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

Duration (unit time) 5 5 8 8 5 5 5

Jobs

Job No. 1 2 3 4 5 6 7

Chargerl

JVo Ho

Discharger

V2

Blender

V4

H,

IVe

H2

f—'

^ — V

B.

B4 |V5

Cleaner

Charger2

Reactorl

V7

Reactor2

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

10

20

i

1 1 i

40

1 i

50

60

.12 1.1/^2.1.1 j

j

j

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\ \

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i

i

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.2.1

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1

1

1 J.lj

••

2.1.1 2.2.1 j 2.3.1 2.4.1 2.5.1 | 2.6.1 2 j j 1—j_J j i_j \i (_J LI I_:_ I : L : i i

Vessel2

.6.2 1.6 .1

:

\3.7.p

il.4.3 1,5.3J 1.6.:^K7.3 1:

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j 113.4.2/1,4.1

J i l l ^6.2^.6,^2 .6.1 1 1 = 1 '^ \'- • = 4•J

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90 100 110 120 f^^'^^m ^^^^^^

3.3.2 13.1

2^5.1I

13.5.2 i.5.3

^

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X.Y. Z ' X:*Vessel; Y: job No.i Z:

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•1

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1

j

1

1

....^ mi^^^^mA

1 1

••^H

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),