkonen, M., Aittamaa, J. Comparison of Various Flow Visualisation Techniques in a Gas-Liquid Mixed Tank Montastruc, L., Azzaro-Pantel, C , Davin, A., Pibouleau, L., Cabassud, M., Domenech, S. A Hybrid Optimization Technique for Improvement of P-Recovery in a Pellet Reactor Mori, Y., Partanen, J., Louhi-Kultanen, M., Kallas, J. Modelling of Crystal Growth in Multicomponent Solutions Mota, J.P.B. Towards the Atomistic Description of Equilibrium-Based Separation Processes. I. Isothermal Stirred-Tank Adsorber Mota, J.P.B., Rodrigo, AJ.S., Esteves, I.A.A.C., Rostam-Abadi, M. Dynamic Modelling of an Adsorption Storage Tank using a Hybrid Approach Combining Computational Fluid Dynamics and Process Simulation Mu, F., Venkatasubramanian, V. Online HAZOP Analysis for Abnormal Event Management of Batch Process Mueller, C , Brink, A., Hupa, M. Analysis of Combustion Processes Using Computational Fluid Dynamics - A Tool and Its Application Novakovic, K., Martin, E.B., Morris, A.J. Modelling of the Free Radical Polymerization ofStyrene with Benzoyl Peroxide as Initiator Oliveira, R. Combining First Principles Modelling and Artificial Neural Networks: a General Framework Oreski, S., Zupan, J., Glavic, P. Classifying and Proposing Phase Equilibrium Methods with Trained Kohonen Neural Network Paloschi, J.R. An Initialisation Algorithm to Solve Systems of Nonlinear Equations Arising from Process Simulation Problems

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Peres, J., Oliveira, R., Feyo de Azevedo, S. Modelling Cells Reaction Kinetics with Artificial Neural Networks: A Comparison of Three Network A rchitectures Perret, J., Thery, R., Hetreux, G., Le Lann, J.M. Object-Oriented Components for Dynamic Hybrid Simulation of a Reactive Distillation Process Ponce-Ortega, J.M., Rico-Ramirez, V., Hernandez-Castro, S. Using the HSS Technique for Improving the Efficiency of the Stochastic Decomposition Algorithm Pongracz, B., Szederkenyi, G., Hangos, K.M. The Effect of Algebraic Equations on the Stability of Process Systems Modelled by Differential Algebraic Equations Pons, M. The CAPE-OPEN Interface Specification for Reactions Package Poth, N., Brusis, D., Stichlmair, J. Rigorous Optimization of Reactive Distillation in GAMS with the Use of External Functions Preisig, H.A., Westerweele, M. Effect of Time-Scale Assumptions on Process Models and Their Reconciliation Repke, J.-U., Villain, O., Wozny, G. A Nonequilibrium Model for Three-Phase Distillation in a Packed Column: Modelling and Experiments Roth, S., Loffler, H.-U., Wozny, G. Connecting Complex Simulations to the Internet - an Example from the Rolling Mill Industry Rouzineau, D., Meyer, M., Prevost, M. Non Equilibrium Model and Experimental Validation for Reactive Distillation Salgado; P.A.C., Afonso, P.A.F.N.A. Hierarchical Fuzzy Modelling by Rules Clustering. A Pilot Plant Reactor Application Salmi, T., Warna, J., Mikkola, J.-P., Aumo, J., Ronnholm, M., Kuusisto, J. Residence Time Distributions From CFD In Monolith Reactors - Combination of Avant-Garde and Classical Modelling Schneider, P.A., Sheehan, M.E., Brown, S.T. Modelling the Dynamics of Solids Transport in Flighted Rotary Dryers Sequeira, S.E., Herrera, M., Graells, M., Puigjaner, L. On-Line Process Optimisation: Parameter Tuning for the Real Time Evolution (RTF) Approach Shimizu, Y., Tanaka, Y., Kawada, A. Multi-Objective Optimization System MOON^ on the Internet Singare, S., Bildea, C.S., Grievink, J. Reduced Order Dynamic Models of Reactive Absorption Processes Skouras, S., Skogestad, S. Separation ofAzeotropic Mixtures in Closed Batch Distillation Arrangements Smolianski, A., Haario, H., Luukka, P. Numerical Bubble Dynamics Soares, R. de P., Secchi, A.R. EMSO: A New Environment for Modelling, Simulation and Optimisation

839

845

851

857 863

869 875

881

887 893

899

905 911

917 923 929 935 941 947

XVI

Thullie, J., Kurpas, M. New Concept of Cold Feed Injection in RFR Tiitinen, J. Numerical Modeling of a OK Rotor-Stator Mixing Device Urbas, L., Gauss, B., Hausmanns, Ch., Wozny, G. Teaching Modelling of Chemical Processes in Higher Education using MultiMedia van Wissen, M.E., Turk, A.L., Bildea, C.S., Verwater-Lukszo, Z. Modeling of a Batch Process Based upon Safety Constraints Virkki-Hatakka, T., Rong, B.-G., Cziner, K., Hurme, M., Kraslawski, A., Turunen, I. Modeling at Different Stages of Process Life-Cycle Yang, G., Louhi-Kultanen, M., Kallas, J. The CFD Simulation of Temperature Control in a Batch Mixing Tank Zilinskas, J., Bogle, I.D.L. On the Generalization of a Random Interval Method

953 959

965 971

977 983 989

Applications in Pulp and Paper Industry Alexandridis, A., Sarimveis, H., Bafas, G. Adaptive Control of Continuous Pulp Digesters Based on Radial Basis Function Neural Network Models 995 Brown, D., Marechal, F., Heyen, G., Paris, J. Application of Data Reconciliation to the Simulation of System Closure Options in a Paper Deinking Process 1001 Costa, A.O.S., Biscaia Jr., E.G., Lima, E.L. Mathematical Description of the Kraft Recovery Boiler Furnace 1007 de Vaal, P.L., Sandrock, C. Implementation of a Model Based Controller on a Batch Pulp Digester for Improved Control 1013 Ghaffari, Sh., Romagnoli, J.A. Steady State and Dynamic Behaviour of Kraft Recovery Boiler 1019 Harrison, R.P., Stuart, P.R. Processing ofThermo-Mechanical Pulping Data to Enhance PC A and PLS 1025 Jemstrom, P., Westerlund, T., Isaksson, J. A Decomposition Strategy for Solving Multi-Product, Multi-Purpose Scheduling Problems in the Paper Converting Industry 1031 Masudy, M. Utilization of Dynamic Simulation at Tembec Specialty Cellulose Mill 1037 Pettersson, P., Soderman, J. Synthesis of Heat Recovery Systems in Paper Machines with Varying Design Parameters 1043 Rolandi, P.A., Romagnoli, J.A. Smart Enterprise for Pulp and Paper: Digester Modeling and Validation 1049 Silva, CM., Biscaia Jr., E. C. Multiobjective Optimization of a Continuous Pulp Digester 1055 Soderman, J., Pettersson, F. Searching for Enhanced Energy Systems with Process Integration in Pulp and Paper Industries 1061

XVll

Virta, M.T., Wang, H., Roberts, J.C. The Performance Optimisation and Control for the Wet End System of a Fluting and Liner Board Mill 1067

Applications in Biotechnology Acufia, G., Cubillos, F., Molin, P., Ferret, E., Perez-Correa, R. On-line Estimation of Bed Water Content and Temperature in a SSC Bioreactor Using a Modular Neural Network model Eusebio, M.FJ., Barreiros, A.M., Fortunate, R., Reis, M.A.M., Crespo, J.G., Mota, J.P.B. On-line Monitoring and Control of a Biological Denitrification Process for Drinking-Water Treatment Horner, D.J., Bansal, P.S. The Role of CAPE in the Development of Pharmaceutical Products Kristensen, N.R., Madsen, H., J0rgensen, S.B. Developing Phenomena Models from Experimental data Levis, A.A., Papageorgiou, L.G. Multi-Site Capacity Planning for the Pharmaceutical Industry Using Mathematical Programming Li, Q., Hua, B. A Multiagent-based System Model of Supply Chain Management for Traditional Chinese Medicine Industry Lim, A.Ch., Farid, S., Washbrook, J., Titchener-Hooker, N.J. A Tool for Modelling the Impact of Regulatory Compliance Activities on the Biomanufacturing Industry Manca, D., Rovaglio, M., Colombo, I. Modeling the Polymer Coating in Microencapsulated Active Principles Marcoulaki, E.G., Batzias, F.A. Extractant Design for Enhanced Biofuel Production through Fermentation of Cellulosic Wastes Sarkar, D., Modak, J.M. Optimisation of Fed-Batch Bioreactors Using Genetic Algorithms: Two Control Variables van Winden, W.A., Verheijen, P.J.T., Heijnen, J.J. Efficient Modeling of C-Labeling Distributions in Microorganisms Wang, F.-Sh. Fuzzy Goal Attainment Problem of a Beer Fermentation Process Using Hybrid Differential Evolution Wongso, F., Hidajat, K., Ray, A.K. Application ofMultiobjective Optimization in the Design ofChiral Drug Separators based on SMB Technology

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European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

Computer Aided Biochemical Process Engineering I.D.L.Bogle Dept of Chemical Engineering, University College London, Torrington Place, London, WCIE 7JE [email protected]

Abstract The growth of the biochemical industries is heating up in Europe after not meeting the initial expectations. CAPE tools have made some impact and progress on computer aided synthesis and design of biochemical processes is demonstrated on a process for the production of a hormone. Systems thinking is being recognised by the life science community and to gain genuinely optimal process solutions it is necessary to design right through from product and function to metabolism and manufacturing process. The opportunities for CAPE experts to contribute in the explosion of interest in the Life Sciences is strong if we think of the 'Process' in CAPE as any process involving physical or (bio-)chemical change.

1. Introduction The biochemical process industries have been in the news, and often headlines, for many years now. There has been a significant impact on Chemical Engineering research in scientific fundamentals but not such a great impact on process design. In the early nineties the European Commission (EC communication 19 April 1991) was predicting that the sales of biotechnology derived products would be between €26 and €41 billion by the year 2000, a three-fold increase on sales in 1985. A recent review of global biotechnology by Ernst and Young (2002) shows that revenues in 2000 in Europe were around €10 billion (M$9,872) but had risen by 39% for 2001 with a figure of around €13 billion (M$ 13,733). So while the sector has not delivered the full promise it is clearly a growing one. Globally the USA dominates the sector with product sales of $28.5 billion in 2001 ($25.7 billion in 2000). A key difference between the USA and Europe is that in the USA the revenues for public companies dominates while in Europe private companies produce nearly half the revenues. For public companies the rest of the world currently contribute only 5.6% of revenues. The European biotechnology industry 'is now starting to play a central role on the global stage ... enabled by a dramatically increased flow of funds into the industry' (Ernst and Young). According to the Ernst and Young report 'the European biotechnology sector is characterized by a high proportion of small early stage companies' so one of the constraining factors is a strain on private equity resources. However the number of companies that have raised more than 20 million euros has risen from 3 in 1998 to 23 in 2001. Also resistance to the industry has been stronger in Europe and this has resulted in tighter controls on both manufacturing and research and development. Regulatory compliance is a key issue in biochemical processes because the regulatory authorities demand well defined operating procedures to be adhered to once approved for a

particular product and process. This has significance for the CAPE community since to have a role it must be early in the development process when there is freedom to make design and operational decisions. Much of the (Bio-)Chemical Engineering design activity aids large scale manufacturing. The modeling effort for biochemical processes is significant because of the specific characteristics of the production (typically fermentation of cells) and separation (often specific chromatographic techniques) operations. However as we will show in this paper there has been significant success in design and operations optimization and that with the continuing improvement in the understanding of metabolic systems and with progress being made elsewhere in facilitating first principles modeling there is considerable scope for improvement and take up of contributions from our community to assist in the development of the industry.

2. Product and Process One of the characteristics of the industry is the rapid generation of new products. This is set to increase particularly for medicinal products since systematic generation based on genome and proteome information are bound to flow from the mapping of the building blocks of living matter in the genes and proteins. Many databases are now Web accessible. The most important driver for CAPE based tools is to be able to provide manufacturing solutions very rapidly based on incomplete information. However tools can also seek to provide guidance for the correct sort of data needed from the laboratory. And also they can seek to provide guidance on the appropriate products for the market place and for manufacturability. The biotechnology sector covers a wide range of products including medicinal products, foodstuffs, specialty chemical products, and land remediation. There is a role for engineers to play in systematic identification of product. The generation of appropriate medicinal treatment based on pharmacological knowledge and modeling once seemed fanciful but with better understanding of functional relationships and with the introduction of gene therapy treatments, where treatment is matched to the specific genetic information of a patient, this may well become commonplace (Bailey). It would also be appropriate for engineers to be specifying systems in which the identification of the product is tied closely in with the function as well as the manufacturability of the product and generating the product and process in a seamless manner. The same may also be true for specialty chemical products produced biologically and of course there is progress in engineering approaches to this problem which would be directly applicable (see for example Moggridge and Cussler). Foodstuffs manufacture should also be thought of in an integrated manner considering the functionality required of the product - taste, mouthfeel, nutritional content - in the specification of product and process. Perhaps this last area is the most difficult because of the difficulty in characterizing much of the functionality in a form that is amenable to quantitative treatment. Biological products are normally produced in fermentation processes. The product is expressed in some type of organism and can i) be excreted and collected, ii) remain inside the cell as a soluble product and the cell must be broken open and the product extracted from the broth, or iii) remain as an insoluble product where again the cell must be broken and particulate recovery methods are also required. There are many choices to be made in the production. Many host organisms are used to express the product:

common bakers yeast, Escherichia coli a common bacterium, Aspergillus niger a fungal bacterium, and mammalian cells are commonly used. If the product is expressed naturally by the organism (such as ethanol by yeast) then there are many choices of strain of the organism to be made, each strain having different levels of expression of the product. But with the advent of genetic engineering it became possible to modify a host organism such that it can produce non-native products. So now the choice is of both host and strain, constrained by limitations of the genetic engineering procedures. It is also possible now to define or modify the expression system within the organisms to optimise production. The whole area of Metabolic Engineering is ripe for greater input for Chemical Engineers and from the CAPE community and Stephanopoulos provides many valuable insights. The topic deserves a review paper of its own but it is worthwhile touching on some of the contributions of our community to this problem. The metabolism is usually represented as a network of well defined chemical reactions although this itself is a simplification as there are other links through enzymatic catalysts present and in the consumption and production of ATP, the main energy transport agent. The CAPE community has much experience of the simulation and optimisation of networks. In the late 60s a general non-linear representation of integrated metabolic systems was first suggested (Savageau) using a power law approximation for the kinetics. Using this formulation it is possible to identify rate controlling steps and bottlenecks, and to optimise the production of individual metabolites. This could be effected practically by changing the environment around the cells or by genetic modification. The optimisation problem can be transformed into a linear progranmiing problem (Voit, Regan et al.) or as an MILP problem (Hatzimanikatis et al) where network structure can also be modified, for example by deactivating paths. The extent to which uncertainty can be directly incorporated has also been tackled (Petkov and Maranas) addressing how likely it is to achieve a particular metabolic objective without exceeding physiological constraints that have been defined probabilistically. Clearly this is a very fertile area but one that must be done in close collaboration with biological scientists since there are many practical issues which limit the modifications that can be made to any metabolic system. It is also possible to assist in the exploration of more fundamental biological problems which the metabolic pathway holds the key to. One example is that pathway proximity gives a measure of how well connected each metabolite is, thus providing us with an objective criterion for determining the most important intermediates of metabolism and this can be formulated as an LP problem (Simeonides et al.). We can expect to see significant opportunities for our community in the area of aiding biological understanding in the future. The ability to manufacture a new product also depends on the ability to purify the product. So the choices can also extend to expressing a product which can easily be separated and then if necessary chemically modified to produce the final usefiil product. One example of this will be discussed later in the paper. So in the manufacture of a new product there are many choices open to the engineers and opportunities to provide CAPE tools to facilitate these thought processes. Some of these choices are shown in fig 1: choices about genetic and metabolic networks, about host organism and type of expression system, and of manufacturing process design.

along with the criteria that influence them: product function and effectiveness (often related to purity) as well as cost, safety and environmental impact (now also with genetic engineering implications). First principles modeling of the entire design process is decades away so the integration of data - both the employment of existing data and the ability to assist in highlighting important data that if collected will significantly enhance the decision making process is critical. Culturally, close interactions with experimentalists is also essential since there is still a significant divide between the life science and the engineering communities with considerable scepticism of the role of computational techniques. However recently there is a much wider recognition of the need for quantitative methods in biology (Chicurel) and so we can be confident of a more receptive response to engineering methods in the future.

Fig 1. Product and process decision making.

3. Process Synthesis We know that it is important to take a systems view of process design. Ideally this also includes all the production and separation aspects and to allow simultaneous treatment of structural and continuous decisions. It should also permit the use of various criteria which must be juggled - economic, technical, environmental and so on. In the following sections I summarise some work we have done on synthesis and design of biochemical manufacturing processes tackling some of these aspects. We are still a long way from comprehensive solutions. In this section I discuss approaches to considering structural flowsheet choices and in the following about choices where the flowsheet has been established and operating conditions are being optimised. The synthesis task here involves a wide range of alternative unit operations and recycle is rare. The problem is often simplified by application of rough guidelines or heuristics, which can be used alone or to simplify the computational task. Leser et al. presented the use of a rule based expert system for use in biochemical process synthesis. In practice an enormous number of heuristics are in common use. Much can be achieved in the early stages of conceptual process design using simple models that encapsulate the key mechanism driving the separation processes. Critical choices between alternatives can be made without having to develop complete simulations. The number of possible configurations increases exponentially as the number of types of separators to be considered increases. The total number of configurations for most practical problems is so large that an exhaustive search is computationally not practical. Clearly because of this explosion it is necessary to use a computationally simple evaluation scheme combined with simple heuristics.

Jaksland et al (1995) developed a property based approach to synthesis of chemical processes which is based on utilising driving forces to characterise the effectiveness of alternative unit operations. Each separation process exploits specific property differences to facilitate purification of the various components in a stream. The key driving force, and corresponding key property, utilised by each technology is identified. Table 1 summarizes properties of several downstream purification operations used in biochemical processes (proposed values of feasibility indices can be found in Steffens et al. 2000a). The approach relies on estimates of the physical properties of the components in the system. While the possibility of predicting all the properties of biochemical systems is still a long way off recent developments in the field for large molecules (polymers) and electrolytic solutions provide encouragement. An extensive UNIFAC group and parameter database of Hansen et al. (1991) was applied to describe activity coefficients of amino acids and peptides using the UNIFAC model. It was demonstrated that the group definition is not appropriate for peptides and therefore proteins. There is considerable research activity going on but it is expected that for the time being the synthesis procedure will be based on measured properties for the system in question and where information is not available to use data from the most similar system. It will of course be necessary to build up a database of data for relevant products and processes but it is hoped that the synthesis procedure will help to guide the experimentation process. Table 1. Separation Processes and key properties (x is particle or molecular diameter that can be handled). Unit operation Centrifugation Sedimentation Conventional filtration Rotary Drum filtration Microfiltration Microfiltration Ultrafiltration Diafiltration Precipitation Two liq phase separation Ion exchange Affinity chromatography Gel chromatography Hydrophobic Int. Chr.

Physical Property Density Density Particle size Particle size Particle size Molecular size Molecular size Molecular size Solubility Partition coefft Charge density Biospecific attraction Lx)g(mol. wt.) Hydrophobicity

Phase S/L S/L S/L S/L S/L I7L L/L L/L L/L UL L/L IVL UL 17L

Notes 0.1<x<100^im x>l ^im x>10^m x>10 ^im 0.05<x<5 ^im 0.05<x<5 ^im 0.001 <x<0.2|Lim 0.001 <x<0.2^m

0.051<x<10^m

SoUds Y Y Y Y Y Y Y Y Y Y N N N N

The synthesis methodology that we have produced (Steffens et al. 2000a) generates and searches the search tree using an implicit enumeration method using the Jacaranda software (Fraga). The screening methodology uses the simple characterizations of the separations. Complex models can be included because the search procedure imposes no requirements on the models' convexity and continuity. Stream characteristics and unit design parameters are discretized hence all searching is done on discrete variables leading to a discrete optimization problem. The algorithm was used to generate alternatives for the manufacture of an animal growth hormone bovine somatotropin or BST. This product is expressed as an insoluble

granule in E.coli and so lessons can be learned for a range of similar expression systems (including one method for the production of synthetic insulin). Figure 2 shows an existing industrial flowsheet for the manufacture of the product and figure 3 shows the optimal flowsheet as generated by the synthesis software. The basic structure of the two flowsheets is the same but Jacaranda suggested the cell concentration step uses microfiltration instead of a centrifuge which is certainly a feasible option. Results for an intracellular product also produced similar flowsheets to those used in practice (Steffens et al 2000a).

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Fig 2. Industrial Flowsheet for the purification of BST (dotted area shows final polishing operations). A powerful advantage of the synthesis methodology is the ability to revise and improve the optimization criteria (Fraga). The synthesis procedure was also posed as a multicriteria optimization problem balancing economic and environmental criteria (Steffens et al. 1999). Here we were able to consider a range of environmental criteria including the life cycle cost (LCA), the critical water mass (CWTM), and the sustainable process index which gives the land mass area required to embed a process sustainably into the environment. We considered the manufacture of penicillin for which a number of processes have been patented. Jacaranda provides a ranked list of best solutions (as many as requested), a very useful feature for process synthesis since some options which may appear to be solutions could have obvious practical problems. Again most of the best solutions were very similar to the industrial flowsheets which include rotary drum filtration, solvent extraction, crystallization, filtration and drying. However when LCA or CWTM environmental criteria are used the solvent extraction process is replaced by cross flow filtration and ion exchange with other potential small changes. This is an expensive option but has clear environmental advantages. The

synthesis problem can easily be modified quickly by the user to meet the business priorities of a company and quickly generate alternatives for further study. Fermenter

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Fig 3. Cost Optimal Flowsheet for BST manufacture generated by Jacaranda. Up to this point the system boundary has excluded the production (cellular fermentation) operation. However if we extend the systems thinking to include this stage further improvements can be made to biochemical processes by changing the product expressed in the fermentation stage into a product that is easily purified. This is done, mostly at bench scale, by adding amino acids to the protein as a tail which will easily bind to a chromatographic adsorption resin. There are twenty amino acids to choose from and any number can be chosen so, again there is a potentially large combinatorial search. We chose to limit the search to a maximum of fifteen amino acids and to base the search on the use of two properties used in adsorption: charge and hydrophobicity (Steffens et al, 2000b). There are approximate methods for predicting these properties. Our procedure searches for the best solution including both production and purification processes assuming that genetic engineering and final tail cleavage costs are the same in all cases. The best three solutions (for BST) were indistinguishable in cost terms but all required the addition of between thirteen and fifteen amino acids and would result in more than halving the manufacturing costs by replacing the section in the dotted box in figure three by one cation exchange column and a cleavage step. These results have not been practically tested but aim to show the potential of using systematic synthesis techniques to suggest ways of searching the huge number of alternatives on offer to the developers of manufacturing processes for new products.

4. Process Design A number of tools have been used for process design once the flowsheet has been established. Bio-Pro Designer (Petrides) has been proposed for this and enables users to put together simple flowsheets for basic sizing and material balancing. However for incorporating more complex models of unit operations we have favoured the use of modelling tools where mechanistic models of separation tasks can be incorporated. Other workers have developed approaches for incorporating business decision making explicitly into the design process developing windows of operation which can be explored (Zhou et al.). We developed a full gPROMS simulation and gOPT optimisation of the BST manufacturing process. To obtain the greatest inclusion body recovery and the highest product purity are conflicting demands. By operating the centrifuge to yield maximal recovery will result in poor purity and these trade-offs are described in more detail in Bogle and Graf. Of course only one of the objectives can be optimised at a time but it is of particular interest what levels of recovery, purity, and productivity can be achieved when the entire process is considered simultaneously. The trade-offs in the multi-criteria optimisation problem can then be explored. Optimisation variables for the process are given in table 2. For the optimisation the fermentation time and the initial fermentation volume have been set. The results of the optimisations are given in table 3. The computational optimisation times for each run were typically 3-4 min on an RS6000. Table 2. Overview of the optimisation variables used. Process Unit

Optimisation variable

Fermenter HarvesterCentrifuge Homogeniser CentrifugeMixer SeparatorCentrifuge

Volumetric throughput (L/h) Settling area (m^) Number of passes (-) Dilution rate (-)

Initial guess 1300 155000 3 3.1

Lower bound 1200 10000 1 1.1

Upper bound 10000 250000 3 4

Volumetric throughput (L/h) Settling area (m^)

1400 105785

1200 10000

10000 250000

Since a desirable target is to maximise the IB recovery, product purity, and productivity, a solution has to be found which introduces an acceptable compromise. The optimisation strategy was changed to include structural decisions and a batchwise recycling of the sediment of the last centrifuge was proposed. The results of the suggested procedure are listed in the final column of table 3. The results show that high levels of all three objectives are achievable: after the second batch, a high purity of 94.6% is reached with an acceptable IB recovery of 83.6% and a productivity of 0.95 kg B.S.T./h which guarantees efficiency of the plant.

Table 3: Results for the maximisation of the IB recovery, purity, productivity, and for an solution where the centrifuge outlet is recycled and reprocessed.

Overall IB recovery (%) Purity (%) Productivity (kg BST /h) Overall process time (h) Final Process Volume (1) Recovered mass of BST (kg)

Maximum Recovery 95 73.8 1.021 37.3 1304 38.1

Maximum Purity 12.7 92.1 0.163 30.6 366 5.1

Maximum Productivity 93.5 55.7 1.16 32.7 815 37.9

Overall Opt. (before/after recycle) 90.7/83.6 80.9/94.6 1.08/0.95 33.6/35.3 1003/370 36.2/33.5

5. New Challenges for Computer Aided Process Engineering The increasing emphasis on quantitative biology means there will be an increasing role for CAPE specialists. There will be opportunities in the design of biochemical products and processes where the complexity is great. The need for a systems view is becoming clear to all and will increase as medicinal products are becoming 'multicomponent'; this can have much greater activity than single active ingredients (Bailey). Our systems view will include function although for medicinal products this challenge is a tough one as it means much more accurate models of living systems. The links to the experimentalists, our ability to help guide useful data collection, and to other disciplines become ever more important. I believe that we have a significant role to play in wider biological problems i.e. if we consider the 'Process' in CAPE to not just be about large scale manufacturing processes but to see it as an entry to any process where physical, chemical and/or biological processes are taking place and the complexity is such that systems approaches are needed. An example project that I am involved in is the modelling of networks from gene through to organ (the liver) building on modelling work being done in a range of Life Science Departments at UCL (http://www.ucl.ac.uk/complex/research/DTI.html). There are huge opportunities for our community to work with a wide range of disciplines and to help tackle some big challenges, not just in the discovery and manufacture of biochemical products but also in some of the biggest problems in this century of biology.

6. References Bailey, J.E. (1999) Lessons from metabolic engineering for functional genomics and drug discovery. Nature Biotechnology, 17 July 1999, 616-618. Bogle, I.D.L., Graf, H. (1997) Simulation as a tool for at-line prediction and control of biochemical processes. In Proc ECCEl, Florence, May 1997, 1933-1936. Chicurel, M. (2000) Mathematical biology: Life is a game of numbers. Nature 408, 900-901. Ernst, Young (2002) Beyond Borders, The Global Biotechnology Report. Fraga, E.S. (1998) The generation and use of partial solutions in process synthesis. Chem. Eng. Res. Des., 76(A1), 45-54.

10 Hansen, H.K., Rasmussen, P., Fredenslund, A., Schiller, M., Gmehling, J. (1991) Vapour liquid equilibria by UNIFAC group contribution. 5. Revision and extension. Ind. Eng. Chem. Res., 30, 2352. Hatzimanikatis, V., Floudas, C.A., Bailey, J.E. (1996) Analysis and design of metabolic reaction networks via mixed integer linear optimisation. AIChE J., 42, 12771292. Jaksland, C.A., Gani, R., Lien, K.M. (1995) Separation process design and synthesis based on thermodynamic insights. Chem. Eng. Sci., 50(3), 511-530. Leser, E.W., Lienqueo, M.E., Asenjo, J.A. (1996) Implementation in an expert system of a selection and synthesis of multistep protein separation processes for recombinant proteins. Ann NY Acad Sci 782:441-455. Moggridge, G.D., Cussler, E.L. (2000) An introduction to chemical product design. Chem. Eng. Res. Des., 78 (Al): 5-11. Petkov, S.B., Maranas, CD. (1997) Quantitative assessment of uncertainty in the optimisation of metabolic pathways. Biotech. Bioeng., 56/2, 145-161. Petrides, D.P. (1994) Biopro designer - an advanced computing environment for modelling and design of integrated biochemical processes. Comput. Chem. Engng., 18,S621-S625. Regan L., Bogle, I.D.L., Dunnill, P. (1993) Simulation and optimisation of metabolic pathways. Comput. Chem. Engng., 17, 627-637. Savageau, M.A. (1969) Biochemical Systems Analysis. 1. Some mathematical properties of the arte law for the component enzymatic reactions. J. Theor. Bio., 25, 370-379. Simeonidis, E., Rison, S.C.G, Thornton, J.M., Bogle, I.D.L., Papageorgiou, L.G. (2003) Analysis of biochemical networks using a pathway distance metric through linear progranmiing. Submitted to Metabolic Engineering. Steffens, M., Fraga, E.S., Bogle, I.D.L. (1999) Multicriteria Process Synthesis for Generating Sustainable and Economic Bioprocesses. Comput Chem Engng., 23, 1455-1467. Steffens, M.A., Fraga, E.S., Bogle, I.D.L. (2000a) Synthesis of downstream purification processes using physical properties data. Biotech Bioeng., 68/2, 218-230. Steffens, M.A., Fraga, E.S., Bogle, I.D.L. (2000b) Synthesis of purification tags for optimal downstream processing. Comput Chem Engng., 24, 717-720. Stephanopoulos, G. (2002) Metabolic Engineering: Perspective of a Chemical Engineer. AIChE J., 48/5,920-926. Voit, E.O. (1992) Optimization of integrated biochemical systems. Biotech Bioeng 40 572-582. Zhou, Y.H., Titchener-Hooker, N.J. (1999) Visualizing integrated bioprocess designs through "windows of operation". Biotechnol Bioeng., 65 (5): 550-557.

7. Acknowledgements I would like to acknowledge the work of many colleagues in Chemical Engineering at UCL whose work over many years made this paper possible: Eric Fraga, Lazaros Papageorgiou, Marc Steffens, Vangelis Simeonides, David Johnson, Sabine Agena, and Holger Graf and to the members of CoMPLEX (Centre for Mathematics and Physics in the Life Sciences and Experimental Biology) also at UCL.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

11

A Two-stage Optimisation Approach to the Design of Water-using Systems in Process Plants Solomon Abebe^, Zhigang Shang^ and Antonis Kokossis^ ^Department of Process & Systems Engineering, Cranfield University, Cranfield, MK43 OAL, UK ^Department of Chemical Engineering & Process Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK

Abstract The minimisation of water and wastewater flows is an objective of increasing value in industries. The paper presents a systematic optimisation approach for the design of the water-using systems in process plants with minimum water usage and capital investment. The proposed approach combines the benefits of water-pinch concepts and mathematical programming techniques. It follows a two-stage procedure, namely targeting stage and network design stage. Both stages rely on the optimisation of a superstructure model with all possible connections between (i) freshwater sources and operations, and (ii) different water-using operations. The approach facilitates the inherent combinatorial nature of the design problem and solves it efficiendy.

1. Introduction The design and analysis of water using systems has received much attention from the research community since 1970s. As the social awareness of the environmental problems caused by extensive industrialisation increases, the need for decision support tools to aid in minimising pollution has been accentuated. Wastewater is generated by processes as byproducts of reaction and when water comes into contact with process materials in mass transfer and extraction operations, direct contact heat transfer and steam ejectors. Also, wastewater is generated by utility systems from boiler feedwater treatment processes, boiler blowdown, cooling tower blowdown, etc. (Nemerow, 1971). A number of approaches have been reported for the optimal design of water-using systems using optimisation techniques. One of the earliest works on the application of optimisation techniques to regional water-using systems is that of Bishop and Hendricks (1971). The authors approached the design task as a transshipment problem and used linear programming techniques to obtain solutions. Takama et al. (1980) used mathematical programming to solve a refinery example. These authors addressed the problem of water management as a combination of water allocation among processes and wastewater distribution to cleanup units. More recently Alva-Argaez et al. (1999) and Huang et al. (1999) presented MINLP or NLP models. Bagajewicz (2000) presented necessary conditions of optimality for water-using systems. These conditions are used later in an algorithmic design procedure.

12 A targeting approach known as water pinch technology was developed by Wang and Smith (1994) for water and wastewater minimisation for the process industries. This technology is conceptually based and represents a systematic tool for the design of water networks. It can effectively pick optimal water reuse solutions. The method is based on assuming: • Constant pollutant load picked up in each process; • Maximum inlet and outlet concentrations in each process. Wang and Smith (1994) introduced a water use representation for a water using operation, which consists of a concentration versus mass load diagram. Based on this representation, every water-using operation can be described with the concept of a limiting water profile. The water profile with maximum inlet and outlet concentrations is defined as the limiting water profile. Once the limiting water profile for every waterusing operation has been obtained, a limiting composite curve can be constructed by combining all the individual profiles into a single composite curve as it is shown in Figure 1 for four processes. The water supply line touches the composite curve at pinch point and determines the minimum overall water consumption. Concentration (ppm)

Concentration (ppm)

8og

800

Mass load (kg/h)

21 41 Mass load (kg/h)

Figure 1. Limiting composite curve construction. Here we will present a two-stage optimisation strategy for the design of water using systems which makes use of the insights provided by water pinch analysis and combines them with mathematical programming tools. Both capital cost and fresh water consumption are minimised.

2. The Two-stage Optimisation Approach The pinch technology is found to be efficient when the number of operations is very few with single contaminate. However, when the number of operations escalates the pinch method becomes impractical to tackle such problems. In the section a new automated methodology for the design of water suing systems is described which makes use of the insights provided by water pinch analysis and combines them with mathematical programming tools. The methodology not only tackles problems with many operations but also problems with multi-contaminates and problems with multiple freshwater

13 sources. The methodology overcomes the limitations that are encountered using pinch method. The design of a water-using system involves water-related elements in the form of a number of freshwater sources available to satisfy the demand and water-using operations described by loads of contaminants and concentration levels. The design task is to fmd the network configuration to minimise the overall demand for freshwater (and consequently reduce wastewater volume) compatible with minimum total annual cost. The investment cost of the network includes piping costs and the cost of mass exchanger units. The approximate length of the pipe can be specified for each possible connection together with the materials of construction. The cost of mass exchange units assumes thermodynamic parameters and equilibrium relationships between the process streams and the water streams for the key contaminants, as well as the corresponding design equations and cost functions. The proposed approach follows a two-stage procedure, namely targeting stage and network design stage. Both stages rely on the optimisation of a superstructure model with all possible connections between (i) freshwater sources and operations, and (ii) different water-using operations. The example of a superstructure with three freshwater sources and three water-using operations is shown in Figure 2. An important feature of the superstructure is that the process streams in the mass exchange operations are considered implicitly through the construction of the limiting water profiles. r 1

•©

*]

Operation 1

Freshwater 2

•

7v

»^

Operation 2

Freshwater 3

x

-*\

Operation 3

*M

I

• Effluent 1

*m

^^ •m

• Effluent 3

Figure 2. Superstructure representation. The number of units in the water network determines existing units and discrete options account for connections between sources and sinks of water. The superstructure is developed so that: • each freshwater stream entering the network is split amongst the water-using operations; • each operation is preceded by a mixer fed by streams from the freshwater splitters and re-use streams emanating from the outlets of all other operations; • each operation is followed by a splitter that feeds the final mixer and the other operations in the system. The objective of the targeting stage is to determine the minimum freshwater cost in a water-using system. The problem is formulated as an NLP model. Once the target is obtained, there are often many network alternatives with the same minimum target. The objective of the network design stage is to obtain one from among these networks one that has minimum capital cost since this will usually correspond to an optimal solution. At this stage it is assumed that the minimum freshwater cost and freshwater flowrates

14 from different sources have been determined at the first stage. An MINLP model is formulated to select the most cost-effective water-using system by minimising the capital cost. The capital cost in the objective function consists of the piping costs and the cost of mass exchanger units. The approximate length of the pipe can be specified for each possible connection together with the materials of construction. The cost of mass exchange units assumes thermodynamic parameters and equilibrium relationships between the process streams and the water streams for the key contaminants, as well as the corresponding design equations and cost functions. As illustrated by the case studies, both the NLP model and MINLP model can be linearised by including constraints to represent necessary conditions of optimality for water-using systems.

3. Case Study The capabilities of the proposed approach have been illustrated with a case study. In this case ten water using operations with single contaminant are considered. The objective is to design a suitable network with the minimum capital cost and minimum freshwater consumption. Table 1 shows the limiting data for a ten processes problem. In this case there is one fixed source of freshwater and ten fixed operations. Each water user can be described by maximum and minimum allowed concentration (inlet and outlet) and the individual mass load of contaminants or the limiting flow rate. Table 1. Limiting data for a ten processes problem (Bagajewicz, 2000). Process ~1 2 3 4 5 6 7 8 9 10

Mass load of contaminant (Kg/hr) 2.00 2.88 4.00 3.00 30.00 5.00 2.00 1.00 10.00 6.50

CriPPrr^ QT (PPf^)

"80 25 90 25 200 25 100 50 50 800 800 400 600 400 100 0 300 50 300 150 Total minimum flow rate te/hr

Minimum freshwater without reuse (te/hr) 25.00 32.00 20.00 30.00 37.50 6.25 3.33 10.00 66.67 21.67 252.42

The problem has been solved in the following two stages: Stage 1 targeting the minimum freshwater flow rate The problem has been formulated as an LP model using the General Algebraic Modeling System (GAMS). The total minimum freshwater flow rate found to be 165.953 te/hr. The freshwater consumption of water is saved by over 34%. The resulting network design is given in Figure 3. As we can see the network consists of some impractical interconnections.

15

-E^n F2,3 (6. 5 t4i)

F2,5 (22.2 t/h)

F2,l(3.43 t/h)

Oppm

-G>

F3,10(22.9t^) ,46.4t/h

•^E-H

166 t/h 920 ppm

F4,7 (0.2

^

-

^0+ i3-

JF9,6(10t/h)

Figure 3. Network design with the minimum freshwater consumption.

4D•EH

Q

-•[T]--'"-'^-*,

F4,10 (13.1 t/h) Fl,3(7.1 t/h)

i52i^h_^gjj'; F3,10(18.7) Oppm 0.57 t/h

im F10,7(llit^)

.[I>--'^'iH F2,9(28.6t^)

^CD *[DJ

F8,10(10t/h)

F9,6(10tAi)

Figure 4. Network design with the minimum capital cost and freshwater consumption.

16 Stage! minimising the capital cost. The optimisation for freshwater saving shown on Stage 1 resulted in a feasible network but the network requires many interconnections. Moreover some of them may be impractical. Once the target is obtained the most cost effective design can be sought by minimising the total capital cost and including the minimum fresh water usage as a constraint. An MINLP model has therefore been formulated to select the most costeffective water-using system by minimising the capital cost. Piping costs are calculated on the basis of the length of the pipe runs, flow velocity, area of the pipe, distance between operation, distance between operation and source, distance between operation and wastewater treatment plant. Figure 4 shows the resulting network with the minimum capital cost and fresh water consumption. It can be seen the number of connections of the network in Figure 4 is lower than that of the network in Figure 3. The network in Figure 4 also avoids irrelevant and uneconomical connections and replaces with economical connections. The final network design shows a reasonable amount flowrate to be discharged from operations, which makes it more economical.

4. Conclusions A methodology for designing a water system that is capable of determining the minimum freshwater usage and minimum total capital cost of the network has been developed. The approach is able to solve problems with multiple freshwater sources and multiple contaminates. The approach can be fully automated and the results from the case study suggest that there are a number of different network configurations that can satisfy the minimum freshwater usage target. The best design should be the network which incurs the minimum capital cost and consumes minimum fresh water.

5. References Alva-Argaez, A., Vallianators, A. and Kokossis, A.C., 1999, A multi-contaminate transshipment model for mass exchange networks and wastewater minimisation problems. Computers & Chemical Engineering, 23. Bagajewicz, M.J., 2000, A review of recent design procedures for water networks in refineries and process plants. Computers & Chemical Engineering, 24. Bishop, A.B. and Hendricks, D.W., 1971, Water reuse systems analysis, J. Sanitary Engng. Div. ASCE. Feb. Huang, C.H., Chang, C.T., Ling, H.C. and Chang, C.C, 1999, A mathematical programming model for water usage and treatment network design. Industrial & Engineering Chemistry Research, 38 (5). Nemerow, N.L., 1971, Liquid waste of industry, theories, practices and treatment. Addison-Wesley Publishing Company, U.S.A. Takama, N., Kuriyama, T., Shiroko, K. and Umeda, T., 1980, Optimal water allocation in a petroleum refinery. Computers & Chemical Engineering, 4. Wang, Y.P. and Smith, R., 1994. Wastewater Minimization. Chemical Engineering Science. 49(7).

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

17

Generation and Screening of Retrofit Alternatives Using a Systematic Indicator-Based Retrofit Analysis Method Niels Kau Andersen, Nuria Coll, Niels Jensen, Rafiqul Gani CAPEC, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark Eric Uerdingen, Ulrich Fischer, Konrad Hungerbiihler Safety & Environmental Technology Group, Laboratory of Technical Chemistry, Swiss Federal Institute of Technology Zurich, CH - 8092 Zurich, Switzerland

Abstract In this work, a new simple, yet effective, systematic method to perform retrofit design and analysis is presented. Based on a path flow analysis approach, a set of indicators is calculated in order to pinpoint unnecessary energy and material waste costs and to identify potentially improved retrofit alternatives. The method requires only steady state design data and a database with properties of compounds, including, environmental impact factor related data and safety factor related data. Given a simulation report corresponding to an actual process (or base case design), the method identifies the material and energy path flows and calculates a set of indicators. The most important design variables are then identified through a sensitivity analysis in terms of their effect on the indicator values, which also defines the limiting values of these variables. The generated retrofit (design) alternatives are classified in terms of reduction targets in cost of operation, raw materials, energy consumption, environmental impact and safety. The well-known HDA-process is used as a case study to highlight the main features of the retrofit analysis method.

1. Introduction The increasing concern and focus on pollution prevention and the never-ending quest for higher profits in order to be competitive on the market, makes the necessity of process optimisation obvious. Although, use of advanced mathematical methods is an obvious solution approach, applications of such methods prove difficult and time consuming for large and complex processes. Also, these approaches are dependent on the availability of reliable mathematical models of the process. An alternative approach is to divide the main problem into sub-problems that are easy to solve without sacrificing the accuracy of the calculations, and where the final step involves solution of a well-defined process optimisation problem. Using available data the indicators can identify the important design variables and the potential for improvement. The indicators, by definition, would also provide estimates of improvements in terms consumption of resources, environmental impact and safety, since they involve the same set of variables. The final results would consist of a list of feasible retrofit (design) alternatives that are guaranteed to provide improvements in comparison to the reference

18 design. These results can also be used to derive a simpler mathematical programming problem with respect to the identified design variables and using the generated retrofit alternatives to determine a superstructure with a well-defined solution space. The objective of this paper is to present the indicator based retrofit analysis method starting from the analysis of the process (plant) data and ending with the generation and evaluation of the generated retrofit alternatives. Although, the last step of deriving and solving the mathematical optimisation problem is not part of the objectives of this paper, the improvements achieved through the application of the method are highlighted through a case study. In the evaluation step, the sustainability metrics defined by IChemE Sustainable Development Working Group (Tallis, 2002), the WAR indicators (Cabezas et al. 1999) and the inherent safety indicators (Hekkila, 1999) are considered.

2. Retrofit Analysis Method The retrofit analysis method consists of 6 main steps, as outlined below. A brief description of steps 2 and 3 are given below. A more detailed description of the methodology can be obtained from the corresponding author ([email protected]). 1. Obtain process (plant) steady state data. 2. Transform the process flowsheet to a process graph, and decompose this graph to identify the path flow diagrams. 3. Calculate the set of indicators ( five for mass and two for energy). 4. Perform sensitivity analysis on the indicators with respect to changes in design variables (to identify the important design variables). 5. Generate retrofit (design) alternatives by changing values of the identified design variables. 6. Evaluate the generated alternatives in terms of improvements with respect to resources (mass & energy), sustainability metrices, environmental impact factors and inherent safety factors. Step 2: (Decomposition of Flows): A process flowsheet consists of unit operations and streams combining these. Uerdingen (2002) applied the graph theory to convert the flowsheet into a process graph where the process units become the vertices and the process streams become the edges that connect the vertices. This helps to identify the flow paths in terms of mass (of each component present in the system) and energy and classify them as supply flows, demand flows or incident flows. A supply flow is either a flow that enters the process or a flow generated in the process. Demand flows are either outlets or flows that are consumed in a reactor. Incident flows are flows that runs between the unit operations. An open path is a flow of a component that enters the process in a supply and leaves in a demand. The path flows are either open, if no recycle occurs, or closed, if recycles are present in the flow sheet. For each recycle, a cycle path is defined for each component in the recycle. The energy demand can exist in two ways - energy leaving with a mass demand flow or as heat transfer. Step 3 involves calculating the set of mass and energy indicators and the most important of these are breifly described below. These indicators, by definition, are implicitly related to the process and operation through variables that indicate how the design/operation can be improved by either decreasing or increasing their values.

19 Material-value added (MVA): For a given open path it is desirable to calculate the value generated from start to end point. This is done by calculating the difference between the value of the component path flows outside the process boundaries and the costs in raw material consumption or feed cost. Negative values for MVA indicates value losses and show that there are potentials for improving the economic efficiency. Energy and waste cost (EWC): The EWC indicator consists of two parts: EC considers the energy costs and WC the process waste costs associated with a given path, by allocating the utility consumption and waste treatment costs. The results will indicate the maximum theoretical saving potential for a given path. High EWC values indicate high energy consumption and waste costs that could be reduced by decreasing the path flow or the duties. For component c in path flow k the equation is: ^

EWCf ^ = m]^^

P^uQu-jj^

+ (Pit)

^Ax\')

(1)

ZJ ^m,uk ^u,uk vm»Pm ) uk=\

Au is an allocation, p j is the density and WAxj is the waste allocation factor. PEu represent the unit price of the utility Q„. Subscript u is the sub-operations index, uk is the index of all component path flows in u and 7 is the path flow index. Reaction quality (RQ): This indicator measures the effect a component path flow may have on the reactions that occur in its path. If the RQ value is positive, the path flow has a positive effect on the overall plant productivity. Negative values indicate an undesirably located component path flow in the process. Accumulation factor (AF): AF is a way of measuring the accumulative behavior of individual components in recycles. .(^) AF=I

(2) EN

OP

a=l

op=l

1 Y^ft^^m

op

where m^^^ is the cycle flow rate. High values of this indicator show that there is a build-up of a component within the system, which possibly could be caused by poor separations or low conversion in the reactive unit. Total value added (TVA): This indicator describes the economic influence a component path flow may have on the variable process costs. Negative TVA values indicate improvement potentials in the process. Still, if a path flow has an high EWC value that is compensated by a high MVA value and gives a positive TVA value it can still be possible to reduce the energy cost. Energy accumulation factor (EAF): The energy accumulation factor (EAF), calculates the accumulative behavior of energy in an energy cycle path flow. Since it is of interest

20 to recycle or recover energy, these factors should be as large as possible in order to save energy. The energy accumulation factor can be calculated as:

EAF^ =—

££

• 'EN

E a=l i=l

^ OP

(3)

^

h op

op=l

where / is the total number of vertices encountered in the energy cycle path flow, and / is the index of these, ec is the index of the cycle energy path flows, ehl is the amount of energy recycled in the particular recycle. Steps 4-6: Once the indicators have been calculated, they are included in a sensitivity analysis in order to pinpoint areas of the process with good improvement potentials and to identify the corresponding set of design variables that may be changed in order to achieve the improvement. The generated retrofit alternatives are evaluated in terms of various performance indices (mass/energy consumption, sustainability metrices, environmental impact factors and safety factors). A process simulation needs to be performed for each alternative. Since the generated retorfit alternatives are usually relatively small changes on the original design, and, a reference flowsheet simulation already exists, these additional simulations are not difficult to make.

4. Case Study Hydrodealkylation of toluene is a process where toluene is converted into benzene by reaction with hydrogen, forming Diphenyl as a byproduct. This is a well known process, which has been studied in numerous publications. The reference design and flowsheet considered in this paper are taken from Seider et al. (1999), where further details can be found. The necessary steady state simulations have been performed with a commercial process simulator, from where the results have been transferred to a software developed for this work to calculate the indicator values. The steady state simulation results are also transferred to ICAS (ICAS Documentation, 2002) to determine the environmental impact factors, the sustainability metrics and the safety factors. Table 1 shows the most important indicator-values from the base case design. A detailed calculation results document can be obtained from the corresponding author. Table 1: Indicator values for base case design. Name CI 02 05 07 09

Description CH4 in gas recycle Diphenyl in stream 26 CH4 in stream 27 CH4 in purge H2 in purge

AF 4.88 -

RQ 0.00 0.00 0.00 0.00 1.06

EWC 484.5 266.8 0.43 7.78 33.98

MVA -13.4 -481.9 -8748.0 -2948.0

TVA -484.5 -280.2 -482.3 -8755.0 -2982.0

The open path flows 05 and 07 score a high negative MVA value because the production of methane from the raw materials is very high compared to the fuel credit

21 given for these paths. Open path flow 09 shows a high negative TVA value. This is because the hydrogen in this path is lost in the purge and the purchase price of hydrogen is high compared to the fuel credit given by incineration. The methane gas cycle CI, shows an AF value above one, which indicates an unfavorable build-up of methane in the system. The low TVA value is caused by the high EWC value, which is again a result of the high flow rate. A sensitivity analysis was performed in order to identify the retrofit alternatives with the largest impact towards an improvement of the process. A component splitter was introduced after the flash operation in order to separate hydrogen and methane before the recycle, which would lead to lower EWC values for the gas cycle paths (see CI value in Table 2). In addition, valuable hydrogen will not be lost in the purge, thus decreasing the negative TVA value of 09. Note that the slight increase in the MVA value for 07 is compensated by the decrease in the MVA values for the other path flows. As hydrogen is fed in excess compared to toluene, reducing the hydrogen feed rate can reduce the amount of hydrogen lost in purge in 09 (see TVA value) as well as the raw material cost, which affects the benefit of the process. Finally, the temperature in the inlet stream to the reactor is optimized (increased) in order to reduce the EWC values of the large streams passing unit E-lOO (pre-heater for the reactor). These suggested changes are implemented and Table 2 shows the improvements in the process and thus in the indicator values for the new process design. Table 2: Indicator values for improved process design. Name CI 02 05 07 09

Description CH4 in gas recycle Diphenyl in stream 26 CH4 in stream 27 CH4 in purge H2 in purge

AF 0.00 -

RQ 0.00 0.00 0.00 0.00 1.04

EWC 0.00 267.2 0.11 6.45 0.06

MVA -12.9 -159.0 -9085.0 -7.5

TVA -484.5 -280.2 -482.3 -8755.0 -2982.0

The sustainability metrices, which show any change (compared to the original design) are summarized in Table 3. As it can be seen, the new design gives an improvement, especially for the energy consumption. Finally, results from the WAR algorithm are listed in Table 4, showing a slight improvement in the GWP and PEI values (all other factors are unchanged). The total inherent safety index (ISI) for the base case process was calculated to be 31. This did not change (as it is closely related to the production rate and identity of the product, in this case, benzene) with the new process design, so no safety or environmental aggravation was encountered by changing the design to a more energy efficient process, using the retrofit alternatives. Besides this HDA case study, the method has been succesfully applied to a range of other processes, including cyclohexane, styrene and monochlorobenzene plants.

22 Table 3: Results from sustainability metrices.

Total net primary energy usage per kg product Hazardous raw material per kg product Net water consumed per unit mass of product

Base case design 78.58E+06 kJ/kg

Improved design 55.24E+06kJ/kg

1.22 kg/kg product 184.6 kg/kg

1.19 kg/kg product 171.3 kg/kg

Table 4: Indicators for the WAR algorithm.

Global Warming Potential (GWP) Potential Environmental Impact (PEI)

Base case design 123.1 573E+03

Improved design 117.6 570E+03

5. Conclusions A systematic and easy to apply computer aided technique for retrofit design has been presented and its application through a well-known case study has been highlighted. An important feature of this technique is that it does not perform any complex calculations but provides feasible retrofit (design) alternatives that show improvements when compared to the reference design. This has been possible because only design variables that are sensitive to the indicators are changed in order to generate the retrofit alternatives. At the same time, since the indicators, by definition, are also functions of the same set of variables as the sustainability metrics, environmental impact factors and inherent safety factors, any generated retrofit alternative that improves the indicator values also improves these factors. For the highlighted case study, it appears that rather than a trade-off between competing factors, the generated retrofit alternatives either improve them or are neutral to them. This means that the process optimisation becomes easier and multiple objectives can be satisfied without resorting to tradeoffs between them. Current work involves developing more case studies so that the question of multiple objectives can be more thoroughly investigated.

6. References Cabezas, H., Bare, J., Mallick, S., 1999, Pollution Prevention with Chemical process Simulators: The Generalized Waste Reduction (WAR) Algorithm, Computers Chemical Engineering, 23 (4-5), 623-634. Heikkila, A.-M., 1999, Inherent Safety in Process Plant Design - An Index-based Approach, Ph.D-Thesis, VTT Automation, Espoo, Finland. ICAS Documentations, 2002, CAPEC Internal Report, PEC02-23, Technical University of Denmark, Denmark. Seider, W.D., Seader, J.D., Lewin D.R., 1999, Process Design Principles, Chapter 3 John Wiley & Sons, Inc., USA. Uerdingen, E., 2002, Retrofit design of continuous chemical processes for the improvement of production cost-efficiency, PhD-Thesis, ETH-Zurich, Switzerland. Tallis, B., 2002, Sustainable Development Progress Metrics, IChemE Sustainable Development Working Group, IChemE, Rugby, UK.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

23

A Comparison of Flowsheet Solving Strategies Using Interval Global Optimisation Methods S. Balendra, and I. D. L. Bogle^ Centre for Process Systems Engineering Department of Chemical Engineering UCL (University College London) Torrington Place, London WCIE 7JE, U.K.

Abstract This paper investigates an approach to process optimisation that allows construction of flowsheets in modular systems that can then be optimised using interval global optimisation methods based on branch and bound methods. The modular flowsheets are constructed with generic unit modules that can provide the interval bounds, linear bounds and derivative bounds using extended arithmetic types. Modular flowsheets are convenient and modular flowsheeting systems very popular. The simultaneous modular approach along with equation-based methods have been used to optimise three case studies. The modular approach has advantages but when optimising there is a price to pay for this. More bounding steps are required resulting in higher computation times although in the case of the water network problem, the most nonlinear of the problems, the price was small.

1. Introduction New methods for global optimization are continually generating interest in chemical engineering. Recent advances in deterministic global optimization methods for the enclosure of all solutions of non linearly constrained problem allow us to consider a wide range of chemical engineering optimisation problems Floudas (1999). Flowsheet optimisation can provide significantly better designs at modest cost during the early stages of design. Modular flowsheeting systems dominate the market and are used by much of the design community. Two important distinctions are identified in formulating flowsheeting problems. In the equation-oriented formulation the flowsheet is treated as a set of mass/energy balance and constituent equations that are solved simultaneously. The alternative sequential modular approach views the flowsheet as interconnected black boxes. Local Modular optimisation methods have been investigated by Schmid & Biegler (1994). Both approaches have their advantages, however the modular approach has the advantage that it matches more closely to the natural structure of the flowsheet. Optimisation can be achieved by the application of global optimisation algorithms to modular flowsheets built from generic models Byrne & Bogle (2000) using methods based on interval analysis.

Corresponding author; d . b o g l e @ u c l . a c . u k ; + 4 4

(0) 20 7679 3803

24 1.1. Interval analysis and automatic differentiation Interval analysis was first introduced by Moore (1966). An interval consists of a lower and an upper bound. Interval arithmetic ensures that the interval result of an operation on two intervals contains all achievable real values. This is useful as continuous real variables can be divided into discrete interval sections. If mathematical operations are carried out on these intervals, according to the rules of interval arithmetic, the result will contain the range of all possible values. As a result, the global optimum can be bounded. Hansen (1992) provides a detailed explanation of some interval methods and their application to global optimization. Certain interval methods make use of interval gradients which require derivatives. Automatic Differentiation (AD) is a method for simultaneously computing partial derivatives using a multicomponent object, called gradient, whose algebraic properties incorporate the chain rule of differentiation. The rules, together with the gradient type, form an extended type that we call AD. This type can be used with intervals.

2. Flowsheet Optimisation Methodology The sequential modular approach can be formulated in a way suitable for interval methods. Modules are connected in the same way but must be modified to handle interval arithmetic. A generic module requires point values or intervals for all the input streams and unit parameters and calculates the conditions for the output streams as respectively values or intervals. Modular flowsheets are constructed with generic unit modules that can provide the interval bounds, linear bounds, derivatives and derivative bounds using extended arithmetic types. Using interval analysis and automatic differentiation as the arithmetic types, lower bounding information is used for optimisation in a branch and bound framework. The interval global optimisation problem is reformulated as a bound constrained linear relaxation problem. Various classes of linear under-estimators, derived from the natural extension and the mean value forms of interval analysis, can be applied to any once differentiable function Byrne & Bogle (1999). These underestimators are combined with the interval bounded linear program to create a rigorous algorithm for constrained global optimisation. These reformulations are used for nonconvex problems.

\Z w

•

f Fig 1. A Generic model allowing multiple types. A generic model, illustrated in Fig 1, is a model that specifies the transformations that need to be applied to some underlying type, T, to obtain the output. The model needs to

25

describe the operations and then the appropriate rules are applied to data of type T. For example, a module, which adds its inputs, should use the interval arithmetic rules if the underlying type is an interval (T = interval) and the rules of AD if the underlying type is an AD type. This formulation also includes models using traditional arithmetic. 2.1. Optimisation of extended- type flowsheets Flowsheets can be built up from generic units and then evaluated using the operations for an extended type, T, which provides the information necessary for the global optimisation algorithm. The variable type being used is intervals. Each unit calculates the output streams (where the input and output streams are usually a vector) and the cost associated with the unit as intervals. The summation of the costs provides the objective function. The design constraints are added outside the module to the optimisation problem. Interval gradient types have been used, and the global optimisation algorithm uses the NE and MV underestimation scheme (Bogle & Byrne, 1999, p.1341-1350) to construct a linear relaxation of the objective function and constraints in terms of the optimisation variables. The solution of this linear relaxation provides the necessary bounds on the optimisation problem. 2.2. Solving recycle problems The recycle stream is torn with a tear block. Then a range of inputs to the flowsheet is selected by the interval optimisation algorithm and the flowsheet is calculated through the interval units to produce a set of outputs which bound all the possible outputs from the flowsheet with the given parameters. Given a guess for the values in the torn stream, XT, the resulting calculated torn stream, Xc, will also enclose all the possible values of the recycle stream with XT as an input. The simultaneous modular approach has been applied. This corresponds to using a recycle module where the parameters are independent variables in the optimisation and the residuals are the residuals of the constraints Xj-Xc = 0. In this case, the recycle is converged as the optimisation converges. 2.3. Equation based flowsheets Interval global optimisation can also be used with equation based systems. Information about the structure of the problem facilitates efficient solution of the constrained NLPs using interval analysis. This is achieved by reformulating the lower bounding procedure as a convex programming problem and allows the inclusion of convex constraints in the lower bounding problem. Bounding procedures here have been taken from Zamora & Grossmann(1998). 2.4. A comparison of the approaches It is interesting to compare the performance of interval methods on modular and equation based formulations of flowsheeting problems. Efficiency and convenience both need to be analysed when making comparisons. The equation based formulation will be more computationally efficient so it is important to know what the price to pay is for having the convenience of a modular formulation. The following sections will demonstrate modular and equation based optimisation for three case studies.

26

3. Case Study I: Haverly Pooling Problem This problem is to blend four feeds into two products to minimize the total cost. Each feed has a composition XA , and cost c [£/(kmol h)]. Each product has a cost, required composition, and flowrate, F. The feeds are mixed to produce products that satisfy the quality requirements using mixer and splitter units to represent the blending tanks. A diagram and details of the problem can be found in Quesada & Grossmann (1995). This problem is a small scale blending problem and is non-convex. The procedure presented here could be used to obtain the global optimum of large scale non-convex blending problems by reusing a very small number of generic units (mixers, splitters, and feed and product units). This problem has a number of local minimizers, and a global minimizer at F= [0, 100, 0, 0,0, 100,100,200]^ and X A = 0.01 with f(x) = -400. This problem requires feeds, products, splitters and mixers. The flowrate is determined by a single input parameter and the cost by multiplying the unit cost by the flowrate. A mixer has two inputs and one output calculated by 'adding' the inputs together; in this case the cost is zero. Splitters divide one input into two outputs based on the input parameter (split fraction) and again the cost is zero. The quality constraint placed on the two product streams become residuals in the product modules, which have one input and no outputs. The equation-based formulation is given in Quesada & Grossmann (1995).

4. Case Study II: Recycle Flowsheet Problem This case study is a reactor-separator-recycle system to produce monochlorobenzene. The operating parameters and sizes for one of the synthesis alternatives are optimised using the detailed models and the costing information provided. Each unit has a capital cost, Cc, and an operating cost, Co, which is incorporated into the objective function through a pay out time of 2.5 years. The principal units are a CSTR and two separation columns. The models have been reformulated in terms of component flowrates, Fsj. The reactor is a continuous stirred tank reactor (CSTR) which models the reaction between chlorine and benzene (A) to produce monochlorobenzene ( B) and dichlorobenzene (C) at a constant temperature. The maximum (global) profit is $2081/day. This flowsheet contains the same units as case study I plus a reactor. The reactor model has a single input stream, F2,i and three parameters, Ai, Bi, and the extent of reaction, v. The equation based formulation is given in Floudas (1995).

5. Case Study III: Alperovits Eight Link Looped Water Network Fig 2 below illustrates a looped water network design configuration of pipe junction (nodes), pressure source (reservoir, pump) and fixed pipe lengths (connecting the nodes). The global optimisation task is to reduce the cost of the network while satisfying the anticipated water pressure head at nodes. A variety of local optimisation schemes have been developed and very few global approaches have been considered Eiger (1994) et al. and Sherali & Subramanian (2001) . This is the first attempt using interval analysis.

27 Reservoir

<2)—L=(i>

a

TO

Fig 2. Water Network Problem. The optimal design problem is to determine the minimal cost combination of pipeline diameters. Each diameter has a corresponding cost per unit length Ck- Each segment k of pipe link i has a particular diameter and a corresponding length X^i (SXki = 1000m) and the objective function is Cost = ^ CjciXf^i-

The global optimum has a cost of $403,657 with the following values for Xi^ for pipe section diameters: 1 (1000m), 2 (795:205m), 3 (1000m), 4 (1000m), 5 (310:690m), 6 (11:989 m), 7 (99:901m), 8 (1000m). For this looped network we have modules for the pipes and the nodes. The objective function is the sum of the cost of the pipe modules. Due to the difference in head between the two nodes, the head constraints are taken as the residuals. The node module can be thought of as a mixer module as in case study I, with an extra stream leaving representing the demand. The equation-based formulation is given in Sherali & Subramian (2001).

6. Results - Number of Iterations and CPU Time for the Case Studies Table 1 - Numerical results. Case Study

Modular Based

Equation Based

CPU/sec

Iterations

CPU/sec

Iterations

I

18.4

13

2.09

3

II

289.2

26

182

15

III

23.56

9

20.94

9

28 The results in Table 1 were generated using Matlab 6.1 on a Pentium III IGHz. As expected the CPU time for the modular approach is longer since there is an inevitable overhead associated with the modular approach. From the results it can also be seen that the number of iterations (interval divisions) is often higher for modular based systems rather than for equations based systems. This is because more relationships are introduced through the interconnections between modules resulting in more bounding procedures required for modular systems. It is also a result of the well known dependency problem Hansen (1992) causing extra bounding if a given variable, which may occur more than once, is treated as a different variable.

7. Conclusions The simultaneous modular approach along with equation-based methods have been used to optimise three case studies. The modular approach has advantages but when optimising there is a price to pay for this. More bounding steps are required resulting in higher computation times although in the case of the water problem, the most nonlinear of the problems, the price was small. Our future work will be exploring the extent to which this can be alleviated by careful implementation of modules to account for interval arithmetic and in particular to avoid the dependency problem. Also in appropriate modules we will introduce an interval Newton method to reduce the number of bounding procedures.

8. References Byrne, R.P. and Bogle, I.D.L., 1999, Global optimisation of constrained non-convex programs using reformulations and interval analysis. Comput chem Engng, 23, 1341-1350. Byrne, R.P. and Bogle, I.D.L., 2000, Global optimization of modular process flowsheets, Ind. Eng. Chem. Res. 39(11), 4296-4301. Eiger, G., Shamir, U. and Ben-Tal, A., 1994. Optimal Design of Water Distribution Networks. Water Resources Research, Vol. 30, No. 9(1194), 2637-2646. Floudas, C.A., 1995, Non-linear and mixed integer optimisation. Fundamentals and Applications. Oxford University Press, New York. Floudas, C.A., 1999, Recent advances in global optimization for process synthesis, design and control: enclosure of all solutions. Comput. Chem. Engng., 23, S963-S973. Grossmann, I.E., 1996, Global optimization for engineering design. Kluwer Academic Publishers. Dordrecht, The Netherlands. Hansen, E., 1992, Global Optimization Using Interval Analysis, Marcel Dekker, New York. Moore, R.E., 1966, Interval Analysis, Prentice Hall, Englewood Cliffs, New Jersey. Schmid, C. and Biegler, L.T., 1994, A simultaneous approach for flowsheet optimisation with existing modelling procedures. Trans. IchemE, 72, 382-388. Sherali, H.D. and Subramanian, S., 2001, Effective Relaxations and partitioning Schemes for Solving Water Distribution Network Design Problems to Global Optimality. Journal of Global Optimisation, 19, 1-26. Quesada, Land Grossmann, I.E.. A global optimization algorithm for linear fractional and bilinear programs. Journal of global optimization, 6:39-76, 1995. Zamora, J.M. and Grossmann, I.E., 1998, Continuous global optimisation of structured process systems models. Comput. Chem.. Engng., 22/12, 1749-1770.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

29

An Integration of Design Data and Mathematical Models in Chemical Process Design B. Bayer, L. von Wedel, W. Marquardt* Lehrstuhl fur Prozesstechnik, RWTH Aachen, D-52056 Aachen, Germany

Abstract Model-based methods, provided by process modeling environments, nowadays support a variety of activities throughout the lifecycle of designing and running chemical processes. On the other hand, computer-aided engineering (CAE) systems have become popular for maintaining the information relevant to describe the function of the process as well as equipment data. This contribution proposes an integration of these two specialized types of systems. First, such an integration allows to understand the design context in which models have been used. Further, an export functionality of the CAE system allows the modeler to generate a skeleton model that can be modified or enriched, instead of starting modeling from scratch for each model-based task.

1. Introduction In chemical process industries there is a growing demand for an improvement of the design process in order to obtain better plants in shorter development cycles. Existing software tools support only isolated parts of the design process. A sustainable improvement of this software support can only be achieved by an integration of tools into an environment combined with the support of work processes (Marquardt and Nagl, 1998). Design data capturing information about the chemical process and the plant as well as mathematical models used for analysis or optimization purposes are major types of information within chemical process design. Design data characterizing a chemical process (such as flowsheets and equipment data sheets) are captured within computeraided engineering (CAE) tools and project databases. Process modeling environments allow developing and solving mathematical models for process analysis. These models are stored in files by the different users who organize them according to personal preferences. Obviously, there are strong dependencies between both sets of information: flowsheet topology and phenomena are reflected by the mathematical model on the one hand; on the other hand, findings based on simulation experiments form the basis for design decisions about the process structure and must thus be re-integrated into the design database. Thus, the integration of tools managing process design data and of tools used for model-based analysis is an important contribution towards the integration of modelbased synthesis and analysis steps during chemical process design. * Correspondence should be addressed to W. Marquardt, [email protected]

30 1.1. Requirements An integration solution to improve upon the use of design data and mathematical models must realize several important requirements: • It must be possible to create a new mathematical model on the basis of the process as it is represented by a process flowsheet. Here, different parts of the model correspond to different parts of the flowsheet. During his/her work, the engineer must be able to switch back and forth between process steps in a flowsheet and corresponding mathematical models. • Based on the design data, a mathematical model cannot be generated completely. Therefore, it must be possible for the user to further extend, modify, and specify the model, ideally with state-of-the-art process modeling tools such as AspenPlus or gPROMS. • If the process flowsheet is modified by the engineer and simulations are going to be performed for this new design alternative, it must be possible to reuse parts of the mathematical models, which have already been specified for the unmodified parts of the process to avoid that the user repeats work already done. • The simulation results must be integrated back into the flowsheet at least partially so that they are available for further design activities. It is further possible, that the user recognizes during modeling and simulation that a modification of the process or its structure is necessary and modifies the model accordingly. Such changes must then be imported back into the flowsheet in order to ensure consistency between the design data and the mathematical model. • During process design, mathematical models on different levels of granularity with varying degree of detail are employed depending on the design context. Mathematical models might represent mass balances with linear descriptions of unit operations for costing considerations, rigorous kinetics and phase equilibria for operating point optimization, or dynamic phenomena for control system design. These different types of models, which are often realized using different process or generic modeling tools, must be maintained. 1.2. State of the art Currently, the functionality described above is mainly performed manually by engineers concerned with process design and model development. Certainly, there is a risk that work in model development is duplicated, inconsistent models are employed for different purposes, or the models used during process design cannot be found in later stages of the project. In commercial tools, the functionality stated as required above is realized partially. As an example, the Aspen Engineering Suite (AES; AspenTech, 2002) realizes an export of a steady-state model in AspenPlus to a dynamic model in AspenDynamics. However, such a point-to-point integration, although useful, is not extensible towards more general model development problems involving different granularity and abstraction levels. Whereas the AES approach considers the AspenPlus model as the core information, from which other model representations are derived, we consider the flowsheet of a process as the relevant piece of information that is used as a starting point for model development (Bayer et al., 2001b). This permits an extensible architecture which can

31 handle the derivation of models from a process flowsheet in a number of different contexts and between tools of different vendors. During the last years, integrated design environments like Aspen Zyqad have been developed. Such tools are tightly linked to the products of a single vendor and do not permit the use of different process modeling tools best suited for different tasks within process design.

2, Tools for Managing Design Data and Mathematical Models In this work, Comos PT (innotec, 2002), a tool holding design data, has been integrated with the model repository Rome (von Wedel, Marquardt, 2002) which is capable of storing and organizing the models which are created and used during process design activities. 2.1. Comos PT Comos PT is a commercial CAE system, which has been originally developed for the support of data management during detailed engineering and construction. It provides a basis for the consistent storage of data. The system has a layered architecture, where the core is built by an object server. Within this server, an object-oriented data model is specified that can be extended and changed in a flexible manner. Further, the server offers standard integration mechanisms like COM and OLE. As a chemical engineering system, Comos PT offers flowsheets in its user interface, where the objects placed on a flowsheet are directly connected to the objects within the database. Comos PT has been extended with parts of the conceptual information model CLiP (Bayer et al., 2001a) as a basis for the support of conceptual process design. Thus, Comos PT is responsible for manipulating and storing design data. The major objects of that extension are process steps representing the different reactions, physical procedures and unit operations of a chemical process and the phase systems representing the material flowing between these process steps. Further, the chemical plant with its equipment and pipes can be specified within that CLiP implementation. 2.2. ROME

Instead of integrating process modeling tools on an individual basis, the design data management system based on Comos PT is hooked up to the model repository ROME (von Wedel, Marquardt, 2002) which takes care of storing and maintaining process models from a variety of sources, such as gPROMS, AspenPlus, or CAPE-OPEN compliant software components. ROME abstracts these incompatible model definitions into a neutral representation and thereby permits access to heterogeneous models through a unified interface. A number of advantages are realized through this neutral representation, among them being able to document, browse, and aggregate models independent from the modeling tools used for their development. The long term goal of the project is the ability to gradually build up a library of mathematical process models relevant for the business domain of a company regardless of the tools being employed in process modeling. ROME is implemented using an object-oriented database (Versant, 2000) which can be accessed via CORE A middleware (Object Management Group, 2000) to ensure that the model repository is easily integrated with in-house or commercial software in a chemical engineering company's intranet, for example. Functionality such as importing.

32 browsing, exporting, or aggregating models can be performed by means of a Windowsbased graphical user interface as part of the ModKit modeling tool (Hackenberg, 2002).

3. Relations Between Design Data and Models The integration approach outlined in this contribution relies on the information model CLiP capturing the relationships between the concepts handled in the two tools to be integrated, i.e. the relations between process steps and phase systems on the left-hand side and mathematical models on right-hand side (cf. Fig. 1).

ProcessStep

f-O

(from DesignData)

\_

pTOC ess

step modeled by Model (from Models)

PhaseSystem (from DesignData)

I

phase system modeled by

l\

1

/^/

i..„ \

1

process port modeled by

ProcessPorl (from DesignData)

dl..rT

\

Process Steps

1

0..n 1

2 cx)nnectivity represented by

PrcxiessState

\ \o..n

Connector (from Models)

0..n ^2

Coupling

(from DesignData)

(from Models)

1..n

O-.n

Mode

Figure 1: Conceptual data model showing relations between process steps and models. In CLiP, the core element to describe the function of a process is a FrocessStep. Examples for process steps are unit operations such as reaction, separation, or mixing (cf. the left-hand side of Fig. 1). A PhaseSystem represents the processing material and defines chemical components as well as the aggregate state. A ProcessPort represents a distinct point within the process with an explicit state of a process step or a phase system (cf. the ProcessState class in Fig. 1). The relations between process ports and states describe the structure of the process. A mathematical Model (cf. the right-hand side of Fig. 1), maintained in ROME, can be specified by equations and variables or by referring to a tool-specific model, such as an AspenPlus input file. A Connector represents a possible connection point of a model and the Coupling denotes connections among connectors. The connector and couplings concepts permit reflecting the structure of a process in the mathematical model. The behavior of process steps and phase systems can be represented by mathematical models (see the modeled-by relations in Fig. 1). In order to map the process topology to the model, process ports and connectors have to be related as well as process states and couplings by corresponding modeled-by relations. It must be considered that the relations between process design and model concepts are rather complex. Depending on the design context, a process step (such as separation) can be represented by different mathematical models (e.g. a linear splitter or a rigorous distillation column) and a certain mathematical model (such as a first-order transfer block) can be used to

33 represent different process steps (e.g. a tank or a first-order reaction mechanism). Thus, the modeled-by relations must be maintained with many-to-many multiplicities.

4. Integration: Implementation and Functionality In this section the integration of Comos PT and ROME is described. In order to create a mathematical model from a design alternative specified in Comos PT, the user selects models for each phase system and process step within Comos PT. Along this work, we have implemented support that provides defaults for this selection for all types of process steps. These selections are grouped into alternative configurations which correspond to a certain model-based application. The first step to apply some model-based application is to specify a suitable model for each process step. Basically, this step establishes the modeled-by relations (cf Fig. 1) between process steps and phase systems on the one hand and models on the other hand. Mapping the process topology to the model to be generated is taken care of by the automatic model generation step. In order to use linear models (e.g. for basic cost estimation), the integrated system provides a configuration linear process model which consists of defaults for linear models for each process step. Another configuration is provided for rigorous steadystate simulations with AspenPlus. Here, all process steps are mapped to corresponding blocks provided by the AspenPlus flowsheeting tool. In addition, the user can create custom configurations and specify arbitrary models to be used, e.g. when custom models for dynamic simulation shall be employed. These models can be selected among the set of models maintained by the model repository ROME. Once mappings for all process steps have been specified in Comos PT through defaults of a certain configuration or user selections, the model can be exported to the model repository ROME. The model is first exported to an intermediate format represented in XML and is subsequently imported into ROME. From the model repository the user can then export the model to different target formats, among them modeling languages like gPROMS, ACM, and Modelica. It should be noted, that the flowsheet topology is preserved through the series of steps executed. Further support realized in Comos PT allows the user to switch between configurations or to create new ones. In order to customize a configuration, the user can override the default mappings, for example to employ a tailored model for a certain process step. The selection of a model for a process step is simplified by a dialogue from which the user can select among the models already available in ROME. The implementation of the conceptual data model shown in Fig. 1 is performed in a number of tables in MS Excel storing the mappings between process steps and models (organized in rows) for the different configurations (organized in columns). Each design project is organized in a separat Excel sheet. Further sheets contain the default configurations. An extension to Comos PT, developed in Visual Basic for Applications (VBA), generates an XML file referring to the selected model configuration stored within the Excel tables. The repository services for model import and model selection can be accessed from Comos PT via the ROME API (von Wedel, Marquardt, 2002).

5. Conclusions and Future Work Based on the conceptual data model CLiP, the integration of the design data management tool Comos PT and the model repository ROME has been presented. The

34

integration improves the use of different model-based analysis techniques along the process design lifecycle. Our realization further permits to generate parts of a mathematical model and to switch between the flowsheet and the corresponding models so that decisions made on the design level can be quickly verified with suitable modelbased techniques. As opposed to proprietary solutions, our approach is open and permits the use of process modeling tools stemming from different vendors. Currently, our approach implements only plain export functionality in order to simplify the transition from a flowsheet to a mathematical model. The use of data integration technology based on the explicit management of relations between heterogeneous documents and integration rules (Becker, Bayer, Nagl, 2003) has shown promising results when it comes to a re-integration of changes of the mathematical model back into the flowsheet. The technology permits incremental updates of mathematical models according to modifications in the flowsheet and vice versa. Such technology should be applied in future extensions in order to improve the capabilities of the implementation and to further simplify the handling of process data and models.

8. References Bayer, B., Becker, S., Nagl, M., 2003, Integration Tools for Supporting Incremental Modifications within Design Processes in Chemical Engineering, 8*** International Symposium on Process Systems Engineering, accepted for publication. Bayer, B., Weidenhaupt, K., Jarke, M., Marquardt, W., 2001a, A Flowsheet Centered Architecture for Conceptual Design, In: R. Gani, S.B. J0rgensen (Eds.): "European Symposium on Computer Aided Process Engineering - 11", Elsevier, 345-350. Bayer, B., Krobb, C , Marquardt, W., 2001b, A Data Model for Design Data in Chemical Engineering - Information Models, Technical report LPT-2001-15, Lehrstuhl fur Prozesstechnik, RWTH Aachen, available online at www.lfpt.rwth-aachen.de. Hackenberg, J., 2002, PhD Thesis, RWTH Aachen, in preparation, innotec GmbH, 2002, innotec online, http://www.innotec.de. Marquardt, W., Nagl, M., 1998, Tool Integration via Interface Standardization?, DECHEMA-Monographie 135, 95-126. Object Management Group, 2002, The Common Object Request Broker: Architecture and Specification, release 2.6.1. VERS ANT Corp., 2000, Versant Database Fundamentals Manual. Fremont, California, von Wedel, L., Marquardt, W., 2002, ROME: A repository to support the integration of models over the lifecycle of model-based engineering processes. In: S. Pierucci, (Ed.): "European Symposium on Computer Aided Process Engineering - 10", Elsevier, 535-540.

7. Acknowledgements This work has been funded by the DFG, Deutsche Forschungsgemeinschaft, in the CRC 476 IMPROVE. The authors thank A. Meyers for the support during implementation.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

35

A Production Planning Strategic Framework for Batch Plants Frederic Berard, Catherine Azzaro-Pantel, Luc Pibouleau, Serge Domenech Laboratoire de Genie Chimique - UMR 5503 CNRS/INPTENSIACET BP 1301 - 5, rue Paulin Talabot - 31106 TOULOUSE Cedex 1 - France [email protected]

Abstract Multipurpose batch plant planning is identified as a combinatorial optimization problem. The overall algorithm framework proposed in this study is based on a twostage approach using an object-oriented discrete-event simulation model (AD-HOC+) in combination with a Genetic Algorithm, since this kind of technique is particularly attractive to treat problems of NP-hard nature. The problem formulation and the results corresponding to a finite-horizon production are presented. This strategy deals with a production organized in only one campaign of a given time horizon H. The objective is to maximize product quantities during the campaign.

1. Introduction Multipurpose flexible batch plants are widely used to produce in small quantities highvalue added fine chemicals. Their production involves a multi-step synthesis and is submitted to strict constraints which are due, on the one hand, to market instability (short life cycles, rapid demand fluctuations) and, on the other hand, to rigorous regulations concerning product quality and environmental aspects. In this context, planning is a very complex problem integrated in supply chain management. The common approach to solve the problem of multipurpose plants planning is to use an MINLP (Mixed Integer Non Linear Programming) formulation (Papageourgiou and Pantelides, 1996). The main limitations of MINLP approaches are attributed to a combinatorial explosion for the treatment of large problems. To overcome this difficulty, a stochastic global optimization technique based on Genetic Algorithms (GAs) was developed previously (Berard et al, 1996a, 1996b). The optimization tool embeds a Discrete-Event Simulation (DES) model (AD-HOC+) using object-oriented concepts and describing the global dynamic behaviour of the production system for evaluation of the objective function. The planning production optimization problem was then solved through different strategies corresponding to various plant scenarios, i.e., cyclic production, finite-horizon production and "just-in-time" production. In each case, a set of production management parameters and a performance criterion computed by the DES simulator are to be defined. More precisely, the recipe priority order of final or intermediate products, determining the batch to be first treated at a given time, leads to a marked combinatorial aspect. In this paper, the problem formulation and the results corresponding to a finite-horizon production are presented. This strategy deals with a production organized in only one campaign of a given time horizon H. The objective is to maximize product quantities

36 produced in the facility during the campaign. An example is presented to illustrate how the proposed methodology can enhance managerial decision making.

2. A Finite-Horizon Production Strategy for Production Planning This part deals with the optimal production strategy within one campaign. The constraint is to carry out production at the end of the imposed time horizon. The campaign is composed of a subset of final products FPi. For a given final product FPi, the produced quantity Qi is divided into a number Ui of batch sizes Si. The production ratios are fixed with reference to Qi. The production parameters chosen to manage the production are the following ones: - Qi' quantity manufactured within the finite-horizon campaign for product FPi; - Hi: number of batches for each FPj of size Si; - Pi: priority order between product recipes for selection of the batch to load first at a given time; - hj, h2: heuristic rules for conflict management; hjis used to choose the batch to load first if several batches have the same priority. Possible rules are the following ones: 1 for the batch which enters first the facility and 2 for the batch which enters first an operation waiting queue; hz is relative to the choice of an equipment item for a given operation. The implemented rules are the following ones: 1 for the equipment item which has been available for the longest time; 2 for the one with the smallest workload; 3 for the one with the smallest waiting queue and, finally, 4 for the one for which the sum of all waiting operating times is minimal. Due to the large induced combinatorial aspect of this kind of optimization problems, classical mathematical methods seem inadequate. Consequendy, a stochastic method, and, more particularly, a Genetic Algorithm (which has proven its efficiency for similar problems) has been used in this study (Goldberg 1994, Cartwright and Long 1993, Azzaro-Pantel et al. 1998). Let us recall that a GA computes a set of individuals (the population) and a set of biologically inspired operators that can generate new individuals from parents. According to the evolutionary theory, only the most suited elements of a population can survive and generate offspring, thus transmitting their biological heredity to new generations. The heredity is enclosed in the chromosomes of the individuals, which are subject to mutation and to crossover mechanisms. The offspring generated by the genetic manipulation is evaluated, via a fitness value, measuring the quality of the solution represented by the chromosome. A selection process then retains the best individuals in the whole population for the next generation. The cycle is repeated, generally until a predefined maximum number of generations is reached. The key points of the GA will be presented in the following sections.

3. Problem Formulation The problem can be formulated as follows. Given: i. a set of NP Final Products FPi, of Ui batches of identical size Si released at the beginning of the campaign , ii. the respective amounts Ri = Qi/ Qi of each product, which are fixed relative to a referential Final Product FPI,

37

the objective is to maximize the global production level Q within the given time horizon. The optimization variables are the aforementioned parameters. 3.1. Parameter encoding Parameter encoding is generally considered as a key-factor in GA success. Special attention has thus been given to production planning encoding (see an example of a genotype in Figure 1). The first string of the chromosome consists of an integer list comprised between zero and a superior limit which depends on the required degree of precision. A similar coding has been adopted for batch number. As expected, the encoding of priority levels between batches plays a crucial role and induces a major part of involved combinatorics. Batch position in priority order is the first choice criterion between several batches which are likely to be loaded simultaneously. When considering the problem of production capacity maximization treated here, the number of genes encoding priorities is equal to the number of recipes considered in a given batch plant. Each gene corresponds to a recipe. The integer value of a gene corresponds to the recipe priority level. It must be noted that if two recipes have the same priority, the corresponding batches will be dissociated according to a loading heuristic rule. For instance, let us consider 3 final products (FPl, FP2, FP3), 2 intermediate products (IPl and IP2). The highest priority (1) is given to batches FPl and IPl, an intermediate one (2) is allocated to IP2 and FP2 and finally, the lowest one (3) to FP3. The corresponding coding is illustrated in Figure 1. GENOTYPE OF AN INDIVIDUAL Production objective

Il246j Q,

Number of batches ofFP

5 2

\L nppi nFP2 npps FPl ^

Priority between recipes

2

3 1

FP2 FP3 IPl

Heuristic rules for conflict

2h IP2

h,

4 hj

Figure 1. Example of a genotype encoding. Note also that this individual may also be represented by the code [13413]. Consequently, the same individual will have several codes, which then violates the unicity principle of individual coding. A double-elimination procedure has then been introduced to verify the encoding validity of an individual generated during the initial population creation phase or resulting from the random application of mutation or crossover operators. Finally, the heuristic rules used for conflict management are coded on the last genes of the chromosome. Each integer value corresponds to the rule number to be applied among the possible values. 3.2. Illustration By lack of place, the example which illustrates the approach will not be presented in detail. The plant is characterized by several interconnected processes involving 16 equipment items for 5 different unit operations. Associated with each process are recipes that describe how raw materials (7) are transformed to output products (3 FPs and 2 IPs). In addition, the facility is characterized by resources that are shared among processes. 3.3. Search space The search interval for all parameters is presented in Table 1.

38 Table 1: Search space for parameters. Parameters Qi : quantity of FPi Hi: number of batches pFj: priority between recipes hi : batch to load hi: equipment to use

Integer coding Genci : [0 ; 2000] Gene2 to gene4: [0;7] [0;5] [0;2] [i;4]

Search space Qi = (10 X gene,) + 25000 •* QiS [25000,45000] n N Hi = gene^ + 7 •> iiiS [7, 14] n N 541 possible orders Cf§2 Cf§2

The treated example illustrates the combinatorial aspect of production management optimization problem and justifies the implementation of a Genetic Algorithm. The order of magnitude of the associated search space is 4,43.10^. 3.4. Genetic operators (Goldberg 1994) The genetic crossover operator adopted here is the k-point crossover. The mutation operator is based on a random sort of a procedure to guarantee the diversity of the explored solutions (random gene replacement, gene permutation ...). The classical Goldberg's biased roulette wheel is used for selection. 3.5. Evaluation function The performance criterion is founded on profit maximization within the campaign and can be expressed as follows: FF3

PF3

P= YB,.«,.., = y 5,..Q, i=PFl

i=PF\

The values of Bi are relative to the profit per product (in 1). The evaluation function has to take into account the constraint Da^H, meaning that the completion time of all products Da must be achieved at the end of time horizon H. For this purpose, the following expression has been considered : F = P if Da < H and F = P - p.(Da - H)^ if Da> H with p = lO"^ The value of p results from successive simulation runs in order to guarantee that P, Da and H have the same order of magnitude. 3.6. GA parameter setting A design of experiment was carried out to select the GA parameters. Finally, the study was conducted with the following choice of parameters (see Table 2). Table 2: GA parameter set. GA parameters Population size Crossover probability Mutation probability Number of generations

Parameter value 80 individuals 0,60 0,12 250

4. Typical results The five best solutions obtained are presented in Table 3.

39 Table 3 : Best solutions obtained by GA. Production ^l^'

FP2

FPl

Net Heuristic rules ''^J^^^"^

Priority order between recipes

FP3

1

ti(l) ni t2(l) n2 t3(l) n3 FPl FP2 FP3 IPl IP2 3508 10 1798 13 1063 11 1 2 1 1 1

2 3 4

4385 3508 3508

8 1798 13 1063 10 1798 13 835 10 1798 13 1169

4385

8

11 14 10

2 1 1

1798 13 1169 10

1

2 2 2

3 2 2

hi hz 1 4

1

][

1

1

]I 1I

1 1

1

1

4 4 4

7.307 7.307 7.307 7.307 7.307

The results obtained point out that: i. In all the runs, Qi varies from 8 to 10 batches, Q2 is always produced in 13 batches whereas Q3 varies from 11 to 14 batches. Since the search space for the number of batches is comprised between 7 et 14 lots, the best solutions are always obtained with a high number of batches, ii. Concerning priority orders, the shared Intermediate Products have a higher priority than Final Products for all solutions and have generally identical priority levels. Final Product FPl comes just after and has a higher priority index than the other FPs. iii. The heuristic rule relative to equipment choice which has the lowest queue length is always chosen (h2 = 4).The batch which enters first the workshop is favoured for h^ The best solution #1 obtained at the 116^ generation is detailed in Table 4. Table 5 presents the comparison between the results obtained by optimization and those obtained by a trial-and-error procedure. sol

I

45 i 40 35 Oi

S30l icl 2 5

f

ki

Fitnessof the best individual Average fitness

20 15' 10] 5 )

20

40

60

80

100 120 Generation

140

160

180

200

Figure 2: Typical evolution of the GA. Note that this procedure, based on the successive runs of ADHOC+, was first used to find a satisfying solution which leads to a high value for net revenue with respect to the time horizon constraint and which is then used as a reference to evaluate the performances of the GA. It can be seen that a substantial improvement is obtained (5.66%).

40 Table 4: Best solution obtained by the GA. Production level Net revenue/month Production plan Priorities between recipes Batch to load first Selected equipment

Qi = 350801 P = 47 936 300 F 10 batches of 3508 1 (350801 of FPl) 13 batches of 1798 1 (233741 of FP2) 11 batches of 1063 1 (11693 1 of FP3) l)FPl,FP3,FPletIP2 2)FP2 1 - the batch entered first 4 - with the highest queue

Table 5 .'Comparison between optimization and empirical Net revenue Empirical method 6 916 672 €

Net revenue AG-DES 7 307 842 €

results. Comparison/empirical + 5,66% i.e., 391 169 €

5. Conclusion The production strategy is particularly interesting for capacity analysis of a facility within a given time horizon. The proposed methodology is well-suited for proposing scenarios under a fluctuating demand, which is typically the case for batch plants. Besides, the approach can be used for a flexibility study, in order to evaluate the performance of various production planning scenarios.

6. References Azzaro-Pantel, C , Bernal Haro, L., Baudet, P., Domenech, S., Pibouleau, L. A twostage methodology for short-term batch plant scheduling : Discrete-Event Simulation and Genetic Algorithm, Computers & Chem. Eng, Vol. 22, n°. 10, 1461-1482 (1998). Berard P., Azzaro-Pantel, C , Domenech, S., Pibouleau, L. "A General Framework for Simultaneous Optimization of Scheduling and Equipment Operating Conditions: A Case Study for Fine Chemistry Batch Plants", ECCE 2, Montpellier, France, 5-6-7 Octobre (1999a). Berard F., Azzaro-Pantel, C , Pibouleau, L., Domenech, S., Navarre, D., Pantel, M., "Towards an Incremental Development of Discrete-Event Simulators for Batch Plants: Use of Object-Oriented Concepts", Computers and Chem Engineering Supplement, S565-S568, (1999b). Cartwright, H.M., Long, R.A. Simultaneous Optimization of Chemical Flowshop Sequencing and Topology Using Genetic Algorihms, Ind. Eng. Chem. Res., 32,2706-2713(1993). Goldberg, D.E., Genetic algorithms in search, optimization and machine learning, Addison (1994). Papageourgiou, L., Pantelides, C , Optimal campaign planning/scheduling of multipurpose batch/semicontinuous plants. 1. Mathematical formulation, Ind. Eng. Chem. Res., vol. 35,488-509, (1996).

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

41

Managing Financial Risk in Scheduling of Batch Plants Aima Bonfiir, Jordi Canton^, Miguel Bagajewicz^, Antonio Espuna^ and Luis Puigjaner^'^ (+)DEQ-ETSEIB-UPC. Av. Diagonal 647, P. G, 2° P. (08028) Barcelona, Spain, e-mail [email protected]; (++) University of Oklahoma, School of Chemical Engineering and Materials Science. 100 E. Boyd St., T - 335, Norman, OK 73019. On sabbatical leave at ETSEIB; (#) Corresponding Author

Abstract The short-term scheduling problem of a multiproduct batch plant with uncertain product demands is addressed in this article. The problem is modelled using a two-stage stochastic approach maximising the expected profit and integrating inventory costs and penahies for production shortfalls. Additionally, risk is controlled using a recently developed methodology.

1. Introduction The scheduling problem in the chemical industry has been extensively studied and alternative methodologies and problem statements have been proposed in the literature to address the combinatorial character of this problem (Shah, 1998). However, most of the formulations presented are based on nominal parameter values without considering the uncertain requirements after the operations are planned and scheduled. The uncertainty from a real environment entails a risk that is initially traduced in a cost but may lead to an unfeasible situation. The aim of the present work is to provide a tool to support the decision making of developing a scheduling policy in an uncertain environment while controlling the variability over the possible scenarios. For this purpose, a deterministic MILP formulation is first presented and used as starting point for modelling a two-stage stochastic optimisation approach. To control the variability over the different scenarios, the concept of risk is introduced. The simultaneously reduction of risk and maximisation of profit results in a multiobjective stochastic optimisation problem. Two alternative risk definitions, one related with financial risk introduced by Barbaro and Bagajewicz (2002a,b) and another considering the downside risk defined by Eppen et al. (1989) are considered and the latter is used as an objective. The outcome is a set of parametric solutions corresponding to different levels of risk.

2. Model The scheduling problem of a multiproduct batch plant under uncertain product demand is addressed with the aim to maximise the expected profit. The scheduling policy involves the number of batches to be produced for each product, the detailed sequence and the starting and final times of each operation performed.

42 To derive the proposed models, one production line with fixed assigned equipment units and zero wait transfer policy is assumed. The scheduling is addressed within a time horizon of one month. Finally, inventory costs and penalties for production shortfalls, proportional to the amount of underproduction, are adopted for each product. 2.1. Deterministic scheduling model The deterministic scheduling model is formulated as a MILP problem based on a batch slot concept. With this formulation, the time horizon is viewed as a sequence of batches, each of which will be assigned to one particular product. The proposed mathematical model is shown in equations (1) to (13). It maximises the expected profit (sales inventory costs - production shortfalls) using X(b,p) as sequencing decision variable (see Nomenclature). A small penalty term on the sum of the initial time of all batches is added to force the schedule to finish in the smallest makespan possible. MaxP = ^[F(/?)-i^r(p) - I{p)'CI{p) - Fr{pyPe{p)]-a^Tin{o,b)

(1)

oJ>

P

subject to: H>TMo,b)

Vo,b

(2)

T(o,b) = '^X{b,p)TOP{o,p)

Vo,b

Tfn{p,b) = Tin{o,b) + T(p,b) Tin{o,b +1) > Tfn{p,b)

yo,b

Tfn{o,b) = Tin{o + \,b) ^X(b,p)
\fo,b

(4) (5)

yo,b

(6)

\/b

nip) = Y,^(b,p)

(3)

("7)

(8)

yp

b

(9)

i>^n(p)

Vip) = mm{D(p), n(p) • BSip))

^p

(10)

I(p) = n(p)-BSip)-V(p)

yp

(11)

43 F(p) = Dip)-Vip)

Vp

(12)

2.2. Stochastic model From the formulation presented in the previous subsection and to derive the two-stage stochastic program, the uncertain product demands are modelled by probability distributions and a set of scenarios is generated using sampling techniques. The number of batches to be produced and the corresponding sequence of products are considered as first-stage decisions, since it is assumed that they have to be taken at the scheduling stage before the realisation of the uncertainty. The sales, inventory and production shortfalls are then recomputed on a second-stage for each scenario generated. Therefore, equations (10) - (12) are rewritten to take into account the different scenarios s. Then the maximisation of the expected profit is defined as: EP = Y^ Prob(s) • Pis) -a'Y,

^Ho, b) =

o,b

-T

Probis) 'J^[V(p,s). Prip) - Iip,s) • CI(p) - F(p,s) • Pe(p)] -a'Y,^in(o,b) (1^) o,b

2.3. Risk management The concept of financial risk defined by Barbaro and Bagajewicz (2002a) and its alternative of downside risk (Eppen et al., 1989) have been incorporated into the stochastic model to support the decision making. Downside risk is finally used. 2.3.1. Financial risk Managing financial risk involves the maximisation of: EP = J^[Prob(s)• P(s)]-a• ^7-m(o,6)-^^^[ProfcC*)• p,. • z^sj)] o,b

s

Pis)>n(i)-U'z(s,i)

5

(14)

i

\/s,i

(15)

2.3.2. Downside risk The utilisation of the alternative downside risk concept requires the redefinition of the objective function and constraints as follows.EP = ju 'Y,[P^ob(s) • P(s)]-a • Y,THo,b) -Y^[Prob(s) • S(s)] o,b

s

S(s)>Q-P(s) ^(^)>0

\/s V^

(16)

s

(17) (18)

44

3. Results and Discussions The proposed methodology to incorporate risk management in the framework of twostage optimisation for scheduling of multiproduct batch plants under uncertainty has been applied to a case study involving four production stages and five different products adapted from Petkov and Maranas (1997). A total number of 500 independent scenarios were simulated using Monte Carlo sampling technique from the given normal demand probability distributions. To assess the importance of the stochastic formulation, the deterministic model using the nominal demand values has been first solved and compared with its stochastic counterpart. The results obtained are detailed in Table 1. The schedules are not shown for space reasons, but they are significantly different. In addition, it is noted that the makespan of the deterministic model is shorter, because the model does not generate inventory to hedge from adverse scenarios, as the stochastic one does. One important thing to notice is that the deterministic model predicts a solution that poorly represents the uncertain environment, i.e. the schedule obtained with the nominal parameters may be unrealistic when another demand is ordered. Indeed, although the profit of the deterministically generated schedule is higher than the expected value of the stochastically generated, when the first one is used to face the uncertainty the expected value of profit drops 16%. The stochastic schedule performs better as it is also reflected in the shift to the left of the risk curve (Figure 1). This is one indication of the danger of using deterministic models in the believe that stochastic models will only "refine" the solution. Table L Results of Deterministic and Stochastic Models.

Products n(p) E[Sales] E[Inv.] E[Penalt.] Profit E[Profit] Makespan

Deterministic schedule P2 PI P4 P3 P5 10 10 15 15 8 726 941 7099 3086 1884 74 59 401 214 116 56 123 25 468 168 79875 (value in nominal scenario) 67165 617

Stochastic schedule P4 PI P2 P3 P5 10 10 16 16 8 726 941 7313 3165 1884 74 59 687 355 116 25 56 254 89 123 76275 (value in nominal scenario) 68539 662

The management of risk has been next performed considering several profit targets (one at a time) along with various weight values reflecting different levels of risk exposure. At each profit target, a schedule with its correspondent risk curve is obtained. Risk values of schedules obtained by managing downside risk with a weight value \x = 0.001 are reported in Table 2. As it was expected, the expected profit value of the schedules approaches the maximum value obtained with the stochastic model (SP) as the profit target is incremented. From a comparison with the stochastic schedule it can be observed that reductions of downside risk of 30% and 16%) are attained at target profits Q. = 60,000 and 65,000, respectively. Selected risk curves are depicted in Figure 2.

45

30000

40000

50000

60000 Profit

70000

30000

40000

50000

60000

70000

80000

90000

Profit

Figure 1. Risk curves from the stochastic Figure 2. Selected downside risk curves for schedules with different profit targets. and deterministic schedules.

Table 2. Risk values of selected schedules when optimising at different profit targets fl. Stochastic solution (SP) FRisk (%) DRisk FRisk (%) DRisk Schedule Target Q E[Profit] 4.2 2 227 102 64,310 50,000 C 8.2 516 7 275 64,442 55,000 D 15.4 1,085 13 770 67,160 60,000 E 27.6 2,140 30.6 1,787 67,160 65,000 F 49.6 4,048 60.6 4,040 67,165 70,000 G 74.6 7,170 74.6 7,170 68,539 75,000 H

4. Conclusions The treatment of uncertainties in batch process planning and scheduling has been addressed as a two-stage stochastic optimisation problem with the incorporation of financial risk management, thus resulting in a multiobjective stochastic system. The proposed methodology has been applied to the scheduling of a multiproduct batch plant and uncertainty in product demands has been first considered and modelled by probability distributions. A comparison between the deterministic and the stochastic formulations has been performed to assess the importance of the stochastic approach. The schedule obtained with the nominal parameter values will poorly perform in most of the probable scenarios. However, with the stochastic modelling a significant improvement is attained and schedules with a good performance over all the scenarios are obtained. The management of risk has been next introduced. From the results obtained it can be noticed that risk can only be managed at the expense of the expected profit. In addition, despite the flexibility introduced by the uncertain parameters and the inventory, different cost-dependent alternatives are required to be able to manage risk in a meaningful way. A variety of alternative schedules are obtained reflecting different risk exposure poHcies.

46

5. Acknowledgements Financial support received from the Spanish "Ministerio de Educacion Cultura y Deporte" (FPU research grant) and "GeneraHtat de Catalunya" (project GICASA-D), and from the European Community (project GlRD-CT-2000-00318 and project GRDl2000-25172) is thankfrilly appreciated. The support of the ministry of Education of Spain for the sabbatical stay of Dr. Bagajewicz at UPC is also acknowledged.

6. Nomenclature Sets: b: i: o: Ps: Parameters: BS(p): CI(p): D(p): H: L: Pe(p): Pr(p): Prob(s): TOP(o,p): U: Q(i): ^(i):

Batches Profit targets Operations Products Scenarios Batch size Inventory cost Demand Horizon time Maximum n** of batches Production shortfall cost Sales benefit Probability Operation time Big value Profit target Financial risk upper bound

P(i): 5(s): l^a: Variables: EP: F(p)/F(p,s): I(p)/I(p,s): MS: n(p): P(s): T(o,b): Tfn(o,b): Tin(o,b): V(p)/V(p,s): X(b,p): z(s,i):

Weight value Downside risk Weight value Low value Expected profit value Shortfall Inventory Makespan Number of batches Profit value Processing time Final time Initial time Sales of product/^ Batch b assigned to prod. p (Binary variable) Binary variable

7. References Barbaro, A. and Bagajewicz, M.J. submitted 2002a, Managing Financial Risk in Planning under Uncertainty - Part I: Theory. Barbaro, A. and Bagajewicz, M.J. submitted 2002b, Managing Financial Risk in Planning under Uncertainty - Part II: Applications and Computational Issues. Eppen, G.D., Martin, R.K. and Schrage, D. 1989, A Scenario Approach to Capacity Planning. Operations Research, 37, 517 - 527. Petkov, S.B. and Maranas, CD. 1997, Multiperiod Planning and Scheduling of Multiproduct Batch Plants under Demand Uncertainty. Ind. Eng. Chem. Res. 36,4864-4881. Shah, N., 1998, Single- and Multisite Planning and Scheduling: Current Status and Future Challenges. Foundation of computer-aided process operations, AIChE symposium series, 340.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

47

A Network Model for the Design of Agile Plants A. Borissova, M. Fairweather and G.E. Goltz Leeds Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, UK

Abstract The network model provides the formalisation and theoretical basis for the generation of options for the design of agile production plants, and the subsequent selection of the most appropriate option when reconfiguring a plant to meet changing product and process demands. The model is developed by applying the concepts of modularisation, standardisation and reconfigurability of plants, and provides the foundation for the development of tools to aid in the analysis of the design of a reconfigurable plant, and to assist in the decision making process. The model represents a plant as a set of nodes and links, with each element of the network, its functionality and the interactions/operations within the network being described in mathematical terms. Plant reconfigurability is described as a transition from one state to another of a plant characterised by specific functionality and level of modularisation. Modularisation and reconfigurability analyses as part of the methodology for the design of agile plants use the network model to simulate the options for plant design.

1. Introduction The life-cycle of a speciality chemicals product is frequently much shorter than the lifecycle of the plant used to produce it. Pisano (1997) and Burgess et al. (2002) show that this requires a redefinition of the business environment. The introduction of a new product, and fitting the new process into a plant, often requires compromises that reduce the yield and simultaneously increase waste and its associated costs. One approach is to develop multi-product reconfigurable modular plants. These are built in modules offsite and assembled on-site in such a way that the modules can be removed, exchanged or re-built as the process requirements change. The design of agile plant seeks to map the equipment performance onto process requirements in terms of ranges rather than points. Standardisation and a systems approach are necessary at all stages, from the draft design to the operating plant. The main elements of the systems approach to process and plant design (Gilles, 1998) are the process and plant structures, process and plant integration, plant properties, modularity and multi-functionality, and systematic process and plant modelling. Process and plant design is a combinatorial task requiring application of sophisticated methods for systems analyses and syntheses. A multi-level presentation of the process and plant structure is given in Table 1. Gilles (1998) considers the lower four levels of the process structure. The first level, considered in this paper, corresponds to the modular concept of the agile plant and represents an addition to Gilles' presentation.

48 Table 1 Process and Plant Structure Levels. Level Module (agile plant)

Components Modules

Device

Devices

Phase

Phases

Bulk property

Continuum

Molecular

Molecules

Interconnections Connections/ Adaptors Valves, pumps, compressors, heat exchangers, etc. Phase boundaries, membranes, valves, pumps, etc. Reactive, diffusive, convective flows Molecular interaction forces

Aggregates -> Plant —> Modules —> Devices -^ Phases -> Bulk properties / Continuum

Through the application of standardized structures and a systems approach to each level, a formal representation (abstraction) of the system can be created, thus allowing the system analyses to be performed on that representation rather than on the real system itself. At the stage of system design, this is the quickest way for simulating and testing the system. The development of a mathematical model of a reconfigurable process plant, representing the structured character and properties of a plant as a system, is the aim of this work. The model describes the plant as consisting of simple entities, or assemblies of simpler entities, that interact with each other in a specific manner. The models used to simulate plant operation should be flexible enough to consider nontrivial decisions, such as relate to safety, which must be taken in the design of an agile plant. For the case of reconfigurable plant design, safety presents additional problems.

2. Network Model of a Process Plant Network models are widely used to model the behaviour of different complex systems, e.g. Cisternas and Swaney (1998), and Farkas and Li (2001). Bulsari (1995) and Lewin (1998) have applied network models to chemical engineering problems. The systems approach to a process plant leads to the concept of the network model of plant structure and operation, and it has been applied to modelling dedicated plants. This work is the first attempt to apply the network approach to the modelling of a reconfigurable plant. A process plant can be represented as a network of units (nodes, modules, clusters of modules) and links (connections) between them. This is shown in Figure 1, where the blocks represent the nodes (modules, or a set of closely-coupled modules) and the lines the connections.

•-H

Figure 1. Agile Plant as a Network.

49

3. Modules as Nodes in the Plant Network The module is a unit, preferably of standard size, with fastening, fitting and termination points, and is characterised by its process functionality, capacity range, utilities and process connections required for its operation. It can be transported and replaced by another module to achieve plant reconfigurability. The module functionality is defined by its "task". For instance, a module may contain a reactor with its peripheral units. The capacity of a module will not only depend on the equipment within the module, but also on the process streams and their properties. Modules can be classified by their functionality, size, etc. The modular concept in reconfigurable plant design requires consideration of many factors, including infrastructure environment, business criteria and constraints. Thus the design of a reconfigurable plant is a multi-objective task and a systems approach is essential for identifying viable options. Applying the building block (or Lego"*"^) concept, a plant could be divided into substructures, including different numbers of modules. Eventually all modules could be divided into their basic components. The smallest unit that cannot be sub-divided is the plant item. Thus the smallest module contains just one plant item. On the basis of this hierarchical structure of the plant, modules are characterised by their level of integration (rank of modularisation). The two extreme ranks correspond to the following cases: where the whole plant is one module (1^^ rank of modularisation); and where each unit of the plant is housed in separate modules, i.e. extreme modularisation. The rank of the module is considered at two levels - external and internal. The external rank characterises the level of decomposition of the whole plant. It is the number of modules in the plant, and thus also represents the rank of the plant. It has the same value for each module in the plant. The internal rank of a module characterises the number of units in that module. It is a specific number for each module.

4. Connections as Links in the Plant Network AH the modules installed in the plant need to be connected to create the plant network. The concept of reconfigurability sets special requirements for the connections between the nodes of the network. There are two kinds of connections in the plant network depending on whether they are inside or outside the modules, i.e. internal and external connections. For reconfigurability purposes, however, every internal connection could become an external one in a decomposition of the module, and vice versa. This makes the standardization of all connections highly desirable. There are three main kinds of flows in the plant network: material, utility and information flows. Material flows transfer materials within and between the modules. Utility flows are steam, cooling water, compressed air, nitrogen, electricity, etc. Information flows are the links between the modules and the computers used to monitor and control the processes in the plant. For the purposes of the reconfigurable plant design, the connections between modules reflect the range of properties of the material flows, and should allow for changes of the properties of both material and utility flows. To minimize the lead-time to reconfigure the plant, connections should be standardized in the range necessary for the family of products and processes considered, and for their scales of production.

50

5. Mathematical Formulation of the Network Model The network model is a formalised representation of a modular plant as a network of modules and connections. Each element of the network (module, connection, plant), its functionality and the concepts the network is based on are described mathematically. The functionality of the whole network and of each module is described as a set of operations (functions, tasks) performed in the plant and by the module. The functionality of each module depends on the functionalities of the units included in it. Let the full range (set) of plant functions (operations) be denoted by F, and the values of the F elements by F,- (for / = l,Nf), where Nf is the total number of functions, hence

(1)

^ = U F /

The following notation is used for the F elements: R for reaction, S for separation, etc. The Boolean symbols c and u are used to denote sub-set and summation operations. The functionality of a module FM is a sub-set of functions of the general set F, i.e. FMI^ F (i = 7,r), where r is the number of modules (rank of the plant) that is defined by both the product and process envelopes. If A^ modules have the same functionality, FM, then the functionality of the network of these modules is F = F^. Thus the functionality of a network of three crystallisers (CR) can be represented by the relation F=CRuCRuCR. In terms of tasks, however, their number is 3. Modules are represented with the expression M"^'^** , where r is the external rank of the module (number of modules in the plant; rank of the plant), u is the internal rank of the module (number of units in the module, used as a characteristic of the complexity of the module), and n^ is the number of elementary tasks performed by the module. Tasks are denoted by Tf, where r is the rank of a task and F is the set of functions (or sub-tasks). The task is considered in the context of both a module and a plant. The task of a module is the set of functions performed by the equipment units in the module. Equipment tasks are derived from the process definition. A set of equipment tasks may correspond to one or more process tasks, and visa versa. The task of a plant is the full set of functions leading to the general objective (set of process tasks) of the plant. The rank of the task is the number of the functions performed. A plant is denoted by F / , where r is the rank of the plant and F the full set of tasks performed by the plant. The following notation is used to represent the connections in the plant: C ^' '*° - internal connection between /* and 7* unit inside module, '•»"..•

C ^'^^^ - external connection between i^ moduleM/' 'f' and/^ module M ^' / in plant, f,Ujj

r ,Uj

r

,Uj

where r is the external rank of the modules, uy the quantitative characteristics of the connection (i.e. flow rate), and/jy the qualitative characteristic of the connection (type of connection).

51 Plant 1

p/•,,«,i ^

_!:"?.

_

HJ [U [A]---[±] Plant 2

,_i"z=i_

'"2'"?,

[±] /57---Z57Z37 Figure 2. Reconfiguring Plant 1 to Plant 2.

6. Reconfigurability Reconfiguring a process plant is an operation of changing the rank and/or functionality of a plant (modules in the plant). The rank of the plant/modules is the number of modules/equipment units, and the rank of a task is the number of functions performed. Equation (2) is the mathematical expression of plant reconfigurability: p'^i^p'^i

(2)

Fl = / l + / 2 + / 3 + •••+/„,

(3)

Fl =/l" +f2 +f3 +

(4)

•••+K

Equations (3) and (4) consider the functionality at the elementary task level. Figure 2 illustrates the case when a plant is reconfigured from state 1 to state 2. The functionality of the first state Fj represented by nj tasks is replaced by the second one F2 performing ^2 tasks. The following cases are possible depending on whether the functionality of the plant is maintained. Case A corresponds to reconfigurability aimed at improving the efficiency of the plant, where the set of tasks is not changed. Case B corresponds to reconfigurability leading to a different set of tasks (i.e. another product). Case A - F; = F2: If r/ ^ r2, typically this means an increase or decrease in the number of modules without changing the functionality. If rj = ri the external rank of the plant does not change, i.e. the number of modules is the same, but some may be replaced by others, e.g. by improved equipment units in new modules. Case B - Fj ^ F2. If r; ^ r2, this is the case where both functionality and plant rank change. Plant reconfiguration is performed through changing the number of modules, leading to a different set of tasks from the existing one (e.g. new product). If ry = r2, the plant functionality may be changed without changing its rank, e.g. by using the same equipment to produce a different product, and applying a different set of elementary tasks.

52

7. Mathematical Operations with Modules and Network Analysis A high-level mathematical language, based on the main arithmetic operations and their physical interpretation in terms of the process plant, includes the following operations: addition, subtraction, multiplication, division, substitution and removal. These mathematical operations correspond to reconfiguring of the plant modular system so that the external rank r and/or the internal rank (number of units) u and functions of the modules (the number n and the functionality F), change. Substitution of modules can be of tv^o kinds: with a new or with an existing module. It is an operation of consecutive removal of one and addition of another module. Two types of network analyses have been proposed, namely modularisation analysis and reconfigurability analysis. Modularisation analysis includes procedures for: determination of the external and internal rank of the modules; determination of the functionality of the modules; setting of criteria for evaluation of the modular plant; visualisation of the modular plant; modular plant option generation and selection. The reconfigurability analysis includes procedures for: setting of the new plant requirements; selection of criteria for the new modular plant estimation; selection of the strategy for reconfiguring (degree of reconfigurability); virtual reconfiguring of the existing modular plant; option evaluation according to the chosen criteria; best option selection; virtual construction of the new modular plant; verification by simulation of the new plant operation. The mathematical operations with modules are used to represent the reconfigurability concept. Not all of the mathematical operations are applicable in practice. For example, division of a 1-unit module is not possible.

8. Conclusions The network model is a formalised, mathematical description of a modular plant which embodies the concepts of modularisation and reconfigurability. It can be used in the generation of options for the design of agile plants, and the subsequent selection of the most appropriate option when reconfiguring a plant to meet changing product and process demands. Modularisation and reconfigurability analyses used in the design of agile plants employ the network model to simulate the options for plant design.

9. References Bulsari, A.B., 1995, Neural Networks for Chemical Engineers, Elsevier, Amsterdam. Burgess, T.F., Hwarng, H.B. Shaw, N.E. and de Mattos, C , 2002, Eur. Man. J., 20, 197. Cisternas, A.L. and Swaney, R.E., 1998, Ind. Eng. Chem. Res., 37, 2761. Farkas, I. and Li, P., 2002, Proc. 4* Int. Conf Cognitive Modelling, Fairfax, Virginia. Lewin, D., 1998, Comp. and Chem. Eng., 22, 1387. Gilles, E.D., 1998, Chem. Eng. Technol., 21, 2. Pisano, G.P., 1997, The Development Factory: Unlocking the Potential of Process Innovation. Harvard Business School, Boston.

10. Acknowledgement The authors wish to thank the EPSRC for their financial support of the work described.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

53

A Vision of Computer Aids for the Design of Agile Production Plants A. Borissova, M. Fairweather and G.E. Goltz Leeds Institute of Particle Science and Engineering, University of Leeds, Leeds LS2 9JT, UK

Abstract Chemical engineers may have to determine the functional requirements for a plant to produce a range of products, rather than just one. This gives rise to the need for process design tools that accept ranges rather than point values. Alternatively, to reconfigure a plant quickly and reliably, a good information model and agreed standards are essential. Existing solid modelling tools can then be used to visualise the changes and ensure that any clashes are detected and resolved before the physical changes are implemented on the plant. This paper describes a combinatorial approach to process, equipment and plant design that is capable of encompassing all these requirements, and contracts this method with traditional approaches. It is shown that traditional design methods may miss options that are identified using the combinatorial approach. Options identified by the latter approach may also lead to novel types of processes and equipment. Application of the new methodology is described in terms of scanning the multidimensional space describing the process, equipment and plant attributes. The new approach is particularly appropriate for the design of agile plants where decisions have to be made as how best to reconfigure an existing facility to manufacture a new product.

1. Introduction According to Pisano (1997) the business environment in which the pharmaceutical, agrochemical and speciality chemical industries operate places a high premium on time to market due to the limited life cycle of their products. Thus, "learning before doing" rather than "learning by doing" becomes important. Business decisions are subject to considerable uncertainty, and computer-based tools can assist in obtaining agreement within a business, even though the final decision is based on "soft" information. Shaw et al. (2001) report on the needs of the UK speciality chemicals industry and the decision processes for the type of plant and its likely capacity. Agile plants that can easily be reconfigured to cope with changing products are likely to be favoured rather than dedicated plants. The challenge is to design plants that are efficient and have either a wide operational envelope or can be interchanged rapidly. Modular plants, where whole modules can be replaced, or pipeless plants may be appropriate. Alternatively, learning from robotic, combinatorial chemistry may be translated to production by replicating rather than scaling-up. Computer aids to help make the right decisions are needed.

54 Traditional methods of process and plant design are often semi-empirical and depend primarily on the ingenuity and experience of engineers. Clark et al. (2000) have indicated how previous designs can be linked to simulation codes. Eggersmann et al. (2002) addressed the issue of the management and re-use of design models. Experience has shown that re-use of P&ID's often leads to over-instrumentation and to the exclusion of the best modern technology. Rudd and Watson (1968) and Douglas (1988) have shown the value of techniques such as process synthesis, while Linnhoff et al. (1985) have demonstrated the benefits of pinch and network technology in obtaining an optimal design for the processes. The advent of modern computers has permitted equipment design based on computational fluid dynamics and molecular modelling. Traditionally, process and plant design has been considered practical in nature, with little fundamental content. Designs have been based on empirical approaches such as the minimum number of units, maximal utilisation of raw materials and energy, and dedicated equipment units that decrease the freedom of the design. The generation of options is, however, a key activity in the design of a plant. Rudd and Watson (1968) describe the creation of plausible alternatives as consisting of three steps: definition of the primitive problem, gathering of cognate facts, and creating specific problems. Douglas (1988) and Biegler et al. (1997) proposed methodologies for option generation. At the equipment level it is well known that engineers tend to favour equipment with which they are familiar as this increases confidence. At the plant level, the layout and detailed design are frequently restricted to a specific process, even if the design remit states that processes for other products may be needed in the future. In the case of both equipment and plant design, the use of point values as input parameters, rather than ranges of the values of the design parameters, has restricted creativity.

2. Combinatorial Approach to Process and Plant Design The combinatorial approach to process and plant design is based on diversity, and this has already been applied in chemistry and materials science, for instance by Engstrom and Weinberg (2000) and by Gordom and Kerwin (1998), to produce millions of potential new chemicals, drugs, sensors and superconductors. Only a few applications in chemical engineering, e.g., solvent selection by Kim and Diwekar (2002), have been identified. The combinatorial approach has been applied to production planning, the selection of manufacturing sites and to scheduling by, for example, Verwater-Lukszo and Otten (1994), Shah and Pantelides (1996) and Pekny (2002). Physico-chemical data are usually treated as point values in design. This ignores the uncertainty in the data, and the fact that different products may have to be produced in the future. This is exacerbated by the complexity of physico-chemical processes involving multi-phase, multi-particulate and multi-component systems, with multi-level interactions within them. The formal design of a complex processing plant, involving several hundred variables with complex interactions, is a formidable, if not an impossible, task. Complexity can be reduced by dividing the process into more manageable steps, identifying key variables and concentrating work where effort will give the greatest benefit. This will not, however, necessarily lead to the optimal design for the whole process.

55

Figure 1. Option generation -from the vision to the real process/plant.

Figure 2. Scanning variable space.

design

Combinatorial design is defined as a theoretical approach to the design of a process and plant. It creates the full set of options for the process and plant without considering the limitations of existing practice. It is applied as a first stage in the design procedure to create the initial process and plant design, or combinatorial, environment. It is not limited either by technical or by business requirements or restrictions. Combinatorial process and plant design is a methodology for the rapid generation of all feasible options for the desired process and plant, and for creating predictive models of their performance and operation. The combinatorial environment is used as a basis for a subsequent Option Generation and Selection methodology for process and plant design that considers the limitations of existing practice (e.g. process parameters and phases, costs, materials of construction, dimensions, etc.). Combinatorial design can also be applied in the research phase of the process and plant design as a tool for the generation of ideas and new design concepts. Supplied with the necessary computer software for the quick generation and evaluation of all possible options, combinatorial design will then be an efficient tool for the design of an agile plant. A General Set of Options (GSO) for the process and equipment design is created mechanistically on the basis of the design variables (see below) in defined ranges that include process routes and equipment diversity. This set of options represents the design envelope. The GSO is an analogue of the "library" used in combinatorial materials science by Gordom and Kerwin (1998), defined as "the array or set of materials to be investigated". The magnitude of this set depends on the complexity of the process and the ranges and steps (precision or granularity) used in defining the design parameters. The initial vision of a process/plant is often in the form of a concept of the future process or plant. Figure 1 represents the development of the process/plant from the conceptual model to the real options. The concept, represented by the top plane, may be the result of technology push or market pull. When the concept is projected on to the requirements plane (denoted by a) the image changes. Even if all the requirements are fulfilled, it might still not have the same shape. Conceptual design should answer the

56 question "how does the process or plant concept project onto the requirements plane". The required plant performance envelope, including ranges of equipment characteristics, is defined in the a plane. Further projection leads to the creation of the real plant configurations/options in the P plane. Different options in the P-plane are possible, some of which may not be feasible. The combinatorial approach requires formalisation. The creation of options is based on changing Design Variables, which are groups of process, plant and equipment characteristics that may be discrete (e.g. type of plant, solvent, etc.) or continuous (e.g. temperature, pressure, etc.). Combinatorial design creates the GSO that gives different values of the Design Variables. Continuous Design Variables are split into discrete intervals. The size of the intervals represents the granularity of information and depends on the level at which the process and plant are considered. The full set of options is then obtained mechanistically by scanning the multi-dimensional space of the Design Variables. Figure 2 illustrates the method of combinatorial design. The hexagon represents the initial design that is satisfied by the seven options shown as stars. An agile plant, however, may also need to accommodate different levels of the Design Variables that are depicted by the pentagon. The possible options are shown as 16-pointed stars. Only three options overlap. The bigger the initial space of the Design Variables the greater will be the agility of the process design. The tools for combinatorial design are based on computer simulations involving mathematical models, databases and the management of information. Together with the emergence of cost-effective and time-efficient computing systems, computational simulations of industrial processes are now a realistic alternative to either the traditional experimental or analytical methods of investigation. A new paradigm in process engineering is therefore emerging, with Edgar (2000) suggesting that computer simulations should be performed even at the discovery phase.

3. Combinatorial Plant Design Combinatorial plant design defines the plant Design Variables; examples are type of plant, plant layout and connections. While it is generally true that no two plants are identical, and therefore the number of plant design options approaches infinity, it is possible to distinguish broad classes of plants. No classification can be guaranteed to be complete, but below are given some suggested types of plant: 1. Dedicated plants - designed to produce a specific product or products throughout the life of the plant. Typically these are plants for bulk chemicals. 2. Versatile plants - designed with fixed plant items, but with the expectation that the piping connecting the plant items will be modified. 3. Re-configurable plants - designed with interchangeable plant items. 4. Modular plants - designed as interchangeable modules containing groups of equipment with pre-defined interfaces to utilities, control and process connection points. 5. Pipeless plants - where vessels are moved between processing stations rather than moving material between vessels.

57 Agile plants can accommodate the change from one product to another quickly in response to changing market needs. Agility generally increases from type 1 to 5. Taking the design of modules as an example, it becomes clear that this is a combinatorial task. Key variables are the functionality, dimensions and the equipment layout within the module, as well as the connections between process modules and to utility modules. Reconfiguring an existing plant for a new product or process is also a combinatorial task. Such a systematic approach aids the decision on the functionality required of each module. Discussion of the standardisation of interchangeable modules (dimensions of the module and the size, type and location of all the external connections) is, however, beyond the scope of this paper.

4. Combinatorial Equipment Design One of the challenges for the design of process equipment is to create the conditions for an agile plant. A way of meeting these requirements is to apply the combinatorial approach to improve the basis for option selection through exploration of a wide range of both existing and novel (unknown) equipment units. Equipment Design Variables considered by combinatorial equipment design include: types of equipment, geometries, materials of construction, etc. The requirements for the type of equipment are derived from the process duty. They can, however, be met in a variety of ways depending on the physico-chemical properties, the driving forces and the fluid dynamics. At the conceptual level the requirement may be to remove heat. At the next level many options may exist. Thus, heat can be removed by direct contact, by making use of the latent heat of vaporisation or by indirect heat transfer. Each of these more specific duties leads to a range of equipment with their associated properties. No list of equipment will ever be exhaustive as new devices are developed to meet particular needs. Multi-functional equipment in particular may extend the range of applications and thus improve agility.

5. Challenges for the Future Apart from developing the tools for combinatorial design, including option generation and selection and a network model to aid both the initial design and subsequent modification of reconfigurable plants, other challenges remain. These include efficient and transparent inter-operability between different software packages, and tools to obtain the maximum information from experimental work at an early stage. Data also need collecting, assessing and presenting in a form that is easily assimilated. Many products are large molecules, so that they are solids under normal conditions. Solids formation is still less well understood than processes involving fluids and there is a lack of reliable models. Furthermore, experimental physico-chemical data that underpin almost all chemical engineering calculations are rarely available. Good, validated estimation methods are needed. Many of the products are biologically active. Predictive models of the toxicity of products, intermediates and by-products in the pure state and as mixtures would be useful at an early stage, and may help to decide between competing process options.

58

If robustly designed laboratory equipment can easily be replicated, then it may be possible to by-pass the scale-up step that has traditionally caused problems.

6. Conclusions The theoretical basis for the development of tools to aid engineers in generating and selecting options for process, equipment and plant design has been described in terms of combinatorial design. The methodology presented minimises the risk of overlooking attractive options. It can be implemented as a computer-aided option generation and selection tool that considers all options at the appropriate level of detail. A knowledgebased information model should be employed to identify all possible options available for reconfiguring an existing plant to manufacture a new product with the fewest, quickest or cheapest changes. This uses the concept of scanning the multi-dimensional space of the Design Variables to create the options. In addition, the ideas of reconfigurable modular plants can be extended using both theoretical and practical approaches. Application of the concepts described is not restricted to design, but can also be used defensively to assess the risk of a competitor developing a more costeffective process. Some challenges to the CAPE conmiunity have been identified.

7. References Biegler, L.T., Grossmann, I.E. and Westerberg, A.W., 1997, Systematic Methods of Chemical Process Design. Prentice Hall, Upper Saddle River. Clark, G., Rossiter, D. and Chung, P.W.H., 2000, Trans. IChemE Part A, 78, 823. Douglas, J.M., 1988, Conceptual Design of Chemical Processes. McGraw-Hill, New York. Edgar, T.F., 2000, Chem. Eng. Prog., 96,51. Eggersmann, M., von Wedel, L. and Marquandt, W., 2002, Chem.Ing.Tech., 74, 1068. Engstrom, J. R. and Weinberg, W. H., 2000, AIChE JL, 46,2. Gordom, E.M. and Kerwin, G.F., 1998, Combinatorial Chemistry and Molecular Diversity in Drug Discovery. John Wiley and Sons, New York. Kim, K.-J. and Diwekar, U.M., 2002, Ind. Eng. Chem. Res., 41, 1285. Linnhoff, B., Townsend, D.W., Boland, D., Hewitt, G.F., Thomas, B.E.A., Guy, A.R. and Marsland, R.H., 1985, User Guide on Process Integration for the Efficient Use of Energy. The Institution of Chemical Engineers, Rugby. Pekny, J.F., 2002, Comp. and Chem. Engng., 26,239. Pisano, G.P., 1997, The Development Factory: Unlocking the Potential of Process Innovation. Harvard Business School, Boston. Rudd, D.F. and Watson, C.C., 1968, Strategy of Process Engineering. John Wiley and Sons, New York. Shah, N. and Pantelides, C.C., 1996, Ind. Eng. Chem. Res., 31, 1325. Shaw, N.E., Burgess, T.F., Hwarng, H.B. and de Mattos, C , 2001, Int. J. Operations and Production Management, 21, 1133. Verwater-Lukszo, Z. and Otten, G., 1994, J. Proc. Cont., 4, 291.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

59

Synthesis of Integrated Distillation Systems Jose A. Caballero , Juan A. Reyes-Labarta and Ignacio E. Grossmann *Department of Chemical Engineering. University of Alicante. Ap. Correos 99, E03080 Alicante SPAIN. Department of Chemical Engineering. Carnegie Mellon University. Pittsburg, PA, 15213, USA.

Abstract The paper presents a novel superstructure based optimization procedure for design a sequence of distillation columns for separating a non azeotropic n component mixture. The separation can be performed using from conventional to fully thermally coupled distillation sequences going through all the intermediate possibilities of partial thermal integration. A two stage procedure is proposed, in the first a feasible sequence of tasks is selected, with an approximation to the total annualized cost that, under some considerations, produces a lower bound to the total annualized cost. In the second stage the configuration in actual columns is selected among all the thermodynamically equivalent configurations. A case study is presented in order to illustrate the procedure.

1. Introduction The fully thermally coupled (PC) configuration has been known for over fifty years (Wright, 1949). Different theoretical studies has shown that thermally coupled configurations can save among 10 to 30% in total and operating costs (see for example, Glinos and Malone 1988 or Triantafillou and Smith, 1992). Petlyuk (Petlyuk et al, 1965) was the first in analyzing the PC system and found it thermodynamically attractive due to the reversible mixing of feeds with internal column streams. Consider a mixing consisting of three components A, B and C, where A is the lightest and C the heaviest. Por some mixtures, for instance when B is the major component and the split between A and B is as easy as the split between C and D, this configuration (Pigure 1) has an inherent thermal inefficiency (Schultz et al, 2002).

r ^

Molar

fraction

/r^ 1

AB

ABC

B in column

^ 2 .,-—"'" B in column

V l ^ B /'' ^ - ^

/ / Bottom

Trays

Top

Figure 1. Concentration profile for component B in a sequence AB/C A/B. Remix ofB occurs in column 1.

60 In the first column, the concentration of B reach a maximum at a tray near the bottom. On trays below this point, the amount of C continues increasing, diluting B. Energy has been using to separate B to a maximum purity but, due to B is not removed at this point B undergone a remixing and it is diluted till the concentration at which it is removed in the bottoms. This remixing is inherent to any separation that involve an intermediate boiling component, and the result can be generalized to a N component mixture. Halvorsen and Skogestad (2001) proved that the minimum energy consumption for a sequence of columns is always obtained with the FC configuration. Petlyuk and coworkers generalized the FC system for n number of components. They defined a FC system as a one with n(n-l) sections for a n component mixture, only one condenser and one reboiler for the entire system, all the components (except the most and least volatile) distributing between the top and the bottom of each column, and all of the product column that is composed of (n-1) binary separation columns built on top of each other. This definition has latter extended and generalized (Agrawal, 1996). In an FC system is not needed that all the products are produced by a main column, the number of column sections goes from (4n-6) -the minimum number of column section for a FC system- to n(n-l) and the condenser and reboiler do not necessarily belong to the same column. Although the total energy consumption is always lower in FC systems than in any other configuration, there are some drawbacks: The number of total sections increases with the reduction in the number of heat exchangers, increasing the total number of trays and then the total cost (in some cases compensated by the integration in a single shell). The energy must be supplied in the worst conditions, at the highest temperature in the reboiler and removed at the lowest temperature, preventing in most cases the use of utilities like medium or low pressure steam. Operation is more difficult due to the large number of interconnections among columns. As the knowledge of these systems increases and operational problems are being solved interest in thermally coupled systems is renewed. However, it is clear that from conventional systems (each column with a condenser and a reboiler) to fully thermally coupled systems there are a large number of possibilities, and the optimum is probably among them. Here we present mathematical programming base procedure for screening among these possibilities. It is a two stage procedure, in the first a sequence of tasks is selected, and in the second the best configuration of columns among those thermodynamically equivalent is selected. The problem addressed in this paper can be stated as follows: Given a number of components, that do not form azeotropes, to be separated into a predefined set of products. The objective is to find an appropriate and cost effective separation scheme. This scheme includes conventional columns, partially linked distillation systems -with any number of heat exchangers between 2 and 2(n-l)- that can produce prefractionators, sloppy splits, side columns etc. Without loss of generality, the products are listed in a decreasing order of volatilities.

2. Integrated Distillation Model Due to the nature of the problem there is not a one to one match between separation tasks and columns that perform a given separation. Even more, a given feasible sequence of separation tasks can be performed by different sequences of thermodynamically equivalent columns. In this paper we present a task based superstructure with intermediate characteristics between the pure State Task Network (STN) (Yeomans and Grossmann, 1999) in which all the separation tasks are explicitly enumerated, and a superstructure in which equipment is previously determined. Figure 2 shows the superstructure for a mixture of 5 components. Although the picture by itself

61 is not new (for example it corresponds to the classical Sargent and Gaminibandara structure (1976). Some important aspects must be remarked that are important at the modeling level. First, individual separation tasks are not considered explicitly. For instance, for the mixture ABCD we consider the most general approach "separate A from D" in which intermediate boiling compounds can or cannot distribute. However, at the level of relation among tasks it is important which separation has taken place. Second, if a group of compounds (state) do not exists in the final solution it is considered as a simple bypass in the superstructure See Figure 2. And third, heat exchangers are not explicitly included in the superstructure, but are considered at the modeling level. In particular, they appear in the final cost, the flow transfer among pseudo-columns (tasks) is very different if there is or there is not a heat exchanger and the presence of a heat exchanger associated to a final product is related to the minimum and maximum number of separation sections. These approach has proved very robust and computationally efficient.

'XX: State does not exist: Bypass.

State ABCDE, for instance, can produce the following separation tasks: A/BCDE; AB/BCDE: AB/CDE; ABC/BCDE ABC/CDE; ABC/DE; ABCD/BCDE; ABCD/CDE; ABCD/DE; ABCD/E

Figure 2. Superstructure for a mixture of 5 components. Note that if a state (group of components) do not exist then becomes in a bypass. Very important, and related to second point of previous paragraph is the question of how generating feasible sequences. Logical connectivity relationships are not enough. It is also convenient to forbid that a given separation can be produced twice, or a given state can be produced simultaneously by two rectifying or stripping sections. Although some authors (Rong and Kralawski, 2001) considered these possibilities they are always suboptimal from the point of view of energy, an it increases the total number of tasks. It could be justified if different concentrations of the same split are considered or if we are interested in some kind of multi-effect heat integration (in our approach, these constraints can be easily relaxed in order to allow these possibilities if desired). Other configurations like that proposed by Kaibel (1987) need more energy than other fully or partially thermally coupled, however due to the reduction in the number of sections it could be interesting in some cases. A set of logical relationships among tasks in terms of binary variables can be included in order to fulfill all these conditions. (Caballero and Grossmann, 2001). Operation conditions into the columns was calculated by Underwood, Fenske equations. However, any other set of equations including rigorous tray by tray calculations could be implemented. The conceptual procedure continue being the same and only the numerical performance would be affected. As an objective the total annualized cost (operating cost, annualized capital cost of columns and heat exchangers) is considered. Procedure proposed by Douglas (1988) has been implemented.

62 The conceptual model is conveniently represented using a disjunctive formulation as follows: min total annualized cost = Annualized Capital Cost + Operation costs s.t.

Underwood equations Fenske equations

V

Calculation Column Area

Bypass of Flows Capital Cost = 0

Capital Cost = fiD, P, N^^^y^ ) ^s Calculation of Qreb or Qcond Calculation of Utilities cost

Transfer of Liquid and Vapor

V

among columns.

Heat exchanger cost - f(Area,UyAT)

Qreb = Qcond = 0

Distillate or Bottom liquid at their buble point

Costs =0

^{z„W,)=True Where s is an index set making reference to the states in the superstructure, Zs is a Boolean variable that takes the value True if a given state exists, Ws is a Boolean variable that takes the value of True is a Heat exchanger associated to that state exists. And the last equation makes reference to the logical relationships among states (tasks) and heat exchangers in order to assure feasible separations. Remark that previous model is linear except for Underwood equations and those equations related to costs estimation. The model has proven to be reliable and computational efficient. Due to the task based approach, the total cost of columns is calculated assuming that a task can be considered a pseudo-column (each pseudo-column with their own diameter), this approach produces a lower bound to the total capital cost. The actual capital cost depends on the final configuration in actual columns. If the capital cost is not the dominant factor (and even in some cases if it is) for preliminary design the previous approach is good enough. With the optimal sequence of tasks it is possible to obtain the best possible rearrangement of these tasks in actual columns (Caballero y Grossmann 2002). In this second stage it is possible include control and operational constrains. Although this second part can be integrated in the model previously presented, due to the large number of thermodynamically equivalent configurations that some sequences of tasks can produce the increase of dimensionality of the problem do not justify it but in some special cases.

3. Case Study As an example we present the separation for a mixture of 5 hydrocarbons. In Table 1 basic data are presented.

63 Table 1. Basic data for example. Component n-Hexane n-Heptane n-Octane n-Nonane n-Decane Total flow Pressure

Feed composition (molar fraction) 02 0.1 0.2 0.2 0.3 200 kmol/h 2atm.

U= 800 W/m^ K Steam cost = 5.09 $/GJ Cold water cost= 0.19 $7GJ Recovery: 98% of heavy key and light key in each separation

The best sequence of tasks is presented in Figure 3a. The solution involve three reboilers and three condensers with a total of 12 column sections. If we do not take into account the possibility of divided wall columns, the minimum number of columns in which the different separation tasks can be performed is equal to n-1, in this case four columns. Taking into account that each thermal link (link between states without heat exchanger) produces two different possibilities of rearrangement of these separation tasks (Caballero and Grossmann 2002), for our solution there are 16 thermodynamically equivalent configurations. The best obtained solution is shown in Figure 3b. The total annualized cost of the best configuration obtained assuming that each separation task is pseudo-column was $1457487 that is a lower bound to the total cost. When we calculate the total annualized cost of the actual configuration -Figure 3b- this cost increases to $1571159, which is around 8% higher. /^r^ r - ^ c

^C2>-i^Q)^^ Figure 3. a) best sequence of tasks obtained, b) Best arrangement in actual columns. It is possible start an iterative procedure in which the previous result is an upper bound, and study the possibility of getting other configurations. Although it has not been presented here it is also possible consider the integration of some columns in a single shell with it is likely to produce some reductions in the investment cost. Note that each integration reduced by 4 the number of thermodynamically equivalent configurations. Note also that there are a good number of configurations with similar performance. The proposed procedure is flexible and it allows study in a easy way other configurations. Some final remarks: In the solution presented the vapor flows always from columns at higher to lower pressures in order to facilitate the operational problems associated to vapor transfer between columns. However, if the number of interconnections among columns makes difficult the control it is possible to implement some of the alternatives like those proposed by Agrawal (2000,2001) for reducing the flow transfer among

64 columns, or if possible try some integration of columns. This lasts points can be implemented at any of the two levels depending on the influence in the total cost.

4. References Agrawal, R., 1996; Synthesis of distillation column configurations for multicomponent distillation. Ind. Eng. Chem. Res. 35, 1059-1071. Agrawal, R., 2000. Thermally coupled distillation with reduced number of intercolumn vapor transfers. AIChE J. 46(11) 2198-2210. Agrawal, R., 2001; Multicomponent distillation columns with partitions and multiple reboilers and condensers . Ind. Eng. Chem. Res. 40. 4258-4266. Caballero, J.A.; Grossmann, I.E.; 2001; generalized Disjunctive programming model for the optimal synthesis of thermally linked distillation columns. Ind. Eng. Chem. Res. (40) 10,2260-2274. Caballero, J.A.; Grossmann, I.E.; 2002; Logic based methods for generating and optimizing thermally coupled distillation systems. Procedings ESCAPE 12, J. Grievnik, and J van Schijndel (Editors), 169-174. Douglas, J.M., 1988, Conceptual design of chemical processes. McGraw-Hill Chemical Engineering Series. Glinos, K, Malone, P., 1988; Optimality regions for complex columns alternatives in distillation systems. Trans IchemE, Part A. Chem. Eng. Res. Des. 66, 229. Halvorsen, I.J., 2001; Minimum energy requirements in complex distillation arrangements.; Ph.D. Thesis, under supervision of S. Skogestad. Norwegian Institute of Science and Technology. Kaibel, G.; 1987; Distillation columns with vertical partitions. Chem. Eng. Tech. 10. 92 Petlyuk, F.B; Platonov, V.M. and Slavinskii, D.M.; 1965. Thermodynamically optimal method of separating multicomponent mixtures. Int. Chem. Eng. 5, 555. Rong. B; Kraslawski, A.; 2001. Procedings ESCAPE 12, J. Grievnik, and J van Schijndel (Editors) (10) 319-324. Sargent, R.W.H. and Gaminibandara, K., 1976. Introduction: approaches to chemical process synthesis. In Optimization in Action (Dixon, L.C. ed) Academic Press, London. Schultz, M.A.; Steward, D.G.; Harris, J.M.; Rosenblum, S.P.; Shakur, M.S.; O'Brien, D. 2002; Reduce cost with dividing-wall columns. Chem. Eng. Prog. May, 6470. Triantafillou, C and Smith, R., 1992; The design and optimization of fully thermally coupled distillation columns. Trans IchemE, Part A. Chem. Eng. Res. Des. 70, 118. Wright, R.O., 1949 US Patent 2,471, 134. Yeomans, H.; Grossmann, I.E., 1999; A systematic modeling framework for of superstructure optimization in process synthesis. Comp. Chem. Eng. 23-709.

5. Acknowledgements Financial support provided by the "Ministerio de Ciencia y Tecnologia", under project PPQ2002-01734 is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

65

A Continuous-Time Approach to Multiproduct Pipeline Scheduling Diego C. Cafaro and Jaime Cerda INTEC (UNL - CONICET) Guemes 3450 - 3000 Santa Fe - ARGENTINA E-mail: [email protected]

Abstract Product distribution planning is a critical stage in oil refinery operation. Pipelines provide the most reliable mode for delivering huge amounts of petroleum products through long distances at low operating cost. In this paper, the short-term scheduling of a multiproduct pipeline receiving a number of liquid products from a single refinery source to distribute them among several depots has been studied. The pipeline operation usually implies to accomplish a sequence of product pumping runs of suitable length in order to meet customer demands at the promised dates while satisfying all operational constraints. This work introduces a novel MILP mathematical formulation that neither uses time discretization nor division of the pipeline into a number of single-product packs. In this way, a more rigorous problem representation ensuring the optimality of the proposed schedule has been developed. Moreover, a severe reduction in binary variables and CPU time with regards to previous approaches was also achieved. A realworld case study involving a single pipeline, four oil products and five distribution depots was successfully solved.

1. Introduction Product distribution planning has become an important industrial issue especially for oil refineries continually delivering large amounts of products to several destinations. Pipelines represent the most reliable and cost-effective way of transporting such volumes of oil derivatives for large distances. This paper is concerned with a distribution system consisting of a single multiproduct pipeline receiving different products from an oil refinery to distribute them among several depots connected to local consumer markets. Because of liquid incompressibility, transfers of material from the pipeline to depots for fulfilling consumer demands necessarily occur simultaneously with the injection of new runs of products into the pipeline. By tracking the runs as they move along the pipeline, variations in their sizes and coordinates with time due to the injection of new runs and the allocation of products to depots can be determined. A few papers on the scheduling of a single pipeline transporting products from an oil refinery to multiple destinations have recently been published. Sasikumar et al. (1997) presented a knowledge-based heuristic search system that generates good monthly pumping schedules for large-scale problems. In turn, Rejowski and Pinto (2001) developed a pair of large-size MILP discrete time scheduling models by first dividing the pipeline into a number of single-product packs of equal and unequal sizes, respectively. This work presents a novel MILP continuous-time scheduling approach that accounts for pumping run sequencing constraints, forbidden sequences, mass balances, tank loading and

66 unloading operations and permissible levels, feasibility conditions for transferring material from pipeline runs to depots, product demands and due dates. The problem objective is to minimize pumping, inventory and transition costs while satisfying all problem constraints. The latter cost accounts for material losses and interface reprocessing costs at the depots due to product contamination between consecutive runs.

2. Problem Deflnition Given: (a) the multiproduct pipeline structure (the number of depots and the distance between every depot and the oil refinery); (b) available tanks at every depot (capacity and assigned product); (c) product demands to be satisfied at every depot at the end of the horizon; (d) the sequence of runs inside the pipeline and their initial volumes at the horizon starting time; (e) the scheduled product output at the refinery during the time horizon (product, amount and production time interval); (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 and (h) the length of the time horizon. The problem goal is to establish the optimal sequence of pumping runs, the run lengths and the product assigned to each one in order to: (1) satisfying every product demand at each depot in a timely fashion; (2) keeping the inventory level in refinery and depot tanks within the permissible range all the time and (3) minimizing the sum of pumping, transition and inventory carrying costs. To do that, variations in sizes and coordinates of new/old runs as they move along the pipeline as well as the evolution of inventory levels in refinery and depot tanks with time are to be tracked.

3. Mathematical Formulation 3.1. Run sequencing constraints Every new pumping run ief^^ should never start before completing the previous one and the subsequent changeover operation. C,-L,>

C,., + T,_, * (>>,_,,. + y,, -1)

where, L , < C , < / i ^

V/€ I'^;s,s'e

S

Vie/""

(1) (2)

3.2. Relationship between the volume and the length of a new pumping run yb„^*L,
vb^*L,

(Zy>,s)*l^
yier"<(Zy,,)n^

seS

(3) \fie I""'

(4)

seS

3.3. Interface size between consecutive runs WF,. > / F , y

* ( J M , . ' + 3^.>

-1)

V/G IJ>ls,s'e

S

(5)

3.4. Upper and lower pipeline coordinates for run iel at time Qy Let F / ' ^ and Fi+/^ ^ be the upper and lower coordinates of run / at the completion time Q' of a later run Vef^"^, respectively. Then,

FJ'^ + W/'"^ = F/'"^ V/G lyve r^'^j'x

(6)

67 3.5. Volume transferred from run iel "^'*' to depots while pumping run i Q/=^/''^+E^/./'^

' ^i'^= ^/'^

V/6/"^"

(7)

3.6. Volume transferred from run i el to depots while pumping a later run TG 7"^'*' The volume of run is I at time C^ is the difference between the size of run / at time C/.i and the volume transferred to depots during the later run i*e I "^^ (/'>/)• ^.(O =^.0'-l) _ J^Dif^

V/G /,V/'G /'^^^,r>/

(8)

jeJ

where X ^ / , / ' ' ^ <w/^""^^ -W/F,-

V/G

/,V/'G

/'^"^,i'>/

(9)

3.7. Feasibility conditions for transferring material from pipeline runs to depots The transfer of material from run i el to depot jeJ is feasible only if the pipeline oudet to depot j is reachable from run /. Fulfillment of such feasibility conditions while pumping a later run i*e f^^ requires that: (a) the lower coordinate of run / at time C,./ must be less than the depot coordinate Pj and (b) the upper coordinate of run / at time C/', decreased by the interface volume WIFi, should be greater than Pj. DJ'^

^ D^'^xJ'^

; F/'"^ -WIF. > P. * jc,./'"^

V/G /, V/^G r^^ ,V> i^je J (10)

3.8. Overall balance around the pipeline during a new pumping run ier^^ The overall volume transferred from runs iel to depots jeJ while pumping a new run Vef^"^ should be equal to the volume injected in the pipeline during run /'. XSD,,/''
Vfe/"--

(11)

3.9. Product allocation constraint A pumping run flowing inside the pipeline just contains a single refinery product. Then, S3',.<1

V/e/«-

(12)

3.10. Fulfillment of market demands The total volume of product s transferred from depots e Js to the local market should be high enough to meet its overall demand qdsj. qmj'

<(C, - C , _ J * v ,

^qmj'^=qd,j

V5G 5,VyG 7,V/G /"^^ \/seSJeJ

(13) (14)

ielnew

3.11. Control of inventory in refinery tanks Assuming that the pipeline injection rate is lower than the processing rate of any production run o, then the worst condition for running out of product s in the assigned tank occurs at the completion time of a pumping run ieT^^ containing product ^^5. In turn, the worst condition for overloading the refinery tank devoted to product s arises at the start of a new pumping run containing s. Then, a^^zu.


V/G r'\oG O

(15)

68 b„ * zl,„ < C, - L,. ;

z/,„

V/ € /"™, o e O

(16)

qu,„
^h.o^B„*zh,

; qh, >vp„*\c,

P,,<M*y,_^

^ier^,seS;

-L. ) - a J - M * z / , „ ^P,.=Q^

'iiel'^.oeO

(17)

Vie / " ' ^ o e O

(18)

^iel"^

(19)

IR°s + X9«,,„ - S^z,. ^ ^^mi".

'^•^eSJel"^

(20)

7/?^ + X < „ - E ^ ; . ^ ^'^max,

V^e 5, ie I"^

(21)

3.12. Control of inventory in depot tanks Let DSi^sf ^ be the amount of product s transferred to depot jsJg from run / during the time interval (Cr - Lr , Cr). Therefore, DStJ''^ = 0 if >;,, =0 and DSiJ''^ = D J ' ' ^ whenever >',;^= 1. Therefore, the following constraints for new pumping runs is f^^ should be satisfied: DSj''
Vie / , . e S,je J^Ve

For old runs j ^ r " ; DS.,J'''^

=DJ'''

\/iG

/"-

I^'^ JG

J^J'e

(23)

T"

Inventory of product 5 in depot jeJs at time C,- , IDsJ' \ is obtained from the one available at time C,-./ by adding the amount (Z, DSi,s.j'' ) supplied by runs iel containing product s, and subtracting deliveries of s to local markets during run i'. IDj'->=IDj'--'>+'ZDS,J'''-qmJ'-> U ID min,,. < ID,."'' < ID max,, S,J

S,J

S,J

^seSJeJ,,

i'e 1"^ (24)

Vi eS.jeJ,, ^ J

i'€ I""" S '

3.13. Initial conditions Old runs ief^^ have been chronologically arranged by decreasing F/*, where F,^ stands for the upper coordinate of run ief^"^ at time t=0. Moreover, the initial volumes of old runs (W^/, ief^^) and the product to which each one was assigned are all problem data. Then, ^i,r-i = ^ ' ' '

V/G r'\r =

first(r''')

(25)

3.14. Problem objective function The problem goal is to minimize the total operating cost including pumping costs, the cost of reprocessing interface volumes and the cost of carrying product inventory in refinery and depot tanks.

69 f

\ d')

s€S jsj[

iel i'slnew

iel i>I

J

1 cardil"'" )1fs

d') jeJs

[i'slnew

J

\i'elnew

4. Results and Discussion The proposed MBLP approach will be illustrated by solving a large-scale multiproduct pipeline-scheduling problem first introduced by Rejowski and Pinto (2001). It consists of an oil refinery that must distribute four products among five depots through one pipeline. Problem data are included in Table 1. Pumping and inventory costs as well as the interface volumes can be found in Rejowski and Pinto (2001). There is initially a sequence of five old runs inside the pipeline containing products (P1,P2,P1,P2,P1) with volumes, in 10^ m \ of (75,25,125,175,75), respectively. The optimal solution was found in 25 s on a Pentium III PC (933 MHz) with ILOG/CPLEX. This represents a threeorder-of-magnitude time saving with regards to the model of Rejowski and Pinto (2001). Figure 1 shows the optimal sequence of new pumping runs as well as the evolution of sizes and coordinates of new/old product campaigns as they move along the pipeline. Four new runs involving products (P2, P3, P2, P4) have been performed.

Run Time

o

interval [hi

Volume [10 " m ^

Figure 1 - Optimal sequence ofpumping runs

5. Conclusions A new continuous approach to the scheduling of a single multiproduct pipeline has been presented. By adopting a continuous representation in both time and volume, a more rigorous problem representation and a severe reduction in binary variables and CPU time have simultaneously been achieved.

70 Table 1 - Problem Data (in l(f m^) Depots Refinery Prod. Level Dl D2 D3 D4 D5 Min 90 90 90 90 90 270 PI Max 400 400 400 400 400 1200 Initial 190 230 200 240 190 500 Min 90 90 90 90 90 270 P2 400 400 400 400 400 Max 1200 180 210 180 180 180 520 Initial Min 50 10 10 10 10 10 P3 Max 350 70 70 70 70 70 Initial 210 50 65 60 60 60 90 90 90 90 90 Min 270 P4 400 400 400 400 400 Max 1200 120 140 190 190 170 Initial 515 Location from 100 200 300 400 475 Refinery [lOW]

Depots D3 D4

]

Dl

Prod. PI

P2

P3

P4

Demand Pumping Cost [$/m^] Demand Pumping Cost [$/m^] Demand Pumping Cost [$/m^] Demand Pumping Cost [$/m^]

D2

D5

100 110 120 120 150 3.5

4.5

5.5

6.0

6.9

70

90

100

80

100

3.6

4.6

5.6

6.2

7.3

60

40

40

0

20

4.8

5.7

6.8

7.9

8.9

60

50

50

50

50

3.7

4.7

5.7

6.1

7.0

6. Nomenclature (a) Sets r^ set of old pumping runs inside the pipeline at the start of the time horizon r"^ set of new pumping runs to be potentially executed during the time horizon (b) Parameters hmax horizon length Pj volumetric coordinate of depot j along the pipeline vb pumping rate qd^ overall demand of product s to be satisfied by depot j Vm maximum supply rate to the local market (c) Variables denoting that product s is contained in run i J'M whenever ^'i^s = 1 denoting that a portion of run i is transferred to depoty while pumping run V denoting that run i ends after the refinery ZM»,. production run o has started denoting that run i begins after the refinery production run o has ended C j , Lti completion time/initial length of the new pumping run iG V^ upper coordinate of run i along the pipeUne Ft at time C,'

S

/ O

iPsy Bo Ooybo

Qi

Du

DSJ

set of derivative oil products set of depots along the pipeUne set of scheduled production runs in the refinery during the time horizon volume of the interface between runs containing products s and s' size of the refinery production run o starting/finishing time of the refinery production run o initial inventory of product s at the refinery initial inventory of product s at depotj volume of run i at time C,' volume of product injected in the pipeline while pumping the new run is T^ volume of product s injected in the pipeline while pumping the new run i volume of run i transferred from the pipeHne to depoty while pumping run V volume of product s transferred from run i to depoty while pumping run V

7. References ILOG OPL Studio 2.1 User's Manual, 1999, ILOG S.A. France. ^nd Rejowski, R., Pinto, J.M., 2001, Paper PIO, Proceedings of T". Pan American Workshop on Process Systems Engineering, Guaruja-Sao Paulo, Brazil. Sasikumar, M., Prakash, P.Patil S.M., Ramani, S., 1997, Knowledge-Based Systems 10, 169.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

71

Optimal Grade Transition Campaign Scheduling in a GasPhase Poly olefin FBR Using Mixed Integer Dynamic Optimization C.Chatzidoukas^'^, C.Kiparissides^ J.D.Perkins^, E.N.Pistikopoulos^'* ^ Department of Chemical Engineering and Chemical Process Engineering Research Institute, Aristotle University of Thessaloniki, PO Box 472,54006 University City, Thessaloniki, Greece. ^ Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College, London SW7 2BY, UK

Abstract Transitions between different polymer grades seem to be a frequent operating profile for polymerization processes under the current market requirements for product with diverse specifications. A broader view of the plant operating profile without focusing only on a single changeover between two polymer grades raises the problem of the optimal sequence of transitions between a certain number of grades. An integrated approach to the optimal production scheduling in parallel with the optimal transition profiles is carried out using Mixed Integer Dynamic Optimization (MIDO) techniques. A remarkable improvement on process economics is observed in terms of the off-spec production and the overall transition time.

1. Introduction Polymerization processes have adopted a character of continuous multiproduct plants, in response to the current demand for polymers. Precisely, the variability observed in the polymer market demand, in terms of product quality specifications, calls upon frequent grade transition policies on the polymerization plants, with legitimate consequences on process economics, due to the regular "necessary" disturbances from steady-state operating conditions. Therefore, the issue of how to operate such process as continuous multiproduct plants, in a global polymer industry environment with intense competitive pressures, emerges nastily. The products produced during a transition are off-spec, since they do not meet the specifications of either the initial or the final product, and consequently must normally be sent to waste treatment facilities. This problem combined with the usual long residence time (-10^ sec) and therefore long transition time of continuous polymerization reactors, results in an exceptionally large amount of off-spec product and consequently in a serious treatment and product loss problem. In order to develop an economically viable operating profile for the process, under the sequential

To whom correspondence should be addressed. Tel: (44) (0) 20 7594 6620, Fax: (44) (0) 20 7594 6606, E-mail: [email protected]

72 production mode of different grades, an integrated approach to a multilevel process synthesis problem is required, taking into consideration, process design, process control, optimisation of transient operation and production scheduling as interacted subproblems. In the present study a unified approach is attempted considering process control, process operation and production planning issues. The problem is examined in relation to a Ziegler-Natta catalytic gas-phase ethylene-1-butene copolymerization fluidised bed reactor (FBR) operating in a grade transition campaign. The process design is totally defined a priori since the polymerization system employed to carry out this research is a unit of an industrial polymer process. A comprehensive kinetic mechanism describing the catalytic olefin polymerization in conjunction with a detailed model of the FBR and a heat exchanger has been developed to simulate the process dynamics and the polymer molecular properties (Chatzidoukas et al., 2002). This model provides the platform for the study of process control, dynamic optimisation of the transient operation between a number of grades and the optimal sequence of transitions. A mixed integer dynamic optimization (MIDO) algorithm enables the above issues to be dealt with simultaneously avoiding the exhaustive calculation of the dynamic optimal profiles for all possible binary transitions, which might be prohibitive from computational point of view when a large number of polymer grades is considered.

2. Problem Deflnition Even though a year-time is a typical time scale for the operating life of an industrial polymer plants, with the observed fluctuations in the market demand a production scheduling on this basis would be hazardous. Therefore, it is expected that in an annual period polymer plants run several production campaigns and production planning for each one would be more efficient. A short-term campaign involving a single batch of four polymer grades (A, B, C, D) has been selected as representative case study in order to illustrate the concepts of our approach to the dimensions of the problem. Each of the four polymer grades is produced at once, without adopting a cyclic mode for the process operation. Therefore the process starts from an initial operating point and does not return to that point at the end of the campaign and hence, the timely satisfaction of the customer orders should be settled on this base. Furthermore, the campaign is studied separately from a previous and a next one, in the sense that the production sequence is determined independently, neglecting how the final grade of this campaign might affect the sequence of a next campaign as a starting point. Similarly, the starting point (Init) of the current campaign is considered as a given final grade of the previous one. Since it is expected that the Init point will affect the sequence of transitions, its polymer properties have been selected on purpose to lie in between the polymer properties of the four desired polymer grades. Furthermore, the polymer properties of the four grades have been chosen in such a way that a monotonous change (either increase or decrease) when moving from one grade to another during the campaign is impossible for the three polymer properties simultaneously. This renders the problem more complicated, reducing the possibility of applying heuristic rules for the selection of the transition sequence.

73 A simplification assumption, particularly for the formulation of the performance criterion, is that the process between the transitions is running at steady state, operating under perfect control, eliminating any disturbance and hence preventing any deviation from on-spec production. With this assumption, the production periods between the transition periods do not need to be considered in this study and the performance index accounts only for the transition periods. Melt index, polymer density and polydispersity are the molecular polymer properties (PP: MI, p, PD) identifying each polymer grade. The four operating points corresponding to the four polymer grades have been found under steady state maximization of monomer conversion with respect to all the available model inputs, so that the process operates with the maximum monomer conversion when running in a production period. In the framework of the integrated approach attempted in this study, selection and tuning of the regulatory and supervisory close-loop feedback controllers is required. From Figure 1, showing a schematic representation of a gas-phase catalytic olefin polymerization FBR, one can identify nine possible manipulated variables: The monomer and comonomer mass flow rates (Fmonb Fmon2) in the make-up stream; the hydrogen, nitrogen and catalyst mass flow rates (FH2, FN2, Feat); the mass flow rate of the bleed stream (Fbieed); the mass flow rates of the recycle and product removal streams (Free, Fout)» and the mass flow rate of the coolant water stream to the heat exchanger (Fwater)- I^ practice, instead of manipulating the comonomer mass flow rate, Fnion2» the ratio of the comonomer to the monomer inflow rate in the make up stream (Ratio = Fmonz/Fmoni) IS Selected as manipulated variable. The structure derived from a relative gain array (RGA) analysis is applied for the range of all the transitions of the campaign and is responsible for holding the reactor's bed level (h), temperature (T), pressure (P) and production rate (Rp) under control in a multiple input-multiple output configuration of PI feedback controllers. Table 1 describes the pairings of the control scheme defining also the manipulated variables. The last two manipulated variables are used by the optimizer to track polymer properties during a transition to their desired values corresponding to each grade.

3. Mathematical Representation The total transition time and the total off-spec production during the campaign are the criteria that should be incorporated in the objective function for the evaluation of the candidate alternatives. Binary variables are used to model the potential assignment of different grades to time slots in the total horizon. The time horizon for the campaign is divided into 20 time slots (5 intervals for each transition). Two integer variables are employed for each polymer grade, one showing when this grade is a starting point (Yix) of a binary transition and one showing when this grade is a desired- final point (Y2x) of each transition. Since the time topology of the Init operating point is known and constant for all the potential campaigns and besides it cannot be a desired grade, only one binary variable is ascribed to this one, which though is known during all the time slots. Hence a total number of eight 0-1 variables are required to describe the fimely distribution of the 4 desired grades. The mathematical formulation of the combined operational and scheduling problem it can be stated as:

74

V

Cyctone

Rec>cie Stream, TaMc 1. Bcst pairiugs of controlled and manipulated variables.

Bleed Stream,

\

FraO

/ (fydiDgen

Cbnpressor

feed, F i e

Bed height (h)—^Product withdrawal (Fout) Temperature (T)^^Coolant feed rate (F^) Pressure (P)

2

tfeat exchanger

Production Inflow rate (Rp) Density (p)

product RemDval,

Nitrogen feed.

T

Manipulated

Controlled

o

Fluidized bed

>-Nitrogen feed rate (FNZ) Monomer make up feed rate (F„,oni) ->-Comonomer ratio (Ratio)

Pure product Cocatalyst Feed

Melt Index (MI)->iIydrogen feed rate (FH2)

Make-up feed, FB™I,F,«2

Figure 1. Gas-phase polymerization FBR unit.

ethylene

h 3

Minimise

O^j = w 1 J 5^ (PPj _transition_dev) dt + w 2 offspec

U(t),YlX(t),Y2X(t)

(1)

0 i=l

where the normalized square transition deviation of the polymer properties PP from their desired values is defined as: PP; transition dev =

K(t)-Y., ^ ,

PP_A - Y,3,, PP_B - Y,c,, PP_C - Y,!,, PP_D)P Yw,.PPJnit + V,PP_A-Y,^.,PP_A + V,PP_B-Y,3,PP_B + Y,e,,PP_C-Y,e,PP_C + Y,o,,PP_D-Y,D,PP_D

subject to: x(t) = f(x(t),x(t),u(t),t)

(2)

y(t) = h(x(t),u(t),t)

(3)

x(to) = x„

(4)

0 < g(x(t), u(t), y(t), Y,x,„ Y,x,„ t)

(5)

where, x, u, y are the state, control and output vectors. A number of inequahty constraints described in Eqn. (5) stem from the definition of the problem and the need for feasible process operation. Precisely, end point constraints have been imposed on selected process variables to guarantee that each transition ends up at the desired steadystate optimal operating point. Finally, constraints on the binary variables were also imposed to make sure the production of all the polymer grades in a sequential transition mode.

75

4. Solution Algorithm-Results The combined structural and operational nature of the problem where both continuous and discrete decisions are involved, is addressed using a Mixed Integer Dynamic Optimization (MIDO) algorithm (Mohideen et al., 1996; Algor and Barton, 1999; Bansal et al., 2002). Under this approach, the problem is iteratively decomposed into two interacted levels-subproblems, in consistency with the hierarchical framework applied to scheduling problems. (Mah, 1990; Rowe, 1997); an upper level (Primal problem) where the operating profile is determined under dynamic optimisation techniques, and a lower level (Master problem) where candidate production sequences are developed. The dual information and the value of the objective function transferred from the Primal to the Master problem, which is solved as a mixed integer linear programming (MILP) problem, are employed to update the candidate production structure until the solutions of the two subproblems converge within a tolerance. The flow rate of hydrogen feed stream, the ratio of comonomer to monomer flow rate in the make-up feed stream and the binary variables constitute the set of the time varying controls, while the controller parameters as well as the length of each time interval are time-invariant decisions. The conmiercial modelling-simulation package gPROMS® in conjunction with the gOPT® optimization interface (Process Systems Enterprise Ltd, Lx)ndon) are used for the integration of the DAE system and the dynamic optimization of the grade transition problem. Additionally, the GAMS/CPLEX solver is used for the solution of the MILP problems resulting form the Master problem. Four iterations between the primal and master sub-problems were adequate for the MIDO algorithm to locate the optimal solution. Table 2 presents the sequence Init->C->A-^B-^D as the optimal production schedule. It also illustrates the remaining three production sequences derived during the four iterations of the algorithm. A comparison between them in terms of the time horizon, the objective function and the total amount of the off-spec product, reveals the excellence of the optimal sequence which results in a 16% reduction of the off-spec product compared to the worst scenario. Figures 2-4 display the optimal profiles for PD, MI and p during the transition campaign. It is noticed that the MIDO algorithm advocates as optimal production planning a sequence with monotonous change in terms of polymer density and polydispersity, however a simultaneous monotonous change is impossible for MI. Table 2. Comparison of the proposed sequences. Sequences _ _ _ _ _

Time Objective Off-spec horizon Function Product _ _

I n i t ^ C ^ A ^ B ^ D 27.16 hr 166.28 Init^D-^A->C-^B 30.63 hr 221.038 Init^D->B^A->C 34.13 hr 185.963

4.8-

Polymer Polydispersity 1

4.6-

c

1":

j^2tn

132 tn 181 to 153 tn

't

•

S

3.83.6-

r^>^

GradeD

I

GradeB

20

25

3.4-

\ _ l

GradeC

3.2-' 0

5

10

15 TimeOir)

Figi ire 2: Optimal PD profile under the optimal production planning.

3(

76

0.25-

1

Polymer Ml |

Grade D

Polymer Density (gr/cm') I

0.20-

0.15-

0.10Initial point

Vll

Grade C

0.05-

^^__^

0.00'

1

'

1

/

X -1

GradeB

Grade A 1

1

15 Time(hr)

Figure 3.: Optimal MI profile under the optimal production planning.

Tiine(hr)

Figure 4: Optimal density profile under the optimal production planning.

5. Conclusions The production sequence in a gas-phase olefin polymerization plant running a grade transition campaign between four polymer grades has been studied in parallel with the optimal transition profile to switch the process from one grade to another. Both the optimal production scheduling and operating profiles for the optimal transition between the polymer grades have been found using a Mixed Integer Dynamic Optimization algorithm. Reduction of the off-spec production and total transition time during the campaign highlights the economic benefits for the polymerization plant resulted from the integrated approach to the problem.

6. References Algor, R.J., Barton, P.I., 1999, Computers. Chem. Eng., 23, 567. Bansal, V., Perkins, J. D. and Pistikopoulos, E. N., 2002, Ind. Eng. Chem. Res. 41, 760. Chatzidoukas, C , Perkins, J.D.; Pistikopoulos, E.N. and Kiparissides, C , 2002, Submitted in Chemical Engineering Science. Mah, Richard S.H., Chemical process structures and information flows. Howard Brenner (Eds.), Butterworths Series in Chemical Engineering, United States of America, 1990, Chap. 6. Mohideen, M.J., Perkins, J.D., Pistikopoulos, E.N., 1996, AIChE J., 42, 2251. Rowe A.D., 1997, PhD Thesis, Imperial College, University of London.

7. Acknowledgements The authors gratefully acknowledge the financial support provided for this work by DGXII of EU the GROWTH Project "PolyPROMS" GlRD-CT-2000-00422.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

77

Environmentally-Benign Transition Metal Catalyst Design using Optimization Techniques Sunitha Chavali\ Terri Huismann\ Bao Lin^, David C. Miller^, and Kyle V. Camarda^ ^Department of Chemical and Petroleum Engineering, The University of Kansas 1530 W. 15^ Street, 4006 Learned Hall, Lawrence, KS 66045 USA ^Department of Chemical Engineering, Rose-Hulman Institute of Technology 5500 Wabash Avenue, Terre Haute, IN 47803 USA

Abstract Transition metal catalysts play a crucial role in many industrial applications, including the manufacture of lubricants, smoke suppressants, corrosion inhibitors and pigments. The development of novel catalysts is commonly performed using a trial-and-error approach which is costly and time-consuming. The application of computer-aided molecular design (CAMD) to this problem has the potential to greatly decrease the time and effort required to improve current catalytic materials in terms of their efficacy and biological effects. This work applies an optimization approach to design environmentally benign homogeneous catalysts, specifically those which contain transition metal centers. Two main tasks must be achieved in order to perform the molecular design of a novel catalyst: biological and chemical properties must be estimated directly from the molecular structure, and the resulting optimization problem must be solved in a reasonable time. In this work, connectivity indices are used for the first time to predict the physical properties of a homogeneous catalyst. The existence of multiple oxidation states for transition metals requires a reformulation of the original equations for these indices. Once connectivity index descriptors have been defined for transition metal catalysts, structure-property correlations are then developed based on regression analysis using literature data for various properties of interest. These structure-property correlations are then used within an optimization framework to design novel homogeneous catalyst structures for use in a given application. The use of connectivity indices which define the topology of the molecule within the formulation guarantees that a complete molecular structure is obtained when the global optimum is found. The problem is then reformulated to create a mixed-integer linear program. To solve the resulting optimization problem, two methods are used: Tabu search (a stochastic method), and outer approximation, a deterministic approach. The solution methods are compared using an example involving the design of an environmentally-benign homogeneous catalysts containing molybdenum.

1. Introduction Transition metal catalysts play a crucial role in many industrial applications, including the manufacture of lubricants, smoke suppressants, corrosion inhibitors and pigments. The development of novel catalysts is conmionly performed using a trial-and-error approach which is costly and time-consuming. The application of computer-aided molecular design

78 (CAMD) to this problem has the potential to greatly decrease the time and effort required to improve current catalytic materials in terms of their efficacy and biological effects. This work applies an optimization approach to design environmentally benign homogeneous catalysts, specifically those which contain transition metal centers. The use of optimization techniques coupled with molecular design, along with property estimation methods allows the determination of candidate molecules matching a set of target properties. For example, it has now been reported (Hairston, 1998) that a computational algorithm has been successfully implemented in order to design a new pharmaceutical which fights cancer. This work employs connectivity indices, which are numerical values which describe the electronic structure of a molecule, to characterize the molecule and to correlate its internal structure with physical properties of interest. Kier and Hall (1976) report correlations between connectivity indices and many key properties of organic compounds, such as density, solubility, and toxicity. The correlations to compute the physical properties are then combined with structural constraints and reformulated into an MINLP, is then solved via various methods to generate a list of near-optimal molecular structures. Raman and Maranas (1998) first employed connectivity indices within an optimization framework, and Camarda and Maranas (1999) used connectivity indices to design polymers which prespecified values of specific properties. An application of connectivity indices to the computational molecular design of pharmaceuticals was described by Siddhaye et al. (2000). In earlier molecular design work, group contribution methods were used to estimate the values of physical properties, as in Gani, et al. (1989), Venkatasubramanian et al. (1995), and Maranas (1996). The connectivity indices, however, have the advantage that they take into account the internal molecular structure of a compound. The property predictions generated from these indices are thus more accurate then those from group contributions, and furthermore, when a molecular design problem is solved using these indices, a complete molecular structure results, and no secondary problem must be solved to recover the final molecular structure.

2. Property Prediction via Connectivity Indices The basis for many computational property estimation algorithms is a decomposition of a molecule into smaller units. Topological indices are defined over a set of basic groups, where a basic group is defined as a single non-hydrogen atom in a given valency state bonded to some number of hydrogen atoms. Table 1 gives the basic groups used in this work, along with the atomic connectivity indices for each type of group. In this Table, the 5 values are the simple atomic connectivity indices for each basic group, and refer to the number of bonds which can be formed by a group with other groups. The 5^ values are atomic valence connectivity indices, which describe the electronic structure of each basic group, including lone-pair electrons and electronegativity. For basic groups involving carbon, oxygen, and halogen atoms, the definitions of these indices are from the work of Bicerano (1996). However, these indices assume the nonhydrogen atom can only have one valency state. For transition metals which can assume multiple valency states, the definition of S" must be extended. We have defined S" based on the number of electrons participating

79 in the bonding, instead of those present in the outer shell. The resulting values for 5^ for molybdenum groups are listed in Table 1, along with values for other groups from Bicerano (1996). Note that atomic connectivity indices can be defined for any basic group, and the small table of groups used here is merely for illustrative purposes. Table 1: Basic Groups and their Atomic Connectivity Indices.

-CH3 -CH2-

8 1 2

5^ 1 2

-CH<

3

3

-CI

1

0.778

-OH -0-

8 1 2

8^ 5 6

1

5

0.139

6

0.171

>Mo<

I >Mo<

I Once a molecule is decomposed into its basic groups, and the atomic connectivity indices for those groups are known, then molecular connectivity indices can be computed for the entire molecule. The zeroth, first and second order molecular connectivity indices \ , *x , and \ axe sums over each basic group, each bond, and each triplet respectively, and are related to the atomic indices in the following manner:

X

ZJ

j-^

ieG\Oi

X

ZJ

IOC

ijeByjOidj

^

/

2J

ijjeT

C C C

^O-djOi

where G is the set of all basic groups in the molecule, B is the set of all bonds, and T is the set of all triplets. The valence molecular connectivity indices are computed analogously using the valence atomic connectivity indices 8^. Once the equations defining the (molecular) connectivity indices are in place, we can use these indices in empirical correlations to predict the physical properties of novel transition-metal catalysts. For example, the correlation derived in this work for density is: >o = 35.81-44.06^-0.2227V -5.748^;^ +0.0522V +31.38';^-0.037V +I5.9l{^zj + 0.0236(V)' -4.203C;rT -0.0022s{'z'J

+0.l592{'zJ

+ 0.0006(';ir7 " 3 7 . 1 8 ^ ^

Since connectivity indices are defined in a very general way, they are capable of describing any molecule, and thus correlations based on them tend to be widely applicable and fairly accurate over a wide range of compounds. Using such correlations, an optimization problem has been formulated which has as its optimal solution a molecule which most closely matches a set of target property values for a molybdenum catalyst.

80

3. Problem Formulation The optimization problem which determines the best molecule for a given application uses an objective function which minimizes the difference between the target property values and the estimated values of the candidate molecule. This can be written as

min ^ = A^V

p scale

P„-/l

target

where R is the set of all targeted properties, P,„ is the estimated value of property m, Pj"^^^^ is a scale factor used to weight the importance of one property relative to another, and P^^^^^ is the target value for property m. The molecule is represented mathematically using two sets of binary variables: a partitioned adjacency matrix with elements a(ij,k) which are one if basic groups / andy are bonded with a A;^''-multiplicity bond, and zero otherwise. In the example presented here, the basic groups can only form single bonds, and thus the index k will be dropped. This matrix is partitioned such that specific rows are preassigned to different basic groups, so that it can be determined a priori what 5i and 5i^ values should be used for each basic group / in the molecule. Since we do not know how many of each type of group will occur in the fmal optimal molecule, the partitioned adjacency matrix will have many rows which do not correspond to a basic group. The binary variable w, is set to one if the ith group in the adjacency matrix exists in the molecule, and is zero otherwise. In order to store the existence of a triplet in the molecule (to compute \), a new binary variable y(ij,l) is defined. An element y(i,j,l) is equal to one if group / is bonded to group j , and group j is bonded to group /. These three sets of variables provide sufficient information to compute the connectivity indices, and thus estimate molecular properties. These data structures are then included within the equations for the connectivity indices to allow the structure of the molecule to be used to estimate physical properties. Along with these definitions, property correlations using the connectivity indices must also be included in the overall formulation. Finally, structural feasibility constraints are needed to ensure that a chemically feasible molecule is derived. In order to guarantee that all the groups in the molecule are bonded together as a single unit, we include the constraints from a network flow problem into the formulation. A feasible solution to a network flow problem across the bonds of a molecule is a necessary and sufficient condition for connectedness, and the constraints required are linear and introduce no new integer variables. Other constraints include bounds on the variables and property values. The problem written in this form is an MINLP, which then must be solved to obtain the desired structures.

4. Solution Methods In this work, two types of solution methods have been tested: the deterministic method known as outer approximation (Duran and Grossman, 1986), and the stochastic algorithm Tabu search (Glover, 1986,1997). While outer approximation guarantees that the global optimum will be found within a finite number of steps for a convex MINLP, the formulation

81 as listed here is nonconvex. Linear reformulations of the equations for y and the objective function have been implemented which leave the property constraints as the only nonlinear equations. The Tabu search algorithm is a meta-heuristic approach which guides a local search procedure and is capable of escaping local minima. Many issues must be addressed when applying Tabu search to molecular design problems. The Tabu search avoids local minima by storing a memory list of previous solutions, and the length of these lists must be set. Furthermore, strategies for determining when a more thorough search of a local region is needed must also be determined. A discussion of these issues is given in Lin (2002). Other applications of Tabu search within chemical engineering are described in Lin and Miller (2000, 2001).

5. Example The example presented here produces a potential molecular structure for a homogeneous molybdenum catalyst for epoxidation reactions. The possible basic groups in the molecule are those listed in Table 1, and the maximum number of basic groups allowed in the molecule is 15. A target value was set for the density, and all structural feasibility constraints were employed. The problem was solved using outer approximation, accessed through the GAMS modeling language on a Sun Ultra 10 workstation. A resource limit of 20 minutes was set, and no guaranteed optimal solution was found. The best integer solution found is shown in Figure 1. The value of the density for this molecule is 4382 Kg/m^, which is far away from the target value of 4173 Kg/m^. S^aOH

I/ CH3--M0—O

^^^ OH

I/

Mo

CI I

NH^

I

OH

CI

Figure 1: Candidate catalyst molecule found using DICOPT. When Tabu search is applied to this example, near-optimal structures are found in a much shorter time. 100 runs of the code were made, each of 90 seconds duration. The best structure found in most of the runs (80%) is presented in Figure 2. This structure has a density of 4172 Kg/m^, which deviates only slightly from the target. Note that many nearoptimal structures were also found, which can be combined into a list which a catalyst designer could use to choose a candidate for synthesis and experimental testing. OH OH

I ; CI—CH2—Mo—CI OH

Figure 2: Candidate catalyst molecule found by Tabu search.

82

6. Conclusions This work has focused on the use of optimization techniques within a molecular design application to derive novel catalyst structures. The use of connectivity indices to relate internal molecular structure to physical properties of interest provides an efficient way to both estimate property values and recover a complete description of the new molecule after an optimization problem is solved. The optimization problem has been formulated as an MINLP, and the fact that the problem has been formulated in a manner which is not computationally expensive to solve (using Tabu search) gives rise to the possibility that the synthesis route for such a molecule could be derived and evaluated along with the physical properties of that molecule. Further work will include such synthesis analysis, as well as the inclusion of a much larger set of physical properties and basic groups from which to build molecules, and will work toward the design of mixtures and the prediction of mixture properties via connectivity indices.

7. References Bicerano, J., 1996, Prediction of Polymer Properties, Marcel Dekker, New York. Camarda, K.V. and Maranas, CD., 1999, Ind. Eng. Chem. Res., 38,1884. Duran, M.A. and Grossmann, I.E., 1986, Math. Prog., 36, 307. Gani, R., Tzouvars, N., Rasmussen, P. and Fredenslund, A., 1989, Fluid Phase Equil., 47, 133. Glover, F., 1986, Comp. and Op. Res., 5, 533. Glover, F. and Laguna, M., 1997, Tabu Search, Kluwer Academic Publishers, Boston. Hairston, D.W., 1998, Chem. Eng., Sept., 30. Kier, L.B. and Hall, L.H., 1976, Academic Press, New York. Lin, B., Miller, D.C., 2000, AIChE Annual Meeting, Los Angeles, CA. Lin, B., Miller, D.C., 2001, AIChE Annual Meeting, Reno, NV. Lin, B., 2002, Ph.D. Thesis, Michigan Technological University. Maranas, CD., 1996, Ind. Eng. Chem. Res., 35, 3403. Raman, V.S. and Maranas, CD., 1998, Comput. Chem. Eng. 22,747. Siddhaye, S., Camarda, K.V., Topp, E. and Southard, M.Z., 2000, Comp. Chem. Eng., 24, 701. Venkatasubramanian, V., Chan K. and Caruthers, J.M., 1994, Comp. Chem. Eng., 18, 9, 833.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

83

Complete Separation System Synthesis of Fractional Crystallization Processes L.A. Cisternas^^\ J.Y. Cueto^^^ and R.E. Swaney^^^ (1) Dept. of Chemical Engineering, Universidad de Antofagasta, Antofagasta, Chile (2) Dept. of Chemical Eng., University of Wisconsin-Madison, Madison, WI, USA

Abstract A methodology is presented for the synthesis of fractional crystallization processes. The methodology is based on the construction of four networks. The first network is based on the identification of feasible thermodynamic states. In this network the nodes correspond to multiple saturation points, solute intermediate, process feeds and end products. The second network is used to represent the variety of tasks that can be performed at each multiple saturation point. These tasks include cooling crystallization, evaporative crystallization, reactive crystallization, dissolution, and leaching. Heat integration is included using a heat exchanger network which can be regarded as a transhipment problem. The last network is used to represent filtration and cake washing alternatives. The cake wash and task networks are modelled using disjunctive programming and then converted into a mixed integer program. The method is illustrated through the design of a salt separation example.

1. Introduction There are two major approaches for the synthesis of crystallization-based separation. In one approach, the phase equilibrium diagram is used for the identification of separation schemes (For example Cisternas and Rudd, 1993; Berry et al., 1997). While these procedures are easy to understand, they are relatively simple to implement only for simple cases. For more complex systems, such as multicomponent systems and multiple temperatures of operation, the procedure is difficult to implement because the graphical representation is complex and because there are many alternatives to study. The second strategy is based on simultaneous optimization using mathematical programming based on a network flow model between feasible thermodynamic states (Cisternas and Swaney, 1998; Cisternas, 1999; Cisternas et al. 2001; Cisternas et al. 2003). In crystallization and leaching operations, filtration, washing and drying are often required downstream to obtain the product specifications. For example, usually filter cake must be washed to remove residual mother liquor, either because the solute is valuable or because the cake is required in a semiclean or pure form. These issues have been discussed by Chang and Ng (1998), who utilized heuristic for design purposes. The objective of this study is to address these issues using mathematical programming. This work constitutes part of our overall effort on the synthesis of fractional crystallization processes. Drying is not included in this method because, as it normally does not involve a recycle stream, the dryer can be considered as a stand-alone operation.

84

2. Model Development 2.1. Networks for fractional crystallization The model proposed in this paper is composed of four networks: (1) the thermodynamic state network, (2) the task network, (3) the heat integration network, and (4) the cake wash network. The first three networks have been described in our previous works; therefore, emphasis here is given to the cake wash network. The first network is based on the detection of feasible thermodynamic states. Using equilibrium data for a candidate set of potential operating point temperatures, a thermodynamic state network flow model is create to represent the set of potential separation flowsheet structures that can result. This representation was presented by Cisternas and Swaney(1998) for two solutes systems, by Cisternas(1999) for multicomponent systems, and by Cisternas et al.(2003) for metathetical salt. Figure 1 shows the thermodynamic state network representation for a two solute system at two temperatures. The structure contains feeds, two multiple saturation points, and products. The second network, which is also shown in Figure 1, is the task network (Cisternas et al. 2001). Each multiple saturation state can be used for different tasks depending on the condition/characteristic of the input and output streams. For example, if solvent is added to an equilibrium state, the task can be: (1) a leaching step, if the feed is solid; (2) a cooling crystallization step, if the feed is a solution with a higher temperature; or (3) a reactive crystallization step, if the feed is a crystalline material that decomposes at this temperature or in the solution fed to this state (for example, the decomposition of carnallite to form potassium chloride). The third network, a heat exchange network, can be regarded as a transhipment problem as in Papoulias and Grossmann (1983). This transhipment problem can be formulated as a linear programming problem. In this representation hot streams and cold streams corresponds to the arcs in the thermodynamic state network. The fourth network is the cake wash network. Cake washing can be accomplished by two methods: (a) The cake may be washed prior to removal from the filter by flushing it with washing liquour. This can be done with both batch and continuous filters, (b) the cake may be removed from the filter and then washed in a mixer. The wash suspension obtained may then be separated with the filter. Figure 2 shows both alternatives for removing the residual mother liquor of concentration y^.i. Figure 2 shows only one stage, but washing may be performed in one or several stages on either batch or continuous filters. In this work countercurrent washing is not considered. As a result, the first stage provides the most concentrated solution and the last stage provides the least. If operation states are near-equilibrium states, then mother liquor concentration in the cake is substantially that of a saturated solution at the final temperature in the process. 2.2. Mathematical formulation Having derived the networks for the separation problem, a mathematical programming formulation is presented for each network to select the optimum flowsheet alternative of the separation sequence.

85

Figure 1. Thermodynamic state network and task network zr, zw. ypw

ywe *

/ c

ymWf WASHING

RESLURRY

FILTER

\

ymr.

rve

17 Figure 2. Cake wash network for stage e. The mathematical formulation for the thermodynamic state network is the same as that developed by Cisternas(1999) and Cisternas et al. (2003). Here a brief description is given. First, the set of thermodynamic state nodes will be defined as: S=(s, all nodes in the system^. This includes feeds, products, multiple saturation points or operation points, and intermediate solute products. The components, solutes and solvents, will be denoted by the set /= {i}. The arcs, which denote streams between nodes, will be denoted by L={1}. Each stream / is associated with the positive variable mass flow rate w/ and the parameter x^ giving the fixed composition of each component in the stream. The constraints that apply are: (a) Mass balance for each component around multiple saturation and intermediate product nodes. se SJ^JE I /65'""(5)

(1)

leLqnS°"'{s)

where Lq is the subset of L of solid stream product, hi is the mass ratio of residual liquid retained in the cake pores to the solid product /, and xyj is the concentration of the mother liquid in equilibrium with solid product /. Also S'^(s) and S^'*^(s) are the sets of

86 input and output streams to node s. (b) Specification for feeds flow rates ^ w, • x^. = C^. , where se S^Je Ip{s) and C^^, is the desired flow rates of specie leF{s)

i in feed s. The heat integration network follows the approach presented by Papoulias and Grossmann(1983). First, it is considered that there is a set K={k} of temperature intervals that are based on the inlet temperatures of the process streams, highest and lowest stream temperatures, and of the intermediate utilities whose inlet temperatures fall within the range of temperatures of the process streams. The only constraints that apply are heat balances around each temperature interval k: R. -^.-. -lQ:^lQn=l OTGVjt

/iGf/jfe

vv, (C^AT)f, - X w, (C^AT)l l^Hk

keK

(2)

/eCjt

where Q,/ , Qn^ and Rk are positive variables that represent heat load of hot utility m, heat load of cold utility n, and heat residual exiting interval k, respectively. (CpAjfik and (CpATfik are known parameters that represent the heat content per unit mass of hot stream leH^ and cold stream leC^ in interval k. //^ Cjt, Vk and Uk are the hot stream, cold stream, hot utility and cold utility set respectively in interval k. A task network is constructed for each multiple saturation point node s. The mathematical formulation, which is close to that in Cisternas et al. (2001), includes mass and energy balance, logic relations to select the task based on input/output stream properties, and cost evaluations. The formulation use disjunctive progranmiing. A cake wash network is constructed for each solid stream product leLq. Let E(l)={e} define the set of washing/reslurry stages in the solid stream product / e Lq. The variables are defined as follows: y^e^ is the concentration of species i in the residual mother liquor of the solid stream / at the output of wash/reslurry stage e. z^ej and riej are the input and output concentration in the washing liquid for the solid stream /, at stage e. ypwie,h ypr^e.h y^^he.h yf^n.e.h ^^uh zr^e.h f^i,e,h and rr/^,, are the concentration of the internal streams in stage e (see figure 2). The wash efficiency parameter, £w/ ^,, for specie i in solid stream / at the stage e can be defined as £w,^,. = {ymwi^. -ypy^iej)/i^i,e,i ~>'P^/,e.,) ^ r le Lq.ee E{1), ie I. The first two constraints in eq. (3) bellow are the efficiency constraint for the wash and reslurry/filter steps. Note that the efficiency for perfect mixing in the wash mixer is equal to 1. The last two constrains in Eq. (3) are the mass balances for specie / at the stage e of washing solid stream /,. Eri^ej rr^ei - Er^^, ypr^^, - ymr,^. + ypr^^. =0

leLq.eE £(/), / e /

87 nwi^e and nrie are parameters that represent the mass ratio of wash liquid to residual liquor in the cake used in wash and reslurry/filter steps respectively. There ratios are referred to as the wash ratio or number of displacements. This network requires the use of discrete variables, ywi^ and yrie to represent the choices of wash, or reslurry/filter, or neither, for each solid product stream I e Lq ai stage e. The corresponding logical relations are: _ y^Le

-^y^i,e

-^yn,e

yn,e

yi,e,i =

y^^i,e,i

yp^i,e,i

= yi,e-i,i

yi,e,i = yi,e,i y^\e,i

y^fiei

ypn,e.i = yi,e-u ytnWi^.

ypn,e.i=^

yp^i,e,i

=

-'yn.e

yi,e,i =

ymr,^.=0 ^^l,e,i

-^y^i,e

ypn,e,i = 0

= 0

y^^i,e,i

- ^

yp^i,e,i

= 0

=0

V \e,i

=0

V

(4)

^^l,e,i=^

^^l,e,i = 0 ^n,ej = Zi,e,i

^^le,i=^

Q^l,e=^^lA

W°

Qfie =nnehi w'

Qn,e=o Cke=Cfw Cvi^ = Cvw

Qw,^=0

Cf,.=Cfr QWf^

Cv.

=CvrQr.

^^l,ej ~ ^l,e,i

Gw,, =0 Qn,e=o Cfl,e=^

Cv,,=0 This logical relation is rewritten as mixed-integer linear equations. The concentration of the last stage / m u s t satisfy the impurity level /L/„ this isy f. hi< IL^^ for le Lqje I. The objective function is to minimize the venture cost. The following equation can be used as an objective function, min X J^iFC,, +VC„ ^c^Ql +cfC,J)+ ^ C ^ G : + l^c„Ql + S S ( C / , , +Cv,,J S&SM teTis)

meV

neU

(5)

leLq e

Eq. (5) represents the total cost given by the investment and utility cost. In this way, the objective function in Eq. (5), subject to constraints in Equations 1 to 4, defines a mixed integer linear progranmiing problem. The numerical solution to the MILP problem can be obtained with standard algorithms. In Eq. (5) Qts^, QJ, VQS and FQs are the heat loads of crystallization or dissolution, the heat loads of evaporation, and the variable costs and fixed costs for the equipment associated with task t of multiple saturation point s.

3. Illustrative Example This example considers the production of potassium chloride from 100,000 ton/year of sylvinite (47.7% KCl, 52.3% NaCl). Data are given in Cisternas et al. (2001). The solution found is shown in figure 3. The problem formulation in 293 equations and 239 variables (27 binary variables) was solved using 0SL2 (GAMS). The optimal solution

divides the feed into two parts. A sensitivity analysis shows that product impurity level and residual liquid retained level in the cake can affect the solution and cost by 20%.

LliAClirNC. at lOOX

iiquui

UNIT

wash liquid

1

WASH UNIT

1

RESLURRY

KCl Cake

Figure 4. Solution for example.

4. Conclusions The objective of this paper has been to present a method for determining the desired process flowsheet for fractional crystallization processes including cake washing. To achieve this goal, a systematic model was introduced consisting of four networks: the thermodynamic state network, the heat integration network, the task network, and the cake wash network. Once the representation is specified, the problem is modelled as a MILP problem. From the example, we can conclude that the model can be useful in the design and study of fractional crystallization processes. Result from the example indicates that product impurity level and the level of residual liquid retained in the cake can affect the optimal solution.

5. References Berry, D.A., Dye, S.R., Ng, K.M., 1997, AIChE J., 43, 91. Chang, W.C, Ng, K.M., 1998, AIChE J., 44, 2240. Cisternas, L.A., Rudd, D.F., 1993, Ind. Eng. Chem. Res., 32, 1993. Cisternas, L.A., Swaney, R.E., 1998, Ind. Eng. Chem., 37, 2761. Cisternas, L.A., 1999, AIChE J., 45, 1477. Cisternas, L.A., Guerrero, C.P., Swaney, R.E., 2001, Comp. & Chem. Engng., 25, 595. Cisternas, L.A., Torres, M.A., Godoy, M.J., Swaney, R.E., 2003, AIChE J., In press. Papoulias, S.A., Grossmann, I.E., 1983, Comp. & Chem. Engng., 707. Turkay, M., Grossmann, I.E., 1996, Ind. Eng. Chem. Research, 35, 2611.

6. Acknowledgment The authors wish to thank CONICYT for financial support (Fondecyt project 1020892).

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. Ail rights reserved.

89

Mathematical Modelling and Design of an Advanced Once-Through Heat Recovery Steam Generator Marie-Noelle Dumont, Georges Heyen LASSC, University of Liege, Sart Tilman B6A, B-4000 Liege (Belgium) Tel:+32 4 366 35 23 Fax: +32 4 366 35 25 E-mail: [email protected]

Abstract The once-through heat recovery steam generator design is ideally matched to very high temperature and pressure, well into the supercritical range. Moreover this type of boiler is structurally simpler than a conventional one, since no drum is required. A specific mathematical model has been developed. Thermodynamic model has been implemented to suit very high pressure (up to 240 bar), sub- and supercritical steam properties. We illustrate the model use with a 180 bar once-through boiler (0TB).

1. Introduction Nowadays combined cycle (CC) power plants become a good choice to produce energy, because of their high efficiency and the use of low carbon content fuels (e.g. natural gas) that limits the greenhouse gases production to the minimum. CC plants couple a Brayton cycle with a Rankine cycle. The hot exhaust gas, available at the output of the gas turbine (Brayton cycle) is used to produce high-pressure steam for the Rankine cycle. The element, where the steam heating takes place, is the heat recovery steam generator (HRSG). High efficiency in CC (up to 58%) has been reached mainly for two reasons: • Improvements in the gas turbine technology (i.e. higher inlet temperature); • Improvement in the HRSG design We are interested in the second point. The introduction of several pressure levels with reheat in the steam cycle in the HRSG allows recovering more energy from the exhaust gas. Exergy losses decrease, due to a better matching of the gas curve with the water/steam curve in the heat exchange diagram (Dechamps,1998). Going to supercritical pressure with the 0TB technology is another way to better match those curves and thus improve the CC efficiency. New improvements are announced in near future to reach efficiency as high as 60%. In the present work we propose a mathematical model for the simulation and design of the once-through boiler. It is not possible to use empirical equations used for the simulation of each part of the traditional boiler. General equations have to be used for each tube of the boiler. Moreover there is a more significant evolution of the water/steam flow pattern type due to the complete water vaporization inside the tubes (in a conventional boiler, the circulation flow is adjusted to reach a vapor fraction between 20% and 40% in the tubes and the vapor is separated in the drum). Changes of flow pattern induce a modification in the evaluation of the internal heat transfer coefficient as well as in the pressure drop formulation. The right equation has to be selected dynamically according to the flow conditions prevailing in the tube.

90 The uniform distribution of water among parallel tubes of the same geometry subjected to equal heating is not ensured from the outset but depends on the pressure drop in the tubes. The disappearance of the drum introduces a different understanding of the boiler's behavior. Effect of the various two-phase flow patterns have to be mathematically controlled. The stability criteria has changed.

2. Mathematical Model 2.1. Heat transfer 2.1.1. Water Mathematical models for traditional boilers are usually based on empirical equations corresponding to each part of the boiler : the economizer, the boiler and the superheater. Those three parts of boiler are clearly separated thus it is not difficult to choose the right equation. In a once-through boiler this separation is not so clear. We have first to estimate the flow pattern in the tube then to choose the equation to be used. "Liquid single phase" and "vapor single phase" are easily located with temperature and pressure data. According to Gnielinski (1993) the equation 1 applies for turbulent and hydrodynamically developed flow. (^/8)(Re^-1000)Pr

_ ^*^

Arw=-

^

1+ 1 2 , 7 7 ( ^ ( p r 2 / 3 _ i j

^

^

•

(1)

•

'

^(i,821og^QRe-l,64)

During vaporization different flow patterns can be observed, for which the rate of heat transfer also differs. In stratified-wavy flow pattern incomplete wetting has an effect on the heat transfer coefficient. A reduction could appear for this type of flow pattern. Computing conditions where a change in flow pattern occurs is useful. A method to establish a flow pattern map in horizontal tube for given pressure and flow conditions is clearly exposed by Steiner (1993). This method has been used in this study. The different flow pattern in the vaporisation zone of the OTB are given in figure 1. The heat transfer coefficient is estimated from numerous data. It is a combination of convective heat transfer coefficient and nucleate boiling heat transfer coefficient. How Pattern Diagram for Horizontal Row (VDI (1993)) Row in tubes with 5.06t^ and 5.166t/h

1 1i

riiistS nular

lE
1£-01

ttoe

1E-03

1E-04

H ^ i-H4l

1 III 1 1

X

Mill

11

f

[Plug

or 5lu

Wavy (2)

-.——r

X

— .— »tra1ified(1) *le-b

uU

Mini l _ J J LL

X-Martinelli parameter

POnoe-throughHFtSG » Tradition^ HRSG|

Figure 1: Flow pattern map in the boiling zone.

Figure 2: Internal heat transfer coefficient 3.

91

= ^'('

conv

(2)

B ,0.37

-2 «(2)..

(l-x)^l.2x^\l-xf^^

T-2

-r-2.2

^li^ Vf^

a

,0.67 \ go 0.01 1+8(1-4

7o

,0.7

(3)

^^^ vc??

cciz)

B --{heatflow,pressure,roughness,geometry} (4) a,lo ttLo is the heat transfer coefficient with total mass velocity in the form of the liquid and OGO is the heat transfer coefficient with total mass velocity in the form of the vapor. The internal coefficients computed for all the tubes of the OTB are presented in figure 2. 2.1.2. Fumes There is no difference between the equations used for a conventional heat recovery boiler and a once trough heat recovery boiler. The main part of the heat transfer coefficient is the convective part (low fumes temperature). The effect of the turbulence has been introduced to reduce the heat transfer coefficient in the first few rows of the tube bundle. The main difficulty to evaluate the heat transfer coefficient for the fume side comes from the fins that enhance the heat transfer, but could also produce other sources of resistance in the heat transfer, such as fouling on the surface of fins or inadequate contact between the core tube and the fin base. There are two methods to evaluate the heat transfer coefficient: • The first one is based on a general equation to evaluate the Nusselt number in cross flow over pipes and the efficiency of the fins. An apparent heat transfer coefficient is then computed with equation 6. • The second one is based on empirical correlations derived from experimental data. For more than four banks in staggered arrangement, equation 7 can be used. It is not obvious to find the most appropriate correlation for a given fin geometry and tube bundle arrangement. The best is to ask finned tube manufacturers to provide their correlations for heat transfer coefficient and fin efficiency corresponding to the required finned tube.

± [•LjQftD-«-FlJMEIN-^VVATERdjf| \"*" Pressure drop - * - vapour fractioni

Figure 3: Heat exchange diagram.

Figure 4: Pressure drop and vapor fraction evolution.

92 A a

=a. * app f

po A

Nu, =0.38Re0.6 d

f

A. fo A

A

(6)

p/3

(7)

2.1.3. Overall heat transfer coefficient Finally the overall heat transfer coefficient is obtained from equation 8. The global heat transferred for each tube is computed with equation 9. We call A7^/ "semi logarithmic temperature difference". It is the best compromise between pure logarithmic temperature difference that has no sense here (only one tube) and pure arithmetic temperature difference that does not allow to follow the evolution of water properties along the tube. The heat exchange diagram of the 0TB is presented in figure 3. l i e 1 — = + :— + a a A A app ;i*_wi a . * - ^ A I A Q = a*A''AT

J si

(8)

\ w2

; AJT, = si In

T

wl) mf

T -T mf wl

+T 2

T -T mf w2 2.2. Pressure drop 2.2.1. Water

AP =

fpV 28

I with d^

/ =

Re 0.3164

(10)

The coefficient f depends on the Reynolds number for flow within the tube. In laminar flow, the Hagen-Poiseuille law can be applied. In turbulent flow the Blasius equation is used. The main difficulty is the evaluation of water pressure drop during transition boiling. The pressure drop consists of three components: friction (APf), acceleration (APm) and static pressure (APg). In once-through horizontal tubes boiler APg=0. The Lockard-Martinelli formulation is used to estimate the friction term. AF

AF O ^2 phases

Miquid

fit

(11)

93

WL.^liquid

(12)

O ^ =1 + — + — - with X = ,r

fit

X

x^

\r^^>

\vapor

The acceleration term is defined with equation 13 where a is the volume fraction of vapor (void fraction). It is reconmiended to discretize the tube in several short sections to obtain more accurate results (figure 4).

AF

o--r

:G^* vap

^

'

(13)

liq

2.2.2. Fumes The pressure drop in a tube bundle is given by equation 14. In this case the number of rows (NR) plays an important role in the pressure drop evaluation. The coefficient f is more difficult to compute from generalized correlations. The easiest way is once more to ask the finned tubes manufacturer to obtain accurate correlation.

AP =

f'P'V

•N

(14)

R

3. Stability Stability calculation is necessary for the control of water distribution over parallel tubes of the same form and subjected to equal heating in forced circulation HRSG and particularly in OTB. The stability can be described with the stability coefficient S. HRSG manufacturers try to keep the stability coefficient in the range (0.7-2). In OTB design inlet restrictions have been installed to increase single-phase friction in order to stabilize the boiler. Based on the 7C-criterion (Li Rizhu, Ju Huaiming, 2002) defined as , the design has been realized with n about 2. This number has to

7r =

be reduced in near future when all various flow instabilities would be identified.

( (

relative change \ in pressure drop/

S =

with

relative change \ in flow rate / S>0 stable S < 0 unstable

d(M) M

Mass flow M

Figure 5: Stability example.

94

4. An Example Results have been obtained for an OTB of pilot plant size (42 rows). WATER (10.25 t/h; Tin=44°C; Tout=500°C) FUMES (72.5 t/h; Tin=592°C; Tout=197°C). In VALIBelsim software in which the simulation model has been implemented, the simulation of the OTB needs 42 modules, one for each row of tubes. Since VALI implements an numerical procedures to solve large sets of non-linear equations, all model equations are solved simultaneously. The graphical user interface allows easy modification of the tube connections and the modelling of multiple pass bundles.

5. Conclusions and Future Work The mathematical model of the once-through boiler has been used to better understand the behaviour of the boiler. Future mathematical developments have still to be done to refme the stability criteria and improve the OTB design. Automatic generation of alternative bundle layouts in the graphical user interface is also foreseen.

6. Nomenclature A Ab Afo Ai ADO

di

AP f G H NR

Nu P

total area of outer surface (m^) bare tube outside surface area fin outside surface area (m^) inside surface area (m^) free area of tube outer surface mean area of homogeneous tube wall specific heat capacity at constant pressure (J/kg/K) tube intemal diameter (m) pressure drop (bar) pressure drop coefficient massflux(kg/m^/s) enthalpyflow(kW) number of rows in the bundle al Nusselt number Nu A pressure (bar)

Pr

Prandl number Pr = — - —

Q Re T

exchanged heat (kW) Reynolds number temperature (K)

V X Xi

a oc(z) X P Tl

A

fluid velocity (m/s) vapor mass fraction component flow rate (kg/s) heat transfer coefficient (kW/mVK) local heat transfer coefficient thermal conductivity (W/m/K) density (kg/m^) dynamic viscosity (Pa.s) or (kg/m/s) fin efficiency

7. References Dechamps, P.J. 1998, Advanced combined cycle alternatives with the latest gas turbines, ASME J. Engrg. Gas Turbines Power 120, 350-35. Gnielinski, V. 1993, VDI heat atlas, GA,GB, VDI-Verlag, DUsseldorf, Germany. Li Rizhu, Ju Huaiming, 2002, Structural design and two-phase flow stability test for the steam generator. Nuclear Engineering and Design 218, 179-187. Steiner, D. 1993, VDI heat atlas, VDI-Verlag, HBB, Dusseldorf, Germany.

8. Acknowledgements This work was financially supported by CMI Utility boilers (Belgium).

European Symposium on Computer Aided Process Engineering- 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

95

Synthesis and Optimisation of the Recovery Route for Residual Products Joaquim Duque^, Ana Paula F. D. Barbosa-Povoa^^ and Augusto Q. Novais^ ^DMS, INETI, Est. do Pago do Lumiar, 1649-038 Lisboa, Portugal ^CEG-IST, DEG, I. S.T., Av. Rovisco Pais, 1049-101 Lisboa, Portugal

Abstract The present work describes an optimisation model for the management of the recovery of residual products originated at industrial plants. The mSTN (maximal State Task Network) representation is used as the modelling framework for the general proposed network superstructure where all possible process transformations, storage, transports and auxiliary operations are accounted for. This is combined with the evaluation of a set of environmental impacts (EI), quantified by metrics (for air, water pollution, etc.) through the minimum environment impact analysis (MEIM) methodology and associated with waste generation at utility production and transportation levels. The final model is described as a MILP, which, once solved, is able to suggest the optimal processing and transport routes, while optimising a given objective function and meeting the design and environmental constraints. A motivating example based on the recovery of the sludge obtained from Aluminium surface finishing plants is explored. This aims at maximizing the quantity of sludge processed and reflects the trade-off between the cost for its disposal, processing, transport and storage, while accounting for the limits imposed in the environment pollutants associated.

1. Introduction Increased awareness over the effects of industrial activities on the environment is leading to the need of providing alternative ways of reducing the negative environmental impacts (Pistikopoulos et al., 1994). In the process industry this problem is highly complex and the potential environmental risks involved forces process manufacturers to undertake special care not only on its production impacts but also on waste disposal, steeping costs and soil occupation. Most of the works looking into these problems addressed the case of designing a plant such that a minimisation of waste produced was obtained (Linninger et al, 1994, Stefanis et al, 1997). A further possible environmental solution, if viable, is the reuse of those waste materials as resources, after total or partial pollutant content removal. In this paper, we explore this problem and propose a model for the synthesis and optimisation of a general recovery route for residual products. The modelling of the general network route is based on the mSTN representation (Barbosa-Povoa, 1994) where all the possible processing, storage and transport operations are considered. A metric for the diverse environmental effects involved is used which is based on the generalisation of the MEI methodology as presented in Stefanis et al (1997).

' Author to whom correspondence should be addressed, e-mail: [email protected], tel:+ 351 1 841 77 29

96 The model is generic in scope and leads both to the optimal network structure and to the associated operation. The former results from the synthesis of the processing steps, while the latter is described by the complete resource time allocation (i.e. processing transport and storage scheduling). A motivating example based on the sludge recovery from Aluminium surface finishing plants is presented with an objective function that maximizes the profit for the proposed network, over a given time horizon. The maximization of the quantity of sludge processed is obtained and reflects the trade-off between the cost for its disposal before and after processing, while accounting for production and transport environment impacts and guaranteeing limits imposed on the environment pollutants.

2. Problem DeHnition and Characteristics The problem of reducing the environmental impact of pollutant products as addresses in this work can be defined as follows: Given: A recovery network superstructure (STN/Flowsheet) characterized by: • All the possible transformations, their process durations, suitable unit locations, capacities, utilities consumption, materials involved and wastes generated. • All waste producers, their location and the quantity of wastes produced along with their pollutants content. • All the reuses and landfill disposals, their locations, utility consumption, capacities and, for the reuse, the wastes generated. • All the possible transport routes, associated suitable transports and duration. Cost data for: • Equipment (processing, transport and storage units). • Reuses and landfill disposal. • Operations and utilities. Operational data for: • Type of operation (Cyclic single campaign mode or short-term operation) • Time horizon/Cyclic time Environmental data (see table 1 Pistikopoulos et al., 1994) • Maximum acceptable concentration limits (CTAM, CTWM) • Long term effect potentials (ex. GWI, SODI) Determine: • The optimal network structure (processing operations, storage locations and transfer routes of materials) • The optimal operating strategies (scheduling of operations, storage profiles and transfer occurrences). So as to optimise an economic or environmental performance. The former can be defined as a maximum plant profit or a minimum capital expenditure accounting for the environmental impacts involved and their imposed limits; the latter can be the minimisation of the environmental impacts where all operational and structural network restrictions as well as cost limits are considered. As mentioned before the mSTN representation is used to model the general network superstructure. This is coupled with a generalization of the MEI methodology so as to account for the waste generation at utility production and transportation levels. For the transport task the environmental impact is calculated based on the fuel oil consumption, therefore at a utility level.

97 Due to the characteristics of the model proposed where the recovery of pollutant products is addressed the system frontier for the environmental impacts is defined at the raw materials level including any type of utilities used. The model has the particularity of considering all possible concurrent transportations and transformations for the same operation (different instances within the superstructure) as well as all raw material producers and re-users. The pollutant is added up for all the different types of waste. The limits on the total waste production and global environment impacts are introduced in the form of waste and pollution vectors, added to the model as additional restrictions. Those limits derive directly from legal regulations for the pollutants considered. The model also considers the possibility of imposing limits on the fmal product amounts required - associated with possible auxiliary operations/removals - as well as on the amount of pollutant materials (raw materials) that should be processed - due to environmental impacts. Table 1. Time dependent environment impact indicators. CTAM ( Critical Air Mass, [kg air/h]) CTWM ( Critical Water Mass, [kgwater/h])

^ polutant emission mass at interval t (kg pollutant/ h) standard limit valu e (kg pollutant/ kg air) C7WM =

polutant emission mass at interval t (kg pollutant/ h) standard limit valu e (kg pollutant/ kg water)

SMD ( Solid Mass Disposal, [kgAi])

SMD

= mass of solids disposed at interval t (kg/h)

^a^t^ CO^I^r^)^^™^^^ ^

^^^ " ^^^^ ^^ P^"- ^^'^^^^^^^t (^^^) ^ ^ ^ ^ (kg C02/kg poll.)

POI ( Photochemical Oxidation Inpact, C2H4 [kg/h]) SODI ( Stratospheric Ozone Depletion Inpact [kg/h])

POl = Mass of poll at interval t (kg poll /h) x POCP (kg Ethylene/kg poll) SODI = Mass of poll at interval t (kg poll /h) x SODP (kg CFCl 1/kg poll)

3. Recovery Route Example In order to illustrate the use of the model proposed, a motivating example based on the optimisation of a recovery route for Al-rich sludge is presented. The anodization and lacquering of aluminium are processes that generate significant amounts of waste in the form of Al-rich sludge. As an economical alternative to disposal, this sludge can be treated and employed as coagulant and flocculant for the treatment of industrial and municipal effluents, or used as agricultural and landfill material. As the surface treatment plant location does not coincide, in general, with the locations for water treatment or landfill location, suitable transports are needed. Based on these characteristics the recovery route network associated with this problem can be described as follows: Given the raw materials differences on pollutant content, two different general types corresponding to state SI and S2 are considered. State SI sludge needs to be processed by task Tl for a two hours period, originating a high pollutant material (S3) that is nonstorable, in the proportions of 1 to 0.97, input and output mass units respectively, and producing a 3% mass units of waste (WTl). State S2 sludge is submitted to a non-aluminium pollutant removal task T2 during two hours, originating a storable intermediate state S4 with the proportions of 2 to 0.98 and originating a 2% waste (WT2), in mass units. This S4 intermediate state is suitable for use as coagulant and flocculant for the treatment of industrial and municipal effluents.

98 The intermediate materials S3 and S4 at respectively 0.6 and 0.4 (mass units) proportions, are then submitted to an aluminium removal task, T3, going on for four hours and originating the final product S5, with the proportions of 1 to 0.99 and originating a 1% waste, in mass units (WT3). This state is stable and has a low pollutant level allowing for its agricultural disposal or the use as a landfill material. Finally the rich aluminium sludge S4 is used for the treatment of industrial and municipal effluents (T4), at a different geographical location, thus requiring a transportation task (Trl) which takes 1 hour of duration. Task 4, leads to the final product S6 and lasts for two hours and has the proportions of 1 input to 0.98 output and originates a 2% waste (WT4) (in mass units). An 8000 tonnes consumption is guaranteed for each final product S5 an S6 to be synthesised from SI and S2, over a production time horizon of 1000 hours with a periodic operation of 10 hours. The STN and the superstructure for the recovery route example are depicted respectively in 0 and 0. The equipment characteristics are presented in Table 2 (raw materials and product storage are unlimited) while impact factors are in Table 3.

Fig. 1. STN Network recovery route.

UA

*h c5

*p

la

1c

Lc C2

V2

I

fl *t>

1b V4

Fig. 2. Recovery route superstructure.

KPciflW

V5

n

2a

C13M

V6

99 The example was solved using the GAMS/CPLEX (v7.0) software running in a Pentium III-E at 863.9 Mhz. The model is characterised by 2046 equations, 1307 variables, of which 144 are discrete, and takes an execution time of 0.110 CPU seconds. The final optimal plant structure is presented in Figure 3 with the corresponding operation depicted in Figure 4. The final recovery route (Figure 3) is characterised by 3 processing steps (in unit lb, Ic and 2a) an intermediate storage location (V4) and a transport route (transport 1, trl). Table 2. Unit characteristics. Units Unit la (la) Unit lb (lb) Unitlc(lc) Unit 2a (2a) Transport 1 Vessel4 (V4) c.u. - currency units

Suitab.

TleT2 TleT2 T3 T4 T5 S4

Capacity (tonne) Max. Min. 150 50 150 50 200 50 200 50 200 50 100 10

Fixed (10' c.u.) 20 20 30 30 0.5 1

Costs Variable (cu/.kg) 0.5 0.5 1 1 0.05 0.1

Table 3. Impact factors. Residues wl_Tl wl_T2 wl_T3 wl_T4 wl_T5 wl_Ul wl_U2 wl_U3 wl_U4

(CTAM) 10 0 1 0 0 0 5 8 2

(CTWM) 0 8 10 8 0 10 0 0 1

u

POCP 0 0 0 0 0 0.05 0 0 0

GWP 0 0 0.03 0.03 0 0 0.004 0.005 0.08

SMD 0.05 0 0 0 0 0 0 0 0

;12

^

I

'

SODP 0 0 0 0 0 0 0.003 0.01 0

L

I—o-J V4 [ 1 1

III Fig. 3. Optimal network recovery route structure. When comparing the options of disposal or processing the materials sludge it can be seen that a value added of 31280 c.u. is obtained against a cost of disposal of 32070 c.u. The recovery option translates a reduction of 95 % in pollutant material with a maximum environmental impact of (ton/hr) CTAM=1.19, CTWM=5.37, SMD=0.005, GWI=0.012 and in POI= SODI=0.

4. Conclusions A model for the synthesis and optimisation of a general recovery route for residual products is proposed. The modelling of the general network route is made through the

100 use of the mSTN representation. This is coupled with a metric for the various environmental effects involved, based on the generalization of the MEI methodology. The proposed model leads to both the optimal network structure, accounting for processing and storage locations of materials, as well as transport, and to the associated operation. The former resulting from the synthesis of the recovery steps (processing, storage and transport), while the latter is described by the complete resource time allocation (i.e. scheduling) where environmental impacts associated not only to the disposal of the materials but also to the utilities and transports utilisation are accounted for. In this way the model is able to suggest the optimal processing and transport route, while reflecting the trade-off between processing and transport costs and environmental worthiness of the modified residual products. It further allows the analysis of the tradeoff existing between the option of the disposal of materials, with a high negative effect to the environment, or their re-processing, while accounting for all the capital, operational, transportation and environment costs associated. As future developments the model is now being extended to account for the treatment of uncertainty in some model parameters. This being investigated on the availability of residual products as well as on the operational and structural levels of the recovery network.

^

h-2_R1a

I

49.98 Tl_R1a

o 2a I 81.63 I T5_Tr1 100 SO

Fig. 4. Scheduling for the recovery route network.

5. References Barbosa-Povoa, A.P.F.D., 1994, Detailed Design and Retrofit of Multipurpose Batch Plants, Ph. D. Thesis. Imperial College, University of London, U.K. Linninger, A.A., Shalim, A.A., Stephanopoulos, E., Han, C. and Stephanopoulos, G., 1994, Synthesis and Assessement of Batch Process for Pollution Prevention, AIchemE Symposium Series, Volume on pollution prevention via process and product modifications, 90 (303), 46-58. Pistikopoulos, E.N., Stefanis, S.K. and Livingston, A.G., 1994, A methodology for Minimum Environment Impact Analysis. AIchemE Symposium Series, Volume on pollution prevention via process and product modifications, 90 (303), 139-150. Stefanis, S.K., Livingston, A.G. and Pistikopoulos, E.N., 1997, Environment Impact Considerations in the optimal design and scheduling of batch processes. Computer Chem. Engng, 21, 10, 1073-1094.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

101

A New Modeling Approach for Future Challenges in Process and Product Design Mario Richard Eden, Sten Bay J0rgensen, Rafiqul Gani CAPEC, Computer Aided Process Engineering Center, Department of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark

Abstract In this paper, a new technique for model reduction that is based on rearranging a part of the model representing the constitutive equations is presented. The rearrangement of the constitutive equations leads to the definition of a new set of pseudo-intensive variables, where the component compositions are replaced by reduction parameters in the process model. Since the number of components dominates the size of the traditional model equations, a significant reduction of the model size is obtained through this new technique. Some interesting properties of this new technique is that the model reduction does not introduce any approximations to the model, it does not change the physical location of the process variables and it provides a visualization of the process and operation that otherwise would not be possible. Furthermore by employing the recently introduced principle of reverse problem formulations, the solution of integrated process/product design problem becomes simpler and more flexible.

1. Introduction As the trend within the chemical engineering design community moves towards the development of integrated solution strategies for simultaneous consideration of process and product design issues, the complexity of the design problem increases significantly. Mathematical programming methods are well known, but may prove rather complex and time consuming for application to large and complex chemical, biochemical and/or pharmaceutical processes. Model analysis can provide the required insights that allows for decomposition of the overall problem into smaller (and simpler) sub-problems as well as extending the application range of the original models. In principle, the model equations representing a chemical process and/or product consist of balance equations, constraint equations and constitutive equations (Eden et al., 2003). The nonlinearity of the model, in many cases, is attributed to the relationships between the constitutive variables and the intensive variables. The model selected for the constitutive equations usually represents these relationships, therefore it would seem appropriate to investigate how to rearrange or represent the constitutive models.

2. Reverse Problem Formulation Concept By decoupling the constitutive equations from the balance and constraint equations the conventional process/product design problems may be reformulated as two reverse

102 problems. The first reverse problem is the reverse of a simulation problem, where the process model is solved in terms of the constitutive (synthesis/design) variables instead of the process variables, thus providing the synthesis/design targets. The second reverse problem (reverse property prediction) solves the constitutive equations to identify unit operations, operating conditions and/or products by matching the synthesis/design targets. An important feature of the reverse problem formulation is that as long as the design targets are matched, it is not necessary to resolve the balance and constraint equations (Eden et al., 2002).

I

Procffi^^ Model Balance and Constraint Equations (Mass, Energy, Momentum) Constitutive Equations (Phenomena model - Function of Intensive Variables)

/ !

Balance and Constraint Equations Identification of design targets by solution of decoupled model

i

REVERSE SIMULATION

D E ^ G N TARGETS
i

REVERSE PROPERTY PREDICTION

Constitutive Equations

Figure 1: Decoupling of constitutive equations for reverse problem formulation. The model type and complexity is implicitly related to the constitutive equations, hence decoupling the constitutive equations from the balance and constraint equations will in many cases remove or reduce the model complexity. Since the constitutive equations (property models) contain composition terms, it is beneficial to solve for the constitutive variables directly, thus removing the composition dependency from the problem.

3. Composition Free Design Methods By rearranging the constitutive equations in a systematic manner, the composition terms can be eliminated from the balance equations. The principal requirement of this new model reduction technique is the choice of a model for the constitutive equations where the constitutive variables, which are calculated through a set of reduction parameters, are linear functions of component compositions. The well-known cubic equations of state such as the Soave-Redlich-Kwong or the Peng-Robinson equations of state satisfy this property requirement. Customized constitutive models may also be generated for this purpose. Michelsen (1986) presented a composition free method for simple flash calculations, where the composition dependent terms of a cubic equation of state are lumped by solving directly for the constitutive variables. This method was extended by Gani & Pistikopoulos (2002) to composition free distillation design. A novel way of representing the constitutive (property) variables of a system is the concept of property clustering (Shelley & El-Halwagi, 2000), where the compositions are eliminated from the process model by characterizing the process streams using physical and chemical properties. The clusters are tailored to possess the two fundamental properties of interand intra-stream conservation allowing for consistent additive rules. Eden et al. (2002)

103 developed cluster based models for fundamental processing units such as mixers, splitters and reactors, through which most sections of process flowsheets can be modeled. The cluster based balance models are derived from the original composition based balance models by systematically removing the composition dependency using property relationships. The clustering approach utilizes property operators defined as:

¥j(PjMix) = 2:x,.VKj(Pjs)

x , = ^

^ i ^ = ^ ^

(^>

S=l

Using an Augmented Property index (AUP) for each stream s, defined as the summation of the dimensionless property operators, the property cluster for property j of stream s is defined: NP

j=l

Cis=—— J' AUR

(3)

The mixture cluster and AUP values can be calculated through the linear mixing rules given by Equations (4) - (5): Ns

Y

-ATTP

CjM.X=EPsqs ' P s - ^ 7 5 ^ s=l

(4)

^^^MIX

AUPM,X=2;'^SAUP,

(5)

s=l

In Equation (4) Ps represents the cluster "composition" of the mixture, i.e. a pseudointensive variable, which is related to the flow fractions (xs) through the AUP values. An inherent benefit of the property clustering approach is that due to the absence of component and unit specifics, any design strategies developed will be generic.

4. Case Study - Recycle Opportunities in Papermaking To illustrate the usefulness of constitutive or property based modeling, a case study of a papermaking facility is presented. Wood chips are chemically cooked in a Kraft digester using white liquor (containing sodium hydroxide and sodium sulfide as main active ingredients). The spent solution (black liquor) is converted back to white liquor via a recovery cycle (evaporation, burning, and causticization). The digested pulp is passed to a bleaching system to produce bleached pulp (fiber). The paper machine employs 100

104 ton/hr of the fibers. As a result of processing flaws and interruptions, a certain amount of partly and completely manufactured paper is rejected. These waste fibers are referred to as broke, which may be partially recycled for papermaking. The reject is passed through a hydro-pulper followed by a hydro-sieve with the net result of producing an underflow, which is burnt, and an overflow of broke, which goes to waste treatment.

Pulp Kraft Digester

^ '

Black L quor

* • • Bleachtng • * •

> » Fiber

Broke

Chemical Cy cle

Waste M

I

raper Product

P^per {Machine

•• »

Reject f

Hydro Sieve

Hydro Pulper

Figure 2: Schematic representation of pulp and paper process. The objective of this case study is to identify the potential for recycling the broke back to the paper machine, thus reducing the fresh fiber requirement and maximize the resource utilization. Three primary properties determine the performance of the paper machine and thus consequently the quality of the produced paper (Biermann, 1996): Objectionable Material (OM) - undesired species in the fibers (mass fraction) Absorption coefficient (k) - measure of absorptivity of light into paper (m^/g) Reflectivity (Roo) - defined as a reflectance compared to absolute standard (fraction) In order to convert property values from raw property data to cluster values, property operator mixing rules are required (Shelley & El-Halwagi 2002; Eden et al. 2002). The property relationships can be described using the Kubelka-Munk theory (Biermann 1996). According to Brandon (1981), the mixing rules for objectionable material (OM) and absorption coefficient (k) are linear, while a non-linear empirical mixing rule for reflectivity has been developed (Willets 1958). Table 1: Properties of fibers and constraints on paper machine feed. Property

Operator

Fibers

Broke

Paper machine

Reference

OM (mass fraction)

OM

0.000

0.115

0.00-0.02

0.01

k(m'/g)

k

0.00115-0.00125

0.001

Rso

(R.)^'^

1

Flowrate (ton/hr)

0.0012 0.0013 0.82

0.90

0.80-0.90

100

30

100-105

From these values it is apparent that the target for minimum resource consumption of fresh fibers is 70 ton/hr (100-30) if all the broke can be recycled to the paper machine. The problem is visualized by converting the property values to cluster values using Equations (1) - (3). The paper machine constraints are represented as a feasibility region, which is calculated by evaluating all possible parameter combinations of the

105 property values in the intervals given in Table 1. The resulting ternary diagram is shown in Figure 3, where the dotted line represents the feasibility region for the paper machine feed. The relationship between the cluster values and the corresponding AUP values ensures uniqueness when mapping the results back to the property domain.

Figure 3: Ternary problem representation.

Figure 4: Optimal feed identification.

Since the optimal flowrates of the fibers and the broke are not known, a reverse problem is solved to identify the clustering target corresponding to maximum recycle. In order to minimize the use of fresh fiber, the relative cluster arm for the fiber has to minimized, i.e. the optimum feed mixture will be located on the boundary of the feasibility region for the paper machine. The cluster target values to be matched by mixing the fibers and broke are identified graphically and represented as the intersection of the mixing line and the feasibility region in Figure 4. Using these results the stream fractions can be calculated from Equation (5). The resulting mixture is calculated to consist of 83 ton/hr of fiber and 17 ton/hr of broke. Hence direct recycle does NOT achieve the minimum fiber usage target of 70 ton/hr. Therefore the properties of the broke will have to be altered to match the maximum recycle target. Assuming that the feed mixture point is unchanged, and since the fractional contribution of the fibers and the intercepted broke are 70% and 30% respectively, the cluster "compositions" (Ps) can be calculated from Equation (4). Now the cluster values for the intercepted broke can be readily calculated from Equation (4), and the resulting point is shown on Figure 5. This reverse problem identifies the clustering target, which is converted to a set of property targets: Table 2: Properties of intercepted broke capable of matching maximum recycle target. Property OM (mass fraction) k(m'/g) Roo

Original Broke 0.115 0.0013 0.90

Intercepted Broke 0.067 0.011 0.879

Note that for each mixing point on the boundary of the feasibility region, a clustering target exists for the intercepted broke, so this technique is capable of identifying all the alternative product targets that will solve this particular problem. Solution of the second

106 reverse problem, i.e. identification of the processing steps required for performing the property interception described by Table 2, is not presented in this work. Most processes for altering or fme tuning paper properties are considered proprietary material, however the interception can be performed chemically and/or mechanically (Biermann 1996, Brandon 1981). C2

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.

Figure 4: Identification of property interception targets.

5. Conclusions Decoupling the constitutive equations from the balance and constraint equations, allows for a conventional forward design problem to be reformulated as two reverse problems. First the design targets (constitutive variables) are identified and subsequently the design targets are matched by solving the constitutive equations. By employing recent property clustering techniques a visualization of the constitutive (property) variables is enabled. A case study illustrating the benefits of these methods has been developed.

6. References Biermann, C.J., 1996, Handbook of Pulping and Papermaking, Academic Press. Brandon, C.E., 1981, Pulp and Paper Chemistry and Chemical Technology, 3rd Edition, Volume III, James P. Casey Ed., John Wiley & Sons, New York, NY. Eden, M.R., J0rgensen, S.B., Gani, R. and El-Halwagi, M.M., 2003, Chemical Engineering and Processing (accepted). Gani, R. and Pistikopoulos, E.N., 2002, Fluid Phase Equilibria, 194-197. Michelsen, M.L., 1986, Ind. Eng. Chem. Process. Des. Dev., 25. Shelley, M.D. and El-Halwagi, M.M., Comp. & Chem. Eng., 24 (2000). Willets, W.R., 1958, Paper Loading Materials, TAPPI Monograph Series, 19, Technical Association of the Pulp and Paper Industry, New York, NY.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

107

Solving an MINLP Problem Including Partial Differential Algebraic Constraints Using Branch and Bound and Cutting Plane Techniques Stefan Emet and Tapio Westerlund* Department of Mathematics at Abo Akademi University, Fanriksgatan 3 B, FrN-20500, Abo, Finland (email: [email protected]) * Process Design Laboratory at Abo Akademi University, Biskopsgatan 8, FIN-20500, Abo, Finland (email: [email protected])

Abstract In the present paper a chromatographic separation problem is modeled as a Mixed Integer Nonlinear Programming (MINLP) problem. The problem is solved using the Extended Cutting Plane (ECP) method and a Branch and Bound (BB) method. The dynamics of the chromatographic separation process is modeled as a boundary value problem which is solved, repeatedly within the optimization, using a relatively fast and numerically robust finite difference method. The stability and the robustness of the numerical method was of high priority, since the boundary problem was solved repeatedly throughout the optimization. The obtained results were promising. It was shown that, for different purity requirements the production planning can be done efficiently, such that all the output of a system can be utilized. Using an optimized production plan, it is thus possible to use existing complex systems, or to design new systems, more efficiently and also to reduce the energy costs or the costs in general.

1. Introduction The problem of efficiently separating products of a multicomponent mixture is a challenging task that is applied in many industries. The objective is to, within reasonable costs, separate the products as efficiently as possible retaining the preset purity requirements. The modeling of different chromatographic separation processes has been addressed in, for example, Saska ^f«/. (1991), Ching ^r a/. (1987) and Guiochon ^f a/. (1994). The optimization of separation processes has been adressed in the pertient literature, for example, in Strube et al (1997) and in DUnnebier and Klatt (1999). A chromatographic separation problem was recently modeled and solved as an MINLP problem by Karlsson (2001). Comparisons of solving the MINLP problem in Karlsson (2001) using the ECP method and the BB method was carried out by Emet (2002). In the present paper, the formulations in Karlsson (2001) and in Emet (2002) are further studied.

108

2. Formulation of the Model Figure 1 shows the different possibilities in a two-column system with two components. At the inlet of a column, it is possible to feed the mixture to be separated (e.g. molasses), the eluent (e.g. water), or the outflow from some other column. At the outlet of a column, one can collect the products or re-use the outcome for further separation. These decisions are modeled using binary variables, y]^,ykij and Xku, as illustrated in Figure 1. The times when these decisions are made are denoted by to, t i , . . . , ^T, where to = 0. The number of intervals is denoted by T and the length of the period by r = tr- The index i denotes which binary variables are valid during the time interval [ti-i,ti]. The indexes k and / denotes the column and the index j the component. The main questions are, thus, what decisions should be made and at which times in order to retain as much separated products as possible.

yu y'^i feed into column k. ykij collect product j from column xiik recycle the outflow from column / to column k.

Column ]

xm ym

Figure 1: A two-column system with two components. 2.1 Dynamic response model The concentration of the component j at the time t > 0 and at the height-position z within column k is denoted by Ckj{t, z). The height of a column is denoted by ZH, and hence 0 < z < ZH' The responses of the concentrations within each column were modeled with the following system of PDEs (Guiochon et ai, 1994):

(l + F ^ , dckj ) ^ + F . ^ f t , ( ^ c , , - ^ + c,,- dt j +u dz ' dt

= Dj

dz'^

(1)

where j = 1 , . . . , C, and k = 1 , . . . ,K. The estimates of the parameters ^j and Pji that were given in Karlsson (2001) were used here. The feed and the recycling decisions provide the following boundary conditions (at the inlet of column k): K

Ckj {t, 0) = yp it) • c f + ^

xik (t) • cij (t,

ZH)

(2)

1=1

The logical functions yp{t)

and xik{t) in (2) are modeled using the following stepwise-

109 linear functions: T i=l T

xik{t) = J2xiik'Si{t)

(4)

where the (Jj(^)-function is defined as

S(t) = l ^ *^

ifte[ti-uti]J

\ 0

=

1,...,T

otherwise.

(5)

The steady state condition of the system (Karlsson, 2001) can be modeled as a periodical boundary condition as follows: Ckj{0,z) =Ckj{r,z)

(6)

That is, the concentrations in a column should be equal at the start and at the end of a period. Conditions on the derivatives can also be formulated in a similar way (Emet, 2002) 2.2 Optimization model The objective function, to maximize the profit over the period, was formulated as:

^^^ ] 7 IZ I ] I ^^*^^ " Y^Pj^f^iJ I [

(7)

where w and pj are parameters that denote the prices of the input feeds, dki, and the collected products Skij • Note that the objective function in (7) is pseudo-convex. The volume of the input feed into column k within the interval i is modeled using the variable dki with the following "big-M" formulation: dki
(8)

where M i > max{dki}' The volumes of the collected products, $kij, are similarly modeled in the following way: Skij < rrikij

(9)

Skij < M2 ' Vkij

(10)

where M2 > max{skij}- The mfcij-variable is defined as the mass of product j within the mterval i at the outlet of column k. These can be formulated as equality constraint as follows rrikij = /

Ckj(t,ZH)dt

(11)

no The nonlinear equality constraints (11) were relaxed as inequalities: rrikij <

/

Ckj{t, ZH)dt + M3 • (1 - ykij) rti

rrikij > /

(12)

J

Ckj{t, ZH)dt - M3 • (1 - V y k u )

(13)

where M3 > max{cfej(t, ZH){U — U-i)}. The purity constraints were formulated as the fraction of the collected product in the total mass of all components: K

T

Z) Z) ^kij '^^^ > Rj

S

(14)

2 Qkij

k=l i = l

where Rj < 1 denotes the purity requirement of component j . The g^^j-variables in (14) are used for measuring the volume of all components within interval i if the component j is collected from column k: c ^

rrikij - Mykij

< Qkij

(15)

The purity constraints (14) were written as linear constraints as follows: K

T

K

T

Rj'YlYl, ^^'3 - IZ m ^**J' - ^ fe=i i = i

fe=i

(^^)

i=i

Linear constraints regarding the order of the timepoints and the binary constraints for the inlet and the outlet were formulated as: fori = 1 , . . . ,T

ti-l

(17)

K

ytl +E Xlik C

E

i=i

1=1 Vkij +

< 1

(18)

X^ Xkil < 1

(19)

K /=1

3. Numerical Methods An analysis of solving the boundary value problem using orthogonal collocation, neural networks and finite differences was conducted in Karlsson (2001). The finite difference method was in Karlsson (2001) reported to be the most robust one (when applied on the chromatographic separation problem), and was hence applied in the present paper. The periodical behavior of the solution was achieved by solving the PDEs iteratively until the changes in the concentrations of two successive iterations resided within a given tolerance

Ill (Emet, 2002). The optimization problem was solved with the ECP method described in Westerlund and Pom (2002). Comparisons were carried out using an implementation of the BB-method for MINLP problems by Leyffer (1999). Whereas the applied BB-method requires both gradient and Hessian information, the ECP-method only requires gradient information. The derivatives needed in each method were thus approximated using finite differences.

4. Numerical Results The profiles of the concentrations of a solution obtained with the BB method are illustrated in Figure 2. Corresponding values are presented in Table 1. The total number of times the system of PDEs has been solved when solving the MENLP problem is also given in Table 1. Note, that most of the CPU-time used in each method was spent on solving the PDEs and calculating the integrals. The purity requirements, (0.8,0.9), were well met using a one-column system. A solution to the two-column problem, obtained with the ECP-method, is illustrated in Figure 3. In the latter problem the purity requirement was (0.9,0.9), and hence recycling was needed. There were, however, severe problems in obtaining any solutions, to the two-column problem, with the BB-method because of the high number of function evaluations needed within each NLP subproblem (Emet, 2002).

Table 1: Results of a one-column system with the purity requirement (0.8,0.9). BB ECP -12.12 -12.28 purity (0.81,0.90) (0.82,0.90) # sub-prob. 124 (MILP) 42 (NLP) # PDE-solv. 11285 1385 1265.4 CPU [sec] 210.0

/•

Figure 2: Profiles of a one-column problem, by BB. Ijl2 (0.01.0.99)

I

^^/; (0.97.0.03)

I

recycle (0.82.0.18)

(0.98,0.02)

(0.12,0.81 2H

(0.8, 0.2)

(0.04,0.96)

(0.23,0.77)

y ^

•

SSH^M

65.6 I

(a) Column 1, recycle to col. 2.

(b) Column 2.

Figure 3: A solution to the two-column problem, f* = —12.4.

recycle

92 9 \ feed

112 3 \

112

5. Discussion A chromatographic separation problem was formulated as an MINLP problem and solved with the ECP method and the BB method for MINLP problems. The dynamics of the underlying separation process was formulated as a boundary value problem that was solved using finite differences. It was shown that, for a lower purity demand, all the outflow of a one-column system could be utilized as products. For a higher purity demand, a more complex system with two or more columns was needed in order to enable the recycling of unpure outflows for further separation. It was further observed that the advantage of the ECP-method was its need for relatively few function evaluations. The main drawbacks of the applied BB-method was the dependency on exact Hessian information. However, improvements in the solving of the boundary value problem, in the solving of the MINLP problem and also within the modeling of these are interesting future research challenges.

6. References Ching C.B., Hidajat K. and Ruthven D.M. (1987). Experimental study of a Simulated Counter-Current adsorption system-V. Comparison of resin and zeolite adsorbents for fructose-glucose separation at high concentration. Chem. Eng. Sci., 40, pp. 2547-2555. Diinnebier G. and Klatt K.-U. (1999). Optimal Operation of Simulated Moving Bed Chromatographic Processes. Computers Chem. Engng Suppl, 23, pp. S195-S198. Emet S. (2002). A Comparative Study of Solving a Chromatographic Separation Problem Using MINLP Methods. Ph.Lic. Thesis, Abo Akademi University. Guiochon G., Shirazi S.G., Katti A.M. (1994). Fundamentals of preparative and Nonlinear Chromatography. Academic Press, San Diego, CA. Karlsson S. (2001). Optimization of a Sequential-Simulated Moving-Bed Separation Process with Mathematical Programming Methods. Ph.D. Thesis, Abo Akademi University. Leyffer S. (1999). User manual for MINLP BB. Numerical Analysis Report, Dundee University. Saska M., Clarke S. J., Mei Di Wu, Khalid Iqbal (1991). Application of continuous chromatographic separation in the sugar industry. Int. Sugar JNL., 93, pp. 223-228. Strube J., Altenhoner U., Meurer M. and Schmidt-Traub H. (1997). Optimierung kontinuerlicher Simulated-Moving-Bed Chromatographie-Prozesse durch dynamische Simulation. Chemie Ingenieur Technik, 69, pp. 328-331. Westerlund T. and Pom R. (2002). Solving Pseudo-Convex Mixed Integer Optimization Problems by Cutting Plane Techniques. Optimization and Engineering, 3, pp. 253-280.

7. Acknowledgements Financial support from TEKES (Technology Development Center, Finland) is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B. V. All rights reserved.

113

Selection of MINLP Model of Distillation Column Synthesis by Case-Based Reasoning Tivadar Farkas*, Yuri Avramenko, Andrzej Kraslawski, Zoltan Lelkes*, Lars Nystrom Department of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland, [email protected] *Department of Chemical Engineering, Budapest University of Technology and Economics, H-1521 Budapest, Hungary

Abstract A case-based library for distillation column and distillation sequences synthesis using MINLP has been developed. The retrieval algorithm, including inductive retrieval and nearest neighbor techniques, is presented. The retrieval method and the adaptation of the solution is tested by a heptane-toluene example.

1. Introduction Distillation is the most widespread separation method in chemical process industry. Since the equipment and utility costs are very high the synthesis of distillation columns and distillation sequences is important task. Whereas it is very difficult due to the complexity of structures and equilibrium models. One of the most popular methods of synthesis is hierarchical approach (Douglas, 1988). The other common method of synthesis is mixed integer nonlinear programming (MINLP). MINLP is also used to perform synthesis and system optimization simultaneously (Duran and Grossmann, 1986). The simultaneous design and optimization method has three steps: (a) build a superstructure; (b) generate the MINLP model of the superstructure; (c) fmd the optimal structure and operation with a proper tool. There are two main difficulties when using MINLP: a) Generating a working accurate MINLP model is a complicated task. Usually, every published paper reports a new MINLP model and superstructure according to the problem under consideration. Up to now only one automatic combinatorial method is reported to generate superstructure (Friedler et al., 1992). However it is hard to use for cascade systems. b) Most of the MINLP algorithms provide global optimum in case of convex objective function and searching space. Rigorous tray-by-tray and the equilibrium models in distillation column design usually contain strongly non-convex equations, therefore finding global optimum is not ensured. In such cases the result may depend on the starting point of calculations. In order to overcome these difficulties, the earlier experiences should be used when solving a new problem. Case-based reasoning (CBR) is an excellent tool for the reuse of experience. In the CBR the most similar case to an actual problem is retrieved from a case library, and the solution of this case is used to solve the actual problem. Finally the solution of the problem is stored in the case library for future use (Aamodt and Plaza, 1994; Watson, 1997). The objective of this paper is to present a case-based reasoning method, which for a new distillation problem - an ideal mixture of components that is to be separated into a number of products of specified compositions - provides proper MINLP model with

114 superstructure and gives an initial state for the design of distillation column or distillation sequence. The creation of the case library of the existing MINLP models and results were considered. The library contains 27 cases of separation of ideal mixtures for up to five components.

2. Case-Based Reasoning Case-based reasoning imitates a human reasoning and tries to solve new problems by reusing solutions that were applied to past similar problems. CBR deals with very specific data from the previous situations, and reuses results and experience to fit a new problem situation. The central notion of CBR is a case. The main role of a case is to describe and to remember a single event from past experience where a problem or problem situation was solved. A case is made up of two components: problem and solution. Typically, the problem description consists of a set of attributes and their values. Many cases are collected in a set to build a case library (case base). The library of cases must roughly cover the set of problems that may arise in the considered domain of application. The main phases of the CBR activities can be described typically as a cyclic process. During the first step, retrieval, a new problem (target case) is matched against problems of the previous cases (source cases) by calculating the similarity function, and the most similar problem and its stored solution are found. If the proposed solution does not meet the necessary requirements of actual situation, the next step, adaptation, is necessary and a new solution is created. The obtained solution and the new problem together build a new case that is incorporated in the case base during the learning step. In this way CBR system evolves as the capability of the system is improved by extending the stored experience. One of the most important steps in CBR is the way of calculation of the similarity between two cases during the retrieval phase.

3. Retrieving Method During the retrieval, the attributes of the target case and the source cases are compared to find the most similar case. There are two widely used retrieval techniques (Watson, 1997): nearest neighbor and inductive retrieval. The nearest neighbor retrieval simply calculates the differences of the attributes, multiplied by a weighting factor. In inductive retrieval a decision tree is produced, which classifies or indexes the cases. There are classification questions about the main attributes in the nodes of the tree, by answering these questions the most similar case is found. Due to variety of specifications of the cases, the two retrieval techniques are combined. First, using inductive method, a set of appropriate cases is retrieved, and then only the cases in the set are considered. Next, the cases in the set are ranked according to theirs similarity to the target case using nearest neighbor method. 3.1. Inductive retrieval There are the following classification attributes in the inductive retrieval: Sharp or non-sharp separation Heat integration: According to this classification there are three possibilities: structure without heat integration; structure with heat integration; thermally coupled structure. In single column configuration only non-heat integrated structure is possible. Number of products: Number of products can change from 2 to 5. This classification is considered because the single column configurations and models do not consist of mass balances for the connection of distillation columns, thus these models cannot be used for three or more products problems.

115 Number of feeds: Cases with 1, 2 or 3 feeds are considered. This attribute is required because of the dissimilarity between the MINLP models with single and multiple feeds. 3.2. Retrieval based on the nearest neighbor method The similarity between the target case and all the source cases is calculated using nearest neighbor method. The evaluation of the global similarity between the target and a source case is based on the computation of the local similarities. The local similarity deals with a single attribute, and takes the value from the interval [0;!]. Thus, from the local similarities the global similarity can be derived as: SIM{T,S)

= YJ ^i' ^^^i / S

(1)

^'

where w/ is the weight of importance of attribute /; sinii is the local similarity between the target (7) and the source case (5); k is the number of attributes. The weight of importance takes an integer value from 1 to 10 according to the actual requirements. Five attributes are used: Components similarity. It is a non-numeric attribute. The similarity of components is based on theirs structure. The similarity tree (Fig. 1), where the nodes represent the basic groups of chemical components, was created. To each component group a numeric similarity value was assigned. For two components the similarity value is the value of the closest common node. The more similar the components are, the higher is the similarity value between them. For the identical components the similarity value isl. components 0

alcohol 0,7 - methanol

hydrocarbon 0,6

/ paraffinic 0,8 - propane - n-butane - iso-butane - n-pentane - n-hexane - n-heptane - n-octane - n-nonane

\

nitrile 0,4 - acetonitrile

aromatic 0,5 - benzene - toluene - o-xylene - diphenyl

keton 0,3 - acetone

unsaturated 0,8 - methylacetylene - tams-2-butene - cis-2-butene

Figure 1. Similarity tree of components. The local similarity of the components {simc) is defined as the average of the similarity values between the components:

116 (2)

um^ =Y,^cj /n

where Xcj is the similarity value of the components from the similarity tree; n is the maximal number of components in the compared mixtures. Boiling point and molar weight of components. These attributes are numeric. The similarity is calculated utilizing simple distance approach: the shorter a distance between two attribute's values the bigger the similarity is. For the higher sensitivity not the original values are used, but normalized one from interval [0;1]. The local similarities for these attributes are defined as: sim^ = l - ^ A f ^ . / n

(3) (4)

/=i

/

where Ati,j is the difference of normalized boiling points; Amj is difference of normalized molar weights; n is the maximal number of components. Feed and product compositions. These are also numeric attributes that are vectors. Comparing vector attributes the distance vector is determined. ? = (^P^2v..,^)

5 = (5,,52,...,5„) r,5G[0;l]; (5)

where T is the attribute vector of the target case; S is the attribute vector of the source case. Because there is a number of product composition vectors, the difference vector and the distance are counted for every product pair. The method is the same in the case of multiple feeds cases. The local similarity of feed compositions {simf) and product compositions {simp) are defined as:

Sim

VJ

(6)

•-\% (7)

Sim

E^,where g is the maximal number of feeds; q is the number of products; e^ are the basis vectors in the J?" space (necessary for normalization). Other attributes can also be considered according to the actual requirements, and the weights are taken from 1 to 10.

117

4. Solution The model consists of a superstructure, the set of variables and parameters, the mass and enthalpy balances and other constraints, but in the original articles usually only the superstructure, the variables and the main equations are detailed. Due to these reasons instead of MINLP models descriptions the original articles have been included in the case base. In the articles usually only a flowsheet and some general data are reported as the optimum of a case. In the CBR program this flowsheet and its mathematical representation are the solution, and basing on these data initial point can be proposed for the MINLP iteration. The base of the mathematical representation of a flowsheet (Figure 2) is a mathematical graph (Figure 3). The vertexes of the graph are: the feed (Fl), the distillation columns (CI, C2,...), the heat-exchangers (condensers: Conl, ...; and reboilers: Rebl, ...), the mixers/splitters (MSI, MS2, ...) and the products (PI, P2, ...); the branches are the streams between the units. This graph can be represented in a matrix form (vertexvertex matrix). In this matrix if fly=l then there is a branch from vertex / to vertex 7, if fly=0, then there is no branch. The streams are signed (SI, S2, ...). There is a set of data describing a stream (temperature, flow rate, main component(s) or mole fractions). These connections are described by vertex-branches matrix, where the starting end ending vertexes of the signed streams are shown. Q55 32.167 MU/hr (L/D) = 9J2 97.1% A 0,732 F

- > $9,9% 8 49 TOTAL TRAYS

H— 0.545>F

n

tsH

Q= 33.907 MU/br

Figure 2. Example of flowsheet.

^^-Ki) Figure 3. Graph representation of flowsheet.

In the graph only simple columns are used with maximum three inputs and two outputs. There are reported as a solution three closest cases and according to actual requirements and engineering experiences the most useful model can be selected from among them. Due to the complexity of the distillation problems there is no adaptation of the found MINLP model. The solution of the closest case is proposed as initial point in the design task.

118

5. Example An example is used to test the method including the retrieval, the revision of the model and the solution of the chosen MINLP model. There is given a heptane-toluene mixture. The flowrate of the equimolar [0.5,0.5] feed is 100 kmol/h. The target is to separate the mixture into pure components with 95% purity requirement at the top and at the bottom. In inductive retrieval, a set of non-heat integrated sharp separation cases with one feed and two products was retrieved. The similarity values between our problem and the cases of the set were calculated using the nearest neighbor formulas. The most similar case was a benzene-toluene system (Yeomans and Grossmann, 2000). Using the MINLP model of this case our problem was solved: the optimal solution is a column with 67 equilibrium trays; the feed tray is the 27* from the bottom; the reflux ratio is 5.928; the column diameter is 3,108m.

6. Summary A case-based program has developed, which in the case of a new separation problem can help to generate a superstructure and an MINLP model for the design of distillation column or sequences. During retrieval the important design and operational parameters are compared. The method is tested by heptane-toluene example, which has been solved from the problem statement through the retrieval.

7. References Aamodt,

A., Plaza, E., 1994, Case-Based: Reasoning, Foundational Issues, Methodological Variations, and System Approaches. AI Communications. lOS Press, Vol. 7 : 1 , 39-59. Douglas, J.M., 1988, Conceptual design of chemical processes, McGraw-Hill Chemical Engineering Series; McGraw-Hill: New York. Duran, M.A. and Grossmann, I.E., 1986, A mixed-integer non-linear programming approach for process systems synthesis, AIChE J., 32(4), 592-606. Friedler, P.; Tarjan, K.; Huang, Y.W. and Fan, L.T., 1992, Graph-theoretic approach to process synthesis: axioms and theorems, Chem. Eng. Sci., 47(8), 1973-1988. Watson, I., 1997, Applying case-based reasoning: techniques for enterprise systems, Morgan Kaufman Publishers, INC. Yeomans, H. and Grossmann, I.E., 2000, Disjunctive programming models for the optimal design of distillation columns and separation sequences, Ind. Eng. Chem. Res., 39(6), 1637-1648.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

119

Discrete Model and Visualization Interface for Water Distribution Network Design Eric S Fraga, Lazaros G Papageorgiou & Rama Sharma Centre for Process Systems Engineering, Department of Chemical Engineering, UCL (University College London), Torrington Place, London WCIE 7JE, United Kingdom ABSTRACT The water distribution network design problem poses challenges for optimization due to the tightly constrained nature of the typical mathematical programming formulation. The optimization of existing water distribution networks has therefore often been tackled through the use of stochastic optimization procedures. However, even these suffer from the need to solve systems of nonlinear algebraic equations. This paper describes the implementation of a hybrid method which combines a fully discrete formulation and visualization procedure with mixed integer nonlinear programming (MINLP) solution methods. The discrete formulation is suitable for solution by stochastic and direct search optimization methods and provides a natural basis for visualization and, hence, user interaction. Visual hints allow a user to identify easily bottlenecks and the aspects of the design that most greatly affect the overall cost. The result is a tool which combines the global search capabilities of stochastic algorithms with the pattern recognition and tuning abilities of the user. The solutions obtained provide good initial points for subsequent optimization by rigorous MINLP solution methods.

1 INTRODUCTION The design of a water distribution network (Alperovits & Shamir, 1977) involves identifying the optimal pipe network, the head pressures of the individual supply and demand nodes, and theflowsbetween the nodes, including both the amount and the direction of flow. The objective is tofindthe minimum cost network which meets the demands specified. The water distribution network design problem poses challenges for optimization tools due to the tight nonlinear constraints imposed by the modelling of the relationship between node heads, waterflowin a pipe, and the pipe diameter. The objective function is often simple, consisting of a linear combination of pipe diameters and lengths. The optimization of existing water distribution networks has been tackled through a variety of methods including mathematical programming (Alperovits & Shamir, 1977; Coulter & Morgan, 1985) and stochastic procedures (Cunha & Sousa, 1999; Gupta et al, 1999; Savic & Walters, 1997). However, even the latter require an embedded solution

120 of systems of nonlinear algebraic equations leading to difficulties in initialization and handling convexity. This paper describes a fully discrete reformulation of the water distribution network problem. This formulation is suitable for directly evaluating the objective function and is particularly appropriate for the use of stochastic and direct search optimization methods. Furthermore, it provides a natural mapping to a graphical display, allowing the use of visualization. Visualization permits the user to interact, in an intuitive manner, with the optimization procedures and helps to gain insight into the characteristics of the problem. The solutions obtained are good initial solutions for subsequent rigorous modelling as a mixed integer nonlinear programme (MINLP). Although the majority of existing work is limited to the optimization of a given network, the new formulation can also generate new network layouts. The visualization and optimization methods have been developed to cater for both the optimization of a given network and the identification of optimal networks. The results presented in this paper, however, are limited to network optimization. 2 T H E PROBLEM STATEMENT The least-cost design problem can be stated as follows. Given the water network superstructure connectivity links for the nodes in the network, the pipe lengths, the demand at each node (assumed to be static) and the minimum flowrate and head requirements, determine the optimalflowrateand direction in each pipe, the head at each node and the diameter of each pipe so as to minimise the total cost of the pipes in the network. 3 T H E DISCRETE FORMULATION AND ITS VISUALIZATION The discrete formulation is based on the modelling of the nodes (both demand and supply) in the network as horizontal lines in a two dimensional discrete space. The position of each line is represented by {x,y). The y value specifies the head at the node. The length of a horizontal line in this discrete space represents the amount of water through the node, irrespective of the actual location along the jc-axis. Transportation of water from one node to another occurs when the lines corresponding to the two nodes overlap (in terms of the x co-ordinates) provided a connection between the two nodes is allowed. The definition of the network is actually a superstructure of allowable pipe connections, pipe diameters and distances between nodes. Given the set of x and y values for the nodes in the network, the allowable connections and the pipe diameter, d, (chosen from a discrete set) allocated to each possible connection, the evaluation of the objective function is based on identifying all the matches defined by the positions of the lines in the discrete space. This evaluation is deterministic and enables the identification of the network layout and the direct evaluation of the cost of the water distribution network. This objective function forms the basis of a discrete optimization problem in jc, y, and d. The discrete formulation provides a natural basis for visualization and, hence, user interaction. Figure 1 presents an annotated screenshot of the visual interface. The graphical interface employs visual hints to allow to user to identify bottlenecks and the aspects of the design that most greatly affect the overall cost. Specifically, the diameter of each

121 mm- %ifitrmi*ff^ m>t^.

*t^ '^mn^m^ ^•ja ism^mif jh^^

W g.q» » « B >^i

^

Indication of excess water

Figure 1: Water distribution network visualization interface for Alperovits & Shamir example. pipe is indicated by its width in the visual display. The violation of demand requirements for a node, or in fact the excess of water delivery to a node, is represented using a small gauge within the horizontal bar representing each node. Although not necessarily apparent in this manuscript, a red colour is used to indicate a shortfall in the demand for the node and a blue colour an excess. The interface allows the user, through use of the mouse or the keyboard, to manipulate the location of each horizontal bar and the diameter of each pipe. Furthermore, the implementation, based on the Model-View-Control design pattern (Gamma et al., 1995) and written in Java, allows the user to interact directiy and easily with the optimization procedures. The user can specify which features to manipulate (e.g. pipe diameters alone) and the specific optimizer to invoke. The choice of optimizer includes a variety of implementations of genetic algorithms and simulated annealing procedures. The user may also export a current configuration as an MINLP model which can be subsequently optimized rigorously, using the GAMS system (Brooke et al, 1998), as described in the next section. The result is a tool which combines the global search capabilities of stochastic algorithms with the pattern recognition and tuning abilities of the user. The solutions obtained provide good initial points for subsequent rigorous optimization with a mixed integer nonlinear model. 4 M I N L P OPTIMIZATION MODEL The objective function expresses the network cost, which is assumed to be linearly proportional to the pipe length and pipe diameter. It is assumed that pipe diameters

122 are available at discrete commercial sizes. The objective function is minimized subject to three main sets of mathematical constraints: continuity (flow balance) constraints, energy loss constraints, and bounds and logical constraints. The first set of constraints represents the mass conservation law at each node of the water network. The second set describes the energy (head) losses for each pipe in the network to relate the pressure drop (head loss), due to friction, to the pipeflowrate and the diameter, roughness, material of construction, and length of the pipe. In this work, the commonly used Hazen-Williams empirical formula (Alperovits & Shamir, 1977; Cunha & Sousa, 1999; Goulter & Morgan, 1985) is used. The third set of constraints includes bounds on variables such as minimum head orflowraterequirements. This set also includes constraints to ensure that only one diameter can be selected for each pipe (stream), a more realistic representation rather than having a split-pipe design. The above problem corresponds to an MINLP model due to nonlinearity in the HazenWilliams correlation. This model is solved using the DICOPT method in the GAMS system (Brooke et al, 1998). DiCOPT invokes MILP and NLP solvers iteratively. In this work, we have used the CPLEX 6.5 MILP solver and four different NLP solvers. 5 ILLUSTRATIVE EXAMPLE An example from the literature (Alperovits & Shamir, 1977) is presented. The results show the improved behaviour, particularly in terms of robustness and consistency, achieved through the combination of the stochastic optimization of a discrete model, user interaction, and rigorous MINLP solution. The problem consists of seven nodes and up to eight pipes. When the viewer is instantiated, the initial values for all the variables default to the mid-point between the lower and upper bounds. From this starting point, the user may immediately interact directly with the viewer to alter the configuration or may request the application of a stochastic optimization step. At any point, the current configuration may be exported as a GAMS input file and solved using the rigorous MINLP formulation. Table 1: Sequence of operations for illustrative example (Alperovits & Shamir, 1977). Step 1. 2. 3. 4.

Operation GA User User User

Objective Function ($'000) 397 411 463 423

Infeasibility Measure

oTs 0.13 0.10 0.13

A typical sequence of steps is presented below. For each step, the current objective value (in discrete space) and a measure of its infeasibility (shortfall in demands met in m^ js) is obtained and these are collated in Table 1. Due to the highly constrained nature of the discrete formulation, an exactly feasible solution is unlikely to be achieved. However, the aim is not so much to solve the problem directly with the visualization tool but to provide good initial solutions for the rigorous optimization procedure.

123 m^mM^^^i^e^^^^^m^Mmi

JM '^Jm^^M^fi'^^T^j^imM

t C - » 1 > t « *ym»mmmtJ)$fm^

faw»
tish'imt,,»>im^i4i^isis&^^^'^mm^^mmm

^*.|»*vfr«ii»ytw»»»»»y tiM*^«* «

Figure 2: Initial and final configurations. 1. As the starting configuration is not particularly good, the first step is to apply a genetic algorithm to achieve a reasonable starting layout. An example initial layout obtained in this manner is shown in Figure 2 on the left. 2. We note that, in this initial configuration, node 3 has none of its requirements met and there is a very small pipe from node 2. We increase the diameter of this pipe four times to diameter 5. The value of the objective function increases, indicating a more expensive network, but one which better meets the requirements specified, as can be seen from the measure of the infeasibility. 3. We now note that all the demand nodes have a shortfall but that the single supply node has an excess (i.e. the full amount available is not being used). We increase the diameter of the pipe connecting the supply node to node 2. This leads to an excess in node 2. Again, we look for small pipes as increasing their size is less damaging to the cost than larger pipes. We start at the bottom of the network, increasing the size of pipe 3^1 and 2 ^ 3 . 4. Now there is an shortfall in node 2 and an excess in node 4 so we decrease pipe 2 ^ 4 . The configuration at this stage is shown in Figure 2 on the right. Thefinalconfiguration obtained through these simple steps is then exported in the form of a GAMS input file, providing an initial starting configuration for the MINLP solution procedure. The results of the subsequent rigorous optimization are presented in Table 2. The results obtained using the initial configuration generated by the user with the visualization tool are better than those obtained otherwise. In particular, all four optimizers used are able to find a good solution with this initial configuration.

124 Table 2: Comparison of solutions (in $ '000s) obtained with different combinations of NLP solvers and initial conditions. Initial Configuration None Allflows= 100 Visualization

CONOPT Failed 456 423

NLP Solver CONOPT2 MINOS 486 446 441 452 420 420

MINOSS

Failed Failed 441

6 CONCLUSIONS A hybrid procedure for solving the water distribution network optimization problem has been presented. This procedure combines a discrete formulation, an interactive visualization interface and a rigorous MINLP formulation. The discrete formulation provides a natural basis for the visualization tool. This tool can interact with the user and, together with embedded stochastic optimization procedures, alternative configurations can be generated easily. These configurations can provide good initial guesses for subsequent rigorous MINLP optimization. In this paper, we have concentrated on the optimization of a pre-defined networks. The discrete formulation and the visualization tool also provide the basis for the design of new networks (the x variable described above). This is the topic of current research.

7 References Alperovits, E. & Shamir, U. (1977). Design of optimal water distribution systems. Water Resource Research, 13 (6), 885-900. Brooke, A., Kendrick, D., Meeraus, A., & Raman, R. (1998). GAMS: A user's guide. GAMS Development Corporation Washington. Cunha, M. & Sousa, J. (1999). Water distribution network design optimization: Simulated annealing approach. Journal of Water Resources Planning and Management, 125 (4), 215-221. Gamma, E., Helm, R., Johnson, R., & Vlissides, J. (1995). Design Patterns. Elements of Reusable Object-Oriented Software. Reading, Massachusetts: Addison-Wesley. Goulter, I. C. & Morgan, D. R. (1985). An integrated approach to the layout and design of water distribution networks. Civil Engineering Systems, 2,104-113. Gupta, I., Gupta, A., & Khanna, R (1999). Genetic algorithm for optimization of water distribution systems. Environmental Modelling & Software, 14, 437-446. Savic, D. A. & Walters, G. A. (1997). Genetic algorithms for least-cost design of water distribution networks. Journal of Water Resources Planning and Management, 123 (2), 67-77.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

125

Optimal Design of Mineral Flotation Circuits E.D. Galvez^^\ M.F. Zavala^^\ J.A. Magna^^^ and L.A. Cisternas^^^ (1) Dept.of Metallurgical Eng., Universidad Catolica del Norte, Antofagasta, Chile. (2) Chemical Engineering Dept., Universidad de Antofagasta, Antofagasta, Chile.

Abstract This study presents a procedure for the design or improvement of mineral flotation circuits, based on a mathematical programming model with disjunctive equations. The procedure is characterized by: 1. The development of hierarchized superstructures, such that the first level represents certain separation tasks. The second level represents circuits of equipment needed to carry out the tasks. 2. A MILP mathematical model is developed which includes the selection of equipment, first principles, and operational conditions. 3. The objective function is the maximization of profits. Examples are included to demonstrate the advantages of the procedure.

1. Introduction In flotation processes the feed may be divided into different fractions by employing differences in surface properties. For example, a concentration plant may be formed by cells grouped into rougher, scavenger, and cleaner banks in order to divide the feed into concentrate and tailings. The behaviour of these processes depends on the configuration of the circuit and the physical and chemical nature of the slurry treated. Some attempts have been described in the literature on automated methods for the design of these types of circuits (Yingling, 1993; Mehrotra, 1988). Studies can be classified as those which consider revenues, operational and capital costs as an objective function (Shena et al., 1996) and those that consider a technical performance function. The latter group may be separated into those that use bank models and those that use cell models (Yingling, 1990). Two groups may also be distinguished between those that use bank models: (a) those that use a first-order model for the flotation kinetics (Mehrota and Kapur, 1974; Dey et al., 1989), and (b) those that use a model indirectly (Green 1984,1992; Renter and Van De venter, 1990). Due to the nonlinear nature of the equations of material balance, the models are required to include simplifications in their mathematical form, or require the development of a specific strategy for the solution of a mathematical model. The present study presents the formulation of a new procedure for the design or improvement of flotation circuits for minerals, characterized by: (a) Superstructures are developed in a hierarchical form, (b) A mathematical model which includes disjunctive expressions for the selection of the equipment, first principles, operational conditions, and logic expressions, (c) The objective function represents maximization of profit. The resultant model represents an MILP model.

126

2. Model Development 2.1. Strategy The design strategy includes two levels of hierarchized superstructures. The upper level includes a task superstructure, in which are included a rougher system (the task of which is feed processing to obtain the maximum separation), a cleaner system (the task of which is purification of the concentrate from the rougher to obtain the final concentrate), and a scavenger system (the task of which is the treatment of the tailings from the rougher to obtain the final tailings). Figure 1 shows the superstructure utilized, where the triangles represent stream mixers or splitters which permit the presentation of a group of alternatives for mineral processing. At the second level, it is considered that each system is formed of three banks of flotation cells: rougher, cleaner, and scavenger banks. Thus, for example in the scavenger system there exist the scavenger-rougher, scavenger-cleaner, and scavenger-scavenger banks. The superstructure for each system is analogous to the task superstructure, but where each system is replace by a bank of flotation cells. This analogy makes easy the mathematical representation. 2.2. Constraints First it is necessary to define some sets, parameters, and variables in order to develop the model. Then, using these definitions, the equations may be developed which include mass balances, yields, operational conditions and logic constraints. The principal sets are: 5 = {5 / ^ is a system}, L = \i/ iisa. stream}, K= {/://: is a species} and M =^/ misa. mixer or splitter}. LA, LC and LT are subsets of L, which include the feeds, concentrates and tailings, respectively, of each system or bank. Also, Lcc = ^£^,£^)/ i^G LA,i^G LC, £ ^ is the concentrate produced from £ ^}, Ltt = ^i^J^)/

i^e LAJ^e

LT J ^ is the tailing produced from £^}. In addition, LL,

LSI and LS2 are subsets of L, which represent the feed, output 1 and output 2 of each stream splitter. Since the superstructures are analogous, all sets are the same for each superstructure. Each stream € of the task superstructure is associated with the variable that represents the mass flow of species k, W^k- Similarly, each stream 6 in each system s is associated with the variable that represents the mass flow of the species k, WIsjxThe material balance for mixers and flow splitter in the task superstructure are: E

^i,k-

E

^a=^

keK,meM

(1)

Where M''(m) and M^"\m) are the sets of input and output streams of the mixer/splitter m. In general it is not common practice to divide the streams in flotation concentration plants. This study, however, considers the possible division of different levels into a set of discrete values for possible levels of division. This is:

127 feed

f

r^

ROUGHER SYSTEM

SCAVENGER SYSTEM

\ >

^

-viv-

tail

A

^ CLEANER SYSTEM

•
?

concentrate

Figure 1. Task superstructure with rougher, cleaner and scavenger systems. Each system has the same superstructure but with rougher, cleaner and scavenger hanks.

je J,kE K jej\

ieLLJ^e

LSlJ^e

LSI

(2)

where/={/7 7G 7 is a fraction level of division}, and £ is the stream which is split into El and £2- ^j is the fraction j of division. Eq. (2) is rewritten as mixed-integer linear equations. Equations similar to equations (1) y (2) hold for the mixer and stream splitter in each system superstructure, but WlsXk. is used instead of WixIn each flotation bank there is '^^5,£^,it ~^S,la,k

^^S,la,k

(i^J^)eLcc,ke

W,,,„, =(l-r,,,^ Jw,,,^,,

(/,,OG

K,seS Ltt,keK,se

(3) S

(4)

where r^^^^ is the ratio of mass flow of concentrate £c and feed l^, of species k, in system s. The ratio T^,^^^, is related to the separation factor fsj^hy

T^j ^k =

fs,ia,k/0^~^ fs,ia,k^' ^^^ separation factor may be obtained from plant data, values from pilot

plants,

or theoretical

or empirical

models.

For example,

fsi k -

128 (l + /:^^^ ^r^^^ j^''« - 1 , where k^j^,^ is the flotation rate for species k, A^^^ the number of cells and r^^ the retention time in the bank fed by /« in system s. Multiple values of 7^^^^ may be implemented because T^i^,^ depends, among other things, on the type of equipment, the number of cells and residence times. For modelling an N set of alternatives, each one with a characteristic value T^^ ^^ „, fixed costs Cy^^^ ^, and variable costs Q,^^ ^, we use eq. (5). Disjunctive equation (5) is expressed as a set of mixed-integer linear equations.

yn

{l^A^)eLcc,{l^,l^)eLtt,

ne N\

ke K,sG 5, f S,la

f

(5)

S,la^n

Feed specification, input and output streams connection between system and task superstructures, and logical constraints must also be included. Others operational conditions, such as streams with zero flow, and upper or lower bounds for flows of each stream are easily included in the model. 2.3. Objective function The optimal selection of the circuit requires that an appropriate objective function be defined upon which the values of the operational and structural variables may be determined. Since in the present case the income depends on the structure and operational conditions, a useful function is the difference between income and costs. Differing relations may be applied for calculation of the income depending on the type of product and its market. For base metals the net-smelter-return formula may be utilized (Schena et al., 1997). Income = U g,W,,,\p(q-Rfc)H-^W,,,[pu

{q-Rfcyirc^

(6)

where ^^Wjo^t is the mass flow of the concentrate, p the fraction of metal paid, jt

^gk^iok

is the mineral grade of the concentrate, gk is the mineral grade of each

species k present in the concentrate, u is the grade deduction, Trc is the treatment charge, and Rfc is the refinery charge. H is the number of hours per year of plant operation, when the flows are in tons per hour. The grade deduction and the fraction of metal paid depend on the recovery efficiency of the smelter. Values of cost and prices of metals are published in specialized journals. Typical values used in the present study are

129 listed in Table 1. It should be noted that as the flows of the species with a high grade increase, so does the profit. However, this increase in flows brings with it an increase in flows of low grade value, which decrease the profits (second term of eq. 6). The annualized costs of the plant may be considered as the sum of operational costs and capital costs. The operational costs include energy, consumption of reagents, labour, and maintenance. The majority of these costs depend more on the feed flow into the plant than on its configuration, and thus are not considered in this analysis. Only the energy costs of mixing the slurry, generation of bubbles, and dispersion were considered. The capital costs include the cost for the banks and pumps, which can be expressed as a linear function of mass flow rates. Thus, the annualized costs are a linear function of the mass flow rates. The objective function subject to constraints 1, 2, 3 and 4 (1, 2 and 5) represent a problem of mixed-integer linear programming (MILP). This is termed Model PI (P2).

3. Applications This section presents the applications of models PI (case 1) and P2 (case 2) to the design of a copper concentration plant, whose species are: k=l (100% chalcopyrite), k=2 (90% silica, 10% chalcopyrite) and k=3 (100% silica). The principal data of the problem are given in Table 1 and 2. Case 1 includes 15 cells per bank in all the stages. Three levels of flow division were considered (100%, 50% y 0%), for all the flow splitters in each of the superstructures. Figure 2 shows the circuit obtained together with the mass flows for each species. The problem, including a total of 548 equations, 307 variables and 58 binary variables, was solved using the GAMS (0SL2 solver). To study the sensitivity of the solution of the problem to other levels of separation, five levels of flow division were considered (100%, 75%, 50%, 25% y 0%). The solution obtained was the same as in the case with three levels of separation. Case 2 includes three levels of cell numbers (10, 15 and 20) per bank in all the stages. The circuit obtained was similar to case 1 (see Figure 2), but without stream division and with 10 cells per bank in the rougher and cleaner, and 20 cells per bank in cleaner-cleaner. A total of 15 cells were maintained only in the scavenger bank. The problem, having a total of 764 equations, 487 variables, and 84 binary variables was solved using the GAMS (0SL2 solver). Table 1. Typical values for a copper concentration plant (minimum grade of concentrate 28%). Parameter P u q, US$/ton metal Rfc, US$/ton metal Trc, US$/ton Con. H, hours/year

Value 0.975 0.015 1764 200 85 7200

Table 2. Data for the example. Feed flow for species k 1 6ton/h 2 3ton/h 3 291 ton/ Flotation rate, species k Rougher system Rougher Banks

Grade of k, mass fraction 0.385 1 0.050 2 0.0 3 1 2 3 4.787

0.946

0.604

Cleaner system Rougher Banks

2.265

0.156

0.08

Cleaner Banks

2.265

0.156

0.04

2.265

0.156

0.250 1

Scavenger system Rougher Banks

130

k case 1 case 2 1 0,15 ~ 0 2 0.8 0

IRQuJsHiRT k case 1 case 2 1 7.2 6.7 2 1,6 1.2 3 118.4 90.2

k case 1 case 2

3 210.6

"ric^5ei^

260,4 k c a s e 1 case 2 1 1.7 1.1 2 1,6 1.2 3 118,2 90,1

["tS^E^NfEf^l

k case 1 case 2 1 1.5 1.6 2 0,3 0,4 3. 38 59,6

k case 1 case 2 0 0.1 .

k case 1 case 2 1 0,5 0,4 2 3 3 3 290,8 290,9

[ytjlities i Sales

Case 1 Case 2 16,7 17,2 Millions yS$ 18,7 19,2 Millions US$

i concentrate

Figure 2. Circuit solution of the application. Cases 1 and 2 have the same circuit, but different values for stream flows.

4. Conclusions A procedure has been developed for the design and improvement of mineral concentration plants. The most important feature of the model is its linearity. The mass balances in stream splitters were represented by disjunctive equations avoiding bilinear terms in the model. The results showed that the division of flows had little effect on determination of the most efficient circuits. This result agrees with practice since it is unusual to split stream in mineral concentration circuits. Modelling of the flotation banks was carried out using disjunctions with discrete values for the concentrate/feed ratio. The model has been useful in the study and design of circuits for mineral concentration. Future study will include extension of the model to examine the possibility of selecting between various types of equipment (columns and banks) and incorporation of intermediate milling.

5. References Dey, A., Kapur, P.C. and Mehrotra, S.P., Int. J. Miner. Process., 26 (1989) 73-93. Green, J.C.A., Int. J. Miner. Process., 13 (1984) 83-103. Green, J.C.A., Chem. Eng. Sci., 37(1992), 1353-1359. Mehrotra, S.P., Miner. Metall. Process., 5 (1988) 142-152. Mehrota, S.P. and Kapur, P.C, Separation Science, 9, (1974) 167. Reuter, M.A. and Van Deventer, J.S.J., Int. J. Miner. Process., 28(1990), 15-43. Shena, G., Villeneuve, J., and Noel Y., Int. J. Miner. Process., 46 (1996) 1-20. Tingling, J.C, Int. J. Miner. Process., 29(1990) 149-174. Yingling, J.C, Int. J. Miner. Process., 38(1993), 21-40.

6. Acknowledgements The authors wish to thank CONICYT for financial support (Fondecyt Project 1020892).

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

131

An MINLP Model for the Conceptual Design of a Carbothermic Aluminium Reactor Dimitrios I. Gerogiorgis and B. Erik Ydstie Dept. of Chem. Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA

Abstract Systematic design and optimization set the standard in today's petrochemical industries, but their impact is limited when considering most processes in metallurgical industries. The present study presents an MINLP model developed for design and optimization of the electrode heating system of a new multistage high-temperature carbothermic reactor. The focus here is the optimization of electrode placement and imposed voltage profile; the model and conclusions can effectively assist ongoing multiscale process modeling.

1. Introduction Metallurgical industries are historically characterized by a high degree of complexity (high-temperature reactions, multiphase flows, complex physicochemical phenomena) and a predominantly experimental, iterative nature of novel process design efforts, both resulting in lack of formal accurate models that could facilitate optimization endeavors. Thus, advances in this field can definitely improve profitability in the globalization era, exactly as petrochemical industries have benefited from MINLP problem formulations and routine use of optimization computer tools that yield significant investment savings. The present paper presents a MINLP model for a novel complex metallurgical process, illustrating its application for the effective design of the reactor electric heating system. Mixed Integer Nonlinear Programming (MINLP) theory and applications have pervaded the field of computer-aided design and optimization of traditional chemical processes. Exemplary processes studied include numerous petrochemical unit operations, such as heat-integrated distillation (Novak et al., 1996; Caballero and Grossmann, 1999; Yeomans and Grossmann, 1999), azeotropic distillation (Bauer and Stichlmair, 1998), reactive (Ciric and Gu, 1994) and cryogenic distillation (Boisset-Baticle et al., 1994), extraction and dehydration (Lelkes et al., 2000; Diaz et al., 2000; Alonso et al., 2001), supercritical fluid extraction (Kalampoukas and Dervakos, 1996), membrane separation systems (Qi and Henson, 20(X)), wastewater treatment (Galan and Grossmann, 1998), heat exchanger networks (Yee and Grossmann, 1990; Aggarwal and Floudas, 1992; Daichendt and Grossmann, 1994; Galli and Cerda, 1998; Bjork and Westerlund, 2002), mass exchanger networks (Papalexandri and Pistikopoulos, 1994) and reactor networks (Esparta et al., 1998; Stein et al., 1999; Rooney and Biegler, 2000; Pahor et al., 2001). Applications include power plants (Manninen and Zhu, 1998), reactive power planning (Chattopadhyay and Chakrabarti, 2002), pump systems (Westerlund et al., 1994), copolymer production (Mantzaris et al., 1999), paper industry (Harjunkoski et al., 1999) and leather industry (Graells et al., 1992), but not the design of metallurgical processes.

132

2. The Carbothermic Aluminium Reactor Carbothermic reduction of aluminium oxide for the production of pure aluminium is an energy-efficient and environmentally benign reduction process with industrial potential. This method has been proposed as a feasible alternative to the prevalent Hall-Heroult electrolytic process; several reactor designs have been tested (Motzfeldt et al., 1989). Nevertheless, reaction complexity poses notable technical obstacles to implementation. The multistage, multielectrode high-temperature carbothermic reactor recently proposed (Johansen et al., 2000; Johansen and Aune, 2002) is a new idea addressing known issues so as to achieve the reactor scaleups that would permit the desired capital cost savings. Nevertheless, its structural and operational complexity entails many design challenges. The most interesting one is the distributed nature of the process, as the electric heating necessary for the endothermic reaction is achieved using independent electrode pairs, both in the first pre-reduction smelting stage as well as in the second reduction stage. The design challenge is to optimize electrode positions and the imposed voltage profile so as to achieve the reaction advance without unnecessary reactor space or energy use. Obviously, dense electrode placement and high voltage result in excessive superheating (a catastrophic effect causing aluminium evaporation, major yield reduction and losses) while sparse electrode placement and low voltage fail to achieve adequate slag heating (an equally undesirable situation resulting in limited conversion and low productivity). Submerged horizontal electrodes also act as obstacles to horizontal molten slag flow; flow and other concurrent multiphase phenomena (Al liquid and CO gas generation) introduce further modeling complications which are not considered in the present study. Figure 1 depicts the structure of the four-stage carbothermic aluminium reactor studied: 1. The first stage of the process is the pre-reduction zone where slag formation occurs. Carbon and aluminium oxide pellets are continuously fed to the electric arc smelter, melt and form a viscous molten slag contained under inert atmosphere and oil cooling. Carbon monoxide and aluminium vapors (AI/AI2O) generated are fed to the third stage. The reaction of AI2O3 with an excess of C to form the A^Cs-rich slag is thus written as: 2Al203(s) + 9C(s) -> (Al4C3+Al203)(siag) + 6CO(g)

(T > 1900 °C)

(1)

2. The second stage is the high-temperature slag reduction zone: the first-stage molten slag flows slowly into the multielectrode submerged arc main reactor, where it is heated to a higher temperature, avoiding local surface superheating caused in open arc reactors. Liquid Al and CO gas are rapidly generated; AI4C3 injection from the third stage assists in shifting the chemical equilibrium towards Al and in avoiding active carbon depletion. The decomposition of the Al4C3-rich slag to form the Al-rich metal phase is written as: (AI4C3 + Al203)(slag) ^

(6A1 + Al4C3)(metal) + 3C0(g)

( T > 2 0 0 0 °C)

(2)

3. The third stage consists of a vapor recovery reactor (VRR), where Al and AI2O vapors react with C to form AI4C3 (unless gas Al species are recovered countercurrent to the incoming solid feed, metal loss has a catastrophic impact on the process economics). 4. The fourth (final) stage of the process is the purification zone: the liquid Al alloy produced floats and flows through an overflow weir to a tank, where dissolved C and entrained AI4C3 particles can be removed by proprietary technology to recover pure Al.

133

3. Carbothermic Reactor Modeling The present study employs a simple finite volume model of the carbothermic reactor: a relatively coarse one-dimensional structured discretization of the domain is considered and a steady state CSTR reactor model is used in each resulting rectangular volume to probe mass, heat and molar balances using temperature-dependent physical properties; the latter have been previously reported in a relevant study (Gerogiorgis et al., 2002). The coarse finite volume decomposition and drastic assumptions are necessary because of the lack of experimental data, and to ensure a computationally manageable model. The presence of electrode pairs (inert conductors) is modeled using binary variables; voltage and intensity profiles are considered piecewise constant along the reactor axis. The advance of the reversible reduction towards Al (liquid) and CO (gas) is considered governed by the overall reaction proposed in a recent kinetic study (Frank et al., 1989): (3)

Al203(s) + 3C(s) -^ 2A1(,) + 3CO,

(g)

The pseudo-first order kinetic model as reported by Frank et al. (1989) has been used, as the presence of metallic solvent (Cu/Sn) in their study is not affecting reaction kinetics. The assumption of instant thermodynamic equilibrium (extremely high temperatures) can be alternatively used to elucidate concentrations within each of the finite volumes; the use of a multiscale model is necessitated in that case (Gerogiorgis and Ydsfie, 2002). A number of simplifying approximations are used for the development of this model. The potential presence of suspended C/AI4C3 particles in the incoming slag is ignored; the generated liquid and gas streams are considered immiscible with the molten slag; species diffusion, horizontal backmixing and vertical recirculation effects are neglected. The Joule heating effect of each electrode is thus confined within the respective volume; the relative concentrations within each volume only depend on the temperature therein, considering only the production of Al (liquid) and CO (gas) without any phase changes. The latter product streams are taken to completely escape the slag at each finite volume. ••CO (Tc p i t o y iacoi«ri F I N I T E V O L U M E M O D E L F O R STAGE 2

«X%A!^^

- StUIDiriCATION FRONT -REAdOR COOLING JAOET

SIDF-FNTW HfdRODtS

CSTR# 1

Figure 1: The conceptual carbothermic aluminium reactor (Johansen andAune, 2002).

134

4. The MINLP Model for Electrode Heating System Design This section presents the formulation of the MINLP finite volume model: the goal here is to perform electrode placement as well as imposed voltage profile optimization for maximization of Al production under mass, heat and molar species balance constraints. The mathematical formulation is based on a CSTR series steady state process model; each finite volume is assumed a CSTR with perfect separation of reactants and products. Thus, the Al maximization objective function and the balance constraints are written as: ^

max

(4)

^ ^ j = 3,i,P ' M , P i=l

S.t.

F,-.,s=I^,s+Fi.P

(5)

Fi-i,s -Cpi-Ls -(Ti., - T , ) = F,s -Cpjs -(Ti - T J + F,p-Cp. p -(T; - T J - Q „ , +Qe, +QR,i (6) Fi-i,s -x j,i-,.s = Fi.s -x j,i,s + Fi.p -x j,i,p +Cj -R, - V Exj,i,s = 1. S x j i,p = 1, x,j.3,,,,s = 0 , X(j.,,,),,p = 0 (i = 1,2,.. N CSTRs) J i Ei = y r V i / L , X y i = Y < N

(7) (8) - (11) (12)-(13)

i

cJi=cJi(Ti) = a,+p,.ln(Ti)

(14)

QH,i=^i(Ei)',Qc,i=U-A.(T,-T,),Q^,=R,V°.Aff Rr=koexd

f-AG^^

•Cj.,,, AG°=aG+bG.T

(15) - (17) (18)-(19)

RTj

Cpi,s/P= S^j,i,s/p-Cpj,s/p,

Cpj,s/P = (ao,j + ai,jT + a2,jT' + a3,jT' + a.2,jT-')

(20) - (21)

j

2173 < T < 2573 (K), 0 < V < 100 (Volts), 0 < x < 1

(22) - (23)

Here, Fi,s and Fi p are the slag and product molar flows exiting finite volume i (CSTR), Xj, i are the molar species fractions, Ti are the temperatures, Cj, i are the concentrations, Vi is the imposed voltage on a pair, Ei is the field intensity, L is the lateral tip distance, Yi are binary variables indicating absence (yi = 0) or presence (yi = 1) of electrode pairs and parameter Y denotes the maximum number of electrode pairs allowed in the reactor. QH,! is the Joule heat production, QR^ is the reaction heat consumption using the kinetic model proposed by Frank et al. (1989), Cj are the stoichiometric coefficients in Eq. (3), Qci, U, A and Tc are cooling rate and parameters, V° is the finite volume of the CSTR, ai(T) is the slag electrical conductivity, and Cp i,s » Cp i,p are the specific heat capacities. The free energy of formation (AG°) for the reaction is published by Frank et al. (1989). Indices i and j refer to position and species (hAliOa, 2:Al4C3, 3:A1, 4:C0), respectively; subscripts S and P denote slag (AI2O3 + C) and product (Al + CO) streams, respectively;

135 N is the total number of isothermal CSTR reactors considered (a sensitivity variable). Temperatures T], concentrations Cjj and fractions Xj^ are the state variables considered. MINLP Model Results The most important results obtained using the MINLP model are presented in Figure 2. IMPOSED ELECTRODE VOLTAGE

2

3 4 FINITE VOLUME #0)

HORIZONTAL (SLAG) FLOWS

ABSOLUTE TEMPERATURE

2

3 4 5 FINITE VOLUME #(i)

VERTICAL (PRODUCT) FLOW^S

MOLAR FRACTION OF Al

Figure 2: MINLP model results for Y -6 electrodes (black) and Y —3 electrodes (gray).

5. Conclusions and Future Work The MINLP model outlined for electrode voltage optimization in a carbothermic reactor captures macroscopic phenomena, giving insight for preliminary heating system design. Electrode positions, voltages and temperatures for maximization of liquid Al production are illustrated in Figure 2, for two different electrode number constraints (Y = 3, Y = 6). Electrode number is equal to the maximum, but heating is most important right at the reactor inlet; temperature increases as slag flows and limiting reactant (AI2O3) deplete. Production increases with power input (6.06 kmol.min'^ / Y = 3, 8.80 kmol.min"^ / Y = 6). More complicated objectives (simultaneous minimization of Al(g) losses and energy use) can also be addressed by augmenting the model with VL equilibrium equations that will account for all 6 species (Al203(i), A^Csd), ^^d)' Al(g), Al20(g), CO(g)) in all fluid streams.

136 The finite volume process model and the conclusions of this study can also be used for multiscale modeling of this complex chemical process (Gerogiorgis and Ydstie, 2002).

6. References Aggarwal, A., Floudas, C.A. 1992, Comput. Chem. Eng. 16 (2), 89. Alonso, A.I., Lassahn, A., Gruhn, G. 2001, Comput. Chem. Eng. 25 (2-3), 267. Bauer, M.H., Stichlmair, J. 1998, Comput. Chem. Eng. 22 (9), 1271. Bjork, K.M., Westerlund, T. 2002, Comput. Chem. Eng. 26 (11), 1581. Boisset-Baticle, L., Latge, C , Pibouleau, L. Comput. Chem. Eng. 18 (S), S99. Chattopadhyay, D., Chakrabarti, B.B. 2002, Int. J. Elec. Power 24 (3), 185. Daichendt, M.M., Grossmann, I.E. 1994, Comput. Chem. Eng. 18 (8), 679. Ciric, A.R., Gu, D.Y. 1994, AIChE J. 40 (9), 1479. Diaz, S., Gros, H., Brignole, E.A. 2000, Comput. Chem. Eng. 24 (9-10), 2069. Esparta, A.R.J., Obertopp, T., Gilles, E.D. 1998, Comput. Chem. Eng. 22 (S), S671. Frank, R.A., Finn, C.W., Elliott, J.F. Met. Mat. Trans. B. 20B (4), 161. Frey, T., Bauer, M.H., Stichlmair, J. 1997, Comput. Chem. Eng. 21 (S), S217. Galan, B., Grossmann, I.E. 1999, Ind. Eng. Chem. Res. 37, 4036. Gerogiorgis, D.I., Ydstie, B.E. 2003, Proceedings of the Foundations Of ComputerAided Process Operations Meeting (FOCAPO 2003), Coral Springs, FL, 581. Gerogiorgis, D.I., Ydstie, B.E. and Seetharaman, S. 2002, Proceedings of the Computer Modeling of Minerals, Metals & Materials Processing Meeting (TMS2(X)2), Seattle, WA, 273. Graells, M., Espuna, A., Puigjaner, L. 1992, Comput. Chem. Eng. 16 (S), S221. Harjunkoski, I., Westerlund, T., Porn, R. 1999, Comput. Chem. Eng. 23 (10), 1545. Johansen, K., Aune, J. 2002, U.S. Patent 6,440,193 (to Alcoa Inc. and Elkem ASA). Johansen, K., Aune, J., Bruno, M., Schei, A. 2000, Proceedings of the Sixth International Conference on Molten Slags, Fluxes and Salts, Stockholm, Sweden (#192). Kalampoukas, G., Dervakos, G.A. 1996, Comput. Chem. Eng. 20 (B), S1383. Lelkes, Z., Szitkai, Z., Rev, E., et al., 2000, Comput. Chem. Eng. 24 (2-7), 1331. Manninen, J., Zhu, X.X. 1998, Comput. Chem. Eng. 22 (S), S537. Mantzaris, N.V., Kelley, A.S., Srienc, F., Daoutidis, P. 2001, AIChE J. 47 (3), 727. Motzfeldt, K., Kvande, H., Schei, A., Grjotheim, K. 1989, Carbothermal Production of Aluminium - Chemistry and Technology, Al Verlag, Dusseldorf, Germany. Novak, Z., Kravanja, Z., Grossmann, I.E. Comput. Chem. Eng. 20 (12), 1425. Pahor, B., Kravanja, Z., Bedenik, N.I. 2001, Comput. Chem. Eng. 4-6, 765. Papalexandri, K.P., Pistikopoulos, E.N. 1994, Comput. Chem. Eng. 18(11-12), 1125. Pettersson, F., Westerlund, T. 1997, Comput. Chem. Eng. 21 (5), 521. Qi, R.H., Henson, M.A. 2000, Comput. Chem. Eng. 24 (12), 2719. Rooney, W.C, Biegler, L.T. 2000, Comput. Chem. Eng. 24 (9-10), 2055. Stein, E., Kienle, A., Esparta, A.R.J., et al., 1999, Comput. Chem. Eng. 23 (S), S903. Westerlund, T., Pettersson, F., Grossmann, I.E. 1994, Comput. Chem. Eng. 18 (9), 845. Yee, T.F., Grossmann, I.E. 1990, Comput. Chem. Eng. 14 (10), 1165. Yeomans, H., Grossmann, I.E. 1999, Comput. Chem. Eng. 23 (9), 1135.

7. Acknowledgments The authors acknowledge the financial support of ALCOA Inc. for the present study (part of the carbothermic aluminium production project co-funded by the U.S. DOE). The first author (D.I.G.) gratefully acknowledges an Institute of International Education Fulbright fellowship as well as an Alexander S. Onassis Foundation doctoral fellowship.

European Symposium on Computer Aided Process Engineering - 13 A. Krasiawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

137

Towards the Identification of Optimal Solvents for Long Chain Alkanes with the SAFT Equation of State Apostolos Giovanoglou^ Claire S. Adjiman^' ^, Amparo Galindo and George Jackson Department of Chemical Engineering and Chemical Technology, Imperial College London, Exhibition Road, London SW7 2AZ. U.K.

Abstract An optimisation framework is presented to enable the identification of immiscibility in binary mixtures of short and long-chain n-alkanes, or polymers. Using the SAFT-HS equation of state and introducing a general thermodynamic criterion implying liquidliquid immiscibility, the largest short-chain n-alkane, which is immiscible with a given long-chain n-alkane is identified. Possible applications of this study can be found in solvent and mixture design formulations in the oil and polymerisation industry, where short-chain alkanes are readily available on-site and can offer good performance.

1. Introduction Fluid phase behaviour is of significant importance in process systems engineering. Understanding and predicting the phase behaviour of a process mixture is an invaluable tool for process design and operation optimisation. In the polymer industry, for instance, processing conditions should be such that polymerisation takes place in a single phase for the end product to be homogeneous. Moreover, in the case when molecular thermodynamic models are available, a tool that guarantees robust phase equilibrium calculations would also be useful as part of a material design framework. Building on the polymerisation example, one may be searching for a solvent that ensures the formation of a single phase inside the polymerisation reactor within the range of operating conditions, or may be seeking a solvent to separate the polymer from the nonreacted monomer in a subsequent product-purification stage. The complexity and dimensionality of the multi-component fluid phase equilibrium/stability means that the development of tools able to account robustly and efficiently for fluid phase behaviour inside process and/or material design formulations is not a trivial task. Such issues have largely been treated either by exploiting prior knowledge of the mixture phase behaviour, or by assuming the number of stable equilibrium phases is known a priori. In this paper a methodology is presented to distinguish between two different types of phase behaviour, which occur in binary mixtures of short and long-chain alkanes or polymers. Extensions of the methodology to the more general case of multi component mixtures can find applications in case studies involving solvent selection and mixture ^ Also affiliated with the Centre for Process Systems Engineering at the same address ^ Corresponding author. Tel: +44(0)20 7594 6638; Fax: +44(0)20 7594 9929; Email: [email protected]

138 design in the oil and polymerisation industries. The choice of solvent in such cases can be narrowed down by noting that short-chain n-alkanes are readily available on-site and can usually offer good performance. The structure of this paper is as follows: in the next section there is a brief description of the problem considered, in section 3 a general thermodynamic criterion for identifying liquid-liquid immiscibility in binary mixtures is introduced, in section 4 the overall problem formulation is presented, and the results are shown in section 5.

2. Problem Statement The aim of this work is to develop a methodology to distinguish between two types of phase behaviour occurring in binary mixtures of n-alkanes of two different lengths: a shorter n-alkane, referred to as the short-chain n-alkane, and a longer n-alkane, referred to as the long-chain n-alkane. Given the size of the long-chain n-alkane, the goal is to identify the short-chain n-alkane with the largest molecular weight such that the mixture exhibits liquid-liquid (L-L) separation; this type of phase behaviour corresponds to type V in the classification of van Konynenburg and Scott (1980) (see figure 1). For molecular weights of the short-chain n-alkane greater than the one identified above, liquid-liquid separation is no longer observed; in the classification of van Konynenburg and Scott (1980) this phase behaviour is the so-called type I (see figure 1). TYPE ll V

L

Cl/ L-V

Wi<Wi'

^is /

J2 ,

Figure 1: Pressure-temperature phase diagrams illustrating the change in phase behaviour from type V to type I in a binary mixture of n-alkanes as the molecular weight (w) of the shortest n-alkane (component 1 and 1 \ respectively) increases. The main characteristics of type V phase behaviour compared to type I are the region of liquid-liquid immiscibility, the so-called cloud curve, close to the critical point of the more volatile component (the short-chain n-alkane), and the appearance of a three-phase line (L-L-V) close to the vapour pressure curve of the same component (see figure 1). Since demixing of the two components is the main difference between these two types of phase behaviour, a criterion to identify liquid-liquid immiscibility is developed. Such a criterion is introduced in the next section. A simplified version of the statistical associating fluid theory (SAFT-HS) is used to model the n-alkane molecules. This approach offers a good representation of the entire n-alkane series (Galindo et ah, 1996) incorporating an intermolecular parameter, which describes the n-alkane size. In this

139 way it is possible to study the behaviour of n-alkane mixtures as a function of the size of the short chain n-alkane.

3. Identifying Liquid-Liquid Immiscibility in Binary Mixtures A mixture reaches equilibrium at the global minimum in its free energy. This sometimes requires the existence of several phases, giving rise to liquid-liquid immiscibility. In the case of a binary mixture, and according to the Gibbs phase rule, the maximum number of liquid phases that can coexist in equilibrium is two. A general criterion to determine immiscibility can be derived directly from the classical thermodynamic rules related to the concept of stability limits. A system is said to be at its limit of stability when even a small perturbation in one of its state variables leads to a phase change (Beegle et al, 1974b). For a binary mixture at a specified temperature and pressure, assuming the absence of a vapour-like density branch at these conditions, the existence of stability limits is a necessary and sufficient condition for liquid-liquid equilibrium to occur over a range of total compositions. This range is bounded above and below by the compositions of the co-existing phases. When non-existence of a vapour-like density branch cannot be guaranteed, the above statement is no longer sufficient, since vapourliquid equilibrium may be more stable than liquid-liquid equilibrium. For the rest of this section non-existence of a vapour-like density branch is assumed, corresponding to high-pressure fluid phase behaviour. Beegle et al. (1974a, 1974b), Modell and Reid (1983) and more recently Firoozabadi (1999) have worked on the derivation of simple and general criteria that can be used to identify stability limits. Starting from the maximum entropy or minimum free energy principle, and making a series of expansions around the state variables, inequalities are developed to identify whether or not a system is indeed in stable equilibrium. Using Legendre transform theory a representation of the derived expressions in different statevariable spaces can be obtained. In the case of a binary mixture it can be shown (Firoozabadi, 1999) that a single liquid phase is stable (or metastable) if and only if:

>0

for/= lor2

(1)

where //, and x, are the chemical potential and the mole fraction of component /, respectively, T is the temperature, and P is the pressure. The above partial derivative becomes negative if the single phase is unstable and the system acquires the global minimum in its energy by separating into two liquid phases. The points at which the above partial derivative vanishes (cf eq. 2) are the limits of stability, and the existence of such points is a signature of liquid-liquid co-existence (spinodal decomposition).

9x

=0

(2)

This is illustrated qualitatively in figure 2 for a model mixture of two spherical molecules of equal diameter. At temperature Ti and pressure P (plots a and c in figure

140 2) the mixture forms one homogeneous liquid phase. At the same pressure P but lower temperature T2 (plots b and d in figure 2), the two components become immiscible as indicated by the existence of extreme points in the chemical potential of component 1, or by the zeros in its partial derivative with respect to composition. In the next section we will discuss how this criterion is used to distinguish between type I and type V phase behaviour in binary mixtures of short and long-chain n-alkanes. One liquid phase

Two liquid phase

Figure 2: Chemical potential and chemical potential partial derivative with respect to composition for a model mixture of two spherical molecules: at conditions T\, P where the two components are miscible (plots a and c), and at conditions T2
4. Problem Formulation In order to derive a mathematical formulation for the problem considered, a thermodynamic model capable of describing the whole series of n-alkanes is required. In this work we use the SAFT-HS approach (Jackson et al, 1989; Chapman et ai, 1989; Galindo et al, 1996), a simplified version of the statistical associating fluid theory (SAFT), which treats molecules as chains of hard-sphere segments with van der Waals interactions. More specifically, n-alkanes are described using a united-atom model where m, hard-sphere segments of equal diameter o; are bonded tangentially to form a chain. Attractive interactions are described with an integrated interaction energy cxa associated with each segment. A simple empirical relationship between the number of carbon atoms in the alkyl chain C, and the number of spherical segments m, has been proposed by Jackson and Gubbins (1989) and Archer et al. (1996): m,= l+(Cr l)/3. The

141 equation can be used in a transferable way to characterise all members of the series in terms of their chain length. This representation gives a reasonable description of the critical point. In the context of this work this is especially important since the onset of liquid-liquid immiscibility first occurs close to the critical point of the short chain nalkane (van Konynenburg and Scott, 1980). Using the SAFT-HS equation and exploiting the immiscibility criterion presented in section 3, the problem can be formulated as a non-linear constrained optimisation program, where for a given long-chain n-alkane, the largest short-chain n-alkane that is immiscible with the long-chain component is identified. The temperature and pressure search area is confined to that close to the critical point of the short chain n-alkane as liquid-liquid immiscibility always appears in this area. The overall formulation is a follows:

max

m,

s.t.

{m^, /?, X,, r) = 0

(3)

T,P

P = Pc,Mx) 0.9 7^
0 < mj < m2

p>0 0 < x <1

where indices 1 and 2 denote the short and long-chain n-alkane, respectively, subscript C stands for critical, //, is the chemical potential, jc, the mole fraction, and m, the SAFTHS chain length parameter of component /, p is the density of the mixture, and P and T denote pressure and temperature, respectively. The partial derivative of the chemical potential with respect to composition at constant temperature and pressure was calculated analytically using the chain rule.

dx.* dp dx.

(4)

JT,P

dx,^ JT.

dp

t,X,

The critical properties of the short-chain n-alkane, which are used to fix the pressure and to bound the temperature are functions of mx only. They are calculated by applying the criticality conditions for component 1, i.e..

^1iTc.vPc.x) = 0,

and

ly^

(rc,„Pc,i) = 0

(5)

142

5. Results The optimisation problem was solved using gPROMS/gOPT (Process Systems Enterprise Ltd.). We have considered long-chain n-alkanes with chain length ranging from 75 up to 9,000 carbon atoms. The results are presented in figure 3. Our calculations suggest a near linear dependence for increasing sizes of the small n-alkane; this is in qualitative agreement with experimental findings (Rowlinson and Swinton, 1986). 800

700

600


SI

o 300 SI

m

200 100

0 1000

2000

3000 4000 5000 6000 long chain size (Cg)

7000

8000

9000

Figure 3: The length of the largest short chain n-alkane which is immiscible with a given long chain n-alkane. The length of the long chain alkane ranges from 75 up to 9,000 carbon atoms.

6. Conclusions An optimisation framework to identify liquid-liquid separation in binary mixtures of nalkanes is presented. A general thermodynamic criterion, based on the concept of stability limits, is introduced to identify the largest short-chain n-alkane which is immiscible in a given long-chain polymer-like n-alkane.

7. References Archer, A.L., Amos, M., Jackson, G. & McLure, I.A., 1996, Int. J. Thermoph., 17, 201. Beegle, B.L., Modell, M. and Reid, R.C., 1974a, AIChE J., 20, 1194. Beegle, B.L., Modell, M. and Reid, R.C., 1974b, AIChE J., 20, 1200. Chapman, W.G., Jackson, G. and Gubbins, K.E., 1988, Mol. Phys., 65, 1057. Firoozabadi, A., 1999, Thermodynamics of Hydrocarbon Reservoirs, McGraw-Hill. Galindo, A., Whitehead, P., Jackson, G. & Burgess, A., 1996, J. Phys. Chem., 100, 6781. gPROMS Version 1.8, www.psenterprise.com. Jackson, G., Chapman, W.G. and Gubbins, K.E., 1988, Mol. Phys., 65, 1. Jackson, G. and Gubbins, K.E., 1989, Pure Appl. Chem., 61, 1021. Modell, M. and Reid, R.C., 1983, Thermodynamics and its Applications, Prentice-Hall. Rowlinson, J.S. and Swinton, F.L., 1982, Liquids and Liquid Mixtures, Butterworths. Van Konynenburg, P.H. and Scott, R.L., 1980, Phil. Trans., A298,495.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

143

Combined Optimisation and Process Integration Techniques for the Synthesis of Fuel Cells Systems Julien Godat, Fran9ois Marechal Laboratory of Industrial Energy Systems, Institute of Energy Sciences, Swiss Federal Institute of Technology , CH-1015 Lausanne mailto:[email protected], tel + 41 21 693 35 16, fax +41 21 693 35 02

Abstract A method that combines process modelling and process integration techniques has been developed to tackle the design of complex integrated systems like fuel cell systems. This method uses the equations of the composite curves as constraints to model the ideal heat exchanger network and the corresponding utility system. When combined with the use of process modelling techniques, this method allows to synthesize optimized fuel cell integrated systems with high efficiency and that integrates the technological design constraints.

1

Introduction

The physical principles behind a fuel cell system is the electrochemical conversion of a fuel into electricity. If the membrane system that allows the separate transfer of the ions and the electrons is the heart of the system, the system integration is of major importance with respect to the system performances(Hirschenhofer, 1998). The Ballard Proton Exchange Membrane Fuel Cell (PEMFC) system (Keitel, R.,) has been used as a basis for this study. It includes a fuel processing system, the fuel cell and the post combustion sub-system. The fuel processing section converts the fuel into a suitable form for the electrochemical reaction, avoiding catalyst poisoning and featuring acceptable catalyzed reaction rates. The fuel processing is a steam reforming system operating at a pressure of 3 bar followed by a shift reactor that converts CO of the reformate into additional CO2 and H2 and a Preferential oxidation reactor (PROX) that converts the remaining CO to avoid fuel cell catalyst poisoning. In our study, we did consider a medium temperature (250°C) shift reactor that allows shift reaction to be realized in one step. A H2 loss by oxidation has been considered in the PROX reactor due to the selectivity of the catalyst. The fuel cell operates at low temperature (less than 100°C). The hydrogen crossing the membrane produces electricity by the electrochemical conversion of the free energy of the hydrogen oxidation reaction. The fuel conversion being lower than 100%, The remaining fuel will be recovered by post combustion to satisfy the energy requirement of the system. In order to reach the operating pressure of the system, the air is compressed by a turbo-compressor driven by the expansion of the flue gases resulting from the post combustion. Coupling

144 PEMFC system Energy Flow Diagram Reforming ^ ^i^irtion

U/

Fuel Processing MT shift

PROX

p l

Fuel Cell

4dW\ (M)cold streams

V(tw)

FIG. 1. Energyflowdiagram of the system of a electricity generator allows producing an additional amount of electricity whose production will depend on the turbine inlet temperature TiT and on the gas turbine system integration. Process integration in fuel cell systems concerns therefore different levels. In terms of chemical conversion, the fuel processing performances affect the fuel cell and the post combustion efficiency, but also in terms of combined heat and power production. A characteristic of the fuel cell system design is the heat exchange system that can not be considered as a conventional network of individual heat exchangers but as a system where heat exchanges take place simultaneously with the chemical and the electrochemical reactions in the same vessel. Fronted with this multi-scale integration problem, our goal has been to develop a methodology that combines process modelling, process integration and optimisation techniques to design better integrated fuel cell systems.

2 Process Synthesis Methodology Thefirststep of the process synthesis methodology is the generation of a simulation model based on the Energy Flow Diagram (fig 1). Knowing the values of the decision variables (P), the energy flow model is used to compute the temperatures, pressures,flowratesand energy flows that define the system requirements. In the integration strategy, some of the flowrates (rhu) have to be computed to close the energy balance and satisfy the heat cascade of the integrated system, we refer to these as being the utility system. The temperatures, pressure and specific energy flows of the utility sub-systems are also computed by energy flow modelling when these are related to decision variables (e.g. the operating pressure or TiT). Theflowrateswill be computed by process integration using the Effect Modelling and Optimisation (EMO) approach (Marechal and Kalitventzeff (1998)). The "ideal but feasible at an acceptable cost" heat exchanger network model is formulated as a linear programming (LP) problem including the heat cascade as constraints and the process efficiency as an objective function. The results of the LP optimisation are then used to compute the objective function of the design and to define the optimal values of the decision variables (P) that maximize the efficiency. In our study, the objective function is the energy efficiency of the system, computed by (1) and the optimisation is stated as (2), where rhu{P) is the solution of the LP problem (3).

rje{P,rhu) =

EFC{P)

+

rhu) - rap,(P) * Ep, + f^NGaddiP^^u) * LHVNG

EGT{P.

rriFc * LHVNG

(1)

145 where EFC{P) and EGT{P, T^U) are respectively the electricity production by the fuel cell system and the net production of the integrated gas turbine system for the decision variables P and the utility flowrates ihw The natural gas (with a lower heating value LHVNG) flowrate entering the fuel processing section {mpc) is a constant, while rriNGadd (^' rh^),the additional natural gas in the utility system results from the LP problem (3). mo2{P) is the pure oxygen flow used in the PROX reactor for the decision variables P and £"02 is the energy consumption of the pure oxygen used in the system (300kWh/tonofO2). Minr]e{PMu{P))

MinFLPobj{rhu, P) = rJiNG^dd (P^ '^u) * LHVNG -

Subject to Heat cascade constraint Mechanical power balance

(2)

EGT{P,

(3)

^U)

(4a) (4b)

In the adopted approach, the model are solved as a simulation problem with enough robustness solving only part of the problem by linear optimisation and analysing the sensitivity of the decision variables (P). This allows not only identifying the optimum but also to represent the shape of the search space. 2.1 Process energy flow model The Energy flow model concerns the calculation of the chemical and electro-chemical reactions as well as the heat exchange requirements, the separation units, compression and expansion. The model has been developed using an equation solver approach (Belsim s,a„ 2001). Although this choice is not critical, it allows an easy modification of the list of specifications during the model development without having to redesign the solving sequence as it would have been the case in the sequential approach. The definition of the hot and cold streams in the energy flow model is critical and should be considered carefully if we do not want to miss energy savings potentials. In the conventional system, the steam is produced in a separated heat exchanger before being mixed with the fuel at the inlet of the reformer (dotted line at the vaporisation temperature on the composite curve of figure 1). In order to recover the partial pressure effect of the steam injection, the energy requirement of the feed preheating has been considered as a liquid-vapour mixture of water and natural gas to be heated up (plain line on the same figure). This implies the use of a special heat exchange equipment. The chemical reactions are modelled assuming (where appropriate) equilibrated reactions. In order to account for the catalyst efficiency, the equilibrium is computed at a different temperature from the heat balance one. The conventional representation of the reformer is to consider the feeds preheating up to the present temperature and then to consider a cold stream representing the heat of reaction Qreac at the constant reforming temperature Treac. In order to better fit the reactor temperature profile, we considered the feed stream preheating to Treac, then the reaction takes place to reach equilibrium at Treac. The heat of reaction is considered into parts :

146 a cold stream from Tint (the reaction startup temperature) to Treac corresponding to the reaction products heating and the balance at constant temperature Treac. This approach will better approximate the real temperature profile in the reactor (dotted line of figure 1) and will allow energy savings for example by additional feed preheating. This definition of heat requirement of the reforming reaction should be kept in mind when it will be necessary to compute the heat exchange network, especially if a pinch point appears in the corresponding temperature range. A similar approach has been used to model the energy requirement of the exothermic reactions (shift and preferential oxidation, combustion as well as the fuel cell it self). For the system optimisation, the pressure, the steam to carbon ratio and the reforming temperature have been considered as decision variables while the temperature of the shift reactor, as well as the conversion in the PROX reactor have been considered asfixed.The fuel utilisation in the fuel cell has not been optimised in our study. The post combustion is modelled assuming the stoechiometric combustion of the fuel not converted in the fuel cell (this fuel contains the remaining methane and hydrogen). The resulting flue gases are then expanded in a turbine with an inlet temperature (TiT) considered as a decision variable. It should be noted that the heat requirement associated with the combustion assumes the possible air and fuel preheatings and the high temperature exchange of the combustion products with the reformer. 2.2 The utility system In order to balance the heat requirement of the system, a utility system will be used. According to the decision parameters, two situations may occur : 1) the heat of the post combustion is not sufficient to balance the heat requirement of the system and additional firing is needed or 2) the system is balanced by the heat of the post combustion and actions have to be taken in order to use the energy excess. These two situations will be represented by adding the two sub-systems in the problem presented on the right of figure 1 (Post combustion sub-system). On the top, the sub-system represents the additional fuel added to the post combustion in order to balance the composite curve, this leads to an additional air requirement (that flows through the compressor, the fuel cell and the air preheating section) and, in the center, an air excess that will be computed in order to maximise the energy conversion into net electricity using the Bray ton cycle. The bottom of the figure represents the post combustion of the non converted fuel. The model used for this representation has been presented in (Marechal and Kalitventzeff, 1998) and has been adapted to account for the effect of the oxygen partial pressure on the electricity production in the fuel cell. This model represents the derivative of the additional fuel and the air excess in the composite curve constraints and the objective function. The limit of this configuration will be a renegerative gas turbine operating at a pressure of 3 bar, without the fuel cell system reaching 26% of electrical efficiency. The model used will allow to represent the possible regenerative exchange, not only between the streams of the gas turbine system, but also with the streams of the process. The difficulty of applying the heat cascade model lies on the fact that it can only be solved by solving an optimisation problem : the solution being defined by the activation of inequality constraints : pinch point or utility flowrate.

147

steam to carbon ratio

FIG. 2. System efficiency as a function of reforming temperature and steam to carbon ratio with and without net production of electricity with the gas turbine

3 Results The visualisation of the objective function with respect to some of the decision parameters is shown on figure 2. Two situations are presented as a function of the reforming temperature and the steam to carbon ratio. The first (lower surface) represents the turbocompressor solution where the TiT is such that the expansion turbine will only drive the compressor without net production of electricity (as it is the case in the original design), while the second (upper) assumes a net electricity production by the gas turbine. The optimal efficiency computed for the system is of 53%, obtained for a steam to carbon ratio of 4 and a reforming temperature of 700°C for the gas turbine case. For the turbo compressor case, the optimum efficiency is of 47% with a reforming temperature of 750°C. These values have to be compared with an efficiency of 36% in the original design. It should be mentioned that the optimal decision are quite different in the two situations indicating that the investment and the choice of the catalyst will be affected by the configuration decision. More results are presented in (Godat and Marechal , 2002). According to design assumptions or limits, the activation of different pinch points, that results from the LP optimisation strategy, will lead pratically to different configuration. Considering as an example the composite curves of figure 3 that have been computed for the same steam to carbon and reforming temperature. On the right, we consider system without electricity production by the gas turbine (turbo-compressor). In this situation, the liquid-vapour feed mixture preheating is necessary in order to reach high system efficiency. Producing steam in a separate heat exchanger (doted cold composite) would have activated a pinch point that would have increased the additionalfiringrequirement. The mixture preheating leads to an increase of 1% of efficiency (from 44.1% to 45.2%). On the left of the figure, we present the results of the regenerative gas turbine integration allowing electricity generation by the gas turbine. In this case, the shape of the composite curve indicates that both

148 2000 1800

_H...

:

With vaporisation Mixture preheating Hot composite curve HptMixture.preheating

—^— - ;r - • • 1 -•,'• — f >• • •

•

I

!'"""

•

With vaporisation Mixture preheating Hot composite curve Hpt Mixture, preheating

— •• -• •

--

1600

Gas turbine net pi-oductioii 1400 1200

•

:

: : : : : : : : :

1000

:

-— i

1

:

^.i.'-''

-,'

/f.---

1

1

:

'•( J

f

/: 1

;-^' >/:

:

i

i

Turbo cdmpresso^

:

:

:

:

•

:

y [/ - :

i

:

1

1

4

' *'~ if :

:

i

i

....

l-^j^

1

i

i

FIG. 3. Composite curves of the system with and without net production with the gas turbine for a) Tref = 800° C, S/C = 2.6 andb) Tref = 800° C, S/C = 2.6 separate production of steam (doted cold composite) and mixture preheating may be envisaged without efficiency penalty. In this case, the system efficiency is of 47.8%. This sensitivity analysis has been made because the objective function (the efficiency) is not the only concern. Other design parameters for example the humidity in the fuel cell and of course the investment have also to be analysed.

4

Conclusion

A model based on the combined use of modelling and process integration techniques has been developed to design optimal integrated fuel cell systems. The use of the process integration techniques solved as a linear programming problem allows modelling the heat exchanges in the integrated system and determining the flowrates in the system even if the pinch point position changes. This approach is especially useful to design integrated systems because it allows modelling the heat exchange system without defining a priori its structure. The proposed modelling method is a first step of the synthesis methodology that will integrate multiple objectives (i.e. the efficiency and the cost) in order to finally design the best system structure. Compared to simultaneous simulation and optimisation, the use of a two level approach (solving the model at a lower level), allows not only the identification of the optimal decision parameters but also the characterisation of the optimal region for the system configurations.

5

References

Hirschenhofer J.H., Fuel Cell Handbook, Fourth Edition, (1998) Godat J., Marechal F, Optimization of a fuel cell system using process integration techniques. Fuel cell conference, Amsterdam, 2002,submitted the Journal of Power Sciences, (2002) Marechal F., Kalitventzeff B., Process integration : Selection of the optimal utility system Computers and Chemical Engineering, Vol 22 SuppL, pp. S149-S156, (1998) Keitel, R., 1996, Application with Proton Exchange Membrane (PEM) Fuel Cells for deregulated market place, ALSTOM BALLARD, Frankfurt, Germany. Belsim - Vali IH, vlO User Guide, Belsim s.a.. Rue Georges Berotte, 29A, B-4470 SaintGeorges-sur-Meuse (Belgium), http ://www.belsim.com. (2001)

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

149

Optimal Design and Operation of Batch Ultrafiltration Systems Antonio Guadix^, Eva S0rensen^*, Lazaros G. Papageorgiou^ and Emilia M. Guadix^ ^Centre for Process Systems Engineering, Department of Chemical Engineering, UCL (University College London), Torrington Place, London WCIE 7JE, U.K. ^'Departamento de Ingenieria Quimica, Universidad de Granada, 18071 Granada, Spain.

Abstract In this paper, an approach for the optimal design and operation of a batch ultrafiltration installation is presented. The approach is based on a dynamic model which takes into account both fouling and cleaning issues. An economic objective function, which includes capital and operating costs, is used and reasonable operating constraints are imposed. The overall problem is formulated as a dynamic optimisation model. A protein ultrafiltration plant involving the use of commercially available tubular ceramic membrane modules is studied. Optimal values for both design and operation variables such as the processing tank volume, the number of membrane modules, the feed and circulation pumps sizing, the work pressure profile and the timing of the operating and cleaning tasks are determined simultaneously.

1. Introduction Batch membrane ultrafiltration is well suited to the processing of biological molecules since it operates at relatively low temperatures and pressures and involves no phase changes or chemical additives, thereby minimising the extent of denaturation, deactivation and degradation of highly labile biological products (Zeman and Zydney, 1996). In many biotechnology systems, the final product is a dilute solution of the desired molecule and batch ultrafiltration can be used in the recovery process for product concentration which can significantly improve the economics and effectiveness of other processing steps. Most of the research work performed on ultrafiltration optimisation has focussed on steady-state techniques, e.g. Liu and Wu (1998) and Belhocine et al. (1998). Unfortunately, these methods do not allow operability considerations to be taken into account. Dynamic optimisation methods, however, can be used to determine optimal values for both design and operation variables simultaneously. In recent years, this technique has successfully been applied to a number of processes (for instance, distillation {Furlonge et al, 1999), reaction (Kvamsdal et al, 1999) or heat exchange (Georgiadis et al, 1998)). In this paper, we consider the application of dynamic optimisation to the optimal design and operation of a batch ultrafiltration system, illustrating the method with a practical case study. To the best of the authors' knowledge, this is the first work in which a formal dynamic optimisation methodology is applied to batch ultrafiltration. ' Corresponding author. Tel: +44 20 7679 3802, E-mail: e. sorensen@ucl . a c . u k

150

2. Problem Description A typical batch ultrafiltration plant is represented in Figure 1. It consists of a processing tank, a feed pump, a circulation pump and a membrane unit with a number of modules in parallel. A permeate is obtained from the membranes while the retentate is recirculated until the desired concentration in the processing tank is reached. Then, a cleaning procedure is performed and the system is ready for the next batch.

Processing tank

Feed pump

RETENTATE

Circulation pump

Membrane unit

^ PERMEATE

Figure 1. Scheme of a hatch ultrafiltration plant.

3. Dynamic Model The physical description of the process described above is based on material balances and equipment performance equations, which incorporate the following key assumptions: • The membrane is fully retentive for the solute considered. • The membrane geometry is tubular. • Permeate flux is governed by the osmotic pressure model (Cheryan, 1998): J=

AP-n

(1)

where J is the permeate flux, AP is the transmembrane pressure, n is the osmotic pressure and RM is the membrane resistance. Fouling occurs according to the cake filtration model (Cheryan, 1998): dR M = aAPPJCr dt

(2)

where CR is the retentate concentration and a and P are parameters. The membrane is perfectly regenerated after each cleaning procedure. The duration of the cleaning process is a linear relationship of the filtration time.

151

4. Optimisation Problem Ultrafiltration installations often produce retentates that need further processing to be marketed (e.g. spray drying). Thus, objective functions based on profit are not appropriate in ultrafiltration processes as revenue data are not generally available. Therefore, the objective function proposed in this study is the total hourly cost (to be minimised). Both capital and operating costs are taken into account. The former includes the costs of the equipment (tank, pumps, membranes) while the latter include the electricity consumption in the pumps and the cleaning costs. Is assumed that: • The capital costs are distributed during the equipment life. • The cost of each cleaning procedure is a function of the membrane area and the final membrane resistance. CC = a + b A R M f

(3)

For batch mode, the plant operation is subject to a number of constraints: • The plant has a minimum capacity requirement. • Feed and product concentrations are fixed due to raw material specifications and quality requirements, respectively. • The work pressure should be below a maximum value recommended by the membrane manufacturer during the entire operation time in order to avoid any irreversible damage to the membrane. The optimal design and operation of an ultrafiltration plant can be formulated as a dynamic optimisation problem. With respect to the optimal design, the following parameters are determined: • Processing tank volume, • Feed and circulation pumps power, • Number of membrane modules (N). Simultaneously, the optimal operation parameters are also found: • Timing of the operating and cleaning tasks, • Work pressure profile. The proposed algorithm to solve this problem is the following: • Relax N to a continuous value. This is reasonable due to the large number of membrane modules. • Solve the resulting dynamic optimisation problem and find N to the closest integer value. Each dynamic optimisation problem is implemented in gPROMS (Process Systems Enterprise Ltd., 2001) which incorporates a control vector parameterisation approach. The work pressure profile is considered to be a linear function of time over the entire time horizon.

5. Case Study and Results As an illustrative example, the optimal design and operation of a protein ultrafiltration plant will be studied. The membrane modules considered are those manufactured by US

152 Filter (US Filter, 2002). Each ceramic module integrates 19 channels 1.02 m long with a diameter of 4 mm for a total area of 0.24m^. Recommended maximum pressure and crossflow velocity are 1000 kPa and 3 m/s, respectively. It is assumed that the batch size is 5000 L and that the plant capacity is at least 1000 L/h. The feed concentration is 5 g/L and the product must have a concentration of 50 g/L. The cost (in US$) of the processing tank, pumps and membranes is calculated using the equations 4, 5 and 6, respectively: CT3„k=120.V°53

(4)

Cp„„p=2590-W 0.79

(5)

CMembrane=1000-A 0.90

(6)

where V is the volume in L, W is the power in kW and A is the area in m^. The equipment lifetime is 20 years for the tank, 10 years for the pumps and 5 years for the membranes. Electricity cost is 0.07 $/kWh. Using the procedure described above, an optimal solution has been found. In Figure 2, the objective function, total hourly cost, is represented versus the number of modules. The relaxed optimum is found at 960.6 modules, where the total hourly cost is 33.1 $/h.

6250 L

8.74 kW

500

750

1000

1250

33.89 kW 961 modules

1500

Number of modules

Figure 2. Objective function.

Figure 3. Optimal design.

153

250

C L E A N

(0 Q.

^200

o> 3

S 150

o a

N G

•Jf 100

o 50 0

1

1

1

2

1

3

4 Time (h)

Operating time (h)

Figure 4. Optimal operation.

Figure 5. Retentate concentration.

For the optimal design (Figure 3), the processing tank volume is 6250 L, the feed pump power is 8.74 kW, the circulation pump power is 33.89 kW and the 961 modules involve a total membrane area of 233.92 m^. For the optimal operation (Figure 4), each batch is 5.00 h long, comprising 2.97 h of filtration time followed by 2.03 h of cleaning. This cleaning time is usual in the food industry and involves rinsing, acid cleaning and basic cleaning stages. During the filtration time, the work pressure should be linearly decreased from 258 to 210 kPa. The evolution of retentate concentration can be seen in Figure 5. The permeate flow rate (Figure 6) is decreasing due to the decrease in the work pressure and, more importantly, due to the presence of membrane fouling. This phenomenon is reflected in the increasing in the membrane resistance Rm (Figure 7).

owu -

2500

^•'•'

E 30

V ^v

3- 2000o o 1500 (0

a> E 1000 -

CL 25

^s^^

^

^v.

u 20 c

^v^ ^^v^^^

(0

.i2 15 ^"^s^^

^^*v,^

0) Q.

^^

500 nC)

CO

2

a> 10 c (0

1 ^ 2

1

2 Time (h)

Figure 6. Permeate flow.

0

C Time (h)

Figure 7. Membrane resistance.

The contribution to the total hourly cost of $33.1 is 12 % capital and 88 % operating costs, respectively. A detailed breakdown of the total capital cost, in total $204 141, is

154 represented in Figure 8, where the membrane cost is highlighted. Operating costs are $146.46 per batch (Figure 9), the cleaning cost being the most significant percentage.

1% 4%

Tank 0 Feed pump D Circulation pump ID Membranes

Figure 8. Capital cost breakdown.

Feed pump D Circulation pump CD Cleaning

Figure 9. Operating cost breakdown.

6. Conclusion This work addresses the optimal design and operation of a batch protein ultrafiltration plant. The dynamic optimisation procedure adopted identifies simultaneously the optimal design parameters and operating policy of the installation. It should be emphasised that the approach can be directly applied to other ultrafiltration processes. This is the first work in which a formal dynamic optimisation methodology is applied to batch ultrafiltration.

7. References Belhocine, D., Grib, H., Abdessmed, D., Comeau, Y., Nameri, N., 1998, J. Membrane Sci., 142, 159. Cheryan, M., 1998, Ultrafiltration and Microfiltration Handbook, Technomic, Lancaster. Furlonge, H.I., Pantelides, C.C, S0rensen, E., 1999, AIChE J., 45,781. Georgiadis, M.C., Rotstein, G.E., Macchietto, S., 1998, AIChE J., 44, 2099. Kvamsdal, H.M., Svendsen, H.F., Hertzberg, T., Olsvik, O., 1999, Chem. Eng. Sci., 54, 2697. Liu, C. and Wu, X., 1998, J. Biotechnol., 66, 195. Process System Enterprise Ltd., 2001, gPROMS Advanced User Guide, London. US Filter, 2002, Ultrafiltration Systems for Wastewater Treatment, Palm Desert. Zeman, L.J. and Zydney, A.L., 1996, Microfiltration and ultrafiltration: Principles and Applications, Marcel Dekker, New York.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

155

Process Intensification through the Combined Use of Process Simulation and Miniplant Technology Dr. Frank Heimann, GCT/A - L540, BASF AG, 67056 Ludwigshafen, Germany

Abstract Various approaches to process intensification can be taken at various levels. At the lowest level, it may be possible to optimise basic physical, thermodynamic and chemical processes, for example, by changing geometries and surface structures, or using catalysts, etc. At the next level, possibilities include the use of cleverly designed plant items such as spiral heat exchangers or centrifugal reactors. Finally, at the highest or process level, improvements may involve carrying out several unit operations simultaneously in a single piece of equipment or making specific process modifications. This paper uses three examples (extractive distillation, reactive distillation column, steam injection) to demonstrate the breadth of possibilities for intensifying chemical processes. The processes were all developed with the help of process simulation and verified experimentally in laboratory-based miniplants. The information gained was essential to the successful design and operation of production-scale plant.

1. What is Process Intensification? Often when examples are given for process intensification, at first there are only examples in which it is possible to combine several unit operations in one piece of equipment. The fact that process intensification is more complex than this is clarified by the definition by Stankiewicsz and Moulijn (2000): Process intensification is any chemical engineering development that leads to a substantially smaller, cleaner and more energy-efficient technology! Intensification measures can thus be carried out at different levels which are different in degrees of complexity. The bandwidth extends from the simplest level, the level of underlying physical and chemical processes (e.g. improving heat transfer by the choice of geometry), to the next more-complex level of equipment and machines (e.g. intensification by an optimum construction design) and on to the most complex level, the process level, in which several unit operations can be combined in one piece of equipment. The examples listed here cover all the levels of complexity. Before these examples are handled in detail, there will be a clarification of what characterises miniplant technology.

2. Characteristics of Miniplant Technology (Heimann, 1998) Miniplants are complete systems for process development in laboratory scale, i.e. typical volumes lie in the range from 0.5 to max. 5 1. The throughputs are

156 correspondingly small at approx. 100 g/h to max. 1 - 2 kg/h. It should be noted here that the miniplant does not represent a true-to-scale, miniaturised simulation of a production plant. It is much more the case that the functions of the future production plant will be simulated in a representative manner. Operation of a miniplant is generally fully automated using a process control system. All of the process steps are integrated in this. It is especially necessary to simulate all important material recycling (e.g. solvents or catalysts). Ultimately the miniplants work out all the information necessary to increase the scale of the production process from the miniplant. Another important aspect of miniplant technology is that the construction design of the equipment and machines is selected in such a way that operation can be carried out under defined process engineering conditions. In this way, general modelling and simulation performed simultaneously with testing is possible and thus the foundation is created for an increase in the scale of the equipment. This will be clarified using column packings as an example. 9 1

1

8 50mbar / ._^/_^^

7

100{nbar

^

-"^^i

400lmbar

10ld mbar 1 1 1 1 1 1 1 1 1 1 1

0,0

1.0

2.0

3.0

F-Factor (Paos)

Figure 1. Separation efficiency with the chlorohenzene/ethyl benzene system. The photo in Fig. 1 shows a packing in miniplant scale with 5 cm diameter. The separating efficiency of these miniplant column packing is measured with defined test mixtures. The thermodynamical properties of these test systems, e.g. the vapour/liquid phase equilibrium, are known exactly. The separating installations can be calibrated with the use of these test mixtures. The graph in Fig. 1 shows a separating efficiency measurement, in which the number of theoretical stages per metre is entered over the vapour load in the form of the F-factor. When the column packings are used with actual material systems, reference can be made to this calibration. Miniplant columns with calibrated internal fittings then make it possible to increase the scale of the equipment directly from the miniplant scale to the production scale. This offers the advantage of a fast and cost-effective process development. Miniplant technology is thus an ideal tool to ensure experimentally process concepts selected with a view to process intensification. This will be demonstrated using three examples.

157

3. Examples 3.1. Example "Extractive rectification" Extractive rectification is an example of process intensification at the process level. In a process chain consisting of reaction, precipitation and centrifuging, a mother liquor develops which contains an alcohol, a chlorinated hydrocarbon, abbreviated as CKW, and a by-product formed during the reaction. The mother liquor must be separated into the individual components in the simplest possible way by a central processing unit. This means, the two solvents CKW and alcohol must be recovered in a high degree of purity in order to recycle them into the process. At the same time, the by-product must be separated from the two solvents. First, using simulation calculations, there will be a search for and development of a simple process concept. The table below in Fig. 2 shows some thermodynamic data for the alcohol/CKW solvent system. The boiling temperature increases from the by-product, to the alcohol and then to the chlorinated hydrocarbon. At the same time, it must be noted that the alcohol and the chlorinated hydrocarbon have an azeotrope. This azeotrope prevents the two solvents from being separated in a single rectification column.

azeotropes of the R-OH / CKW solvent system (at 1.013 bar) comp.1

comp.2

H,0 by-product by-product H,0 CKW H,0 R-OH H^O CKW R-OH R-OH CKW

Xi

X2

kg/kg

kg/kg

0.07

0,93

0.84 0.55

0.16 0.45

0.19

0.81

T X 68 79 88 93 100 112 118 121

hetero-az. Iietero-az. hetero-az. azeotrop

Figure 2. Azeotropic compositions and boiling temperatures of the material system. Extraction comes into play here. By adding another component, in this case water, three additional hetero-azeotropes form. By breaking down into an aqueous and an organic phase, an additional material separating effect is obtained, which can be used for processing the mixture. This will become clear from the following diagram (see Fig. 3). The rectification column developed on the basis of the process simulation calculations is shown here. According to the boiling temperatures of the three heteroazeotropes in the column, three side streams can be drawn off and each sent to a phase separator, in which each azeotrope breaks down into the aqueous phase and the organic phase. The organic phases consist of the purified solvents and/or the concentrated by-product. The aqueous phases are each returned to the column. At the column bottom, a waste water stream

158 then occurs which will be disposed of and/or in part will be returned to the head of the column.

aqueous NaOHc;)

N

^

C>NP,96%

OCKW

ao 0,1% R-OHO.5%

feed tf^

ao 0,5%

waste R-OH O^l'ro

Figure 3. Extractive rectification column. Extractive rectification offers another advantage. The chlorinated hydrocarbon can hydrolyse, i.e. splits off hydrogen chloride which leads to corrosion in the column. If aqueous sodium hydroxide solution is used instead of water as the extraction medium, it is possible to neutralise the hydrogen chloride which develops. The process concept was confirmed experimentally in a miniplant column and the foundations were set up for an increase in scale to production scale. Open questions tested in the miniplant related to the correct description of the vapour/liquid phase equilibriums in the simulation, testing of the fluid dynamics behaviour on the basis of the two liquid phases and the corrosion problems. In the mean time, the production column has been put into operation successfully. The specifications required for the alcohol and the chlorinated hydrocarbon are achieved and no corrosion occurs. 3.2. Example "Reaction column" In an equilibrium reaction, an educt is converted using aqueous hydrochloric acid as solvent. In this process, acetone develops in addition to the product. The disadvantage of this reaction is that it is an equilibrium reaction, in which the equilibrium is greatly on the side of the educt. What is advantageous is that the equilibrium state is reached quickly. By removal of acetone, the equilibrium can be moved towards the product side. The fact that no thermal stress can be put on the product is something which will also have to be considered with all process concepts selected for removal of the acetone. Among the alternative solutions tested, a reaction column is the most elegant possibility. Since the chemical equilibrium occurs very quickly in this example, it

159 mainly offers the advantage that in parallel to the reaction, distillative separation can also be carried out. It was also possible to prove this process concept experimentally using miniplant technology. A bubble tray column, 30 mm in diameter, was used as the miniplant column. The advantage of the bubble tray column is that there is a hold-up for each tray giving the advantage that the residence time in the column can be varied by the variation of the feed flow into the column. In this way, the foundation was set up for the increase in scale using thermodynamic and fluid dynamic simulation on the production column. This has a diameter of 600 mm and was manufactured of glass due to the corrosive nature of the aqueous hydrochloric acid. miniplant

acetone ^HCI

production

diameten iilMBiil bubbletray: iilBllli: residence timeftraiiiilliHl

educt^l HCI water

^j>roduct HCI

30mm^ 25 trays 4min

bubble tray coluillil of glass with PTFE-bubbiiil

testing of • residence time • number of trays, energy consumption • optimum position of feed tray

Figure 4. Increase in scale of the reaction column from miniplant to production scale. In this example of process intensification at the level of equipment, as well, the technical realisation was completed successfully. The column is in operation since 2 years. 3.3. Example "Steam stripping" The example explained in the following illustrates process intensification at the level of basic chemical and physical processes. Again, it concerns an equilibrium reaction, in which the equilibrium is strongly on the educt side and a slightly volatile component has to be removed from the system to displace the equilibrium. However, the equilibrium does not occur spontaneously, so the use of a reaction column is not possible. Therefore, a high-stress field develops with high yield and duration of thermal stress. Different process technology alternatives for removal of the low-boiling fraction were computer-simulated. Direct discharge of water vapour steam offers the most favourable option which protects the product.

160 A problem of the reduction in scale of the production to the miniplant scale developed in the simulation of the discharge of steam, since the volume and the cross-section area change by different orders of magnitude. This means it is not possible to keep both steam load and steam introduction duration constant during the reduction in scale from production to the miniplant. An elegant solution is to carry out separate experiments regarding the influence of thermal stress duration and the influence of fluid dynamic load. In addition, the question of simulating the discharge of steam in the miniplant scale was of central importance. In order to achieve the finest possible distribution of steam with the greatest steam bubble surface, it was planned to use special steam discharge valves, which were constructed on the basis of a fluid dynamic simulation in the miniplant (see Fig. 5). In this example, again it was possible to successfully ensure the process concept experimentally using miniplant technology. This production plant is already successful in operation.

production plant 3 valves 80 mm 0 with 216 holes, ea. 3,5 mm 0 miniplant: 1 pipe 10 mm 0 with 5 holes, 3 mm 0

^^^^^^^*^^

6,3 m3. reactor

Figure 5. Reduction in scale of the steam discharge from production to miniplant scale.

4. Closing Remarks Worldwide competition, the necessity of protecting natural resources and minimising environmental stress will continue to play a central role in the development of new processes. The examples presented above show that cost-effective as well as sustainable solutions can been found using process intensification. Miniplant technology is an important tool for quickly and cost-effectively experimental ensuring of solutions which have been proposed, in view of process intensification.

5. References Heimann, F., 1998, CIT 9,1192. Stankiewicsz, A. and Moulijn, J., 2000, Chem. Eng. Progress 1,22.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

161

A Constraint Approach for Rescheduling Batch Processing Plants Including Pipeless Plants W. Huang and P.W.H. Chung Department of Computer Science, Loughborough University, Loughborough, Leicestershire, LEll 3TU, UK

Abstract In the process industries batch plants are attracting attentions because of their suitabiUty for producing small-volume, high-value added commodity chemicals. Pipeless plants have also been developed and built to increase plant flexibility. Unexpected events, such as the failure of a processing unit, sometimes happen during operations. To avoid risk and to utilise the remaining resource, it is important to reschedule the production operation quickly. The constraint model in BPS has been extended to include constraints for rescheduling. These additional constraints are described in this paper and a case study is used to demonstrate the feasibility of the approach.

1. Introduction Efficient scheduling of batch plants is required since it harmonizes the entire plant operation to achieve the production goals. The scheduling of batch plants is challenging, especially for pipeless batch plants where the plant layout has to be considered as well. Many researchers addressing these issues use the Mixed Integer Linear Programming (MILP) approach, where an elaborate mathematical model is required to describe a problem. Kondili et al. (1993) suggested a general algorithm for short-term batch scheduling formulated in MILP using a discrete time representation. Pantelides et al (1995) presented a systematic and rigorous approach for short-term scheduling of pipeless batch plants. However, as the complexity of a plant increases, scheduling problems become harder to formulate in MELP. Constraint Satisfaction Technique (CST) has been used to solve problems ranging from design to scheduling. CST does not require elaborate mathematical formulae but requires a problem to be stated in terms of its constraints. Das et al (1998) investigated a simple but typical production scheduling problem and found it is possible to develop CST-based scheduling solution within very modest computation time. Huang and Chung (1999) developed a constraint model to represent a common class of traditional batch plant scheduling problems and a simple scheduling system. Batch Processing Scheduler (BPS) was produced based on this model. Das et al (2000) compared the approach developed by Huang and Chung (1999) with established mathematical programming approaches and concluded that it is relatively easy to represent complicated batch plant scheduling problems by using the constraint-based approach. Huang and Chung (2000) proposed a constraint model to represent scheduling problems in pipeless batch plants and improved the scheduling system BPS accordingly. Unexpected events, such as the failure of a processing unit, sometimes happen during plant operations. These events will make the original schedule invalid. To avoid risk and to utilise the remaining resource, it is important to reschedule the production operations quickly. However, few papers have reported on the investigation on rescheduling of chemical batch plants. Ko et al (1999) proposed a rescheduling approach for pipeless

162 plants. Their system can overcome unexpected events by adjusting the starting time of reactions and re-determining the sequence of equipment to be processed. Although the paper took plant layout into account, transportation time was ignored, which means the generated schedule would not be feasible in practice. This paper reports on the rescheduling capability as an extension to BPS. The extended constraint model can be applied to solve rescheduling problems for both traditional and pipeless batch plants, where the transfer time between stations is considered.

2. Constraint Model For Rescheduling 2.1. A typical pipeless plant process The constraint model for rescheduling is described with the help of a typical pipeless plant process. The production process is shown in Fig. 1. Circles and rectangles denote states and jobs respectively. The process starts with clean vessels being charged with A and B in an appropriate amount. The charged vessels are then taken to a blender, where the content is homogenized in a blending operation to form material AB. Following this, AB reacts with a third raw material C to form another intermediate material. Int.. Three final products PI, P2 and P3 are formed by blending Int. with three different additives Al, A2 and A3 respectively. The corresponding products PI, P2 and P3 are discharged through a discharge station and the empty dirty vessels must be cleaned before they can be used again. Finally, the clean vessels must move back to the start point waiting for A to be charged. The plant layout is shown in Fig. 2.

Blended AB in vessel

Empty dirty vessel Fig. 1: Production processes of a pipeless batch plant

2.2. Rescheduling constraints Unexpected events can be formulated as additional constraints on the original problem. The goal of rescheduling a problem must is to find a feasible solution so that what has been done before the failure cannot be changed and the breakdown resource cannot be used during its down time. In order to achieve this the failed resource is allocated to a "breakdown" activity in BPS.

163 BA^F,^ STiBA) = Ts md ET(BA) = T,

(1)

Where BA and Fj. represent a "breakdown" activity and the failed resource respectively. Ts and T^ represent the start and end time of the failure period of the breakdown resource respectively. The above formulae show that the failed resource is allocated to the "breakdown" activity to ensure that other jobs cannot use it. Its start and end time {ST and ET) are equal to T^ and T^ respectively. If ET(Jd < ST(BA) then ST\Jd = ST(Jd, ET\Jd = ET{Jd and Sp{Jd = Sp(Jd

(2)

This formula means that if in an original solution a job ended before T^, which is equal to the start time of the "breakdown" activity introduced in rescheduling the problem, the start and end time of the job as well as the selected resource will remain unchanged. ST*(J{) and ET*{J{) represents the job's corresponding start and end time respectively, and ^p* represents the corresponding resource in the rescheduled solution. Essentially, the above constraints "freeze" the part of the original schedule that has already happened. If Then

ST{BA) < ET{Ji) < ET{BA) either (BA) < ST\J{) & ST\Jd = TV^, or J^ <- S^

(3)

Where Ji represents a job that required the failed resource and ended after T^ but ended before T^ in the original scheduling solution. This formula means that in the rescheduled solution, either the job is delayed to start after the failure period or the job selects another suitable resource if there is one. The decision is made by the system according to constraint propagation. If the job is delayed, the exact start time TVr will be determined by the system as well. 5q represents another suitable resource for the job. If Then

ET(BA)<ET{Jd {ST\jd = ST(Jd or

ST\J0

= TV^} and {Sp(Jd = Sp(Jd or J.^S^}

(4)

This formula means that if a job ended after T^ in the original solution, in the rescheduled solution either its start time remains unchanged or it is delayed, which is also possible. In the meantime either the selected resource will remain unchanged or the job selects another suitable one. These decisions are made by the system according to constraint propagation. After a problem is rescheduled, the makespan in the new solution is probably extended because some jobs that required the failed resource during the failure period in the original solution are delayed now. In order to avoid an arbitrary increase of the makespan during rescheduling, an upper bound on the makespan needs to be introduced. The upper bound is set as the original makespan plus the largest possible delay among those delayed jobs. There is a possibility that a delayed job just ended after (i.e. one unit time after) the start of failure period in the original solution and its duration is the largest one among all jobs, so the largest possible delay is the failure duration plus the job's duration minus one. M:<M, + {T,-T,) + D^a.-l

(5)

164 Where Ms* represents the current makespan for rescheduling and Ms represents the original makespan. Dmax represents the maximum duration among the jobs and {T^-T^ indicates the duration of the breakdown activity i.e. the failure period. The rescheduling optimal criterion is either to minimize makespan or to minimize the number of changes of the start time of all jobs compared with the original solution: If

ST\J^ = STiJO then Vi = 0 else V^ = 1

(6)

A^v=2V,

(7)

1=1

Mm(A^v) or Min(M,)

(8)

Where V^i is a binary variable that represents whether the start time of a job has changed. If the start time remains the same, then Vi is assigned to zero, otherwise it is assigned to one. A^v represents the total number of changes i.e. the sum of Vi. Min(N^) means to minimize the total number of changes and Min{M^ means to minimize the makespan.

3. Case Study The process described above is used as a case study to demonstrate the feasibility of the proposed model. The production demands are shown in Table 1 and the time is defined in terms of unit time, which is 0.1 hour, in the schedule. Eight processing stations of six distinct types are considered and the relevant details are shown in Table 3. The plant layout in Fig. 2 is used. The tracks between stations are divided into 11 segments, which are 8 vertical tracks (VO - V7) and 4 horizontal tracks (HO - H3). The moving time for a vessel to pass each track segment is 0.1 hour. Buffers (Bl - B4) are placed in the cross points where vessels can wait for the next track segment to become available. The information on failed resource is provided by the user as shown in Table 2. There are two rescheduling criteria in BPS: 1) minimize the total number of changes to the original schedule; 2) minimize the makespan. Chart 1 shows the optimal solution found given the criterion to minimize the makespan. It illustrates that time and resources are allocated properly considering the failure of Reactor 1. The failure period is shown by the shaded area. The Chart also indicates that Reactor 1 was not allocated to any jobs during the failure period. Compared with the original solution obtained (not shown here), what happened before the breakdown of Reactorl was unaffected. BPS also successfully obtained correct solutions when the criterion is to minimize the number of changes was used. Again, results are not shown here due to space limit. Table 1: The production demands. Products PI

P2 P3

Amounts (m') 20 20

10

Delivery time (unit) 180^^^^ 2 ^ 240^^

Suitable vessels V I , V2 V3 V I , V2

Table 2: Failed resource. Failed Resource Reactorl

Start of Failure (unit time) 30^^

End of Failure (unit time) 3gth

165 Table 3: Duration and suitable stations for each job.

Charge A Charge B Blend A+B Reaction Blend Additives + Int. Discharge Cleaning

Blenderl

Suitable Station Charger 1 Charger 2 Blender 1, Blender 2 Reactor 1, Reactor 2 Blender 1, Blender 2 Discharger Cleaner

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Blender

V4

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Reactor2

Fig. 2: The layout of a pipeless batch plant. 0 (Stations)

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Chart 1: The optimal solution by minimizing the makespan.

^^^•M^^J

166

4. Conclusion In this paper, a constraint model for rescheduling batch processing plants including pipeless plants is proposed. This research progress is achieved by adding rescheduling capability as an extension to Batch Processing Scheduler (BPS), in which unexpected events such as the failure of resource are treated as additional constraints and the problem will be rescheduled using the original solution as a guide. Essentially, the constraints "freeze" the part of the original schedule that has already happened and stop the failed resource being used during the breakdown period. The feasibility of the model has been demonstrated by a case study.

5. References Das, B.P., Shah, N. and Chung, P.W.H. 1998, "Off-line scheduling a simple chemical batch process production plan using the ILOG scheduler". Computers and Chemical Engineering, Vol. 22, pp. S947-S950. Das, B.P., Shah, N., Chung, P.W.H. and Huang, W. 2000, "Comparative Study of TimeBased and Activity-Based Production Scheduling", Hungarian Journal of Industrial Chemistry, Vol. 28, pp7-10, HU ISSN: 0133-0276. Huang, W. and Chung, P.W. 1999, "Scheduling of Multistage Multiproduct Chemical Batch Plants using a Constraint-Based Approach", Computers and Chemical Engineering, Vol. 23, ppS522-S514, ISSN 0098 1354. Huang, W. and P.W.H. Chung, 2000, "Scheduling of Pipeless Batch Plants Using Constraint Satisfaction Techniques", Computer and Chemical Engineering, Vol. 24, No. 2-7, pp377-383, ISSN: 0098-1354. Ko, Daeho, Seonghoon Na, II Moon and Min Oh, 1999, "Development of a Rescheduling System for the Optimal Operation of Pipeless Plants", Computer and Chemical Engineering, suppl. S523-S526. Kondili, E., Pantelides, C.C. and Sargent, R.W.H. 1993, "A General Algorithm for Short-Term Scheduling of Batch Operations - I. MILP Formulation", Computers Chem. Engng, Vol. 17, No. 2, pp. 211-277. Pantelides, C.C. and Realff, M.J. and Shah, N. 1995, "Short-Term Scheduling of Pipeless Batch Plants", Chemical Engineering Research and Design, Vol 73, NO.A4,431-444.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

167

Integrated MINLP Synthesis of Overall Process Flowsheets by a Combined Synthesis / Analysis Approach N. Irsic Bedenik\ B.Pahor^ and Z.Kravanja^ 1 Faculty of Chemistry and Chemical Engineering, University of Maribor P.O.Box 219, Maribor, SI - 2000 Slovenia e-mail: [email protected] and [email protected] 2 Sika, Ltd., Prevale 13, Trzin, SI - 1236, Slovenia

Abstract This paper describes an integrated MINLP synthesis of overall process schemes using a combined synthesis / analysis approach. The synthesis is carried out by a multilevelhierarchical MINLP optimization of the flexible superstructure, whilst the analysis is performed in an economic attainable region (EAR). The role of the MINLP synthesis step is to obtain a feasible and optimal process structure, and the role of the subsequent EAR analysis step is to verify the MINLP solution and to propose in the feedback loop, any profitable superstructure modifications for the next MINLP. The main objective of the integrated synthesis is to exploit interactions between the reactor network, separator network and the remaining part of the heat/energy integrated process scheme.

1. Introduction The concept by which a reaction/separation network is the kernel of a chemical plant in which other process units have to support, gives rise to the hierarchical strategy of process synthesis (Douglas, 1988). However, due to the many varied interactions between the subsystems, the only way to explore these interactions integrally is to perform simultaneous synthesis of the overall process schemes using the mathematical programming approach. The most efficient way to perform discrete and continuous decisions simultaneously is to apply mixed-integer nonlinear programming (MINLP). Even with the important advantages of this approach; e.g. optimality and feasibility of solution, the direct synthesis of overall process schemes by MINLP is still limited by small and medium size problems and its complexity. The most important deficiency of the superstructure approach is that the search for the optimal solution is within the reach of an abundance of proposed alternatives. On the other hand model complexity, nonlinearities and nonconvexities may give rise to poor optimal solution even when good quality alternatives are proposed in the superstructure. In order to upgrade the capabilities of the MINLP approach, a multilevel MINLP is applied which is combined with sequential analysis of intermediate MINLP solutions in order to propose a more and more profitable evolutionary superstructure. This paper presents an integrated methodology for MINLP process synthesis in an equation-oriented environment, which is upgraded by a sequential geometric analysis of the economic attainable region (EAR). This synthesis is performed within a systematic frame work of the multilevelhierarchical MINLP synthesis of the process schemes (Kravanja and Grossmann, 1997) from reactor network (Level 1) to reactor/separation network (Level 2) and, finally, to the overall heat integrated process scheme (Level 3). The combined MINLP synthesis and EAR analysis approach was first applied to the synthesis of pure reactor networks at

168 Level 1 (Pahor et al, 2000) and, more recently, to the synthesis of reactor/separator networks at Level 2 (Irsic Bedenik et al., 2001). Now it has been extended to synthesis of the overall process schemes at Level 3.

2. Combined Multilevel MINLP Synthesis and Economic Attainable Region Approach The main feature of the MINLP synthesis is to obtain appropriate trade-offs between continuous/discrete cost decisions, whilst the main feature of the attainable region (AR) technique is to identify an optimal reactor network structure by which the maximal conversion, selectivity, yield, etc. can be achieved. The drawback of the MINLP is that it can converge to a poor local optimal solution and the drawback of the geometric AR approach is to that it is limited to 2-D or at most 3-D problems. The main idea of the combined MINLP/AR approach is to upgrade the capabilities of both approaches: the MINLP synthesis is thus performed to obtain appropriate economical trade-offs of multi-D problems and analysis in the AR is carried out to prescreen the solution space, to verify the optimal MINLP solution and, if there exists any extension to the optimal MINLP solution, to propose profitable modifications to the superstructure. In this way a flexible concept of compact superstructures is introduced which enables the solution of synthesis problem areas and to obtain superior solutions. Since the conventional AR is constructed in the concentration space using already mentioned technological criteria, it does not directly reflect process economics and, consequently, the obtained solutions may lie far from the true economic trade-off solution. The same criterion is used in both steps in order to restore consistency in the synthesis and analysis steps. Economic, rather than technological, criterion is used to define the objective function in the MINLP step and, therefore, the conventional attainable region was modified and transformed into an economic one by constructing 2-D projections in economical, rather than concentrated, spaces. Beside the reaction rate vector R(x) which is used to construct a concentration attainable region (CAR), the economic objective function from the MINLP model is now used to transform the CAR into the economic attainable region (EAR). E.g., the profit function:

PiRix)) = Z(c-/^;)-Cp-Z(^;"-^r)-c, p

(1)

peprod ^^ heat

-0

^ heat

-C

^ ^ cool

- 0

^ cool

C

T/- ret

-V

^ ret

C

X ' ^ sep

~ Z^^i

^ HEN

~^

gives rise to 2-D EAR projection of the annual profit produced vs. retention time along the reactor network and molar profit function: P''{R{x)) = P/F^,^^^

(2)

gives rise to 2-D EAR projection of the profit per mol of product produced (P^ in $/mol) vs. flow rate of desired product produced along the reactor network (Fp^desked)- The former EAR is more suitable for direct verification of MINLP solution in the AR and the latter one is more suitable for analysis of the MINLP solution to propose profitable modifications to the superstructure. It should be mentioned that many other useful 2-D projections can be generated. In this way, the conventional trajectories in CAR are now modified to reflect the economic performance of the system: at Level 1 the trajectories reflect the economic performance of the reactor network (reactor efficiency curves), at Level 2 they reflect the mutual performance of the reactor/separator network

169 (reactor/separator efficiency curves) whilst now at Level 3 they resemble complete efficiency curves and reflect the economic performance of the overall process. Level 3 is thus an integrated synthesis of the entire chemical process based on information from Level 2. A combined approach is performed until the analysis in EAR suggests no profitable extensions. The DAE formulation of the process models is exact and it's integration into the process superstructure is relatively easy. The combined MINLP synthesis and EAR analysis approach introduces a certain degree of flexibility and adaptability to the modular flowsheet superstructure which, in this way, becomes more compact so that MINLP synthesis can be performed more simply. This in turn favours simpler, and hence, more realistic process flowsheets, where economy of scale, connectivity, and heat integration can be appropriately accounted for in the selected units. The multilevel MINLP synthesis and EAR analysis approach, is implemented in the MIPSYN (Mixed-Integer Process Synthesizer) computer package and the analysis in the EAR in the MATHCAD 2000 Professional. •1 —|»<2>K>«0 FEED-2 - < ) - * 0

1:

Legend for

interconnection

nodes

n

SINaE CHOICE STREAM SPLITTER

O

MULTIPLE CHOICE STREAM SPLITTER

O

SINGLE CHOICE STREAM MIXER

O

MULTIPLE CHOICE STREAM MIXER

Figure 1: Reactor /separator general superstructure. The multilevel MINLP/EAR is thus performed hierarchically by the following 3-level scheme: Start: General reactor network superstructure (Fig. 1) Level 1 - Reactor network synthesis: MINLP with detailed reactor and very simple separator models with a simultaneous heat integration model (Duran and Grossmann, 1986). EAR - proposes profitable reactor/separation superstructure. Level 2 - Reactor/separator network synthesis: MINLP with detailed reactor and detailed separator models or statistical separator model based on rigorous simulation, Duran's model for simultaneous heat integration to identify process hot and cold streams. EAR - proposes final compact superstructure with only the most attractive alternatives. Level 3 - Reactor/separator/HEN synthesis: Detailed reactor and detailed separator model, modified model for the simultaneous synthesis of heat integrated HEN (Yee and Grossmann, 1990). Stop: When the analysis in EAR suggests no profitable extensions.

3. Case Study A case study of allyl chloride production described in Pahor et al. (2001) is taken to demonstrate the multilevel MINLP/EAR approach. Two consecutive reactions are

170 A + C I 2 — ^ B +HCI (principal one) and B4-CI2 —^^^^C + HCland one parallel reaction A + CI2 —'^^—> D (A propene, B allyl chloride, C 1,3 - dichloro propene, D 1,2 -dichloropropane;ki,o= 1.5 • 10"^ s"\ k2,o = 4.4-10^ s'\ k3,o= 100 lmor^s'\ and Ex = 66 271J/mol, £2 = 99 410 J/mol, £3 = 33 140 J/mol). The reaction rate vector R(x) for components A, B, C, D and CI2 is: (3) ^ 2 ^ B ' ^Cl »

^ 3 ^ A • ^Cl » ~ ^ l ^ A ' ^Cl ~ ^ 2 ^ B ' ^Cl ~ ^ 3 ^ A ' ^Cl J

The objective is to maximize annual profit at a fixed production of allyl chloride (7.560 mol/s). 3.1 Level 1: Reactor network synthesis The general reactor network superstructure was first used without intermediate separation and with ad hoc cost for the final separation. The profit was 17.154 M$/a with one PFR. Analysis in the EAR (Fig. 2a) shows that the actual PFR trajectory is significantly below the horizontal boundary of the AR which would be obtained when CB is kept zero. This observation indicates that additional profit can be gained if suitable intermediate separation of B can be found. When the MINLP synthesis was performed with intermediate separation (IS) and no cost for IS was charged to the profit, the optimal topology resuhed in a set of three reactors, the first was PFR and the next two were recycle PFRs with a profit of 18.773 M$/a. The analysis in the EAR (Fig. 2b) shows reactor trajectories at higher molar profit.

0.756

1.51

2.27

3.02

3.78

4.54

5.29

6.05

6.80 7.56

Molar flow rate of component B (mol/L)

Figure 2a: Reactor trajectory without IS.

434

5.»

t.MI

7Si

Molar flow rate of component B (mol/L)

Figure 2b: Reactor trajectories with IS.

3.2 Level 2: Reactor/separator network synthesis MINLP was repeated with a more detailed statistical separation model and separation cost based on rigorous simulation. The solution without IS of allyl chloride yielded a profit of 19.109 M$/a gained in one PFR. When the solution was analysed in the EAR all IS ahematives was found to be unattractive (Fig 3a). The only possible improvement could be achieved on the final separation. Six final separation alternatives (FS) were analysed in the EAR (Fig. 3b) to suggest new superstructure. The new superstructure comprised one PFR, no IS and the best four final separation alternatives. The optimal MINLP solution yielded a profit of 20.079 M$/a and the alternative with the least expensive condensation of propene was selected for the final superstructure.

171 0.0920

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SS" 0.0903 0 ~" —

>%

5 0.0839 u •O 0.0812

^^^^^-^^^:^:^'~^'^^^

O- 0.0785 e •3 0.0758

au 0.0731

-

•

-

.

_

.

_

19 109 S 18 935 ^ 18 456*5 18 310 >-

^

Legend: No IS IS is prefractionation with inert component 2 0.0677 IS is prefractionation with flash 0k - • - IS is conventional prefractionation 0.0650 0.75 1.51 2.27 3.02 3.78 4.54 5.29 6.05 6.80 7.56 Molar flow rate of component B (moi/s)

^

0.0704

Figure 3a: Reactor/intermediate separator trajectories.

VI

-^ 0.0886 n ts ,g 2 0. 0 Z, 0

0.0869 0.0852 0.0835 0.0818

" " * • " ' • " •

—

— •—.. ^

" ' •

in

""""'""* — — -.

aZ 0.0801

20 079 19 896 ' ^ 19 6 7 1 ^ 19 350 ^ C 18 899 2 18 467

e«

?" 0.0784

aS

0.0767 0.0750

0.75 1.51 2.27 3.02 3.78 4.54 5.29 6.05 6.80 Molar flow rate of component B (mol/s)

Figure 3b: Reactor/final separator trajectories.

3.3 Level 3: Reactor/separator/HEN network synthesis More detailed heat integration with different utilities (cold water, refrigerator, steam), restrictions and forbidden matches was carried out simultaneously with the synthesis of the reactor/separator/HEN network. Reactors were modelled as adiabatic reactors due to practical constraints. 0.0820 Without heat integration: The MINLP c.=0 0.0813 was first performed in one PFR as "o 0.0806 suggested at Level 2 and the solution ^ 0.0799 ^ 0.0792 yielded a profit of 17.791 M$/a. The 2 0.0785 selectivity of allyl chloride production a .:f"-N. u 0.0778 with respect to the consumption of CI2 is "o 0.0771 very low (Table la) not only because the 0.0764 0.0757 number of passes of propene through the 0.0750 "0 0.756 iM 2J7 3^2^jr^.54 5.29 6.05^780 7.56 rcactor is Small due to very high H MIPSYN 1

0t

Molar flow rate of component B (mol/L)

Figure 4a: Reactor/separator trajectory without heat integration.

COUSUmptioU o f U t i l i t i e s b u t alsO bcCaUSC

of the very wide temperature range in the reactor. (See the rapid decrease of the molar profit in Fig. 4a.)

Simultaneous heat integration: The MINLP was repeated for reactors with a side feed stream in order to decrease the temperature range in the reactor. The profit was increased to 20.393 M$/a by a two PFR with a side cold shot. The selectivity significantly increased (from 0.81 to 0.95). Table 1: MINLP solutions at Level 3. Option Without heat integration Profit, M$/a 17.791 HU, M$/a 0.221 CU, M$/a 0.271 HEN, M$/a / Selectivity 0.81 5.24 N° passes IPFR Topology

Heat integration 20.393 0 0.262 / 0.95 8.44 2 PFR, side feed

Simultaneous HEN synthesis 20.103 0.011 0.250 0.240 0.89 8.40 IPFR

172 Simultaneous HEN synthesis: The MINLP synthesis was carried out by the use of a onestage synthesis model for HEN (Modification of Yee's model) with 5 hot streams(2 segments for one non-isothermal process stream, 2 hot isothermal process streams, one hot utility stream - steam) and 9 cold streams (4 segments for two non-isothermal process streams, 3 isothermal process streams and 2 cold utilities - cold water and refrigerator). The profit obtained in the 23'^ MINLP iteration was 20.103 M$/a and the molar profit in the EAR (Fig.4b) was significantly increased compared to that of the non-integrated solution. It is interesting that the optimal topology (Fig. 5) comprises only one PFR without the side cold feed in order to increase the temperature driving force in HEN. The selectivity was decreased to 0.89 (Table Ic) and 240 k$/ a of investment cost for HEN was charged to the profit.

0.756

1.51

2.27 3.02 3.78 4.54

5.29 6.05

6.80 7.56

Molar flow rate of component B (moI/L)

Figure 4b: Reactor/separator/ HEN trajectory.

T^< Figure 5: Optimal structure of the reactor/separator/HEN network.

4. Conclusions The main advantage of the integrated synthesis approach is to obtain appropriate tradeoffs between product income and raw materials, and operating and investment costs. In this way, any particular improvement in any process subsystem can have a synergistic effect on any improvement to the others, e.g. processes which recycle any increase of reactor efficiency, reduction of separation costs or integration of heat or energy not only directly increase the profit, but can significantly reduce the consumption of raw material, too. One the other hand neglecting parts of the process cost, e.g. HEN cost, overestimates the profit not only because the cost are not subtracted from the profit but because the reactor efficiency and, hence, the income is overestimated, too. It should be noted that the synthesis by the hierarchical multilevel MINLP/EAR approach is guided by engineering creativity which may give rise to new innovative design solutions.

5. References Douglas, J.M., 1988, McGraw-Hill, New York. Kravanja, Z. & Grossmann, I. E., 1997, Comp. Chem. Engng, 21, S421-S426. Pahor, B., Irsic N., & Kravanja Z., 2000, Comp. Chem. Engng, 24, 1403-1408. Irsic Bedenik, N., Pahor, B. & Kravanja, Z., 2001, Supplementary proceedings of ESCAPE-11, CAPEC, Denmark, 59-64. Duran, M.A., & Grossmann, I.E., 1986, AIChE J, 32, 123-138. Yee, T. F., & Grossmann, I. E., 1990, Computers chem. Engng, 14,1165.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

173

Computer Aided Design of Sty rene Batch Suspension Polymerization Reactors C. Kotoulas, P. Pladis, E. Papadopoulos and C. Kiparissides Department of Chemical Engineering & Chemical Process Engineering Research Institute, Aristotle University of Thessaloniki, P.O. Box 472, 540 06, Greece

Abstract The present paper deals with the development of a comprehensive CAD tool for a styrene free-radical batch suspension polymerization reactor. The gPROMS© simulation platform is employed for describing the dynamic behavior of the batch polymerization system. The kinetic model accounts for both thermal and chemical initiation mechanisms, thus, the model can be employed over an extended range of polymerization temperatures. A generalized free-volume model is derived to account for diffusion-controlled reactions (e.g., termination, propagation and chemical initiation). The overall reactor model includes also appropriate dynamic energy balances for the reaction medium and the coolant in the reactor jacket. An equation of state model is employed to calculate the concentration of the various species (e.g., monomer, solvent, H2O) in the various phases present in the reactor. A Windows^^ user-friendly interface, based on DELPHI progranmiing language, has been developed to link the gPROMS model with the input file containing the necessary design and reactor operating data. It is shown that the model can successfully simulate the operation of batch styrene suspension polymerization reactors, and predict the polymerization rate, temperature, pressure and molecular weight distribution of polystyrene.

1. Introduction Polystyrene (PS) is a commercially important thermoplastic, mainly produced by both bulk and suspension free-radical polymerization. The bulk polymerization of styrene is difficult to control and, thus, is being replaced by the suspension process, which produces PS in the form of white granules. In the presence of volatile hydrocarbons (C4 - C6), foamable PS beads can be produced by the suspension process. At low temperatures (e.g., < 100 *^C), the free-radical polymerization of styrene is commonly carried out in the presence of chemical initiators (e.g., azo compounds and peroxides). At higher temperatures (e.g., 100 - 200 °C), the polymerization of styrene can readily proceed via thermal initiation. The main advantage of thermal polymerization of styrene is that pure PS of desirable molecular weight can be produced by simply varying the polymerization temperature. However, formation of low molecular oligomers and close control of the polymerization temperature are the two disadvantages of the thermal polymerization process. Based on the original developments of Mayo (1968) and the later work of Pryor and Coco (1970) regarding the thermal initiation mechanism of styrene, a comprehensive kinetic mechanism was developed to describe the combined thermal and chemical free-radical polymerization of styrene. A key difference between the present work and previous modelling approaches is the use of a comprehensive

174 thermal initiation mechanism, as well as the use of dynamic molar balances for all species related to the formation of 'live' radicals. The complete polymerization model was build in gPROMS© (an equation-based modelling environment) following an open-system architecture. The final model consists of several modelling elements including a comprehensive kinetic model, a thermodynamic model used for equilibria calculations, a gel-glass effect model, etc.). A Microsoft® Windows™ based interface developed in Borland® Delphi™, is used for: (i) the input of process data and model-related parameters, (ii) the selection/editing/storage of the appropriate modelling components, (iii) the construction of the overall model, (iv) the simulation, and (v) the processing of the simulation results.

2. The Batch Suspension Polymerization Process The batch suspension polymerization system considered in the present study, is schematically shown in Figure 1. It consists of a well mixed jacketed vessel. In the suspension polymerization process, liquid styrene is dispersed in the continuous aqueous phase by the combined action of stirring and the use of suspending agents. The reaction takes place in the monomer droplets. For modelling purposes, each droplet can be treated as a small batch bulk polymerization reactor. The heat of polymerization is transferred from the dispersed droplets to the aqueous phase and then to the coolant flowing through the reactor's jacket. Gas Phase:

Monomer and Pentane Fig. 1: Batch suspension polymerization

Suspending medium reactor.

A cascade control system consisting of a master PID and two slave PI controllers was employed to maintain the polymerization temperature within ±0.1 °C of the setpoint value by manipulating the cold and hot water flowrates to the reactor jacket. The master controller monitors the reaction temperature and its output drives the setpoint of the slave controller. The latter monitors the outlet temperature of the jacket fluid and drives the two separate control valves. For the accurate prediction of the reactor pressure with respect to time under both isobaric and nonisobaric conditions, a detailed account of monomer distribution in the various phases is required. In the suspension styrene polymerization process, three

175 different phases can exist, namely, the vapor, the aqueous and the organic phase. During polymerization, the three phases are assumed to be in equilibrium. The fugacities of styrene and pentane in the gas phase are calculated using the Soave-Redlich-Kwong Equation of State (EOS), whereas the corresponding activities in the polymer phase are calculated using the Flory-Huggins equation.

3. The Polymerization Kinetic Mechanism A comprehensive kinetic mechanism is proposed to describe the combined chemical and thermal free-radical polymerization of styrene. Thus, besides the commonly employed reactions (e.g., chemical initiation, propagation and termination), thermal initiation and chain transfer to monomer and to Diels-Alder adduct reactions are included. In particular, the so-called AH thermal initiation mechanism of Mayo comprises a reversible Diels-Alder dimerization of styrene to form 1-phenyl-1,2,3,9tetrahydronaphtalene (AH), the formation of a styryl (M) and a 1-phenyltetralyl radical \A) via the reaction of AH with monomer, the initiation of new polymer chains and the formation of "dead" trimers via the reaction of AH with styrene. Assuming that the quasi-steady approximation for the concentration of the intermediate species, AH, holds true, one can derive a second- or third-order initiation rate model with respect to the styrene concentration, depending on the reaction step that is considered to be the dominant one in the thermal initiation mechanism (Hui and Hamielec, 1972, p.749). To our knowledge this is the first attempt to model the combined chemical and thermal initiation of styrene without the application of quasi-state approximation for all the intermediate thermal initiation species. In summary, the postulated free-radical polymerization mechanism of styrene includes the elementary reactions presented in Table 1 (Kotoulas et al). In the kinetic scheme, the symbols /, R' and M denote the initiator, primary radicals and monomer molecules, respectively. The symbols R^ and Dn identify the respective "live" and "dead" polymer chains of length n. Table 1: Comprehensive Kinetic Mechanism for Styrene Polymerization. '

Chemical Chain Initiation:

Propagation:

I ^^ )2R* R ' + M *"' )Ri

R„+M-^^^R„,,

Thermal Chain Initiation:

Chain Transfer to Monomer:

2^^C$(^) 1

R^+M

Ph

1

•

AH+M—!^ riT J(A)+ ^^/^>.J/^ Ph

•f^

nW K^

^^ >Ri+Dn

Chain Transfer adduct:

R„+AH

to

Diels-Alder

^^^ >Dn+A

A + M-J^^->R3 Termination by Combination:

AH + M

^' ) trimers

R„+R,-^^^D„„

176 The method of moments is employed to calculate the variation of the leading moments of the number chain length distributions of "dead" and "live" polymerization chains with time. The cumulative molecular weight distribution of the polymer is calculated as a weighted sum of all the "instantaneous" weight chain length distributions produced during a batch run. At low to moderate monomer conversions or/and at high temperatures, the polydispersity index of the polystyrene (i.e., P.D = M^/Mn) will be low (e.g., P.D < 2) and the 'instantaneous' weight chain length distribution (WCLD) will follow the two-parameter Schulz-Flory distribution. Diffusion-controlled phenomena affecting the termination and propagation reactions, as well as the initiator efficiency (gel-, glass- and cage effect, respectively) are expressed in terms of a reaction-limited term and a diffusion-limited one (Keramopoulos and Kiparissides, 2002). The latter depends on the diffusion coefficients of the corresponding species (i.e., polymer and monomer) and an effective reaction radius.

4. Windows based gPROMS Application The model for the batch suspension polymerization reactor was developed using in the gPROMS© simulator. A windows based interface developed in Delphi programming language was employed to build, modify and run the reactor model. The model can predict the monomer conversion, initiator(s) and blow agent (pentane) concentrations, polymerization rate, molecular weight distribution of polystyrene, external jacket inlet/outlet temperatures, and the reactor temperature and pressure. The windows based application calls the gPROMS simulation engine in asynchronous mode, thus, allowing the real-time display of the simulation results. Some features of the application are: (i) storage, modification and retrieval of process operating conditions and parameters of the mathematical model, (ii) user defined gel/glass effect functions, (iii) user-defmed thermodynamic model for phase equilibria calculations, (iv) user-defined set-point policy for reactor temperature, (v) user-defmed initiator, pentane and water flowrates during the course of polymerization, (vi) run-time display of simulation results, (vii) generation of report files with gPROMS simulation activity and simulation results, and (viii) extended graphics output capabilities including comparison with experimental data and among different simulation runs. Major points of consideration in the software developments were the simulation speed, the user friendliness of the interface, and the capability of process model modification by the user. Several options are available for editing/modifying both the gel/glass/cage effect models and the EOS used for thermodynamic calculations. In fact, the user can introduce a completely new model, modify an existing relationship or/and import a user-supplied model in the form of a gPROMS Foreign Object.

5. Simulation Results The predictive capabilities of the new kinetic model were demonstrated by a direct comparison of model predictions with experimental measurements on monomer conversion, number and weight average molecular weights and molecular weight distribution. The polymerization was carried at different temperatures in a batch, bulk polymerization system. In the temperature range of 100 - 150 °C, a chemical initiator (e.g., Dicumyl Peroxide, DCP) was employed in combination with the thermal initiation of styrene. On the other hand, at higher temperatures (150 - 180 °C), the polymerization was initiated exclusively by the thermal initiation mechanism.

177 In Figures 2 and 3, experimental and model results on monomer conversion and number and weight average molecular weights are plotted with respect to the polymerization time at 100°C. The initial concentration of DCP was equal to 4,000 ppm. It is apparent that a very good agreement exists between model predictions and experimental results. Figure 4 shows a comparison between simulation results (continuous lines) and experimental data (discrete points) on monomer conversion at three different temperatures (e.g., 150, 160 and 170°C). The polymerization was carried out in the absence of a chemical initiator. As can be seen, for all reactor temperatures, there is close agreement between experimental conversion measurements and simulation results. In Figure 5, a comparison between model predictions and experimental GPC measurements on weight average molecular weight is shown.

1.0-

0.8-

•/

.2 0.6-

1 O

•/^

0.4-

0.2-

• 9^ Time (min)

Fig. 2: Predicted and experimental Fig. 3: Predicted and experimental conversion-time histories (T =100 ^ C, [IQ] average molecular weights (T =100 ^C, = 4,000ppm DCP). [lol = 4,000ppm DCP).

1.0^.-—S-

^ "X-^^^^^^^^—

0.8-

a

c

.2 2 5 >

•/

y

0.6-

8 i

• 0.2•

D T = 150°C 1 • Tsieo'c * T = 170*'C 1

0.0-1

1 Monomer Conversion

Fig. 4: Predicted and experimental conversion-time histories for thermal polymerization (T = 150 - 17(fC).

Fig. 5: Predicted and experimental weight average molecular weights (T = 150-

i7orc).

In general, very good agreement is observed at all reactor temperatures. It is important to point out that weight average molecular weights, exhibit a characteristic decrease with monomer conversion as it has been reported in the literature. This due to the chain transfer to adduct (AH) reaction.

178

1.0-

1 "o a. •5 c

1 iS

0.8-

Conversion • 21.4% O 56.8 % • 71.2% D 100%

k\

0.6-

f^\ d'' \

PS

0.4-

u.

s 1

0.20.0-

M^

°5.\

^^:

'^^fer^

Molecular Weight

Fig. 6: Predicted and experimental molecular weight distributions at different conversion levels. Finally in Figure 6, model predictions are compared with Experimental GPC measurements on molecular weight distributions at 130°C. Simulation results and the corresponding experimental distributions are plotted at four different conversion levels. It must be noticed that the molecular weight distributions are scaled with respect to monomer conversion. Apparently, the calculated molecular weight distributions are in excellent agreement with the GPC measurements over the whole conversion range.

6. Conclusions A batch suspension polymerization reactor model has been developed in gPROMS, including a comprehensive kinetic mechanism for the combined chemical and thermal polymerization of styrene, a generalized model for the prediction of gel/glass effect, molar species and energy balances for the reactor/jacket and the dynamics of the reactor controllers. The predictive capabilities of the proposed model were demonstrated by the successful simulation of experimental data on styrene conversion, number and weight average molecular weights and molecular weight distributions, over a wide range of temperatures. The gBA can be used as a tool to speed-up considerably the training of new engineers, carry out what-if scenarios for the production of new products and the optimization of temperature and/or initiator addition policies.

7. References gPROMS User Guide, 2002, Process Systems Enterprise Ltd. Hui, A.W. and Hamielec, A.E. 1972, J. App. Polym. Sci, 16,749. Keramopoulos, A. and Kiparissides, C. 2002, Macromolecules, 35,4155. Kotoulas, C., Krallis, A., Pladis, P. and Kiparissides, C. (submitted to Macromolecular Chemistry and Physics). Mayo, F.R., J. Amer. Chem. Soc. 1968,90,1289. Pryor, W.A. and Coco, J.H. 1970, Macromolecules, 3, 500.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

179

Waste Heat Integration Between Processes III: Mixed Integer Nonlinear Programming Model Anita Kovac Kralj and Peter Glavi^ Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova 17, Maribor, Slovenia Phone:+386 62 2294454 Fax:+386 62 2527 774 E-mail:[email protected]

Abstract The simultaneous heat and power integration between processes using mixed integer nonlinear progranmiing (MINLP) contains equations of structural and parametric optimization of the nonretrofitted or retrofitted plants. High pressure steam production and generation of electricity using a steam turbine are included in the integrated structure. MINLP can predict: the optimum energy target of the integration between processes, steam and electricity production. The approach has been illustrated by four complex processes (solvent production, formalin production, methanol production and oil refinery) using MINLP. The objective function have maximized the annual profit of heat and power integration to 303,2 kUSD/a.

1. Introduction Integration between processes can reduce waste heat. It can be performed either by pinch analysis or by mixed integer nonlinear progranmiing, MINLP. The pinch analysis does not guarantee the global optimal solution because it cannot be used simultaneously with material balances but it quickly proposes good integrated structures between nontrivial complex processes. Heat integration between processes was first introduced into the literature by Ahmad and Hui (1991). The paper describes a method that, considering an overall plant consisting of many processes, leads to ''total site integration" where heat recovery from one process to another occurs using their utilities. Rudman and Linnhoff (1986) included a turbine which reduced energy usage among the processes. Bagajewicz and Rodera (2000) developed targeting procedures for direct and indirect integration in the special case of many plants. A very popular MINLP algorithm (Biegler et al., 1997), which is based on the mathematical programming can be used for the integration between processes. Although simultaneous it is difficult to converge for complex and energy intensive processes because the number of variables increases with the number of combinations.

2. Waste Heat and Power Integration Between Processes The processes operating within one location can be mutually integrated. Energy consumption can be lowered, if more waste heat can be recovered. The heat transfer between the processes can reduce waste heat, CO2 and SO2 emissions and thereby pollution. We have extended the method of waste heat integration between processes with the simultaneous generation of electricity using the steam turbine (Kovac Kralj et al., 2002). The method for waste heat integration between processes is composed of three steps: 1. retrofit of individual processes (Kova^ Kralj et. al, 2000), 2. analysis of efficient heat transfer between nonretrofitted or retrofitted processes.

180 3. simultaneous integration between some nonretrofitted and some retrofitted existing processes using mixed integer nonlinear programming (MINLP). The integration between processes can be carried out by all the steps, or by the first and the third step or only by the last step depending on the complexity of the problems. All the steps can be carried out simultaneously and the MINLP algorithm applied with or without the first and the second step. The mathematical model is using the MINLP algorithm, performing the simultaneous heat integration between processes and generation of electricity. The MINLP model contains equations of structural and parametric optimization of the nonretrofitted or retrofitted plants. The high pressure steam production and generation of electricity using the steam turbine are included in the integrated structure. MINLP can predict: the optimum energy target of the integration between processes, steam and electricity production. The procedure does not guarantee a global cost optimum, but it does lead to good, perhaps near-optimum designs. 2.1. The steam turbine system The steam turbine system is a closed - cycle one. It is used to drive the process reducing steam pressure from high or medium pressure to low or atmospheric pressure. The design pressure of the high or medium pressure turbine can be varied. The power of the high or medium pressure turbine (Ptur) is a function of the pressure respectively or of the inlet (rtur,in) and outlet (Tiur.out) temperatures (a, b and c being constants): ^tur = ^tur + ^tur 'Ttm,m + ^tur *'' tur,out

(1)

The efficiency of the high or medium pressure turbine (//tur) is a quadratic function of the inlet (Ti^a,in) temperature: ^tur = ^ef + Kf -TturM + ^ef '(T^An)

(2)

The heat flow rate of the condenser (C^con) is a function of the inlet (rtur.in) and the outlet (T'tur.out) temperatures: ^con ~ ^con "^ ^con * ^ tur,m "^ Qon "^ tur,out

W/

The annual depreciation of the high or medium pressure turbine (Cd,tur in USD/a) is a function of the inlet {Ttar,m) temperature. The quadratic equations is composed of two equations (Biegler et al., 1997, pp. 688): Cd,tur = 925 0 9 0 - 4 2 7 2 -7^,^+ 5,09(7^^,^'

(4)

The annual depreciation of the high or medium pressure pump (Cd,pum in USD/a) is a function of the inlet (rtur,in) temperature (Biegler et al., 1997): Cd,pum = 368 + 7,5 'T^^]n

(5)

3. Case Study Four existing nonretrofitted processes: solvent production from a primary oil, formalin production from methanol and air, oil refinery (atmospheric distillation), low-pressure Lurgi methanol production, are operating within one location and, therefore, the method

181 of waste heat integration between them for steam and electricity production can be used. The MINLP model contains equations of structural and parametric optimization of the nonretrofitted or retrofitted plants. The MINLP model is based on the superstructure (Fig. 1). Hot and the cold process streams of the existing nonretrofitted processes (Kovac Kralj et al., 2002): solvent recovery (E204), the refinery (FG, E211, E210, S80), the formalin (ElO, E5, E6) and the methanol (ACl) or retrofitted methanol (SG) or retrofitted refinery (RS80) which are heated or cooled by utility, are included in the superstructure. The superstructure is including the integration between: the synthesis gas stream of the retrofitted methanol plant and the stream 80 of the existing nonretrofitted refinery (rMsG-Rs8o)» the synthesis gas stream of the retrofitted methanol plant and the stream ElO of the nonretrofitted formalin plant (rMsG-FEio)» the synthesis gas stream of the retrofitted methanol plant and the stream RS80 of the retrofitted refinery (rMsG-rRRS8o)» generation of electricity is using surplus heat in the retrofitted methanol plant (rMsG-TUR) and heat flow rate of condensers can be used for process heating in the nonretrofitted formalin plant (KI-FEIO and K2-FE5), the flue gas stream of the nonretrofitted refinery and the stream of the 37 bar steam production (RFG-P37), the flue gas stream of the nonretrofitted refinery and the stream 80 of the nonretrofitted refinery plant (RFG-RS8O)» the E211 stream of the nonretrofitted refinery and the stream E5 of the nonretrofitted formalin plant (RE2irFE5)» the E211 stream of the nonretrofitted refinery and the stream of water preparation for 37 bar steam (RE2irP37), the E211 stream of the nonretrofitted refinery and the stream E5 in split A of the nonretrofitted formalin plant (RE2irFE5A)» the E211 stream of the nonretrofitted refinery and the stream E6 of the nonretrofitted formalin plant (RE2II-FE6)» the ACl stream of the nonretrofitted methanol and the stream ElO of the nonretrofitted formalin plant (MACI-FEIO)» the E210 stream of the nonretrofitted refinery and the stream E204 of the nonretrofitted solvent plant (RE2IO-SE204) and the E210 stream of the nonretrofitted refinery and the stream E6 of the nonretrofitted formalin plant (RE2IO-FE6)The selected hot streams (/; / = SG, FG, E211, E210, ACl; / = 1,.. /) and cold streams (/; j = S80, P37, ElO, E5, E6, E204, RS80; j = 1, .. 7) are binary variables for possible splitting in structures A or B or C (yi/^, yt^, ytc, yjA, yjB, yjc) or D for the generation of electricity. The binary variables are determining the integration between processes. The redundant heat flow rate of the retrofitted methanol plant can be transferred to the nonretrofitted refinery CVSGA = yssoA = 1) or to the formalin process O^SGB = JEIOA = 1) or to the retrofitted refinery (JSGC = JRSSO = 1) or to generation of electricity O^SGD = }^tur =1)-

The heat of the flue gas can be used for the 37 bar steam production CVFGA = yp3i = 1) or for heating the nonretrofitted refinery stream (JFGB = yssoB =1)- The waste heat of stream E211 in the nonretrofitted refinery can heat the stream E5 and water for 37 bar steam production (yEiuA = >'E5B = yp3i = 1) or E5 and E6 streams of the formalin process CVE2IIB = JE5A = JE6A = 1)- The stream ACl of the existing methanol plant can be integrated with ElO of the formalin one O'ACI = >'EIOB = !)• The heat flow rate of E210 in the nonretrofitted refinery can be transferred to the formalin plant CVE2IOB = yE6B = 1) or to E204 of the solvent production process CyE2ioA = }^E204 = !)•

182 rMsr.-TUR 2096 k W i

875 °C K2-Fpj

. 14761 kW

83:

•

rMsG-Rs80

BOS kW

£)

821,3 °(I

synthesis g^

as split A

- J I — l _ r ) ytur , ^^^70^

rMsG-rRRSj retrofitted methanol

m

"HI-

70''C '

Bl

,^,^o^

3HB kW 2QZ2kW

3178 kW

^^^-^"C 0

I

2072 kW

369°C 0

1

313 °C

ysG 3178 kW 16427 kW K54,6°C ^Bl

875 °C existing refinery A 345,5^^ flue gas

o

RpG-Rs8(J

B

ypG

rMsG-Fmo 313 °C

P37 150 °C 220 °C

o o a o -P37

existing refinery

A

182,7 °C.

yE2ii

E211

B

existing methanol ACl

136 °C|

95 °C

%211-f E5A 136 °C\

110,7°C

P^ACI-FEIO

127,5

O

t

yAci

114 °C RE21irSE204 A ^ 130,8 °C

existing refinery 169,7 °d

A yE210

E210

RE2IO"FHS

134,6 °C

l ^ ^ 'S80A

. 4 existing refinery ' 175,4 °C stream 80

__>-<.

2096,2 kW

ys8o B

233,5 °C M ^S80A

246 °C

6

667,5 k\M

94,25 °C

<—

loc 94,18 °C^

55,1 °C I

•^ existing formalin

2072 kW

94 °C

1840,5 kW

ElO

X j i

II

\

U|^39,2k\7^39,2kW

1

I

53,3 °C E5

aa 75,3 kW 213 °C

'1664,6 kW

Fig. 1: Grid diagram of heat and power integration between the processes.

y^s

existing formalin 15 °C

75,3 kW

Or,

yEio

existing formalin

139,2tW^^

139,2kW,

114,6°C 358 °C

yp37

O

Q

1464,4 kW

^ElOB

37 bar steam production

32 °C

122 k\M

1040 ktV

94,22 °C

.54°C

o

99°(C

6

B

83,5 kW

yE6 E^ existing solvent 69,2 °C

yE204 E204 retrofit refmery yRsso RS80

183 The MINLP model is including the equations of structural and parameter optimization. The hot and cold streams can split to streams A or B or C or D for the generation of electricity: yiA-^yiB-^yic + yiD^i

/=i,.../

(6)

yjA-^yjB

j=l,.-J

(7)

+ yjc^^

The binary variables can influence the structural dependence. The 37 bar steam production is including the preparation of water (yp^i = yEiuA = !)• yFGA+ yp3i ^ 2 yFGA + }'E211A^2

(8) (9)

In integrating the retrofitted methanol with the nonretrofitted refinery (ysGA= >'S80A= 1) or the retrofitted one (JSGC = ^RSSO = 1) the furnace is not needed; therefore, there are no flue gas and 37 bar steam production (ypcA = JFGB = JSSOB = yp3i = yEiuA = 0): JSGA + ySGC + >^FGA ^^ 1 JSGA+^'SGC+yPGB^l ySGA + >'SGC + >'S80B ^ 1 JSGA+ySGC+JP37^ 1 >'SGA+ ySGC+ yE211A^ 1

(10) (11) (12) (13) (14)

The generation of electricity CVSGD) is including the condensation (ytur)* ysGD-ytm'^0

(15)

The MINLP model is using additional annual profit of heat and power integration criterions. The additional annual income of integration sums up the additional savings of: fuel, 5 bar steam, 8 bar steam, cooling water and 37 bar steam and electricity production. In the model the existing areas can be used (AHE,ex) by enlarging them with additional areas (AHE,add)- The additional annual depreciation of enlarged and new areas (AHE,new) of heat exchangers and pipings (Table 1), is multiplied by the payback multiplier (r = 0,2448) to obtain the maximum annual profit of heat and power integration: Max annual PROFIT = Cfuei-[^G-jFGA+^GB+^8o-}'s80A+^s80B ] + Q ' [ ^ 1 0 A + ^ 1 0 B + ^ 1 0 C +^5-tyE5A+ }'E5B+ ^'ESC) + ^6-CVE6A+3^E6B)] + Cg'^204-JE204 + Ccw[^E2irCVE211A+3^E211B) + ^ E 2 1 0 A + ^ E 2 1 0 B ] + Q i -Ptur'^tur

+ Qr^i

-[S(670.

AHE,add'''')-l,8 +1(8600+670. AHE,new'''')-l,8

- Cd,tur - Cd,pum - Cpip • ( S ( yi^A+ yi,B + yi,c) + ? ( J;,A+ }';,B+ >';,c) )]' r

(16)

The simultaneous heat and power integration as optimized by MINLP is selecting the generation of electricity using the high pressure turbine (40 bar with the efficiency of 82 %, 7;ir,in = 500 °C, T^^out = 125 °C, ptur,out = 2 bar ) and the boiler rMsG-TUR in the retrofitted methanol plant (VSGD = ytur= 1; grey heat exchanger in Fig.l). The condensers KI-FEIO and K2-FE5 are transfering total heat flow to the nonretrofitted formalin (y^^ = jEioc = ^Esc = 1 ) - The flue gas is integrated with the process stream in the nonretrofitted refinery process (JFGB = yssoB = 1; RFG-RSSO)- New or additional areas of heat exchangers are: rMsc-TUR (with 2096 kW) of 8,7 m ^ KI-FEIO (with 1464,4 kW, TKI out= 117,7 °C) of 85,7 m ^ K2-FE5 (with 139,2 kW) of 8,5 m\ RFG-RS8O (with 667,5 kW) of 57,5 m\ The

184 structure enables the generation of 496,6 kW of electricity and savings of 5 bar 1603,6 kW of steam and (2-667,5 kW) of fuel. The additional annual depreciation of: the high pressure turbine, pump, insulation piping, new and additional areas of heat exchanger are 176,8 kUSD/a. The additional annual income of electricity production, saving of fuel and 5 bar steam are 480 kUSD/a. The additional profit of the integration is estimated to be 303,2 kUSD/a. Table 1: Cost data for example processes. 4,

(8 600,0+670A^'^^)-3,6 17,06 4,17 2,95 2,60 0,40 4,43 2380,0

Installed costs of heat exchanger : Cost of electricity (Q/)**: Cost of 37 bar steam (Q7)**: Cost of 8 bar steam (Cg)*^: Cost of 5 bar steam (Cs)^: Cost of cooling water (Ccw)^Cost of fuel {Cfueif: Cost of insulation piping (Cpjp)^:

&

Ahmad; Tjoe and Linnhoff, i A=area in m Swaney;

USD USD/(GJ) USD/(GJ) USD/(GJ) USD/(GJ) USD/(GJ) USD/(GJ) USD

Perry, - Ciric and Floudas,

4. Conclusions We have extended the simultaneous integration method to exchange waste heat between the processes with the simultaneous generation of electricity using the steam turbine. Simultaneous heat and power integration between processes can be performed using the MINLP algorithm, in which alternatives of the heat transfer between several existing nonretrofitted or retrofitted processes can be included. We have carried out simultaneous heat and power integration of four existing, nontrivial plants. The objective function has maximized the annual profit to 303,2 kUSD/a.

5. References Ahmad, S. 1985. Heat exchanger networks: Cost tradeoffs in energy and capital. Ph. D. thesis. University of Manchester, Manchester, 113 -306. Ahmad, S. and Hui, C.W. 1991. Heat recovery between areas of integrity. Computers chem. Engng, 15, 809-832. Biegler, L.T., Grossmann, I.E. and Westerberg, A.W. 1997. Systematic methods of chemical process design. Prentice Hall PTR. Upper Saddle River New Jersey. Bagajewicz, M.J. and Rodera, H. 2000. Energy savings in the total site. Heat integration across many plants. Comput. chem. Engng 24, 1237 - 1242. Ciric, A.R and Floudas, C.A. 1989. A retrofit approach for heat exchanger networks. Comput. chem. Engng 13/6, 703-715. Kovac^ Kralj, A., GlaviC, P. and Kravanja, Z. 2000. Retrofit of complex and intensive processes II: stepwise simultaneous superstructural approach. Comput. chem. Engng 24/1, 125-138. Kovac Kralj, A., Glavic, P. and Krajnc, M. 2002. Waste heat integration between processes. Applied Thermal Engng 22, 1259-1269. Perry, R.H. 1974. Chemical engineer's handbook, McGraw-Hill, New York, 25-19. Rudman, A. and Linnhoff, B. 1995. Process integration: planning your total site. Chemical Technology Europe January/february. Swaney, R. 1989. Thermal integration of processes with heat engines and heat pumps. AIChE Journal 35/6, 1010. Tjoe, T.N. and Linnhoff, B. 1986. Using pinch tehnology for process retrofit. Chem. Engng. 28,47-60.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

185

Integration of Process Modelling and Life Cycle Inventory. Case Study: i-Pentane Purification Process from Naphtha L. Kulay^^\ L. Jimenez^^\ F. Castells^^\ R. Banares-Alcantara^^^ and G. A. Silva^*^ (1) Chem. Eng. Dept., University of Sao Paulo, Av. Prof. Luciano Gualberto tr.3 380, 05508-900 Sao Paulo, Brazil. E-mail: {luiz.kulay, gil.silva}@poli.usp.br (2) Chem. Eng. Dept., University Rovira i Virgili, Av. Paisos Catalans 26,43007 Tarragona, Spain. E-mail: {Ijimenez, fcastell, rbanares}@etseq.urv.es

Abstract A framework for the assessment of the environmental damage generated by a process chain and based on a life cycle approach is proposed. To implement it, a methodology based on the integration of process modelling and environmental damage assessment that considers all the processes of the life cycle was developed. This integration is achieved through an eco-matrix formed by eco-vectors containing the most relevant environmental loads. To verify the methodology, a case study on the deisopentaniser plant of REPSOL-YPF (Tarragona, Spain) has been carried out. The environmental profile of the alternative scenarios is improved when co-generation and heat recovery are considered.

1. Introduction Modern society demands a constant improvement on the quality of life. One of the actions of the administration is to guarantee a better environment. In this context, chemical process industries suffer an increasing pressure to operate cleaner processes. To achieve this goal, environmental aspects and the impact of emissions have to be considered in the design of any project using one of the procedures already developed [ISO, 1997]. Life Cycle Assessment (LCA) is the most common tool for the evaluation of the environmental impact of any industrial activity. The LCA is chain-oriented procedure that considers all aspects related to a product during its life cycle: from the extraction of the different raw materials to its final disposal as a waste, including its manufacture and use. According to ISO 14040 [ISO, 1997], LCA consists of four steps: goal and scope definition, inventory analysis, impact assessment and interpretation. The LCA identifies and quantifies the consumption of material and energy resources and the releases to air, water and soil based upon the Life Cycle Inventory (LCI). The procedure as it is applied to chemical processes has been previously described by Aelion et al. (1997). The results from the LCI are computed in terms of environmental impacts, which allow the establishment of the environmental profile of the process. For environmental assessment the application of potential impacts is restricted to the estimation of global impacts. For example, the amount of CO2 released is used as an indicator of climate change due to its global warming potential. One kilogram of CO2 generated by an industrial process in any of the different stages of a product life cycle

186 contributes equally to the climate change. However, this is not the case for sitedependant impacts, such as the potential impact of acidification measured as H"^ release. Unfortunately, the LCA does not accommodate for site-specific information of different process emissions. To include it, weighting factors across the system boundaries have to be selected, a task which is beyond the objective of this work [Sonneman et al., 2000]. For this reason, a methodology that includes environmental aspects in the analysis of processes has been developed. Applying the LCA perspective to different scenarios for electricity generation and steam production provides key information to decision makers at a managerial and/or political level.

2. Methodology This section describes a proposed methodology to evaluate the environmental impact of a chemical industrial process chain in the most accurate way possible. It includes a procedure to compute the LCI based on the concept of eco-vectors [Sonneman et al., 2000]. Each process stream (feed, product, intermediate or waste) has an associated ecovector whose elements are expressed as Environmental Loads (EL, e.g. SO2, NOx) per functional unit (ton of main product). All input eco-vectors, corresponding to material or energy streams, have to be distributed among the output streams of the process (or subsystem). In this sense, a balance of each EL of the eco-vector can be stated similarly to the mass-balance (inputi = outputi + generation,). This is the reason why all output streams are labelled as products or emissions. The eco-vector has negative elements for the pollutants contained in streams that are emissions and/or waste. Figure 1 illustrates these ideas for an example of a chain of three processes that produces a unique product. The proposed procedure associates inventory data with specific environmental impacts and helps to understand the effect of those impacts in human health, natural resources and the ecosystem.

3. Problem Statement The methodology has been applied to the debutaniser and depentaniser columns of a naphtha mixture processed in the REPSOL-YPF refinery (Tarragona, Spain). The process PFD is shown in Figure 2. The first column is fed with a naphtha stream rich in C4 (= 28.3 tonh"^). This unit is a debutaniser and removes n-butane and lighter components (= 0.50 tonh"*). Perfect separation is not achieved since capital investment must be balanced against operating costs to arrive at an acceptable economic payout. As a result, it is more convenient to think of the debutaniser as having a cut point between n-butane and i-pentane, which is removed as top product from the second column (= 16.3 tonh'^). The intermediate naphtha input stream (C5 rich-naphtha = 71.5 tonh'^) comes from another plant in the same refinery. Production under design conditions is 83.0 ton•h'^ Proper understanding of recovery in both columns can improve refinery economics, due to the downstream effects of light components. The plant has four heat exchangers, and two of them (HX-1 and HX-3) recover process heat. Both condensers are air cooled, and thus plant utilities are electricity and steam. The production of these two utilities consumes additional natural resources and generates additional releases to the environment, and thus they were included.

4. Results The LCI was computed using process simulation as a support tool. This approach is appropriate for both, the design of new processes and the optimisation of existing ones. The use of process simulators to obtain the LCI guarantees a robust approach that

187 allows LCA to exploit their advantages in terms of availability of information, and reduces the uncertainty associated with data in the early phases of design. However, we can expect that on a long-term perspective, relative and uncertain values are valid when comparing among alternatives. The models for the naphtha plant, the electricity generation, the steam production and the heat recovery system were developed using Hysys.Plant®, and were validated using plant data. To build accurate models for all alternatives is not practical, and thus the models were reused for the different alternatives considered. The key simulation results were transferred to a spreadsheet (Microsoft® Excel), through macros programmed in Visual Basic™. Despite the fact that emissions were produced at different locations (e.g. those related to its extraction, transport and refining), the eco-vector has a unique value for each stream, i.e. it does not considers site-dependant impacts. The eco-vectors associated to all the inputs and outputs of the process are computed per ton of product (i-pentane). The aspects included in the eco-vector were divided into two categories: > Generated waste: in air (CO2, SO2, NO^, and VOC; estimated as fugitive emissions), wastewater (chemical oxygen demand, COD) and solids wastes (particulate matter and solids).

Raw material

Process I

(^^A + \

J RM

Process 3

(soA

^ (^0^]

+

NO,

\

Process : 2 '

NO,

\

)1

CO^ NO,

+

J2

\

J3

-> Product

=

fsoA co^ NO,

\

J%CA

Figure 1. Life cycle inventory analysis according to the eco-vector principle. Econd D6-C4

HX_1

I

Econd De-iC5

De-C4

Figure 2. Simplified PFD of the REPSOL-YPF plant. >

Consumption of natural resources: depletion of fossil fuels (fuel-oil, gas-oil, carbon, natural gas and oil), consumption of electricity and water. The plant consumes medium-pressure steam, while electricity generation and steam

188 production may use high or low pressure steam. The eco-vectors that correspond to these streams are also considered. The environmental loads of the process inputs were retrieved from the ETH Report [Frischknecht et al., 1996] and the TEAM™ database [TEAM, 1998]. The use of different scenarios allows the comparison among alternatives. The scenarios were chosen based on the source of steam and the generation of electricity (Table 1). Three of them focus on the environmental impacts of the original process (scenarios VI, VII and VIII) where changes related to the production of steam were compared. All other cases compare alternatives for a possible future implementation, e.g. those considering co-generation to produce electricity. For each one of the scenarios the eco-vector was divided into the three different processes: steam production, electricity generation and naphtha plant. As an example, the eco-vectors of scenario III are shown in Table 2. The results indicate that: • To reduce the CO2 and the BOD we have to focus on the production of steam. For scenarios VI, VII and VIII the electricity generation has also a certain impact (^ 3 to 29%). • To decrease the SO2 changes should be made in the production of steam and/or in the generation of electricity (Figure 3). The scenarios that include cogeneration radically minimise this value. • NOx, VOC and solid wastes are produced completely by the generation of electricity. • H2O consumption is mainly due to steam production. As expected, heat integration allows the reduction of this amount by 91%. Results (Figure 4a) show that scenarios VII, VIII and, to some extent, scenario V concentrate most of the consumption of fossil fuels, while the best alternatives in terms of water consumption are scenarios III and IV. As expected, heat recovery has a great impact on the results of scenarios III, IV, VI and, to a lesser extent, scenario VIII. If cases III and VIII are compared, the impact of co-generation on ELs is easily detected. Concerning the consumption of natural resources, the best alternative is scenario III (cogeneration, downgrading of steam and heat recovery). In terms of atmospheric releases (Figure 4b), the best options are scenarios III and IV. On the contrary, the most significant impacts were observed in scenarios VII and VIII. Nevertheless, the releases of NOx, SO2 (scenario V) and VOC's (scenario VIII) must be highlighted. Table 1. Main characteristics of the scenarios considered.

I II III IV V VI VII VIII

Electricity generation Co-generation Co-generation Co-generation Co-generation Expansion of steam in a turbine Spanish energy grid Spanish energy grid Spanish energy grid

Steam production Generation of steam Expansion of steam Generation + heat recovery Expansion + heat recovery Fuel oil & fuel gas burning Fuel oil & fuel gas burning + heat recovery Fuel oil & fuel gas burning Generation + heat recovery

189 Table 2. Eco-vectors for scenario 111.

Natural gas/kg Water/kg Electricity/kW High pressure steam/kg Medium pressure steamykg Electricity/kW High pressure steam/kg Medium pressure steam/kg COz/kg SOa/kg NO,/kg VOC/kg Particulate matter/mg DQO/mg

• Steam production

Steam Electricity production generation Inputs 0. 1.410"' 0. 1.5-10' 0. 0. 0. 1.8-10-' 0. 0. Outputs 3.410"" 0. 1.810"' 0. 0. 1.810"' Atmospheric emissions ^ 0. 3.7-10"' 0. 0. 0. 0. 0. 0. 1.5-10" 0. 1.510" Liquid efluents 3.9-10"' 0.

Plant operation

Total /ton i-Cs

0. 1.510"' 3.4-10"^ 0. 1.810"'

1.410"' 3.0-10"' 3.4-10"^ 1.810"' 1.810-'

0. 0. 0.

3.4-10"'' 1.8-10"' 1.810"'

0. 0. 0. 0. 0.

3.7-10" 0. 0. 0. 1.510 1.510"

0.

3.910"'

I Electricity generation

Figure 3. Comparison of the SO2 generation, (a) Scenario VI; (b) Scenario VII; (c) Scenario VIII. With respect to wastewater generation, there are a few scenarios with low impact (III, IV, VI and VIII) while the rest exhibit very similar values. If all aspects are analysed simultaneously, the best alternatives are scenarios III and IV, while the worst one is scenario VII. It is noteworthy to say that all environmental loads considered in the ecovector have to be balanced to reach a compromise, as their impacts in the ecosystem and human health differ widely. Also, note that some of the impacts are local (e.g. steam production), while others are distributed in different regions (e.g. extraction, external electricity generation) even though the LCA approach does not allow to differentiate among them.

190

I

n

m

IV

V

VI

B Natural gas

H Fuel oil

BFuelgas

QOil

a Water

D Electricity

vn

vffl

• Carbon

I

n

in

IV

V

VI

IZ1C02

BS02

• NOx

0 Particulate

^QOD

• Sobd wastes

vn

Vffl

HVOC

Figures 4a and 4b. Percentage of the impact on different Environmental Loads for each scenario, (a) Raw materials consumed; (b) Emissions.

5. Conclusions Significant progress in the integration of environmental aspects with technical and economic criteria has been achieved to date, although limitations still exist due to the uncertainty of the available data. The proposed methodology shows that the use of process simulators to obtain the LCI guarantees a robust approach. Furthermore, the methodology provides valuable information to compare alternatives for future implementation by assessing and preventing environmental impacts. This study will be extended with the application of models to predict the damage on human health, natural resources and the ecosystem. For the case study two different types of environmental profile can be identified (scenarios I-IV and scenarios V-VIII). The use of co-generation to produce electricity decreases the total damage, as its relative impact is lower than the one resulting from the use of the Spanish electricity grid.

6. References Aelion, V., Castells, F. and Veroutis, A., 1995, Life cycle inventory analysis of chemical processes. Environ. Prog., 14 (3), 193-195. Frischknecht, R., Bollens., U., Bosshart, S. and Ciot, M., 1996, ETH report, Zurich, Switzerland. ISO 14040, 1997, Environmental management. Life cycle assessment. Principles and framework, ISO, Geneve, Switzerland. Sonnemann, G.W., Schuhmacher, M. and Castells, F., 2000, Framework for environmental assessment of an industrial process chain, J. Haz. Mat., 77, 9 1 106. TEAM®, 1998, Ecobilan Group, Paris, France.

7. Acknowledgements One of the authors (L. Kulay) wishes to thank CAPES (Ministry of Education of Brazil) for the financial support. We also acknowledge the cooperation of REPSOL-YPF, and Hyprotech (now part of Aspentech) for the use of an academic license of Hysys.Plant®.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

191

Superstructure Optimization of the Olefin Separation Process Sangbum Lee, Jeffery S. Logsdon*, Michael J. Foral*, and Ignacio E. Grossmann Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA15213, USA;*BP, Naperville, IL60563, USA

Abstract The olefin separation process involves handling a feed stream with a number of hydrocarbon components. The objective of this process is to separate each of these components at minimum cost. We consider a superstructure optimization for the olefin separation system that consists of several technologies for the separation task units and compressors, pumps, valves, heaters, coolers, heat exchangers. We model the major discrete decisions for the separation system as a generalized disjunctive programming (GDP) problem. The objective function is to minimize the annualized investment cost of the separation units and the utility cost. The GDP problem is reformulated as an MINLP problem, which is solved with the Outer Approximation (OA) algorithm that is available in DICOPT++/GAMS. The solution approach for the superstructure optimization is discussed and numerical results of an example are presented.

1, Introduction The olefin process involves a number of steps for producing and separating hydrocarbon components consisting of hydrogen and Ci-Cs components. We address the optimization of the separation system, where the goal is to select a configuration of separation tasks and their corresponding units, as well as pressure and temperature levels in order to perform heat integration. The objective is to minimize the total annualized cost of the separation system. Figure 1 shows the superstructure of the olefin separation system. There are number of states and separation tasks. The white boxes represent sharp split separations and the shaded boxes represent non-sharp split separations. We consider 8 components in the separation system and they are hydrogen, methane, and C2~C5 components. Since we are mainly concerned with the recovery of ethylene and propylene, we assume that the C4 mixture and the C5 mixture can be treated as a single component. As shown in Figure 1, there are 25 states including final products and 53 separation tasks. Non-sharp split separations have intermediate components which appear in both the top and bottom products. For each separation task, there is a subset of technologies available depending on the separation task. Table 1 shows 7 separation technologies considered in the separation process. Dephlegmator is a separation unit where heat exchange and mass transfer take place at the same time. Cold box is a cryogenic separation unit that is based on Joule-Thomson effect. Each separation task can be performed by a number of separation technologies, which are selected based on the components involved in the feeds.

192

Figure 1: Superstructure of separation system. Table 1: Separation technologies. Tl T2 T3 T4 T5 T6 T7

Distillation column Physical absorption tower Membrane separator Dephlegmator Pressure Swing Adsorption (PSA) Cold Box Chemical Absorption tower

2. GDP Model We propose a generalized disjunctive programming model for optimizing the superstructure of the separation system shown in Figure 1 (see Yeomans and Grossmann, 1999a, 1999b). The first level in the embedded disjunction corresponds to the selection of the separation task. Once the separation task is selected, the second level disjunction is for the selection of the separation technologies. For example, if a distillation column is chosen, then the mass and energy balances for distillation column are enforced and the corresponding cost term is considered. An additional disjunction is the heat integration for the distillation columns, and another disjunction is for compression, pumping or pressure reduction of each state. For the separation units, simple mass/energy balances are used. Assumptions for modeling the separation system are as follows: 1) Vapor pressure of the stream is calculated with Raoult's law and by the Antoine equation (Reid et al., 1977) 2) Utility (cooling water/hot steam) cost is given by a function of temperature (see Figure 2) 3) Investment cost is given by concave cost functions (Douglas, 1988)

193 Based on these assumptions, the following nonconvex GDP model is constructed: Indices Distillation column I States k Separation technology s Separation task st Sets K Distillation column k / States / STs Separation technology st for task s Separation task s for state / Si Parameters Minimum T difference EMAT CRu Upper bound for comp. Ratio Lower bound for comp. ratio CRL Variables r, Temperature of state / Xi Flowrate of state / ICi Investment cost for separation of / Pressure of state / Pi Compressor cost for state / CQ UCi Utility cost for separation of / Selection of separation task yz,jt Selection of heat integration for YSi,s state / YCi Selection of compression for state / Selection of separation tech. Y^ s,st RBi Bottom recovery ratio of state / Top recovery ratio of state / RTi Heat transferred from state / to distillation column k QEXu Heat generated or consumed by state / Qi Condenser temperature in distillation column for / Tf Reboiler temperature in distillation column k Model Olefin 1: a) Minimize the annualized cost of capital investment, compression and utility min Z = ^ {iCi + CCi + UC^)

b)

Overall mass balances s.t.

c)

Ax = 0

Pressure and temperature calculation by Antoine equation Pi=fa(Ti),

d)

V/G/

Embedded disjunction for the separation task

xf" = RT^xfi"' xf"" = RB^xf'"'

Vie/

YT

V SES:

mass balance: ftn{Xi) = 0 V steST,

energy balance: /e(jc,, 7;, /^, Q,-) = 0 cosf fuction:iiq,UCi)

=

fc(xi,Ti,Pi,Qi)

194 e)

Disjunction for the heat integration

T[^>T^ + EMAT

r -•I'Za

e£X,.,>0

MQEX,.,-0

\/ieI,\/keK

(/C,.,f/C,) = ^(x,,7;.,i^.,(2£X,.,)J f)

Disjunction for the compressors/pumps

(Ti,Pi)ou.=JPliTi,Pi)in CR[^
v ^ / ' M )out "" v ^ / ' ^ / «

/Pl''
VlG/

CC, =0

g) Logic propositions

\/ieI

rs,i,s h)

\/steST^yseSiyieI .YZi^j, \/ste ST^,\/seSiyieiykGK

vYT^s,st

Variable bounds

0
V/

0
V/

YSi,, YT^^^, YZij^, YCi e [true, false] 0
V/, s, st, k

yi,k

In the above modoi fa, fm, fe, fc, fz, Jpu and ^ 2 are the corresponding functions for the calculation of pressure, mass balance, energy balance, investment and utility cost, heat exchange cost, and compressor/pump cost, respectively. We adopt simple model equations for the cost calculation of the process units and compressor T/P (Douglas 1988; Biegler et al., 1997). The above GDP model is transformed into an MINLP using the big-M formulation for the disjunctions (Lee and Grossmann, 2000).

3. Utility System The process streams and separation units require individual cooling/heating for the temperature changes. We consider heat integration with a number of available utility streams with different temperature. Due to the discrete choices of the temperature and

195 cost, the optimal selection of the utility stream yields a MINLP. However, as shown in Figure 2, the utility cost can be approximated by a smooth function of the temperature. In this way, we avoid introducing 0-1 variables and simplify the modeling of utility system. We construct a third order regression of the utility cost, which yields a good approximation that generally provides an underestimation of the actual cost of the utility streams due to the continuous relaxation of the temperature levels of the utilities.

Figure 2: Utility stream temperature. Total cost: 110.82 M$/yr

^^^P
C2H4

Q .3.P 0 " " ©

C2H6

Figure 3: GAMS optimal solution.

4. Numerical Results Figure 3 shows the optimal solution for the superstructure shown in Figure 1. First the compressors are used to increase the pressure of the feed stream to the dephlegmator, which separates the hydrogen and methane from the heavier components. Then the hydrogen/methane mixture is sent to the cold box and hydrogen is separated from methane. The cold box operates at the low temperature and high pressure which requires

196 additional refrigeration and compression. The C2-C5 mixture is sent to the deethanizer (distillation column) and the C2 mixture is recovered as top product. The C3 mixture is separated by the depropanizer, and the C4-C5 mixture is sent to the debutanizer. A chemical absorber is used for the C2 split and distillation column is used for the C3 split. All the separation units perform sharp separations. Note that there is a heat exchange between the depropanizer and the C3 splitter to reduce the utility cost. The annualized capital cost of the process is 39.1M$/yr. The power cost for the compressors is 29.8M$/yr and the utility cost for the separation units is 41.9M$/yr. The energy cost is about 75% of the total cost. Since the olefin separation process is highly energyintensive, a significant amount of utility cost can be saved by the heat integration. Table 2 shows the statistics of the problem, where it can be seen that the MINLP problem is very large. This MINLP was solved in about 2 hours on a Pentium PHI PC using GAMS/DICOPT++, an algorithm for MINLP problems that is based on the Outer Approximation (OA) with Equality Relaxation and Augmented Penalty (Viswanathan and Grossmann, 1990). CPLEX was used for the MILP solver and C0N0PT2 was used for the NLP solver in GAMS (release 20.7). The heuristic termination was used that is based on the lack of improvement in the objective. Table 2: GAMS computational results. MINLP problem size Number of constraints Number of variables Number of binary variables

52,703 24,475 5,851

DICOPT++ solution Number of iterations 5 CPU seconds 8,778 First integer solution 142.9 M$/yr

5. References Brooke, A., Kendrick, D.., Meeraus, A. and Raman, R., 1997, GAMS language guide. Release 2.25, Version 92. GAMS Development Corporation. Biegler, L.T., Grossmann, I.E. and Westerberg, A.W., 1997, Systematic methods of chemical process design. Prentice Hall, New Jersey. Douglas, J.M., 1988, Conceptual design of chemical processes. McGraw-Hill, NY. Duran, M.A. and Grossmann, I.E., 1986, An Outer-Approximation Algorithm for a class of Mixed-Integer Nonlinear Programs. Math. Prog., 36, 307. Lee, S. and Grossmann, I.E., 2000, New Algorithms for Nonlinear Generalized Disjunctive Programming, Comp. Chem. Eng. 24, 2125. Reid, R.C., Prausnitz, J.M. and Sherwood, T.K., 1977, The properties of Gases and Liquids, 3*^^ edition. McGraw-Hill, New York. Viswanathan, J. and Grossmann, I.E., 1990, A Combined Penalty Function and OuterApproximation Method for MINLP Optimization, Comp. Chem. Eng. 14, 769. Yeomans, H. and Grossmann, I.E., 1999a, A Systematic Modeling Framework of Superstructure Optimization in Process Synthesis, Comp. Chem. Eng. 23, 709. Yeomans, H. and Grossmann, I.E., 1999b, Nonlinear disjunctive programming models for the synthesis of heat integrated distillation sequences, Comp. Chem. Eng. 23,1127.

6. Acknowledgments The authors would like to thank BP for financial support of this project

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

197

Batch Extractive Distillation with Intermediate Boiling Entrainer Z. Lelkes, E. Rev, C. Steger, V. Varga, Z. Fonyo, L. Horvath* Chemical Engineering Department, Budapest University of Technology and Economics, H-1521 Budapest, Hungary *Res. Lab. Mat. & Env. Sci., Chem. Res. Center of HAS, H-1525 Budapest, Hungary

Abstract Feasibility of batch extractive distillation in rectifying column with middle boiling entrainer is studied. Separation of methyl acetate and cyclohexane (forming minimum boiling azeotrope) using carbon tetrachloride, and separation of chloroform and ethyl acetate (forming maximum boiling azeotrope) using 2-chlorobutane are theoretically studied based on profile maps and rigorous simulation. Non-extractive distillation with pre-mixing the entrainer to the charge is also studied in both cases. Feasibility of the processes are demonstrated with laboratory-scaled experiments. Versions of BED according to the types of the azeotrope and of the entrainer are compared; and the decisive properties are pointed out.

1. Introduction Extractive distillation is an efficient separation method for non-ideal and azeotropic mixtures; see amongst others Widagdo and Seider (1996), Knapp and Doherty (1994), Wahnschafft and Westerberg (1993). For realisation of the extractive distillation in batch (BED), the simplest configuration is the rectifier with a continuous entrainer feeding into the column, as shown in Fig 1. More sophisticated configurations such as a middle vessel column (e.g. Safrit et al. (1997), Warter and Stichlmair (1999)) could be also used; but so far BED experimental results have been published mainly for the rectifier (Yatim et al., 1993; Lang et al., 1994; Lelkes et al., 1998b; and Milani, 1999). According to Laroche et al. (1991), the entrainer for homoazeotropic distillation can be the lightest, the heaviest, or even the intermediate boiling component in the system. Lang, Lelkes, and co-workers (1998, 1999) analysed feasibility of separating minimumboiling azeotrope applying BED with light and heavy entrainers and maximum-boiling azeotrope applying BED with heavy entrainer. Another possibility for separating mixtures applying entrainers is the so-called solvent enhanced batch distillation (SBD). In the case of SBD the entrainer is not fed continuously into the column; rather it is pre-mixed to the mixture at the beginning of the process, see e. g. Bernot et al. (1991), Rodriguez-Donis et al. (2001a). Even heteroazeotropic batch distillation (Rodriguez-Donis et al (2001b) could also be used. Our test mixtures, selected according to didactic viewpoints, are methyl acetate and cyclohexane with carbon tetrachloride for minimum boiling azeotrope, and chloroform and ethyl acetate with 2-chlorobutane for maximum boiling azeotrope. Operation steps (sequencing), limiting flows, and limiting stage numbers are determined by feasibility study, based on profile maps; the design is validated by rigorous simulation.

198 Comparison of SBD and BED using intermediate entrainer, according to effectiveness, and the use of light intermediate and heavy entrainer are presented. Cyclohexane (B) 1 1

X (rectificatiot section)

(extractivesection)

Extractive profiles

0.8 j

Rectification profiles

0.6 j 0.4 j

Q \ L^J^^J^v VT>^^^\

0.2 j

ut/7>^^^/^^ p

0 ! 0

0.2

ca4(E)

Figure 1 Sections of BED.

SN W 0.4

^ 0.6

F/V=0.5 R= infinite XD=[0.9; 0.05; 0.05]

^

1 0.8 1 Methyl acetate (A)

Figure 2 Extractive and rectification profiles at R = oo, F/V = 0.5.

2. Minimum Boiling Azeotrope with Intermediate Boiling Entrainer 2.1. Feasibility of SBD Determination of the separation sequence applying SBD is based on the residue curve map. According to Bernot et al. (1991), the separation with SBD is feasible in a stripper only. In a rectifier the first product is the azeotropic mixture, regardless to the initial position of the still composition. Thus, separation of minimum boiling azeotropes with SBD in a rectifier is infeasible. 2.2. Feasibility of BED Using continuous entrainer feeding into the column the separation becomes feasible (Rev et al., 2003). Rectification and extractive profiles at F/V=0.5 and R = oo are shown in Fig 2. A feasible rectification profile is drawn in the figure by bold line. There is a stable node (SN) of the extractive profiles near the A-E edge. As all the extractive profiles arrive at the neighbourhood of SN, they all cross the specified rectification profile; therefore the rectification profile can be reached by any extractive profile from the still even if the still composition is in the middle of the composition triangle. On the basis of the residue curve map and that of the map of feasible extractive profiles, the operation steps can be established as is shown in Table 1 (column c). Moreover, the locus of SN does not depend on the still composition; thus roughly constant distillate composition can be maintained during the production step of the process. 2.3. Simulation results Simulation of steps 2 and 3 is performed with Nextr=15, Nrect=15, Q=1.5kW, F = 0.085 kmol/h, R = 10.0, Xch = [0.5; 0.5; 0.0], H = 6 litre = 0.0645 kmol. The given feed flow rate and boiling power roughly correspond to a feed ratio of F/V ~ 0.5. The computed recovery ratio varies between 85 % (at high productivity) and 97-98 % (at lower productivity). The results are in good agreement with our expectations.

199 Table 1: Step sequences of BED using different type entrainers. Azeotrope: Entrainer: heat-up run-up V'cui CO

ex CO

2"^ cut S'^'cut

b Maximum Heavy R = ooF = 0 R = ooF = 0 ( R = oo R = ooF>0 F>0) R0 R0 A A R
Residue: E

Residue: E

c d Minimum Maximum Intermediate R=:ooF = 0 R = ooF = 0 R = ooF>0 R0 A R
reload

E

R0 EA R
Residue: B

Residue: B

load EA

R0

EA R
A

Lx)adEA R
Residue: E

Residue: A

R
4'*'cut 5^^ cut Main contaminant . in A Bubble point ranking

e Minimum Light R = ooF = 0

B

B

E

E

E

AB, A, B, E

A, B, AB, E

AB, A, E, B

A, E, B, AB

E,AB,A,B

3. Maximum Boiling Azeotrope with Intermediate Boiling Entrainer 3.1. Feasibility of SBD and BED Producing Pure A By Bernot et al. (1991), separation of a maximum boiling azeotrope is feasible applying SBD in a rectifier, because the full composition triangle constitutes a single distillation region. Rigorous simulations have been performed (Lelkes et al., 2002) to validate this process. However, even moderately pure chloroform (XAD ^ 0.9) could not be produced with a great number of theoretical stages (N = 100) and unacceptable great reflux ratio (R = 70). We concluded that pure product cannot be achieved in this way. After the study on the feasibility of BED the same results were achieved, thus the separation is not feasible either with continuous entrainer feeding. 3.2. Feasibility of SBD and BED producing AE Mixture in the first production step Although pure A cannot be produced in the first production step, a mixture of A and E (chloroform and 2-chlorobutane) can be produced, and later separated, because A and E do not form any azeotrope in our text mixture. In order to obtain pure A in a later step, reduced molfraction of A, XAR = XA/(XA+XB), in the distillate is specified. With a high enough value, e.g. XAR = 0.98, this assigns a narrow triangle along the A-E edge, as a range of acceptable distillate compositions. The feasible region for R = 9 and the evolution of the still paths for both SBD and BED are shown in Fig 3. The separation of the azeotrope is feasible in both cases, but BED is more advantageous, because the continuous feeding of the entrainer drives the still path in the direction toward edge B-E. Since the feasibility region valid for SBD reaches edge B-E, feeding to the still is sufficient. That is, the feed need not be applied to the

200 column directly, and distillation in step 2 (in terms of Table 1) with the same recovery specification can be started with less amount of pre-mixed entrainer. Ethyl Acetate (B) 1 Still path for SBD

Still path for BED

0 0,2 2-Chlorobutane (E)

0,8 1 Chloroform (A)

Figure 3 Expected still path directions for BED and SBD. 3.3. Simulation Results Simulations of step 2 of SBD and BED are performed. The two simulation runs are specified in a way that they provide the same purity (XAR = 0.98) in the accumulator and consuming the same amount of entrainer (90 mol). According to the results, BED produces the same purity and recovery of component A (= 92 %) in shorter time (10.0 h vs. 11.3 h) and the still hold-up by BED is half of that by SBD (7.1 litre vs. 15.5 litre).

4. Experimental Results Feasibility of the novel processes was demonstrated with experiments in a laboratory scale packed column (Rev et al., 2002). The column was made of glass with a height of 1.5 m and inside diameter of 5 cm. The initial still hold-up was 1 litre in all of the experiments. For demonstrating the feasibility of separating the minimum boiling azeotrope with middle boiling entrainer, equimolar binary mixture was initially charged into the still. The distillation path in step 2 crossed the isovolatility curve. It means that the azeotrope can be broken in this way; and the separation of a minimum boiling azeotrope with intermediate boiling entrainer is possible by applying BED in a rectifier. In the case of a maximum boiling azeotrope, the distillation path can be driven along the AE side of the triangle by applying BED with intermediate boiling entrainer. For demonstrating this possibility, two experiments were performed with identical specifications. The distillation path in the SBD experiment turned sharply inside of the triangle when the still path reached the boundary of the feasible region. On the contrary, the distillation path in the BED experiment ran along the AE side. This latter result can be considered as an effect of the continuous entrainer feeding into the still. It can be

201 concluded that BED is more advantageous separating a maximum boiling azeotrope with middle boiling entrainer than SBD.

5. Comparison of the Different Cases Separation of minimum boiling azeotropes with light and heavy entrainers, and that of maximum boiling azeotrope with heavy entrainer, all applying BED, have earlier been investigated. The study on separating minimum and maximum boiling azeotropes with intermediate boiling entrainer makes possible to conclude viewpoints of designing an effective separation process. Table 1 presents the separation steps for the different cases. Table 2 summarises the main limiting parameters of the separating processes. On the basis of comparing the corresponding columns of these two tables, the most important information for designing a BED process is the relative position of the entrainer to the azeotrope according to the series of the characteristic bubble points in the studied system. Table 2: The essential limiting parameters of the studied separation process. Azeotrope Entrainer ^min

N • rect A^min, N ^^max, rect N • extr ^^min,

a Minimum

b Maximum Heavy

+ + + +

+ +

c d Minimum Maximum Intermediate

+ + + +

e Minimum Light

+ +

+ +

Envelope of the rectification profiles (This can be extended marginally by extractive profiles.)

Envelope of the rectification profiles (This can be extended marginally by extractive profiles)

^pre-mix, min

• *F/V ' ' mm (at R = 00)

Boundary

Separatrix of the extractive profiles

Specified rectification profile and the corresponding extractive profile

If the bubble point of the entrainer is higher than that of the azeotrope then pure products can be maintained, and the operation steps and limiting parameters are almost the same for all the three systems (Table 1 column a-c). There are some differences for the maximum boiling azeotrope with heavy entrainer. The run-up step (Table 1 column b), that serves for the purification of the first cut product, can be omitted if Xch,A is greater than XAZ,A (see Lang et al, 2000). The other difference is the non-existence of the limiting parameters (Table 2 column b) Nmax, rect and F/Vmin at R = ©o. These parameters do not appear here because the 1^^ cut is an unstable node of the residue curve map in the case of separating a maximum boiling azeotrope, and is a saddle point in the case of separating a minimum boiling azeotrope. If the bubble point of the entrainer is lower than that of the azeotrope then pure products cannot be maintained at the beginning of the process, but binary mixtures, without any azeotrope, can be produced. The separation schemes for minimum boiling azeotrope with light entrainer and for maximum boiling azeotrope with intermediate entrainer are

202 similar, and even their other characteristics are identical. SBD is feasible in both cases; BED is applied just for increasing the effectiveness of the process. The entrainer (component E), instead of B, becomes the main contaminator of A if the entrainer is not the heaviest component. This can be an important viewpoint if A should be produced as free of B as possible.

6. Conclusion Feasibility of batch extractive distillation in rectifying column with middle boiling entrainer was studied for both minimum and maximum boiling azeotropes. Separation of a minimum boiling azeotrope with intermediate boiling entrainer is feasible in rectifier applying BED. Separation of a maximum boiling azeotrope with intermediate boiling entrainer is feasible in rectifier applying either SBD or BED; but application of BED is more advantageous. The results of the feasibility method were validated by rigorous simulations. The main steps of the separations were justified by laboratoryscaled experiments. The results of the studies on separating minimum and maximum boiling azeotropes with light, intermediate, or heavy entrainers are compared according to their operation steps and feasibility domains. The decisive property for designing an effective BED process, separating azeotropes, is the relative position of the entrainer to the azeotrope in the bubble point series. But the type of the azeotrope (minimum or maximum) can modify the existence of some limiting parameters (F/Vmin, Nmax, rect)-

7. References Knapp, J.P., Doherty, M.F., 1994, AIChE J., 40, 243 Lang, P. et al, 2000, Comp. Chem. Eng., 24, 1665 Lang, P., et al, 1999, Comp. Chem. Eng., 23, S93 Lang, P., et al, 1994, Comp. Chem. Eng. 18, 1057 Lelkes, Z., et al, 1998, AIChE J., 44, 810 Lelkes, Z., et al, 1998, Chem. Eng. Sci., 7, 1331 Milani, S.M., 1999, Trans IchEmE., 77, 469 Rodriguez-Donis, I., et al, 2001a, Ind. Eng. Chem. Res., 40, 2729 Rodriguez-Donis, I., et al, 2001b, Ind. Eng. Chem. Res., 40, 4935 Safrit, B.T, Westerberg, A.W., 1997, Ind. Eng. Chem. Res., 36,436 Wahnschafft, O.M, Westerberg, A.W., 1993, Ind. Eng. Chem. Res., 32, 1108 Warter, M., Stichlmair, J., 1999, Comp. Chem. Eng., 23, S915 Widagdo, S., Seider, W.D., 1996, AIChE J., 42, 96 Yatim, H.P., et al, 1993, Comp. Chem. Eng., 17, S57 Bernot, et al., 1991, Chem. Eng. Sci., 46, 1331 Rev, et al., 2003, Ind. Eng. Chem. Res., 42, 162 Lelkes, et al., 2002, AIChE J., 48, 2524 Rev, et al. 2002, Proc. of Distillation and Absorption 2002, Baden-Baden, Germany

8. Acknowledgement: This study has been supported by OTKA T037191, F035085, T030176, and AKP 2001112.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

203

Short-cut Design of Batch Extractive Distillation using MINLP Z. Lelkes, Z. Szitkai, T. Farkas, E. Rev, Z. Fonyo Budapest Univ. Dept. Chem. Eng., 1521 Budapest, [email protected]

Abstract An automatic design method for batch extractive distillation, one of the most important techniques for separating low relative volatility or azeotropic mixtures, is presented. Example calculations are performed to the acetone-methanol mixture using water as entrainer. The NLP and MINLP problems are solved with applying GAMS DICOPT++.

1. Scope For realizing extractive distillation in batch (BED), the simplest configuration is the rectifier with a continuous entrainer feeding in the column (Fig. 1). More sophisticated configurations, such as a middle vessel column, could be also used (e.g. Safrit et al., 1997; Warter and Stichlmair, 1999); but so far BED experimental results have been published mainly for the rectifier (Yatim et al., 1993; Lang et al., 1994; Lelkes et al, 1998ab; and Milani, 1999). To our best knowledge, automatic design method for batch extractive distillation has not been yet elaborated. In the case of the well-elaborated continuous distillation and conventional batch distillation processes, the reflux ratio plays a single deterministic role, and methodologies for determining the minimum flow rates and the minimum number of theoretical stages are well known and easily applicable. On the contrary, design of BED is far from being a trivial task. Even the feasibility of the process is always a question. Not just the optimal values, but even the feasible range of the essential parameters, namely of the reflux ratio and the feed ratio, both at a given heat duty, are difficult to estimate. The feasibility of the process can be easily failed by blind search for appropriate flow rates. That is why special methodologies for determining the feasible range have to be developed. Any search for optimal design parameters cannot effectively performed before a good estimation of minimum and maximum values is given. The most important limiting values of BED are the minimum feed flow rate (Fmin) at given reflux ratios (R), particularly at infinite reflux ratio (R=^), minimum reflux ratio (^min)» minimum number of theoretical stages in the extracting section (A^min,extr)» and minimum and maximum numbers of theoretical stages in the rectifying section (A^min,rect and A^max,rect)- Maximum reflux ratio is, in some cases, also an interesting property of continuous extractive distillation. However, this phenomenon does not occur in the most frequent case of this process, that we consider now (see the next paragraph), if V/L is high enough. There are several cases of BED, according to the type of the system to be separated and to the type of the residue curve map of the system formed with the entrainer. We deal with the most common case of separating a minimum boiling azeotrope with a heavy boiling entrainer not forming any new azeotrope. Our example mixture is (acetone / methanol)+water. The short-cut design methodology is based on the feasibility analysis developed by Lelkes et al (1998a), and using MINLP. The design methodology consists of two main parts: Limiting values of the most important design and operating

204

parameters are first determined; then optimization is performed; both steps using mathematical programming tools.

2. Feasibility Method for BED Here we shortly review the feasibility analysis (Lelkes et al, 1998a). We deal with BED performed in a batch rectifier consisting of three parts (see Fig. 1) namely (1) a rectification section (RS) including the condenser, the reflux divider, and the stages above the feed, (2) an extractive section (ES) including the feed stage and the stages between the feed and the still, and (3) the still itself The feasibility study is based on analysis of a map of feasible column profiles and still path. The following assumptions are applied in the model: No holdup exists apart from the still, dynamics are approximated through quasi steady states, constant molar overflow and boiling point feed and reflux streams are assumed. The concentration profiles are described by the differential eq 1: dx/dh=±(V/L)(y(x)-y*(x)); where y*(x) is the equilibrium vapor composition, and y(x) is calculated from the operating line. XD is applied as initial value for solving eq 1 in the RS; the momentary composition in the still is applied as initial value in solving for the ES; with appropriately changed sign of eq 1. The actual value of VIL and D is a function of V, R and F. For example, the following relations hold in the rectification section: (V/L)rect=V/(y-D), {VIL\^f^VI{yD+F), D=V/(R-\-l). The still path is determined by differential component balance eq 2: d(//sXs)/dt=FxF-Z)xD; the initial value is the charge in the still. BED is called feasible if a column state with the specified product purity (even with zero recovery) can be reached from the initial state (charge in the still, and empty column). A necessary and sufficient condition for feasibility is existence of an extractive profile connecting the still path to a rectification profile reaching the specified distillate composition. This can be checked by analyzing the profile maps (see Fig. 2). r

Methanol (B)

^ (1)^

1^, •^^D

rf^ IfV

SJ^

^~~-—-i^--^-^--''

-XtJ^^ f

1

(3)-<

TT^

Figure 1.

R=oo Possible extractive profile

\ /

,

Residue curves

Z ^ ^ ^ " *

/^^ ^^<—'•

^—r^

J

FA^=0.58

J^^^X^v"^ WJ Iter

(E)

SN

Acetone (A)

Figure 2.

In case of heavy solvent, with total reflux and appropriately selected feed flow rate, the feasible EPs from any point in the composition triangle (A) run to a stable node (SN) situated near or on the AE edge. From the neighborhood of this SN point, high purity distillate composition can be reached by rectification profile. Having the profile maps analyzed, the following operation sequence can be concluded: Step 1: /?=oo, F=0: heat-up; its time is A^i. Step 2: /?=oo, F>0: start-up; its time is At2. Step 3: /?0: production of component A; its time is At^. Step 4: /?
205

3. Basic Data, Targets and Tools Before outlining the method in details, we provide a list of general considerations: Specified data: Charge composition, distillate composition, stage holdup, vapor rate or boiling duty, and either operation time or minimum recovery. Limiting values to be determined: {Fmin, Nmin,extr^ and A^minjectl at /?=oo, and /^min for a given feasible F feed flow rate. Target: Determination of near optimal design and operation parameters with operating policy of constant R and F. Operating the column is much more convenient this way comparing to variable flow rates, and it is shown by Lelkes et al. (1998b) that this strategy is not very far from the optimal one. Objective: In our article we apply the following objective function eq 3:

c

Q-

(A^«+A^£)+

c

: 0.6729 mol"

where CQ and Cf are costs related to heat duty and to the entrainer consumption, respectively, while C/v is specific capital costs for a stage. The total cost is related to this roughly estimated capital. Specific cost ratios are thus applied in the objective function. Computation: All the short-cut computation, including both the equation solving and the optimization steps, is performed with using GAMS DICOPT++ (Brook A. et al, 1992). Example: Our example mixture is (acetone (A) / methanol (B)) + water(E); XD,spec=[0.94; 0.025; 0.035], F=760 torr, y=48 mmol/s. The charge is 170.82 mol with equimolar A-B composition: Xch=[0.5; 0.5; 0.0]. The specified recovery of A (Acetone) is Z D A = 7 0 mol; i.e. 77=0.8196. Volumetric hold-up per tray is //v=70 ml.

4. Finding Limiting Values with JMathematical Programming 4.1. Minimum feed flow rate {F^^ Fmin is minimal at given R and V if A^=oo is necessary to achieve the specified separation (xs to XD) even with zero recovery. We determine F^J^R=co) because Fmin(^=°o)>Fnun(^Frr^^. As is seen in Figure 3, SN just sits on the rectification profile of a pure enough distillate composition if F=F^^.

"71 ,

Methanol (B)

1

1. F=0.008 mol/s; F>F„i„

1

2. F=0.007 mol/s; F=Finin 3. F=0.006 mol/s; F
// ' /^ /""^^

Wa er(E)

Figure 3.

___^ " "~—

~^-^^^^X.

4. F=0.004 mol/s; F
active tray \

<

11

D=0,

•

XD

5. F=0.002 mol/s; F
~^

inactive tray ^4

^ 's-^ ;3 ^ ><-^x 1 2

i"-

Acetone (A)

L,x

Figure 4.

v,ys

206 Since the rectification profile runs along the AE edge, SN is on AE or under it (outside the A) for F>Fmin. If SN is inside the A then F0.0 and finding an SN point, in function of F/V, with XB=e. The criterion of a point being SN is the equality of y to y*. On the other hand, SN compositions inside the A all coincide with the isovolatility curve aAB=l with total reflux (Safrit et al, 1997; Lelkes et al, 1998a), therefore F^n(R='^) can be determined based on the isovolatility curve, as well. This task can be accomplished by assigning a small 6>0.0 and finding a point of the property of isovolatility with JCB=^. Then the corresponding F/Y ratio can be determined according to this point being on some extractive profile [y=(F/y+l)x-(F/V)xF], thus (F/V)min=|>*A(x)-JCA]/[xA-JCF,A]- In this way the SN criterion (y = y*) is not used. Both methods were tried for XD=[0.94; 0.025; 0.035], F=760 torr, V=48 mmol/s, with different trial values of e, giving the same results: Finin=6.133 mmol/s (6)=0.01). 4.2. Minimum stage numbers (A^miii,extr and A^miyect) (^D,A)min should be specified for determining minimum stage numbers. A stage number Nmin is minimal at R=co and given F/V if {^D,A^(-^D,A)min at N^^ and XD,A<(^D,A)min at ^
R=4 FA^=0.58

(B) Bourrlary approximated by a sequence of points

V J ^

Boundary

^s,,^

R=4,10 FA^=0,833

Extractive profiles

Possible extractive profiles

Xo<

Water (E)

Figure 5.

Acetone (A)

Water (E)

Acetone (A)

Figure 6.

A reflux ratio /^min is minimal (at a constant F/V) if XD is reachable from XCH at R=Rjmn but with zero recovery. The specified XD is reachable if there is a still path leading to a momentary Xs that can be connected to XD with a column profile. The actual situation of the feasibility boundary depends on R. All the points of the calculated still path lie in Region-II for any R
207 R=Rrmn- Therefore, at R^in the still path is tangent to the boundary (Lelkes et al, 1998a). That is why the boundary is to be calculated for determining /?min. The approximation of the boundary is based on three observations: (1) Location of UN is rather insensitive of F/V and R; it is situated near corner E. (2) No extractive profile exists starting from edge AB and reaching the neighborhood of E. (3) The feasibility region is convex; the tangents drawn to any point of the boundary lie outside the region. The boundary is approximated by finite differences, as follows (see Fig. 6). The tangent of any point Xp of the boundary can be given as x=Xp+/lAx where Ax is the actual slope of the boundary; the latter can be approximated as Ax=(V/L)[y(xp)y*(xp)]A/i, according to eq 1. The boundary can thus be approximated by a sequence of points {xo, Xi, ..., XK} satisfying the following relations: |XK-XUN|<^small positive real, ^K,E> ^K-i,E> •••> JCo,E= 0.0, and Xp+i=Xp+/lpAx; for some real Ap where Ax=(V/L)[y(xp)y*(xp)]A/i. Although XUN could be determined, XUN~XE= [0.0,0.0,0.0] may be substituted. Thus JCK,E=1-£^' is applied instead of |XK-XUN|<^ above. Apart from the details of calculating the equilibrium vapor composition y*(x), the boundary for given Xp, R, and F/V can be determined by solving an equation system. Rrain cau be determined by modifying the above system of equations as follows. Denote the points of the straight-line section connecting Xch to Xp (in our case XF=XE, the corner E) by xlp and the points of the approximating boundary by Xp. Discretize the composition domain [0.0; 1.0] of molfraction of entrainer into K equal parts and assign the points Xp and xlp so that JCP,E=JC7P,E. Thus, the xlp points are all known. Then search for the maximum R, subject to the condition that all the points of the still path lie outside of the feasible region. In practice, the boundary with the property that the still path is tangent to it is searched for. Fig. 7 demonstrates our results for F=28 mmol/s and y=48 mmol/s (F/y=0.5833) with K=20. The calculated minimum is /?min==0.597. The boundary touches the still path of the second step of the process; and the still path is tangent to the boundary. The computed boundary correctly approaches the real boundary. Methanol (B)

Methanol (B) 1.0-rs^ 0.90 8-" 0.7 0.60.5 0.40.30.2 0.1 0.0 Water (E)

Still path

R=0.597 F=28 mmol/s

1,0 0,9 -

^y>^

Estimated boundaiy

0,8 0,7 -

>\Ch

Estimated boundary

R=3.384 F=0.039mol/s

^^^*\^^ /Still padi y'^V\Xch

0,5 -

Extractive profiles

0,4 • 0,3-

0,2 -

-^ 0.2

0.4

Figure 7.

\ 0.6

0.8

1.0 Acetone (A)

0,1 -

/—Xo^^^

0.0

0.2

Water (S)

0,4

0,6

0,8

1,0

Acetone (A)

Figure 8.

5. Optimal Design Process design of batch extractive distillation is a most complicated task not just for the difficulties encounter in feasibility analysis but also because there are too many essential design parameters. These are the reflux ratio, the feed ratio, stage numbers in the two column sections, and the length of the process steps at specified charge composition, charge amount, product purity, recovery, and heat duty in the still. There are also many constraints to be taken into account (inequality constraints for the limits determined in the previous sections, equality constraints modelling the column profiles and the still path, and additional equality constraints applied in estimating the boundary that constitutes a limit for the still path). Determining a near optimal design and

208 operation via simulation with trial and error is a tedious and rather inefficient procedure. Instead, near optimal parameters can be quickly determined with the suggested method. MINLP optimization can be applied, based on the following considerations. There is rather litde change in XD during step 3 at constant R and F, thanks to the semibatch character of the process. If XD is taken as constant, the still path can be calculated at given R, F, and Xp (see Fig. 8). At the end of the second step of the process (at time t2=^ti+At2), the actual still composition x^ can be calculated from a simple component balance. The still path of step 3 can be determined by integrating eq 2 started from Xs=Xt2. The solution is a straight line if XD is constant. The theoretical end of step 3 is the time when the still path reaches the boundary; therefore, Xt3 is estimated by the intersection of the still path with the boundary. Once Xt2 and Xt3 are known, the amount of used solvent, the amount of yielded distillate, and the final recovery can be calculated. Ideally all the variables R, F, At2, Ats, A^extr, and Afreet can be considered as design variables. However, optimising them together proved to be too complex task for the solver. Therefore, a two-phase, iterative, optimization strategy is applied. In the first phase R, F, and At^ are optimized with fix stage numbers and At2. In the second phase the stage numbers and At2 are optimized with fix flow rates. The cycle ends if the flow rates do not change. Numerical results are shown in Table 1. After two iteration steps the algorithm concluded to the values: /?=3.384, F=39 mmol/s, Ar2=788.5 s, A^3=6802 s, A^extr=8, A^rect=4. Thus the optimization is successfully accomplished. The optimal still path can be seen in the Fig. 8. The results are validates by rigorous simulation. Table 1. Results of the iteration steps and the optimal parameters (recovery=0.7). Iter.

Reflux

F (mol/sec)

Step 2. (sec)

1/a 1/b 2/a 2/b 3/a

3.29

0.042

1105

Step 3. (sec) 6655

3.384

0.039

788.5

6802

3.384

0.039

788.5

6802

Extr. stages 12 (init. est.) 8

Rect . stages

8

4

4

6. References Brook, A., et al: "GAMS. A User's Guide; Release 2.25.", boyd & fraser, USA, 1992. Lang, P., Yatim, H., Moszkowicz, P., Otterbein, M. Comp. Chem. Eng. 18, 1057, 1994. Lelkes, Z., Lang, P., Benadda, B., Moszkowicz, P., AIChE J., 44, 810, 1998a. Lelkes, Z., Lang, P., et al, Chem Eng. Sci., 53, 1331, 1998b. Milani, S.M., Trans. IchemE., 77, 469, 1999. Safrit, B., Westerberg, A.W., Ind. Eng. Chem. Res. 36, 436, 1997. Warter, H., Stichlmair, J., Comp. Chem. Eng., 22, S915, 1999. Yatim, H., Moszkowicz, P., Otterbein, M., Lang, P. Comp. Chem. Eng., 17, S57, 1993. Yeomans, H. and Grossmann, I.E., Ind. Eng. Chem. Res. 39, 1637-1648,2000.

7. Acknowledgement To Hung, grants: OTKA F035085, T037191, and AKP 2001-112.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

209

A Conflict-Based Approach for Process Synthesis with Wastes Minimization Xiao-Ning Li, Ben-Guang Rong, Andrzej Kraslawski*, and Lars Nystrom Department of Chemical Technology, Lappeenranta University of Technology, P.O.Box 20, FIN-53851, Lappeenranta, Finland. *E-mail: [email protected]

Abstract This paper presents a conflict-based analysis approach for process synthesis with wastes minimization for dealing with the conflicts of multi-objective nature in the early design stage. A three-level hierarchical procedure is proposed for carrying out the identification of waste sources, the generation of pollution prevention alternatives and mathematical optimization. It has been shown that the superstructure aimed at the wastes minimization can be systematically formulated on the basis of the proposed strategy. The proposed approach has an important potential for achieving a more efficient solution in the stage of mathematical optimization. The approach is illustrated by a case study: air-based direct oxidation process for the production of ethylene oxide.

1. Introduction With the increasing public pressure and restrictive regulations, wastes treatment has become more and more important issue for chemical process synthesis. Traditionally the end-of-pipe treatment approach, which is aimed to eliminate the produced pollution, is not an efficient method in the view of the sustainable development. Current research efforts put attention on considering the reduction of the waste sources using the hierarchical approach, such as Douglas hierarchical procedure (Douglas, 1992) and onion diagram (Smith, 1995). However, the wastes minimization itself is a complex decision task that involves wastes handling and multi-objective analysis. The wastes treatment always generates the contradictions among design objectives. Those contradictions cannot be handled in the satisfactory way using existing hierarchical decision-making methods. Therefore it is an important theoretical and practical issue to develop a new approach to deal with the emerged contradictions during the design of the processes aiming at the wastes minimization. The objective of this paper is applying the multi-objective based analysis for the process synthesis with wastes minimization. A step-by-step systematic approach is proposed to ensure the reduction or elimination of the conflicts with regards to the waste handling and multi-objective synthesis. The pollution prevention alternatives are identified and the superstructure aimed at wastes minimization is formulated for the further mathematical optimisation. A case study, air-based direct oxidation process for the production of ethylene oxide, is presented for the illustration of the proposed approach.

210

2. Methodology A three-step approach is proposed for the generation of wastes minimization alternatives (Fig. 1). In the first step, the base case is used to evaluate the current performance of the process and to detect the concerned characteristics that are related with the waste sources. Next, in order to improve those concerned characteristics, a developed matrix is used for selecting the suitable heuristics or techniques, which ensure the reduction or elimination of the conflicts with regards to the wastes handling and multi-objective synthesis. Then, the pollution prevention alternatives are identified. Together with the base case, the superstructure aimed at wastes minimization is formulated. The supersturcture is modified and verified by checking the identified key parameters of waste sources and repeating conflict-based analysis. In the third step, the design alternatives obtained from the superstructure are evaluated using multi-objective optimisation. The procedure is realised by applying simulated annealing with the process simulator ASPEN PLUS.

Stepl* problem analysis and diagnosis

Step2. superstructure generation

Define wastes minimization problem with concerned multi-objectives

ijidentify available heuristics of pollution prevention by WM matrix

Analysis characteristics of streams and processes

Multi-objective conflict analysis for evaluation and screen of alternatives

Identify the key parameters for waste sources

Formulate superstructure aimed at waste minimization

Steps* superstructure optimization Simulated annealing + ASPEN | ^ Fig. 1. Three-step design methodology. 2.1. Conflict-based methodology Conflict-based approach is derived from the TRIZ methodology (Theory for solving inventive problems) (AltshuUer, 1998). TRIZ is a methodology to identify the system's conflicts and contradictions for solving the inventive problems. The main idea of TRIZ consists in the modification of the technical system by overcoming its internal contradictions. Therefore, it is an efficient method for handling the conflicts among the objectives in order to identify the promising pollution prevention alternatives. 2.2. Matrix of wastes minimization (WM matrix) A matrix of wastes minimization is formulated for organizing the available heuristics and techniques of wastes minimization. The process is based on the analysis of the heuristics and techniques that improve the characteristics related with the waste sources

211 and their contributions to the process design objectives. Twelve parameters for identification of the sources of wastes minimization are extracted. They are placed in the left column of the matrix as shown in Table 1. There are following objectives considered in this matrix: the economic criteria, product quality, safety and controllability. Every objective is composed of its sub-objectives, which are listed in Table 2 (Douglas, 1998). In this paper there are selected 31 heuristics based on Halim et.al. (2002) and Dantus et.al. (1996). The details of the heuristics are not given here since the space limitation. The heuristics are divided into four groups that deal with: the changes of product, transformation of input material, modifications of technology and good manufacturing practice. Table 1. Characteristics (parameters) of wastes minimization source. 7. recycle ratio 8. purge or emission ratio 9. side product treatments 10. product specifications 11. heat utility efficiency 12. process configuration

1. raw material conditions 2. raw material efficiency 3. reaction conversion 4. reaction selectivity 5. separation solvent 6. separation efficiency

Every heuristics is placed into the intersectional cell between the concerned characteristics and the influenced design objectives. Table 2 shows a fragment of the wastes minimization matrix. The symbols '+ -' are assigned to the available heuristics. The symbol '+' means that the concerned process objective is improved when applying the heuristics; '-' means its deterioration. It indicates that the use of the heuristics of wastes minimization result in the changing of the values of different objectives. This may lead to the conflicts among the concerned objectives. Therefore, via this matrix, the suitable heuristics of wastes minimization can be evaluated and selected based on the analysing the conflicts among the process objectives. Tahlel. A fragment of the wastes minimization matrix. Design objectives Economic Product quality l.raw material cost 1.product species 2. equipment cost 2. product amount 3. utility cost 3. product purity ^ 4. product profit J 5. start-up cost ^ 1

El H6(+)

2

Hll(+) H22(+)

...

E5

Hll(-) H30(-)

Ql

H22(+)

Q3 H4(+) H5(+) H30(+)

Safetv Lionising risk 2.explosion risk 3. toxicity risk 4.hi^^h T/P risk SI

S4

ControUabilitv 1. operating condition 2. process flow control 3. recycle control 4. unit operability Cl H6(-)

...

H22(-)

C4

212 We have derived the meta-heuristics for selecting the wastes minimization heuristics based on the objective conflict-based analysis as folio wings: 1. selecting the heuristics having the positive influence '+' on the concerned design objectives and screening out the heuristics which have the negative effect '-'on the design objectives. 2. trading off the heuristics having simultaneously positive and negative influences on various design objectives. Based on the objective-oriented analysis of the heuristics, the alternatives of pollution prevention are evaluated and refined. Moreover, the potentially optimal structures from the point of view of the particular objectives are indicated by the respective analysis of the objectives.

3. Case study The proposed approach is applied to the air-based direct oxidation process for the production of ethylene oxide. The following discussion focuses mainly on the identification of the waste sources, evaluation of the flowsheet alternatives based on the analysis of conflicts among the objectives, and systematic generation of superstructure aimed at the wastes minimization. A schematic flow diagram of the ethylene oxide process is shown in Figure 2. JE

r^ iV

Primary reactor

Purge J reactor I Primary y absorber

Purge absorbdrl

T Air

"^ Power, heat recovery from vent gas Ethylene

Refiner Waste liquid

Fig. 2. Air-based direct oxidation process for ethylene oxide. 3.1. Process description Referring to the Encyclopaedia of Chemical Technology (1980), the process can be divided into three major sections: reaction system, oxide recovery, and oxide purification. In the first section, as described in Chemical and process technology encyclopaedia (1974), a mixture of ethylene, air and recycle gas, in which the ethylene content is 3-5 vol% is conducted under a pressure of 10-20 atm gage to a tubular reactor with fixed-bed silver catalyst. The following reactions take place during the oxidation of ethylene. The per pass ethylene conversation in the primary reactors is maintained at 20-50% in order to ensure catalyst selectivity. CH2 =CH2 + j ^ 0 2 ->C2H40 CH2 = CH2 + 3O2 -^ 2CO2 +2//2O

213 The second section is ethylene oxide recovery from the crude product gas. The produced ethylene oxide is dissolved by the water solvent in absorber. The unabsorbed gas from the main absorbed overhead is split into two portions. The largest portion is recycled to the primary reactor. A smaller portion is fed to the purge reactor system. Its purpose is to allow reaction of a substantial portion of the ethylene content of the purge gas. The gas leaving the purge reactor entered a purge absorber. In the third section, the ethylene oxide-rich water absorbent streams from both absorbers are combined and feed to a desorber. The oxide is distilled at the top with some light gases, which are separated in a stripper. The partially purified oxide is sent to a final refining column. 3.2. Identifying the key parameters for the reduction of the wastes sources Based on the analysis of the process flowsheet, there are generated several sources of wastes. An attempt will be made to minimize or eliminate the following wastes: 1. the vent gases from the purge absorber. 2. the vent gas from the stripper. 3. the waste liquid from the refinery column. 4. the generation of by-product. 5. the heat loss of the process streams The vent comes from the purge absorber and strippers. It consists of spent air, carbon oxide and traces of ethylene oxide. It is closely related with the input raw material composition and the purge ratio; the reaction conversion determines flowrate of generated by-product; the amount of the discharged waste liquid is affected by the separation efficiency of oxide recovery and purification process; the heat loss prevention is achieved by the efficient heat matching strategies. Therefore the following five key parameters are identified to reduce the waste sources: SI-raw material conditions (1); S2-reaction conversion (3); S3-separation efficiency (6); S4- purge or emission ratio (8); S5-heat utility efficiency (11). 3.3. Generating the superstructure aimed at the wastes minimization In this work, the following objectives are considered: the economic criteria, product quality and process controllability. Based on the identified key parameters for the waste source reduction and the specific process information, the suitable heuristics of wastes minimization are identified and analysed via WM matrix. For example, from the WM matrix, it is seen that there are three heuristics related with changing the raw material condition (SI). Heuristics 4(material purification), 6 (material updating quality) are selected since there are no clear conflicts among the design objectives. Heuristic 5 (material substitution) is screened out since it may bring conflicts between economic criteria and controllability. For improving the reaction conversion (S2) to reduce the generation of the by-product, based on the specific process. Heuristic 13 (changing configuration of reactor) and Heuristic 14 (optimising the reaction condition) are selected. However they could increase the equipment cost and cause the difficulties in process controllability as indicated by the WM matrix. Based on the objective-oriented analysis of the heuristics, the pollution prevention alternatives are evaluated and screened. Moreover, the potentially optimal structures from the point of view of the particular objectives are indicated by the respective analysis of the objectives.

214 As a result of the analysis of the conflicts among the objectives, the suitable heuristics are selected for the generation of the superstructure aimed at the wastes minimization. Figure 3 shows the superstructure with the highlighted waste sources. It involves those alternatives, such as improving the input material by adding the air purifier (H4), using highly purified oxygen (H5), using two parallel reactors (H13) and improving the higher pressure of reactor (H14) to increase the conversion rate, adding the catalytic converter at the main process vent for modifying the emission ratio (H27-material loss prevention), putting additive to water for more efficient absorption (H15-choice the suitable separation solvent), optimising heat exchange network for improving the heat utility efficiency (H19-heat integration) etc. In consequence there is formulated the superstructure favourable to pollution prevention. The compact and efficient superstructure is the foundation for the search of the optimal solution through the multiobjective optimisation.

waste liquid AP-air purifier CV-catalytic converter P- high pressure A-additive — prcx:ess alternatives

Fig. 3. The illustration of wastes minimization centred superstructure.

3. Conclusions An approach based on conflict analysis is presented for process synthesis with wastes minimization. It deals with the conflicts among the objectives in the early design stage. A matrix of wastes minimization is formulated to assist in the conflicts analysis. It contains 12 characteristics and 31 heuristics for the wastes minimization. A three-level hierarchical procedure is proposed for carrying out the identification of waste sources, the generation of pollution prevention alternatives and mathematical optimization. In order to implement the proposed approach, there is studied air-based direct oxidation process for the production of ethylene oxide. It has been shown that the superstructure aimed at the wastes minimization can be systematically formulated on the basis of the proposed strategy. It has an important potential for facilitating the generation of the efficient solutions in the stage of mathematical optimization.

4. References Altshuller, G., 1998,40 principles: TRIZ keys to technical innovation, Inc.MA, USA. Chemical and process technology encyclopaedia, 1974,443, McGraw Hill, USA. Dantus, M.M., High, K.A., 1996, Ind. Eng. Chem. Res., 35,4566. Douglas, J. M., 1998, Conceptual design of chemical process, McGraw Hill, New York. Douglas, J.M., 1992, Ind. Eng. Chem. Res., 31, 238. Encyclopaedia of Chemical Technology, 1980, third edition, 9,441, Wiley-Interscience. Halim, I., Srinivasan, R., 2002, Ind. Eng. Chem. Res., 41, 196. Smith, R., 1995, Chemical process design, McGraw Hill, New York.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

215

A New Continuous-Time State Task Network Formulation for Short Term Scheduling of Multipurpose Batch Plants Christos T. Maravelias, Ignacio E. Grossmann* Department of Chemical Engineering, Carnegie Mellon University Pittsburgh, PA15213, USA

Abstract A new continuous-time MIL? model for the short-term scheduling of multipurpose batch plants is presented. The proposed model relies on the idea of the State Task Network (STN) and addresses the general problem of batch scheduling, accounting for resources other than equipment (utilities), variable batch sizes and processing times, various storage policies (UIS/FIS/NIS/ZW) and batch splitting/mixing. Compared to other general continuous STN formulations, the proposed model is more efficient. Compared to event-driven formulations, it often gives better solutions being equally fast. The application of the model is illustrated through an example problem.

1. Introduction The problem of short-term scheduling of multipurpose batch plants has received considerable attention during the last decade. Kondili et al. (1993) introduced the notion of State Task Network (STN) and proposed a discrete-time MIL? model, where the time horizon is divided into time periods of equal duration. Shah et al. (1993) developed a reformulation and specific techniques to reduce the computational times for discretetime STN models. Pantelides (1995) proposed the alternative representation and formulation of the Resource Task Network (RTN); Schilling and Pantelides (1996) developed a continuous-time MILP model, based on the RTN representation, and a novel branch-and-bound algorithm that branches on both continuous and discrete variables. Mockus and Reklaitis (1999) and Zhang and Sargent (1996) proposed MINLP continuous-time representations for the scheduling of batch and continuous processes. lerapetritou and Floudas (1998) proposed a new MILP formulation, based on time events, for the scheduling of batch and continuous multipurpose plants. Several authors have recently proposed related models for the scheduling of multipurpose batch plants (Castro et al. (2001); Lee et al. (2001)). In this work, we propose a new general State Task Network MILP model for the shortterm scheduling of multipurpose batch plants in continuous time that accounts for resource constraints other than equipment (utilities), variable batch sizes and processing times, various storage policies (UIS/FIS/NIS/ZW) and allows for batch mixing/splitting. The proposed model can be extended to account for multiple intermediate due dates. It is computationally more efficient than other general STN/RTN models and equally efficient to the less general event-based models. Extensive computational comparisons can be found in Maravelias and Grossmann (2003). The key features of the proposed model are the following: (a) the time horizon is divided into a continuous time grid.

* To whom correspondence should be addressed. E-mail: [email protected]

216 common for all units, (b) assignment constraints are expressed using binary variables that are defined only for tasks, not for units, (c) start times of tasks are eliminated, and (d) a new class of valid inequalities that improves the LP relaxation is added to the MILP formulation.

2. Problem Statement We assume that we are given: (i) a fixed or variable time horizon (ii) the available units and storage tanks, and their capacities (iii) the available resources and their upper limits (iv) the production recipe (mass balance coefficients, utility requirements) (v) the maximum batch size and processing time data (vi) the amounts of available raw materials (vii) the prices of final products The goal is to determine: (i) the sequence and the timing of tasks taking place in each unit (ii) the batch size of tasks (i.e. the processing time and the required utilities) (iii) the amount of final products sold The proposed model can acconwnodate various objectives, such as maximization of profit, or the minimization of the makespan for specified demand.

3. Mathematical Model A common, continuous partition of the time horizon is used to account for all possible plant configurations and resource constraints other than those on units. The idea of decoupling tasks from equipment, as proposed in lerapetritou and Floudas (1998), is also used. Assignment constraints are expressed through task binaries Wsin and WfinBinary Wsin is 1 if task / starts at time point n, and binary Wfi„ is 1 if task / finishes at or before time point n. The start time, Tsin, of task / is always equal to time point r„ and thus time matching constraints are used only for finish time, Tfin, of task i. The batch size of task / that starts at, is being processed at, and finishes at or before time point n is denoted by Bstn, Bpin and Bfin, respectively. The amount of state s at time point n is denoted by Ssn and the amount of resource r consumed by various tasks at time point n is denoted by Rm- The amount of state s consumed (produced) by task / at time point n is benoted by ^isn (B^isn)- The details and derivation of the proposed model can be found in Maravelias and Grossmann (2003). 3.1. Assignment constraints Constraint (1) is the main assignment constraint and enforces the condition that not more than one task can be processed in a unit at any time. Constraint (2) enforces the condition that all tasks that start must finish, while constrsaints (3) and (4) enforce the condition that not more than one task can start or finish on a specific unit at any time:

E KWs^-Win)^^ Sw'^.=Sw/;„ v/ n

(D (2)

n

XW5,,<1 y/,Vn te'(;)

V;,Vn

(3)

217 ^Wf^
V;,Vn

(4)

3.2. Duration and timing constraints The duration. Din, and the finish time, % , of a task are calculated through constraints (5), and (6) and (7), respectively. The elimination of start times, Tsin, is made through constraint (8) and the time matching between time points and finish times is achieved through constraints (9) and (10). Note that in the general case a task may finish at or before a time point n [constraint (9)], whereas a task must finish exactly at a time point [constraints (9) and (10)] if it produces a state for which zero-wait policy applies: A„=«,W^^,„+A55,„

V/,Vn

(5)

Tf,„
\/iyn

(6)

Tf,„>Ts^+D,„-H(l-Ws,„)

Vi,Vn

(7)

Ts,„=T„

V/,Vn

(8)

Tf^.,
VJ,Vn

Tf.„_,>T„-Ha-WfJ

(9)

V/GZWOXVn

(10)

3.3. Batch-size constraints and material balances Constraints (11) and (12) impose upper and lower bounnds on the batch sizes Bstn and Bsin, while constraint (13) enforces variables Bsin and Bfin to be equal for the same task. The amount of state s consumed, B^isn, and produced, B^isn, by task / at time n is calculated through constraitns (14) and (15) respectively. Constraint (16) is the mass balance for state s at time n, where SSsn is the amount of state s sold at time n. Constraint (17) is a capacity constraint, where Q is the storage capacity: B^^^Ws.^
V/,Vn

(11)

BrWfi„
^U^n

(12)

BSi,_,^Bp,^_,=Bp,^+BU

"^U^n

(13)

Kn=PisBSin

yU\/n,yseSI(i)

(14)

Bl-PisBU

yiyn,\/sGSO(i)

(15)

Ssn + SS,^ = 5,,., + X B,?„ - S BL |G0(5)

S^
V5, Vn

>1

(16)

l€/(5)

Vs,Vn

(17)

3.4. Resource constraints The amount of renewable resource r required by task / that starts at n, R^^n^ is calculated by constraint (18). The same amount is "released" when task / finishes, R^rn^ and is calculated by constraint (19). The total amount of resource r required at time n is calculated in (20) and bounded, not to exceed the maximum availability RJ^"^^ by (21): Kn=rirWSin+S,,,Bs,„

V/,Vr,Vn

(18)

218

<=r.wy;,+«5,„B/;, v/,vr,v/i Rn,=Rm-^-lRL^+lRL

Vr,V«

I

R^
(i9) (20)

I

yr,yn

(21)

3.5. Time ordering Equations (22) - (24) define the start and the end of the time horizon and enforce an ordering among time points: T„^i=0

(22)

T„.m=H

(23)

T„.i^T„

Vn

(24)

3.6. Tightening constraints The addition of valid inequalities (25), (26) and (27) tightens the LP relaxation and significantly reduces the size of the branch-and-bound tree. llD^n^H

Vj

(25)

te/(y) n

X ^D^.
V/Wn

(26)

jG/(y) n>n

S S(«,w/;,. + AB/;,.)
(2?)

ie/(;)n'
3.7. Objective function While various objective functions can be acconmiodated within the proposed model (e.g. minimization of makespan or production cost for fixed demand), the maximization of income from sales is used here.

maxZ = XS^.'^^.« s WSiru WfinElOJl

(28)

n BSir, Bpi,,

Bfi„^ S^ru SS^r,

T^

Tfir, D^n, B^isru B""isruR\rru R^'inu Rm>0

(29)

The proposed MILP model comprises of constraints (1) - (29), where (8) is used to eliminate Tsin4. E x a m p l e The proposed model is used for the scheduling of the state task network of Figure 1, whose data are given in Table 1. There are six units (Ul, U2,.. .U6) available for the ten tasks. Unlimited storage is available for states Fl, F2, INTl, INT2, PI, P2, P3 and WS; finite intermediate storage is available for states S3 (15 kg) and S4 (40kg); no intermediate storage is available for states S2 and S6, while zero-wait policy applies for states SI and S5. States Fl, F2, and S4 are initially available in sufficient amounts. Furthermore, each task requires one of the there following utilities: cooling water (CW), low pressure steam (LPS), and high pressure steam (HPS). The maximum availability

219 for CW, LPS and HPS is 25, 40 and 20 kg/min, respectively. Constant processing times are assumed.

Figure 1: Sate Task Network of Example.

Table 1: Example data (B^^^ in tons, a in hr, yin kg/min, Sin kg/min per ton). Task Unit

Tl Ul 5 2 LPS 3 2

r»MAX

Dur (a) Utility Y 6

T2 U2 8 1 CW 4 2

T4 Ul 5 2 HPS 3 2

T3 U3 6 1 LPS 4 3

T6 U4 8 2 HPS 4 3

T5 U4 8 2 LPS 8 4

T7 U5 3 4 CW 5 4

T8 U6 4 2 LPS 5 3

T9 U5 3 2 CW 5 3

TIO U6 4 3 CW 3 3

The optimal solution yields the Gantt chart of equipment in Figure 2, and the resource utilization graph in Figure 3. In the optimal solution, 10 tons of product PI and 3 tons of product P3 are produced. As shown in Figure 2, task T6 is not performed since unit U4 is assigned to task T5 only, and thus, product P2 is not produced. Cooling water is the limiting utility, as its utilisation is equal to its availability from t=2 to t=4. The optimal solution is found when the 12-hour time horizon is divided into 8 intervals. The MILP problem consists of 3067 constraints, 180 binary and 1587 continuous variables. Its LP relaxation is $19,500 and its optimal solution is $13,000. The optimal solution was found in 62.8 sec and 2,107 nodes.

Ul U2 U3 U4 U5 U6

Tl

Tl

J3.

T4

itl

_T4

J^ T3

T3

T3 TS

T5 T9 T8

teg^TO

i(^|i^| 10

Figure 2: Equipment Gantt chart for Example.

12

t(hr)

220 50 40

.— ^ " 1 30

^

r 1 1

20

1

r

10 H 0

2

;

L_

1

0

_l

4

6

8

10

12

Figure 3: Resource utilisation level for Example.

6. References Castro, P., Barbosa-Povoa, A.P.F.D., Matos, H., 2001, An Improved RTN ContinuousTime Formulation for the Short-term Scheduling of Multipurpose Batch Plants, Ind. Eng. Chem. Res., 40, 2059-2068. lerapetritou, M.G., Floudas, C.A., 1998, Effective Continuous-Time Formulation for Short-Term Scheduling. 1. Multipurpose Batch Processes. Ind. Eng. Chem. Res., 37,4341-4359. Kondili, E., Pantelides, C.C., Sargent, R., 1993, A General Algorithm for Short-Term Scheduling of Batch Operations - 1 . MILP Formulation. Comput. Chem. Eng., 17,211-227. Kyu-Hwang Lee, Heung II Park, In Beum Lee, 2001, A Novel Nonuniform Discrete Time Formulation for Short-Term Scheduling of Batch and Continuous Processes. Ind. Eng. Chem. Res., 40,4902-4911. Maravelias, C.T., Grossmann, I.E., 2003, A New General Continuous-Time State Task Network Formulation for the Short-Term Scheduling of Multipurpose Batch Plants. Submitted for Publication. Mockus, L., Reklaitis, G.V., 1999, Continuous Time Representation Approach to Batch and Continuous Process Scheduling. 1. MINLP Formulation. Ind. Eng. Chem. Res., 38, 197-203. Pantelides, C.C, 1994, Unified Frameworks for the Optimal Process Planning and Scheduling. In Proceedings on the Second Conference on Foundations of Computer Aided Operations, 253-274. Schilling, G., Pantelides, C.C, 1996, A Simple Continuous-Time Process Scheduling Formulation and a Novel Solution Algorithm. Comput. Chem. Eng., 20, S1221-1226. Shah, N.E., Pantelides, C.C, Sargent, R., 1993, A General Algorithm for Short-Term Scheduling of Batch Operations - II. Computational Issues. Comput. Chem. Eng., 17, 229-244. Zhang, X., Sargent, R.W.H., 1996, The Optimal Operation of Mixed Production Facilities - General Formulation and Some Approaches for the Solution. Comput. Chem. Eng., 20, 897-904.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

221

Life Cycle Analysis of a Solar Thermal System with Thermochemical Storage Process Nur Aini Masruroh, Bo Li and Jiri Klemes Department of Process Integration, University of Manchester Institute of Science and Technology (UMIST), PO Box 88, Manchester M60 IQD, United Kingdom [email protected]

Abstract A new more efficient solar heating / cooling system has been developed for houses and buildings by an EU co-fmanced SOLASTORE (5FW ENERGIE) project with a consortium of partners from France, Spain, Portugal and the UK. It is targeting a considerable reduction of CO2 emission by improvement of the solar energy system efficiency and the extended utilization of the solar energy using reversible chemical reactions as energy storage. Although solar energy is considered environmentally friendly, the whole life cycle of a solar energy production has to be evaluated. The production targets for the SOLARSTORE system are potentially thousands units. This makes it very important to explore the total environmental impacts caused during its whole life cycle. This work employs Life Cycle Analysis (LCA), an ISO 14040 based technique for evaluating the total environmental impacts associated with a product, to analyse the total environmental impacts of SOLARSTORE system during its whole life cycle. The standard LCA methodology has been extended and modified to cope successfully with this task. The LCA results show the total environmental impacts to achieve 1 GJ energy by using SOLARSTORE system: global warming potential ranging in 6.3 - 10 kg CO2, acidification potential in 46.6 - 70 g SO2, eutrophication in 2.1 - 3.1 g phosphate and photochemical oxidant in 0.99 - 1.5 g C2H4. The raw material acquisition processes contribute 99% to the total environmental impacts. A LCA based comparison has been made analysing the total environmental impacts of a traditional solar heating system, a traditional fossil fuel heating system and SOLARSTORE system. It shows that SOLARSTORE provides a better solution for reduction of negative environmental impacts by using solar energy.

1. Introduction Solar energy is offering a considerable potential to limit the greenhouse effect. It enables substitution for fossil fuels used for energy generation, and consequently avoids the atmospheric emissions and other polluting residuals associated with conventional, mainly fossil, energy production processes. The major problem is that solar energy is provided independently of the needs, which leads to a low efficiency of the installations, covering only 30 to 60% of heating requirements and domestic hot water. The majority

^ Corresponding [email protected]

222

of thermal storage systems available on the market are based on a hot water tank (sensible storage) or a phase change material (PCM). These systems need a large area in the house and are not suited for long life of storage. The storage period needed can be as long as five days and a sensible or latent storage would lead to an important loss of heat during this period of storage. SOLARSTORE project is developing a more efficient solar heating/cooling system based on a pair of salts-water endothermic / exothermic reactions. Integration of this thermo-chemical storage process enables to store the solar thermal energy when heat requirements are lower than heat production and restore it when the heat production cannot cover the requirements. Therefore, it is possible to save the thermal solar energy, which would be normally lost. The need of auxiliary energy such as electricity or gas decreases, which is reducing negative environmental impacts due to the use of conventional energy resources. Is it really solar energy "green" and if to what extent? Is a developed solar energy unit environmentally friendly? The production targets for SOLARSTORE system are expected to be thousands units, which makes it very crucial to assess the environmental impacts associated with such systems. A comprehensive appreciation of the environmental impacts associated with the SOLARSTORE system requires an assessment of the emissions released and the consumption of energy and materials during its entire life cycle, from raw material acquisition to waste disposal. Life Cycle Analysis (LCA), which is based on ISO 14040 (Burgess, A.A. and Brennan, D.J., 2001), is an effective tool to make a quantitative assessment of the environmental aspects and potential impacts associated with a product during its entire life cycle. This a 'cradle to grave' (from raw material extraction to waste disposal) approach, providing a systematic way of evaluating the environmental impacts of a product, identifying and quantifying the emissions and material consumption that affect the environment at all stages of the entire product life cycle.

2. Objectives and Basic Specification 2.1. Objectives The objective is to explore the environmental impacts and raw material consumption associated with the SOLARSTORE system, by applying the LCA technique. Further objective is to fmd out whether SOLARSTORE system could create less negative environmental impacts, by comparing the environmental impacts of SOLARSTORE system, traditional fossil fuel heating system and traditional solar heating system. 2.2. Basic specification of SOLARSTORE system The SOLARSTORE system consists of two major units that can be separated physically, a general solar heating unit and a thermo-chemical storage unit. The general solar heating unit consists of a solar collector, a backup boiler, heat exchangers, pumps, connections, valves, and sensors. The thermo-chemical storage unit consists of reactors, evaporators, condensers and reactive compounds that are constructed by compressing certain inorganic salts and certain inert supporting structures together.

223

3. LCA for SOLARSTORE 3.1. LCA framework Fig 1 gives the technical framework for conducting LCA, showing how the basic components, goal and scope definition, inventory analysis, impact assessment and inventory assessment, are interrelated.

Ammsm 1. Goal and scope definition

Data analysis

Constructing the process flow chart

IMTACr 6. Classification

iMmov]iNi:^>ir Reporting and improvement assessment

Characterisation Defining the system boundaries

8. Valuation

Impacts to be evaluated Collecting the data

Processing the data

Detailed Execution step

Fig. 1. Technical Framework for LCA. 3.2. System deHnition and major assumptions SOLARSTORE system consists of two major units that can be physically separated, therefore, the LCA study can be performed for these two units separately. Previous LCA study of general solar heating system (Mirasgedis, S., et al, 1996) provided useful starting point, whilst LCA study of the thermo-chemical storage system has to be newly developed. The processes involved include raw material acquisition processes, manufacturing processes of all components, assembling process of each unit, installation and maintenance processes, processes of using SOLARSTORE system, disassembling process of each unit, disposal processes of the components and recycling processes of the materials. The transportation processes between different sites should also be considered. The difficulties to obtain the full data set (the SOLARSTORE system is still under the development) and the complexity of this analysis dictated the system definition to be modified to cope successfully with the task: L The usable lifetime of SOLARSTORE system is assumed to be 15 years. Since SOLARSTORE system is able to store / release solar thermal energy when necessary without consuming any other energy resources, it can be reasonably assumed that zero emission would be created by SOLARSTORE system during its usable lifetime. Therefore, the use phase of SOLARSTORE system is excluded

224

2.

3.

4.

from the analysis. The installation and maintenance processes are also excluded from the analysis due to the absence of data. SOLARSTORE system should be disposed off when it loses the ability of storing/releasing solar thermal energy. This should be taken into the consideration when assessing the environmental impacts. After being disposed, the equipment might be recycled to produce the material with the same quality (primary recycle) or the one with lower quality (secondary recycle). Although this recycling might be energy intensive and create significant emissions, this phase is excluded from the system boundary. This is because firstly only limited information is available for this recycling and secondly it is assumed that the emissions resulted from the primary recycle process have been considered in the processes of raw material acquisition and manufacturing. Railway and road transport are assumed to be major means for transportation and distribution processes.

Generally the environmental impacts to be considered include the resource depletion, human health and ecological consequences (Masruroh, N.A., 2002). In this study the problem is simplified and only the global warming potential, acidification, eutrophication and photochemical oxidant are evaluated. 3.3. Functional unit The SOLARSTORE system is developed to improve the efficiency of traditional solar heating system. The size of hardware equipment and the amount of the reactive compounds are directed by the potential of energy savings that can be achieved by the system. The functional unit in this study is per GJ of energy provided by SOLARSTORE system. Considering the other expected results of the project, reducing CO2 emission, such a functional unit makes it easier to compare the emissions released by SOLARSTORE during its life cycle with the emissions released by a traditional solar heating system or fossil fuel heating system. 3.4. LCA results In this LCA study are four options for selection of appropriate salt combinations and binders, three situations in which different energy requirements are to be fulfilled by using SOLARSTORE system, and two possible market places. Twenty-four LCA case studies have been carried out to select appropriate reactive compounds for different situations and different market places. The LCA results show that the total global warming potential impacts range in 6.3 - 10 kg CO2/GJ, acidification potential in 46.6 - 70 g SO2/GJ, eutrophication in 2.1 - 3.1 g phosphate/GJ, and photochemical oxidant in 0.99 - 1.5 g C2H4/GJ. It is also shown that the major part of emissions comes from the raw material acquisition phase (around 99%).

225

4. Comparison with Other Heating Systems Although SOLARSTORE system could improve the efficiency of traditional solar heating system, it cannot fulfil the total annual heating requirement in most location around Europe. A backup boiler is used to accommodate the rest heat requirement. kg COz/annum

SOLARSTORE

Conventional Solar Heating System

® Equipment

Natural Gas

Low Sulphur Heating Oil

* Fossil Fuel

Fig. 2. Annual Global Warming Potential Impacts for one Case Study. Fig 2 shows the annual global warming potential impacts caused by using different systems. A lifetime of 15 years is assumed for evaluation. SOLARSTORE system creates more environmental impacts during its manufacturing processes. It is caused by the use of the thermo-chemical unit and the reactive materials. More material and energy is required for this phase. However, SOLARSTORE system could replace 72% of fossil fuel, which consequently results in a significant reduction of the total environmental impacts and the total annual environmental impacts are considerable lower than by using other systems. SOLARSTORE system provides a better solution for reduction of negative environmental impacts by using solar energy, which encourages further development and production from the environmental point of view.

226

5. Conclusion This work employed the LCA to study environmental impacts associated with a new solar heating / cooling system, which is integrated with a thermo-chemical storage unit to improve the efficiency of traditional solar heating system. Twenty-four case studies have been carried out for consideration of different situations, different salt combinations and binders and different market places. The total environmental impacts to achieve 1 GJ energy by using this novel system are: global warming potential impacts ranging in 6.3 - 10 kg CO2, acidification potential in 46.6 - 70 g SO2, eutrophication in 2.1 - 3.1 g phosphate and photochemical oxidant in 0.99 - 1.5 g C2H4. The raw material acquisition processes contribute 99% to the total environmental impacts during the whole life cycle. The results provide a clear comparison of total environmental impacts of SOLARSTORE system, traditional solar heating system and traditional fossil fuel system. It shows that SOLARSTORE provides an advantageous solution for reduction of negative environmental impacts.

6. References Burgess, A.A. and Brennan, D.J., 2001, Application of Life Cycle Assessment to Chemical Processes, Chemical Engineering Science, 56, 2589 - 2604. Masruroh, N.A., 2002, Life Cycle Analysis of a Solar Thermal System with Thermochemical Storage Process, MSc Dissertation, Department of Process Integration, UMIST, Manchester, UK. Mirasgedis, S., Diakoulaki, D. and Assimacopoulos, D., 1996, Solar Energy and the Abatement of Atmospheric Emissions, Renewable Energy, 7, (4), 329 - 338.

7. Acknowledgement The financial support from the EC Project ENERGIE NNE5-2000-00385 "Improvement of the efficiency of solar thermal systems by integration of a thermo-chemical storage processes - SOLARSORE" and the collaboration from project partners CREED, CLIPSOL, ADAI, CNRS and Dalkia are gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

227

Hybrid Synthesis Method For Mass Exchange Networks Andrew K. Msiza and Duncan M. Fraser Department of Chemical Engineering, University of Cape Town, Private Bag, Rondebosch, 7701 South Africa.

Abstract A hybrid tool for the synthesis of mass exchange networks is presented in this paper. The tool uses targets to measure the quality of solutions generated by a mixed-integer non-linear (MINLP) model. The components making up the hybrid tool are a total annual cost target of the expected flowsheet, a physically meaningful initial flowsheet, a driving force diagram and an MINLP model. The total annual cost target represents the best cost scenario for the flowsheet, an initial flowsheet is used to initialise the MINLP solver and the driving force plot assists the designer to generate alternative initial solutions to improve the generated MINLP solution. The hybrid tool produces mass exchange networks whose total annual costs are within 10% of previously reported pinch solutions and networks that are similar or better than those obtained from the MINLP approach alone. The designer has confidence in the quality and optimality of the solutions due to the available targets and the visual driving force diagrams.

1. Introduction Process synthesis can be approached in three different ways: heuristics, physical and thermodynamic insight, and mathematical programming. Hybrid methods where two or all of the synthesis methods are combined are now becoming used, taking advantage of the combined strength of the individual techniques. In Grossmann and Daichendt (1996) the question of how the optimisation and targeting approaches, and heuristics for that matter, can be combined "in such a way that on the one hand the integration is conceptually consistent and rigorous, and on the other hand it exploits the strengths of each approach" is highlighted as one of the important challenges to be solved. In this paper we will adress this challenge using the following work as a basis. Kravanja and Glavic (1997) proposed a match-dependent heat-exchanger area targeting method followed by an NLP optimisation of the structure meeting the area targets. This method fixes the utilities before estimating the heat exchanger area. Papalexandri tt al. (1994) proposed an MINLP model for the simultaneous generation of a network and the determination of the TAC without resorting to any pinch decomposition concepts. The reported total annual costs of most of the problems solved by Papalexandri et al. (1994) were poor when compared to those obtained by Hallale (1998) using a pinch approach, yet the MINLP framework itself was versatile enough to contain even those solutions proposed by Hallale. It would then seem plausible that a transfer of some techniques from pinch technology to MINLP optimisation would expose the actual optimum solutions embedded in the MINLP hyperstructure.

228 Hallale (1998) showed how the capital and operating cost (El-Halwagi and Manousiouthakis, 1989) through supertargeting could be used to optimise the total annual cost (TAC) of a mass exchange network before design. Key features of the supertargeting approach were the determination of a network's total annual cost and a set of network generation criterion based on available driving force. Full details of all this may be found in Hallale (1998) and Hallale and Fraser (1998, 2(X)0a, and 2000b). The key objective of this paper is therefore to propose a new method of synthesis for mass exchange networks such that the techniques of pinch technology developed by ElHalwagi and Mathousiouthakis (1989) and Hallale (1998) are combined with the MINLP hyperstructure approach proposed by Papalexandri et al (1994).

2. Proposed Hybrid Synthesis Method The philosophy behind the integration is described by Figure 1. Determine Supertargets

Set up Superstructure as an MINLP model

^

P

Construct an initial flowsheet

\^

1%

^ ^r Optimise the MINLP model

Analyse DP plot for an alternative initial flowsheet ik

^.-^TA 1.1

^new ^

^V^

N

1 Av^target-^

Optimum Figure 1: The philosophy of the hybrid synthesis method. Most MINLP-models are non-convex and their solutions are not guaranteed to be global, therefore, total cost can be used to measure the optimality of MENs generated by MINLP. The installed cost of process units is commonly estimated from cost charts and cost indices which estimate the costs within 20-30%. These costs are then annualised by factors in the range 20-40% before being added to annual operating costs to give TACs. This means that a 10% approach of the TAC targets can be regarded as being optimal.

229 In the hyperstructure model of Papalexandri et ah (1994) we incorporate physically meaningful structures to initialise the MINLP solver. These initial structures may be: a. An initial solution whereby the mass-exchange duty is completed by external mass separating agents. This approach is analogous to HEN where the heating and cooling duties are completed by externally derived steam or cooling water; or b. A pinch-based initial solution. Once an initial solution is incorporated into the MINLP model, the model is solved via the DICOPT solver employing the Outer approximation algorithm for equality relaxation and augmented penalty (OA/ER/AP). If the resulting solution does not meet the 10% TAC margin, an alternative initial flowsheet is presented to the MINLP solver. A driving force diagram is used to help the designer identify the regions in the reported network that do not make use of the available driving force. The model is then solved with the new initial flowsheet and if the solution is within the target margin, it is accepted as an optimal solution.

3. Case Study 3.1. The problem statement The selected case study involves the dephenolisation of two aqueous streams, Rj and /?2, by solvent extraction (Hallale, 1998). The process MSAs are gas oil {Si) and lube oil {S2). The external MSA is light oil {Ss). The problem data is given in Tables 1 and 2. Table 1: Stream data for the dephenolisation problem. Rich Streams Ri R2

Lean Streams Si S2 S3

G (kg/s) 2 1

y^ (mass fraction) 0.050 0.03

y^ (mass fraction) 0.10 0.006

Density (kg/m3) 1000 1000

L^ (kg/s) 5 3

x^ (mass fraction) 0.050 0.03 0.0013

x^ (mass fraction) 0.10 0.006 0.015

Density (kg/m3) 880 930 830

00

M

b

2 1.53 0.71

0 0 0.001

Table 2: Equipment data for the dephenolisation problem. Exchanger cost (installed) t Eo

Annualisation factor

$9 050V"^ (volume in m^) 10 minutes per stage 100% 0.2

Cost (k$/yr)/(kg/s) 0 0 239.4

230 3.2. The approach Step 1: The supertargets This step involves the determination of the total annual cost target for the expected flowsheet. Using the supertargeting results reported by Hallale (1998), the total annual cost for this problem is $226000 with $158400 contributing to the annual operating cost and $338000 (annualised by multiplying by 20%) accounting for the annual capital cost. Step 2: The superstructure The MINLP model is similar to that of Papalexandri et al (1994). The practical issues regarding the handling of logical operators in the MINLP model are discussed in Zsitkai ^r a/. (2001 and 2002). Step 3: Constructing an initial flowsheet The flowsheet is initialised by using all the available external MSA (S3) to recover the phenol from the rich streams. Step 4: Optimising the MINLP model The hybrid model is implemented in GAMS (Brooke et al., 1988) on a PIT Celeron 533 MHz PC and solved using DICOPT solver implementing an Outer Approximation algorithm. The solution for the dephenolisation problem is similar to the proposed initial structure and has a total annualised cost of $2 236 000 which, is far beyond the 10% margin of the target. The operating and capital cost contributions to this cost are $2 230 000 and $6000 respectively. The MINLP solver did not add other exchangers or use an of the available process lean streams. Si and S2. This can be attributed to the fact that the solver could have been trapped in a local optimum (which is a characteristic of MINLP optimisation solvers). Step 5: Driving force analysis An analysis of the flowsheet in terms of the use of driving force by the selected matches will help in the selection of a new initial flowsheet. It is envisaged that the new flowsheet will re-route the MINLP solution search path to an optimal solution according to the criteria of the hybrid method. The method of constructing a driving force diagram is discussed in detail in Hallale (1998). In Figure 2, the Exchangers 1 and 2 are superimposed in the composite operating line. The exchangers are shown to be making too much use of the available driving force. To illustrate Step 5 we now initialise the MINLP solution with a pinch-derived flowsheet. The final hybrid solution obtained from initialising with a pinch solution is given by Figure 3. The hybrid solution is similar to the pinch solution except for the distribution of the number of stages among the exchangers and the reduction in the final composition of S2. Table 3 compares the results obtained for different initialisations. The hybrid solution is achieved through the simultaneous optimisation of the capital and operating cost and the generation of a network structure and through the iteration between the economic objective and the mass transfer driving force.

231

Figure 2: Driving force plot for the solution obtained by initialisation with an external MSA only. Exch. Nst Load

7 1 0.00125

6 7 0.006

.m-(?} 9.006

0.0106

<7)M11^

0.005

3 13 .0369

5 4 6 13 0.0034 0.0096

3.71 kg/s

(^_^)

0

0.0154 0

2 6 0.0146

1 2 0.0321

0.0339 Q M ^ ^ 2

0.0154

00.00761

Flowrate (kg/s)

Q

ao3JV1 1

0.015

0.0073981 0.01

0.01486

^ ^ ^ ^ _ 0 J L O 2 5 5 ^ 2.34

3.65xlOi

001^

>0.53

Figure 3: Hybrid solution resulting from a pinch-derived initial flowsheet. (CAP = $76600, OPC = $158400) Table 3: Cost of the optimum solutions from tested initialisations. Initialisation External MSA External MSA + S2 External MSA + Si+ S2 Pinch based

TAC ($/yr) 2 236 000 960 700 272 000 235 000

CAP ($/yr) 6 000 18 400 80 000 76 600

OPC ($/yr) 2 230 000 942 300 192 000 158 000

Number of units 2 3 4 7

232

4. Conclusions This paper has presented and tested a design philosophy for the synthesis of mass exchange networks whereby an MINLP approach is integrated with pinch analysis tools. At the heart of the integration is the use of pinch-based total cost targets to evaluate the optimality of MINLP solutions and driving force diagrams to identify different initial solution structures. A case study was solved to illustrate the hybrid philosophy. An important conclusion from the case study is that although the hybrid approach is able to meet the total annual cost target criterion of 10% it still suffers the MINLP limitations in terms of the solver getting trapped in local optima. The result of this is that solutions generated tend to be similar to initial structures given to the solver.

5. References Brooke, A., Kendric, D. and Meeraus, A. (1988). GAMS, A user's guide. The Scientific Press, San Fransisco. El-Halwagi, M. and Manousiouthakis, V. (1989). Synthesis of mass exchanger networks, AIChE J., 35(8), 1233-1244. Grossmann, I. and Daichendt, M.M. (1996). New trends in optimisation-based approaches to process synthesis, Comp. Chem. Eng., 20(6-7), 665-683. Hallale, N. (1998). Capital cost targets for the optimum synthesis of mass exchange networks, PhD thesis. University of Cape Town. Hallale, N. and Eraser, D.M. (1998). Capital cost targets for mass exchange networks. A special case: Waste minimisation, Chem. Eng. Sc, 53(2), 293 - 313. Hallale, N. and Eraser D.M. (2000a). Capital Cost Targets for Mass Exchange Networks, Parts I-II, Computers and Chemical Engineering, 53(2), 293-313. Hallale, N. and Eraser D.M. (2000b). Supertargeting for Mass Exchange Networks, Parts I-II, Trans I Chem E, 78, Part A, 202-216. Kravanja, Z. and Glavic, P. (1997). Cost targeting for HEN through simultaneous optimisation: a unified pinch technology and mathematical programming design of large HEN, Comp. Chem. Eng., 21(8), 833-853. Papalexandri, K.P., Pistikopoulos, E.N. and Floudas, C.A. (1994). Mass exchange networks for waste minimisation: a simultaneous approach. Trans. Inst. Chem. Eng, 72(Part A), 279-294. Wang, Y. and Smith, R. (1994). Wastewater minimisation, Chem. Eng. Sci, 49, 9811006. Zsitkai, Z., Lelkes, Z, Rev, E. and Fonyo, Z. (2001). Solution of MEN synthesis problems using MINLP: Formulation of the Kremser equation. Proceedings Escape-11 Conference, Kolding, Denmark, European Symposium on Computer Aided Process Engineering -11,1109-1114, Elsevier, Amsterdam. Zsitkai, Z., Rev, E., Fonyo, Z., Msiza, A.K. and Eraser, D.M. (2002). Comparison of different mathematical programming approaches for mass exchange network synthesis. Proceedings ESCAPE-12 Conference, Eds: Grievink, J., Schijndel, J. van. The Hague, The Netherlands, 361-366, Elsevier, Amsterdam.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

233

Multiperiod Synthesis and Operational Planning of Utility Systems with Environmental Concerns A. P. Oliveira Francisco^ and H. A. Matos^ ^Dep. de Eng. Quimica, Inst. Sup. de Engenharia de Lisboa, 1949-014 Lisboa, Portugal ^Dep. de Engenharia Quimica, Instituto Superior Tecnico, 1049-001 Lisboa, Portugal

Abstract Utility plants supply the required energy demands to industrial processes. Several authors were addressed the synthesis and design of those plants. However, a multiperiod model for utility systems including environmental concerns wasn't described until now. This paper presents an extension of Iyer and Grossmann (1997, 1998) model to synthesis and multiperiod operational planning in order to include the global emissions of atmospheric pollutants issues coming from the fuels burning. A new four steps algorithm is introduced to solve this multiobjective model. One motivation example enables us to compare the different units and fuel selection and also the operation periods of an industrial utility system taking in account the electrical power import/export policy and environmental concerns.

1. Introduction Utility plants supply the required energy demands to chemical processes, namely, mechanical, electrical and thermal power (different levels of steam). Changes in specifications, composition of feed and seasonal product demands create several process conditions with the corresponding variation in the utility demands during one annual horizon. Several authors were addressed the synthesis and design of utility plants. Among these authors, Papoulias and Grossmann (1983) described a MILP model for the synthesis and design of utility systems, for fixed demands. Iyer and Grossmann described models for multiperiod operational planning (1997) and synthesis and operational planning (1998) of utility systems. Chang and Wang (1996) described a multiobjective programming approach to waste minimization in the utility systems of chemical process, using the concept of global emissions of gaseous pollutants. This model merging economic and environmental concerns in the utility system synthesis was stated for fixed utility demands. Oliveira Francisco (2002) described a methodology for the synthesis and multiperiod operational planning of utility systems in a heat integrated industrial complex. This comprises a multiperiod model for utility systems including environmental concerns. The purpose of the present paper is to show the structure of this modified model and the resolution algorithm, applied to a simple example problem.

234

2. Problem Deflnition Given a set of time variable (multiperiod) demands of steam at various levels of pressure, electricity and mechanical power, the problem of synthesis and operational planning of the utility system consists in a structural and parameter optimization from a superstructure of alternatives. The superstructure will be decomposed in a set of feasible configurations. For each feasible configuration the unit sizes are such that allow demands satisfaction in all operation periods. In a single objective problem - only economic optimization - the configuration with the lowest total cost (investment and operational costs) for the horizon of planning should be chosen. If in addition to economic optimization we have to satisfy to other objectives, for example, environmental concerns, the problem arises to a multiobjective problem and a different optimization strategy should be adopted. The superstructure of utility system adopted in this work is derived from superstructures described by Papoulias and Grossmann (1983) and Iyer and Grossmann (1997, 1998). Figure 1 exemplifies the superstructure adopted for the Example Problem. Purchased Power 1 Power 1 Exports

Power 1 from Turbines

fel Purchased VHP Steam — n

Power 2 from Turbines

Unit 21

Figure 1. Superstructure for Example Problem.

Power 1 Demands

Power 2 Demands

235 This superstructure includes several steam headers at various pressure levels (VHP, HP, MP and LP). Steam can be generated in either conventional fired boilers (units 1, 2 and 20) or with waste heat boilers (units 13 and 28) receiving hot gases from gas turbines. There is a deaerator (unit 11) receiving make-up water and condensates returned from process utilizations. A condenser (unit 8) is provided for condensation of LP steam from unit 4. Power can be generated with several types of steam turbines, gas turbines (units 12, 27 and 30). Electrical generators can be driven by steam turbines or gas turbines. Gas turbines can operate in a stand-alone basis or associated with waste heat recovery boilers. There are also several types of auxiliary equipment as fans, pressure reducers and pumps.

3. Model Formulation Our model for the utility system is an extension of the multiperiod models described by Iyer and Grossmann (1997, 1998) in order to include the concept of global emissions of the gaseous pollutants that came from fuel burning. Following Smith and Delaby (1991) global emissions comprises local emissions derived from the production of utilities in industrial site and the balance between increasing/lowering of the emissions in the regional power station due to electricity imports and exports to regional power network by the utility system. The extended mathematical model for the utility system can be formulated as follows: P

zp=

min

fo(yd'^)-^^ft(xt^yt)-^^

y^,y^,d,x,

t=l

s-t. ht(d,y,.y,.xt.et)^0,

P

K

lAkEGkt

d)

t=\k=\

t = l...,P

(2)

jc,-Q"y,<0,

f = l,...,P

(3)

xr-a'y,>0.

t = 1,..., P

(4)

y, > y , ,

f = l,..., P

(5)

iy,
(6)

EGia-LEMk(llQ„r,)^0

(7)

n r

d& R\x,e

R'^XR^, y ^ G { 0 , i y ,

y,G{0,iy'''

Where y^ are integer variables (0-1) defining the selection of units for the design; d design variables defining the sizes of units; y^ integer variables (0-1) that determine the operational status on/off for period t; Xt the state and control variables for period t, Q the parameters (e.g, utility demands) for period t, EGkt the global emissions of pollutant k, in period r, Q^rf ^^^ production of level r steam, in the unit n, in period t, as the absorbed heat in the steam generator, LEMj^ the limit of global emissions of pollutant k, expressed in relation to the absorbed heat in the steam generator, Xk the weighted

236 parameter meaning the pollutant k contribution to the objective function, i^Q,i^Q are valid limits, lower and higher , respectively, P the number of periods and a a scalar lower than P. The objective function includes the investment cost for the design (fo) and the sum of the operation costs (ft) for all periods r = 1, ..., P., as well as the above referred weighted terms of global emissions of pollutants. Specific integer variables (binary, 0-1) in appropriate restrictions of the mathematical model allow the selection of operation on/off status and operations modes, e.g. extraction or condensing steam turbine. In the Example Problem given below we adopted a MILP formulation for the utility system optimization.

4. Decomposition Algorithm Iyer and Grossmann (1998) proposed a bilevel decomposition algorithm for solving his model. In the described algorithm, the first step is solving a design problem (DP) obtained from the principal model by making zero all fixed operation costs in the objective function, removing constraints of type (4) and (6) and by replacing yt with y^ in the constraints of type (3). The solution of model DP gives a lower bound for the objective function of principal model and provides values for design integer variables yd to use in the next step. In a second step a planning model (OP) is solved by fixing in the main model variables y^ obtained in first step. Solution of OP gives a higher bound for the objective function of principal model and provides an operational plan for the next time DP is solved. Iterative procedure with adding of appropriate cuts converges to the solution of main model. Then a modification of the Iyer and Grossmann algorithm was implemented: a) Fixing values of weighted parameters ^j^. b) Solving the utility system model with Iyer and Grossmann (1998) bilevel decomposition algorithm. In this step we obtain a design and operational plan for the utility system. c) Fixing the values calculated in step b) for binary variables ya and yt in constraints and solving the model obtained by replacing objective function (1) with a second objective function (8). ZE

= min E Z /lit ^^kt

^^^

t k

This step provides a utilization plan for fuels (binary variables) in the utility system arising to a minimum of global emissions. d) Fixing binary variables associated with the selected units for design (y^) and with the utilization plan of fuels obtained in c) and solving the model with objective function (1). Solutions obtained in steps b), c) and d) correspond to diverse importance given to economic and environmental concerns. Less pollutant fuels have higher costs than more pollutant content fuels. Thus, total cost for these three solutions will be b) < d) < c). Since all three solutions will satisfy the global emissions limitations the selected solution depends from the user criteria.

237

5. Example Problem A set of multiperiod utility demands of a new industrial complex is shown in Table 1 (one year with twelve equal periods). The synthesis of the utility system for this site is based in the superstructure represented in Figure 1. Table 1. Steam/BFW and power demands for the industrial complex for each period. Period Steam VHP (tAi) HP MP LP BFWfor Process (t/h) Power 1 (P) 2 (MW)

1 55 150 140 350 50

2 40 149 145 360 55

3 35 143 135 370 55

4 60 155 140 350 50

5 50 150 120 365 50

6 7 8 60 65 35 180 150 150 170 130 150 380 370 370 50 55 50

9 55 180 170 390 50

10 55 120 130 300 50

11 60 165 150 373 50

12 40 120 145 300 55

19.7 6

18 4

17 4

17.5 5

18 4.1

19 5

17 6

18 4

17 4

16.2 5

17.2 4.4

19.5 6

p=\ - electrical power; p=2 - mechanical power; VHP - 10 MPa; HP - 5 MPa; MP - 2 MPa:; LP - 0.35 MPa.

This problem was formulated as a MILP and solved for two situations: Case A - the utility system is not allowed to import electrical power from regional network; Case B electricity imports are allowed. For each case we solve different models: Model 1.1 - Iyer and Grossmann model with local and global emissions calculation. Model 1.2 - Iyer and Grossmann objective function with constraints (2)-(7). Model II -This paper work model (solution from d) in above algorithm). Results are shown in Tables 2 and 3. An increase of the total cost is obtained moving towards the different models, since they take in account more environmental constraints. Moreover, Model II shows a smaller exploit of the Gas Turbines compared with Model 1.2 and the most intensive use of Steam Turbines. Table 2. Selection and operational plan (^WP) of units for Case A/Case B.

Unit. Operation mode 1 (HP boiler) 2 (MP boiler) 13 (HP boiler) 20 (VHP boiler) 28 (VHP boiler) 3.1 (ST) 3.2 (ST) 4.1 (ST) 12.1(GT) 27.1 (GT) 30.1 (GT)

#WP

Model LI Total Cost

12/12 8/7 -/12/12 1/11 / -/-/-/1/-/3

Case A: 68.58 M$/year CaseB: 71.42 M$/year

#WP

Model 1.2 Total Cost

12/12 4/11 10/6 12/12 11/11 -/-/-/10/6 11/11 11-

Case A: 77.30 M$/year Case B: 76.70 M$/year

#WP 12/12 9/8 -/12/12 4/-/1 11/10 10/9 -/4/-/-

#WP- Number of Working Periods; ST- Steam Turbine; GT Gas Turbine

Model II Total Cost

Case A: 90.10 M$/year Case B: 90.44 M$/year

238 Table 3. Fuel usage and Global Emissions of CO2 and SO2 for Case AI Case B.

Fuel usage (in units 1,2 and 20) (kt/year)

Fuel

Model LI

Model 1.2

Model II

1

-/-

-/0.6

387.2/393.9

2

-/-

3

-/-

298.2 / 347.4 -/-

-/-/-

4

448.8/422.5

65.9/44.1

-/-

448.8/422.5

364.1/392.1

387.2/393.9

1272/1544

1275 /1372

861/851

33.7 / 36.9

13.4/13.4

-2.44/-2.70

Total Global Emissions

CO2 (kt/year) SO2 (kt/year)

Fuel: 1 - 75.38% C; 0.1% S; 2 - 86.47% C; 1.35% S; 3 - 87.26% C; 0.84% S; 4 - 84.67% C; 3.97% S.

The fuel consumption reduction obtained by solving the models is also due to reach optimal power import/export strategy (Oliveira Francisco, 2002). Moving towards the models a decrease in Global Emissions could be found, but a significant one is achieved in the Model II for CO2 and SO2. The negative values in the SO2 Global Emissions means that a power is exported from the industrial site causing a necessary lower working level at the Regional Power Station (RPS). The model was solved assuming that RPS burns a coal with 74.5% of C and 2.0% of S.

6. Conclusions Present work formulation is useful for preliminary design and can be applied to grassroots projects or to the revamping of existing utility plants. A motivation example enables us to compare total cost between models. The introduction of environmental terms in the objective function and in the set of constraints show us a different choice of the fuel with a increase of about 7 - 31 % of the Utility Plant annual total cost. This also corresponds a significant reduction in the Global Emissions - about 32 % and more than 100% in C02and SO2, respectively.

7. References Chang, C.-T. and Hwang, J.-R., 1996, A Multiobjective Programming Approach to Waste Minimization in the Utility Systems of Chemical Processes. Chem. Eng. Sci., 51(16), 3951-3965. Iyer, R. and Grossmann, I.E., 1997, Optimal Multiperiod Operational Planning for Utility Systems. Comput. Chem. Eng., 21(8), 787-800. Iyer, R. and Grossmann, I.E., 1998, Synthesis and Operational Planning of Utility Systems for Multiperiod Operation. Comput. Chem. Eng., 22(7-8), 979-993. Oliveira Francisco, A.P., 2002, MSc Thesis, Lisbon, I.S.T., U. T. L. Papoulias, S.A. and Grossmann, I.E., 1983a, A structural optimization approach in process synthesis -1 Utility systems. Comput.Chem. Eng., 7(6), 695-706. Smith, R. and Delaby, O., 1991, Targeting flue emissions. Trans. IchemE, 69(A), 492505.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) • © 2003 Elsevier Science B.V. All rights reserved.

239

Sizing Intermediate Storage with Stochastic Equipment Failures under General Operation Conditions Eva Orban-Mihalyko^ and Bela. G. Lakatos^ ^Department of Mathematics and Computing , ^Department of Process Engineering University of Veszprem, H-8201 Veszprem, PO Box 158, Hungary email:[email protected], [email protected]

Abstract An algorithm and simulation program have been developed for sizing intermediate storages of batch/semicontinuous systems taking into account stochastic equipment failures under general operation conditions. The method is based on the observation that any process of this system can be built up from a random sequence of failure cycles of finite number. By means of simulation and statistical evaluation of the results of the simulation runs the storage is sized at a given significance level. The computation time is favourable, and it appears to be a linear function of the number of the failure cycles.

1. Introduction The intermediate storage has an important role in improving operating efficiency of batch processing systems. It increases the variability of the system and reduces the process uncertainties. Over a long time horizon, it can also buffer the effects of equipment and batch failures when it is sized adequately. The sizing of an intermediate storage often can be treated as a deterministic problem, but, when the equipment and batch failures are significantly of random nature, then its sizing becomes a stochastic rather than deterministic task. Deterministic variations in the failure frequency and recovery time have been considered by Karimi and Reklaitis (1985) and Lee and Reklaitis (1989), while stochastic variations have been studied by Odi and Karimi (1990,1991), and Mihalyko and Lakatos (1998). In these studies, however, constants filling and withdrawing intensities were assumed. The aim of the present contribution is to study the problem under generalized conditions, i.e. when the intensity of filling and withdrawing of material into and from the intermediate storage may be changed arbitrarily during the operation.

2. Process Model Let us consider a non-continuous processing system with n upstream and m downstream units (usually n?^) with an intermediate storage. We assume that the processing units are operated periodically, and stochastic failures of the units under general conditions may occur. Furthermore, we suppose that the filling and removal rates may vary in time arbitrarily, i.e. they are described by general functions exhibiting at most finite number of jump discontinuities. Let o\^,... co^^ and^2,1 v^2,m denote the operation periods of the upstream and downstream units, while t^^ ,-hn

^^^ h,\ ^"•h,m ^^^ the filling and removal times, respec-

tively. Further, let t^^ ,..• ^i°„ and t^^ .— tl^m denote the corresponding delay times. We

240 suppose that t^^ +1^^^ < co^^ for any unit. Then, the mathematical model of the process is formulated under the following assumptions: 1. The ratio of two arbitrary periods is a rational number. 2. Only one upstream unit may suffer failure at the same time. Let its index be 1. 3. The failed unit does not transfer material into the storage during its repairing. 4. The failure of a unit does not affect the operation of the remaining ones. 5. The differences between the serial numbers of the failure periods, denoted by ^„ are integer random numbers of the same distribution having bounded range. We suppose that 4 /=1,2,... are independent. j

Then the serial number of the f^ period of failure is expressed as ^ ^ / , its initial /=i

moment is ^{^i -1)^1,1 , and the fmal moment is ^ ^ / ^ ^ • As a consequence, the/^ j-i

failure cycle is, by definition, the interval

S^/-^u'S^/-^i,

as it shown in Fig. 1.

The filling and removal rates are described by the following functions showing at most finite number of discontinuities: 0, if

0< CO, 'd,s

\(o.'d,s bef.Ai)-

fciM

CO,

t^ +t

M,s

), if

CO, 'd,s

(1)

0),

\co.

!lilh±<. t \co.'d,s co,^

0, if

where /^^ > 0 is some positive function, while d=l and s=l,....n for the upstream, and d=2 and ^=l,....m for the downstream units. The amount of the material transferred by the s^^ unit during an operation period is t=0

1

'

^i'i

tt•

^^^^'^

•

1 L

(^7+&)^7.7

1

[ ik i L

t

•

^ ^

^ ^ w 2^^ failure cycle w Moment of the 7^' Moment of the 2"' failure failure

V^ failure cycle

Fig.l. Characteristic time intervals of the process with equipment failures. ^
\bef,,{x)dx.

(2)

241 and the total amount of the material transferred by the s^^ unit in the time interval [0,f] may be expressed as

Vj-{t)^\bef,,{x)cbc.

(3)

When a failure of the 7" upstream unit occurs, then the filling intensity is described by the function ^e/i,(0,

7 >

fg

if

^ •«i.i /=1

befli^^(t) =

0, if

7J

re

(4)

j

•^u )

and the total amount of material transferred of the V unit is expressed as f

(5)

Then, the amount of material in the intermediate storage is varied in time according to /o

\

0

"

0

'^

0

(6) 5=2

5=1

where (taf) denotes a vector of dimension (n+m) of the delay times.

3. Sizing of the intermediate storage In order to have material in the intermediate storage always sufficient to operate the system without problem, it is necessary to have an initial amount y(0) in the starting moment of operation as

-minVh^'At).

(7)

Oil
There will no overflow if the volume of the storage is equal to maxVh^'\t)

+ V(.0)

(8)

As a consequence, the volume of the storage sufficient to operate of the system is expressed

0
0
(9)

Since in the present case the failures of the units are stochastic, so is also the function (,o )

Vh ''\ and the goal is to determine the distributions of the maxima and minima of this very function. In order to achieve this we proceed in the following way. We divide the process in the interval [0,0 into sub-processes according to the failure cycles and investigate the variation in time of the amount of material in the storage in

242 these sub-processes consecutively. The method developed is based on the following statements. Consider the function in the/'' failure cycle having the following form Vh^'''Xt)-Vh^''\^^i

'CO,0 for te

S^/-^U'S^i

CO,

. Then we have the

Statement 1. The actual delay times related to the initial moment of the /^ cycle becomes modified compared to the original ones, and are given as a function of the initial moment the cycle 7-1

^1,1

y-1 1=1

'(^ny w...+^".-E^/'^u+^'/.^-^

(0,

rl(Z^rco,0 =

(10) •7-1

" 7-1

S^/-^i.i

/=!

1=1

,+^°.+'.,.-Efi'^u
1=1

_ while the amount of material in the storage is varied in time according to Vh'^^'\t)-Vh^''\Y^^,

•co,,)=:Vh '' -

( / - ^ f , -co,,).

(11)

Statement 2. The number of actual delay times r^^ for all upstream and downstream units is finite. Statement 3. The number of vectors \fd,s} formed from the possible actual delay times 1. TT TT u ^u Pu IS equal to I I ^1 ^ • I I ^2 5 » where —— = '

s=2

5=1

'

CO,s

q,^,

^1,1 ,

P2,s =

(O^^s

Q2,s

. . , , and p^ ^ and q^ ^ are rel-

ative primes. The direct consequence of the Statement 3 is the Statement 4. The number of sub-processes arising in an arbitrary process is finite and is n

m

given by A' • J][^i^ '11^2,^ ' where K is the number of possible values of ^^. Statement 5. The maximum and minimum problems, providing the maximum and minimum values of the variation of amount of material in the intermediate storage in any failure cycle, are reduced to finding maxima and minima of finite number of functions. Statement 6. Let M^'-'^k) and m^^'^k) denote the global maximum and global minimum of problem of Statement 5, where k stands for the possible values of random variable ^1. Then the maximum and minimum value of the amount of material in the intermediate storage in the whole/^ failure cycle can be obtained as a sum of the initial /0

)

(0

\

amount of the cycle, and the global maximum M^'^''(^') and minimum m^'^'^^p, respectively. Subsequently, the maximum and minimum values in the whole interval of the process can be obtained recursively.

243 Statement 7. Any process can be built up from a random sequence of functions related to the failure cycles of finite number. By means of simulation and statistical evaluation of the results of simulation runs the storage can be sized at a given significance level.

4. Example For the sake of illustrating the method developed, consider a batch system with two upstream and two downstream units the operation parameters of which are as follows: ^1,1 = '7 ' ^1,2 = 4, 6^2,1 = '7 '^2,2 = ^ ' ^1,1 = 4, t^2 = 3' ^2,1 = 5, ^2 2 = 2 , t^^ = 2, ^1^2 = ^ ,

^21 = 1, ^2,2 "= i • Let us assume that the filling and removal rates of the units are described by the functions of the form: f^^{t) = 4t, fiji^) = 4t, /2,i(0 = i, fi,!^^) - St. Then, the number of the possible vectors of delay times is equal 12 that are given in Table 1. If the first failure of the unit 1 occurs in the 7^^ 2""^ or 3'"^ period of operation, respectively, then 36 different sub-process variations of the changes of the amount of material in the storage during the first failure cycle are possible. Three such subprocesses, corresponding to the vector of delay times (2,0,1,1), are shown in Fig.2, the Vh'"'"'•"(t)

\

\ \

V

a) ' b) ' c) ' Fig. 2. Variation of the amount of material in the storage in the r^ failure cycle when the r^ failure occurs in the a) V^ period, b) 2" period, c) 3^ period of operation Table 1. The characteristics of the possible vectors of delay times. m(k) and M(k) minimum and maximum for failure in the k^ period of operation; EVh - expected value of the amount of the transferred material in the storage during one cycle Vector of the delay times (2,0,1,1) (2,0,1,0) (2,0,1,-1) (2,1,1,1) (2,1,1,0) (2,1,1,-1) (2,-2,1,1) (2,-2,1,0) (2,-2,1,-1) (2,-1,1,1) (2,-1,1,0) (2,-1,1,-1)

m(l) -18.5 -20 -20.5 -24.5 -24.5 -30.5 -16.5 -18.5 -26.5 -10.5 -16 -22.5

Mil) 3.6 0 0 0 0 0 10 6 10 11.5 2 3.5

m(2) -1 -11 -13 -8 -17 -8 -17 -15 -4 -9 -10 -8

M(2) 23.5 19.5 13.5 19.5 9.5 11.5 19.5 17 17 21.5 21.5 21.5

m(3) 0 -8.5 -10 -8 -14.5 -12 -4 -6.5 -6.5 0 -0.67 -6.5

M(3) 33 31 31 30.5 26.5 21 39 35 27 41 31 33

EVh 3 -13/6 -11/3 -3 -25/3 -29/3 13/3 -1 -113 19/3 1 -1/3

values of minima and maxima obtained for these 36 variations, together with the expected values of the amount of transferred material in the storage during one cycle, are presented in Table 1. The global minima and maxima of these functions were

244 determined numerically by the combination of the grid and modified simplex method. According to Statement 7, each process of the system under investigation can be built

1000

1200

1400

t

a) b) Fig. 3. Variation of the amount of material in the storage through a) 15 and b) 100 randomly selected failure cycles, corresponding to the vector of delay times (2,0,1,1). up from these 36 sub-processes. These processes differ from each other in the sequence of the sub-processes sequenced randomly one after the other. These processes can be generated by computer simulation, selecting one of the possible sub-processes randomly according to a defined probability distribution. Such process is shown in Fig.3 that consists of 15 and 100 failure cycles, respectively, the sequence of which were generated randomly by using the discrete uniform distribution. Carrying out 10,000 simulation runs, consisted of 100 failure cycles under the same operation and simulation conditions, we obtained mean value of minima=-483.08, mean value of maxima=27.9316, and mean value of their differences=509.79. Based on the nu-merical results, it can be concluded that the difference is smaller than 684.1619 with probability 0.95, hence 684.2 is a sufficient size for the storage at significance level 95%. Notice that, in the example, the expectation of the transferred material in the r^ cycle is positive on the basis of the initial delay time but the remaining delay times, as it well seen in Table 1, cause a decreasing tendency in the variation of the process.

5. Conclusions A method and simulation program has been developed for sizing intermediate storages in batch/semi-continuous systems taking into account stochastic equipment failures under general operation conditions. The method is based on the observation that any process of this system can be built up from a random sequence of failure cycles of finite number. With the aid of the analysis of the problem, optimisation on large time intervals of the processes is replaced by optimisation on smaller intervals of the sub-processes of that very process. By means of simulation and statistical evaluation of the results of the simulation runs the storage may be sized at a given significance level. The computation time is favourable, since it is a linear function of the number of the failure cycles.

6. References Karimi, LA. and Reklaitis, G.V., 1985, AIChE Journal, 31,44. Lee, E.S. and Reklaitis, G.V., 1989, Computers chem. Eng., 13, 1235. Mihalyko, E.G. and Lakatos, B.G., 1998, Computers chem. Eng., 22, S797. Odi, T.O. and Karimi, LA., 1990, Chem. Eng. Sci., 45, 3533. Odi, T.O. and Karimi, LA., 1991, Chem.Eng.Sci., 46, 3269.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

245

Synthesis, Design and Operational Modelling of Batch Processes: An Integrated Approach Irene Papaeconomou^ Sten Bay J0rgensen^ Rafiqul Gani^ and Joan Cordiner^ ^CAPEC, Department of Chemical Engineering, Technical University of Deimiark, DK-2800, Lyngby, Denmark ^Syngenta, Grangemouth Manufacturing Centre, Earls Road Grangemouth, Stirlingshire, FK3 8XG, United Kingdom

Abstract The objective of this paper is to present a general methodology for the synthesis and design of batch processes. However, for the synthesis to be complete the operational modelling of the individual batch operations, such as reaction and separation, needs to be performed. The general methodology comprises a set of algorithms that supply the batch operational routes, which are a sequence of sub-tasks performed in order to achieve a specific objective for the reaction or separation task. That sequence is the operational model for every unit. Three algorithms are highlighted for the operational design of batch reactors, distillation columns and crystallizers. The algorithms are tested on case studies and the application results, including verification of the generated operational sequences through dynamic simulation, are presented.

1. Introduction The recent increase in the production of high-value-added, low-volume specialty chemicals, fine chemicals, pharmaceuticals and biochemicals has created a growing interest in batch processing technologies. In order to achieve a specific objective for the product, a number of tasks usually need to be performed for a period of time. The synthesis of batch operations requires the identification of the necessary tasks and their sequence. However, only when the individual tasks are fiilly characterized is the synthesis of batch operations complete. This can be achieved by simultaneous modelling and design of the operation of each batch task, where the objective is the minimization of a number of variables, such as time, utility costs or a combination. The operational modelling and synthesis in our approach entails the identification of subtasks and the order they need to be performed so as to reach the specified objective for the overall task. This provides the batch recipe for the individual task. The information acquired from the synthesis and the operational design is important for plaiming, scheduling and control design for batch operations. The general methodology consists of a number of algorithms that generate feasible batch recipes for specified operational and end constraints. The algorithms that have been developed so far are applicable to one-phase batch reaction, non-azeotropic batch distillation and also to batch crystallization and/or two-phase single unit separation. The algorithms, which are rule-based, provide the identity of the operational sub-tasks to be performed and the end of each sub-task and thereby, simultaneously synthesize, design and model the batch operations. The process design, the chemical hazard, the envirormiental impact and the safety risk of the processes define a set of constraints for the problem, which are then used to identify the end of the sub-tasks and to reject

246 infeasible operational schemes. Thermodynamic and physical insights are used to determine the next feasible sub-task, until the product constraints are met. The sub-tasks are defined as operations where the manipulated variables remain constant during the period of the sub-task. For example, operating at a specific reflux ratio and/or vapour boilup rate could be a sub-task considered for batch distillation. The algorithms also identify the principal operational parameters and a corresponding operational model where these parameters are the main variables. The operational model can be verified either experimentally or/and through simulation. Dynamic simulation has been used to analyse and validate the algorithms. The presentation will highlight the overall methodology through illustrative case studies.

2. Methodology The objective for the synthesis of batch operational sequences is to minimize the operating time and/or cost of operation. The focus in some cases might be the optimal time, while in others the minimization of energy/ operating costs. As there is a trade off between these two objectives, ultimately an optimization problem will have to be formulated and solved, where appropriate weights can be given to time and operating costs. However, all optimum solutions have to be feasible. Therefore, a methodology has been developed for the synthesis of batch operational routes, which consists of a set of algorithms that generate feasible/near optimum batch recipes for specified operational and end constraints. The conmion ground of these algorithms is the existence of a number of constraints that need to be satisfied at all time and the usage of manipulated variables to ensure feasible operation. The algorithms handle the operational modelling of each task by identifying the sequence of sub-tasks that need to be performed in order to achieve the objectives of the specified operation. An important feature of the algorithms is that the insights employed by the algorithm actually identify near optimum solutions without use of advanced numerical optimization techniques.

3. Algorithm for the Operational Design of Batch Reaction The algorithm for the design of the operation of batch reactors, with existent only one phase, multiple reactions taking place and operational constraints on temperature present, has been presented earlier (Papaeconomou et al., 2002). The key factor is the existence of desired reactions and of competing reactions, where the latter need to be suppressed. In addition to the operational constraints, there are also end constraints/objectives, namely the molefraction of the limiting reactant in the reaction of interest that should be as low as possible and the progress of the reaction of interest that should be as high as possible. At least one of the end constraints has to be satisfied. In this algorithm, apart from the operational constraints, a supplementary constraint on the projection in the end of selectivity is used. Selectivity Sij of reaction i over competing reaction j is defined as the ratio of the reaction rate of reaction i to the reaction rate of reaction j . The algorithm helps to identify the first operating step (subtask) based on the highest selectivity. For the generation of the recipe, rules are employed at all points to identify the end of each sub-task and to determine the next feasible sub-task, such as isothermal operation, adiabatic operation, heating, cooling, etc. The procedure is repeated until at least one of the product (end) objectives is met. Short example: The case is a batch reactor where a set of reactions is proceeding and operational constraints on the reactor temperature are present [300K = Tmin < T < Tmax = 360K]. There are reactions leading to the product, which are desired, while there are

247 also competing side reactions that need to be suppressed: Reaction 1: (Rl) + (R2) ^ (II) Reaction 3: 2 (11)-^ (12) + (B) + (H2) Reaction 2: (Rl) + (Il)-> (A) Reaction 4: (12) + (Il)<-> (C) The desired product is 12 and the desired intermediate product is II. Thus, reactions 1 and 3 are wanted, while reactions 2 & 4 are unwanted. Therefore, selectivity Sn and S34 must be high and above a certain value Sconstraim (example: Sconstraint=15). The application of the algorithm described above provides briefly the following sequence of operations. Table 1. Operational sequence for the case study generated from the algorithm. Sub task no 1 2 3 4

Type of operation Isothermal operation Heating Cooling Heating

Operating conditions 300 K Different amounts of heat Different amounts of heat Different amounts of heat

Operating time 0.1 hr varies varies varies

For this example, operating isothermally or adiabatically at any (starting) temperature in the accepted temperature range, leads to infeasible operation, because either the temperature or the selectivity constraint is eventually violated. However, isothermal operation at 300K is the best starting point and therefore, it is selected as sub-task 1. As soon as the selectivity constraint was about to be violated the end of this sub-task was detected and according to rules, the next sub-task was identified. Sub-task 2 was found to be heating, because it promotes reaction 1 (less exothermic) instead of reaction 2 (exothermic). A number of alternative feasible operational sequences were generated, as different amounts of heat from a range of available heat input were applied in sub-task 2. That also meant that the operating time for this step varied. The end of sub-task 2 was detected as the temperature constraint was about to be violated and cooling was applied as sub-task 3. The last sub-task was heating for the same reasons as sub-task 2. A detailed description of the results can be obtained from the author. The operational sequences were generated together with corresponding information related to the number, type and operating conditions of the sub-tasks. This information was then used to verify the feasibility of the alternatives through dynamic simulation with BRIC in the ICAS environment.

4. Algorithm for the Operational Design of Batch Distillation The algorithm for the generation of operational sequences for the case of batch distillation has been discussed in Papaeconomou et al., 2003 for the separation of multicomponent non-azeotropic mixtures. In this paper, a case study of binary azeotropic mixture is presented. The algorithm is applied, in order to obtain an operational route that will remove the azeotrope in minimum time and/or cost, so that the desired high purity product will remain in the vessel. The objective of the algorithm is to apriori identify the necessary sequence of sub-tasks in order to achieve desired specified end objectives for the products. These objectives are the product purity and the amount of product (yield) and they both have to be fulfilled. The algorithm employs a repetitive procedure to determine the operating conditions (reflux ratio and vapour boilup rate) along with a very good approximation of the operating time, for each sub-task. The only given data needed is the amount and composition of the initial charge and the desired product (distillate) specifications. The algorithm uses a set of simple equations for the distillation column (Diwekar, 1995) and adapts well-known methods, such as the driving force approach and the McCabe-Thiele

248 diagram to find quickly a near optimum recipe for the separation task. The strong feature of this algorithm is the use of the driving force approach to find the minimum reflux ratio and the reflux ratio used for the specific feed. The existence of a driving force is what makes the distillation feasible, and that is why it is not possible to cross a distillation boundary, such as an azeotrope where there is no driving force. As it has been discussed in Gani and Bek-Pedersen, 2000 operating at the largest driving force leads to the near minimum energy expenses. The advantage of using the driving force approach is that it gives you the physical insights to operate in an easy and near optimum energy costs way. For a specific feed composition, the largest driving force corresponds to the minimum reflux ratio, which however can only be supported by an infinite number of plates. Thus, for a specific number of plates a larger reflux ratio has to be used but still it should be as close to the minimum as possible. The end of each sub-task is detected as the following violation takes place. At some point the reflux ratio used approaches the actual minimum value for the corresponding composition in the vessel. At this point a new reflux ratio has to be used. The limiting composition at the end of the sub-task is found using the simple graphical method of McCabe-Thiele. The distillate amount and the amount remaining in the vessel are calculated from simple mass balance equations. The operating time of the sub-task is found from the overall material balance around the top of the column. This procedure is repeated until the desired yield is achieved. Short example: A mixture of methanol and methyl-acetate (15% kmol MeOH and 85% kmol MeAc) is to be distilled. The objective is to achieve a 99 % purity methyl-acetate left at the bottom of the column, with a 95 % recovery of the maximum yield. In the case of minimum boiling azeotropic mixtures, the azeotrope is considered to be the first product. The algorithm uses the azeotropic composition as the distillate specification. The application of the algorithm provides the following sequence of sub-tasks. The simulation engine in ICAS for batch processes, BRIC, has been employed for dynamic simulation to verify the suggested recipe. The operating conditions for each sub-task were defined, with the distillate composition being the end constraint for the sub-task, except for the last sub-task, where the purity of MeAc left in the column was the end constraint. The results are listed in table 2. Table 2. Operational sequence for obtaining the azeotrope, leaving pure MeAc in the column. Sub task no 1 2

Reflux ratio 4.8 10

Vapour boilup rate 100 100

Operating time 0.942 hr 0.465 hr

Simulated operating time 1.176 hr 0.459 hr

Ach. MeAc purity 95.89% 99.05%

Ach. MeAc recovery 95.91%

Table 3. Results for constant refl\ux ratio operation. Operation

No of intervals

Reflux ratio

Vapour boilup rate

Simulated operating time

Ach. MeAc purity

Ach. MeAc recovery

a) b) c) d)

1 1 1 2

4.8 8.5 10 [4.8,10]

100 100 100 100

1.615 hr 2.324 hr 2.629 hr 1.635 hr

99.05% V 99.05% V 99.05% V 99.05% V

84.90% 95.05% V 96.90% V 95.91% V

The operational sequence Hsted above was compared with constant reflux ratio operation. In that case, it was found that for low values of the reflux ratio, the two end

249 objectives could not both be achieved. For high values of the reflux ratio, the operating time was significantly higher than the one achieved by the operational sequence. Compared to operation with a constant reflux ratio, where both product objectives are achieved, the time in the generated recipe is by 30 % faster, as it can be seen in table 3.

5. Algorithm for the Operational Design of Batch Crystallization The algorithm for the operational design in batch crystallization is illustrated in Figure I. The objective of the algorithm is to identify in advance the necessary sub-tasks and their sequence, in order to achieve specified objectives for the separation task, namely the recovery of solutes (yield). The algorithm is using insights obtained from solidliquid equilibrium diagrams, with the purpose of generating a sequence of feasible/near optimum operational steps. The algorithm consists mainly of a repetitive procedure that identifies the nature of each sub-task and the operating conditions. The initial step is the actual generation of the phase diagram. The phase diagram is derived by drawing the solubility curves for a given temperature range for the operation of the crystallizers. In the repetitive procedure, the feed location is pinpointed to the diagram and the feasibility of the precipitation of the desired solid solution is checked. This is done by relating the feed point with the invariant point connected to the desired solute at each temperature. For the specific feed, the solute to precipitate is identified and the operational task is specified, in terms of choosing the operating temperature, removing or adding solvent, or mixing streams. The exact amount of solvent to evaporate or add can be found from the lever principle, since the material balances can be represented on the phase diagrams in the form of tie lines. It is significant to avoid regions on the diagram, where two solids precipitate, since this is not effective separation. For that reason evaporation is always less than the maximum and dilution is more than the minimum. Knowing the exact location of the slurry, the product yield can be computed, with the lever principle. The composition of the mother Hquor in equilibrium with the precipitated solute can be located on the phase diagram and treated as a new feed. The above-described procedure is repeated until the desired or maximum yield for the feed and range of operations is achieved. GIVEN DATA

I DRAW PHASE DIAGRAM

HjO

1

/^

1

/

\

SELECT OPERATIONAL TASK AND CONDITIONS

/

S/L SEPARATION

^' ^*--**^°°^

/^*t!fML2ff=3

1

/

/

••'

\

^N»ML2;§fc2—WW ^*°'^

'"^513

'ON

\

"'^A

//>'' ^^ ,

Figure 1. Schematic presentation of the algorithm for batch crystallization.

,

20

,

30

,

40

,

50

,

60

,

70

,

,

Figure 2. Phase diagram for the ternary system H20-NaCl-KCl

\

250 Short example: A ternary mixture of water, sodium chloride NaCl and potassium chloride KCl (85, 15 and 5 % w.t. respectively) is to be separated. The objective is to recover 95% of the dissolved NaCl. The permitted range of temperature is 0 to 100 ^C. At first the ternary phase diagram is drawn for the temperature range. For simplification reasons, only the minimum and the maximum temperature are shown in Figure 2. The precipitation of NaCl is feasible at any temperature in the range. However, the slurry density (and thus the yield) is higher as the temperature increases, and so the operating condition for the crystallizer is set to be 100 °C. The mother liquor is treated as a new feed and the procedure is repeated. The second sub-task is chosen to be crystallization at 0 °C. The mother liquor from that sub-task is treated similarly to Feed 1 and a cycle option is created. The results are given in table 4. Table 4. Operational sequence for the batch crystallizer, suggested by the algorithm. Sub-task no

Operation

Temperature

Saltpptd

Yield

1 2 3 4 5

Evaporative crystallization Cooling crystallization Evaporative crystallization Cooling crystallization Evaporative crystallization

100 °C OT 100 °C OT 100 °C

NaCl KCl NaCl KCl NaCl

73.6% 62.5% 90.1% 86.0% 96.3% > 95%

6. Conclusion A general methodology that allows the simultaneous synthesis, design and operational modelling of batch processes has been developed. For that reason a set of algorithms is used, which identify the necessary sub-tasks and their sequence, along with the principal operational parameters creating the operational model of the process. However, the strong feature of the algorithms is that they generate the operational model apriori with no use of rigorous models and minimum computational effort. All the algorithms were tested against case studies and results were briefly presented. Dynamic simulation verified that all the generated operational sequences were feasible, achieving all end constraints, and actually superior to one interval operation with constant values for the manipulated variables. The methodology, the algorithms and the associated computer aided tools provide a systematic and integrated approach to the solution of problems involving batch operation sequence and verification.

7. References Diwekar, U.M., 1995, Batch Distillation: Simulation, Optimal Design and Control. Taylor & Francis, USA, 15-30. Finch, B., 1970, How to Design Fractional Crystallization Processes, Ind. Eng. Chem., 62,6. Gani, R. and Bek-Pedersen, E., 2000, Simple New Algorithm for Distillation Column Design, AIChE J., 46, (6), 1271. Papaeconomou, I., Jorgensen, S.B. and Gani, R., 2002, A General Framework for the Synthesis and Operational Design of Batch Processes, Comput. Chem. Eng., (In Press). Papaeconomou, I., J0rgensen, S.B., Gani, R. and Cordiner, J., 2003, A Conceptual "design" Based Method for Generation of Batch Recipes, Proceedings of FOCAPO 2003, Coral Springs, 473.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

251

Modelling, Design and Commissioning of a Sustainable Process for VOCs Recovery from Spray Paint Booths Sauro Pierucci, Danilo Bombardi\ Antonello Concu\ Giuseppe Lugli^ Department of Chemistry, Materials and Chemical Engineering Politecnico di Milano, Milano, Italy ^ CTP: Costruzioni Termodinamiche Parmensi Parma, Italy

Abstract Air emissions from surface coating operations result from the evaporation of the organic solvents in the coatings and consist primarily of volatile organic compounds (VOCs). Aim of this paper is to present an innovative and sustainable process based on VOC absorption. An absorption tower is fed on the top by oil which efficiently absorbs at low temperature the VOCs contained by the off-gas which enters the tower at its bottom. Saturated oil from the column is then stripped at high temperature in a vacuum system which condenses VOCs at a temperature slightly below the ambient temperature. Stripped oil is then recycled to the absorption tower. The paper will provide a complete description of an industrial site located in Italy including modeling, design, commissioning, industrial operating conditions and economic evaluations.

1. Introduction Many manufactured items receive surface coatings for decoration and/or protection against damage. In general terms, the surface coating process comprises several distinct steps: surface preparation, application of coatings, and curing of coatings. Air emissions from surface coating operations result from the evaporation of the organic solvents in the coatings and consist primarily of volatile organic compounds (VOCs). In order to limit VOCs emissions, two possible actions are today foreseen (Gay 1997, Stone 1997): VOC destruction or VOC recovery. VOC destruction is accomplished via incineration (Darvin et al 2000). In general, costs of incineration can go up dramatically as the temperature is raised and when auxiliary fuel is required to accomplish the incineration. This can happen if the concentration of VOCs in the air stream is below 1000 ppm.(Vasilash 1997) There are two major types of VOCs recovery: refrigerated condensation (Stone 1997) and adsorption, followed by refrigeration (Hussey and Gupta 1997, Kent 1999). Although there are several types of condensation systems the most common adopted is a reverse Rankine cycle where a closed-cycle heat pump with a separate working fluid is used to condense VOCs. Adsorption is a process whereby the VOCs in the air stream are captured physically on the surface of a solid such as carbon. Steam or inert gas is

252 then used to regenerate the solid beds by stripping the concentrated VOCs from the surface before it becomes saturated. Aim of this paper is to present an innovative and sustainable process based on VOC absorption. An absorption tower is fed on the top by oil which efficiently absorbs at low temperature the VOCs contained by the off-gas which enters the tower at its bottom. The mass ratio between oil and gas is approximately around 1, so that a tray configuration results more efficient than an alternative packed column. Saturated oil from the column is then stripped at high temperature in a vacuum system which condenses VOCs at a temperature slightly below the ambient temperature. Stripped oil is then recycled to the absorption tower. The paper will provide a complete description of the plant including modeling, design, commissioning, industrial operating conditions and economic evaluations. The research project in the scope of this paper was jointly conducted by CMIC Department of 'Politecnico di Milano\ Faculty of Chemical Engineering and CTP, 'Costruzioni Termodinamiche ParmensV, an Italian Industry recently created and operating in the area of air cleaning for environmental purposes.

2. Absorption Process The absorption process proposed by this paper is sketched in Figure 1. Contaminated air at ambient temperature and pressure is cooled in C-1 to a value of approximated 4 °C, before entering the absorption tray-tower which absorbs contaminants with oil fed at the same temperature (4-5 °C) in the top of the column. Exhausted oil from the column bottom is preheated to 180"C in the plate heat exchanger E-2. A vacuum stripper (0.2 absolute bars) provides the separation of contaminants from oil through a top condenser working at a temperature slightly lower than ambient temperature. Regenerated oil is then cooled in E-2, flowing countercurrently with the exhausted oil-flow arriving from the column bottom. Regenerated oil is then fiirtherly cooled in the plate heatexchanger C-2. Clean air from the top of the absorption column, pre-cools the air from booths in E-1. Recirculating Oil

Air from Booths Air to Atmosphere

Absorber

Figure 1. Process schematic diagram.

Stripper

253 The cooling utilities required by C-1, C-2 and by the stripper condenser are provided by specific refrigeration systems electrically driven. The heating utility required by the stripper reboiler is supplied electrically with specific finned explosion resistants. The whole process is therefore requiring only electrical power at its battery limits.

3. Process Thermodynamics A typical contaminants composition is reported in table. 1. The TOC ranges normally from 1200 to 2500 mg/Nm^ in the air flow which is maintained practically at the controlled flowrate of 14000 Nm^/h. In special conditions the TOC may reach values up to 3500 mg/Nm^. Table 1. Typical contaminants composition. mg/Nm Acetone

31

mg/Nm Ethyl Acetate

Methyl Ethyl Ketone 683 Toluene

29

mg/Nm Butyl Acetate 492

523 Xylenes

802

The Ester Alcohol 2,2,4-Trimethyl-l,3-Pentanediol Monoisobutyrate was chosen as absorbent oil. Fig.2 reports the experimental vapor pressure dependance on temperature. Laboratory tests were carried out to evaluate the absorbance of contaminants into oil and for validating a thermodynamic model aimed to the prediction of components volatilities in the mixture. A good agreement was found assuming the vapor phase as ideal while the liquid phase activity coefficients were estimated by a standard UNIFAC model. Vapor pressure correlations for pure contaminants were derived from Perry and Green (1997).

350

400

450

500

550

Temperature [K] Figure 2. Vapor Pressure vs Temperature of the absorbent oil

254

4. Contaminants Quality The contaminants quality depends on the TOC value, so that the assumption of constant relative components ratio is not suited for a proper analysis of the process performances. The rational of such a situation depends on the coating adopted for each desired product. Asymptotically it might be expected that each coated product line provides a specific value of the TOC. Extensive on site analysis of air contaminants demonstrated this assumption.

• MethyEthyl Ketone • Xylenes A Buthyl Acetate • Toluene

0.15 1500

2000

2500

3000

3500

4000

TOC

Figure 3. Experimental contaminants mass fractions (relative) vs TOC. Moreover it was experimentally discovered that the dependence of TOC total value with internal contaminants composition varied almost linearly. Figure 3 reports the contaminants relative mass fractions as they result from experimental data. The assumption of a linear dependence arises with an acceptable approximation. Data derived from Figure 3 are useful for analysing the performance of the process at various values of the TOC in the off gas from the spray paint booths.

5. Process Design The basic design of the process was obtained by using the commercial simulator PRISMA. The 'engineering' was provided by the equipments suppliers. Table 2 reports the specifications used for the design. The dependence of internal relative composition of contaminants vs TOC was assumed to vary linearly as it was demonstrated by experiments previously reported in Fig.3. The design phase was conducted with the aim of finding an optimal compromise between costs and performances. This is a trial and error procedure which is strongly dependent also on the client requirements and utility availability. The optimum was, at the end, found with the main specifications reported in Table 2. It was assumed a tray efficiency in the absorber tower of 0.6 so that a 17 valve-trays column was constructed.

255 Table 2. Process Design specifications and main results. Design SpeciHcation Air Flowrate 14000 Nm-^/h TOC in the inlet stream 1500-2500 mg/ Nm^ TOC to atmosphere < 500 mg/ Nm^

Design Main Results Absorption Tower Theoretical Trays 10 Temperature 5'C Pressure 1 Atm Stripping Tower Theoretical Trays 12 Reboiler Temperature 190 X Subcooled Condenser Temperature 5°C Pressure 0.2 Atm 10 mVh Recirculating Oil Tot. heat-exch. surface 480 m^ Total energy absorbed 180 Kw

The stripping column adopted the same efficiciency and tray type. All the heatexchangers were biased-plate exchangers which warranted a good compromise in reducing the volume equipments per cost unit.

6. Commissioning and Performances The plant was constructed early 2001. Due to the innovative solution intrinsically proposed, an extensive test run period was necessary before commissioning the plant to the client. In that occasion also the testing of the model adopted for simulating the plant was also possible. Some typical results are compared in figure 4, were the discharged TOC value is plotted vs a parameter which is the product of two terms: inlet-TOC value times airflowrate value. 1000 900 1

800

I .as Q

600

g

500

700

• TOC Exp. • TOC Predicted

400 300 15

20

25

30

35

TOC*Air-flow*le-6

Figure 4. Comparison between experimental and predicted TOC values. The model demonstrated a good agreement with experiments at design conditions, while had the trend of overestimating the discharged TOC values for higher TOC and Air

256 flowrate. The predictions were in any case conservative in favour of a better performance of the real plant.

7. Process Costs The operational costs are mainly related to the total energy absorbed as electricity for a value of about 180 Kw. Of those about 50% are required by the boiler in the stripping section together with the oil cooling heat exchanger C-2. This value may be reduced almost linearly by increasing the investment costs of the heat exchanger E-2, i.e. by increasing its surface. The actual solution is in principle a compromise between investment and operational costs. Nevertheless it is important to point out that the plant may provide flexibility for changing this optimum in both directions, investments and operational, giving in such a way the possibility time to time to adopt the most convenient solution. The investment costs are intrinsically low due both to the simplicity of the process and to its operating conditions. This is however true for a limited interval of the inlet conditions, that is the total air flowrate and its TOC: in other words the plant capacity is limited to an upper limit of about 20000 NmVh of treated air with a TOC < 1500. Whenever this upper limit is violated the plant cost is practically doubled being more effective to double the plant itself. Whenever this occasion occurs alternative technologies such as incineration are more convenient from the economical point of view although less safe for the environmental impact and sustainability.

8. Conclusions An innovative process has been described for the reduction of TOC in the effluents from spray paint booths. The process pays the advantages of being simple and operating at acceptable conditions. The costs, both investment and operational, are limited and competitive, provided that the plant capacity is below a specified upper limit. The process has undoubtedly the advantage of having a zero impact to the environment and of being totally sustainable being required only electricity as unique utility at its battery limits. The performances are acceptable and in respect of the design specifications. They may be enhanced by increasing either the operational costs of about 50% or the total surface area of specific heat exchangers devoted to the heat recovery.

9. References Darvin, C.H., Proffitt, D. and Ayer, J., 2000, Modern Paint and Coatings, 87,10. Gay, R., 1997, Environmental Technology, 5,45. Hussey, F. and Gupta, A., 1997, Advanced Coatings Technology Conference, April 710, Detroit, Michigan. Kent, S., 1999, Chemical Engineering, 106, 1. Perry, H.R. and Green, D.W., 1997, Perry's Chemical Engineers' Handbook, VII Edition, Mc Graw Hill, Malaysa. Stone, J., 1997, Products finishing, 7, 85. Vasilash, G.S., 1997, Automotive Production, 108,4.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

257

Comparison Between STN, m-STN and RTN for the Design of Multipurpose Batch Plants Tania Pinto^, Ana Paula F. D. Barbosa-Povoa^^ and Augusto Q. Novais^ ^DMS, INETI, Est. do Pago do Lumiar, 1649-038 Lisboa, Portugal ^CEG-IST, DEG, I. S.T., Av. Rovisco Pais, 1049-101 Lisboa, Portugal

Abstract This paper looks into the design problem by each of the three types of representation, STN, m-STN and RTN, with a goal to establish their relative merit and derive a set of guidelines concerning their applicability. From this analysis it was also possible to identify aspects of design, which require further research and a number of recommendations is put forward to this effect. Some cases are described illustrating the flexibility and the applicability of the three types of representation, along with their numerical results.

1. Introduction In multipurpose batch plants, a wide variety of products can be produced via different processing recipes by sharing all available resources, such as equipment, raw material, intermediates and utilities. In order to ensure that any resource in the design can be used as efficiently as possible, an adequate methodology is necessary in order to address such type of problems without creating ambiguities in the process/plant representation. The first general methodology for batch plant design (Shah, 1992), that aimed to account for this aspect, was the State-Task Network (STN). Later on, this methodology was improved and the maximal State-Tasks Network (m-STN) emerged. This considers a more general detailed representation where some deficiencies present in STN were overcome (Barbosa-Povoa and Macchietto, 1994). The process recipes and the plant structure (units and connections) are combined into a single framework that represents the plant topology and all legal transfers of material within the plant. More recently, a new representation, the Resource-Task Network (RTN), was applied to the design of batch plants (Barbosa and Pantelides, 1997). However, some detail related to the full plant topology is not addressed explicitly. This paper considers the application of STN, m-STN and RTN methodologies over two examples of design multipurpose batch plant with the goal to emphasise their conceptual and computational differences and to set a guideline concerning their applicability. A discrete time formulation for a non-periodic single campaign mode of operation was considered.

^ Author to whom correspondence should be addressed, e-mail: [email protected], tel:+ 351 1 841 77 29

258

2. Comparison Between STN, m-STN and RTN When dealing with batch process design, three main aspects must be considered: the process, the plant and the operation. The STN representation as presented by Kondili et al. (1988) addresses only the modelling of the process recipe. Its application to the design case (Shah, 1992) assumes full plant connectivity where no location of material is considered explicitly. Two types of nodes characterise this representation, the State and the Task nodes. The State nodes (denoted as circles) represent the different types of materials within the process recipe while the Task nodes (denoted as rectangles) represent the transformation of materials from one state to another. Later on, BarbosaPovoa and Macchietto (1994) when addressing the detailed design of batch plants used the mSTN representation where the process and the plant topology are considered simultaneously. Four types of nodes are considered: the eStates, the i/oStates, the eTasks and the tTasks. These correspond respectively to the dedicated storage of material, location of material, processing tasks and transfers of material. The RTN representation considers two types of nodes: Tasks and Resources. The tasks, are operations that consume/produce a specific set of resources while resources model the different types of resources needed in the plant. When addressing the detailed design of batch plants, process operation and plant topology must be considered. The application of the above representations resulted in the need of paying a special attention to three modelling aspects. These are respectively the modelling of the storage tasks, the transfers/ location of material in the plant and the instantaneous characteristics of the storage and transfer tasks. In order to illustrate these aspects, a motivating example is studied followed by the presentation of the results obtained for a second and more complex example. The GAMS/CPLEX (v 7.0) software was used running in a Pentium III at 333 Mhz. 2.1. Motivating example A plant is to be designed at a maximum profit so as to produce 80 ton of a single product (S3) from two raw materials, (SI) and (S2). Two different processing tasks are considered. Task Tl that transforms SI into S3 after 1 hour and task T2 that processes S2 during 2 hours and generates S3. A single campaign non-periodic mode of operation was assumed over a time horizon of 5 hours. In terms of equipment, three storage tanks are available (VI, V2 and V3) to store respectively, SI, S2 and S3, and a multipurpose reactor is suitable to process task Tl and T2. Vessels VI and V2 are connected to reactor Rl (connections cl and c2), while the latter is also connected to vessel V3 (connection c3). The plant design should provide in detail the plant structure as well as the operational schedule. 2.7.7. State Task Network - STN In order to address explicitly all the possible transfers of material, storage and processing tasks the application of the STN methodology results in the representation shown in Figure 1.

259

Figure 1. STN Process representation. In here the concept of State and Task was preserved as presented by Shah (1992). The resulting STN representation involves 17 nodes - 8 tasks and 9 states. The Tasks model: the storage of material (Tal, Ta2 and Ta3 - for SI in VI, S2 in V2 and S3 in V3), the processing (Tl and T2 both in Rl) and the transfers of material (pil, pi2 and pi3 - for SI, S2 and S3). The States represent not only the type of material (SI, S2 and S3) but also its location in the plant (Sla, Sib, S2a, S2b and S3a, S3b). 2.7.2. Maximal State Task Network (mSTN) The resulting maximal State Task Network (m-STN) is shown in Figure 2. Eleven nodes are obtained where storage, processing and transfers of material are handled explicitly, as well as the materials location. Thus, we have three dedicated storage (Sl/Vl, S2/V2 and S3/V3), two iStates (iel, ie2) one oState (iol), three transfer tasks (pil/cl, pi2/c2 and pi3/c3) and two processing tasks (eTasks Tl/Rl and T2/R1).

pi3/c3

Figure 2. m-STN, Process representation. 2.1.3. Resource Task Network For the Resource-Task Network, RTN and considering directly the definitions established by Pantelides (1994) for Tasks and Resources the resulting RTN leads to 24 nodes (Figure 3).

©*-|

©^ Ta3

Figure 3. RTN process representation. These correspond to 16 resources (7 equipment resources and 9 material states) and 8 tasks (3 storage, 3 transfers and 2 processing). Note that a material resource may differ not only due to the type of material involved but also due to its location (ex: Sla, Sib).

260 As referred above the main differences between the three types of representations explored are due to the need of addressing explicitly the storage, transfer and location of materials and to the fact that transfers of material are assumed instantaneous. In addition, material in storage must be available continuously. Below, these points are explored. 2.7.4. Storage tasks When modelling a storage task, the availability of material must be considered in a continuous form, while the utilisation of suitable equipment must be made explicit. Considering the application of STN concepts, the usage of the storage vessel is handled through the definition of a task where the allocation of the equipment is accounted for (Figure 4a). Furthermore, and since the availability of material must be instantaneous, an auxiliary state (SIa) was defined. In this way the vessel utilisation is guaranteed, otherwise the model characteristics would result in the non-utilisation of the vessel since state SI would be always available at no storage cost. In the m-STN the equipment allocation is implicit in the eState definition (Sl/Vl, Figure 4b). As for the RTN, a storage task is also created (Figure 4c). This consumes two types of resources - the material (SI) and the vessel (VI) and produces instantaneously an auxiliary material (SIa) and, after one time unit, the equipment resource (VI). Again the need for the auxiliary resource is explained by the instantaneous characteristic of the task, that unless associated with a fictitious transformation of resources, would never be used.

Ta1

S1/ V1

Ta1

Figure 4a. STN.

Figure 4b. m- STN.

- H Sla

Figure 4c. RTN.

Note that, if the direct application of the STN concepts would not be followed the representation for the STN and m-STN could be the same. That is, if it would be assumed that in the STN, a state would model not only the type of material but also its allocation to the storage vessel. This is explored in terms of model resolution as it can be seen in Table 2. 2.1.5. Transfer Task/Material Location Either in the STN or RTN methodologies, the transfer tasks are treated as a normal task. These tasks although not transforming the state/resource in terms of type material, moves it from one place to another - resulting in a different state/resource (Figure 5 a and 5c) - and uses an extra resource to perform it a suitable connection (cl). As for the m-STN (Figure 5b) the transfer of material is handled explicitly, through a transfer task (pil) that uses a suitable connection (cl). Comparing the STN and the m-STN representations, it can be concluded that they are similar although in terms of model statistics the first results in more variables and constraints, as it will be seen later (see Table 2). This is due to the mathematical formulation associated. For the RTN, on the other hand, the number of instances is larger which reflects accordingly in the model statistics. Again, and as before, for the storage task the instantaneous characteristic of these tasks implies the need for creating auxiliary state/resources nodes (Sla).

261

->(^^r)->^^

(^^j\-p^yc^_^,^^ pil

Figure 5a. STN.

Figure 5b. m-STN.

Figure 5c. RTN.

Solving the motivating example using the three representations explored above and the data expressed in Table 1, the results obtained are shown in Table 2. These corresponds to a 0% margin of optimality and to an objective function of 1248,54 x 10^ monetary units where units Rl, V3, CI and C3, with 80 units of capacity where chosen. Table 1. Capacities and equipment cost.

Capacity [u.m/m ] max:min Cost[10^ C.U.] fix;var

VI ^^^

V2 ^^j

V3 ^^S.Q

Rl 200:0

0

0

1:10'^

10:10'^

CI 200:0

C2 200:0

C3 200:0

10'^ 10'^

(c.u.= currency units; u.m= mass units; unl.= unlimited) Analysing the model statistics it can be seen that the m-STN representation results in a smaller problem both in terms of variables and constraints, followed by the STN and RTN. As for the general versus the adapted STN, the latter results in a smaller model. The model statistics influence the CPU times, as it can be seen in Table 2. The m-STN is solved more quickly (0.234) followed by the STN (0.312) and finally the RTN (0.359). However the differences are not very marked. Table 2. Computational data. Methodology STN -general STN - adapted m-STN RTN

N** Variables 137 98 75 364

N** Binary 48 36 24 127

N" Constraints 227 176 122 511

CPU time (s) 0.313 0.312 0.234 0.359

LPs 6 5 7 16

STN - general (dedicated storage model as a task); adapted (state/unit allocation) 2.2. Example 2 Using an example proposed by Barbosa-Povoa and Macchietto (1994), the above representations are again explored. In here, a plant must be designed at a maximum profit so as to produce three final products, S4, S5 and S6, with production capacities between [0:80] ton for S4 and S5, and [0:60] for S6, from two raw materials, SI and S2. The process operates in a non-periodic mode over a time horizon of 12 hours. The results in terms of model statistics are shown in Table 3. The problem modelled through the mSTN presents the smallest statistics followed by the STN-adapted and finally the RTN. The same behaviour is observed when analysing the computational times associated.

262 These facts indicate that again the m-STN representation appears as the most adequate for the modelling/solution of the detailed design of batch plants. Table 3. Computational data. Methodology STN -general STN- adapted m-STN RTN

N** Variables 974 794 600 2615

N^ Binary 358 298 116 1018

N"* Constraints 1743 1503 918 3662

CPU time (s) 8.734 4.469 4.187 123.765

LPs 570 523 522 5029

3. Conclusions This paper discusses the applicability of STN, m-STN and RTN representations to the detailed design of batch plants, where a discretisation of time and a non-periodic operation mode were assumed. The main differences identified were concerned with three important aspects that are related. The need of explicitly considering the storage tasks, which account for the continuous availability of material and the usage of a suitable equipment. The need of considering the different locations of material in the plant and consequently the definition of transfers of material with suitable equipment associated. And, finally the instantaneous characteristic of each one of these tasks. These representations resulted in larger models when using the RTN methodology and consequently harder models to be solved. For the STN also larger models where obtained with regards to the m-STN representation. In conclusion, within the scope of the problem characteristics covered, the m-STN appears as the most adequate representation to the detailed design of batch plants, since it explores the problem characteristics reducing the need of auxiliary instances in the representation, as well as reducing the mathematical formulation statistics associated. Thus, the choice of an adequate representation for the solution of a given problem should, as much as possible, explore the problem intrinsic characteristics. However, it is important to note that the work presented should be further explored and more examples should be solved so as to confirm this conclusion. Also, other problem characteristics such as set-ups dependency, cleaning needs, connectivity suitability, amongst others, should also be studied. This is now ongoing research by the authors.

4. References Barbosa-Povoa, A.P.F.D. and Machietto, 1994, Detailed design and retrofit of multipurpose batch plants. Computer Chem. Engng, 18, 11/12, 1013-1042. Barbosa-Povoa, A.P., Pantelides, C.C., 1997, Scheduling and design of multipurpose plants using the resource-task network unified framework. Computer Chem. Engng, 21b, S703-S708. Kondilli, E., Pantelides, C.C. and Sargent, R.W.H., 1988, A general algorithm for scheduling bath operation. In Proc. of 3"^^ Ind. Symp. on Process Systems Engineering, pages 62-75, Sydney, Australia. Pantelides, C.C, 1994, Unified framework for optimal process planning and scheduling. In D.W.T. Rippin and J. Hale, editors. In Proc. Second Conf. on Foundations of Computer Aided Operations, CACHE Publications, pages 253-274. Shah, N., 1992, Efficient scheduling, planning and design of multipurpose batch plants. Ph. D. Thesis, Imperial College, University of London, U.K.

European Symposium on Computer Aided Process Engineering- 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

263

Generalized Modular Framework for the Representation of Petlyuk Distillation Columns p. Proios and E.N. Pistikopoulos* Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College, London SW7 2BY, U.K.

Abstract In this paper the Generalized Modular Framework (Papalexandri and Pistikopoulos, 1996) is used for the representation of the Petlyuk (Fully Thermally Coupled) column. The GMF Petlyuk representation, which avoids the use of common simplifying assumptions while keeping the problem size small, is validated for a ternary separation, by a direct comparison of its results to those obtained by a rigorous distillation model.

1. Introduction The Petlyuk column (Petlyuk et al, 1965) is an energy efficient distillation system which, along with its thermodynamically equivalent Dividing Wall Column (Wright, 1949), has been reported of being able to lead to energy savings of even up to 40% when compared to conventional simple column arrangements (Glinos and Malone, 1988 and Schultz et a/., 2002). The importance of this complex distillation column has compelled the development of numerous methods for its design and analysis. These methods can be classified into two main categories, namely, those using simplified (shortcut) models and those using rigorous (detailed) models. Petlyuk et a/. (1965) used shortcut calculations for the minimum reflux based on constant relative volatilities and internal flowrates. Cerda and Westerberg (1981) developed a shortcut model for the minimum reflux assuming sharp separations for the Petlyuk column. In Fidkowski and Krolikowski (1986) the Petlyuk column was studied for ternary mixtures and sharp calculations through a shortcut model for the minimum vapour flowrate based on the Underwood method. Glinos and Malone (1988) and Nikolaides and Malone (1988) designed the Petlyuk column using shortcut calculations under constant relative volatilities and equimolar flowrates. Carlberg and Westerberg (1989) and Triantafyllou and Smith (1992) used a three-simple-column approximation of the Petlyuk column. The former proposed a shortcut model for minimum vapour flowrate for nonsharp separations whilst the latter based their design on the Fenske-Underwood-Gilliland shortcut techniques. Halvorsen and Skogestad (1997) used a dynamic shortcut model based on assumptions of equimalr flowrates and constant relative volatilities for their Petlyuk/Dividing Wall Column model. Agrawal and Fidkowski (1998) used Underwood's method for their Petlyuk design and Fidkowski and Agrawal (2001) proposed a shortcut method for the separation of quarternary and higher mixtures in To whom correspondence should be addressed. Tel.: (44) (0) 20 7594 6620, Fax: (44) (0) 20 7594 6606, E-mail: [email protected]

264 Petlyuk arrangements extending the Fidkowski and Krolikowski (1986) method. Shah and Kokossis (2001) designed the Petlyuk columns in their framework based on the Triantafyllou and Smith (1992) shortcut procedure. Finally, Amminudin et ah, (2001) proposed a shortcut method for the design of Petlyuk columns based on the equilibrium stage composition concept. It must be noted that the above methods provide fast and simple ways of designsing and analysing the performance of the Petlyuk column. However, the fact that they are based on simplifying assumptions can place a limitation on their accuracy and applicability, notably for the cases where these assumptions do not hold. This limitation can be overcome through the use of rigorous methods, not relying on simplifying assumptions. Chavez et al. (1986) examined the multiple steady states of the Petlyuk column through a detailed tray-by-tray model under fixed design, which was solved with a differential arc-length homotopy continuation method. Dtinnebier and Pantelides (1999) designed Petlyuk columns using a detailed tray-bytray distillation model based primarily on the rigorous MINLP distillation model of Viswanathan and Grossmann (1990). Also based on the latter, Yeomans and Grossmann (2000) proposed a disjunctive programming model for the design of distillation columns including Petlyuk arrangements. These methods are based on detailed and accurate models with general applicability. However, they do generate considerably larger nonlinear programming problems which lead to an increase of the computational effort. The scope of the presented work is twofold: a) to provide a valid method for representing and analyzing the performance of the Petlyuk column with respect to its energy efficiency potential at a conceptual level and b) based on this, to put the foundations for the extension of the method to the synthesis level, that is, for the generation and evaluation of all column arrangements for this separation problem, involving simple and also (partially) thermally coupled columns. These will be realized in an integrated way, from a process synthesis point of view, and without generating a large optimization problem (as the rigorous methods), while avoiding the common limiting assumptions, characteristic of the shortcut methods.

2. The Generalized Modular Framework In this work the Petlyuk column is represented through the Generalized Modular Framework (GMF) (Papalexandri and Pistikopoulos, 1996), which is an aggregation framework for process synthesis/representation. The GMF is based on the fact that since a large number of process operations are characterized by mass and heat transfer phenomena (for instance the mass and heat exchange between liquid and vapour streams in distillation), using a generalized method for capturing those, the process operations in question can be systematically represented in a compact and unified way. The GMF through its generalized mass and heat exchange modelling, aims towards that direction. In brief, it can be stated that the GMF is a superstructure optimization method and, alike most of the methods belonging to this class, consists of a Structural Model, responsible for the generation of the (structural) process alternatives and a Physical Model, responsible for the evaluation of the latters' performance/optimality.

265 Cooler

Heater

6

-D

a—o Pure Heat Module

Pure Heat Module

Figure 1: GMF Building Blocks (Ismail et al 2001)' The Structural model consists of: (i) the GMF building blocks and (ii) their interconnection principles. The GMF building blocks (Figure 1) are representations of higher levels of abstraction and lower dimensionality where mass/heat or pure heat exchange take place. The existence of the building blocks is denoted mathematically through the use of binary (0-1) variables. The Interconnection Principles define the way the various building blocks should be connected to each other for the generation of physically meaningful alternative units and their resulting flowsheets. The mathematical translation of these principles is realised through a set of mixed and pure integer constraints, which define the backbone of the GMF structural model. The GMF Physical Model is employed for the representation of the underlying physical phenomena of the generated structures. Each building block is accompanied by its physical model, which is based on fundamental (and thus general) mass and heat exchange principles at the blocks' boundaries, consisting of mass and energy balances, molar fraction summation corrections and appropriate Phase Defining and Driving Force Constraints arranging the mass and heat transfer. The complete GMF mathematical model, as a combination of the structural and physical models is a Mixed Integer Nonlinear Programming problem (MINLP), and can be found in detail in Papalexandri and Pistikopoulos (1996) and Ismail et al. (2001). For the GMF representation of the Petlyuk column a minimum number of 6 mass/heat and 2 pure heat modules are employed (Figure 2). The connectivities of the building blocks are appropriately arranged so that the complex structure of the Petlyuk column is obtained. This is done by fixing the corresponding binary variables to 0 or to 7 for the respective nonexistence or existence of building blocks and their interconnections. For the Petlyuk column representation, each mass/heat module represents a column section (aggregation of trays), where a separation task takes place. The pure heat exchange modules represent the condenser (cooler) and the reboiler (heater) of the Petlyuk column. It must be noted that since a tray-by-tray model is not employed, the equilibrium constraints are being replaced by Driving Force Constraints at the two ends of each one of the six mass/heat modules, according to the type of contact (countercurrent for distillation). These constraints along with the Phase Defining Constraints and the conservation law constraints ensure mass and heat transfer feasibility and define the distribution of the components in the existing building blocks. However, the main motivation for representing the Petlyuk column through the GMF lies on the latter's main representational advantages, which for the examined case are summarised below: (i) the GMF physical model captures efficiently the underlying

266

rSJ^^

xCl^

LS^.

Qreb

P2

y-^ Qh

f-~-^

Figure 2: Petlyuk Column (Conventional and GMF representation). mass/heat transfer phenomena, since it is not based on simplifying and limiting assumptions such as sharp splits, equimolar flowrates, constant volatilities and it does not involve any shortcut calculations, (ii) the GMF physical model can accomodate any thermodynamic model, (iii) the GMF structural and physical models allow the represention of the Petlyuk column in an aggregated way, leading to a smaller and easier to solve optimization problem (iv) the framework can be potentially extended to the evaluation of other (distillation) systems through a superstructure based on the existing six mass/heat modules and by allowing more interconnections. In the following section the above advantages and the framework's validity and representational merit will be demonstrated through a GMF/Petlyuk column case study.

3. Numerical Results - Validation The GMF representation of the Petlyuk column is employed for the separation of the ternary mixture of Benzene, Toluene and 0-xylene. The problem data was taken from Chavez et al (1986) and it involves the separation of a saturated liquid feed of 211.11 mol/s, with molar fractions of Benzene, Toluene and 0-xylene, 0.2, 0.4 and 0.4, respectively, into three product streams with molar fractions of 0.95, 0.9 and 0.95, in the above components. The objective is the minimization of the utility cost. For a fixed (Petlyuk) structure, the corresponding GMF mathematical problem is a nonlinear programming problem (NLP) which was solved in GAMS (Brooke at al, 1992) using the solver C0N0PT2. Due to the inherent stream mixing and splitting terms the problem is nonconvex which is solved only to local optimality. However a systematic procedure has been employed with appropriate initial guesses and bounds for the stream flowrates, temperatures and molar fractions in order to find a local optimal point which represents the potential (energy consumption levels) of the examined Petlyuk column. From the optimization runs for the mixture and feed composition examined, the GMF provided the energy consumption levels (heater duty of 9,026.3 kW) and the operating conditions of the Petlyuk column, using the mass/heat exchange principles of the GMF physical model.

267 However, since the GMF physical model is an aggregated (and, thus, nonconventional) model, the validity of the GMF results for the Petlyuk representation was evaluated by comparing these results quantitatively and qualitatively, to those derived from a conventional tray-by-tray model. For these purposes, the rigorous model of Viswanathan and Grossmann (1990) was used for the minimization of the operating cost, with the problem definition and the column design taken also from Chavez et al. (1986). From the results of the optimization, the two models are found to be in quantitative agreement, since the reboiler heat duty in the rigorous model was 10530 kW, which is very close to that of the GMF heater, indicating that the GMF model predicted correctly the energy consumption of the Petlyuk column. The small divergence between the two is possibly due to the fact that in the GMF the bottoms product stream is removed before the heater (with less liquid entering it, Figure 2). However, such a quantitative agreement needs to be the product of a qualitative agreement (that is, in the components' distribution over the various column sections). Since the GMF does not provide information at the tray level, in order to enable a comparison of the composition and temperature profiles of the two models, the points of the feeds, interconnections and side streams of the GMF representation were placed on the corresponding points (tray locations) of the tray-by-tray model, in a common x-axis. In Figure 3 are shown the profiles of the Toluene composition and of the temperature in the main column of the Petlyuk arrangement. From these it is apparent that the two models are also in qualitative agreement in the main column (similar results were derived for the prefractionation column, as well). This qualitative agreement shows that the GMF provided insights on the performance of the Petlyuk column, with respect to its energy consumption, based on a sound physical model which is capable of capturing efficiently the mass and heat transfer phenomena of the examined system. Another point of importance is related to the size of the generated optimization problem. Due to the aggregated nature of the GMF representation (where variables and equations are accounted for only at the building blocks' boundaries and not at the tray level, as in the rigorous models), a size reduction of 75% in the number of variables and constraints, respectively, has been noted when using the GMF instead of the trayed model (depicted

I

3

5

7

9

11

13

15 17 19 Travs/Moduks

21

23

25

27

29

31

Figure 3: Qualitative Comparison of GMF and Rigorous Models (Petlyuk Column).

268 in Figure 3 with the fewer GMF points), with direct effects in the computational effort. Of course, as it can be observed in Figure 3, the GMF does not provide detailed results and profiles, as the rigorous model does, but this is beyond the aim of the framework, which is not a simulation but a synthesis/representation tool, at a conceptual level.

4. Conclusions As shown, the GMF provides a sound and useful tool for the representation and evaluation of the Petlyuk column and its underlying physical phenomena providing valid information about the energy consumption levels of the fully thermally coupled column. Moreover, the GMF results, which were derived using an aggregated physical model and thus generating a significantly reduced optimization problem, were evaluated for their consistency and validity through their comparison with a well-established rigorous distillation model. Finally, having validated the GMF physical model for the examined system, the complete GMF model, with its physical model, as it was used in the presented work, and with its full structural model (without incorporating a fixed structure but with an adequate number of building blocks and their interconnections to be determined by the optimizer) can now be used for the synthesis problem, i.e. the generation and evaluation of all the alternatives of interest (simple and complex) for the examined separation problem, which is the scope of our current research.

5. References Agrawal, R. and Fidkowski, Z.T., 1998, Ind. Eng. Chem. Res., 37, 3444. Amminudin, K., Smith, R. Thong, D. and Towler, G., 2001, Trans IChemE, 79(A), 701. Brooke, A., Kendrick, D. and Meeraus, A., 1992, GAMS - A User's Guide, Scientific Press, Palo Alto. Carlberg, N.A. and Westerberg, A.W., 1989, Ind. Eng. Chem. Res., 28, 1386. Cerda, J. and Westerberg, A.W., 1981, Ind. Eng. Chem. Process Des. Dev., 20, 546. Chavez, R.C., Seader, J.D. and Wayburn, T.L., 1986, Ind. Eng. Chem. Fundam.,25, 566. Dunnebier, G. and Pantelides, C.C., 1999, Ind. Eng. Chem. Res., 38,162. Fidkowski, Z.T. and Agrawal, R., 2001, AIChE J., 47(12), 2713. Fidkowski, Z.T. and Krolikowski, L., 1986, AIChE J., 32(4), 537. Glinos, K. and Malone, M.F., 1988, Chem. Eng. Res. Des., 66, 229. Halvorsen, I.J. and Skogestad, S., 1997, Comp. Chem. Eng., 21, S249. Ismail, S.R., Proios, P. and Pistikopoulos, E.N., 2001, AIChE J., 47(3), 629. Nikolaides, LP. and Malone, M.F., 1988, Ind. Eng. Chem. Res., 27(5), 811. Papalexandri, K.P. and Pistikopoulos, E.N., 1996, AIChE J., 42, 1010. Petlyuk, F.B., Platonov, V.M. and Slavinskii, D.M., 1965, Int. Chem. Engng, 5(3), 555. Schultz, M.A., Stewart, D.G., Harris, J.M., Rosenblum, S.P., Shakur, M.S. and O'Brien, D.E., 2002, CEP, 98(5), 64. Shah, P.B. and Kokossis, A.C., 2001, Comp. Chem. Eng., 25, 867. Triantafyllou, C. and Smith, R., 1992, Trans IChemE, 70 (A), 118. Viswanathan, J. and Grossmann, I.E., 1990, Comp. Chem. Eng., 14(7), 769. Wright, R.O., Fractionation Apparatus, 1949, U.S. Patent 2,471,134. Yeomans, H. and Grossmann, I.E., 2002, Ind. Eng. Chem. Res., 39,4326.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

269

A Multi-Modelling Approach for the Retrofit of Processes A. Rodriguez-Martinez\ I. Lopez-Arevalo^, R. Banares-Alcantara^* and A. Aldea^ ^Department of Chemical Engineering, ^Department of Computer Engineering and Mathematics, Universitat Rovira i Virgili, Tarragona, SPAIN.

Abstract The retrofit of an existing process is a complex and lengthy task. Therefore, a tool to support the retrofit by reasoning about the existing process and the potential areas of improvement could be of great help. A proposal for a retrofit approach based on a multimodelling knowledge representation is presented in this paper. The use of structural, behavioural, functional and teleological models allows the designer to work with a combination of detailed and abstract information depending on the retrofit step. The proposed retrofit process consists of four steps: data extraction, analysis, modification and evaluation. The HEAD and AHA! prototype systems were implemented for the two initial steps. These systems have been applied in a case study to the ammonia production process.

1. Introduction Industrial processes require periodic evaluations to verify their correct operation, both in technical and economical terms. These evaluations are necessary due to changes in the markets, and safety and environmental legislation. In order to satisfy these demands it is necessary to investigate process alternatives that allow the optimal use of existing resources with the minimum possible investment. The retrofit of processes is a methodology of analysis and evaluation of possible changes to an existing process in order to improve it with respect to some metric (economical, environmental, safety, etc). Historically, the retrofit of processes has been largely centred on energy savings. In the last decades significant advances in this area were obtained through the use of the pinch methodology (Linnhoff and Witherell, 1986) and mathematical programming techniques (Grossmann and Kravanja, 1995). Other systems, such as the one proposed by Fisher et al. (1987), combine heuristic rules with decision hierarchies. These methods generate process alternatives based on the modification of the process structure or the dimensions of the items of equipment. A possible improvement to these approaches would be the reduction of the complexity originated by the use of detailed information. As an alternative approach we propose the use of multiple models (structural, behavioural, functional and teleological) to represent detailed and abstract knowledge for the retrofit of artifacts in general and chemical processes in particular.

To whom correspondence should be sent. Email: [email protected]

270

2. Methodology The proposed methodology for retrofit consists of four steps and the use of a multimodel knowledge representation. 2.1. Retrofit process Our proposed retrofit process is shown in Fig. 1. HEAD

Data Extraction

AHA!

Design Analysis

knowledge AcquisitionL

£

Data Abstraction

i Data Analysis

3:

Alternatives Generation Design Modification Alternatives Adaptation

RETRO Design Evaluation

3:

Alternatives Evaluation

TProposed Alternative

Fig. 1. The retrofit process based on a multi-model knowledge representation. The main steps of the retrofit process are: • Data Extraction. Information of the artifact is extracted from an initial representation (the simulation output from HYSYS^^ in our case). The HEAD system performs the data extraction, see Section 3. • Design Analysis. Extracted information is abstracted at several levels based on a set of hierarchical functions and precedence rules. This abstracted information is analysed to identify promising sections for retrofit. The AHA! system performs the design analysis, see Section 3. • Design Modification. Alternatives are generated based on the application of new specifications to the original artifact. • Design Evaluation. The generated alternatives are evaluated with respect to their specifications. If an alternative does not satisfy the specifications, the Design Modification step is repeated until they are satisfied. The RETRO system is being implemented for the design modification and evaluation steps (see Section 4). 2.2. Knowledge representation We propose a multi-modelling approach for the representation of knowledge as suggested by Chittaro et al. (1993). In our approach, a unit (i.e. the building block of an artifact; in the case of a chemical process it corresponds to an item of equipment or a section of the process) is represented by the following types of models: • Structural, i.e. the class of a unit and its connectivity.

271 • • •

Behavioural, i.e. how the unit works. Functional, i.e. the role of the unit within the artifact. Teleological, i.e. the objective and justification of the unit.

Depending on the retrofit step and the abstraction level we can use detailed information (structural and behavioural models) or abstract information (functional and teleological models) to reason about a unit.

3. Application of tlie Methodology and Results For the data extraction step we have implemented the HEAD system (HYSYS ExtrAction Data). HEAD is programmed in MS Visual Basic™ and its goal is to extract information from a process flow diagram (PFD) taking advantage of the Programmability features of HYSYS™. The extracted information is then sent to AHA! (Automatic Hierarchical Abstraction tool), a Java based prototype system that generates different levels of abstraction from the initial PFD in order to identify sections where retrofit can be applied. In the near future, the output results of AHA! will be used by RETRO (Reverse Engineering Tool for Retrofit Options). RETRO (now being developed in Java) will generate and evaluate process alternatives. 3.1. Generation of meta-units Initially, the information extracted by HEAD from HYSYS™ is used by AHA! to generate Units (process blocks). A Unit consists of four models: structural, behavioural, functional and teleological. The models of a Unit are built as follows: the behavioural model is obtained by comparing its input and output values. The type of Unit and its connectivity constitute the structural model. Furthermore, each Unit is associated with a functional model. Finally, the teleological model defines on an abstract manner the goal and purpose of a Unit inside an artifact. The Units are abstracted by means of inference mechanisms. During this process Metaunit(s) are generated as a result of abstracting two or more Unit(s) and/or Meta-unit(s). These inference mechanisms are implemented as a rule-based system based on (a) Douglas methodology (Douglas, 1988); (b) the identification of generic blocks (Turton et al., 1998); and (c) application of a hierarchy of functions (Teck, 1995). A reduced version of the hierarchy of functions is shown in Table 1. These functions are prioritised according to the precedence shown in Fig. 2. The abstraction process trail can be interpreted as an inverse record of a plausible design history.

Reaction |—HSeparation —" Temperature Change—" Pressure Change —A Flow Change +

Precedence

Fig. 2. Functional precedence in AHA!

272

Table 1. Hierarchy of Functions. General Function Reaction Separation Temperature_change Pressure_change Flow_change

Associated operations Reaction Decantation, extraction, distillation, absorption, stripping, adsorption, crystallisation, leaching, drying, and membranes Heating, cooling Pressure_decrement, Pressure_increment Mixing, splitting

3.2. Case study We have applied HEAD and AHA! to the ammonia production process, see Fig. 3. In this process, a hydrogen/nitrogen stream is fed to three catalytic reactors in series. The NH3 produced is fed to the separation section (V-100, V-101) to obtain a 95% pure product stream. Two heat exchangers are used for energy recovery and two coolers are used to obtain flash conditions. *

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^s£ Fig. 3. Ammonia production process in HYSYS ^ The initial ammonia process representation generated by AHA! (abstraction level 0) is shown graphically in Fig. 4. Every Unit (icon) in the figure is modelled according to Section 2. All the relevant information of Units and streams can be accessed through windows, menus, and buttons. Two abstract levels above. Fig. 5 shows the second abstract level of the ammonia process. In this abstract level the corresponding Units of FlowjChange (mixers and splitters) have been abstracted due to their lower precedence. Meta-units are represented as boxes. The designer can navigate through the abstract levels that have been generated and fmd the relations between Units and/or Meta-units at different abstract levels. Browsing through the trail of the abstraction process a designer can identify the sections of an artifact.

273 mUBBM mt em JM»«8«60r» Tw^m

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4. Discussion The use of structural, behavioural, functional and teleological models allows the designer to work with a combination of detailed and abstract information depending on the retrofit step. With this information it is possible to identify automatically sections of a artifact, such as the reaction and separation sections, just as a human designer does (Turton et al, 1998). We are planning for RETRO to generate process alternatives by means of methodologies grouped within the area of greener process design, and thus propose

274 processes with adequate environmental and safety performance (Sylvester et al. 2000). Together with these methodologies we plan to apply: 1. Conflict-based analysis (design objectives vs. principles), to exemplify the generation of innovative alternatives which is necessary at the abstract end of the abstraction hierarchy (Xiao-Ning et al. 2002). 2. Identification/selection of alternative solvents (Hostrup et at. 1999), as an example of process modifications applicable at the middle of the abstraction hierarchy. 3. Inclusion of effluent treatments, generally made after designing the rest of the process.

5. Conclusions We have presented a multi-modelling approach for the retrofit of processes. Based on a multi-model knowledge representation (structural, behavioural, functional and teleological models) we can generate the artifact at different levels of detail to facilitate its retrofit (data extraction, design analysis, modification, and evaluation steps). The HEAD and AHA! prototype systems have been implemented for the data extraction and design analysis steps respectively. In particular, AHA! can automatically abstract an artifact in order to identify the process sections where the retrofit task should be focused.

6. References Chittaro, L., Guida, G., Tasso, C. and Toppano, E., 1993, IEEE Trans. Sys. Man. Cybern., SMC-23, 1718-1751. Douglas, J., 1988, Conceptual Design of Chemical Process, Mc Graw Hill, New York. Fisher, W. R., Doherty, M. F. and Douglas, J. M. (1987) Ind. Eng. Chem. Res., 26, 2195-2204. Grossmann, I. and Kravanja, Z., 1995, Comp. Chem. Eng., 19, Suppl., S189-S204. Hostrup, M., Harper, P.M. and Gani, R., 1999, Comp. Chem. Engng., 23, 1395-1414. Linnhoff, B. and Witherell, W.D., 1986, Oil & Gas J., 84, 54-65. Sylvester, R., Smith, W. and Carberry, J., 2000, AIChE Symp. Ser., 96, 26-30. Teck, T., 1995, MSc. Information Technology dissertation. Department of Artificial Intelligence, University of Edinburgh, Edinburgh. Turton, R., Bailie, R.C., Whiting, W.B. and Shaeiwitz, J.A., 1998, Analysis, Synthesis and Design of Chemical Process, Prentice Hall, New Jersey. Xiao-Ning, L., Ben-Guang, R. and Kraslawski, A., 2002, In European Symposium on Computer Aided Process Engineering - 12, Elsevier, 241-246.

7. Acknowledgments We thank Hyprotech (now part of ASPENTech) for the use of an academic license of HYSYS™. Also we would like to thank the Universitat Rovira i Virgili (Spain) for the PhD scholarship of I. Lopez-Arevalo and to the Universidad Autonoma del Estado de Morelos (Mexico) for the PhD scholarship of A. Rodriguez-Martinez.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

275

Synthesis of Partially Thermally Coupled Column Configurations for Multicomponent Distillations Ben-Guang Rong*, Andrzej Kraslawski and Ilkka Turunen Department of Chemical Technology, Lappeenranta University of Technology, P.O. Box 20, FIN-53851 Lappeenranta, Finland. *E-mail: [email protected]

Abstract The synthesis of partially thermally coupled column configurations for a multicomponent distillation has been studied in the context of the thermodynamic equivalent structures. There has been formulated a complete space of the possible thermodynamic equivalent alternatives of the partially coupled (PC) configurations for multicomponent mixtures. A formula is presented to calculate the number of all the partially coupled schemes for any n-component mixture. The formulated altematives of all the possible arrangements of PC configurations provide a complete subspace for optimal design of multicomponent distillation systems not only for the economics, but also for column equipment designs.

1. Introduction Thermal coupling technique has been used to design multicomponent distillation systems which have the potentials to significantly reduce both energy consumption and capital cost compared with conventional simple column configurations. A considerable research works have been conducted on thermally coupled systems for ternary mixtures. The mostly studied ternary thermally coupled schemes are the side-stripper (SS), the siderectifier (SR) and the fully coupled scheme (FC) (Petlyuk column) (Petlyuk et al., 1965). For thermally coupled schemes for mixtures with four or more components, there are only a few papers in the literature that are mostly concerned with the finding of the possible structures of the thermally coupled schemes (Sargent & Gaminibandara, 1976; Agrawal, 1996; Christiansen et al. 1997). It is well-known that the side-rectifier (SR), the side-stripper (SS), and the dividing-wall column (DWC) are the mostly employed thermally coupled systems for temary mixtures. In an analysis on the relationships of the known thermally coupled configurations for temary mixtures, we observed that these well-known systems are the thermodynamic equivalent arrangements of the original thermally coupled configurations. Those original thermally coupled configurations are produced from the corresponding conventional simple column configurations by only removing condenser(s) and/or reboiler(s) associated with submixtures of two or more components (Rong & Kraslawski, 2002). The synthesis of the PC configurations with only side strippers and (or) side rectifiers for any n-component mixture has been studied in our earlier work in terms of the economics evaluation (Rong & Kraslawski, 2003). We observed that even though the difference of the capital costs among the thermodynamic equivalent structures will not change the optimal PC system, there are still some differences between the thermodynamic equivalent structures for a specific PC configuration with regard to the column equipment designs. Thus, it needs a further investigation for optimal design of the partially thermally coupled (PC) systems among all of the possible thermodynamic equivalent structures in

276 terms of not only economics evaluation, but also column equipment design. The main objective of this paper is to systematically synthesize the possible partially thermally coupled configurations for four or more component mixtures, with the emphasis on the optimal design of the partially coupled systems among all of the possible thermodynamic equivalent structures.

2. Generation of the Original Partially Thermally Coupled (OPC) Column Configurations It is known that in a conventional simple column configuration for an n-component distillation, there are totally n-1 simple columns (Thompson & King, 1972). Each simple column has a rectifying column section with a condenser and a stripping section with a reboiler. As a consequence, each simple column configuration has totally 2(n-l) column sections, as well as 2(n-l) condensers and reboilers. It is observed that among 2(n-l) column sections in a simple column configuration, there are n column sections which produce the desired pure products from the corresponding condenser(s) and reboiler(s). Each of these n column sections is enriched with one of the components in the feed mixture. While the remaining n-2 column sections do not produce the desired pure products but their condenser(s) and/or reboiler(s) have the submixtures with two or more components. For each of the n-2 column sections enriched with a submixture of two or more components, there is an inevitable remixing at the end of the column section due to the existing of the condenser (reboiler) for supplying the needed reflux (boilup) for the column section. This remixing will produce the separation inefficiency in the distillation system. According to Petlyuk et al. (1965), this remixing can be avoided by removing the condenser or the reboiler at the end of the column section and interconnecting the column units by the two-way liquid and vapor streams, i.e. the thermal coupling streams. Each rectifying (stripping) column section after removing its condenser (reboiler) will require the liquid reflux (vapor boilup) from its subsequent column unit.

^

rJTnAB.

x^,

Column 2

Column 2

jf

i3^

ABCDE Column

CDE Column 4

JColumn 4 Column 3

61

P L_

Column 3

DE

iji-: (a)

(b)

Figure 1. A five-component simple column configuration and its original thermally coupled configuration.

277 As an example, Figure la illustrates the conventional simple column configuration of a five-component separation sequence of (AB/CDE—•A/B->C/DE->D/E). It is seen from Figure la that there are three column sections whose products are internal submixtures with two or three con^onents. Column 1 has rectifying section 1 with condenser AB and stripping section 2 with reboiler CDE. Column 3 has stripping section 6 with reboiler DE. By eliminating the condenser(s) and the reboiler(s) with the internal submixtures, the partially thermally coupled scheme is produced as shown in Figure lb. This partially coupled configuration of Figure lb has exactly the same structural arrangements of the three column units as its counterpart of the conventional simple column configuration of Figure la. We define it as the original partially thermally coupled configuration (OPC) with regard to the introduced thermal couplings for the simple columns of the conventional simple column configuration. Obviously, each of the conventional simple column configurations will produce an original partially thermally coupled configuration by directly replacing of those condensers and/or reboilers associated with submixtures of two or more components with thermal coupling streams. Thus, for any n-component mixture, the total number of the original partially thermally coupled configurations (OPC) is equal to the number of the conventional simple column sequences (SC) for an ncomponent mixture. It can be calculated by the following equation of Thompson & King (1972).

,

fez])! "

(1)

n!(n-l)!

3. Generation of the Thermodynamic Equivalent Partially Coupled (TEPC) Configurations It is seen that in an OPC, each rectifying (stripping) column section, after removing its condenser (reboiler), will receive the needed reflux liquid (boilup vapor) flow from the corresponding rectifying (stripping) section of its subsequent column. From Figure lb, it is seen that by replacing condenser AB of column 1 in Figure la with the thermal coupling streams AB, the reflux liquid in rectifying section 1 of column 1 is supplied by rectifying section 3 of its subsequent column 2. Both reflux liquids of sections 1 and 3 are from the same condenser A of column 2 in Figure lb. Thus, there is generated a structural degree of freedom by the introduced thermal coupling AB that the thermally linked two rectifying column sections 1 and 3 can be combined to receive the needed reflux liquids from the same condenser A. Or in other words, column section 3 of column 2 can be moved to column 1. Similarly, the introduced thermal coupling CDE in Figure lb will bring a structural degree of freedom to combine column section 6 of column 3 with column section 2 of column 1, or the column section 6 is movable, and the structural degree of freedom from the thermal coupling DE will make column section 8 movable. It is observed that for any n-component conventional simple column configuration, the removing of a condenser (reboiler), associated with two or more components of a prior column, will make the rectifying section (stripping section) of its subsequent column movable. Therefore, each thermal coupling introduces a structural degree of freedom in the thermally coupled system for the rearrangements of the column sections that will produce the thermodynamic equivalent arrangements. A thermodynamic equivalent structure is defined as that it has the different arrangement of the column sections among the column units from the original thermally coupled configuration, while it has the same individual splits, the same thermal coupling streams for the same submixtures as its

278 original thermally coupled configuration. In Figure lb, the introduced three thermal couplings AB, CDE and DE generate three structural degrees of freedom that make the three colunm sections 3, 6, and 8 movable among the column units. Thus, it will produce different thermodynamic equivalent structures by different movements of the movable column sections among the column units. If we once move one column section of 3, 6, or 8 there will be produced three thermodynamic equivalent arrangements from the original thermally coupled configuration of Figure lb, as shown in parts a-c of Figure 2, respectively. If we once move two column sections of (3, 6), (3, 8) or (6, 8) there will be produced other three thermodynamic equivalent arrangements as shown in parts d-f of Figure 2, respectively. If we simultaneously move all of the three movable column sections of (3, 6, 8), it will result in a thermodynamic equivalent arrangement as shown in part g of Figure 2.

Figure 2. Thermodynamic equivalent thermally coupled arrangements of Figure 1(b). There are some significant differences of the structural features of the thermodynamic equivalent arrangements in comparison to the original partially thermally coupled configuration. As illustrated in Figure 1, there are two column sections of each of the column units in the original thermally coupled configuration. It is exactly the same

279 structure as its counterpart of the conventional simple column configuration. However, the distribution of the 8 column sections among the 4 column units in the thermodynamic equivalent arrangements of Figure 2 is different from each other. This difference results from the different movements of the movable column sections designated in the original thermally coupled configuration. Depending on the number of the column sections being moved, a column unit in the thermodynamic equivalent structures of Figure 2 can have 1, 2, 3, 4, or 5 column sections. This will significantly affects the design of the column equipment of the thermodynamic equivalent configurations. Furthermore, for a thermally coupled distillation configuration, the introduced thermal coupling streams are perceived to be the source of operating problems. Usually, it is expected that pressure of the column withdrawing a vapor flow, should be a little higher than that of the column receiving the vapor flow in a thermally coupled system (Carlberg & Westerbergl989). Thus, there exist constraints in determination of the pressures of the thermally linked column units for design a PC configuration (Rong et al. 2001). Even though all of the thermodynamic equivalent structures of a partially thermally coupled configuration have the same number of the thermal couplings, their constraints on pressures among the column units might be different. It is so since each movement of a column section will change the vapor flow direction of the corresponding thermal coupling streams. As discussed earlier, in any conventional simple column configuration for an ncomponent distillation, there are n-2 column sections whose condenser(s) and/or reboiler(s) are associated with submixtures of two or more components. Thus, there can introduce n-2 thermal couplings for a conventional simple column configuration for an ncomponent distillation. It means that there will introduce n-2 structural degrees of freedom in a partially thermally coupled configuration. It also means that there are n-2 column sections in a partially thermally coupled configuration that are movable among the column units. The following formula is derived for the calculation of the number of thermodynamic equivalent partially coupled configurations for an n-component simple column configuration {n>i).

Tn =2^1-2 =2"-'

(2)

Where C^_2=l designates the original partially coupled configuration without movements of column sections (e.g. Figure lb); C^_2 (/=1, n-3) designates the number of thermodynamically equivalent arrangements by once moving / column sections (e.g. parts a-c or parts d-f in Figure 2); C^22 =1 designates the side-column thermodynamically equivalent arrangement by simultaneously moving all of the n-2 column sections (e.g. Figure 2g). Thus, the total number of the thermodynamically equivalent partially coupled configurations for all of the conventional simple column configurations of an ncomponent mixture can be calculated from the following formula.

P„=5„xr„=fe:i>llx2"-

(3)

n\{n-i)\ Table 1 illustrates the number of the original partially coupled configurations, as well as the number of the total thermodynamic equivalent thermally coupled configurations generated from the conventional simple column configurations for feed mixtures with different number of components.

280 Table 1. The number of thermodynamic equivalent thermally coupled schemes generated from the simple column configurations for an n-component mixture. No. of No. of SC No. of OPC No. of total TEPC components configurations configurations configurations

3 4 5 6 7 8 9 10 11

2 5 14 42 132 429

2 5 14 42 132 429

1,430 4,862 16,796

1,430 4,862 16,796

4 20 112 672 4,224 27,456 183,040 1,244,672 8,599,552

Obviously, the thermodynamic equivalent partially coupled column configurations have formulated a unique search space of the possible thermally coupled alternatives for optimal design of distillation systems for multicomponent separations. Because of the space limit, the optimal design of the partially thermally coupled systems among all of the TEPC configurations for some specific multicomponent mixtures will be presented in the future publications.

4. Conclusions In this work, the synthesis of the partially thermally coupled column configurations for a multicomponent distillation has been studied with regard to the thermodynamic equivalent structures. There has been formulated a complete space of the possible thermodynamic equivalent alternatives of the partially coupled configurations for multicomponent mixtures. A formula is presented to calculate the number of all the partially coupled schemes for any n-component mixture. The formulated alternatives of all the possible arrangements of PC configurations provide a complete search space for optimal design of multicomponent distillation systems not only for the economics, but also for column equipment design. This can help designers to find the final optimal thermally coupled distillation systems with concerns of both economics and equipment designs.

5. References Agrawal, R., 1996, Ind. Eng. Chem. Res., 35,1059. Carlberg, N.A. and Westerberg, A.W., 1989, Ind. Eng. Chem. Res., 28, 1386. Christiansen, A.C., Skogestad, S. and Lien, K., 1997, Comput. Chem. Eng., 21, S237. Petlyuk, F.B., Platonov, V.M. and Slavinskii, D.M., 1965, Int. Chem. Eng., 5, 555. Rong B.-G., Kraslawski, A., Nystrom, L., 2001, Comput. Chem. Eng., 25, 807. Rong B.-G. and Kraslawski, A., 2002, Ind. Eng. Chem. Res., 41,5716. Rong B.-G. and Kraslawski, A., 2003, AIChE J., 49, xxx. Sargent R.W.M. and Gaminibandara, K., In Optimization in Action; L.W.C. Dixon, Ed.; Academic Press: London, 1976, p. 267. Thompson R.W. and King, J., 1972, AIChE J., 18, 941.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

281

A Multicriteria Process Synthesis Approach to the Design of Sustainable and Economic Utihty Systems Zhigang Shang Department of Process & Systems Engineering, Cranfield University, Cranfield, MK43 OAL,UK Antonis Kokossis Department of Chemical Engineering & Process Engineering, University of Surrey, Guildford, Surrey GU2 5XH, UK

Abstract The proper design criteria for a modern utility plant should include both environmental and economic requirements. In other words, not only the capital and operating costs of a utility plant but also the corresponding utility wastes must be minimised. The paper presents a systematic multicriteria process synthesis approach for designing sustainable and economic utility systems. The proposed approach enables the design engineer to systematically derive optimal utility systems which are economically sustainable and economic by embedding Life Cycle Assessment (LCA) principles within a multiple objective optimisation framework. It combines the merits of total site analysis, LCA, and multi-objective optimisation techniques

1. Introduction In process industries, large amount of gaseous emissions is generated by combustion processes associated with the utility systems. The emissions can result in many impacts on the surrounding environment. As a result of serious concerns about environmental problems in recent years, development of process synthesis methods for waste reduction purpose has become a research issue of growing importance. Thus, the proper design criteria for a modern utility plant should include both environmental and economic requirements. In other words, not only the capital and operating costs of a utility plant but also the corresponding utility wastes must be minimised. Many applications have been presented previously to address the problem of synthesis and design of utility systems. (Papoulias and Grossmann,1983; Colmenares and Seider ,1989; Bruno et ai, 1998; Wilkendorf et al, 1998; Rodrguez-Toral et al, 2001). It should be noted that all studies mentioned above addressed the utility system design problem only based on economical considerations and none of them adopted waste minimisation as one of their design criteria. Research in the latter area has not received much attention until recently. Smith and Delay (1991) tried to establish the minimum targets for the flue gas emissions in the utility system. Linnhoff (1994) proposed an approach to the minimisation of environmental emissions through improved process integration, i.e. the pinch technology. However, these approaches were not able to put a cost against emissions. As the impact of a process on the environment is dependent on its structure and design characteristic, environmental issues and economic ones should

282 be considered simultaneously as an integral part of process synthesis and design (Fredler et al., 1994; Linninger et aL, 1994). This invariably requires some trade-off between these issues. The mathematical programming approach should be in general more comprehensive and less-prone to trade-off these issues as long as all essential engineering insights are formulated in the mathematical models. To address this idea of including environmental impact considerations into process design, Life Cycle Assessment (LCA) is gaining wider acceptance as a method in identifying more sustainable options in process design. Recently, LCA has started to be coupled with multi-objective optimisation to provide a framework for process design by simultaneously optimising on environmental, economic and other criteria (Stefanis et al., 1997; Azapagic, 1999). These developments are still underway. The multi-objective optimisation techniques used by these works can only obtain Pareto-optimum solutions which provide infinite number of options for optimal design. Therefore, other multicriteria decision-making (MCDM) techniques are further required to identify the best compromise solutions. Furthermore, few works have been reported to generate utility system designs based on the integration of LCA and multiobjective optimisation. Here we will present a systematic multicriteria process synthesis technology for designing sustainable and economic utility systems. The technology should be able to generate the best compromise solutions by simultaneously optimising on environmental, economic and other criteria, rather than obtain Pareto-optimum solutions which provide infinite number of options.

2. Multicriteria Process Synthesis The proposed multicriteria process synthesis technology enables the design engineer to systematically derive optimal utility systems which are economically sustainable and economic by embedding LCA principles within a multiple objective optimisation framework. It combines the merits of total site analysis, LCA, and multi-objective optimisation techniques. It follows a four-step procedure as follows: (i) Design candidates identification using total site analysis technology; (ii) Environmental impact assessment using LCA principles; (iii) Formulation of the multi-objective optimisation model to incorporate environmental impact criteria as process design objectives together with economics; (iv) Multi-objective optimisation using goal programming techniques. Step 1: Design candidates identiHcation using total site analysis technology The first step in the formulation of the synthesis problem of utility systems is to consider systematically many alternative configurations by including them in a superstructure. In this step, the technology screens various utility units and identifies the efficient utility units that will be implemented into a superstructure from which the optimum design will be selected. There are enormous number of utility units which can be employed in a utility system, namely boilers, back-pressure /condensing turbines, gas turbines, electric motors, steam headers at different pressure levels, condensers, auxiliary units, and all of their different combinations. If all of them are included in a superstructure, it will be too large to be

283 solved. In this approach, the Total Site Profiles (TSP) (Dhole and Linhoff ,1992) are used to locate the feasible utility units in the context of a total site that may be used to satisfy the heat and power demands of a production site. TSP give a simultaneous view of surplus, and heat deficit, for all the processes on the site and reveal the cogeneration potential for the whole site. Thus the TSP can be used as a conceptual tool to screen and target feasible utility units for the site, such as the location of the steam headers and cogeneration units. The Thermodynamic Efficient Curve (TEC) (Shang and Kokossis, 2001) is then employed to identify the efficient utility units by screening among the feasible units. These efficient utility units will form a superstructure. The TEC tool is able to compare the efficiencies of utility units. Only the units with promising efficiencies will be included in the superstructure. Therefore, the superstructure derived by the proposed approach will be much smaller than a general superstructure that includes all possible units. Step 2: Environmental impact assessment using LCA principles The second step of this approach involves carrying out LCA study of the superstructure. The LCA principles are used to estimate the environmental impact of each candidate unit included in the superstructure. The LCA study considers a broad system which considers not only the utility system but also all processes associated with raw material extraction and imported electricity generation. Raw materials such as fuels and water are assumed to be available at no environmental penalty. In this approach, a typical coal-fired power plant is included to generate the electricity that needs to be imported by the utility system as shown in Figure 1. The advantage of the broad system is that input wastes (to the utility system) by importing electricity can be also accounted for together with output emissions (from the utility system). Next, the LCA study involves estimating the amount and type of each waste leaving the system boundary. Once the inventory has been determined, the impact of each waste on the surrounding environment is quantified. Here we use the widely accepted approach described by Heijungs (1992) in which the wastes are grouped according to the environment on which they will impact. Impacts related to global warming, ozone depletion, acidification, nitrification, photochemical oxidation, resources depletion and human toxicity are considered. The advantage of using such environmental impacts is that the information provided is directly linked to impact on the environment rather than for instance mass flowrates of waste materials. Local Enmssions

Local Emissions

ih::. Process Plant

Figure 1. The broad system boundary.

Central Power Station

284 Step 3: Formulation of the multi-objective optimisation model Having developed the superstructure for the utility system, one can then formulate a mathematical program accordingly for the synthesis of the utility system. In order to consider environmental criteria as distinct objectives together with economics in the design problem of the utility system, a multi-objective optimization formulation is considered to select the most sustainable and economic utility system from the superstructure by minimising all the environmental impacts from, the utility system simultaneously, while minimising the total cost of the utility system subject to the given set of utility demands. The numerical values of the environmental impacts and costs are dependent on design characteristics of the utility system. Therefore, the eight environmental impact criteria identified and quantified in the LCA study step and the total cost of the utility system are considered as independent, distinct minimisation functions in the multi-objective optimisation model. The cost objective function is the sum of annualised capital and operating costs. The former includes the fixed and variable costs of all system units. The latter consists of the costs of fuels, fresh water and purchased electricity. The material and energy balance equations associated with every unit in the superstructure are included as the equation constraints of the optimisation problem. Other than the balance equations associated with all units, models of gas emissions and environmental impacts are also integrated into the optimisation model. Binary variables are used to signify the existence or non-existence of units in the superstructure. The resulting multi-objective optimisation problem is formulated as an MINLP model. The decisions to be made by the multi-objective optimisation model include the configuration of the utility system, the values of the operating pressures and temperatures of different steam headers, the types of fuels used by the units, and all stream flowrates. Step 4: Multi-objective optimisation using goal programming techniques Both structural and parameter optimisation in the superstructure are performed for the multi-objective MINLP model on all environmental and cost objective functions to locate the best utility systems with minimal environmental impact and the desired economic performance. The multi-objective MINLP model is solved with goal programming (GP) techniques so as to provide the optimal configure from a superstructure that has embedded many feasible utility systems. By being able to tradeoff incommensurable objectives, e.g. environmental impacts and economic requirements, the GP methods are able to avoid the well-known problems encountered, for instance, weighting objectives, infinite number of non-inferior solutions, etc. In this approach, the objectives are ranked and then minimised lexicographically using the nonArchimedean GP to identify the best compromise solution. The best performance of each of the criteria over the specified operating ranges are used as the goals for the multi-objective optimisation problem. Rather than attempting to achieve solution optimality for single-objective problems, the approach of the GP is to find the best compromise solution that comes as closely as possible to satisfy the design goals.

285

3. Case Study The methodology is illustrated as it has been applied to an industrial complex. The case study considers a design problem for a site utility system in the industrial complex. Figure 2 shows the superstructure for the utility system that is to be designed for satisfying utility demands of the industrial complex. The utility system should meet the demands of VHP, HP, MP, LP steam and power demands. The superstructure consists of three main boilers (Bl, B2, B3) which use different fuels (natural gas, coal and oil), one gas turbine boiler (GT boiler), two local boilers (PI and P2), six steam turbines (Tl to T6), two gas turbines (GTl and GT2) which use natural gas and oil respectively, one BFW pump and the deaerator. There are five steam levels (VHP, HP, MP, LP and VLP) and one vacuum level. Steam can be generated at two levels: very high pressure (Bl, B2, B3, GT boiler and P2) and high-pressure (PI). Letdown steam from higher levels is also available. The utility system is interconnected with the utility grid. Connection to the grid allows import of electricity in case of a need. There are options to export excess electricity.

-

Emissions

i

Oil

-,

Natural gas

^Vm^ Emissions iissions BFW pump

1 5^

ElectricitvJ

/ — | - \ Central Fmmr Vrif Statton

C^ E

Figure 2. The superstructure of a utility system.

The problem is formulated as a multic-objective optimisation model and is solved using Goal Programming technique. The optimal solution includes one oil boiler (B3), one

286 natural gas turbine (GT2), one gas turbine boiler (GT Boiler), two local boilers (PI, P2) and four steam turbines (Ti , T3, T4 and T6).

4. Conclusions A systematic multicriteria synthesis technology for the design of sustainable and economic utility systems has been developed. The proposed technology enables the design engineer to systematically derive optimal utility systems which are economically sustainable and economic by embedding Life Cycle Assessment (LCA) principles within a multiple objective optimisation framework. The best design should be the utility system which incurs the minimum environmental impact and capital and operating costs.

5. References Azapagic, A. and Clift, R., 1999, The application of life cycle assessment to process optimisation. Computers & Chemical Engineering 23. Bruno, J.C., Fernandez, F., Castells, F. and Grossmann, I.E., 1998, A rigorous MINLP model for the optimal synthesis and operation of utility plants. Chemical Engineering Research & Design. 76. Colmenares, T.R. and Seider, W.D., 1989, Synthesis of utility systems integrated with chemical processes. Ind. Eng. Chem. Res. 28. Dhole, V.R., and Linnhoff, B., 1992, Total site targets for fuel, co-generation, emissions and cooling. Computers & Chemical Engineering, 17. Friedler, F., Varga, J.B. and Fan, L.T., 1994, Algorithmic approach to the integration of total flowsheet synthesis and waste minimisation. American Institute of Chemical Engineering Symposium Series, 90. Heijungs, R., et al., 1992, Environmental Life Cycle Assessment of Products Background and Guide. Leiden: Centre of Environmental Science. Linnhoff, B., 1994, Use pinch analysis to knock down capital costs and emissions. Chem. Engng Prog 90. Linninger, A.A., Ali, S.A., Stephanopoulos, E., Hanand, C. and Stephanopoulos, G., 1994, Synthesis and assessment of batch processes for pollution prevention. American Institute of Chemical Engineering Symposium Series 90. Papoulias, S.A., and Grossmann, I.E., 1983, A structural optimization approach in process synthesis - 1 : Utility systems. Computers & Chemical Engineering 7. Rodriguez-Toral, M.A., Morton, W. and Mitchell, D.R., 2001, The use of new SQP methods for the optimization of utility systems, Comp. Chem. Engng., 25. Shang, Z.G. and Kokossis, A.C., 2001, Design and synthesis of process plant utility systems under operational variations. ESCAPE-11, Denmark. Smith, R. and Delaby, O., 1991, Targeting flue gas emissions. Trans IchemE, 69. Stefanis, S.K., Livingston, A.G. and Pistikopoulos, E.N., 1997, Environmental impact considerations in the optimal design and scheduling of batch processes. Computers & Chemical Engineering, 21. Wilkendorf, F., Espuna, A. and Puigjaner, L., 1998, Minimization of the annual cost for complete utility systems. Chemical Engineering Research & Design, 76.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

287

A Decision Support Database for Inherently Safer Design R. Srinivasan^'*, K.C. Chia^ A-M. Heikkila^ and J. Schabel^ ^ Department of Chemical & Environmental Engineering National University of Singapore 10 Kent Ridge Crescent, Singapore 119260 ^ VTT Industrial Systems P.O. Box 1306 Tampere, Finland

Abstract An inherently safer process relies on naturally occurring phenomena and robust design to eliminate or greatly reduce the need for instrumentation or administrative controls. Such a process can be designed by applying inherent safety (IS) principles such as intensification, substitution, attenuation, limitation of effects, simplification, etc. throughout the design process, from conception until completion. While the general principles and benefits of IS are well known, a searchable collection of inherently safer designs that have been implemented in industry has not been reported. Such a database of inherently safer design (ISD) examples would assist the process designer in the early stages of the design lifecycle when critical design decisions are made. In addition to examples of IS design which have been successfully carried out, the database that we have developed contains process incidents which could have been averted by the application of ISD. In this paper, details of the database, the query engine, and potential applications are presented.

1. Introduction Inherent safety is the pursuit of designing hazards out of a process as opposed to using engineering or procedural controls to mitigate risk. This is usually achieved through intensification, substitution, attenuation, limitation of effects, simplification, avoiding knock on effects, making incorrect assembly impossible, making status clear, tolerance of misuse, ease of control and computer control (Kletz, 1998). Using the above principles, a more robust plant can be designed where departures from normal conditions are tolerated without serious consequences for safety, production, or efficiency. Despite the obvious importance of ISD, there has only been limited work for developing tools that support the assessment of IS. INSET V/SLS developed to promote IS principles, and contains a set of tools which support the adoption of IS principles into process development and design (Malmen et al., 1995; van Steen, 1996, Turney et al. 1997). Recently, an expert system that supports ISD by identifying safety issues and proposing inherently safer alternatives was reported (Palaniappan et al., 2002a; 2002b). One important criticism of toolkits and expert systems is that due to their 'generic' nature and the need to be applicable to a variety of processes, they cannot account for the subtle

' Corresponding Author. Tel: +65 67732671; Fax: +65 67791936; e-mail: [email protected]

288 nuances and special cases that occur during process design. Another issue relates to the link between safety, health, environmental aspects, economics, and the operability of a chemical plant (Palaniappan et al., 2002c). Since safety is rarely considered in isolation, there can be many synergies and tradeoffs between the different facets. Again it is not easy to foresee all the tradeoffs and judgement calls are required. To overcome these shortcomings, IS toolkits and expert systems can be complemented by a knowledgebase of design examples describing scenarios where IS principles have been used. Such a database would also help the process designer by illustrating possible synergies and tradeoffs between safety and other aspects during practical plant design. Such a decision-support database, called iSafeBase, is presented in this paper. The remainder of this paper is organised as follows: in the next section, the conceptual and implementation phases of iSafeBase are described. Two case studies are used to illustrate the use of iSafeBase in Section 3. Conclusions and future work directions for this work are presented in Section 4.

2. Database Design and Development The following were some key considerations during the design of iSafeBase: • Expandable: A database is useful only if it has a sufficiendy large dataset of examples. In order to enable this, it should be easy to enter new examples into the database, not only by the designer familiar with the internal details of the system, but also by any user by means of a simple interface. • Customisable: As mentioned above, safety is related to numerous aspects of process design, not all of which can be pre-enumerated. The design of the database should allow new classes of information to easily be added. • Open architecture: It should have an open and flexible architecture that permits the exchange of information with other design support tools such as flowsheeting packages, CAD systems, or safety evaluation systems. Examples of ISD would then be available while working with those systems. After comparing various database development software packages (including Filemaker, Microsoft FoxPro, Corel Paradox, Microsoft SQL Server and Oracle), Microsoft Access was selected as the preferred platform because of its ubiquitous availability and ease of use. Two distinct steps were needed to develop a structure that met these objectives: designing the data structures and constructing relationships between them. These are described below. 2.1. Data structures The following major classes of information are important: 1. Material properties - such as toxicity, corrosivity, reactivity, explosiveness, and flanmiability. 2. Design-related information - including design stage (chemistry route selection, chemistry route detailed evaluation, process design optimisation, process plant design, etc.), chemistry, and equipment. 3. Safety-related information - including hazards, and IS principles. 4. Design alterations - involving chemistry, material, or equipment modifications. 5. Accident-related information. Tables are used to organise the above data in iSafeBase. Each table comprises a number of fields which store the necessary various attributes for that class. Table 1 shows some example tables and their fields. The reader should note that references are provided for each design example and accident in order to enable the designer to explore further.

289 Table 1: Database tables and their fields. Table IS Design Accidents IS Principles Modification Type of Hazard

Fields Description, Illustration, Design Stage, Equipment, Reference Outcome, Initiating Event, Contributing factors. Consequences, Description, Equipment, Reference Principle, Suggestion Modification, Cost savings Type of hazard. Properties, Role, Unit Operations

2.2. Relationships Once the types of data have been specified, the relationships between the tables must be defined. The primary data tables provide a unique identifier (ID) for each record. Linking tables were created to relate records from different tables, and these links use the identifier to reference data across tables and enable one-to-one, one-to-many, many-to-one and manyto-many relationships. For example, a substance can have more than one hazardous property and a hazardous property can be present in many substances. A many-to-many relationship would be described for a substance (say with ID=1) that is toxic (ID=1) and flammable (ID=3) - this would be captured through one entry in the Materials table, two entries in the Properties table, and two rows in a material-properties link table (where the field 'Material' would have a value of 1, and the field TD-Properties' would have values 1 and 3 respectively). A simplified representation of the various relationships in iSafeBase is shown in Figure 1.

f

3

Materials ID (materials) .•

( ID-Role 1^ ID(RQle)

^ J <-!

f ID-Properties^ »|^ID(PrQpertie^^

[Type of Hazard] Properties Role Unit Ops ID(Hazard)

ID-Unit Ops ^ ID (Equipment)!

•k

n

M

IS Design ID (Pre-Design)1 ID (Post-Design) Design Stage Equipment J

Pre-Design ID J>ost-DesignlDj

pD-Design Stage^

i-J^

ID (Stage) J

{ ISprindples ^ • [lD(Suggestion)J ^

Equipment I^ID(Acddents)J

Figure 1: Relationships in iSafeBase. 2.3. Querying the database Once the examples have been collated, they need to be retrieved. A key consideration for the acceptability of a database is the ease in which it can be queried. Queries have been

290 implemented in iSafeBase to allow searches by specific equipment, hazard, substance, IS principle, modification, design stage, or outcome. Free text searches which search through every field in the database can also be performed. Additionally, the functionality to browse all the cases in the database related to a specific category, through a hierarchical interface, has also been implemented. 2.4. Graphical user interface Developing the graphical user interface (GUI) was the last step in producing a functional database. Figure 2 shows the GUI for the two ways of querying iSafeBase as described.

^ iSafeBase

^ iSafeBase

Bipofe Keyword [confcenbl

Input l^eywQfd Contents ^

Inputfeeyvvord;| Equipment

Querybyi

Hazard

p

IS Principle

€o!

Design Stage Modification Outcome

Figure 2: Querying iSafeBase by (a) Keyword search, and (b) Category specific browsing.

3. Case Study: Keyword 'React' The current version of iSafeBase has forty design examples and accidents. Figure 3 lists the number of examples in each design stage while Table 2 lists the different sources from which the design and accident examples were selected.

O)

Process plant design

CO

CO c .5^ o O

Process design optimisation Chennistry route detailed evaluation Chemistry route selection

No. of cases: o Figure 3: Design examples in each design stage.

10

15

20

291 Table 2: Sources of design examples. Different sources Kletz, T.A., Process Plants: a handbook for inherently safer design, 1998, Taylor & Francis. Chementator, Chemical Engineering, (journal) Proceedings of International Conference & Workshop on Process Safety Management and Inherently Safer Processes, October 8-11, 1996, Orlando, AIChE. Bollinger, R.E. et al.. Inherently Safer Chemical Processes - A Life Cycle Approach, 1996, AIChE. Total

Cases 22 8 7 3 40

A query on the keyword 'react' is used to illustrate the different facets of the program. Twenty-eight different design examples and thirteen accidents were returned for this case from 'air contexts. Two such design examples are outlined in Tables 3 and 4. Table 3: Design example summary from Case study 1.

Hazardous Scenario IS Principle Suggestion Design stage Example of Modification Reference

Case description MIC reacted with alpha-naphthol to make carbaryl. Large inventories of MIC kept in plant. Substitution - Use another process route that involves less hazardous material or conditions. Chemistry route selection. Different sequence of reactions: Alpha-naphthol and phosgene are reacted together to give an ester that is then reacted with methylamine resulting in same product. No MIC is produced. (Pilot tested by Makhteshim, an Israeli company) Kletz, T.A. (1998). Process Plants: A Handbook for Inherently Safer Design, p.68

4. Conclusions While the importance of inherently safer design of chemical plants has been widely accepted, this has not been practised partly because of the lack of support tools. A database of examples of inherently safer designs has been reported in this paper. The software quickly retrieves cases of design modifications and related accidents for a given scenario. By making it possible to retrieve specific examples of ISD through a simple query process, it is hoped that this tool would guide plant designers in their effort to develop safer chemical plants. It would also promote IS in the mindsets of management, since concrete examples of what has been successfully implemented and the associated rewards can easily be presented.

292 Table 4: Design example summary from Case study 2, Hazardous Scenario IS Principle Suggestion Design stage Suggested Modification Example of Modification Reference

Case description Reaction runaway. Ease of control - Use physical principles instead of other measures that may fail or be neglected. Chemistry route detailed evaluation. Use another catalyst. ICI Chemicals & Polymers has developed oxy-anion promoted catalysts in which the selectivity promoter is adsorbed onto the catalyst to activate it. Any temperature excursion in the reactor results in desorption of the activator. Thus, reaction mnaway potential has been eliminated. Hawksley, J.L., and M.L. Preston (1996). "Inherent SHE: 20 Years of Evolution."

5. References Kletz, T., 1998, Process plants: a handbook for inherently safer design. Philadelphia: Taylor & Francis, pp. 1-19, 152-180. Malmen, Y., Verwoerd, M., Bots, P.J., Mansfield, D., Clark, J., Tumey, R. and Rogers, R., 1995, Loss Prevention by Introduction of Inherent SHE Concepts, SLP Loss Prevention Conference, December 1995, Singapore. Palaniappan, C , Srinivasan, R. and Tan, R., 2002a, Expert System for Design of Inherently Safer Processes - Part 1: Route Selection Stage, Industrial and Engineering Chemistry Research, Vol.41(26), pp.6698-6710. Palaniappan, C , Srinivasan, R. and Tan, R., 2002b, Expert System for Design of Inherently Safer Processes - Part 2: Flowsheet Development Stage, Industrial and Engineering Chemistry Research, Vol.41(26), pp.6711-6722. Palaniappan, C , Srinivasan, R. and Halim, I., 2002c, A Material-Centric Methodology for Developing Inherently Safer and Environmentally Benign Processes, Computers & Chemical Engineering, Vol. 26(4/5), pp.757-774. Tumey, R., Mansfield, D., Malmen, Y., Rogers, R., Verwoerd, M., Suokas, E. and Plasier, A., 1997, The INSIDE Project on inherent SHE in process development and design - The Toolkit and it's application, IChemE Major Hazards XIII, April 1997, Manchester, UK. van Steen, J., 1996, Promotion of inherent SHE principles in industry, IChemE - 'Realising an integrated management system', December 1996, UK.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

293

Using Design Prototypes to Build an Ontology for Automated Process Design* IDStalker^ ESFraga^ LvonWedel^ AYang^ ^Centre for Process Systems Engineering, Department of Chemical Engineering, UCL, London WCIE 7JE, UK ^Lehrstuhl ftir Prozesstechnik, RWTH Aachen, 52056 Aachen, Germany E-mail: i . s t a l k e r @ u c l . a c . u k

Abstract Recently there has been an increased interest in agent-based environments for automated design and simulation (Garcia-Flores et al. 2000). In such environments, responsibility for decision making is partly removed from the engineer to the underlying agent framework. Thus, it is vital that pertinent knowledge is embedded within this framework. This motivates the development of an ontology (Gruninger & Lee 2002) for the particular domain. An important first step is a suitable organisation of the knowledge in a given domain.

1. Introduction Automated process design is a complex task that typically makes use of an array of computational tools, for example thermophysical packages. Agent based systems, such as COGents (Braunschweig et al. 2002), offer a potential solution to the dynamic access and configuration of such tools.. To realise this potential an automated design agent requires both process design domain knowledge — that is an ontology — and appropriate knowhow to apply this domain knowledge. This paper describes the use of design prototypes to organise domain knowledge as a first step towards the development of an ontology for process design and the mechanisms needed to invest a design agent with the domain knowledge.

2. A Design Prototype for Conceptual Process Design Design prototypes arose in mechanical engineering but the ideas apply to generic design processes. The conceptual basis is the Function-Behaviour-Structure (FBS) framework (Gero 1990) which is motivated by the following: [...] the metagoal of design is to transform function F (where F is a set) into a design description D in such a way that the artefact being described is capable of producing these functions. (Gero 1990) *Work funded by Project COGENTS, Agent-Based Architecture For Numerical Simulation, funded by the European Community under the Information Society Technologies Programme (1ST), under contract IST-200134431.

294 Documentation

Formulation

F Bg S Bs D

Function Expected Behaviour Structure Actual Behaviour Design Documentation

Figure 1. The Function-Behaviour-Structure (FBS) Framework

This design description represents an artefacts elements and since there is generally no function in structure nor structure in function, the transformation from function to description proceeds in stages. Gero (1990) introduces the FBS framework, Figure 1, to elaborate these stages working on the premise that It is function, structure, behaviour and their relationships which form the foundation of the knowledge which must be represented (Gero 1990). The goal of conceptual process design is to generate and select good process designs, usually represented by aflowsheetwith design parameters and often supplemented with design rationale (Banares-Alcantara 1997) This is the Design Artefact. A design problem begins with the desired products, reactions of interest, available processing technologies, raw materials and a set of criteria for ranking. We seek a process which will derive the desired products from raw materials: this is the function F of our design artefact. Employing the FBS framework allows us to model process design as a combination of the the following activities: formulation^ to realise F a sequence of expected behaviours. Bey such as separation, reaction, etc., is formulated; synthesis, the expected behaviours are used to synthesise an appropriate structure 5; analysis, the structure is analysed for cost and actual behaviours, B^; evaluation, the actual behaviours are compared with the expected behaviours: ideally actula behaviours will be an acceptable superset of the expected behaviours; reformulation, as design problems are typically underdefined, we are likely to find that the first few drafts of aflowsheetare incomplete (Laing & Fraga 1997) and so the expected behaviours and function are reformulated; documentation,finally, the final design artefact is fully documented in (D). Examples of FBS for a generic prototype for conceptual design are shown in Table 1. A Design Prototype is a knowledge representation schema which abstracts "all requisite knowledge appropriate to that design situation" (Gero 1990). Symbolically, a prototype proforma is expressed ^ = {F,B,S,D,K,C)

295 where K = {Kr,Kg,Kc,K^,Kj^) is a tuple of, respectively: relational knowledge, which provides and makes explicit the dependencies between the variables in the function, behaviour and structure categories; qualitative knowledge, which provides information on the effects of modifying values of structure variables on behaviour and function; computational knowledge, which specifies mathematical and symbolic relationships between variables in the function, behaviour and structure categories; constraints or contextual knowledge identifies exogenous variables for a design situation; and reflexive knowledge, a pair K^ = {T,P) comprising, respectively, the typology which identifies the broad class to which the prototype belongs and a partition representing the subdivision of the concept represented by the prototype. Examples are shown in Table 1. C denotes the context in which the design is activity is taking place. In our case, this is the context of process engineering and does not need further elaboration. Two common approaches to developing aflowsheetfor a given engineering process are a hierarchical approach (Douglas 1988) and an algorithmic approach, typically through mixed integer nonlinear progranmiing (MINLP) (Grossmann et al. 1999). These are different mechanisms to transform the expected behaviours identified in the prototype into a suitable structure. Both begin with the statement of the function of the final process. Accordingly, the approaches refine the same base prototype in different directions. The hierarchical approach refines the prototype in small steps: starting with the coarse-grained top level information of process type and applying a number of heuristics to derive the additional (refined) information; this approach emphasises qualitative knowledge. The algorithmic approach refines the prototype in large steps: a minimum of required information is developed and this is used to develop a number of sections of the prototype by appealing to external search mechanisms; this approach emphasises computational knowledge. The two approaches are largely complementary and share a minimum of overlap. Accordingly, to ensure a broad application we have extracted, organised and collated into a single prototype design knowledge from a representative of each approach (Douglas 1988, Fraga et al. 2000).

3. Towards an Ontology, OntoCAPE An ontology may be defined to be "an explicit specification of a conceptualisation" (Gruber 1993). The underlying FBS framework provides natural categories for an ontology of process design. Ontologies were originally motivated by the need for sharable and reusable knowledge bases. However, the reuse and sharing of ontologies themselves is still very limited. Those seeking to reuse a particular ontology do not always share the same model as those who built it: thus, it is often difficult to discover tacit assumptions underpinning the ontology and to identify the key distinctions within it (Gruninger & Lee 2002). The use of a prototype to develop an ontology circumvents these problems: the key distinctions derive from the framework of prototype; if a prototype has been fully developed, then all assumptions are made explicit in the knowledge categories. OntoCAPE specifies a conceptualisation of process modeling, simulation, and design. A skeleton ontology has been developed in which the major categories of COGents concepts

296 Table 1. Generic Prototype for Conceptual Process Design

Function

to convert raw materials to desired products subject to specified constraints: inputs —> outputs

Behaviour

Structure

Kr

Behaviours

separation, reaction, mixing, heating, cooling, recycle, etc.

Variables

recoveries, rates, duties, etc.

Elements

flash, distillation column, reactor, mixer, heater, etc.

Variables

number of units, volume of reactor, heights of distillation columns, reaction temperature, operating pressure, etc.

Properties

component thermophysical properties, thermal conductivity, tray efficiency, etc.

Function to Behaviour

If function is to isolate pure product, the required/expected behaviour would be ''separation."

Behaviour to Behaviour Variables

Recovery specification for separation units.

K,

Recycle structure required; economic potential has an inverse relationship with raw material costs; etc.

Kc

Unit models; cost correlations; product specifications; reaction equilibria; etc.

^ct

Plant data, such as amortisation period; site constraints; ambient conditions; etc.

UR

Typology

process flowsheet

Partition

separation, reaction, reaction-separation, with recycle, without recycle, etc.

297 Application Specific Concepts

process design

process modelling

process simulation

Common Concepts chemical process system processing subsystem realisation

function

behaviour

processmg material

software system

Figure 2. OntoCAPEfigure

are identified and key concepts given for each category. The resulting top level structure of OntoCAPE is illustrated in Figure 2. The full ontology is currently being developed and will provide more detailed class hierarchies, class definitions, attributes, relations and constraints. OntoCAPE comprises of a number of relatively independent partial models. In particular, there are partial models conmion to different CAPE applications nd those peculiar to specific applications. The processing subsystem in the skeleton OntoCAPE has three distinctive aspects: realisation, function, and behaviour. This corresponds naturally to the FBS framework of in design prototypes. Accordingly, design prototypes, especially concrete examples, provide a suitable organisation of material for use in refining the concepts and relations of skeleton ontology relevant to process design. Moreover, the full ontology, in turn, can be used to provide more formal specification of design prototypes. The formal specification of the full ontology will be expressed in DAML+OIL ( h t t p : / /www. d a m l . o r g ) .

4. From Design Prototype to Design Agent To function in an agent based system, the design agent must supplement knowledge of both what is, domain knowledge, with know-how, problem solving knowledge. To this end, ontologies and problem solving mechanisms (PSMs) (also, called problem solving methods or generic task models), go hand-in-hand (van Heijst 1995): ontologies capture domain knowledge; PSMs capture the task-level application of the domain knowledge. Since FBS framework separates knowledge from the computational processes which operate upon it, a design prototype provides a basis from which to develop a systematic approach to identifying PSMs. The transformations broadly embrace the computational processes through which one category of knowledge is developed into another. We apply PSMs to function io formulate expected behaviour; behaviour to synthesise structure;

298 structure to analyse for actual behaviour; expected and actual behaviour to evaluate actual behaviour. Thus, well-developed prototypes are invaluable in developing a design agent: an ontology is derivable from the prototypes; the transformation processes of the FBS framework provide us with a basis for a systematic approach to discovering PSMs.

5. References Banares-Alcantara, R. (1997), *Design support for process engineering III. Design rationale as a requirement for effective support'. Computers and Chemical Engineering 21, 263-276. Braunschweig, B. L., Fraga, E. S., Guessoum, Z., Paen, D. & Yang, A. (2002), COGents: Cognitive middleware agents to support e-cape, in B. Stanford-Smith, E. Chiozza & M. Edin, eds, 'Proc. Challenges and Achievements in E-business and E-work', pp. 1182-1189. Douglas, J. M. (1988), Conceptual Design of Chemical Processes, McGraw-Hill International Editions. Fraga, E. S., Steffens, M. A., Bogle, I. D. L. & Hind, A. K. (2000), An object oriented framework for process synthesis and simulation, in M. F. Malone, J. A. Trainham & B. Camahan, eds, 'Foundations of Computer-Aided Process Design', Vol. 323 of AIChE Symposium Seriesy pp. 446-449. Garcia-Flores, R., Wang, X. Z. & Goltz, G. E. (2000), 'Agent-based information flow for process industries supply chain modelling'. Computers chem. Engng 24,11351142. Gero, J. S. (1990), 'Design protoypes: A knowledge representation schema for design', AI Magazine Winter, 26-36. Grossmann, I. E., Caballero, J. A. & Yeomans, H. (1999), 'Mathematical programming approaches to the synthesis of chemical process systems', Korean J Chem Eng 16(4), 4 0 7 ^ 2 6 . Gruber, T. R. (1993), 'A translation approach to portable ontology specifications'. Knowledge Acquisition 5(2), 199-220. Gruninger, M. & Lee, J. (2002), 'Ontology applications and design: Introduction', Communications of ACM 45(2), 39-41. Laing, D. M. & Fraga, E. S. (1997), 'A case study on synthesis in preliminary design'. Computers & Chemical Engineering 21(Suppl.), 53-58. van Heijst, G. A. C. M. (1995), The role of ontologies in knowledge engineering. Thesis, University of Amsterdam.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

299

Engineer Computer Interaction for Automated Process Design in COGents* ID Stalker^ R A Stalker Firth^ E S Fraga^ ^Centre for Process Systems Engineering, Department of Chemical Engineering, UCL, London WCIE 7JE, UK ^Summertown Solutions Ltd, Suite 140, 266 Banbury Road, Oxford 0X2 7DL, UK E-mail: i . stalker@ucl .ac.uk

Abstract We identify those interaction issues necessary to foster creativity in automated process design. We apply the key distinctions of Engineer Computer Interaction (Stalker & Smith 2002) to ensure that these are included in the development of a process design agent within the COGents framework (Braunschweig et al. 2002, COGents n.d.). The formalism is used to develop a blueprint for interactivity between a designer and a design agent which fosters creativity in design.

1. Automated Process Design in COGents A process design problem begins with the desired products, reactions of interest, available processing technologies, raw materials and a set of criteria for ranking. The result of process design is a flowsheet supplemented with design rationale: this is our Design Artefact (Baiiares-Alcantara 1997). This is a complex task and benefits greatly from the use of automated tools. Recently, agent based systems (Ferber 1999) have received an increased interest for application to automated design and simulation (GarciaFlores et al. 2000). COGents is a European project to use cognitive agents to support dynamic, opportunistic interoperability of CAPE-OPEN compliant software over the internet (COGents n.d., Braunschweig et al. 2002). It is essentially 2L proof of concept for numerical simulation using agent technology, software components and web repositories with the chosen context being computer aided process engineering. Part of this work involves the development of a process design agent which will make use of an automated design tool, Jacaranda (Fraga et al. 2000), in coordination with other agents. The current usage scenario for the Jacaranda System is typical of design tools. The user input is comprehensive: the user sets up the system; fully defines the problem; defines the nature of the solution space through units available for a problem; defines the granularity of the solution space through discretisations of continuous parameters; provides cost *Work funded by Project COGENTS, Agent-Based Architecture For Numerical Simulation, funded by the European Community under the Information Society Technologies Programme (1ST), under contract IST-200134431.

300

Figure 1. Current Usage Scenario Use Case Diagram

models, material components and raw material specifications. We sunmiarise a use case analysis of the current usage scenario in Figure 1. In COGents, we seek to remove the onus from the user through the use of agents. As a necessary step we have identified how to redistribute the use cases appropriately among the design agent, a design tool and the additional COGents framework. We illustrate the anticipated final distribution in Figure 2. The design agent prepares the problem definition with minimum input from the user, obtaining information from other agents in the COGents platform and employing its own knowledge to undertake appropriate decisions.

2. Interaction Issues Advantages of an agent based approach to process design include the automation of routine tasks, access to up-to-date information, access to new technologies and access to an increased range of solution mechanisms. Reducing the burden from the the designer allows him to focus on more creative aspects, increasing the likelihood of truly novel designs. However, an agent based approach not only removes the onus from the user, it also removes a certain amount of control. Consider, in Figure 1 the user controls the information employed by the design tool, through level of discretisation, values for variables and the constants used, and so forth. He can make use of the design tool for preliminary explorations of a given solution space, a key to successful design (Navinchandra 1991, Smithers 1998); for example, through the use of partial solutions (Fraga 1998, Fraga et al. 2000). In Figure 2 the level of automation seems to prevent this creative use of the design tool: the designer must either accept the results of the system without question or seek an alternative; should a design problem remain unsolved, there is no indication of neamess to a solution, nor of those constraints which may have restricted particular design alternatives. Thus, there is no information available to guide a reuse of the system or to take on board when preferring an alternative design tool.

301

E>esign Tool

COGents

Figure 2. Anticipated Final Usage Scenario Use Case Diagram

We seek to realise the full potential of an agent based approach by using the technology to reduce the burden and including mechanisms through which to re-introduce the designer into the loop. One way is to allow a choice of responsibility from the current situation of Figure 1 to the final situation of Figure 2. This returns control but also returns the burden. A preferable way is to promote an increased interactivity, allowing the designer to supervise the design agent. This returns control without the burden. Engineer Computer Interaction (ECI) is a methodology for coordinating aspects of HCI with domain specific knowledge to facilitate the development of more appropriate software systems to support engineers. ECI developed in Structural Engineering (Stalker & Smith 2002). Application of ECI to a given discipline requires the development of three elements: Organisational Schema A representation of the important stages in the life cycle of a design artefact which can be translated into a software structure for computer implmentation. Task Decomposition A decomposition of the generic tasks in developing the artefact through its life cycle. The decomposition available for each task in the original ECI blueprint offers the following modules: Data Management to examine the input information for fitness for use; Model Selection to offer a choice of underlying assumptions; Model Use to allow appropriate revisions and tuning of models; Viewpoints to encourage exploration of the space of solutions from different perspectives; and Comparison of

302 Documentation

Formulation

F Bg S Bs D

Function Expected Behaviour Structure Actual Behaviour Design Documentation

Figure 3. The Function-Behaviour-Structure (FBS) Framework

multiple interpretations. Engineer Identikit A set of generic engineering representations to facilitate the development of domain specific user system interaction.

3. Automated Process Design with Engineer Computer Interaction Organisational Schema We employ the Function-Behaviour-Structure (FBS) Framework (Gero 1990), illustrated in Figure 3. The function F of our design artefact is to represent a process which will derive the desired products from raw materials. To realise this function, a sequence of required behaviours, such as separation, reaction, etc. (expected behaviours, Be) is formulated; these are used to synthesise an appropriate structure 5; the structure is analysed for cost and actual behaviours, B^; as design problems are typically underdefined, we are likely to find that the first few drafts of a flowsheet are incomplete (Laing & Fraga 1997) and so the expected behaviours and function are reformulated. Finally, thefinaldesign artefact is documented in D. Task Decomposition Of particular interest to process design are: Model Selection and Use Appropriate model selection and use are vital to synthesis and analysis tasks. For process design in COGents we have access to models within our design tool and also from the additional COGents framework. Access to model parameters is essential: these are often problem specific, for example, amortisation periods, selectivity, conversion, recoveries; a designer oftens makes a number of choices of discretisation during preliminary explorations (Fraga 1998, Laing & Fraga 1997). Viewpoints and Comparison Results from a number of different models are extremely useful for evaluation and reformulation of behaviours. We compare the actual behaviours of the synthesised structure with the formulated behaviours; we compare full and partial solutions generated in order to maximise insight. For example, the primary design tool in COGents, Jacaranda (Fraga et al. 2000), generates the best N solutions, as requested, by the user. Engineer Identikit Generic engineering representations identified for process design are:

303 Classification such as physical properties databases and thermophysical packages; ontologies and information technology based data models (Bayer et al. 2001); subproblem classifications, such as the subproblem dependencies, qualifiers and solution hierarchies in (Fraga 1998); and cost tables. Procedure and Sequence such as the necessary order of unit operations; procedural information subsists in computational methods. Graphical Representations includingflowsheetreaders such as HYSYS; simple tools for reading tables of subproblems, for example (Laing & Fraga 1997); traditional sketches of graphs. Formulae including mathematical formulae; reaction equations; potentially clauses of logic programs to capture design heuristics of hierarchical approaches, such as developed in (Douglas 1988). Symbols depicting the various unit operations and theflowsheetsthemselves. Customs and Practice including standards, guidelines and other information observed as a general practice by process designers and engineers. Tables and Lists of physical properites; unit specifications and constants; subproblem listings with status measures (Fraga 1998). We note, for example, applying dynamic programming techniques to process design is based on the use of cost tables (Fraga 1998). Natural Language to enlarge upon or provide a commentary to the information in the other categories.

4. Discussion Agent based systems offer enormous benefits to automated process design, reducing the burden of effort, increasing access to information, models and solution techniques and so forth. However, it is imperative that we provide an interactivity to ensure that the designer has a creative input; that he retains control and has access to partial solutions to foster a systematic search of design space and a computational efficiency. We have applied the key distinctions of EC! to ensure that development of the process design agent accommodates these needs. Enhancing the potential interactivity with a design agent invested with design expertise encourages a less expert user to employ the system in a creative manner similar to that of a more experienced designer. The impact of the inclusion of ECI on the development of a process design agent is minimal. It does not affect the progression suggested by the differences in Figures 1 and 2. Rather we are increasingfinalsystem and it is only in light of system that we can properly determine whether the desirable interaction issues are best served through extending the functionality of the design agent; or through the introduction of a personal assistant agent (Ferber 1999). Nothwithstanding, there are ontological implications: we must ensure that our design ontology embraces relevant additional concepts such as partial solutions, cost tables, preliminary exploration, coarseness of discretisation, subproblem dependencies, dependency qualifiers, solution status, and similar.

304

5. References Banares-Alcantara, R. (1997), 'Design support for process engineering III. Design rationale as a requirement for effective support'. Computers and Chemical Engineering 21, 263-276. Bayer, B., Krobb, C. & Marquardt, W. (2001), A data model for design data in chemicalm engineering - information models. Technical Report LPT-2001-15, Lehrstuhl fuer Prozesstachnik, RWTH Aachen. Braunschweig, B. L., Fraga, E. S., Guessoum, Z., Paen, D. & Yang, A. (2002), COGents: Cognitive middleware agents to support e-cape, in B. Stanford-Smith, E. Chiozza & M. Edin, eds, Troc. Challenges and Achievements in E-business and E-work\ pp. 1182-1189. COGents (n.d.). The COGents Project Agent-based Architecture for Numerical Simulation', http;//w WW. cogents.org. Douglas, J. M. (1988), Conceptual Design of Chemical Processes, McGraw-Hill International Editions. Ferber, J. (1999), Multi-Agent Systems: An Introduction to Distributed Artificial Intelligence, Addison Wesley. Fraga, E. S. (1998), The generation and use of partial solutions in process synthesis', Chemical Engineering Research and Design 76(A1), 45-54. Fraga, E. S., Steffens, M. A., Bogle, I. D. L. & Hind, A. K. (2000), An object oriented framework for process synthesis and simulation, in M. F. Malone, J. A. Trainham & B. Camahan, eds, 'Foundations of Computer-Aided Process Design', Vol. 323 of AIChE Symposium Series, pp. 446-449. Garcia-Flores, R., Wang, X. Z. & Goltz, G. E. (2000), 'Agent-based information flow for process industries supply chain modelling'. Computers chem. Engng 24,11351142. Gero, J. S. (1990), 'Design protoypes: A knowledge representation schema for design', AI Magazine Winter, 26-36. Laing, D. M. & Fraga, E. S. (1997), 'A case study on synthesis in preliminary design'. Computers & Chemical Engineering 21(Suppl.), 53-58. Navinchandra, D. (1991), Exploration and Innovation in Design: Towards a Computational Model, Springer-Verlag. Smithers, T. (1998), Towards a knowledge level theory of design process, in J. S. Gero & F. Sudweeks, eds, 'Artificial Intelligence in Design '98', Kluwer, pp. 3-21. Stalker, R. & Smith, I. (2002), 'Structural monitoring using engineer-computer interaction'. Artificial Intelligence for Engineering Design, analysis and Manufacturing 16(5). Special Edition, Human-Computer Interation in Engineering Contexts.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

305

Developing a Methanol-Based Industrial Cluster Rob M. Stikkelman\ Paulien M. Herder^, Remmert van der WaP, David Schor^ Delft University of Technology ^Interduct, Delft University Clean Technology Institute ^Faculty of Technology, Policy and Management; Energy & Industry Section The Netherlands

Abstract We have conducted a study in collaboration v^ith the Port of Rotterdam in which we explored possibilities for developing a methanol-based industrial cluster in that area. The study had two main goals. The first goal was to develop a realistic methanol-based industrial cluster, supported by technical and economic data. For our cluster we have considered plants and processes from the entire production chain. The second goal of the study was to bring together various actors in the field of our proposed methanol cluster. In order to create a common language among the actors and to get the actors involved actively, we developed a virtual prototype of the cluster. During a workshop with the actors, we used the virtual prototype as a vehicle to initiate discussions concerning technical and economic issues and improve upon the proposed cluster. The key actors that are needed to bring about innovative changes are expected to continue the discussions and explorations in this field together in the future.

1. Introduction The Rotterdam port area in The Netherlands is the main hub in the world-wide methanol infrastructure. About 1 million ton of methanol is imported, stored and sold each year. The importance of methanol in the Rotterdam port area is expected to increase, and possibly double, in the future, as the application of methanol in fuel cells may be a promising option for improving the sustainability of the road transportation sector. The world-wide transportation sector currently depends on oil for roughly 98% of its operations. These oil-based fuels contribute considerably to urban air pollution in the form of emissions of CO2, ground-level ozone precursors (NOx), carbon monoxide (CO) and particulate matter (PM). The application of these fuels in conventional combustion engines is also a source of noise pollution. The application of methanol in fuel cells, however, increases energy efficiency and decreases noise and emission levels compared to the conventional combustion engine. When methanol is to be applied broadly in the transportation sector, the current methanol demand will increase far beyond the current world production levels for the downstream production of fuel additives and adhesives. In order to produce the required amounts of methanol, new, sustainable production routes are being explored and developed world-wide (e.g.. Herder and Stikkelman, 2003). Accordingly, the importance of existing methanol hubs in the world is expected to increase significantly.

306 We have conducted a study in collaboration with the Port of Rotterdam, in which we explored futuristic, and sometimes unusual possibilities for developing a methanolbased industrial cluster based upon the existing methanol infrastructure in that area. The study had two main goals. The first goal was to develop a realistic methanol-based industrial cluster, supported by technical and economic data. The second goal of the study was to bring together the various actors in the field of our proposed methanol cluster, and to create support for the envisaged transformation.

2. Theoretical Background 2.1. Cluster modelling A number of approaches have been reported in literature that deal with the modelling of a cluster of industrial processes. A conventional systems engineering approach to modelling clusters, using mass and energy balances for the chain and its subsystems was introduced by Radgen et al. (1998). It was reported to be a valuable way of modelling and analysing production networks and chains. The authors used existing process simulators, using mass and energy balance calculations to build and analyse chains. In this work, however, we decided to develop a dedicated tool, based on spreadsheets, in order to simplify the building of the virtual cluster. Some other studies aim at optimising an entire cluster with respect to economic and/or ecological objectives. In our study we did not yet aim at obtaining an optimised cluster, but merely at identifying the design space of the methanol cluster. The functional approach as suggested by Dijkema and Reuter (1999) and Dijkema (2001) was used in this study to identify and explore the design space for designing our methanol cluster in the Rotterdam port area. The functional approach can deal effectively with system complexity as it focuses on system functionality in stead of system contents, and the functional characteristics of a system are technology-free. A technology-free, functional design of a methanol cluster provided us with the necessary structure for the definition of the cluster design space without compromising or going into detail of the wide array of technical solutions. 2.2. Transition management The theoretical development of a methanol cluster is of no use when the actors that will have to invest in the new cluster are not involved from the very beginning. These actors can enrich the design space of the methanol cluster with new ideas and alternative plants and processes. The transformation to a methanol-based cluster will likely be a gradual transformation. We, therefore, used the transition management body of knowledge (e.g., Rotmans et al, 2001) to build our theoretical framework with respect to creating involvement of various actors in the change processes. Transitions are modelled as Scurves divided into four phases. A pre-development phase is followed by a take-off phase. Then the acceleration phase takes place which is concluded by a phase of stabilisation. Transition management concepts can help to create involvement, to expose barriers for change and to support the taking down of those barriers. An important tool that is offered by transition management theories is the design of a transition agenda that

307 Table 1. Overview ofsubgoals and research methods. Subgoal 1. To develop a theoretical framework 2. To explore and map the design space broadly 3. To bound the design space 4. To quantify the design space 5. To design a viable methanol-based industrial cluster 6. To design a viable transition process

Research method Literature survey Functional modeling Interviews and literature survey Virtual Prototype Workshop with relevant actors Workshop with relevant actors

w^ould indicate which stage the transition process is in, and would give an indication of how to reach the next stages by creating a long term vision and short term actions.

3. Research Approach In order to achieve our goals we have divided the study into a number of subgoals, and we used different research approaches for each step. The subgoals and associated research methods are summarised in table 1. We conducted a literature survey in order to build a manageable and useful theoretical framework. This framework was described in the previous section. Second, we developed a functional design of a methanol cluster, using the approach described by Dijkema, and using our current knowledge and expertise regarding the developments in the Rotterdam port area. This functional design was used to identify which actors should be approached if this cluster was to be realised. Through interviews and further literature study we were able to identify the most relevant actors and consult with them in order to obtain a realistic design space. We also used the interviews to get a quantitative feel for the cluster, by asking the various actors about their long-term vision with respect to the developments concerning methanol in the broadest sense. We then turned these interview results into a quantitative model, the Virtual Prototype, describing our design space of alternative methanol-based clusters and allowing users to modify the cluster and get an impression of the viability of alternative cluster designs. Finally, we will use the Virtual Prototype in a workshop with relevant actors as a means to further the transition process. The intended results of the workshop are a well thought out methanol-based industrial cluster in the Rotterdam port area, and the start of a platform or community of actors who need and want to get involved in developing such cluster.

4. Results 4.1. The methanol cluster For the functional design of our cluster we have considered plants and processes from the entire production chain, ranging from fossil and renewable fuels to methanol derivatives, such as fiber board plants that make use of formaldehyde. In addition, the cluster includes industries that process or use by-products' such as hydrogen and platinum. The cluster comprises five main functional areas. For each of these functional areas we have made an inventory of possible interactions, flows and subsystems:

308 1. 2. 3. 4. 5.

power production waste processing transportation fuel s methanol and derivatives spin-off processes

The functional design of the cluster is shown in Figure 1.

Bectridty

Biomass

Innport

Crg. waste

Fossil fuels

n

Methanol

ICE car FCcar

Derivates

Rber board

H2

R recycling

Airplane FC production H

Furniture

Figure 1. Functional design of methanol cluster. Power production Power plants currently use fossil fuels as their main feedstock, but are interested in supplementing their feedstock with biomass. A quick calculation, however, shows that under the current market conditions the application of biomass in a power plant is not economically viable. The economic variable cost margin of the conversion of biomass into electricity would be 10% at most. This is too small a margin to justify the use of biomass in electricity production at this moment. Biomass can, however, be used more economically for the production of synthesis gas by gasification, which can be turned into methanol. Roughly, 1 ton of biomass can be converted into 1.2 tonnes of methanol, rendering the variable cost margin at a more attractive 60%. Waste processing The presence of a gasification unit opens up possibilities for the gasification of all kinds of organic wastes, such as solid waste, plastics, sludge, rubber wood and household waste (Schwarze Pumpe, 2002). Transportation fuels Fossil fuels are practically the sole provider of energy for transportation of goods over the road infrastructure, in the form of natural gas, petrol and diesel. The application of methanol, however, as a replacement fuel in conventional internal combustion engines (ICE) is promising. Only strict economic considerations hold back a large scale introduction of methanol into ICE cars. The use of methanol in cars powered by fuel

309 cells has a brighter future, as methanol can be a convenient and safe hydrogen carrier. The viability of implementing a methanol fuel cell into cars has been demonstrated, among others, by DaimlerChrysler (2002), who has developed a series of demonstration models (NECAR). Methanol and derivatives The supply of methanol to the area is expected to grow in the future. This will attract new large-scale installations that process methanol to convert it into derivatives, such as olefins, through the Methanol to Olefins process (MTO) and it will cause expansion of the production of formaldehyde. At its turn, formaldehyde can be used in the production of fiber board, a key ingredient for the furniture industry. In addition to the import of biomass for gasification purposes, imported wood chips can be used in the production of fiber board. Spin-off processes Finally, we introduced a subsystem of spin-off processes to capture any processes that are not directly linked to methanol production or processing, but may come to play a significant role in the future. Generally the life span of fuel cells is shorter than the life span of cars, so we introduced a platinum recycling industry in order to process used fuel cells. In addition, we added an extreme example of using the hydrogen surplus as an aeroplane fuel, since the energy-mass ratio for hydrogen is 3 times higher than for kerosene. This scenario, however, may well be realised only in the very far future. 4.2. Actor involvement The relevant actors come from a very wide range of industries. In order to create a common language among the actors and to get the actors involved actively, we developed a virtual prototype of the cluster, based upon our functional design and the interview results. Some key conclusions and trends that could be extracted from these interviews were: • a main obstacle for methanol cluster development is a high initial investment • relatively inexpensive natural gas inhibits wide-scale research into biomass applications • there is a need for research into a large-scale biomass gasifier • there is a lot of tacit knowledge within companies concerning future developments During a workshop to be held with the actors, we will discuss and detail our ideas and proposals for a methanol cluster, and we will use the virtual prototype as a vehicle to initiate discussions concerning technical and economic issues of the cluster., and extract the tacit knowledge that is present in the actors. The workshop will comprise a panel of representatives from actors considered in the Virtual Prototype. Sessions will include surveys, hypothetical scenarios, and free exchange of ideas to refine our methanol cluster model and develop a consensus on necessary developments along a transition path. As an example, a hypothetical scenario may take as fact near term, significant and enduring cost increases in petroleum. Under such supposed conditions the panel's thinking with regard to creating and operating a methanol cluster at Rotterdam will be captured through survey instruments.

310

5. Discussion and Conclusions The preliminary results of our study support many of our ideas about possibilities for a methanol cluster. The functional design of the cluster proved to be useful in identifying a wide array of possible processes and actors. Secondly, many of the key actors that are needed to bring about such innovative industrial clusters have been interviewed and indicated to be very willing to be brought together in a workshop. These actors are expected to further their discussions and explorations in this field by means of several other transition management initiatives that are currendy being deployed by the Dutch Ministry of Economic Affairs. We trust that this research contributes to the research body of knowledge concerning the development of industrial clusters, as well as to a healthy and competitive methanol-based Rotterdam port area.

6. References Dijkema, G.P.J, and Renter, M.A., 1999, Dealing with complexity in material cycle simulation and design, Computer and Chemical Engineering, 23 Supplement, pp. S795-S798. Daimler-Chrysler, 2002, Study Cites Low Cost for Methanol Refueling Stations, methanol.org, March. Dijkema, G.P.J., 2001, The Development of Trigeneration Concepts, Proc. 6*^ World Congress of Chemical Engineering, Melbourne, Australia. Herder, P.M. and Stikkelman, R.M. 2003, Decision making in the methanol production chain, A screening tool for exploring alternative production chains. International Conference on Process Systems Engineering 2003, Kunming, China. Radgen, P., Pedernera, E.J., Patel, M. and Reimert, R.,1998, Simulation of Process Chains and Recycling Strategies for Carbon Based Materials Using a Conventional Process Simulator, Computer and Chemical Engineering, 22 Supplement, pp. S137-S140. Rotmans, J., Kemp, R., van Asselt, M.B.A., Geels, F., Verbong, G., Molendijk, K.G.P. and van Notten, P., 2001, Transitions & Transition management: The case for a low emission energy supply, ICIS BV, Maastricht, The Netherlands. Schwarze Pumpe, 2002, Sekundarrohstoff-Verwertungs-zentrum Schwarze Pumpe (SVZ), http://www.svz-gmbh.de/.

7. Acknowledgements This study benefited from the support and expertise of the municipal authority of the Port of Rotterdam, and the authors would like to thank Pieter-Jan Jongmans and Anne van Delft for their co-operation. The authors would also like to acknowledge the valuable contributions of Hugo Verheul (Delft University of Technology) to the study, specifically in the area of transition management.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B. V. All rights reserved.

311

Risk Premium and Robustness in Design Optimization of Simplified TMP Plant Satu Sundqvist*, Elina Pajula, Risto Ritala KCL Science and Consulting, P.O.Box 70, FIN-02150 Espoo, Finland

Abstract This paper illustrates issues related to optimal design under uncertainty in a simplified TMP (thermomechanical pulp) plant design case. Uncertainty in the case study is due to four dynamic scenarios of the paper machine pulp demand serviced by the designed TMP plant. Both a risk premium approach and a multi-objective optimization technique were employed. In the latter the worst-case scenario (representing the highest cost) was taken as the robustness measure of the design, and the design parameters were determined as a trade-off between the optimum of the mean cost model (i.e. the stochastic model) and of the worst-case scenario. The TMP model is a general example of an industrial case having parallel on/off production units and time-variant productions costs. Therefore, the design case could also be interesting for other fields of chemical industry than paper manufacturing, and the optimization procedures can be applied for risk premium and robustness studies in general dynamic optimization cases.

1. Introduction In papermaking, TMP (thermomechanical pulp) plant has to satisfy the pulp demand of the paper machine. Design optimization of the simplified TMP plant includes the number of refiners (A^Ref) and the storage tank volume (Ftank) as design parameters. The optimization is genuinely a dynamic problem having paper machine demand and production costs, and thus — when optimally operated — also the number of active refiners varying in time. In the TMP plant design, the optimum of the total costs is found via a subtask of minimizing the capital costs and the production costs in operations and scheduling optimization. The TMP design optimization is a MINLP (mixed-integer non-linear programming) problem since it has both a discrete, A/Ref, and a continuous, Fiank, design parameter. The operational optimization subproblem has integer decision variables (number of active refiners in time) affecting the continuous state of intermediate tank volume through process dynamics. The tank volume is constrained to stay between a minimum and a maximum volume. In the operational optimization, the task is to schedule startups and shutdowns of refiners in order to minimize the production cost when the demand of the paper machine and the price of the electricity are known over a given time horizon.

312

2. Optimization Procedure 2.1. Operations and scheduling optimization In general, the operations optimization task is to find suitable set point trajectories for the controllers. As the controllers are omitted from our simplified TMP system model, no setpoint optimization is included in the study. However, the refiner scheduling optimization can also be considered as operations optimization with refiner activity set point trajectory as binary valued (on/off) function of time. In this case, the operations optimization over a time horizon of some one hundred decision time intervals took approximately one minute by using a low-end PC and Matlab environment and the simulated annealing algorithm (Otter and van Ginneken, 1987). 2.2. Design optimization The MINLP problem in the TMP case is simple in that the NPV (net present value) per capital employed can be determined by first treating both the design parameters (A^Ref and Ftank) as discrete ones and then interpolating a continuous cost function Cost = X^tank) for the optimal number of refiners. Consequently, no advanced MINLP solvers are needed. 2.3. Objective function With a given scenario of the paper machine TMP demand, the production schedule can be optimized and with a given probabiUty distribution of all scenarios (p^), the operational costs as a function of n(t) and V(t) can be calculated. By adding the capital costs, the optimal values for the decision-making amongst the studied design alternatives (A^Ref, Ktank) are obtained. DESIGN LEVEL:

C t {f P'^^"'°' ('' ^-'""- ^^^ ""capital (^-' ^- J

^'^

subject to OPERATIONS LEVEL:

«^°H^;^Ref,^.ax) = argming{nW}

(2)

"(0 100

gHt)} =Y.''At)+K"up+ h^^n^^ dV_ -t-^="(0/..-/4 dt 0
(3)

(4) (5)

n(t)e [0,\,...N^J

(6)

where/^f is production capacity of one refiner, fp^is paper machine demand and h-, refers the daytime and night time electricity costs per refiner at each time interval. The capital cost can be written as ^capital

~ ^Ref "^ ^lank

~ '^Ref^Ref.i

" ' " ' ' O V ten* ' ' ^ o )

^ '

313 where Qe/ is the capital cost of a refiner, which, in real cases, is a function of the capacity (in MW) of the refiner. In the tank cost, the exponent a is usually from about 0.6 to 0.7 (Biegler and Grossmann, 1999) and Co and FQ are the base capacity and base cost, respectively. 2.4. Case calculations In the over-all design optimization, four different demand scenarios of the paper machine were considered. Figure I. All scenarios are expected to be equally likely, i.e. p^ = 0.25. Scenario C

Scenario A

c"

r u

1 1

^

\

Decision interval

1

1 Decision interval

Decision interval

Decision interval

Figure 1. Demand scenarios of the paper machine in the simplified IMP case calculations. Parameter values for the TMP model to be optimized are shown in Table 1. The time horizon is divided into 7=100 decision intervals, where A/=30 min, corresponding to a total of approximately two-day time period for the case calculations. Table 1. Parameter values for the simplified TMP model. Model Parameter

Value

TMP demand - average A-C / D - min - max Number of refiners Refiner production Tank volume - maximum, Vmax - minimum, Vmin - initial volume, Vo(/=0) • end volume, Vend(/=100) Electricity costs - night time - daytime - up/down costs

Units per decision interval (At = 30 min) 7.6/10.4 0-16.5 NRef=3,4,5,6 3.6 Units Vmax = 20, 30, 50, 70, 100, 200,400 5%V„^ 15% Vn^ 2 5 % V n u x - 35%Vn..x

Units per decision interval 3 5 3

The over all feasible region covered in the optimization was obtained by combining the feasible regions of all scenarios resulting the following:

N=3-^V> 200; N=4-^V> 100; N=5-^V> 30 andN= 6^V> 30. The non-feasible regions were due to the fact that paper machine demand could not be satisfied. These values were considered to have infinite large cost values and thus omitted from the optimization.

314 In the design optimization, the interest on capital costs was neglected, and thus the capital cost was simply the annual depreciation. The number of the depreciation years, m, for the refiners and the storage tank was studied in the range of m = [1, 2, 4, 10, 20]. The capital cost due to refiners, A^Ref = [3, 4, 5, 6], is calculated as: 1 •N C (8) 'Ref ^^ Ref

^RefJ

where m is the number of years for depreciation, and CRef,i = 200 is the cost of one refiner (in the units relative to the two-day time period of electricity costs). Similarly, the capital cost due to the intermediate tank, Ftank = 20 - 400, is calculated as: (9) where m is the number of years for depreciation and b = CQ/VQ'^ = 10 is the relative unit cost of the tank.

3. Optimal Design and the Effect of a Risk Premium In the design with a risk premium, the expected value based on the probabilities of all scenarios was calculated for each discrete design parameters, A^Ref and Ftank- The risk premium was defined proportional to the standard deviation of the operational costs under the four equally likely scenarios, with a proportionality factor a = 0...3. The objective fimction to be minimized is expressed as Co. = t/7^g(Az(0) + C,,,,w +aa'.

(10)

Figure 2 shows that with these parameters the risk premium affects the design only at intermediate number of depreciation years. It was obvious that the number of the depreciation years (affecting the importance of capital costs versus operational costs) had a strong effect on the optimal design alternative. At 10 years depreciation time, the risk premium factor had an influence on the optimal design increasing both the number of refiners, A^Ref, and the continuous design parameter, Ftank. a)

b)

Number of refiners for the optimal design in a simplified TMP case

6 z If 5

s

A

1'

• •

•

CO

l>

^ 3

• fl =0-3 A a=0 X a=3

1 1 5

10 15 20 Number of years for depreciation

400

E 3 O

X A

300 200


0 )

Storage tank volume for the optimal design in a simplified TMP case

100

•

•

•

A

• a =0-3 A a =0 X fl=3

0

25 Number of years for depreciation

Figure 2. Risk premium weighing effect (a = 0 - 3) on the optimal design in the simplified TMP case with different number of years for depreciation: (a) number of refiners and (b) storage tank volume. The optimum of the design parameters was found in the studied range of A^Ref and Ftank for the depreciation times 1-10 years, where the capital costs dominates the total costs.

315 As for the 20 years of depreciation time, the optimum number of refiners is observed to reach the maximum (A^Ref = 6) indicating that the parameter range should probably be larger than studied. It was therefore calculated that the minimum costs in operational optimization (based on maximum production rate and storage tank volume at low energy price period) are to be found amongst the number of refiners up to A^Ref = 13 and ^tank = 550. However, the studied range (A^Ref = 3 - 6 , Ftank = 20 - 400) was adequate to find the optimal design parameters when the depreciation time of the relative capital costs is restricted to maximum of 10 years.

4. Robust Design Optimization The robust optimization study was based on the worst-case scenario analysis (Suh and Lee, 2001). The best robust solution was chosen amongst the Pareto optimal design alternatives. 4.1. Multiobjective optimization In the MOO (multiobjective optimization) method expected cost and robustness measure are simultaneously optimised. The robust model is based on the stochastic model (Eq. 10, with a = 0) having an additional objective of controlling the variability of performances of individual scenarios. The worst-case scenario is taken as the objective variable for the robustness measure and a decision-making procedure is applied to choose the best robust design alternative for the case study. 4.2. Decision-making The best robust solution for the decision-making (with the studied model parameter range and the depreciation years m =10) was found by using an L^-metric method, where the robust model parameters are obtained nearest to the ideal point. Figure 3. Pareto Curves

O.obO \

0,200 I Ideal I

0,400

Figure 3. Robust optimization of the simplified IMP case with four different demand scenarios of the paper machine. The best robust solutions based on the worst-case analyses are found with N = 6 and with the indexes k = 5 and k = 8 for the different scaling factors (probability of the worst-case scenario) p^ = 0.25 orpy^= 1 (no scaling), respectively. The optimum solution withp^ = 0.25 corresponds the storage tank volume of Vtank-350.

316 The scaling factor, /?w, is a function of a probability of the worst-case scenario, i.e. /7w = 0.25. The resuh was also calculated without any scaling (p^ = 1). The selected robust optimal solution is closer to the stochastic model solution E(^=0) for smaller p^, and closer to the worst case analysis solution W(k=Np) for larger/>w

5. Results and Discussion For the simplified TMP design case, stochastic model gives A^ = 5 refiners and Ftank = 320 for the optimal design. Both the risk premium study and the robust optimization study prefer N= 6 refiners. In both studies, the optimum storage tank volume is Fiank = 350. Design optimization with a stochastic model does not take into account any uncertainty in design. The TMP design alternatives are based on the over all feasibility region of all scenarios. However, if one of the scenarios is strongly restricting the feasibility region and, in addition, is quite infrequent, the scenario can be omitted from the optimization. This might cause a situation where the TMP line is temporarily unable to produce pulp for the paper mill. Then the question to be answered is, what will be an additional cost of such a scenario, and in more general, how the extra cost should be handled in the design optimization.

6. Conclusions In the paper, the optimization with a risk premium, stochastic optimization and robust optimization were compared. The TMP plant design, even though extremely simplified, had all the characteristics of mixed-integer and dynamical design problems. Therefore, the study offers a suitable application for comparison of the design principles when uncertainty is considered in decision making of optimal design parameters.

7. References Biegler, L.T., Grossmann, I.E., Westerberg, A.W., 1999, Systematic Methods of Chemical Process Design, Prentice Hall, New Jersey. Otten, R.H, van Ginneken, L.P., 1989, The Annealing Algorithm, Kluwer Academic Publishers. Suh, M., Lee, T., 2001, Robust Optimization Method for the Economic Term in Chemical Process Design and Planning, Ind. Eng. Chem. Res., 40, 5950.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

317

Process Design as Part of a Concurrent Plant Design Project Timo L. Syrjanen Jaakko Poyry Oy PO Box 4, 01621 Vantaa, Finland, email: [email protected]

Abstract This paper describes methods and tools developed and in use in a large engineering company when process design forms part of a concurrent plant design project. One of the most important aspects is how to handle the information flow between different disciplines. The methods and tools to solve the information-sharing problems are using new ICT technologies such as the Extensible Markup Language (XML) and the Web. Also the measuring of concurrent plant design and engineering performance as for the information existence, accuracy, completeness and timing is discussed. As a case example of how the process design can be integrated with other disciplines by using new ICT technology, Jaakko Poyry Oy's MODE concept is described.

1. Introduction The world economy is continuously changing and new requirements and challenges are set also for the plant design. Global competition has increased and a new situation on the market has forced the engineering companies to cut costs, slice time and improve quality in their design work. One solution to meet these requirements is to use concurrent design and integrate process design in the concurrent plant design. This paper describes those methods and tools which can be used in the process design when it is part of the concurrent plant design. The process design has an important role in the whole plant design process. Design processes can be divided into two parts. The internal process consists of the proper process design and the interface process defines how the process design interacts with other disciplines. In this paper the main interest is focused on the interface process. In successful plant design handling of the information flow between different discipline interfaces is critical. Information must be managed correctly. Connecting the information flow to a schedule is obligatory. It is important to have measures for information existence, accuracy, completeness and timing. There are different methods of organising the information flow between the process design and other disciplines. Information can be transferred by using transfer files or storing design information in a common repository, which can be accessed with different tools for various reasons. This method also gives possibilities to use new web technologies to access design information.

318

2. Plant Design Project 2.1. Combined project involving different disciplines A plant design project is an effort in which a project company delivers a unique product to an external client. The projects are characterized by their product orientation. The objective of the project is to create a physical entity, i.e. the mill. A typical plant design project consists of designing a paper or pulp mill. Every new paper or pulp mill project requires individual engineering work. Manufacturing or procurement activities cannot be performed before appropriate engineering activities have been completed. The work in different disciplines must be harmonized to complete the project. 2.2. Engineering input data problem Today the plant design projects are becoming larger and more complex. The unit sizes are growing both in mill, engineering and contractor organizations. The reason for the growth is financial, i.e. to keep the projects feasible, and consequently large units seem to be the right solution. One of the main problems in implementing plant design projects is how to execute project plans efficiently, i.e. on schedule and correctly. The time schedules become shorter and shorter, which means that the project tasks and works must be divided between different organizations to keep the time schedule. Today concurrent design is applied to almost every pulp and paper mill design project. To succeed in design work, the basic input data for engineering must be accessible as early as possible and it should also be correct and complete. When information is shared between organizations efficiently, the quality of plant design projects increases. It is not an easy task to share the knowledge and information. The knowledge comprises all information flows in the project and the involved parties' organizations. It includes hard and soft, structured and unstructured, official and unofficial knowledge and data. For each design process it is relevant to know which input data are accessible and what is their status. The status varies from preliminary through released for design and released for construction to final.

3. Process Design Interacting with Other Disciphnes 3.1. Process design The process design acts as a base for all the other design tasks. Some parts of the process design may be performed in quite an early phase of the project. The process design can be divided into two different phases, i.e. preliminary engineering, in which conceptual design is carried out, and detail engineering. The conceptual design starts with balance calculations and preliminary studies. After that the block diagrams of the processes are created, which can be completed into preliminary flow sheets in the basic engineering phase. In this phase all necessary main equipment inquiry specifications, as well as other process equipment, pump, motor and tank lists are created. As the data and information on the main equipment form the basis for creating the final flow sheets, the detail engineering cannot be started until the main equipment has been purchased. The preliminary flow sheets and calculations are checked and the flow sheets are completed incrementally by adding information on the pipe sizes.

319 instrumentation and connections starting from larger sizes, which are the most decisive for space reservation. The sizes and types of all tanks and vessels needed in the mill are calculated. At the same time the preliminary specifications of pumps and motors are defined, and a preliminary procurement specification is created based on this information. The sizes and types of pumps and equipment are checked during the design. The dimensioned flow sheets are completed concurrently in accordance with the instrumentation design, and the flow sheets become PID diagrams. Although the creation of PID diagrams is a joint venture between the process, mechanical and automation disciplines, the process engineer is responsible for the diagrams. After the diagrams have been finished, the process design prepares the operation instructions and logic diagrams in co-operation with automation and electrical engineers. 3.2. Concurrent work between process and mechanical design The process and mechanical design are closely related and the engineering tasks are performed concurrently. For example pipe routing is started before the flow sheets are ready (see Figure 1). This is necessary because the results of the piping design are needed for the structural design and procurement in an early phase. To succeed in concurrent design is normally difficult for both process and mechanical design. From the process engineer's point of view the piping engineer is asking for the process information much before it even exists, and from the piping engineer's point of view the process engineer delivers the data much too late for successful project execution. What makes the problem even more difficult is that also external information is needed, such as the client's comments on and approval of the flow sheets. The improvement of concurrent design can be achieved in two ways; either by improving the design as its own process or by improving the data sharing between the disciplines. Process design Design Criteria

Preliminary Process design

Mechanical design

Modified Process design

Piping design

Modified Piping design

Figure 1. Process and piping design information flow.

4. Data Flow and Sharing The information sharing within a plant design project organisation is a key element for successful project execution. Today's design and manufacturing time schedules are set so exact that there is no room for delays or misunderstandings for lack of information. All information must be available for everyone in the project at all times. The projects are executed by using concurrent design, the project teams can be located in different

320 places even in different countries, and knowledge must be shared between them successfully. The project manager is responsible for the knowledge sharing. In the project it is important to decide on the interfaces between the disciplines. The shared information must be specified and a schedule must be given for when and how information is shared. Is the information pushed from the creators to its users or are the users pulling the information when they need it? Special interest must be given to change management.

5. Tools for Data Sharing 5.1. Mode - mill database architecture In Jaakko Poyry Oy the data-sharing problem between disciplines was observed for a long time ago (Talvio). One effort to solve the problem was the implementation of the MODE (MOdel Driven Engineering) design architecture. It is a collection of engineering applications sharing the same mill database. The mill database is a relational database application with structures for process, piping, automation, electrical engineering and project management data. The model consists of functions, which are the requirements for a specific task, and of components, which fulfil the function requirements. The functions and components area hierarchically connected. The engineering applications are independent from the database. The applications can be implemented with either legacy tools or commercial ones. Most of the MODE applications have been developed as legacy applications in Jaakko Poyry Oy. In the mill database the data may have one of the three status values; Current, RED (released for design) or RFC (released for construction). The current data are the latest and most up-to-date version of the data. The discipline owning the data can change the data at any time. When the data reach the status that they are ready to be released for design (RED), the data are saved in the RED fields. The other disciplines can use RED data values as a basis for their design. Data may be changed, but it shall be carried out in accordance with a predefined procedure. When the data will be released for construction (RFC), they may be considered final. Changing of the RFC data requires a complete study of the consequences due to the change. Most often the project manager or the client must approve the change.

5.2. Process design information as part of the WWW application Just like product models can be used as part of the WWW application (Siltanen), also plant design applications can benefit from web applications. Typically web applications are 3-tier applications (Figure 2).

HTML/XML

Client

i

Q Engineering system XML <

Document Database

> ^ - ^

Application ^=^>.—^ _ S

server Figure 2. Web application

architecture.

L_J

A

Drawmg

database

321 The requirement to create an independent modularised and maintainable system is to standardise the exchange protocol between the application server and back ends. The exchange format must be system-neutral and platform-independent, and it must be widely known and easy to implement. In the modern web application XML is an obvious choice. With XML the process design data can be exchanged and shared so that the application server connection with back end can be implemented. The client system is a typical Internet browser, with some plug-ins for drawing rendering. The purpose of the client is to act as a user interface to the whole application package. The application server contains all the application logic and its main role is to integrate the data from different sources, i.e. process design data and other discipline data components. The back ends are traditional repository applications such as engineering databases, document management, ERP systems, other application servers, etc. 5.2.7. Project portal Jaakko Poyry Oy has developed a project information publishing system WebPub, which is a web technology-based document publishing system. Through WebPub the user can view and print all general project documents and information. During the course of a project, the system is mainly active in the project group's Intranet (Kiiskinen). Within the WebPub structure, all the project information is divided logically into relevant groups of their own. For example, the Process Page is a group containing process PID diagrams connected with equipment information and standards. After the information has been segmented in a rational way and links designed for easy and fast searching, the requested information can be conveniently found and retrieved. 5.2.2. Application integration In the Jaakko Poyry MODE concept the process application is integrated with a 3D plant design system. All information between the systems is transferred in an application-independent XML format. Using the application server in integration gives possibilities to share design work in different locations within the company or even between different companies. Currently Poyry's own legacy XML schema is used, but when standard schemas are published, those should be used.

6. Concurrent Design Performance Measurements When concurrent design is used in a plant design project, it is important to know how the design work progresses and how well the information sharing is accomplished. Performance measurement is useful in controlling the design project and it can be used as a project management tool. 6.1. Mill Database Completeness The mill database can be used for measuring data sharing. When the process engineer inputs the data into the mill database, the input data are simultaneously released to other disciplines. It is quite easy to develop a measurement system which can measure the completeness of the input data.

322

The estimated number of equipment in each equipment class, i.e. main equipment, tanks, pumps, valves, pipelines, motors, etc, is needed as preliminary data. The preliminary data can be collected from previous projects or experienced designers can estimate the numbers. Each equipment class will be measured by different data attributes specific to the class. These attributes may have the status of current, RFD or RFC. Based on these values, it is easy to measure the completeness of the process data. The completeness of the project may be calculated with the formula: Completeness for Design = Has RFD value/Number of equipment in class Completeness for Construction = Has RFC value/Number of equipment in class 6.2. Piping application coherence When a piping application is used, to measure design completeness with process design is to count equipment in the mill database and equipment in the 3D piping application. For example how many valves are there in both applications and are there any discrepancies between the equipment attribute values. This is a good measurement and it is quit easy to implement. Some plant design system vendors provide checking routines to verify the process design against the mechanical design or vise versa.

7. Summary In the plant design projects the process design acts as a basis for all other design tasks. Time is the most critical factor in a plant design process. Therefore we use concurrent design in the plant design in which the process design has the most important role. It is critical how well the data sharing between the disciplines is accomplished. Measures and methods have been developed, but research is needed especially in change management. The tools for data sharing are important. Currently the tools are more and more webbased applications and use XML as the communication language. This trend will continue. For many years Jaakko Poyry Oy has concentrated on building the MODE architecture in which its heart, the mill database, has the key role in information sharing. The results have been promising, but using it as a quality tool and measuring the design completeness need to be further developed.

8. References Kiiskinen, J., Harkonen, K., 1999, WebPub - A pioneering document publishing and distribution system. Know-how wire, June, Jaakko Poyry Oy, Vantaa, Finland. Peltopuro, J., 1999, Master Thesis: Plant design development in 3D CAD system, HUT, Machine Design Espoo,Finland (in Finnish). Siltanen, P., Syrjanen T., Kuusisto M., 1999, XML-based meta-data modelling for product data management. In Proceedings of PDT Europe '99. Stavanger, Norway. Talvio, P. 1987, Today's design systems keep all parties involved on a daily basis.. Pulp and Paper, September, USA.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

323

A New MINLP Model for Mass Exchange Network Synthesis Z. Szitkai, T. Farkas, Z. Kravanja*, Z. Lelkes^, E. Rev and Z. Fonyo Chemical Engineering Department, Budapest University of Technology and Economics, H-1521 Budapest, Hungary; [email protected] * Faculty of Chemistry and Chemical Engineering, University of Maribor, Smetanova 17, P.O. Box 219, SI-2000 Maribor, Slovenia

Abstract Based on the principles of a simultaneous optimisation model developed by Yee and Grossmann (1990) for heat exchanger network synthesis, a robust optimisation model for mass exchange network synthesis has been developed. Superstucture, essential modelling equations, and example problems with their solutions are presented. The new model is fairly linear and is applicable to systems of both packed and staged vessels, and multicomponent problems as well.

1. Introduction Mass exchange network synthesis (MENS) is an efficient tool for pollution prevention through process integration, and was originally developed mainly based on the ideas of heat exchanger network synthesis (HENS). The first, pinch-based, solution methodology of El-Halwagi and Manousiouthakis (1989) was extended by Hallale and Eraser in 1998 and later in 2000. Using their advanced targeting methods both the capital cost and the total annual cost (TAC) of the network can be predicted ahead of any design. Still, pinch technology for MENS does not provide a systematic way for deriving the optimal network structure. The network design includes trial and error elements, especially when large or multiple component problems are considered. Design methods based on simultaneous optimisation offer the possibility of designing the MEN in a single automated step. The whole MENS problem is formulated as a mathematical optimisation problem that has to be solved for global optimum. Most conveniendy, binary variables are used to represent the network structure, hence the optimisation problem to be solved is usually a mixed integer non-linear programming (MINLP) problem. The first simultaneous MINLP model for MENS was presented by Papalexandri et al. (1994). Comeaux (2000) aimed at simplifying the model formulation, and adopted pinch principles to be able to formulate the MENS problem as a moderate size non-linear programming (NLP) problem.

2. Motivation and Aim of the Work Szitkai et al. (2002a) presented an extensive comparison of the methods mentioned above and showed that so far the best method for MENS is the MINLP model of Papalexandri et al. (1994). Using her model, most of the advanced pinch based designs of Hallale and Eraser can be reproduced or improved. Papalexandri's model is also superior to the insight based NLP method of Comeaux (2000). Still, as it was shown, Papalexandri's MINLP method sometimes delivers worse solutions than the advanced pinch design method of Hallale and Eraser. The most probable reason is that

324 Papalexandri's MINLP model cannot always be solved for global optimality with the commercially available algorithms because her model contains plenty of bilinear mass balances, which set up a nonconvex search space. The aim of this work has been to develop a robust MINLP model for MENS. Regarding the assumptions and modelling principles of the simultaneous optimisation model of Yee and Grossmann (1990), that was originally developed for designing HENs, it was expected that a similar modelling technique would be applicable to MENS as well, resulting in a fairly linear MINLP model.

3. Superstructure and MINLP Model Assuming iso-concentration mixing in the network, mass balance equations can be formulated linearly by using merely concentrations and the amounts of transferred masses. This assumption can only be applied when the stagewise MEN superstructure shown in Figure 1 is used. concentration location 1

S'^^S^ ^

concentration location 2

Stage Z concentration location 3

• j ^ ' ^ . l ^ ^ yi,s

y2,s

Fig. 1: Stagewise superstructure for single component MENS. As Figure 1 shows, only rich and lean stream concentrations at the stage borders (concentration locations, k) are used instead of in- and outlet concentrations of the individual mass exchangers, hence the mass balances for the mixing points become linear. In Figure 1 the superstructure is shown for two rich streams, two lean streams, and two stages. Generally any of the rich and lean streams can be matched once in each of the stages. This superstructure allows somewhat less complex network structures compared to that of Papalexandri et al. The minimum number of superstructure stages can be calculated based on the concentration data of the streams, just as at HENS. R and S represent rich and lean stream flowrates; y and x are rich and lean mole fractions; the indices S and T denote source and target concentrations. The analogy with the Yee-Grossmann HENS model can be closely kept in case of single component MENS problems and packed columns as mass exchangers. The concentrations of all the streams at the concentration locations, at the bounds of the composite intervals, have to be the same in pinch technology; but this constraint does not appear in our model. The only restriction applied is that there cannot be more than

325 one unit in any stage between two streams. This difference usually results in less number of necessary concentration stages than composite intervals in pinch technology. When extending the model to compatible multiple component MENS problems, linearity can be maintained by applying special modelling frame with identical superstuctures applied to the individual components. In case of incompatible components nonlinear balances have to be included. In the new MINLP model, some equations prescribe mass balances at the concentration borders; other equations assume monotonity of the concentrations. Equation 1 sets the mass exchange me to zero if the unit does not exist; otherwise its value is constrained by Q (big-M technique). Equations 2 and 3 force the exact calculation of the driving forces of the units {dy) only if the given units do exist in the solution; F is a constraint. Continuous 0
dyuj^k ^ yuk - ^i,jXj,k - Kj + ^ui,k (1 - zuj,k)

(2)

dyi,jM\ ^ yiMi - ^ij^jMi

(3)

- Kj + hj,k (1 - Zij,k)

bZij,k - Zij^k - PZi,j,k + ^Zij,k = 0

(4)

Obj = Obj _ genuine + w S (pz/,y,^ - sZi^j^^ f

(5)

ij,k

Indices / and j stand for the rich and lean streams, respectively. Originating from the definition of the MENS problem (El-Halwagi and Manousiouthakis, 1989), rich stream flowrates (R) are fixed while lean stream flowrates (5) are model variables. This renders the MENS model slightly more nonlinear compared to the original HENS model. Logarithmic mean differences are approximated with the method of Chen (1987):

Imcdijj^

dyuj,kdyi,jMi

(6)

—^—-—

Kremser equation has to be applied for using staged vessels (Szitkai et al., 2002b), which, unfortunately, spoils the linearity of the model. MINLPs were solved using the GAMS package (Brooke et al., 1992). 3.1. Example problem I (packed columns) Example problem 4.1 from the PhD Thesis of Hallale (1998) is reconsidered (Table 1). Packed columns are specified as mass exchangers, and the exchanger mass based costing method of Hallale is used with the following costing equations: 1

^^/ ik

mass,j^, =-—

TCC =

LIN„,J61S

1 1

'f I E masSijj^ Uhk N • ^' units

(K^ = 0.02 kg NHss"^ kg-^)

(7)

\

(8)

The total capital cost (TCC) of the MEN involves both the cost of the column shells and the cost of the packing. Using the targeted, minimum external lean stream flowrate

326 (5i=2.48 kg/s) Hallale's solution featured a total capital cost of $298,000. Using our MINLP model, relaxed binary variables, and a penalty in the objective function to force them equal to zero or to one were introduced. This stabilised the optimisation process. Fixing the external MSA {S3) flowrate to 2.48 kg/s our solution's optimal TCC was $307,000. Optimising for the TAC (annualisation factor of the capital cost is 0.225, cost of the external MSA is taken 0.001 $/kg and 8150 hr/yr is assumed) we obtained a solution with a TAC of $134,000. The latter solution is shown in Figure 2. Summary of the solutions is shown in Table 2. Table 1: Stream data for example problem L Rich streams

G (kg/s) 2 4 3,5 1,5 0,5

Ri R2 R3 R4 R5

(mass fraction) 0,005 0,005 0,011 0,010 0,008

MSAs (kg/s) 1,8 1

s, S2

CX)

S3

(mass fraction) 0,0017 0,0025 0

y (mass fraction) 0,0010 0,0025 0,0025 0,0050 0,0025 x' (mass fraction) 0,0071 0,0085 0.017

m

b

1,2 1 0.5

0 0 0

Table 2: Cost results of example problem I. objective TCC

comments pinch technology minimal utility MINLP model minimal utility MINLP model

TCC TAC

TCC($)

7>lC($/yr)

298000

140000

307000

142000

218000

134000 - ^ ^ ' ^ 2 kg/s

-<3)-

-Qy

-"^^-"-^^ 4 kg/s ^ ^ ^ ^ 3.5 kg/s

•<J}

^ ^ ^ ^ ^ 1 ^ 1.5 kg/s

<^

^ ' ^ ^

0.5 kg/s

0.015719

2.904 kg/s

oO-

m^ ^O

-O-

7

Fig. 2: Solution of example problem I.

r^^

TAC=$134000/yr TCC=$218000

327 3.2. Example problem II (staged columns) In this example the target is removal of sulphur dioxide (SO2) from four gaseous streams. Only one external MSA is available, pure water (Si). The stream data are available in Table 3. Tray columns are used as mass exchangers. The capital cost is based on the shell cost $12800//,^-^^D^-^ and the cost $608^^^^ per tray; where D is the column diameter, and Ht is the total column height. The overall efficiency of the trays is fixed as 20%. The inactive height is 3m; the tray spacing is 0.5m. The number of stages is calculated with Kxemser equation. This is a highly non-convex equation. Therefore, the global optimum is not ensured by the MINLP; and the time for finding a solution is much longer. Moreover, the local optima found depend on the initial values. The solution of Hallale, with pinch technology, was rCC=$860000 (rAC=$427000/yr). In our model the objective function was the annual cost. Annualisation factor was 0.225; 8150 hr/a were assumed and $0.003/kg or $0.054/kmol cost for the external MSA were assumed. The optimal solution is shown in Fig.3. Table 3: Stream data for example problem II. Rich streams Ri R2 R3 R4

G (kmol/hr) 50 60 40 30

(mol fraction) 0,01 0,01 0,02 0,02

MSAs (kmoVhr) Si

00

(mol fraction) 0

y (mol fraction) 0,004 0,005 0,005 0,015 x' (mol fraction) -

m

b

26.1

-0.00326

Rl ^0.005

(D--

50 kmol/lir

R2i 60 kmol/hr

-Qy

R3I 40 kmol/hr R 4 30 kmol/hr

SI

0^ / ^

strays

\

0.000305

6 trays

O^^^^^^^O^^^^ 1969 kmol/hr 26 trays

5 trays

TAC=$359000/yr TCC=$339000 Fig. 3: Optimal solution of Example II. In this case the flowrate of the external MSA is a bit greater than the minimum (in Hallale's solution it was 5i=1593 kmol/hr). Therefore the capital cost and the annual cost are decreased.

328 3.3. Example problem III (multicomponent problem) The COG example of Papalexandri et al (1994), originally by El-Halwagi and Manousiouthakis (1989), was also solved. The target is the removal of H2S and CO2 from COG (a mixture of H2, CH4, CO, N2, NH3, CO2 and H2S), (RO and the tail gases of a Claus unit (R2). Available lean streams for the purification are aqueous ammonia (Si) and chilled methanol (S2). Perforated-plate columns are considered for applying both solvents. TAC results are as follow: Papalexandri et al., 1994 (MINLP): 917880; Hallale and Fraser, 2000 (Pinch): 427000; our optimum: 436289 $/yr.

4. Conclusions A new, robust and fairly linear MINLP model for the synthesis of MENs has been developed, based on the superstructure and optimisation model developed by Yee and Grossmann (1990) for designing HENs. Using the new model we can obtain the proper trade-off between capital and external MSA costs by taking all the driving forces as optimization variables. The model's main advantage can be fully exploited in the case of packed columns. However, the model can be extended to handle staged columns as well by introducing non-linear expressions in the MINLP problem. The numerical solution's stability is enhanced by using relaxed binary variables with additional constraints and penalty function to enforce the relaxed variables to take binary values. Solutions of example problems justify the applicability of the model and predict that the new model could be applied to design the MEN part of more complex process synthesis problems.

5. References Brooke, Kendrick, Maereus, GAMS. A User's Guide, Rel. 2.25, Scientific Press, 1992. Chen, J.J. (1987). Letter to the Editor: Comments on improvement on a replacement for the logarithmic mean. Chem. Engng. Sci., 42, 2488. Comeaux, R.G., (2000), Synthesis of MENs With Minimum Total Cost, MSc Thesis, Dept.of Process Integration, UMIST, Manchester, England. El-Halwagi, M.M, and Manouthiousakis, V., (1989), Synthesis of Mass Exchange Networks, AIChE Journal, 35, (8), 1233-1244. Hallale, N. and Fraser, D.M., (1998), Capital Cost Targets for Mass Exchange Networks, Part I-IL, Chem. Eng. Science, 53(2), 293-313. Hallale, N. and Fraser, D.M., (2000), Supertargeting for Mass Exchange Networks, Part I-IL, Trans I Chem E, 78, Part A, p.202-216. Hallale, N., (1998), Capital Cost Targets for the Optimum Synthesis of Mass Exchange Networks, PhD thesis. University of Cape Town, Dept. of Chemical Engineering. Papalexandri, K.P., Pistikopoulos, E.N. and Floudas, C.A. (1994), Mass Exchange Networks for Waste Minimization, Trans IChemE, 72, Part A, 279-293. Szitkai, Z., Msiza, A.K., Fraser, D.M., Rev, E., Lelkes, Z., Fonyo, Z. (2002a), Comparison of different mathematical programming techniques for mass exchange network synthesis, p. 361-366, Proc. ESCAPE-12, The Hague, Netherlands, 26-29 May, 2002; Eds. J. Grieving & J. van Schijndel, Elsevier, 2002. Szitkai, Z., Lelkes, Z., Rev, E., Fonyo, Z. (2002b). Handling of removable discontinuities in MINLP models for process synthesis problems, formulations of the Kremser equation. Computers Chem. Engng., in press. Yee, T.F., Grossmann, I.E. (1990), Simultaneous optimization models for heat integration II. Heat Exchanger Network Synthesis, Computers Chem Engng 14 (10), 1165-1184.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

329

A Knowledge Based System for the Documentation of Research Concerning Physical and Chemical Processes System Design and Case Studies for Application M. Weiten, G. Wozny Dipl.-Ing. Moritz Weiten, Technical University of Berlin, Department of Process and Plant Technology, Sekr. KWT-9, StraBe des 17. Juni 135, 10623 Berlin; Prof. Dr.-Ing. Giinter Wozny, Technical University of Berlin, Department of Process and Plant Technology, Sekr. KWT-9, StraBe des 17. Juni 135, 10623 Berlin

Abstract A technical framework is presented in this paper, which allows scientific institutions to establish a knowledge based management of their research results. The system incorporates general principles of information management and relies modem techniques of knowledge engineering. It allows scientists to store research results in standard data formats as well as to include knowledge about the resources and their interconnections. The underlying methodology is based on the standardization of scientific data at different levels and on the concept of ontologies.

1. Introduction Great parts of the results of many research projects dealing with physical and chemical processes get lost due to the lack of an integrated and complete documentation. At least published work can be retrieved with the help of digital libraries. Even within an institution, researchers find it hard to comprehend the work of their colleagues and gather the corresponding data without the help of the originators. Despite some few exceptions, most research institutions dealing with physical and chemical processes leave the task of information management to the individual researcher. On the other hand, research institutions and individual researchers need a technical platform enabling them to store and retrieve their data and information in a standardized way. The framework and the system implementation presented in this paper focuses on the latter aspect. The development of a knowledge based system is described, which helps to manage the results of scientific research in the area of physical and chemical processes.

2. Goals/Requirements The following are some general goals of information management (Weiten et al., 2002a): storage, management and integration of heterogenous resources (text-based, data-based, images, etc.); long-term storage and access; efficient information retrieval; modular storage and access. 2.1. Management of heterogeneous resources Research concerning physical and chemical processes typically has a heterogeneous output in form of data files, spreadsheets, publications, etc. A concept for the manage-

330

ment of such resources has to take into account the different ways the information is structured at each case. Such a concept has to provide a way to gather existing links between resources, based on their context (e.g. a text document and a spreadsheet referring to the same experiment). An interface for the integrative access to those heterogeneous resources has to be supplied. Appropriate data formats (or wrappers/mediators^) are required, in order to realize some certain functionality (e.g. extraction, filtering and linking). Heterogeneous resources require integration concepts, in order to allow an efficient access without knowledge about the particular source (Paton et al., 2000). In this project an integration concept based on common data models has been developed. It helps users to query and access information sources with the help of graphical user interfaces visualizing basic concepts of their scientific domain. 2.2. Long-term storage Long-term storage requires appropriate data formats and standards, which in return require interfaces to standard applications and broad user-support. Standardization often is a difficult job. The standards of individual organisations or corporations (such as a plant data model for CAE-related tasks and tools) are designed to perfectly satisfy their particular requirements. This kind of standard turns out to be insufficient for organisations sharing resources with others (e.g. on the base of collaboration). On the other hand do international, widespread standards tend to be either too complex to maintain (cp. the comments of Batres et al. (1999) on STEP) or too simple to provide a base for real-world applications. The solution lies within the standardization at different levels. In this project, several XML-extending standards have been chosen as basis for long-term storage. Appropriate tools (converters, viewers) have been developed. 2.3. Efficient information retrieval Efficient retrieval is equivalent to obtaining the required information with the highest possible precision (the lowest overload) and little effort. Widespread retrieval techniques have been developed especially for text-based information sources (e.g. in form of search engines). These techniques rely on the natural language, with all its ambiguity and complexity. Alternative approaches for text-based information have -among othersbeen developed for texts with very regular structure that can be represented by a data model (Embley et al., 1998), and for engineering data (Moss et al., 1999). Databases provide a structure and a flexible query language, making precise queries possible. The major drawback is the required knowledge about the particular data model. Approaches of information integration approaches target this problem. In this project an integration approach developed in the field of knowledge engineering (based on ontologies) has been chosen (Studer et al., 1998). It allows to access information from the viewpoint of common concepts within a scientific domain. 2.4. Modular storage and access Modularity is obviously important for large information resources and when there is no or little support for filtering. Database applications for example offer such filtering capabilities. This does not hold for typical file-based data sets such as spreadsheets. In this case, the information or data can only be provided as a whole, except specialized interfaces for certain file formats are available. Standard data formats for scientific data allow the creation of standardized interfaces that are capable of modular access. ^ See also Wiederhold (1992) and Muslea et al. (2001)

331 The importance of a modular for text-based information in form of publications has been strongly emphasized by Kircz (1998). The standard data formats used in this project allow a modular access to information at different levels of detail.

3. Methodology and System Design 3.1. Incorporation of the ontology-concept The framework developed relies on the concept of ontologies (Uschold and Gruninger, 1996) which can be seen as 'a shared and common understanding of some domain that can be communicated across people and computers' (Studer et al., 1998). Ontologies as "knowledge data models" have been applied in different areas, such as information integration (Paton et al., 2000) and expert systems (Ceccaroni et al., 2001). In the system presented here, ontologies provide the base for a formal description and a classification of information resources. Ontologies have been implemented in order to describe the relation of scientific documents (publications, reports), similar to the "ScholOnto"-approach developed by Motta et al. (2000). Additional ontologies describe concepts of scientific research that have to do with the development of mathematical models (Weiten et al., 2002 and Weiten et al., 2002b). These allow a linking of different resources based on conmion concepts (e.g. model parameters). 3.2. Usage of standard data formats Standard data formats are a requirement of long-term storage and platform-independent access. Furthermore do certain standard data formats provide useful a functionality for retrieval and manipulation of data. As already mentioned, can the development of standards for certain fields be very demanding, since a standard must satisfy the needs of its potential users in terms of a least common denominator. The framework presented relies on an incremental standardization. XML forms the basic standard, with a wide range of tools available for data access and manipulation (linking, parsing, filtering, transforming, etc.). Text documents coded in XML are annotated with additional data for bibliographic information on the base of the Dublin Core Standard (Weibel, 2000). The DocBook-standard (Walsh and Muellner, 1999) is the base for standardization of the document-structure. A standardized structure allows a modular storage and access of documents. Scientific data is stored in the Extensible Data Format (XDF). XDF itself follows the philosophy of an incremental standardization. It is an XML-based data format, which provides some basic features (e.g. definition of physical units, n-dimensional data structures). XDF can be extended to meet the requirements of certain scientific fields. Different XDF-based standards are always compatible at the level of the basic XDF functionality. In this project, XDF has been chosen as the basis for numerical and experimental data. The DocBook-standard defines the structure for text documents, with bibliographic information in terms of Dublin Core. 3.3. Technology The system consists of different parts. A central database stores data and information in form of data files in standardized format and ontology-related additional information about resources. The central repository is based on a DB2^^-Database, with the XMLExtender'T^ and the Text-Extender"^^. Web-based user interfaces provide maintenance and retrieval functions. Office'^^-Templates (with Visual Basic Wizards) form the other

332 end of the system. These support users in generating standardized resources and submitting them to the central repository. Java-applications perform a conversion process (from proprietary office formats to XML-based formats). They allow to register resources with parts of standard data models (ontologies) and to define interconnections. The generation and maintenance is realized with Protege 2000, a tool for knowledge based systems, developed in Stanford University.

4 Use Cases 4.1. "Personal" information management

Documesf^-Wlndow
Man tnMfcr m»*tl fcr MMfOtnr Further expemnnttt hove been carried out w .at anionic twfactant SDES and the NF mnabrane D5K (O aoioca) m order to set q> a masf transfer model Earlier NF experiments with surfactant Iiaasport of the sohite ocean -difrw»n model based on been developed to predict Quz is given b^.

Pc^p-Menu Tree-Vlew (shows selectable parts of

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(1) In equation ( 1 ) r w represents the hydraulic membrane 1 resistance. It can be dftmnmfMl flrom the mire watnr flinr

Fig. 1: Formal description of information resources with an editor.

In this situation, a researcher works on a process model, including the experimental investigation. He/she has performed several experiments on the base of a certain strategy. The latter has been conceptualised with the background of the mathematical model development. The approach chosen for the mathematical model requires the determination of certain model parameters. The researcher has gathered several files of raw data from these experiments. A spreadsheet-software is used for filtering and curve fitting. The derived values are used in the implemented mathematical model of the process. The researcher obtains simulation results in form of data files, which are again processed with the help of spreadsheet software, in order to perform and visualize model characteristics and the validation with experimental data. When the research project has reached a certain status, the researcher decides to prepare a publication. In the present situation, a "paper version" of the publication would in many cases be the only output accessible some time after the termination of the project. With the help of the system presented in this paper, the researcher first of all uses templates, enabling him/her to create standardized spreadsheets. A database for references together with document templates allow the researcher to create a publication, which meets the particular layout required, and at the same time serves as a base for a standardized XMLfile (to be automatically created). The created files as well as raw data files are submitted to the central database, which validates the structure and "asks" for additional information about the resources supplied and their interconnections. The latter can be edited with a graphical user interface (figure 1), which provides access to the particular struc-

333 ture of a resource. Colleagues or successors of the researcher within the institution use a web-based interface to "browse" the research results submitted. They can use that interface to view texts and data. Hyperlinks provide additional information about resources, such as the determination of model parameters for example. 4.2. Collaborative research Concerning the tasks of scientific work, this situation is similar to the previous one. However, there are some new aspects. The central database with allows the institutions involved to access the data and information of the participants without the need to install any special software. Possible contradictions (e.g. two participants referring to the same physical parameter with different terms and different values or functions) can be discovered in time, since the system checks single concepts (such as parameters) against the appropriate ontology. The standard file formats can be extended by each discipline participating in order to meet particular requirements. Compatibility can still be guaranteed at different levels (e.g. XML, XDF for data files). Data can be exchanged on the base of a common denominator.

5. Conclusions and Outlook Modem techniques in the fields of knowledge engineering and information management allow research institutions to increase the value of research results in form of electronically stored resources. Two typical use cases indicate how the system presented in this paper represents an approach to technically support scientists in an enhanced information management. The system is still to be integrated in a complete framework, which includes the social and organisational aspects of information- and knowledge management. Such a framework is for example presented by the CommonKADS-Methodology (Schreiber et al., 2000).

6. References Batres, R., Asprey, S.P., Fuchino, T., Naka, Y., 1999. A KQML Multi-Agent Environment for Concurrent Process Engineering. Computers and Chemical Engineering, 23, 653-656. Buckingham, S., Motta, E., Domingue, D., 2000. ScholOnto: an ontology-based digital library server for research documents and discourse. International Journal on Digital Libraries, 3, 237-248. Ceccaroni, L., Cortes, U., Sanchez-Marre, M., 2001. OntoWEDSS - An Ontology-based Environmental Decision-Support System for the management of Wastewater treatment plants. Thesis (PhD), Universitat Politecnica de Catalunya. Embley, D.W., Campbell, D.M., Smith, R.D., Liddle, S.W., 1998. Ontology-Based Extraction and Structuring of Information from Data-Rich Unstructured Documents. Proceedings of the International Conference on Information and Knowledge Management., New York: ACM Press, 52-59. Kircz, J.G., 1998. Modularity: the next form of scientific information presentation?. Journal of Documentation, 54 (2), 210-235. Moss, M.A., Jambunathan, K., Lai, E., 1999. A knowledge based database system for engineering correlations. Artificial Intelligence in Engineering 13, 201-210.

334

Motta, E., Shum, S.B., Domingue, J., 2000. Ontology-Driven Document Enrichment: Principles, Tools and Applications. International Journal of Human Computer Studies, 52, 1071-1109. Muslea, I., Minton, S., Knoblock, C.A., 2001. Hierarchical wrapper induction for semistructured information sources. Journal of Autonomous Agents and MultiAgent Systems, 4 (1/2), 93-114. Paton, N.W., Goble, C.A., Bechhofer, S., 2000. Knowledge based information integration systems. Information and Software Technology, 42, 299-312. Schreiber, G., Akkermans, H., Anjewierden, A., de Hoog, R., Shadboldt, N., Van de Velde, W., Wielinga, B., 2000. Knowledge Engineering and Management: The CommonKADS Methodology., Massachusetts: MIT Press. Studer, M., Benjamins, V.R., Fensel, D., 1998. Knowledge Engineering: Principles and methods. Data & Knowledge Engineering, 25, 161-197. Uschold, M., Gruninger, M., 1996. Ontologies: Principles, Methods and Applications. Knowledge Engineering Review, 11 (2), 93-136. Walsh, N., Muellner, L., 1999. DocBook., Sebastopol, CA: O'Reilly. Weibel, S., 2000. The Dublin Core Metadata Initiative. D-Lib Magazine, 6 (12) [online] http://www.dlib.org/. Weiten, M., Goers, B., Wozny, G., 2002. Information Management for Engineering Sciences. In: Novosad, J. (Process Engineering Publisher), Eds. Proceedings of the 15th International Congress of Chemical and Process Engineering., 155156. Weiten, M., Wozny, G., Goers, B., 2002a. Wege zum Informationsmanagement fur die interdisziplinare Forschungsprojekte und Entwicklung eines prototypischen Systems. Chemie Ingenieur Technik (to appear in Vol. 74, 11, 2002). Weiten, M., Wozny, G. and Goers, B., 2002b. In: Luczak, H., Cakir, A. E. and Cakir, G., Eds. Proceedings of the 6* International Conference on Work With Display Units., Berlin: ERGONOMIC GmbH, 624-626. Wiederhold, G., 1992. Mediators in the architecture of future information systems. IEEE Computer, 25, 38-49.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

335

A Semi Heuristic MINLP Algorithm for Production Scheduling Mehmet Yuceer, Ilknur Atasoy and Ridvan Berber Department of Chemical Engineering, Faculty of Engineering, Ankara University Tandogan 06100 Ankara, Turkey

Abstract A large number of process synthesis, design and control problems in chemical engineering can be formulated as a mixed integer nonlinear programming (MINLP) model, involving continuous variables and integer decisions. In this paper, we present an MINLP formulation for production scheduling of multi-product batch plants. The binary (0/1) integer variables of the non-convex MINLP problem make it impossible to use the general purpose algorithms for solution. In order to overcome this difficulty, a semi-heuristic algorithm for production scheduling was developed. Using this approach, the non-convex MINLP problem is first considered as an MILP problem without dividing the orders. Thus, the order that causes prolonged delivery time can be identified. Constraints for this order are then relaxed and MELP problem is re-solved using the new constraints. Having reached the new schedule, the quantitative distribution of the specific order to different units can be determined by solving the LP problem that does not contain integer variables since allocation of the orders to the units and processing order are known. The results obtained with some example problems indicate improvements over previous schedules and therefore, give promise that the suggested strategy might be used in moderately-sized industrial applications.

1. Introduction The single stage multi-product plants with non-identical parallel production units are common to processing, pharmaceuticals, polymer, food industries and also machinery. Hard industrial competition requires that customer orders not only fulfilled on time, but also manufactured with utmost economic benefit in such plants. This, in turn dictates a strict scheduling of orders in available equipment. If one adds many constraints with regard to the scheduling, such as predecessors/successors, cycles to be avoided and makespan, the problem becomes a huge one, right at the 'formulation' phase, even before attempting to solve. The solutions provided until late 80s had not been considered satisfactory to prevent production tardiness. After, probably, the first attempt towards the solution of this NPcomplete problem by Pekny and Miller (1991), some approaches using heuristics (by Mussier and Evans 1989), MILP formulation in discrete time (by Kondili 1993 a, b) and continuous time with heuristic (by Cerda et al 1997) have been proposed. However, one major difficulty with MILP formulations is that the problem size increases exponentially with the number of units/orders. In a most recent work, Berber and

336 Ozdemir (2003) identified one deficiency and two misconception about the formulation of such problems. They claimed that, contrary to the foregoing statement, the fact that every order can be processed in every unit or after every order in one unit is more contributive to the size of such problems. In our previous work (Berber and Ozdemir 2003), an automatically generated MILP formulation was used to schedule a set of orders in non-identical parallel processing units without diving any order. However, if the process time of any of the orders in one unit is very long, then it becomes necessary to divide this order into two or more pieces so that other units may also be used to process it. This strategy will undoubtedly help meet the customer expectations and prevent tardiness. The special difficulty associated with such a strategy, which results in an MINLP formulation, is that the objective function becomes nonlinear, and furthermore non-convex due the multiplicative appearance of integer and real variables. Since available MINLP algorithms are for convex functions only, the problem is seemingly very difficult to solve. This work tackles with such problems, and defines a semi-heuristic algorithm for the solution, and shows that it is effective for moderately sized cases.

2. Problem Statement and Model The scheduling problem in single-stage, parallel unit, multi-product plants is considered. Customer orders, each composed of only one product, are to be processed in a subset of the available processing units. Total production time is chosen as the objective to be minimized. The model accounts for a number of logical physical constraints, which are likely to occur in practice, such as follows: • Orders may have predecessor and successors • Both the predecessor and the successor to a given order must be manufactured in the same processing unit • Each equipment has only one single order to be first processed in it • Each order can be first processed in only one processing unit • Makespan is considered as a constraint to ensure that a due date for the whole set of orders to be processed is met • Cycle constraints were included such that a job can not be simultaneously both the predecessor and the successor to another one • Release time of units, i.e. the time needed for any unit to become available, is incorporated in the formulation of the objective function The original problem is first handled as an MILP problem without any interest in dividing the orders. The solution to this problem identifies the order that extends the processing time, therefore, indicating where the need is for dividing an order to be processed in multiple units. Then, constraints for this unit are relaxed so that it is allowed to be processed in more than a unit, and the MILP problem is re-solved under these circumstances. This solution provides the schedule that the particular order is to be processed in multiple units in an optimal setting. As the allocation to the units and the processing order becomes, thus, known and the integer variables are eliminated; then the real amount to be processed in each unit remains to be determined, which is done by solving the corresponding linear problem (LP).

337 The solution algorithm developed in this study is presented in Figure 1 as a flow diagram. Modeling non-convex MINLP Problem

Solving MINLP problem as an MILP problem without dividing the orders

Determination of the order to be divided and the number of units it is to be processed (manual interpretation)

Relaxation of the constraints and re-solving the problem in MILP form

Solving the fmal problem converted into LP form

Figure 1. Semi-heuristic algorithm for the solution of non-convex MINLP problem. 2.1. Objective function The objective of the problem we propose here is the minimization of a function comprising the total processing time of orders being considered, as represented by the following mathematical statement:

El E (^^/ +Xn,n>T, *XM, + X^™v *TCL„„ IEL

iel

I L PR// T,7 TCLmi/ Xmi/ just XFi/ XM.il

mePRil

V"

mEPRil

: Set of available orders : Set of available units : Set of customer orders that can be processed just before O, in unit /. : Total processing time of order Oi in unit /. : Cleaning time for the ordered pair of jobs (Oi, Om) in unit / : Binary variable denoting that the processing of order Om takes place in unit / before the campaign for Oi : Binary variable denoting that order Oi is the first to be processed in unit / : Amount of the O, order to be processed in unit /

A MATLAB program was developed to automatically formulate the problem such that it can be solved by a branch and bound algorithm when in MILP form. The program

338 takes the data related to the properties of the orders and production units, creates the model, i.e. objective function and all the constraint equations, produces the input files for MINOS package (Murtagh and Saunders 1995) to be run in Fortran environment, and necessary other files for easy interpretation of the MINOS output files. The user, then, easily extracts the results of the optimum schedule, i.e. allocation of orders into the production units and the schedule in each unit, to be drawn as a Gantt chart.

3. Example and Results A set of example problems were solved in order to test the proposed method. The one which will be presented here is the spesific problem tackled by Cerda et al. (1997), and later reconsidered and solved by Berber and Ozdemir (2003) with an objective of minimizing the total production time. This example is composed of 10 orders to be processed in 4 units, has 47 binary variables and 648 constraint equations All units are assumed to be available at the time of scheduling. Table 1 and 2 show the production and batch capacities of orders in every unit and set of predecessors, respectively. Production times of one batch of each product are given in Table 3, whereas the cleaning times are indicated in Table 4. First the problem was solved with an MILP formulation, i.e. without resorting to dividing any order. Makespan was considered as a constraint and an optimum schedule, with an objective function value of 81.4 days and a completion time of 26.25 days, was found. However, the results, as shown in Figure 2a, indicated that dividing the order 6 would have resulted in even better optimal solution in terms of fulfilling a possible customer demand of earlier completion of the set of orders. When the solution strategy proposed in this work was implemented for this example, the optimum schedule shown in Gantt diagram of Figure 2b was found. The objective function reached was 81.5 days, and the orders were to be completed within 23.85 days. These results are clearly indicative of the fact that, with a relatively small sacrifice of 0.1 days in the objective function, the set of orders would be completed 2.4 days earlier.

4. Conclusions This work considered optimal scheduling of a set of orders in multi-product batch plants with non-identical, single stage, parallel processing units. Particular emphasis was placed in dividig one order into multiple units, and a semi-heuristic algorithm was proposed to solve the MINLP problem with a non-convex objective function. The results obtained with some example problems indicate improvements over previous schedules where such emphasis was not considered, and therefore, show promise that the suggested strategy can be used for implementation in industrial environment.

339 Table 2. Input data, batch capacities.

Table 1. Input data, predecessors and order quantities.

Products Products

Predecessors

01 02 03 04 05 06 07 08 09 OlO

0 3 , 06, 09, OlO 03,07 02, 06, 09, OlO 0 5 , 06, OlO 04, 07, OlO 01, 05, 09 03, 05, 08 05,07 0 1 , 0 3 , 06, OlO 01, 03, 04,09, 06

Quantity (kg) 550 850 700 900 500 1050 950 850 450 650

01 02 03 04 05 06 07 08 09 OlO

Unit 1 1.7 ~ 1.25 — — 2.4 — ~ 1.6 2.6

Unit 2 — — ~ 1.7 1.4 1.8 — — 1.9

Unit 3 — 0.9 1.1 — ~ ~ 1.05 ~ -

Table 3. Production times of one batch of orders in units (Ti day/batch). Products Ol 02 03 04 05 06 07 08 09 OlO

Unitl (kg/batch) 100 — 140 — — 280 ~ — 200 250

Unit 2 (kg/batch) — ~ ~ 120 90 210 ~ ~ — 270

Unit 3 (kg/batch) ~ 210 170 — ~ — 390 ~ — ~

Unit 4 (kg/batch) ~ — — — 130 — 290 120 -_ -

Table 4. Cleaning times. Predecessors Successors

i

01 02 03 04 05 06 07 08 09 OlO

01 — 1.0 — — 1.4 — — 2.1 1.5

02 03 04 05 — — — — — — 1.1 — — — 0.15 — — — — 0.05 — 0.3 — — 0.3 0.7 — — 0.85 1.8 — — — — — — 1.25 — — —- 0.6 0.75 0.5

06 0.65 — — — 0.7 — — — 0.8 0.1

07 — 0.3 — 0.9 —— 1.65 — —-

08 0 9 OlO — 0.85 0.4 — — — — 1.6 0.2 — — 0.5 — 0.6 — — 1.2 — — 0.45 — — — — — — 0.65 .... 0.7 -—

Unit 4 — ~ 0.85 1.65 2.1 --

340 4 Units -10 Orders

4 Units -10 Orders

-

08

06

05

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-

08 TCL

03

02

-

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Figure 2. Solution of the example problem, (a) without dividing the orders (Berber and Ozdemir 2003), (b) when order 6 is divided between units (this work).

5. References Berber, R. and Ozdemir, Z., 2003, Production scheduling in single stage multi product batch plants: A Critical Evaluation and Some Improvement, Paper submitted to Ind. Eng. Chem. Res. Cerda, J.; Henning, G.P. and Grossmann, I.E., 1997, A Mixed - Integer Linear Programming Model for Short -Term Scheduling of Single Stage Multiproduct Batch Plants with Parallel Lines, Ind. Eng. Chem. Res., 36, 1695. Kondili, E.; Pantelides, C.C. and Sargent, R.W.H., 1993, A General Algorithm for Short-Term Scheduling of Batch Operations - 1 , Computational Issues, Comp. & Chem. Engng., 17,211. Kondili, E.; Pantelides, C.C. and Sargent, R.W.H., 1993, A General Algorithm for Short-Term Scheduling of Batch Operations - 2 , MILP Formulation, Comp. & Chem. Engng., 17, 228. Murtagh, B.A. and Saunders, M.A., 1995, MINOS Ver. 5.4 User's Guide, Systems Optimization Laboratory, Stanford University, Stanford, CA. Mussier, R.F.H. and Evans, L.B., 1989, An Approximate Method for the Production Scheduling of Industrial Batch Processes with Parallel Units, Comp. & Chem. Engng., 13,229. Pekny, J.F. and Miller D.L., 1991, Exact Solution of the No-Wait Flowshop Scheduling Problem with a Comparison to Heuristic Methods. Comp. & Chem. Engng., 15,741.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

341

Roles of Ontology in Automated Process Safety Analysis Chunhua Zhao, Mani Bhushan, Venkat Venkatasubramanian* (chunhua, mbhushan, venkat) @ecn.purdue.edu Laboratory for Intelligent Process Systems (LIPS), School of Chemical Engineering Purdue University, West Lafayette, IN 47907. USA

Abstract Process safety analysis is an information intensive task. Collecting all the necessary information from different sources is time consuming and error prone. Most of the information may already be available in some electronic formats. Sharing and reusing this process information can save significant time and effort. Using ontology can greatly enhance the communication and inter-operability among different systems. In this work, ontologies are designed for various kinds of process information and safety analysis results. PHASuite, an intelligent software system for performing automated process safety analysis, has been built based on these ontologies. Appropriate information sharing schemes have been proposed and implemented in PHASuite. It is found, based on several industrial case studies, that information sharing can greatly reduce time and errors associated with reentering information.

1. Introduction Process safety analysis is an information intensive task. For a typical chemical process, the basic information includes the material information, P&ID, process chemistry, and operating conditions. Different process design and analysis systems may use different aspects of this information. For example, simulation software use physical and chemical properties of materials, P&ID and operating conditions to quantitatively model the process. Process safety analysis software, such as PHASuite (Process Hazards Analysis Suite, an intelligent automated tool for process safety analysis developed in LIPS Laboratory at Purdue University, details can be found in Zhao, 2002), needs most of the information required by simulation tools, with some additional information, on such as the hazardous material properties. Better understanding of the process provided by simulation results, such as the calculated separation ratio of a separation, could also be used in safety analysis. Rather than collecting all the necessary information from different sources and reentering this information into PHASuite, which is time consuming and error prone, sharing and reusing this process information can lead to significant savings in time and effort. The very first requirement for information sharing between different software systems is that these software have an open structure, i.e. the information to be shared should be syntactically readable by other software, and not just stored through object serialization. More and more software are choosing this open approach. However, in order to meaningfully share the information, a common understanding is necessary to reduce or eliminate conceptual and terminological confusion. Such an understanding can help in achieving (1) better communication between people; and (2) inter-operability among systems (Uschold and Gruninger, 1996). The latter is achieved by translating between

342

different models, paradigms, languages and software tools. 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. Although the implicit conceptualization may be embodied in a piece of software, for example, a process simulation tool presumes views on concepts as unit operation, operation and process, an explicit and standardized conceptualization is much more useful. In fact, ontology is defined as an explicit specification of a conceptualization (Gruber, 1993). The requirements for a useful ontology include: clarity, coherence, extensibility, minimal encoding bias, and minimal ontological commitment (Gruber, 1993). In this work, the design of ontologies consists of the following steps: (1) identifying purpose and scope; (2) building the ontology including ontology capture, ontology coding, and integrating existing ontologies; (3) evaluating; (4) documenting. 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. Ontologies can play a significant role in information sharing and knowledge reuse in process safety analysis. In this paper, we define ontologies related to process safety analysis and propose an ontology-based information sharing scheme, which have been implemented in PHASuite to achieve inter-operability with other software systems. While the specified details presented here pertain to PHASuite (based on HAZOP methodology), we believe that the general scheme of ontology-based information sharing will be applicable to and useful for other process safety analysis systems. To the best of our knowledge, as of now there are no well-defined standards for sharing information for process safety analysis. Our work is an attempt towards developing a standardized structure for information sharing for this important task. The language used to define the ontologies is currently informal, i.e. mostly are defined in natural language. Although this kind of definition is sufficient for current implementation, definitions created using more formal language are desired for further implementation. To develop formal ontologies, some specification languages have to be used. For example, KSL Ontology Server (Farquhar et al., 1995), based on Ontolingua, is a mechanism for writing ontologies in a canonical format. Recently, built on earlier efforts and inspired by three building blocks including Web integration, frame-based systems and description logics, DAML+OIL (Connolly et al, 2002), has been proposed as an ontology specification language. Besides the specification language, acquisition support and reuse of ontologies are also active research areas.

2. Ontologies in PHASuite In PHASuite, the main required information can be divided into four types: material, P&ID, chemistry and operating procedures. Based on various types of information, ontologies have been developed for operation related and safety related information. 2.1. Operation related ontologies For the operation related information, concepts for operating procedures, operating conditions, and parameters are necessary. The hierarchical level of ISA-S88.01 standard (ANSI/ISA-S88.01, 1995), which decomposes a process into different levels, namely procedure, unit procedure, operation, and phase, has been followed in this work. To specify a piece of operating procedure, parameters and operating conditions are needed. Definition of process chemistry is straightforward and can be divided into reaction and

343 separation. A reaction is specified by reaction type, reactants, products, excessive reactants, inhibitors, catalysts and solvents. A separation is specified by input materials, names of different phases, and materials involved in each phase. Equipment is specified by design properties, such as design temperature, pressure and capacity, as well as some structural specifications including whether the equipment has a jacket, etc. 2.2. Safety related ontologies Safety related ontologies are of two types: (i) for sharing information required for safety analysis, and (ii) for sharing safety analysis results. Besides operation related information, safety analysis requires additional information, e.g. the material hazardous properties. The properties, which are currently used in PHASuite can be in Boolean type i.e. true or false, for example, corrosive, cryogenic, dust explosibility, hygroscopic, racemic etc., or take real values (or classification levels) such as boiling temperature, fire hazard level etc, or text strings, such as risk phrases. Material hazardous properties usually exist in Material Safety Data Sheets (MSDS). Some other useful information, available in the MSDS but not being used in current version of PHASuite, can be defined in a similar manner. Besides developing ontologies which enable PHASuite to gather the required input information, it will also be useful to define ontologies for sharing the analysis results with other systems. A typical result, generated by safety analysis, includes the information on: (1) location of the deviation; (2) the equipment; (3) deviation; (4) deviation type; (5) consequence; (6) cause; (7) location of consequence and location of cause; (8) safeguards, and (9) recommendation, as well as other useful information such as (10) cause causal path and consequence causal path etc.

3. Information Sharing Scheme for PHASuite When single ontologies (global ontologies) are used as shared vocabulary for same kind of information by different software tools, information sharing is straightforward since tools can access the information directly. If multiple explicit ontologies are used for different software tools, information sharing is a little complex, but inter-ontology mapping can be created to translate information in one ontology to another. However, currently common ontologies for process information/knowledge related to process safety analysis are hardly developed, and most of the systems were developed without the guidance of ontologies. To handle this situation, ontologies are first created in PHASuite, based on which adapted ontologies are created and imposed on other software tools, either as the information supplier or consumer. A two-step procedure has been developed as the information sharing scheme. As shown in Figure 1, for information importing, the first step is to access and extract information, based on the customized ontologies, from other information sources. The second step is to translate the acquired information into format understandable by PHASuite guided by a dictionary as the inter-ontology mapping. The information is then stored in an information repository. Both the dictionary and the information storage are created based on the predefined ontologies. During run-time, objects are generated from the interface storage. For exporting the information, the first step is to store the information from PHASuite in a results repository based on the predefined ontology, and the second step to convert the information to the format required by other software tools. The following sections demonstrate this scheme using examples of sharing operating procedure information with Batch Plus® and safety analysis results with PHAPro®.

344 Approaches to use this scheme to share information with MSDS and P&ID are also proposed.

Process Information

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Figure 1 Information sharing scheme in PHASuite.

3.1. Sharing process information with process simulation tools Batch Plus® (Aspen Technology Inc.) is a batch simulation tool. It needs information about the operating procedures, equipment and some properties of materials. Most of this information is also necessary for carrying out safety analysis. Process information in Batch Plus is stored in several separate database files. Process information is dispersed in different tables in the database files. Queries in SQL were designed to gather the information from different tables using the relations between tables. Material and reaction information are gathered from the material database, and the Unit procedure and operation details are collected from operation database. Since separations are not specified explicitly in Batch Plus, this information has to be gathered through the stream information from simulation results. Equipment information is better organized in results database, so it is gathered from that source. Dictionaries, constructed under the guideline of ontologies, are used to guide the translation of the information gathered from Batch Plus to information accessible through PHASuite. The dictionaries are implemented in a database. As an example, the dictionary to map operation in Batch Plus to the corresponding operation in PHASuite includes the corresponding operation name from PHASuite for each operation in Batch Plus. This information is then stored in an interface database which is readily accessible by PHASuite. The corresponding object representation of this information is created and used in PHASuite during run-time. Figure 2 illustrates the procedure for importing information from Batch Plus®. This information sharing scheme has been tested using several industrial case studies. It was found that approximately 90% to 95% of the process information required by PHASuite can be gathered from Batch Plus®. The remaining information is mainly the information that has not been specified in Batch Plus® such as the material hazardous properties. Sharing information has greatly reduced the time and error associated with reentering the information. In addition, it makes the cooperation between these different tools possible.

345

o^^

Figure 2 Importing process information from BatchPlus® to PHASuite. 3.2. Sharing results with safety documentation tools The results generated using PHASuite are stored in results database following the ontologies designed for the safety results. Although PHASuite itself provides facilities for results documentation and reporting, it may also be useful to export the results to other safety results documentation tools, such as PHAPro® (Dyadem International Ltd.). It is fairly straightforward for PHASuite to export its results to PHAPro®. PHAPro® can access a hierarchical text file as input. Ontologies for the analysis results are used to guide the design of the import field mapping file used by PHAPro® to map the fields in the text file to the fields understandable by PHAPro®. The results export facility of PHASuite constructs the text file by reading results from results database and exporting the results to a hierarchical text file. 3.3. Sharing material information with MSDS Material properties, especially those related to safety, are important information for safety analysis. Material safety information is normally stored in the form of Material Safety Data Sheet (MSDS), which is typically a text file with different sections devoted to different aspects of material properties and safety concerns. It is very hard to access the information stored in such a text format, although some parsing tools, such as Perl, can be used to extract certain information by string searching, even though the information obtained in this manner may be ambiguous. In recent years, XML has emerged as a popular file format for exchanging information. Some efforts have been made to convert the MSDS to standardized XML format (e.g. WERCS® from The WERCS Ltd.). In the proposed approach to access material safety information automatically from MSDS-XML, the central component will be a XML parser and a dictionary or translator defined using ontologies. Similar to other information, the material information will be stored in an interface database of PHASuite, and the object representation for materials will be constructed from this database at run-time. 3.4. Sharing P&ID information with CAD tools P&ID is another important information source for process safety analysis. For a modern chemical process, P&ID is normally very complex and it is a tedious process to recreate such a drawing in PHASuite. These days, most of the P&ID drawings are in some electronic format, such as AutoCAD®, SmartPlant P&ID® etc. The drawings created using older version of CAD tools are composed of lines or curves. In recent years, with the development of object oriented programming, newer CAD tools are object-based and the basic drawing components are blocks instead of lines, and some of them are

346 data-centric. This data-centric approach makes it possible for PHASuite to share information with them. Some code (possibly in Visual Basic for Applications), using algorithms similar to those currently coded in PHASuite, can be embedded in the CAD software to generate process flow diagram (PFD) from P&ID. The information can then be translated into an interface database accessible by PHASuite, guided by the dictionary created under the guidance of ontologies for equipment. It may also be possible to move the P&ID drawing facility in PHASuite to CAD software by using its drawing facility to further specify the stream information in PFD.

4. Conclusions Promising roles of ontology in automated process safety analysis were discussed in this paper. The design process, methodologies and tools used for authoring were briefly discussed. Ontologies were designed for various kinds of process information and safety analysis results. Based on the ontologies, schemes for information sharing were proposed and implemented in PHASuite. The schemes were illustrated for batch processes using examples of sharing information with other systems or sources, including importing process information from Batch Plus and exporting safety analysis results to PHA documentation tools. This type of automated information sharing can greatly reduce time and effort, and also eliminate errors that may be introduced while manually reentering the process information. In addition to the information intensive nature, process safety analysis needs extensive safety related knowledge for various operations and equipments. This knowledge is also useful for other purposes, such as fault diagnosis and operator training and support. The approaches used here will also be useful for design and implementation of ontology to support safety related knowledge sharing and reusing, which will be further investigated. The ontologies designed here for sharing information and reusing knowledge can serve as a first step towards a standardized methodology for process safety analysis, and can be extended to other types of tools for chemical processes.

5. References ANSI/ISA-S88.01, 1995, Batch Control-Part 1: Models and terminology. Connolly D. et al. Eds, 2001, DAML+OIL Reference Description, www.w3.org. Farquhar, A., Fikes, R., Pratt, W. and Rice, J., 1995, Collaborative Ontology Construction for Information Integration, Stanford University. Gruber, T.R., 1993, International Workshop on Formal Ontology. Italy. Uschold, M. and Gruninger, M., 1996, The Knowledge Engineering Review, 11(2). Zhao, C , 2002, Knowledge Engineering Framework For Automated HAZOP Analysis, Ph.D. Thesis. Purdue University.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

347

Operator Support System for Multi Product Processes Application to Polyethylene Production J. Abonyi^, P. Arva*, S. Nemeth*, Cs. Vincze*, B. Bodolai*, Zs. Dobosne Horvath*, G. Nagy*, M. Nemeth* ^University of Veszprem, Department of Process Engineering Veszprem, P.O. Box 158, H-8201, Hungary www.fmt.vein.hu/softcomp, abonyij @fmt.vein.hu *Tiszai Vegyi Kombinat Ltd., Tiszaujvaros, P.O. Box 20, H-3581, Hungary

Abstract Process manufacturing is increasingly being driven by market forces and customer needs and perceptions, resulting in necessity of flexible multi-product manufacturing. The increasing automation and tighter quality constraints related to these processes make the operator's job more and more difficult. This makes decision support systems for the operator more important than ever before. Based on the three-level model of skilled operators, this paper proposes a modular Operator Support System (OSS). As the proposed approach extensively uses process data, the OSS is based on a data warehouse designed with the help of enterprise and process modeling tools. For human-computer interaction, front-end tools have been worked out where advanced multivariate statistical models are applied to extract the most informative features. The concept is illustrated by an industrial case study, where the OSS is designed for the monitoring and control of a high-density polyethylene plant.

1. Introduction To meet the growing demands of a global economy, many industries strive to remain competitive by providing multiple grades of a large volume, high value product using the same process equipment. Lost production capacity and grade transitions, are major costs associated with the production (Kosanovich). One such example is the production of different grades of polyethylene. Because each transition to a different product grade must be made efficiently with simultaneous objectives of minimal off-specification product and feed stock waste, and non-violation of safety and environmental constraints, the monitoring and control of such flexible multi-product processes owes much to operator control skills and intelligence. These necessaries the design of an Operator Support System (OSS) that can help the operators in transition control. In Section 2, this paper proposes a modular OSS designed for multi-product processes. While the primary contribution is the prototype implementation of the strategy, certain elements of this approach are novel contributions. The latter include the application of enterprise and process model based data-warehouse and synergistic integration of multivariate statistical models to the operator interfaces. This concept is illustrated in Section 3, where the prototype of the proposed OSS is applied to high-density polyethylene (MDPE, HDPE) plant.

348

2. Structure of the OSS The operator has many tasks, such as to keep the process running as closely as possible to a given condition, to preserve optimality, to detect failures, and to maintain safety. Figure 1. shows a three-level model of the performance of skilled operators, which is an excellent sketch for human behavior. As this scheme suggests, there is a need for OSS which indicates intuitive and essential information on what is happening to avoid the operator mental overload and gives suggestions according to operator's experience and skills (Huang, Lane, Lindheim). Hence, the OSS of flexible processes should be the combination of information systems, and mathematical models and algorithms aimed to extract relevant information (signs, e.g. process trends and symbols) to "ease" the operators' work. In the following the main elements of this kind of system are described. Extensive use of historical process data. As new products are required to be introduced to the market over a short time scale to ensure competitive advantage, the development of process monitoring models of multi-product manufacturing environment necessitates the use of empirical based techniques as opposed to firstprinciples models, since phenomenological model development is unrealizable in the time available (Lane). Hence, the mountains of data, that computer-controlled plants generate, must be used by the operator support systems to distinguish normal from abnormal operating conditions and to plan and schedule sequences of operating steps. Data warehouse. Traditional OSS focuses only on specific tasks, which are performed. In case of flexible processes, the design of integrated information system is extremely important. This kind of focus on process approach means stronger focus on the material and information flow through the entire enterprise, where the OSS follows the process through the organization instead of focusing separate divisions. This also means that most of the information moves horizontally within the organization, thus requiring a higher degree of cooperation and communication across the different divisions in the plant (Lindheim, Mjaavatten). This requires the integration of data taken from various production units into a data warehouse with focus on the specialties of the technology. This model-based information system consists of only consistent, non-violate, preprocessed, historical data, and it is working independently from the distributed control system (DCS). This archival database is useful to query, group and analyze the data related to the production of different products and different grade transitions. Goals

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Stored Rules

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Rule-based Behavior Recognition Signs

Skill-based Behavior Feature Formation

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Figure L Three-level model of skilled human operator.

349 Enterprise and process modeling. The design of a data warehouse is based on the sincronization of the events related to the different information sources which requires the understanding the material, energy and information flow between the units of the plant. For this purpose not only first-principles models of the main process units have to be identified, but enterprise modelling (EM) tools have to be also used. The application of EM is extremely important, as this process describes the organization, maps the work-processes, and thereby identifies the needs of OSS. Formulated products (plastics, polymer composites) are generally produced from many ingredients, and large number of the interactions between the components and the processing conditions all have the effect on the final product quality (Lakshminarayanan). When a reliable model is available that is able to estimate the quality of the product, it can be inverted to obtain the suitable operating conditions required for achieving the target product quality (MacGregor). If such model is incorporated to the OSS, significant economic benefits can be realized. In this study, the important process variables having effect to the product quality have been selected by cluster analysis. Self-Organizing Maps. Front-end tools. Chemical reactors, in particular polymer reactors are multivariable, exhibit nonlinear characteristics, and often have significant time delays. In this case the operator cannot easily visualize what is happening in the process, so the computer should aid for visualization of the process state and its relation to the quality of the final product. As the final product quality is measured in the quality control laboratory, not only WYSIWYW (What you see is what you want) interfaces between the operator and the consol are important but WYSIWIS (What you see is what I see) interfaces between the operators (operators at the reactor, at the product formation process, and at the laboratory) are needed to share the information horizontally in the organization. Process monitoring based on multivariate statistical analysis. Plant operators are skilled in the extraction of real-time patterns of process data and the identification of distinguishing features (see Figure 1.). Hence, the correct interpretation of measured process data is essential for the satisfactory execution of many computer-aided, intelligent decision support systems that modern processing plants require. In supervisory control, detection and diagnosis of faults, product quality control, and recovery from large operation derivations, determining the mapping from process trends to operating conditions is the pivotal task. The aim of multivariate statistical based approaches is to reduce the dimensionality of the correlated process data by projecting them down onto a lower dimensional latent variable space where the operation can be easily visualized. These approaches use the techniques of principal component analysis (PCA) or projection to latent structure (PLS). Beside process performance monitoring, these tools can be used for system identification (MacGregor, Wang), ensuring consistent production and product design (Moteki). The potential of existing approaches has been limited by its inability to handle more than one recipe/grade. There is, therefore, a need for methodologies from which process representations can be developed which simultaneously handle a range of products, grade and recipes (Lane). In this paper PCA and self-organizing maps are applied to the visualization of the highdimensional state of the production system.

350

3. Application Example The proposed approach is appHed in a case study that is the data-based product quality monitoring and control of a polyethylene plant at Tiszai Vegyi Kombinat (TVK) Ltd. The aim of the OSS is to help the operators to follow the way of the products from polymer powder production through its storage and processing to granulate storage. An interesting problem with the process is that it is required to produce about ten product grades according to market demand. Hence, there is a clear need to minimize the time of changeover because off-specification product may be produced during transition. There are other reasons why monitoring the process is advantageous: Only a few properties of the product are measured and sometimes these are not sufficient to define entirely the product quality. For example, if only rheological properties of polymer are measured (melt index), any variation in end-use application that arise do to variation of chemical structure (branching, composition, etc.) will not be captured by following only these product properties. In these cases the process data may contain more information about events with special causes that may effect the product quality. Data warehouse. The technology consists of three locally segregated units: polymerization unit (reactors, separation and recovery system), granulation unit and quality control laboratory. The polymerization unit is controlled by a Honeywell DCS, hence the relevant process and calculated variables such as reactor temperature and polymer production rate are collected and stored by a PHD-module. The frequency of the laboratory qualification of the polymer powder and granulate is around two hours. Based on these data-sources, the prototype of the information system has been implemented with the use of MySQL SQL-server, general office programs (Access), and professional engineering prototyping language (MATLAB, Database Toolbox). Enterprise and process modeling. To detect and analyze causal relationships, the laboratory measurements and the operating variables of the reactors and extruders have to be synchronized based on the model of the main process elements (e.g., pipes, silos, flash-tanks). For this purpose, based on the models of the material and information flows, MATLAB scripts were written to collect all the logged events of the whole production-line and to arrange and re-calculate the time of these events according to the "life" of the product from the reactor to the final product storing. Table 1. Number of transitions between the main product grades stored in the database. A B C D £ F G H I J K L

A 0 4 4 2 0 0 0 O

B 1 0 1 0 0 0 0 O 1 0 0 0 0 0

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351 'Jtm-m's,v, IK

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Figure 2. Grade transition from product A to product E. (left: reactor process variables, right: quality-related variables, lab. measurements). The melt index (MI) and the density of the polymer (ro) are monitored by off-line laboratory analysis after drying of the polymer that causes about one-hour time-delay. Since, it would be useful to know if the product is good before testing it, the monitoring of the process would help in the early detection of poor-quality product. For this purpose black-box models have been worked out, which estimate the product quality []. Front-end tools. Based on the historical data of the previous half-year, all of the productions and grade transitions (see Table 1.) have been pre-processed by the above mentioned models. As Figure 2 shows, based on the database of the grade transitions, we have designed special figures that can be used by the operators as patterns of control strategies. Not only tools for the visualization of time-series have been developed by but plots illustrating the safety constraints (see Figure 3a). Process monitoring based on multivariate statistical analysis. The difficulty of the problem comes from the fact that there are more than ten process variables to consider (e.g., reactor temperature (T), monomer (C2), comonomer (C6), chain transfer agent (H2) concentrations, etc.). As Figure 3b. shows, the proposed OSS consists of PCAbased visualization tools were not only the two-dimensional space of the transformed variables are plotted but the Hoteling T^ and Q measures to detect faults. .<^ y

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352

4. Conclusions In this paper the structure of a data-driven OSS has been proposed for the monitoring and control of flexible multi-product processes. As the proposed approach extensively uses process data, the OSS is based on a data warehouse designed with the help of enterprise and process modeling tools. For human-computer interaction, front-end tools have been worked out where advanced multivariate statistical models are applied to extract the most informative features. The concept is illustrated by an industrial case study, where the OSS is designed for the monitoring and control of a high-density polyethylene plant. The prototype of the information system has been implemented with the use of MySQL SQL-server, general office programs (Excel, Access), and professional engineering prototyping language (MATLAB, Database Toolbox). Based on half-years of data collection, with the proposed tools more than 120 and 80 grade transitions were collected and analyzed in the two production-lines of the process. We hope that based on the application of these tools significant economic benefits will be realized in the near future.

5. References Doymaz, F., Chen, J., Romagnoli, J.A., Palayoglu, A., A Robust Strategy for Real-Time Process Monitoring, Journal of Process Control , 1 1 , 2001, 343-359. Huang, S-H., Qian, J-X, and Shao, H-H., Human-Machine Cooperative Control for Ethylene Production, Artificial Intelligence in Engineering, 9, 1995, 203-209. Kosanovich, K.A. and Piosovo, M.J., A Dynamical Supervisor Strategy for MultiProduct Processes, Computers & Chemical Engineering, 21, 1997, 149-154. Lakshminarayanan, S., Fujii, H., Grosman, B., Dassau, E., Lewin, D.R., New product design via analysis of historical databases. Computers and Chemical Engineering 24, 2000, 671-676. Lane, S., Martin, E.B., Kooijmans, R., Morris, A.J., Performance Monitoring of a Multi-Product Semi-batch Process, Journal of Process Control, 11,2001, 1-11. Lindheim, C. and Lien, K.M., Operator Support Systems for New Kinds of Process Operation Work, Computers & Chemical Engineering, Volume 21, 1997, S113-S118. MacGregor, J.F., Kourti, T., Statistical process control of multivariate processes. Control Eng. Practice, 3, 1995,403-414. Mjaavatten, A. and Foss, B.A., A modular system for estimation and diagnosis. Computers & Chemical Engineering, Volume 21, 11, 1997, 1203-1218. Moteki, Y. and Arai, Y., Operation planning and quality design of a polymer process, IFACDYCORD, 1986, 159-165. Nishitani, H., Human-Computer Interaction in the New Process Technology, Journal of Process Control, 6, 1996,111-117. Wang, X.Z., Data Mining and Knowledge Discovery for Process Monitoring and Control, Springer, 1999.

6. Acknowledgements The authors would like to acknowledge the support of the Cooperative Research Center (VIKKK) (project 2001-II-lA), and founding from the Hungarian Ministry of Education (FKFP-0073/2001) and from the Hungarian Research Found (OTKA T 037600). Janos Abonyi is grateful for the financial support of the Janos Bolyai Research Fellowship of the Hungarian Academy of Science.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

353

Combination of Measurements as Controlled Variables for Self-Optimizing Control Vidar Alstad and Sigurd Skogestad Department of Chemical Engineering, Norwegian University of Science and Technology (NTNU), N-7491 Trondheim, Norway, email: [email protected], [email protected]

Abstract A new method for selecting controlled variables (c) as linear combination of measurements (y) is proposed based on the idea of self-optimizing control. The objective is to find controlled variables, such that a constant setpoint policy leads to near optimal operation in the presence of low frequency disturbances (d). We propose to combine as many measurements as there are unconstrained degrees of freedom (inputs, u) and major disturbances such that Acopt{d) = 0. To illustrate the ideas a gas-Uft allocation example is included. The example show that the method proposed here give controlled variables with good self-optimizing properties.

1. Introduction Although not widely acknowledged, controlling the right variables is a key element in overcoming uncertainty in operation. Control systems often consist of several layers in a hierarchical structure, each operating on a different time scale. Typically, layers include scheduling (weeks), site-wide optimization (day), local optimization (hours), supervisory/predictive control (minutes) and regulatory control (seconds). The layers are interconnected through the controlled variables c. Optimal operation for a given disturbance d can be found by solving the following problem. min/(jc,M,^)

(1)

u

f{x,u,d)=0 g{x,u,d) < 0

xex,ue

u,de "D

where / is the process model, g the inequality constraints, u the independent variables (inputs), d the disturbances in which we cannot affect, and x the states. J is the scalar economic performance metric and since the economics are primarily decided by steadystate operation, only steady-state models are used in this analysis. Solution of (1) give the optimal inputs and states, Uopt{d) and Xopt{d) respectively, and also the optimal value

354 of the measurements, yopt{d), as a function of d. As shown in Skogestad (2000a) we assume that all optimally active constraints are implemented (active constraint control). Self-optimizing control follows the idea of Morari et al. (1980) and may be summarized as: Self-optimizing control (Skogestad 2000a) is when an acceptable loss can be achieved using constant setpointsfor the controlled variables (without the need to re-optimize when disturbances occur). The central issue when searching for the self-optimizing control structure is to decide how to best implement the optimal policy in the presence of uncertainty. This is accomplished by selecting the right set of controlled variables c to be kept at constant setpoints Cj, in spite of disturbances d and implementation error n. The goal is to minimize the loss, L = y(c, d) —Jopt{d), with a constant setpoint strategy, where the loss is the difference between the value of the objective using a constant setpoint policy and the value of the true optimal objective. For a review of self-optimizing control see (Skogestad 2000^). Skogestad et al. (1998) propose two methods for selecting controlled variables with good self-optimizing properties based on a Taylor series expansion of the loss function. Candidate controlled variables are not limited to single measurements, as shown by Morud (1995) who, by seeking all possible directions of the output space, was able to find a linear combination of the measurements with good self-optimizing properties. Here a much simpler method is proposed.

2. Proposed Method for Selecting Controlled Variables as Linear Combinations of Measurements We show in this section, that if we neglect the implementation error in controlHng c (e.g caused by poor control or measurement error), then it is possible from a Unear point of view to find a linear combination of the available measurements with zero loss ("perfect self-optimizing control"). By eliminating the states jc, we may write the measured variables y as a function of the independent variables (degrees of freedom) u and disturbances d. y = fy{u,d)

(2)

In general the set y also includes the independent variables u. The controlled variables c ("primary outputs") are to be selected as combinations of the measured variables ("secondary outputs"), c = h{y)

(3)

where the generally non-Hnear function h is free to choose, except that we assume that the controlled variables are independent and that the number of controlled variables (c's) equals the number of degrees of freedom (u's). We will here consider the case where the function h(y) is Unear. We may then write c = h{y) as

355 Ac = H^y

(4)

where the matrix H is free to choose. We assume that the operation is nominally optimal, that is, we have Cs = Copt{d*) where d* is the nominal disturbance. We assume that there is no implementation error (n = 0), which impUes that we will have c = Cs (constant) for all disturbances d. This constant setpoint policy will be optimal (with zero loss) provided the optimal value of c{d) remains constant, that is, is Copt{d) is independent of d. This simple insight may be used to find the optimal linear combination (i.e. find the optimal choice for the matrix H). We consider small changes (disturbances) from the nominal disturbance. Then the change in the optimal value of the measurements is given by ^yopt = yopt,d ~ yopt4* =F{d-d*)=

FAd

(5)

where the sensitivity matrix F = - ^ may be obtained numerically by solving the optimization problem (1) for small changes in the disturbance variables d, and from this obtain Uopt{d) as well as yopt{d). We assume that Ugpt and Xopt are continuous in ^ in a neighborhood of the nominal point. From (4) the corresponding change in the optimal value of c is Acopt = H Ayopt- Now require that Acopt = 0 which gives Acopt = HFAd = 0. This need to be satisfied for any Ad so we must have that HF = 0

(6)

In other words, we should select H to be in the left null space of F (H £ fA^(F^)). We assume that we have n unconstrained degrees of freedom (the length of vectors u and c are n), use m independent measurements when forming c, and have k independent disturbances. We than have that F is a m x A: matrix and / / is a n x m matrix. By assuming m>k and m>n and by assuming independent inputs and disturbances it follows that rank{F) = k. The fundamental theorem of linear algebra (Strang 1988) tells that the left null space of F, fAt(F^), has rank m — r, where r = K — Rank{F). Since H G 0^{F^) we have that dim{H) —m — k and by assuming that the number of controlled variables must be equal to the number of inputs we get rank{H) = n m-k

= n^m

= n-\-k

(7)

so that #y = #d-\-#u , e.g. the minimum number of measurements needed is equal to the number of inputs plus the number of disturbances. We then have Theorem 2.1 Assume we have n unconstrained independent variables u, k independent disturbances d, and m measurements y, of which at least n-\-k are independent. It is the possible to select measurement combinations Ac = HAy

(8)

356 such that HF = 0 where F = - ^ . Keeping c constant at its nominal optimal value then gives zero loss when there are small disturbances d. The matrix H is generally not unique. In summary, the main idea is to select the selection matrix H such that Acopt = HAym^opt — 0 by using m = n-\-k independent measurements. If the number of available measurements exceeds the number of inputs and major disturbances, there is some freedom to choose these as to reduce the implementation error and to maximize the observabihty of the disturbances in the measurements, see Alstad & Skogestad (2002) for further details.

3. Example: Gas-Lift Allocation Optimization In many oil/gas fields the production of oil, gas and water are constrained by the processing capacity and other process constraints such as available flow-line transportation capacity. Wang et al. (2002) point out that the available literature does not provide robust procedures on how to formulate and solve typical optimization problems for such systems. Often, the "optimization" consider the constraints sequentially, .or only subproblems are considered (e.g by not including the transportation system to the processing facility). Dutta-Roy & Kattapuram (1997) considered the effect of including process constraints for a two-well case that share a common transportation line to the process. They found that failing to include the process constraints (in this case the transportation line) gave a sub-optimal solution of the problem. Here, we focus on how to implement the optimal operation in the presence of low frequency disturbances. In typical oil/gas producing systems there are large uncertainties (e.g. reservoir properties, models) and few measurements, so methods that can help operate the process optimally when disturbances occur are of great value. In this paper we consider the gas-Uft structure in Figure 1 with the data given in Table 2. The model used is a distributed pseudo one-phase flow model (Taitel 2001) assuming black oil compositional PVT behavior (Golan & Whitson 1996). The valves are modeled as one-phase with a linear characteristic. The flow model represent a two-point boundary value problem and the partial differential equations are discretized using orthogonal collocation. The two wells (W\ and Wi) are connected to a common transport line {T). We assume that the system is dynamically stable. Gas is injected through valves {CV(, and CV-]) to increase the production from the reservoir by making the static pressure (head) less. The operating objective is to maximize the profit, J — Y,i=o,g,giPi^i where indices o,g,gi are oil, gas and injected gas respectively, pi is the price for phase and m/ is the mass rate for phase /. We have neglected water in this analysis. The inputs in this case are u = [Vi V2 V3 V4 V5 V^ V-j]^ where Vi is the valve position for valve /. We assume that the level and pressure of the separator are controlled at the setpoints using CV4 and CV5 respectively. These setpoints can not be manipulated, thus removing 2 DOR In typical offshore systems, the ratio of oil and gas (GOR, the ratio of stock-tank gas mass to stocktank oil mass) from each well is not exactly known, so we assume that the low frequency disturbance is the ratio of gas and oil (d = [GORi GOR2f[^^^]) in the reservoir, where the GOR is given at reservoir properties. The available measurements are the pressure upstream the valves for the wells (/Vi and /V2) and the injection gas mass rates (m^/^i and mgi^2)- It is assumed that there is a upper Umit in the gas processing capacity in the process.

357 due to compressor limitations in the process. The optimally active constraints (for all disturbances) are [nig^tot Vi Vi ^3] so we have DOF = 1 -l-A—X unconstrained DOR Since it is optimal to control the total gas massflowat the constraint, we can reformulate the objective to only consider the cost of injecting the gas into the well (7 = Z/=o,gi Pii^i)- In this case we have assumed that po — 0.17[$//:^] and p^i — -0.05[$/^g] corresponding to a oil price of $ 20 per barrel. The cost for recycling gas in the system has been assumed to be half the sale price of natural gas which was assumed to be 0.1$/5m^. Following the procedure in Section 2 we have that m = n - f / : = l - f 2 = 3, sowe need three measurements. We select the measurements /Vi, /V2 and m^/^as measurements. The optimal sensitivity function (F) is calculated by imposing the above constraints and upon requiring HF — 0, this result in the controlled variable cuc-Hy[0.76 - 0.65 0.09][fVi Fyi ^gi,^- The loss is calculated for several structures and is given in Table 1. We see that controlling c = Cue have good self-optimizing properties with the lowest average and worst case loss. A constant setpoint policy for the other controlled variables give a higher loss.

Table 1. Loss for the alternative control variables for the gas optimization case.

Rank

c

1 2 3 4 5

Cue Pvi mgi,2 rrigi^x PV2

GOR\ 0.03-4 0.06 0.0 1.5 2.0 0.8 3.2

Loss (in million $/year) GORi GORi : 0.03 -+ 0.06 0.10-^0.13 GO/?2:0.10 ^ 0 . 1 3 0.16 0.0 1.0 1.9 4.5 0.5 1.4 5.3 4.1 2.7

Average 0.05 1.5 2.3 2.5 3.3

Table 2. Data for the gas lift allocation example. Parameter L'W\,W2 Dw\,W2 LT DT Rivs,l Pres,2

PIresA PIres,2

Psep Pi P2 M, GOFfl GOlf^

Figure 1. Figure of the well network.

"^g,tot

Value 1500 0.12 300 0.25 150 155 lE-7 0.9SE - 7 50 750 800 20 0.03 0.10 15

Unit m m m m bara bara m3 sPa s Pa

bara

1 kmole kg kg

i

Comment Lepgth well 1 and 2 Diameter well 1 and 2 Length transportation line Diameter transportation line Pressure reservoir well 1 Pressure reservoir well 2 Production index well 1 Production index well 2 Pressure separator Black oil density reservoir 1 Black oil density reservoir 2 Molecular weight gas Nominal gas oil ratio Nominal gas oil ratio Maximum gas capacity

358

4. Conclusion We have derived a new method for selecting controlled variables as linear combination of the available measurements, that from a hnear point of view have perfect self-optimizing properties if we neglect implementation error. The idea is to calculate the optimal sensitivity function {^yopt = FAd) and select controlled variables as linear combination of the measurements c = Hy, such that HF = 0. The method has been illustrated on a gas-Uft allocation example. The example illustrate that in a constant set-point control structure, selecting the right controlled variables are of major importance.

5. References Alstad, V. & Skogestad, S. (2002), 'Combinations of measurements as controlled variables; application to a petlyuk distillation column'. Submitted to ADCHEM 2003. Dutta-Roy, K. & Kattapuram, J. (1997), A new approach to gas-lift allocation optimization, in *paper SPE38333 presented at the 1997 SPE Western Regional Meeting, Long Beach, CaHfomia'. Golan, M. & Whitson, C.H. (1996), Well Perfomance, 2 edn. Tapir. Morari, M., Stephanopoulos, G. & Arkun, Y. (1980), 'Studies in the synthesis of control structures for chemical processes, part I: Formulation of the problem, process decomposition and the classification of the controller task, analysis of the optimizing cotnrol structures', AIChE Journal 26(2), 220-232. Morud, J. (1995), Studies on the Dynamics and Operation of Integrated Plants, PhD thesis, Norwegian Institute of Technology, Trondheim. Skogestad, S. (2000a), Tlantwide control: the search for the optimal control structure', J. Proc. Control 10,487-507. Skogestad, S. (2000Z?), * Self-optimizing control: the missing link between steady-state optimization and control', Comp. Chem. Engng. 24, 569-575. Skogestad, S., Halvorsen, I. & Morud, J. (1998), * Self-optimizing control: The basic idea and tay lor series analysis', In AIChE Annual Meeting, Miami, FL . Strang, G. (1988), Linear Algebra and its Applications, 3 edn, Harcourt Brace & Company. Taitel, Y. (2001), Multiphase Flow Modeling; Fundamentals and Application to Oil Producing System, Department of Fluid Mechanics and Heat Transfer, Tel Aviv University. Course held at Norwegian University of Science and Technology, September 2001. Wang, P., Litvak, M. & Aziz, K. (2002), Optimization of production from mature fields, in 'Proceedings of the 17th World Petroleum Congress', Rio de Janeiro, Brazil.

6. Acknowledgements Financial support from the Research Council of Norway, ABB and Norsk Hydro is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

359

Integrating Budgeting Models into APS Systems in Batch Chemical Industries Mariana Badell, Javier Romero and Luis Puigjaner Chem. Engng. Dept, UPC, E.T.S.E.I.B., Diagonal 647, E-08028 Barcelona, Spain. e-mails: [javi.romero, mariana.badell, luis.puigjaner]@upc.es

Abstract This work is our proposal for a new conceptual approach to include in enterprise management systems. It addresses simultaneous integration of the supply chain outflows with scheduling and budgeting in short term planning in batch chemical process industries. A cash flow and budgeting model coupled with an advanced planning and scheduling (APS) procedure is the key of the advance. The model development made in this paper and the results suggest that a new conceptual approach in enterprise management systems consisting of the integration of the enterprise finance models with the company operations model is a must to improve overall earnings.

1. Introduction The new economy sets more challenges to overcome in the industry, especially in the batch chemical processes. Here inherent batch process flexibility is to be exploited to obtain maximum enterprise-wide earnings. This flexibility is transformed in complexity to its cash flow management due to the large product portfolio, assortment of material resources, equipment, manpower and so on. Hence, in this work we propose the financial to take advantage of the scheduling and planning level to improve the overall enterprise earnings. Accounting systems, which have been used up until today, are insufficient and will not stand the contest from the increasingly efficient capital market. Consequently the value added given by the transactional-based enterprise systems and its metrics is in doubt. As a first aid answer trends give more weight to treasury and budget than to accounting and planning. Indeed, the reinforcement of cash flow models is a way to put the investors in the focus to take into account the factors that affect them. The majority of companies cannot drive cash flows matching them in the best manner with the operations and other functional decision tasks that provoke them due to the lack of integrated cross-functional links. This means that almost any company has an automatic solution equivalent to a MRP for the resource "liquidity". If companies cannot drive liquidity they cannot control it, being the insolvency the first step into the bankruptcy path of enterprises. Hence, it is the most important to create the integrated tool for simultaneous optimal solutions.

2. Financial Problem Formulation and Previous Work System integration has got quite big attention but lacks prediction, which reflects the same lack of theoretical background as happened with MRP systems in the sixties. Today the lack of adequate enterprise computer-aided systems capable of managing optimally the working capital forces CFO to make decisions using out of date, estimated

360 or anecdotal information. It is like driving by looking through the rear-view mirror. In that position it is not possible to see where the entity is going, only where it has already been, not knowing if damage was provoked. The common issue to begin a budget is to ask about the sales to place the cash inflows. That is the difference with our approach: a simultaneous solution of the production demanded is determined in unison following the guidelines and contraints of CFO. A review of the previous theoretical works in the literature reveals that while in the area of deterministic models of cash management most of them were developed focusing more in the individual financial decision types; at the stochastic side of cash management models, two basic approaches were developed. Baumol's model (1962) had an inventory approach assuming certainty. On the contrary. Miller and Orr (1966) assumed uncertainty. At the sixties linear programming was introduced to the area of finance, allowing the consideration of intertemporal aspects. Orgler, 1969, used an unequal period LP model to capture the day-to-day aspect of cash management problem to minimise the budget cost over the planning horizon subject to constraints involving decision variables. Commercial offthe-shelf financial budgeting software uses toolboxes to add forecasts and other facilities, but no budgeting model functionally integrated to work on line at enterprise level was found in the literature either in the market.

3. The Integrated Model The proposed framework is shown through a specific case study. This case study consists of a batch specialty chemical plant with two different batch reactors. Here, each production recipe basically consists of the reaction phase. Hence, raw materials are assumed to be transferred from stock to the reactor, where several substances react, and, at the end of the reaction phase, products are directly transferred to lorries to be transported to different customers. Plant product portfolio is assumed to be around 30 different products using up to 10 different raw substances. Production times are assumed to range from 3 to 30 hours. Product switch-over basically depends on the nature of both substances involved in the precedent and following batch. Cleaning time ranges from 0 up to 6 hours till not permitted sequences. Scheduling & Planning Model The problem to solve is a 13-week period. Equations 1 to 23 show the scheduling and planning model. The first week is planned with known product demands and the others with known (regular) and estimated (seasonal) demands. Here, orders to be produced are scheduled considering set-up times (cleaning times). This way, the sequence of orders to satisfy customer requirements and the equipment unit to order assignment that minimises the overall required cleaning time is calculated for the first week. For the rest of weeks, sudden demands are just known with one week in advance but as their overall number can be estimated, the model lefts enough idle time to accommodate these 'unknowns'. Besides, it is assumed that sudden orders may be accepted in function of the actual plant capacity. In this way, the model is to be rerun every week as forecasts develop into real orders. Next weeks from the first one are not exact. Indeed, they probably won't be executed as calculated, but their planning is useful to know if there will be enough room to accommodate coming orders. Here, no exact sequence is calculated, and so, no set-up times are considered. The amount of raw materials final products stored at every week-period is also monitored in function of the amount stored in the precedent period, the amount bought or produced and the amount consumed or

361 sold in that period. With this, the model will be able to decide when to ask for raw materials, considering a minimum possible order-size or a relationship between unitary raw material cost and order size.

TPH = S J^TOP^nx^^,^, + X^^o. o p

(1)

o

TPfw^ < 168 {week production time)

(2)

CT„, = E SCT„.x^„,x^,„_,^, o>\

(3)

CT^^ - 0 (initial required cleaning time) o = \

Yj^p.o,e^Yj^p,o-X,e

X

(6)


(7)

p,o,e

^•Xp,o,e^f^p.o,e

(8)

Xp.o,ei =0 if product p is of type 2

(9)

^p,o,«2 = 0 ««^ Xp,o,e3 =^ if product p is of type 1

(10)

TP,,=^TOP,..nw,,,

k>l

(11)

TPi^^ <(168-6^) (week production time) Wu,e^nw^,^^

k>l

(12)

k>l

(13)

M.W,,k,e^nw^,^^ k>l

(14)

^p,k\er -^ if product p is of type R2 k>l

(15)

^p,k\e2' ~^ ^"^ ^p,k\e3' -^ if P^oduct p is of type Rl k>l

(16)

^^p,k=l,e=^^p,o,e

(17)

satisfaction,^^,^^^_^ff, = 1

^^^^

P_Stock^^ =P_Stocky,,, +Yi^e'^^pxe - S^Pi'satisfaction, e

P_Stocky, > 0

i\k-D,+d i\prodj=p

R_StocK, = R_StocK,.,-Y,

J^^r^-n^pxe +^^r^^a-i e

p\Rp=r

(lyj)

R-Stock^, >0

(22)

Budgeting Model Short-term budgeting decisions can be taken every week-period. Week production expenses will consider an initial stock of raw material and products. An initial working capital cash is considered beneath which a short-term loan must be requested. The minimum net cash flow allowed is determined by the CFO considering its variability.

362 Production liabilities incurred in every week-period are assumed to be due to buy of raw materials and production exogenous cash-flows incurred in every week to sale of products. A short term financing source is represented by a constrained open line of credit. Under agreement with banks, loans can be obtained at the beginning of any period and are due after one year at a monthly interest rate (i.e 5%). This interest rate might be a function of the minimum cash. The portfolio of marketable securities held by the firm at the beginning of the first period includes several sets of securities with known face values in monetary units (mu) and maturity week-period k' incurred at month-period k. All marketable securities can be sold prior to maturity at a discount or loss for the firm. Introducing these equations into the budgeting model presented give an integrated model for production scheduling and planning and enterprise budgeting. Wcashj^ > Min _ Cash

. .

R_Liability,_, =^qb^- rb^j, • CostRaw^

(25)

r

Exogenous_cas\ = ^ satis^qp. -SaleP^

(26)

i\D,=k

Debt^ < Max _ debt Debt^ = Debt^_^ + Borrow^ - Out _ Debt^ + F • Debt^_^ MS_net_cashflow^ =-^

(27)

[MSinv^,^^ -MSsale^,^^^

k '=k+l1

(28) k-l

+ S {^k,k ^^Sin\k' - ^k,k MSsale,,,) With this, cash balance is as follows. Exogenous_cas\ -R_liability^^ + Borrow,^ - Out_Debt^ MS _ net _ Cashflowj^ + WCas\_^ + others^_ = WCas\

(29)

Objective function: For m = 3, 6, 9 and 12, cash is withdrawn from the system in form of shareholder dividend. Objective function will consist of maximising these dividends as follows: others^^-^^912 ~ ~ s h a r e _ d i v i I = 1,2,3,4 ' v^ O.F. = msix 2^ai'share _divI

(30)

4. Results of Integration of Models The model is run for a plant product portfolio of 30 different products using up to 10 different raw substances. Production times are assumed to range from 3 to 30 hours. Product switch-over basically depends on the nature of both substances involved in the precedent and following batch. Cleaning time ranges from 0 up to 6 hours till not permitted sequences.

363 Case Study Planning results The model proposed has been implemented in GAMS/CPLEX and solved at a 1 GHz machine. Optimal solution is achieved in 190 CPU seconds. Figure 1-a shows stock of raw materials and final products profile during the three month period. Figure 1-b shows a diagram with the different number of batches of products to be produced at each week. 1000 900 800

8 '°° i

600

2 c

- Product sstcxjk

500-^

-Raw Stock

I 400-1 ^

300 200 100 0

1

2

3

4

5

6

7

8

9 10 11 12 13

Figure 1 (a and b). Planning results when solving the planning&scheduling model. Case study Budget results For the first set of the budgeting model, it is assumed no marketable securities invested at the beginning of the period, an initial cash equal to the minimum cash (20000 u.), an open line of credit at annual interest of 10% and a set of marketable securities at 5% annual interest. In the 12-months horizon it is assumed that cash is withdrawn for dividend emission at 4, 8 and 12 period (month). With this, it is solved the LP problem proposed and results give Figure 2, where overall marketable securities and cash borrowed during the first 3 months are shown. Cash withdrawn in the year is 185.588 u. 40000 35000 30000 25000 w 20000 15000 © o 10000 O w 5000 0

90000 4- 80000 70000 60000 + 50000 40000 30000 20000 10000 0 10

15

Week

Figure 2. Budgeting results when solving the sequencial procedure.

- Marketable securities Debt

364 Integrated Model. Figures 3 and 4 shows the results of integration of models. 1000 900 800

8 ^°° i 600 o

- Product s stock

c 500-1

I 400 ^

-Raw Stock

300 200 100 0

1 2 3 4 5 6 7 8 9 10 11 12 13

Figure 3. Planning results when solving the integrated model. 70000

90000

- Marketable Securities - Debt

Weeks

Figure 4. Budgeting results when solving the integrated model. The overall cash withdrawn during the year, when using the integrated framework, is of 203.196 u.

5. Conclusions The concept behind improved enterprise resource planning systems is the overall integration of the whole enterprise functionality through financial links. This framework is able to support in real time optimal schedule budgets. A difference of 9.5% in earnings/year is achieved in the case study when integrated approach is used. Armed with up to the minute information on the overall budget status, costs and schedules, allocation of resources, reschedules and cost of capital, the enterprise is ready to respond efficiently to events as they arise. The financial support from Generalitat de Catalunya (CIRIT), EC-VIPNET (G1RDCT2000-003181 & GCO (BRPRCT989005) projects are acknowledged.

6. References Badell, M., Puigjaner, L. "Discover a Powerful Tool for Scheduling in ERM Systems", Hydrocarbon Processing, 80, 3, 160, 2001. Badell, M., Puigjaner, L., "A New Conceptual Approach for ERM Systems". FOCAPO AIChE Symposium Series No.320, V 94, pp 217- 223 (1998). Baumol, W.J., "The Transactions Demand for Cash: An Inventory Theoretic Approach," Quarterly Journal of Economics, Vol. 66, No.4 (1952), 545-556. Miller, M.H., Orr, R., "A Model of the Demand for Money by Firms," The Quarterly Journal of Economics, Vol. 80, No.3 (1966), 413-435. Orgler, Y.E., "An Unequal-Period Model for Cash Management Decisions", Management Science, Vol. 20, No.lO (October 1970), 1350-1363. Srinivasan, V., 1986, "Deterministic Cash Flow Model", Omega, 14, 2,145-166.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

365

A System for Support and Training of Personnel Working in the Electrochemical Treatment of Metallic Surfaces Athanassios F. Batzias and Fragiskos A. Batzias Laboratory of Simulation of Industrial Processes, Industrial Management Dept. University of Piraeus, Karaoli & Dimitriou 80, Piraeus 185 34, Greece

Abstract Fuzzy multicriteria analysis is used for decision making in a network of procedures that describes a complete electrochemical finishing plant. The decision alternatives result by means of fault tree analysis and neuro-fuzzy reasoning; the criteria are categorized as objective and subjective. The training of the technical staff is achieved in a cooperative environment by playing with 'what if scenarios based on real and simulated data.

1. Introduction For many reasons, productivity, safety, reliability, liability, and quality conditions require a significant degree of skill from the technical personnel. In order to face lack of skill and/or unexpected events in operation and product quality problems, special cooperative procedures in the domain of Computer Aided Process Engineering (CAPE) should be developed. The basic idea is to change the operational space by means of a Knowledge Based System (KBS), allowing (a) a human operator to interact with the process via less knowledge intensive rules and (b) the process/quality/knowledge engineers to select the relevant data and to design/develop/implement a neuro-fuzzy mechanism producing these rules in cooperation with the operator. Such a cooperation is indispensable when several persons from different human user classes are involved within the same computerised system (Johanssen 1997; Johanssen and Averuk 1993). This work deals with a KBS which can provide rules and guidance to technical personnel working in the electrochemical treatment of metallic surfaces, creating also a cooperative environment between members of the staff that belong to different hierarchical levels. The same system creates/enriches a local knowledge base and performs Fault Tree Analysis (FTA) when a critical defect has been detected, increasing traceability according to ISO-standards of 9000-series. The KBS consists of the discrete sub-systems CIS, EIS, TIS, and the envelop-system EDS. The CIS (Chemical Interactive Sub-system) provides rules to the operator concerning the conditions he must keep in order to obtain the product within an allowed region as regards defects, according to specifications. The CIS is suitable for a chemical process that takes place in a homogeneous bath and is based on a neuro-fuzzy classification algorithm. The EIS (Electrochemical Interactive Sub-system) provides rules to the operator concerning the conditions he must keep in order to obtain both, defect-free surface and quality according to specifications set by the client or the market, with minimal cost. The EIS is suitable for an electrochemical process that takes place in a non-homogeneous bath and

366 is based on a neuro-fuzzy approximation algorithm performing in combination with an external heuristic procedure. The TIS (Topological Interactive Sub-system), which is hierarchically under the EIS, provides prohibitive rules and offers consultance to the operator concerning the arrangement of jigs and racks within the tank of electrochemical processing to avoid defects and ensure the desired quality. This is a very difficult task described in technical manuals to be rather an art than a technology, demanding continuous feedback by the operators and the quality control laboratory. The FDS (Fault Diagnosis System) is an envelop-system which contains the above described sub-systems and the necessary procedures for complete FTA.

2. Methodology The methodology followed is heavily based on fuzzy multicriteria analysis performed by the technical personnel twice in the computer aided integration of procedures described subsequently in this chapter and depicted in Figure 1 (21 steps interconnected with 8 decision nodes). In step 2, application of neurofuzzy network predicts product quality (output) from treatment conditions (input); subsequently given output, in the form of a vector of accepted interval values, defined by the client or the market demand, determines input vectors in clusters by means of the input-output mapping which has been constructed in the learning section of the neurofuzzy network; last, clusters are filtered through minimal accepted width of values of input variables and the remaining form a set of alternatives among which the best is chosen by means of multicriteria analysis, applying a fuzzy modification of PROMETHEE (Geldermann et al. 2000) with the following criteria: fixed cost, fi; energy cost, fa; physical productivity (or treatment rate, dependent mainly on current density with consequences on surface structure and defect appearance), f^', rest variable or operation cost, f^, environmental impact, fy, contribution to inter-lot convenience, depended mainly on the number, size, quality requirements, and priority of lots programmed, f^; contribution to intra-lot convenience, depended mainly on the ranges of treatment control variables (voltage, current density, anodizing time, electrochemical efficiency, concentration, temperature), allowed by production specifications, in relation with production facilities available, f-j. In step 10, the kind of defect observed is put as the 'top event' in the root of a fault tree, where each cause - effect link is quantified by a fuzzy index of significance of this causal relation, given by experts on the basis of (i) the relative frequency of occurrence in the past and (ii) relevance to scientific theory and experimental data; consequently, the leaves of the tree are the suggested ultimate causes which must be examined experimentally in order to find out the real cause and subsequently to make the proper remedial proposal. The order of tests to be used for this experimentation is determined by applying a fuzzy multicriteria method like the one mentioned above, with the following criteria: test significance, supported by FTA, gi; equipment availability, g2; reliability, based on analysis of variance (ANOVA) of experimental results obtained under similar treatment conditions in the past, gy, cost, g^; ratio of time required to time available due to production constraints/conmiitments, g^; expected contribution to explainability, i.e. relation to the corresponding scientific background, g^. It is worthwhile noting that criteria fi, fa, f4, g2, gs, g4 are rather objective, while criteria f3, fs, f6, fy, gi, g5, g6 are rather subjective. The row elements of the multicriteria matrix

367 used as input, which correspond to subjective criteria, are evaluated by six members of the technical staff (2 engineers/managers, 2 scientists working in the quality laboratory, 2 operators), according to a 3-stage DELPHI method incorporated within the integrated KBS. More specifically, the 2 operators evaluate (assign grades on) the elements corresponding to criteria fe, f?, gs, while the other 4 members of the staff evaluate the elements corresponding to the rest subjective criteria fs, fs, gi, ge- All 6 members of the staff evaluate the elements of the weight vector used as input. The whole KBS can be used for both support and training, even by an isolated operator, as all variables and parameter values are provided by the System in real time, depicting current conditions. Similarly, the operator can 'play' with one of the past representative cases saved in the System. During a training session, the trainee activates the KBS by introducing values/choices/situations and receives the System's response; the steps where the initiative belongs to the trainee or the System are symbolized with t or s, respectively. 11. Input of (i) product requirements/specifications set by the client or the market and (ii) raw material or semi finished product quality assessment which took place during the previous stages of production/treatment. 2t. Application of CIS or EIS if the process is chemical or electrochemical, respectively, to determine the best conditions for production/treatment by means of fuzzy multicriteria analysis. 3 t. Application of TIS, which is necessary in the case of EIS. 4 s. Chemical or electrochemical treatment, registration of (i) changes in conditions and (ii) observations of any unexpected event or failure occurring during processing. 5 s. Visual inspection of the product, accompanied with simple measurement in situ. 61. Post treatment remedial actions for eliminating recognizable light defects. 7 s. Separation of defected articles. 8 s. Sampling by the Quality Control Committee (QCC). 9 s. Offline product quality control in Laboratory. lOt. Application of (i) FT A to suggest the ultimate cause of the observed defect and (ii) fuzzy multicriteria choice of best experimental route among candidate alternatives, to confirm or reject the suggestion. 1 Is.Realization of confirmation testing via the chosen experimental route. 12t. Rejection of defected articles by the QCC; decision on recycle or disposal. 13t. Realization of special surface treatment to bring the articles back to their initial condition, according to the remedial directive issued by the Laboratory. 14t. Implementation of special treatment chosen among reconmiended practices , e.g. local plating/anodizing, on condition that it is acceptable by the client. ISs.Transient storing of additionally treated defective articles till the issue of Laboratory testing results. 16t. Sampling among apparently good items according to standard or recommended or agreed practices and dispatch to Laboratory for offline testing. 17s. Transient storing of apparently good items till Laboratory testing. 18s. Knowledge processing for support and training.

368 f START \

f

PREVIOUS STAGE/STORING t

NEXT STAGE/STORINGn^—T

END

\

2 t

f~

A

>

20^1

i X—H

18

»9t|-

1 ves no

I

I Activity Node

^ \

Decision Node

P. Are there defected articles after remedy? R. Is there another alternative experimental route? U. Are the quality testing results acceptable? W. Was the initial fault caused by human mistake?

(

j Initiation/Termination

Q. Is the suggestion confirmed? T. Is oxide stripping feasible? S. Is surface restoration feasible? Z. Are there defective articles?

Figure 1: Flow Chart of procedures constituting a complete process in an anodizing/electroplating plant, according to the 21-step CAPE plan described in the text (t: trainee's initiative and demand; s: System's response and supply).

369 19t. Sensitivity analysis performance for changing weight values of subjective criteria in the multi criteria input vector. 20t. Sensitivity analysis performance for changing parameter values of the generalized function in the special multi criteria method adopted. 2Is.Storing of defected articles.

3. Implementation and Specimen Results The methodology described in the previous chapter has been applied successfully by the authors in the case of a complete plant of aluminium anodizing, which consists of the subsequent processes: cleaning, etching, polishing, electrolytic brightening, sulphuric acid anodizing, dyeing, sealing, finishing. A specimen run concerning the application of step 2 (see Figure 1) in the process of sulphuric acid anodizing of aluminium is presented herein, based on data provided by the Hellenic Aerospace Industry S.A. The input vector consists of the following six variables: voltage, current density, anodizing time, electrochemical efficiency, electrolyte concentration, and bath temperature, which take values within the ranges ( 9 - 2 1 V), (0.8 - 7.6 A/dm^), ( 1 0 - 8 0 min), (80 - 90 %), (5 - 30 g H2SO4/L), and ( 1 0 - 2 8 °C), respectively. The output vector consists of two variables, thickness of oxide and porosity of anodic layer, which take the values 12±0.5 jam and 11±1% respectively, as set by the client in the case of the specimen run under consideration. The input-output mapping resulted after learning gave 252 six-to-two input-output combinations satisfying the specifications set by the client. These combinations were clustered to 10 groups, which were reduced to 5 after filtering, constituting the set of alternatives Ai (i=l,2,..., 5). The criteria weight vector used in the fuzzy PROMETHEE was fj: 18, 2, 1; f2: 10, 1, 2; fy 15, 1, 3; f4: 8, 1, 1; fs: 6, 1, 3; fe: 16, 1, 4: ff. 27, 2, 4, where each triadic fuzzy number appears in the usual L,R form. The generalized preference function used was the linear one, with two parameters: q for defining the indifference region (lower threshold) and p for defining the end-of-linearity in preference change (upper threshold). The results shown in Figure 2 are (a) at high sensitivity level with low p, q values (p=0.50, q=0.25) and (b) at low sensitivity level with medium p, q values (p=1.0, q=0.50). These diagrams reveal the possibility of trainees/operators to influence the choice of best alternative by changing the weight values corresponding to subjective criteria, f^, fs, fe, f?; this possibility is significant only at high sensitivity level. On the contrary, the possibility of the rest members of the staff, who participate in training and operating, is more expressed through monitoring the parameter values of the generalized preference function. In this way, all participants, although belonging to different technological cultures and hierarchical levels, learn to cooperate closely during operation and training, as they determine together the conditions of real or simulated production via the KBS. One of the problems that may appear in implementing the present training and support System is that some times technical personnel which belongs to different hierarchical levels, with different culture, uses linguistic terms with varying contextual meaning, e.g. in describing/evaluating defects, like the ones presented by Batzias and Batzias (2002).

370

1

(a)

A5

A4 A3 A1 A2

o O) 0,8 •o .9- 0,6 in

» E

0,4

I

0,2

Figure 2. Results at (a) high sensitivity level with low p, q values and (b) low sensitivity level with medium p, q values; the contribution of trainee/operator to resolution increase for distinguishing the proposed alternative may be proved decisive. A solution to this problem might be the creation of an ontological communication protocol. A similar technique has been suggested by Batzias and Marcoulaki (2002), for the creation of local knowledge bases in the fields of anodizing and electroplating, but we have not incorporated yet this technique to the System described herein.

4. Conclusions CAPE, in the form of a network of procedures/decisions, can effectively include the human factor to achieve both, technical support and staff training. We designed/ developed/implemented a Knowledge Based System (KBS) which uses, inter alia, fuzzy multicriteria analysis to determine (i) optimal conditions for chemical or electrochemical surface treatment of metals and (ii) preferable experimental routes for investigating the causes of failure in production. The specimen run of the corresponding software presented herein, based on data supplied by the department of aluminium anodizing of a large industrial firm, shows how members of the technical personnel, belonging to different technological cultures and hierarchical levels, can cooperatively learn throughout a computer integrated production system.

5. References Batzias, A.F. and Batzias, F.A., 2002, Computer-Aided Chem. Engineering 10,433. Batzias, F.A. and Marcoulaki, E.C., 2002, Computer-Aided Chem. Engineering 10, 829. Geldermann, J., Spengler, T. and Rentz, O., 2000, Fuzzy Sets and Systems, 115,45. Johannsen, G., 1997, Control Eng. Practice, 5(3), 349. Johannsen, G., and Averukh, E.A., 1993, Proc. IEEE Int. Conf, on Systems, Man and Cybernetics, Le Touquet 4, 397.

6. Acknowledgements Aluminium anodizing data supply from the Hell. Aerospace Ind. S.A. and financial support provided by the Research Centre of the Piraeus Univ. are kindly acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

371

Sensor-Placement for Dynamic Processes C. Benqlilou\ M. J., Bagajewicz^, A. Espuna\ and L. Puigjaner^* ^Universitat Politecnica de Catalunya, Chemical Engineering Department, E.T.S.E.I.B., Diagonal 647, E-08028 - Barcelona (Spain), Tel.: +34-93-401-6733 / 6678, Fax: +34-93-401-0979. ^University of Oklahoma, 100 E. Boyd T-335, Norman, OK 73019, USA. On sabbatical stay at E.T.S.E.I.B., *Corresponding author.

Abstract This article presents a methodology to design instrumentation networks for dynamic systems where Kalman filtering is the chosen monitoring technique. Performance goals for Kalman filtering are discussed and minimum cost networks are obtained.

1. Introduction In general, the optimal location of measurement points should take into account aspects that improve plant performance such as process variable accuracy, process reliability, resilience, and gross-error detectability (Bagajewicz, 2000). These performance indicators (e.g. estimation precision, reliability) of a sensor network represent the constraints in the sensor placement design problem. Among different monitoring techniques like Kalman filters and various Data Reconciliation schemes, Kalman filter presents good variance reduction, estimation of process variables and better tracking in dynamic changes of the process (Benqlilou et al 2002). This performance, however, varies with the position and quality (variance) of the sensors. This paper focuses on the determination of the optimal sensor placement for the use of Kalman filtering.

2. Kalman Filter Algorithm A linear, discrete, state-space model of a process is usually described by the following equations. X. = Ax._i +5w._i +v._i

(1)

y. =CX. +W.

(2)

being x, the n^ dimensional state vector at instant / (representing time instant t = iT), T the sampling period, u is the n^ dimensional known input vector, v the (unknown) zero mean white process noise with covariance Q^ = £[y.v^ J, and w the unknown zero mean white measurement noise with known co variance R^ -

E\A;.W^

J.

In this work it is assumed that the A, JB and C matrices coefficients are known at all times and do not change with time, that is the resulting model is a Linear TimeInvariant (LTI) system model. Given a set of measurements (>',) it is desired to obtain

372

the optimal estimators of the state variables x,. These estimates (X...) are obtained using all measurements from time t = 1... i.By using all the measurements from the initial time onwards to derive the estimates, one is automatically exploiting temporal redundancy in the measured data. The Kalman Filter (Narasimhan S. and C. Jordache, 2000) starts by assuming an initial estimator of the state variables and an estimator of its error covariance matrix P:

XQ

= E[XQ]

(3)

Cov[xo]=Po

(4)

These quantities are used for the prediction of the state variable (no control input is considered, that is u=0) and the error covariance matrix P of the state estimate as follows:

x^/,_i=Ax,_i/,._i+Bw,_i

(5)

/^•/,-i=A/^-i//-iA^+G

(6)

The next phase is the updating of the state estimation and its error covariance matrix by using the process measurements.

Pui=(I-KC)P,n-i

(8)

where kt is the Kalman filter gain given by:

ki =Pi/i-lC^(CP^i-lC^+R)

^

(9)

The corrected values are obtained by formally minimising the sum of squares of the differences between the estimates and true values of state variables, and is thus an extension of the well-known deterministic least squares objective function.

3. Instrumentation Performance Measure If the Kalman filter is to be used as the monitoring paradigm, then it is necessary to choose or develop the desired performance measures. We define the performance f^p^^f of the estimation of the variable j by averaging its error variance element [Pi/i]jj over the entire time horizon:

'^Perf

Kvfe'll n 1=1 L^,7,Jy

373 Pi/i has been selected as a basis for the evaluation of the performance index since it can be determined a priori and without any previous knowledge of the measurements. The parameters required for its computation are R, Q and PQ. The measurement error covariance R is given by the quality of the sensors while the process noise covariance Q is generally more difficult to determine because one does not have the ability to directly observe the process. If an ideal process is assumed, where all variability sources are included in the model, Q = 0. Finally, the value of PQ is selected to be equal to R (practical initialisation for the filtering process). Under conditions where Q and R are constant, both the estimations of Pj/i error covariance and the Kalman gain ki stabilise quickly and then remain constant. Therefore, the asymptotic value of Pi/i can also be used as performance measure. In fact, when the Kalman filter is applied to a system that is continuous and dynamic, the latter is preferred, whereas when conditions reflect short lived batch systems the former is more appropriate. It is clear that performance can be constructed for any set of sensors if and only if the variables are observed. Thus, any design model needs to be able to guarantee observability, either independently or through the model equations. One possible global performance index can be constructed by comparing the measuring system performance with the one corresponding to the same system but in which all variables are measured. When only a few variables are of interest, only these will be considered, being S the set of variables of interest:

K^ Perf,l

_ _

•Si

(11) Perf _Current

Perf _Optimum\

being ko an smoothing value. However, an alternative performance index can be constructed by adding all the indices of the variables included in S:

n \p^

^Perfa-Zj

abs\ -

seS

V

•

-^^S^abs\ki ^Perf _Current ]

(12)

seS

4. Observability Given the topology of the process and the placement of the sensor, variable classification procedure aims to classify measured variables as redundant and nonredundant and the unmeasured variables as observable and unobservable. This is an

374 important task for the performance of DR, since the presence of unobservable or nonredundant variables may generate a singular matrix that could lead to the failure of the DR procedure. Bagajewicz (2000) and other authors have considered the classification procedure in the case of linear DDR or linearised DDR. This procedure allows obtaining the set of redundant variables, which are introduced in the Kalman filter algorithm via the matrix C. That is, for each measured variable a value of one in the corresponding diagonal element of C is introduced. Once the Kalman filter returns back the variance-covariance matrix of the adjusted variables, the variancecovariance matrix of the unmeasured but observable variables is obtained by using the observability model obtained by the classification variable procedure. In this way one can get the variance-co variance of all variables.

5. Design Model The minimum cost model proposed is the following: min (N^)

subject to: fiKp^^nf*

(13)

Required observability where/ is certain given threshold. For a given number of sensors A^^, the determination of the optimal sensor placement is found by determining the diagonal elements of the observability matrix C (if C„ = 1 the variable / is measured and if C„ = 0 it is not measured). To obtain the best performance, matrix C is varied. One difficulty with this formulation is that the threshold values/ are difficult to assess. It is possible to substitute the required observability constraints by the required variance of the state variable estimator. The unobservable variables are then represented by a variable with a very high variance. Since the optimisation problem includes binary variables, the solution is obtained by enumeration. The optimisation strategy is as follows: 1. Determine the optimum performance, given by the case when each process variable involved in the dynamic mass balance is measured i.e. the observability matrix is the identity matrix. 2. Eliminate one sensor and obtain the list of sensor networks from the total set of combination alternatives that satisfies the constraints. 3. Obtain the system performance by selecting the minimum value of the objective function given the list obtained in step 2. 4. Repeat steps 2,3 and 4 until Ns is equal to the minimum number of sensor that allows the system observability.

375 Only when the performance index can be expressed in the same units as cost, one can construct a true cost minimization algorithm. Before that is obtained, one needs to look at a spectrum of solutions and decide the best trade-off of performance vs. cost. In any case, the Pareto optimum space over the different objectives can be determined.

6. Case Study Figure 1 shows a process network used as a Case Study to evaluate the proposed sensor placement methodology, taken from Darouach and Zasadzinski (1991): eight streams and four nodes form it. Simulated measured data were generated from the true values that obey the balance relations with an addition of normally distributed random errors with zero mean and known variance-covariance matrix.

Q8 "^^

• Wl

Q2

w

f

)

Q7

Q3

w

T

1

w

04

[• W\

W4

^'

• W

Figure 1. Process Network. In this case study, both level and flow-rate sensors are considered with no more than one sensor per variable (multi-observation is not considered). In figure 2.a it can be seen the behaviour of system performance based on comparison with asymptotic performance (equation 11).

Number of sensor

Figure 2.a. Correlation between Ns and the system performance using Eq. 11

10 Number of sensor

Figure 2.b. Correlation between Ns and the system performance using Eq.l2.

In figure 2.b system performance is based on the sum of individual performances (equation 12). The unmeasured variables are emulated by given an initial guess value with a highly variance. It can be seen form these figures the results of both approaches and the advantage of these procedures for improving the sensor network design decision making. The first approach shows a significant jump in performance when going from 9

376 to 10 sensors, and suggest that a good choice is using 10 sensors, because the improvements afterwards are marginal. Figure 2b, however, does not detect this feature.

7. Conclusions A new approach to design instrumentation networks for dynamic systems based on the Kalman filtering techniques is presented. Different performance measures are proposed and compared through a Case Study. The optimisation problem is solved in an enumerative way. Also the observability was tackled by two approaches; the same results can be obtained, and the difference between them mainly affects to the mathematical characteristics of the resulting models (and the required solving procedures), as well as to the need of a classification based on observability.

8. References Bagajewicz, M., 2000, Design and Upgrade of Process Plant Instrumentation. (ISBN: 156676-998-1), CRC (formerly published by: Technomic Publishing Company) (http://www.techpub.com). Benqlilou C , Bagajewicz, M.J., Espuria, A. and Puigjaner, L., 2002, A Comparative Study of Linear Dynamic Data Reconciliation Techniques, 9th Mediterranean Congress of Chemical Engineering. Barcelona, Nov. 26-30. Darouach, M. and Zasadzinski, M., 1991, Data Reconciliation in Generalised Linear Dynamic Systems, AIChE J., 37(2), 193. Narasimhan, S. and Jordache, C , 2000, Data Reconciliation and Gross Error Detection: An Intelligent Use of Process Data, Gulf Publishing Co., Houston, TX.

9. Acknowledgements Support form the Ministry of Education of Spain for Dr. Bagajewicz sabbatical stay at E.T.S.E.I.B. is acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

377

Chaotic Oscillations in a System of Two Parallel Reactors with Recirculation of Mass Marek Berezowski, Daniel Dubaj Cracow University of Technology, Institute of Chemical Engineering and Physical Chemistry, 31-155 Krakow, ul. Warszawska 24, Poland, e-mail: [email protected]

Abstract The paper deals with the analysis of the dynamics of a system of two non-adiabatic reactors, operating in parallel. An effect of recycle degree and division of feedstock on generation of temperature-concentration chaotic oscillations in the system is investigated.

1. The Model The system of two independence chemical reactors, operating in parallel, is presented in Fig.l. REACTOR

9

1 1-f , —*^—^ ,

Q

a ,0 1

1

"s.^s

REACTOR

l-q '

r^

^

2

2*

2

/ Fig. 1. Conceptual scheme of the system. To the inlet of the system a stream of feed is introduced, with the normalized flowrate equal to 1-f. On the other hand, to the inlet to individual reactors the streams, according to the division q and l-q are introduced. The outlet streams of the products undergo mixing with each other, yielding the resulting degree of conversion and temperature according to the relation:

a^ = qa, + (1 - q)a^;

0^ = qG, + (1 - q)Q,

(1)

378 The whole system operates as a recirculating one, which enables one to recover the nonreacted mass and heat evolved in reactors. For tank reactors the corresponding balances are presented by equations: Mass balance of reactor 1:

da,''1 dz

= q{fa^-a,)^(l),{a,,@,)

(2)

Heat balance of reactor 1

^,^=9(yB.-0,)+<2>,(«n©,)+(i-/)<^(0«-0,)

(3)

at Mass balance of reactor 2 d (y

8—^ = (l-q)(fa^-a^)-t(/>^(a^,0^) dt

(4)

Heat balance of reactor 2 at Kinetic of reaction of respective reactors are described by Arrhenius type relations:

(t>, {a,, 01) = (1 - f)Da{\ - a, Y e x p ( r - ^ ^ )

(6)

1+ ^ 1

(/>,(a,,e,) = {l-f)8Daa-a,rtxpiy/^

)

14-/782 As it is well known, each of the reactors can generate autonomic temperatureconcentration oscillations (M. Sheintuch and D. Luss, 1987; L.F. Razon and R.A. Schmitz, 1987; W. Zukowski and M. Berezowski, 2000). Their period depends on the values of reactor's parameters. If the reactors differ from technological viewpoint, the generated oscillations may differ in frequencies. In this situation the mixing of two outlet streams may lead to time series of multiperiodic or quasiperiodic character. It comes out that if a part of the resulting stream is mixed with the feed, such a system may generate chaotic changes of concentrations and temperature in individual reactors. This has been proved by numerical analysis. In Fig.2 the Feigenbaum diagram is

(7)

379 presented, which illustrates the character of dynamics of the system under consideration as a function of the recirculation coupling/.

Fig. 2. Feigenbaum diagram; q=0.5. On the vertical axis of the diagram the extreme values of the conversion degree Ct^ are indicated. Fig.2 shows clearly the interval of periodic oscillations (lines), of quasiperiodic oscillations (shaded areas generated in the point/=0) as well as intervals of chaotic oscillations (shaded areas preceded by the scenario of doubling the period). The only one steady state is marked by broken line. It is the unstable steady state. The character of individual intervals has been confirmed both by the sensitivity of the model with respect to the initial conditions and to the corresponding Poincare sections. In Fig. 3 the analogous Feigenbaum diagram is presented, which illustrates the character of dynamics of the system under consideration as a function of the division of stream of feed degree q.

380

OJ

0.2

03

0.4

05

0.6

0.7

0.8

0.9

1

Fig. 3. Feigenbaum diagram; f =0.1. Three areas are seen in it. On the left side of the figure there is area of triple steady states. On the bottom part of this area, the unstable branch is seen (broken lines). The middle part of figure includes an area of stable (continuous line) and unstable (broken line) single steady states. Unstable steady states generate both periodic solutions (single lines) and chaotic solutions (shaded area). On the right side of the figure there is an area of triple steady states. The bottom unstable fragments (broken line) generate stable periodic solution (continuous lines). Poincare set confirming the chaotic character of the solution is presented in Fig.4. All the calculations have been performed for the following parameters values: Da=0.02, n=1.5, p = 2 . 7 , y=l5, 0=1,5, Sfj

= 0 . 0 1 , o, = ^ 2 = 1 . 1 , 6 = 1 . 1 .

381

Fig. 4. Poincare set; f^O.l

q=0.525.

2. Conclusions It is interesting that two reactors, operating in parallel and coupled by the recirculation loop, can generate chaotic oscillations. Joining in parallel the apparatus, fed by the streams of the same composition and identical flowrates means, namely, nothing else as the increase of volume, in which the reaction process occurs. Thus, it seems that two reactors operating in parallel are, from the model point of view, equivalent to one larger reactor. On the other hand, the application of recycle in a single apparatus does not introduce qualitative changes in the system. The situation looks like that, when the system operates as a steady-state one. In such case all inertial constants are of no importance. The situation is different when one has to do with unsteady states. Different volumes of reactors and so-different residence times in individual reactors - may generate in them various types of dynamics. In the example presented the constant S = 1 . 1 , connected with the ratio of the volume of reactor 2 to the volume of reactor 1. In the conclusion, we have to point out with reference to that, the tubular reactor with axial dispersion may be modeled by the cascade of tank reactors, the obtained in this study qualitative results can be transposed to the solutions of the system made up of a parallel tubular reactors. It means that, the parallel heterogeneous tubular system with

382 recycle may also generate temperature-concentration quasiperiodic and chaotic oscillations, although the single apparatus offers the single periodic oscillations only.

3. Symbols Da f n q Ct

Damkohler number recycle coefficient order of reaction partition coefficient conversion degree

)6

coefficient related to enthalpy of reaction

6

dimensionless heat transfer coefficient

8

ratio of volume of reactor 2 to volume of reactor 1

y

dimensionless number related to activation energy

O

dimensionless capacitance of reactor

0

dimensionless temperature

Subscripts 1,2 refers to reactor 7 or 2 s refers to outlet from the system H refers to heat exchanger temperature

4. References Razon, L.F. and Schmitz, R.A., 1987, Chem. Engng Sci., vol. 42, 1005: Multiplicities and instabilities in chemically reacting systems - a review. Sheintuch, M. and Luss, D., 1987, Chem. Engng Sci., vol. 42, 41: Identification of observed dynamic bifurcations and development of qualitative models. Zukowski, W. and Berezowski, M., 2000, Chem. Engng Sci., vol. 55, 339: Generation of chaotic oscillations in a system with flow reversal.

5. Acknowledgements This work was supported by the State Committee for Scientific Research (KBN-Poland) under grant number PBZ/KBN/14/T09/99/01d.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved,

383

Control Structure Selection for Unstable Processes Using Hankel Singular Value Yi Cao^ and Prabikumar Saha School of Engineering, Cranfield University, Bedford MK43 OAL, UK

Abstract Control Structure Selection for open loop unstable processes is the main theme of this paper. Hankel singular value has been used as a controllability measure for input-output selection. This method ensures feedback stability of the process with minimal control effort as well as it provides a quantitative justification for the controllability. Simulation results with Tennesse-Eastman test-bed problem justify the proposed theory.

1. Introduction One of the most important issues in Control Structure Selection is choosing appropriate screening criteria, viz. controllability measure, for input and output combinations. I/O selection is performed based on a plant model and a proposed set of candidate actuators and sensors. Reasons for not using all the available devices could be the reduction of control system complexity. Various controllability measures are available in the literature; foundation is often laid by singular value decomposition such as singular vectors, relative gain array, I/O effectiveness factor etc. However, few of them address the combinatorial issue involved in I/O selection from a large number of candidates particularly for open loop unstable processes. Sometimes it may be desirable to perform I/O selection for an open-loop unstable plant that is already equipped with the devices which may be used to control certain outputs to ensure feedback stability prior to further design of control system (McAvoy & Ye, 1994). However these decisions were made solely on the basis of engineering understanding. The aim of the present work is to find a quantitative measure which can be used to select a large number of candidate inputs and outputs for open loop unstable processes.

2. Theoretical Background Glover (1986) studied the robust stabilization of a linear multivariable open-loop unstable system modelled as (G+A) where G is a known rational transfer function and A is a perturbation (or plant uncertainty). G is decomposed as G1+G2, where Gy is antistable and G2 is stable (Figure 1). The controller and the output of the feedback system are denoted by K and y respectively. Gy is strictly proper and K is proper. Glover (1986) argued that the stable projection G2 does not affect the stabilizability of the system, since it can be exactly cancelled by feedback. The necessary and sufficient condition for G to be robustly stabilized is to stabilize its antistable projection Gy. ^ Author for correspondence ([email protected])

384

rHZ

nw (7)\ w

H=^ ^

k.

?l

1 j 1j

->

—UtFj

Antistahle projection

whole process

Gi

K_ ^

^

Stable projection

BzH [Ci D2J FAZ

Figure 1: Closed loop system subject to plant uncertainty A Consider, RIT will denote the space of proper rational transfer functions with no poles on s-jw with norm denoted by • I ; RH" will denote the subspace of RLT with no poles in the closed right half plane; A* is the conjugate transpose of matrix A, whereas for a rational function of 5, Gj* denotes [Gi^-s)]*. The above feedback system is internally stable iff Gi*, 5 ,

KS,

SG^, I-KSG^e

RH'

(1)

dei{l-GiK)(oo)^0

(2)

S

(3)

:={l-GiKy^

where S is the sensitivity matrix. The objective is to find a controller K that stabilizes (G7+A) for all allowable perturbations A. In other words, the problem is to achieve feedback stability by a controller K with minimal control effort i.e. to minimize IKS^^ . Francis (1986) argues that for technical reasons it is assumed that Gj has no poles on the imaginary axis; thus Gj belongs to /?L~, but not RfT". In that case, the minimum value of l^'S'l^ over all stabilizing i^s equals the reciprocal of minimum Hankel singular value of Gj , <7^n (T^*) i.e. the square root of the smallest nonzero eigen value of r^*r^* where r^* is the Hankel operator with Gj*. Francis (1986) proves that the operator r**r^* and the matrix LcLo share the same non-zero eigenvalues where Lc and Lo controllability and observability gramians respecively. If the system has M inputs and A^ outputs, state space matrices of Gj can be written as: B,=lb, C,=[c''

b^ .... bj^] c^

....c^f

(4) (5)

where {bj,j=\...M} and {c„ j=l...A^}are state space matrices of subsystems with 7"' input and i* output. Their controllability and observability gramians will be

385

A,% + 4,Ai=c/c,.

(7)

The minimum HSV of that subsystem will be ^,; := ^™„ (re- ) = jA~iLr*L;j

(8)

where A^^ (•) denotes the minimum eigenvalue. Understandably, it is possible to extract subsystems with m selected inputs and n selected outputs from Gj. Suppose the selected inputs and outputs have index sets, J={ju jiy •••» 7m} and /={/i, ii, ..., in), respectively. ControllabiUty and observability gramians for any such subsystem will be je J

/e /

and the HSV can be calculated in a similar manner as in Eqn 8. It is observed that if GU is the HSV of the selected subsystem and cr^ is that of the whole process then cT/y is always smaller than Go and the numerical value of Cu decreases monotonically with further elimination of input(s) and output(s). Thus, it is possible to find out a set of inputs and outputs such that - a subsystem consisting of those particular inputs and outputs will satisfy the argument, CTQ - (J/y < S , where (Jean be arbitrarily chosen. However, interaction between candidate inputs and outputs immensely affect the numerical values of HSV vector. Thus, minimum value of HSV vector alone is not sufficient to identify the correct I/O combination. Instead, the sum of all the elements of HSV vector, which is normalized by the HSV of the whole process, is used as a controllability measure in this work (Lim, 1996). Presence of pure integrators in the system will invalidate the above theory as the matrix A J in Eqns (6) & (7) will be zero. To counter this problem, a diagonal matrix, having small negative magnitude as elements, can be added to the system matrix A before decomposing into stable and antistable parts. Through this operation, the poles will shift slightly towards right without disturbing overall characterisfics of the process. However, the pure integrators will move to the RHS of imaginary axis and will be converted into small positive poles which can later be extracted in Gj.

3. Tennessee-Eastman Process The Tennessee Eastman test-bed problem (Downs & Vogel, 1993) involves the control of five unit operations. The simulated plant has 41 process variables and 12 manipulated variables as illustrated in Figure 2, which are modeled with 50 state variables. Out of 41 process variables there are 22 controllable outputs including level, pressure, temperature, flow and 19 composition indicators. The chemical reactions are irreversible and occur in the vapor space of the reactor. The formation of an inert byproduct, F, is undesirable. The products G and H accumulate in the reactor. In this paper the desired set point is 50% G and 50% ^ on a mass basis. By-product F may be present in the product with 97.5% of the product being composed of G and H.

386

^.^JH

©

Figure 2: A schematic diagram of Tennesse-Eastman process A model of the process is generated in Simulink® software. Details of the process data are available elsewhere (Downs & Vogel, 1993). Open loop simulation of model indicates that the process is unstable in nature. The control objective is to select the inputs & outputs in order to stabilize the complete system.

4. Results and Discussions 4.1. Control structure selection The entire analysis has been carried out through MATLAB® software. Due to wide range of the numerical values of the base case I/O variables, proper scaling is essential for reliable analysis. Although the manipulated inputs are already scaled between 0 to 100% rather than their original engineering units, further scaling factor of 5% of their maximum possible variation in either side of base case value, is used to avoid input saturation during real time control. On the other hand, various scaling factors are used for outputs depending on their relative importance during the run of the process. Flow, pressure and level variables are provided respectively with 10%, 2.5% and 2% of their nominal values as scaling factor whereas that of the temperature variables is only 1°C. Resulting scaled process is decomposed into stable and antistable subsystems using STABPROJ subroutine of the Robust Control Toolbox. The antistable subsystem has two pairs of positive complex poles, 3.0648 ± 5.0837/ & 0.024973 ± 0.15521/ and two pure integrators (numerical value is of the order of 10'^).

387

12.5

Figure 3: HSVs of subsystems with one input (or output) and all outputs (or inputs). To observe the effect of individual inputs and outputs on the process, only one input (or output) has been taken at a time along with all the outputs (or inputs) for analysis. Hankel singular values are calculated and shown in the Fig. 3 which clearly shows dominance of liquid levels in stripper and the separator (outputs 12 & 15 ) and reactor cooling water flow (input 10) over the other inputs and outputs. From engineering understanding it can be concluded that outputs can be controlled with stripper and separator liquid flow and reactor cooling water flow can be used to control the reactor temperature. Further analysis using a Branch & Bound method has proven this selection correct (Saha & Cao, 2002). 4.2. ControUer design & closed loop results The graphical user interface SISOTOOL is a design tool in MATLAB® software which allows one to design single-input/single-output (SISO) compensators by interacting with the root locus, Bode and Nichols plots of the open-loop system. PI controllers are designed for TE process using this tool by closing one loop at a time (Table 1). Table 1. Controller settings for TE plant. Lx)ops Output 12 vs Input 7 Output 15 vs Input 8 Output 9 vs Input 10

Controller settings Gain Reset -0.1 0.01 -0.1 0.01 -7.2 0.01

388 Controlled output profiles

0

0.2

0.4 0.6 Time (hr)

0.8

Manipulated Input profiles

1

^

0

0.2

0.4 0.6 Time (hr)

0.8

1

Figure 4: Closed loop response of TE plant using stabilizing PI controller. The closed loop simulation results are shown in Figure 4. PI controller renders the desired stability.

5. Conclusion It is shown in this work that Hankel singular value can be used as an I/O controllability measure in the control structure selection for open-loop unstable processes. This method ensures feedback stability of the process with minimal control effort as well as it provides a quantitative justification for the controllability. Simulation results with Tennesse-Eastman test bed process show that the selected I/O set is effective and prediction made by the new I/O selection measure is valid.

6. Literature Cited Downs, J.J and Vogel, E.F., 1993, Comput. Chem. Engng., 17(3), 245-255. Francis, B.A., 1987, Lecture Notes in Control and Information Sci, A Course in Hoc Control theory, Eds, M.Thoma and A.Wyner, Springer-Verlag, Heidelberg (Germany), 140. Glover, K., 1986, Int. J. Control, 43(3), 741-766. Lim, K.B., 1996, J. Guidance, 20(1), 202-204. McAvoy, T.J. and Ye, N., 1994, Comput. Chem. Engng., 18(5), 383-413. Saha, P. and Cao, Y., 2002, PSE 03, China. Accepted for presentation.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

389

Neural Networks Based Model Predictive Control of the Drying Process Mircea V. Cristea, Raluca Roman, §erban P. Agachi "Babe§-Bolyai" University of Cluj-Napoca, Faculty of Chemistry and Chemical Engineering, 11 Arany Janos, 3400 Cluj-Napoca, Romania, [email protected]

Abstract The paper presents the simulation results of using Neural Networks (NN) for building a statistical model, afterwards used for Nonlinear Model Predictive Control (NLMPC) of the drying process. Important incentives of the NN approach are explored, such as modelling the drying process for which detailed governing rules may be difficult to formalize as first principle models and reducing the computation time in nonlinear model based control. Different control structures are tested, using direct or inferred (NN based observer) measured process variables. Incentives and drawbacks of the different control approaches are outlined and the most favourable control scheme is pointed out. Simulation results reveal clear benefits for the NN based NMPC using the NN based observer approach, compared with traditional control methods, and prove incentives for industrial implementation.

1. Introduction The high-voltage electric insulator production implies a first step batch drying process in order to reduce the moisture content of the drying product from 18-20% to 0.4% in special gas-heated drying chambers. The second step is carried out in high temperature ovens, to achieve the desired moisture content of the final product. Gas and air flow rates are controlled according to a special program, during a period of about 100 hours, in order to obtain the desired moisture content and avoiding the risk of unsafe tensions in the drying products. The main control problem for the drying process performed in the gas heated chambers is the lack of direct measurement of the product moisture content, needed for feedback control. Building a detailed first principle model able to thoroughly describe the spatial and temporal evolution of properties inside the electric insulator body, needed in model based control, is complex and not yet reliable. The NNbased control may overcome some of these problems. The main studied outputs of the process are the moisture content of the drying product X, the outlet air temperature To and the air humidity XQ. The considered inputs of the process are the natural gas y^ and fresh air ^ . flowrates, as manipulated inputs, and the temperature T^ and moisture Xe content of the inlet air together with the heating capacity of the natural gas Hf, as disturbances. The gas-heated chamber may be considered divided into three sections as shown in figure 1. Section 1 represents the air volume within the drying chamber, section 2 the direct surroundings of the drying product. Section 3 represents the drying product itself

390

"^^nrr

XT" ^Section

Figure 1. Description of the drying chamber.

The manipulated input and output variables together with the above mentioned disturbances have been chosen based on practical (industrial) considerations and results obtained in previous studies (Cristea et al. 2000).

2. Methods Founded on an idealised model of the biological neuron, the calculation paradigm of NN is able to represent information on complex systems. Neural Networks are composed of simple elements, neurons, operating in parallel. The network function is determined mainly by the connections between its neurons. The weighted connection paths link every two neurons to each other, the weighting structure providing the total network performance. The main benefits of the NN approach consist in their remarkable ability of learning, generalisation and robust behaviour in the presence of noise. As a consequence, the NN may be successfully used for modelling systems in which detailed governing rules are unknown or are difficult to formalise, but the desired input-output set is known. They also present incentives for cases when input-output data are noisy and when high processing speed is required. The employed NN architecture was of multilayer feed-forward structure, using the backpropagation training algorithm for computing the network biases and weights. Two layers of neurons have been considered, having the tan-sigmoid transfer function for the hidden layer and the purelin transfer function for the output layer. The quasi-Newton Levenberg-Marquardt algorithm was used for training the NN and an early stopping method was applied for preventing the NN overfitting and improving generalization (Hagan and Menhaj, 1994).

3. Research Results 3.1. Neural network design and training Building the neural networks model has been the first step in performing the NN based NLMPC. The NN model of the dryer has been developed to serve two goals. The first one is to provide information on time evolution of target variables, inherently needed for prediction in the NLMPC algorithm. The second one is to infer the moisture content

391 of the drying product, based on available measured variables, model that is later used for NN observer based NLMPC. The NN developed model has the complimentary property of requesting reduced computation effort supplying the algorithm with speed necessary for real time implementation. The structure of the NN consists in two layers of neurons having as NN-inputs: the natural gas flow rate, the moisture content of the drying product, the outlet air temperature and the chamber air humidity (considered with values at the current sampling time t). The last three variables are the state variables of the process. The NNoutputs are the same three state variables but considered at the next sampling time t+At. The trained NN is designed to predict one step into the future the behaviour of the state variables. Applied repeatedly, the dynamic NN predicts the time evolution of the state variables over a desired time horizon. As the drying process of electric insulators is performed batch wise, the process presents as particularity the lack of steady states. According to this behaviour, the training procedure of the NN has been achieved on the basis of a special prepared set of training data. The training set of data has been chosen in accordance to the industrial control practice. Good training performance has been obtained, proved by the close to unity correlation coefficients between the training data set (targets) and the NN simulation data set (NN response). Following the testing step, the trained NN has been used to simulate the drying process having imposed different drying programs, compared to those used for training. The favourable fit was also preserved for the testing subsets of data demonstrating a good generalization property of the NN. The prediction capability of the NN has been subsequently exploited for the observer based nonlinear model based predictive control. 3.2. NN based model predictive control The NLMPC structure obeys the current control practice, i.e. driving the evolution of the moisture content of the drying product in the desired way by means of controlling the air temperature inside the chamber. Usually, the desired decreasing profile of the drying product moisture content is obtained by imposing an increasing ramp-constant profile on the air temperature. The NN based Nonlinear Model Predictive Controller uses the previously trained NN to perform its prediction tasks. Step response models, simulated by the NN, have been used in two approaches: single model approach and multiple models approach. The second approach uses updated models for every of the ramp-constant time segments of the drying programme. First, the setpoint following capacity was tested in the absence of disturbances. Simulation results, for drying chamber air temperature control, are presented in figure 2. The results revealed a very good behaviour, particularly for the NLMPC case using multiple models. The control performance shows reduced overshoot and short settling time, compared to the simple PID control structure (Cristea et al. 20(X)). Afterwards, control performance testing was carried out in the presence of three significant disturbances typically occurring in the industrial practice: 10 ^C inlet air temperature T^ drop (from 16 ^C io 6 ^Q, 10 % heating power capacity Hf drop of natural gas and 20 % inlet air moisture content x^ rise.

392 Chamber Temp.

1

1.5

2

Time [s]

3.5 xlOP

Figure 2. Setpoint following ability of the NN based MFC for single (solid line) and multiple (dashed line) model approach.

All of the three disturbances have been introduced as steps at time t= 120000 s. NNbased NMPC control result, for the heating power capacity Hf (and most important) disturbance is presented in figure 3. Chamber Temp. I PC]

1.5

Time [s]

2 X 10

Figure 3. Disturbance rejection ability of the NN based MFC for the heating power capacity Hf drop, single (solid line) and multiple (dashed line) model approach.

393 Disturbance rejection aptitude of the NN-based NLMC presents favourable control performance results both with respect to the setting time, overshoot and to the zero offset, for all of the tested disturbances. Taking into account that the target variable, the moisture content of the product, is not available for direct measurement, a NN based state observer is proposed for its estimation. The data provided by the NN state observer is used for feedback nonlinear model predictive control of the product moisture content, as shown in figure 4.

NN B A S E D MODEL PREDICTIVE C CONTROLLER

S e tp o in t I \^ N — N.

I i

L^

NN B A S E D STATE OBSERVER mi

;j C e r a m ic

m ai

mass

Figure 4. Structure of the control system for direct moisture content control using NN based state observer and NN based NLMPC controller.

Product Moisture Content

1.5

2

Tinne [s]

2.5

3.5

4 x10^

Figure 5. Setpoint (dashed line) following and disturbance rejection ability for direct moisture content control using NN based state observer and NN NMPC (solid line).

394 The time dependent setpoint selection for the moisture content is based on practical and theoretical considerations concerning the time evolution of the product drying-rate. The conditions stated by the above mentioned considerations are best fulfilled by a sevensegment ramp function, which is actually used as setpoint. Simulations were conducted using this control structure and the results, for two 10% heating power disturbances applied at both t=3000 s and t=1250000 s, are presented in figure 5. The simulation results for this control structure show both good setpoint following and disturbance rejection capability. Although slight decrease of the control performance quality has been noticed, this alteration presents reduced influence on overshoot, response time and offset. The ability to perform direct control of the product moisture content may be highly appreciated. The applied model predictive algorithm has a few special features that make it more effective: operates with constraints on manipulated variables and controlled variables; a nonlinear form of the MPC algorithm was used to obtain feasible control performance; the NLMPC controller was tuned according to the dynamic sensitivity analysis.

4. Conclusions The proposed NN based observer of product moisture content coupled with the NN based model used for NLMPC prove to be a good strategy for controlling the drying process of electric insulators. The results obtained simulating NN based NLMPC reveal good setpoint tracking performance as well as an effective disturbance rejection. Its high performance is owing to the use of the direct control of the product moisture content relying on the NN based state observer, to the calculation speed provided by the NN based model to the NLMPC algorithm, and to the optimal manipulation of both the inlet air and gas flow rates. The NN based model offers the incentives of capturing the intrinsic behaviour of the drying process, otherwise difficult to be described in first principle models. Utilization of this method should be carefully performed with respect to the quality of the training set of data. Increasing the confidence for this set of data may be obtained by expunging the outliers, filtering the data presenting errors in the NN simulation steps and repeating the NN training procedure, both preceded by a careful analysis of the physical feasibility of the training data. For the industrial plant, the NN based NLMPC may result in more efficient energy management, higher productivity and improved product quality.

5. References Cristea, V.M., Baldea, M., and Agachi, §.P., 2000, Model Predictive Control of an Industrial Dryer, ESCAPE-10, Florence. Hagan, M.T., and Menhaj, M.H., 1994, Training feedforward networks with the Marquardt algorithm, IEEE Transaction on Neural Networks, 5, 989.

6. Acknowledgements Financial support from The Swiss National Science Foundation within the Institutional Partnership Project no.7 IP62643, with ETH Zurich, is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Krasiawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

395

Real-Time Optimization Systems Based On Grey-Box Neural Models F.A. Cubillos^^^ and E.L. Lima^^^ ^^^ Depto. Ing. Quimica, Universidad de Santiago de Chile. Casilla 10233, Santiago, Chile. Fax: 56-2-6817135 , email: [email protected] ^^^ Programa de Engenharia Quimica, COPPE, Universidade Federal do Rio de Janeiro. C.P. 68502 CEP 21945-970, Rio de Janeiro, RJ, Brasil.

Abstract This paper investigate the feasibility using of grey-box neural type models (GNM) for design and operation of model based Real Time Optimization (RTO) systems operating in a dynamical fashion. The GNM is based on fundamental conservation laws associated with neural networks (NN) used to model uncertain parameters. The proposed approach is applied to the simulated Williams-Otto reactor, considering three GNM process approximations. Obtained results demonstrate the feasibility of the use of the GNM models in the RTO technology in a dynamic fashion.

1. Introduction The online optimization of chemical plants has enjoyed considerable industrial interest because of it capacity to achieve competitive advantages in the marketplace. Numerous successful applications of the real-time optimization in industrial practice have been reported (Nath and Alzein, 2000). The economic performance of an RTO system is measured by the expected profit achieved, which is strongly influenced by the quality of the model used (Loeblein and Perkins, 1998). The RTO systems reduce the plant/model mismatch by updating the model using actual and historical plant data sets (Yip and Marlin, 2002). Because the RTO execution is time consuming, simple phenomenological steady state models are currently used. In practical situations, however, it is difficult to reach the steady state among each RTO execution period, leaving the plant in a permanent state of slow dynamic changes. Under this condition model is not entirely consistent and an inefficient update process could reduce the economic performance of the plant. The key to solve this problem is the use of phenomenological dynamical plant models, that have the disadvantages of being difficult to obtain and difficult to update in real time. An alternative way of solving this difficulty is the use of dynamical models, based on combinations of first principles and neural networks (NN), called grey-box neural models (GNM). A GNM normally consists of a phenomenological part (heat and/or mass balances differential equations) and an empirical part (a neural network in this work). Due to the inherent flexibility of NN, models based on this structure are well suited to represent complex functions such as those encountered in chemical reaction processes. This work proposes incorporate in the RTO system a dynamical GNM of the

396 plant based on phenomenological principles and neural networks. The model update is equivalent to the network training. But, the main reason for the use of this approach is the fact that a steady state equivalent model may be easily derived from the dynamical GNM and used efficiently in the optimization step.

2. Grey-Box Neural Models (GNM) Neural networks are non-parametric, massively connected models that perform quite well for approximating nonlinear, multivariable functions. This unique property has allowed using them successfully in predictive control of nonlinear processes. Grey-box Neural Models combine a phenomenological model of the system with neural networks, which estimate the uncertain parameters of the process. This technique enables the synthesis of simpler mathematical models than purely phenomenological ones, with more robust generalization properties than purely NN models. These two properties make the GNM especially attractive in tasks associated with Process Identification, Process Control and Optimization, (Cubillos and Lima, 1998; Xion and Jutan , 2002). The GNM technique consists on formulating a process model, formed by equations derived from phenomenological principles - such as mass, energy and momentum balances - and neural networks, dedicated to estimate those parameters difficult to model or uncertain. This form of representation is an attempt to add prior knowledge to black-box neural models, in order to reduce its complexity and improve their adaptive and predictive properties (Psichogios and Ungar, 1992). Thompson and Kramer (1994) classified these grey-box models into two main types: NN bringing intermediate values (parameters or variables) to be used by the phenomenological model {series grey-box models) or NN in parallel with the dynamic model compensating the plant/model mismatch (parallel grey-box models). Figure 1 shows the series scheme for a Grey-box model as used in this work.

Inputs

Phenomenological

Outputs

Dynamic Model Parameters

Figure 1: The GNM approach.

397

3. Process Descriptions In this work we applied the proposed approach to the simulated CSTR reactor from the Otto-Williams benchmark plant modified by Forbes and Marlin (1996) that may be described by elementary kinetics. The reaction sequences are: A+ B->C

(1)

BH-C-> P + E

C + P->G Instantaneous profits can be expressed as a function of the feed and product flowrates as (Forbestetal.,1994) P = 1143.38*X(P)* Fr + 25.92 X(E)*Fr - 76.23*Fa - 114.34*Fb

(2)

The ideal CSTR had no reactor temperature dynamic, and the manipulated variables to optimize where Tr and flowrate of B component (Fb). Fa and M were set to [ 2 Kg/s, 10220 Kgs]. GNM synthesis To study the feasibility of the use of the GNM type models in the RTO technology, three different modelling schemes were selected as described in Fobest et al. (1994): i) ii) iii)

Single reaction approximation (Ml): [ A + 2B -> P +E] Two reactions approximation (M2): [A + 2B ^ P +E ; A +B +P -> G] Complete three reactions system (M3) as described in (1).

Each GNM was synthesized considering the non stationary mass balance for each species. Feedforward neural networks were added to estimate the hypothetical reaction rates with unknown kinetics. Target reaction rates were calculated directly from discretized mass balances. For example, for a single reaction model (Ml), P component balance may be used to estimate unique reaction rate given by: R, = (Fr*X(P)/M)k+(X(P)k-X(P)k.i)/To

(3)

In order to obtain adequate data estimation for the reaction rates, PRBS input sequences in Fb and Tr were introduced, using a sample time of 1000 sec. Operation conditions and outlet concentrations were register to train the neural networks. The model update that consists of the NN adaptation was carried out using a second order recursive algorithm. The best NN structures were found by a systematic training procedure, considering outlet concentrations of A and B components and the reactor temperature as the inputs to the networks. Finally, networks with one hidden layer with four nodes and sigmoidal activation functions were selected. Based on the updated dynamic GNM it was possible to derive an equivalent steady state model able to be used for optimization purposes.

398 To illustrate the approach, considering the two model approximation (M2), the model has to estimate two reaction rates (Rl and R2) using a neural networks. In the steady state the model equations are: Fa - (Fa+Fb)*X(A) - Rl*M - R2*M = 0 Fb - (Fa+Fb)*X(B) - 2*R1*M - R2*M = 0 - (Fa+Fb)*X(P) + R1*M - R2*M =0 - (Fa+Fb)*X(E) + 2*R1*M =0 - (Fa+Fb)*X(G) + 3*R2*M =0

(4)

A similarly approach was used to derive the other GNM models, where the NN' were used to estimate the respective reaction rates. Figure 2 shows the prediction of the outlet concentration for E product using M2 model. Similarly results are found for the Ml and M3 models showing that the GNM scheme is able to adequately track the process dynamic.

4. RTO results The GNM approach with the three alternative adapted models were tested in the RTO scheme considering similar operation conditions as used by Forbes and Marlin (1996), with feed flow rate and reactor temperature as the optimization variables. The optimization problem is to maximize the profit, as indicated in Equation 2, constrained by the corresponding dynamical GNM models. A dynamical test applied considering the reactor operating in a non optimum point. At a pre-established time, the RTO is connected to the plant, running each sample time, in order to position the process at the optimum. Current reactor states were using as initial guess to the next optimization step. Figure 3 shows the behavior of the RTO system for the three GNM models and the true model over a time horizon of 22000sec (21 RTO executions). Results indicate that all GNM models were able to find an optimally set of inputs close to the true optimum and maintained this conditions over the time. It can be observed that the deviations respects to the nominal optimum are more severe when more inexact is the process model using in the RTO. Other issue observed is the sensitive of the RTO/GNM system to the initial conditions in the optimizer. In order to compare the performance of each model considered in this work, a dynamic performance index, defined as the total profit obtained over the time window was calculated and shown in Table 1. Results show that a more exact model brings best performance, specifically the three reaction model. Table 1: Cumulative profit.

MODEL Total Profit ($)

True 8663

GNM/Ml 8237

GNM/M2 8537

GNM/M3 8576

399 0.38-1

K-,

1

0.36-

0.34-

5?

_h H

1

•

11

I

il

li

0.30-

)

hj

i > j

0.32-

0.28 —1 C

h

ij

1

•

50

h [f

1

1

h

1

150

100

200

S a m pies

Figure 2: Actual (cont) and prediction (dash) E concentration by GNM/M2 model.

<^

10

15

Samples Figure 3: Instantaneous profits.

5. Conclusions The obtained results demonstrate the feasibility of the use of the GNM models in the RTO technology in a dynamic fashion. We considered that this approach introduce improvements in the RTO technology, allowing extension to highly non linear plants, feasibility of on-line adaptation using dynamical information and the integration among MPC - RTO systems by using current plants models. However, issues as models adequacy to optimization task should be analyzed in depth.

400

6. Notation Fa,Fb = Inlet flow rates Fr = Outlet flow rate M = Reactor Mass holdup P = Economic objective function R = Reaction rate (in mass) To = Sample time Tr = Reactor temperature X(i)= composition of component i in mass fraction Subscripts i = component i k= Sample instant

7. References Cubillos, F. and Lima, E., 1998, Adaptive hybrid neural models for process control. Computers and Chemical Engineering, Vol 22, S989-S992. Forbest, F., Marlin, T. and MacGregor, J., 1994, Model Adequacy Requirements For Optimizing Plant Operations, Computers and Chemical Engineering, Vol 18, pp. 497-510. Forbes, J.F. and Marlin, T.E., 1996, Design Cost: A Systematic Approach to Technology Selection for Model^Based Real-Time Optimization Systems. Computers and Chemical Engineering, Vol 20,717-734. Loeblein, C. and Perkins, J, 1998, Economic analysis of different structures of on-line process optimization systems. Computers and Chemical Engineering, Vol. 22, pp.1257-1269. Nath, R. and Alzein, Z., 2000, On-line dynamic optimization of olefins plants. Computers and Chemical Engineering, Vol 24, 533-5338. Psichogios, D. and Ungar, L., 1992, A hybrid neural networks-first principles approach to process modeling, AIChE J., 38, 1. Thompson, M. and Kramer, M., 1994, Modeling chemical processes using prior knowledge and neural networks, AIChE J., 40, 132. Xiong, Q. and Jutan, A., 2002, Grey-box modelling and control of chemical processes. Chemical Engineering Science, Volume 57, 6, 1027-1039. Yip, W.S. and Marlin, T.E., 2002, Multiple Data Sets for Model Updating in Real-Time Operations Optimization. Accepted for publication in Computers and Chemical Engineering.

8. Acknowledgments The authors wish to acknowledge the support provided by FONDECYT (Projects 1020041 and 1010179).

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

401

Change Point Detection for Quality Monitoring of Chemical Processes Belmiro P. M. Duarte^* and Pedro M. Saraiva^ GEPSI - PSE Group, Instituto Superior de Engenharia de Coimbra, Portugal ^GEPSI - PSE Group, Dept. of Chemical Engineering, University of Coimbra, Portugal

Abstract This paper addresses a class of problems typically faced by process engineers and operators: the detection of assignable variation causes in retrospective data series corresponding to quality or process variables. The detection of average and/or variance changes is dealt as a classical change-point problem analysis where the two main questions raised are: 1) "Did a change really occur?" and 2) "When did it occur?". The approach adopted for achieving such a goal is based upon Change-Point Analysis (CPA) performed over CUSUM operators. To handle any type of data structure, the detection step is performed by a nonparametric bootstrapping procedure that estimates a probability distribution, according to which the existence of process shifts is determined. We tested the above approach through its application to typical chemical engineering case studies, covering a simulated CSTR and industrial data collected from a Portuguese pulp plant.

1. Introduction The detection of process shifts in retrospective discrete time data series can be treated as a classical change-point problem (Basseville and Nikiforov, 1993; Chen and Gupta, 2000; Darkhovsky and Brodsky, 1993). The basic goal underpinning this paradigm is to find the point(s) in time where a certain statistic did suffer pronounced behaviour changes through enumerative procedures. Some of the most commonly used statistics in parametric detection are the Geometrical Mean Average (Hines, 1976), CUSUM (Page, 1957), or the Generalized Likelihood Ratio (Lorden, 1971), while Mann-Whitney (Darkhovsky and Brodsky, 1993) and CUSUM (Csorgo and Horvath, 1997) values have been employed for non-parametric change detections. Sullivan and Woodall (1996) used a likelihood ratio test to detect change-points in retrospective time series and introduced the so called Likelihood Ratio Test (LRT) control charts, aimed at establishing whether a process is under statistical control (Turner et al., 2001). Taylor (2001) introduced a tool based upon CUSUM statistics to identify change-points on the values for a given monitored variable, through a nonparametric bootstrapping procedure. In this article we describe a Change Point Analysis (CPA) methodology for identification of process behaviour changes associated with the quality performance of a

Author to whom correspondence should be addressed: Departamento de Engenharia Quimica, Instituto Superior de Engenharia de Coimbra, Quinta da Nora, 3030 Coimbra, Portugal.

402 given chemical process, and illustrate its practical value through the presentation of two specific case study applications.

2. Change Point Analysis Approach The strategy that we will use to detect process shifts in retrospective data sets is based upon the CUSUM operator described by Basseville and Nikiforov (1993), Csorgo and Horvath (1997) and Taylor (2001) for off-line types of problems. The choice of such an operator is justified by its optimal properties (Lorden, 1971). Let us suppose that a data set D comprises m independent observations x^ for / = l,---,m, with x^ following a generic probability distribution PQ with 6 G 91 being a vector of relevant parameters (such as the mean or standard deviation). If a change in the mean occurs for observation mj, then the observations through m^ are described by a distribution PQ^ and all the subsequent ones by PQ^Assuming for now that only changes in the mean do occur, and focusing our attention on their identification, let us further consider that the observations are: Xi=H-^Zi

(1)

where z, is a stationary signal with mean 0 and finite covariance that exhibits short range dependence. The cumulative sum operator at the i* point, 5,, is given by:

Si = tzk

(2)

it=i

with the change-point, t^ , placed at ^0 =argmax|5,|

(3)

To estimate the confidence levels associated with each change point we do compare the CUSUM operator range with its distribution obtained by re-sampling the original data, assuming that the range of 5 , , designated as r, is given by: r - max 5. - min 5. \
(4)

\
The decision regarding change-points significance is achieved by a bootstrapping procedure with the points z, randomly sampled without replacement (Efron et al., 1994). A large number of bootstrap samples (n^) is required to achieve a robust decision on how much r would vary if no change took place. The number of bootstrap instances with ranges, r^, superior to r, designated as n^ , can be expressed as:

403 "b

(5)

"'=^,'M) and the occurrence of a significant shift determined from d:

(6)

cl = 100.0—

According to values of cl, a three-level discrimination function, del, may be defined as: \l

if

c/G {[lOO.Ox(1.0-cri);100.0]u[0.0;100.0xai]}

dcl = 1

if

c/G {[I00.0x(1.0-a2);100.0x(1.0-ai))u(l00.0xai;100.0xcir2]}

0 if

(7)

c/6{(l00.0xa2;100.0x(1.0-a2))}

where a^ and a2 ^^^ two different type I acceptance errors. Values of del = 1 and del = 2 provide, respectively, evidence and strong evidence that a change occurred at point ^0 . For the detection of variance change points, a similar approach is used, based upon the d^ statistic, proposed by Inclan and Tiao (1994):

d.=

Izt

*=i

(8) 2

I 2*

m

which is monitored and used to support a change point analysis. After locating a first major shift, the basic Change Point detection algorithm is recursively applied to each of the subintervals generated. In each of the time subintervals resulting from the above time partition, designated as j , and containing nij points, confidence intervals for the mean can be built according to the t-Student critical values:

Mn\j

h-a/2,mj-l

'^Mrrii

'^h-al2,mi

^'V^

(9)

For the standard deviation, each of the points represented, $,, is given by:

?, =k->«» and the confidence limits are built according to the x'^ distribution:

(10)

404

(11)

^ruj

3. Case Studies 3.1. Simulated CSTR The first example chosen to illustrate the CPA capabilities in detecting mean and variance process shifts reports to a simulated continuous stirred tank reactor (CSTR) where a reversible reaction A<-^R is carried out (Economou and Morari, 1986). Each combination of feeding stream properties, i.e. the triplet (C^,, Cj^^, 7,), leads to a set of corresponding output values of ( C ^ , C/j, T). White noise was added to the simulated data thus obtained, through a term N(0,0.1) added to C^,, C^ and C^ , and N(0,1.0) added to 7} and T, where N(//,o) represents a normal distribution with mean // and standard deviation o . A set of 200 points was obtained by performing four step or ramp variations over C^, and T^ (Table 1). Table 1. Disturbances used to generate data for average change detection. Observations #Region Comment 1 1-30 Default case (C^, = 1.0 mol/1; T^ = 430 K) 31-60

2

Positive step change in concentration (C^, = 1.1 mol/1)

61-100

3

Positive step change in temperature (T, = 438.6 K)

101-140

4

Negative step change in concentration (C^, =0.9 mol/1)

141-200

5

Positive slope ramp concentration (slope

disturbance of C^j

change in = 0.1/60

mol/(l.observation); initial value of C^, = 0.9 mol/1) Output C/j was chosen to apply our CPA algorithm, with n^ set to 2000, a^ to 0.05, a2io 0.1, and a to 0.027. The results thus obtained are provided in Figure 1 (where vertical ranges correspond to mean confidence intervals) and Table 2, showing that all of the shifts were indeed identified. Table 2. Change Point Analysis Results. Observation Region Start End 1 1 30 2 60 31 3 61 100 4 101 140 5 141 200

Average (mol/1) 0.5078 0.5607 0.5101 0.4617 0.4912

cl (%) 100.00 100.00 100.00 97.35 100.00

405 3.2. Industrial data from a pulp plant The set of industrial data considered here for CPA application corresponds to a particular pulp quality variable (brightness), collected every hour from a magnesium bisulphite Portuguese pulp mill. For this quality characteristic the plant does have a target value of 88.2 "ISO, together with a minimum allowed specification of 87.5 °ISO. The data available covers a period of almost 200 operating hours, and a CPA, performed over both average and standard deviation behaviours (Figure 2), does show that several significant changes did occur for both of the parameters, and allows us to identify them hierarchically, from top level events to increasingly less significant shifts. Process engineers may stop this recursive addition of detail in an interactive way, whenever they feel that no further added value derives from more time partitioning, even though it may be statistically significant. This interaction and hierarchical identification of process changes can provide powerful insights regarding a better understanding of available data, their interpretation and lead to increased knowledge about the underlying process behaviour, why, how and when real changes did take place.

4. Conclusion In this paper we propose an algorithm based on CUSUM statistics to detect changes in average and/or variance for retrospective data series. It does not depend on any parametric assumption about underlying probability distributions, given that a bootstrapping procedure is adopted to identify statistically significant changes. Since many chemical processes do not behave under stable steady state conditions, but rather with very frequent changes over time, rather than trying to monitor them through control charts or similar techniques, a Change Point Analysis approach (as the one pointed out here) seems to provide a better way for monitoring quality variables and achieve process performance improvements, through a top down identification of the most significant changes that took place over time. Our algorithm was tested over simulated data describing the operation of a CSTR where a reversible reaction occurs, as well as with industrial data collected from a Portuguese pulp plant.

17

33

49

65

97 113 Batch

129

145

161

177

193

Figure 1. Mean Change Point Analysis monitoring for the CSTR.

406

Figure 2. Pulp brightness CPA monitoring for: a) Mean; b) Standard Deviation.

5. References Bassevile, M. and Nikiforov, I.V., 1993, Detection of Abrupt Changes: Theory and Applications. Prentice Hall, New Jersey. Chen, J. and Gupta, A.K., 2000, Parametric Statistical Change Point Analysis. Birkhauser, New York. Csorgo, M. and Horvath, L., 1997, Limit Theorems in Change-Point Analysis. Wiley, New York. Darkhovsky, B.S. and Brodsky, B.E., 1993, Nonparametric Methods in Change Point Problems. Kluwer Academic Publishers, Amsterdam. Economou, C.G. and Morari, M., 1986, Ind. Eng. Chem. Process Des. Dev., 25, 403. Efron, B., Tibshirani, R.J. and Efron, B., 1994, An Introduction to the Bootstrap. CRC Press, New York. Inclan, C. and Tiao, G.C., 1994, Journal of the Amer. Stat. Assoc, 89, 913. Hines, W.G.S., 1976, IEEE Trans. Information Theory, 22,4,210. Lorden, G., 1971, Annals Mathematical Statistics, 42, 1897. Page, E.S., 1957, Biometrika, 44, 248. Sullivan, J.H. and Woodall, W.H., 1996, Journal of Quality Technology, 28, 3, 265. Taylor, W.A., 2000, Change-Point Analysis: A Powerful New Tool for Detecting Changes. Web: http://www.variation.com/cpa/tech. Turner, CD., Sullivan, J.H., Batson, R.G. and Woodall, W.H., 2001, Journal of Quality Technology, 33, 2, 242.

6. Acknowledgments The authors would like to acknowledge financial support provided by FCT through research project POCTI/1999/EQU/32647.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

407

Selecting Appropriate Control Variables for a Heat Integrated Distillation System with Prefractionator Hilde K. Engelien, Sigurd Skogestad Norwegian University of Science and Technology (NTNU) Department of Chemical Engineering, 7491 Trondheim, Norway

Abstract A heat integrated prefractionator arrangement is studied for a ternary separation of a propane-butane-pentane solution. The prefractionator arrangement has large energy savings compared with the best of the direct or indirect sequence with no heat integration. A heat integrated distillation system can be more difficult to control than a non-integrated arrangement, so good control systems are essential. In this work the focus is on the selection of control variables. The method of self-optimizing control has been used to provide a systematic procedure for the selection of controlled variables, based on steady state economics.

1. Introduction For ternary separations there are three classical separation schemes: direct split, indirect split and prefractionator arrangement. Energy savings can be achieved for these separation schemes by running one of the columns at a higher pressure and integrating the reboiler/condenser. For these multi-effect systems there are two modes of integration: forward integration, where the heat integration is in the direction of the mass flow, and backward integration, where the integration is in the opposite direction of the mass flow. Cheng and Luyben (1985) compared the steady state designs for several multi-effect configurations for a benzene/toluene/xylene separation. The result showed 50% energy reduction and that the best configuration for the separation studied was a prefractionator/sidestream column arrangement with reverse integration. Ding & Luyben (1990) presented control studies of both forward and backward integrated prefractionator systems for ternary separation of benzene-toluene-xylene. A direct split system is used for comparison. The configurations suggested has "total Q" control and also control of the two impurities in the sidestream (from main column) by controlling the sidestream flowrate and the sidestream draw-off tray. For the low-purity case they find that the prefractionator arrangement is dynamically about the same as the conventional direct split configuration. For the high purity case both systems are controllable, but the direct split configuration gives much better load rejection. The control of the sidestream toluene composition is particularly poor. Bildea & Dimian (1999) also investigated the controllability for a system with a prefractionator and a sidestream main column. For the forward and backward integrated case they looked at four different designs, depending on the light/heavy split in the

408 prefractionator. The authors concluded that in general the forward heat integration scheme is the easiest to control. In this work a heat integrated arrangement consisting of a prefractionator and a main column with sidestream is studied for the ternary separation of a propane-butanepentane solution. The objective of this work has been on the selection of controlled variables, that is, finding which variables that should be controlled. The concept of selfoptimizing control (Skogestad, 2000), which is based on steady state economics, is used to provide a systematic framework for the selection of the controlled variables. This method involves a search for the variables that, when kept constant, indirectly lead to near-optimal operation with acceptable economic loss. In self-optimizing control, rather than solving the optimization problem on-line, the problem is transferred into a simple feedback problem (Skogestad, 2000). In practice, this means that when the plant is subject to disturbances it will still operate within an acceptable distance from the optimum and there is no need to re-optimize when disturbances occur.

2. The Integrated Prefractionator Arrangement The system studied in this paper is a ternary separation of propane-butane-pentane. The separation is carried out in two columns operating at different pressures (See Figure 1). The first column is a high pressure (HP) prefractionator, which performs the propane/pentane split. Both the distillate and the bottom products from the HP column is fed to the second, low pressure (LP) column. Here propane, butane and pentane are the products from the distillate, sidestream and bottom stream, respectively. In the LP column the top part of the column (above sidestream) performs the propane/butane split while the bottom part (below the sidestream) performs the butane/pentane split. The feed to the HP eulumn ia 300 mol/s (liquid feed), feed compOKitinn ig (0.25 0.5 0.25) and there are 20 and 40 stages in the HP and LP columns, respectively (10 in each section). The heat integration between the two columns is in an integrated reboiler/condenser, where the condensing heat from the HP column is used to boil the LP column.

JZ (ABC) HR

JT (AB

i

(BC^

\^L^

(A)

(B) LP

L Figure 1. The heat integrated prefractionator arrangement.

(C)

409 2.1. Energy savings for the integrated prefractionator arrangement A prefractionator arrangement with no heat integration saves about 30% energy compared to the best of the direct or indirect sequence. A prefractionator with further heat integration where the columns are run at different pressures, can have savings of around 50% compared to the best of the direct or indirect sequence (Ding & Luyben, 1990). For both the arrangements the energy saving is dependent on the recovery of the middle component from the prefractionator. Figure 2 shows a comparison of the minimum vapour flowrate required for the integrated and non-integrated prefractionator arrangement. The calculation is based on the Underwood shortcut equations for minimum vapour flowrate for sharp splits and constant relative volatility. In the prefractionator (propane/pentane split) the minimum vapour flowrate as a function of the recovery of the middle component rB,Db is calculated from:

{ V.min,\

cc^z A'-A

+

^A-^B

^B ^B,D ^B

(1)

The Underwood roots, 0A and OB. are found from the feed equation (King, 1980). The vapour flowrate in the second column is calculated from Kings equation (King, 1980) for binary mixtures. Note that the effect of pressure on the separation is not included in these formulas. Vmin for Prefractionator With and Without Heat Integration

Prefractbnator arrangement with no integration: V =V +V min

0

0.1

0.2

pref

main

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Recovery of middle component (B)

Figure 2. Comparing Vmin for prefractionator arrangement with and without integration, sharp split, propane-butane-pentane; ZF = [0.15 0.7 0.15].

410 Based on these minimum vapour flowrate calculations Table 1 presents comparisons between energy requirements of integrated prefractionator arrangements and other integrated schemes. The energy savings are given as percentage improvement compared to the best of the non-integrated direct or indirect sequence. The Petlyuk arrangement has also been included for comparison. In all cases one or both of the integrated prefractionator arrangements has higher energy savings compared to the other schemes. The highest savings occur when there is a high concentration of the middle component. For feed composition (0.15 0.7 0.15) both the integrated prefractionator arrangements have savings of 63.1 %, compared to the best of the direct or indirect non- integrated sequence. In terms of energy the best of the other integrated schemes is a direct split arrangement (with forward or backward integration), which has 37.7 % savings. Table 1. Comparison of energy savings (Vmin) of different systems (compared to the best of the non-integrated direct or indirect sequence), sharp split: propane-butane-pentane. ZF

[1/3 1/3 1/3] [0.7 0.15 0.15] [0.10.45 0.45] [0.15 0.7 0.15] [0.45 0.10.45] [0.15 0.15 0.7] [0.45 0.45 0.1]

DSF (%) 45.5 19.8 32.1 37.5 27.6 32.5 42.0

DSB (%) 45.5 19.8 32.1 37.5 27.6 32.5 42.0

DSF- direct split forward integrated, ISF - indirect split forward integrated, PF - prefractionator forward integrated.

ISF (%) 28.6 20.1 25.0 28.4 29.2 21.2 29.0

ISB (%) 28.6 30.2 25.0 28.4 30.0 21.2 29.0

PF (%) 58.11 25.6 Sin 63.1 34.1 46.7 54.7

PB(%) 59.1 41.6

Sin 63.1 43.7 46.7 58.1

Petlyuk (%) 28.6 19.85 25.0 28.4 27.6 21.2 29.0

DSB - direct split backward integrated ISB - indirect split backward integrated PB - prefractionator backward integ rated

3. Self-Optimizing Control The objective of the study is to implement a simple "optimal" control scheme for the integrated prefractionator arrangement by finding and controlling the variables in the system that will directly ensure optimal economic operation. Then, when there are disturbances in the system, there is no need to re-optimize. The self-optimizing control procedure (Skogestad, 2000) consists of six steps: 1) a degree of freedom (DOF) analysis, 2) definition of cost function and constrains, 3) identification of the most important disturbances, 4) optimization, 5) identification of candidate controlled variables and 6) evaluation of loss with constant setpoints for the alternative sets of controlled variables. The first important step in this systematic procedure is to analyse the number of degrees of freedom (DOF) for the system. For the integrated prefractionator arrangement there are eleven DOF, when assuming a fixed feedrate. These are: the boilup in the HP column, the condensation rate in the HP column, reflux, distillate and bottom flowrate from both columns, sidestream flowrate in the LP column, boilup in the LP column and condensation rate in the LP column (see Figure 1).

411 For this distillation system there are four holdups in the reboilers and condensers that have to be stabilised, but these have no steady-state effects and therefore no effects on the cost function. This then leaves seven degrees of freedom for optimization. In the formulation of the objective function there are two 'conflicting' elements: to produce as much valuable product as possible, but using as little energy as possible. For a given feed, the cost function is defined as the amount of propane, butane and pentane from the LP column (at 0.99 mol% or more) multiplied by the relevant product prices, minus the cost of boilup: J = PD^LP

+ Ps SLP + PBBLP

- PQ QHP

(2)

where po, Ps» and pe are the prices of the propane, butane and pentane products, respectively and pq is the price of boilup. In this study all the products are assumed to have the same value (po = Ps = PB = p)Having defined the objectives, the system constraints must be defined. In addition to requiring positive flows, the following seven constraints have been specified: • The pressure in the LP column should be greater than or equal to 1 bar. • The pressure in the HP column should be less than 15 bar. • The reboiler duty in the LP column (QB,LP) ^ust equal the condenser duty in the HP column (QcHp) (equality constraint). • The product purities in the distillate (XA,D)» side (XB,S) and bottom stream (XC,B) should be above or equal to 99 mol%. • The area in the combined reboiler/condenser should be less than or equal to AmaxIn practice this can be implemented by allowing the area to vary by using a bypass. The optimization problem can then be formulated as: min (-Jx(x,u,d)), subject to: gi(x,u,d) = 0 (model equations) and g2(x,u,d) < 0 (operational constraints). Here; x are state variables, u are independent variables that can be affected (DOF for optimization) and d are independent variables that can not be affected (disturbances). Then the optimal operating point for the system with no disturbances is found by solving the optimization problem. This gives the optimal steady state values for all the variables in the system. Then the optimization is repeated for the various disturbances. The most important disturbance that has been considered is variations in the feed flow of ± 20 % and variations in feed compositions. From this optimization the active constraints of the system is found. When a variable is at a constraint then active constraint control is implemented. For this system we normally find that the three product compositions, the pressure in the LP column and the area of the exchanger are active constraints. This then leaves us with one unconstrained degree of freedom for which a control variable has to be selected. However, there may be cases when the above constraints are not active. Take, for instance, a case when there are changes to the feed composition, such that the condensation in the HP column is higher than the energy requirements of the LP column. In terms of Figure 2 this means that the minimum vapour flowrate curve for the prefractionator will lie above the curve for the main column, for all recoveries of the middle component. In order to balance the columns it may then be optimal to overpurify the least valuable product in the main column, thus one purity constraint is no longer

412 active. Another possible operation is that the prefractionator no longer performs a sharp A/C split and the light component (A) will appear in the bottom stream in order to reduce the prefractionator duty. It is therefore important for the column operation and control system to study the feed composition and the effects of expected disturbances. If the condensation in the prefractionator is less than the boilup in the main column this can result in the purity requirements of the LP column not being met, or that we get pure A at the top, or pure C at the bottom of the prefractionator. Another factor that can change the active constraints is the price of the products. When the prices are the same it is most profitable to produce each product at the minimum purity specification. However, if the price of one product is higher then the others then the products with the lower prices may be overpurified in order to produce as much as possible of the high value product. For the unconstrained degree of freedom the suggested control variables tested were one of the following: boilup in the HP column, fixed boilup to feedrate ratio (QB/F), the pressure in the HP column, reflux ratio in the HP column, fixed reflux to feedrate ratio, distillate flow in HP column, bottom flowrate in HP column, temperatures in the HP column, temperatures in the LP column, distillate composition in the HP column and bottom composition in HP column.

4. Conclusions The method of self-optimizing control is applied to a heat integrated prefractionator arrangement. This system has a total of eleven degrees of freedom with six DOF available for optimization when variables with no-steady state effects have been excluded and the duties of the two columns are matched. From the optimization it is found that there is one degree of freedom left for which there is not an obvious choice of control variable. The method of self- optimizing control will be used to find a suitable control variable that will keep the system close to optimum when there are disturbances.

5. References Bildea, C.S., Dimian, A.C., 1999, Interaction between design and control of a heatintegrated distillation system with prefractionator, Tans IChemE, Vol. 77, Part A, 597-608. Cheng, H.C., Luyben, W., 1985, Heat-integrated distillation columns for ternary separations, Ind. Eng. Chem. Process Des. Dev., 24, 707-713. Ding, S.S., Luyben, W., 1990, Control of a heat-integrated complex distillation configuration, Ind. Eng. Chem. Res., 29, 1240-1249. King, C.J., 1980, Separation Processes, McGraw-Hill Book Co. Lenhoff A.M., Morari, M., 1982, Design of resilient processing plants - I: Process design under consideration of dynamic aspects. Chemical Engineering Science, Vol. 37, No.2,245-258. Skogestad, S., 2000, Plantwide control: the search for the self-optimizing control structure, J. Proc. Control, Vol. 10,487-507.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

413

A Holistic Framework for Supply Chain Management A. Espuna^, M.T. Rodrigues^, L. Gimeno^ and L. Puigjaner^ ^ Departament d' Enginyeria Quimica, Universitat Politecnica de Catalunya, ETSEIB, Avda. Diagonal 647, pab. G-2, E-08028 Barcelona, Spain, email:[email protected] ^ Departments of Electrical and Chemical Engineering, State University of Campinas, UNICAMP C.P. 6101, 13083 Campinas S.P, Brazil, email:[email protected]

Abstract A new approach to Supply Chain Management (SCM) is proposed that considers different structures conceived as module components of a holistic framework. In this way, decision support is supplied at different levels and for different functionality. Thus, the system may be also used for multi-objective assistance to decision making, while systematically considering the time and other intrinsic constraints associated to the structure of the supply chain. This approach is applicable to the different supply chain layers, from the individual single sites to the global Supply Chain optimisation, including multi-site (single company) competitive strategic decisions, or the independent management of a similar objective (i.e. benefits, client satisfaction, etc.) for different companies.

1. Introduction Although the trend towards optimum management of single manufacturing sites has been driven by de integration of aggregate planning and detailed scheduling (Erengug et al., 1999), the consideration of multi-site manufacturing networks and their co-operative supply chain systems requires a revised perspective and complementary decision making structures. A number of approaches have been presented in order to address the supply chain issue (Arntzen et al., 1995; Vidal et al., 1997; Romberg, 1998). An important conclusion is that within all these approaches, at least one of the following is not addressed properly: (i) the SCM systems do not take into advantage of the modern computing architectures (e.g. open systems) available nowadays (ii) the planning and scheduling problems are partially tackled (iii) they do not suit for many manufacturing technologies and (iv) they do not address the whole multi-enterprise supply chain allowing individual manufacturing components to dynamically connect and adapt according to market changes and opportunities. More specifically, the intrinsic dynamics and complexity of the supply chain systems, the special characteristics of the different manufacturing networks and the existence of other considerations (e.g. environment) which must be taken into account, are not adequately covered by current approaches. The proposed approach in this work includes different structures that are conceived as module components of a holistic framework. In this way, decision support is supplied at different levels and for different functionalities (general manager, marketing.

414 production, distribution, sales, etc.)- The planning problem is modeled following the three-phase procedure described below.

2. Solution Approach Firstly, a sequential approach in phases is proposed for the planning problem: The goal of the first phase is to obtain the more adequate supply chain configuration for the specific demand considered. The results of this phase include decisions about which sites will be used, their run times and the transportation needs between sites, without proceeding to time allocation. All this information is dependent on production rates initially supplied by site managers, which may not be accurate enough, since they will depend on the final work load allocation made in a competitive way. Thus, these production rates should be negotiated in view of the initial and subsequent planning results and their consequences when low level site-specific constraints are applied. The second phase proceeds to time allocation of sites production and transportation in order to minimize completion times of final products with acceptable costs for the whole SC as far as for partners. For that it utilizes run times already determined in phase one as bounds in a multi-agent environment. Finally, a third phase would deal with detailed sites planning. In this way the main characteristic of the sequential approach proposed is to deal with the supply chain configuration problem considering only the required run times to ftilfill production needs and without dealing with production and transportation time allocation. Each one of these three phases is solving one part of a global problem, and imposing constraints to the next one, so no guarantee of global optimality can be provided. In order to deal with these problems, additional procedures have to be developed in order to identify constraints relaxation at each phase that eventually may lead to global improvements. This information should be back propagated in the form of modifications of the previous phase scenario. Since the third phase of the proposed procedure has been already object of extensive research, only phases 1 and 2 will be addressed in the next sections.

3. First Phase This phase selects sites to be utilized and determines runtimes for production sites, throughput at storage sites and quantities transported between sites. The cost function minimized involves: i) production costs as a function of runtimes or quantities produced, ii) transportation costs between sites which depend on quantities transported of each state and iii) manipulation costs at storage sites as a function of the manipulated mass of each state (throughput). Production sites are characterized by states production and consumption rates in each possible site operating mode. Storage sites can also operate under different operating modes that determine which states can be stored. During the time horizon each site can utilize only one mode of operation. Once the solver has determined selected sites, runtimes and quantities transported it is possible to build a Gantt chart in two limit situations: i) "continuous" transportation of sites output products, that is transportation can occur immediately after sites start times and ii) transportation only after total production. Any real situation will lie between

415 these two limits. The following sets, parameters and variables are utilized. / s m Pim^s Ri^rn.s Ds Iriis, Outis linkiia ^opim,s ^ocims stoTi istOis t(Um) bint(Um) sto(i,m,s) qt(ii,i2,s )

sites (production and storage sites) states sites operating modes production rate of state s at production site / operating under mode m consumption rate of state s at production site / with mode m total external demand (kg) of state s = true if site / consumes (produces) state s - true if site /; can supply some intermediate state to site i2 = true if site / under mode m produces state s = true if site i under mode m consumes state s = true if site / is a storage site; false if site / is a producer site initial storage of state s at site / (continuous) run time of production site / under mode m (binary) = 1 if producer or storage site / utilizes mode m (continuous) mass throughput of state s at storage site / in mode m (continuous) mass (kg) of state s transported from site /; to site (2

Demand for end products: demand can be external and internal as these products can be also intermediates; sites run time and/or storage sites throughput must allow to fulfill these demand on end products (only conditions false are signaled explicitly). S

Pims'^(i^^)+

X

[sto(i,m,s) + istOi^]>D^+

Outi,,mpi^, stori=f

^

qt{Ui2^s) [1]

/,/2 ,m Outi^Irii^,

i,m Outi, stori ^Pims

Induced demand: intermediates and raw materials needs must be fulfilled through transportation. Equations 2a and 2b are utilized for producer or storage sites respectively. X

^K^'i'^'2"^)= X

/i

m

\ms''^^h^^)'^

X

Qt(ihh^^)=

/j

linki^2

X

sto(i2,m,s)[2ab]

m

linki^2

Transportation: limited by production or storage. Equations 3a and 3b are utilized for producer or storage sites respectively. X

qt(iiJ2^s)<

^

1*2

m

^%s linki^i^

^Piims

Pi^^^^t(ii,m);

^ (2 ^2S linki^^^

qt(iiJ2^s)<

^ m ^Piims

Binary variables definition: Producer and storage sites respectively

sto(^,m,s)[3ab] +''^^15

416 M ^bint(im) > t{i,m)

M ^bint(i,m) >

stored(i,m,s)

bint(i,m) < t{i,m)

bmt(i,m) < stored {i,m,s)

[4a,b]

Sites operation mode: each site operates under only one mode during the planning horizon. ^bint(i,m)
[5]

m

The kind of results obtained is illustrated with the example shown in Figures la,b. Cost minimization leads to a makespan of 251 h with a cost value of 90000. Accepting a degradation until 120000 makespan becomes 99 h mainly through the utilization of external supply of one of the final products through site S47 (which has a higher cost, thus not being utilized when cost is minimized). The above formulation does not consider final products demand due dates. Cost minimization can lead to unacceptable run times since the implied completion times can prevent fulfilling due dates. If completion time estimates are not acceptable other supply chain configurations, utilizing alternative suppliers and/or producer sites can be preferable in spite of higher production or transportation costs. Instead of combining these two aspects in a single cost function, it seems preferable to allow the user to enter some acceptable cost degradation and minimize a cost function that estimates completion times. This reformulation includes all the previous equations with objective transformed into a constraint plus conditions below modeling completion times. CT(i2) > t(i2, m) + delta{i2, ^i, s) delta(i2,/i, s) - CT(ii) - transp contr - manip contr > -M [1 - wt{ii, ^2 )] delta(i2, ii, s) - CT(ii) - transp contr - manip contr < M [1 - wt{ii, i2 )] delta{i2 Ji,s)<M

"^ wt(ii,/2)

For a site i2 its completion time must be greater than its runtime plus any contribution from previous sites sending materials to it. The contribution of any site /; in turn is given by its completion time plus transportation and manipulation times. Detailed model is presented by Gimeno and Rodrigues (2002). Accepting some cost degradation, the obtained result is shown in Figure lb with a smaller time to fulfill demand. Again, the new selected structure is also indicated.

4. Second Phase In this phase the objective is to allocate in time production and transportation in order to fulfill a specific demand of end products characterized by quantities and due dates, with acceptable costs for the whole SC as far as for partners in the SC network. This multiobjective situation is addressed through a multi-agent implementation. Every single actor in the Supply Chain may be modeled through an individual autonomous agent, capable to make any local decisions affecting the links between this actor and the rest of

417 the system (SC). Active SC structure, production and transport allocation, and best and worst completion times estimates from the first phase are used to constrain the search effort. ••lg|»l

JM

M=g—1 Figure la. Supply Chain structure for minimum cost(90000) at left and with cost degradation (120000) at right. Ihou^pil cf skiayBsilES

9f7

916

r^ ^

^

^

^

•

^

"

•

^

913

911/914

\ 2D0O

4000

\ eooo

800O

Figure lb. Runtimes for selected productions sites and throughput for selected storage sites. White bars correspond to the non-degraded situation, black to cost degradation. Then, the proposed approach is based on an evolutionary procedure, where each agent is allowed to reconsider its decisions while the rest of agents also evolve. This leads to an continuous changing scenario for each agent that, for one part, might not converge to a final state and, for another part, in the case of convergence, will not necessarily lead to a desired global optimum (if it can be even defined). In order to ensure the evolution of the system towards a compromise between individual agent objectives and global objectives, two additional controlling agents have been

418 introduced: a coordinating agent and a smoothing agent. The coordinating agent calculates the range of global costs (upper and lower bounds) looking at the SC as a global supplier that should accomplish different internal constraints, defined through aggregation of the individual characteristics of each site. This may lead to a significant reduction in the decision making range of the individual agents. The smoothing agent enforces convergence in a similar way, but based on the assessment of the evolution of the system.

5. Conclusions A sequential approach for Supply Chain Management has been presented. Structurally, the different phases are conceived as module components of a holistic framework. In this way, decision support is supplied at different levels and for different functionalities (general manager, marketing, production, distribution, sales, etc.). Additional support is provided by modules contemplating financial issues (cash-flow management, risk assessment) forecasting facilities, etc., and the use of different optimisation tools. Thus, the system may be also used for multi-objective assistance to decision making, while systematically considering the time and other intrinsic constraints associated to the structure of the supply chain. This approach is applicable to global Supply Chain optimisation, including multi-site (single company) competitive strategic decisions, or the independent management of a similar objective (i.e. benefits, client satisfaction, etc.) for different companies. The proposed holistic approach has been devised for this type of integration/negotiation in a multi-objective environment allowing different modules to interact. It is perceived as a configurable modular system provided with interfaces that strictly adheres to consolidated and emerging standards (ISA, CO, ...) Thus, software transparency and interoperability is guaranteed allowing to easy customisation and agile reusability of existing software.

6. References Arntzen, B.C., Brown, CO., Harrison, T.P., Trafton, L.L. 1995. Global supply chain management at digital equipment corporation, Interfaces 25, 69-93. ErengU9 S.S., Simpson, N.C., Vackaria, A.J., 1999, Integrated production/distribution planning in supply chains: An invited review. European Journal of Operational Research, 115. Gimeno L., Rodrigues, M.T., 2002, Sequential Approach to Production Planning in Multisite Environments, 15th IFAC World Congress, Barcelona, Spain. Homburg, C , 1998, Hierarchical multi-objective decision making, European Journal of Operational Research, 105, 155-161. Mele, F.D., Espuna, A., Puigjaner, L. 2(K)2, Discrete Event Simulation for Supply Chain Management in AIChE Annual Meeting, Nov. 3-8, Indianapolis, USA (Accepted). Vidal, C.J., Goetschalckx, M. 1997, Strategic production-distribution models: A critical review with emphasis on global supply chain models, European Journal of Operational Research, 98, 1-18.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

419

Management of Financial and Consumer Satisfaction Risks in Supply Chain Design G. Guillen(-H-), F. D. Mele(++), M. Bagajewicz(+), A. Espuna(++), and L. Puigjaner(++)(#) (-H-)Universidad Politecnica de Catalunya, Chemical Engineering Department, ETSEIB, Diagonal 647, 08028 Barcelona, Spain; (+) University of Oklahoma. School of Chemical Engineering and Materials Science, 100 E. Boyd St., T-335, Norman, OK 73019, USA. On sabbatical leave at ETSEIB; (#) Corresponding author.

Abstract In this article the design of a supply chain consisting of several production plants, warehouses and distribution centers is considered introducing uncertainty and using a two stage stochastic model. The model takes into account profit over the time horizon and considers consumer satisfaction. Financial risk and the risk of not meeting the consumer satisfaction are considered and managed at the design stage. The result of the model is a set of pareto optimal curves that can be used for decision making.

1. Introduction Supply Chains (SC), which started to be studied in the early 90s, include several decision variables: strategic, tactical and operational. Strategic decisions include the supply chain design, which consists of the determination of the optimal configuration of an entire SC network: number, location and capacity of plants, warehouses and distribution centers to be set up, the transportation links and the flows and production rates of materials. In this work, we present a two-stage stochastic model for SC design with management of financial and consumer satisfaction risks. The model is presented next.

2. Deterministic Model This model considers several production plants, warehouses and distribution centers. It is similar to previous SC models (Tsiakis et al., 2001). However, some modifications have been introduced. The NPV instead of the cost is used as objective function. In addition, the capacities of the plants/warehouses are considered in the determination of the capital investment and in the calculation of the operational associated costs. 2.1. Constraints • Mass balance: the steady state is supposed through the SC

420 ^Pj,t

(1)

j

(2)

^P.j.t i

k

Y^^pjia^ Demandp,^

•

^

(3)

pXt

Capacity constraints: there are maximum and minimum capacity constraints for the plants and warehouses of the SC

Zll^Pur^pi

Vi,t

(4)

Cap.^ < Cap.

\fi,t

(5)

Capf < 'Caf, < Cap^

V/

(6)

p

= Cap,

J

2^2^^pjh 'Ppj 2.-£-i

SF.-= Capj,

(7)

\/jj

Cap J, < CapJ

^j,t

(8)

Y^B.^-Capj^=C^.

^J,t

(9)

2.2. Objective function The objective function is to maximize the NPV and the consumer satisfaction MaxNPV MaxTCSat j^py ^ y CashFlow,

(10) (11)

Cashflow, = -CI = -{FCI+ WC)

t=\

(12)

Cashflow^ = - Re venues, - DE, - IE, - Taxes,

t -2...T

(13)

Cashflow^ = - Re venues, - DE, - IE, - Taxes, +WC

t=T

(14)

FCI = Y,(FClt'Aj

+C^rri)

+ ZZ^C^Jc-^jc

'•

J

(1^)

c

revenues, = ^Salesp, • price^

"^t^p

(16)

p

Sales ^,=Y.Qp>. IE.=Y,i.IEfA,+C^rili)

+ YI.^Ejc-Bic

"^t'P

(1"^)

V<

(18)

DE. =IZe„, -vc, + I E I y , . -/^c,, + I I I X , , .rc,, + i

p

j

p

k

j

j

p

P

k

k

P

^j

I

j

(19)

421 Taxes^ = {revenues^ - Depreciation, )-tr 1 ^ Sales ^, Hp ^ Demandp, TCSat = -TCSat,

\/t

Vr

(20) (21) ^^^^

3. Stochastic Model The stochastic problem is characterised by two essential features: the uncertainty in the problem data and the sequence of decisions. In our case, the demand is considered as a random variable with a certain probability distribution. The binary variables associated to the opening of a plant/warehouse as well as the continuous variables that represent the capacity of plants/warehouses are considered as first stage decisions. The fluxes of materials and the sales of products are taken as second stage or recourse variables. The objective functions are therefore the expected net present value and the expected consumer satisfaction.

4. Financial and Consumer Satisfaction Risk The financial risk associated with a design project under uncertainty is defined as the probability of not meeting a certain target profit (Barbaro and Bagajewicz, 2002a,b). In this work, the risk of not meeting consumer satisfaction is defined in a similar way, that is, as the probability of not meeting a certain target consumer satisfaction. A composite risk is defined using two aspiration levels or targets (a profit Q. and a consumer satisfaction Q') as follows: Crisk (x, Q,Q') = P(FO(x)< Q A FO \iC)< Q')

(23)

In the case where the probabilities are independent, this risk results in the product of both risks. This is the assumption used in this article. Risk management Three different objectives: NPV, consumer satisfaction and compounded risk are considered. If one uses a utility function, the compounded risk can be manipulated by changing the weights of the objectives for different aspiration levels Q and Q.\ In order to avoid the use of binary variables the concept of downside risk (Drisk(x,Q)), introduced by Eppen et al. (1989), is used, as explained by Barbaro and Bagajewicz (2002a,b).

5. Case Study We considered a problem with two possible production plants locations, three warehouses and four markets. The aim of the problem is to determine the optimal SC configuration that

422 maximises the NPV of the investment while maximise at the same time the consumer satisfaction. Figure 1 shows the Pareto curve for the deterministic case. This curve was obtained maximizing the NPV and constraining the consumer satisfaction. The curve shows that only above a 66% consumer satisfaction level some trade off between the objectives exists. Below 66% of requested consumer satisfaction the solution is the same as that of the model without constraining consumer satisfaction and therefore all the pareto solutions accumulate at the end point on the left. Figure 2 shows the same curve for the stochastic model. Figures 3 and 4 show the corresponding consumer satisfaction andfinancialrisk curves of the pareto solutions of the multiobjective stochastic problem. Unsupported solutions are suspected to exist, but this could also be the effect of the small number of scenarios (100) used. In future work this matter will be resolved.

Consumer Satisfaction (%)

Figure 1. Deterministic Pareto Curve.

Consumer Satisfactiwi (%)

Figure 2. Stochastic Pareto Curve.

Figures 4 depicts the financial risk curves associated with each point of the Pareto Optimal curve. For example the curve with no restriction on the consumer satisfaction (SP_E(CSAT)>0) is the one with largest expected NPV. As the consumer satisfaction is constrained the curves move to the left, thus reducing the expected net present value. The shape of the curves, however, remains fairly constant. The corresponding curves of consumer satisfaction risks are shown in Figure 3. The curves move to the right as the expected net present value is reduced. The shape in this case becomes steeper. To reduce the risk associated to the consumer satisfaction the design was modified by limiting the downside risk at certain targets. In figure 5 the different risk curves associated to the penaUsation of consumer satisfaction risk at 69%, 72% and 75%. When the risk is limited, the expected profit (figure 6) is reduced, that is the financial risk curves move to the left. One important thing to notice is that the consumer satisfaction risk curves do not intersect. This is because the consumer satisfaction is not maximised, but the expected net present value is. In addition, the resulting designs present a higher expected consumer satisfaction. Figure 7 shows the composite risk curves (the consumer satisfaction is not

423 constrained). Figure 8 shows one composite risk pareto curve and another composite risk curve where the risk is constrained at a target of 75%. . 1

J

.

.SP_E0

i"

SP_E(CSAT)>80

f

SP_E(CSAT>>95

1

/

SP E(CSAT>>=100»

1 // ''

r

,.y f

.'

/

/ 2.50

2.75

3.00

Consumer Satisfactbn (%)

Figure 3. Consumer Sat Pareto Risk Curves.

3.25 3.50 NPV(niiIL of euros)

3.75

4.00

Figure 4. NPVPareto Risk Curves.

100%^

y>Yj::

80% 60% -

i

•o!

»!

If/ 1 j* '1 ^

/ y *

.E(CSAT)>0

""

/J/ -

40% -

-n=69 -n-72

20%

0% 2.50

2.75

3.00

3.50

3.75

NPV (irin. of euros)

Consumer Satisfaction (%)

Figure 5. Consumer Sat. Risk Curves.

3.25

• •n=75

Figure 6. NPV Risk Curves.

• • • '

•

/

H><

^><""'>^ Cmvmm

Figure 7. Composite Risk Pareto Curves.

^

•j^*-'''^"'*M

25

Figure 8. Composite Risk Curves.

4.00

424

6. Conclusions A definition of composite risk is presented and several pareto optimal curves have been obtained. A stochastic programming approach was used to manage financial and consumer satisfaction risks in the design of supply chains.

7. Nomenclature p products i plants j warehouses k markets c discrete types t interval times CVpi: Variable cost ofp at / CHpj : Handling cost of/? aty CTif. Cost of transport between / andy CTjk'. Cost of transport betweeny and k ir: Interest rate tr: Taxes rate n: Usefiil plant life Hp : Number of products FCf^i, Yi: Fixed cost coefficients at / lE^i, rji'. Indirect expenses coefficients at / lEjc'. Indirect expenses aty of c CSatt: Consumer satisfaction in t TCSat: Total consumer satisfaction

Ai'. Binary variable (Ai =1 if i is opened, Aj =0 otherwise) Bjc'. Binary variable (Bic =1 if j of c is opened, Bjc =0 otherwise). cXpf Production capacity factor of/? at / J3pj: Handling capacity factor of/? aty CO/. Inventory cost aty X/. Turnover inventory rate aty SFji Security design factor ofy Demandpkt'. Demand of/? atkint Pricep. Price of p Capjc'. Capacity ofy of c Capit'. Capacity of/ in t Capjt: Capacity ofy in t Capf. Capacity of plant / Cap/. Capacity of warehouse/' Qpit'. Amount of/? fabricated at / in / Xpijt'. Amount of/? transported from / toy" in t Ypjkt: Amount of/? transportedfromyto A: in ^

8. References Barbaro, A.F. and Bagajewicz, M. 2002a. Managing Financial Risk in Planning under Uncertainty, Part I: Theory, AIChE Journal, Submitted. Barbaro, A.F. and Bagajewicz, M. 2002b. Managing Financial Risk in Planning under Uncertainty, Part II: Applications, AIChE Journal, Submitted. Tsiakis, P., Shah, N. and Pantelides, C.C. 2001; Design of Multi-echelon Supply Chain Networks under Demand Uncertainty. Ind. Eng. Chem. Res. 40, 3585-3604. Simchi-Levi, D.; Kamisky, P.; Simchi-Levi, E., 2000; Designing and Managing the Supply Chain. Concepts, Strategies, and Case Studies. Irwin McGraw-Hill.

9. Acknowledgements Financial support received from European Community (project GROWTH Contract GlRDT-CT-2000-00318) is fully appreciated. Support from the Ministry of Education of Spain for the sabbatical stay of Dr. Bagajewicz is also acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

425

Operator Training and Operator Support using Multiphase Pipeline Models and Dynamic Process Simulation: Sub-Sea Production and On-Shore Processing Morten Hyllseth & David Cameron Fantoft Prosess AS, PO Box 306, NO-1301 Sandvika, Norway Kjetil Havre Scandpower Petroleum Technology AS, Postboks 3, NO-2027 Kjeller, Norway

Abstract Recent advances in sub-sea oil production technology have changed the way off shore oil fields are developed. Many new field developments use sub-sea production facilities and pipe a multiphase mixture of gas, oil and water back to an existing platform or onshore facilities for separation and processing. These pipelines can be very long (up to 100km long) and complex - with complicated branching and crossovers. Dynamic features of multiphase flow, such as slugging, can cause disturbances in the processing system. Operators need help in handling these. Model-based estimates of pressure, holdup and flow along the pipeline are thus needed. An integrated system for operator support and operator training is being delivered for a large sub-sea gas field in the Middle East. It builds upon a dynamic process simulator (D-SPICE) and a multiphase flow simulator (OLGA 2000). The simulator incorporates methods for simulating multiphase flow in closed-loop networks and tracking of hydrate inhibitors. The system is tuned to measured process performance. The system also supports predictive simulation facilities. The paper provides an industrial case study of computer-aided process engineering in a technically challenging environment. Novel methods for multiphase modelling in closed loops, real-time model system design and model tuning are presented.

1. Introduction and Objectives: Sub-Sea Processing and Transport Oil production technology has changed drastically in recent years. Whereas once an oil or gas field would be built with a platform and on-site processing of fluids, now fields are being developed with sub-sea production equipment and long multiphase pipelines to existing platforms or shore facilities. These facilities have lower capital and operating costs than conventional platforms, and enable the development of what would be otherwise marginal fields. These new developments give rise to interesting operational challenges, most of which are related to the multiphase transport of oil, gas and water to the processing facilities. A mixture of oil, gas and water in a pipeline flows in a highly non-linear way. Depending on the topography of the pipeline and the total flow rate through the line, large accumulations, or slugs of liquid can be produced. For this reason, a slug catcher a separator with large total volume and small normal operating volume - is used to provide enough inventory to handle a slug. However, if a pipeline is long, it is likely that the liquid volume in the pipeline far exceeds the economically defensible volume of the slug catcher. The process must therefore be operated in such a manner unacceptable amount of slug flow is avoided.

426

Export Gas

Onshore Facilities Condensate

Produced Water

Figure 1. A simplified schematic of the production system. The glycol recovery and distribution system is not shown. Operation of complex sub-sea networks with long tie-backs are not straightforward. Consider the process shown in Figure 1. Throughput for the pipelines is controlled using the choke valves on the wells. Additional control can be obtained by manipulating pressure in the slug catcher on shore. Note that the control elements, the choke valves, are installed 100km from the variable to be controlled, namely slug catcher level. Deadtimes are dominant, and a model is needed to predict the effect of a change in choke position on onshore behaviour. This paper describes the application of multiphase dynamic modelling to the monitoring and control of the process shown in Figure 1. This process is a gas development in the Middle East. The system that is delivered simulates process behaviour to provide estimates of local flow rate and inventory in the transport pipelines. Predictive simulations are used to identify actions that will cause slug problems.

2. Multiphase Modelling The core of the monitoring system is a multiphase model of the transport pipelines. This uses an widely-accepted simulation program called OLGA 2000. The principles behind this program have been described in detail elsewhere (Bendiksen, 1991, Scandpower 2001).

3. System Modelling and System Integration 3.1. Overview The system model consists of two elements: (1) a D-SPICE model of on-shore facilities and sub-sea utilities and (2) an OLGA 2000 model of the sub-sea production wells and pipelines. These two models are fully integrated and share a common, D-SPICE, user interface. 3.2. OLGA modelling The OLGA model consists of 202 km of piping, a reservoir inflow model for eight wells 22 valves, the pipeline surroundings and sources for methanol and glycol injection.

427 3.2.1. Closed-loop modelling The structure of the transport system posed a technical challenge. Multiphase flow models have been developed for merging flow networks, where the nominal flow is in one direction from the branches of the tree (the production wells) to the root of the tree (the land facilities). However in this system, the dual export line and crossover arrangement impose a diverging flow network. The closed multiphase flow loops imposed by the parallel export pipelines in the Scarab/Saffron fields required expanding the multiphase flow network solver of OLGA to diverging network. 3.2.2. Glycol tracking and methanol distribution It is possible that the natural gas can react with water to form solid hydrates in the pipeline. If this happens the pipe will be blocked with solids. For this reason, hydrate inhibitors such as glycol or methanol, are injected into the sub-sea system. The process described here uses ethylene glycol (MEG) as a primary inhibitor and methanol as a backup inhibitor. MEG is recovered from the system in the onshore facilities, but methanol is discharged with the produced water. Both the MEG and the methanol systems are poorly instrumented. The total flow rate to the entire system is measured, but there is no measurement of glycol or methanol at each injection point. We therefore developed a hydraulic model of the glycol and methanol distribution networks and interfaced this with the onshore facilities for MEG recovery and the OLGA model. MEG tracking has been implemented in OLGA. MEG is included as a separate component in the aqueous phase in the pipeline. The MEG concentration in the aqueous phase can therefore be monitored to ensure that the pipeline system stays outside the hydrate formation region. 3.3. Modelling of onshore facilities A model of onshore facilities is needed for the following reasons: (1) the pressure control in the onshore facilities influences the behaviour of the transport pipelines and (2) the transport pipelines and wells must be operated so that constraints in the onshore facilities, such as vessel liquid capacities, system pressures and unit throughputs, are not violated. A simplified model was built of the onshore facilities. This model represents the main pieces of onshore equipment and represents all important throughput and capacity constraints. Constraints modelled are slug catcher level, slug catcher pressure, condensate separator level, pressure in condensate separators, product gas demand, coalescer interface level, level in storage tanks for condensate, produced water, MEG and the unseparated MEG-water mixture and the capacity in MEG separation and condensate stabilisation. These constraints are modelled and monitored. An alarm is raised if the calculated value of these constraints goes out of its normal range or is predicted to do so in the near future. The alarming on predicted values is done through the regular execution of a look-ahead simulation. 3.4. Look-ahead simulations One of the most valuable features of the system is its ability to run predictive simulations on a routine basis. These look-ahead simulations are run using a copy of the process model. This model is initialised with a snapshot of the current conditions in the real-time model. It is then run, as fast as possible, for a specified time into the future. Key variables in the model are monitored for alarm conditions. If an alarm is raised it is sent to a special look-ahead alarms list and is reported to the operator. Future operator actions can be simulated by using a script file that executes the required actions on the

428 look-ahead model. This script is written in D-SPICE's proprietary scripting language, called Model Control Language (MCL). The predictive behaviour of key variables can be shown through a predictive trend display, as shown below. Historical data is shown to the left of the vertical cursor, and predicted data to the right.

tAAtMM Q««rP«»«i»

> f{ iPi»x|"''«l''i's«"l Toast P^ISTsSir] ii jj^l a^xj idF\ M

2a8f| ^i\ ^ i ^f\ > tj iicj rasj »ci incj ^tii j&f{ wcj j s | wcj m4 MIE^

^ ^

3

11 m

(»R

|B#il^«j^'' w:»"

Figure 2. A screen dump of the user interface showing the look-ahead trend and lookahead simulator control panel. This example shows a very important monitoring variable, namely the level in the slug catcher. It is all too easy to operate the pipeline system so that liquid accumulates in the export pipelines. If this liquid comes out rapidly, as a slug, it is possible to overfill the slug catcher and shut down the onshore processing. The look-ahead simulator allows operators to predict whether an sub-sea operation, such as bringing another well on stream, will give rise to problems some time later. It also enables them to evaluate alternative ways of avoiding problems. 3.5. System integration The system is integrated with the customer's process control and SCADA system. This is done using D-SPICE's DCS interfacing system. Since the client's control system supported the OLE for Process Control (OPC - http://www.opcfoundation.org) standard, we were able to use the standard D-SPICE OPC client interface without modification. Thus, an interface that we originally developed for an ABB control system was used successfully to communicate with a Yokogawa system. This is a radical improvement over the situation only a few years ago, where each control system

429 required a proprietary and expensive interface that often involved the purchase of extra control system hardware. In our opinion, OPC is a key enabling technology for applying computer-aided process engineering in real processes. For testing, we have replaced the control system with a copy of the model and an OPC server. This model simulates the process and allows the behaviour of the real-time system to be evaluated and tested.

Maintenance HMI Client

Operator HMI Client

Figure 3. System architecture for a typical multiphase process monitoring system. 3.6. Tuning Tuning is essential for the correct performance of the system. Thus, measurements of flow and pressure are used to adjust well parameters and pipe friction. Temperature measurements are used to adjust heat transfer coefficients. Single-loop tuning algorithms are used. A system of logic and data validation is used to ensure that bad measurements are not used.

4. Operator Interface and Operator Support Tools A custom operator interface was built for this system. This interface is used in parallel with the control system. It has a similar look and feel to the control system, but concentrates specifically on variables that are estimated by the model. The interface provides access to estimated quantities; measured quantities used in the model; trends of key variables, and alarms on present estimates and predicted values. All graphical elements are animated to enable process status to be seen at a glance.

5. Results At the time of writing the system had been successfully passed through factory acceptance testing (FAT). This means that the system had been demonstrated to be able to communicate with the control system and had been able to monitor the performance of a simulated process. The process is being installed in November 2002 and is expected

430 to be in use from early 2003. Operational experience will therefore be presented at the meeting. On the basis of the FAT, we expect that the system will be a necessary tool for operating the difficult sub-sea production system.

-Holdup 20 I n c h Nol [ f r a c t ] -Gas tlmr [UMSCFB] -Agueovs Pliase Hbldiqp [fract] 1 - £00 -

1

0 8 - 500 - 0 0 0 6 -

400 -

0 6

300 0 4 0

2 •

0 -J

200 •

0 4

100 " 0 2

0 "J

0

5000

10000 Blstajuce DnJ

15000

20000

Figure 4. An example of the user interface for one of the two export pipelines. The profile is seen by the operator and shows liquid hold-up (the highest curve, left-most axis, gas flow (next axis to the right, next highest curve) and aqueous phase holdup (left-most axis and lowest curve). The operator can see at a glance that there is a low gas flow rate, with the risk of slug formation.

6. Conclusions Novel multiphase technology has been coupled with dynamic process simulation, open control system interfaces and a custom user interface to provide a necessary tool for process operators. We hope to be able to report interesting experience and observations from the commissioning of the system.

7. References Bendiksen, K.H., et al, (1991), "The Dynamic Two-Fluid Model OLGA: Theory and Application", SPE Production Engineering, May 1991, 171-180. Cameron D.B., 0degaard, R.J. and Glende, E., (2001), "On-line Modelling in the petroleum industry: Successful applications and future perspectives", in: Gani, R, and Bay J0rgensen, S., (eds.), "European Symposiym on Computer Aided Process Engineering - 11", Elsevier, Amsterdam, 111-116. Scandpower Petroleum Technology AS, (2001), "OLGA 2000 User's Manual", Kjeller, Norway.

8. Acknowledgements This work was carried out by a team that, with the authors, included J0rgen 0degaard, Erik Glende, Johnny Nylund, Sverre J0rgensen, Gunnhild Baekken, Iris Andersen, Kersti Ekeland Bjurstr0m and Zheng Gang Xu. Their substantial contribution is acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Scierlce B.V. All rights reserved.

431

Unstable Behaviour of Plants with Recycle Anton A. Kiss, Costin S. Bildea*, Alexandre C. Dimian and Piet D. ledema University of Amsterdam, Nieuwe Achtergracht 166, 1018 WV, Amsterdam *Delft University of Technology, Julianalaan 136, 2628 BL Delft, The Netherlands

Abstract This article considers processes involving two reactants and two reactions. It is demonstrated that plantwide control relying on self-regulation results in regions of state multiplicity or unfeasibility, even if the stand-alone reactor has a unique, stable operating point. Moreover, when selectivity reasons require low per-pass conversion, instability is very likely.

1. Introduction In today's economically competitive environment, chemical plants must cope with large changes in production rate, product specification and feedstock quality. In addition, exploiting system's nonlinearity for an optimal design is a current practice. However, the combination of non-linearity, disturbances and design uncertainty might lead to undesired phenomena: jumps to a new low-performance operating point, oscillatory or even chaotic behaviour. State multiplicity and instability in CSTR, tubular reactor with axial dispersion or catalytic particle are classic problems in chemical reaction engineering. Other representative systems are heat-integrated reactors, binary, thermally coupled, azeotropic or reactive distillation. With very few exceptions, the non-linear studies considered stand-alone units. However, coupling stable units does not guarantee the stability of the resulting system. Instability could occur due to inability of the plantwide control system to manage the mass balance of the plant. For recycled reactants, the reactor must ensure that the entire amount fed in the process is transformed into products. Reactor - separation - recycle systems are self-regulating, if only one reactant is involved as in the case of A-^ P reaction. Control structures allowing floating recycle and relying on the selfregulating property work well, if the reactor is large enough (Larsson and Skogestad, 2000). If heat effects are considered, the recycle systems involving either CSTRs (Pushpavanam and Kienle, 2001) or PFRs (Bildea et ai, 2002) may exhibit state multiplicty and instability. These occur also in polymerization reactors (Kiss et al, 2002). When the reactor volume and the nominal conversion are small, the plant is very sensitive to disturbances. In this case, fixing the recycle and changing the reaction conditions (volume, temperature, pressure) results in better performance (Luyben et al, 1999). The above-cited studies considered the A -> P reaction that can seldom be found in real plants. In this article we consider processes involving two reactants and two reactions. We demonstrate that plantwide control relying on self-regulation leads to regions of state multiplicity or unfeasibility, even if the stand-alone reactor has a unique, stable operating point. Moreover, when selectivity reasons require low per-pass

432 conversion, instability is very likely. Due to space limitations, we restrict the discussion to liquid phase reactions, and wellmixed reactor (CSTR). The results are equally applicable to PFRs and gas-phase reactions. The analysis is based on dimensionless models. In general, f, and z^j are dimensionless flow rates and concentrations, respectively. Subscripts / and k define streams and components, respectively.

2. One Recycle Systems This section analyses the consecutive parallel reactions A + B->P A + P-^R taking place in an isothermal CSTR-Separator-Recycle system. Such chemistry is common, for example in butane - butene alkylation for iso-octane production, or reaction between ethylene oxide and alcohols. Usually, the intermediate product P is of interest. We present results for the case of adjacent reactants volatility, when the flowsheet has only one recycle {Figure 1). When both reactants are completely recycled, feasible operation is possible only if the ratio of reactants in the feed matches exactly the stoichiometry. For this reason, one reactant feed is on flow control (/A,O=1), while the feed flow rate of the second reactant (fB,o) is used to control its inventory in the process. We assume a good separation, in such a way that the product is pure. The reactants are completely recycled and the molar fraction of the product in the recycle stream is very low. The model includes reactor and separation equations, as well as the relation for the feed flow rate of second component imposed by the control structure (Eqs 1 to 8).

a=0.1 0.8 \ 0.6

0.5

/"'^^v,

1 A+B-*P A+P->R

0.4\

\

5

0.2-

^

^

^

^

^

1—1—1—1—I—I—1—,—1—1—1—1—•-

u -1

40

=

=

=

=

' -'• r ' ' ' ' 1 ' ' ' ' 1 Da 60 100

Figure 1. Control structure relying on Figure 2. Selectivity of product P for self- regulation for a one-recycle plant. different kinetics (a=k2/kj).

^ ^ ' (^A,2 • ^B,2 + ^ • ^A,2 • % 2 ) + / 2 * ^A.2 " / s ' ^A,3 = 1

(1)

/ B , 0 + / a • ^B,3 - {fl

(2)

' ^B,2 + ^ « • ^A,2 ' ^B.2 ) = ^

433

fl

' ^P,2 - ^ «

• (^A,2 • ^B,2 - ^

• ^A,2 * ^P,2 ) =

(3)

^

(4)

1+ / R - / 2 = 0

(5)

/22A,2-/3^A,3=0

(6)

/2^B,2 ~ / 3 ^ B , 3 ~ ^

(7)

^A,3 "^ ^3,3 "^ ^P,3 ~ ^ /R ~/3

(8)

~"/B,0~^

Two steady state solutions are possible. The selectivity of product P, 5P/A is given in Figure 2 as a function of Damlohler number. Figures 3 and 4 show the conversion of the key component, X^, for different values of the separation performance (zp^) and recycle flow rate (/R). All diagrams exhibit an unfeasibility region at low Damkohler values. When the Damkohler number exceeds the critical value corresponding to the turning point of the Da - XA diagram, two feasible steady states exist. The critical value Da" represents a limit point of the balance equations. Then, the following feasibility conditions (i.e. existence of steady states) can be derived: Da>

4(1^/R/

(9)

A higher recycle rate (Figure 3) shifts the limit point to lower conversion and Damkohler number values. As a result, the state multiplicity has a diminished practical importance for high recycle rates. However this might not be economically feasible due to the increased costs involved by a higher recycle rate. In addition, at a given recycle rate, a poorer separation - i.e. higher molar fraction of product in the recycle - shifts the fold to higher conversions and Damkohler numbers (Figure 4). Consequently the critical reactor volume required in a recycle system increases. In order to minimize the effects of state multiplicity it is recommended to have a good separation - i.e. no product in the recycle stream. _

Ja=0.2

^^^^^^

]


/A^2 0.4

1 r'^L^ A^-^^

0.2 J

1 llp

0

A+B->P A-t-P-^R

50

100 Da

150

200

Figure 3. Da-X bifurcation diagram for different recycle flow rates fR.

0

50

100 Da

150

200

Figure 4. Da-X bifurcation diagram for different separation performances, Zps-

434

f

0.5 n 04 -

A+B- ^P A+P-

Selectivity

^^0.3-

r1 -08 -0.6 2

Conversion

<

^0.2-

- 0.4 05" 0.1 - 0.2 0.0-

—

i

—

1

—

<

—

,

—

,

—

,

—

^

time/[h]

-0

Figure 5. Instability of low conversion operating point in one-recycle systems. In order to assess the stability of the two different steady states, an AspenPlus simulation was developed. The physical properties of A, B, P, and R species correspond to butene, butane, iso-octane and C12H26, respectively. The operating point was chosen near the fold, on the low-conversion high selectivity branch. The units were designed and rigorous steady-state simulation was performed. The flowsheet was exported to AspenDynamics, where control loops were provided and tuned. It turned out that the nominal operating point is unstable. Figure 5 shows the shift from low to high conversion branch. The change of operating point is also accompanied by a decrease of selectivity.

3. Two-Recycle Systems In this section we consider the consecutive reactions:

2A^P-\-R This chemistry can be found, for example, in the Tatoray process. r~~|

A Recycle

A Feed Product

Figure 6. Control structure relying on self- regulation for a two-recycle plant.

435 Depending on the physical properties of the species involved, several flowsheets are possible. If the reactants A and B are lighter and heavier, respectively, than the main product P, the flowsheet involves two recycle streams. Plantwide control includes control loops for reactor level and temperature as well as distillation columns top and bottom purity or, equivalendy, temperatures (Figure 6). One reactant feed (A) is on flow control,/A^ = 1, relying on self-regulation. The main advantage of this configuration is that the production rate can be easily set. The flow rate of reactant B at reactor inlet/RB is fixed. The feed rate of reactant B,fB^, is used to control the inventory of reactant at some location, for example an intermediate storage tank. For this control structure, the following equations can be easily derived: ^ « • (^A,2 • ^B,2 + ^ • ^1,2 Yfl'

(10)

^A,2 " /s * ^A,3 = ^

/B,0 + / 5 - ^ B , 5 - ( / 2 - ^ B , 2 + ^ « ' ^ A , 2 - ^ B , 2 )

(11)

= 0

/2^A,2 ~/3^A,3 ~ ^

(12)

/2^B,2 ~/5^B,5 ~^

(13)

JR,B ~ J2~

(14)

J5~/B,O~^

J3~

J5~

(15)

/B,0 ~ ^

Figures 7, 8 and 9 show conversion versus Damkohler number bifurcation diagrams, for different recycle rates, separation performances and kinetics. In all cases the lowconversion branch is closed-loop unstable, independent on the separation dynamics. In order to assess the stability of the two different steady states, an AspenPlus simulation was developed. The physical properties of A, 5, P, and R species correspond to toluene, tri-methyl-benzene, xylene and benzene, respectively. The operating point was chosen near the fold on the low-conversion branch.

0.8-

0.8 -

- ' ' 1 0 ^ ^ ^ ^ •^]]^^j5-

3 ^

Z B , 5 = 1 J ^

0.6-

0.6-

f//^

0.4 -

^A.3=1

-""50

A+B^2P 2A->P+R *

^

1

1

1

20

1

^

- ^ ^ ' ^ i , K

0.4 •

1

r

' 1 • ' ' ' 1 ' ' ' 40 Da 60

Figure 7. Da-X bifurcation diagram for different recycle flowrates, f^.

a=0.1

0.2-

n-

.ir^..

= 3

ZA,3-1

^^^-^"6^1

a =0.1

0.20

ZB,5=1

A+B-^2P 2A-»P+R '

'

1 '

40

•

'

Da

'

1 '

60

Figure 8. Da-X bifurcation diagram for different separation performances, ZBS-

436 0.5 0.4 -7-0.3

0.1

A+B->2P 2A->P+R

0.0

10

Da 15

Figure 9. Da-X bifurcation diagram for different kinetics (a-k2/kj).

10

time/[h]

20

30

Figure 10. Instability of low conversion operating point in two-recycle systems.

The units were designed and rigorous steady-state simulation was performed. The flowsheet was exported to AspenDynamics, where control loops were provided and tuned. It turned out that the nominal operating point is unstable. Figure 10 shows the shift from low to high conversion branch. This occurs after a long period of misleading stationary behaviour.

4. Conclusions - State multiplicity occurs in systems involving two reactants if the control structure implies self-regulation of the mass balance for one reactant. Feasible operating points exist only if the reactor volume (i.e. Da number) exceeds a critical value. - When multiple states exist, the low conversion ones are unstable. The instability manifests as a jump to high conversion points, or infinite accumulation of some reactant. - In multi-reaction systems, economical optimality implies high selectivity. This can be achieved at low per-pass conversion operating points that might be unfeasible due to the low-conversion instability. - Considering only the nominal steady state, the operating point can lead to a difficult to control or even un-operable plant. Nonlinear analysis is a way to identify and avoid such dangerous situations at the design stage.

5. References Bildea, C.S., Cruz, S.C, Dimian, A.C. and ledema, P.D., 2002, European Symposium on Computer Aided Process Engineering - 12, The Hague, The Netherlands. Kiss, A.A., Bildea, C.S., Dimian, A.C. and ledema, P.D., 2002, Chemical Engineering Science, 57(2), 535. Pushpavanam, S. and Kienle, A., 2001. Chemical Engineering Science, 56, 2837. Larsson, T. and Skogestad, S., 2000, Modelling, Identification and Control, 21, 209. Luyben, W.L., Tyreus, B.D. and Luyben, M.L., 1999, Plantwide Process Control, McGraw-Hill, New York.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

437

Development of an Intelligent Multivariable Filtering System based on the Rule-Based Method S. p. Kwon, Y.H. Kim, J. Cho and E. S. Yoon Institute of Chemical Processess, Seoul National University, San 56-1, Shillim-dong, Kwanak-gu, 151-744 Seoul, Korea (ROK), e-mail: [email protected], [email protected], jacque(a)pslab.snu.ac.kr, [email protected]

Abstract In this v^ork an intelligent multivariable filtering system (IMPS) based on the rule-based method is developed for on-line monitoring of the states of a transient chemical process. Basically, IMPS consists of three main components, the inference engine, the knowledge database and the state estimation. Once in a while, it is not normal to observe the states of such a transient process only by a fixed filter. For that reason the filter should be often changed along with the inconsistent situation during the overall period of state estimation. In IMPS a certain filter is chosen by the cooperation of the inference engine and the knowledge database. Since the rule-based method makes use of well-established knowledge of long experience, IMPS gives consistent and reliable results. Moreover, the decision rules integrated in IMPS can be flexibly changed for the variation of the standard operating manual. In practice IMPS is built on the environment of SIMULINK. As a case study a continuous polymerization reactor was stochastically simulated and sequentially filtered by two different filters.

1. Introduction There are more and more demands for special chemical products with beneficial properties. Thus, chemical reaction processes, which are related to the production of fine and specialty chemicals, are exactly estimated by using on-line estimation techniques. Therefore, the main activities of process operators of the full-automated chemical plants are fault detection and diagnosis, and correcting deviated states, which are based on process variables estimated, such as temperature, pressure and density. In practical stochastic observers, which are simply called filters, are implemented for estimating the complete state vector extracted from the noisy process data measured, and then all variables can be derived from the state vector estimated (Kwon and Wozny, 1999; Vankateswarlu and Avantika, 2001). Por that reason a widely variety of filter algorithms have been developed and a number of works have been carried out for online monitoring of various nonlinear chemical processes (Jazwinski, 1970; Ramirez, 1994; Guiochon, et al., 1995). Especially, Kalman filter algorithms have been often used for on-line monitoring of polymerization reaction processes (Schuler and Suzhen, 1985; Gagnon and McGregor, 1991; Kozub and McGregor, 1992; Boem and Roeck, 1994; Wang, et al., 1995; Mourikas, et al., 1998).

438 Practical applications of the selected filter are highly divers, with each case having peculiarities of its own (Haykin, 2002). A steady-state filter, which is called the Wiener filter, is effective for stationary inputs, but it is not sufficient for dealing with situations, in which the signal and noise is not stationary. In this case the optimal time-varying filter, which is called the Kalman filter, is available for a range of applications. In addition the adaptive Kalman filter, in which the observation noise covariance is sequentially updated by using FIR (finite-duration impulse response) filter algorithm, is practical because of its tracking capability (Chen and Rutan, 1996). Occasionally, a type of filter is not sufficient to carry out on-line monitoring of process transitions, because chemical processes at the abnormal situation show an extremely large change from one steady state to another. For instance there are frequent manual changes in the product grade in continuous chemical processes. It was emphasized that manual errors keep count about 40 percents of all causes of accidents in the chemical and petrochemical industry (Bhagwat, et al., 2001). On-line monitoring systems that detect faults during process transition are very significant to reduce the manual errors.

2. Optimal Filtering Algorithms In general, the nonlinear time-variant process model and the nonlinear observation model with measurement noise are represented by x(t) = f{x,u,t)-\-w{t),

A:(O)=XO,

y{t) = h{x,u,t)-\-v(tl

(1) (2)

where x(t) is n dimensional state vector, u(t) is m dimensional input vector, / is a nonlinear state fimction of x(t) and u(t). w(t) and v(t) are additive white noises with zero-mean. Initial state vector jc(0) is a Gaussian random vector with mean XQ. y(t) is r dimensional output vector, /i is a nonlinear measurement function of JC(0 and u(t). w{t) and v(t) are independent of jc(0). In addition the covariance matrices of (jc(0) - XQ), w(t), and v(0 are PQ, Q{t) and R(t), respectively. 2.1. Steady-state optimal filter Inherently, the Kalman filter is an optimal algorithm, in which the linear state-space model is used to predict state vector x(t) between the sampling intervals, and then all the estimated states are filtered by using the past state estimate and the newly obtained measurement vector y(t). The optimal state estimate is carried out through minimizing the quadratic performance functional, in which both of state and measurement uncertainties are included in this criterion consistently. By using the boundary conditions for minimizing this performance functional the Riccafi's equadon can be solved. As a result, the Kalman filter algorithm is obtained. i = Fx + PH^R-' {y - Hx),

(3)

P = PF^ + FP + Q-PH^R-'HP,

(4)

439 where JCQ and PQ are initial state estimate and its covariance. The symbol x is the state estimate, and P is the covariance of state estimation error, which is calculated from the known final value backward in time. The filter gain K is defined as PlfPT^ and can be computed independently from the dynamic state response, because it is only a fiinction of system and performance parameters. If the calculation of P is examined at infinite fime, then Eq.(4) will come close to a steady state. Besides, the filter gain becomes a constant value, if the system is observable and controllable (Ogata, 1987). 2.2. Time-variant optimal filter The steady-state optimal Kalman filter can be generalized for time-variant systems or time-invariant systems with non-stationary noise covariance. The time-varying Kalman filter is calculated in two steps, filtering and prediction. For the nonlinear model the state estimate may be relinearized to compensate the inadequacies of the linear model. The resuhing filter is referred to the extended Kalman filter. If once a new state estimate is obtained, then a corrected reference state trajectory is determined in the estimation process. In this manner the Filter reduces deviations of the estimated state from the reference state trajectory (Kwon and Wozny, 1999; Vankateswarlu and Avantika, 2001). In the first step the state estimate and its covariance matrix are corrected at time 4 by using new measurement values j(4).

k{t,) = Fx[t,\t,_,)+K{tMh)-H^h\t,_^), K{t,)=l{t,\t,^)H'[R+Hl{t,\t,^)H'y,

(5) (6)

P{t,)={l-K{t,)H)p{t,\t,_X

(7)

where the process and observation matrices mean F = {df/dx)^^^ and H = {dh/dx)^^^. In the second step the state estimate and its covariance are predicted forward to the next sampling time by integrating the deterministic fiinctions (Kwon and Wozny, 1999). 2.3. Adaptive recursive least-square filter For the regular filter the observation noise covariance J? is a constant matrix determined before state estimation. On the other hand, the measurement noise covariance R(t) may be adjusted to compensate for estimation errors. Using finite-duration impulse response (FIR) filter algorithm the observation noise covariance can be adjusted during the state estimation process.

R{h) = t^]{vk

-tj)-^'ih

-tj)]-H'P{t,)H

,

(8)

7=1

where the filter order p is the number of delay-elements corresponding to a smoothing window. The symbol oj is the respective tap weight, and the asterisk denotes complex conjugation. The second term of right-hand side is use to describe the parameter estimation errors. According to Eq.(8) the on-line observation residual v(4), which is the difference between the observation and prediction, will result in a large observation

440

noise covariance, if another component makes a contribution to the observation. Hence, if the on-Hne residual becomes too large, then the small weight factor will turn off the filter, and the number of delay-elements will not be used to estimate the parameters (Haykin, 2002; Ogata, 1987).

3. Intelligent Multivariable Filtering System (IMFS) For the state estimation a certain filter can be automatically selected by the cooperation of the inference engine and the knowledge database in IMFS, as shown in Figure 1. The knowledge database means the sum of knowledge about facts and rules, whereas the inference engine is the general problem-solving knowledge. The rules represented by "if-then sentence" are an effective method to represent recommendation, direction, strategy, etc. The interpreter compares the fact and the condition. If the fact satisfies the given condition, then the instructed action is executed (Suh, 1997). Filters can be used for estimating state variables of a transient process sequentially. The rule-based method makes use of well-established knowledge of long experience and gives consistent and reliable results. It can also find a suitable filter more rapidly than the other knowledge representation methods, such as the procedural method and the formal logic. Furthermore, the decision rules integrated in the knowledge database are flexibly changed on account of the variation of the standard operating manual. IMFS Disturbed Sgnals

^

Qven

^

Situation

1 Multivariable Filter |c4=t>

i 1

tr

inference Engine

Filtered Signals

step

BiiHi

|

C

B

knowledge Database

\

1 Situation 1 |
•S

1 Situation N | < - ^ [ Filter N |

Figure 1. On-line monitoring of the transient states by using IMFS.

Figure 2. Integration of the nonlinear model in a block ofSIMULINK.

4. Continuous Polymerization Reactor: A Case Study The polymerization reaction system, which is studied in this work, consists of Methyl methacrylate (MMA) as monomer, Azo-bis-isobutyronitrile (AIBN) as initiator, and Ethyl acetate as solvent. Free radical polymerization reaction is assumed to work in a continuous stirred tank reactor with a cooling water jacket. This polymerization reactor can be designed to produce an amount of polymer product, i.e. the rate of output stream is constant. The rigorous nonlinear process model of the continuous polymerization reactor consists of a number of differential and algebraic equations about the reaction kinetics, the gel and glass effect, the volume change, the gas-liquid phase equilibrium in the reactor, the energy balance, and the polymer molecular weight moments (Kwon and Wozny, 1999; Guiochon, et al., 1995; Boem and Roeck, 1994; Wang, et al, 1995). The

441 material balance consists of three terms for the accumulation, the reaction and the mass flow. These equations are valid for four components such as the initiator, the monomer, the solvent, and the chain transfer agent. The general mechanism of polymerization reaction gives the reaction rates of each component under the assumptions, QSSA (Quasi-steady state approximation) and LHC (Long chain hypothesis). The energy balance contains four terms for the heat accumulation, the heat generation, the heat flow and the heat removal through the cooling jacket. The polymer molecular weight and its distribution are described by the balances of the lowest three moments of active polymer molecules. By using the rigorous nonlinear model developed the dynamic behavior of the continuous polymerization reactor can be simulated accurately. The nonlinear model was programmed in MATLAB, and then for convenient uses it was inserted into a block of SIMULINK, which is a commercial dynamic simulator in the MATLAB package, as shown in Figure 2. Using the symbolic model in SIMULINK stochastic simulation can be carried out with no trouble. In Figure 3 and 4 we can see that the polymerization process reaches a steady state about 3 hours after the reaction start, and then there is a transition in 20 hours. There are drastic changes of the conversion, the molecular weight, the temperature. Furthermore, the steady-state Kalman filter and the time-varying Kalamn filter can be effectively switched in order to estimate the state of the continuous polymerization reactor. Both of the filters showed satisfactory performances at the steady state region, that is three hours after the reaction startup of the polymerization reaction. However, we can see clearly that the time-varying Kalman filer is preferred to the steady state one at the drastically varying region, as shown in Figure 5 and 6. At abnormal situations it is recommended to use more than two different filters sequentially according to the condition. The selection method, which is called IMFS, was suggested for practical applications. IMFS is a reliable and consistent system for the reason that it bases on a well-established knowledge of long experience. As the case study, the continuous polymerization reactor is investigated. The nonlinear model is developed and integrated in a block of SIMULINK for the convenient use. By using the program stochastic simulations are carried out. In addition a few different filter algorithms were evaluated by simulation. f'tt^'Vr'UHWl-S**^

i70

*t^»i^'f^t'|^>iM^Y»t«»^i4<Mi»M'h*»*''j5

10

15 Time [h]

20

25

20

25

30

|M^¥<»I^^ 10

15 Time [h]

20

Figure 3. Stochastic simulation on the conversion and the molecular weight.

5

10

15 Time [h]

Figure 4. Stochastic simulation on the temperature and the coolant feed.

442

Time [h]

Time [h]

Figure 5. Filtering of the temperature and the conversion using a fixed filter.

Time \h]

Figure 6. Filtering of the temperature and the conversion using two filters.

5. Conclusions At abnormal situations it is recommended to use more than two different filters sequentially according to the condition. IMPS could suggest a suitable filter for the practical application. IMPS is a reliable and consistent filtering system based on the well-established knowledge of long experience. The continuous polymerization reactor was investigated as a case study. The nonlinear model is developed and integrated in the block of SIMULINK for the convenient use. By using the program stochastic simulations were carried out and filter algorithms were evaluated. One of the most important advantages of IMPS is that it can help operators to reduce the time and effort necessary to find proper filters.

6. References Bhagwat, A.M., Srinivasan, R. and Krishnaswamy, P.R., 2001,4'^ IP AC WS on On-line Pault Detect. & Super. Chem. Proc. Ind., 75. Boem, D. and Roeck, H. 1994, 3'^ IEEE Confer, on Contr. Appl, 1277. Chen, J. and Rutan, S.C, 1996, Analtica Chemica Acta, 3351-10. Gagnon, L. and McGregor, J.P., 1991, Can. J. Chem. Eng., 69, 648. Guiochon, S., Defaye, G., Vidal, C. and Caralp, L., 1995, DYCORD+'95, 238. Haykin, S., 2002, 3'"^ Eds., Adaptive Pilter Theory, Prentice Hall, NJ. Jazwinski, A.H., 1970, Stochastic Process and Piltering Theory, Academic Press. Kozub, D.J. and McGregor, J.F., 1992, Chem. Eng. Sci. 47,1047. Kwon, S.P. and Wozny, G., 1999, Com. & Chem. Engng. Suppl., 273. Mourikas, G., Moorris, A.J. and Kiparissides, C, 1998, DYCORD+'98, 682. Ogata, K., 1987, Discrete-Time Control Systems, Prentice Hall, Chap.7. Ramirez, W.F., 1994, Process Control and Identification, Academic Press. Schuler, H. and Suzhen, Z., 1985, Chem. Eng. Sci., 40, 1891. Suh, J.C, 1997, Dissertation, Seoul National University, 59-78, (in Korean). Vankateswarlu, C. and Avantika, S., 2001, Chem. Eng. Sci., 56, 5771. Wang, Z.L., Pla, F. and Corriou, J.P., 1995, Chem. Eng. Sci., 50, 2081.

European Symposium on Computer Aided Process Engineering - 13 A. Krasiawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

443

Multiple-Fault Diagnosis using Dynamic PLS Built on Qualitative Relations Gibaek Lee\ En Sup Yoon^ ^Department of Industrial and Engineering Chemistry, ChungJu National University, Chungbuk, 380-702, Korea, email: [email protected] ^School of Chemical Engineering, Seoul National University, Seoul, 151-742, Korea

Abstract This study suggests the hybrid method of qualitative model and quantitative data-based method to improve diagnosis accuracy and resolution, and promote reliable diagnosis of multiple-fault. The proposed method is based on signed digraph offering a simple and graphical representation for the qualitative relationships between process variables. On local causal relationships of each variable in signed digraph, PLS model is built to predict the target variable of the causal relationships. In order to handle accurately process dynamics, the input of PLS uses the current value of source variables as well as the past values of source and target variables. The measured value and predicted one are compared to diagnose fault.

1. Introduction Fault diagnosis is used to analyze the process data on-line, monitor the process trends, and diagnose faults at abnormal situation. It helps operators in decision-making and ultimately assist operators to more efficiently keep operation continuous and safe. Considering the characteristics of chemical processes, the minimum requirements for the fault diagnosis methodology have been suggested as like speed, accuracy, resolution, robustness, portability, and reliability (Finch, 1989). Among these factors, reliability means that accurate diagnosis can be expected for all faults, including novel faults and predictable multiple-fault. Multiple-fault is more than two faults that happen simultaneously or sequentially and can be classified into four categories as induced fault, independent multiple-fault, dependent multiple-fault, and masked multiple-fault (Lee et al., 1999). Masked multiple-fault is the faults of which some can explain all symptoms from the others, and cannot be recognized using the qualitative method only. Diagnostic methods for chemical processes are broadly classified as ones that use process model, and ones that rely on process history data. And they are classified as qualitative ones and quantitative ones, respectively (Venkatasubramanian, 2000). This study suggests a new hybrid method based on signed digraph (SDG) in qualitative model-based methods, and partial least squares (or projection to latent structures, PLS) in quantitative history data-based methods. The proposed method will be illustrated with the case study of a heat exchanger and a CSTR. This process is originally used by Kramer (1987) and is simulated by the model of Sorsa (1991). The sampling interval is 5 s, and total diagnosis time is 2000 s. The first or single fault occurs at 100 s, and the second fault occurs at 100 or 200 s. Diagnosis result of this study will be compared with the one of the qualitative method

444

Figure. 1. Reduced digraph of the CSTR process. suggested in our previous study (Lee et al., 1999).

2. Suggested Method 2.1. Off-line analysis 1. Modification of SDG: After SDG is built, the reduced digraph is obtained by removal of unmeasured nodes from the SDG (Kramer, 1987). The reduced digraph of CSTR process is shown in figure 1. And, physically feasible faults for each piece of equipment are defined and added on the root node in order to handle only physically meaningful faults (Lee et al., 1999). 2. Dynamic PLS model: Each arc in SDG represents the instant effect from source node to target node. All source nodes connected with the arcs to each target node have the direct influence on the target node. That is, only the source nodes connected to a target node can affect the target node. Therefore, the PLS model based on the source variables connected to a target variable can predict the value of the target variable. The output Y of the model is each target variable, and the input X of the model is the source variables of the target variable. In order to handle accurately process dynamics, PLS is integrated with ARMAX, referred to as dynamic PLS (DPLS). The resulting input of DPLS for a target variable includes the current value of source variables as well as the past values of the target variable and source variables. For example, the DPLS model based on measured variable, FR, FW, and T can predict TR in CSTR process. If the current value and one previous value are used as input data, the input matrix X for the estimation of TR is formed as F,(l)

F^(l)

7(1)

TM

F.iO)

iv(0)

T{0)

F,(2)

F^(2)

T{2)

T,{2)

F,{1)

^.(1)

T{1)

X= F,(t)

F„it)

T(t)

T,it-l)

F,{t-l)

/v(f-l)

(1) T{t-l)

445 3.

Learning data: Operation data is needed to build DPLS model. In the suggested method, each DPLS uses only data set representing the local relations from input variables to output variable. The required data set for each model can be provided by normal operation data set such as set-point changes, which are frequently occurred. Therefore, the suggested method does not need faulty case data set, which is rarely available. 4. Determination of model parameter: The necessary number of time lags / and the principal components (PC) are determined from learning data. The number / is usually 1 or 2 which indicates the order of the dynamic system. The design method is analogous to the method used in the study of dynamic PCA (Ku et al., 1995), and uses the cross-corelation plots of the scores to determine the number of PCs. The number of time lag and PCs for the DPLS model of the CSTR process are shown in Table L The input matrix X as equation (1) is made with the determined number of time lag, and DPLS model is developed by multivariate statistical package PlantAnalyst®. 5. Preparation of set table: The fault detection is performed by the observation of the residual, which is the difference of measured value and predicted value by DPLS. Thus, the faults inducing the variation of each residual are classified with the sign of the residual. The qualitative state of the residual of (+) or (-) becomes symptom, Table 1. Number of PCs, time delay, and fault table of the CSTR process. Residual variables CAO FO TO CL CR CT FP FR FW L T TR CA CB

Positive (+) Sign of residual FEED-CCH FEED-FCH FEED-TCH LC-SVCL FC-SVCH TC-SVCL VL-BH, FS-BH

Number of PCs 2 2 2 2

Time delay 1

2

1

VR-BH, FS-BH

1 4 7

1 2 2

3

1

5 5

2 2

VT-BH LS-BH, PUMP-EF TS-BH, FS-BH, LS-BL CW-TCH, HX-PL, FS-BL, TS-BL LS-BH, TS-BH LS-BL, TS-BL

Negative (-) sign of residual FEED-CCL FEED-FCL, FP-BK FEED-TCL LC-SVCH FC-SVCL TC-SVCH VL-BL, PP-BK, PUMP-EF, FS-BL VR-BL, FS-BL, PUMP-EF, RP-BK VT-BL, WP-BK LS-BL, RX-LK TS-BL, FS-BL, LS-BH CW-TCL, FS-BH, TS-BH LS-BL, TS-BL LS-BH, TS-BH

which is expressed as with the pair of the output variable and the sign of the residual. The classified faults are stored in a set (called as fault set). Also, The faults can be classified into two types. One type of faults is ones added to the output variable. The sign of the symptom by the faults are same with the one of arc connecting the fault

446 to the output variable. An another type of faults is sensor faults of measured variables except output variables in DPLS model. This paper does not consider independent sensor faults. The sign of the symptom by the faults is the reverse direction of the product of the sign of the sensor faults and the sign on the arc connecting the input variable to the output variable. The fault set for the example process is shown in Table 1. 2.2. On-line diagnosis (1) Detection method: The residual variation is detected by CUSUM. CUSUM has the recurrent computation form suitable for real time analysis and does not need filtering. It uses two parameters of minimal jump size and threshold size. In this study, 6o of residual distribution as the minimal jump size and 3 o of CUSUM distribution as the threshold was used (Lee et al., 1999). (2) Diagnosis using fault set: The basic diagnostic strategy is to obtain the set of minimum faults that can explain all detected residuals. The diagnosis procedure is as follows. ® The fault sets corresponding to the detected symptoms are listed as named as the list of fault sets. The union of the fault sets in the list becomes the set of initial fault candidates. Among the elements of the initial fault candidates set, each sensor fault is pre-examined whether the residual of the measured variable of the sensor fault is detected in the direction of the sensor fault. Otherwise, the sensor fault is removed from the initial fault candidates set. It can improve diagnosis resolution. © In order to decide how many symptoms each fault candidate, F can explain, the number of how many fault sets in the list of fault sets involve F is calculated. The number is named as nES (number of explained symptoms). The fault candidates having the biggest nES are included in the set of first fault candidates. If all detected symptoms cannot be explained by single faults of first fault candidates, multiple-fault will be searched at the next step. ® First element in the set of first fault candidates is selected. After the fault sets including the first fault candidate are removed in the list of fault sets, the remaining list of fault sets is assigned to the first fault candidate. The union of the fault sets in the list of fault sets assigned to the first fault candidate becomes the set of multiple-fault candidates for the first fault candidate. The nES of each fault in the obtained multiplefault candidates set is calculated. The fault candidates having the biggest nES are included in the set of second fault candidates for the first fault candidate. When the nES of second fault candidate is same with the number of the fault sets in the list of fault sets assigned to the first fault candidate, double-faults of the first and second fault candidates can explain all symptoms. If all detected symptoms are not explained, this step will be repeated. For instance, consider the double fault case. In this case, the level sensor is lowly biased at 100 s (LS-BL). After 100 s, the reactor temperature is highly biased (TS-BH). The symptom of L(-) is detected at 105 s, CA(-) at 175 s, CB(+) at 200 s, T(+) at 205 s, and TR(-) at 215 s. The diagnosis procedure will be explained with the data of 215 s. The initial fault candidates set is {LS-BL, RX-LK, TS-BL, TS-BH, FS-BH, CW-TCL} and TS-BL and FS-BH is removed because T(-) and FR(H-) are not detected. Therefore, the initial fault candidates set is {LS-BL, RX-LK, CW-TCL, TS-BH}. Because LS-BL among these faults has the biggest nES of 4, LS-BL is selected as first fault candidates. In the next step, the fault sets of {CW-TCH, TS-BH} is assigned to LS-BL. The final fault candidate is two double-fault of {{LS-BL, TS-BH}, {LS-BL, CW-TCL}}. In this example, though the diagnosis is later than the time of fault occurrence, it is accurate. The qualitative method failed to obtain the true solution because it is masked multiple-

447 fault (Lee et al., 1999). Also, it shows good diagnosis resolution as the final fault candidate set has two elements.

3. Case Studies 3.1. Diagnosis description The selected situations can be found in our previous study (Lee et al., 1999). They are 15 single faults and 37 double faults which are generated randomly, and the step function is used for the simulation of a fault. Eight DPLS models for eight measured variables are obtained. Also, three PLS models are made for three control output variables. As the learning data for each PLS model, this example uses seven data sets of set-point change and external disturbance. These situations are frequently occurred in normal operation. The same data are used to determine the parameters of CUSUM of minimal jump size and threshold size. The constraint variable suggested in our previous study of fault-effect tree model (Lee et al., 1999) are used to increase the resolution. It represents the quantitative governing equation such as the balance equation and valve relation as variables. The previous study used a mass balance and two control valve equations for CSTR. As the control valve equations are expressed by DPLS model, this study uses only mass balance equation. Reactor leaking (RX-LK) is a root cause of the positive deviation of the constraint variable, DF that is defined as F^ - Fp 3.2. Result of single fault cases To measure the diagnostic performance, three parameters are used. Accuracy is 1 if the diagnosis is accurate, that is, a true fault is involved in the final fault candidates set. Otherwise, accuracy is 0. Robustness is the number of wrong detected symptoms independent to the true faults. When accuracy is 1 and robustness is 0, resolution denotes the number of final fault candidates. In all selected single fault cases, accuracy is 1 and robustness is 0. For the case of VLBH, our previous method based on the qualitative model gave double-fault during 45 s (Lee et al., 1999), but the suggested method shows robust result during all diagnosis periods. Though the resolution for 2 cases of RX-LK and LS-BL is worse than our previous method, the resolution by the suggested method is better for 4 cases of WP-BK, VL-BH, VT-BH, and FS-BL. 3.3. Result of multiple-fault cases Our previous qualitative method for 9 cases failed because these cases are masked multiple-faults in which one fault can explain the symptom of the other fault. However, Table 2. Diagnosis result of the selected double faults. No. 1 7 6 10 13 14

Robustness 0.96 / 1 0/0 0/0 0/0 0/0 0/0

Resolution

No.

1.09/4 2.23/4 1.01/4 3.84/4 4.0/4

15 17 19 20 28 31

Robustness 0.99 / 1 0/0 0/0 0/0 0.2/1 1/1

Resolution 3.82/4 1.17/4 8/8 4/4

448 the proposed method showed the results that only 1 case among 37 cases fails and the diagnosis for other 36 cases are accurate during all diagnosis periods. The diagnosis for the double-fault of RX-LK and PP-BK fail, because process variations resulted from PP-BK are too weak to detect symptoms for FP-BK. In table 2, the former is average over the total results taken by the frequency of 5 s during the simulation period of 2000 s, and the latter is the worst result during all diagnosis periods. Table 2 shows the diagnosis result of the selected double-fault except a failed case and 24 cases of the worst resolution under 2. Case 20 of FV-BL and WPBK shows the worst resolution of 8. In the case, the primary fault candidates of {VT-BL, WP-BK} and {VR-BL, FS-BL, PUMP-EF, RP-BK} from the detected residuals of FW(-) and FR(-) are obtained, respectively. Thus, 8 (2 X4) double-faults became the final fault candidates. Though 33 cases among 36 cases show the robustness of 0, three cases (1, 15, and 28) detect a variable independent to the true solution in short periods. This wrong detection is due to that smaller CUSUM parameters than necessary were used. In order to prevent wrong detection, CUSUM parameters are doubled for the diagnosis. With the new parameters, the wrong detection of two cases is not occurred. And, fault detection for most cases is delayed for 5-30 s. However, diagnosis accuracy and resolution for 33 cases are not effected to be same with the previous parameters.

4. Conclusion This study is about the fault diagnosis by the hybrid method of qualitative model-based method and quantitative history data-based method. The diagnosis is performed by the observation of measured value and predicted value by DPLS model built on the local causal relationships of SDG The proposed method has the advantages to improve diagnosis accuracy and resolution, and facilitate diagnosis of masked multiple-fault.

5. Reference Finch, F.E., 1989, Automated Fault Diagnosis of Chemical Process Plants Using Modelbased Reasoning, Sc.D. Thesis, Massachusetts Institute of Technology. Kramer, M.A. and Palowitch, B.L., 1987, AIChE J. 33, 1067. Ku, W., Storer, R.H. and Georgakis, C , 1995, Chemometrics Intell. Lab. Syst. 30, 179. Lee, G, Lee, B., Yoon, E.S. and Han, C , 1999, Ind. Eng. Chem. Res. 38, 988. Sorsa, T. and Koivo, H.N., 1991, IEEE Trans. Systems. Man. Cybern. 21, 815. Venkatasubramanian, V., 2000, Proc. of the PSE Asia 2000. 597.

6. Acknowledgement This work was supported by grant No. (R05-2002-000-00057-0) from the Basic Research Program of the Korea Science & Engineering Foundation.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

449

Integration of Design and Control for Energy Integrated Distillation Hongwen Li, Rafiqul Gani, Sten Bay J0rgensen CAPEC, Department of Chemical Engineering Technical University of Denmark DK-2800, Lyngby, Denmark

Abstract A method for development of control structures is presented for an energy integrated distillation column. The method contains three levels. First the feasible operating region is determined, second the feasible static control structures are proposed and screened, and third, the additional degrees of freedom stemming from process dynamics are handled using additional actuators and control loops. The advantage of the three-layered strategy is that the first two layers can be dealt with early during process development while the third layer may be added at the appropriate design point where information on the dynamic behaviour is available.

1. Introduction The systematic computer aided pre-solution analysis of process models for integrated design and control presented earlier by Russel et al. (2002) is further investigated in this paper for an energy integrated distillation pilot plant. This paper investigates aspects of design and control of the integrated distillation column with the model analysis method and validates the results through simulation and operational analysis of the energy integrated distillation column. First the model analysis is presented for a single distillation column; subsequently the column analysis is extended with the analysis for a heat pump. Finally, the method for development of control structures is presented and verified through simulation.

2. Process Description The heat integrated distillation pilot plant considered in this paper is shown in Figure 1. It contains two main sections, namely a distillation column section and a heat pump section. The heat pump section is physically connected to the distillation column through the condenser at the top and the reboiler at the bottom of the column. The heat pump consists of four heat exchangers, two compressors, one expansion valve, a large tank, OCfjy^ and Ctcv9 ^^^ ^^^ control valves. While the refrigerant circulates within the heat pump it changes phase, and through absorbing heat of vaporization at low pressure and releasing it again at high pressure it carries heat from the column condenser to the column reboiler. A more detailed description of this pilot plant is given by Eden et al. (2000). The process model analysis of these two sections is discussed individually.

3. Process Model Analysis Model analysis first determines the available degrees of freedom for design and for control, which then identifies the "common" variables used in design as well as control. The analysis subsequently identifies the important constitutive equations, their dependent process variables and the corresponding derivative information with respect to the identified "common" variables. This analysis employs the mass and energy

450 balance equations and the constitutive equations to generate information related to process sensitivity, process feasibility, and design constraints. The model analysis is decomposed into two parts: first the analysis is carried out for the distillation column and thereafter, the heat pump system.

_g^^CV9__ Condenser ( ^ j Expansion valve j

(DecanteT)

-^3—d_s—• D.XQ

r-€H

-SF.Xp

Compressors

h©

Superheating

( ReceiverJ

Secondary Z ' * ^ Condenserv-*^

i=F^

B.X.

Figure 1: Flow sheet of the heat integrated distillation column. 3.1. The process model analysis for the distillation column Five degrees of freedom (determined from the model analysis) are related to five design and control variables. The design problem considered determines the optimal values of the design variables so that some process variables attain their desired values while the control problem maintains the same process "conmion" variables at their desired values by manipulating the same "common" design variables when there is a disturbance. As the design and control problems involve the same set of "conmion" variables, they are integrated and solved simultaneously, once an integrated problem has been formulated. From a control point of view, for dual composition control of the distillation column, both the top product purity and the bottom product purity need to be controlled. The hold ups of the condenser and the reboiler here need to be controlled to stabilize the system. For example the optimisation variable or design variable D (distillate flow rate) is used to control top composition xo and vapour flow rate at the bottom VB is used to control bottom purity jc^, where vapour flow rate is manipulated by heat duty of the reboiler QB- The column pressure is controlled by heat removed from the condenser QcThe holdup of the condenser MD, is controlled by reflux flow rate LQ and the holdup of reboiler MB is controlled by bottom product B. Hence for control purpose, the design optimisation variables, QB, QC, T), LQ, B may be chosen as the manipulated variables. This illustrates the relationship between design and control issue for a conventional distillation column.

451 From a design point of view, the five candidate design variables are selected first. The product rate D and B need to be specified to meet the external mass balance and the market needs. Vapour flow rate V, the condenser heat duty Qc and reflux flow rate LQ are needed in the column to fulfil the separation process. From a control point of view, then design variables are also considered as "actuator" variables and it is necessary to identify the appropriate process variables that could be "controlled" through them. 3.2. The model analysis for the energy integrated distillation column From the model analysis, two degrees of freedom are obtained for the heat pump section. Here high pressure on heat pump section PH and low pressure PL are chosen as controlled variables. Two actuators are valves Ctcvs ^^^ ^cv9 •

4. Operation Window for the Energy Integrated Distillation The appropriate variables that can be controlled through the identified "common" design/actuator variables can be identified through an investigation of the operation window. In the case of this heat integrated column with sieve trays operated primarily in the spraying regime, the limits forming the operating region are the flooding limit, weeping limits, maximum column pressure, maximum heat pump high pressure, maximum heat pump low pressure, maximum cooling power of the heat pump system, maximum pumping capacity. Inside this region is the operation window, within which the operation point must be located to ensure the separation process (as illustrated through Figure 2). The empirical correlations for flooding and liquid weeping are described below and the limits related to the high and low pressures of the compressor system are determined through simulation. 4.1. Flooding and liquid weeping curves The following derivations are based on empirical correlations estimated by several authors and collected by Zuiderweg (1982) on his review paper on the state of the art for sieve trays. Let LQ and V be the volumetric flow rates of reflux and boil-up in m^/s, and let pi and pg be the liquid and gas densities in kg/m^. The weeping limit in terms of the minimal vapour flow rate is then found by the following empirical correlations:

^min ~ ^^w '^t-ij

(1)

\ Pl Where: CFmax is the tray capacity factor on bubbling area, m/sec At is the tray area, m^ This correlation is plotted as the weeping limit, i.e. Curve 1 in Figure 2 The flooding limit in terms of the maximal vapour flow rate is used as the flowing correlation:

(2) Where CF^ax is the capacity factor at start of flooding, m/sec. This correlation is plotted as the flooding limit, i.e. Curve 3 in Figure 2.

452 4.2. Maximum and minimum PL The limits of the operation region imposed by the heat pump are obtained by simulation in total reflux mode. Curve 2 in Figure 2 is mapped by switching on a controller to maintain heat pump low pressure PL at its maximum, i.e., 600kPa and then gradually decrease high pressure PH until intersection with the weeping limit. Going along this trajectory the number of active cylinders reduced as appropriate such that the pressure drop through CV9 has a reasonable level (50-200kPa). If the pressure drop exceeds these limits retuning of the low pressure controller is necessary due to the nonlinear valve characteristic. Curve 4 in Figure 2 is mapped by keeping CV9 open and all cylinders active, and then gradually decrease high pressure PH- This way the low pressure is at all time kept as low as possible, decreasing as the high pressure is reduced. The lower limit represents the lowest possible column pressure, and it crosses the weeping limit at a point, which thus is the point of lowest possible column pressure and boil-up rate at which the column can be operated.

5. The Static Actuator Configuration of the Integrated Distillation Column 5.1. The static actuator conHguration For integrated distillation column QB and Qc are not the manipulated variables, which are controlled by PH and PL on the heat pump section. Through the analysis of the column the actuator structures it appears that PH+PL (on the heat pump side) is suitable to the control column pressure while PH-PL (on the heat pump side) may be used to control the vapour flow rate. With these control actuator configuration, the column pressure and vapour flow rate control loops are decoupled. This also means that the actuator (design) variables on the distillation column side are determined through the "control" variables on the heat pump side. Rigorous simulations have been performed to confirm the actuators configuration with the dynamic model of Koggerb0l (1995). The simulation results are plotted in Figure 2, where the curve A in Figure 2 is at constant PH+PL» while PR-PL change. From curve A one can see that column pressure is nearly constant for constant PH+PL for many different PH-PL. From curve B one can see that the vapour flow rate is nearly the same at constant PH-PL in spite of different PH+PL- This confirms the design and control issues stated above that one could control the vapour flow rate in the integrated distillation column by manipulating the pressure difference between the high pressure and the low pressure of the heat pump side and the column pressure by manipulating the sum of the two heat pump pressures.

6. Control Structure for Dynamic Integrated Distillation Column 6.1. Dynamic control structure for colunm section For the distillation column, the overall control for the column section has five outputs XD, XB, MD, MB and P. Comparing to the static control problem, two more holdup variables, i.e., MD and MB, are introduced. Suppose that the column pressure and the reboiler vapour flow have the same control configurations as the steady state. For such kind of "standard" control problem, the most widely accepted control structures are "LV-configuration" or "DV-configuration. The issue of this kind of control configuration has been investigated using frequency dependent formulations of measures such as the condition number, the Relative Gain Array by Bristol (1966) and the Relative Disturbance Gain by Stanley et al (1985). This paper will focus on discussing the dynamic control structure on the heat pump section and how each dynamic control structure affects on the stability of the integrated distillation column.

453 6.2. Control structure on the heat pump section As discussed above, PH+PL and PH-PL are used to control column pressure and vapor flow rate. In turn, PH and PL are controlled by manipulating two actuators Ctcv^ ^^^ Ct(^yg. The pair of these two process variables and two control valves play a very

60 80 100 Column pressure P(kPa)

120

Figure 2: A curve: PH+PL ^t constant, PH-PL change. B curve: PH-PL ^t constant, PH-^PL change.

important part in terms of stabilization of the integrated distillation column. First let us discuss how disturbance affects the heat pump high pressure PH and low pressure PL SO as to decide the pair problems. Consider, for example, the plant at steady state with only liquid level controllers for the reboiler and the condenser has been implemented. If suddenly the energy balance is disturbed by a small amount 5H, for instance due to a disturbance in the feed preheater in the feed composition, or perhaps in the temperature of the cooling medium in the secondary condenser, then the changed heat input starts to accumulate in the plant. If the disturbance reduces the cooling rate this will immediately affect the high pressure PH such that PH begins to increase. Thereby the compression work is continuously increased, but also the cooling rate will gradually increase as the temperature gradient in secondary condenser and in the air coolers will increase with PH. The increase in the high pressure affects boil-up rate, and as a result of this, the column pressure and the heat pump low pressure PL simultaneously increase. Assuming that the enthalpy of the feed remains constant after the disturbance, the behavior of the entire plant becomes unstable if the compressor work increases faster than the sum of all the outgoing heat flows. For this integrated distillation column the compressor work does indeed increase faster than the sum of all the outgoing heat flows within part of the operating region. Therefore a small disturbance in the overall energy balance can initiate a drift of the plant towards increasing or decreasing pressures depending on the sign of the disturbance. To reject disturbance so as to stabilize the system, high pressure PH and low pressure PL need to be controlled by manipulating suitable actuators. In theory either the low pressures or the high pressure could be paired with Ct^y^ and thereby stabilized the system. However, the gain from Otcvs ^^ ^^^ ' ^ ^ pressures is relatively small (Koggerb0l, 1995) so if CX^y^ is to be used for stabilization it should be preferably be paired with the measurement of PH-

454 The valve CLQ^^ does not directly affect the energy balance but it can be used to stabilize the plant if it is paired with a suitable measurement. Suppose that PL is stabilized by manipulating the valve CXQ^^^ then a disturbance, which tends to increase PL, will be neutralized by the valve opening being increased by the controller. This way PL is maintained at setpoint. The main result of the discussion above is that high pressure PH should be controlled and that the cooling valve OL^y^ is preferred as actuator for this purpose. So, in conclusion, a control loop manipulating 61! ^^g based on a measurement of the high pressure PH is suggested to stabilize the plant. The low pressure PL is controlled by control valve OL^^y^ to stable the system. In the reboiler the saturation pressure PH is a sufficient measure of the condition on the freon side for heat transport into the column, This condition is now going to be controlled using 61!^^g. In the condenser, which is the other contact point between the heat pump and the column, the saturation pressure PL is a sufficient measure of the condition on the freon side for heat transport from the column. So this control structures, i.e., valve OLQ^^ control low pressure and valve dJ^yg control high pressure, can reject the disturbance and stable the system.

7. Conclusion With a systematic computer aided analysis of the process model inspired by Boris et al, the control and design problems for an energy integrated distillation column are carried out. The relationships between design and control problems are discussed through analysis of the static process model to result in a more suitable control actuator configuration for the integrated distillation column. Rigorous simulation results verify this analysis. This paper addresses how to select and combine actuators in order to achieve nearly independent actuator actions. Thereby the interactions between basic control loops in the integrated distillation column are significantly reduced which is the basis for optimising control.

8. References Bristol, E.H., 1966, On a New Measure of Interactions for Multivariable Process Control; IEEE Trans. Automat. Control, AC-11, 133-134. Eden, M.R., K0ggersb0l, A., Hallager, L. and J0rgensen , S. B. 2000, Computer and Chemical Engineering, 24, 1091-1097. Eden, M.R., L0ppenthien, C. and Skotte, R., 2000, Distillation Column Startup Manual, Technical University of Denmark, Lyngby, Denmark. Koggersb0l, A., 1995, Distillation Column Dynamics, Operability and Control, Ph. D Thesis, Technical University of Denmark, Denmark. Russel , B.M., Henriksen, J.P., J0rgensen , S.B. and Gani, R., 2002, Computer and Chemical Engineering, 26(2), 213-216. Stanley, G., Marino-Galarraga, M. and Avoy, Mc, 1985, Shortcut Operability Analysis. The Relative Disturbance Gain; Industry Engineering Chemistry, Process Design Development, Vol. 24(4), 1181-1188. Zuiderweg, F.J., 1982, Sieve Trays: A view on the State of the Art; Chemical Engineering Science. Vol. 37(10), 1441-1464.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

455

Process Monitoring Based on Wavelet Packet Principal Component Analysis Li Xiuxi, Yu Qian*, Junfeng Wang School of Chemical Engineering, South China University of Technology, Guangzhou, 510640, P. R. China

Abstract For improving performance of principal component analysis (PCA) for process monitoring with noise, this paper proposes a wavelet packet PCA (WPPCA). It integrates ability of wavelet packet in de-noise and ability of PCA to de-correlate the variables by extracting a linear relationship. Process monitoring is simulated in a two-inputs, two-outputs dynamic process with noise. The simulation result shows that the wavelet packet PCA eliminate effects of noise effectively with better monitoring performance. Finally, the proposed approach is successfully applied to Tennessee Eastman process for dynamic monitoring.

1. Introduction Process monitoring is applied to improve reliability and safety of process operation. The main functions of process monitoring include: monitor the system operation status; detect the occurrence of fault; quantitative analysis of the abnormal extent; determine the type, time, extent, exterior, action ways and influence extent of faults. PCA as an effective method of data analysis techniques has been widely applied in process monitoring (Wise and Ricker, 1991; Nomikos and MacGregor, 1995). However, as PCA mainly analysis the linearity and steady state of process variables, its application on complicated process system is restricted. Barkshi et al (1998) had proposed a multi-scale PCA (MSPCA) to improve the local analysis of time-frequency, which combines wavelet analysis with conventional PCA. Qin et al (1999) applied the MSPCA to fault diagnosis and detective of sensor, and simulated the tubular reactor and furnace, which got good results. But the wavelet analysis just divides low-frequency part of signal. Since it ignores high-frequency part, the de-noise performance of it is restricted. To improve the PCA monitoring performance in process with noise, this paper proposes wavelet packet PCA (WPPCA), combining wavelet packet analysis and PCA.

2. Wavelet Packet PCA Wavelet packet PCA integrates PCA and wavelet packet analysis. Wavelet packet analysis decomposes the high-frequency part further, which wavelet analysis not does, and adaptively selects relative frequency bond based on character of signal to be analyzed. The steps in the WPPCA methodology are shown in Figure 1, and the detailed procedures are given as follows.

Corresponding author, Tel: +86(20)87112046, E-mail address: [email protected]

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^

>< t-^ o ^ R ^\ /7 p \\J/ 3. X

inSHi

': h ^ V <- —— N

V

\ni? a-

W,1,2

• /

•

•/

1

/

^

1

P I

\

/

I P

I \r

^-!

-

y ••'

^ • ' ~ " '

W 1/ *

V^ L,0 J

1-Hg

I 1 ^ '" I I

_ —^^—1 — _ —

L...>

M't/-

F/^. 7. Methodology of wavelet packet PCA.

(1) For each column in data matrix, select wavelet packet function ^jXn{t) and wavelet packet dividing level L and compute wavelet packet decomposition coefficients {WL,0,WL,b..-,WL/-l};

(2) For each variable, use the same best full wavelet packet base algorithm to process wavelet packet decomposition tree and find best wavelet packet decomposition coefficients; (3) Select these coefficients as column vector to build wavelet packet coefficients matrixes with different tree nodes {X^oi ^L,U""XL,I^.\]^ the row number of these matrix is n/2^ and the column number is m; (4) For these coefficients matrixes, respectively use conventional PCA to confirm the retain number of principal components and compute principal components score matrixes {7^,0, 71,i,...,r^/.i} and load matrixes {PL,Q, PL,U"',PL,I-\}\ (5) Use retain score matrixes and load matrixes to rebuild wavelet packet coefficients matrixes {X\^Q, ^ ' / . b - - - ^ L / - I } ;

combines corresponding column (6) For each column in [X\^Q, X\^i,...^\^2^.x}, vectors to get rebuild wavelet packet coefficients; (7) For these coefficients, respectively use wavelet packet de-noise limit method to process these coefficients and get de-noising coefficients; (8) Use wavelet packet rebuild algorithm to get each variable samples {x\,X2,...yXm}', (9) Build new data matrix X* and use PCA to select the retain number of principal components and compute score matrix T and load matrix P\ The WPPCA combines the ability of PCA to de-correlate the variables by extracting a

457

linear relationship with that of wavelet packet analysis to extract auto-correlated measurements. To combine the PCA method and wavelet packet analysis efficiently, each measurement variable, which is also the column vector of the original data matrix, are decomposed to wavelet packet coefficient column vector using the same best full wavelet packet base. That is, the original data matrix X is transformed to WpX. In which Wp is an nxn standard orthogonal matrix, and Wp denotes the transform factor which includes the filter coefficients.

In which WPi^2.i(i=0,l,...,L) denotes the wavelet packet filter coefficient matrix. The relations between principle component analysis for X and the principle component analysis for WpX are given by following two theorems: Theorem 1: The principle component load vector for WpX is same as the principle component load vector for X, and the principle component score vector for WpX is the wavelet packet transform of the principle component score vector for X. Proving: Because each column of matrix X is analyzed with the wavelet packet using the same wavelet packet transform matrix Wp, the relativities among the columns of matrix WpX and the columns of matrix X are unchanged. From: (WpXfiWpX) = X''w\WpX=X''X We will see that when number of sampling points are large enough, the columns mean value of the matrix WpX are equal to the colunm mean value of the original data matrix X. And their covariance matrix is the same too. The above equation shows that after the transformation the principle component load vectors of the matrix WpX are the same with that of the original data matrix X. From PCA, we can get: X = TP^ So: WpX = (WpT)P'^ It shows that the principle components score vectors of the matrix WpX are the wavelet packet transformations of the principle components score vectors of the matrix X. Done. Theorem 2: When no principle component is ignored in any scales and no wavelet packet coefficient are eliminated by the threshold value, the result of WPPCAis equal to the result of PCA. Proving: From the properties of wavelet packet transformation and wavelet packet reconstruction we will see that if the wavelet packet coefficients are not treated, the wavelet packet reconstructed signals are the same as the original signals. When all principle components are reserved, the reconstructed data matrix is the same with the original data matrix. Done.

3. Algorithm Performance Simulation To test the performance of wavelet packet principle component analysis in dynamic process monitoring with noise, a 2-in-2-out three order dynamic system with noise is employed. The mathematical models are:

458 z{k)-.

0.087 -0.102 0.118 -0.191 z{k-\) + z(k-2) 0.847 0.264 0.638 0.147 [0.053

-0.091

[0.476

0.128

z(k-3) +

1

2

3

-4

luik-V)-^

0.8 0.8

a(k-l)

y{k) = z{k)+v{k)-\-0.%o{k) where u is the input variable.

u(k) =

0.811

-0.226

0.477

0.415

M(A:-1) +

-0.328

0.143

0.096

0.188

0.455

-0.162

0.135

0.242

\u(k-3) +

\u(k-2)

0.193

0.689

-0.320

-0.749

\8(k-l)-\-

0.8 0.8

cr(k-l)

where f'is a random white noise which mean value is 0 and variance is 1, v is a random white noise which mean value is 0 and variance is 0.1, (J is a random white noise which mean value is 0 and variance is 1. 1000 normal samples are selected, and a MSPCA model and a WPPCA model are established respectively. The SPE and T^ and control limitation are calculated. When the confidence region is 95%, the control limitations are: 5P^«=1.7564, 7^«=7.0356.

jAJJiMiM

,. . ^1 A./v.^l^AAA7^A 20 40 60 80 100 120 140 160 180 200

20 40 60 80 100 120 140 160 180 200

20

Sample (a) Fig. 2. SPE and f plot with variance error, (a)WPPCA,

40

60 80 100 120 140 160 180 200 Sample

(b) (b)MSPCA.

200 sampling real-time data are monitored using the proposed model. To test the monitoring performance, a variance error disturbance is introduced at the 160th sampling time and canceled at the 162nd sampling time. The plots of SPE and 7^ are shown in Fig. 2. From Fig. 2(a), only few sampling points are over control limitation before the 160 time because of the noise, and the disturbance is detected successfully. It shows that the WPPCA will detect the abnormal status very well, and monitor the dynamic process with noises efficiently. Fig.2(b) is the result of MSPCA based on

459 wavelet analysis. Neither the SPE plot nor the T^ plot can detect the disturbance occurrence at the 160th sampling time. The results show that the WPPCA is better than MSPCA based on wavelet multi-frequency analysis in process monitoring.

4. Case Study In this Section, the proposed wavelet PCA approach is applied to the monitoring problem of the Tennessee Eastman (TE) process. Tennessee Eastman process, which was developed by Downs and Vogel (1993), consists of five major unit operations: a reactor, a condenser, a vapor-liquid separator, a recycle compressor, and a product stripper. Some disturbances are programmed for researching the characteristics of the control system, listed in Table 1.

Table 1. Process disturbance for the Tennessee Eastman. Case IDV(l) IDV(2) IDV(3) IDV(4) IDV(5) IDV(6) IDV(7) IDV(8) IDV(9) IDV( 10) IDV( 11) IDV(12) IDV( 13) IDV(14) IDV(15) IDV(16)

Disturbance A/C feed ratio, B composition constant B composition, A/C ratio constant D feed temperature Reactor cooling water inlet temperature Condenser cooling water inlet temperature A feed loss C header pressure loss - reduced availability A, B, C feed composition D feed temperature C feed temperature Reactor cooling water inlet temperature Condenser cooling water inlet temperature Reaction kinetics Reactor cooling water valve Condenser cooling water valve Unknown

Type Step Step Step Step Step Step Step Random variation Random variation Random variation Random variation Random variation Slow drift Sticking Sticking Unknown

The reference set contains 1000 samples from normal operation with a sampling interval of 3 min. For the sufficient representation of the normal status of the TE process, these data are sampled in 10 groups, and the mean values of them are regarded as normal operation data. A WPPCA model is developed from these data. Nine principal components are selected, which capture 90.32% of the variation in the reference set. The control limits shown in every plot correspond approximately to the 95% confidence region, which is determined by using the methodology presented by Nomikos and MacGregor (1994): 5P£:«=7.1509, 7^«=75.0008. The simulation is run under the first disturbance IDV(l), which is loaded at the 300th time step. SPE plot and T^ plot are shown in Figure 4. From these plots, disturbance is quickly detected, although before the 200 time there still are some sampling points of SPE and T^ over control limit to false alarm. After the 300th time, the SPE and the T^ plots are far over the control limit. Figure 5 shows the scores plot. The figure clearly illustrates that process projection points are away from the normal situation. This result shows that for the TE process the WPPCA will get well effect in process monitoring.

460

1000

1000

Fig. 4. SPE and t^ plots ofWPPCAfor IDV(l).

-10 -180

-140 -100 -60 -20 The First Principal Component

Fig. 5. Scores plot ofWPPCAfor IDV(l).

5. Conclusions In this paper, a wavelet packet PCA is proposed, which integrate performance of wavelet packet analysis de-noise and what of PCA. WPPCA algorithm and two theorems were presented. A dynamic 2-in-2-out three-order process with noise was employed to compare the WPPCA and the MSPCA based on wavelet analysis. The result shows that the WPPCA has the better performance than the MSPCA based on wavelet analysis. Finally, the WPPCA is used in the state monitoring for TE process. Application of TE process shows that the proposed WPPCA approach is effective.

6. References Bakshi, B.R., (1998), Mutiscale PCA with application to multivariate statistical process monitoring. AIChE J., 44(7), 1596-1610. Downs, J.J. and Vogel, E.F., (1993), A plant-wide industrial process control problem. Computers and Chemical Engineering, 17(3), 245-255. Jaffard, S. and Laurencot, P., (1992), Orthonormal wavelets, analysis of operations and applications to numerical analysis. Proceedings of the 3*^^ China-France Conference on Wavelet. Nomikos, P. and MacGregor, J.F., (1994), Monitoring batch processes using multiway principal component analysis, AIChE Journal, 40(8), 1361-1375. Qin, J.S., Lin, W. and Yue, H., (1999), Recursive PCA for adaptive process monitoring, IFAC Congress'99, July 5-9, Beijing, CHINA. Wise, B.M. and Ricker, N.L., (1991), Recent advances in multivariate statistical process control: improving robustness and sensitivity. Proceedings of IFAC ADCHEM Symposium, 125.

7. Acknowledgments Financial support from the National Natural Science Foundation of China (No. 29976015), the China Excellent Young Scientist Fund, China Major Basic Research Development Program (G20000263), and the Excellent Young Professor Fund from the Education Ministry of China are gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

461

Information Criterion for Determination Time Window Length of Dynamic PC A for Process Monitoring Xiuxi Li, Yu Qian*, Junfeng Wang, S Joe Qin^ School of Chemical Engineering, South China University of Technology, Guangzhou 510640, China ^ Department of Chemical Engineering, The University of Texas, Austin TX78712, USA

Abstract Principal component analysis (PCA) is based on and suitable to analysis of stationary processes. When it is applied to dynamic process monitoring, the moving time window approach is used to construct the data matrix to be analyzed. However, the length of the time window and the moving width between time widows are often empirically tested and selected. In this paper, a criterion for determining the time window length is proposed for dynamic process monitoring. A new algorithm of dynamic monitoring is then presented. The proposed selection criterion is used in the new algorithm. Finally, the proposed approach is successfully applied to a two-input two-output process and Tennessee Eastman process for dynamic monitoring.

1. Introduction For safety and good product quality of process plant, it is important to monitor process dynamic operation and to detect upsets, abnormalities, malfunctions, or other unusual events as early as possible. Since first principle models of complicated chemical processes are in many circumstances difficult to develop, data based approaches have been widely used for process monitoring. Among them, the principle component analysis (PCA) extracts a number of independent components from highly correlated process data, has been applied successfully for process monitoring. A limitation of PCA-based monitoring is that the PCA model is built from the data, which is stationary, while most of real industrial processes are dynamic. When it is used to monitor process with dynamic characteristics, it is hard to exactly identify whether faults or normal dynamic varieties. A number of efforts have been done to improve performance of PCA based monitoring techniques (Ku, 1995, Qian, 2000, Kano, 2001, Qin, 2001). However, these articles have not pointed out the criteria how to select the time window length. In this paper we propose a criteria for determining the time window length by using Information Criteria (IC) to compare dynamic monitoring characteristics with different time window length. Equipped with the proposed window length selection criteria, a new dynamic monitoring algorithm is presented.

2. Augment Data Matrix with the Moving Time Window Approach The moving time window approach uses a length-invariable window and moves it along the time axis with a fixed step. With the approach, local dynamic characteristics of data Corresponding author, Tel: +86(20) 87112046, E-mail address: [email protected].

462 series could be captured and varieties of data series could be timely analyzed. Two major parameters of the approach are the window length and the moving width between windows. Selection of the two parameters is critical and not easy. For example, if the window length is selected too large, computational complexity would be augmented enormously. On the other hand, if it is too small, certain of dynamic characteristics might be lost. The key to choose the moving width is to balance the computation complexity and the degree of losing alarm. In practice, it is chosen with operation experience of the industrial processes. Let raw data matrix be Xe3i^^. X^eSR^^'is depicted as follows:

In dynamic PC A models, the augmented matrix

x,{t-l) ^mit + ^-l)

r= x^{t+nw-w) "•

x^{t-\-nw-w-l)

x^{t-\-nw-w) '"

(1)

x^{t-^nw-w-l)Jn'yn{

where / and w are the time window length and the moving width between windows, n' and m' are inferred as follows: n ' = int(( n - Z ) / w ) + 1

(2)

m' = (I + l)m We use AR models to denote the time-lagged variables within the X' matrix, which is represented as Xi(t)+aiiXi(t-l)+..

.-k-aiiXi(t-l)=^t)

(3)

where / is the order of the AR model, equivalent to the time window length, and / G [ 1 , m]. Thus we select the time window length in a way based on the approach of determination the order of AR model.

3. Information criteria for determining the time window length In Section 2, we introduce model identification to interpret dynamic PCA, and find that the selection of the time window length can be accordingly solved with the approach of determination the order of AR model. Identification of a system model may be regarded as confirming the probability distribution of a stochastic process. From this understanding, the principle of information criteria is to select appropriate model structure to maximize the approximate extent between the real probability distribution and the estimated probability distribution based on observation data. Shannon entropy is always used to measure the approximate extent, which is represented as:

H,=lf(x)lnfix)dx where jc is a continuous stochastic variable.

(4)

463 Let stochastic variable x, y be the output variable and observation variable of the system to be identified respectively. Let / {x) be the real probability density of the stochastic process, and g (x| y) be the estimative probability density based on observation variable y. The difference between the entropy of the real probability distribution and the entropy of the estimative probability distribution is regarded as the approximate extent variable of the two probability distributions. It is given by: Uf. g) = - J / W i n f{x)dx - (-J/Win g{x\y)dx) = -\ fix)\n[--^]dx

^^^

Taking into account the model parameter vector a, which is the function of the observation variable y, then ^(x|y)=^[x|a(};)]. Thus the information criterion is defined as: select a model order / to maximize the function / (g), which is given by J{g) = E^{L\fix\g(x\a{y))}

(6)

Based on the same observation data, different estimative parameter vector ai is determined from a number of different model order, /. Accordingly, different probability density function is calculated. The model order is thus determined by maximizing the J{g), as the most appropriate order. Let ao denote the estimative parameter, which maximizes the £';c{ln^[^|^Cy)]}» and a^Lbe the maximal likelihood estimative variable within the ao. Neymann and Pearson have proposed an important asymptotic relation, which is represented as follows:

21„|lteJ|~X;

(7)

That is: 2lng\y\ dML\-2\ngly\aoh X]

(8)

where ^Qy|aAfL] is the maximal likelihood function of the observation variable 3^, and / i s the free degree of the X^ distribution. Akaika have proved that: £,{21ng[^ao]-21ng[x|a^J-X,^

(9)

From Eqns. 8 and 9, we have -2£^fe[lng(;c|a^,]}=-2£jng[y|a^,]}+2r

(10)

Let

/C = -2[lng();|a^J+2/

(11)

then computation of the maximal value of the J(g) is transformed into computation of

464 the minimal value of the IC. The computation of the logarithm maximal likelihood function \ng{y\dMd follows following relationship,

ln^(y|5MJ = ~ l n < 5 |

(12)

where n is the sample number and Sj is the variance of the residual ^. Jenkins and Watts have proved 51-—^-—y^ii

(13)

For dynamic PCA, the residual can be inferred as follows:

S(^;-^;)'-S(^,-^,)'

II =J^

tL

(14)

m where X is the raw data matrix and X is the recursive data matrix after processed by the conventional PCA. Then, from Eqns. 11, 12, 13 and 14, we conclude the information criteria as follows: selecting the moving time window length / to make:

/C = nln -ii^i^:

.

^

^ + 2r

(15)

m(n-2l-l) minimal, where y is the number of the estimative parameters and equal to / in the AR model.

4. A dynamic monitoring scheme using moving time window To make the proposed parameters selection algorithms useful in real plants, we propose a dynamic monitoring scheme that addresses the issues of operation steady situations varying with time. With the tolerance limits Qa and 7^a» a complete procedure for dynamic process monitoring, including moving time window approach and parameters selection criteria, is implemented in real time, as follows: 1) Use variables correlation analysis approach to determine the raw data matrix X. 2) Calculated, rand X. 3) Depends on operational experience, select the moving width w between time windows. 4) Select time window length set: [/i, I2 ... h], and respectively calculate the augment matrix [X'l ... X's]. 5) Calculate [ P ^ . . . P ' s ] , [ r i . . . r s ] and [x;.-.x:J. 6) Calculate [ICi ... IQ] from Eqns. 15. Select the minimal value ICmin from [ICi ... ICs\ and the corresponding /, X\ P\ T and X' be selected at last. 7) For real time data, calculate Q^ and f^i. If Q\>Qa or f^i>f^a^ further identify

465 which variable arises the abnormal situation by variable contribution plot. 8) Otherwise, set / = / + 1 and go to step 7.

5. Application to dynamic process monitoring In this Section, the proposed dynamic monitoring scheme is applied to the monitoring problem of the Tennessee Eastman process. Tennessee Eastman process, which was developed by Downs and Vogel (1993), consists of five major unit operations: a reactor, a condenser, a vapor-liquid separator, a recycle compressor, and a product stripper. The process has 41 measurements, including 22 continuous process measurements and 19 composition measurements, and 12 manipulated variables. Some disturbances are programmed for researching the characteristics of the control system, listed in Table 1. Table 1. Process disturbance for the Tennessee Eastman. Case IDV(l) IDV(2) IDV(3) IDV(4) IDV(5) IDV(6) IDV(7) IDV(8) IDV(9) IDV(IO) IDV( 11) IDV(12) IDV( 13) IDV(14) IDV(15) IDV(16)

Disturbance A/C feed ratio, B composition constant B composition, A/C ratio constant D feed temperature Reactor cooling water inlet temperature Condenser cooling water inlet temperature A feed loss C header pressure loss - reduced availability A, B, C feed composition D feed temperature C feed temperature Reactor cooling water inlet temperature Condenser cooling water inlet temperature Reaction kinetics Reactor cooling water valve Condenser cooling water valve Unknown

Type Step Step Step Step Step Step Step Random variation Random variation Random variation Random variation Random variation Slow drift Sticking Sticking Unknown

The reference set contains 1000 samples from normal operation with a sampling interval of 3 min. Considering the performance of dealing with multivariate process of the PC A, we selects time window length / set as [1 2 3]. From Eqns. 15, we can accordingly compute the IC values of different /. Based on the proposed IC approach, the / is chosen as 3. The window moving width w is chosen as 4. Thus the data matrix is a (250x64) array, where 250 is the number of available data windows, 64 is the number of variables. A linear DPCA model is developed from the data matrix. Seventeen principal components are selected, which capture 97.7% of the variation in the reference set. The control limits shown in every plot correspond approximately to the 95% confidence region, which is determined by using the methodology presented by Nomikos and MacGregor. To verify the effectiveness of the proposed IC approach, four comparative simulations for the DPCA model and the CPCA are made. In the first case, the disturbance IDV(l) is introduced at sample 200. The result is shown in Fig. 1. Using the CPCA, many SPE values have been out of the control limit even if the process is normal. However, the DPCA is able to well detect the disturbance. The second case involves the disturbance IDV(2), and the result is shown in Fig. 2. In general, the performance of dynamic PCA with appropriate / and w should be better than conventional PCA.

466

250

400

600

1000

Sample

Fig.l SPE plots of data characterizing IDV(l) projected onto the DPCA model and the CPCA model.

Fig. 2 SPE plots of data characterizing IDV(2) projected onto the DPCA model and the CPCA model.

6. Conclusions Inspired from the principle of identification dynamic time-series model by determining the model order, we present in this paper an Information Criteria (IC) approach to select the time window length in the dynamic PCA. Then a new dynamic monitoring algorithm with the proposed IC approach is presented. Application of TE process proved that the proposed IC approach is effective. The dynamic PCA with appropriate time window length and windows moving width is able to detect and identify faults and abnormal events better than conventional PCA approach.

7. References Downs, J.J. and Vogel, E.F., 1993, A plant-wide industrial process control problem. Computer and Chemical Engineering, 17, 245-255. Jenkins, GM. and Watts, D.G, 1968, Spectral analysis and its applications. San Francisco: Holden-Day. Kano, M., Hasebe, S. Hashimoto, I. and Ohno, H., 2001. A new multivariate statistical process monitoring method using principal component analysis. Computer and Chemical Engineering, 25, 1103-1113. Ku, W., Storer, R. and Georgakis, C , 1995, Disturbance detection and isolation by dynamic principal component analysis. Chemometrics and Intelligent Lab. Systems 30, 179-196. Li, Weihua and Qin, S.J., 2001. Consistent dynamic PCA based on errors-in-variables subspace identification. Journal of Process Control, 11, 661-678. Lin Weilu, Qian, Y. and Li, X.X., 2000, Nonlinear dynamic principal component analysis for on-line process monitoring and diagnosis. Computer and Chemical Engineering, 24,423-429.

8. Acknowledgments Financial support from the National Natural Science Foundation of China (No. 29976015), the China Excellent Young Scientist Fund, China Major Basic Research Development Program (G20000263) are gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

467

Tendency Model-based Improvement of the Slave Loop in Cascade Temperature Control of Batch Process Units Janos Madar, Ferenc Szeifert, Lajos Nagy, Tibor Chovan, Janos Abonyi University of Veszprem, Department of Process Engineering Veszprem, P.O. Box 158, H-8201, Hungary, [email protected]

Abstract The dynamic behaviour of batch process units changes with time and this makes their precision control difficult. The aim of this paper is to highlight that the slave process of batch process units can have a more complex dynamics than the master loop has, and very often this could be the reason for the non-satisfying control performance. Since the slave process is determined by the mechanical construction of the unit, the above mentioned problem can be effectively handled by a model-based controller designed using an appropriate nonlinear tendency model. The paper presents the structure of the tendency model of typical slave processes and presents a case study where real-time control results show that the proposed methodology gives superior control performance over the widely applied cascade PID control scheme.

1. Introduction In the pharmaceutical and food industry high-value-added products are manufactured mainly in batch process units. The heart of units is generally a jacketed stirred tank in which not only chemical transformation, but distillation, crystallisation, etc. can also be performed. As the aim of pharmaceutical industry is to produce high quality and purity products, the optimisation and control of operating conditions is the most efficient approach to produce efficiently, as well as to reach specific final conditions of the product in terms of quality and quantity (Cezerac, 1995). The 888.01 batch control standard defines three types of control needed for batch processing (ECES, 1997): • Basic control comprises the control dedicated to establishing and maintaining a specific state of the equipment and process. Hence, basic control includes regulatory control, interlocking, monitoring, exception handling. • Procedural control directs equipment-oriented actions to take place in an ordered sequence in order to carry out a process-oriented task. Hence, procedural control is characteristic of batch processes. • Co-ordination control directs, initiates and/or modifies the execution of procedural control and the utilisation of equipment entities. Examples of co-ordination control are algorithms for supervising availability of capacity of equipment, allocating equipment to batches, etc. When these control types are applied to the equipment, the resulting equipment entities provide suitable process functionality and control capability. However, lots of theoretical and practical problems have to be solved for the successful implementation.

468 Recently, the research focuses on the higher hierarchical levels (co-ordination control like scheduling and optimisation, and procedural control) (Garcia, 1995; Terwiesch, 1998; Book, 2(XX)), and the basic control is assumed to be the same as the control of continuous processes. However, in the batch environment, there may be higher requirements on the performance of basic control (Fisher, 1990). Due to the complexity of the chemical synthesis and the difficulty to estimate reactant compositions on-line, the control of reactors remains basically a temperature control problem, commonly performed directly or indirectly through heat exchangers with a heat transfer fluid circulating in the jacket surrounding the reactor. For this purpose, generally simple cascade control systems are used (Cezerac, 1995) and usually not very much attention is paid to the tuning of the slave control loop (i.e. in practice simple proportional controllers are used). However, according to our industrial experience, the performance of the complex and hierarchical solutions is primarily constrained by the performance of the split-range controller in the slave-loop. Hence, this paper focuses on the slave-loop control and presents a detailed case study where the impact of the slave-loop is illustrated by the temperature control of a pilot plant presented in Section 2. The tendency model of the jacket of the reactor is given in Section 3, while in Section 4 this model is utilized in a model-based control algorithm. Based on the real-time control results presented also in this section, some conclusions will be drawn in Section 5.

2. Process Description: Prototype of Pharmaceutical Process Systems To study the control strategies of multipurpose production plants a prototype of pharmaceutical process systems was conceptualized. The physical model of this system was designed and installed in our laboratory. The P&I diagram of the process is shown on Figure 1. As depicted in Figure 1, the central element of the process unit is a 50 liter stirred autoclave with heating-cooling jacket. The unit contains feeding, collector and condenser equipments.

Figure 1. The prototype of the pilot process unit.

469 Through the jacket the direct heating-cooling system allows cooling with chilled water or heating with steam in steam or hot water mode. In the hot water heating mode the water is circulated by a pump, the steam is introduced through a mixer, while the excess water is removed through an overflow. Since the system is multipurpose and operates in batch regime, the precision temperature control is not a simple problem. In the industrial practice, cascade structure is used to decompose the problem into two parts. Contrary to the classical PID-PID cascade scheme, in this paper model-based controllers are applied at both the master and slave levels. The manipulated variable at the master level is the jacket temperature; the disturbance (that can be indirectly determined in model-based solutions) is the heat flux of the processes taking place in the reactor. The manipulated variables of the slave process are the valve signals (VI: steam valve, V2: cooling water valve); the disturbance is the reactor temperature; the output is the characteristic jacket temperature. The latter can be defined as the inlet, outlet or average temperature of the jacket. This choice will influence the dynamics of both the slave and master loop processes. Based on dynamical simulation, experimental results and experience gained on other industrial systems we assigned the inlet temperature of the jacket as the output of the slave process. Applying the above decomposition, the master process can be modelled as a first order plus time delay (FOPTD), while the slave process should be modelled as a more complex nonlinear system, as it will be presented in the following section.

3. The Model of the Jacket The jacket and the circulating liquid can be described using the common lumped parameter enthalpy or heat balances given in the chemical engineering literature. In the model, zero-volume distributors and mixers are applied and the overflow as well as the feed of the steam and the fresh cooling water are taken into account. The obtained simplified first principle model can be regarded as the tendency model (Filippi-Bossy, 1989) of the most important phenomena. Its scheme is given on Figure 2 where TH is the temperature of the cooling water coming from the environment, TF is the equivalent steam temperature calculated from the boiling temperature, the latent heat and specific heat. The valve characteristics are given in form of second order polynomials. The two first order transfer functions are obtained from the lumped parameter model of the jacket and the model of the thermometer at the jacket inlet. The Kl, K2, and K3 constants can be calculated from the parameters of the first-principles model of the process or can be identified using experimental data. For this purpose open-loop experiments were conducted on the whole operating range of the composite manipulated variable u (because of the split-range control: VI and V2 are not opened at the same time, u=100% means that VI is opened fully, u=0% means that V2 is opened fully). For comparison, beside the proposed tendency model (Ml) a FOPTD (M2) model with was identified based on the data shown of Figure 3. The significant deviation between the two models supports our practical experience that controller design based on linear models cannot provide good control performance in the slave loop. To prove this assumption in the following section real-time control experiments will be presented where the previously presented tendency model will be applied in model-based temperature control of the batch process unit.

470

reactor temperature

T1,T2 DT K KAR

Time constant Time-delay Gain Nonlinear valve characheristic

Figure 2. Schematic model of the reactor jacket.

Figure 3. Comparison of slave models and the process.

4. Temperature Control The proposed simple, but structurally transparent model can be easily utilised in several model-based control algorithms. We chose the so called Predictor-Corrector Controller (PCC) scheme which was developed and tested by us in many pharmaceutical applications in the previous decade (Abonyi et al., 1999). The basic scheme of the PCC algorithm is shown in Figure 4. Similarly to the Internal Model Control (IMC) scheme, the model is modified in every time-instant according to the measured process variables (correction). The control signal is calculated analytically based on this corrected tendency model without solving any optimisation problem. The operation of the proposed slave loop controller is demonstrated as a part of the complete reactor temperature control, where the master model-based controller was based on an FOPTD model. The parameters of the models were determined using the experimental data given of Figure 3. For comparison, a classical PID-PID cascade controller was also designed to the process and its parameters were optimized on the models of the master and slave processes and fine-tuned experimentally. The performance of this cascade PID-PID controller in a heat-up operation is shown on Figure 5. (The manipulated variables are constrained because of the physical limitations of the system). The same experiment was conducted using the model-based PCC-PCC controller scheme, and the

471 result is given on Figure 6. This result shows that the proposed methodology gives superior control performance over the widely applied cascade PID control scheme. As the master process is a simple FOPTD system that is easy to control, we have realized that mainly the slave-controller determines the overall control performance. Model Linear dynamic, Steady-state nonlinearity, Physical constrains

•

I I zlj

Corrector

Predictor

^

handling modelling error

P-inverse model

PCC

.

^

!

I

measurement

Process

control input

Figure 4. Scheme of PCC algorithm. -Y_mastef

—SP_»live

—Y_slava

—VI

—V2

|

Figure 5. Reactor temperature control using a PID controller. I

—SP_nw»tf

Ev^

Figure 6. Reactor temperature control applying a PCC controller.

472 This is because the proposed model-based slave loop controller is able to effectively handle the nonlinearities and the constraints of the valves and accurately describes the dynamics of the jacket of the reactor. This observation confirms our practical experience gained during the installation and tuning of model-based controllers in the Hungarian pharmaceutical industry in the last ten years. The advantages of PCC are the following: superior performance over PID control, effective constraint handling (no windup), the parameters of the controllers can be easily determined by simple process experiments, and the complexity of the controller is comparable to that of a well furnished PID controller. Furthermore, the analysis of the modelling error gives the possibility of process monitoring.

5. Conclusions The reason for the non-satisfying control performance of batch process units very often is the slave process that can have a more complex dynamics than the master loop has. As the slave process is determined by the mechanical construction, it is straightforward to design a model-based controller based on a nonlinear tendency model of the slave process. It has been shown that the parameters of the model-based slave controller (namely the parameters of the tendency model) can be easily determined by simple process experiments, and the complexity of the controller is comparable to that of a well furnished PID controller. Real-time control results showed that the proposed controller effectively handles the constraints (no windup) and gives superior control performance.

6. References Cezerac, J., Garcia, V. Cabassud, M., Le Lann, M.V. and Casamatta, G., 1995, Comp. Chem.Eng., 19,S415. European Committee for Electrotechnical Standardisation, 1997, S88.01, EN 61512-1. Garcia, V., Cabassud, M., Le Lann, M.V., Pibouleau, L. and Casamatta, G., 1995, The Chem. Eng. Biochem. Eng. J., 59, 229. Terwiesch, P., Ravemark, D., Schenker, B. and Rippin, D.W.T., 1998, Comp. Chem. Eng., 22, 201. Book, N.L. and Bhatnagar, V., 2000, Comp. Chem. Eng., 24, 1641. Fisher, T.G., 1990, Batch Control Systems - Design, Application and Implementation, Instrument Society of America. Abonyi, J., Chovan, T., Nagy, L. and Szeifert, F., 1999, Comp. & Chem. Eng., 23, S221. Filippi-Bossy, C , Bordet, J., Villermaux, J., Marchal-Brassely, S. and Georgakis, C , 1989, Comp. Chem. Eng., 13, 35.

7. Acknowledgements The authors would like to acknowledge the support of the Cooperative Research Center (VIKKK) (project 2001-1-7 and II-IB), and founding from the Hungarian Ministry of Education (FKFP-0073/2001 and 0063/2000) and from the Hungarian Research Found (OTKA T0376(X)). Janos Abonyi is grateful for the financial support of the Janos Bolyai Research Fellowship of the Hungarian Academy of Science.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

473

Consistent Malfunction Diagnosis Inside Control Loops Using Signed Directed Graphs Mano Ram Maury a", Raghunathan Rengaswamy^, and Venkat Venkatasubramanian^'* "Laboratory for Intelligent Process Systems, School of Chemical Engineering, Purdue University, West Lafayette, IN 47907, USA. ^Department of Chemical Engineering, Clarkson University, Potsdam, NY 13699-5705, USA.

Abstract Though signed directed graphs (SDG) have been widely used for modeling control loops, due to lack of adequate understanding of SDG-based steady state process modeling, special and cumbersome methods are used to analyze control loops. In this article, we discuss a unified SDG model for control loops (proposed by Maury a et al. (2002b)), in which both disturbances (sensor bias etc.) as well as structural faults (sensor failure etc.) can be easily modeled. Various fault scenarios such as extemal disturbances, sensor bias, controller failure etc. have been discussed. Two case studies are presented to show the utility of the SDG model for fault diagnosis. A tank-level control system is used as first case study. The second case study deals with fault diagnosis of a multi-stream controlled CSTR.

1. Introduction Various types of faults occurring in a chemical plant can be broadly categorized as (1) faults originating outside control loops and (2) faults originating inside control loops. A properly functioning controller (emulating integral control action) masks the faults since the effect of disturbances is passed to the manipulated variable even though the error signal is zero. Thus, presence of control loops makes fault diagnosis more challenging. Among many models such as fault trees, completely numerical models etc., signed directed graphs (SDG) have been widely used for modeling control loops. Iri et al. (1979) were the first to use SDG for modeling a chemical process. Later, Oyeleye and Kramer (1988) discussed about SDG-based steady state analysis and prediction of inverse response (IR) and compensatory response (CR). Recently, Chen and Howell (2001) presented fault diagnosis of controlled systems where SDG has been used to model control loops. Previous researchers used special methods to deal with control loops since SDGbased steady state modeling was not fully explored. Recently, Maurya et al. (2(X)2c) presented a systematic framework for SDG-based process modeling and analysis. We also proposed a unified SDG-model for control loops in which both disturbances (e.g.

* Author to whom all correspondences should be addressed, e-mail: [email protected], phone: (765) 494 0734, fax: (765) 494 0805.

474 sensor bias) as well as structural faults (e.g. sensor failure) can be easily modeled and analyzed (Maurya et ai, 2002Z?). In this article, we explore the fault diagnostic applications of the proposed model. This article is organized as follows. In the next section, we present a brief overview of our SDG-related work. In section 3, we discuss the unified SDG model for control loops. Various fault scenarios are also analyzed. In section 4, two case studies are presented to show the diagnostic efficiency of the proposed framework for fault diagnosis of systems with control loops. The article is concluded with discussion on future work.

2. Overview of SDG-based Process Modeling and Analysis A brief discussion on SDG-based process modeling and analysis is presented here. A detailed discussion can be found in (Maurya et al, 2002c). A SDG for a process can be developed from the model equations of the process. A process can be described by differential equations (DE), algebraic equations (AE) or differential algebraic equations (DAE). The initial response of a DE system can be predicted by propagation through the shortest paths from the fault node to the process variables. The initial response of a DAE system with only one perfect matching (or only negative cycles) in the algebraic part can be predicted by propagation through shortest paths assuming that arc length for differential arcs and algebraic arcs are 1 and 0, respectively. A perfect matching between the equations and dependent variables is a complete matching in which each equation is matched with a variable and no variable or equation is left unmatched. The response of an AE system can be predicted by analyzing the corresponding qualitative equations or propagation through the SDG (provided that the AE system has only one perfect matching or there are no positive cycles in the SDG for the AE system). The steady state response of a dynamic system can be predicted by using the SDG for the corresponding steady state equations. Maurya et al. (2002^) have shown that the qualitative equations ensure correct prediction of the steady state behavior of systems that exhibit CR. This leads to considerable simplification in SDG-based steady state analysis of control loops. A succinct discussion is presented next. For detailed discussion, see (Maurya et al, 2002a).

3. Control Loops- a Unified Framework Most of the control loops used in the industry are PI control loops (as far as their behavior is concerned). All control loops considered in this section are assumed to be PI control loops unless otherwise stated. Oyeleye and Kramer (1988) have analyzed PI control loop as a system exhibiting CR. It has already been shown that CR is implicitly handled by the steady state equations, no special method is needed to analyze control loops (Maurya et al, 2002b). Depending upon the qualitative state of the error signal, appropriate changes in the perfect matching handle the underlying scenario. 3.1. Model and preliminary analysis of a control loop The fault variables considered are the bias in the measurement, the controller signal and the valve position, set point (in the context that set point can be changed by an external agent), and failure in the measurement, the controller signal and the valve position. The model for a PI controller is given below.

475 External system

External system

csfaii fM<^y

CS fail 0

^ ^•"•W"

CSbias #^ ^ Positive arcs ^ Negative arcs k>0 kc>0 kv>0

8([CSfail])'''' (a) Information flow for e;^0

CS,

x^

(b) Information flow for e=0

Figure 1. SDGfor a PI control loop. ,bias m

(2)

~ ^m

CSp

(3) KQ.S

dt CS VP

(1)

^

ri S{CSfail).{CSp +

(4)

CSi)-hCStia

^{VPfail).K.CS^VPuas

(5) (6)

In the above equations, X, CS and VP refer to the controlled variable, controller signal (controller output) and valve position (or manipulated variable), respectively. The subscripts m, P and / refer to measurement, P control and I control, respectively, kc and ky are the controller gain and the valve gains, respectively. Failure inside the control loop is modeled by introducing non-zero deviations in the corresponding failure and bias variables. For example, sensor failing high is modeled as Xmjaii = 1 and Xm,bias ='+' etc. The effect of VP and external variables (say Xj') on X is modeled as: X = k.VP -h ttijfXjf

(7)

Usually the above equation is matched with X = Xiin the absence of a control loop and k represents the process gain (kp). The system described by equations 1-7 has two perfect matchings. One of the SDGs of this DAE system for [kc] = [k] = [ky] ='+' is shown in Figure 1(a). There is only a negative feedback cycle in the AE part of the SDG and hence propagation is valid (Maurya et ah, 2002c). Now we discuss initial and steady state response of the PI controller. Initial response: Figure 1(a) shows the SDG for the DAE system. Initial response can be predicted by propagation through the shortest paths in this SDG. The controller effectively behaves as a P controller. Thus equation 4 and CSj can be eliminated from analysis. The remaining equations constitute model of a P controller. For non-zero disturbances or bias, the error, e^O (corresponds to imperfect control). Information flow is as expected. The SDG also shows the interaction between the control loop and the extemal system.

476 Steady state response: Figure 1(b) shows the SDG for the corresponding AE. Ideally speaking, steady state refers to the state when all the derivative vanish i.e. e = 0 in equation 4. The arc (e -> CSp) becomes ineffective. Now X^^ = Xm and as observed in the previous section, perfect matchings change (the AE system has only one perfect matching) and information flow is exactly opposite to that of the previous case. Perfect control is achieved under such conditions. Figure 1(b) also shows the interaction of the control loop with the extemal system in steady state. Notice the signs of the arc Xjf —> X (sign is [aijf]) in Figure 1(a) and the arc Xjf —> VP (sign is [—aijf/k]) in Figure 1(b). In another situation, controller and (or) valve opening saturate(s). When X has reached a constant value, in a loose sense one can say that the system has reached steady state. Still, e ^ 0. For all practical purposes, controller saturation can be modeled through P control action with suitably modified gain (that corresponds to the ratio of the saturated value of {CSp + CSi) to thefinalvalue of e). This situation corresponds to imperfect control and is explained through Figure 1(a). Thus the concept of perfect matching handles everything within the proposed framework guaranteeing completeness. Further, no spurious solutions are generated and such a framework is useful for large-scale applications. Now a number of fault (disturbance) and failure scenarios are discussed with respect to perfect control and imperfect control. 3.2. Perfect control The controller can be modeled as integral controller (Figure 1(b)) because e = 0. Various faults are discussed below. Changes in external disturbances: Integral action keeps the controlled variable at its set point. The information flow is:

X^' -^Xm-^X

-^VP and xy -^VP^CS^

CSj.

Faults inside the control loop: Three types of faults are: • Sensor bias: The propagation is Xm,bias —> X. Qualitatively, [X] = -[Xm,bias]' • CS bias: The propagation is CSuas -^ CSj. Further, C5='0' and X ='0\ • VP bias: [CS] = -[VPbias] and VP = X ='0\ 3.3. Imperfect control Imperfect control is exhibited due to large extemal faults or control loop failure. The error signal is non-zero (Figure 1(a)). CS builds up till the controller saturates. Two scenarios are: (i) large extemal disturbance, set point change or sensor bias in which the controller behaves as a P controller and, (ii) failure inside the control loop in which the control loop is open. Three types of failure are: • Sensor failure: The arc X —» Xm is cut. Propagation yields [X] = -[Xm^bias]• Controller failure: The paths from e to CS are cut and CS = CSbias• Control valve failure: The arc CS —» VP is cut and X = VP = VPtias-

4. Case Studies Case study 1 deals with fault diagnosis in a tank level-control system. Case study 2 deals with fault diagnosis of a CSTR system.

477 Jo

^n

VP fail 0 ^ kc<0

\

/VP xv"^

\ ^«

y cs, • Positive arcs (a) The controlled tank system

X;;^ Negative arcs

(b) SDG for the perfect control case

Figure 2. The tank-level control system and its SDG. 4.1. Case study 1: Tank-level control system The importance of this case study is three-fold: (1) to explain simple concepts, (2) comparison with the results discussed in the literature and, (3) to emphasize the ability to perform multiple fault diagnosis. The controlled tank and its SDG under the perfect control scenario are given in Figure 2 (a) and (b), respectively, fi and fo are the inlet and outlet flowrates, respectively. L is the level of the liquid in the tank, kc is negative. The measurements are fo, Xm and CS. Diagnosis for two fault scenarios is discussed below. Positive sensor bias: The observed pattern is [fo Xm CS] = [0 0 -f ]. Any fault in fi or set point is ruled out. The candidate faults are VP^ias = ' - ' (=> X='0') or Xm,bias ='+' (=> X ='-'). Further resolution cannot be achieved. Negative sensor bias and positive inletflowrate: One observed pattern could be [fo Xm CS] [+0 0]. fi ='+' is inferred by direct propagation. But this alone cannot explain CS ='0\ Forward simulation shows that if fi ='+' were the only fault then CS ='+\ So the assumption of multiple faults is necessary. One can easily see that the other fault is VPtias

= -^' (X

='0')

or XmMas

= -' (X

= V ) .

A similar case study has been presented by Oyeleye and Kramer (1988) to explain SDGbased analysis of compensatory response. 4.2. Case study 2: A multi-stream controlled CSTR The case study has been taken from Chen and Howell (2001). A detailed SDG-analysis of this case study has been presented elsewhere (Maurya et ai, 2002a). In this section, we present SDG-based control loop diagnosis for this case study. The SDG for the stable system under perfect control scenario is shown in Figure 3. A similar SDG has been presented by Maurya et al. (2002^?) to show that the proposed framework can model type-A interaction. There are no cycles in the SDG. Thus qualitative simulation or fault diagnosis can be performed by using forward or backward propagation, respectively. For a sample comparison with the results discussed in the literature (Table 5 of (Chen and Howell, 2001)), consider fault 1 i.e. L-sensor-bias-high (Lm,bias ='+')• Forward propagation to node LC shows that LC ='-\ Similarly other results can be reproduced. Let us consider diagnosis of the same scenario. The measurements are [LC FC TC FJC FJ CA] = [ + - 4-]. Back-propagation from node FC reveals that the candidate fault set is {FVuas ='-\ FMuas ='-\ LM^as ='+'}•

478

LV.:,

*" Positive arcs Negative arcs

Figure 3. SDGfor the multi-stream controlled CSTR- perfect control. The first two candidates are ruled out since they cannot produce LC ='-'. Thus the fault is LMbias ='+' (complete fault resolution).

5. Conclusions and Future Work A brief discussion on our SDG-related work followed by a detailed discussion on the SDG-based modeling and analysis of control loops has been provided. Two case studies have been presented to elucidate the use of the framework for fault diagnosis. In future, the framework would be used for control loop monitoring and distributed fault diagnosis in large-scale systems.

6. References Chen, J. and Howell, J. 2001, A self-validating control system based approach to plant fault detection and diagnosis, Comp. & Chem. Engg., 25, 337-358. Iri, M., Aoki, K., O'Shima, E. and Matsuyama, H. 1979, An algorithm for diagnosis of system failures in the chemical process, Comp. & Chem. Engg. 3(1-4), 489-493. Maury a, M.R., Rengaswamy, R. andVenkatasubramanian, V. 2002a, A signed directed graph-based systematic framework for malfunction diagnosis inside control loops. Technical Report CIR\C-02-2 Purdue University. Maurya, M.R., Rengaswamy, R. and Venkatasubramanian, V. 2002Z?, A systematic framework for the development and analysis of signed digraphs for chemical processes: Part II- Control loops andflowsheetanalysis; Submitted to Ind. Engng. Chem. Res. Maurya, M.R., Rengaswamy, R. andVenkatasubramanian, V. 2002c, A systematic framework for the development and analysis of signed digraphs for chemical processes: Part I- Algorithms and analysis^ Submitted to Ind. Engng. Chem. Res. Oyeleye, 0.0. and Kramer, M.A. 1988, Qualitative simulation of chemical process systems: Steady-state analysis, AIChE J., 34(9), 1441-1454.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

479

Financial Risk Control in a Discrete Event Supply Chain Fernando D. Mele^"^\ Miguel Bagajewicz^"^^, Antonio Espuna^"^^ and Luis Puigjaner^"^^^*^ (+) Chemical Engineering Department, Universitat Politecnica de Catalunya, ETSEIB. Diagonal 647, E-08028, Barcelona, Spain., Phone: +00 34 934016733. (++) School of Chemical Engineering and Materials Science. University of Oklahoma. 100 E. Boyd, T-335, Norman OK 73019, USA. On sabbatical leave at ETSEIB. (#) Corresponding Author

Abstract In this work, a discrete event supply chain is modeled from the point of view of one of the members. The model takes into account uncertainty and it determines an optimal ordering policy so that profit is maximized and financial risk is controlled. Two cases are considered. In one case, uncertain the behavior of the other members of the chain is known while in the other they are not.

1. Introduction A Supply Chain Management (SCM) problem by means of discrete-event simulation is studied in this paper. The paper is an extension to discrete event modeling of the models presented by Perea-Lopez et al. (2001). We add uncertainty in the form of two-stage modeling and financial risk management (Barbaro and Bagajewicz, 2002a,b). This paper is organized as follows: The SC dynamic modeling is first described. In the following sections, the deterministic and the stochastic models are described. Next, the risk concept utilized is explained. Finally, some conclusions and ideas for future work are exposed.

2. Modeling the Supply Chain It has been consider a supply chain (SC) with all entities acting as independent agents, each of these being represented by a collection of states and transitions (Figure 1). The model has been constructed using two toolboxes of Matlab: Stateflow and Simulink, and it considers the SC as a decentralized system where there is no global coordinator and every entity in it makes decisions locally. The demand has been modeled as a set of events distributed over the time horizon of the study, each of them having an associated amount of material and time of occurrence. The inter-arrival intervals are uniform but the associated amounts are distributed according to a normal distribution.

480 ORDER input (ORin)

^ Order ; Reception

ORDER output {ORou\

i Ordering

Delivering j M { \ T E R I A L output {MAout)

\ Material • I Reception :

MATERIAL input (MAin)

f

Figure 1. Generic unit scheme. The inventory policy aims at determining when should a replenishment order be placed and how large should this order be at each time. At every time R, the inventory position / is checked. All the members of the supply chain, except the one in consideration, behave like follows: If / is below the reorder threshold s, a replenishment quantity is ordered according to a known law. One example of such law is the proportional one used by Perea-Lopez et al. (2001): If the inventory is above a threshold 5, nothing is done until the next review, otherwise an order u is done according to the proportional law, u = k {s - J). Total profit is used as performance index. It considers sales, purchasing costs and storage costs for materials and orders over the simulation time horizon.

3. Deterministic Model Six generic units have been connected as Figure 2 shows. The material flow moves from the entity SIP to the customers and the ordering flow moves in the opposite direction. The inventory control policy beforehand described has been applied in all the entities belonging to the model, except in the DIB.

Rest of the system

,I ORout

DRin

-I

Customer demand

DIB MA

Figure 2. Supply Chain Scheme.

MAout

Figure 3. Relation between the SC and one entity.

The case posed considers that a given plant wishes to make decisions in order to maximize its own profit. The manager of this plant knows the modus operandi of all the chain by means of a simulation model, and has information about the future demand. In

481 our case study, the distribution center DIB receives orders that the system places (ORin). It can either respond by delivering materials (MAout) or save the order if it has not enough material. On the other hand, the system sends materials to DIB (MAin), and if it is necessary, DIB places orders (QRout) to the system. The variable that has to be manipulated to modify the profit of DIB is Orout. The question to answer is what is the quantity of material that should be ordered in time TQ, T'I, x'2 and T'3 in order to maximize DIB's profit. Thus, there exist three possible discrete values at each of the four time instants. One of the permitted values is chosen at each time TQ, T'I, x'2 and T'3, and one simulation of the system is executed. For each simulation, the profit is calculated and the one with largest profit is kept.

Figure 4. Demand and Time instants in which orders have to be placed.

4. Stochastic Model The demand is modeled using normal distributions and sampling scenarios. The amount ordered in time TQ is considered as a first-stage variable, that is, a decision made before the uncertainty is revealed, whereas the amounts of materials ordered in the next periods, T'I, T'2 and T'3, are considered second-stage variables, decisions made after the uncertainty materialization.

5. Financial Risk This work applies the financial risk concept defined in Barbaro and Bagajewicz (2002a). Financial risk is the probability of a certain design x of not meeting a certain target profit level Q. Figure 5 represents a typical curve that describes the risk as a function of different profit targets. The objective is to reduce the risk for certain aspiration levels.

Risk{x,Q) = YJ P^P^^fi^s W < ^ ) SES

(1)

482

Figure 5. Typical risk curve.

6. Results Since the size of the orders that has to be request is chosen between three values, and, in addition, there are four time instants in which an order has to be placed, there are 81 possible combinations for simulating in each scenario. For each one of these configurations, taking into account each scenario, the expected values of the profit (E(profit)) has been calculated and the one with the largest expected profit is picked. In the deterministic case the values for the demand have been chosen in 7 units of product A each five simulations steps and 3 units of B with the same frequency. Moreover, the value for the safety inventory level has been set in 50 units for all the entities except in SIP and PI where the selected value has been 100 units. In the first case below described, a variance of 3 and 2 has been added to both deterministic values of the demand size. In the second case, a variance of 30 has been added to the deterministic value of the safety inventory level. 6.1. First case. Uncertain demand In this case, it has been considered that uncertainty is only in the demands. The model used 100 scenarios and three discrete values at each time. Three curves of maximum profit has been generated (Figure 6). Decisions can be taken by observing the chart and by comparing the expected profit E(Profit) and risk values for each alternative (Table 1). It is important to notice that these curves represent the maximum E(Profit) achieved for each value of TQ. The negative profit values correspond to scenarios in which the sales are minor to the purchases or storage costs in the simulation. For example, if a customer asks for materials and the inventory level is not high enough, the orders are accumulated, then, DIB incurs in a penalization cost.

0.900.80 0.70 0.60 Risk 0.50 0.40 0.30 0.200.10-

0.90 0.800.70 0.600.500.40 0.30 0.20 0.10

/

TO = 0

TO=10 TO=20

i-f^^

,

,

,

Figure 6. Risk curves for the stochastic first case

-3000

^ /

^

TO = 0

.TO=7

J^

TO=14

JJ

/v

/it^

^ ^ -2000

-1000

1000

2000

3000

4000

5000

Figure 7. Risk curves for the stochastic second case.

483 Table 1. Results for the stochastic first case. Order size at TQ 0 10 20

E(Profii) [€] 1043 952 897

Risk{Q = 1000) [%] 46 45 50

Risk(n=: 2000) [%] 86 88 87

6.2. Second case. Uncertain ordering policy in third parties In this case, it has been considered that uncertainty is in one of the parameters of the ordering policy of the entity RIB. It has been supposed that the uncertain parameter is the reorder point s of the inventory control policy of RIB, and the values for this parameter belongs to a normal distribution with a given mean value and variance. The same procedure than in the first case has been applied. Results can be seen in Figure 7 and Table 2. Table 2. Results for the stochastic second case. Order size at TQ E(Profit) [€] RiskjQ = 1000) [%] 0 940 47 7 857 52 14 780 56

Riskj^ = 2000) [%] 89 92 92

6.3. Risk management In both cases above, as the profit is maximized for each option of the first stage variable (size of the order at TQ) the risk also increases. Given the simulation-based approach used, solutions with smaller risk are found by inspection. Consider case one (uncertainty in demands) and an aspiration level of Q, = 500. The risk at this level was computed for all the simulations and the smaller was chosen. The curves corresponding to maximum profit and reduced risk are shown in Figure 9. The size of the order picked for the reduced risk case is now TQ- 10, as opposed to zero for the maximum profit case. The expected profit reduces from 1043 to 940. The risk at an aspiration level of 500 is reduced from 34 % to 28 %, which is significant. For an aspiration level of 0, that is, the risk of loosing money is reduced for this solution from 19 % to 14 %, again a significant reduction. The value of the downside risk at an aspiration level of 0, that is, the integral of the financial curve from -oo to 0 (Barbaro and Bagajewicz, 2002a), also decrease from 40 to 30.

484

Figure 9. Maximum Profit and Reduced Risk curves.

7. Conclusions A SC is modeled in this paper, determining the optimal ordering policy of one of the members in conditions in which the behavior of the other members is perfectly known and the demands are uncertain. A second case was considered where the demands are certain and the parameters of the order policy models of the other members are uncertain. It has been shown how financial risk can be managed. Extensions to the consideration of more uncertain parameters as well as decentralized control with sharing of information or centralized control are work in progress.

8. References Applequist, G.E., Pekny, J.F. and Reklaitis, G.V., 2000, Risk and uncertainty in managing chemical manufacturing supply chains, Comp. Chem. Eng., 24. Barbaro, A.F. and Bagajewicz, M., 2002a, Managing Financial Risk in Planning under Uncertainty, Part I.* Theory, AIChE Journal, Submitted. Barbaro, A.F. and Bagajewicz, M., 2002b, Managing Financial Risk in Planning under Uncertainty, Part II: Applications. AIChE Journal, Submitted. Law, A.M. and Kelton, W.D., 1991, Simulation Modeling & Analysis, McGraw-Hill International Editions. Perea-Lopez, E., Grossmann, I.E., Ydstie, B.E. and Tahmassebi, T., 2001, Dynamic Modeling and Decentralized Control of Supply Chains. Ind.Eng.Chem.Res., 40.

9. Acknowledgements Financial support received from Generalitat de Catalunya, FI programs, and project GICASA-D, and European Community project VIPNET (GlRDT-CT-2000-00318) is fully appreciated. Support form the Ministry of Education of Spain for the sabbatical stay of Dr. Bagajewicz is acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

485

Control Application Study Based on PROCEL Q.F. Meng, J.M. Nougues, MJ., Bagajewicz and L. Puigjaner* Universitat Politecnica de Catalunya, Chemical Engineering Department, Av. Diagonal 647, E-08028 - Barcelona (Spain), Tel.: +34-93-401-6733 / 6678, Fax: +34-93-401-0979. *To whom correspondence should be addressed E-mails: [email protected]

Abstract This is the compare study of control strategy in different operating conditions. To achieve this, a configurable process scenario at pilot plant scale (PROCEL) has been built at the Universidad Politecnica de Catalunya (UPC). In this work, the following study has been carried out in sequence: 1. Walk through the general steps for process control development 2. In Sattline DCS, different configurations have been programmed for continuous mode case study. 3. Using the commercial software MATLAB ,there have been reviewed the performance of various tuning techniques optimisation techniques Genetic Algorithm Results of the above study have been tested.

1. Introduction Objectives: The object is to study of different control strategy using pilot plant data It is a simple control problem, but the aim is to apply different techniques. The majority of the controllers used in industry are of PID type. A large industrial process may have hundreds of these type of controllers. They have to be tuned individually to match the process dynamics in order to provide good and robust control performance. Traditionally there is several methods: 1. Thumb rule. According to the different process, experienced value of PID is applied. 2. Trial and error. 3. Critical point method Including ZN method and TL method. 4. Performance Index, ISE or ITAE. 5. Automatic tuning. This is a series of automatic tuning methods, such as Relay feedback tuning method. By automatic tuning (or auto -tuning), we mean a method which enable the controller to be tuned automatically on demand from an operator or an external signal. In this work, an ITAE index acts as object function. And two optimisation methods Newton search method and Genetic Algorithm are both carried out. Genetic Algorithms' Overview: The Genetic Algorithms is a stochastic global search method that mimics the metaphor of natural biological evolution. GAs operate on a population of potential solutions

486 applying the principle of survival of the fittest to produce better and better approximations to a solution. At each generation, a new set of approximations is created by the process of selecting individuals according to their level of fitness in the problem domain and breeding them together using operators borrowed from natural genetics. This process leads to the evolution of populations of individuals that are better suited to their environment than the individuals that they werecreated from, just as in natural adaptation. GAs versus Traditional Methods: It can be seen that the GA differs substantially from more traditional search and optimisation methods. The four most significant differences are: GAs search a population of points in parallel, not a single point. GAs do not require derivative information or other auxiliary knowledge ;only the objective function and corresponding fitness levels influence the directions of search. GAs use probabilistic transition rules, not deterministic ones. GAs work on an encoding of the parameter set rather than the parameter set itself (except in where real-valued individuals are used). In cases where a particular problem does not have one individual solution, for example a family of Pareto-optimal solutions, as is the case in multi-objective optimisation and scheduling problems, then the GA is potentially useful for identifying these alternative solutions simultaneously. Methodology: 1. System Identification In pilot plant, real-time test to obtain data. Extracting data to do a curve fitting 2. Using mass balance and energy balance equation to calculate the math model of the process 3. Adjust the model to fit the data, compare the fitting between the data and methodology. Using Matlab simulates and develops a tuning parameter ,model validity in case study This paper is arranged as the following part 2, History review of PID controller tuning techniques. In part 3 there is a brief introduction to the PROCEL pilot plant, on e model is presented in part 4,in part 5,a discussion .

2. Tuning controller s techniques The most of the controllers used in industry are of PID type .A large industrial process may have hundreds of this type of controllers. They have to be tuned individually to match the process dynamics in order to provide good and robust control performance. About the tuning techniques: The output of a PID controller is: w (t) =

Kp

= Kp

{e

+ i y \ \

' e + K J y

{T )d T + T ^

e {T ) d T +

K j^

de dt

^ ) dt (1)

487 Traditionally there is several methods: 1. Thumb rule. According to the different process, experienced value of PID is applied. 2. Trial and error. 3. Critical point method. Including ZN method and TL method. 4. Performance Index , ISE or ITAE In this work ITAE will be used. 5. Automatic tuning. This is a series of automatic tuning methods, such as Relay feedback tuning method.

Relay Feedback system

Figure 1. Relay Feedback System. By automatic tuning (or auto-tuning),we mean a method which enable the controller to be tuned automatically on demand from an operator or an external signal. Automatic tuning needs identify the dynamics of a certain process. Usually Relay was mainly used as an amplifier in the fifties and the relay feedback was applied to adaptive control in the sixties. The exciting to a process loop make it reach the critical point. The critical point, i.e , the process frequency response of the phase lag of pi(7i),has been employed to set the PID parameters for many years since the advent of the ZieglerNichols(Z-N) rule. From then several modified identification methods are

^

Ad

Ku=

(2)

an proposed. The controller Cohn-Coon method requires an open-loop test on the process and is thus inconvenient to apply. The disadvantage of the Yuwana and Seborg method and the Bristol method is the need of large set-point change to trigger the tuning which may drive the process away from the operating point. To acquire more than one point of dynamics of process Proposed method: performance index ITAE.

3. PROCEL Description PROCEL, the PROcess CELl pilot plant, has been built at UPC in order to test real time applications. It is constituted by three tank reactors, three heat exchangers and the necessary pumps and valves to allow changes in the configuration. Equipment of the P ROCEL is fully connected and the associated instrumentation allows the change of configuration by software. PROCEL is designed to work in different operation modes. An appropriate set of electric valves makes the plant configurable in different modes of

488 operation in an easy way, from strictly batch operation to continuous or hybrid scenarios. The plant is also provided with a distributed control system (DCS). The Sattline DCS is connected to a PSP(Planning , Scheduling and Programming) Server and Data Server using XML message via TCP/IP network. This flexibility allows making experiments in batch, continuous and batch-continuous mode simply configuring the control software. The DCS is Sattline (ABB). This physical system allows validating different methodologies with a case study that can be transported to complex production structures (i.e. petrochemical plants).

Figure 2. PROCEL Control Configuration.

Tcold

U/.f.) Tl

I^^Ki^" Out I F3 Jhot

Figure 3. Heating Temperaure Control.

2200 2400 2600 2800 3000 3200 3400 360Q 3800 Mm 42Q|||

Figure 4. STEP Response of the system.

4. System Identification The pilot plant contains three glass reactors, EQl, EQ2, Eq3 each with a volume of 10 litres .A highly flexible connectivity between the three vessels is achieved via a network of pipes, pumps and valves.The case to de studied is with EQl, cold water flow Fl, temperature of Tcold is feeding from the top of EQl,one electrical heater is applied to control the temperature Tl,then the heated water is discharged from the bottom with the flow F3,and temperature Tl.To minimise the level fluctuation level loop is facilitated.When the process is stable, a step input of Rl is applied to the process. The

489 process data is collected via MMS OLEGateway + VB program, then the data of CSV format is imported to Matlab workspace. The variable curve is plotted: Then the process dynamic is obtained as the following,in the form of FOPTD ,eq (3),(4)

G(5) =

Gis) =

(3)

250^ + 1

(4)

Ts + l

In the same time ,on the basis of material balance and energy balance , a differential equation is got.

£»(r„j/rf/=AF,fry-rR,j+F2fr2-r;j/;+F5(r5-rR,)7A'R,+ARiVj,;-Zo5i_R;(rRr«m6)y/wM«/CpVR,

(5)

The most important parameter of the model is the gain, delay, and time constant. The necessary adjusting is made to best fitting the process curve.

S.ControUer Design After the model is obtained, the PID parameter tuning is committed

Q]^

{B Out1

o

-KD

Figure 5. ITAE Calculation Block. Here we continue use the PID controller.

ITAE = j'^t-abs(e(t))dt

(6)

In this work , an ITAE index acts as object function. And two optimisation methods Newton method and Genetic Algorithm is both carried out. In this case the object function is a function of index ITAE= f(Plant model(K,I ;D), Integral time, SP, Disturbance) Optimisation parameters procedure: Software enviroment: Matlab 6 relaesel2 Simulink4.0 That is the spent time is 20 minutes and 29 seconds

490 Above is optimisation of Newton search Method That is the spent time is 7 minutes and 7 seconds. The basic genetic algorithm is as follows: 1. Create an initial population (usually a randomly generated string) 2. Evaluate all of the individuals (apply some function or formula to the individuals)

^^^;i9e?5i'

Figure 6. GA Initial Populations 3. Select a new population from the old population based on the fitness of the individuals as given by the evaluation function. 4. Apply some genetic operators (mutation & crossover) to members of the population to create new solutions. 5. Evaluate these newly created individuals. 6. Repeat steps 3-6 (one generation) until the termination criteria has been satisfied (usually perform for a certain fixed number of generations) This code is to generate a population of 10 individuals, and the boundary of explorer is [1.1 9], the evaluation functions "mygademoleval.m", Here we use Genetic Algorithm for Function Optimisation Toolbox ,see reference.

6. Discussion and Conclusion We use a pilot plant to acquire process data and to test controller strategy. A tuning procedure is also proposed based on Optimisation techniques Genetic Algorithm. In the future, an online tuning method will be developed and tested, and applying to MultiVariable, Multiloop system.

7. References Astrom, K.J., Hagglund, T., Huang, C.C, Ho, W.K., 1993, Automatic tuning and adaptation for PID controller-a survey,Control Eng.Practice,(4)(1993) 699-714. Astrom, K.J., Hagglund, T., 2001, The future of PID control-Control Eng. Practice, (9) 1163-1175. Chipperfield, A., Fleming, P. Pohlheim, H., Fonseca', C., Genetic Algorithm Toolbox User's Guide 1-3. Houck, C.R., Joines, J.A., Kay, M.G., 1999, A genetic Algorithm for Function Optimisation: A Matlab Implementation. Tan, K.K., Lee, T.H., Jiang, X., 2001, On-line relay identification, assessment and tuning of PID controller. Journal of Process Control, (11), 483-496. Yuval, D., Genetic Algorithms and Robotics: a heuristic strategy for Optimisation.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

491

Challenges in Controllability Investigations of Chemical Processes Mizsey, P., M. Emtir, L. Racz\ A. Lengyel\ A. Kraslawski^ and Z. Fonyo Department of Chemical Engineering, Budapest University of Technology and Economics, H-1521 Budapest, Hungary ^MOL Rt. (Hungarian Oil Trust Co.) Szazhalombatta, Hungary ^Lappeenranta University of Technology, Lappeenranta, Finland

Abstract The controllability investigation of any kind of chemical process is the interactive and challenging part of process design or development. The investigation works on several levels and uses different methods. First, the control targets are defined, the set of controlled variables are determined and the set of possible manipulated variables are selected. The proper pairing of the controlled and manipulated variables, that is the design of the control structure, consists of first, the study of steady state control indices and then dynamic behaviours in the cases of open and closed control loops of the promising control structures. This investigation is presented on the design of energy integrated separation schemes. A new challenging method is offered by the Rough Set Theory (RS), which has been already successfully used in several areas of artificial intelligence and data analysis e.g. for the discovery of patterns and dependencies in data. Its use for controllability investigations is a new area at the revision of control structures of existing plants, retrofit modifications, because it can detect the dependencies among the possible controlled and manipulated variables with the analysis of the measured data and helps to fulfil the requirements of the control target. RS theory indicates also the measure of the dependencies among the variables. The RS theory is used for the improvement of the control structure of a complex chemical process, which is the fluid catalytic cracking unit (FCC). The analysis of the data of existing FCC unit shows that the product quality significantly depends on the temperature in the regenerator unit and its control is necessary. After considering the degrees of freedom, a new control loop is designed for the proper control of the temperature in the regenerator unit, which is accepted by the industry and it will be included in the control structure of the FCC plant.

1. Introduction Controllability investigations are integral part of process design and they are mutually influencing each other. According to previous studies, theories, and practice there is a classical way for the design of control structures (e.g. Mizsey and Fonyo, 1990, Mizsey et al, 1998). It starts already on the short-cut level of process design and counts for the degrees of freedom for the possible control loops. After defining the control targets the set of controlled variables and the set of manipulated variables are determined. This selection is based on engineering judgement and heuristics but the result of exhaustive mathematical modelling is also considered. After defining the sets of controlled and manipulated variables, steady state controllability indices like Niederlinski index, relative gain array, Morari resiliency index, condition number are determined (e.g. Luyben, 1990). The evaluation of the

492 steady state indices gives indication for the most promising control structures which are finally tested by dynamic simulation methods before the final selection. This controllability investigation works properly at the design stage of processes if there is a reliable model of the system and also for modification of existing plants' control strucutre if we have reliable model. In case of revision of existing plants there is, however, another alternative where the revision and/or improvement of the control structure can be supported with the use the Rough Set theory (e.g. Pawlak, 1982) which helps to detect dependencies in the system to be controlled. For this activity the RS theory needs measured data of the plant to be investigated. After detecting the dependencies and also their measures the control structure can be revised and modified.

2. Demonstration of Interaction between Design and Control The example for the comprehensive design of five energy integrated separation schemes demonstrates the interaction between process design steps: economic optimisation and controllability investigations. A three-component-alcohol-mixture is separated in five distillation based energy integrated two-column separation systems: two heat integrated distillation schemes (forward and backward heat integration), fully thermally coupled distillation column (also known as Petlyuk or Kaibel system), and sloppy separation sequences with forward or backward heat integration. The schemes are economically optimised for the total annual cost (TAC) and than controllability investigation takes place. The results compared to the non-integrated base case and each other. The results of the rigorous optimization can be summarized as follows: the heat-integrated schemes are always more economical than the conventional distillation schemes, direct sequence with backward heat integration (DQB) shows the maximum TAC savings 37 %. direct sequence with forward heat integration (DQF) shows the smallest TAC savings, 16 %, the sloppy schemes show TAC savings of 34 % for forward heat integration and 33 % for backward heat integration, Petlyuk system (SP) shows 29 % TAC saving value and the highest utility demand compared to the other energy integrated structures, sloppy schemes with forward (SQF) or backward heat integration (SQB) have the lowest values of utility demand but because of using middle pressure steam the utility cost will be higher. Secondly, the optimum schemes are investigated from controllability point of view. The controlled variables are the product compositions and the set of manipulated variables is also determined. This is based on engineering judgement. The possible manipulated variables are the following: distillate 1, reflux flow, distillate 2, reflux flow 2, bottom rate 2, heat duty, side product flow. Ratio control structures are not considered. The steady state indices are determined and compared. The results are shown in Table 1 and they indicate the following: • serious interactions can be expected for the sloppy schemes (SQF & SQB) and for the Petlyuk system (SP) due to poor RGA values and also for other indices, • base case (D) and heat integrated schemes (DQF and DQB) show less interactions than those of the sloppy schemes and Petlyuk system, • for D, DQF, and DQB the selection of the D1-L2-B2 manipulated variables for the control of product compositions shows good controllability features.

493 Table 1. Steady state controllability indices of selected control structures for the economically optimized schemes. Studied Schemes D-iDl-L2-B2) DQF-(D1-L2-B2) DQB-(D1-L2-B2) SP-(D-S-Q) ST-(L-S-B) SQF-(D-S-Q) SQF-(L-S-B) SQB-(D-S-Q) SQB-(L-S-B)

NI 1.137 1.136 1.093 3.515 7.438 6.470 4.030 5.080 1.287

MRI 0.099 .024 0.023 0.182 0.089 0.010 0.008 0.038 0.022

CN 8.890 36.32 39.660 6.890 14.38 137.4 158.1 33.31 64.388

xn 1.0 1.0 1.0 1.0 0.130 1.000 0.250 0.997 0.770

X22 0.880 0.88 0.910 0.320 0.570 0.250 0.250 0.470 0.827

X33 0.880 0.88 0.910 0.280 0.990 0.150 0.998 0.196 1.0

Dynamic simulations are carried out at equimolar feed composition and feed rate of 100 kmol/hr, base case. The disturbances are 100 to 100.5 kmol/hr for feed rate, and (0.33/0.33/0.33) to (0.32/0.34/0.32) for feed composition, respectively. First, the schemes are studied without any composition control (open loop) and then with closed composition control loops. It can be concluded: 1- In the case of open composition control loops the schemes, also the non-integrated base case, show quite similar dynamic behaviour but the sloppy schemes with backward heat integration (SQB) is significantly slower than the others. For the base case (D) and for the heat integrated schemes (DQB and DQF) the D1-L2-B2 set of the manipulated variables show good controllability performances 2- In the case of closed composition control loops, for the base case (D) and for the heat integrated schemes (DQB and DQF) the D1-L2-B2 set of the manipulated variables show good controllability performances. The heat integration does'nt influence the dynamic behaviours. 3- The more complex energy integrated structures, Petlyuk system and sloppy heat integrated structures, show worse dynamic behaviour (settling time, overshoot) than those of the base case and the simple heat integrated scheme. 4- SQB has the worst controllability features among the all, 5- Forward heat integration schemes (DQF and SQF) prove to be better than backward heat integration schemes (DQB and SQB). This can be due to stronger interactions that can take place because of the opposite direction of material and energy flows. Considering the economic disadvantage of the DQF, it is not preferred to DQB. On the contrary, SQF and SQB show similar economic features but since SQB shows the worse controllability features among the all and SQB is not recommended. In this case the controllability features make the decision. The case study solved by the classical way proves that this is an effective methodology, however, the selection of the sets of the controlled and manipulated variables is quite easy because the systems are simple.

3. New Challenge in Control: the Rough Set Theory The Rough Set theory or Rough Set Data Analysis (RSDA) is widely used for the determination of non-linear relationships in many different areas. Rough set theory is a method of information analysis and especially reduction of data sets, discovery of data patterns, classification of the objects into sets and generation of decision rules, e.g. Pawlak, (1982, 2002). Rough set theory does not need any preliminary information about data like probability distribution (as in probabilistic analysis), basic probability

494 assignment (as in Dempster-Shafer theory) or membership function (as in fuzzy set theory). It performs an analysis of properties of the data, allowing for the identification of the redundant or irrelevant attributes. In consequence, it enables obtaining of the simple rules among input and output variables from the database by reducing the redundant attributes while keeping the original degree of consistency. The feature of the RSDA that it can discover dependencies among variables can be utilised for the controllability investigation. Namely, at the early step of the control structure design the determination of the sets of controllability and manipulated variables is usually based on heuristics, experiences, and engineering judgement. This synthesis activity works quite straight if the system to be controlled is simple, well known by the experienced engineer, and data about system are reliable. However, in the case of complex systems the proper selection of the controlled and manipulated variables which fulfil the control targets is not always obvious even for the experienced designer. Some dependencies can be unnoticed. But this synthesis activity can be aided if the RSDA is used to support this activity to avoid unnoticing the dependencies which are needed for the proper control of the complex plant. The RSDA is tested and used for a complex system, for an existing Fluid Catalytic Crack unit.

4. Rough Set Theory to Improve the Control of FCC Unit The control of the FCC unit is an exhaustively studied topic in the literature as well as in the industrial practice. Since the FCC units produce large amount of valuable products their control has a paramount importance. There have been several works to improve its control e.g. Pohlenz, (1970), Lee et al. (1989), Kurihara, (1967), Worldwide Refining Survey (2001) and Advanced Control and Information Systems (2(X)1). For the improvement of the control of the existing FCC plant the Rough Set Theory is tested and used. The rough set data analysis is realised by ROSETTA software, a toolkit for analysing tabular data within the framework of rough set theory. ROSETTA (0hm and Komorowski, 1997) is designed to support the overall data mining and knowledge discovery process. For the RSDA carried out by the ROSETTA, about 140 measured operating points of the FCC industrial unit are collected and analysed. This analysis gives results about the dependencies of an existing plant, which are suitable to reconsider the control structure of the plant as well. The product quality (motor octane number, MON) depends on the properties of the feed, steam, catalyst, and air flows. Table 2 contains the values of the measured variables. They are selected as attributes (input data) influencing the decision (output data) - product quality. The first problem, when applying rough set theory, is to determine the number of the data intervals. If the number of the intervals is too high, then too many rules (if - then connections among the input and output variables) will be obtained. On the other hand, if the number of interval is too low then the set of rules will be too small and in an extreme case it becomes empty. Therefore the optimal number of intervals is a crucial point in the use of rough sets. After determining the intervals of the variables, the ROSETTA toolkit determines the rules, in the form of if-then connections between the variables. In the case of the investigated FCC unit, the rules are checked by the statistical model of the FCC unit. Based on the statistical model 8 rules are correct out of 150 rules. The system can be controlled if the rules, connecting the attributes and decision, are known. This kind of control is similar to the fuzzy control, but "rough set control" is not so subjective and complicated as fuzzy control. The different rules can be compared to check if they influence the same decision. Finally, the right rule can be

495 selected for control purposes considering the simplicity of the control structure, its cost and time of the operation (settling time). Table 2. Measured points of the FCC unit. Techn. parameters Feed oil

Steam

Stripper Dispersion Fluffing Emergency

Catalyst Air

Location

Variables Mass flow (t/h) Pressure (bar) Reactor Temperature ( T ) Sulphur containing Mass flow (t/h) Mass flow (t/h) Reactor Mass flow (t/h) Mass flow (t/h) Temperature ("C) Reactor Catalyst / feed oil Coke content (%) Regenerator Flow (kNm'/h) Regenerator Temperature ("C)

Values 100.0-203.04 4.39-8.33 60.56 - 131.39 0.01 -0.12 1.5-3.6 2.17-3.80 0.15-0.60 0.18-1.21 657.07 - 684.05 6.24-10.34 1.5-3.5 66.01-90.51 160.02-208.18

In the case of the studied FCC unit, it is found that several rules are already used for control purposes. It can be also seen from the results that the temperature of the catalyst is an important attribute because if it increases in the range of possible operation, the product quality, MON also increases. The temperature of the catalyst is fixed in the regenerator where the coke being on the catalyst's surface is burned away. The coke is formed in the reactor part of the FCC during the cracking of heavy hydrocarbons. The temperature of the catalyst is not controlled in the investigated FCC unit yet, so a control loop should be designed to improve the operation of the actual control structure. In the first step, the analysis of degrees of freedom is carried out and a possible manipulated variable is found: the coke formation in the reactor can be controlled by the feed flow of the bottom product of the main distillation column (BMC) which contains heavy hydrocarbons. (This main distillation column separates the products of the FCC unit.) This flow is free for this control and it is selected as manipulated variable. Since the too high temperature in the regenerator unit must be avoided, the temperature profile in the regenerator should be followed and the highest temperature is selected by a so called "high selector (HS)". The recommended new control structure is presented in Figure 1. Afterburning in the dilute phase of the regenerator can be avoided with our recommendation.

5. Conclusions The Rough Set Theory proves to be successful for the improvement of control structure of an industrial FCC unit because it can detect dependencies between all of the process variables, attributes (input data) and the decision (output data) - product quality, the control target. For this activity Rough Set needs measured data of the plant. The modification of the existing control structure detected by the Rough Set Theory is recommended and accepted by the industrial experts.

496 to maii

Flue

f

columi

--©j new control loop (TC3)

i

Reacto

\

a

r-A0--

.JxW_>

Steam of fluffing

BMC

feed

steam of dispersion

Figure 1. FCC unit with control loops and with the new control loop (TC3).

6. List of References Advanced Control and Information Systems, 2001, Control of FCC unit. Hydrocarbon Processing, September. Kurihara, H., 1967, Optimal control of FCC processes, PhD. Thesis, Mass. Inst, of Techn., Cambridge. Lee, L.L., Chen, Y.W., Huang, T.N. and Pan, W.Y. 1989, Four-Lump Kinetic Model for Fluid Catalytic Cracking Process, The Canadian Journal of Chem. Engng., 67, pp. 615-619. Luyben, W.L., 1990, Process Modelling Simulation and Control for Chemical Eng., McGraw-Hill. Mizsey, P. and Fonyo, Z., 1991 Assessing plant operability during process design. Computer-Oriented Process Engineering, Elsevier, 411-416. Mizsey, P., Hau, N.T., Benko, N., Kalmar, I. and Fonyo, Z. 1998, Process control for energy integrated distillation schemes, Comp chem Eng, 22, S427. 0hrn, A., Komorowski, J. 1997, ROSETTA: A Rough Set Toolkit for Analysis of Data, Proc. Third International Joint Conference on Information Sciences, Fifth International Workshop on Rough Sets and Soft Computing (RSSC'97), Durham, NC, USA, March 1-5, Vol. 3,403-407. Pawlak, Z., 1982, Rough set. International Journal of Computer Information Sciences 11,341-356. Pawlak, Z., 2002, Rough sets decision algorithms and Bayes' theorem, European Journal of Operational Research, 136, 181-189. Pohlenz, J.B., 1970, Oil and Gas Journal, 68, 33, 158-165. World-wide Refining Survey, 2001, Oil and Gas Journal, Dec. 24.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

497

Analysis of Linear Dynamic Systems of Low Rank Satu-Pia Reinikainen^\ Agnar Hoskuldsson^^ ^^ Lappeenranta University of Technology, P.O. Box 20, 53851 Lappeenranta, Finland, Email: [email protected] ^^ Technical University of Denmark, IPL, Bldg 358, 2800 Lyngby, Denmark, Email: [email protected]

Abstract We present here procedures of how obtain stable solutions to linear dynamic systems can be found. Different types of models are considered. The basic idea is to use the Hprinciple to develop low rank approximations to solutions. The approximations stop, when the prediction ability of the model cannot be improved for the present data. Therefore, the present methods give better prediction results than traditional methods that give exact solutions. The vectors used in the approximations can be used to carry out graphic analysis of the dynamic systems. We show how score vectors can display the low dimensional variation in data, the loading vectors display the correlation structure and the transformation (causal) vectors how the variables generate the resulting variation in data. These graphics methods are important in supervising and controlling the process in light of the variation in data.

1. Introduction Past years have shown great advances in measurement equipments. Sensors and optical equipments are examples of data collection means that have become very popular. These new instruments will have great influence on the future developments. E.g., many process companies are using NIR (Near Infra-Red) instruments for process control, because investment in NIR based control only costs around 10% of traditional process equipments. There are other important aspects of the new ways of process control. These new instruments do not touch the materials, and it is cheap to store and send the data onwards. There is great need for new methods that can handle data from these modem types of instruments. The reason is that we typically receive large amount of data that need to be processed and the data usually show very low rank. E.g., NIR data from a chemical process control gives us a data matrix X=XNXK with K=1050. The actual rank in these data may be four or five. Typically, the algorithms available in program packages assume that the data have frill rank, or they only check for the numerical precision of the used algorithms. When these methods are used these types of data, the solution vectors tend to be unstable and provide with unreliable predictions. Looking at the linear least squares methods can show the problems involved. Suppose the response variable, y, represents some quality measure. The linear least squares method is looking for a solution, b, such that the measure |Xb-yp is minimized. The exact solution is given by b=(X'^X)"^X'^y. For NIR data the matrix X'^X will be

498 1050x1050, but the solution should be based on a four or five dimensions. If the number of samples, N, is sufficiently large, we may be able to compute this solution, possible using extended precision. But the solution will have 1050 values, many of which are large, and it will be useless for prediction purposes. The approach chosen here is to use the H-principle of mathematical modelling (Hoskuldsson (1996)). The basic idea is to carry out the modeling in steps and at each step compute a rank one approximation to the solution. This rank one solution is based on optimizing the balance between the improvement in fit and the associated precision that can be obtained by such an improvement in the solution. Thus, each of the rank one part is a result of optimization task involving fit and precision, such that all parts are in certain sense optimal at the respective step of the analysis.

2. Mathematical Models Suppose that there are given values of the instrumental variables that has been collected in a matrix X. A standard assumption in standard assumption is to assume that the response variable can be derived linearly from X apart from small random values that are assumed normally distributed. We write it as y=Xp+8, or y~N(Xp,a^I). This indicates that the residuals have the same variance, a^. The linear least squares methods is concerned finding the value of p that minimizes the measure of fit, |Xp-yp ->min. The exact solution, bj, to this task is given by bi=(X^X)'^X^y. Sometimes there is a requirement that the solution vector in some sense should be as small as possible This can be included in the optimization task as minimizing the sum P^Vp + |Xp-y|^ ->min. The exact solutions are b2=(X'^X+V)-^X'^y. The matrix V can be the unity matrix, I, a constant times the unity matrix, kl, the covariance matrix for the b's or some other positive definite matrix. A common choice for V is kl, where the constant k is chosen by some external condition, e.g., the value that gives the smallest leave-one-out predictions. This is the popular Ridge Regression method. When working with dynamic systems we are interested in the changes in time in the solution vector. We shall look closer at the Kalman filter approach in finding the solutions. Let X^ be the instrumental data up to time t, (xt,yt) the sample values at time t, the and St= Xt^Xt+V. Then the solution at time t, b2,t, can be written as b2,t

= (Xt.iXi+V+Xt x7)-kXt.i V i + Xt^yO

= b2,t-i + kt(yt - x j b2,t-i), with kt= St-i'^x/gt, and gt=l+xj St.f^Xt. This follows from the rewriting XjXt= Xt./Xt.i+ Xt Xt^, X/yt = Xt-i^yn + x/yt, and the application of the matrix inversion lemma. This leads to the Kalmanfilterequations 1. Sample variance: gt=l+x7 St.f^Xt. 2. Kalman gain: kt= St.f^Xt/gt. 3. Update the solufion: b2,t = b2,t-i + kt(yt - x7 b2,t-i). 4. Update the inverse: St"^ = SM"^ - gt kt kt^. In these equations at time zero So=V. Otherwise the matrix V does not enter the equations. Apartfiromthese equations there may be some further ones on requirements to the solution vector. When there are many variables the recursive updating equations tend to give unstable solutions. E.g., in the case of NIR instruments S would be

499 1050x1050. Even if we start with a diagonal V, the updating becomes unstable because the difference matrix S-V is typically of rank 3-6 for NIR data. The present approach is concerned with finding stable solution in the case the data show low rank like in the case of NIR data. The algorithm proposed is independent of V. Thus, V can be zero or any other prior choice. The solution is based on the H-principle of mathematical modeling that we shall consider closer.

3. The Basic Algorithm H-principle is a recommendation of how we should carry out the modelling procedure for any mathematical model: 1) Carry out the modelling in steps. You specify how you want to look at the data at this step by formulating how the weights are computed. 2) At each step compute expressions for i) improvement in fit, AFit, and ii) the associated prediction, APrecision 3) Compute the solution that maximizes the productAFit x APrecision 4) In case the computed solution improves the prediction abilities of the model, the solution is accepted. If the solution does not provide this improvement, it stops. 5) The data is adjusted for what has been selected and start again at 1). The H-principle suggests that we should find a weight vector w that gives us a solution of step 3 (Hoskuldsson (1996)). The solution suggested is given by the eigen vector of the leading eigen value to the eigen value problem, X'^YY'^XW = Xvf

In case there is only one response variable, Y=y, there is a closed form expression for w

w = xVlx^y|. The next task is to compute the loading vector, p, as p=Sw/d, where d=w^Sw. The score vector, t, is defined as t=Xw. Besides these vectors we need one type more, the transformation or causal vectors r. It is defined such that p=Sr. These computations are carried out at each step. At the end of the computations the data is adjusted for what has been selected. The algorithm is as follows: 0. Initialize variables. Xo=X, So=S, Yo=Y, EO=IK, B = 0 . For a=l,2,..., K, 1. Find the weight vector Wai solve Xa-i^YY^Xa-iWa = K^a, or Wa = Xa-iV/|Xa-/yl2. Compute scaling constant dai da=Wa^Sa-iWa, loading vector pai Pa=Sa.iWa/da, and score vector ta=Xa.iWa.

3. Transformation vectors r^: ra=Ea.iWa; Adjust transformation matrix: Ea=Ea.i-daraPa^ 4. Compute new solution coefficients B: Ba = Ba-i + dgraqa^, with qa=Y^ta/da. 5. Adjust X:Xa=Xa.i-taPa'^. 6. Adjust S: Sa=Sa.i - da PaPa^.

7. Check if this step has improved the prediction aspect of the model, and if X-a or da are not too small. If it pays to continue, start a new iteration at 1.

500 The results of this algorithm is an expansion of the matrices as follows: X =tiPi^ + t2P2^+...4-tAPA^+...+ tKpJ

=TPl

S = di pi pi^ + d2 P2 P2^ + ..+ dA PAPA^ + ... + dK P K P J S-' = di ri ri^ + d2 r2 rj"^ + ...+ dA rArA^" + ... + dK TKFJ B = di ri qi'' + d2 r2 q2'' + ... + dA FAQA^ + ... + dK TKQK^

= PDP^. = RDR\ = RDQ\

Here the vectors are collected in a matrix, e.g., T=(ti,t2,...,tK). D is a diagonal matrix with da's in the diagonal. The decomposition of S is a rank one reduction, meaning that the rank of say Sa is one less than that of Sa-i. (Follows from SaWa=0). Thus SK will be the zero matrix. The matrix R satisfies R^P=D'\ or ri^pj=5ij/di. It can also be written as (RD''f(?D'')=l or RDP'^=I. The score vectors (ta) are not orthogonal, ti^tj^O for i^j. This algorithm is carried out for each time point t. Note, that if V=0, S=X^X and the algorithm reduces to PLS regression. In that case the score vectors become orthogonal. We can view the algorithm as an approximation, B = s-^X^Y = (diriri^+...)(piti^+...)Y = (riti^+...)Y = (diriqi^4-...). Note that only A terms in the expansions are used. The choice of the weight vector w at each step reflects the covariance that is left. The expansion stops, when there is no covanance left, Xa'^Y=0. When there are many variables, it is often necessary to be careful in finding the weight vector w. A collection of methods has been developed that optimise the choice of w (Reinikainen, Hoskuldsson (2002)). In general it is needed to auto-scale the data, i.e., to centre data and scale to unit variance. The choice of V should reflect the choice and be of same units as the scaled data. For further details see the appendix.

4. Graphics Display The same types of graphic analysis for any choice of the matrix V are used. Here an example of the graphic analysis based on an industrial on-line data is presented. The figures illustrate results of static linear PLS model, in which NIR data from an oil refinery is used to model density of the product. The vectors in the algorithm are displayed graphically to illustrate the structure and variation in data. The basic plots are: 1. ta versus 4: The vectors (ta) decompose the data matrix X. Therefore the plots of ta versus tb show us the sample (fime) variation in data. Fig 1 reveals that the process (samples) is changing with the time. Arrows in Fig 1 visualise the drift on 1.-4. PLS components. The dynamic behaviour can be clearly seen even on the first two score vectors. Therefore, it cannot be expected that the same model will be valid at the Table 1. R^ values of thefirstfour latent variables of the PLS example. LV 1 2 3 4

S R^(X), % 34.17 75.83 97.08 98.99

S R^(Y), % 59.77 80.52 82.95 87.48

501 0.6 ^3 0.4

12 •s^g

0.2

.

•^^"94

17i<—

> 0

^"?

-0.2 -04

J

i^90

19

•95

J

^

^4

0

1

h ,4

-0.3

-0.2

-0.1.

0

0.1

0.2

0.3

Figure 1. Score vectors presenting sample (time) variation. 0.05

1190cm-i

0.04

1

0.03 0.02 P4

0.01 0

1 ^ cm-' ^ * » % '» ^ 0 0 cm'^h.2

-0.15

-0.1

-0.05

0

0.05

0.1

1

1

1 ci? cm' •\ Jm ^|L«n — - j t - ir^--i"-w

1^1

1 1 1

-0.01 1210 cm-i

0.15

-0.06

^ 9 5 0 cni' ••J^ieoocli-

-0.04

-0.02

0

0.02

0.04

0.06

P3

PJ

Figure 2. Loadings revealing variables (wave numbers) contribution to the PLS model. -Pi

P i - - - Ps

1200

P4

spectrum

1000

0.2

1200

1000

800

wavenumber, cm'^ wavenumber, cm'^ Figure 3. Loading vectors (p), scaling vectors (r) and an example ofspectrums. beginning of the later time period and at the end of the period. In this case the change should not only concern the solution vector found in dynamic modeling, but the whole model should be changed. 2. Pa versus pb'. The loading vectors (pa) are generated as Pa=Sa-iWa, where Wa is found by some optimising considerations. We look at these plots to see how the variables contribute at the individual steps. Especially in spectral data the changes in data might be small. With Fig 2 it is easy to identify the wave numbers causing the drift. A spectrum together with loading vectors is presented in Fig 3. 3. Ta versus r^: The transformation vectors (ra) are generated from Pa=Sra. They also satisfy da'^ta=Xra. Thus, these vectors tell us how the variables contribute to the analysis, and, how the covariance structure in S has been used. We can also multiply element-wise X and ra to see which variable contribute most to the score vectors.

5. References Hoskuldsson A., 1996, Prediction Methods in Science and Technology, Colourscan, Warsaw Poland Reinikainen S-P., Hoskuldsson A., 2002, COVPROC Method: Strategy in Modeling Dynamic Systems, Journal of Chemometrics (accepted).

502 Appendix. Analysis of linear dynamic systems of low rank Proposition 1. The weight vectors (wj are orthogonal to later loading vectors

(pj,

pjwa=0,forb>a. P r o o f . N o t e that Wa^Pa=l a n d Wa^Sa = Wa^ (Sa.i - da Pa Pa^) = da Pa^ " da (Wa^Pa) Pa^ = 0.

Pb=Sb.iWb/db. We write Sb-i as Sb-i

= Sb.2 - db-i Pb-i Pb-i^ = Sb.2(I - Wb-i Pb-i^ ) = Sb-iUo = SaUi

Here Ui is some matrix that is not used. This gives Wa^Pb= Wa^Sb-lWb/db = Wa'^ Sa UiWb/db = 0 .

This completes the proof. The important property of the algorithm is Proposition 2. The matricesP=(pi,...,PK)

^f^dR=(r],...,rf^

satisfyR^P=D^.

Proof. The vectors ra are defined as Pa=Sra. If a=l we get Pi = SoWi/di = S Wi/di, or ri= Wi. This gives Pi'^ri = pi^ wi/di = wi'^ S wi/di^ = 1/di. For a=2 we get P2 = SiW2/d2 = (So - di Pi Pi"^) W2/d2 = S(I - Wi Pi^) W2/d2 or r2=(I - Wi pi^) W2/d2 This gives Pi^r2 = (pi'^ W2 - (Pi Vi)(pi'^ W2))/d2 = ( p / W2 - (pi'^ W2))/d2 = 0 P2^r2 = (P2'^ W2 - (P2Vi)(pi'^ W2))/d2 = (p2'^ W2) /d2 = l/d2 since (p2^Wi) = 0 fi*om Proposition 1. For higher values of the indices a and b we proceed in a similar way as in Proposition 1. Proposition 3. The weight vectors (wj are mutually orthogonal, Wiy^Wa=0,forb^. Proof. Suppose that a>b. Note that Xa-i^YY^Xa.iWa = A^aWa. It gives W a V = Wa'^ Xa.i^YY'^Xa-iWb.

From definition of Xa-i we get Xa-l = X b . i - (tbPb^ + . . . + ta.iPa-1^).

From Proposition 1 we get Xa-lWb = (Xb-i - (tbPb'^ + . . . + ta.iPa-l'^)) Wb = Xb-i Wfe- tb(Pb'^ Wb) = t b " tb = 0 .

This shows that the weight vectors are mutually orthogonal.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

503

Data Based Classification of Roaster Bed Stability Bjom Saxen^ and Jens Nyberg^ ^Outokumpu Research Oy, P.O. Box 60, nN-28101 Pori, Finland, bjom. saxen @ outokumpu.com ^Outokumpu Zinc Oy, P.O. Box 26, FIN-67101 Kokkola, Finland, jens.nyberg @ outokumpu.com

Abstract An on-line application of a self-organizing map (SOM) has been developed for detecting and predicting instability of a fluidised bed furnace. In the application, which has been in use at the roster of Outokumpu Kokkola zinc plant for over one year, SOM is utilised for compressing multi-dimensional process measurement data and for visualising bed stability changes as a path on a two-dimensional map. Instability, which normally causes operational problems and lowered production, has been detected quite reliably. A rule-based system for proposing correcting actions is being developed as an extension to the SOM.

1. Introduction Roasting of zinc concentrates at Outokumpu Kokkola plant is carried out in two fluidised bed furnaces. Occasionally, the bed of a furnace moves into instability, which leads to operational problems and lowered production. Reasons, indicators and remedies for bed instability have been investigated during the last few years. Generally, instability is a consequence of changes in the chemical or physical properties of the concentrate feed, but the causal connections are complex. There is a fairly large amount of real-time data available at the roaster, e.g. temperature, flow and pressure measurements, and also less frequent off-line analyses of the chemical composition of the streams. Although a period of instability can be recognised from history data, real-time interpretation of the high-dimensional data is difficult and there is a need for a data refining and compressing tool. The self-organizing map (SOM) is a method for visualisation, clustering and compressing data (Kohonen, 2001). The SOM can effectively refine multi-dimensional process data as reported by e.g. Alhoniemi et al. (1999) and has been shown suitable for process monitoring and fault diagnosis also in mineral and metal processing (Rantala et al., 20(X), Jamsa-Jounela et al., 2001, Laine et al., 2000). In addition to detection of roaster bed instability, there is also a need for identification of the underlying reasons. This task requires expertise knowledge, since there are many factors to

504 be considered. Rule based systems represent a straightforward approach for applying apriori knowledge in supervision and fault detection (Isermann, 1977).

2. The Roasting Process Roasting is an essential part of a zinc electrowinning process. In Kokkola zinc plant, the process contains departments for roasting, leaching and purification, electrowinning and melting & casting. There are two roasting furnaces, both of fluid bed type (Lurgi), with a grid area of 72 m^. The mix of zinc concentrates is fed to the furnace by rapid slinger belts, and air is fed from the bottom of the furnace. Around 22 t/h concentrate and around 42 000 NmVh air is fed to each furnace. The reaction between sulphides in the concentrate and oxygen is exothermic and heat is generated; the furnace temperature is kept at about 920 950 C by cooling. The products are solid oxide material, called calcine, and sulphur dioxide gas. The gas, which also contains solids, is lead to a waste heat boiler, cyclones and electrostatic precipitators before it is cleaned in a mercury removal step and in a sulphuric acid plant. Along with the roasting, some of the concentrates are directly leached. This enables higher flexibility in the acquiring of concentrates; some concentrates are more suitable for roasting and others for direct leaching. 2.1. Challenges and development Roasting is in principle a simple process, but there are many influencing variables and sometimes it is very difficult to control the furnace. The main difficulty is that every concentrate behaves differently, because of its specific mineralogy. The move to concentrates with finer grain size influences the furnace behaviour, and impurities like Cu and Pb have a great impact. High impurity level can lead to sintering of the bed; i.e. molten phases and sulphates are formed. Another problem is that the bed sometimes becomes very fine (no coarsening occurs) and this hinders the fluidisation. To master the process, it is essential to maintain a stable bed with good fluidising properties and good heat transfer. During last years many plant test runs have been carried out with the aim to better understand the roasting mechanism and to find out optimal run conditions (Metsarinta et al., 2002). Among the tested parameters are impurity levels (Cu, Pb), concentrate particle size, water injection to different spots, oxygen use etc. The number of measurements has been increased, which has brought more information about the state the furnace. New control strategies and advising systems have been developed by utilising knowledge gained theoretically and through tests, but also by data based studies of the process behaviour. 2.2. Process control Basic measurements and control loops of one furnace line are shown in Figure 1. The furnace control can roughly be divided into three levels: 1. The Conventional level includes standard controller for flows, pressures, etc.

505 The Advanced level includes sophisticated use of the large amount of measurement data; fuzzy temperature control by concentrate feed, oxygen enrichment control by 02-feed and furnace top temperature control by water addition. Also, this level includes process monitoring by means of SOM, as well as an advisory system based on expert rules (under development). The Ultimate level implies changing the concentrate mix into a "safe" region, i.e. a composition with coarse particles and little impurities.

CONCENTRATE MIX

mi FU2ZY CONTROL

T

m^hCHEMICAL ANALYSIS

^

GRAIN SIZE DISTRIBUTION

Figure 1. Flow chart and basic instrumentation of one furnace line.

3. Data Based Methods To support the investigations on the chemical and physical mechanisms of the roasting process, plant data have been analysed mathematically. This has resulted in tools for process control, especially for bed stability monitoring and management. To verify earlier observations and to serve as a base for the development of control methods, a correlation analysis was carried out with process data from one year of operation. Variables included were measurements of flow, temperature and pressure, origins of the concentrates in the feed mix, chemical analyses of feed and product compositions and grain size distribution of the product. In addition, some calculated quantities used in the furnace operation were also included. The study was carried out using linear correlation analysis and by time series plots of selected variables. Although the bed stability was the main focus of

506 the analysis, the correlations were analysed in general and no single response (output) variable were selected. Separate analyses were carried out for both furnace lines. Along with the correlation analysis, SOM was used as a tool for data mining and correlation exploring. The SOM algorithm quantizes the observations into a set of prototype vectors and maps them on a two-dimensional grid. The updating method forces the prototype vectors of neighbouring map units to the same direction so that they will represent similar observations. The number of prototype vectors is chosen essentially smaller than the number of observations in training data. Thus, the algorithm generalizes correlations in the data and clusters the observations, being thereby suitable for data visualisation.

4. Results Based on process data studies with the SOM, an on-line tool for detecting instable furnace behaviour from process measurements was developed. The software was developed and implemented in MATLAB® using version 2.0beta of SOM Toolbox (2002). Models for both furnace lines were made. The measurement variables were concentrate feed, air feed, oxygen feed, oxygen coefficient, water feed, windbox pressure, furnace and boiler temperatures at different spots, boiler steam production, boiler offgas oxygen content, calcine composition (S^", Na, Si, K, Cu, Pb) and fraction fine particles in calcine. The temperature measurement signals were pre-treated by mean value calculation and a rulebased exclusion of non-representative signals. One-day mean values from around two years of operation were used for training. Observations from process shut-downs were excluded from the data, occasional erroneous values (due to probe or data transfer failures) were labelled as non-available and the variables were normalised by linearly scaling to unit variance. The dimension of the data vector fed to each SOM was 20. The SOM grid size was set to 9x6, i.e. 54 prototype vectors was set to represent around 600 observations in the data set. In the training data, the algorithm clustered most periods of instability close to each other and a rough classification into stable and instable areas of the map could be made. The classification was based on the knowledge that low concentrate feed, low windbox pressure and large fraction of fine particles in the calcine correlate with instability. The SOM component planes in Figure 2 show how these variables are represented in the prototype vectors. It should be noted that although these variables correlate with bed stability, none of them could alone be used as stability indicator. For the on-line interface, the map units correlating with instability was coloured red, the units close to this area yellow, and the other units green.

507 Windbox pressure (mbar) n270

Concentrate feed (t/h) Fraction <71 pim in calcine (%) ^N^>vs.«^v^N n24.6 - - - - - n37

21.9

22.6

1242

^^^^^^^^

•20.5

^-^-"-'-•^''^^^'^

-6.75

Figure 2. Component planes for three important variables in the SOM for furnace 2. In the on-line application, the feed data is 8-hour mean values achieved from the history database at the plant. The interface shows changes in bed stability by a five-days path (5x3 observations) of the best-matching unit (BMU) on the map. The BMU is the unit representing the prototype vector with shortest distance to the input vector. Also, the application outputs a plot of the quantization error (Euclidean distance between BMU and input vector) for the same period, which can be used as an indicator of model reliability. The on-line SOM tool has been in use for over one year, and has detected bed instability tendencies quite reliably. The BMU path on the map is easy to interpret, and gives a quick generalization of the situation in the furnace. Figure 3 shows the SOM interpretation of the stability of furnace 2 during five days in September 2002. During this period, the bed was moving from instability back to normal behaviour. The quantization error plot in Figure 3 indicates that the explanation of the first observations in the period is unreliable.

18-Sep-2002 14:00:00 - 23-Sep-2002 06:00:00 w:1

Quantization error Normal (green)

I Dubious (yellow)

I Unstable (red)

Figure 3. SOM visualisation of a bed stability path of furnace 2; the smallest circle represents the match of the first observation and the star shows the latest match. A plot of the quantization error for the same period is given to the right.

508

5. Conclusions and Further Work Detection of fluidised bed instability requires multidimensional data and appropriate methods for its analysis. The SOM-application at the roaster performs data analysis which, in opposite to a human observer, is systematic and consequent. The application reliably monitors bed stability, and gives valuable support for operation. However, most of the process variables clearly correlating with instability show only consequences, and some of them are manipulated variables in control loops. The underlying reasons for a particular instability period may be so nested that they are hard to detect. Hence, the development of a rule based system for isolating instability reasons and providing correcting actions has been started. The rules are based on metallurgical and practical process know-how. Known inappropriate combinations of feed composition and process parameters are checked through, and when such a combination is found, the system gives advises for correcting actions. For instance, one rule is: IF calcine Cu > 0.6% AND Oxygen coefficient < 1.2 THEN Increase oxygen coefficient! Further work will include refining and tuning of the rules based on upcoming process situations.

6. References Alhoniemi, E., Hollmen, J., Simula, O. and Vesanto, J., 1999, Process Monitoring and Modeling using the Self-Organizing Map, Integrated Computer Aided Engineering, vol. 6, no. l,pp. 3-14. Isermann, R., 1977, Supervision, fault-detection and fault-diagnosis methods - an introduction. Control Engineering Practice, vol. 5, no. 5, pp. 639 - 652. Jamsa-Jounela, S-L., Kojo, I., Vapaavuori, E., Vermasvuori, M. and Haavisto, S., 2001, Fault Diagnosis System for the Outokumpu Flash Smelting Process, Proceedings of 2001 TMS Annual Meeting, New Orleans, USA, pp. 569-578. Kohonen, T., 2001, Self-Organizing Maps, volume 30 of Springer Series in Information Sciences. Springer, Berlin, Heidelberg. Laine, S., Pulkkinen, K. and Jamsa-Jounela, S-L., 2000, On-line Determination of the Concentrate Feed Type at Outokumpu Hitura Mine, Minerals Engineering, vol. 13, no. 8-9, pp. 881-895. Metsarinta, M-L, Taskinen, P., Jyrkonen, S., Nyberg, J. and Rytioja, A., 2002, Roasting Mechanisms of Impure Zinc Concentrates in Fluidized Beds, accepted for Yazawa International Symposium on Metallurgical and Materials Processing, March 2003, CaUfomia, USA. Rantala, A., Virtanen, H., Saloheimo, K. and Jamsa-Jounela, S-L., 2000, Using principal component analysis and self-organizing map to estimate the physical quality of cathode copper. Preprints of IFAC workshop on future trends in automation in mineral and metal processing, Helsinki, Finland, pp. 373-378. SOM Toolbox, 2002, http://www.cis.hut.fi/projects/somtoolbox [18 October 2002].

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

509

A Two-Layered Optimisation-Based Control Strategy for Multi-Echelon Supply Chain Networks p. Seferlis and N. F. Giannelos Chemical Process Engineering Research Institute (CPERI) PO Box 361, 57001 Thessaloniki, Greece, email: [email protected], [email protected]

Abstract A new two-layered optimisation-based control approach is developed for multi-product, multi-echelon supply chain networks. The first layer employs simple feedback controllers to maintain inventory levels at all network nodes within pre-specified targets. The feedback controllers are embedded as equality constraints within an optimisation framework that incorporates model predictive control principles for the entire network. The optimisation problem aims at adjusting the resources and decision variables of the entire supply chain network to satisfy the forecasted demands with the least required network operating cost over a specified receding operating horizon. The proposed control strategy is applied to a multi-product supply chain network consisting of four echelons (plants, warehouses, distribution centres, and retailers). Simulated results exhibit good control performance under various disturbance scenarios (stochastic and deterministic demand variation) and transportation time lags.

I. Introduction A supply chain network is commonly defined as the integrated system encompassing raw material vendors, manufacturing and assembly plants, and distribution centres. The network is characterised by procurement, production, and distribution functions. Leaving aside the procurement function (purchasing of raw materials), the supply chain network becomes a multi-echelon production/distribution system (Figure 1). The operational planning and direct control of the network can in principle be addressed by a variety of methods, including deterministic analytical models, stochastic analytical models, and simulation models, coupled with the desired optimisation objectives and network performance measures (Beamon, 1998; Riddalls et al., 2000). Operating network cost, average inventory level, and customer service level are commonly employed performance measures (Thomas and Griffin, 1996; Perea et al., 2001). In the present work, we focus on the operational planning and control of integrated production/distribution systems under product demand uncertainty. For the purposes of our study and the time scales of interest, a discrete time difference model is developed. The model is applicable to networks of arbitrary structure. To treat demand uncertainty within the deterministic supply chain network model, a receding horizon, model predictive control approach is suggested. The two-level control algorithm relies on a

510 decentralised safety inventory policy, coupled with the overall optimisation-based control approach.

Figure 1. Multi-echelon supply chain network.

2. Supply Chain Model Let DP denote the set of desired products (or aggregated product families) of the system. These can be manufactured at plants, P, by utilising various resources, RS. The products are subsequendy transported to and stored at warehouses, W. Products from warehouses are transported upon customer demand, either to distribution centres, D, or directly to retailers, R. Retailers receive time-varying orders from different customers for different products. Satisfaction of customer demand is the primary target in the supply chain management mechanism. Unsatisfied demand is recorded as back-orders for the next time period. A discrete time difference model is used to describe the supply chain network dynamics. The duration of the base time period depends on the dynamic characteristics of the network. The inventory balance equation, valid for warehouses and distribution centres, is:

>'a(0-ya('-l)+S^a',*('-V*)-E%.*'(0

V ke^,D}t^T,ie

DP

(1)

yi^k is the inventory of product / stored in node k . x-j^^j^ and x^^^-r denote the amounts of the i-th product transported through routes (k^,k) and {k,k^), respectively, where k^ supply k and A:^^are supplied by k. L^^j^ denotes the transportation lag for route (k^,k). The transportation lag is assumed to be an integer multiple of the base time period. For retailer nodes, the inventory balance considers the actual delivery of product / attained, denoted by J^-

y>At)=y>A'-})+I,h^'A-W,)-daif)

V keR,teT,ieDP

(2)

511 The balance equations for unsatisfied demand (e.g., back-orders) take the form: BO,,{t)^BOj-l)+R,,{t)-d,,{t)-LO,,{t)

ykeRjeTJe

DP

(3)

where Rtjt) denotes the demand for product / at retailer k and time period t. LOtJt) denotes the amount of cancelled back-orders (lost orders). At each node capable of carrying inventory (nodes of type W, D, and R), capacity constraints are in effect that account for a maximum allowable inventory level: y,{t)=J,oc,y,,it)^vr

yke^,D,R}tET

(4)

i

where Y^ denotes the actual inventory of the node, Oi the storage volume factor for each product, and Vk^^ the maximum capacity of the node. A maximum allowable transportation capacity, T/"/^, is defined for each permissible transportation route within the supply chain network: 5;Ax,,,,.(f)
\/ke{P,W,D}teT

(5)

i

where J3i denotes the transportation volume factor for each product. For each manufacturing resource RSp a maximum level of availability, CJ^, in each plant node is specified: SE'^..A*.r(O^Cj i

ykePjeTJeRS

(6)

k'

where K. j denotes the usage factor of thej-th resource for the /-th product.

3. Control Strategy for Supply Chain Management Supply chain management is performed within a two-layered approach. The first layer aims at keeping inventory levels around pre-specified targets. A single dedicated controller is used for each inventory node. Disturbances are generated by demand fluctuations at downstream nodes. The second level of control is a model predictive optimisation-based scheme that considers the entire network dynamics, embedding the inventory controllers of the first layer and a stochastic model for demand variation. 3.1. Inventory control Proportional-integral-derivative (PID) controllers are derived for the feedback control of inventory levels. The PID control law in discrete velocity form is given by the following relationship (Marlin, 1995):

512

mvXt)=mv,{t-l)-K^

1+ T,

kkYK l + 2^y(r-l)-/^feV(?-2) (7)

+ -^ At ^

J

\

)

where mv^/j is the value of the manipulated variable for the inventory controller. At the discrete control interval, Kc the proportional gain, T/ the reset time for the integral mode, and r^ the reset time for the derivative controller mode. The manipulated variable for the inventory control of each node is the total amount of the products transferred from all supplying nodes to node k:

^^*(0=SS^/.o(^~^o)

(8)

i

k'

The choice of the manipulated variables imposes a constraint on all incoming material to a particular node. The PID controllers are tuned to allow for fast set-point tracking and good disturbance rejection dynamics, taking into consideration the transportation delay between nodes. 3.2. Optimisation-based model predictive control Supply chain management requires a number of decisions to be determined at every time period. The main objectives of the supply chain network can be summarised as follows: (i) maximise customer satisfaction, and, (ii) keep operating supply chain costs low. The first target is attained by the minimisation of back-orders for a period of time, while the second target is achieved by minimising transportation and inventory (storage) costs associated with the supply chain network. Based on the fact that past and present control actions affect the future response of the system, a receding-time horizon is selected. The trajectory of the system is predicted and compared to the desired trajectory. The control actions are then determined from the minimisation of a performance index over the given time horizon, th-

,W.

|VV„

t

ke{R}

i

T,i,k ,k \ri,k ,k

t kG^,D,R}

(9)

i

The performance index, /, includes a term penalizing back-orders at all retailer nodes, and a term accounting for the transportation costs. The weighting factors WBO and wj reflect the relative importance of the controlled (back-orders) and manipulated (transportation of products) variables. The overall optimisation model-based predictive controller for the supply chain network takes the following form: Min

J

X

s.t. Supply chain model Eq. 1-6 Feedback inventory controllers Eq. 7 Stochastic disturbance model

(P)

513 All variables in the supply chain network are assumed to be continuous. This is definitely valid for bulk commodities and products. For unit products, continuous variables can still be utilised, with the addition of a post-processing rounding step to identify neighbouring integer solutions. This approach, though not formally optimal, may be necessary to retain computational tractability in systems of industrial relevance. The computational cost for solution of linear programme (P) increases with the size of the receding time horizon, which has to be carefully chosen in order to balance good control performance with robustness to external disturbances. The time horizon should be selected at least as large as the largest transportation delay in the system.

4. Simulated Results A four-echelon supply chain system consisting of two production nodes, two warehouse nodes, four distribution centres, and 16 retailer nodes is studied. All possible connections between immediately successive echelons are permitted. There is a number of low-cost routes between successive echelons that carry the bulk of the supply, and a number of more expensive alternative routes that will be used periodically when the cost of accumulated back-orders becomes significant. Five product families are being distributed. The size of the network model is 650 variables per time period with 358 product quantities along transportation routes and 80 back-order quantities as optimisation variables. 4.1. Deterministic disturbance in demand The given network can accommodate step changes in the order of 50% for each product family. Retailer inventories resume their set-points within typically 10 time periods, whereas 15 time periods are required in the larger warehouse nodes. The maximum deviation from inventory set-points is kept below 20% (figure 2). 4.2. Stochastic disturbance in demand A stationary stochastic model is used to describe the demand variation over the simulated time span. Typical simulation results are reported in table 1 and figure 3. Demand satisfaction is optimised at high levels in most cases. The performance index, reflecting network operating costs, increases at higher demand variances and transportation delays. Larger transportation lags require a more conservative controller tuning in order to avoid controller-induced instability. However, there is a compromise between tight inventory control (small inventory variance) and achievable minimum performance index. Cases 4-5 and 7-8 exemplify the impact of proper receding horizon selection to supply chain network performance. In case 4, a time horizon equal to 3 time periods achieves a higher demand satisfaction rate at the expense of higher transportation costs than case 5, where a time horizon equal to 5 is selected. In case 6, the control horizon is equal to the maximum transportation lag in the system (5 time periods), resulting in a relatively high performance index and lower customer satisfaction. By increasing the control horizon to 6 time periods, a significant improvement is observed. In general, shorter time horizons lead to more aggressive control actions, but larger time horizons may render the control scheme more susceptible to demand variations.

514 '1 +

» E

\

0

- e - Wnode l l -X- Dnode —H- Rnode

V 0

5

4

i\

+

10

15

20

25

30

35

40

45

50

Time period

Figure 2. Inventory levels for a 50% step change in demand for product A.

Figure 3. Inventory levels for case I.

Table I. Results of simulated cases Case 1 2 3 4 5 6 7 8 9

Transport, lags [Lpw LwD LDR] [111] [111] [111] [2 11] [2 11] [4 2 1] [5 2 1] [5 2 1] [5 3 1]

Receding horizon th 5 5 5 3 5 5 5 6 6

Demand satisfaction % 99.9 99.6 94.8 99.9 99.7 98.9 90.5 99.7 98.9

Variance in prod, demand 0.1 0.2 0.5 0.1 0.1 0.1 0.1 0.1 0.1

7/time period 21.86 22.02 24.57 24.30 21.86 26.16 40.42 24.87 26.77

5. Conclusions A two-layered control strategy was described for supply chain management purposes. The strategy combines feedback controllers to account for the fast dynamics at the inventory nodes, while utilising the power of a fully-centralised optimisation-based model predictive controller to achieve an optimal operating policy for the supply chain network over a selected time horizon.

6. References Beamon, B.M., 1998, Int. J. Production Economics, 55, 281. IVIarlin, T.E., 1995, Process Control, ]VIcGraw-Hill, New York. Perea-Lopez, E., Grossmann, I.E., Ydstie, B.E. and Tahmassebi, T., 2001, Ind. Eng. Chem. Res., 40, 3369. Riddalls, C.E., Bennet, S. and Tipi, N.S., 2000, Int. J. Syst. Sci., 31,969. Thomas, D.J. and Griffm, P.M., 1996, Eur. J. Oper. Res., 94, 1.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

515

Dynamic Control of a Petlyuk Column via ProportionalIntegral Action with Dynamic Estimation of Uncertainties Juan Gabriel Segovia-Hernandez^, Salvador Hernandez^, Ricardo Femat'^ and Arturo Jimenez^ ^Instituto Tecnologico de Celaya, Depto de Ingenieria Quimica, Av. Tecnologico y Garcia Cubas s/n, Celaya, Gto., 38010, Mexico, [email protected] ^Universidad de Guanajuato, Facultad de Quimica, Noria Alta s/n, Guanajuato, Gto., 36050, Mexico. ^ Departamentos de Matematicas Aplicadas y Sistemas Computacionales, IPICYT, Apdo. Postal 3-90, 78231, Tangamanga, San Luis Potosi, SLP, Mexico.

Abstract A three point control configuration based on a proportional-integral controller with dynamic estimation of unknown disturbances was implemented in a Petlyuk column. The proposed controller comprises three feedback terms: proportional, integral and quadratic actions. The first two terms act in a similar manner as the classical PI control law, while the quadratic term (double integral action) accounts for the dynamic estimation of unknown disturbances. Comparison with the classical PI control law was carried out to analyze the performance of the proposed controller in face to unknown feed disturbances and set point changes. The results show that the closed-loop response of the Petlyuk column is significantly improved with the proposed controller.

1. Introduction Since the energy consumption of distillation columns can have a significant influence on overall plant profitability, several strategies have been suggested to improve their energy efficiency. One strategy is the use of thermal coupling, in which the transfer of heat is accomplished by direct contact of material flow between two columns. For the separation of ternary mixtures, the Petlyuk column (also known as the fully thermally coupled distillation column) provides a choice of special interest (Figure 1). The Petlyuk column had not gained interest in the process industries until recent times (Hairston, 1999) even though its concept was established some 50 years ago (Brugma, 1937; Wright 1949). Savings in both energy consumption and fixed investment can be accomplished through the implementation of such a separation scheme. Theoretical studies have shown that Petlyuk columns can save up to 30% in energy costs compared to conventional schemes (e.g. Petlyuk et al, 1965; Glinos and Malone, 1988). Such results have promoted the development of more formal design methods (Triantafyllou and Smith, 1992; Hernandez and Jimenez, 1999a; Amminudin et al, 2(X)1; Muralikrishna et al, 2002). To promote a stronger potential for industrial implementation, a proper understanding of operation and control aspects are needed to complement the energy savings results. Recent efforts have contributed to the understanding of the dynamic properties of the Petlyuk column (Wolff and Skogestad, 1995; Abdul-Mutalib and Smith, 1998; Hernandez and Jimenez, 1999b; Serra et al, 1999; Jimenez et al, 2001).

516

K^ ^ 3 -»• A

^ -*•

B

\<^

L-kFigure 1. Petlyuk column. The expectance that the dynamic properties of Petlyuk columns may cause control difficulties, compared to the rather well-known behavior of the conventional direct and indirect sequences for the separation of ternary mixtures, has been one of the factors that has contributed to their lack of industrial implementation. In this work, we analyze the closed-loop behavior of Petlyuk columns when a proportional-integral controller with dynamic estimation of unknown disturbances is implemented (Alvarez-Ramirez et al., 1997). The performance of the integrated column under such a controller is compared to the behavior under a traditional proportional-integral controller. The analysis is based on rigorous dynamic simulations, and two cases are considered: (i) set point tracking and (ii) output regulation under load disturbances in the feed mixture.

2. Design of Petlyuk Columns A base design for the Petlyuk column was first obtained, followed by an optimization procedure to detect the base operating conditions under which the minimum energy consumption for such a design was achieved. The optimization procedure has been described by Hernandez and Jimenez (1999a). An ODE model was formulated with equations for total mass, component mass and energy balances, along with ideal VLE and stage hydraulics relationships. After the model is formulated, the design problem of the Petlyuk column shows five degrees of freedom; three of them are consumed by the implementation of three control loops, and the two additional degrees of freedom are used as search variables to detect the operation with minimum energy consumption. The search variables we used were the flowrates of the liquid and the vapor interconnecting streams (LF and VF, Figure 1).

3. The PI Control with Dynamic Estimation of Uncertainties The implementation of the output feedback control for distillation column can be configured such that only the liquid composition of the output flowrate is regulated (i.e., uncoupled one-point configuration control; see second example by Alvarez-Ramirez et al., 1998). In such a configuration, the liquid compositions for the main product streams A, B and C (see Figure 1) were taken as the controlled variables whereas, respectively.

517 the reflux flowrate, the side stream flowrate and the reboiler heat duty were chosen as the manipulated variables. The ideas behind the simulations are (i) to show that Petlyuk column can be controlled by exploiting a simple control configuration and (ii) to improve the closed-loop performance by implementing a proportional-integral feedback with dynamic estimation of unknown disturbances (also called PII^). The main idea behind the proposed controller is to estimate the input d = J(t) from the system output and, if the estimated value is close to the actual one, substitute it with a Pl-like control law. The PI control law can be written as the following dynamic system (Luyben, 1990)

u=

Kr{y-r)-z (1)

z=

K,{y-r)

where r stands for the input reference, y denotes the system output and z is the integral of the control error. The constants KQ and Kj = KjTi (where T; denotes the reset time) stand for the proportional and integral gains, respectively. The estimated value of the input d is computed via the following equations:

y = — y + KpU + d + gXy-y) z 'd = gXy-'y)

(^) (3)

where d and y are, respectively, the estimated values for d and y whereas ^i and g2 are estimation constants, which_must be strictly_positive to guarantee convergence of the estimation errors ei = {y - y) and 62 = (d~ d) to the origin, i.e., if ^1,^2 > 0 then (^i,^22 -^ (0,0) for all time t > to > 0 and any initial condition ^10 = ^i(O), ^2,0 = ^i(O) =^ y ^ y and J -^ to > 0 and any initial condition at the physically realizable operation of the column (Femat et al., 1999). Note that equations (1) - (3) are linear; therefore, one can readily obtain a transfer function for the system. Indeed, the transfer function takes the form: C(s) = u{s)/ec(s) = A'c + Kj/s + ^£/s(TnS + 1), where s = (oj, j = (-1)^^^ and eds) = (y{s) - r(s)); KE = Ksigugi) and Tn = Tii(^i,^2) stand for the gain and characteristic time of the dynamic estimation term (namely KE/S{TIIS +1)). Note that such a term is quadratic and provides a dynamic estimation of the input d, which can represent load disturbances (regulation problem) or step changes in references (servocontrol problem). For further details on tuning and closed-loop stability analysis of the PII^ controller, see Alvarez-Ramirez et al. (1997) and Femat et al. (1999), respectively. The performance of the PII^ controller was compared with the performance of the classical PI control action, which is a widely-used type of controller in the chemical industry. Both controllers were tuned following the criterion of the integral of the absolute error (lAE), such that the values of the control gains (Kc, Ki and Ti in the case of PI controllers, or Kc, g\ and g2 in the case of the PII^) that provided a minimum value of lAE for a set point change for each separation scheme were detected.

4. Separation Objective and Control Goals The analysis presented in this work is based on the separation problem of three different ternary mixtures with molar compositions (A, B, C) equal to (0.40, 0.20, 0.40) and product purities of 98.7, 98 and 98.6 percent, respectively. The three mixtures

518 considered were n-pentane, n-hexane and n-heptane (mixture 1), n-butane, isopentane and n-pentane (mixture 2), and isobutane, n-butane and n-hexane (mixture 3). Two set of simulations were carried out. (i) Servo-control. Step was induced as set point changes for each product composition under SISO feedback control at each output flowrate (see Figure 1) and (ii) Regulation under load disturbances: the effect of feed composition disturbances was induced to test and compare the performance of the proposed controller (a 5% change in the composition of one component with the same total feed flowrate).

5. Dynamic Simulations and Results The dynamic results are presented on a comparative basis to allow for a better assessment of the controllers performance. For mixture 1, the results of the lAE values for the case of responses in the face to feed disturbances show that the PII^ controller provides a better behavior than the PI controller. Table 1 shows how the lAE values for the PII^ controller are smaller than those for the PI controller. The highest values for lAE, which reflect the most difficult control task, are obtained for the stabilization of the intermediate component. This is probably because the dynamic behavior of the composition of the intermediate component under open loop operation shows an inverse response. However, it should be noted that the most significant improvement of the PII^ controller over the PI controller was obtained for the control of the intermediate component (in contrast to the control problem of the lightest and heaviest components). Table 1. lAE results for the mixture 1 under load disturbances at feed compositions. Component A B C

Flf 1.2296x10"^ 2.8259 X 10-^ 1.745939x10'^

PI 2.2082 x 10"^ 8.7463 x lO"^ 3.1119x10-^

A more detailed analysis of the dynamic performance obtained for the lightest (A) component and the heaviest (C) component follows. Figure 2 displays the simulation results obtained for the control analysis of component A. When load disturbances were induced, the PII^ controller adjusts the composition of product A smoothly, while the PI action shows a significant time period of product quality deterioration (Figure 2a). The control effort, measured through the changes in the control valves positions (Figure 2b), reflects the superior performance of the PII^ controller accordingly. When a set point change in the composition of component A was imposed, the controllers showed a fairly similar behavior, as observed in Figures 2c and 2d. Figure 3 shows some results obtained for the control of the heaviest component. A superior behavior of the PII^ option is again evident. Although for the set point tracking case (Figure 3c), the use of the PII^ controller shows only a slightly better performance than the PI controller, a remarkable improvement of the use of the PII^ controller is obtained when responses against feed disturbances were considered (Figure 3a). For the case of set point tracking, the responses of the system under the action of either the PII^ controller or the traditional PI controller were not significantly different, although the use of the PII^ controller provided generally a faster adjustment with fewer oscillations. When the response of the column to feed disturbances was analyzed, the PII^ controller provided a remarkable improvement over the use of the PI controller; while in several cases the implementation of the PI controller yielded extremely high

519 settling times, the PII^ controller showed an excellent capability to eliminate the feed disturbance fast and without overshoot problems. As far as control efforts are concerned, the implementation of the PII^ controller provided smoother control actions; the variations in control valves positions were minor, in contrast with the results for the Pl-classical control mode, in which the valves even became saturated (or completely closed) in several of the tests conducted. e o J

•" 50 A 49«

!

1

«•-

"o

45 -

1^

»***iiiitAl!ihtow—• • • • • • • "• , — , — , — , — • — i 43 \— , — 1 — , — ,

-*—pira

"

K 6

7

8

9

j

8

10

12

14

10

a) Response to feed disturbance in composition A

b) Response in the control valve to feed disturbance in component A

—*—PU*2 1 -••-PI

1 :::

I ..»W«»=*™

1 g 54 • 1 ; 53 • J 521 51 • 1 50 <

c) Response to set point change in composition A

d) Response in the control valve to set point change in component A

Figure 2. Some representative dynamic responses (component A) for the separation of mixture 1.

I 0.995

\fm-

|o.»5r*-'—^^"' 0.98 -I

1

I

5«

,—

a) Response to feed disturbance in composition C

b) Response in the control valve to feed disturbance in component C

-g

56

Kj-^ 0

1

2

3

5

6

7 Time,hr

c) Response to set point change in composition C

d) Response in the control valve to set point change in component C

Figure 3. Some representative dynamic responses (component C) for the separation of mixture 1.

520 When mixtures 2 and 3 were subjected to the same tests, similar trends on the dynamic responses of the Petlyuk column were obtained. Particularly, the PII^ controller provided a remarkable performance when load changes in the feed composition were considered. The smooth performance of the PII^ controller is induced by its disturbance estimator, which resembles the structure of linear state observers.

6. Conclusions The control of a Petlyuk column with a proportional-integral controller with dynamic estimation of uncertainties was analyzed. The dynamic behavior of this action was compared to the Petlyuk column performance under a proportional-integral controller. Set point tracking and responses to feed composition disturbances were analyzed. The results obtained for three case studies show that, after optimizing the controller parameters of each control policy, the closed loop behavior under the PII^ control mode was significantly better than the responses obtained with a PI controller. The superiority of the PII^ control option was particularly noticeable when the column was subjected to feed disturbances. The properties of the PII^ controller allow a proper detection of disturbances and a proper corrective action to prevent the controlled output from significant deviations from the desired operation point. In general, the PII^ controller has been found to have an excellent potential for the control of the Petlyuk column.

7. References Abdul Mutalib, M.I. and Smith, R., 1998, Trans Inst. Chem. Eng., 76, 308. Alvarez-Ramirez, J., Femat, R. and Barreiro, A., 1997, Ind. Eng. Chem. Res., 36, 3668. Amminudin, K.A., Smith, R., Thong, D.Y.-C. and Towler, G.P., 2001, Trans Inst. Chem. Eng., 79, 701. Brugma, A.J., 1937, Dutch Patent No. 41, 850, October 15. Femat, R., Alvarez-Ramirez, J. and Rosales-Torres, M., 1999, Comp. Chem. Eng., 23, 697. Glinos, K. and Malone, F., 1988, Chem. Eng. Res. Des., 66, 229. Hairston, D., 1999, Chem Eng., April, 32. Hernandez, S. and Jimenez, A., 1999a, Comp. Chem. Eng., 23, 1005. Hernandez, S. and Jimenez, A., 1999b, Ind. Eng. Chem. Res., 38, 3957. Jimenez, A., Hernandez, S., Montoy, F.A. and Zavala-Garcia, M., 2001, Ind. Eng. Chem. Res., 40, 3757. Luyben, W.L., 1990, Process modeling, simulation and control for chemical engineers, 2nd Ed., McGraw-Hill, Singapore. Muralikrishna, K., Madhavan, K.P. and Shah, S.S., 2002, Trans Inst. Chem. Eng., 80, 155. Petlyuk, F.B., Platonov, V.M. and Slavinskii, D.M., 1965, Int. Chem. Eng., 5(3), 555. Serra, M., Espuna, A. and Puigjaner, L., 1999, Chem. Eng. Process., 38, 549. Triantafyllou, C. and Smith, R., 1992, Trans Inst. Chem. Eng., 70,118. Wolff, E.A. and Skogestad, S., 1995, Ind. Eng. Chem. Res., 34, 2094. Wright, R.O., 1949, U.S. Patent 2, 471, 134, May 24.

8. Acknowledgements Financial support from Conacyt and Concyteg, Mexico, is gratefully acknowledged.

European Symposium on Computer Aided Process Engineering - 13 A. Kraslawski and I. Turunen (Editors) © 2003 Elsevier Science B.V. All rights reserved.

521

Dynamic Study of Thermally Coupled Distillation Sequences Using Proportional - Integral Controllers Juan Gabriel Segovia-Hernandez^, Salvador Hernandez^, Vicente Rico-Ramirez^ and Arturo Jimenez^ ^Instituto Tecnologico de Celaya, Departamento de Ingenieria Quimica, Av. Tecnologico y Garcia Cubas s/n, Celaya, Gto., 38010, Mexico. ''Universidad de Guanajuato, Facultad de Quimica, Noria Alta s/n, Guanajuato, Gto., 36050, Mexico, [email protected]

Abstract A comparative study of the energy requirements and control properties of three thermally coupled distillation schemes and two conventional distillation sequences for the separation of ternary mixtures is presented. The responses to set point changes under closed loop operation with proportional-integral (PI) controllers were obtained. Three composition control loops were used, and for each separation scheme, the parameters of the PI controllers were optimized using the integral of the absolute error criterion. The effects of feed composition and of the ease of separability index were considered. The results indicate that there exist cases in which integrated systems may exhibit better control properties than sequences based on conventional distillation columns.

1. Introduction Distillation process, the most widely-used separation method in industry, is characterized by its high energy consumption. Alternate arrangements to the conventional distillation columns (one input, two outputs) have received noticeable attention in recent years. Through the use of recycle streams between two columns, several thermally coupled distillation systems have been proposed. The three thermally coupled systems that have been analyzed to a greater extent are the system with side rectifier (TCDS-SR, Figure la), the system with side stripper (TCDS-SS, Figure lb), and the fully thermally coupled distillation system (or Petlyuk column. Figure Ic). Several studies have shown that those TCDS schemes can save up to 30% on energy consumption with respect to the direct and indirect sequences based on conventional columns (Tedder and Rudd, 1978; Alatiqi and Luyben, 1985; Glinos and Malone, 1988; Fidkowski and Krolikowski, 1991; Finn, 1993; Yeomans and Grossmann, 2000). Most of these results were obtained through energy consumption calculations at minimum reflux conditions, and they spawned the development of more formal design procedures. Hernandez and Jimenez (1996, 1999a) have reported the use of optimization strategies for TCDS to detect designs with minimum energy consumption. When comparing the energy savings of the integrated schemes, it has been found that in general the Petlyuk system offers better savings than the systems with side columns. However, the complex column configurations that can potentially produce larger energy savings are not commonly used in industrial practice, largely because of control concerns (Dunnebier and Pantelides, 1999). Recent research efforts have been conducted to understand the

522 operational properties of TCDS. The works of Wolff and Skogestad (1995), AbdulMutalib and Smith (1998), Hernandez and Jimenez (1999b) and Jimenez et al. (2001) have shown that some of these integrated options are controllable, so that their potential implementation would probably not be at the expense of control problems. In this work, we present an analysis on the closed loop behavior of three TCDS, and compare their responses to those of the conventional direct and indirect distillation sequences. The analysis is based on rigorous dynamic simulations using changes in set points of product compositions.

2. Design procedure The design of the three TCDS under consideration was carried out following the procedure suggested by Hernandez and Jimenez (1996, 1999a). The method provides a tray structure for the integrated systems by a section analogy procedure with respect to the design of a conventional sequence; the TCDS-SR is obtained from the tray arrangements of a direct sequence, the TCDS-SS from an indirect sequence, and the Petlyuk system from a sequence of a prefractionator followed by two binary distillation columns. The degrees of freedom that remain after design specifications (one degree of freedom for the systems with side columns, and two for the Petlyuk system) were used to obtain the operating conditions under which the integrated designs provide minimum energy consumption.

/KIFI I

H -#(a) TCDS-SR

->c

(b)Ta)S-SS

(c) Petlyuk Coluim

Figure 1. Thermally coupled distillation sequences. The search procedure provided the optimal values of the interconnecting vapor flowrate (VF) for the TCDS-SR (Figure la), the interconnecting liquid flowrate (LF) for the TCDS-SS (Figure lb), or both streams for the case of the Petlyuk column (Figure Ic). Rigorous simulations, using the dynamic model developed by Hernandez and Jimenez (1996), were conducted to test the designs. The model is based on the total mass balance, component mass balances, equilibrium relationships (assuming ideal VLB), summation constraints, energy balance and stage hydraulics (Francis weir formula). Because of the coupling between the columns, the set of equations must be solved simultaneously.

523

3. Dynamic Simulations and Case Studies Although more formal techniques to define the control loops for the integrated columns may be used (for instance the relative gain array method), we based our selection on practical considerations. Thus, the control of the lightest component was manipulated with the reflux flowrate, the heaviest component with the reboiler heat duty, and the control of the intermediate component was a function of the integrated structure; for the TCDS-SR it was tied to the reflux flowrate of the side rectifier, for the TCDS-SS to the heat duty of the side stripper, and for the Petlyuk column to the product stream flowrate. The closed loop analysis was based on proportional-integral controllers. The parameters of the controllers, proportional gains (Kc) and the reset times (Xi), were optimized for each conventional and integrated scheme following the integral of the absolute error (lAE) criterion. The case studies were selected to reflect different separation difficulties and different contents of the intermediate component of the ternary mixtures. Three mixtures with different values of the ease of separability index (ESI, the ratio of relative volatilities of the split AB to the split BC, as defined by Tedder and Rudd, 1978) were considered. The selected mixtures were n-pentane, n-hexane and n-heptane (Ml, ESI = 1.04), n-butane, isopentane and n-pentane (M2, ESI = 1.86), and isobutane, n-butane and n-hexane (M3, ESI = 0.18). To examine the effect of the content of the intermediate component, two types of feed compositions were assumed. One feed with a low content of the intermediate component (where mole fractions of A, B, C, were equal to 0.40, 0.20, 0.40, feed Fl) and another one with a high content of the intermediate component (A, B, C equal to 0.15, 0.70, 0.15, feed F2), were used. The total feed flowrate for all cases was 45.5 kmol/h. Specified product purities of 98.7, 98 and 98.6 percent for A, B and C respectively were assumed.

4. Energy Requirements The results on energy requirements reflect the optimization procedure carried out on the recycle streams for the three integrated sequences. 4.1. Mixture Ml Table 1 shows the energy requirements for each integrated scheme and conventional sequences when mixture Ml was considered. The Petlyuk system shows the best potential, offering savings in energy consumption of up to 50% with respect to the conventional distillation sequences. The TCDS-SR and TCDS-SS require between 14 and 20% less energy consumption than the conventional sequences. 4.2. Mixtures M2 and M3 The superior behavior on energy efficiency of the Petlyuk column was also observed for mixtures M2 and M3 (Segovia-Hernandez, 2001). In the case of mixture M2 the Petlyuk column can offer savings in energy consumption of up to 15% with respect to the conventional sequences, while the savings achieved by the TCDS-SR and TCDS-SS schemes are in the order of 10%. In the case of mixture M3 the Petlyuk column requires between 40 and 50% less energy consumption, whereas the TCDS-SR and the TCDSSS options offer energy savings of up to 30% with respect to the conventional sequences. Table 1. Energy requirements (Btu/h)for separating mixture Ml. Feed Direct Sequence indirect Sequence TCDS-SR TCDS-SS Fl 3,263,772.2 3,547,190.0 2,521,007.0 2,730,465.2 F2 4,127,083.9 4,356,343.8 3,167,085 3,511,610.3

Petlyuk column 1,709,474.1 2,142,722.5

524

5. Dynamic Results The dynamic analysis was based on individual set point changes for product composition on each of the three product streams. The three control loops for each conventional and integrated sequence were assumed to operate under closed loop fashion. 5.1. Mixture Ml, composition Fl Table 2 shows the lAE values obtained for each composition control loop of the distillation sequences under analysis. It is observed that the Petlyuk column offers the best dynamic behavior, which is reflected in the lowest values of lAE, for the control of the three product streams. The dynamic response of each control loop when the Petlyuk column was considered is displayed in Figure 2, where a comparison can be made to the response obtained with the widely-used direct sequence. One may notice in particular how the direct sequence is unable to control the composition of the intermediate component, while the Petlyuk column provides a smooth response, with a relatively short settling time. It is interesting to notice that for this mixture with an ESI = 1, and a low content of the intermediate component in the feed, the Petlyuk column offers the highest energy savings and also shows the best dynamic performance from the five distillation sequences under consideration.

j|A^sf 0 0.10.2 0.30.40.50.60.7 0.80 9 "

a) Conponent C (Petlyuk)

S

0 0.1 0.2 03 04 05 06 07 08 09 lamtr

d) Conponent C (Direct sequence)

V'- < » > • » • > 0 0.10.2 0.30.40.5 0.60.7 0.80.9 1 Ihichr

b) Conponent B (Petlyuk)

I:3 i ^ y ^ ^ 0

0,5

1

1.5 2 Tlm.hr

2.5

3

c) Conponent A (Petlyuk)

k/vvwvvv |lvww—— 1.5

e) Component B (Direct sequence)

2

25

3

f) Component A (Direct sequence)

Figure 2. Dynamic responses of the Petlyuk column and the direct sequence. 5.2. Mixture Ml, composition F2 When the content of the intermediate component in the feed was raised from 20 to 70 percent, significant changes in the dynamic responses of the distillation systems were observed. The first remark is that the Petlyuk column does not provide the best choice from an operational point of view. A second observation is that the best choice depends on the control loop of primary interest. When the control of the light (A) or the heavy (C)