18th EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING
COMPUTER-AIDED CHEMICAL ENGINEERING Advisory Editor: R. Gani Volume 1: Volume 2: Volume 3: Volume 4: Volume 5:
Volume 6: Volume 7: Volume 8: Volume 9: Volume 10: Volume 11: Volume 12: Volume 13: Volume 14: Volume 15: Volume 16: Volume 17: Volume 18: Volume 19: Volume 20: Volume 21:
Volume 22: Volume 23: Volume 24: Volume 25:
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. Pallai and Z. Fonyó, 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. Jørgensen, Editors) European Symposium on Computer Aided Process Engineering-12 (J. Grievink and J. van Schijndel, Editors) Software Architectures and Tools for Computer Aided Process Engineering (B. Braunschweig and R. Gani, Editors) Computer Aided Molecular Design: Theory and Practice (L.E.K. Achenie, R. Gani and V. Venkatasubramanian, Editors) Integrated Design and Simulation of Chemical Processes (A.C. Dimian) European Symposium on Computer Aided Process Engineering-13 (A. Kraslawski and I. Turunen, Editors) Process Systems Engineering 2003 (Bingzhen Chen and A.W. Westerberg, Editors) Dynamic Model Development: Methods, Theory and Applications (S.P. Asprey and S. Macchietto, Editors) The Integration of Process Design and Control (P. Seferlis and M.C. Georgiadis, Editors) European Symposium on Computer-Aided Process Engineering-14 (A. Barbosa-Póvoa and H. Matos, Editors) Computer Aided Property Estimation for Process and Product Design (M. Kontogeorgis and R. Gani, Editors) European Symposium on Computer-Aided Process Engineering-15 (L. Puigjaner and A. Espuña, Editors) 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering (W. Marquardt and C. Pantelides) Multiscale Modelling of Polymer Properties (M. Laso and E.A. Perpète) Chemical Product Design: Towards a Perspective through Case Studies (K.M. Ng, R. Gani and K. Dam-Johansen, Editors) 17th European Symposium on Computer Aided Process Engineering (V. Plesu and P.S. Agachi, Editors) 18th European Symposium on Computer Aided Process Engineering (B. Braunschweig and X. Joulia, Editors)
COMPUTER-AIDED CHEMICAL ENGINEERING, 25
18th EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING Edited by
Bertrand Braunschweig IFP, France
and
Xavier Joulia LGC - ENSIACET - IPT, France
Amsterdam – Boston – Heidelberg – London – New York – Oxford Paris – San Diego – San Francisco – Singapore – Sydney – Tokyo
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Contents
Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi International Scientific Committee. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxiii National Organising Committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxvi
Plenary Lectures Model Parameterization Tailored to Real-Time Optimization Benoît Chachuat, Bala Srinivasan and Dominique Bonvin. . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Challenges for Multi-Scale Modeling of Multiple Failure Modes in Microelectronics Juergen Auersperg, Bernhard Wunderle, Rainer Dudek, Hans Walter and Bernd Michel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Design and Integration of Policies to Achieve Environmental Targets René Bañares-Alcántara. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 Computational Chemical Engineering Modeling Applied to Energy and Reactor Design Luc Nougier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Curricular and Pedagogical Challenges for Enhanced Graduate Attributes in CAPE Ian T. Cameron and Daniel R. Lewin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Topic 1 – Off-Line Systems Keynote Lectures Chemical Product Engineering: The 3rd Paradigm Michael Hill.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Simulation in Nuclear Engineering Design Christian Latgé. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Oral Communications Supply Chain Risk Management Through HAZOP and Dynamic Simulation Arief Adhitya, Rajagopalan Srinivasan and I.A. Karimi.. . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 A New Approach for the Design of Multicomponent Water/Wastewater Networks Débora C. Faria and Miguel J. Bagajewicz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Effect of Catalytic Reactor Design on Plantwide Control Strategy: Application to VAM Plant Costin S. Bildea and Alexandre C. Dimian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
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Model of the Product Properties for Process Synthesis Peter M.M. Bongers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model André B. de Haan, Norbert J.M. Kuipers and Maartje Steensma. . . . . . . . . . . . . . . . . . . . . .61 Synthesis of Cryogenic Energy Systems Frank Del Nogal, Jin-Kuk Kim, Simon Perry and Robin Smith . . . . . . . . . . . . . . . . . . . . . . . 67 Study of a Novel Heat Integrated Hybrid Pervaporation Distillation Process: Simulation and Experiments M.T. Del Pozo Gómez, P. Ruiz Carreira, J.-U. Repke, A. Klein, T. Brinkmann and G. Wozny. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 A Novel Network-Based Continuous-time Formulation for Process Scheduling Diego M. Giménez, Gabriela P. Henning and Christos T. Maravelias. . . . . . . . . . . . . . . . . . 79 Excipient Interaction Prediction: Application of the Purdue Ontology for Pharmaceutical Engineering (POPE) Leaelaf Hailemariam, Pradeep Suresh, Venkata Pavan Kumar Akkisetty, Girish Joglekar, Shuo-Huan Hsu, Ankur Jain, Kenneth Morris, Gintaras Reklaitis, Prabir Basu and Venkat Venkatasubramanian. . . . . . . . . . . . . . . . . . . . 85 Optimal Column Sequencing for Multicomponent Mixtures Andreas Harwardt, Sven Kossack and Wolfgang Marquardt. . . . . . . . . . . . . . . . . . . . . . . . . 91 Systematic Design of Production Processes for Enantiomers with Integration of Chromatography and Racemisation Reactions Malte Kaspereit, Javier García Palacios, Tania Meixús Fernández and Achim Kienle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 The Application of a Task-Based Concept for the Design of Innovative Industrial Crystallizers Richard Lakerveld, Herman J.M. Kramer, Peter J. Jansens and Johan Grievink. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Cell Cycle Modelling for Off-line Dynamic Optimisation of Mammalian Cultures Carolyn M. Lam, Kansuporn Sriyudthsak, Cleo Kontoravdi, Krunal Kothari, Hee-Ho Park, Efstratios N. Pistikopoulos and Athanasios Mantalaris. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 New Configuration for Hetero-Azeotropic Batch Distillation: I. Feasibility Studies Peter Lang, Ferenc Denes and Xavier Joulia. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 Integrated Design of Solvent-Based Extractive Separation Processes P. Lek-utaiwan, B. Suphanit, N. Mongkolsiri and R. Gani. . . . . . . . . . . . . . . . . . . . . . . . . . 121 Development of a Novel Petri Net Tool for Process Design Selection Based on Inherent Safety Assessment Method Fakhteh Moradi and Parisa A. Bahri.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
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Population Balance Modeling of Influenza Virus Replication in MDCK Cells During Vaccine Production Thomas Müller, Josef Schulze-Horsel, Yury Sidorenko, Udo Reichl and Achim Kienle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 A Population Balance Model Approach for Crystallization Product Engineering via Distribution Shaping Control Zoltan K. Nagy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 Uncertainty Patterns and Sensitivity Analysis of an Indicator Based Process Design Framework Stavros Papadokonstantakis, Agarwal Siddharta, Hirokazu Sugiyama and Konrad Hungerbühler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 Batch Scheduling with Intermediate Due Dates Using Timed Automata Models Subanatarajan Subbiah, Thomas Tometzki and Sebastian Engell. . . . . . . . . . . . . . . . . . . . 151 A Decomposition Approach to Short-Term Scheduling of Multi-Purpose Batch Processes Norbert Trautmann, Rafael Fink, Hanno Sagebiel and Christoph Schwindt . . . . . . . . . . . 157
Posters Combined Nitrogen and Phosphorus Removal. Model-Based Process Optimization Noelia Alasino, Miguel C. Mussati, Nicolás Scenna and Pío Aguirre. . . . . . . . . . . . . . . . . 163 A Systematic Procedure for Optimizing Crude Oil Distillation Systems Hasan Y. Alhammadi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 Evaluation of Pervaporation Process for Recovering a Key Orange Juice Flavour Compound: Modeling and Simulation W.A. Araujo, M.E.T. Alvarez, E.B. Moraes and M.R. Wolf-Maciel . . . . . . . . . . . . . . . . . . . 175 A Microeconomics-Based Approach to Product Design Under Uncertainty Craig Whitnack, Ashley Heller and Miguel J. Bagajewicz. . . . . . . . . . . . . . . . . . . . . . . . . . 181 Model Predictive Control Based Planning in the Fruit Industry Aníbal Blanco, Guillermo Masini, Noemi Petracci and Alberto Bandoni . . . . . . . . . . . . . . 187 Optimize Process Condensate Reusing System for Ammonia Plant by the Synthesis of MEN Li Chen, Jian Du, Zhihui Gao, Pingjing Yao and Warren D. Seider. . . . . . . . . . . . . . . . . . 193 Entrainer-Based Reactive Distillation versus Conventional Reactive Distillation for the Synthesis of Fatty Acid Esters M.C. de Jong, A.C. Dimian and A.B. de Haan. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 199 Supply Chain Optimization with Homogenous Product Transport Constraints Tivadar Farkas, Zoltán Valentinyi, Endre Rév and Zoltán Lelkes. . . . . . . . . . . . . . . . . . . . 205 A Sensitivity Analysis on Optimal Solutions Obtained for a Reactive Distillation Column Rui M. Filipe, Steinar Hauan, Henrique A. Matos and Augusto Q. Novais . . . . . . . . . . . . 211
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Synthesis of Zero Effluent Multipurpose Batch Processes Using Effective Scheduling Jacques F. Gouws and Thokozani Majozi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217 Design of a Syngas Infrastructure Paulien M. Herder, Rob M. Stikkelman, Gerard P.J. Dijkema and Aad F. Correljé. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Implementation of a Reactive Dividing Wall Distillation Column in a Pilot Plant Rodrigo Sandoval-Vergara, Fabricio Omar Barroso-Muñoz, Héctor Hernández-Escoto, Juan Gabriel Segovia-Hernández, Salvador Hernández and Vicente Rico-Ramírez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229 Optimisation of a Bio-ethanol Purification Process Using Conceptual Design and Simulation Tools Patricia M. Hoch and José Espinosa . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Improvement of Operating Procedures through the Reconfiguration of a Plant Structure Satoshi Hoshino, Hiroya Seki, Tomoya Sugimoto and Yuji Naka. . . . . . . . . . . . . . . . . . . . . 241 Graph-Theoretic Approach to Optimal Synthesis of Supply Networks: Distribution of Gasoline from a Refinery Young Kim, L.T. Fan, Choamun Yun, Seung Bin Park, Sunwon Park, Botond Bertok and Ferenc Friedler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247 Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications Mohamed T. Mahmud, Iqbal M. Mujtaba and Mansour Emtir. . . . . . . . . . . . . . . . . . . . . . . 253 An Integrated Framework for Operational Scheduling of a Real-World Pipeline Network Suelen Neves Boschetto, Luiz Carlos Felizari, Lia Yamamoto, Leandro Magatão, Sérgio Leandro Stebel, Flávio Neves-Jr, Lúcia Valéria Ramos de Arruda, Ricardo Lüders, Paulo César Ribas and Luiz Fernando de Jesus Bernardo . . . . . . . . . . . . 259 An Optimization Framework of Multibed Pressure Swing Adsorption Systems Dragan Nikolic, Michael C. Georgiadis and Eustathios S. Kikkinides . . . . . . . . . . . . . . . . 265 Multi-Objective Design of Multipurpose Batch Facilities Using Economic Assessments Tânia Rute Pinto, Ana Paula F.D. Barbósa-Póvoa and Augusto Q. Novais . . . . . . . . . . . . 271 Oil Products Pipeline Scheduling with Tank Farm Inventory Management Susana Relvas, Henrique A. Matos, Ana Paula F.D. Barbosa-Póvoa and João Fialho. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 Methodology of Conceptual Process Synthesis for Process Intensification Ben-Guang Rong, Eero Kolehmainen and Ilkka Turunen . . . . . . . . . . . . . . . . . . . . . . . . . . 283 Process Plant Knowledge Based Simulation and Design Jelenka B. Savkovic-Stevanovic, Snezana B. Krstic, Milan V. Milivojevic and Mihailo B. Perunicic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
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Study of Arrangements for Distillation of Quaternary Mixtures Using Less Than N-1 Columns Dulce María Méndez-Valencia, María Vázquez-Ojeda, Juan Gabriel Segovia-Hernández, Héctor Hernández and Adrián Bonilla-Petriciolet. . . . . . . . . . . . . . . 295 A Hybrid Meta-Heuristic Method for Logistics Optimization Associated with Production Planning Yoshiaki Shimizu, Yoshihiro Yamazaki and Takeshi Wada . . . . . . . . . . . . . . . . . . . . . . . . . 301 Model-Based Investment Planning Model for Stepwise Capacity Expansions of Chemical Plants Andreas Wiesner, Martin Schlegel, Jan Oldenburg, Lynn Würth, Ralf Hannemann and Axel Polt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307 Divided Wall Distillation Column: Dynamic Modeling and Control Alexandru Woinaroschy and Raluca Isopescu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
Topic 2 – On-Line Systems Oral Communications Optimization of Preventive Maintenance Scheduling in Processing Plants DuyQuang Nguyen and Miguel Bagajewicz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319 Predictive Optimal Management Method for the Control of Polygeneration Systems Andrés Collazos and François Maréchal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Comparison of Model Predictive Control Strategies for the Simulated Moving Bed Adrian Dietz and Jean-Pierre Corriou . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331 Model Reduction Techniques for Dynamic Optimization of Chemical Plants Operation Bogdan Dorneanu, Costin Sorin Bildea and Johan Grievink . . . . . . . . . . . . . . . . . . . . . . . 337 A Mathematical Programming Framework for Optimal Model Selection/Validation of Process Data Belmiro P. Duarte, Maria J. Moura, Filipe J.M. Neves and Nuno M.C. Oliveira. . . . . . . . 343 Towards On-line Model-Based Design of Experiments Federico Galvanin, Massimiliano Barolo and Fabrizio Bezzo . . . . . . . . . . . . . . . . . . . . . . 349 Sensor Placement for Fault Detection and Localization Carine Gerkens and Georges Heyen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355 Using Kriging Models for Real-Time Process Optimisation Marcos V.C. Gomes, I. David L. Bogle, Evaristo C. Biscaia Jr. and Darci Odloak . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements Héctor Hernández-Escoto, Ricardo Aguilar-López, María Isabel Neria-González and Alma Rosa Domínguez-Bocanegra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
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Optimal Control of Batch Processes Using Particle Swam Optimisation with Stacked Neural Network Models Fernando Herrera and Jie Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375 Online LQG Stabilization of Unstable Gas-Lifted Oil Wells Esmaeel Jahanshahi, Karim Salahshoor and Riyaz Kharrat . . . . . . . . . . . . . . . . . . . . . . . . 381 Analysis of the Constraint Characteristics of a Sheet Forming Control Problem Using Interval Operability Concepts Fernando V. Lima, Christos Georgakis, Julie F. Smith and Phillip D. Schnelle . . . . . . . . . 387 Real-Time Optimization via Adaptation and Control of the Constraints Alejandro Marchetti, Benoît Chachuat and Dominique Bonvin . . . . . . . . . . . . . . . . . . . . . . 393 Integration of Engineering Process Control and Statistical Control in Pulp and Paper Industry Ana S. Matos, José G. Requeijo and Zulema L. Pereira . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399 A Combined Balanced Truncation and Multi-Parametric Programming Approach for Linear Model Predictive Control Diogo Narciso and Efstratios Pistikopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 Fault Detection and Isolation Based on the Model-Based Approach: Application on Chemical Processes Nelly Olivier-Maget, Gilles Hétreux, Jean-Marc Le Lann and Marie-Véronique Le Lann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411 Computer Aided Operation of Pipeless Plants Sabine Piana and Sebastian Engell. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417 Off-line Design of PAT Systems for On-line Applications Ravendra Singh, Krist V. Gernaey and Rafiqul Gani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
Posters New Method for Sensor Network Design and Upgrade for Optimal Process Monitoring Miguel J. Bagajewicz, DuyQuang Nguyen and Sanjay Kumar Sugumar . . . . . . . . . . . . . . . 429 A Novel Proactive-Reactive Scheduling Approach in Chemical Multiproduct Batch Plants Elisabet Capón, Georgios M. Kopanos, Anna Bonfill, Antonio Espuña and Luis Puigjaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 Model Predictive Control of the Waste Water Treatment Plant Based on the Benchmark Simulation Model No.1-BSM1 Vasile-Mircea Cristea, Cristian Pop and Paul Serban Agachi. . . . . . . . . . . . . . . . . . . . . . . 441 Load Balancing Control System of a Furnace from Atmospheric Distillation Unit Cristian Patrascioiu and Sanda Mihalache . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 Optimal Operation of Sublimation Time of the Freeze Drying Process by Predictive Control: Application of the MPC@CB Software N. Daraoui, P. Dufour, H. Hammouri and A. Hottot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
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Improving Steady-State Identification Galo A.C. Le Roux, Bruno Faccini Santoro, Francisco F. Sotelo, Mathieu Teissier and Xavier Joulia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459 Application of Adaptive Neurofuzzy Control Using Soft Sensors to Continuous Distillation Javier Fernandez de Canete, Pablo del Saz-Orozco and Salvador Gonzalez-Perez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465 Correlation-Based Just-In-Time Modeling for Soft-Sensor Design Koichi Fujiwara, Manabu Kano and Shinji Hasebe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 471 Integrating Strategic, Tactical and Operational Supply Chain Decision Levels in a Model Predictive Control Framework José Miguel Laínez, Georgios M. Kopanos, Mariana Badell, Antonio Espuña and Luis Puigjaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477 Hybrid Strategy for Real Time Optimization with Feasibility Driven for a Large Scale Three-Phase Catalytic Slurry Reactor Delba N.C. Melo, Adriano P. Mariano, Eduardo C. Vasco de Toledo, Caliane B.B. Costa and Rubens Maciel Filho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 Adaptive Control of the Simultaneous Saccharification – Fermentation Process from Starch to Ethanol Silvia Ochoa, Velislava Lyubenova, Jens-Uwe Repke, Maya Ignatova and Günter Wozny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 Advanced Control Monitoring in Petrobras’ Refineries: Quantifying Economic Gains on a Real-Time Basis Rafael Pinotti, Antonio Carlos Zanin and Lincoln Fernando Lautenschlager Moro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation Diego Martinez Prata, José Carlos Pinto and Enrique Luis Lima . . . . . . . . . . . . . . . . . . . 501 State Estimation for Dynamic Prediction of Hydrate Formation in Oil and Gas Production Systems J. Rodriguez Perez, C.S. Adjiman and C.D. Immanuel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 RCS for Process Control: Is There Anything New Under the Sun? Manuel Rodríguez and Ricardo Sanz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 Data Treatment and Analysis for On-line Dynamic Process Optimization Nina Paula G. Salau, Giovani Tonel, Jorge O. Trierweiler and Argimiro R. Secchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519 Nonlinear Model Predictive Control of a Swelling Constrained Industrial Batch Reactor Levente L. Simon, Z.K. Nagy and Konrad Hungerbühler . . . . . . . . . . . . . . . . . . . . . . . . . . 525 An Adapted SLAB Model Using Sensor Data for the Prediction on the Dispersion of Hazardous Gas Releases Won So, Dongil Shin and En Sup Yoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531
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Topic 3 – Computational & Numerical Solutions Strategies Keynote Lecture Expanding Process Modelling Capability through Software Interoperability Standards: Application, Extension and Maintenance of CAPE OPEN Standards Ray Dickinson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
Oral Communications Optimization of WWTP Control by Means of Multi-Objective Genetic Algorithms and Sensitivity Analysis Benoit Beraud, Jean-Philippe Steyer, Cyrille Lemoine and Eric Latrille. . . . . . . . . . . . . . . 539 A Model Reduction-Based Optimisation Framework for Large-Scale Simulators Using Iterative Solvers Ioannis Bonis and Constantinos Theodoropoulos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 545 Rigorous Flowsheet Optimization Using Process Simulators and Surrogate Models José A. Caballero and Ignacio E. Grossmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 551 MILP-Based Decomposition Method for the Optimal Scheduling of an Industrial Batch Plant Pedro M. Castro, Augusto Q. Novais and Alexandre Carvalho . . . . . . . . . . . . . . . . . . . . . . 557 Design of Constrained Nonlinear Model Predictive Control Based on Global Optimisation Michal C ižniar, Miroslav Fikar and M.A. Latifi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563 Biclustering of Data Matrices in Systems Biology via Optimal Re-ordering Peter A. DiMaggio Jr., Scott R. McAllister, Christodoulos A. Floudas, Xiao-Jiang Feng, Joshua D. Rabinowitz and Herschel A. Rabitz. . . . . . . . . . . . . . . . . . . . . 569 Optimum Experimental Design for Key Performance Indicators Stefan Körkel, Harvey Arellano-Garcia, Jan Schöneberger and Günter Wozny . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575 Inductive Data Mining: Automatic Generation of Decision Trees from Data for QSAR Modelling and Process Historical Data Analysis Chao Y. Ma, Frances V. Buontempo and Xue Z. Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . 581 The Solution of Very Large Non-Linear Algebraic Systems Davide Manca and Guido Buzzi-Ferraris. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587 Multi-Operations Time-Slots Model for Crude-Oil Operations Scheduling Sylvain Mouret, Ignacio E. Grossmann and Pierre Pestiaux . . . . . . . . . . . . . . . . . . . . . . . . 593 A Framework for Analysis of Computational Load of CAPE Tools Pablo A. Rolandi and Alejandro Cano . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 An Implementation of Parallel Computing for Hierarchical Logistic Network Design Optimization Using PSO Yoshiaki Shimizu and Hiroshi Kawamoto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
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Service-Oriented CAPE: A New Direction for Software Applications Iain D. Stalker, Eric S. Fraga, Aidong Yang and Nikolay D. Mehandjiev . . . . . . . . . . . . . 611 Using Grid Computing to Solve Hard Planning and Scheduling Problems Michael C. Ferris, Christos T. Maravelias and Arul Sundaramoorthy . . . . . . . . . . . . . . . . 617 Benchmarking Numerical and Agent-Based Models of an Oil Refinery Supply Chain Koen H. van Dam, Arief Adhitya, Rajagopalan Srinivasan and Zofia Lukszo . . . . . . . . . . 623 Large-Scale Nonlinear Programming Strategies for the Operation of LDPE Tubular Reactors Victor M. Zavala and Lorenz T. Biegler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
Posters Simulis® Thermodynamics: An Open Framework for Users and Developers Olivier Baudouin, Stéphane Dechelotte, Philippe Guittard and Alain Vacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635 A New Approach for Chemical Transfer Reaction Models Zakia Benjelloun-Dabaghi, Renaud Cadours, Sylvie Cauvin and Pascal Mougin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641 Modeling and Simulation of the Particle Size Distribution for Emulsion Polymerization in a Tubular Reactor Ala Eldin Bouaswaig, Wolfgang Mauntz and Sebastian Engell . . . . . . . . . . . . . . . . . . . . . 647 Composite Zeolite Membranes Characterization by using a Transient State Experimental Technique and a Parameter Estimation Procedure Lucile Courthial, Arnaud Baudot, Mélaz Tayakout-Fayolle and Christian Jallut . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653 MPC@CB Software: A Solution for Model Predictive Control Bruno da Silva, Pascal Dufour, Nida Othman and Sami Othman . . . . . . . . . . . . . . . . . . . . 659 Detection of Multiple Structural Changes in Linear Processes Through Change Point Analysis and Bootstrapping Belmiro P.M. Duarte and P.M. Saraiva. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665 Applications of Grey Programming to Process Design Edelmira D. Gálvez, Luis A. Cisternas, Pamela S. Patiño and Kathy L. Ossandon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671 Flexible and Configurable MILP-Models for Meltshop Scheduling Optimization Iiro Harjunkoski and Guido Sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 677 Functional Data Analysis for the Development of a Calibration Model for Near-infrared Data Cheng Jiang and Elaine B. Martin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683 Application of Global Sensitivity Analysis to Biological Models Alexandros Kiparissides, Maria Rodriguez-Fernandez, Sergei Kucherenko, Athanasios Mantalaris and Efstratios Pistikopoulos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
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Development of a Sophisticated Framework for Complex Single- and Multi-Objective Optimization Tasks Matthias Leipold, Sven Gruetzmann, Georg Fieg, Dietrich Maschmeyer, Jörg Sauer and Holger Wiederhold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 Towards Resilient Supply Chains: Uncertainty Analysis Using Fuzzy Mathematical Programming Kishalay Mitra, Ravindra D. Gudi, Sachin C. Patwardhan and Gautam Sardar. . . . . . . . . 701 Modeling and Identification of the Bio-ethanol Production Process from Starch: Cybernetic vs. Unstructured Modeling Silvia Ochoa, Ahrim Yoo, Jens-Uwe Repke, Günter Wozny and Dae Ryook Yang. . . . . . . . 707 Particle Swarm Optimisation in Heat Exchanger Network Synthesis Including Detailed Equipment Design Aline P. Silva, Mauro A.S.S. Ravagnani and Evaristo C. Biscaia Jr. . . . . . . . . . . . . . . . . . 713 A Single Stage Approach for Designing Water Networks with Multiple Contaminants Krzysztof Walczyk and Jacek Jezowski . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 719
Topic 4 – Integrated and Multiscale Modelling and Simulation Keynote Lecture Multiscale Molecular Modeling: A Tool for the Design of Nano Structured Materials Maurizio Fermeglia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725
Oral Communications Energy-Preserving Method for Spatial Discretization: Application to an Adsorption Column Ahmed Baaiu, Françoise Couenne, Laurent Lefevre and Yann Le Gorrec . . . . . . . . . . . . . 727 MEXA goes CAMD – Computer-Aided Molecular Design for Physical Property Model Building André Bardow, Sven Kossack, Ernesto Kriesten and Wolfgang Marquardt. . . . . . . . . . . . . 733 Modeling the Phase Equilibria of Nitriles by the soft-SAFT Equation of State Abdelkrim Belkadi, Mohamed K. Hadj-Kali, Vincent Gerbaud, Xavier Joulia, Fèlix Llovell and Lourdes F. Vega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 739 Application of a Digital Packing Algorithm to Cylindrical Pellet-Packed Beds Richard Caulkin, Michael Fairweather, Xiaodong Jia, Abid Ahmad and Richard A. Williams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 Modelling and Simulation of a Membrane Microreactor Using Computational Fluid Dynamics Paris Chasanis, Eugeny Y. Kenig, Volker Hessel and Stefan Schmitt . . . . . . . . . . . . . . . . . 751 Modeling of Catalytic Hydrogen Generation from Sodium Borohydride André Gonçalves, Pedro Castro, Augusto Q. Novais, Carmen M. Rangel and Henrique Matos . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 757
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Towards a New Generation Heat Exchanger Models Geert W. Haarlemmer and Jérôme Pigourier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763 Brownian Dynamics and Kinetic Monte Carlo Simulation in Emulsion Polymerization Hugo F. Hernandez and Klaus Tauer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 769 Biodiesel Production by Heat-Integrated Reactive Distillation Anton A. Kiss, Alexandre C. Dimian and Gadi Rothenberg . . . . . . . . . . . . . . . . . . . . . . . . 775 Modeling Comparison of High Temperature Fuel Cell Performance: Electrochemical Behaviours of SOFC and PCFC Jean-Marie Klein and Jonathan Deseure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 781 An Integrated Framework for Model-Based Flow Assurance in Deep-Water Oil and Gas Production Eduardo Luna-Ortiz, Praveen Lawrence, Constantinos C. Pantelides, Claire S. Adjiman and Charles D. Immanuel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787 Enhanced Modeling and Integrated Simulation of Gasification and Purification Gas Units Targeted to Clean Power Production Mar Pérez-Fortes, Aarón Bojarski, Sergio Ferrer-Nadal, Georgios M. Kopanos, José Ma Nougués, Enric Velo and Luis Puigjaner . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793 Absorption of Aromatic Hydrocarbons in Multicomponent Mixtures: A Comparison Between Simulations and Measurements in a Pilot Plant Diethmar Richter, Holger Thielert and Günter Wozny . . . . . . . . . . . . . . . . . . . . . . . . . . . . 799 A Comprehensive Population Balance Model of Emulsion Polymerisation for PSD & MWD: Comparison to Experimental Data S.J. Sweetman, C.D. Immanuel, T.I. Malik, S. Emmett and N. Williams . . . . . . . . . . . . . . . 805 Prediction of Partition Coefficients Between Food Simulants and Packaging Materials Using Molecular Simulation and a Generalized Flory-Huggins Approach Olivier Vitrac and Guillaume Gillet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811 Shape – The Final Frontier Xue Z. Wang, Caiyun Ma and Kevin J. Roberts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 817
Posters Computational Fluid Dynamics: A Tool to the Formulation of Therapeutic Aerosols Nathalie Bardin-Monnier, Véronique Falk and Laurent Marchal-Heussler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 823 Large Eddy Simulation of Particle Dispersion in a Straight, Square Duct Flow Michael Fairweather and Jun Yao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 829 Test Bench Dimensioned by Specific Numerical Tool Nicolas Gascoin, Philippe Gillard, Gregory Abraham and Marc Bouchez . . . . . . . . . . . . 835 Optimization of SOFC Interconnect Design Using Multiphysic Computation Dominique Grondin, Jonathan Deseure, Mohsine Zahid, Maria José Garcia and Yann Bultel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 841
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Multi-Objective Scheduling for Environmentally-Friendly Batch Operations Iskandar Halim and Rajagopalan Srinivasan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847 Operability Analysis and Conception of Microreactor by Integration of Reverse Engineering and Rapid Manufacturing André L. Jardini, Maria Carolina B. Costa, Aulus R.R. Bineli, Andresa F. Romão and Rubens Maciel Filho . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 853 Optimisations with Energy Recovery for Oxidative Desulphurization of Heavy Gas Oil Hamza A. Khalfalla, Iqbal M. Mujtaba, Mohamed M. El-Garni and Hadi A. El-Akrami . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 859 Ion-Specific Potential of Mean Force Between Two Aqueous Proteins Eduardo R.A. Lima, Frederico W. Tavares and Evaristo C. Biscaia Jr. . . . . . . . . . . . . . . . 865 A Heteronuclear Group Contribution Method for Associating Chain Molecules (SAFT-γ) Alexandros Lymperiadis, Claire S. Adjiman, Amparo Galindo and George Jackson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 871 An Analytical-Numerical Method for Solving a Heap Leaching Problem of one or more Solid Reactants from Porous Pellets Mario E. Mellado and Luis A. Cisternas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 877 Thermochemical Multi-phase Models Applying the Constrained Gibbs Energy Method Risto Pajarre, Peter Blomberg and Pertti Koukkari . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 883 Industrial Applications of Multi-Phase Thermochemical Simulation Risto Pajarre, Pertti Koukkari and Karri Penttilä . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 889 Prediction of the Melting Point Temperature Using a Linear QSPR for Homologous Series Inga Paster, Mordechai Shacham and Neima Brauner . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895 A General Mathematical Model for a Moving Bed Gasifier Sauro Pierucci and Eliseo Ranzi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 901 Modelling of an Hybrid Wastewater Treatment Plant Marie-Noëlle Pons, Maria do Carmo Lourenço da Silva, Olivier Potier, Eric Arnos and Philippe Battaglia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 907 Dimension Reduction of Two-Dimensional Population Balances Based on the Quadrature Method of Moments Andreas Voigt, Wolfram Heineken, Dietrich Flockerzi and Kai Sundmacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 913 Predictions of the Consequences of Natural Gas-Hydrogen Explosions Using a Novel CFD Approach Robert M. Woolley, Michael Fairweather, Samuel A.E.G. Falle and Jack R. Giddings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 919
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Topic 5 – Cape for the Users! Oral Communications Support of Strategic Business Decisions at BASF’s Largest Integrated Production Site Based on Site-Wide Verbund Simulation Stefan Brüggemann, Nanette Bauer, Eberhard Fuchs, Axel Polt, Bernhard Wagner and Michael Wulkow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 925 A Generic Scientific Information Management System for Process Engineering Sylvie Cauvin, Mireille Barbieux, Laurent Carrié and Benoît Celse. . . . . . . . . . . . . . . . . . 931 Rapid Process Design and Development of Complex Solution Copolymers Yadunandan L. Dar and Tahir I. Malik . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 937 Troubleshooting and Process Optimisation by Integrating CAPE Tools and Six Sigma Methodology Dr. Guido Dünnebier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 943 A Compliance Management System for the Pharmaceutical Industry Julie Fisher, Arantza Aldea and René Bañares-Alcántara . . . . . . . . . . . . . . . . . . . . . . . . . 949 Business Process Model for Knowledge Management in Plant Maintenance Tetsuo Fuchino, Yukiyasu Shimada, Masazumi Miyazawa and Yuji Naka . . . . . . . . . . . . . 955 Practical Challenges in Developing Data-Driven Soft Sensors for Quality Prediction Jun Liu, Rajagopalan Srinivasan and P.N. SelvaGuru . . . . . . . . . . . . . . . . . . . . . . . . . . . . 961 Process Analytical Technologies (PAT) – The Impact for Process Systems Engineering Zeng Ping Chen, David Lovett and Julian Morris . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 967 Decision Support for Control Structure Selection During Plant Design Jan Oldenburg, Hans-Jürgen Pallasch, Colman Carroll, Veit Hagenmeyer, Sachin Arora, Knud Jacobsen, Joachim Birk, Axel Polt and Peter van den Abeel . . . . . . . 973 Production-Line Wide Dynamic Bayesian Network Model for Quality Management in Papermaking Aino Ropponen and Risto Ritala . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 979 OntoMODEL: Ontological Mathematical Modeling Knowledge Management Pradeep Suresh, Girish Joglekar, Shuohuan Hsu, Pavan Akkisetty, Leaelaf Hailemariam, Ankur Jain, Gintaras Reklaitis and Venkat Venkatasubramanian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985 OntoCAPE 2.0 – a (Re-)Usable Ontology for Computer-Aided Process Engineering Jan Morbach, Andreas Wiesner and Wolfgang Marquardt . . . . . . . . . . . . . . . . . . . . . . . . 991
Posters CAPE Methods and Tools for Systematic Analysis of New Chemical Product Design and Development Merlin Alvarado-Morales, Naweed Al-Haque, Krist V. Gernaey, John M. Woodley and Rafiqul Gani . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997
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Hazop Support System and its Use for Operation Koji Kwamura, Yuji Naka, Tetsuo Fuchino, Atsushi Aoyama and Nobuo Takagi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003 Acceleration of the Retrieval of Past Experiences in Case Based Reasoning: Application for Preliminary Design in Chemical Engineering Stephane Negny and Jean-Marc Le Lann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1009 Visual Exploration of Multi-State Operations Using Self-Organizing Map Yew Seng Ng and Rajagopalan Srinivasan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1015 Multi-Criteria Decision Making in Product-driven Process Synthesis Kristel de Ridder, Cristhian Almeida-Rivera, Peter Bongers, Solke Bruin and Simme Douwe Flapper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1021 Improvement of the Production Process of Leached Optical Fibers in a Technological and Organizational Context Daniëlle T. Stekelenburg, Zofia Lukszo and Jeff Lowe . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1027 Quality Assurance of Simulation Results Laurent Testard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1033 Decision Tree Based Qualitative Analysis of Operating Regimes in Industrial Production Processes Tamás Varga, Ferenc Szeifert, József Réti and János Abonyi . . . . . . . . . . . . . . . . . . . . . . 1039 Mobatec Modeller – A Flexible and Transparent Tool for Building Dynamic Process Models Mathieu R. Westerweele and Jan Laurens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045
Topic 6 – Cape and Society Keynote Lecture Sustainable Energy Futures, and what we can do about it Cav. Prof. Sandro Macchietto . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1051
Oral Communications A Methodology for Designing and Evaluating Biomass Utilization Networks Nasser Ayoub, Hiroya Seki and Yuji Naka . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1053 Integrated Gasification Combined Cycle (IGCC) Process Simulation and Optimization F. Emun, M. Gadalla and L. Jiménez . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1059 IDEF0 Activity Modeling for Integrated Process Design Considering Environmental, Health and Safety (EHS) Aspects Masahiko Hirao, Hirokazu Sugiyama, Ulrich Fischer and Konrad Hungerbühler . . . . . . 1065 A Prototype Agent-Based Modeling Approach for Energy System Analysis Bri-Mathias Hodge, Selen Aydogan-Cremaschi, Gary Blau, Joseph Pekny and Gintaras Reklaitis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1071
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A Systematic Framework for Biorefinery Production Optimization Norman E. Sammons, Jr., Wei Yuan, Mario R. Eden, Burak Aksoy and Harry T. Cullinan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077 Economic Analysis and Process Integration of Hydrogen Production Strategies Wei Yuan, Norman E. Sammons Jr., Kristin H. McGlocklin and Mario R. Eden . . . . . . . 1083 Design of Heat-integrated Power Systems with Decarbonisation Xuesong Zheng, Jin-Kuk Kim and Robin Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1089
Posters Mathematical Modeling of Limestone Dissolution in Batch Stirred Tank Reactors in Presence of a Diluted Strong Acid Cataldo De Blasio, Jarl Ahlbeck and Frej Bjondahl . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1095 Biodiesel Production from Vegetable Oils: Operational Strategies for Large Scale Systems Nívea de Lima da Silva, Elmer Ccopa Rivera, César Benedito Batistella, Danilo Ribeiro de Lima, Rubens Maciel Filho and Maria Regina Wolf Maciel . . . . . . . . 1101 Minimization of Life Cycle Greenhouse Emissions and Cost in the Operation of Steam and Power Plants Pablo E. Martinez and Ana Maria Eliceche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1107 Developing a Lake Eutrophication Model and Determining Biogeochemical Parameters: A Large Scale Parameter Estimation Problem Vanina Estrada, Elisa R. Parodi and M. Soledad Diaz . . . . . . . . . . . . . . . . . . . . . . . . . . . 1113 Computer Aided Design of Occupationally Healthier Processes Mimi H. Hassim and Markku Hurme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1119 Energy Management in a Stand-Alone Power System for the Production of Electrical Energy with Long Term Hydrogen Storage Dimitris Ipsakis, Spyros Voutetakis, Panos Seferlis, Fotis Stergiopoulos, Simira Papadopoulou, Costas Elmasides and Chrysovalantis Keivanidis . . . . . . . . . . . . 1125 Mapping Environmental Issues within Supply Chains: A LCA Based Approach José Miguel Laínez, Aarón Bojarski, Antonio Espuña and Luis Puigjaner . . . . . . . . . . . 1131 Exergy Analysis of Biological Hydrogen Production Ala Modarresi, Walter Wukovits and Anton Friedl . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137 Sensitivity Analysis of a Model for Atmospheric Dispersion of Toxic Gases Nishant Pandya, Eric Marsden, Pascal Floquet and Nadine Gabas. . . . . . . . . . . . . . . . . 1143 A Generic Framework for Modeling, Design and Optimization of Industrial Phosphoric Acid Production Processes Athanasios I. Papadopoulos and Panos Seferlis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149 Fisher Information: A Generalized Sustainability Index? Vicente Rico-Ramirez, Pedro A. Quintana-Hernandez, Jesus A. Ortiz-Cruz and Salvador Hernandez-Castro . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155 Towards Improved Cleaning of FMCG Plants: A Model-Based Approach A. Yang, E.B. Martin, G.A. Montague and P.J. Fryer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1161
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Contents
Topic 7 – Cape in Education Oral Communications Development of Sustainable Energy Systems: A New Challenge for Process Systems Engineering Education Catherine Azzaro-Pantel, Christophe Gourdon, Xavier Joulia, Jean-Marc Le Lann, Stéphan Astier, Guillaume Fontes, Maria David and Alain Ayache. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1167 Enhancing the Understanding and Insights of Students and Industry Operators in Process Engineering Principles via Immersive 3D Environments Christine Norton, Ian Cameron, Caroline Crosthwaite, Nicoleta Balliu, Moses Tade, David Shallcross, Andrew Hoadley, Geoff Barton and John Kavanagh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1175 CAPE Tools in Biotechnology: Why, When, What, Who, Which Ones and Where? L. Jiménez, I. Katakis, A. Fabregat, T. Schafer, S. Rodriguez, J.M. Mateo, M. Giamberini, B. Rivera, P. Argüeso, E. Calero, L. Vico, F. Hernandez, R. Genc, M. Medir, J.R. Alabart and G. Guillén-Gosálbez . . . . . . . . . . . . . . . . . . . . . . . . 1181 What is “In” and What is “Out” in Engineering Problem Solving Mordechai Shacham, Michael B. Cutlip and Neima Brauner . . . . . . . . . . . . . . . . . . . . . . 1187
Poster Virtual and Remote Laboratory for Robotics E-Learning Carlos A. Jara, Francisco A. Candelas and Fernando Torres . . . . . . . . . . . . . . . . . . . . . 1193 Author Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1199
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Preface This book contains papers presented at the 18th European Symposium on Computer Aided Process Engineering, ESCAPE-18, held in Lyon, France, June 1–4, 2008. A complementary CD-Rom contains all the papers presented at the symposium. ESCAPE-18 is the 40th event of the CAPE (Computer Aided Process Engineering) Working Party of the European Federation of Chemical Engineering (EFCE). The ESCAPE series started in 1992 at Elsinore, Denmark, on a strong foundation of 23 events of the CAPE WP. The first event was organized in Tutzing, Germany, in 1968. The most recent symposia were organized in Barcelona, Spain, 2005, Garmisch-Partenkirchen, Germany, 2006 and Bucharest, Romania, 2007. The ESCAPE series brings the latest innovations and achievements by leading professionals from the industrial and academic communities. The series serves as a forum for engineers, scientists, researchers, managers and students from academia and industry to: – present new computer aided methods, algorithms, techniques related to process and product engineering, – discuss innovative concepts, new challenges, needs and trends in the area of CAPE. This research area bridges fundamental sciences (physics, chemistry, thermodynamics, applied mathematics and computer sciences) with the various aspects of process and product engineering. The main theme for ESCAPE-18 is CAPE for the Users! CAPE systems are to be put in the hands of end users who need functionality and assistance beyond the scientific and technological capacities which are at the core of the systems. User-friendliness, on-line or web-based advice, decision support, knowledge management, organisational issues, are important points that must be taken care of when deploying a CAPE system. These issues were addressed in a special session and industrial case studies illustrating CAPE methods and tools were encouraged. The other four main topics cover the usual scope of ESCAPE series: – – – –
off-line systems for synthesis and design, on-line systems for control and operation, computational and numerical solutions strategies, integrated and multi-scale modelling and simulation,
and two general topics address the impact of CAPE tools and methods on Society and Education. More than 580 abstracts were submitted to the conference. Out of them 420 were invited to submit a full paper and 342 were finally selected for oral or poster presentation. Their authors came from 41 different countries. The review of abstracts, review of manuscripts and final selection
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of revised manuscripts were carried out by an International Scientific Committee (ISC). We are very grateful to the 84 members of the ISC for their efficient and fruitful collaboration. In addition to the accepted papers, eleven outstanding speakers were invited for giving plenary or keynote lectures on state-of-the art, challenges and future needs in all main topics. ESCAPE celebrates its 18th anniversary this year, reaching the adult stage! It is true that ESCAPE is quite an established conference in the realm of computer-aided process engineering, but it continues to attract innovative young researchers from around the world. We are confident that it will go on as such in the forthcoming year, keeping the young spirit together with the experience acquired over its first eighteen years. We hope that this book will serve as a valuable reference document to the scientific and industrial community and will contribute to the progress in computer aided process and product engineering.
Bertrand Braunschweig Xavier Joulia ESCAPE-18 Co-Chairmen
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International Scientific Committee
Conference Co-Chairpersons Bertrand Braunschweig, IFP, France Xavier Joulia, LGC – ENSIACET – INPT, France
Topic Area Co-Chairpersons Off-line Systems Rafiqul Gani, Technical University of Denmark, Denmark Jan van Schijndel, Shell Global Solutions International, The Netherlands
On-line Systems Chonghun Han, Seoul National University, South Korea Martin Wolf, Bayer Technology Services, Germany
Computational and Numerical Solution Strategies Lorens Biegler, Carnegie-Mellon University, USA Michel Pons, Michel Pons Technologie, France
Integrated and Multiscale Modelling and Simulation Luis Puigjaner, Universitat Politècnica de Catalunya, Spain Costas Pantelides, Process Systems Enterprise, UK
CAPE for the Users! Tahir I. Malik, ICI Strategic Technology Group, UK Wolfgang Marquardt, RWTH Aachen University, Germany
CAPE and Society Peter Glavic, University of Maribor, Slovenia Sophie Jullian, IFP, France
CAPE in Education Ian Cameron, University of Queensland, Australia Georges Heyen, University of Liège, Belgium
Members Off-line Systems Ana Barbosa-Póvoa, Instituto Superior Tecnico, Portugal David Bogle, University College London, UK Michael Doherty, University of California, USA
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International Scientific Committee Andrzej Gorak, University of Dortmund, Germany Johan Grievink, Delft University of Technology, The Netherlands Ignacio Grossmann, Carnegie Mellon University, USA Ludovit Jelemensky, Slovak University of Technology, Slovakia Zdravko Kravanja, University of Maribor, Slovenia Christian Latgé, CEA, France Henrique Matos, Instituto Superior Tecnico, Portugal Xuan Meyer, LGC – ENSIACET – INPT, France Ka Ming Ng, Hongkong University of Science and Technology, China (Hongkong) Sauro Pierucci, Politecnico di Milano, Italy Heinz Preisig, Norwegian University of Science and Technology, Norway Eva Sorensen, University College London, UK Petr Srehlik, BRNO University of Technology, Czech Republic
On-line Systems Dominique Bonvin, Ecole Polytechnique Fédérale de Lausanne, Switzerland Didier Caudron, Sanofi Pasteur, France Yann Creff, IFP, France Sebastian Engell, University of Dortmund, Germany Antonio Espuña, Universitat Politècnica de Catalunya, Spain Sten Bay Jorgensen, Technical University of Denmark, Denmark Marie-Véronique Le Lann, LAAS, France Iqbal Mujtaba, University of Bradford, UK Jose Pinto, Universidade de São Paulo, Brazil Sigurd Skogestad, Norwegian University of Science and Technology, Norway Venkat Venkatasubramanian, Purdue University, USA Günter Wozny, Technical University of Berlin, Germany Toshko Zhelev, University of Limerick, Ireland
Computational and Numerical Solution Strategies Guido Buzzi-Ferraris, Politecnico di Milano, Italy Benoit Chachuat, Ecole Polytechnique Fédérale de Lausanne, Switzerland Pascal Floquet, LGC – ENSIACET – INPT, France Christodoulos Floudas, Princeton University, USA Jacek Jezowski, Rzeszow Technical University, Poland François Maréchal, Ecole Polytechnique Fédérale de Lausanne, Switzerland Hervé Pingaud, ENSTIMAC, France Stratos Pistikopoulos, Imperial College London, UK Mordechai Shacham, Ben-Gurion University of the Negev, Israel Alain Vacher, ProSim, France Peter Verheijen, Delft University of Technology, The Netherlands
Integrated and Multiscale Modelling and Simulation Claire Adjiman, Imperial College London, UK Ana Maria Eliceche, Plapiqui, Argentina Christian Jallut, LAGEP – Université Lyon 1 – CPE, France Thokozani Majozi, University of Pretoria, South Africa Fernando Martins, FEUP, Portugal Natalia Menshutina, D.I. Mendeleev University of Chemical Technology, Russia
International Scientific Committee Gintaras Reklaitis, Purdue University, USA George Stephanopoulos, MIT, USA Jan Thullie, Politechnika Slaska, Poland Gilles Trystram, GénIAl – ENSIA, France
CAPE for the Users! Rafael Batres, Toyohashi University of Technology, Japan Sylvie Cauvin, IFP, France Gabriella Henning, INTEC, Argentina Andrzej Kraslawski, Lappeenranta University of Technology, Finland Jean-Marc Le Lann, LGC – ENSIACET – INPT, France Jack Ponton, University of Edinburgh, UK Rajagopalan Srinivasan, National University of Singapore, Singapore Lars Von Wedel, AixCAPE, Germany
CAPE and Society Arsène Isambert, LGPM-ECP, France Emilia Kondili, TEI of Piraeus, Greece Sandro Macchietto, Imperial College London, UK Peter Mizsey, Budapest University of Technology and Economics, Hungary Yuji Naka, Tokyo Institute of Technology, Japan Claudio Oller do Nascimento, Universidade de São Paulo, Brazil Valentin Plesu, University Politehnica of Bucharest, Romania En Sup Yoon, Seoul National University, Korea
CAPE in Education David Bogle, University College London, UK Marie Debacq, CNAM, France Urban Gren, Chalmers University of Technology, Sweden Daniel Lewin, Technion, Israel
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National Organising Committee
Chairman Bertrand Braunschweig, IFP
Members Didier Caudron, Sanofi Pasteur Stéphane Déchelotte, ProSim Pascal Floquet, LGC – ENSIACET – INPT Arsène Isambert, LGPM – ECP Christian Jallut, LAGEP – Université Lyon 1 – CPE Xavier Joulia, LGC – ENSIACET – INPT Christian Latgé, CEA Frédérique Léandri, IFP Francis Luck, Total Francis Nativel, Axens Hervé Roustan, Alcan Philippe Vacher, RSI
Symposium Secretariat ESCAPE 18 c/o COLLOQUIUM 12 rue de la Croix-Faubin 75011 Paris – France
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
1
Model Parameterization Tailored to Real-time Optimization Benoît Chachuat,a Bala Srinivasan,b Dominique Bonvina a
Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne (EPFL), Station 9, CH-1015 Lausanne, Switzerland b Département de Génie Chimique, Ecole Polytechnique de Montréal, C.P. 6079 Succ. centre ville, Montréal (QC), H3C 3A7, Canada
Abstract Challenges in real-time process optimization mainly arise from the inability to build and adapt accurate models for complex physico-chemical processes. This paper surveys different ways of using measurements to compensate for model uncertainty in the context of process optimization. A distinction is made between model-adaptation methods that use the measurements to update the parameters of the process model before repeating the optimization, modifier-adaptation methods that adapt constraint and gradient modifiers, and direct-input-adaptation methods that convert the optimization problem into a feedback control problem. This paper argues in favor of modifier-adaptation methods, since it uses a model parameterization, measurements, and an update criterion that are tailored to the tracking of the necessary conditions of optimality. Keywords: Measurement-based optimization; Real-time optimization; Plant-model mismatch; Model adaptation; Model parameterization.
1. Introduction Optimization of process performance has received attention recently because, in the face of growing competition, it represents the natural choice for reducing production costs, improving product quality, and meeting safety requirements and environmental regulations. Process optimization is typically based on a process model, which is used by a numerical procedure for computing the optimal solution. In practical situations, however, an accurate process model can rarely be found with affordable effort. Uncertainty results primarily from trying to fit a model of limited complexity to a complex process. The model-fitting task is further complicated by the fact that process data are usually noisy and signals do not carry sufficient excitation. Therefore, optimization using an inaccurate model might result in suboptimal operation or, worse, infeasible operation when constraints are present [8]. Two main classes of optimization methods are available for handling uncertainty. The essential difference relates to whether or not measurements are used in the calculation of the optimal strategy. In the absence of measurements, a robust optimization approach is typically used, whereby conservatism is introduced to guarantee feasibility for the entire range of expected variations [18]. When measurements are available, adaptive optimization can help adjust to process changes and disturbances, thereby reducing conservatism [9]. It is interesting to note that the above classification is similar to that found in control problems with the robust and adaptive techniques. An optimal solution has to be feasible and, of course, optimal. In practice, feasibility is often of greater importance than optimality. In the presence of model uncertainty,
2
B. Chachuat et al.
feasibility is usually enforced by the introduction of backoffs from the constraints. The availability of measurements helps reduce these backoffs and thus improve performance [6]. Generally, it is easier to measure or infer constrained quantities (e.g. temperature or pressure) than estimate gradients of the cost and constrained quantities. These elements clearly set a priority of actions in the framework of adaptive optimization. This paper discusses three major approaches in adaptive optimization that differ in the way adaptation is performed, namely (i) model-adaptation methods, where the measurements are used to refine the process model, and the updated model is used subsequently for optimization [7,17]; (ii) modifier-adaptation methods, where modifier terms are added to the cost and constraints of the optimization problem, and measurements are used to update these terms [8,10,20]; and (iii) direct-input-adaptation methods, where the inputs are adjusted by feedback controllers, hence not requiring optimization but a considerable amount of prior information regarding control design [9,21,25]. These approaches are surveyed and compared in the first part of the paper. A critical discussion follows, which argues in favor of modifier-adaptation methods that share many advantages of the other methods. An important issue not addressed herein concerns the availability of reliable measurements. Also, note that the intended purpose of the models presented here is optimization and not prediction of the system behavior.
2. Static Optimization Problems For continuous processes operating at steady state, optimization typically consists in determining the operating point that minimize or maximize some performance of the process (such as minimization of operating cost or maximization of production rate), while satisfying a number of constraints (such as bounds on process variables or product specifications). In mathematical terms, this optimization problem can be stated as follows:
( ) ( ) := g ( , y ) 0
minimize: p ( ) := p , y p
subject to: G p where n and y p respectively; n
ny
ny ny
gp :
(1)
p
stand for the process input (set points) and output vectors,
p : n ng
p
is
the
plant
performance
index;
and
is the vector of constraints imposed on the input and output
variables. In contrast to continuous processes, the optimization of batch and semi-batch processes consists in determining time-varying control profiles, u(t), t 0 t t f . This typically involves solving a dynamic optimization problem, possibly with path and terminal constraints. A practical way of solving such problems is by parameterizing the control profiles using a finite number of parameters , e.g., a polynomial approximation of u(t) on finite elements. Although the process is dynamic in nature, a static map can be used to describe the relationship between the process inputs and the outcome of the batch y(t f ) . Hence, the problem can be regarded as a finite-dimensional static optimization problem similar to (1), and the optimization approaches discussed in the following sections can also be used in the framework of run-to-run optimization of
Model Parameterization Tailored to Real-Time Optimization
3
batch and semi-batch processes (see, e.g., [9]). In practice, the mapping relating the process inputs and outputs is typically unknown, and only an approximate model is available,
y = f ( , ) with y
ny
(2)
representing the model outputs, and n the model parameters, and n
f : n n y the input-output mapping. Accordingly, an approximate solution of problem (1) is obtained by solving the following model-based optimization problem:
minimize: ( , ) := ( , y, )
subject to: y = f ( , )
(3)
G ( , ) := g ( , y, ) 0
Provided that the objective and constraint functions in (1) and (3) are continuous and the feasible domains of these problems are nonempty and bounded, optimal solution points p and are guaranteed to exist for (1) and (3), respectively [2]. Note that such optimal points may not be unique due to nonconvexity. The KKT conditions – also called necessary conditions of optimality (NCO) – must hold at an optimal solution point provided that the active constraints satisfy a regularity condition at that point [2]. For Problem (3), the KKT conditions read:
(
)
G , 0, 0 ,
(
)
(
)
G , + , = 0, G , = 0
(
(4)
)
n
where g is the vector of Lagrange multipliers. The KKT conditions involve the G , which are denoted collectively by subsequently. quantities G, and
3. A Classification of Real-time Optimization Schemes Real-time optimization (RTO) schemes improve process performance by adjusting selected optimization variables using available measurements. The goal of this closedloop adaptation is to drive the operating point towards the true plant optimum in spite of inevitable structural and parameter model errors. RTO methods can be classified in different ways. This section presents one such classification based on the parameters that can be adapted, as illustrated in Fig. 1; note that repeated numerical optimization is used in the methods of columns 1 and 2, but not in those of column 3. 3.1. Model-Adaptation Methods The standard way of devising a RTO scheme is the so-called two-step approach [1], also referred to as repeated identification and optimization in the literature. In the first step, the values of (a subset of) the adjustable model parameters are estimated by using the available process measurements. This is typically done by minimizing the lack of closure in the steady-state model equations (2), such as the weighted sum of squared errors between measured outputs y p and predicted outputs y [17].
4
B. Chachuat et al.
Figure 1: Optimization scenarios that use measurements to adapt for feasibility and optimality.
A key, yet difficult, decision in the model-update step is to select the parameters to be updated. These parameters should be identifiable, represent actual changes in the process, and contribute to approach the process optimum; also, model adequacy proves to be a useful criterion to select candidate parameters for adaptation [8]. Clearly, the smaller the subset of parameters, the better the confidence in the parameter estimates, and the lower the required excitation. But too low a number of adjustable parameters can lead to completely erroneous models, and thereby to a false optimum. In the second step, the updated model is used to determine a new operating point, by solving an optimization problem similar to (3). Model-adaptation methods can be written generically using the following two equations (see Fig. 2):
(
)
k = k1 + upd y p ( k1 ) y( k1 , k1 ) ,
(5)
= opt (
(6)
k
k
)
where upd is the map describing the model-update step, such that upd (0) = 0 ; opt , the map describing the optimization step. Note that the handles for correction are a subset of the adjustable model parameters . The use of auxiliary measurements ( y p ) presents the advantage that any available measurement can be used.
Figure 2. Model-adaptation method: Two-step approach
5
Model Parameterization Tailored to Real-Time Optimization
It is well known that the interaction between the model-update and reoptimization steps must be considered carefully for the two-step approach to achieve optimal performance. In the absence of plant-model mismatch and when the parameters are structurally and practically identifiable, convergence to the plant optimum may be achieved in one iteration. However, in the presence of plant-model mismatch, whether the scheme converges, or to which operating point the scheme converges, becomes anybody's guess. This is due to the fact that the update objective might be unrelated to the cost or constraints in the optimization problem, and minimizing the mean-square error in y may not help in our quest for feasibility and optimality. To alleviate this difficulty, Srinivasan and Bonvin [23] presented an approach where the criterion in the update problem is modified to account for the subsequent optimization objective. Convergence under plant-model mismatch has been addressed by several authors [3,8]; it has been shown that an optimal operating point is reached if model adaptation leads to a matching of the KKT conditions for the model and the plant. Theorem 1. Let the parameter adaptation (5) be such that the plant measurements p match those predicted by the model, . Then, upon convergence, the model-adaptation scheme (5-6) reaches an (local) optimum operating point of the plant. A proof of this result is readily obtained from the assumption that the KKT conditions predicted by the model equal those achieved by the plant. With such a matching, the converged solution corresponds to a (local) plant optimum. Although Theorem 1 is straightforward, the KKT-matching assumption is difficult to meet in practice. It requires an “adequate” parameterization so that all the components of the KKT conditions can match, as well as “adequate” measurements and an “adequate” update criterion. 3.2. Modifier-Adaptation Methods In order to overcome the modeling deficiencies and to handle plant-model mismatch, several variants of the two-step approach have been presented in the literature. Generically, they consist in modifying for the cost and constraints of the optimization problem for the KKT conditions of the model and the plant to match. The optimization problem with modifiers can be written as follows: ( , ) := ( , ) + T minimize: ( , ) := G ( , ) + G + GT k 0 subject to: G
(
where G
ng
)
(7)
is the constraint bias, n the cost-gradient modifier, and
n n
G g the constraint-gradient modifier; these modifiers are denoted collectively by subsequently. • The constraint bias G represents the difference between the measured and predicted constraints, G := G p ( ) G( , ) , evaluated at the previous operating point k . Adapting only G leads to the so-called constraint-adaptation scheme [6,8]. Such a scheme is rather straightforward and corresponds to common industrial practice [17]. • The cost-gradient modifier represents the difference between the estimated and predicted values of the cost gradient, T := p , evaluated at the previous
6
B. Chachuat et al.
operating point k . The pertinent idea of adding a gradient modifier to the cost function of the optimization problem dates back to the work of Roberts [19] in the late 1970s. Note that it was originally proposed in the framework of two-step methods to better integrate the model update and optimization subproblems and has led to the so-called ISOPE approach [4]. • The constraint-gradient modifier G , finally, represents the difference between the estimated and predicted values of the constraint gradients, T := G p G , G
evaluated at the previous operating point k . The idea of adding such a first-order modifier term to the process-dependent constraints, in addition to the constraint bias G , was proposed recently by Gao and Engell [12]. This modification allows matching, not only the values of the constraints, but also their gradients. Overall, the update laws in modifier-adaptation methods can be written as (see Fig. 3):
(
k1 , ) k = k1 + upd p ( k1 ) (
= opt ( k
k
)
)
(8) (9)
:= G, G where , , with , G as defined in Problem (7); and the modifier update map, upd , is such that upd (0) = 0 . The handles for correction are the modifier parameters instead of used in the context of model-adaptation schemes. Also, the measurements p required to make the adaptation are directly related to the KKT conditions; auxiliary measurements are not used in this framework. Observe the one-toone correspondence between the number of measurements/estimates and the number of adjustable parameters. In particular, identifiability is automatically satisfied, and so are the KKT-matching conditions.
Figure 3. Modifier-adaptation method: Matching the KKT conditions
Modifier-adaptation methods possess nice theoretical properties, as summarized by the following theorem. Theorem 2. Let the cost and constraint functions be parameterized as in Problem (7). Also, let the information on the values of p be available and used to adapt the modifiers . Then, upon convergence, the modifier-adaptation scheme (8-9) reaches an (local) optimum operating point of the plant.
Model Parameterization Tailored to Real-Time Optimization
7
A proof of this result is easily obtained by noting that, upon convergence, the modified in (7) match the plant constraints G , and the gradients of the modified constraints G p cost and constraint functions match those of the plant (see also [10]). It follows that the active set is correctly determined and the converged solution satisfies the KKT conditions. Hence, there is a close link between the model- and modifier-adaptation methods in that the parameterization and the update procedure are both intended to match the KKT conditions. Essentially, modifier-adaptation schemes use a model-predictive control with a one-step prediction horizon. Such a short horizon is justified because the system is static. However, since the updated modifiers are valid only locally, modifieradaptation schemes require some amount of filtering/regularization (either in the modifiers or in the inputs) to avoid too aggressive corrections that may destabilize the system. 3.3. Direct-Input-Adaptation Methods This last class of methods provides a way of avoiding the repeated optimization of a process model by transforming it into a feedback control problem that directly manipulates the input variables. This is motivated by the fact that practitioners like to use feedback control of selected variables as a way to counteract plant-model mismatch and plant disturbances, due to its simplicity and reliability compared to on-line optimization. The challenge is to find functions of the measured variables which, when held constant by adjusting the input variables, enforce optimal plant performance [19,21]. Said differently, the goal of the control structure is to achieve a similar steadystate performance as would be realized by an (fictitious) on-line optimizing controller. In the presence of uncertainty, the inputs determined from off-line solution of problem (3) for nominal parameter values satisfy the NCO (4) but typically violate the NCO related to the plant itself. Hence, a rather natural idea is to correct the input variables so as to enforce the NCO for the plant [1,9,14]; in other words, the controlled variables are chosen as the NCO terms, with the corresponding set points equal to zero. Tracking of the NCO (4) consists of three steps: (i) determining the active set (positivity condition on Lagrange multipliers), (ii) following the active constraints, and (iii) pushing the sensitivity to zero. Determining the active set requires a switching strategy, whereby a constraint is included in the active set when it is attained, and deactivated when its Lagrange multiplier goes negative [29]. This switching logic renders the scheme more complex, and in the interest of simplicity, it may be assumed that the active constraints do not change. Note that such an assumption is always verified in the neighborhood of an optimal solution and is observed in many practical situations. Once the active set is known, the inputs are split into : (i) constraints-seeking directions that are used to track the active constraints, and (ii) sensitivity-seeking directions that are adapted to force the reduced gradients to zero. The active constraints G ap and the
G ap I P+ P , with P := , need to be measured. Since, in general, the constraint terms are easily measured, or can be reliably estimated, adjusting the inputs in the constraint-seeking directions to track the active constraints is rather straightforward [4,25,27]. Adjusting the sensitivity-seeking directions is more involved, mainly due to the difficulty in the measurement of the gradient terms. François et al. [9] proposed a two-time-scale adaptation strategy, wherein adaptation in the sensitivity-seeking directions takes place at a much slower rate than in the constraint-seeking directions.
reduced cost gradient r p :=
p
8
B. Chachuat et al.
Direct-input-adaptation methods obey the following equations (see Fig. 4):
(
k = k1 + con G ap ( k1 ), r p ( k1 )
(G
a p
)
(
( k ), r p ( k ) = swi p ( k )
)
)
(10) (11)
where con is the map describing the controller, such that con (0, 0) = 0 ; swi , the map describing the switching logic for determination of the active set. The handles for correction are the process inputs , i.e., no specific parameterization is required here. Both the active constraints and the reduced cost gradient are forced to zero, e.g., with a discrete integral-type controller.
Figure 4. Direct-input-adaptation method: Tracking the NCO using control
Direct-input-adaptation methods also possess nice theoretical properties, as summarized by the following theorem. Theorem 3. Let the information on the values of p be available and used to adapt the inputs and the active set given by (10-11). Then, upon convergence, the direct-inputadaptation scheme (10-11) reaches an (local) optimum operating point of the plant. Note that the active process constraints and reduced gradients are both zero upon convergence. Moreover, since the positivity of the Lagrange multipliers is guaranteed by the switching logic, the active set is correctly identified and the NCO are satisfied. The key question lies in the design of the controller. Unlike optimization-based schemes, the required smoothening is provided naturally via appropriate controller tuning. 3.4. Evaluation of the various methods A systematic approach for evaluating the performance of adaptive optimization schemes, named the extended cost design, has been presented in [30]. It incorporates measures of both the convergence rate and the effect of measurement noise. Interestingly, it is shown that in the presence of noise, a standard two-step algorithm may perform better, in terms of the proposed metric, than modified algorithms compensating for plant-model mismatch such as ISOPE. Another approach to performance characterization for adaptive optimization has been proposed in [15], which considers the backoff from active inequality constraints required to ensure feasibility. Therein, better adaptive optimization approaches produce smaller backoffs.
4. Use of Measurements for Feasible and Optimal Operation This section discusses the two main rows in Fig.1. The feasibility issue is addressed first, and various gradient estimation techniques are summarized next. 4.1. Feasible Operation In practical applications, guaranteeing feasible operation is often more important than achieving the best possible performance. Hence, first priority is given to meeting the
Model Parameterization Tailored to Real-Time Optimization
9
process constraints (such as safety requirements and product specifications) and only second priority to improving process performance in terms of the objective function. Interestingly, the results of a variational analysis in the presence of small parametric error support the priority given to constraint satisfaction over the sensitivity part of the NCO [6]. More specifically, it has been shown that, in addition to inducing constraint violation, failure to adapt the process inputs in the constraint-seeking directions results in cost variations in the order of the parameter variations ; in contrast, failure to adapt the inputs in the sensitivity-seeking directions gives cost variations in the order of 2 only. The ability to guarantee feasible operation is addressed next for the three classes of methods presented above. In model-adaptation methods, since the plant constraints are predicted by the process model, constraint matching – but not necessarily full KKT matching – is needed to guarantee feasibility; however, this condition may be difficult to meet, e.g., when the model is updated by matching a set of outputs not directly related to the active constraints. With modifier-adaptation methods, feasibility is guaranteed upon convergence, provided that all the constraint terms are measured [6]; yet, ensuring feasibility does not necessarily imply that the correct active set has been determined due to the use of possibly inaccurate cost and constraint gradients, e.g., when gradient modifiers are not considered. Finally, in direct-input-adaptation methods, feasibility is trivially established when the active set is known and does not change with the prevailing uncertainty. However, as soon as the active set changes, tracking the current set of active constraints may lead to infeasibility. A switching logic can be used to remove this limitation, but it requires experimental gradient information to be available; the use of a barrier-penalty function approach has also been proposed [26]. If feasibility cannot be guaranteed, conservatism can be introduced in the form of constraint backoffs. Such backoffs are also introduced to enforce feasibility when some of the constraints are difficult to measure. 4.2. Gradient Estimation Taking a system from a feasible to an optimal operating point requires accurate gradient information. In model-adaptation schemes, since the updated model is used to estimate the gradient, convergence is relatively fast. In the other two schemes, the gradient information has to be estimated experimentally, thereby slowing down convergence significantly. Perhaps the major bottleneck in modifier- and direct-input-adaptation schemes lies in the estimation of this gradient information. The finite-difference scheme used in the original ISOPE paper [19] is known to be inefficient for large-scale, slow and noisy processes. Hence, alternative techniques have been developed, which can be classified as either model-based approaches or perturbation-based approaches. Model-based approaches allow fast derivative computation by relying on a process model, yet only approximate derivatives are obtained. In self-optimizing control [12,21], the idea is to use a plant model to select linear combinations of outputs, the tracking of which results in “optimal“ performance, also in the presence of uncertainty; in other words, these linear combinations of outputs approximate the process derivatives. Also, a way of calculating the gradient based on the theory of neighbouring extremals has been presented in [13]; however, an important limitation of this approach is that it provides only a first-order approximation and that the accuracy of the derivatives depends strongly on the reliability of the plant model. The idea behind perturbation methods is to estimate process derivatives using variations in the operating point. Extremum-seeking control [1,14] attempts to obtain the cost
10
B. Chachuat et al.
sensitivity by superposing a dither signal to the plant inputs. In dynamic model identification, the plant is approximated by a dynamic model during the transient phase between two successive steady states [16,31,11]. Since the derivatives are calculated from the identified dynamic model, the waiting time needed for reaching a new steady state is avoided. Other perturbation-based approaches, which remove the disadvantage of requiring additional dynamic perturbations, consist in using current and past (steadystate) measurements to compute a gradient estimate based on Broyden’s formula [16]. For the case of multiple identical units operating in parallel, Srinivasan considered perturbations along the unit dimension rather than the time dimension, thereby allowing faster and more accurate derivative estimates [22]. In principle, the smaller the difference between the operating points, the more accurate the derivative approximation, but conditioning issues might arise due to measurement noise and plant disturbances. A way of avoiding this latter deficiency is presented in [10].
5. Discussion In this section, we take a critical look at the three classes of adaptive optimization methods described above in terms of various criteria. We also argue in favor of modifier-adaptation methods, in the sense that they provide a parameterization that is tailored to the matching of the KKT conditions. The analysis presented in Table 1 shows many facets of the problem. It is interesting to see that modifier-adaptation methods can be positioned between the model-adaptation methods and direct-input-tracking methods; several attractive features are shared between the first and second columns, while other features are shared between the second and third columns. The methods differ mainly in the handles and in the measurements that are used for correction. The major drawback of model-adaptation schemes is that KKT matching is required for convergence to a (local) plant optimum, which can be very difficult to satisfy with the (arbitrary) parameterization and (arbitrary) auxiliary measurements y p . In comparison, modifier-adaptation methods resolve the challenging task of selecting candidate parameters for adaptation by introducing the modifiers as handles. Also, the measurements p are directly related to the KKT conditions, and their number is equal to that of the handles , i.e., there results a square update problem. Hence, since these parameters are essentially decoupled, no sophisticated technique is required for the update of . Moreover, KKT matching becomes trivial, and reaching a (local) plant optimum is guaranteed upon convergence. This leads us to argue that modifier-adaptation methods possess the “adequate” parameterization and use the “adequate” measurements” for solving optimization problems on-line. Direct-input-adaptation methods differ from model- and modifier-adaptation methods in that a process model is not used on-line, thus removing much of the on-line complexity. Another important element of comparison is the use of experimental gradient information. The modifier- and direct-input-adaptation methods make use of experimental gradients to guarantee (local) optimality. However, obtaining this information is usually time consuming and slows down the entire adaptation scheme. Note that the use of an updated process model gives the ability to determine changes in the active set and typically provides faster convergence. Yet, in practice, the convergence of the model- and modifier-adaptation methods is often slowed down by the introduction of filtering that is required to avoid unstable behavior that would result because the corrections are local in nature.
11
Model Parameterization Tailored to Real-Time Optimization
Model-adaptation methods
Modifier-adaptation methods
Direct-input adaptation methods
Adjustable parameters
Dimension of parameters
n
ng + n (ng + 1)
n
Measurements
yp
p
p
Dimension of measurements
ny
ng + n (ng + 1)
ng + n (ng + 1)
p
None
y yp
Update criterion
2
2
Exp. gradient estimation
No
Yes
Yes
Repeated optimization
Yes
Yes
No
On-line use of process model
Yes
Yes
No
Model predictive
Model predictive
Any
Smoothening
External filter
External filter
Controller tuning
Choice of active sets
Optimization
Optimization
Switching logic
Requirement for feasibility (no gradient information)
Constraint matching
None
Correct active set
Requirement for optimality (with gradient information)
KKT matching
None
None
Controller type
Table 1. Comparison of various real-time optimization schemes
6. Conclusions This paper provides a classification of real-time optimization schemes and analyzes their ability to use measurements to track the necessary conditions of optimality of the plant. The similarities and differences between the various schemes are highlighted, and it is shown that modifier-adaptation schemes use a parameterization, measurements, and an update criterion that are tailored to the matching of KKT conditions. To improve the performance of adaptive optimization, it may be useful to combine specific features of the various methods. For example, the combination of model adaptation (which ensures fast convergence for the first few iterations and detects changes in the active set) with direct-input adaptation (which provides the necessary gradients in the neighborhood of the plant optimum) has been demonstrated in [24]. Another interesting combination would be to use a modifier-adaptation approach at one time scale and perform model adaptation at a slower rate, thus giving rise to a two-timescale adaptation strategy.
References 1. Ariyur K. B. and Kristic M., “Real-Time Optimization by Extremum Seeking Feedback”, Wiley, 2003. 2. Bazaraa M. S., Sherali H. D. and Shetty C. M., “Nonlinear Programming: Theory and Algorithms”, second ed., John Wiley and Sons, New York, 1993. 3. Biegler L. T., Grossmann I. E. and Westerberg A. W., “A note on approximation techniques used for process optimization”, Comput Chem Eng 9(2):201-206, 1985.
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4. Bonvin D. and Srinivasan B., “Optimal operation of batch processes via the tracking of active constraints”, ISA Trans 42(1):123-134, 2003. 5. Brdys M. A. and Tatjewski P., “Iterative Algorithms For Multilayer Optimizing Control”, World Scientific Pub Co, London UK, 2005. 6. Chachuat B., Marchetti A. and Bonvin D., “Process optimization via constraints adaptation”, J Process Control, in press. 7. Chen C. Y. and Joseph B., “On-line optimization using a two-phase approach: an application study”, Ind Eng Chem Res 26:1924-1930, 1987. 8. Forbes J. F. and Marlin T. E., “Model accuracy for economic optimizing controllers: the bias update case”, Ind Eng Chem Res 33:1919-1929, 1994. 9. François G., Srinivasan B. and Bonvin D., “Use of measurements for enforcing the necessary conditions of optimality in the presence of constraints and uncertainty”, J Process Control 15:701-712, 2005. 10. Gao W. and Engell S., “Iterative set-point optimization of batch chromatography”, Comput Chem Eng 29(6):1401-1409, 2005. 11. Golden M. P. and Ydstie B. E., “Adaptive extremum control using approximate process models”, AIChE J 35(7):1157-1169, 1989. 12. Govatsmark M. S. and Skogestad S., “Selection of controlled variables ans robust setpoints”, Ind Eng Chem Res 44(7):2207-2217, 2005. 13. Gros S., Srinivasan B. and Bonvin D., “Static optimization via tracking of the necessary conditions of optimality using neighboring extremals”, Proc ACC 2005, Portland OR, pp. 251-255, 2005. 14. Guay M. and Zang T., “Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainty”, Automatica 39:1283–1294, 2003. 15. de Hennin S. R., Perkins J. D. and Barton G. W., “Structural descisions in on-line optimization”, Proc Int Conf PSE‘94, pp. 297-302, 1994. 16. Mansour M. and Ellis J. E., “Comparison of methods for estimating real process derivatives in on-line optimization”, Appl Math Mod 27:275-291, 2003. 17. Marlin T. E. and Hrymak A. N., “Real-time operations optimization of continuous process”, Proc 5th Int Conf on Chemical Process Control (CPC-5), Tahoe City NV, 1997. 18. Mönnigmann M. and Marquardt W., “Steady-state process optimization with guaranteed robust stability and feasibility”, AIChE J 49(12):3110-3126, 2003. 19. Morari M., Stephanopoulos G. and Arkun Y., “Studies in the synthesis of control structures for chemical processes, Part I”, AIChE J 26(2):220-232, 1980. 20. Roberts P. D., “An algorithm for steady-state system optimization and parameter estimation”, Int J Syst Sci 10:719-734, 1979. 21. Skogestad S. “Plantwide control: The search for the self-optimizing control structure”. J Process Control 10:487–507, 2000. 22. Srinivasan B., “Real-time optimization of dynamic systems using multiple units”, Int J Robust Nonlinear Control 17:1183–1193, 2007. 23. Srinivasan B. and Bonvin D., “Interplay between identification and optimization in run-torun optimization schemes”, Proc ACC 2002, Anchorage AK, pp. 2174–2179, 2002. 24. Srinivasan B. and Bonvin D., “Convergence analysis of iterative identification and optimization schemes”, Proc ACC 2003, Denver CO, pp. 1956-1961, 2003. 25. Srinivasan B., Primus C. J, Bonvin D. and Ricker N. L., “Run-to-run Optimization via Constraint Control”, Control Eng Pract 9(8):911-919, 2001. 26. Srinivasan B., Biegler L.T. and Bonvin D., “Tracking the necessary conditions of optimality with changing set of active constraints using a barrier-penalty function”, Comput Chem Eng 32(3):572-579, 2008. 27. Stephanopoulos G. and Arkun Y., “Studies in the synthesis of control structures for chemical processes, Part IV”, AIChE J 26(6):975-991, 1980. 28. Tatjewski P., “Iterative optimizing set-point control–The basic principle redesigned”, Proc 15th IFAC World Congress, Barcelona, 2002.
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29. Woodward L., Perrier M. and Srinivasan B., “Multi-unit optimization with gradient projection on active constraints”, Proc 8th Int Symp on Dynamics and Control of Process Systems (DYCOPS), Vol 1, pp. 129-134, 2007. 30. Zhang Y. and Forbes J. F., “Extended design cost: A performance criterion for real-time optimization systems”, Comput Chem Eng 24:1829-1841, 2000. 31. Zhang Y. and Forbes J. F., “Performance analysis of perturbation-based methods for realtime optimization”, Can J Chem Eng 84:209-218, 2006.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Challenges for multi-scale modeling of multiple failure modes in microelectronics Juergen Auersperg, Bernhard Wunderle, Rainer Dudek, Hans Walter, Bernd Michel Abstract Design studies of electronics components on the basis of parameterized Finite Element Models and DoE/RSM-approaches (Design of Experiments/Response Surface Methods) are more and more performed for optimizations at early phases of the product development process. That is why electronics components especially in the field of RF (Radio Frequency), optoelectronics, high temperature and power applications are often exposed to extreme thermal environmental conditions, mechanical shock and vibrations. However, a continuous industry drive for miniaturization and function integration forces the development of feature sizes down to the nanometer regime. Simultaneously, the well known thermal expansion mismatch problem of the several materials, residual stresses generated by several steps of the manufacturing process and various kinds of inhomogeneity attribute to interface delamination, chip cracking and fatigue of interconnects, in particular. The applied methodologies typically base on classical stress/strain strength evaluations or/and life time estimations of solder interconnects using modified Coffin-Manson approaches. Recent studies show also how the evaluation of mixed mode interface delamination phenomena, classical strength hypotheses along with fracture mechanics approaches and thermal fatigue estimation of solder joints can simultaneously be taken into account. Over and above that, new materials will be introduced especially in Back-end of line (BEoL) layers of advanced Cu/Low-k 90, 45, … , 22 nanometer CMOS (Complementary Metal-Oxide Semiconductor) technologies. So, black diamond-I or black diamond-II as new materials are increasingly porous and interconnect materials or new functional layers come up as nano-particle filled high-tech compounds. Thus, it is to be checked whether it can be handled as homogeneous materials anymore. For sure, this will have most important impacts on the thermo-mechanical performance of the total IC (Integrated Circuit) tack. The problems appearing during packaging of CMOS-ICs at least showed that IC and package reliability are strongly interacted. Thus, the challenge for simulations in this field is not only the wide range of structural dimensions but also, the different approaches that have to be combined: Molecular or atomistic level simulations and “conventional” Finite Element Analysis (FEA) with global-local modeling, substructuring as well as fracture and damage mechanics, cohesive zone models, viscoelasticity, plasticity and creep of homogeneous constitutive models. Furthermore, it is known that multiple failure modes competitively act simultaneously wherefore, design optimizations have to incorporate all failure modes that are essential for the overall reliability. Moreover, considering that variables of the simulation models are naturally stochastic parameters leads to the consequence that all results show also scattering. First steps towards robust designs show the potential of the utilized FEA-based RSM/DOE approach to evaluate the thermo-mechanical reliability of various electronics assemblies in a more complex way giving at the same time a more solid basis for design optimizations.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Design and integration of policies to achieve environmental targets René Bañares-Alcántara Department of Engineering Science, University of Oxford, UK
Abstract Few problems are as urgent and important as climate change. Climate change mitigation policies are geographically and culturally dependent given the variability of resources, of access to technology and of national political constraints such as ensuring energy security, affordability and social acceptability. Thus, climate change mitigation hinges on devising integrated policies involving many mutually reinforcing and coordinated efforts in order to exploit synergies between policy tools and to avoid policy conflicts. The possible roles of chemical engineers in this problem are: • a traditional one, as providers of improved and new technologies, e.g. in the development of CO2 capture technologies, • a less conventional and recent one, as participants in the framing and development of policies, e.g. influencing the formulation of the UK energy policy [Clift 06], • a future role as providers of tools, methods and systems to support policy formulation, i.e. the development of effective and acceptable courses of action to reach explicit goals. The talk will address the last role. Important insights into a policy formulation methodology can be elicited from engineering design. It will be argued that engineering design and synthesis methodologies offer a productive framework and a suite of practical tools for supporting policy design and integration, i.e. providing alternative configurations of policy tools to use and how to schedule their phasing and implementation in order to achieve a reduction in greenhouse gas emissions. However, process and policy design are not identical and, as a result, complementary approaches have to be used to take into account their differences, in particular the pervasiveness of non-quantifiable factors. These ideas will be exemplified with two support systems being developed for energy and transport policy formulation.
References Clift, R. “Sustainable development and its implications for chemical engineering”. Chemical Engineering Science 61:4179-4187, 2006.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Computational chemical engineering modeling applied to energy and reactor design Luc Nougier IFP, France
Abstract Chemical engineering is the combination of physical, chemical, biological …operations on an energy or chemical plant. For process design, we have to carry out optimisations based on a multiple of parameters all the more so since the needs of processes in industry change very rapidly. These industries have to integrate new constraints linked to the energy cost and the environmental impact coupled with a need for more and more technical product. Chemical engineering will play a key role to maintain the efficiency of the industry in a global market in which the processes offer become more and more technological and has to take into account : . • higher system integration to minimised energy consumption by coupling different process steps (ie : coupling of endothermal and exothermal steps, reaction and separation….), . • better optimisation of units design, . • higher product selectivity to avoid or limit by-product, . • production of new products. To achieve these new developments the approach cover a large domain of technical disciplines and also a multiscale approach in time and length. This new complexity require to increase the relative weight of modeling and scientific calculation in the process development. For exemple, CFD calculation is currently used for the development of reactor technologies and reactor internal, but most of the time it is difficult to couple hydrodynamic modelisation and reaction modelisation. A lot of improvement are expected by coupling these two approaches. The molecular modelisation has also a large potential in process development and has to be coupled with more classical approach. For process integration, the thermodynamic optimisation is very useful mainly for developing new processes (pinch technology). The modeling tools have to be used in all the steps of process development taking into account a multiscale approach and without forgetting the measurement technologies needed for model validation.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Curricular and pedagogical challenges for enhanced graduate attributes in CAPE Ian T Camerona, Daniel R Lewinb a. School of Engineering, The University of Queensland, Brisbane, AUSTRALIA, 4072 b. PSE Research Group, Dept Chemical Engineering, Technion, Haifa 32000, ISRAEL
Extended Abstract Computer Aided Process Engineering (CAPE) undergirds and informs a wide range of decision making in the product and process life cycle. Life cycle phases that span the planning and conceptualization of product and process, through research and development and then onto design, construction, operation and decommissioning are permeated by CAPE activities. The importance of CAPE activities and their central role in the global engineering enterprise cannot be underestimated. These activities require the use of techniques and tools for informed decision making are shown in Figure 1.
EIA models
Finance models
Enviro
Prelim Elementary flowsheets flowsheets Pilot Physical properties
Logistics Optimization RCM models models
Flowsheet models
Planning Decon
Control models
Bioremed
at e R em ed i
D ec om
m
is si on
CFD
pe ra te
Molecular modelling C on ce pt
Nano
R &D
Reaction networks
CPM
Mechanical CFD
Micro
CPM
SCOR models
O
Meso
RMgt
D e de tail si ed gn
Macro
CPM
In st al l
Scenario planning
St ra te gi c
Length-time scale
Mega
Life cycle phase Figure 1 Some CAPE application areas across the life cycle phases
Yet, how well do we tackle the challenges of CAPE in curriculum design and deployment in higher education? What are the keys to effective development of graduate attributes and skills in the CAPE domain that can be achieved through innovative curricula and the learning environments that inform, challenge and prepare engineering graduates for work in a “model centric” world? What are the technological and informational forces that are rapidly shaping the way engineering is practised in the global context?
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I.T. Cameron and D.R. Lewin
In this presentation, the authors seek to address some of these questions by reference to current trends in educational practice and the application of active learning principles that have been developed, deployed and assessed at institutions in Australia, Israel and elsewhere. In most cases these approaches have found extensive use over many years. It is vital that the debate is centred not just on individual, isolated courses that touch on some aspects of the CAPE issue, but that we start with holistic or systems thinking on curriculum development that provides integration and cohesion in the curriculum and leads to graduate attributes and skills necessary for the next generation of engineers. The curriculum challenge is seen as a cohesive pathway that exercises a strong thread of CAPE activities. Pathways need to build upon basic concepts, integrate new content which illustrates the relationships amongst the principal learning components and then drives that learning with realism and relevance to maintain student engagement. The curriculum challenge has to address the major issues of: • • • •
WHAT has the be learned: the content issue WHY it is to be learned: the rationale HOW it is to be learned: the process and methods WHEN it has to be learned: the pathway to be adopted
In terms of processes, there are numerous options available with the most effective focusing on active learning strategies. Figure 2 illustrates some well documented pedagogic approaches that have been adopted into curriculum delivery. They include problem and project based learning (PBL), project centred curricula (PCC) and Conceive, Design, Implement and Operate (CDIO) approaches.
Figure 2 Active learning pedagogies in curriculum delivery
The authors will explore these key issues and illustrate holistic approaches that impact on curriculum innovation. They will draw examples from a range of applications of these important pedagogic concepts.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
23
Chemical Product Engineering: The 3rd Paradigm Michael Hill M Hill & Associates LLC, Mahwah, New Jersey 07430, USA, and Columbia University, New York, NY 10027, USA
Abstract New chemical products have historically been created by combining a broad knowledge of existing chemical products with scientific experimentation. Since a combinatorial explosion of product options will inevitably limit all experimental techniques, it should be preferable to minimize experimentation through a systematic consideration of product formulations prior to experimentation. This is the essence of product design and engineering. While the design of a chemical product and its manufacturing process are analogous, some critical differences are so fundamental that a new paradigm and new approaches are needed to successfully solve product design problems. In addition, chemical product design requires a methodology or algorithm to apply chemical engineering fundamentals. Product design techniques should draw largely on heuristics when data are limited, followed by more detailed calculations when data become available. Significant work is still needed to establish a comprehensive generic methodology for engineering chemical products in the absence of complete data. Keywords: Product Design, Product Engineering, Chemical Engineering Paradigm
1. Introduction Chemical Product Engineering and the related area of Chemical Product Design have recently received much attention within the chemical engineering community, with an exponential increase in published papers over the past decade. [1]. A chemical product may consist of an individual chemical, but more frequently it will be a mixture of chemicals with a set formulation and often a set microstructure. Chemical products of industrial interest include performance chemicals, semi-conductors, paints, cosmetics, inks, pharmaceuticals, personal care products, household products, and foods. [2,3] While new chemical product development has historically been the domain of chemists, the use of chemical products by consumers invariably involves some transformation of the product due to applied stresses, temperature gradients, physicochemical hydrodynamics, mass transfer, etc., making product use a “process” in the chemical engineering sense. [2,4] Thus the analysis of product behavior ultimately requires the same fundamentals as the analysis of process behavior, and is well suited to study by chemical engineers.
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M. Hill
Notwithstanding the commonalities in the engineering analyses of a chemical product’s behavior and its manufacturing process, there are fundamental differences between the design of a chemical product and its manufacturing process. For example, chemical process design primarily seeks to identify the lowest cost process. Even process related issues like reliability, controllability, and pollution control ultimately translate into costs that must be minimized. Thus, process design easily lends itself to a mathematical treatment. In contrast, chemical product design seeks to obtain the most added value for a product through enhanced product properties. This is far more complex than a mathematical treatment to maximize profit, as profit will depend in some unidentified way upon a complex set of product properties that may not even be identified at the outset. Thus, product design and engineering must not only require new chemical engineering approaches, but even more fundamentally, a new mindset. 2. The 3rd Paradigm While various comments on chemical engineering paradigms have appeared over the years [1,5-7], an overuse of the word paradigm by society in general may have led to some confusion over the meaning of the term. One is reminded of the Dilbert comic strip where every engineer says his project is a paradigm but no one seems to know what that means! The term paradigm was popularized by Thomas Kuhn in his book, The Structure of Scientific Revolutions, first published in 1962. Borrowing the word from linguistics, Kuhn used the term to indicate a specific way of viewing scientific reality, the mindset of a scientific community. Some of Kuhn’s examples include Copernican astronomy, Newtonian dynamics, and quantum mechanics. Each of these paradigms affected the choice of problems that were considered worthy of solution, as well as acceptable approaches to solving those problems. [8] As pointed out by Kuhn, even when paradigms are known to be inadequate, their inadequacies are frequently minimized or even ignored by a scientific community. But if and when a paradigm reaches a crisis where its technical inadequacies are brought into focus, perhaps driven by social requirements, a new paradigm will arise to explain what the prior paradigm could not. Thus the inadequacies of Newtonian mechanics in explaining some observations that had been viewed as anomalies eventually led to Einsteinian dynamics, and the success of this new paradigm in explaining those observations opened up an entirely new set of problems as worthy of consideration. [8] Of course Newtonian mechanics is still useful and may even be considered as a special case of Einsteinian dynamics.
Chemical Product Engineering: The 3rd Paradigm
25
From this perspective, it should be appreciated that originally chemical engineering had no paradigm. Chemical processes were studied within the context of various industries, and so engineers studied processes to make soap, dyestuffs, sugar, etc. Without the mindset of a unifying principle, engineers did not look for and hence failed to see commonality between these processes. [9] Chemical engineering received its first paradigm in 1915 with the introduction of the unit operations concept. [3,9,10] This mindset allowed engineers to recognize commonalities between elements of chemical processes despite their use in different industries. Under this paradigm, chemical engineering was no longer the study of how to manufacture a specific commodity, but rather the study of unit operations. As a consequence, chemical process design became a matter of deciding which sequence of unit operations was most appropriate to manufacture a desired product. While still useful to the present day, the unit operations paradigm proved inadequate for solving some important classes of problems. This awareness led to the emergence of chemical engineering science as a second paradigm in the late 1950’s, as best exemplified by the textbook Transport Phenomena. [3,9-11] This approach taught engineers to analyze problems by thinking in terms of their underlying fundamental chemical and physical sciences, writing mathematical equations to describe the phenomena, and then solving those equations. The chemical engineering science paradigm may also be described as the “first principles” approach. The chemical engineering science paradigm is widely used today. In fact, its application has been broadened by the incorporation of biological science and new information technology tools. But as important as these latter elements have been, they have been incorporated into the existing chemical engineering science paradigm rather than lead to a new mindset. Similarly, specific techniques for solving various classes of chemical engineering problems are not new paradigms, for they fall within the current chemical engineering way of thinking. On the other hand, until recently the chemical engineering community largely ignored all product issues other than purity as irrelevant, focusing exclusively on processing while leaving product development to chemists. In the minds of many, chemical engineering is synonymous with process engineering. Hence product engineering will require a new mindset in addition to new chemical engineering approaches, and should therefore be recognized as a third chemical engineering paradigm, as first hinted in 1988. [9] Of course, product engineering as a paradigm does not preclude other paradigms from emerging, nor does it replace previous paradigms. Process engineering may even be considered as a special case of product engineering.
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But a product engineering mindset is essential if chemical engineers are going to be able to solve problems where both the product and its manufacturing process must be identified, an entirely new and important class of problems. 3. Product Design Methodologies New chemical products have historically been created by combining a broad knowledge of existing chemical products with scientific experimentation. Product development is also at times accelerated through high-throughput experimentation, where large numbers of products are simultaneously made in small quantities, or through experimental design, where statistical techniques reduce the number of experiments performed. Nevertheless, these techniques have their limitations. For example, it is impractical to use high-throughput experimentation to make large numbers of structured products (like emulsions or composite powders) in small quantities. Similarly, experimental design can help determine optimal levels of a specified component but a combinatorial explosion will frequently prevent selection from a list of all potential components. Thus, chemical product development is all too often random trialand-error experimentation at present. However, the systematic identification of problem solutions should be superior to a random identification of solutions, either because better solutions can be identified or because acceptable solutions can be identified sooner or with less resource. So while it is unrealistic to eliminate all experimentation, it would be desirable to minimize experimentation through the introduction of a systematic consideration of product formulations prior to experimentation. From this perspective, the object of product design is to specify a small set of formulations likely to meet the product requirements, and which can be confirmed or refined through experimentation. Thus, chemical product design and engineering should be viewed as a phase of chemical product development that should precede a more focused experimental program. Analogous to chemical process design, chemical product design requires a methodology or algorithm to apply chemical engineering fundamentals. Cussler and Moggridge proposed a generic framework for chemical product design, suggesting a 4-step algorithm: (1) identify customer needs, (2) generate ideas to meet those needs, (3) select among the ideas, and (4) manufacture the product. They also admit that this framework is a simplification that tries to come down on the side of universal applicability rather than effectiveness in specific cases. [12] While this framework is an excellent starting point, it may be useful to expand on it. People who specialize in understanding consumers and market trends typically identify customer needs, often before chemical engineers are assigned to a product design project. Nevertheless, chemical engineers can help refine the
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understanding of consumer needs through their understanding of what is physically possible. Issues surrounding the design of a manufacturing process for complex chemical products have been discussed elsewhere [2,13,14], so I will focus on the remaining two steps, namely how ideas can be generated to meet customer needs, and how to best select from among those ideas. These steps must be at the heart of a chemical product design methodology. In practice, significant guidance is needed as to how to generate options and how to best select from among them. This is not simply a matter of brainstorming ideas and selecting the best option. While brainstorming and other creativity techniques are often useful for generating novel approaches to problems, a generic methodology is needed to systematically transform each novel approach into a specific set of product alternatives, and to quantitatively analyze those alternatives so as to select from among them. 4. Design of Homogeneous Products 4.1. Overview Having taught chemical product design to undergraduates at Columbia University, my colleagues and I have developed a useful methodology for designing homogeneous chemical products when limited data are available. This methodology has nine steps, and can guide a student team through a product design problem of moderate difficulty, each step requiring one week for a team of 3-4 students to complete, except steps 3, 4 and 5, which likely need two weeks each. Thus the course neatly fits into the time constraints of a university semester. The methodology assumes that the target behavior of the new chemical product has already been specified, eliminating the need for a step to determine customer needs. Also, since the required products are assumed homogeneous, their properties will result solely from their components and not a product microstructure generated during processing. This allows us to design the product and process sequentially rather than simultaneously, greatly simplifying the methodology and making it well within the grasp of undergraduates. Thus the procedure loosely follows the 4-step procedure of Cussler and Moggridge [12], but adds additional important details. For example, this procedure includes an analysis of market realities. A chemical product cannot be designed without a consideration of whether the proposed product will be profitable. Hence specific steps to assess the marketplace and determine profitability are included. In addition, recognizing that product design is only the first stage of product development and must be followed by a focused experimental program, the procedure includes an analysis of all uncertainties that should be followed up by experimentation.
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In addition, the methodology recognizes a key difference between the economics of commodities and specialty products that is easily overlooked. There is little risk that a commodity chemical manufactured by a new manufacturer or plant will go unsold if it is priced comparable to the competition. This is because manufacturers are generally unable to differentiate their commodity products from those of their competitors if they are priced the same, and so by the laws of supply and demand, any small increase in supply will lead to a small decrease in price for all manufacturers of the commodity as the market absorbs all the commodity produced by the new manufacturer. As all of the commodity manufactured at a new plant will sell at this new market price, the primary business decision is whether the investment in a new plant is justified by its return. On the other hand, since chemical products are differentiated by their performance specification, a new product will be governed by its own supply and demand equilibrium, and there will be no guarantee that a new chemical product can be sold at any price. There is no point in trying to calculate the return on investments (a cash flow transient) if the business proposition is not profitable in the steady state, i.e., with investments ignored. Hence before a prospective manufacturer considers whether the investment is justified by its return, ongoing profitability must be assessed first. This is typically a calculation of the market size that must be achieved for revenue to cover fixed costs, a situation referred to as “break-even”.1 [15] The methodology follows below. 4.1.1. Investigate Current Products The designer should begin by investigating current products, if any, in the marketplace – price, composition, the specific function of any components, strengths and weaknesses (from both a customer/consumer and a supplier perspective), any hidden costs, and total market size. Even if there is no product just like an intended product currently in the market, there may be other kinds of products indirectly fulfilling the same end function. For example, instead of using a device to purify drinking water, people may be drinking impure water and going more often to the doctor to treat water-borne illness. This will all be important information for setting an appropriate price for the new product, which in turn will be critical for determining whether the new product will be profitable.
1
Break-even, the market size size needed for revenues to cover ongoing fixed costs, is not the same as the payback period, the time required for cash flow to cover an investment. Break-even deals with steady state issues and is measured in either units of money or product volume; payback period deals with the cash flow transient and is measured in units of time.
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4.1.2. Initial Technical Analysis The mechanism(s) by which the new product may be able to work should be analyzed next. Consider the implications each mechanism will this have on the physical properties of the product. Also, identify the underlying chemical engineering phenomena (e.g. thermodynamics, reaction kinetics, transport phenomena, etc.) that will be relevant to understanding the behavior of the product. Where there are multiple properties that must be met simultaneously, consider if there are classes of compounds that can provide some of the required properties if they were present as components. If so, assume that the complete required property set can be decomposed into subsets of properties which can be achieved separately through their own components. This will allow the complete property set to be achieved by combining all components. Also identify any classes of compounds that would be inappropriate in the new product. This fundamental understanding will be later used to model the properties of the product. For example, consider the problem of formulating a biodegradable deicer for airplane wings. One would likely decide that freezing point depression is a more appropriate deicing mechanism than raising surface temperature by heat generation, as the latter effect would be temporary. This suggests that the product should contain a freezing point depressant. However, the product must also adequately wet and spread over the aircraft surface, not cause corrosion to wet metal surfaces, and biodegrade at acceptable rates. As it is unlikely that one compound will meet all these criteria, it can be assumed that the product will consist of (1) compounds that adequately depress the freezing point yet also biodegrade at acceptable rates, (2) compounds to ensure wetting, i.e. surfactants, and (3) compounds to prevent corrosion, i.e. anti-corrosion agents. 4.1.3. Build Product Property Models For each property subset, the understanding of the underlying chemical engineering phenomena can be used to derive a set of equations that can predict the relevant behavior as a function of composition. While simplifying assumptions may be made, be careful not to oversimplify. Verify qualitatively that the models will be useful for predicting the relevant behavior. Next, list all physical parameters that will be needed to apply the model with any candidate compound. In the absence of direct experimental data, decide how the needed physical parameters will be obtained (e.g. tabulated data, appropriate correlations, group contribution methods, etc.) For example, designing a biodegradable aircraft deicer would require a model of freezing point depression so that one could predict the mass of ice melted per mass of deicing compound at a given temperature. However, assuming ideal solution behavior leads to the unlikely conclusion that the only property governing freezing point depression is molecular weight, so solution ideality is
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clearly an oversimplification. In addition, the design would require a model of drainage rate off aircraft surfaces so that one could predict time to product failure, as well as a model of biodegradation. These models in turn lead to a need for various physical parameters, including activity coefficients, heats of fusion, and viscosity. 4.1.4. Generate Alternatives For each property subset, generate as large a list of potential candidates as is possible, based on an understanding of the underlying chemistry. This may be done by computer generation of alternatives or by searching through tabulated databases. Using the various product property models and any other relevant factors, cull each list by eliminating candidates that are inappropriate. 4.1.5. Select Product Composition For each property subset, define overall performance by assigning a weighting factor to each property in the set. In the example of the aircraft deicer, while there may minimum targets for freezing point depression and biodegradation that must be simultaneously achieved for a formulation to be given further consideration, assigning appropriate weighting factors to these properties will allow the product designer to consider performance tradeoffs in identifying the formulation with the best performance. Next obtain raw material costs for compounds that simultaneously meet all the important criteria within that property subset, and using the property models and weighting factors, rank all remaining candidates for their raw material costs on an equal overall performance basis. Identify any compounds that are less expensive than those used in current products on an equal overall performance basis, including hidden costs. Assuming that the complete required property set can be achieved by combining the components for each property subset, identify an overall composition to recommend for experimental study. 4.1.6. Design the Process For the preferred composition, chose a base case plant capacity and perform a preliminary process design. This preliminary process design should include a process flow sheet, a material balance for each stream, and sizing of all major equipment. Determine how much capital will be required to build this plant as a function of capacity. 4.1.7. Analyze the Risks Identify the key technical risks associated with this project, and recommend how these risks should be managed. This should include a listing of all key assumptions that were made in designing the product and its process, and an
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experimental plan for corroborating the conclusions drawn from these assumptions. 4.1.8. Analyze Finances for Ongoing Costs Based on cost/performance of the preferred composition and current products, identify a recommended selling price for the new product. Considering all available factors, identify the market share that may be expected at the recommended selling price. Making reasonable estimates, identify the expected variable costs and fixed costs associated with the new product.2 Identify the market share required for break-even, and compare to the expected market share to determine if the new product is likely to be profitable on an ongoing basis. Calculate the net profit expected on an ongoing basis. 4.1.9. Analyze Finances for Investments Making reasonable estimates, calculate the investment expenses that will be required. Given the expected market share and reasonable assumptions for the ramping up of sales, calculate how long will it take to recoup the initial investment while meeting the internally required discount rate. Based on this analysis, decide if the investment should be recommended. 4.2. Discussion This product design methodology will identify a product that meets the preliminary performance specification, and although it assesses both ongoing profitability and return on investments, it guarantees an acceptable level of neither. However, as with all design, product design should be approached iteratively. Once a product designer completes the last step of this method, he will know the various factors that influence product performance and economics. In addition, there may have been multiple product possibilities identified by the methodology, some of which may have been eliminated prematurely. Hence the product designer will be in a position to take a fresh look at all previous decisions and explore the impact of these decisions on ongoing profitability and return on investment. It is also possible that the product designed by this procedure can be the starting point for mathematical optimization. Since the product that offers maximum performance regardless of costs is unlikely to be the product that offers 2
Variable costs are ongoing costs proportional to sales volume, and include items like raw materials and delivery charges. Fixed costs are ongoing costs treated as independent of sales volume, although more correctly they are step functions of sales volume. These include items like depreciation and administrative overheads. [15] Some costs, like labor and utilities, fall somewhere in between these two idealizations, and may be treated as either. Note that a fixed capital investment, unlike depreciation, is not an ongoing cost, and hence is not a fixed cost.
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maximum profitability, there is value in simultaneously simulating and optimizing the effects of product performance, consumer response, and microeconomics. [16] As the focus of the product design must be sufficiently narrowed to permit this approach, the procedure outlined above is a good starting point. 5. Design of Structured Products The methodology proposed above assumes that a homogeneous product can achieve all the required product properties. This ignores the class of chemical products known as structured products, which achieve their properties through a microstructure that is determined by the interaction of its components and the manufacturing process. [17] Product engineering for structured products will be particularly difficult, as the product and process must be designed simultaneously. [2] Here again, a generic methodology is needed to systematically transform each novel approach into a specific set of product alternatives, and to quantitatively analyze those alternatives so as to select from among them. As with process design, this product design methodology would likely be hierarchical and iterative. Two primary approaches are possible: (1) generation and systematic reduction of the number of alternatives through heuristics, and (2) optimization of the set of all potential alternatives through mathematical programming. By analogy to what has been concluded about process design, it can be expected that product design techniques will draw largely on heuristics when data are limited, followed by more detailed calculations later on. [18] Where sufficient data to enable a complete mathematical representation of the product-engineering problem exists, mathematical techniques exist for their solution. However, significant work is still needed to establish a comprehensive generic methodology to generate and systematically reduce the number of alternatives through heuristics, so that product engineering can be accomplished even in the absence of complete data. Recent work has established how to mathematically represent the generic product-engineering problem [19], and mathematical programming has been successfully applied to these problems. [20] Of course, these techniques can only be applied where sufficient data are available to enable a complete mathematical representation of the product-engineering problem. Conversely, in the early stages of design when such data are generally lacking, heuristics are needed to systematically generate and analyze alternatives. Others have begun to identify product-engineering heuristics within specific product contexts [21-23], but a comprehensive generic methodology to generate and systematically reduce the number of alternatives through heuristics has yet to be established for the general problem.
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6. Conclusions The methodology for design of homogeneous products outlined in Section 4 highlights some of the real issues that chemical engineers face in product design. These problems may be quite rich despite the constraint that the product has no microstructure. On the other hand, a comprehensive generic methodology for structured products as suggested in Section 5 would be significantly more complex and would require significant work to develop. However, this methodology would allow structured products to be engineered even in the absence of complete data, accelerating new product development well beyond the capabilities of purely experimental techniques.
References [1] R. Costa, G. D. Moggridge, and P. M. Saraiva, AIChE J, 52 (2006) 1976 [2] M. Hill, AIChE J, 50 (2004) 1656 [3] E. Favre, L. Marchal-Heusler, and M. Kind, Trans IChemE, 80 (2002) 65 [4] M. F. Edwards, Chem. Eng. Res. Des., 84 (2006) 1 [5] J. Villermaux, Chem. Eng. Sci., 48 (1993) 2525 [6] R. A. Mashelkar, Chem. Eng. Sci., 50 (1995) 1 [7] G. Stephanopoulos and C. Han, Comp. Chem. Eng. 20 (1996) 143 [8] T. S. Kuhn, The Structure of Scientific Revolutions, University of Chicago Press, Chicago, 1996 [9] Committee on Chemical Engineering Frontiers, Frontiers in Chemical Engineering: Research Needs and Opportunities, National Academy Press, Washington, 1988 [10] J. Wei, ChemTech, 26 5 (1996) 16 [11] R. B. Bird, W. E. Stewart and E. N. Lightfoot, Transport Phenomena, Wiley, New York, 2002 [12] E. L. Cussler and G. D. Moggridge, Chemical Product Design, Cambridge University Press, New York, 2001 [13] F. M. Meeuse, J. Grievink, P.J.T. Verheijen and M.L.M. Van der Stappen, “Conceptual Design of Processes for Structured Products” in M. F. Malone, J. A. Trainham and B. Carnahan (eds.) Fifth International Conference on Foundations of Computer Aided Process Design, AIChE Symp Ser No 323, 2000, pp. 324-328 [14] F. M. Meeuse, “Process Synthesis for Structured Food Products” in K. M. Ng, R. Gani, and K. Dam-Johansen (eds.) Chemical Product Design: Towards a Persepective Through Case Studies, Elsevier, Amsterdam, 2006, pp. 167-179 [15] W. C. Lawler, “Cost-Volume-Profit Analysis” in J. L. Livingstone and T. Grossman (eds.) The Portable MBA in Finance and Accounting, Wiley, New York, 2002, pp. 102-124 [16] M. J. Bagajewicz, AIChE J 53 (2007) 3155 [17] M. F. Edwards, IChemE North Western Branch Papers No. 9 (1998) [18] J. M. Douglas and and G. Stephanopoulos, “Hierarchical Approaches in Conceptural Process Design: Framework and Computer-Aided Implementation”, in L. T. Biegler and M. F. Doherty (eds.), Fourth International Conference on Foundations of Computer Aided Process Design, AIChE Symp Ser No 304, 1995, pp. 183-197 [19] R. Gani, Comp. Chem. Eng., 28 (2004) 2441 [20] A. K. Sunol, “A Mixed Integer (Non) Linear Programming Approach to Simultaneous Design of Product and Process”, in L. T. Biegler and M. F. Doherty (eds.), Fourth
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Ser No 304, 1995, pp. 276-279 [21] K. Y. Fung and K. M. Ng, AIChE J, 49 (2003), 1193 [22] C. Wibowo and K. M. Ng, AIChE J, 48 (2002) 1212 [23] C. Wibowo and K. M. Ng, AIChE J, 47 (2001) 2746
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Simulation in nuclear engineering design; Christian LATGE C.Latgé, Research Director, French Atomic Energy Commission, CEA-DEN-DTN , Cadarache Research Center, 13108 Saint Paul lez Durance FRANCE
Abstract The development of a new system or process in nuclear field requires generally first to select structural material and coolant and identify associated critical issues, which are inherent in the design and safe operation of the system or process which has to be developed. The design of a system or process has to deal with neutronics, thermal hydraulics, mass and heat transfer, and their consequences on heat deposition, materials structure mechanics, coolant technologies, control systems and operational procedures. All these related studies, using analytical, numerical and experimental approaches, have the following main objective: assessment of reliability and safety aspects which might endanger the integrity and operability of the system, during the life duration; this assessment contributes to the definition and evaluation of control systems, countermeasures, and more generally the preparation of licensing. Selection of best design options requires the use of simulation tools in order to size the individual components and demonstrate the reliability of the whole system or process. Thanks to some examples, ie the design of a spallation target for nuclear waste transmutation, within the framework of an international project, we will illustrate the design strategy of a prototypical integrated system. An extension to some other specific fields of research in chemical engineering for nuclear applications will be performed. Keywords: nuclear engineering, integrated prototypical systems, simulation tools
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Supply Chain Risk Management through HAZOP and Dynamic Simulation Arief Adhityaa, Rajagopalan Srinivasana, b, I.A. Karimib a
Institute of Chemical and Engineering Sciences, 1 Pesek Road, Jurong Island, Singapore 627833, Singapore b Department of Chemical and Biomolecular Engineering, National University of Singapore, 4 Engineering Drive 4, Singapore 117576, Singapore
Abstract In today’s globalized economy, supply chains strive to be increasingly efficient and effective by adopting strategies such as outsourcing, just-in-time practices, and lean inventory. However, these measures to operate the supply chain more efficiently often lead to increased fragility. As uncertainties become more prevalent and disruptions arise from many sources, supply chain risk management has become imperative. Considering the complexity of today’s supply chains and their operations, this paper proposes a systematic framework for supply chain risk management. Within the framework, this paper presents a structured methodology for risk identification and consequence analysis. Following the well-established HAZard and OPerability (HAZOP) analysis method in process safety, supply chain risk identification can be performed by systematically generating deviations in different supply chain parameters, and identifying their possible causes, consequences, safeguards, and mitigating actions. Consequence analysis can be conducted using a dynamic simulation model of the supply chain operations. The application and benefits of the proposed approach are demonstrated using a refinery supply chain case study. Keywords: Disruption Management, Uncertainty, Refinery, Supply Chain Modeling.
1. Introduction A supply chain (SC) comprises all the entities and activities required to deliver final products to end-customers – encompassing procurement, transportation, storage, conversion, packaging, etc. Present-day SCs involve numerous, heterogeneous, geographically distributed entities with varying dynamics, complexities, and uncertainties. Complex maze of the network, unpredictable dynamics, information delay, limited visibility, and involvement of disparate entities with varying goals complicate SC decision making. Furthermore, today’s SC operations are subject to various operational and disruption risks. Operational risks are uncertainties expected in day-to-day operations such as variations in supply, demand, production, transportation, and cost. Disruption risks arise from natural or man-made adverse events which cause variations beyond the expected range such as earthquakes and terrorist attacks. SC risk management is critical to ensure continuity of profitable operations amidst these risks. In this paper, we present a framework for SC risk management and demonstrate its application in a refinery SC. The refinery SC has many sub-processes such as crude procurement, planning, scheduling, oil trading, logistics, etc. At the center of this SC lie the oil refining operations. Refining is a complex process which involves a number of operations to transform crude oil into valuable products. The refinery SC begins from the oil
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reservoirs, found most abundantly in the Middle East region, and tapped via both ground fields and offshore platforms. Transportation of the crude to various processing plants/refineries around the world is carried out mostly by large ships called Very Large Crude Carriers (VLCCs) or pipelines. Even with extensive networks and carefully planned schedules, transportation times are relatively long; it takes 4-6 weeks for a VLCC carrying crude oil from the Middle East to reach refineries in Asia. Such long periods make crude supplies easily susceptible to disruptions, leading to failure to meet customers’ demands or a crude stock out. This is a critical problem as it would compel unit shutdowns and result in large losses. A single crude mix allows numerous products and their variants to be produced through a suitable alteration of processing conditions. Accordingly, refineries must adapt their operations to the different crude batches to maintain the required product specifications, which gives rise to differing operating costs. Further, since crude oil prices, product demands and prices fluctuate highly, optimization needs to be done frequently. Other key features of the refinery SC are large inventories, need for safety-first, sensitivity to socio-political uncertainties, environmental regulations, and extensive trading. Hence, there is clearly a need for risk management in the refinery SC. 1.1. Literature Review SC risk management is a growing research area. Chopra and Sodhi (2004) group SC risks into eight categories (disruptions, delays, systems, forecast, intellectual property, procurement, receivables, inventory, and capacity) and give general mitigating strategies for each category. Kleindorfer and Van Wassenhove (2004) discuss two types of risk management issues in global SCs: matching supply to demand and addressing disruptions to SC activity. Mishra, et al. (2003) present an agent-based decision support system to manage disruptions in a refinery SC. In the event of a disruption, agents collaborate to identify a holistic rectification strategy using heuristic rules. Since there is limited literature on structured and elaborate methodology for SC risk management, this paper attempts to propose one such methodology.
2. Framework and Methodology for Supply Chain Risk Management The proposed framework for SC risk management is illustrated in Figure 1 and comprises the following steps: 1. Risk identification: The first step is to recognize uncertainties and risks faced by the SC. With globalization and increased outsourcing practices, the number of parties involved in the SC and the links connecting them have increased significantly. Hence, some risks may not be obvious and it is important to have a structured method for risk identification, as presented in Section 2.1. 2. Consequence analysis: Once the risks have been identified, their consequences have to be analysed using an appropriate model of SC operations. The disruptions due to one particular risk or a combination of risks can be simulated and propagated through the SC model and the effects analysed. In a complex SC, there could be important domino effects. These should be explicitly considered in the analysis. Section 2.2 presents a dynamic simulation model of the integrated refinery SC which enables such analysis. 3. Risk estimation: Risk is usually quantified in financial terms and/or ranked according to some pre-defined criteria. The frequency or probability of each risk materializing is estimated. The risk is quantified in two dimensions: its frequency/probability and its severity/consequence, taking into account the effects of mitigating actions and safeguards, if any.
Supply Chain Risk Management Through HAZOP and Dynamic Simulation
Risk identification
List of detected risks
Consequence analysis
Risk estimation
List of risks and their estimates
List of risks, their safeguards and mitigating actions
Significant changes such that risk study is necessary
Risk monitoring
List of risks and their effects
KPIs and supply chain changes
Risk mitigation
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Risk assessment No
Supply chain operation
Risk acceptable? Yes
Figure 1. Proposed framework for SC risk management
4. Risk assessment: The risk management team decides whether the risk quantified in the previous step is acceptable based on experience, industry standards, benchmarks, or business targets. If not, additional mitigation actions or safeguards are required. 5. Risk mitigation: Mitigating actions and safeguards such as emergency procedures and redundancies have to be developed for the risks, based on both the SC model and inputs from the risk management team or relevant personnel. Two types of mitigating action can be differentiated – preventive and responsive. Once the risks have been deemed acceptable, SC operations proceed with the appropriate safeguards and mitigating actions in place. 6. Risk monitoring: The SC structure and operation do not remain stationary but changes regularly due to, for example, new suppliers, new regulations, new operating conditions, new products, etc. The risk management team should continually monitor the SC for new risks. The team might be required to start from step (1) to consider the new risks arising from these changes. 2.1. Risk Identification through HAZOP For risk identification, this paper proposes to employ the HAZard and OPerability (HAZOP) analysis method from chemical process risk management. SC networks are in many ways similar to chemical plants. Drawing from this analogy, we propose to represent SC structure and operations using flow diagrams, equivalent to process flow diagrams (PFDs). A simplified flow diagram of the refinery SC is shown in Figure 2. Following the well-established HAZOP method, SC risk identification can be performed by systematically generating deviations in different SC parameters, and identifying their possible causes, consequences, safeguards, and mitigating actions. The deviations are generated using a set of guidewords in combination with specific parameters from the flow diagrams. Table 1 gives a non-exhaustive list of these guidewords and parameters. The guideword “Low” can be combined with a flow to result in, for example, the deviation “Low demand”. Possible causes and consequences can be identified by tracing the flows in the diagram. Safeguards are any items or procedures which help to protect against a particular deviation. It could protect against the deviation before it occurs, i.e. reducing the frequency, or help to recover quickly and minimize impact after it occurs, i.e. reducing the severity. An example of the former is safety stock, which protects against demand uncertainty; an example of the latter is insurance. Mitigating actions are additional items or procedures on top of any existing safeguards which are deemed necessary to manage the deviation.
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Figure 2. Simplified refinery SC flow diagram Table 1. Sample guidewords and parameters for HAZOP
Guidewords No High Low Early/late Parameters Material flow Information flow Finance flow
Meaning None of the design intent is achieved Quantitative increase in a parameter Quantitative decrease in a parameter The timing is different from the intention Raw material, side product, energy, utility, etc Order, quote, forecast, message, signal for action, etc Cash, credit, share, receivables, pledge, contract, etc
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2.2. Consequence Analysis through Dynamic Simulation For consequence analysis, we have developed a dynamic simulation model of the refinery SC, called Integrated Refinery In-Silico (IRIS) (Pitty et al., 2007). It is implemented in Matlab/Simulink (MathWorks, 1996). Four types of entities are incorporated in the model: external SC entities (e.g. suppliers), refinery functional departments (e.g. procurement), refinery units (e.g. crude distillation), and refinery economics. Some of these entities, such as the refinery units, operate continuously while others embody discrete events such as arrival of a VLCC, delivery of products, etc. Both are considered here using a unified discrete-time model. The model explicitly considers the various SC activities such as crude oil supply and transportation, along with intra-refinery SC activities such as procurement planning, scheduling, and operations management. Stochastic variations in transportation, yields, prices, and operational problems are considered. The economics of the refinery SC includes consideration of different crude slates, product prices, operation costs, transportation, etc. The impact of any disruptions or risks such as demand uncertainties on the profit and customer satisfaction level of the refinery can be simulated through IRIS.
3. Case Study This case study is based on the refinery SC flow diagram in Figure 2. We consider the parameter “Crude arrival”, which is the material flow from the jetty to the refinery crude tanks (marked by a star in Figure 2), and the guideword “No” to derive the deviation “No crude arrival”. To study the possible causes of this deviation, we trace backward from the crude arrival flow and find the jetty, shipper, and supplier entities. No crude arrival could be caused by unavailability or disruption to any of these entities, e.g. jetty closure, shipper unreliability, or supplier stock-out. The possible consequences can be examined by tracing forward from the crude arrival flow, from which we find the crude tanks, processing units, product tanks, shipper, and customers. Thus, the possible consequences of no crude arrival are low inventory in the crude tanks, possible out-ofcrude situation which leads to operation being disrupted, low inventory in the storage tanks, low product shipment to customers, and unfulfilled demand. Safeguards for this deviation are required to cover for the crude which is not arriving. These could be in the form of crude safety stock or emergency crude procurement. Since shipper unreliability is one possible cause, a suitable mitigating action could be to consider engaging a more reliable shipper. Other mitigating actions include establishing better communication and transparency with suppliers and shippers for timely notice of any delay, and rescheduling to avoid shutdown by reducing throughput until the crude arrives. These HAZOP results are summarized in Table 2. Consequence analysis of no crude arrival due to delay in transportation is performed using IRIS simulations. In this case, the refinery would like to evaluate the mitigating action of engaging a more reliable shipper. The existing shipper has a 10% probability of late crude delivery while the new shipper is more reliable with a 5% probability of delay. However, the new shipper on average costs $30million more than the existing one. The refinery also considers having a safeguard in the form of safety stock. Hence, four cases are evaluated: with and without safety stock for each shipper option. The resulting profit and customer satisfaction from these cases are shown in Table 3. Safety stock can increase customer satisfaction to 95% despite low existing shipper reliability. However, profit suffers a lot from low shipper reliability. This is because of high shutdown costs. Demand backlog can be satisfied in the next immediate cycle, hence customer satisfaction does not suffer much from shutdown. Safety stock cannot make
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up for poor performance of shipper. In both cases (with and without safety stock), the new shipper increases the profit by more than $50million. Since the increase in profit is more than the increase in cost, it is recommended to switch to the new shipper. Further, safety stock is also recommended as it increases both customer satisfaction and profit.
4. Concluding Remarks Risk management is critical for today’s SCs. In this paper, we propose a systematic framework for SC risk management and structured methodology for risk identification and consequence analysis, demonstrated in a refinery SC. The proposed HAZOP method for risk identification has two notable advantages. It is systematic, because the deviations studied are generated using pre-defined guidewords and pertinent system parameters, as opposed to ad-hoc scenario analysis. It is also complete, because it is structured around a representation of the whole process in the form of flow diagrams, as opposed to other methods with limited scope such as checklist. Consequence analysis is performed through IRIS, a dynamic simulation model of the refinery SC. Risk probability estimation, cost-benefit analysis and optimization of risk management strategies are the direction of our current work.
References S., Chopra and M. S. Sodhi, 2004, Managing Risk to Avoid Supply Chain Breakdown, MIT Sloan Management Review, 46, 1, 53-61. P. R. Kleindorfer and L. N. Van Wassenhove, 2004, Managing Risk in Global Supply Chains, In H. Gatigon and J. Kimberly (eds.), The Alliance on Globalization, Cambridge University Press, Chapter 12. MathWorks, 1996, Using Simulink: Version 2. M. Mishra, R. Srinivasan, and I. A. Karimi, 2003, Managing disruptions in refinery supply chain using an agent-based decision support system, Presented at the AIChE annual meeting, San Francisco, CA, Nov 16-21. S. S. Pitty, W. Li, A. Adhitya, R. Srinivasan, and I. A. Karimi, 2007, Decision Support for Integrated Refinery Supply Chains. 1. Dynamic Simulation, Computers and Chemical Engineering (In Press). Table 2. HAZOP results for crude arrival delay
Deviation No crude arrival
Causes
Consequences
Safeguards
Jetty unavailability; Shipper disruption; Supplier stockout
Low stock, outof-crude; Operation disrupted; Demand unfulfilled
Safety stock; Emergency suppliers
Mitigating Actions More reliable shipper; Frequent check with supplier /logistics; Rescheduling
Table 3. Consequence analysis results for the risk of crude arrival delay
Safety Stock
Yes No
Average Customer Satisfaction (%) Shipper Existing New 95 98 91 95
Average Profit ($, million) Shipper Existing New 38 93 27 83
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
43
A new approach for the design of multicomponent water/wastewater networks Débora C. Faria and Miguel J. Bagajewicz University of Oklahoma, 100E. Boyd, Norman – OK 73019, USA
Abstract Water allocation problems have nonlinearities and non-convexities due to bilinear terms. To address this issue we propose to discretize one of the variables of the bilinear terms. As a result an MILP model is generated, which provides a lower bound. To reduce the gap between this lower bound and the upper bound (a feasible solution found using the original NLP model), an interval elimination procedure is proposed. As a result, the feasible space shrinks after each iteration and the global optimum is identified. We illustrate the methodology for minimum water allocation problems. Keywords: water networks, multicoponent, bilinearities, discretization, lower bound.
1. Introduction The design of water/wastewater networks where water is reused and/or regenerated in processes plants is one important problem in industry as it leads to important water and cost savings. To accomplish this task for multicomponent systesm, mathematical programming is needed (Bagajewicz , 2000). The models contain a large number of bilinear, non-convex terms, which make the identification of a global optimum cumbersome. To overcome this difficulty, some authors have presented methodologies to find feasible solutions for these systems (Bagajewicz et al.,2000; Alva-Argaez et al., 1998,2007; Ullmer et al.,2005). With the exception of the work presented by Karuppiah and Grossmann (2006), no other present a methodology to find the global optimum solution. In this paper we present a new discretization methodology based on an interval elimination procedure that guarantees global optimality. We present the nonlinear model first, followed by a description of the discretization model and the solution procedure. Finally, an example is presented.
2. The Nonlinear Model Problem statement: Given a set of water using units, freshwater sources, wastewater sink and available regeneration processes with their limiting data, a globally optimum for the freshwater consumption is sought. The corresponding non-liner model to solve this water allocation problem (WAP) written in terms of contaminant mass load is: Water balance at the water-using units
¦ FWU w,u + ¦ FUU u*,u + ¦ FRU r ,u w
u*
=
r
¦ FUS u ,s + ¦ FUU u ,u* + ¦ FURu*,r s
u*
∀u
(1)
r
FWU, FUU, FRU, FRR and FUR are the freshwater to unit, unit to unit, regeneration unit to units, regeneration to regeneration and unit to regeneration flowrates.
D.C. Faria and M.J. Bagajewicz
44
Water balance at the regeneration processes
¦ FURu ,r + ¦ FRRr*,r = ¦ FRU r ,u + ¦ FRRr ,r* + ¦ FRRr ,u u
r*
u
r*
∀r
(2)
u
Contaminant balance at the water-using units
¦ (CWw,c * FWw,u ) + ¦ ZUU u*,u ,d + ¦ ZRU r ,u,d w
u*
+ ΔM u ,c
r
= ¦ ZUU u ,u*,d + ¦ ZUS u , s ,d + ¦ ZURu ,r ,d u*
s
(3)
∀u, c
r
CWw,c is the pollutant c concentration in freshwater. In turn, ZUU, ZRU, ZUS and ZUR are mass flows of contaminants between units, regeneration to units, units to disposal and units to regeneration units. Finally ΔM u ,c is the mass load of component c. Maximum inlet concentration at the water-using units
¦ (CW w,c * FUW w,u ) + ¦ ZUU u*,u ,c + ¦ ZRU r ,u ,c w
u*
r
· § ≤ Cinmax u ,c * ¨¨ ¦ FUW w,u + ¦ FUU u*,u + ¦ FRU r ,u ¸¸ u* r ¹ ©w
(4) ∀u , c
Maximum outlet concentration at the water-using units
¦ (CW w,c * FUW w,u ) + ¦ ZUU u*,u ,c + ¦ ZRU r ,u ,c + ΔM u ,c w
u*
r
· § ≤ Coutmax u ,c * ¨¨ ¦ FUU u ,u* + ¦ FUR u , r + ¦ FUU u ,u* + ¦ FUS u , s ¸¸ ∀u , c r u* s ¹ © u*
(5)
Cinmax and Coutmax are maximum inlet and outlet concentrations. Contaminant balance at the regeneration processes
ª º ZRrout ,c = « ¦ ZURu , r ,c + ¦ ZRRr *, r ,c » *(1 − XCRr ,c ) r* ¬u ¼ ª º + « ¦ ZRU r ,u ,c + ¦ ZRRr ,r *,c + ¦ ZRRr ,r *,c » * XCRr ,c r* r* ¬u ¼
(6)
∀r , c
Here XCRr ,c is a binary parameter that determines is a contaminant is removed or not. Capacity (CAP) of the regeneration processes CAPr = ¦ FURu ,r + ¦ FRRr *,r ∀r u
(7)
r*
Contaminant mass loads These constraints are written in a general form where i can be any water using unit or any regeneration process; and j can be a water using unit, regeneration process or sink.
ZIJ i, j ,c = FIJ i, j * Couti, j
∀i ∈ {U , R}, j ∈ {U , R, S}, c
(8)
A New Approach for the Design of Multicomponent Water/Wastewater Networks
45
Freshwater consumption – Objective function
Min¦¦ FWU w,u w
(9)
u
3. The Discrete Methodology 3.1. Model Discretization The proposed approach discretizes one variable (concentrations used here or flowrates) of the bilinear term generated at the splitting points. As a result, a mixed integer linear programming (MILP) model is generated. The discretized concentrations are now parameters ( DC d,c,u for the water using units; DCR d,c,r for regeneration processes). Eq. 8 (the only bilinear one) is substituted by the following “big M” constraints, that force the outlet concentrations to be in between two discrete concentrations. ZIJ i , j ,c − DC d ,c ,i * FIJ i , j ≥ DC d ,c ,i * Fmax * (XI i,c,d − 1) ∀i ∈ {U , R}, j ∈ {U , R, S }, c, d < dmax ZIJ i , j ,c − DCd +1,c,i * FIJ i , j ≤ DCdmax,c,i * Fmax * (1 - XIi,c,d ) ∀i ∈ {U , R}, j ∈ {U , R, S }, c, d < dmax
(10)
(11)
To guarantee that only one interval is picked, we write:
¦ XIi,c,d = 1 d
∀i ∈ {U , R} , c
(12)
Thus, the contaminant mass load of each stream is calculated through a relaxation between two discrete points. Finally, to ensure that there is no contaminant mass load when flowrate does not exist, we write: ZIJ i , j ,c ≤ DC dmax ,c ,i * FIJ i, j
∀i ∈ {U , R}, j ∈ {U , R, S }, c
(13)
The discretized model provides a lower bound (because it is relaxing one constraint), but most important, it also points to a set of intervals that might contain the optimum. In addition, a good upper bound can be obtained using the solution of this lower bound as a starting point of the original NLP problem.
Once a lower bound and an upper bound of the problem are found, one can evaluate the lower bound solution and determine which intervals might be part of an optimum solution. The ones that are proved not to be in the optimum solution are eliminated and the remained intervals of the discrete concentration parameters are discretized again. This is done as follows. 3.2. Interval Eliminations In each iteration, after a lower and an upper bound are found, we implement the following procedure for each discrete concentration: 1. The interval selected by the lower bound model is forbidden to be selected (this means the correspondent binary is fixed to zero) 2. The discrete model is then run again. Two possibilities exist:
D.C. Faria and M.J. Bagajewicz
46
a.
The solution is feasible (a solution between the current lower and upper bound exists). In this case, it is possible to have an optimum solution outside of the investigated interval. Thus, nothing is done. The solution is infeasible (there is no feasible solution between the current lower and upper bound outside of the investigated interval). Thus, the optimum solution needs is inside of the investigated interval. Thus, the region outside of the investigated interval is disregarded.
b.
4. Illustration of The Methodology We now illustrate the method a small example with two water-using units and two contaminants (Wang and Smith, 1994) (Table 1). For this example, two intervals (dmax=3) are used. Figure 1 shows how the discrete concentrations are being divided at the beginning (initialization step). Process 1 2
Table 1 – Limiting data of illustrative example Mass Load Cin,max Contaminant (Kg/h) (ppm) A 4 0 B 2 25 A 5.6 80 B 2.1 30
Cout,max (ppm) 100 75 240 90
Figure 1 – Illustrative example of the discrete approach - initialization.
In this case, the lower bound is 52.895 ton/h and the upper bound is 54 ton/h. All the selected intervals of the discrete concentration are in the second interval. When the lower bound model is re-run forbidding the selected intervals (intervals evaluation), it is found that none of the first intervals have the possibility of hosting the optimum solutions. Thus, the intervals between the first and second discrete points can be eliminated and the second intervals re-discretized.
Figure 2 – Illustrative example of the discrete approach – 1st iteration.
A New Approach for the Design of Multicomponent Water/Wastewater Networks
47
With this new intervals in the second iteration the lower and upper bound do not change (LB = 52.895 ton/h and UB = 54 ton/h), but the intervals are smaller, so a new elimination procedure can be conducted. The same procedure is repeated until the lower bound solution is equal (or has a tolerance difference) to the upper bound solution. In this example, using two intervals, is solved in 11 iterations and 11.6 seconds. Note that hen the elimination is not possible more intervals are used.
5. Examples The proposed method is applied to a refinery case presented by Koppol et al. (2003). This example has four key contaminants (salts, H2S, Organics and ammonia), six water using units, and three regeneration processes. The limiting data of the water using units are shown in the original paper. The solution when freshawater consumption is minimized, without allowing the addition of regeneration processes, is presented in Figure 3. A freshwater consumption of 119.332 ton/h was achieved. Only one iteration is needed and the solution is found in 0.81 seconds. The solution when regeneration processes are introduced (Reverse osmosis, which reduces salts to 20 ppm; API separator followed by ACA, which reduces organics to 50 ppm; and, Chevron wastewater treatment, which reduces H2S to 5 ppm and ammonia to 30 ppm) has a freshwater consumption of 33.571 ton/h. Only one iteration is needed to find the solution in 2 seconds. However, the found solution present several regeneration recycles and very small flowrates. This is an undesirable situation for the practical point of view. To overcome this issue, we added binary variables to control a minimum allowed flowrate if the connection exits and to forbid recycles as well. The new solution (also 33.517 ton/h) is found in two iterations (34 seconds). The flowsheet obtained is not shown for space reasons.
Figure 3– Optimum for Multicomponent Example. No regeneration
Further, we no longer consider the regeneration processes with fixed outlet concentrations of the key contaminants. Instead, we evaluate what would be these concentrations if we want minimize the need for regenerations at the found freshwater consumption (33.571 ton/h). To translate this goal to a mathematical form, we use the total removed contaminant mass load (that is the combination between flowrate and concentration reduction) as the objective function. Now, the outlet concentrations of the keys contaminants in the regeneration processes can have any value higher than the ones previously presented. The optimum solution found after 2 iterations (66 Seconds) shows the regeneration processes having the following features: Reverse osmosis needs to reduce salts to 85 ppm instead 20 ppm originally proposed. The API separator
D.C. Faria and M.J. Bagajewicz
48
followed by ACA need to reduce organics to 50 ppm as before. Finaly, the Chevron wastewater treatment should keep the 5 ppm reductions for H2S, but can operate to reduce ammonia to 120 ppm instead 30ppm. The suggested network is presented in Figure 4.
Figure 4– Optimum for Multicomponent Example. With Regeneration
6. Conclusions The suggested approach has showed good results on the minimum water allocation problems. The methodology also allows handling the outlet concentration of the key contaminants of the regeneration processes as a variable. This arises to be important when one wants to determine optimum contaminats reduction without define the regeneration processes beforehand. As future work, the methodology will be extended to the optimization of WAP using other objective function.
References M. Bagajewicz, 2000, A review of recent design procedures for water networks in refineries and process plants, Computers and Chemical Engineering, 24, 2093-2113. M. Bagajewicz, M. Rivas and M. Savelski, 2000, A robust method to obtain optimal and suboptimal design and retrofit solutions of water utilization systems with multiple contaminants in process plants, Computers and Chemical Engineering, 24, 1461-1466. A.A. Alva-Argaez, C. Kokossis and R. Smith, 1998, Wastewater minimization of industrial system using an integrated approach, Computers and Chemical Engineering, 22, S741-S744. A.A. Alva-Argaez, C. Kokossis and R. Smith, 2007, A conceptual decomposition of MINLP models for the design of water-using systems, Int. J. of Env. and Pollution, 29(1-3), 177-205. C. Ullmer, N. Kunde, A. Lassahn, G. Gruhn and K. Schulz, 2005, WADO: water design optimization – methodology and software for the systhesis of process water systems, Journal of Cleaner Production, 13, 485-494. R.Karuppiah and I.E. Grassmann, 2006, Global optimization for the systhesis of integrated water systems in chemical processes, Computers and Chemical Engineering, 30,650-673. Y.P. Wang and R. Smith, 1994, Wastewater Minimization, Chem. Eng. Science, 49(7), 981-1006. A.P.R. Koppol, M.J. Bagajewicz, B.J. Dericks and M.J. Savelski, 2003, On zero water discharge solutions in the process industry, Advances in Environmental Research, 8, 151-171.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
49
Effect of catalytic reactor design on plantwide control strategy: Application to VAM plant Costin S. Bildea1 and Alexandre C. Dimian2 1
University “POLITEHNICA” of Bucharest, Polizu 1, Bucharest, Romania University of Amsterdam, Nieuwe Achtergracht 166, Amsterdam, The Netherlands
2
Abstract The paper demonstrates that the kinetic behaviour of a catalyst is a key element in developing a plantwide control strategy. The “inverse problem” is also important: design a catalyst whose kinetic behaviour fulfils at best the performance criteria of the plant. So far, these problems have not been systematically investigated. The methodological tool is based on the bifurcation analysis of the structure Reactor / Separation / Recycle. This analysis allows finding regions in the space of design parameters where performance criteria are met and stability is guaranteed. The catalytic chemical reactor must be a flexible unit. The recycling strategy is determined by the kinetic effect of each reactant, as well as by the sensitivity of the elementary reaction steps to concentration and temperature. When selectivity and catalyst properties require low per-pass conversion, manipulating the reactor temperature profile is an effective means for steering the plant between different operating points. Keywords: design, plantwide control, catalytic reactors, vinyl acetate
1. Introduction Controlling the inventory of reactants in plants with recycles can be performed in two ways [1]. The first one is evaluating the inventory of each reactant and controlling it by feedback, using the corresponding fresh feed as manipulated variable. A practical way is to fix the flow rates of reactants at reactor inlet. Production rate changes can be achieved a) by modifying the flow rates of reactants, which works when the process is designed for large conversion and b) by changing the reactor operation parameters, which is recommended at low values of conversion. The second approach is fixing the fresh feed rate of reactants and using the self-regulation property of the mass balance [2]. This strategy offers a direct way of changing the production rate. However, it can be applied only when the per-pass conversion of the limiting reactant has a high value. Previous studies [3] highlighted the interaction between reactor design and the control of plants with recycles and considered the generic Reactor / Separation / Recycle system as fundamental structure for developing plantwide control strategies. In the present paper, we consider the design and control of a process involving a complex LHHW catalytic reaction scheme. The Vinyl Acetate monomer (VAM) process has been proposed as benchmark for developing a plantwide control procedure [4], and received the attention of several studies [5-7]. However, our evaluation of these works indicates that the control strategy suffers of high sensitivity since the kinetics of the chemical reaction was implemented on a pre-determined reactor and plant design. Our approach considers the kinetics of the catalytic process as the starting point in designing the plant with recycles, as well as in developing the plantwide control strategy.
50
C.S. Bildea and A.C. Dimian
2. Process design The manufacturing of vinyl acetate by the oxy-acetylation of ethylene is described by the following gas-phase catalytic reaction: C2H4 + CH3COOH +0.5O2 ĺ C2H3OOCCH3 + H2O
ΔrH = -176.2 kJ/mol
A highly undesired secondary reaction is combustion of ethylene to CO2, which lowers the yield and complicates the removal of the reaction heat: ΔrH = -1322.8 kJ/mol
C2H4 + 3O2 ĺ 2CO2 + 2H2O
The catalyst plays a crucial role in the technology. A typical modern catalyst consists of 0.15-1.5 wt% Pd, 0.2-1.5 wt% Au, 4-10 wt% KOAc on silica spherical particles of 5 mm [8]. The very fast reaction takes place inside a thin layer (egg-shell catalyst). Preferred conditions are temperatures around 150 to 160 °C and pressures 8 to 10 bar. Hot spots above 200 °C lead to permanent catalyst deactivation. The excess of ethylene to acetic acid is 2:1 to 3:1. Because of explosion danger, the oxygen concentration in the reaction mixture should be kept below 8%. Small amount of water in the initial mixture are necessary for catalyst activation. The dilution of the reaction mixture with inert gas is necessary because of high exothermic effect. Accordingly, the reactor is designed at low values of the per-pass conversions, namely 15 – 35% for the acetic acid and 8-10% for ethylene. The above elements formulate hard constraints both for design and for plantwide control. Analyzing the mechanism of the catalytic reaction allows the identification of the major factors that affect the reactor design. The reaction kinetics is not sensitive to the concentration of the acetic acid, but the presence of some water is necessary to activate the catalyst. On the contrary, ethylene and oxygen are involved in kinetics through a complex adsorption/surface reaction mechanism. The catalyst manifests high activity and selectivity. The power-law kinetics involves only ethylene and oxygen [8]: α1 rVA = k1 pC p β1 H O 2
4
2
where Į1 is 0.35 - 0.38 and ȕ1 0.18 - 0.21. The reaction constant is given by k1 = A1 exp(− E1 / RT ) in which the energy of activation depends on the Pd content, for example 39 kJ/mol for Pd 1% and 17.3 kJ/mol for Pd 5%. A similar kinetic expression describes the secondary combustion reaction, but with reaction orders very different compared to the main reaction: α2 rCO2 = k 2 pC pβ2 H O 2
4
2
Table 1. Kinetic parameters for vinyl acetate synthesis over a Pd/Au/SiO2 catalyst [9,10]
Reactions
Power-law kinetics C2H4 O2 C2H4+CH3COOH+0.5O2 0.36 0.20 C2H4 +3O2 ĺ 2CO2 + 2H2O -0.31 0.82 * reaction rate in mol/litre-catalyst/sec.
Kinetic constants E (J/mol) 15000 21000
A1 2.65E-04 7.50E-04
A2 7.95E-05 2.25E-04
Effect of Catalytic Reactor Design on Plantwide Control Strategy
51
R-GAS HX R-IN SEP ETHENE MIX1
PFR
SEP
OXYGEN MIXER
ACETIC R-OUT R-ACETIC
Figure 1 Design of the reactor for vinyl acetate manufacturing in a recycle system
Figure 1 presents the Reactor / Separation / Recycle structure used for performing reactor design and bifurcation analysis. Because of incomplete conversion, both ethylene and acetic acid are recycled. The recycle policy should maintain an ethylene/acetic acid ratio of 3 : 1, as well as oxygen concentration at reactor inlet bellow 8 vol%. The choice of gaseous inert is a key design decision. Some reports [4-7] consider ethane (impurity in the fresh feed), but this solution is not adopted here. Because CO2 is produced by reaction in large amount, its use as inert in a concentration of 10-30 % vol is the most economical [8]. However, the presence of CO has to be prevented since this is a catalyst poison.
3. Plantwide control The main goals of the plantwide control system are to ensure safe operation, desired production rate and product quality, and to optimize the efficiency of using the material and energetic resources. Figure 2 presents the control structure around the chemical reactor. Safety is essential. Therefore, the oxygen is added under concentration control, in a mixing chamber placed behind concrete walls. Secondly, the cooling should avoid reaction runaway. Several temperature measurements are placed along the reactor bed and the highest value is selected as the process variable. The manipulated variable of the control loop is the steam generator pressure, which directly influences the coolant temperature. The water level in the steam generator is controlled by the water makeup. Note that using a simple feedback loop may not work. When the steam rate increases, the correct action is to add more water as makeup. However, the pressure simultaneously decreases. The lower pressure means that, initially, the steam bubbles will occupy a larger volume, and the liquid level will increase. A feedback levelcontroller will wrongly decrease the water make-up rate. Therefore, the steam rate is measured and the required water makeup is calculated. This feedforward action is combined with the feedback provided by the level controller. As recommended in previous works, the inventory of reactants in the plant is maintained by fixing the reactor-inlet flows. Acetic acid is taken with constant rate from a storage tank, and the fresh feed is added on level control. The gas rate going to the evaporator is a good estimation of the ethylene inventory. Therefore, this flow is kept constant by adjusting the fresh ethylene feed. The fresh oxygen rate is manipulated by a concentration control loop, as previously explained.
52
C.S. Bildea and A.C. Dimian
TC Steam
O2
F FF
C2H4 recycled
+
PC
TC
CC
+
LC
T
Reactor
T
HS
FC
T
Steam generator
C2H4 fresh
FC AcOH recycled
PC
TC
Evaporator
AcOH fresh
VAc crude to separation
FC
LC AcOH storage
FC AcOH to separation
Figure 2. Control structure for fresh feeds and around chemical reactor CO2 removal
CO2
C2H4 recycled
FC CC
AcOH
PC FC AcOH
C-4 C-1 LC
PC PC
TC
3Flash
C-1
Decanter
LC TC
FC
LC C-5
LC PC
TC LC
PC LC LC
VAc
C-3
T-1 VAc crude from reactor
PC
LC
TC
FC C-6 TC Water
Water AcOH to storage
Figure 3. Control structure of the separation section
Effect of Catalytic Reactor Design on Plantwide Control Strategy
53
The separation section takes advantage from the heterogeneous azeotrope formed by vinyl acetate and water. Significant energy saving, up to 70 %, can be obtained by making use of a dehydration gas pre-treatment. In this way the exothermic reaction can cover up to 90 % from the energy requirements of the distillations. The control of the separation section is presented in Figure 3. Because the distillate streams are recycled within the separation section, their composition is less important. Therefore, columns C-3, C-5 and C-6 are operated at constant reflux, while boilup rates are used to control some temperatures in the lower sections of the column. For the absorption columns C-1 and C-4, the flow rates of the absorbent (acetic acid) are kept constant. The concentration of CO2 in the recycle stream is controlled by changing the amount of gas sent to the CO2 removal unit. Temperature and pressure control loops are standard. In Reactor / Separation / Recycle systems, two strategies can be employed to achieve production rate changes. The first one, by manipulating the reactor inlet flows, does not work here: the acetic acid does not influence the reaction rate, the per-pass conversion of ethylene is very low (10%), while the reactor-inlet oxygen concentration is restricted by the safety concerns. Therefore, the second strategy manipulating the reaction conditions is applied.
4. Results Figure 4 shows results of simulation in Aspen DynamicsTM, for the following scenario: the plant is operated at the nominal steady state for 1 hour. Then, the coolant temperature is increased from 413 K to 425 K and simulation is continued for 2 hours. The maximum temperature inside the reactor increases from 455 K (at 0.8 m from reactor inlet) to 469 K (at 1.2 m from inlet). The higher temperature results in higher reaction rates, less reactants being recycled. The gas recycle is the fastest, and the ethylene feed is the first to be adjusted. Then, more oxygen is added by the concentration controller. The dynamics of the liquid recycle is slower and it takes about 0.5 hours until the acetic acid feed reaches the new stationary value. The vinyl acetate production rate increases from 154 kmol/h to 171 kmol/h. At time t = 3 hours, the coolant temperature is reduced to 400 K, and the simulation is run for another 2 hours. The maximum reactor temperature drops to 452 K (near reactor inlet) and the production rate is decreased to 134 kmol/h. During the entire simulation, the oxygen concentration stays very close to the setpoint of 6%. Moreover, the concentration of the vinyl acetate product is above the 99.98% specification. Similarly to our approach, Luyben and co-workers [4, 5] proposed to fix the reactorinlet flow rate of acetic acid and to use the fresh feed to control the inventory in the bottom of the acetic-acid distillation column. The two control strategies are equivalent (a)
(b)
Ethylene
180 160
Acetic acid 140 120
Oxygen
100 80
180
Water
160
Vinyl acetate
40 30
140 20
120
CO2 10
100 80
0
1
2
3
time / [h]
4
5
Flow rate / [kmol/h]
50
200
Flow rate / [kmol/h]
Flow rate / [kmol/h]
200
0 0
1
2
3
4
5
time / [h]
Figure 4. Dynamic simulation results as flow rates of a) fresh reactants and b) products
54
C.S. Bildea and A.C. Dimian
from a steady state point of view. However, Olsen et al. [6] showed that Luyben’s structure has an unfavourable dynamics due to the large lag between the manipulated and controlled variables. The other important control loops in [5] paired the oxygen feed with oxygen concentration, and ethylene feed with pressure in the system. The production rate was also manipulated by the setpoint of reactor temperature controller. Chen and McAvoy [7] applied a methodology where several control structures, generated on heuristic grounds, were evaluated using a linear dynamic model and optimal control. Their results also indicate that fixing the reactor-inlet flows is the recommended strategy.
4. Conclusion The case study of vinyl acetate synthesis emphasises the benefits of an integrated process design and plantwide control strategy based on the analysis of the Reactor / Separation / Recycles structure. The core is the chemical reactor, whose behaviour in recycle depends on the kinetics and selectivity of the catalyst, as well as on safety and technological constraints. Moreover, the recycle policy depends on the reaction mechanism of the catalytic reaction. The approach in steady state reactor design finds a dynamic equivalent in the plantwide control strategy. Because of low per pass conversion of both ethylene and acetic acid, manipulating the flow rate of reactant at reactor inlet has little power in adjusting the production rate. The reaction temperature profile becomes the main variables for changing the reaction rate and hence ensuring the flexibility in production. The inventory of reactants is adapted accordingly by fresh reactant make-up directly in recycles. Productivity higher than 1000 kg VAM/m3-catalyst/h can be achieved working at higher temperature and shorter residence time, as well as with good temperature control. This approach can be seen as generic for low per pass reactions.
References [1] Bildea C.S., Dimian A.C., Fixing flow rates in recycle systems: Luyben’s rule revisited. Industrial and Engineering Chemistry Research. 2003; 42: 4578. [2] Downs J., Distillation Control in a Plantwide Control Environment. In Practical Distillation Control; Luyben W., Ed.; van Nostrand Rheinhold: New York: 1992. [3] Bildea C.S., Dimian A.C., Cruz S.C., Iedema P.D., Design of tubular reactors in recycle systems, Computers & Chemical Engineering 28 (1-2): 63-72, 2004. [4] Luyben M.L. and Tyreus B.D., An industrial design / control study for the vinyl acetate monomer process, Comp. Chem. Eng., 1998, 22, 867 [5] Luyben M.L., Tyreus B.D., Luyben W.L. , Plantwide control design procedure, AIChE Journal, 43 (12), 3161-3174, 1997 [6] Olsen, D., Svrcek, W., Young, B., Plantwide control study of a vinyl acetate monomere process design, Chem. Eng. Comm, 192 (10), 1243-1257, 2005 [7] Chen, R. and McAvoy, T., Plantwide control system design: methodology and application to a vinyl acetate process, Ind. Eng. Chem. Res., 42, 4753 – 4771, 2003 [8] Renneke, R. et al., Development of a high performance catalyst for the production of vinyl acetate monomer, Topics in Catalysis, 38(4), 279-287, 2006 [9] Han, Y. F., Wang J. H., Kumar, D., Yan, Z., Goodman D. W., A kinetic study of vinyl acetate synthesis over Pd-based catalysts, J. Catalysis, 232, 467, 2005 [10] Han, Y. F., Kumar, D., Sivadinarayana C., Goodman, D. W., Kinetics of ethylene combustion in the synthesis of vinyl acetate, J. Catalysis, 224, 60, 2004
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
55
Model of the Product Properties for Process Synthesis Peter M.M. Bongers Unilever Food and Health Research Institute, Olivier van Noortlaan 130, 3130 AC,Vlaardingen, The Netherlands
Abstract In the hierarchical decomposition method, or, process synthesis one only looks at the input-output structure of the process at the first level. In subsequent levels more detail is added, finally ending with the entire flowsheet. Design decisions are made by using heuristics and models. The amount of detail in the models depend on the level at which the models are applied. The models are used to describe how processes behave in terms of bulk properties. However, during the product-process design, the product is judged on sensory attributes. The models need extension to sensory attributes (the property model). The sensory attributes depend on physical attributes, as can be predicted by the models, and ingredients. This dependency range from constant to highly non-linear. This paper describes how the problem of determining the lowest complexity model for the property function can be formulated and solved for an ice cream example. The estimated property function model provides a good estimation of the sensory attributes. In combination with a process function model we are able to related ingredients and process conditions with sensory attributes. Keywords: product-process design, sensory models, neural networks.
1. Background Process synthesis is regarded as the invention of conceptual process designs. These designs are expected to be reliable, economic attractive and generated within a limited time frame. Thus, process synthesis is the generation of alternatives and choices to reduce the number of alternatives in all conceptual process engineering steps within the innovation process. As the number of possible alternatives to perform a desired task can be easily about 104 to 109, methodologies are required to reduce this explosive number to manageable levels. The development of those methodologies to aid engineers to better design a process is not a novel challenge. In the chemical industry, first academic publications and successful industrial implementations related to process synthesis methodologies are well established, see Douglas (1988), Sirola (1996). In the hierarchical decomposition method developed by Douglas (1988) one only looks at the input-output structure of the process at the first level. In subsequent levels more detail is added, finally ending with the entire flowsheet. Design decisions are made by using heuristics and models. The amount of detail in the models depend on the level at which the models are applied. Historically, process models are used to describe how processes behave in terms of bulk properties such as flow, temperature, pressure, concentration, etc. However, our consumer goods, such as soups, mayonnaise or ice cream, are not bought on their bulk properties, but on how consumers perceive the products. During the product-process
P.M.M. Bongers
56
design stages, the product is judged on measured sensory attributes, such as mouth feel, bite, creamy texture, etc. Hence, there is a need to extend process models with sensory attributes. Figure 1 shows how the process model can be extended into a model chain from raw materials, equipment and operational conditions through sensory attributes to consumer liking. OPERATIONAL CONDITIONSL
EXTERNAL DISTURBANCES
PROCESS FUNCTION
CONSUMER LIKING
SENSORY ATTRIBUTES
PHYSICAL ATTRIBUTES
RAW MATERIALS
PROPERTY FUNCTION
PRESSURE TEMPERATURE AIRCRYSTAL SIZES
CONSUMER FUNCTION
SMOOTHNESS ICINESS CREAMINESS
Figure 1 Process, property and consumer function for ice cream
Products are bought by the consumers based on their perceived benefits. A product design should therefore aim at satisfying specific consumer benefits. To be more precise, one needs to be able to relate the ingredients, equipment and processing conditions to the consumer benefits. In the design phase there is the need to evaluate concepts without ‘large’ and expensive consumer trials. For this purpose sensory attributes measured by a trained QDA panel, are used to measure consumer benefits. Previously reported work describes dynamic process model for ice cream freezers (Bongers, 2006) and extruders (Bongers and Campbell, 2008) to relate operating conditions, equipment geometry with physical attributes, such as extrusion temperature. This leaves the property function as the unknown to be found. As no fundamental relations are currently available on which to develop a model, we have to revert to experimental relations. Then, for analysis purposes, the property function should be determined from physical attributes to sensory attributes. For synthesis purposes, the property function should be determined from sensory attributes back to physical attributes. In the past various attempts have been made to determine the property functions for all kinds of products. Almost all of these use linear regression techniques (see for example Powers and Moskovitz, 1974) to deal with the measured data. By the fact that most of the property function is highly non-linear, these techniques fail. In addition to the linear regression, a linear regression on non-linear functions of the attributes can be used. The drawback is that the non-linear functions of the attributes have to be defined by the user. At present this have to be done by trail-and-error and turns out to be a very tedious. Based on the above observations, a successful approach to determine the property function has to be based on a generic non-linear function description. One such approach is to use neural networks as a non-linear describing function.
Model of the Product Properties for Process Synthesis
57
2. Data manipulation 2.1. Data set The dataset of 30 experiments contains: • 1 equipment type (usage of a freezer or a freezer and single screw extruder) . This is a nominal parameter (-1 for only freezer, +1 for both freezer and single screw extruder) • 1 process parameter (exit temperature). This is a continuous parameter between -6oC and -13oC with a resolution of 0.1oC • 1 ingredients parameter (fat level). This is a continuous parameter between 8% and 12% with a resolution of 1% • 25 sensory properties of the icecream. These are ordered intervals between 0 and 10 with a resolution of 0.1 The property model has 3 independent inputs and 25 outputs. This multi-input-multioutput system can also be described as a multiple (decoupled) system of multi-inputssingle-output (Ljung, 1999). 2.1.1. Data analysis Basic statistical analysis on the sensory properties (variance, kurtosis and min-max) showed that 4 sensory parameters where not influenced by the inputs and hence excluded from the analysis (later on, they will be indicated as constant). Correlation analysis between the sensory attributes showed 3 sensory attributes having a correlation coefficient of 0.95 or higher with each other. For this cluster only one of the sensory attributes is taken forward in the analysis. As a result, only 17 sensory attributes will be analysed.
3. Property model The property model should be as simple as possible, but not too simplistic That means that for each of the senory parameters we need to determine the ‘simplest’ relation. On the data set two types of describing functions will be determined: a linear regression or neural network to describe the non-linearities. Which of the models to use will be determined by trading-off the prediction error against the number of parameters used, i.e. the AIC (Akaike, 1974). 3.1.1. Linear regression Multiple linear regression can be applied to determine a linear function having the following form: Sensory attribute(n) = p1 ⋅ Fatlevel + p2 ⋅ Temperature + p3 ⋅ FreezerType + p4 3.1.2. Neural network A neural network consists of a number of nodes, called neurons, connected to the inputs and outputs, having the following structure for this application.
P.M.M. Bongers
58
fat level extrusion temperature
sensory attribute
freezer type
The neurons weight all inputs and provide an output via the activation function. The complexity of the neural networks used will be determined by the number of nodes in the hidden layer (2,3,5 or 7). The activation applied in this application is a hyperbolic tangent function. In mathematical terms, the output of neuron j is defined by: output of neuron j With: yj n wiu i input from neuron i (or input i), weighted with wi y = tanh( Σ w u ) i i
j
i=1
The weightings wi in the neural network are determined by an optimisation algorithm using the error between the measured outputs and the outputs predicted by the neural network. The work of Rumelhart et.al. (1985) is recommended for more details about this type of neural networks and examples. In theory one hidden layer neural network is sufficient to describe all input/output relations. More hidden layers can be introduced to reduce the number of neurons compared to the number of neurons in a single layer neural network. The same argument holds for the type of activation function and the choice of the optimisation algorithm. However, the emphasis of this work is not directed on the selection of the best neural network structure, activation function and training protocol, but to the application of neural networks as a means of non-linear function fit.
4. Model parameter estimation 4.1. Training set In order to be able to perform validation of the model, not all 30 cases can be used to determine the model. Also care must be taken to which cases will be used for validation and which cases for determination of the model. Because it is easy with an experimental model to fit noise in the data, a ‘large’ validation set has been chosen (5 cases in the validation set and 25 cases remaining in the set to determine the model (=training set) ). To avoid coincidental results, the whole procedure is repeated 5 times with different training sets and validation sets, where the cases in the validation set have been selected randomly. 4.2. Error Criterion The next step is to determine the error criterion on which to decide the predictive value of the model and to decide which prediction type to use for which sensory attribute. For each of the sensory attribute, the root mean square of the prediction error, ε, will be used to evaluate the properties of the prediction model type. With: yˆ predicted output for case i N
ε :=
1 N −1
¦
i =1
( yi − yˆ i ) 2
i
yi N
measure output for case i number of cases
Model of the Product Properties for Process Synthesis
59
4.3. Results The whole analysis (including the penalty for over parametrising) has been implemented in Matlab (Mathworks 2007) using the public domain neural network tool of Norgaard (1995). The following predictor type, and mean square errors for the sensory attributes have been obtained. predictor type
Sensory attribute No Name . 1 Firmness on spooning
0.10
Neural (3*)
predictor type
Sensory attribute No Name . 14 powdery
0.02
Constant
2
Initial firmness
0.11
Neural (2)
15 vanilla pods
0.06
Neural (3)
3
Chewiness
0.05
Neural (3)
16 flavour melt
0.05
4
Coldness
0.18
Linear
17 creamy flavour 0.44
Correlated with 10 Linear
5
Crumbliness
0.08
Neural (2)
18 sweetness
0.03
Constant
6
inital smoothness
0.08
Neural (2)
19 sharp/yogurt
0.02
Constant
7
I/C quantity in mouth
0.11
Neural (7)
20 fruity
0.12
Neural (2)
8
I/C/ size in mouth
0.11
Neural (2)
21 vanilla flavour 0.07
Neural (2)
9
Rate of melt
0.17
Linear
22 boiled milk
0.14
Linear
10 Creamy texture
0.12
Neural (5)
23 other flavour
0.04
Constant
11 Thickness
0.14
12 final smoothness
0.15
Correlated with 10 Neural (2)
24 unexpected 0.15 flavour 25 final mouth- 0.16 coating
13 grittiness
0.07
Neural (2) sum of errors
Linear Neural (2)
2.78
As an example for the validation, one of the validation cases is shown below. It can be seen that almost all sensory attributes are predicted within the accuracy of the data. Sensory model validation (case 3) firmness on spooning initial firmness chewiness coldness crumbliness inital smoothness I/C quantity in mouth I/C/ size in mouth rate of melt creamy texture thickness final smoothness grittiness powdery vanilla pods creamy flavour sweetness sharp/yogurt fruity vanilla flavour boiled milk other flavour unexpected flavour final mouth-coating mouthdry/astringent
measured predicted 0
*
2
4 6 8 sensory score (st. dev.= 0.1242)
Denotes the number of neurons in the hidden layer.
10
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P.M.M. Bongers
5. Conclusions and future work The process models predicting bulk physical attributes have been augmented by a properties model describing the relations between the physical attribues and the sensory attributes. For each of the sensory attribute the lowest complexity model has been determined. Instead of an trial-and-error approach, a neural network with one hidden layer has been used as a generic non-linear function. The complexity of the neural network can thus be seen as the number of nodes in the hidden layer. The performance of the property function model obtained by the above described procedure has verified with the validation set and the property function model provides a good estimation of the sensory attributes.
References Akaike, H (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control 19 (6): 716–723. Bongers, P.M.M. (2006) A Heat Transfer model of a scraped surface heat exchanger for Ice Cream, Proc. 16th European Symposium on Computer Aided Process Engineering Bongers, P.M.M., I. Campbell (2008) A Heat Transfer Model of an Ice Cream Single Screw Extruder, Proc. 18th European Symposium on Computer Aided Process Engineering Bruin, S. (2004) Lecture notes ‘Product design’, Technical University of Eindhoven, The Netherlands Douglas, J.M. (1988). Conceptual design of chemical process, McGraw Hill, New York. Lennart, L. (1999). System Identification — Theory For the User, 2nd ed, PTR Prentice Hall, Upper Saddle River, N.J. Matlab (2007). User guide, Norgaard, M. (1995). Neural Network based system identification toolbox, for use with MATLAB, Report 95-E-773, Institute of Automation, Technical University of Denmark. Powers, J.J., H.R. Moskowitz (1974). Correlating sensory objective measurements; new methods for answering old problems, Amer. Soc. Testing Materials, Philadelphia. Rumelhart, D.E., G.E. Hinton, R.J. Williams (1986). Learning internal representation by error propagation, Parallel Distributed Processing, MIT Press. Siirola, J.J. (1996). Industrial applications of chemical process synthesis, Advances in Chemical Engineering, 23, J.L. Anderson (Ed.), 1996 Wildmoser, J. (2004), Impact of Low Temperature Extrusion Processing on Disperse Microstructure in Ice Cream Systems, Dissertation ETH no. 15455.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
61
Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model André B. de Haan,a Norbert J.M. Kuipers, b Maartje Steensmac a
Eindhoven University of Technology, Faculty Chemical Engineering and Chemistry, PO Box 513, 5600 MD Eindhoven, The Netherlands b University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands c Akzo Nobel Salt bv,PO Box 10, 7400 AA Deventer, The Netherlands
Abstract Chiral compounds are important products in the pharmaceutical and fine chemical industry. Fractional reactive extraction (FREX) is a promising enantiomer separation method but knowledge on translation into industrial practice is very scarce. In this work the combinations of process and product parameters that generate a specified yield and product purity have been evaluated using a multi-stage equilibrium model. The simulations demonstrated that the influence of changes in process parameters (pH, T, concentrations) can be predicted with the multistage equilibrium model for reactive extraction of phenylglycinol and phenylethylamine. A higher pH, lower temperature, higher concentrations and a higher excess of extractant all result in higher purities. Implementation of reflux results in somewhat higher product purities (or less stages), but a significant loss in capacity. Recovery of product and extractant by backextraction should be carried out by pH shift, preferably with CO2 to prevent salt formation. For separating racemic mixtures with a minimal single stage selectivity of 1.5 a multiproduct extractor should contain 50 stages, evenly distributed over the wash and strip section. Keywords: Multistage modeling, Fractional extraction, Enantiomer
1. Introduction In the pharmaceutical and fine chemical industry, chiral compounds play an important role as intermediates and end products. Most of these products are produced in a multiproduct environment. Fractional reactive extraction (FREX) is a promising alternative to existing enantiomer separation methods. In this technique an enantioselective extractant is employed as separating agent in the fractional extraction scheme that employs a wash stream to remove the less strongly bonded enantiomer from the extract. [1]. So far, (fractional) reactive extraction has been studied by a number of authors for chiral separation of amino acids [2-7] and occasionally for other enantiomer classes [812]. However, knowledge on translation of lab-scale FREX into industrial practice or into a general multi-product design is very scarce. In our previous work, we have established an azophenolic crown ether based solvent system as a versatile, i.e. multiproduct, and highly selective extractant for various amines and amino alcohols [13]. The single-stage extraction equilibria including back-extraction were investigated [14] as well as the kinetics of the complexation reactions [15].
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As a step towards industrial implementation, this work aims to elucidate which combinations of process and product parameters generate a specified yield and product purity in a multistage extractor. To reach this goal, a multi-stage equilibrium model has been constructed based on a single stage description comprising the chemical and physical equilibria of the system. Simulations have been performed to study the effect of process parameters and the consequences for the design of a multi-product extractor. EXTRACT R, C
WASH
aq
org pK
HR+ HS+
pK
H+ + R H+ + S
P
P
R+C S+C
KR
KS
1
RC
FEED R,S
wash section
2
3
SC
strip section
4
RAFFINATE S
SOLVENT C
Figure 1: (left) Single extraction stage: main equilibria between enantiomers ‘R’ and ‘S’ and enantioselective extractant ‘C’; (right) fractional extraction scheme with wash stream (KR > KS).
2. Multi-Stage Equilibrium Model For the previously established azophenolic crown ether extractant a predictive single stage equilibrium model (Figure 1) was constructed and validated [14]. The extent of extraction is characterised by the distribution ratios DR and DS for each enantiomer:
DR =
[ R ]org ,allforms [ R ]aq ,allforms
=
[ R ]org + [ RC ]org +
[ R ]aq + [ HR ]aq
and
DS =
[ S ]org ,allforms [ S ]aq ,allforms
(1)
The operational selectivity αop is defined by the ratio of these distribution ratios. Its upper limit is the intrinsic selectivity αint, which is the ratio of the complexation constants:
α op =
DR DS
(assuming DR > DS)
and
α int =
KR KS
(2)
In fractional extraction equipment, additional degrees of freedom are the solvent-to-feed ratio (S/F), the wash flow (as W/F or W/S), the number of stages and the location of the feed stage. As measure for optical purity of the raffinate and the extract, the enantiomeric excess (e.e.) is used [16]. The e.e. and yield of the enatiomer R in the extract are given as:
e.e. =
[ R] − [ S ] [ R] + [ S ]
yield R , EXTRACT =
total R extract total R feed
[mol ] (3) [mol ]
The concentrations of extractant and enantiomer are characterised by the ‘concentration level’ and the ‘extractant excess’ defined as:
Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model
excess extractant =
63
S ⋅ [C ] solvent F ⋅ [rac] feed
(4)
In the multistage equilibrium model all single stages are connected countercurrently (Figure 1). The multistage model is implemented in gPROMS (PSE Ltd., London, UK). All equilibrium conditions and mass balances are solved simultaneously. To reduce the simulation time, the influence of process conditions is studied at a fixed number of stages of 4 (2 in each section) with the specification to ‘reach equal e.e. in each stream’. This specification is used to ensure that a ‘symmetrical’ separation (equal purity in extract and raffinate) is obtained. In each simulation the wash flow (expressed as W/S or W/F) is adapted to reach the point where the e.e. in the raffinate equals the e.e. in the extract.
3. Results and discussion 3.1. Influence of process parameters Figure 2 and 3 show that for both phenylglycinol (PG) and phenylethylamine (PEA) an increase in extractant excess, an increase in pH, a decrease in temperature or a higher overall concentration level all result in an ‘equal e.e.’ point at a higher e.e. in both streams and at a higher W/F ratio. By each of these changes, the extent of complexation between crown ether and both enantiomers increases (see Figure 1). If the wash stream is not adapted, the yield in the extract increases, but e.e. decreases. Vice-versa, the purity in the raffinate increases, but the yield decreases. If now the wash stream is increased as well, more enantiomer is washed back from the extract, and equal yield and purity are obtained in extract and raffinate. 3.2. Influence of number of stages The influence of pH and concentration level on the W/F ratio and required number of stages that yield a product purity of 0.98 e.e. are presented in Figure 4. It can be seen that lower pH or lower extractant excess results in a lower e.e. in four stages and thus also in a larger stage requirement to reach e.e. = 0.98. 1
PG
20
0.8
30
W/F
0.4
e.e.
W/F
0.6 PEA
0.8
PG
15
PEA
20
1
0.6
PEA
10 PEA
10
PG
0 0
10
20
T [°C]
30
0.2
5
0
0
0.2
PG
7.5
0.4
e.e.
40
8.5
9.5
0 10.5
pH
Figure 2: Influence of temperature (left) and pH (right) on ‘equal e.e.’ points (W/F, e.e.) for separation of PEA (pH=9.4) or PG (pH=9.1); S/F=2 with [rac] =0.01 M and [C]=0.01 M.
64
A.B. de Haan et al. 20
0.9
40
1
30 [C]= 0.01
10 0.8
S/F=1
5
W/F
0.85 e.e.
W/F
15
PG
0.8
PEA
0.6
20 0.4
PEA
10
e.e.
S/F=1
0.2 PG
0
0
0.75 0
2
4
6
8
0
10
0 0.04
0.02 [C] = [rac], M
extractant excess [-]
40
40
30
30
30
20
20
10
10
10
0
0
15 20 10 5 0 8.5
9
9.5
N
W/F
20
40
W/F
25
10
N
Figure 3: Influence of extractant excess on PG separation (left, pH=9.1) and concentration level on equal e.e. points (W, e.e.) for separation of PEA (pH=9.4) or PG (right), S/F=2
0 0
pH
2
4
6
8
10
extractant excess [-]
Figure 4: Influence of pH (left) and extractant excess (right, pH=8.6) on W/F ratio and stage requirement N for PEA separation; e.e.=0.98 in both extract and raffinate, S/F=2, [rac]=0.02 M. 1
2.4
0.88
extract
0.87
0.9 raffinate
0.8
0.86
e.e.
W/F
e.e.
2.2
2 0.85
0.7
1.8 0
0.0005 [R-PG] in wash
0.001
0
0.0005
0.84 0.001
[R-PG] in wash
Figure 5: (left) Effect of reflux of R-PG in wash stream in PG separation on e.e. in extract and raffinate, fixed W/F=2.3, [rac]feed=0.01 M, S/F=2 with [C]=0.01 M (right) influence on location of equal e.e. points: W/F and e.e.
Performance Analysis and Optimization of Enantioselective Fractional Extraction with a Multistage Equilibrium Model
65
3.3. Minimal excess of extractant It was observed in the simulations that if there is no excess of extractant over the enantiomers, a full separation can never be obtained. Under these circumstances, the extractant will eventually become fully loaded, and adding more stages will not increase the product purity any further. Therefore, a minimal excess around 1.5 is required for the conditions and systems studied in this paper.
Wash stream W
3.4. Reflux The effect of reflux (addition of R-PG to wash stream) on e.e.’s in separation of PG is given in Figure 5(left) for a constant wash stream. It can be seen that the purity in the extract increases and the purity in the raffinate decreases. New ‘equal e.e.’ points were determined by adapting the wash stream. They are presented in Figure 5(right). It is concluded that reflux of the strongly bound enantiomer in the wash stream indeed results in a better e.e. (or lower stage requirement) and lower W/F ratio at the operating point. However, for an appreciable effect a rather large concentration of one enantiomer has to be present in the wash stream, so a large fraction of the W2 aq. stream product stream (raffinate 2) needs to be refluxed. Especially with a F high W/F ratio, application of fractional back Feed reflux may be uneconomical. extraction extraction (R,S) Figure 6: Conceptual flow sheet comprising fractional extraction and back-extraction unit with recycle of solvent stream. Assumption: R is preferentially extracted ( KR > KS)
solvent, C clean
solvent, R,C loaded
Raff. 2 R in water
Raff. 1: S in water
6
6
4
4
W2/F
W2/F
N=2 N=2
2
N=3
0
N=3
2 0
5.5
6 pH
6.5
5.5
6
6.5
pH
Figure 7: Back-extraction of PEA (left) and PG (right) by pH shift, aqueous stream W2 (as ratio to feed F) requirement for 99.5 % recovery. Data for N=2 and N=3, loading conditions: 5 °C, S/F=1.5, [C]=[rac]=0.02 M.
3.5. Back-extraction To recover the strongly bound enantiomer product and the extractant, the loaded solvent stream can be treated in a back-extraction unit (Figure 6). A convenient way to achieve back extraction by pH shift without producing salts is the addition of low-pressure CO2 [14]. The model results for back-extraction of PEA (left) and PG (right) by pH shift are
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presented in Figure 7 for 2 and 3 equilibrium stages. It can be seen that the W2/F ratio decreases with decreasing pH and increasing number of stages. W2/F determines the dilution of the product in raffinate 2 compared to the feed meaning that for W2/F<1 (below dotted line), the product concentration has increased compared to the feed.
4. Design considerations in a multi-product environment Conventionally, an extractor is designed to separate a specific compound in the most economical way. However, for multi-product applications the extractor should contain sufficient stages for each component of (future) interest. It was found with the multistage model that if a multi-purpose extractor with 50 stages is built, all systems with αop > 1.5 can be succesfully separated, and with 30 stages, all systems with αop > 2.0. Any ‘excess’ stages for a certain component opens possibilities to increase the capacity or reduce costs in that specific separation. The multistage model can be used as a tool for optimization.
5. Conclusions The availability of the versatile crown ether extractant in combination with the multistage model results in a unique separation tool in a multi-product environment. The influence of changes in process parameters (pH, T, concentrations) can be predicted with the multistage equilibrium model for reactive extraction of phenylglycinol and phenylethylamine. The purity and yield can be improved by each measure that results in a higher extent of complexation; a higher wash flow rate is required then to obtain a good yield and purity in both product streams. Implementation of reflux results in somewhat higher product purities (or less stages) at a slightly smaller W/F ratio, but a significant loss in capacity. Recovery of product and extractant by backextraction should be carried out by pH shift, preferably with CO2 to prevent salt formation.
References [1] T.C. Lo, M.H.I. Baird, C. Hanson, 1983, Handbook of Solvent Extraction. Wiley-Interscience, New York [2] T. Takeuchi, R. Horikawa, T. Tanimura, 1984, Anal. Chem., 56, 1152-1155. [3] H.B. Ding, P.W. Carr, E.W. Cussler, 1992, A.I.Ch.E.J., 38, 1493-1498. [4] Y. Yokouchi, Y. Ohno, K. Nakagomi, T. Tanimura, Y. Kabasawa, 1998, Chromatography, 19, 374-375 [5] H. Tsukube, J. Uenishi, T. Kanatani, H. Itoh, O. Yonemitsu, 1996, Chem. Comm., 4, 477-478. [6] M. Pietrasckiewicz, M. Kozbial, O. Pietraszkiewicz, 1998, J. Membr. Sci., 138, 109-113. [7] P.J. Pickering, J.B. Chaudhuri, 1997, Chem. Eng. Sci., 52, 377-386. [8] Y. Abe, T. Shoji, M. Kobayashi, W. Qing, N. Asai, H. Nishizawa, 1995, Chem. Pharm. Bull., 43, 262-265. [9] Y. Abe, T. Shoji, S. Fukui, M. Sasamoto, H. Nishizawa, 1996, Chem. Pharm. Bull., 44, 15211524. [10] V. Prelog, Z. Stojanac, K. Kovacevic, 1982, Helv. Chim. Acta, 65, 377-384. [11] V. Prelog, S. Mutak, K. Kovacevic, 1983, Helv. Chim. Acta, 66, 2279-2284. [12] V. Prelog, M. Kovacevic, M. Egli, 1989, Angew. Chem. Int. Ed. 28, 1147-1152. [13] M. Steensma, N.J.M. Kuipers, A.B. de Haan, G. Kwant, 2006, Chirality, 18, 314-328. [14] M. Steensma, N.J.M. Kuipers, A.B. de Haan, G. Kwant, 2006, J. Chem. Techn. Biotechn., 81. 588-597. [15] M. Steensma, N.J.M. Kuipers, A.B. de Haan, G. Kwant, 2007, Chem Eng. Sci., 62, 13951407. [16] R.A. Sheldon, Chirotechnology, Industrial synthesis of optically active compounds. Marcel Dekker Inc., 1993.
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Synthesis of Cryogenic Energy Systems Frank Del Nogal, Jin-Kuk Kim, Simon Perry and Robin Smith Centre for Process Integration, The University of Manchester, PO Box 88, Manchester, M60 1QD,United Kingdom
Abstract The use of cold energy should be systematically integrated with process streams in lowtemperature systems for energy savings and sustainable low-carbon society. In this paper, new design methodology for cascaded mixed refrigerant systems with multistage heat exchanges has been proposed, which systematically screens, evaluates and optimizes key decision variables in the design of refrigeration cycles (i.e. economic trade-off, partition temperature, refrigerant compositions, operating conditions, refrigerant flowrate). The integrated design and optimization for overall cryogenic energy systems is also addressed to reflect system interactions between driver selections and design of refrigeration systems. Two case studies are illustrated to demonstrate the advantage using developed design methods. Keywords: Low temperature energy systems, Mixed refrigerants, Power systems, Synthesis, Optimization
1. Provision of low-temperature cooling The provision of cold energy to process industries has gained far less attentions from process engineering community, compared to energy systems which is based on hightemperature energy carrier (e.g. steam), although sub-ambient cooling has a significant potential for energy saving in practice. Effective use of cold energy is vital to ensure the cost-effectiveness of low-temperature processes, as significant power requirement for compression is one of major energy consumptions in the provision of cryogenic cooling to process streams. One of widely-used techniques to save energy requirement in the cryogenic energy systems is to apply a heat integration technique, such that most appropriate levels and duties for refrigeration are determined to match them against GCC (grand composite curve), as shown in Figure 1 (Linnhoff et al., 1982; Linnhoff and Dhole, 1989; Smith 2005). The GCC represents overall characteristics of energy systems, and this provides better understanding how to design the refrigeration cycles. Figure 1 illustrates the cycle in which pure refrigerant is employed as a working fluid, and two levels of cooling for process streams are facilitated by using multiple expansion. If one level of refrigeration is provided, all the cooling duty is provided at Level 2, which results in large compressor shaftpower requirements. The thermodynamic efficiency of the simple cycle can be improved by introducing economizer, vapor cooler and inter-cooler with multi-level expansion (Wu, 2000, Smith 2005). The cascading two simple cycles, in which different refrigerant is used, is a useful way to reduce shaftpower requirements for compressor when large temperature range is to be covered by refrigeration. Another important degree of freedom for energy
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saving in refrigeration system is the decision for how to reject heat to or remove heat from process stream(s). These considerations often lead to have a complex cycle with multi-levels and/or cascaded arrangement, which consists of large number of unit.
T*
Level 1
Q1
Level 1 W
Q2
Level 2 Level 2
Q1
(A)
ΔH
Q2 (B)
Figure 1. Refrigeration with pure refrigerant The use of mixed refrigerants in the cycle can simplify the structure of refrigeration cycle as well as reduce compression duty significantly. As illustrated Figure 2a, the close match between hot (process) stream and cold (refrigeration) stream can be achieved by using mixed refrigerant, while pure refrigerant cannot avoid thermodynamic inefficiency due to large gap existed between two streams. The shape of refrigeration stream in Figure 2a depends on the composition of refrigerants and its operating conditions. When large temperature range is to be cooled by mixed refrigerant systems, cascade arrangement is also possible (Figure 2b). Other structural variations to obtain a better match between hot and cold stream profiles had been suggested, for example, repeated partial condensation and separation of the refrigerant stream (Finn et al., 1999), and a self-cooling mixed refrigerant cycle (Walsh, 1993). T
Process stream T
Process stream Upper cycle
Pinch Point Evaporator (mixed refrigerant)
Partition temperature
Lower cycle Evaporator (pure refrigerant) H
H (A)
(B)
Figure 2. Mixed refrigerant systems In order to explore the advantages from mixed refrigerant systems, it is aimed to develop a systematic design and optimization framework for mixed refrigerant systems, in which design interactions are systematically investigated, as well as all the available structural and operating options are fully screened to provide optimal and economic design. The developed new design method also overcomes shortcomings which had not
Synthesis of Cryogenic Energy Systems
69
been fully addressed in previous works done by Lee (2001) and Vaidyaraman and C. Maranas (2002): i) ii) iii) iv)
enforcement of minimum temperature difference (ΔTmin) throughout the heat recovery systematic trade-off between capital and operating cost multi-stage compression with inter-cooling, and avoiding being trapped in local optima.
2. Optimization of Mixed Refrigerant Systems Mixed refrigerant systems are optimized with the superstructure shown in Figure 3. The superstructure used in this work is arranged with multi-stage heat exchangers in which mixed refrigerant cycle provides not only cooling for a process stream, but also cooling of a hot gas stream. The liquid refrigerant is separated from hot refrigerant stream, and this can be further subcooled in the exchanger before expansion or can be expanded without subcooling. Both cases can be considered within the superstructure proposed in the study. The complexity of the multi-stage arrangement is further increased by introducing cascading of two cycles. The composition of refrigerants and operating conditions for each cycle can be chosen differently, which provides great flexibility in the design as the cooling profile can be closely matched with process stream. The heat recovery is integrated between upper and lower cycles. It should be noted that economic trade-off should be made to justify gains obtained from complex structures at the expense of capital cost.
.....
Process Stream
Figure 3. Superstructure for cascaded mixed refrigerant systems The key optimization variables in the design are: flowrate and composition of mixed refrigerants for each cycle, intermediate temperature between stages for each cycle, and operating pressures of stream after and before compressor for each cycle. The optimization formulation includes: •
Objective function
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• • •
Material and energy balances for each stage Pressure, temperature and enthalpy profiles Multistage compression arrangement with inter-cooling
The developed optimization is solved with genetic algorithm as the previous study based on deterministic optimization techniques showed that it is often trapped in local optima, due to highly non-linear nature of formulations in the model. The simulation model and genetic algorithm is interacted to produce high quality optimal solution(s), although computational time is relatively expensive. It should be mentioned that one of important features in the developed model is to ensure feasibility of heat recovery in every exchanger. The potential candidate (design) produced during optimization, is simulated, and cold and hot composite curves are produced. Then this is rigorously checked against given ΔTmin.
3. Case study 1 First case study is to liquefy gas stream from 25 oC to -163 oC by single mixed refrigerant cycle with a single stage. The energy data for process stream is given in Figure 4. The objective function is to minimize the shaftpower demand for compression. When 5 oC of ΔTmin is considered, the optimal cooling systems with 27.8 MW of minimum power demand are given in Figure 4, in which compositions of refrigerants and operating conditions (flowrate, pressure) are shown as well. The comparison between Lee’s (2001) method and new method is made, which shows 8 % of improvement in power demand from new method. 30 oC
2.81 kmol/s 45.1 bar 1.8 bar
Process Stream
25 oC
-163 oC
N 2 14.5 % C 1 19.5 % C 2 39.3% C 3 0.04% n-C4 26.67 %
Temp ( oC) ΔH (MW) 25 -6 -57.7 -74.6 -96.5 -163
20.2 18.3 14.5 10.2 5.9 0
Figure 4. Case study 1: Optimal design for single mixed refrigerant systems
4. Case study 2: Integrated design for low-temperature energy system with driver selection The second case study is to cool gas stream from 35 oC to -160 oC, and the detailed energy flow is given in Figure 5. In this example, cascade mixed refrigerant systems is optimized with 3 oC of ΔTmin.
Synthesis of Cryogenic Energy Systems
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As low-temperature energy systems employs a series of compressor, the driver selection (i.e. matching between mechanical power demands and available direct drivers) is very important in the overall system design. The design of refrigeration systems (i.e. number of compressor and its duty) inevitably affects the driver selection, and therefore, an integrated design between refrigeration and driver selection should be made. The simultaneous optimization between two design problems are carried out, which provides more realistic and applicable design. (Figure 6) The optimized variables are shown in the Figure 5, at the minimum power demand with 216.06 MW. It should be noted that the design results from an integrated optimization of overall low-temperature energy systems, with the full consideration of driver selections. It is clearly illustrated that the composition and operating conditions per each cycle are optimized to serve for each operating range. One stage for each cycle is chosen in this case, as multi-stage arrangement is not favored, due to large capital expenditure. F = 20.3 kmol/s N2 0.1 % C1 9.8 % C2 41.6 % C3 11.8 % n-C4 37.3 %
37.3 bar 4 bar 35 oC
Process Stream
Temp ( oC) ΔH (MW) 35 4.5 -21.9 -54.0 -80.0 -131.4 -160.0
42.2 bar
212 186 158 120 65 22 0
F = 12.9 kmol/s N 2 11.1 % C 1 40.1 % C 2 35.3 % C 3 13.0 % n-C4 0.5 %
1.9 bar -160 oC
Figure 5. Case study 2: Optimal design for cascade mixed refrigerant systems Genetic Algorithm
Objective function
Set of operating conditions with structural options
Refrigeration simulator Updated power demands
Driver selection
Integrated design
Figure 6. Integrated design for low-temperature energy systems
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5. Summary The developed new synthesis method for mixed refrigeration system provides not only energy saving in cryogenic systems but also conceptual understanding of the design problem in cold energy management. The effective way for providing cold energy is exploited from cascaded multi-stage mixed refrigeration cycles, which can be very effective to reduce compression power in low-temperature systems. Also the integrated design of refrigeration and driver selection is also developed and discussed from the case study.
References A. Finn, G. Johnson and T. Tomlinson (1999) Developments in Natural Gas Liquefaction, Hydrocarbon Processing, 78 (4) G. Lee (2001) Optimal design and analysis of refrigeration systems for low temperature processes, PhD Thesis, UMIST, Department of Process Integration, Manchester, UK B. Linnhoff and V. Dhole (1989) Shaftwork Targeting for Subambient Plants, AIChE Spring Meeting, Houston, US B. Linnhoff, D. Townsend, D. Boland, G. Hewitt, B. Thomas, A. Guy and R. Marsland (1982) User Guide on Process Integration for the Efficient Use of Energy. IChemE: Rugby, England, 1982 R. Smith (2005) Chemical Process Design and Integration, John Wiley & Sons, Ltd., UK S. Vaidyaraman and C. Maranas (2002) Synthesis of Mixed Refrigerant Cascade Cycles, Chemical Engineerng Communications, 189 (8) B. Walsh (1993) Mixed Refrigerant Process Design, Off. Proc. Comb. Conf., 6th Conf. Asia Pac. Confederation. Chemical Engineering, 1, 59/1-64/1 G. Wu (2000) Design and Retrofit of Integrated Refrigeration Systems, PhD Thesis, UMIST, Manchester, UK
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Study of a novel Heat Integrated Hybrid Pervaporation Distillation Process: Simulation and Experiments a b
M.T. Del Pozo Gómez, a P. Ruiz Carreira, a J.-U. Repke, a A. Klein, T. Brinkmann, a G.Wozny,
a
Institute for Process Engineering, Berlin University of Technology, Strasse des 17. Juni 135, Berlin 10623, Germany b GKSS Research Centre GmbH, Department of Process Engineering, Institute of Polymer Research, Max-Planck-Straße 1, Geesthacht D-21502, Germany
Abstract In the present work a new developed heat integrated hybrid pervaporation distillation process is modeled and experimental studies are carried out to analyze the effect of the heat integration in the process. With the results of the experiments, the model is validated and a comparison between industrial scale non heat integrated and heat integrated processes is done. As a result, three main advantages are presented in the approach: a) reduction of the necessary external energy supply into the process, b) improvement in the pervaporation separation performance and c) reduction in the necessary membrane surface. Keywords: heat integration, hybrid process, pervaporation, azeotropic mixtures
1. Introduction The separation of homogeneous azeotropic mixtures has always been a highly energy consuming process in the chemical industry. Many efforts have been done in the last decade to find new and more efficient processes that improve the thermal separation techniques in practice. Between the different studied alternatives outstands the hybridpervaporation distillation process [F. Lipzinski, 1999]. It has been seen in previous studies [P. Kreis, 2004] that this technique can lead to a considerable reduction in the process costs by decreasing the total energy consumption. But despite of these promising results, only the application in the field of organic solvents dehydration has gained a bigger importance in the chemical industry [A. Jonquières, 2001], and the only way to increase its use is with the improvement of the pervaporation technique using a more efficient module design or a better performance membrane. In the present paper, for the bettering of the pervaporation process, the necessary external energy supply will be reduced. The pervaporation process is a separation process, which is based on the selective transport through a dense membrane combined with a phase change of the permeating components from liquid to vapor [F. Lipnizki, 2001]. To make the change of state (liquid – vapor) possible, energy is required. That is normally reflected in a temperature drop between the inlet feed and the outlet retentate streams, what makes the use of external heat exchangers necessary after consecutive pervaporation modules. In previous studies [M. T. Del Pozo Gomez, 2007] it has been found, that the use of the saturated vapor going out at the top of the distillation column as a heating medium inside the pervaporation module (see fig.1) can lead to a lower energy consuming process avoiding the need of external heat exchangers minimizing
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the temperature drop along the module, and increasing the permeate flux. In the present work, the use of the heat integration in the process is studied in detail and experimentally demonstrated. For that aim, a heat exchanger has been built and integrated with a flat sheet membrane module and a model for the whole hybrid process has been built and experimentally validated. Finally, the total energy saving in an industrial scale heat integrated process is calculated.
Figure 1: Hybrid pervaporation distillation process flow sheet. Left with external heat exchangers, right with heat integration.
2. Study of the heat integration concept 2.1. Model of the process For the study of the process, a set of partial differential model equations for a flat sheet pervaporation membrane with an integrated heat exchanger (see fig.2) has been developed. The temperature dependence of the permeability coefficient is defined like an Arrhenius function [S. Sommer, 2003] and our new developed model of the pervaporation process is based on the model proposed by [Wijmans and Baker, 1993] (see equation 1). With this model the effect of the heat integration can be studied under different operating conditions and module geometry and material using a turbulent flow in the feed. The model has been developed in gPROMS® and coupled with the model of the distillation column described by [J.-U Repke, 2006], for the study of the whole hybrid system pervaporation distillation. § EA J p ,i = Qreference,i ⋅ exp¨ i ¨ R ©
§ 1 1 ⋅¨ − ¨T T feed © reference
·· ¸ ¸ ⋅ X i , feed ⋅ γ i , feed ⋅ p i0, feed − p i , permeate ¸¸ ¹¹
(
i Xi
Component in the mixture Mole fraction (mole/mole)
pi0 R Q
Pressure for the pure component (bar) Ideal gas constant (J/ mol K) Permeability (kg/m2 hr bar)
)
(1)
Jp
γi
Permeate flux (kg/m2 hr) Activity coefficient
pi T
Partial pressure (bar) Temperature (K)
Study of a Novel Heat Integrated Hybrid Pervaporation Distillation Process: Simulation and Experiments
75
Figure 2: Flat membrane module with heat integration. Left, whole module structure, right, picture of the heat integration part.
2.2. Experimental work For the model validation and the analysis of the heat integration in the hybrid pervaporation distillation process, a laboratory plant has been built at the TU -Berlin and prepared for the connection with the distillation column (see fig. 3). With this plant experiments with a flat PVA-based (Polyvinylalcohol from GKSS) hydrophilic membrane have been done. A heat exchanger has been built within the pervaporation module. The temperature in the heat exchanger has been necessary to avoid the temperature drop between feed and retentate streams in the pervaporation process. In the process a 2-Propanol/ Water mixture has been separated. The concentration of 2Propanol in the feed is between 80 and 90 % in weight and the temperature range in the experiments was between 70 and 90°C. The feed flow is turbulent and the system fully insulated to avoid heat looses. The pressure in the permeate side has been kept at 30 mbar and the feed pressure at 1.5 bar.
Figure 3: Pervaporation pilot plant in the TU- Berlin. Left process diagram, right pilot plant.
With help of a Freelance ABB process control system, the process was monitored and controlled and important variables of the system were recorded.
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3. Results and discussion 3.1. Membrane characterization and validation of the model After experimental work, the value of the activation energy (EA) and the reference permeability (Qref) for a PVA-based (from GKSS) pervaporation membrane and mixture in use have been obtained (see table1), and the model for the pervaporation process with and without heat integration has been successfully validated. The absolute error between the model and the experimental permeate fluxes is under 8% (see fig.4), and almost insignificant for the water purity in the permeate side (under 0.5%) obtaining a permeate stream with up to 99.9% in water. Table 1. Results of the membrane characterization for a reference temperature of 70°C. EA (J/mol)
Qref (kg/m2 hr bar)
2- Propanol
-69663.2
6.4E-4
Water
-230.73
1.483
Jp (kg/m 2 hr), model
Compound
8 % Absolute error
0.6 0.5 0.4
W ithout heat integration
0.3 0.2 0.1
W ith heat integration
0 0
0.1
0.2
0.3
0.4
0.5
0.6
2
Jp (kg/m hr), experimental Figure 4: Model validation. Permeate flux (Jp) experimental and model results, using a flat PVA based organic module by dehydratation of a 2- Propanol/ Water azeotropic mixture. The temperature was kept between 70 and 90°C and experiments with and without heat integration were done.
3.2. Influence of the heat integration in the pervaporation process Experiments with and without heat integration have been done under the same conditions in order to study the effects of the heat integration in the process. It has been found, that by supplying the energy necessary for the pervaporation, the total permeate flux increased more than 13% (see fig.5) and, if the total energy provided by the condensation of the vapor is supplied, even a higher increase in the permeate flux can be achieved (up to 22%) getting permeate fluxes around 0.36 kg/ m2 hr. The increase in the permeate flux has an important influence into the process, making possible, either the reduction of the necessary membrane area (for a desired product purity), or the increase of the product purity (if the membrane area is kept constant). No need of external heat exchangers between two pervaporation modules is required, and
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all the energy supplied into the pervaporation module can be obtained from the condensation of the distillate stream [A. Klein, 2006].
Jp (kg/m2 hr)
0.35 Experiments with heat integration Model with heat integration
0.33 0.31 0.29
Experiments without heat integration Model without heat integration
0.27 0.25 86.8
87
87.2
87.4
87.6
87.8
88
% wt. 2-Propanol in Feed
Increase in the permeate flux due to the heat integration
Figure 5: Influence of the heat integration in the permeate flux at a feed temperature of 70°C.
3.3. Comparative study of the industrial scale process with and without heat integration With the validated model, and on the basis of the industrial scale operation parameter presented by [S.Sommer, 2004] (see table 2), the configurations with and without heat integration have been compared for an industrial scale process. It has been found that the total energy supply in the process per kg final product can be reduced about 28% and that a higher product purity is obtained (see table 3) due to the heat integration effect. This is reflected not only in the reduction of the energy consumption, but also in a smaller necessary membrane area, if the desired purity of the product is constant. Table 2. Operation conditions of the industrial scale simulation processes. Pressure in the column
1.015 bar
Number of stages in the column
8
Feed wt% 2- Propanol in the column Feed wt% Water in the column
Feed flow rate in the column
1875 kg/hr
80
Bottom wt% Water in the column Membrane Area
99.8 125 m2
20
Permeate pressure
20 mbar
Table 3. Comparison between the energy conssumption in the two processes lay -out. [kW] Reboiler
[kW] External
[kW] Condenser
[kg/hr] product
[kJ/kg product]
With heat integration
509.87
46 (compressor)
311.63
1490.59 (90.6% wt. 2-Propanol)
2095.14
Without heat integration
525
170 (membrane feed reheating)
520
1500 (90% wt. 2Propanol)
2916
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4. Conclusions In the present paper, the influence of the novel heat integration concept has been successfully demonstrated and studied in detail. For that purpose, a heat exchanger has been built including a flat membrane module. A new model describing the heat integrated process has been developed in gPROMS® and experimentally validated. It has been proven that an important effect of the heat supply is the increase in the total permeate flux up to 22%. That will be directly reflected in higher product purity for a constant membrane area or in a smaller membrane surface requirement if the desired product purity is fixed, having a more profitable process. The concentration of water in the permeate side has been within the desired values (over 99.9%) and the model predictions of the separation process for the azeotropic mixture 2-Propanol/Water are adequate. The comparison of the industrial system with and without heat integration has been done. As a result, in the case with heat integration the total energy supply in the process can be reduced about 28% and the product purity can increase. In the presentation, the results of the model and experiments and the comparison of the process with and without heat integration will be shown in further detail and the advantages of the new heat integration concept will be proven.
5. Acknowledgements The authors would like to thank EFRE (request number 10134788) for sponsoring this project, and PolyAN GmbH for the cooperation in the present research work.
References M.T. Del Pozo Gómez, A. Klein, J.-U. Repke, G. Wozny, 2007, Study and Design of a Heatintegrated Hybrid Pervaporation-Distillation Process, ECCE-6 1357 Distillation, Absorption & Extraction. A. Klein, J.-U. Repke, M. T. Del Pozo Gómez, G.Wozny, 2006, Hybrid -PervaporationDistillation processes – a novel heat-integration approach, AJChE 409 Separation Design. J.-U. Repke, F. Forner, A Klein, 2006, Separation of Homogeneous Azeotropic Mixtures by Pressure Swing Distillation – Analysis of the Operation Performance, Chem. Eng. Techn., vol. 28, 1151-1557. S. Sommer, T. Melin, 2004, Design and Optimization of Hybrid Separation Processes for the Dehydration of 2-Propanol and Other Organics, Ind. Eng. Chem., vol. 43, 5248-5259. P. Kreis, 2004, Prozessanalyse hybrider Trennverfahren, Dissertation, Dortmund, Germany. S. Sommer, 2003, Pervaporation and vapour permeation with Microporous Inorganic Membranes, PhD Thesis, RWTH Aachen, Germany. J. Lipzinski, G. Trägardh, 2001, Modelling of Pervaporation, Models to analyze and predict the mass transfer transport in Pervaporation, Separation and Purification Methods, vol. 30(1), 4925. A. Jonquières, R. Clément, P. Lochon, J. Néel, M. Dresch, B. Chrétien, 2001, Industrial state-ofthe-art of pervaporation and vapour permeation in the western countries, Journal of Membrane Science, vol. 206, 87 -117. F. Lipzinski, R.W. Field and P.-K. Ten, 1999, Pervaporation-based hybrid process: a review of process design, applications and economics, Journal of Membrane Science vol. 153, 183 – 10. J.G. Wijmans, R.W. Baker, 1993, A simple predictive treatment of the permeation process in pervaporation, Journal of Membrane Science, vol. 79, 101-113.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
A Novel Network-based Continuous-time Formulation for Process Scheduling Diego M. Giménez,a Gabriela P. Henning,a Christos T. Maraveliasb a
INTEC (Universidad Nacional del Litoral - CONICET), Güemes 3450, S3000GLN Santa Fe, Argentina b Department of Chemical and Biological Engineering, University of Wisconsin – Madison, USA
Abstract We present a novel network-based continuous-time formulation for process scheduling that addresses multiple limitations of existing approaches. Specifically, it handles nonsimultaneous transfers of input/output materials to/from processing units; it employs a more flexible time representation; and it explicitly accounts for unit connectivity. This is accomplished via the modelling of two key issues: (i) the state of a processing/storage unit, and (ii) the material transfer between processing and storage units. The proposed formulation allows us to model many complexities associated with process scheduling and obtain solutions to problems that cannot be addressed by existing methods. Keywords: process scheduling; network-based continuous-time formulation.
1. Introduction Existing network-based scheduling formulations are based on the state-task network (STN) or the resource-task network (RTN) representation (Kondili et al., 1994; Pantelides, 1994). In these formulations it is implicitly assumed that: a) material transfer between units is always possible, i.e. all processing units are connected to all the vessels that are used for the storage of the corresponding input and output materials; b) all input/output materials of a task are transferred simultaneously to/from the processing unit when the task starts/ends; and c) stable output materials can be temporarily stored in a processing unit after a task is completed, but stable input materials cannot be temporarily stored before a task starts, i.e. in continuous time representations the beginning of a task must coincide with a time point and at such point all the materials should be available. However, these assumptions do not always hold. For example, in recovery and purification processes the solvent can be drained earlier. Similarly, in certain chemical reactions reactants are fed before the beginning of the task, which actually occurs when the catalyst is added. Interestingly, despite the large number of methods recently proposed to tackle process scheduling, there are very few attempts to address these limitations. Barbosa-Póvoa and Macchietto (1994) discuss the issue of connectivity and material transfer in the context of discrete-time formulations. However, to our knowledge none of the existing methods deals with the shortcomings due to assumption (c). The goal of this paper is the development of a novel approach that overcomes these shortcomings. The key ideas of the proposed method are presented in section 2. The main variables and constraints of the mixed-integer linear programming (MILP) formulation are presented in section 3. The advantages of the new method are illustrated through a small example problem in section 4.
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2. Proposed Approach 2.1. Time Representation We introduce a new global continuous-time representation: a set of global time points kK={1, 2, …K} span the scheduling horizon from 0 to H delimiting a set of K-1 time intervals of unknown length, where interval k starts at time point k and ends at k+1. The novelty of this new representation is that tasks do not have to start (or finish) exactly at a time point. In other words, a task assigned to start on a unit at time point k can actually start any time within interval k (late beginning) as Fig. 1a shows. Similarly, a task that is assigned to end at time point k can actually end at any time within interval k-1 (early end). Thus, the new representation can potentially lead to formulations with fewer time points. 2.2. Process States Unlike previous network-based models, a processing unit can be used both for carrying out process tasks or storing input/output materials before/after the start/end of a task. Furthermore, input/output materials do not have to be simultaneously transferred to/from a unit. Hence, a unit jJ can be in three different states during time interval k (Fig. 1b): a) idle state (Wj,k=1); b) storage state; and c) execution state (Ej,k=1). If used for storage, then it can either be used for input (SIj,k=1) or output (SOj,k=1) materials. The execution state is delimited by the formal task boundaries, which are given by the values of the event variables associated with task beginning and end. If a task iIj is assigned to start in unit j within interval k (at or after time point k) then Xi,j,k=1, where Ij is the set of tasks that can be carried out in unit j. If a task is assigned to end within interval k-1 (at or before time point k) then Yi,j,k=1. In addition, an auxiliary variable indicates when a task started before time point k is still being processed in unit j at such time (Zj,k=1). 2.3. Time Balances To accurately account for a late beginning or early end of a task in unit j after and before time point k, respectively, we introduce two new variables: a) T j LB , k that denotes the lateness within interval k in starting a task, and b) T j EE , k that denotes the earliness within interval k-1 in finishing a task. We also introduce variables to model the time a S processing unit remains idle ( T j ID , k ) or is used for storage T j , k , during interval k (Fig. 1c). Early end within [Tk’-2, Tk’-1] Output
Late beginning within Input [Tk+1,Tk+2] Task T: A + B o C + D storage
Idle
storage
Task T Tk-1
Tk
Tk+1
Tk+2
Tk’-2
Tk’-1
Tk’
(a) Proposed time representation W j ,k 1 1 S
I j ,k
O j , k ' 1
1 E j ,k 1 1 E j ,k 2 1 X T , j ,k 1 1 Z j ,k 2 1
Z j ,k' 2
E j ,k '2 1 S 1 Y j ,k' 1 1
1
Task T Tk-1
Tk
Tk+1
Tk+2
Tk’-2
Tk’-1
Tk’
(b) States of processing units T j ST ,k
T j ID , k 1
T
T
LB j , k 1
Processing Time
EE j ,k ' 1
T j ST , k ' 1
Task T Tk-1
Tk
Transfer of A at Tk
Tk+1 Transfer of B at Tk+1 B
A
Tk+2
Tk’-2
Tk’-1
Tk’
(c) Time balances Consumption of A & B by task T
Production of C & D by task T
Transfer of Transfer C at Tk’-1 of D at Tk’ D
C
Task T Tk-1
Tk
Tk+1
Tk+2
Tk’-2
(d) Material transfer
Figure 1. Key concepts of the proposed formulation
Tk’-1
Tk’
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2.4. Material Transfer and Material Balances Material transfer is formulated explicitly via flow variables. In the context of this contribution, the concept of flow represents an instantaneous transfer of material from a storage/processing unit to another physically connected storage/processing unit. Only one material can be stored in a storage unit vV in any time interval, but multiple input/output materials can be simultaneously stored in a processing unit before/after a task starts/ends. Material balance constraints in storage units include only incoming and outgoing flows. The corresponding balances in processing units include the incoming and outgoing flows as well as production and consumption terms that correspond to the transformation of materials by process tasks (Fig. 1d).
3. Mathematical Formulation In addition to the event ( X ijk ,Yijk ), state ( W jk , E jk , S Ijk , S Ojk ) and auxiliary ( Z jk ) binary variables, time corresponding to point k (Tk), and timing variables ( T jkLB , T jkEE , T jkID , T jkST ), the following continuous variables are defined: VV VU x Flows FmUV, j , v , k , FmUU , j , j ', k , Fm , v , v ', k , Fm , v , j , k to represent instantaneous transfers of material m at time point k between storage vessels (V) and processing units (U), where the letter sequence in the superscript denotes the direction of the transfer. x Batch-sizes BiS, j , k , BiP, j , k , BiF, j , k to denote the total amount of task i that starts to be processed, that keeps processing and finishes, respectively, in unit j at time point k. x Inventory I mV , v , k of material m in storage vessel v during time interval k, and inventory I mUI, j , k / I mUO, j , k of input/output material m in processing unit j during time interval k. To facilitate the presentation, in the remaining we use capital letters for variables, small letters for parameters (with the exception of horizon H) and bold capital letters for sets. 3.1. State Constraints Clearly, a processing unit has to be in exactly one state during each time interval:
E j ,k W j ,k S Ij ,k S Oj ,k
1, j ,k K
(1)
A unit is in the execution state during interval k if a task starts within such interval, i.e. at or after point k, or another task started in a previous interval is still being executed:
E j,k
Z j , k ¦ X i , j , k , j , k K
(2)
i I j
Finally, the Zj,k auxiliary variable (denoting that at time point k unit j continues executing a task previously started) can be defined as follows:
Z j ,k
Z j ,k 1 ¦ X i , j ,k 1 ¦ Yi , j ,k iI j
j, k ! 1
(3)
iI j
3.2. Timing Constraints A late beginning (early end) with respect to time point k can only occur if a task is assigned to start (end) in unit j at such time point, as the following inequalities indicate:
T j LB ,k d H
¦X
i, j,k
i I j , iI cZW
, j , k K ;
T j EE ,k d H
¦Y
i, j ,k i I j , i I pZW
, j , k ! 1
(4)
where IcZW/IpZW are the sets of tasks consuming/producing unstable materials for which late beginnings and early ends are forbidden. Similarly, storage and idle times occur only if the unit is in the corresponding state:
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T j ID j , k K , k d HW j , k ,
I O T j ST j , k K ; , k d H ( S j , k S j , k ),
(5)
In that case, the idle and storage times should be equal to the length of the time interval: ID Tk 1 Tk H (1 S Ij ,k S Oj ,k W j ,k ) d T j ST , k T j , k d Tk 1 Tk
j, k K
(6)
3.3. Time Balance Constraints Constraints (7)-(9) are used to define the continuous-time grid and enforce the appropriate timing constraints without resorting to big-M terms: LB ST ID Tk t ¦¦ (aijYi , j ,k ' bij BiF, j ,k ' ) ¦ T j EE j, k ! 1 ,k ' ¦ (T j ,k ' T j ,k ' T j ,k ' ), k 'dk iI j
k 'dk
(7)
k 'k
¦¦ (a
LB ST ID X i , j ,k ' bij BiS, j ,k ' ) ¦ T j EE j, k K (8) ,k ' ¦ (T j ,k ' T j ,k ' T j ,k ' ) d H Tk ,
¦ (T
ID ST F T j EE , k T j , k T j , k ) ¦¦ ( aijYi , j , k bij Bi , j , k )
ij
k 'tk iI j
k
LB j,k
k '!k
k 'tk
H , j
(9)
i I j k
where aij and bij are the fixed and proportional processing time constants. 3.4. Batching constraints Batch-size variables are constrained as follows:
E jMIN X i , j ,k d BiS, j ,k d E jMAX X i , j ,k , i I , j J i ,k K
(10)
BiF, j ,k d E jMAX Yi , j ,k , i I ; j J i ,k ! 1
(11)
BiS, j ,k BiP, j ,k
(12)
where
ȕjMIN/ȕjMAX
BiP, j ,k 1 BiF, j ,k 1 , i , j J i ,k K is the minimum/maximum capacity of unit j.
3.5. Material Balances 3.5.1. Storage Vessels The material balance constraint in storage vessels is expressed as follows:
I mV , v , k
I mV , v , k 1
¦F
VU m,v, j ,k
jJ v
¦F
VV m , v , v ', k
v 'V v
¦F
UV m, j ,v, k
j J v
¦F
VV m , v ', v , k
,
v 'V v
(13)
m ( M NIS M ZW ), v Vm , k where Jv/Vv are the sets of units/vessels connected to vessel v, MNIS/MZW are the sets of tasks for which non-intermediate storage/zero-wait storage policies are enforced, and Vm is the set of vessels that can be used to store up material m. The inventory is constrained not to exceed the maximum storage capacity 9m,vMAX by expression (14).
I mV , v , k d 9 mMAX m ( M NIS M ZW ), v Vm , k ,v ,
(14)
3.5.2. Processing Units The corresponding material balances in processing units for input and output materials are expressed via equations (15) and (16), respectively:
I mUI, j ,k
I mUI, j ,k
¦F
VU m ,v , j , k
vVi Vm
¦F
UU m , j ', j , k
j 'J j
¦J
C iI j I m
im
BiS, j ,k , m, j , k
(15)
A Novel Network-Based Continuous-time Formulation for Process Scheduling
I mUO, j ,k
I mUO, j ,k
¦J
iI j I mP
im
BiF, j ,k
¦F
PS m , j ,v , k
vV j Vm
¦F
PP m , j ', j , k
, m, j , k
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(16)
j 'J j
where ImC/ImP are the sets of tasks consuming/producing material m, Jj/Vj are the sets of units/vessels connected to unit j, and Ȗim is the stoichiometric coefficient of material m in task i (negative if consumed). Note that inventory level changes in processing units are due to material transfer as well as material consumption and production by processing tasks. Obviously, input/output materials can only be stored in a processing unit if the unit is in the corresponding state:
¦I
UI m, j , k
d E jMAX S Ij , k ,
j , k K ;
m
¦I
UO m , j ,k
d E jMAX S Oj ,k , j , k K
(17)
m
3.6. Utility Constraints The total amount Rr,k of utility r consumed at time interval k is calculated through equation (18), and constrained not to exceed the maximum availability ȡrMAX by (19):
Rr , k
Rr , k 1 ¦ ¦ [ f ijr ( X i , j , k Yi , j , k ) gijr ( BiS, j , k BiF, j , k )], r , k K (18) i I r jJ i
Rr ,k d U rMAX , r , k K
(19)
where Ir is the set of tasks requiring utility r, and fijr and gijr are the fixed and proportional, respectively, constants for the consumption of utility r by task i in unit j. 3.7. Objective function The proposed model consists of expressions (1)–(19) and can be used to tackle various objective functions. In this short communication the profit maximization is studied:
z
max
¦ ¦S
mM FP vVm
V m m ,v , K
I
(20)
where ʌm is the price of material m and MFP is the set of products that can be sold.
4. Example A scheduling problem corresponding to a simple multipurpose batch plant is studied in order to show the main advantages of the proposed formulation. The process structure, task information and material data are described in Fig. 2. The profit maximization for a time horizon of 8 hours (H=8) is pursued. The problem instance was solved with the aim of getting an optimal schedule in a case where existing models cannot even obtain a feasible solution. In this example it is easy to note that, since no intermediate initial inventory is held, the only way to obtain final products is by performing task T2 first (so INT1 and INT2 can be available), then executing T1 (so INT3 can be available), and finally either T3 or T4. Nevertheless, since a NIS policy is adopted for INT2, T4 should begin immediately after task T2 finishes. However, this is infeasible for current approaches because INT3 cannot be available at that time (INT3 is produced by T1, which cannot start until T2 finishes since it consumes INT1). The proposed formulation overcomes this limitation by allowing a temporal storage of INT2 in unit R-103 until INT3 becomes available. Thus, the material load/discharge is decoupled from the task beginning/end.
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Elements
Tasks Stoichiometric Relations
Processing Units: R-101, R-102, R-103 Tasks: T1, T2, T3, T4 Vessels: V-101, V-102, V-103, V-104, V-105, V-106 Materials: RM1, RM2, INT1, INT2, INT3, P1, P2 Utilities: Hot Steam (HS), Cooling Water (CW)
T1 T2 T3 T4
Material Data m ʌm ($/kg) v
Plant Topology 9 mMAX ,v
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RM1 RM2 INT1 INT2 INT3 P1 P2
UIS UIS FIS (200) NIS FIS (500) UIS UIS
1000 1000 0 0 0 0 0
0 0 0 0 0 30 40
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0.8 RM1 + 0.2 INT1 o INT3 RM2 o 0.3 INT1 + 0.7 INT2 INT3 o P1 0.6 INT2 + 0.4 INT3 o P2
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Task Information i
j
aij (h)
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r
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T1
R-101 R-102 R-101 R-102 R-103 R-103
0.5 0.5 0.75 0.75 0.25 0.5
0.025 0.04 0.0375 0.06 0.0125 0.025
40 25 40 25 40 40
HS HS CW CW HS CW
6 4 4 3 8 4
T2 T3 T4
80 50 80 50 80 80
0.25 0.25 0.3 0.3 0.2 0.5
(kg/min)
30 30 30 30 30 30
Figure 2. Example of a very simple multipurpose facility
Figure 3 presents the optimal schedule obtained by implementing the proposed MILP model in GAMS/CPLEX 10.0 on a Pentium IV (3.0 GHz) PC with 2 GB of RAM, adopting a zero integrality gap. It can be seen that six global time points (five time intervals) were required to obtain this optimal solution. The model instance involved 87 binary variables, 655 continuous ones, and 646 constraints. An optimal solution of $3592.2 was found in only 0.87 s by exploring 282 nodes. Units
T2
T1
T3
T4 INT3 (16.00) from V-104 T4 (46.67)
INT2 (28.00)
R-103
T5 T6 INT3 (5.33) from V-104 T4 (40.00) T3 (66.66)
INT2 (24.00) R-102
T2 (34.29) INT2 (28.00) T2 (40.00) INT1 (4.00) to V-103
R-101
2
INT3(61.33)
INT1 (10.29) INT3 (18.67) T1 (40.00) T1 (61.33) INT3 (21.33) INT1 (8.00) to V-104 INT1 (1.98) from V-103
2.250
0
INT2 (24.00)
3.750
5.417
4
Time (h)
6.917
6
Figure 3. Optimal schedule for the motivating example
References A. P. Barbosa-Póvoa and S. Macchietto, 1994, Detailed design of multipurpose batch plants, Comp. Chem. Eng., 18, 11/12, 1013-1042. E. Kondili, C. C. Pantelides, and W. H. Sargent, 1993, A general algorithm for short-term scheduling of batch operations-I. MILP formulation, Comp. Chem. Eng., 17, 2, 211-227. C. C. Pantelides, 1994, Unified frameworks for optimal process planning and scheduling. In: Foundations of computer-aided process operations, New York, 253-274.
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Excipient Interaction Prediction: application of the Purdue Ontology for Pharmaceutical Engineering (POPE) Leaelaf Hailemariama, Pradeep Suresha, Venkata Pavan Kumar Akkisettya, Girish Joglekarb, Shuo-Huan Hsub, Ankur Jaine, Kenneth Morrisc, Gintaras Reklaitisa, Prabir Basud and Venkat Venkatasubramaniana1 a
School of Chemical Engineering, Purdue University, West Lafayette IN 47907 USA Discovery Park, Purdue University, West Lafayette, IN 47907 USA c Department of Industrial and Physical Pharmacy, Purdue University, 585 Purdue Mall, West Lafayette, IN 47907 USA d National Institute for Pharmaceutical Technology and Education, Purdue University, 315 Hovde Hall, 610 Purdue Mall, West Lafayette, IN 47907 USA e Enterprise Optimization, United Airlines, Chicago, IL 60007 USA b
Abstract A drug product consists of a drug substance and one or more excipients that play specific roles in rendering desired properties to that product, from improvement of flow to control of the release of the drug substance. Inter-excipient and drug substanceexcipient chemical reactions are to be avoided and formulators often use heuristics and past experience to avoid potential interactions during drug product development. Multiple tools are present to mechanistically predict chemical reactions: however their utility is limited due to the complexity of the domain and the need for explicit information. In this work, the Purdue Ontology for Pharmaceutical Engineering (POPE) was used to develop an excipient reaction prediction application that made use of structural, material and environmental information to predict reactions Keywords: Excipient Interaction, Product Development, Ontology, Rule Language
1. Introduction A drug product includes the drug substance along with compounds that enhance processing and effectiveness, called excipients, which perform such functions as improvement of flow or increase of tablet mass. The drug product is expected to be chemically stable to avoid formation of toxic compounds and loss of the drug substance: however reactions between the drug substance and excipients and amongst the excipients are possible. These interactions may be avoided by careful design based on experience, rigorous experimentation or using software packages to predict reactions. These packages include mechanistic tools and knowledge-based reaction prediction tools. Mechanistic tools that have been developed to predict reactions include the CAChe WorkSystem (see URL) and SPARTAN (see URL). Knowledge-based systems include reaction predictors like ROBIA (Reaction Outcomes By Informatics Analysis) 1
Corresponding author:
[email protected]
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(Socorro et al, 2005) and the LHASA (Logic and Heuristics Applied to Synthetic Analysis) software (see URL). However, the current solutions to chemical reaction prediction have several limitations. Secondary and tertiary interactions are rarely considered and there is little work on chemistry reasoning which is valuable for chemical stability analysis but would require an explicit information model. In addition, there is little scope for integration of the reaction information (which might describe conditions in microsolutions found between solid particles) with the solid information. In this work a prototypical reaction prediction system which makes use of known reaction information, the molecular structure of reactants and structural and environmental information, like the backbone of the molecule and the reaction pH, is presented. First the POPE ontology, which includes descriptions of the material, chemical reaction and structure descriptors, is briefly presented. The next section is dedicated to the description of the prototype reaction prediction system, followed by application examples. The last section discusses other potential applications of the ontological approach and future work.
2. Introduction to the Purdue Ontology for Pharmaceutical Engineering Several options exist for the explicit representation of information. XML (eXtensible Markup Language: see URL) is one. XML does not have a fixed set of tags but allows users to define tags of their own, much like the English language versus Chemistry or Biology. An example of XML Schema (glossary) examples is the Chemistry Markup Language (CML: see URL) for molecule information. XML does not provide any means of defining the semantics (meaning) of the information. The needs for explicit expression and capture of semantics are met by ontologies, which are defined as follows: “An ontology defines the basic terms and relations comprising the vocabulary of a topic area as well as the rules of combining terms and relations to define extensions to the vocabulary.” (Gomez-Perez et al., 2004). For the pharmaceutical domain, the ‘basic terms’ could be a ‘material’ and a ‘material property’ and their relations could be ‘<material> has <material property>’. An example of a simple ontology is shown in Figure 1. Figure 1: An ontology example The powder flow rate (a material property) of the API (a material) has an average value of 1 g/s within the range of [0.8, 1.2]. The source of the reported value was the experiment ‘API: Flow Measurement’ at a given context (78% relative humidity) The collection of the different concepts e.g. material, material property etc and their relation e.g. has Value, comprise an ontology. The Purdue Ontology for Pharmaceutical Engineering (POPE) was developed to address the information modeling needs mentioned previously. POPE includes several smaller interrelated ontologies; the Purdue Ontology for Material Entities (POME)
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which describes materials; the Purdue Ontology for Degradant Structures (PODS) which describes the chemical structure of materials with respect to molecular fragments; the Purdue Ontology for Reaction Expression (PORE) which describes the interactions between materials including chemical reactions; the Purdue Ontology for Material Properties (POMP) which describes the physical, chemical and mechanical properties of materials and the Purdue Ontology for Description of Experiments (PODE). 2.1. Material Ontology (POME) There had been some work done to describe materials in an explicit manner including the Standard for the Exchange of Product Data STEP (ISO 10303) and OntoCAPE, which included descriptions of phases, chemical components and reactions (Yang and Marquardt, 2004). However, in the data models above, experiments and solid properties get little treatment. POME builds on the concepts defined by OntoCAPE and includes solid and pharmaceutical properties. The material is described in terms of its substance entity (environment independent) and its phase system entity (environment dependent: solid, liquid, vapor, mixtures) and its role in a mixture (e.g. for solids: flow aid, dilunt etc). The phase system would be described by the fraction and identity of the phases comprising it (phase composition). Each phase would have a chemical composition, which describes the species and their relative abundance in the given phase as well as the environmental conditions e.g. temperature, pressure. For instance, the antibiotic Seromycin ® is manufactured as a tablet which may include several components like Cycloserine and Magnesium Stearate. The tablet is a solid mixture; the phase composition including phase, substance and amount information (e.g. Cycloserine: Solid: 83% m/m) and the role of Cycloserine being an Active Pharmaceutical Ingredient (API). The chemical composition describes a pure component. The substance aspect includes molecular structure information e.g. as a SMILES string (NC1CONC1=O). 2.2. Degradant Ontology (PODS) Previous work on representation of chemical structures includes the EcoCyc Ontology (http://ecocyc.org/) for metabolites and the Chemical Markup Language (CML) among others. Ontologies developed to describe molecules include those by Feldman et al (2005) and Villanueva-Rosales and Dumontier (2007). PODS builds on the above for the pharmaceutical domain by making use of common molecular fragments (shown in Figure 2). Each fragment is part of a ‘fragment-entity’ which might participate in a reaction and is connected to (or identified as) a backbone group. For Cycloserine, the fragment entities include a five- member ring, two amine groups and a carbonyl group. PODS can be coupled with the PORE to represent chemical systems and with POME to describe a material during product development. 2.3. Reaction Ontology (PORE) The concept of a reaction may include physical and chemical changes. Some work had been done previously to model chemical reactions including the EROS (Elaboration of Reactions for Organic Synthesis) system (Gasteiger et al, 2000) and work by Sankar and Aghila (2006). PORE was developed to represent reactions as interactions between functional groups/phase systems. Each reaction would have a reaction_context, which describes the pertinent descriptors of the reaction e.g. at what temperature it occurs, at
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what pressure, pH etc. For instance, the context for Cycloserine hydrolysis captures the temperature (600C), pH range (1-7) and phase (liquid). Several restrictions such as the requirement of at least one reactant and one product for a reaction were put in place. 2.4. Property Ontology (POMP) Previous work on explicit modeling of material properties includes CAPEC (Sousa et al, 1999) and OntoCAPE (Yang and Marquardt, 2004). POMP extends the properties in OntoCAPE to include interproperty relations and solid material properties. The property structure includes generic properties like heat, mass and momentum transfer properties (e.g. heat capacity, diffusivity and density respectively) as well as a separate description for solid properties. Solid properties were described at three levels; substance properties (pertaining to the molecular level e.g. molecular structure), particle properties (pertaining to single crystals or amorphous particles e.g. unit cell dimensions) and powder (bulk) properties (e.g. particle size distribution). Each property value would be correlated to a set of environmental conditions during measurement (e.g. temperature, pressure) and a source (experiment, mathematical model or literature). 2.5. Experiment Ontology (PODE) Noy and Hafner (2000) developed a representation of molecular biology experiments using ontologies. Hughes et al (2004) developed a laboratory ontology which captured the relationship between materials and processes through a hierarchy of actions. PODE links experiments to material properties. Experiments have some generic characteristics which include the time and place of the experiment as well as the experimenters. Equipment and experimental procedures were modeled as a collection of actions, which could be observation /measurement actions, processing actions or operation actions. For instance the measurement of Cycloserine bulk density involves a specific experimental procedure (put powder on top of sieve: (processing action); turn on sieve (operation action); observe powder volume (observation step)).
3. Prediction of reactions between drug product components POPE had previously been used to support a decision support system for pharmaceutical product development and modeling of solid unit operations (Venkatasubramanian et al, 2006). In this application, reactions between the drug substance and the excipients are predicted through the following steps. A survey of the drug degradation domain was made and a set of common molecular fragments are collected as in Figure 2. Once the chemical structure of the new drug substance is known, the active fragments are sought through the Chemistry Development Kit (CDK) tools. Figure 2: List of molecular fragments
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Reactions involving the identified active fragments are sought from among the reaction ontology instances which describe the participant active fragments. For user input including the molecular structure (described by PODS) and reaction conditions, the relevant reactions are returned. The reaction conditions would include the environment (temperature, pressure, pH: captured by PORE), phase information (described by POME and POMP) and reported experiment procedure (captured by PODE). The ontology was coded using OWL (Web Ontology Language) using the Protégé 3.3 interface. Search was performed using the Semantic Web Rule Language (SWRL) plugin of Protégé. The reaction database is populated from free online databases from SigmaAldrich® and Metasynthesis®. A schematic representation is shown in Figure 3.
Figure 3: Reaction prediction system (a) overall scheme (b) SWRL input The system was used to predict reactions for several drug compounds. For instance, the system correctly predicted the hydrolysis, oxidation and isomerization of Cycloserine based on the compound’s similarity to γ-Butyrolactone hydrolysis, Imipramine hydrochloride oxidation and Pilocarpine epimerization. Knowledge of the possibility of Cycloserine oxidation may exclude the use of Crospovidone, which has hydrogen peroxide, a strong oxidizing agent, as a common impurity. Capturing multiple types of information, possible through the ontological approach, is useful for interaction prediction in pharmaceutical product development.
4. Summary The Purdue Ontology for Pharmaceutical Engineering (POPE) was developed with its component ontologies for descriptions of materials, chemical structures, reactions, material properties and experiments. Based on POPE an excipient interaction prediction/diagnosis application which made use of structural and environmental information was presented. There are several challenges in the horizon, which include the consideration of rates of reaction to determine relevance and evaluation of multiple measures of molecular similarity.
Acknowledgements The work was done through the financial support of the Engineering Research Center for Structured Organic Particulate Systems (ERC-SOPS), the Indiana 21st Century Fund and Eli Lilly and Company. The authors thank Balachandra Krishnamurthy and researchers at Lilly Research Laboratories (Henry Havel, Brian Good, Gus Hartauer, Steve Baertschi, Ahmad Almaya, Aktham Aburub, and David Long) for their support.
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References S. Baertschi (2005) Pharmaceutical Stress Testing: Predicting Drug Degradation in Drugs and the Pharmaceutical Sciences, Vol. 153, Taylor and Francis Group, Boca Raton FL. Cache: http://www.cache.fujitsu.com/ CML: http://www.xml-cml.org H. J. Feldman, M. Dumontier, S. Ling,., N Haider, C.W.V. Hogue (2005) CO: A Chemical Ontology for Identification of Functional Groups and Semantic Comparison of Small Molecules, FEBS Letters, 579, 4685-4691. J. Gasteiger, M. Pförtner, M. Sitzmann, R. Höllering, O. Sacher, T. Kostka, N. Karg (2000) Computer-assisted synthesis and reaction planning in combinatorial chemistry, Perspectives in Drug Discovery and Design, 20, 245–264. A. Gomez-Perez., M. Fernandez-Lopez, O. Corcho. (2004) Ontological Engineering: with examples from the areas of knowledge management, e-Commerce and the Semantic Web. Springer-Verlag London. G. Hughes, H. Mills, D. de Roure, J. Frey, L. Moreau, M.C. Schraefel, G. Smith, E. Zaluska (2004) The semantic smart laboratory: a system for supporting the chemical eScientist, Organic and Biomolecular Chemistry, 2, 1-10. LHASA: http://www.lhasalimited.org N. Noy, C. Hafner (2000) Ontological foundations for experimental science knowledge bases, Applied Artificial Intelligence, 14, 565-618. N. Pandit (2007) Introduction to the pharmaceutical sciences Lippincott, Williams and Wilkins, Baltimore, MD. P. Sankar, G.J. Aghila (2006) Design and development of chemical ontologies for reaction representation, Journal of Chemical Information and Modeling, 46, 6, 2355-2368. I.M. Socorro, K. Taylor and J.M. Goodman (2005) ROBIA: A Reaction Prediction Program, Organic Letters, 7, 16, 3541-3544. SPARTAN : http://www.additive-net.de/software/spartan/index.shtml V. Venkatasubramanian, C. Zhao, G. Joglekar, A. Jain, L. Hailemariam, P. Suresh, V. Akkisetty, K. Morris, G.V. Reklaitis (2006) Ontological Informatics Infrastructure for chemical product design and process development, Computers and Chemical Engineering, CPC 7 Special Issue, 30(10-12), 1482-1496. N. Villanueva-Rosales, M. Dumontier (2007) Describing chemical functional groups in OWL-DL for the classification of chemical compounds, OWL: Experiences and Directions (OWLED 2007), co-located with European Semantic Web Conference (ESWC2007), Innsbruck, Austria. XML: http://www.w3.org/XML/ A. Yang, W Marquardt (2004) An Ontology-based Approach to Conceptual Process Modeling In: A. Barbarosa-Póvoa, H. Matos (Eds.): European Symposium on Computer Aided Process Engineering -14, 1159-1164.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimal column sequencing for multicomponent mixtures Andreas Harwardt,a Sven Kossack,a Wolfgang Marquardt a a
Lehrstuhl für Prozesstechnik, RWTH Aachen, Templergraben 55, 52056 Aachen, Germany,
[email protected]
Abstract The separation of a multicomponent mixture using distillation is usually possible in a large number of different sequences, which will provide the same products but have different energy demand. In this contribution, we provide a systematic method to find the optimal column sequence based on exergy demand. The screening of design alternatives is done within a superstructure framework, which allows for the decomposition of the separation sequences into unique separation tasks. The use of the task concept significantly reduces the computational work. The individual separation tasks are evaluated using shortcut methods. For the application to azeotropic mixtures, the mixture topology is determined and feasibility checks are performed for every split. In this context, azeotropes are treated as pseudo-components. Keywords: sequence synthesis, multicomponent, rectification body method,
state task network 1. Introduction In distillation network synthesis, the separation of multicomponent mixtures is possible in a large number of different column sequences, where the sequences, although they result in the same products, have different energy demand. A nonoptimal choice of the separation sequence can lead to significant additional cost during the operation. Several approaches for column sequencing can be found in the literature. Hendry and Hughes [1] introduced the separation task concept, where the distillation network is decomposed into the individual separation tasks, which are evaluated using the ideal thermodynamic based UnderwoodFenske-Gilliland method. This idea was extended to complex distillation systems by Shah and Kokossis [2]. The idea of a superstructure for distillation column networks was introduced with the state task network by Sargent and Gaminibandara [3]. Thong and Jobson [4] suggested a sequential approach for the column sequencing for azeotropic mixtures. The major problem with column sequencing is the large number of possible sequences, which grows exponential by the number of products. This contribution presents a stepwise procedure to identify the optimal sequence.
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In the first step, the design alternatives are automatically generated using a superstructure. In the second step, the design alternatives are evaluated using the rectification body method (RBM) [5], a nonideal thermodynamic based shortcut method. Unlike simulation studies or MINLP optimization, shortcut methods allow fast evaluation of the single separation task without detailed specification of the distillation column. 2. Methodology 2.1. Zeotropic mixtures
Assuming a four component mixture and simple two product splits, Fig. 1 shows all possible separation sequences into the pure components under the assumption of sharp splits. If the number of components is increased, an exponential growth of the number of sequences is observed (Fig. 2, sequences). This behaviour is well known [6] and can be described by N=
(2(n − 1))! n!(n − 1)!
(1)
where n is the number of products and N is the number of sequences.
Figure 1: Sequence alternatives for the separation of a four component mixture
The same separation steps (same feed and product compositions) can occur in different sequences. This can be seen in Fig. 1, where the first and the second sequence have the first separation in common. This property is used in a superstructure to reduce the complexity of the multicomponent systems. The state task network [3] is applied. In this superstructure, every possible composition, which can be attained, is called a state. The states represent the feed, possible intermediate products and products of the separation sequence. A task is defined as an operation connecting three different states, the feed state and the two product states [1]. The tasks can be automatically generated by performing all possible separations of every state composition into the intermediate products or products. Every separation sequence can be seen as a
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valid combination of tasks. A combination of tasks is valid if it starts with the feed state and ends at the product states. The application of the state task network requires the specification of linearly independent products. If products are linearly dependent, which in this case means that they could be attained by mixing other products, the state task network formulation is not applicable. This is due to the fact that the tasks would not be independent from the sequence. The main advantage of superstructure is that the number of tasks only grows with the third power of the number of products, compared to the exponential growth of the number of sequences (Fig.1) [2]. 500 Sequences Tasks
400
300
200
100
0 2
3
4
5
6
7
8
Components
Figure 2: Growth of the number of tasks and sequences
2.2. Azeotropic mixtures
The application of the superstructure for the separation of azeotropic mixtures requires some modifications. Separation is limited by azeotropes and the corresponding distillation boundaries, which form distillation regions [7]. For a feasible separation, top and bottom product composition have to be in the same distillation region. Boundary crossing (where the feed and the two product compositions are located in different distillation regions) is possible in the presence of curved distillation boundaries, but is not considered in this work. The required information about the distillation boundary is obtained from the pinch distillation boundary (PDB) feasibility test [8]. The information is stored in the reachability matrix, as introduced by Rooks et al. [9], which represents the topology of the residue curve map of the mixture. A feasible set of linear independent products has to be selected, where products can be pure components, azeotropes or a chosen product composition. This set is feasible if all products are part of the same distillation region. The singular points of a distillation region usually provide a good set of possible product compositions. The azeotropes are treated as pseudo-components.
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2.3. Shortcut calculations
The evaluation of a separation sequences requires information about the feasibility and the cost of the individual separation tasks. Determining the minimum energy demand of a separation has been found to be a good way of estimating the cost of a distillation system, because operation cost are dominated by the energy demand and investment cost are closely related to the vapor flow rate in the column [10]. The minimum energy demand can be calculated using the RBM shortcut. The feasibility of the individual separation tasks can be checked with the application of PDB feasibility test. The sequence evaluation is performed sequentially. At first, the superstructure including states and tasks is generated automatically. For every task, the PDB feasibility test is performed. If the split is feasible, the RBM calculates the minimum energy demand for the separation of the feed into the top and the bottom product. Once the minimum energy demand (QB) has been calculated, the exergy demand (EB) can be determined. The exergy of the energy represents the part of the energy that can be converted into mechanical energy using the ideal Carnot cycle. The required information about the reboiler temperature (TB) is provided by the RBM calculations. The evaluation based on the exergy demand accounts for the different temperature levels of the energy requirement. Once all task energy and exergy requirements have been calculated, the sequence energy and exergy demand is determined. The feasible sequences are automatically generated for the given number of products. Information about the active tasks for every single sequence is provided by the algorithm. The separation of the mixture into n products requires n-1 tasks. The sequences are found by combinatorial search with all identified tasks, where invalid branches of the combinatorial tree are cut to significantly reduce the computational demand. The sequence evaluation is done by the summation of the energy or the exergy demands of the active task of the sequence, which is computationally inexpensive. This summation is done for every sequence. After all sequence exergy demands have been calculated, the sequence with the lowest exergy demand is selected to be the optimal one. 3. Case studies In a first case study, the zeotropic mixture of pentane, hexane, heptane and octane is supposed to be separated into the pure components. Five different sequences are possible (Fig. 1), which have ten individual separation tasks. They are referenced as sequence one to five according to the labeling in the figure. Assuming a pressure of 1.013 bar, an equimolar feed and a total flowrate of 10 mol/s, the energy and exergy demands are calculated for the ten tasks using the RBM shortcut. Sequence five, which corresponds to the direct sequence, is found to be optimal. Obviously, the optimal sequence depends on
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the feed composition. The sequence exergy requirement is calculated to be 157 kW, where the energy requirement is 637 kW. In a second case study, a zeotropic mixture is separated into ten products. The mixture contains the ten nalkanes from propane to dodecane. 4862 Sequences, with 165 shortcut calculations for the tasks, are evaluated in less than ten minutes (Windows 2003 Intel Xeon Dual 3.06 GHz 3840 MB RAM). In a third case study, the mixture of acetone, chloroform, benzene and toluene is investigated. Acetone and chloroform are known to form a high boiling azeotrope. The composition space is separated into two distillation regions. The superstructure is used to identify optimal sequences in both distillation regions. In this case, the feed is set to be of equimolar composition at a flowrate of 10 mol/s and a pressure of 1.013 bar. The separation takes place in the convex region of the composition space, which can be identified from the information in the reachability matrix. For the given feed composition all five separation sequences are feasible. Table 1 displays the task exergy (EB) and energy (QB) requirements for the separation using the RBM, the labeling corresponds to Fig.1. Table 1. Task energy and exergy requirements task #
feed
top
bottom
QB [kW]
EB [kW]
1
ABCD
ABC
D
366
91
2
ABCD
AB
CD
602
127
3
ABCD
A
BCD
242
42
4
ABC
AB
C
595
110
5
ABC
A
BC
257
40
6
AB
A
B
311
46
7
BCD
BC
D
329
82
8
BCD
B
CD
465
98
9
BC
B
C
476
88
10
CD
C
D
193
48
Table 2. Sequence energy and exergy requirements
active tasks
sequence #
QB [kW]
EB [kW]
6
1272
247
1
1
4
2
1
5
9
1100
219
3
2
6
10
1107
222
4
3
7
9
1047
211
5
3
8
10
900
188
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The reachable products are the pure components/pseudo-components of the convex distillation region, which are acetone (A), acetone/chloroform (B), benzene (C) and toluene (D). The information about the single task energy and exergy requirements provides a good insight in the behaviour of the system. The energy and exergy demand of a sequence can now easily be calculated by the summation of the energy and exergy demand of the present tasks of every sequence, the information is provided in Table 2. It can be seen, that in this case, sequence five, which consists of three direct splits, gives the optimal solution with the lowest exergy requirement. 4. Summary and conclusion This contribution aims to identify the optimal sequence for a distillation column network. The method for column sequencing presented here is based on ideas from previous contributions presented in the introduction. The application of a superstructure allows for the decomposition of the sequences into individual separation tasks, which significantly reduces the computational work. The use of the nonideal thermodynamic based RBM shortcut method has significant benefits over the use of the Underwood-Fenske-Gilliland method, since it allows the extension to azeotropic mixtures. The automatic generation of the superstructure and the fast evaluation with the shortcut allows the application on large systems up to 10 products (zeotropic system), which is significantly larger than other examples in the literature. Telling from the zeotropic and azeotropic case studies presented in this contribution, it can be seen that this superstructure generation and evaluation is a useful tool in distillation network design, because it allows for rapid evaluation of design alternatives. It provides a small selection of promising design alternatives, which can then be investigated in more detail. The method can be applied within the process syntheses framework [11] for process variant generation and evaluation.
References [1] Hendry, J.E., Hughes, R.R.: Chem. Eng. Prog. 1972, 68, 6, 71. [2] Shah, P.B., A.C. Kokossis: AIChE Journal 2002, 48, 527. [3] Sargent, R.W.H, K. Gaminibandara: Optimization in Action; L.C.W. Dixion, Ed.: Acadamic Press; London, 1976. [4] Thong, D.Y.C., Jobson, M.: Chem. Eng. Sci. 2001, 56, 4417. [5] Bausa J., R.v. Watzdorf, W. Marquardt: AIChE J. 1998, 44, 2181. [6] Thompson, R.W., C.J. King: AIChE J. 1972, 18, 941. [7] Doherty, M.F., M.F. Malone Conceptual Design of Distillation Systems, McGraw-Hill, New York, 2001. [8] Brüggemann, S.: PhD Thesis, RWTH Aachen 2005. [9] Rooks, R.E., V. Julka, M.F. Doherty, M.F. Malone: AIChE J. 1998, 44, 1382. [10] Bausa, J.: , PhD Thesis, RWTH Aachen 2001. [11] Kossack, S., K. Krämer, W. Marquardt: submitted to Chem. Eng. Res. Dev.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Systematic Design of Production Processes for Enantiomers with Integration of Chromatography and Racemisation Reactions Malte Kaspereit,a Javier García Palacios,a Tania Meixús Fernández,a Achim Kienle a,b a
Max-Planck-Institut für Dynamik komplexer technischer Systeme, Sandtorstr. 1, D-39106 Magdeburg, Germany b Otto-von-Guericke Universität, Lehrstuhl für Automatisierung/Modellbildung, Universitätsplatz 2, D-39106 Magdeburg, Germany
Abstract A systematic study is performed of integrated processes that combine chromatographic separation and racemisation reaction for production of pure enantiomers. In a theoretical case study, processes of different degrees of integration are investigated by optimization of corresponding models. Concepts studied range from reactor-separator-recycle systems to fully integrated schemes with distributed reactivity. Physico-chemical parameters were determined experimentally for a model system. Data are reported together with first results for a simple flowsheet-integrated process. Keywords: process integration, chromatography, racemisation, enantiomers
1. Introduction Enantiomers are stereoisomers structured like mirror-images (see Fig. 1). A main problem related to producing a pure single enantiomer is that selective synthesis is often not feasible or too expensive. In contrast, conventional synthetic procedures are less expensive but non-selective (they deliver the racemic 1:1 mixture). Since usually only one enantiomer has the desired physiological effect (the other might be ineffective or harmful), such mixtures need to be separated; for example, by kinetic resolution, crystallisation, or chromatography. However, the yield achievable by this approach is inherently limited to 50% only. a
a C b
d c
A
C
d
b
c
B
Figure 1: Schematic representation of two enantiomers (here denoted as A and B). The two forms differ only in the spatial arrangement of the functional groups
Against this background it appears highly desirable to combine enantioseparations with an interconversion (racemisation) of the undesired enantiomer. Ideally, this should allow for a yield of 100%. Since racemisations are equilibrium-limited (with 1:1
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equilibrium composition), process integration appears as viable concept. Here we will investigate processes that combine (continuous) chromatography and racemisation.
2. Theoretical Case Study 2.1. Problem statement Fig. 2 shows the task to be resolved by the processes considered here. The constraints resemble a pharmaceutical problem, where purity requirements are very high and – due to significant synthesis costs – a high conversion of the undesired form is desirable. (continuous) chromatography
50% A 50% B
≥ 99.9% A 0.1% B
racemisation A'B
Figure 2: Schematic problem statement for the production of enantiomer A.
Subject of the study are integrated processes without waste stream that yield the desired enantiomer with 99.9% purity. This corresponds to a conversion of 99.8%. Further, also a less restrictive case is investigated (90% purity and 80% conversion). Mail goal is here to identify general trends with respect to integrating continuous chromatography and racemisation. Therefore, we consider a countercurrent of stationary and mobile phases (i.e., True Moving Bed, TMB). While a feasible technology would require column switching (i.e., Simulated Moving Bed, SMB), the development of such system is out of scope here. Details on TMB/SMB systems are given in, e.g., [1]. 2.2. Processes investigated There is a rather large number of options to integrate continuous chromatography and racemisation reaction. Fig. 3 shows a selection of possible schemes for the production of the weaker adsorbing enantiomer A. a)
S SR
F
A
c)
S
b)
S
F
A
d)
S
reaction
separation
F
SR
F
A
A
reaction & separation
Figure 3: Selected schemes for the production of A (F – feed, S – solvent, SR – solvent removed). a) Reactor-separator-recycle system w/ four zones and solvent removal. b) Partially integrated process w/ three zones and side reactors. c) Fully integrated process w/ four zones, distributed reaction and solvent removal. d) Fully integrated scheme w/ three zones and distributed reaction.
Concerning the level of integration, classical flowsheet-integrated processes as reactorseparator-recycle systems (Fig. 3a) and the use of side reactors (“Hashimoto process”,
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Fig. 3b) are considered. Furthermore, fully integrated schemes are possible (i.e., chromatographic reactors). While one option is to apply a constant reaction rate parameter (i.e., Damköhler number, Da) throughout the unit, here we also consider the option to use different values for Da in the individual zones (Fig. 3c). Finally, since four-zone processes require a recycle (and the removal of solvent), also integrated processes with three zones are studied (Fig. 3d). Please note that here we focus on the schemes shown in Fig. 3 (and their corresponding “counterparts” for the production of enantiomer B). However, there are more options. For example, a four-zone Hashimoto system with internal recycles was suggested [2]. 2.3. Process model and optimisations All processes are modeled as series of countercurrent equilibrium cells. Parameters were determined experimentally (section 3). A liquid-phase reaction is accounted for by Da = (rate constant)x(cell volume)/(solid flow rate). Adsorption is described by the biLangmuir model. All equations were implemented in the simulation environment DIVA [3]; details on the implementation of a largely analogous model can be found in [1,4]. The following set of performance parameters were used to evaluate each process: ⋅ ⋅ ½ ⋅ ciout V SR ° VS ° out out , = , = , = SR PR V c EC ® Pi = out ¾ i PR ° PR c A + c Bout °¯ ¿
i = ( A, B)
(1)
with purity Pi, productivity PR, specific eluent consumption EC, specific solvent removal SR, and ciout as product concentrations. Note that PR can be scaled by the solid volumetric flow (here equal to unity). Furthermore, solvent removal is assumed ideal (i.e., no losses, obtains feed concentration level for higher concentrated solute) and that side reactors (Fig. 3a and 3c) are in reaction equilibrium. Optimisations were performed using an SQP algorithm in DIVA with EC as objective function and the purity as nonlinear constraint. Variables were Da-numbers and the relative zone flow rates, m j ( j=I...IV) (i.e., ratio of liquid and solid flow in each zone). 2.4. Results Table 1 lists the obtained optimisation results for the process schemes in Fig. 3. As expected, the conventional setup a) is a feasible option. It performs somewhat better for the strongly adsorbed component B. The reason is that for producing A, the recycle load is higher due to the strongly diluted stream of B at the extract port. The Hashimoto process (b) was found to be infeasible for 99.9% purity. In fact, the process is thermodynamically infeasible for the production of pure A. The scheme achieves only low performance for 90% purity. This is in agreement with literature [2]. The hypothetical option of a fully integrated process with distributed reactivity (c) allows for a significant improvement of process performance. This holds in particular for component A, where SR and EC are strongly reduced. The main reason is that here the required m I –value is 16% lower than in case (a); m I is even lower than the Henry constant of B. The explanation is that any B in the reactive zone I also reacts to produce A, which is desorbed more easily and transported towards the non-reactive zones. A similar benefical effect (which is somewhat less pronounced) is found for m IV, which is higher for the fully integrated schemes than for the flowsheet-integrated processes. As a last option, integrated three-zone processes (d) were studied. These cannot achieve a purity of 99.9%. However, a comparison of the results for 90% purity demonstrates a significant potential. Considering that these schemes have no recycle or solvent removal, they appear very attractive for tasks with limited purity requirements.
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Table 1: Optimisation results for the process options shown in Fig. 3. The first column marks the process scheme according for Fig. 3 and the target component. *) PR is scaleable by solid flux. P [%] 99.9 99.9 90.0 90.0 99.9 90.0 90.0 99.9 99.9 90.0 90.0 99.9 90.0 90.0
a) A a) B a) A a) B b) b) A b) B c) A c) B c) A c) B d) d) A d) B
m I / Da I [-] 23.47 / 19.33 / 19.47 / 18.03 / -
m II / Da II [-] 11.54 / 14.71 / 10.58 / 12.57 / -
m III / Da III m IV / Da IV EC [-] [-] [l/g] 17.34 / 13.26 / 11.7 20.22 / 12.24 / 9.67 18.67 / 13.54 / 5.30 20.41 / 13.20 / 5.01 not feasible 18.97 19.85 13.63 16.8 20.51 13.54 14.84 12.2 -4 -18 -18 19.69 / 1039 11.69 / 10 17.24 / 10 12.26 / 10 8.54 22.69 / 10-16 14.62 / 10-11 20.55 / 10- 3 15.05 / 10 9 8.94 16.37 / 1068 11.25 / 10- 4 18.49 / 10-18 13.09 / 10-18 2.87 19.29 / 10-18 13.03 / 10-18 20.56 / 10- 4 15.54 / 10 9 3.61 not feasible (max. PA= 98.9%, max. PB = 99.4%) 16.65 / 4061 19.04 / 10-18 13.08 / 10-18 4.19 19.85 / 10-18 12.79 / 10-18 15.68 / 458 4.10
SR [l/g] 9.54 5.56 3.50 2.13
PR [g/l]* 0.87 0.77 1.12 0.96
0 0 3.87 4.40 0.93 0.36
0.32 0.47 0.87 0.85 1.14 1.04
0 0
0.85 1.02
3. Investigations for a model system The model substance used in this work is chlorthalidone (CT), which has (in racemic form) some use as a diuretic and anti-hypertensive drug. CT is stereolabile (i.e., it can be racemised rather easily) [5]. Chemicals were purchased from Merck (Darmstadt, Germany), with the exception of CT (Sigma Aldrich, Steinheim, Germany). 3.1. Chromatographic parameters Experiments were performed using an analytical column (200x4mm) with a chiral stationary phase (Nucleodex β-OH, Macherey-Nagel, Germany) at 10°C with a flow rate of 0.5 ml/min. The mobile phase was 40/60 (v/v) methanol/water, 50mmol triethylamine at pH=5.0 (acetic acid). Conventional HPLC equipment was applied (Knauer, Berlin, Germany and DIONEX, Idstein, Germany). The porosity was determined from an acetone pulse. NTP-values were determined from small injections of 0.4 g/l racemic CT in mobile phase (corresponds to solubility). 0.4 0.3 c i [g/l]
t R,i [min]
16 14 12 10
0.2 0.1
0
0.05
0.1 0.15 c i [g/l]
0.2
0 10
20
30 t [min]
40
50
Figure 4: Determination of adsorption isotherms. Left – perturbation data and corresponding fit by isotherm model (lines). Right – overloading experiments (points, injection volume: 0.13...5ml) and simulations (lines).
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Adsorption isotherms of the bi-Langmuir-type were measured (see Tab. 2). An initial set of parameters was obtained by the perturbation method [6]. Subsequently, a “peak fitting” approach based on the equilibrium-dispersive model was used for refinement (for details, see [4]). Fig. 4 shows a good agreement between models and experiments. 3.2. Kinetics of racemisation reaction The thermal racemisation of CT was investigated using batch experiments. Since CT is available only in racemic form, first purified fractions (ca. 2ml each) were obtained from HPLC runs, which then were allowed to racemise at different temperatures (15°C to 60°C). Samples were taken for HPLC analysis. Fig. 5 (left) shows an example data set. -6
4
-8
3
ln k
c i [10-5 mol l-1]
5
2
-12
1 0
-10
0
100 200 t [min]
-14 29
300
31 33 1/T [10-4 K-1]
35
Figure 5: Left – example of a batch racemisation experiment at 40°C. Symbols: concentrations of the enantiomers (HPLC analysis). Lines: calculated from Eq. (2). Right – Arrhenius diagram obtained from batch experiments between 15°C and 60°C.
Data were fitted by adjusting the rate constant of the first-order kinetic expression
c1 (t ) =
c10 + c20 § 0 c10 + c20 · ¸ exp(− 2kt ) + ¨¨ c1 − 2 2 ¸¹ ©
(2)
Fig. 5 (right) shows the resulting Arrhenius plot from which activation parameters were determined (Tab. 2). Fig. 5 (left) shows the resulting fit obtained from these parameters and the rate expression (2). A good agreement was obtained for all experiments. Table 2: Summary of experimentally obtained parameters for chromatography and racemisation. Adsorption isotherms I
II
I
II
qS / qS bi / bi
length / diameter / porosity
B
A 94,17 / 0,244 20cm / 0,4 cm / 0,796
number of theoretical plates Racemisation kinetics
0,207 / 6,395
0,141 / 3,192 680 12 -1
k0 =3,77⋅10 s
/ EA = 99,9 kJ/mol
3.3. Recycling chromatography combined with thermal racemisation The above theoretical study shows that it is useful to fully integrate racemisation and continuous chromatography. However, corresponding technology is not yet available. Since the conventional reactor-separator setup was demonstrated to be feasible, as a first step single-column recycling chromatography was investigated experimentally. A thermostatted CSTR (40°C) was connected to the column in a recycle setup. A part of the front of each chromatogram was collected as product A; the rest was recycled to the
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reactor. To maximise productivity, the process was operated in “touching band” mode. Due to dispersion in the system, the product average product purity achieved was 95%. Reactor concentrations remained close to the 1:1 mixture. Since no solvent removal could be used at this small scale the process expectedly suffered from strong dilution. 100
5 0
0
10 cycle
20
100 yield [%]
10
EC [l/g]
PR [g/d/l]
15
50
0
0
10 cycle
20
50
0
0
10 cycle
20
Figure 6: Performance of single-column recycling with (open symbols) and without solvent removal (filled) in comparison to an SMB-based process with ISR in steady state (dashed lines).
Fig. 6 shows performance predictions obtained with the equilibrium-dispersive model for such single-column recycling with and without ideal solvent removal (ISR). The same requirements were used as in section 3. The process is basically infeasible without ISR. Also shown is the steady state performance of an SMB-based process (6 columns, ISR, cf. Fig. 3a). As is often found, the SMB process achieves a lower productivity, but at the same time allows for significantly lower solvent consumption.
4. Summary For the production of pure enantiomers from racemic mixtures it is desirable to combine the enantioseparation with an interconversion (racemisation) of the undesired form. Corresponding concepts that integrate chromatography and racemisation were studied theoretically, ranging from classical flowsheet integration to fully integrated processes with distributed reactivity. The latter options – although being hypothetical – have a significantly improved performance. However, it was also found that internal recycles and solvent removal are necessary if high purity is required. Parameters for racemisation kinetics and chromatographic separation of a model system were determined experimentally. Model predictions and first-stage experiments were performed for flowsheet integrated processes. Single-column systems were found to be an interesting alternative to SMB-based schemes. Current work focuses on theoretical investigations of further process schemes under a broader range of product and problem specifications. Furthermore, technological options are studied for fully integrated processes and intermediate solvent removal.
References [1] M. Kaspereit et al., J. Chromatogr. A (2007) 2 – 13 [2] T. Borren, Untersuchungen zu chromatographischen Reaktoren mit verteilten Funktionalitäten, PhD thesis, VDI Verlag, Düsseldorf, Germany, 2007 [3] M. Mangold et al., Chem. Eng. Sci. 55 (2000) 441 – 454 [4] M. Kaspereit, Separation of Enantiomers by a Process Combination of Chromatography and Crystallisation, PhD thesis, Shaker Verlag, Aachen, Germany, 2006 [5] K. Cabrera et al., J. Chromatogr. A 731 (1996) 315 – 321 [6] C. Blümel et al., J. Chromatogr. A 865 (1999) 51 – 71.
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The Application Of A Task-Based Concept For The Design Of Innovative Industrial Crystallizers Richard Lakervelda, Herman J.M. Kramera, Peter J. Jansensa, Johan Grievinka a
Delft University of Technology, Leeghwaterstraat 44, 2628 CA Delft, The Netherlands
Abstract There is a need for a more synthesis-focused design approach for industrial crystallizers. In this paper a new task based design approach is applied to design a crystallization process unit. The approach aims to conceptually build-up the crystallization process from fundamental building blocks called physical tasks. Two lines of research are followed. First of all, the design and key results of several small scale experiments are discussed which demonstrate practical feasibility of the concept by isolating single tasks. Secondly, a model of a task based crystallizer consisting of two compartments has been developed. A dynamic optimization of the model shows that tight specifications on product quality can be achieved, because it is possible to control tasks independently from each other. This increase in flexibility for design and operation is of significant value for the development of future crystallizers. Keywords: Crystallization, Process synthesis, Task based design, Process optimization.
1. Introduction Crystallization is one of the oldest and economically most important separation technologies in chemical industry. The design of crystallization processes is complicated compared to liquid processes, because besides purity also properties like shape, polymorphic form and size distribution have to be taken into account. The selection of crystallisation equipment is traditionally done from a limited number of state-of-art industrial crystallizers followed by optimization of that particular type of equipment. This reduces the design space and creative input of a designer. This contribution discusses the application of a novel approach for the conceptual design of crystallization process units, which is called a task based design approach [1]. The aim of the work is twofold. Small scale experiments illustrate that by combining several technologies the task based design approach can be realized in practice. Secondly, a model based optimization study aims to illustrate the increase in flexibility for design and operation.
2. Task based design approach Current industrial crystallizers facilitate many physical phenomena. The control over each of these individual physical phenomena is not possible because in present industrial crystallizers these phenomena are strongly entangled. To improve on these drawbacks a more functionally-driven design approach is proposed called task-based design [1]. In the task-based design approach an attempt is made to conceptually construct the crystallization process from fundamental building blocks called physical tasks. A task is a design concept indicating a preferred change in the state of matter to a target state, to be effected by means of a physical or chemical event under a specified range of operating conditions and kinetics. The concept shows similarities with the state
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task network as was introduced by Kondili et. al [2] for process scheduling. Tasks can be connected in a network to accomplish the complete transition of a given feed into a desired product. The aim is to generate alternative ways of structuring the tasks, leading to a task superstructure that contains all possible and relevant tasks and their interconnectivity. Optimization of the task superstructure can be realized based on product quality, throughput or economic evaluation of the process and can be dependent on design constraints. The task based design approach is more flexible than traditional design approaches and allows for the optimization of individual crystallisation tasks. In this way a larger solution space is created which is needed to improve product quality.
3. Experimental isolation of single crystallization tasks One of the key challenges of the development of a task based design approach for crystallization processes is the ability to control crystallization tasks independently from each other, which makes optimization of that particular task possible. To demonstrate the practical feasibility of the approach an experimental program has been designed and conducted. The objectives of the experimental work are as follows: 1. Minimize attrition as it competes with growth 2. Keep supersaturation below nucleation threshold to isolate crystal growth 3. Evaluate technology which can induce nucleation at low supersaturation The next three sections discuss experiments which are each dedicated to one of these objectives. The focus will be on the design of the experiments and key results. 3.1. Experimental isolation of task crystal growth by minimizing attrition The setup that was selected to minimize attrition consists of a bubble column in which supersaturation is created by simultaneous cooling and evaporation of the solvent by sparging air. The crystals are kept in suspension by the upward velocity of the bubbles, eliminating the need for a stirrer or a circulation pump. In this way attrition caused by crystal-impeller collisions is absent. Seeded batch experiments on lab-scale show the feasibility of the concept by comparing the growth of a seeded population with so-called ideal growth behaviour. Ideal growth behaviour means that the number of crystals stays constant during the batch. In that case the final product size reaches a maximum, which can be estimated by setting up a mass balance over the seed population [3]. The results from the bubble column show a different trend compared to agitated crystallizers. In particular it can be said that the results are much closer to ideal growth behaviour, which means that the number of crystals stay constant during the batch and attrition is indeed minimized [4]. 3.2. Experimental isolation of task Supersaturation Generation with membranes The second objective of the experimental work is related to tight control of supersaturation at any place in a future crystallizer to prevent spontaneous nucleation bursts and to maximize crystal growth. Membranes offer an interesting opportunity to control supersaturation gradients in new crystallizer designs as a designer can move a boiling zone to any desired place. Furthermore additional process actuators are available by changing the conditions around a membrane, for example pressure or osmotic pressure at the permeate side in case of reverse osmosis. An experimental setup has been constructed and tested to assess the potential application of membranes for crystallization processes (Figure 1).
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105
flux [ kg m-2 h-1]
16
12
8
4
0 0
4
8
12
16
time [hours]
Figure 1: Process flow diagram setup combining crystallization and membranes
Figure 2: Measured flux for four successive experiments
It is concluded that a stable flux of approximately 2.5 kg m-2 h-1 can be achieved (Figure 2). This value will be an important input for the optimization studies of the design of a task based crystallizer in the next section. 3.3. Experimental isolation of task nucleation by using ultrasound Ultrasound is an interesting tool to induce nucleation at low supersaturation in a controlled way. It can be used to produce a large amount of nuclei with a narrow monodispersed distribution by applying pressure as a driving force [5]. An ultrasound generator is placed inside a supersaturated solution. An Ultrasonic field is applied for 2 minutes at various power inputs. The supersaturation is low to avoid spontaneous nucleation. The objective of the experiments is to evaluate the reproducibility of the production of nuclei and to relate the power output to the number of nuclei produced. During each experiment crystals were observed approximately one minute after insonation. It is concluded that nuclei can be generated at low supersaturation with a nucleation rate that is constant and not very sensitive for power input (Figure 3). The value of the nucleation rate will be used in the optimization studies. Produced crystals [#]
1.E+08
1.E+07
Gas Solvent
1.E+06
I
Ultrasound
M/L
G/L/S
1.E+05 40
50
60
70
80
Gas
Power input [W/l]
Figure 3: Measured number of crystals as function of ultrasonic power input.
I
Figure 4: compartmental structure task based crystallizer
4. Modeling and optimization of a task based crystallizer The experiments described in the previous chapter aim to demonstrate that the task based design approach is practically a feasible approach. Single crystallization tasks can be isolated, which makes optimization of that particular task possible. Combination of the technologies allows for the construction of a task based crystallizer in which each of the tasks can be controlled independently from each other. In this chapter an example of such a crystallizer is modeled and optimized.
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4.1. Modeling of a task based crystallizer A schematic drawing of the modeled system is given in figure 4. It involves a compartment with gas, liquid and solid phase which is used to grow crystals with negligible attrition. From this compartment a clear solution is taken which is fed to a second compartment which contains a membrane surface which is used to selectively remove solvent. Ultrasound can be applied within the GLS compartment to produce nuclei also at low supersaturation and with a constant rate. The system is operated in batch mode. The model will be used in an inverse problem and there exists a large difference in order of magnitude between the values of the moments of the crystal size distribution. Therefore special attention has been paid to proper scaling and simplification of the model. Therefore, instead of the full population balance the moments of the distribution are used, which yields a set of ordinary differential equations. The equations of the GLS compartment are written into dimensionless form to obtain a better scaled model. The component mass balance for the GLS compartment and the total mass and component balance for the ML compartment complete the model. This yields the following set of equations, where x0, .., x4 represent the scaled moments, y is the dimensionless solute concentration, İ is the liquid fraction and ș is the dimensionless time.
dx0 dT
K uD ,
dyGLS dT
UL
1
H
dVML dT
dx1 dT
yGLS x0 ,
dx2 dT
2 yGLS x1 , dH dT
1
yML yGLS J yGLS H
J AM W GLS
,
I
dCML dT
dx3 dT
VML
3 yGLS x2 ,
,H
dx4 dT
4 yGLS x3
1 kV x3
CGLS CML W GLS
(3)
(4)
CML dVML VML dT
(5)
Where Į represents the scaled nucleation rate, ȕ a growth rate constant, c0 and c* a reference and saturated concentration respectively, Ȗ is a dimensionless crystal density:
D
B W GLS E
3
E
0
* TGLS
kGW GLS c c
J
Ucrystal cT*
GLS
0
* TGLS
c c
W GLS
VGLS
I
(6)
The dimensionless state variables are defined as follows:
x0
yGLS
m0 E 3 , x1
m1E 2 , x2
cGLS cT*GLS c 0 cT*GLS
, yML
m2 E , x3
cML cT*GLS c 0 cT*GLS
m3 , x4
m4 E 1
(7)
(8)
4.2. Base case simulation The model of the task based crystallizer having two compartments has been implemented in gPROMS Modelbuilder 3.0.0. (PSE Enterprise, London). A base case simulation has been done with the settings as given in Table 1. The initial values correspond in both vessels to a clear saturated liquid.
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Table 1. Fixing degrees of freedom for base case simulation Parameter VML(t = 0) VGLS
Value
Unit
0.005
3
Physical meaning
m
Volume ML compartment
3
0.005
m
Volume GLS compartment -2
-1
J
2.5
kg m h
Mass flux from experiments (Figure 2)
Am
0.192
m2
Membrane surface area
B
3.5.108
# m-3 s-1
Maximum nucleation rate (Figure 3)
TGLS
298
K
Temperature GLS compartment
TML
323
K
Temperature ML compartment
ȝU
0.2 (t < 500 s)
-
20% of the reactor is insonated for 500s
0.0 (t > 500s) ij
l min-1
0.6 .
kG
6.0 10
-9
Flow rate between compartments
4 -1
-1
m s kg
-
The results of the base case simulation are depicted in Figure 5 and 6. It can be seen that crystals with a mean size of 265 ȝm can be produced with a solid fraction of 27%. The supersaturation and growth rate show a peak in the beginning which can be explained by the supersaturation build up from the increasing concentration in the ML compartment and supersaturation consumption by the increasing crystal surface area. 300
40
0.9
30 20
0.8
1.6 Mean size Supersaturation
Mean size [um]
50
1.2 200 0.8 100 0.4
10 0
0.7 0
2
4 Time [h] 6
8
Figure 5: Growth rate and liquid fraction in GLS compartment for the base case
0
Supersaturation [%]
1 Growth rate liquid fraction
liquid fraction [-]
Growth rate [nm/s]
60
0 0
2
4 Time [h] 6
8
Figure 6: Mean size and Supersaturation in GLS compartment for the base case
4.3. Model based optimization of a task based crystallizer The base case simulation can be optimized by introducing an objective function and by adding constraints to the model. The objective function of the dynamic optimization is the crystal mean size (m4/m3). The following constraints are subject to the simulation in addition to those indicating limits of the physical possible domain: x G = kg(C – C*) < 15.10-9 m s-1 (maximum growth rate, minimize defects) < 592 kg m-3 (prevent scaling on membrane surface) x CML = 0.75 (minimum liquid fraction) x İ(t = tend) The manipulated variables for the optimization are the mass flux over the membrane (J) and the ultrasound utilization (ȘU). Figure 7 shows the optimal trajectories of the manipulated variables. The results illustrate the strength of the task based design approach. In this case a very tight constraint on the growth rate has been imposed. It can be seen how both the flux and the utilization of ultrasound work together to maximize the crystal mean size. In the initial phase the ultrasound and flux are both high to create
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quickly a crystal population that can consume supersaturation and push the growth rate to its constraint (Figure 8). As the growth rate approaches the constraint the flux drops to reduce the supersaturation. At this point the utilization of ultrasound is still high to increase the surface area in the GLS compartment. As the crystals start to grow and consume more supersaturation, the flux can increase and the utilization of ultrasound can decrease to create less nuclei and therefore increase the mean size. Note that the total amount of solvent that has to be removed, which is proportional to the surface below the flux, is fixed because there is a constraint on the production. The flux therefore only has limited flexibility to force the growth rate below the constraint. It is possible to achieve the constraint on product quality, because now we are able to manipulate the task nucleation in addition to the task supersaturation generation. It should be noted that all the degrees of freedom are not explored yet, but already for this simple case a significant improvement in flexibility for design and operation is found. 20 Flux
16 12
Mean size [um]
1.5
10
8
0.5
4
40
0
0
0
1
2 Time [h] 3
4
Figure 7: Flux and insonation fraction maximizing mean size (only first 4 hours)
15
120
1
0
Mean size [um] Growth rate [m/s]
160
Fraction insonated
eta [%]
Flux [kg/m2/h]
2
20
200
80 5
Growth rate [nm/s]
2.5
0 0
2
4 Time [h] 6
8
Figure 8: Mean size (objective function) and growth rate (limiting constraint).
5. Conclusions In this paper a task based design approach is applied for the design of crystallization process units. The task based design approach considers fundamental crystallization tasks as building blocks for design. An experimental program and equipment have been identified which allows for the isolation of single crystallization tasks. It shows that the task based design approach is practically feasible. The experimental results are input for modeling and optimization of the design of a task based crystallizer, which consists of two compartments with different thermodynamic phases. A compartment in which the task crystal growth and nucleation are executed is connected to a compartment in which the task supersaturation generation can be executed. A dynamic optimization study shows that tight constraints on product quality can be achieved, because tasks can be controlled independently from each other. It allows for the design of novel crystallization equipment with improved flexiblity to manipulate product quality.
References [1] Menon, A.R. and A.A. Pande and H.J.M. Kramer and J. Grievink and P.J. Jansens, Ind.Eng.Chem.Res., 46 (2007) 3979 [2] E. Kondili and C.C. Pantelides and R.W.H. Sargent. Computers chem. Engng (1993), 17, 211 [3] N. Doki and N. Kubota and A. Sato et al., AIChE 45 (1999) 2527 [4] R. Lakerveld and A.N. Kalbasenka and H.J.M. Kramer and P.J. Jansens and J. Grievink, Proceedings of 14th Internationcal Workshop on Industrial Crystallization (2007) 221 [5] C. Virone and H.J.M. Kramer and G.M. van Rosmalen et al. Journal of Crystal Growth 294 (2006) 9
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Cell Cycle Modelling for Off-line Dynamic Optimisation of Mammalian Cultures Carolyn M. Lam,a Kansuporn Sriyudthsak,a Cleo Kontoravdi,a Krunal Kothari,a Hee-Ho Park,a Efstratios N. Pistikopoulos,a Athanasios Mantalarisa a
Centre for Process Systems Engineering, Dept. of Chem. Eng., Imperial College London, South Kensington Campus SW7 2AZ, UK.
Abstract Mammalian cell cultures producing high-value biopharmaceuticals are expensive and time-consuming to study due to their exclusive dependence on experimentation. A mathematical model has been developed that describes batch/fed-batch hybridoma suspension cultures under normal and chemically-arrested conditions, which is also used to optimise the fed-batch cultures. The optimised strategy was tested experimentally demonstrating that product concentration was closely predicted though the viable cell concentration was partly underestimated. Overall, the model has assisted in reducing the number of experiments required to determine optimal cell culture conditions. Further work is required to improve the model predictability. Keywords: mammalian, hybridoma, off-line, modelling, optimisation.
1. Introduction Biologicals, such as monoclonal antibodies (MAbs), are important drugs for the treatment of various diseases. The global market for MAbs is projected to increase to US$16.7 billion in 2008 (Reichert and Pavlou 2004). Mammalian cells are the preferred expression system in order to achieve functional products. However, large infrastructure investments, high costs of experimentation and long cultures necessitate the reduction in costs and time-to-market. Once the best cell-line and media composition have been selected, the feeding strategy for fed-batch cultures would need to be optimised to maximise the production potential of the cell culture. Continuous improvements in mammalian culture technologies are also important to maintain their competitiveness versus other alternatives such as transgenic plants and animals (Ma et al., 2003; Dyck et al., 2003). Modelling offers advantages in providing insight into the production process and guiding experimentation, thus elimination any unnecessary experiments. Furthermore, it also enables in silico determination of best and worst case scenarios, which help focusing resources on beneficial trials. In this study, modelling of a hybridoma suspension culture based on first principles for off-line optimisation of time-varying process strategies was performed. By tracking the population in various phases of the cell cycle (G0/G1, S, and G2/M), the specific productivity of each sub-population was taken into account, which reflected the culture’s intrinsic properties more accurately.
2. Materials and Methods 2.1. Batch and Fed-Batch Cultures The mouse-mouse hybridoma CRL-1606 cell line producing IgG1 monoclonal antibody (MAb) against human fibronectin was obtained from ATCC. Batch cultures
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were inoculated at 1.5-2.0x105 cell ml-1 in 100ml medium containing DMEM with 25mM glucose and 4mM glutamine (GIBCO), 2.5% CBS (ATCC) and 1% Pen-Strep (GIBCO) in shake-flask incubated at 37oC and 5% CO2. Samples were taken every 8 h. Three out of six batch cultures were arrested with 0.5% DMSO (Wang et al., 2004) at 44 h. A fed-batch culture was first tested in triplicates with the same initial conditions as the batch cultures and concentrated glutamine (Sigma) at 200 mM was added twice a day. Three sets of triplicate fed-batch cultures were then performed following an optimised feeding strategy with three different cell cycle-arrest times at 78 h, 96 h, and 126 h respectively. The feed contained DMEM (GIBCO) with 200mM glutamine and 500mM glucose (Sigma). 2.2. Cell Culture Analyses Cell concentration and viability were measured with a Neubauer haemocytometer (Assistant, Germany) and trypan-blue (Sigma). Glucose, glutamine, lactate, and ammonium were detected using BioProfile200 (NOVA Biomedical) pre-calibrated with internal standards. Cells were fixed and stained with propidium-iodide (Sigma-Aldrich) for cell cycle analysis with flow cytometry (Beckman Coulter). The concentration of MAb was measured using an in-house sandwich ELISA assay.
3. Modelling 3.1. Model Structure The model was adapted from Kontoravdi et al. (2005) for cell growth/death, nutrient uptake, and major metabolism. The model was further developed to include description of cell cycle sub-populations. The cell cycle representation was based on the yeast model of Uchiyama & Shioya (1999) and the tumour cell model of Basse et al. (2003). Eq.(1)-(4) express viable cell concentration(Xv[cell L-1]) in terms of cells in G0/G1, S, and G2/M phases. As a simplification in notation, G0/G1 cells will be indicated as G1 unless otherwise stated. XG1, XS, XG2/M [cell L-1] are concentrations of viable cells in G0/G1, S, and G2/M phase, respectively, whereas Fout[L h-1] is the outlet flowrate. V[L] is the cell culture volume; b, k1, k2 [h-1] are the transition rates of cells from G1 to S, S to G2, and M to G1 respectively; and μd[h-1] is the specific death rate. (1) X v = X G1 + X S + X G 2 / M dX G1 F = 2b ⋅ X G 2 / M − k1 ⋅ X G1 − μ d ⋅ X G1 − ( out ) ⋅ X G1 dt V dX S Fout = k1 ⋅ X G1 − k 2 ⋅ X S − μ d ⋅ X S − ( )⋅ XS V dt dX G 2 / M F = k 2 ⋅ X S − b ⋅ X G 2 / M − μ d ⋅ X G 2 / M − ( out ) ⋅ X G 2 / M V dt
(2) (3) (4)
k1, k2, b can be rearranged and expressed in terms of the specific growth rate, μ [h-1]: 2 − xG1 (5) k1 = ⋅μ
xG1 1 + xG 2 / M ⋅μ k2 = xS
b=
μ
(6) (7)
xG 2 / M
where xi is fraction of cells in cell cycle phase i. xi is related to the specific growth rate (Uchiyama & Shioya, 1999; Slater et al., 1977) and are expressed as follow:
Cell Cycle Modelling for Off-line Dynamic Optimisation of Mammalian Cultures
x G1 = 1 −
(t S + t G 2 / M ) ⋅ μ − θ S − θG2 / M log 2
111
(8)
tS ⋅ μ +θS log 2
(9)
x G 2 / M = 1 − x G1 − x S
(10)
xS =
where θi represents the fraction of cells in cell cycle phase i when growth rate is zero, and tS and tG2/M [h] represent the time spent in S and G2/M phase respectively. Eq.(11)-(12) are the specific glucose uptake rate, Qglc[mmol cell-1 h-1], and the specific lactate production rate, Qlac[mmol cell-1 h-1], modified from Kontoravdi et al. (2005) based on results of the initial fed-batch culture (see Fig.2). A maintenance term for glucose uptake was removed and the glucose uptake and lactate production rates were linked to glucose concentration. In the equations below, μ[h-1] is the specific growth rate, Yx,glc[cell mmol-1] is the cell-yield from glucose, KQglc[mM] is the halfsaturation constant for glucose uptake, [GLC] is the glucose concentration [mM], Ymax -1 lac,glc[mmol mmol ] is the maximum yield of lactate from glucose, Klac,glc[mM] is the half-saturation constant for lactate production with respect to glucose concentration. [GLC ]2 μ (11) ⋅ Q = glc
2 Yx , glc K Qglc + [GLC ]2
Qlac = Ymax lac , glc ⋅
[GLC ] K lac , glc + [GLC ]
(12)
Eq.(13)-(14) take into account the production of MAb by each cell cycle phase, where v(%) is viability, QMAb,G1 , QMAb,S , QMAb,G2/M[mg cell-1 h-1] are specific MAb production rates of the corresponding cell-cycle phases, [MAb] is the concentration of monoclonal-antibody [mg L-1], KMAb[%] is an inhibition constant for MAb production with respect to cell viability. The introduction of viability in QMAb was based on the results of Glacken et al. (1988) which demonstrated that cell culture productivity was affected by low viability; these findings were also observed in our experiments that specific productivity decreased for CRL-1606 during death phase. F d [ MAb] (13) = f (v) ⋅ (Q ⋅X +Q ⋅X +Q ⋅X ) − ( out ) ⋅ [ MAb] dt
where
MAb ,G1
0 ° ° 1 f (v ) = ® ° K MAb °¯1 + v
G1
, v ≥ 80%
MAb , S
S
MAb ,G 2 / M
G2 / M
V
(14)
, v < 80%
3.2. Parameter Estimation and Dynamic Optimisation The model was implemented in gPROMS (Process Systems Enterprise Ltd.) and the parameters were estimated based on the batch and initial fed-batch data. The same set of parameters was used to generate the simulation results for the batch, fed-batch, and cell growth arrested cultures. The model consists of 13 differential equations and 32 parameters of which 7 were altered in the arrested cultures with their values programmed to switch automatically in the model when the cell cycle-arresting chemical was introduced. As a case study for product yield optimisation, the amount of feed and the cell cycle-arrest time were varied while all other cell culture conditions, e.g. feed compositions, time intervals etc., were fixed. The model-based optimisation was done using a mixed-integer dynamic optimisation algorithm (Bansal et al., 2003) with a grid of initial values for the degrees of freedom concerned. The best fed-batch strategy was selected for experimental validation with a variation in cell cycle-arrest time in two additional fed-batch cultures to test the predictability of the model.
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4. Results and Discussion 4.1. Batch Cultures The model was able to capture the reduction in growth rate and the corresponding increase in the G0/G1 phase population when cells were arrested at 44 h (Fig.1). Although the viable cell concentration of the arrested culture at late exponential phase and the final MAb concentration of the normal culture were slightly lower than predicted, it is important to note that the relative growth rates and productivity in the two cultures were in accordance with model prediction. There was a time-lag of approximately 10 h in the change in G0/G1 and S phase distribution at the beginning of the cell culture as compared with the model simulation. This might suggest the need of a lag term in the model in order to represent the delayed response of the cells.
Fig.1: Batch culture data showing (a) viable cell (Xv) and antibody (MAb) concentration; and (b) cell cycle distribution for normal(n)/arrested(ar) cultures. Simulation results are shown by lines.
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4.2. Fed-batch Cultures
Fig.2: Initial fed-batch culture data showing (a) viable cell(Xv) and antibody(MAb) concentration; and (b) glutamine(Gln), ammonium(Amm), glucose(Glc), and lactate(Lac) concentration. Simulation results are shown by lines.
Fig.3: Optimised fed-batch data showing (a) viable cell(Xv) concentration; and (b) antibody (MAb) concentration for cell cycle-arrest at 126h and two other cell cycle-arrest times at 78h and 96h. Simulation results are shown by lines.
The initial fed-batch culture performed revealed a rich dynamic response of the cells when glutamine was continuously added throughout the cell culture. The simulated viable cell, MAb, glutamine, and ammonium concentrations followed the experimental trends (Fig.2). However, the cells appeared to consume less glucose and, consequently, produced less lactate after about 60 h. The model over-predicted the lactate production only near the end of the culture, suggesting that certain metabolic changes had taken place which has not been fully captured by Eq.(11)-(12). The model-based dynamic optimisation results that were obtained from a fixed feed composition, same initial condition as the batch culture, and a feeding interval of 6-12 h, suggested an optimal cell cycle-arrest time at 126 h and supplementation with feed from 48 h onwards. The results of three different fed-batch cultures with identical supplementation strategies but various cell cycle-arrest times are shown in Fig.3. The viable cell concentration, Xv, was closely predicted up to about 80 h. However, after 100h, Xv decreased significantly in all three cultures. The predicted MAb concentration was in accordance with the experimental results with only a slight under-prediction around 80-100 h. Both model predictions and experimental results indicated a small difference in MAb yield when the cultures were arrested at different times. The optimised fed-batch experiments involved a total of 9 shake flask cultures so the
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deviation between the data and model predictions for Xv appeared to suggest a deficiency in the model. Overall, with the aid of model predictions, fewer experiments were needed in order to explore the possible limits of the cell culture production capacity. In the optimised fed-batch culture, the culture life-time was extended as indicated by the Xv peaking at about 100 h while the corresponding peaking time for the initial fed-batch and batch cultures were about 90 h and 65 h respectively; and the MAb yield reached ~3.5x103 mg L-1 as compared to ~2.5x103 mg L-1 in the initial fed-batch culture and ~1.3x103 mg L-1 in the batch cultures.
5. Conclusion The model was able to predict the culture dynamics for batch, fed-batch, and cell growth arrested cultures, especially up to the exponential growth phase, after which certain variable predictions deviated from the experimental results in fed-batch cultures, e.g. the viable cell concentration in the optimised fed-batch culture tended to be overestimated, and the simulated glucose uptake rate near the end of the fed-batch cultures was higher than observed. The model closely predicted the monoclonal antibody concentration in the optimised fed-batch culture despite an underestimation of the viable cell concentration. The model developed was able to direct experimental efforts to a more focused area in this case study. The monoclonal antibody yield in the optimised fed-batch culture was ~3.5x103 mg L-1 which was about 40% higher than the initial fed-batch culture. Further improvement of the model structure may be necessary to enhance its predictive capability.
References V. Bansal, V. Sakizlis, R. Ross, J.D. Perkins, E.N. Pistikopoulos, 2003. New algorithms for mixed-integer dynamic optimization. Computers and Chemical Engineering, 27, 647-668. B. Basse, B.C. Baguley, E. S. Marshall, W. R. Joseph, B. van Brunt, G. Wake, D. J. N. Wall, 2003. A mathematical model for analysis of the cell cycle in cell lines derived from human tumors. Journal of Mathematical Biology, 47, 295-312. M.K. Dyck, D. Lacroix, F. Pothier, M.-A. Sirard, 2003. Making recombinant proteins in animals - different systems, different applications. Trends in Biotechnology, 21(9), 394-399. M.W. Glacken, E. Adema, A.J. Sinskey, 1988. Mathematical descriptions of hybridoma culture kinetics: I. Initial metabolic rates. Biotechnology and Bioengineering, 32(4), 491-506. C. Kontoravdi, S.P. Asprey, E.N. Pistikopoulos, A. Mantalaris, 2005. Application of global sensitivity analysis to determine goals for design of experiments: An example study on antibody-producing cell cultures. Biotechnology Progress, 21, 1128-1135. J.K.-C. Ma, P.M.W. Drake, P. Christou, 2003. The production of recombinant pharmaceutical proteins in plants. Nature Reviews Genetics, 4, 794-805. Process Systems Enterprise Ltd. 2007. URL: www.psenterprise.com. J.M. Reichert and A.K. Pavlou, 2004. Monoclonal antibodies market. Nature Reviews Drug Discovery, 3(5), 383-384. M. L. Slater, S. O. Sharrow, J. J. Gart, 1977. Cell cycle of Saccharomyces cerevisiae in populations growing at different rates. Proceedings of the National Academy of Sciences of the United States of America, 74, 3850-3854. K. Uchiyama and S. Shioya, 1999. Modeling and optimization of α-amylase production in a recombinant yeast fed-batch culture taking account of the cell cycle population distribution. Journal of Biotechnology, 71, 133-141. X. Wang, S. He, Y. Zhang, J. Xu, Q. Feng, L. Li, L. Mi, Z. Chen, 2004. DMSO Arrested hybridoma cells for enhanced antibody production. Sheng Wu Gong Cheng Xue Bao, 20, 568571.
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New Configuration For Hetero-Azeotropic Batch Distillation: I. Feasibility Studies Peter Langa , Ferenc Denesa and Xavier Jouliab a
BUTE Dept. of Building Services & Process Engineering, H-1521 Budapest, Muegyetem rkp. 3-5, bLGC-ENSIACET-INPT, 118 route de Narbonne, 31077 Toulouse, France
Abstract For heterogeneous batch distillation a new double column configuration operating in closed system is suggested. This configuration is investigated by feasibility studies based on the assumption of maximal separation and is compared with the traditional batch rectifier. The calculations are performed for a binary (n-butanol – water) and for a ternary heteroazeotropic mixture (isopropanol – water + benzene as entrainer). Keywords: heteroazeotrope, batch distillation, feasibility studies.
1. Introduction If components of a mixture form a heteroazeotrope or by the addition of an entrainer (E) a heteroazeotrope can be formed, the azeotropic composition can be crossed by decantation. In the pharmaceutical and fine chemical industries batch processes including the batch heteroazeotropic distillation (BHD) are widely applied. As far as we know the BHD was exclusively applied in the industry in batch rectifiers (equipped with a decanter) in open operation mode (with continuous top product withdrawal). The batch rectifier (BR) was investigated with variable decanter holdup by Rodriguez-Donis et al. (2002) and with continuous entrainer feeding by Modla et al. (2001, 2003) and Rodriguez-Donis et al. (2003), respectively. Recently the BHD was extensively studied for the BR and multivessel columns by Skouras et al. (2005a,b). The objectives of this paper are - to suggest a new double-column system (DCS) for the BHD, - to investigate this configuration by feasibility studies, - to compare its performance with that of the traditional BR. Calculations are performed for a binary (n-butanol – water) and for a ternary heteroazeotropic mixture (isopropanol – water + benzene).
2. The column configurations studied First the BR then the new DCS is studied by assuming maximal separation. 2.1. Batch rectifier (Fig. 1.) First the separation of the binary then that of the ternary mixture is presented. Separation of a binary mixture If the charge (feed) composition (xch,A (mole fraction of component A)) is in the Br Ar heterogeneous region ( x AZ, ) it is worth to separate it by decantation A < x ch,A < x AZ,A Ar into an A-rich ( x AZ, ) and a B-rich ( x Br ) phase before the start of the distillation. A AZ,A
One production cycle consists of two distillation steps. In the first step we select the phase to be distilled so that the overall quantity of the two products in the first cycle be
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Fig. 1. BR producing A from mixture A-B
Fig. 2. DCS for binary mixture
maximal. It can be derived (for pure products) that we have to distil the A-rich phase Br Ar Br first if x ch ,A > x AZ ,A /[1 − ( x AZ,A − x AZ,A )] . Step 1: Production of A: The A-rich phase ( x Ar ) of the heteroazeotrope (xAZ,A) is reAZ,A Br fluxed and the B-rich one ( x AZ, ) is withdrawn as distillate. The bottoms is product A. A
Step 2: Production of B: The B-rich phase(s) is (are) distilled. The B-rich phase of the azeotrope is refluxed and the A-rich one is withdrawn as distillate. The bottom residue is product B. The main disadvantages of the BR are that in one step only one component can be produced (in the residue) and that the recovery is limited since the other component in the distillate is saturated with this component. Separation of the ternary mixture The separation of a homoazeotropic isopropanol (A) – water (B) mixture is considered. Addition of an entrainer, in a small amount, is needed. The steps of a production cycle are: Er
Step 1: Production of A: The E-rich phase ( x TAZ ) of the ternary azeotrope ( x TAZ ) is Br
refluxed and the B-rich phase ( x TAZ ) is withdrawn as distillate, which is distilled in Step 2. The bottom residue is product A. Step 2: Removal of E: The B-rich phase of the azeotrope is refluxed and the E-rich phase is withdrawn as distillate. The bottom residue still contains some A. Step 3: Purification of B from A: A is removed (from the bottom residue of Step 2) in the form of binary A-B homoazeotrope ( x BAZ ) in the distillate and the bottom residue is product B. 2.2. The new double column system (Fig. 2.) The two column system is operated in closed mode (without continuous product withdrawal) with a single decanter. The two components are simultaneously produced as bottom residues. Separation of a binary mixture A heterogeneous charge is separated by decantation. The A-rich phase is filled in the reboiler of the column α (producing A) and a B-rich one to the other reboiler β. A homogeneous charge can be divided between the two reboilers. The top vapour of both columns is of azeotropic composition. The A-rich phase is sent to the top of column α and the B-rich one is fed to the top of column β.
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Separation of the ternary mixture The homogeneous charge can be arbitrarily divided between the two reboilers.The entrainer, which is filled at the start only in the reboiler of column α, circulates in the system. The top vapour of the column α is ternary azeotrope and that of column β is AB binary azeotrope. The E-rich phase is sent to the top of column α and the B-rich one (containing negligible amount of E) is fed to the top of column β.
3. Feasibility method Our aim is to estimate the duration of the processes and the amount of products. A simplified model was applied based on the following assumptions: maximal separation, negligible hold-up on the trays and in the decanter, constant molar overflow, the flow rates do not vary with the time, one-phase liquid streams leave the decanter, negligible duration of pumping between the operation steps (BR), no entrainer loss (in the case of the ternary mixture). The total and component material balances for one column and the decanter are analytically solved. For the DCS we assume that both products reach the prescribed purity at the same time, that is, the duration is minimal. The process time (τ) for both configurations and for the DCS the optimal division (vα) of total vapour flow rate (V) between the two reboilers and that of the charge (Ubα/Uch) are shown. 3.1. Equations for the BR Separation of a binary mixture jr ( x irAZ,i − x AZ U ,i )( x e ,i − x b ,i ) Duration of a step: τ = ir ⋅ b jr V ( x AZ,i − x AZ,i )( x e,i − x AZ ) ,i
where i, j: components (i is produced in the given step); x b,i , x e, i : mole fraction of i in the reboiler at the beginning and end of the step; U: molar holdup in the reboiler. Distillation of the ternary mixture Step 1: We suppose that product A does not contain E (it is polluted only by B). Er Br ( x TAZ U , A − x TAZ, A )( x spec, A − x ch , A ) ⋅ ch , Duration of this step: τ(1) = Er Br ( x TAZ, A − x TAZ, A )( x spec, A − x TAZ, A ) V where x spec,A is the specified purity of product A. Step 2: The top vapour has ternary azeotropic composition. Duration of this step: Br Br x Er ,A − x TAZ ,A x TAZ,E U b τ ( 2) = TAZ ⋅ ⋅ Er Er V x TAZ ,A − x TAZ,A x TAZ,E Step 3: In this step only A and B are present, the top vapour is the homoazeotrope. There is no need for a decanter. Duration of this step: x b,A − (1 − x spec,B ) U τ (3) = ⋅ (1 + R ) ⋅ b , where R is the reflux ratio. x BAZ,A − (1 − x spec,B ) V 3.2. Equations for the double column system Separation of the binary mixture β Br For a heterogeneous charge: x αb,A = x Ar AZ,A and x b ,A = x AZ,A . For a homogeneous one:
x αb, A = x βb, A = x ch , A , the number of independent equations is less by one than in the previous case, hence one of the unknowns ( U αb , U βb , v α ) must be specified. The value of the main operational parameters:
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τ=
Br Ar Δ( U α x αA ) − ΔU α x AZ − x Br Δ( U α x αA ) − ΔU α x AZ, A x Ar , A x AZ, A − x AZ, A AZ, A , vα = ⋅ Ar ⋅ AZ, A α α α Ar Br Δ( U x A ) − ΔU x AZ, A x AZ, A − x Br x AZ, A − x AZ, A x AZ, A − x AZ, A AZ, A
where ΔU α = U αe − U αb , Δ( U α ⋅ x αA ) = U eα ⋅ x spec,A − U αb ⋅ x αb,A , U αb =
x ch ,A − x βb,A x αb,A − x βb,A
⋅ U ch
Separation of a ternary mixture Initially only the reboiler α contains E. We neglect the content of E of the B-rich phase. Hence there is no E in column β whose top vapour is A-B binary azeotrope. The number of unknowns is more than the number of independent equations by one. Hence one of the unknowns must be specified. The composition of the phases is a function of vα but this function can be mathematically expressed with difficulty which would make the solution of the set of equations difficult. Hence we specify vα. The values of the main parameters of the operation: U αe ⋅ ( x spec,A − x ch ,A ) x Er − x , U αb = U eα + E ErTAZ, E ⋅ v α ⋅ V ⋅ τ , τ = Er α Er xE L ⋅ ( x A − x ch ,A ) + v ⋅ V ⋅ ( x ch ,A − x TAZ,A ) U eα =
x ch ,A − (1 − x spec,B ) x spec,A − (1 − x spec,B )
⋅ U ch
4. Calculation results The total vapour flow rate of the DCS was taken equal to that of the BR ( V = 20 kmol/h ). (The heat duty is proportional to the vapour flow rate.) For the DCS we determine the optimal division of the charge between the two reboilers (and the division of the total vapour flow rates belonging to it). In all cases the amount of charge is 100 kmol and the specified purity (xspec,i) is 99.5 mol% for both products. 4.1. Separation of binary mixtures (n-butanol(A) – water(B)) The composition of the heteroazeotrope and that of the A-rich and B-rich phases, Ar
Br
respectively: x AZ = [0.2562, 0.7438] , x AZ = [0.568, 0.432] , x AZ = [0.012, 0.988] All possible cases are studied: two homogeneous charges (one rich in A and the other rich in B) and a heterogeneous one. 4.1.1. Homogeneous charge rich in A a.Batch rectifier: x ch = [0.9, 0.1] . In Step 1 A is produced (Table 1). b. Double Column System We determine τ and vα for different ratios Ubα/Uch (Figs. 3. & 4.) The best operational policy (Table 1) is when the total amount of the charge is fed into reboiler α ( U αb / U ch = 1 ).The duration of the cycle is nearly equal for the two configuBR Step 1 Step 2 Ubα,β/Uch Div. of vap. fl.rate Duration [h] 0.862 0.014 Prod. A [kmol] 90.336 0.000 Prod. B [kmol] 0.000 9.544 Byprods. [kmol] 0.120 Byps. comp. [mol%] 56.80
DCS Col. α Col. β 1.00 0.00 0.9844 0.0156 0.880 90.404 0.000 0.000 9.596 0.000 -
BR Step 1 Step 2 Ubα,β/Uch Div. of vap. fl.rate Duration [h] 0.101 0.034 Prod. A [kmol] 0.502 0.000 Prod. B [kmol] 0.000 99.112 Byprods. [kmol] 0.386 Byps. comp. [mol%] 1.12
DCS Col. α Col. β 0.00 1.00 0.2538 0.7462 0.136 0.505 0.000 0.000 99.495 0.000 -
Table 1. Results (binary mixture rich in A) Table 2. Results (binary mixture rich in B)
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New Configuration for Hetero-Azeotropic Batch Distillation: I. Feasibility Studies
BR Step 1 Step 2 α,β Ub /Uch Div. of vap. fl.rate Duration [h] 2.006 0.100 Prod. A [kmol] 29.298 0.000 Prod. B [kmol] 0.000 69.823 Byprods. [kmol] 0.879 Byps. comp. [mol%] 56.80
DCS Col. α Col. β 0.5180 0.4820 0.9530 0.0470 2.141 29.798 0.000 0.000 70.202 0.000 -
Step 3 0.261 0.000 30.723 5.224 BAZ
DCS Col. α Col. β 0.9981 0.0019 0.9650 0.0350 8.494 67.576 0.000 0.000 32.424 0.000 -
Table 4. Results (ternary mixture)
25
1.0
20
0.8
15
0.6
10
0.4
5
0.2 0.0
0 0.0
0.2
0.4
0.6
U bα /U ch
0.8
0.0
1.0
0.2
0.4
0.6
U bα /U ch
0.8
1.0
Fig. 4. Rel. vap. flow rate of column α (binary mixture rich in A)
Fig. 3. Duration of the process (binary mixture rich in A)
1.0
16
0.8
U bα /U ch
12
τ [h]
BR Step 2 0.010 0.000 0.000 0.160 TAZ
vα
τ [h]
Table 3. Results (bin. heterogeneous mix.)
Step 1 Ubα,β/Uch Div. of vap. fl.rate Duration [h] 8.055 Prod. A [kmol] 64.001 Prod. B [kmol] 0.000 Byprods. [kmol] Byprods. compn. -
8 4
0.6 0.4 0.2 0.0
0 0.5
0.6
0.7
v
α
0.8
0.9
Fig. 5. Duration of the process (ternary mixture)
1.0
0.5
0.6
0.7
vα
0.8
0.9
1.0
Fig. 6. Division of the charge (ternary mixture)
rations. In the case of DCS by the best policy the whole amount of A is already in the reboiler α at the start and only B must be eliminated from it. The reason of the small value of vβ is that the B-rich phase flowing from the decanter into column β has very high B-content ( x Br AZ,B = 0.988 ). Hence only a small amount of A must be removed in the form of azeotrope for the purification of B. The main advantage of the DCS is that there is no residue at all. 4.1.2. Homogeneous charge rich in B a. Batch rectifier: x ch = [0.01, 0.99] . In Step 1 B is produced (Table 2). b. DCS: We determined τ and vα for different divisions of the charge. The best operational policy (Table 2) is when the total amount of the charge is fed into reboiler β. The duration of the cycle is nearly equal in the two cases. The ratio of the duration of the two steps for the BR: τ (1) / τ ( 2) = 2.971 The ratio of vapour flow rates of the two columns for the DCS: v β / v α = 2.940
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The values of these two ratios show that energy demand of the production of each component is nearly the same for the two configurations. The division of the charge can be explained similarly as in the case of the previous charge composition. 4.1.3. Heterogeneous charge Before the distillation the charge of composition x ch = [0.3, 0.7] is separated by decantation into an A-rich ( U Ar = 51.8 kmol ) and a B-rich ( U Br = 48.2 kmol ) phases. a. Batch rectifier: In Step 1 the A-rich phase is distilled and A is produced (Table 3). b. DCS: The preliminary decantation provides the division of the charge which determines the value of vA. Hence only one solution exists (Table 3). The duration of the cycle is nearly equal in the two cases. 4.2. Separation of the ternary mixture (isopropanol (A) – water (B) + benzene (E))
Binary azeotropic charge ( x BAZ = [0.674, 0.326,0] ) is separated by the application of an entrainer (E). The composition of the ternary IPA – water – benzene heteroazeotrope and those of its E-rich and B-rich phases: Er
Br
x TAZ = [0.238, 0.239, 0.523] , x TAZ = [0.277, 0.048, 0.675] , x TAZ = [0.103, 0.894, 0.003] a.Batch rectifier. Calculation results are shown in Table 4. b.DCS: We determine τ and U αb / U ch for different rel. vapour flow rates of column α (Figs. 5-6). Calculation results for the best operational policy are shown in Table 4. The duration of cycle is nearly equal in the two cases. The amount of the final residue is more than 5 % of the charge for the BR, whilst there is no residue at all by the DCR.
5. Conclusion We suggest using a new double column system (DCS) for heterogeneous batch distillation. It is operated in closed mode without continuous product withdrawal. This configuration was investigated by feasibility studies based on a simplified model (maximal separation, negligible holdup) and was compared with the traditional batch rectifier (BR). The calculations were performed for the mixtures n-butanol – water and isopropanol – water + benzene (entrainer). The performance of the DCS was compared with that of the BR. The main benefit of the DCS is that it produces no residue to be separated later. The DCS proved to be feasible and in the cases studied competitive with the BR. In comparison with the BR it gave for the ternary mixture better and for the binary one similar results, respectively. Feasibility studies were completed by rigorous simulations. The results of these calculations based on much less simplifying assumptions are published in a separate paper.
References Modla G., P. Lang and K. Molnar, (2001). Batch Heteroazeotropic Rectification … 6th WCCE, Melbourne, Australia, (10 pages on CD),. Modla G., P. Lang , B. Kotai and K. Molnar, (2003). AIChE J, 49 (10), 2533. Rodriguez-Donis I, V. Gerbaud, X. Joulia, (2002). AIChE J, 48 (6), 1168. Rodriguez-Donis Y., J. Equijarosa, V. Gerbaud, X. Joulia, (2003). AIChE J, 49, 3074. Skouras S., V. Kiva , S. Skogestad, (2005a). Chem. Eng. Sci., 60, 2895. Skouras S., S. Skogestad, V. Kiva, (2005b). AIChE Journal, 51 (4), 1144-1157.
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Integrated Design Of Solvent-Based Extractive Separation Processes P. Lek-utaiwana,b, B. Suphanita, N. Mongkolsirib, R. Ganic a
ChEPS, Dept of Chem Eng, King Mongkut’s Univ of Technical Thonburi, Bangkok , 10150, Thailand b SCG Chemicals, Rayong,21150, Thailand c CAPEC, Dept of Chem Eng, Technical Univ of Denmark, DK-2800 Lyngby, Denmark
Abstract The objective of this paper is to present a systematic methodology for integrated design of solvent-based extraction processes for recovery of desired chemicals and to highlight the application of this methodology through the solution of an industrial case study involving the recovery of two highly valued with high demand chemicals, ethylbenzene (EB) and mixed-xylenes, from a C8-aromatics mixture. The computer aided molecular design (CAMD) technique integrated with process design has been used to design the solvent-based extractive separation process. The details of the systematic methodology are presented and highlighted through the results from the industrial case study. A sensitivity analysis of the design to uncertainties in thermodynamic properties has been performed to evaluate their effect on process economy and environmental impact. The sensitivity analysis also provided input to design of experiments for measurements of important uncertain properties. Keywords: solvent-based separation, solvent selection, extractive distillation, CAMD
1. Introduction Increasing the value of a product is an important issue in almost all chemical processes. This is particularly true in naphtha cracking processes where there are opportunities for improvements of a large range of chemical products, which are usually intermediates for a wide range of chemicals-based consumer products. In this way, they enhance the value of the naphtha cracking unit product. Among many options, two commonly employed alternatives to upgrade byproducts is to separate and purify them to high-value (pure) chemicals or to convert them to another higher value chemical through reaction pathway. In this work, the first option of purifying the chemical product is investigated. The design objective for the solvent-based purification process is to not only satisfy the process-product specifications, but also to have a good economic return and reliability of performance. The key to success in this case is not only the process design, but also the effect of solvent selection on the process economy, process operability and the environmental impact. In this work, a systematic methodology integrating the solvent (design) selection issues with the extractive separations issues, the process economy and industrial operational as well as environmental constraints. Various design approaches have been proposed for separation process design and optimization, such as heuristic, insights based approach, graphical or geometric approach and numerical. In this work, the driving force based design, proposed by Gani & Bek-Pedersen [2] for synthesis, design and operation of the separation processes, especially for distillation based separation system is applied. Successful solvent-based
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extraction system design also requires the use of a good (environmentally acceptable) solvent that can increase driving force of interesting key components.
2. Methodology for design of solvent-based extraction processes The systematic methodology integrates the solvent design (selection) issues with the extractive separation issues, the process economy and industrial operational as well as environmental constraints. The CAMD technique [1] is combined with analysis of residue curve maps and separation driving forces to generate feasible solvent-based extractive separation process flow-diagrams. The best process is identified as the one that satisfies all the product-process constraints as well as being economic and environmentally acceptable. Figure 1 shows the main steps of the systematic methodology.
Figure 1: Block diagram of the integrated design of solvent-based separation process sequencing algorithm
The methodology highlighted in Fig 1 employs a number of computer aided methods & tools. For solvent selection, it employs the ProCAMD software [4] that designs/selects solvents for specified solvent target properties. The solvent (entrainer) plus the binary mixtures to be separated forms ternary systems whose distillation boundaries and residue curve maps are analyzed to identify the suitable solvent. ICASPDS is used for this purpose. As the solvent-based ternary systems are non-ideal mixtures, the accuracy of the predicted vapor-liquid phase equilibria are verified, where possible, with available experimental data and compared with more than one property model. In this case, the following software, ICAS®, Aspen Plus®, Aspen Distill®, or DistillDesigner® have been used. For solvent recovery column design, the driving force
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approach of Gani and Bek-Pedersen [2] has been used while for the two-feed extractive distillation column, the method proposed by Petlyuk [3] has been used. For a feasible process configuration, the operational costs as well as the equipment costs are calculated to obtain the final economic analysis. The type of solvent used and its loss with the products provides an account of the environmental impact. In a business (industrial) world, the most important issue is not just operational feasibility but also economic feasibility. Therefore, an economic evaluation is needed before any new process investment can be made. However, before any such investments, any uncertainties in the design need to be quantified. Therefore, a sensitivity analysis of the uncertain parameters to investigate the effects on process economy is performed as the last task of the systematic design methodology. The conclusions of the sensitivity analysis helps the engineers to decide if further experimental work is necessary.
3. Industrial case study This case study involves the recovery of highly valued and high demand ethylbenzene (EB) and mixed-xylenes (comprising of p-xylene (PX), m-xylene (MX) and o-xylene (OX)) from a C8-aromatics mixture (C8A). As point out above, C8A is isomers mixture, so their separation (recovery) is not simple, that why there is only one commercial process of liquid-phase adsorptive separation available for EB recovery from C8A. [8] However, this process requires high investment cost and generates huge volume of waste adsorbent that may become an environmental problem. Therefore, another green process should be considered for the EB purification. The ratio of various properties of the key components (EB and PX) were tested to examine the possibly alternatives. The result showed, by vapor pressure ratio, the solvent-based extractive distillation can be employed for their purification. [7] 3.1. Solvent selection The problem of identifying solvents for the separation of EB from PX by extractive distillation is considered first. The target solvent properties are solubility parameter, the normal boiling point, the normal melting point and selectivity (Sij = γi∞/γj∞). Specifying the above constraints to ProCAMD, a list of feasible solvents were obtained, from which, a selection is listed in Table 1. Table 1 Selected solvent by ProCAMD Result no
1 2 3 4 5 6 7 8 9
Solvent Name
Solubility parameter at 298 K (MPa1/2)
Normal Melting point (K)
Normal Boiling point (K)
Selectivity
Aromatic-Aldehyde-1 (AAD1) Acyclic-Ester-1 (AE1) Cyclic-Ketone-1 (CK1) Acyclic-Ester-2 (AE2) Acyclic-Ketone-1 (AK1) Cyclic-Ketone-2 (CK2) Acyclic-Ketone-2 (AK2) Aromatic-Alcohol-1 (AAL1) Cyclic-Amide-1 (CAD1)
21.44 21.42 17.86 19.84 17.69 19.88 17.88 24.09 23.16
247.15 254.15 265.05 234.15 209.23 244.91 232.4 248.81 249.15
453.51 475.15 488.35 453.95 422.02 419.32 451.08 466.67 475.15
1.23 1.22 1.22 1.20 1.19 1.19 1.18 1.13 1.13
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As result in table 1, the solvent that claimed by Berg’s patent [7] was also presented in the list at the fifth rank. This means successful in solvent selection could be achieved because the better solvents in term of both selectivity and solvent recovery can be acquired. (Berg’s solvent has closed boiling point to OX, so this becomes solvent recovery problem.) Due to its concentration-independent, the selectivity is the primary criterion chosen to be considered for selecting the suitable solvent in stead of the driving force. However, the selection of the best solvent based on only Sij is inadequate because it does not directly relate to the distillation design. The suitable criterion should return to how significant the solvent could alter the driving force between the key components. 3.2. Analysis of the solvents in terms of driving force diagrams The performance of the solvents were checked through solvent-free driving force diagrams for different choices of the property models. Figure 2 shows the solventfree driving forces obtained for the same systems with the original UNIFAC-VLE model and the UNIFAC-Do model [5]. As solvent AE1 (acyclic-ester-1) appears to have desired predicted behavior with both models, it is selected for further studies. One important point of difference is the predicted values of Dy (see Figures 2a-2b). With the UNIFAC-VLE model, it is 0.045 while with UNIFAC-Do, it is 0.145. Therefore, experimental verification is necessary to establish the true value and a sensitivity analysis to determine the solvent property effects on process economy needs to be checked before a decision for pilot plant studies can be made. Diving force curve-UNIFAC-DMD Diving force curve-UNIFAC
0.16
0.06 No-Solvent AAD1 AE1 CK1 AE2 AK2 CAD1 AK1 CK2 AAL1
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No-Solvent AAD1 AE1 CK1 AE2 AK2 CAD1 AK1 CK2 AAL1
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DF
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-0.02
xEB
(a) by UNIFAC
xEB
(b) by UNIFAC-Do
Figure 2: Solvent-free driving force curves plots for selected solvents
Assuming that one of the models is correct, the design calculations can be continued to obtain the process economic analysis. At the same time, the environmental impact can also be investigated. As our selected solvent is an ester, it’s MSDS shows low human effect, which may only act as an irritant to skin, eye and respiratory, and do not have any other environmental effect. So, it can be concluded that solvent is suitable for separation of EB from PX by extractive distillation. 3.3. Process design Solvent-based separation through extractive distillation consists of two distillations. The first is an extraction column with two feed (Aspen Distill® was used designing this column), while the second is a simple distillation column (the driving force concept was used for designing this column). The design was then verified by rigorous simulation using Aspen Plus®. The residue curve map (see Fig. 3) was used
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Integrated Design of Solvent-Based Extractive Separation Processes
for the design of the first column to have consistent bottom and top products. The design details for this column for both models are given in Table 2. For the solvent recovery column, fifty theoretical stages were required for total recovery the solvent with degree of purity to level of 99.99%mol. Key components for this column were AE1 and OX. By driving force concept, at Dx = 0.4, the feed location was at 30th stage. The conventional distillation for separating EB to the required purity was also designed to compare with the extractive distillation approach. Since C8 aromatics mixture is an ideal mixture, so the same results were obtained from both property packages [6], which total number of stage was 298 stages, feed location was at 179th stage (Dx = 0.4, Dy = 0.0145), reflux ratio was 20, reboil ratio was 23.3. Separation of EB by a single conventional distillation column is obviously not feasible. However, the data can be used to compare with extractive distillation system in terms of investment cost and operating cost.
AE1
AE1
(a) Feed and products specifications
(b) Complete design
Figure 3 Residue curve maps of EB-PX-AE1 system Table 2 Input data and results from Aspen Distill® for extraction column design
Input Parameter
Value
EB/PX mix. rate EB/PX mix. composition AE1 rate
1.0
AE1 composition Distillate composition
AE1 = 1.0
Bottom product compositon Reflux ratio Operating pressure
EB = 0.6 PX = 0.4 2.5
EB = 0.995 PX = 0.005 AE1 = 1e-6 EB = 0.031 PX = 0.121 AE1 = 0.848 20 1 atm
UNIFAC Output Parameters Number of theoretical stages Feed location
UNIFAC-Do Value 78
Output Parameters Number of theoretical stages Feed location
Value 44
EB/PX mix. stream AE1 stream
33th
0.53
Distillate product rate
0.53
Bottom product rate
0.47
Bottom product rate
0.47
Reboil ratio
2.20
Reboil ratio
2.52
EB/PX mix. Stream AE1 stream
58th
Distillate product rate
7th
(Note: Dy = 0.045)
(Note: Dy = 0.145)
8th
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3.4. Sensitivity analysis A sensitivity analysis was performed to identify the effect of the driving force on the utility cost and the equipment cost. The results are shown in Fig. 4 and they confirm that the driving force is inversely proportional to the ease of separation and therefore the cost. This means that over-prediction of the driving force may lead to infeasible separation while under-prediction of the driving force may lead to waste of resources. The equipment costs were estimated by Aspen ICARUS® and utility pricings were based on general pricings in Thailand. Equipm ent cost sensitivity analysis
Utility cost sensitivity analysis 3,800
10.00
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0
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Dr i v i ng f or c e ( D y )
(b) Equipment cost
Figure 4 Sensitivity analysis on uncertainty effect of thermodynamic property prediction
4. Conclusions A systematic methodology where solvent selection and process design have been integrated, has been developed and tested through the solution of an industrial case study involving a difficult separation problem. While the methodology and the corresponding tools were found to be applicable for industrial problems, uncertainties in property model predictions were noted. This pointed out that experimental verification of the model-based results is necessary and the sensitivity analysis provided enough information to plan the experimental effort, as future work for this project. Finally, it can be concluded that the available computer aided methods and tools can significantly reduce the time and effort to solve the class of problems highlighted in this work.
References [1] AT Karunanithi, LEK Achenie, R Gani, 2006, Chemical Engineering Science 61, 1247-1260. [2] R Gani and Bek-Pedersen, 2000, AIChE Journal, 46, 1271-1274 [3] F.B. Petlyuk, 2004, Distillation Theory and Its Application of Optimal Design of Separation units, Cambridge series in chemical engineering [4] R. Gani, 2006, ICAS-Program Package, CAPEC Report, DTU, Lyngby, Denmark (www.capec.kt.dtu.dk) [5] U. Domanska et. al., 2005, Fluid Phase Equilibria 235, 182-190. [6] W.L. Rodrigues, S. Mattedi, J.C.N. Abreu, 2005, Brazilian Journal of Chemical Engineering [7] L. Berg, Sep. of EB form PX by Ex. Dist, US Patent No. 5 425 855 (1995). [8] UOP LLC, 2004, Process Technology and Equipment
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Development of a novel Petri net tool for process design selection based on inherent safety assessment method Fakhteh Moradi, Parisa A. Bahri * School o, Electrical, Energy and Process Engineering, Murdoch University, Murdoch, WA 6150, Australia
Abstract Safety assessment can be implemented using different tools during process design stage. As part of this assessment, the implementation ability and the flexibility of the tools are of great concern. In this paper, a new user-friendly approach using Petri nets as modelling and implementation tool has been presented. Inherent safety methodology is used to assess the safety level of different process options and I2SI indexing system is employed to quantify safety factors. The applicability of this tool is demonstrated through revisiting an aclyric acid production case study taken from literature. Keywords: Petri net, inherent safety, process design.
1. Introduction Due to the importance of safety in process industries various safety and risk assessment methods have been developed to provide the opportunity of considering safety issues in early design stages. Meanwhile several studies have been undertaken to create appropriate implementation tools for developed assessment methodologies (Palaniappan et al., 2002a, Khan and Amyotte, 2004 and 2005). In this paper, inherent safety method and Petri nets modelling have been selected as the safety assessment and implementation tool, respectively. Section 2 briefly describes inherent safety methodology and adapted indexing tool and proposed modifications. Section 3 gives some information about Pteri nets and the related modelling approach undertaken in this research. In section 4 the proposed method is illustrated using a case study. Some discussions are given in section 5 and finally the paper concludes with reviewing the advantages of the proposed method.
2. Inherent safety method Inherently safer design, as one of the assessment techniques used in early design stage, aims at making processes inherently safer by using key principles such as elimination, minimization, substitution, moderation, and simplification (Kletz, 1985, Hendershot and Berger, 2006). Inherent safety methodology applies these principles to a basic process in order to eliminate or reduce the hazards. Using less hazardous materials, minimizing the inventory of hazardous material and changing the form and/or condition of using hazardous materials are some examples of application of these guidewords (Hendershot, 1997, Khan and Amyotte, 2005).
*
Author to whom correspondence should be addressed:
[email protected]
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From the financial point of view, considering inherently safer options in process deign will reduce the process lifetime costs. Although conventional systems may have less fixed and operational costs, inherently safer options turn to be the cost-optimal ones given their lower maintenance and safety measure costs. In application of inherent safety concepts, I2SI indexing system is used for quantification of process units and equipment response.
2.1. Indexing system The I2SI indexing system for inherent safety evaluation as developed by Khan and Amyotte (2005) has been adapted in this study. Their final inherent safety index (I2SI) shows the potential applicability of the inherent safety keywords to the process. The index value greater than unity means positive response to inherent safety principles. The larger index indicates better response. A less than unity I2SI indicates that the equipment does not respond to inherent safety guidelines which is a weakness of the process route containing that equipment. In financial analysis two final indices are available: Conventional Safety Cost Index (CSCI) which is the ratio of conventional safety measures of the system over the probable loss cost, and Inherent Safety Cost Index (ISCI) which is the relative amount of the cost of inherent safety measures added to the system to the loss cost (Khan and Amyotte, 2004). Smaller ISCI in comparison to CSCI shows enviable impact of safety features on safety costs. In other words the smaller the ISCI/CSCI fraction the better the response. In this study the total number of non-responding equipment in each route is considered as the first comparison factor named Penalty. It is also proposed that I2SI to be divided by ISCI/CSCI ratio to obtain a unique index called Safety-Cost Ratio which represents a combination of safety and cost factors for each piece of equipment (Equation 1). Since a large I2SI and a small ISCI/CSCI ratio is always desirable, larger values of SafetyCost Ratio will indicate better response to inherent safety principles. In addition the Total Safety-Cost Ratio of each route is calculated as the sum of the individual SafetyCost Ratios of all the equipment existing in that route (Equation 2). These calculations provide decision-makers with a unique index for each route as a judgment base instead of simple assessment of different factors of different equipment in Khan and Amyotte (2005). These modifications will dramatically reduce human intervention into decisionmaking process. Safety-Cost Ratio = I2SI / ( ISCI / CSCI ) Total Safety-Cost Ratio =
¦
n
(1)
(Safety- Cost Ratio)
i 1
i
(2)
n is the total number of equipment Finally, to make decision about the best route, the Penalty factor would be considered in the first step. The route with the smallest Penalty factor is considered as the safest route. At the second level, among the routes with the same and smallest Penalty factors, the best one is the route with the largest Safety-Cost Ratio.
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3. Petri net model The implementation tool has to offer a comparative base to evaluate different process routes and to choose the best possible option. Different factors will come into account to define the efficiency of the tools. Flexibility, complexity and the number of routes that can be evaluated at certain time can be noted as some of these factors. Petri net modelling tool can be considered as a suitable implementation tool for risk assessment due to its flexibility and process simulation ability (Vernez et al., 2004). In addition, different feasible process options can be modelled in a Petri net as a super model, and assessed from safety point of view. A Petri net is a directed bipartite graph including places (drawn as circles) and transitions (drawn as bars). Places contain tokens which are shown as dots. The set of arcs are divided into input and output arcs with an arrowhead on their destinations. A transition is called enabled if all input places have at least the same number of tokens as all its output places. An enabled transition fires by removing tokens from input places to output places. Places, transitions and arcs all can be weighted. Weight is an additional feature that can carry critical attribute of related node through the nets (Gu and Bahri, 2002) In this paper, the first step has been to adapt a type of Petri net to model the process route(s). Initially, the basic route of producing a desired product is chosen. All possible combinations of process units to optimize the production yield and operating conditions of the basic route are considered as new routes. All the possible routes are then put together to create the supernet model of the system. This supernet is divided into various subnets based on the similarities and differences between production alternatives. Similar processing units of different routes build up subnets which are shared between some routes while unlike processing parts may create subnets which are used in one route only. Petri net model is able to automatically create different combinations of these subnets to define all possible process routes. The type of Petri net model used in this research is Place Weighted Petri net. Places represent equipment, transitions show starting and finishing of operations and tokens are raw material, semi-finished and finished products. The weights on places indicate Safety-Cost Ratios for equipment.
4. Case study The selected acrylic acid production process involves catalytic oxidation of propylene in the vapour phase at 190°C and 3 atm pressure. Two side reactions of this one-step process result in production of carbon dioxide and acetic acid with water (Khan and Amyotte, 2005). Three main options from different possible combinations of process units have been previously studied (Khan and Amyotte, 2005, Palaniappan et al., 2002b). The first option is the base case with no additional inherent safety features. The second and third options are revised versions of the first one. Modifications can include some or all of the following: a quench tower to reduce the temperature, change of solvent to lower the severity of the operating conditions, an extraction column, a solvent mixer to optimize the use of solvent and efficiency of acid extraction and the use of solvent recycle. Option 3 (Figure 1) which contains all basic and additional processing units can be described as follows. Acrylic acid is produced by partial oxidation of propylene in a fluidized-bed catalytic reactor. To prevent any side reaction, a cold recycle quench is used immediately after reactor. Deionized water in the off-gas absorber absorbs off-gas from the quench tower, containing acetic acid, acrylic acid, unreacted propylene, and byproducts. In the next step, an acid extractor is used for liquid-liquid extraction to
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separate the acid from water using diisopropyl ether as the solvent. After that diisopropyl ether is recovered and recycled in the solvent tower from the organic phase of extractor products. The bottom stream from this solvent tower is sent to the acid tower to separate and cool the acetic acid and acrylic acid and send them to storage. A waste tower is used to recover and recycle the solvent from acid extractor’s aqueous phase product. The bottom wastewater stream, containing acetic acid and small amount of solvent, is sent to wastewater treatment (Palaniappan et al., 2002b). In order to create the supernet of this process involving all processing units of the three mentioned options, the basic parts of routes are included in the main structure of the supernet. Moreover some groups of one or more units have been created and modelled as subnets. As a result, the following unit groupings/subnets have been considered: x Subnet A: including air compressor (Figure 2a). x Subnet B: including distillation column I, distillation column II, and distillation column III (Figure 2b). x Subnet C: including solvent splitter (Figure 2c). x Subnet D: including acid extraction tower, distillation column I, distillation column II, distillation column III, and solvent mixer (Figure 2d). The Petri net model of the supernet (Figure 2e) is implemented in Visual C++ and the total number of routes generated by Petri net is found to be 8. The results of Total Safety-Cost Ratio and Penalty factor estimations for these routes are presented in Table 1.
5. Discussion The results in Table 1 illustrate that the 8 generated routes have Penalty factors between 2 and 6 and Total Safety-Cost Ratios between 32.25 and 3.6 depending on their added inherent safety feature(s). Routes 3 and 4 with Penalty factor of 2 have the lowest, specifying them as safer options which are the same as options 2 and 3 respectively in Khan and Amyotte (2005). Between these two routes, route 4 has Total Safety-Cost Ratio of 32.25 which is higher than 29.98 for option 3 and the highest among all routes resulting in route 4 to be the best option. Route 5 which is the base case with no added inherent safety feature shows the highest Penalty factor of 6 and the smallest Total Safety-Cost Ratio of 3.6. In comparison with previous methods, the proposed method has significantly reduced human intervention in decision-making process. Route selection can be based on Total Safety-Cost Ratio which is a combination of safety and cost indices of all equipment in each route instead of assessing different factors separately. Moreover this approach has the capability to automatically generate possible process options and carryout safety calculations simultaneously. The automation of route generation which means creating all possible combinations of subnets and the base case is one of the most important advantages of using Petri net model. This minimizes the likelihood of missing any possible combination.
6. Conclusion This paper proposed place weighted Petri nets as a novel tool for selection of process design based on inherent safety technique. Inherent safer design is a methodology to achieve fundamentally safer plants. The impacts of applying inherent safety principals in process design can be quantified using I2SI indexing system.
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The proposed approach provides designer with the opportunity of considering more feasible routes faster through its automatic route generation ability and easier evaluation and comparison of their safety and costs through simultaneous calculation of Total Safety-Cost Ratios. Table 1. Total Safety-Cost Ratio of each route
Penalty factor Total SafetyCost Ratio
Route1
Route2
Route3
Route4
Route5
Route6
Route7
Route8
5
5
2
2
6
6
3
3
8.65
9.57
29.98
32.25
3.6
4.52
24.93
27.20
Figure 1. Aclyric acid production route including all inherent safety features.
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Figure 2. Petri net model of aclyric acid production routes, a: subnet A, b: subnet B, c: subnet C, d: subnet D, e: supernet.
References Gu, T. & A. Bahri, P., 2002, A survey of Petri net applications in batch processes, Computers in Industry, 47, 99-111. Hendershot, D., 1997, Inherently safer chemical process design, Journal on Loss Prevention in the Process Industries, 10, 3, 151-157. Hendershot, D. & Berger, S., 2006, Inherently safer design and chemical plant security and safety, American Institute of Chemical Engineering, Khan, F. & Amyotte, P., 2004, Integrated inherent safety index (I2SI): A tool for inherent safety evaluation, Process Safety Progress, 23, 2, 136-148. Khan, F. & Amyotte, P., 2005, I2SI: A comprehensive quantitative tool for inherently safety and cost evaluation. Loss Prevention, 18, 310-326. Kletz, T. A., 1985, Inherently safer plants, Plant/Operation Progress,4, 3, 164-167. Palaniappan, C., Srinivasan, R. & Tan, R., 2002a, Expert system for the design of inherently safer processes. 1. Route selection stage, Ind. Eng. Chem, 41, 26, 6698-6710. Palaniappan, C., Srinivasan, R. & Tan, R., 2002b, Expert system for the design of inherently safer processes. 2. Flowshhet development stage, Ind. Eng. Chem, 41, 26, 6711-6722. Vernes, D., Buchs, D. R., Pierrehumbert, G. E. & Bersour, A., 2004, MORM-A Petri net based model for assessing Oh&S risks in industrial processes: Modeling qualitative aspects. Risk Analysis, 24, 6, 1719-1735.
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Population balance modeling of influenza virus replication in MDCK cells during vaccine production Thomas Müllera, Josef Schulze-Horselb, Yury Sidorenkob, Udo Reichla,b, Achim Kienlea,b a
Otto von Guericke Universität Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany b Max Planck Institut für Dynamik komplexer technischer Systeme, Sandtorstraße 1, D39106 Magdeburg, Germany
Abstract In this contribution a population balance model of influenza A virus replication during vaccine production in Madin-Darby canine kidney (MDCK) cell cultures is developed. Differentiation on the population level is described by a degree of infection, which is proportional to the amount of intracellular viral proteins. This can be measured directly using flow cytometry. It is shown that the model shows reasonable agreement with experimental data, although not all details of the inner dynamics can be fully reproduced. Keywords: population balance modeling, distributed populations, virus replication, vaccine production, microcarrier cell culture.
1. Introduction In influenza vaccine production the use of permanent mammalian cell lines becomes more and more important. Besides sophisticated cell culture technologies and downstream processing methods, mathematical modeling plays a crucial role in improving production efficiency. Most notably for analysis and optimization of the process, the benefit of combining extensive experiments with mathematical modeling approaches is obvious. Thus, this strategy will contribute to the investigation of dynamic and kinetic phenomena and their link to the measured data. One can distinguish between structured and unstructured models, the latter neglecting intracellular phenomena. On the contrary, structured models account for intracellular processes and states in different compartments of the cell or include explicit kinetics for various intracellular steps of virus replication. Despite the high social relevance of infectious diseases and widespread use of animal cell lines in vaccine production, the application of even unstructured models for quantitative analysis and parameter estimation has not been common practice in bioprocess optimization. So far, research concerning influenza vaccine production in MDCK cell cultures has focused on the characterization of metabolism, growth of different cell lines and virus yields in various production systems [1,2].
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Based on the experimental investigation of the infection status of cells by measuring immunofluorescence of intracellular viral proteins with flow cytometry [3] mathematical models are required, which are able to describe distributed populations of cells with different degrees of infection. For this purpose, in the present paper an internal coordinate is introduced to quantify the degree of infection and the previous approach by Möhler et al. [4] is extended accordingly.
2. Model formulation The population balance model of Möhler et al. [4], which forms the basis for the presented approach, describes the replication of influenza A viruses in MDCK cells growing on microcarriers. It is unstructured and includes three concentrated state variables, which are the number concentrations of uninfected cells Uc, infected cells Ic and free virus particles V. It is assumed that at the time of infection (t0) all microcarriers are completely covered with cells, which corresponds to the maximum cell concentration ( U c , 0 = C max = 1.2 ⋅10 6 ml −1 [4]). Virus seed is added to the microcarrier cell culture and infection takes place. The amount of infectious virus particles added is described via MOI (multiplicity of infection, number of infectious virions per cell at t0 [5]). Virus particles instantly attach to uninfected cells. Consequently, the latter become infected with the infection rate kvi. After a certain time delay (τ = 4.5 h) due to intracellular processes, infected cells start releasing virus particles with the release rate krel and carry on until they die (kcd). Free virions can either attach to still available uninfected cells (kva) or simply degrade (kvd). Attachment to infected cells is neglected. In Möhler et al. [4] it is shown that the simple unstructured model is able to show good agreement between simulated outer dynamics and hemagglutination (HA) assays, which allow to estimate the total number of virus particles in the supernatant. However, the intracellular progress of infection is not considered, and therefore a comparison with flow cytometric fluorescence data characterizing the cell’s status during infection is impossible. To change this situation and to allow differentiation between cells the degree of infection δ is introduced as an infected cell’s property:
I c (t , δ ) = I c ,δ (t ) with δ ∈ N, [1, ∞] The degree of infection specifies the intracellular amount of viral protein and corresponds to the equivalent number of virus particles inside the cell assuming that a complete virus particle comprises 4000 viral proteins M1 and NP (3000 M1/virion +1000 NP/virion [6]). Schulze-Horsel et al. [3] show that the intracellular amount of viral M1 and NP proteins is coupled linearly with the cell's fluorescence caused by immunostaining against influenza A virus M1 and NP. The uptake or production of 4000 viral M1 and NP proteins or 1 virus particle respectively will lead to an increase of δ by 1; the cell’s fluorescence will increase by 2.66 FU/virion (fluorescence units, data not shown). Because not only infected cells but also uninfected cells with no intracellular viral protein show unspecific fluorescence intensity due to unspecific antibody binding, it seems suitable to change the internal coordinate from the degree of infection δ to a more
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general degree of fluorescence ϕ, where every step from one degree to another accounts for a change of the cell’s fluorescence intensity by 2.66 FU. Thereby, also the distributed unspecific fluorescence of uninfected cells can be taken into account: U c (t , ϕ ) = U c ,ϕ (t )
I c (t , ϕ ) = I c ,ϕ (t ) with ϕ ∈ N, [1, ∞ ]
The change of behavior along ϕ is characterized by two processes: virus replication increases fluorescence intensities with the replication rate krep while virus release decreases it respectively with the release rate krel. These two processes describe the inner dynamics of the system. 2.1. Model equations It can be shown that growth and death of the uninfected cells can be neglected due to medium exchange, limited space on microcarriers and fast progression of infection. Therefore, only infection is considered for description of the uninfected cell’s behavior: dU c ,ϕ dt
= −kvi U c ,ϕ V
(1)
As an initial condition, uninfected cells are considered to be normally distributed over the logarithmically scaled fluorescence axis to ensure good agreement with flow cytometric data collected by Schulze-Horsel et al. [3]. Infected cells emanate from uninfected cells, intracellular virus replication starts and the number of infected cells deceases with the specific death rate kcd. As described above convection along ϕ occurs due to virus protein accumulation and release. Every step from one degree of fluorescence to another is associated with the intracellular production or release of one virus particle respectively, so that the actual degree of fluorescence of every infected cell is controlled by these two effects. For brevity only the equation for ϕ > 1 is shown: dI c ,ϕ dt
= k vi U c ,ϕ −1V − kcd I c ,ϕ − k rep (I c ,ϕ − I c ,ϕ −1 ) + k rel (I c ,ϕ +1 − I c ,ϕ )
(2)
Free virions emerge from infected cells with ϕ > 1 by means of virus release. They are able to attach to uninfected cells (kva) or degrade with time (kvd). ∞ ∞ dV = k rel ¦ I c ,ϕ −kvd V − k va ¦ U c ,ϕ V dt ϕ =2 ϕ =1
(3)
Additionally, dead cells are included in the process because intact dead cells show up in the flow cytometric data. For simplicity all dead cells are considered to stay intact and keep the specific ϕ they possessed at time of death.
3. Parameters As the focus of this work is on the further development of the model of Möhler et al. [4], parameter identification was skipped for the time being and the “best-fit” parameter
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set was adopted. It is worth noting that the parameters used here have the same significance as in the undistributed model, except for the replication rate krep which has been introduced for the present model; its value has been derived from the flow cytometric data by means of sum-of-least-squares method (data not shown). Initial conditions are in agreement with the same set of experimental data of Schulze-Horsel et al. [3]. Table 1 summarizes the applied parameters and initial conditions, which differ from the ones published by Möhler et al. [4, Tab. 1, p. 50]. Table 1. Applied parameter set and initial conditions (note, that not every virus particle is infectious and non infectious virions have to be considered) Parameter
Value
Unit
krep
502 3 120 360
h -1 106/ml 106/ml 106/ml
V0 (MOI = 0.025) V0 (MOI = 1.0) V0 (MOI = 3.0)
4. Simulation results All simulations were performed with the dynamic simulator DIVA and visualized with MATLAB. For simplicity the delay behavior between infection and virus release was reproduced by simply shifting the simulation results by tshift = 4.5 h [4]. 4.1. Outer dynamics Figure 1 shows the evolution of virus yields over time for two of the three observed initial conditions. There is no detectable difference between the present structured model and the unstructured approach of Möhler et al. [4]. That is because of the unstructured model being included in the structured model as the zeroth order moment.
Figure 1. Outer dynamics in comparison with model of Möhler et al. [4]: virus yield vs. time post infection for different MOI (circles: experimental results, solid line: unstructured model, dashed line: structured model, tshift = 4.5 h)
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Figure 2. Inner dynamics: number density function qc vs. fluorescence intensity for specific time points post infection. (dots: experimental results, solid line: simulation results, MOI = 3.0, tshift = 4.5 h)
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4.2. Inner dynamics The inner dynamics are determined by the cell distribution over the fluorescence changing with time. For comparability the cell concentrations have to be converted into number density functions, which are obtained by normalization with the overall cell concentration at the specific time point and division by the specific class width in logarithmic scale. All cells (uninfected, infected and dead) contribute to the distribution as they all show fluorescence. Figure 2 shows the comparison between simulation results and the flow cytometric data reported by Schulze-Horsel et al. [3] for MOI = 3.0. The simulation peak lags behind in the beginning and catches up for later time points, but the overall tendency of increasing mean values can be reproduced quite well. However, the present model has a drawback: for an unknown biological reason the experimental distributions fall back to smaller fluorescence intensities at later time points (data not shown). So far, this effect cannot be simulated with the presented model formulation adequately.
5. Conclusion A new deterministic population balance model with distributed cell populations has been presented. The model is based on the unstructured approach of Möhler et al. [4]. Concerning outer dynamics the present model is equivalent to the unstructured model which proved to be sufficient to predict virus yields for different initial conditions [4]. The characteristics of the inner dynamics can be simulated except of the decrease of fluorescence intensity at later time points. The biological reasons for this effect are unclear. Presumably there are more states that have to be considered during virus replication like intercellular communication, extent of apoptosis or specific stage in cell cycle. Future computational and experimental research will aim in this directions and concentrate on structured descriptions of the virus replication in mammalian cell culture.
References [1] J. Tree, C. Richardson, A. Fooks, J. Clegg, D. Looby, 2001. Comparison of large-scale mammalian cell culture systems with egg culture for the production of influenza virus A vaccine strains. Vaccine 19, 3444–3450. [2] Y. Genzel, R. Olmer, B. Schäfer, U. Reichl, 2006. Wave microcarrier cultivation of MDCK cells for influenza virus production in serum containing and serum-free media. Vaccine 24 (35–36), 6074–6084. [3] J. Schulze-Horsel, Y. Genzel, U. Reichl, 2007. Quantification of intracellular accumulation of M1 and NP of influenza A virus – monitoring of infection status of production cells during vaccine production by flow cytometry, Submitted to BioMedCentral Biotechnology. [4] L. Möhler, D. Flockerzi, H. Sann, U. Reichl, Apr. 2005. Mathematical model of influenza A virus production in large-scale microcarrier culture. Biotechnology and Bioengineering 90 (1), 46–58. [5] P. Licari, J. Bailey, 1992. Modeling the population dynamics of baculovirus-infected insect cells: optimizing infection strategies for enhanced recombinant protein yields. Biotechnology and Bioengineering 39 (4), 432–441. [6] D. Knipe, P. Howley, D. Griffin, 2001. Field’s virology, 4th Edition. Lippincott Williams & Wilkins, Philadelphia.
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A population balance model approach for crystallization product engineering via distribution shaping control Zoltan K. Nagy Chemical Engineering Department. Loughborough University, Loughborough, LE11 3TU, United Kingdom
Abstract The paper presents a practical control approach, which can be used to directly design the shape of a crystal size distribution, to robustly achieve desired product properties. The control approach is implemented in a hierarchical structure where on the lower level a model-free crystallization control methodology, the supersaturation control, drives the system in the phase diagram, rather than in the time domain, whereas on the higher level a robust on-line model based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modeled using the population balance equation, which is solved using an efficient implementation of the method of characteristics. Keywords: distribution shaping control, population balance modeling, method of characteristics, optimal control, quadrature method of moments.
1. Introduction Crystallization is one of the key unit operations in pharmaceutical, food and fine chemicals industries. Despite the long history and widespread application of batch crystallization, there remains a disproportionate number of problems associated with its control [1], mainly related the complex nonlinear dynamics with non-ideal mixing, and various disturbances characteristic to these systems. The operating conditions of the crystallization process determine the physical properties of the products which are directly related to the crystal size distribution (CSD), shape or polymorphic form. These properties determine the efficiency of downstream operations, such as filtration, drying, and tablet formation, and the product effectiveness, such as bioavailability and shelflife. With the recent change of industrial procedures from Quality-by-Testing (QbT) to Quality-by-Design (QbD) and the advent of process analytical technology (PAT) initiative, especially in the pharmaceutical industries, approaches which can be used to design desired product properties are of great interest. The classical control objectives expressed in characteristics of the size distribution (e.g. maximize average size, minimize coefficient of variation) can lead to conservative and economically inefficient designs of the crystallization systems [2]. The paper presents an approach which can be used to directly design the shape of a crystal size distribution, to achieve desired product properties. Since dissolution rate depends on the shape of the CSD, when the resulting crystals represent the final product (e.g. drugs for inhalers) controlling the shape of the CSD can provide novel applications in the area of drug delivery, or environmentally friendly dosage of pesticides, where particular multimodal distributions can be designed to achieve desired concentration level of the active compound. The crystallization system is modeled via a population balance equation which is directly used in the
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optimization procedure where the objective function is expressed in terms of the shape of the entire CSD. The population balance model (PBM) is solved using an efficient implementation of the method of characteristics [3] when nucleation and growth are the governing mechanisms, and with the quadrature method of moments (QMOM) when agglomeration and breakage are also considered [4]. It is shown that in special cases when constant supersaturation control is applied analytical solution of the PBM is possible for the case of generic power law growth kinetics. The optimization problem is solved using an efficient multistage approach implemented in the optimization package OptCon. The proposed approach is corroborated in the case of a simulated crystallization system.
2. Population balance modelling of the batch crystallization process 2.1. PBM with growth and nucleation kinetics only Considering a single growth direction with one characteristic length L , and a wellmixed crystallizer with growth and nucleation as the only dominating phenomena the population balance equation (PBE) has the form sfn (L, t ) s{G (S , L; Rg )fn (L, t )} B(S ; Rb )E(L0 , L) , st sL
(1)
where fn (L, t ) is the crystal size distribution expressed in the number density function (number of crystal per unit mass of slurry), t is time, G (S , L; R ) is the rate of crystal growth, B(S ; Rb ) is the nucleation rate, S = (C-Csat) is the supersaturation, C is the solute concentration, Csat = Csat(T) is the saturation concentration, and Rg and Rb are vectors of growth and nucleation kinetic parameters, respectively. Equation (1) can be transformed into a homogeneous hyperbolic equation with boundary condition f (L0 , t ) B(S )/G (S ) and initial condition given by the size distribution of seed, f (L, 0) fseed (L0 ) . The partial differential equation can be reduced to a system of ODEs by applying a combination of the method of characteristics (MoC) and method of moments (MoM). The aim of the MoC is to solve the PDE by finding characteristic curves in the L t plane that reduce the PDE to a system of ODEs. The L t plane is expressed in a parametric form by L L(2 ) and t t(2 ) , where the parameter 2 gives the measure of the distance along the characteristic curve. Therefore fn (L, t ) fn (L(2 ), t(2 )) , and applying the chain rule gives: g
dfn dL sfn dt sfn d 2 d 2 sL d 2 s t
.
(2)
Considering size independent growth and comparing (2) with (1) we find 2 t and the characteristic curve is given by dL G . dt
(3)
Adding (3) to the equations which results by applying the MoM, we can calculate the characteristic curve and boundary conditions f (L0 , t ) by the following ODEs,
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d N0 B dt d Nj G Nj 1 BLj0 , j 1, 2, 3 , (4) dt dL G dt with initial conditions x 0 [N0 (0), N1 (0), N2 (0), N3 (0), 0] where the jth moment Nj is
defined by Nj
¨
d
Lj fn (L, t )dL,
j 0, !, d .
(5)
C (t ) C (0) kv Sc (N3 (t ) N3 (0)) ,
(6)
0
The solute concentration is given by
where Sc is the density of crystals and kv the volumetric shape factor. 2.2. PBM with breakage and agglomeration kinetics The dynamic population balance equation for a closed homogenous system considering a single characteristic size is written,
1/ 3
1/ 3
3 3 3 3 fn M
d sfn L
L2 L C L M , M fn L M
¨ b L, M a M fn M dM ¨ dM 2/3 3 3 L 0 st 2 M
L
birth due to breakage
birth due to agglomeration
(7)
d s G L fn L
E 0, L B0 a L fn L fn L ¨ C L, M fn M dM
0 sL
nucleation death due to breakage growth
death due to agglomeration
where ȕ, a, G, B and b are the aggregation kernel, breakage kernel, growth rate, nucleation rate and the daughter particle size distribution, respectively. The quadrature method of moment (QMOM) is based on the transformation d
Nk
¨
N
fn L Lk dL x wi Lki
(8)
i 1
0
After moment transformation and applying the quadrature rule the model is given by N N N k /3 dNk 1 N wia Li b k, Li wi w j L3i L3j C Li , Lj wia Li Lki dt 2 i 1 j 1 i 1 i 1
birth due to breakage N
N
birth due to agglomeration
N
death due to breakage
(9)
wi Lki w j C Li , Lj k wi Lki 1G Li E 0, k B
i 1 j 1 i 1 nucleation
death due to agglomeration
growth
The breakage and agglomeration kernels depend on mixing conditions. Optimizing the power input to the system which determines the turbulent kinetic energy it is possible to minimize breakage or agglomeration.
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3. Application of the batch NMPC for crystallization product design For the case studies crystallization of paracetamol in water was considered as the model system, for which both the 1D and 2D growth kinetics were determined, by performing D-optimal experimental design. Samples were taken every 10 minutes and the characteristic sizes were determined by using image analysis. Different product design problems were considered, when various objective functions expressed as function of the CSD ( f (CSD; R) ) were optimized, by determining the required temperature profile, seed characteristics (distribution and mass) as well as mixing characteristics (overall turbulent kinetic energy), which can be expressed by the generic robust formulation min{(1 w ) [ f (CSD; R)] wV [ f (CSD; R ]}
T (t ) Seed Mixing
(10)
where (¸) and V (¸) are the mean and variance of the performance index, respectively corresponding to the uncertain model parameter vector R . Equation (10) generally is subject to various operational, productivity and quality constraints. In the first case study the optimization problem is expressed as follows min
T (t ),mseed ,Lseed ,Tseed
{(1 w ) (fn (Lk , t f ; Rˆ) fndesired (Lk , t f ))2 wV [ fn (L, t f ; R ]} (11)
s.t.
k
Tmin b T (t ) b Tmax dT b Rmax dt C (t f ) b C max Rmin b
(12)
mseed ,min b mseed b mseed ,max Lseed ,min b Lseed b Lseed ,max Tseed ,min b Tseed b Tseed ,max
where Rˆ is the nominal parameter vector. The seed distribution is considered to be described by a Gaussian probability distribution function with mean Lseed and standard deviation Tseed . The optimization provided the optimal seed characteristics Lseed 56 Nm , Tseed 12 Nm and amount mseed 2.4 g . The temperature profile is given in Figure 1, together with the linear profile for comparison. For the linear profile the optimal seed characteristics were used as initial conditions. Figure 2 shows the microscopic images of the crystals obtained when the profiles in Figure 1 were implemented at a laboratory scale crystallizer. The entire evolution of the size distribution during the batch is given in Figure 3. It can be seen that the optimal operating policy results in a significant bias of the distribution toward large particle sizes. The schematic representation of the practical implementation of the approach is shown in Figure 5. The proposed control strategy involves two controllers: (i) a tracking controller that follows a reference trajectory in the phase diagram, and (ii) a supervising controller that adapts the reference to changing operating conditions. At near to optimal conditions, the operating curve is usually close to the nucleation curve and even small errors in the tracking can lead to spontaneous nucleation and compromised crystal quality. The feedback controller is designed that takes concentration and temperature
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measurements and adjusts the jacket temperature so that a predefined (using on openloop optimization design case) concentration vs. temperature operating is followed. The initial profile is predefined but it is adapted online using the model based predictive control approach. Concentration measurement is provided in the experimental implementation via ATR-UV/Vis coupled with robust chemometrics. Variations in operating conditions, such as quality and amount of seed, undesired secondary nucleation due to impurities in the system, disturbances in fluid dynamics, etc. require the adaptation of the operating curve both on-line and from batch to batch. The adaptation of the operating curve is especially important for complex organic molecules for which the metastable zone width might not be well defined and/or reproducible. The constrained optimization based nonlinear model predictive control strategy is used to estimate dynamic changes in shape and crystal size distribution. 32
(A)
T (qC)
31
30
(B)
29
28
0
40
80 Time (min)
120
160
0.04
pdf
0.03 0.02 0.01 0 0
80 60
200
40 400
L (Pm)
20 0
time (min)
Fig. 3. Evolution of the pdf along the whole batch for case B.
Probability density function
Fig. 1. The resulted optimal temperature profile Fig. 2. Microscopic images of the crystal products obtained with linear (A) and optimal (continuous line with plusses) and the linear cooling (B), using the optimal seed in both cases. cooling profile (dashed line).
0.6
Initial distribution
0.5 0.4
Optimized final distributon
0.3 0.2
Final distribution
0.1 0 0
200
400 600 L (Pm)
800
1000
Fig. 4. CSD in the case of controlled and uncontrolled agglomeration.
In the second case study the agglomeration is modeled by considering and hydrodynamic agglomeration kernel C (Li Lj )3 . An optimization problem similar to (10) is formulated but using the turbulent kinetic energy as optimization variable.
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Figure 4 illustrate the results of the fluid dynamics optimization. The PBM with the agglomeration kernel is solved using the QMOM with four quadrature points, represented as bars on Figure 4. The distribution is reconstructed from the moments using a modified Gamma distribution with fourth order orthogonal Laguerre polynomials. In both cases bimodal distribution is obtained. The optimized final distribution shows significantly less agglomeration. In this case a perfectly mixed tank is considered with uniform kinetic energy in the volume. Current research considers the use of multi-compartmental model in conjunction with off-line CFD simulation to estimate the distribution of turbulent kinetic energy for optimized mixing conditions.
Fig. 5. Architecture for robust control of crystal habit and shape of CSD for batch cooling crystallization.
4. Conclusions A robust optimization based control algorithm is described, which is able to design crystalline product properties, via optimization of cooling profile, seed properties or hydrodynamics. The approach provides robust performance by taking the parametric uncertainties into account in a distributional multi-objective optimization framework. The crystallization model is solved using a combination of method of characteristics and standard method of moments or quadrature method of moments, leading to a computationally very efficient approach which can be used even in real time. The two level control strategy which includes at the lower level a supersaturation controller and a model based control on the higher level was implemented on a laboratory scale crystallizer. Both the simulation and experimental results illustrate the advantages of the proposed crystallization control approach. Acknowledgements The author would like to acknowledge the financial support from the Engineering and Physical Sciences Research Council (EPSRC) UK, project EP/E022294/1.
References [1] R. D. Braatz, Annual Reviews in Control, 26, (2002) 87. [2] M. Fujiwara, Z. K. Nagy, J. W. Chew, R. D. Braatz, Journal of Process Control, 15, (2005), 493. [3] R. LeVeque, Numerical Methods for Conservation Laws, Birkhauser, 1992. [4] R. McGraw, Aerosol Science and Technology, 27, (1997), 255.
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Uncertainty patterns and sensitivity analysis of an indicator based process design framework Stavros Papadokonstantakisa, Agarwal Siddhartaa, Hirokazu Sugiyamaa, Konrad Hungerbühlera a
Swiss Federal Institute of Zurich, Wolfgang Paulistr. 10, Zurich 8093, Switzerland
ABSTRACT In recent years, many chemical companies have adopted the concept of sustainable development as a core business value. With focus on early phases of process design for continuous processes (Methyl Methacrylate process) this study tests the robustness of an established design framework, which integrates monetary, environmental, health and safety objectives. The framework comprises four stages of process modeling, each one being characterized by the available information for reaction route, yield, reaction time and separation scheme. Since several important factors are available in detail only at later phases of process design, a variety of evaluation indicators is used, which are then aggregated to a total score, realizing a multi-objective assessment. Although this is a popular approach in chemical engineering, especially when the development of rigorous models appears to be problematic or time consuming, the uncertainty issues arising must be clearly identified and analyzed, in order for the decision-maker to be able to evaluate correctly the value and limitations of the framework. The heuristical definition of the evaluation indicators, the experience based and often process specific weighting factors, the unknown nature of interactions between the aforementioned parameters, and the relative ranking based on type of designs taken into account form the ensemble of major uncertainty sources. The present study systematically detects the conditions under which these uncertainties become important and focuses more on those cases that the implementation of such a framework would fail to reach a statistically significant conclusion. A variety of uncertainty patterns and sensitivity analysis methods were applied for each defined stage and the proposed analysis is demonstrated on the design of a Methyl Methacrylate continuous process, considering six different synthesis routes. The crucial limitations identified in the results set the framework boundaries, assisting in this way the decision-maker to evaluate its scope and importance. Keywords: early phase process design, multi-objective assessment, heuristical indicators, uncertainty patterns.
1. INTRODUCTION Among several possible methods for such multi objective decision-making, e.g. spider plots [1] or Principal Component Analysis (PCA) for comparing various Safety, Health and Environmental aspects [2], the present study uses an aggregation approach, i.e.
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Design stages
different indicator results are aggregated into a single evaluation score using weighting factors [3]. Process Chemistry I (PCI)
Process Chemistry II (PCII)
Conceptual Design I (CDI)
Reaction
Reaction
+ Separation + Waste treatment
+ Equipment
Model includes
Stoichiometry, 100% yield (ideal)
Conversion, selectivity, auxiliary, catalyst, solvent, byproduct, heat of reaction
Shortcut process models, simple property data
Rigorous process models, non-ideality, reaction kinetics, detailed property data
Decision structures
No decision forced screen routes with serious problems
Select some reaction routes
Considered aspects
D1 Raw material cost Raw material cost (theoretical minimum) (updated)
Supplemental indicator
Multiobjective evaluation indicators
Economic performance Proxy for gate-to-gate costs /environ. impacts
Conceptual Design II (CDII)
Select process Optimize parameters option(s) &/or route(s) by sensitivity analysis by multiobj. evaluation of all feasible options D2 D3 D4 Production cost
Net present value
Mass Loss Indices (MLI)
Energy Loss Index (ELI)
CED in raw material production (theoretical minimum)
CED in raw material production (updated)
Cradle-to-gate CED
Cradle-to-gate CED (updated)
Hazard in E/H/S
EHS method (substance-level)
EHS method (incl. reaction mass)
EHS method (incl. process mass)
EHS method (updated)
Technical aspects
#Reaction steps; Raw material availability; Patents; Blacklist substances
Technical problems (e.g. long-term catalyst activity)
Process complexity
Equipment specification
Life-cycle environmental impacts
Figure 1: Overview of the framework: definition of design stages and appropriate modeling approaches as well as evaluation indicators for each stage.
This process design framework includes four stages of process modelling and multiobjective decision-making. Focusing on early design phase, Process Chemistry I/II and Conceptual Design I/II, are defined according to the available information as a basis for process modelling and assessment. For each defined stage, appropriate modelling methods and evaluation indicators regarding economy, life-cycle environmental impacts, EHS hazard and technical aspects have been selected. Based on the evaluation results, multi-objective decision-making is performed systematically at each stage (Figure 1). This framework has been previously evaluated in a case study (Methyl Methacrylate, MMA), where it was mimicked step-by-step with 6 synthesis routes as a starting point. By comparing the evaluation profile of these six routes over different stages, several factors were identified that are available in detail only at later stages, and which cause significant updates to the results. An example of the aggregation procedure r
in this framework is depicted in Figure 2. X s ,i is the evaluation indicator of route r at design stage s (i.e. from Process Chemistry II to Conceptual Design II ) in considered category i, (i.e.
Esr , Psr , Lrs , SH sr , HH sr , EH sr ), the different elements being the
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evaluation indicators for economy, proxy for gate-to-gate energy related economic and environmental impacts, life-cycle environmental impacts, and hazards in safety, health and environment, respectively. Before aggregation, the indicator values are normalized by the maximum (i.e. the worst) indicator value of all routes in the respective category i, as follows:
X
r s ,i
=
X sr,i max( X sr,i ) r
Level 1: Normalized scores
X
r PCII ,i
Raw mat. cost: E
Level 2: Mid-point scores
Aggregation step 1
w1,i
M
r PCII , j
Level 3: Total score
Aggregation step 2
r TPCII
w2 , j
x w1,RM-Cost(=0.77)
+
Cost
+
CED
x w2,Cost(=0.50)
x w1,ELI-Cost(=0.23) Proxy by ELI: P
Raw mat. CED: L
Safety hazard: SH
Health hazard: HH Env. hazard: EH
x w1,ELI-CED(=0.23)
x w2,CED(=0.20)
x w1,RM-CED(=0.77)
+
Total score
x w1,S(=0.40)
x w1,H(=0.20)
+
Hazard
x w2,Hazard(=0.30)
x w1,E(=0.40)
Figure 2: Aggregation scheme at Process Chemistry II. Values of weighting factors are those used in the case study.
From the normalized scores at Level 1 three mid-point scores are calculated (Aggregation Step 1 in Figure 2), in cost, overall cumulative energy demand (CED) and hazard (Level 2). In aggregation step 1, weighting factors within cost category are based on industrial statistics about the ratio of raw material and separation cost. The same weighting factors are applied in CED category, for which such empirical values were not available. The adopted values are from commodity industry and in other processes weights can be different, e.g. in fine or specialty chemicals raw material costs are typically higher. Within the hazard category, the indicated weighting factors are chosen according to the respective number of sub-categories, i.e. 4 in safety, 2 in health and 4 in environment. In aggregation step 2 the mid-point scores (Level 2) are aggregated in order to provide the final total score (Level 3). In this second aggregation step the weighting factors reflect company’s culture to rank cost, CED and hazard.
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2. UNCERTAINTY ISSUES AND SENSITIVIY ANALYSIS IN THE FRAMEWORK Despite the promising results after the framework implementation in a complex case study, the assessment of the framework robustness should consider the uncertainties involved in it. These could arise from subjective scaling and weighting of various parameters in the definition of indicators, subjective weighting in the aggregation steps, unknown significance level in differences of the indicator values, as well as limited coverage of the field under consideration for each indicator Among these different sources of uncertainty the present study focuses on the impact of uncertainty in the indicator values and the weights aggregating them, in particular on the identification of those regions where the selection between the best route and the rest becomes statistically insignificant. This problem was approached by examining the ratios of weighting factors which represent the order of relative importance of an indicator or mid-point score over the other. Each defined weight ratio was updated from each original value using a gradient descent method to the direction of minimization of the total scores differences. At each update step of this weight ratio the indicators values were also updated using the same approach, and an uncertainty was incorporated in terms of sampling from a normal distribution. Those regions were identified in which a statistical t-test was indicating that the total score of the best route is not significantly different from the one of its competing route. Following this approach a variety of scenarios was tested, regarding the width of the distribution depicting the uncertainty effect, the combinations of weight ratios and indicator values considered uncertain, the normalization effect based on the worst considered route, and the correlations between the indicators.
3. RESULTS AND ANALYSIS The aforementioned approach for detecting the impact of uncertainties in the regions of specified weight and indicator values was implemented in the MMA case study. The respective MMA data regarding routes chemistry and process information can be found in open literature [4]. Some typical results are presented in Figure 3. For each step of the outer loop of weight ratios update, an inner loop of indicators update is executed a predefined number of times. For each route r the algorithm is updating the indicator X according to the respective first-order partial derivative: X(t) = X(t-1) - Ș ∂ (¨Total Score)/ ∂ X where (¨Total Score) = Total Score route r – Total Score route best.
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Figure 3: The effect of uncertainty in combinations of indicator values with a sequentially forward selection.
At each step of the indicator update, the new value of the indicator is used as the mean of a normal distribution with predefined width, which represents the imposed uncertainty pattern. This results in a distribution of the total score for each route, which is compared with the respective distribution of total score of the best route using a t-test for means. In this way it can be identified which indicator is the “fastest” in affecting the inference based on the total score, “fastest” meaning requiring the minimum percentage change. In this procedure of indicators updating the value of the indicator for the worst route is kept constnat in order not to change the normalization of the system. Since the weight ratios remain constant for all routes, their updating step, which is also calculated on the basis of the first-order partial derivative, is averaged using “sum of digits” method, (i.e. since there are 6 routes considered, the weight ratio update based
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on the second best route receives a weight of 5/15, the third best one 4/15 etc. and finaly the weighted mean of all indicated updating steps determines the weight ratio update). In Figure 3 x-axis represents the number of update steps taken to shift the weight ratios, while y-axis represents the range of percentage change which is required in the indicator values for the decision to become uncertain. The error bars indicate the range of percentage change required for a statistically insignificant decision, while straight horizontal lines refer to indicators whose uncertainty pattern has not influenced the inference at all. For example, an uncertainty in indicator E between 10 and 15% (Figure 3, first graph) can cause a statistically insignificant decision for the selection of the best route. The uncertainty in all other indicators, when taken alone, is not affecting the descision-making. Once such a result has been reached, a sequentially forward selection is performed, i.e couples of E, which is the most sensitive indicator when considered alone, with other indicators are tested and when the most sensitive couple is identified, it forms the base for considering triplets and so on. The results of this procedure are depicted in the rest of the graphs of Figure 3, where it can be seen that the total score is more sensitive to the couple E-HH and the triplet E-HH-L respectively.
4. CONCLUSIONS & OUTLOOK Our analysis has quantified some expected trends but has also revealed some cases for further analysis. The main study result is that the importance of uncertainty in indicators seems to be greater than that of the weights. Therefore, further analysis needs to be carried out to determine and if possible correct the primary source of uncertainty in indicators which arises from their definition and data accuracy used in their calculation, while uncertainty in weights is a matter of design.
REFERENCES [1] J. Gupta, D. Edwards, 2003, A simple graphical method for measuring inherent safety, Journal of Hazardous Materials, 104, 15-30. [2] R. Srinivasan, N. Nhan, 2007, A statistical approach for evaluating inherent benigness of chemical process in early design stages, Process Safety and Environmental Protection Official journal of the European Federation of Chemical Engineering: Part B, Available Online. [3] H. Sugiyama, U. Fischer, M. Hirao, K. Hungerbühler, 2006, A chemical process design framework including different stages of environmental, healt and safety assessment, Computers Aided Chemical Engineering, 21, Part 1, 1021-1026. [4] H. Sugiyama, Decision-making framework for chemical process design, PhD Diss. ETH No. 17186.
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Batch Scheduling With Intermediate Due Dates Using Timed Automata Models Subanatarajan Subbiaha, Thomas Tometzkia, Sebastian Engella a
Process Control Laboratory (BCI-AST), Department of Biochemical and Chemical Engineering, University of Dortmund, 44221 Dortmund, Germany.
Abstract In the process industries, the problem of scheduling multi-product batch plants to satisfy the demand for various end-products within specified due dates occurs frequently. In contrast to the state-of-the art approach of using mathematical model formulations to solve such scheduling problems, an alternative approach is to use reachability analysis for timed automata (TA). In this paper, we discuss an extension of our earlier work on scheduling using TA models where the problem of makespan minimization was addressed. We extend the formulation to the meeting of due dates, modelled as causing additional costs (e.g. penalties for late delivery and storage costs for early production). The proposed solution by reachability analysis of priced timed automata is tested on a case study to demonstrate its successful application. Keywords: Batch plants, scheduling, timed automata, reachability analysis.
1. Introduction Multi-product and multi-purpose batch plants offer the advantage of increased flexibility with respect to range of recipes that can be handled and the production volumes compared to continuous plants. Batch scheduling is particularly difficult due to numerous constraints arising from the process topology, the connection between the pieces of equipments, inventory policies, material transfers, batch sizes, batch processing times, demand patterns, changeover procedures, resource constraints, timing constraints, cost functions and uncertainties. Particularly in batch plants, the problem of satisfying the demands of the various end-products within due dates occurs very often. Most of the solution approaches proposed in the last years solve such problems by modeling them by mathematical programming formulations (MILP or MINLP) and applying commercial solvers. In [8], the authors proposed a slot-based formulation with a continuous time representation which they showed to be suitable for network-based production schemes involving mass balances and product flows. The work presented in [7] proposed a MILP formulation in which the product stocks and mass balance constraints were ignored by fixing the batch sizes to discrete values. The formulation was tested on scheduling a real-life example which resulted in a model with reduced complexity and the results showed increased solution efficiency. The contribution [6] describes an extension of the previous work on continuous time formulations to deal with intermediate due dates with significant improvement in computational efficiency. However, the application of these approaches is hindered by the effort needed to formulate mathematical models and requires experience in algebraic modeling and a deep knowledge of the solver and its internal algorithms. Recently, the approach to solve scheduling problems by reachability analysis for timed automata has gained great attention. The framework of TA has been originally proposed
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by [1] to model timed systems with discrete dynamics. User friendly tools (e.g. Uppaal [3], TAOpt [5]). have been developed to model and to analyze such systems. Previous work on the TA based approach to scheduling problems with makespan minimization on hard job shop benchmarks were reported in [2] and [5]. The particular appeal of this approach comes from the modular and partly graphical modeling which enables inexperienced users to build models. Another advantage is the availability of powerful search algorithms that can be modified and extended for special purposes. The primary objective of this work is to extend the TA based formulation to address the problem of scheduling batch processes with multiple release dates and intermediate due dates with the objective of minimizing tardiness. In the TA based approach the resources, recipes and additional timing constraints are modeled individually as sets of priced timed automata with costs for transitions and cost rates for staying in locations. The sets of individual automata are synchronized through synchronization labels and are composed by parallel composition to form a global automaton. The global automaton has an initial location where no operations have been started and at least one target location where all operations required to produce the demanded quantities of end-products within the specified due dates have been finished. A cost optimal symbolic reachability analysis is performed on the composed automaton to derive schedules with the objective of minimizing the overall cost incurred as the sum of costs due to transitions and the integral costs for staying in locations.
2. Test Problem In order to illustrate the approach, a case study is considered. The case study is a multi-stage multiproduct chemical batch plant demonstrator with a plant topology similar to flexible flow shops. Two recipes to produce the end-products are given. The endproducts blue (B) and green (G) are produced from three raw materials, yellow (Y), red (R) and white (W). Each batch of the product results from two batches of the raw materials. The production process considered is: two batches of material Y and W reacts to produce one batch of Figure 1: P&ID of the multi-product batch plant product B ; similarly two batches of R and W reacts to produce one batch of product G. The plant consists of 3 stages in which the first stage consists of three buffer tanks which are used to store the raw materials Y, R and W (see Fig. 1). The buffer tanks in the first stage may contain at most only two batches of the raw materials. The second stage consists of three reactors that perform the reaction process to produce the end-products. Each reactor can be filled from each raw material buffer tank in the first stage; implying that it is possible to produce either product B or product G in each reactor. After processing the materials, a reactor may contain at most one batch of the product. The third stage consists of two buffer tanks which are used to store the end-products B and G exclusively. Each of the buffer tanks
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has a maximum capacity to store three batches of the respective products. Operations once started should be finished without any interruption (non-preemptive scheduling). The production of one batch of a recipe (B or G) consists of 6 operations and involves timing constraints between individual operations. After the materials are processed by the reactors the end-products must be drained into the buffer tanks in the third stage immediately imposing a zero-wait constraint between the operations. We consider the task to produce 23 orders in total, 12 batches of product B and 11 batches of product G, for which 138 operations have to be scheduled. Each batch of raw material is released at different points of time and for every 3 batches of a product a due date has to be met. The release dates and the due dates are known in advance and a penalty cost is incurred for missing a due date. The objective is to produce the demanded amount of products with minimal penalty cost.
3. Background of Timed Automata Timed Automata (TA) are finite state automata extended by the notion of clocks to model discrete event systems with timed behaviour. A timed automata is defined by a tuple, TA = ( L , C , Ĭ , inv , l0 , F ) in which, L represents the finite set of discrete locations, l0 , F ∈ L , where l0 represents the initial location and F represents the set of final locations. The set of clocks assigned to the TA are represented by C. The relation Ĭ ⊂ L × ϕ × Act × U(C) × L represents the set of transitions between the locations where, ϕ is a set of guards specified as conjunctions of constraints of the form ci ⊗ n or ci - cj ⊗ n , where ci , cj ∈ C, ⊗ ∈ { , = = , , < , >, ≠ } and n ∈ N. The set of actions (e.g. invoking a new event or changing the value of a variable) while taking a transition is denoted by Act. U(C) represent the set of clocks that are reset to zero after taking the transition. inv represent a set of invariants that assign conditions for staying in locations. The invariant conditions must evaluate to true when the corresponding location is active and the automaton is forced to leave the location when the invariant evaluates to false. A transition between a source location l and target location l' with a guard g ∈ ϕ (C), performing an action a ∈ Act and resetting the clocks r ∈ U(C) is denoted by (l, g, a, r, l'). A transition can occur only when the guard conditions are satisfied. An extension of TA with the notion of costs is known as priced TA [4]. A priced TA is equipped with an additional function P : L * Ĭ → R0 which assign cost rates to locations and costs to transitions. The cost of staying in a location with cost rate ƛ for d time units is given by P(L) = ƛ · d . The scheduling problem is modeled using the priced TA framework in a modular fashion. The resources, jobs and timing constraints are modelled as sets of priced TA. The interaction between the automata sets are established by synchronized transitions and shared variables. Two transitions are said to be synchronized when they have the same synchronization labels and the corresponding automata can only change their locations simultaneously. Such sets of automata are composed using parallel composition thereby forming one composed global automaton by considering the synchronization labels. The composed automaton represents the model of the complete system and a cost-optimal reachability analysis can be performed in order to derive schedules. The reachability analysis technique starts from the initial location of the composed automaton that represents the initial state of the system and evaluates the successor states created by a successor relation. This enumerative process is continued until the final target location specified is reached with minimal cost. In the search, branch-and-bound techniques are used in order to explore the solution space quickly.
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4. Priced TA model The idea of modeling the scheduling problem using priced TA is explained using a simple example process. Consider a process that consists of tasks T1 and T2 performed in resources R1 and R2, respectively. Let task T1 be followed by T2 and the time taken to perform T1 be p1 and T2 be p2. The process has a release date ri and a due date di. A storage cost is incurred if the process is finished before the due date and a penalty cost is incurred for missing the due date. The basic principles of modeling the process using a priced timed automata is shown in Fig. 2. The automata on the left hand side model the process and the automata on the right hand side model the required resources. The upper automaton on the left models the release date and the operations, the due date with the penalty cost is modeled by the automaton below. Initially, the process automaton is in the location wait T1 and wait dd representing that the process has not yet started. The release date ri of the process is modeled by the guard ci ri . Once the guard is enabled and the resource R1 is available, the first automaton can take the transition from wait T1 to exec T1 thereby allocating the resource and simultaneously making the resource automaton R1 transit from idle to busy by the synchronization label α1. The clock ci is reset to measure the duration of the task T1 modeled by the invariant ci p1 and the guard ci p1. After p1 time units have elapsed the first part of the process automaton is forced to transit from location exec T1 to wait T2 modeling that task T1 is finished and the process is waiting to perform task T2. At the same time the resource automaton R1 transits back from busy to idle representing that the resource is released by the synchronization labeled by ϕ1. The operation of performing task T2 in R2 is modeled in a similar fashion. Basically the α transitions represent the allocation of a resource and the ϕ transitions represent the release of a resource. The second automaton on the left at the start of the run takes a transition from wait dd to exec dd irrespective of the transitions in the first part of the process automata. At the same time when the transition takes place, the clock cd is reset to measure the due date using the invariant cd di and guard cd di. In the case where the process is finished before the due date, i.e. the second part of the process automaton is still in the state exec dd and the first part is in state exec T2 with the guard ci p2 enabled, the first process automaton transits to the location early and stays there until the due date is reached. The incurred storage cost is calculated using the cost rate at the location early and the time period for which the location is active. Once the due date is reached then the synchronized transition labeled by į is taken thereby representing the termination of the process. On the other hand, for the case where the finishing time of the process is beyond the due date, i.e. the upper process automaton is still in one of the states before early and the second automaton is in state exec dd with the guard cd di enabled; the wait T1
exec T1 α1
ϕ1
wait T2
ci > ri ci > p1 ci := 0 ci < p1
wait dd
exec dd
cd < d i
ci := 0
exec T2
ci < p 2
tardy cd > di
cd := 0
α2
early ϕ2
α1
finish’ δ
ci > p2
idle
Resource R1 α2
finish’’ δ
cd = delay cost
Example Process
busy ϕ1
ci = storage cost
idle
busy ϕ2 Resource R2
Resource Automata
Figure 2: Priced TA model of the simple example process and the corresponding resources
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second automaton transits to the location tardy and stays there waiting for the last operation of the process to finish. The incurred delay cost is calculated using the cost rate at the location tardy and the time period for which the location tardy is active. Once task T2 is finished then the synchronized transition labeled by į is taken thereby representing the end of the process. Apart from the individual clock a global clock is present to model the completion time of the process. Using these principles, the priced TA model for the case study considered can be derived by defining interacting priced TA for the recipes and resources. Each production order (a job) consisting of a release date, due date, recipe number, storage cost and delay cost is modeled as a priced TA with an individual clock. The general structure of each job automaton depends on the corresponding topology of the recipe. Operations that can be performed in alternative resources are modeled using alternative transitions starting from the same location. The parallel operations in a recipe such as pumping the raw materials yellow (red) and white to produce blue (green) is modeled by individual automata with synchronization points established by synchronized transitions. The zero-wait constraint in the process is modeled by imposing the waiting location of the corresponding operation as an urgent location. A reactor which is allocated for preparing the end-product is occupied when the operation of draining the corresponding raw material starts. It is released only after finishing the draining of the end-product to the corresponding buffer tank. This is modeled by synchronizing the transition that represents the start of the draining operation of the raw material in the recipe automata with the transition that represents the allocation of the corresponding (reactor) resource automaton, and the transition that represents the finish of the draining operation of the end-product in the recipe automata is synchronized with the transition that represents the release of the corresponding (reactor) resource automaton.
5. Experimental Results In order to test the proposed modeling and solution approach the prototypic tool TAOpt developed at the Process Control Laboratory is used. It consist of a reachability algorithm for priced TA to perform a symbolic reachability analysis to explore the solution space and to derive production schedules with minimal cost. Various search space reduction techniques introduced in [5] are realized in order to prune parts of the solution space that lead to sub-optimal solutions. Given the process information, priced TA models are created in a modular fashion automatically by TAOpt. The process information consist of the resource data (capacity, equipment purpose), the recipe data (duration of operations, sequence of operations, timing constraints between tasks, materials processed) and the table of production orders (due date, release date, delay cost). Once the individual automata have been created the composed automaton is realized on the fly and the reachability tree is created. The reachability tree consists of nodes and transitions; a node represents a combination of state and clock valuations of all clocks including the global clock. A cost-optimal reachability analysis is performed starting from the initial location where no jobs are started and trying to find a path to the target location where all jobs are finished within the defined due date. The objective is to minimize the penalty cost. The search algorithm used to explore the reachability graph was a combination of maximum depth and minimum cost. The search space reduction techniques weak non-laziness, sleep-set method and passed list inclusions were employed to prune parts of the reachability tree (for detailed explanations see [5]). The number of nodes for all the tests performed with TAOpt was limited to 2.6 million explored nodes. A continuous time based formulation with resource constraints
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Table 1. Tardiness minimization: (Tcpu) computation time in CPU sec., (Tfirst) computation time required to reach the first feasible solution, (Obj.) objective value, (Opt.sol.nodes) total number of nodes explored to reach the optimal solution, (disc.) number of discrete variables, (cont.) number of continuous variables, (eqns.) total number of equations.
Orders
Tcpu
6 12 18 23
53 75 1082 1930
TAOpt 1st sol Tfirst Obj. 0.02 320 0.04 74 0.05 105 0.08 115
Opt.Sol. nodes 330302 335548 1670659 1998302
Tcpu 66 3037 11885 30621
GAMS/CPLEX 1st sol disc. Tfirst Obj. 66 0 1566 3037 0 3132 3629 1 4640 22325 4 6148
cont.
eqns.
3913 6635 9265 11895
16803 36706 60016 87382
presented in [6] was implemented and tested. The TA based solution approach was compared with the MILP-based solution approach for different instances of the test problem. The number of event points considered for the instances with 6, 12, 18 and 23 production orders were 27, 54, 80 and 106, respectively. The objective value of the optimal solution for all the instances was zero. The MILP model was solved with GAMS 22.5 and CPLEX 10.2. For CPLEX the standard configuration with an optimality gap of 0 was chosen. Both approaches were tested on a test environment of a 3.06 GHz Xeon machine with 2 GB memory and Linux O.S. The results obtained for various instances considered are shown in Tab.1. The investigation clearly revealed that both the approaches could reach the optimal solution with zero penalty cost. However TAOpt could compute the first feasible solution and the optimal solution faster compared to the approach proposed in [6]. Except for the first instance for all other instances considered CPLEX took more than 3000 sec to compute the first feasible solution.
6. Conclusions This work presents a successful application of the TA based approach to solve production scheduling with multiple release dates and intermediate due dates and the test results revealed that the TA based approach is competitive compared to state-of-art approaches. Future work will investigate on using decomposition techniques to solve large scale problems and employing the TA based optimization algorithm to solve them. The authors gratefully acknowledge the financial support from the NRW Graduate School of Production Engineering and Logistics at Universität Dortmund.
References 1. 2. 3. 4. 5. 6. 7. 8.
R. Alur and D.L. Dill, 1994, A theory of timed automata. Y. Abdeddaim and O. Maler, 2001, Job-shop scheduling using timed automata. K.G. Larsen, P.Pettersson and W. Yi, 1997, UPPAAL in a nutshell. G. Behrman, A. Fehnker, T.S. Hune, K.G. Larsen, P.Pettersson, J. Romijn and F.W. Vaandrager, 2001, Minimum-cost reachability for linearly priced timed automata. S. Panek, S. Engell, and O. Stursberg, 2006, Efficient synthesis of production schedules by optimization of timed automata. M.G. Ierapetritou, C. Floudas, 1999. Effective Continuous-Time Formulation for ShortTerm scheduling: III. Multiple intermediate due dates. S. Panek, S. Engell, and C. Lessner, 2005, Scheduling of a pipeless multi-product batch plant using mixed-integer programming combined with heuristics, Proc. ESCAPE. J. M. Pinto and I.E. Grosmann, 1994, Optimal cyclic scheduling of multistage continuous multiproduct plants, Comp. and Chem. Eng. 18.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A Decomposition Approach to Short-Term Scheduling of Multi-Purpose Batch Processes Norbert Trautmann,a Rafael Fink,b Hanno Sagebiel,b Christoph Schwindtb a
University of Bern, Schützenmattstrasse 14, 3012 Bern, Switzerland Clausthal University of Technology, Julius-Albert-Straße 2, 38678 ClausthalZellerfeld, Germany
b
Abstract Batch processes are generally executed on production plants consisting of multi-purpose processing units and storage facilities of limited capacity. We deal with the problem of computing a minimum-makespan production schedule for given primary requirements. Our solution approach is based on a decomposition of the problem into two subproblems. The first subproblem consists in computing an appropriate set of batches for each process. We present a novel formulation of this problem as a mixed-integer linear program of moderate size. The second subproblem is to schedule the processing of these batches on the processing units subject to material-availability and storage-capacity constraints. We tackle the latter problem with a new priority-rule based scheduling method. Computational experience with a sample production process presented in Maravelias and Grossmann (2004) shows that with the decomposition method near-optimal production schedules can be computed in a very small amount of CPU time. Keywords: Multi-purpose batch plants, Scheduling, Decomposition, MILP
1. Introduction In the process industries, low volumes of multiple products are typically produced on multi-purpose batch plants. In batch production mode, the total requirements for the final products and the intermediates are split into batches. To process a batch, first the inputs are loaded into a processing unit, then a transformation process is executed, and finally the output is unloaded from the unit. We consider multi-purpose processing units, which can operate different processes. The duration of a process depends on the processing unit used. Between consecutive executions of different processes in a processing unit, a changeover with sequence-dependent duration is necessary. The minimum and maximum filling levels of a processing unit give rise to a lower and an upper bound on the batch size. In general, raw materials, intermediates, and final products can be stored in storage facilities of finite capacity. Some products are perishable and therefore must be consumed immediately after they have been produced. The short-term scheduling of multi-purpose batch plants has been widely discussed in the literature. Recent reviews can be found in Floudas and Lin (2004), Burkard and Hatzl (2005), and Méndez et al. (2006). Roughly speaking, monolithic and decomposition approaches can be distinguished. The major limitation of the former approaches consists in the impractical amount of computation time which is required for solving problem instances of practical size (cf. Maravelias and Grossmann 2004). Decomposition approaches divide the problem into a planning and a scheduling problem. Planning determines the batch size and the number of executions for each process, and scheduling
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allocates the processing units and storage facilities over time to the processing of the corresponding batches (cf. Neumann et al. 2002). In this paper, we present a novel formulation of the planning problem, which allows for considering alternative processing units with unit-specific lower and upper bounds on the batch sizes. In contrast to the nonlinear model presented in Trautmann and Schwindt (2005), the new formulation represents a mixed-integer linear program, which can be solved to optimality using standard mathematical programming software. For approximately solving the resulting scheduling problem, we propose a priority-rule based method. The remainder of this paper is organized as follows. In Section 2, we formulate the planning problem as a mixed-integer linear program. In Section 3, we present our schedule-generation scheme for the scheduling problem. In Section 4, we report the results of an experimental performance analysis that is based on a sample production process presented in Maravelias and Grossmann (2004).
2. Planning Problem 2.1. Problem Statement In the following, we interpret each combination of a transformation process and a processing unit as a task. For example, if two processing units are available for executing a process, then we define two tasks for this process. The planning problem consists in determining the batch size and the number of executions for each task such that the given primary requirements for final products are satisfied, the prescribed intervals for the batch sizes are observed, each perishable product can be consumed immediately after production, and the total bottleneck workload is minimized. 2.2. Formulation as a Mixed-Integer Linear Program In our model formulation, we use the following notation: Sets G set of all groups of processing units P , P p set of all products, set of all perishable products 7 set of all tasks 7S , 7S set of all tasks producing product S , set of all tasks consuming product S 7X set of all tasks that can be processed on unit X UJ set of all processing units in group J Parameters DWS proportion of product S in batch size of task W ( 0 for input products, ! 0 for output products) E , E W lower bound on batch size of task W , upper bound on batch size of task W W
QW upper bound on number of executions of task W US primary requirements of product S V S , TS storage capacity for product S , initial stock of product S Variables EW , EWP batch size of task W , batch size of P -th execution of task W HWP binary; equal to 1, if task W is executed at least P times, and 0, otherwise ZJ workload of group J of processing units
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2.2.1. Constraints The batch sizes must be chosen within the prescribed bounds, i.e.,
E W d EW d E W
( W 7 )
(1)
and such that for each perishable product S P p , the amount consumed by one execution of any task W 7S equals the amount produced by one execution of any task W '7S , i.e.,
DW ' S EW '
( S P p ; W ,W ' 7S u7S )
DWS EW
(2)
The final inventory of product S P must be sufficiently large to satisfy the primary requirements US , but it must not exceed the given storage capacity V S , i.e., QW
US d T S ¦ DWS ¦ EWP d US V S W T
(S P )
(3)
P 1
Eventually, we link the variables EW , EWP , and HWP as follows: 0 d EWP d EW
EW (1 İ IJȝ ) E W d EWP d H WP E W
(W T; P
1, ,Q W )
(4)
It is readily seen (cf. Neumann et al. 2002) that inequalities (4) imply the equivalences HWP 1 EWP ! 0 EWP EW ( W T ; P 1,,Q W ). The linear ordering of the binary variables HWP belonging to the same task W serves to reduce the size of the feasible region significantly without any loss of generality:
H W1 t H W2 t t H WQW
(W T )
(5)
2.2.2. Objective Function Our primary objective is to minimize the total bottleneck workload, which we compute as follows. We divide the processing units into as many groups as possible in such a way that first, each processing unit belongs to exactly one group and second, each transformation process can only be executed on processing units of one and the same group. The set of all these groups is denoted by G . The bottleneck of group J G is the processing unit with the maximum potential workload maxXU J ¦W T pW ¦QPW 1H WP , X where pW denotes the processing time of task W ; we refer to the workload of this bottleneck unit as the workload ZJ of group J G , i.e., QW
ZJ t ¦ pW ¦ H WP W TX
( J G;X U J )
P 1
(6)
Often there are several feasible solutions minimizing the total bottleneck workload. Therefore we additionally try to minimize the workload on the non-bottleneck units (second-order criterion) and the total unneeded inventory (third-order criterion). With G1 and G 2 being sufficiently small constants, we formulate our objective function QW
QW
P P ¦ ZJ G1 ¦ pW ¦ H W G 2 ¦ ¦ DWS ¦ EW
J G
W T
P 1
S P W 7
P 1
(7)
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Optimization Problem In sum, the planning problem reads as follows:
P
Min. (7) ° ®s.t. (1) to (6) ° H WP ^0,1` W 7 , P ¯
1, ,Q W
3. Scheduling Problem 3.1. Problem Statement A solution to planning problem (P) provides us with the set of task executions yielding the required amounts of intermediate and final products. For what follows we refer to a task execution as an operation, and O denotes the set of all operations. The scheduling problem consists in determining a start time S i t 0 for each operation i O in such a way that no two operations are processed simultaneously on the same processing unit, the processing units can be changed over between consecutive operations, sufficient amounts of the input materials are in stock at the start of each operation, there is enough storage space available for stocking the output products at the completion time of each operation, and the completion time of the last operation (i.e., the production makespan) is minimized. The immediate consumption of perishable intermediates is ensured by associating each product S P p with a fictitious storage of capacity zero. 3.2. Scheduling Method The first step of our algorithm consists in generating an operation-on-node network. Each operation i O corresponds to one node of the network. The nodes are connected by arcs representing minimum and maximum time lags between the start times of the operations. If the scheduling problem is solvable, then there always exists an optimal schedule for which all those temporal relationships are satisfied. Assume that we have arranged the operations belonging to the same task in some arbitrary order. Since the task can only be processed on one unit, the operations have to be executed one after another. Accordingly, we define a minimum time lag which is equal to the task’s processing time between any two consecutive operations in the sequence. We may add further arcs by exploiting the input-output relationships between the tasks. If an intermediate is produced by exactly one task, we can identify minimum time lags which are necessary to the timely availability of the input materials. If an intermediate is consumed by exactly one task, we can add arcs to avoid capacity overflows in a similar way. Those arcs correspond to maximum time lags between producing and consuming operations. Next, we determine the strong components of the network, i.e., the -maximal sets of nodes such that the network contains a directed path from each node to each other node of the set. Since any two nodes of a strong component are mutually linked by temporal relationships, all operations belonging to the same strong component are scheduled consecutively in our method. The basic idea of the scheduling method is very simple. In each iteration we schedule one eligible operation, which is selected based on priority values. The operation is started at the earliest point in time at which the minimum and maximum time lags of the network are satisfied, the operation can be executed on the processing unit, and a sufficient amount of input materials is available. The operations of a strong component are eligible to be scheduled if (i), all of those operations' predecessors in the network out-
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side the strong component have already been scheduled, (ii), there is enough input material available to process all operations of the strong component, and (iii), there is no other strong component for which some but not all operations have been scheduled. Thus far we have not taken the limited capacity of the storage facilities into account. The storage-capacity constraints are considered via capacity-driven latest start times. If in some iteration of our method we have generated a capacity overflow in a storage facility at a time t , we temporarily force eligible operations consuming the product stocked in this facility to start no later than time t . Those latest start times are maintained until the capacity overflow has been removed. As a consequence it may happen that an eligible operation can no longer be scheduled because the capacity-driven latest start time is smaller than the earliest feasible start time. If no eligible operation can be selected, we perform an unscheduling step in the following way. At first, we determine the operation i that produced the material which cannot be stocked. Next, we select one of the eligible operations, say, operation j . We then increase the earliest completion time of operation i to the earliest feasible start time t of operation j by introducing a release date of t pi for operation i , where pi denotes the processing time of operation i . If operations i and j belong to the same strong component, we remove all operations of this strong component from the schedule and resume the scheduling method. Otherwise, we remove all operations and restart the scheduling procedure from scratch. The unscheduling step may generate unnecessary idle times, which can easily be removed in a postprocessing step. The algorithm can be implemented as a multi-start procedure by randomly disturbing the priority values of the operations. In our implementation the initial unbiased priority values are based on earliest feasible start times, the sizes of the strong components, and the capacity-driven latest start times of the operations.
4. Performance Analysis 4.1. Implementation and Settings We have tested the performance of our decomposition approach on a set of 28 test instances, which have been generated by varying the primary requirements for the four final products of the Maravelias and Grossmann (2004) sample process. We compare our method to the results obtained with the monolithic time-indexed problem formulation of Kondili et al. (1993). The tests have been performed on an AMD personal computer with 2.08 GHz clock pulse and 1 GB RAM. The mixed-integer linear programs of the planning problem and the monolithic model have been solved with CPLEX 10.2, and the multi-pass priority-rule based scheduling method has been implemented in C++. For the latter method, we have imposed a run time limit of 1 second. 4.2. Results Table 1 shows the optimum makespans computed with the monolithic model and the CPU times in seconds, including the time required to prove the optimality of the solution. The last two columns of the table list the makespans and the CPU times obtained with the decomposition approach. Out of the 28 instances, 17 could be solved to optimality, and the maximum relative optimality gap is less than 7 %. The results obtained for the larger instances indicate that our method scales quite well. The maximum CPU time is less than 3 seconds, versus more than two hours for the monolithic approach. In sum, the analysis shows that the decomposition approach is able to provide good feasible schedules at very modest computational expense. Hence, the method is well-suited
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for the planning and scheduling of real-life processes, where due to various types of uncertainties a frequent rescheduling of the operations is often necessary. Instance MG-01 MG-02 MG-03 MG-04 MG-05 MG-06 MG-07 MG-08 MG-09 MG-10 MG-11 MG-12 MG-13 MG-14 MG-15 MG-16 MG-17 MG-18 MG-19 MG-20 MG-21 MG-22 MG-23 MG-24 MG-25 MG-26 MG-27 MG-28
Primary req. (3,3,7,7) (3,7,7,3) (7,7,3,3) (3,7,3,7) (7,3,7,3) (7,3,3,7) (5,5,5,5) (6,6,14,14) (6,14,14,6) (14,14,6,6) (6,14,6,14) (14,6,14,6) (14,6,6,14) (10,10,10,10) (9,9,21,21) (9,21,9,21) (21,21,9,9) (9,21,9,21) (21,9,21,9) (21,9,9,21) (15,15,15,15) (12,12,28,28) (12,28,28,12) (28,28,12,12) (12,28,12,28) (28,12,28,12) (28,12,12,28) (20,20,20,20)
Kondili et al. (1993) Makespan CPU time 17 19 17 17 17 16 16 29 28 29 26 26 22 25 41 37 41 35 35 28 34 53 47 53 44 44 35 41
1.74 2.11 1.35 1.63 1.79 4.04 7.99 6.41 10.29 0.79 3.68 3.22 33.39 9.58 23.93 31.88 13.98 30.44 17.24 385.18 137.33 190.24 329.47 42.80 221.04 25.43 8804.97 156.93
This paper Makespan CPU time 18 20 17 17 17 17 17 29 29 29 26 26 23 26 41 38 41 35 35 29 35 53 47 53 44 44 37 41
1.34 2.16 1.39 1.57 2.06 1.59 1.27 1.59 1.69 1.75 1.59 1.42 1.80 1.57 1.91 1.54 1.56 1.93 1.70 1.40 1.81 1.70 1.85 2.39 1.94 1.63 2.38 1.40
Table 1: Computational results for the 28 problem instances
References Burkard, R.E., Hatzl, J., 2005. Review, extensions and computational comparison of MILP formulations for scheduling of batch processes. Comp. Chem. Eng. 29(8), 1752–1769. Floudas, C.A., Lin, X., 2004. Continuous-time versus discrete-time approaches for scheduling of chemical processes: a review. Comp. Chem. Eng. 28(11), 2109–2129. Kondili, E., Pantelides, C.C., Sargent, R.W.H., 1993. A general algorithm for short-term scheduling of batch operations: I. MILP formulation. Comp. Chem. Eng. 17(2), 211–227. Maravelias, C.T., Grossmann, I.E., 2004. A hybrid MILP/CP decomposition approach for the continuous time scheduling of multipurpose batch plants. Comp. Chem. Eng. 28(10), 1921– 1949. Méndez, C.A., Cerdá, J., Grossmann, I.E., Harjunkoski, I., Fahl, M., 2006. State-of-the-art review of optimization methods for short-term scheduling of batch processes. Comp. Chem. Eng. 30(6-7), 913–946. Neumann, K., Schwindt, C., Trautmann, N., 2002. Advanced production scheduling for batch plants in process industries. OR Spectrum 24(3), 251–279. Trautmann, N., Schwindt, C., 2005. A MINLP/RCPSP decomposition approach for the short-term planning of batch production. In: Puigjaner, L., Espuña, A. (eds.) European Symposium on Computer Aided Process Engineering — 15. Elsevier, Amsterdam, pp. 1309–1314.
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Combined Nitrogen and Phosphorus Removal. Model-Based Process Optimization Noelia Alasino, Miguel C. Mussati, Nicolás Scenna, Pío Aguirre INGAR Instituto de Desarrollo y Diseño (CONICET-UTN), Avellaneda 3657, (S3002GJC) Santa Fe, Argentina.
Abstract An optimization model based on a superstructure embedding several activated sludge process configurations for nutrient removal is formulated and solved. Simultaneous optimization of the process configuration (process synthesis) and operation conditions for given wastewater specifications and influent flow rate in steady state operation are investigated. The performance criteria selected is the total annual operation cost minimization while predicting compliance with the effluent permitted limits. As the piece of equipment is supposed given, investment costs are not considered. The Activated Sludge Model No. 3 extended with the Bio-P module for computing biological phosphorus removal are used to model the reaction compartments, and the Takács model for representing the secondary settler. The resulting mathematical model is a highly non-linear system, formulated as a Non-Linear-Programming Problem, specifically as a DNLP. The model is implemented and solved using GAMS and CONOPT, respectively. The optimal solution computed from the superstructure model provides cost improvements of around 10% with respect to conventional processes. Keywords: Activated superstructure, DNLP.
sludge
process,
ASM3+BioP,
process
optimization,
1. Introduction In previous works, the COST benchmark wastewater treatment plant model (Copp, 2002) to evaluate control strategies for N removal based on the Activated Sludge Model No. 1 had been used as starting point for optimization of the operation conditions as well as for synthesis of activated sludge WWTPs. Based on the ASM3 model (Gujer et al, 1999), the aim was to minimize the total annual operating cost (Alasino et al, 2006a and 2006b) and the total cost (investments and operating costs) (Alasino et al, 2007). Optimization of P removal facilities is nowadays a key issue. Indeed, biological P removal is often persuade in European treatment plants as an alternative to chemical P removal based on P precipitation with salts such as FeCl3 (Gernaey and Jorgensen, 2004). In Gernaey and Jorgensen (2004) a benchmark WWTP for combined N and P removal is developed for evaluating and comparing WWTP control strategies, and a number of scenario evaluations focusing on the selection of DO set points are described to illustrate the simulation benchmark. Here, optimal operation conditions for a superstructure embedding the most widely used configurations for combined nutrient removal aiming at minimizing operating annual costs will be investigated for given wastewater specifications and flow rate. The plant lay-out used as the departing model is that proposed by Gernaey and Jorgensen (2004), which corresponds to the A2/O process. The other configurations embedded are the UCT process (VIP process), the modified UCT process and the Bardenpho process.
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2. Problem Definition The problem addressed is the simultaneous optimization of the process configuration (process synthesis) and the operating conditions (flow rates of aeration, recycles and fresh feed to each reaction compartment and external carbon source dosage) of ASWWTPs for combined biological N and P removal, aiming at minimizing the total annual operating cost. It is assumed: - influent wastewater specifications, - effluent permitted limits, - a process superstructure model, - a cost model computing operation costs, and - process unit sizes.
3. Process Description b) UCT – VIP
a) A2/O process E
D2 ANAE
S
E
RI2 ANAE
RI1
REC PUR
RI
c) Modified UCT process E
RI2 ANAE
ANOX
OX
ANOX
D2
S
OX
ANOX
ANOX
OX RI1
D2
S
REC PUR
RI
REC PUR
d) Modified Bardenpho process
E ANAE
ANOX
OX
ANOX
D2
OX
S
REC PUR
Figure 1. Most widely used ASWWTP configurations for combined nutrient removal
In ASPs, the WW stream is exposed to different environmental conditions (anaerobic, anoxic and aerated zones) to facilitate the different microbiological processes such as the release or uptake of P, nitrification and denitrification. Reduction of carbonaceous matter and nitrification (ammonium is converted to nitrate by autotrophs) are favored by aerobic conditions; while denitrification (nitrate is converted to N gas by heterotrophs) is favored by anoxic ones, if readily biodegradable C is available. Biological P removal relies on P uptake by aerobic heterotrophs (known as phosphate-accumulating organisms PAOs) capable of storing orthophosphate in excess of their biological growth requirements. Under anaerobic conditions, PAOs convert readily available C (e.g., VFAs) to C compounds called polyhydroxyalkanoates PHAs. PAOs use energy generated through the breakdown of polyphosphate molecules to create PHAs. This breakdown results in P release. Under subsequent aerobic or anoxic conditions, PAOs use the stored PHAs as energy to take up the P that was released in the anaerobic zone, as well as any additional phosphate present in the WW. Figure 1 presents the most widely used ASWWTP configurations for combined N and P removal. The A2/O process presents a sequence of anaerobic reactors (to promote the growth of PAOs) followed by a sequence of anoxic to promote denitrification, and finally aerobic reactors. It has one internal and one external recycle stream. The internal recycle stream conducts a fraction of the nitrified liquor from the last aerobic to the 1st anoxic compartment, and the external recycle conducts a fraction of the sludge from the underflow of the sedimentation tank to the 1st compartment. In the UCT process, both recycle streams are feed to the anoxic zone and a second internal recycle stream is present from the anoxic to the anaerobic compartment. The modified UCT process has 2 internal recycles and 1 external one as in the original UCT process but the anoxic zone is divided into 2 zones. The external recycle is directed from the underflow of the decanter to the 1st anoxic zone. The 1st internal recycle stream conducts a fraction of the nitrified liquor from the aerobic to the 2nd anoxic zone. Finally, the second internal recycle stream pumps a fraction of the mixed liquor from the 1st anoxic back to the anaerobic compartment. The Bardenpho process configuration has also an external
Combined Nitrogen and Phosphorus Removal. Model-Based Process Optimization
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recycle from the sedimentation tank to the anaerobic zone and has an internal recycle from the 1st aerobic zone to the 1st anoxic zone. In general, the addition of external C to the anoxic zone could be detrimental to P removal in a EBPR plant, as the ordinary heterotrophs have competing advantages for nitrate over the denitrifying PAOs, resulting in poor anoxic P uptake. It is recommendable that the external C to be added to the anaerobic zone of an EBPR plant short of COD. The C source is taken up by PAOs to form intracellular C storage compounds, the use of which improves both P and N removal under anoxic conditions.
4. Process Optimization Model The superstructure embeds the four process alternatives described in the preceding section as can be appreciate in Figure 2. As mentioned, the basic plant adopted as starting point for developing the superstructure model is that proposed by Gernaey and Jorgensen (2004), which consists of 7 mixed reaction compartments with a total volume of 6749 m3, and 1 secondary settler of 6000 m3. The 1st and 2nd compartments are anaerobic units; the following 2 are anoxic zones and the last 3 formed the aerated region. This configuration has 1 internal and 1 external recycle stream, and corresponds to the A2/O process. The other process configurations are incorporated into the superstructure by allowing more recycles streams. The superstructure also allowed the distribution of the main process streams. Figure 2. Proposed superstructure Air
uTECSD
Qef
QTfresh M1
kLa1 kLa2 kLa3 kLa4 = 0 d-1 S1 M2 = 0 d-1 S2 M3 = 0 d-1 S3 M4 = 0 d-1 S4 M5 QTr,int,1
QTr,int,2
QTr,int,3
QTr,int,4
kLa5
kLa6
QTr,int,5
kLa7 S6 M7
S5 M6
QTr,int,6
S7
QTr,int,7 QTr,ext
Qwaste
4.1. Reactor model For the aeration tanks, steady state CSTR model is considered. The ASM3 model (Gujer et al, 1999) extended with the Bio-P module (Rieger et al., 2001) is chosen to model the biological processes. The stoichiometric coefficients and kinetic constants are interpolated to 15 oC as proposed by Gujer et al. (1999). The volumes of the reaction compartments are set as follows: 500 m3 for Reactor 1; 750 m3 for Reactors 2, 3 and 4; 1333 m3 for Reactors 5, 6 and 7. The following constraints are considered for the mass transfer coefficient kLai in each compartment i: kLai=0 for Reactors 1, 2, 3 and 4; 0 <= kLai<= 360d-1 for Reactors 5, 6, and 7. kLai,max=360d-1 is the maximum operating limit. 4.2. Secondary settler model The secondary settler is modeled as a non-reactive settling tank subdivided into 10 layers of equal thickness, using the double-exponential settling velocity model (Takács et al.1991). A fixed settler depth of 4 m and a cross area of 1500m2 are adopted. 4.3. Splitter and mixer mass balances. Splitters and mixers models are also needed to represent the proposed superstructure. 4.4. Effluent quality limits These effluent thresholds values were used as specification constraints (Copp, 2002; Gernaey and Jorgensen, 2004): SNH,ef: 4 gN m-3; Ptot ef: 1.5 gP m-3; NTOT,ef: 8 gN m-3; BODef: 10 gCOD m-3; CODef: 100 gCOD m-3; XSS,ef: 30 gSS m-3.
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4.5. Maximum values for operation variables The maximum values for the operation variables taken from Copp (2002) are: Qr,ext: 36892m3d-1; Qr,int: 92230m3d-1; Qwaste:1844.6m3d-1; uECSD: 2*103 kgCODd-1; kLai:360 d-1. 4.6. Objective Function The total annual operating cost (OC) is adopted as the objective function to be minimized. The operation cost is computed as follows (Vanrolleghem and Gillot, 2002): OC = OCa + OC pump + OCEQ + OCSLDGD + OCECSD
where OCp is the annual operating cost of unit p. EQ, Ea, Epump, uSLDGD and uECSD are the effluent quality index, aeration energy demand, pumping energy demand, waste sludge production rate and external carbon source dosage rate, respectively, which expressions are given in detail in Alasino et al. (2007) and Gernaey and Jorgensen (2004). The annual unitary operation costs are (Vanrolleghem and Gillot, 2002; Mussati et al., 2002; Gernaey and Jorgensen 2004): ĮEQ: 50 Euro day (kgPU year)-1; ĮE: 25 Euro day kWh year)-1; ĮSLDGD: 75 Euro day (kgSS year)-1; ĮECSD: 109.5 Euro day (kgCOD year)-1. The effluent quality index EQ (kg contaminating unit d-1), which is related to the fines paid due to contaminant discharge, is computed by weighting the compounds loads having influence on the water quality that are usually included in the legislation. 4.7. Influent Wastewater Specifications The influent WW flow rate is set at 18446 m3 d-1. The influent WW composition used consists of the original flow weighted average dry weather influent composition for ASM1 proposed in COST, modified to make it compatible with the ASM3+BioP model. The influent PO4= concentration (SPO) has been taken from Gernaey and Jorgensen (2004). The nonzero input concentrations for compounds are: SI: 30 gCOD m-3; SS: 69.5 gCOD m-3; XI: 51.2 gCOD m-3 ; XS: 202.32 gCOD m-3; XH: 28.17 gCOD m-3; XSS: 215.493 gSS m-3; SNH: 40.60 gN m-3; SALK: 7 gCOD m-3; SPO4: 9.01 gP m-3.
5. Results and Discussion The resulting mathematical model is a highly non-linear system, formulated as a Nonlinear Programming with Discontinuous Derivatives DNLP, with constraints. The model is used for optimization of the operation conditions for the influent wastewater specifications described in the preceding section. A multiple starting point strategy was adopted and, as expected, several locally optimal solutions were found. The solution showing the minimal OC value is presented. Fig. 3 shows the optimal configuration and main optimization variable values for the operating conditions for the proposed superstructure. Table 1 shows the main variables optimal values and costs. Optimization models for the conventional processes (A2/O, UCT, modified UCT and Bardenpho process) have also been implemented. These models were developed simultaneously with the superstructure model development in order to validate the preliminary results obtained. These results are presented in Fig. 4 and Table 1. All optimal solutions predict external C source dosage. Reactors resulted to be anaerobic, anoxic or aerobic compartments depending on the DO (SO) and NOx (SNO) concentrations. Fig. 3 shows C source dosage to the 2nd reactor, influent WW distribution to 1st and 2nd compartment, external recycle distribution to 1st and 4th compartment and an internal recycle from the 7th to the 4th one. It presents a zone (1st reactor) with anoxic conditions (SO=8*10-4gm-3; SNO=0.4gm-3) followed by a zone (2nd and 3rd reactors) with anaerobic conditions (SO<1*10-5gm-3; SNO=6*10-3 and 4*10-4gm3 ), an other zone (4th reactor) with anoxic conditions (SO=1*10-3gm-3; SNO=0.5gm-3), and
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Combined Nitrogen and Phosphorus Removal. Model-Based Process Optimization
finally an alternate aerated zone (SO=0.9, 3*10-3 and 0.6gm-3; SNO=9.0, 2.9 and 8.7gm-3). The OC decreases around 7% with respect to the plant and operating conditions proposed by Gernaey and Jorgensen (simulation results not shown), and effluent meets the quality conditions while the last one does not. Figure 3. Optimal configuration and main process variable values Superstructure optimization (OC= 762 678) uECSD,2 = 65904 gCODSs d
-1
Qef = 18159 3 -1 md
3 -1
Qr,int,7,4 = 2533 m d Qfresh,1 = 17279 Qfresh,1 = 1167 3 -1 3 -1 md md -1 -1 kLa1=0d kLa2= 0 d -4 -3 -3 SO,1=8 10 gm SO,2=0 gm -3 -3 -3 SNO,1=0.4gm SNO,2=6.10 gm
-1
-1
kLa3=0 d -3 SO,3=0 gm -4 -3 SNO,3=4.10 gm
-1
kLa4= 0 d -3 -3 SO,4=1.10 gm -3 SNO,4=0.5gm
3 -1
-1
kLa5=307d -3 SO,5=0.9gm -3 SNO,5=9.0gm
-1
kLa6=0d -3 -3 SO,6=3.10 gm -3 SNO,6=2.9 gm
kLa7=227 d -3 SO,7=0.6gm -3 SNO,7=8.7gm Qwaste = 287 3 -1 md
3 -1
Qr,ext,1 = 9119 m d
Qr,ext,4 = 12148 m d
Figure 4. Main process variable values for each configuration optimization Qef = 18147 3 -1 md
a. A2/O process configuration optimization (OC = 801 929) Qfresh,1 = 18446 3 -1 md
uECSD,3 = 379552 gCODSs d -1
kLa1= 0 d -3 -3 SO,1=2.10 gm -3 SNO,1=0.7gm
-1
3 -1
Qr,int,7,3 = 0 m d
-1
-1
kLa2= 0 d -5 -3 SO,2=1.10 gm -2 -3 SNO,2=5.10 gm
-1
k L a 3= 0 d -3 SO,3=0 gm -3 -3 SNO,3=3.10 gm
-1
k L a 4= 0 d -3 SO,4=0gm -4 -3 SNO,4=2.10 gm
-1
kLa5= 334 d -3 SO,5=1.0gm -3 SNO,5=9.6gm
kLa6= 0 d -3 -3 SO,6=3.10 gm -3 SNO,6=2.6 gm
-1
kLa7= 217 d -3 SO,7= 0.5gm -3 SNO,7= 8.1gm Qwaste = 299 3 -1 md
3 -1
Qr,ext,1 = 20853 m d
b. VIP process configuration optimization (OC = 779 166) Qef = 18147 3 -1 md
3 -1
Qr,int,4,1 = 13666 m d
3 -1
Qr,int,7,3 = 0 m d
uECSD,3 = 176491 -1 gCODSs d -1
-1
kLa1= 0 d k L a 2= 0 d -3 -3 SO,1=0gm SO,2=0gm Qfresh,1 = -3 -3 -4 -3 SNO,2=2.10 gm 18446 SNO,1=4.10 gm 3 -1 3 -1 md Qr,ext,1 = 24539 m d
-1
kLa3= 0 d -3 -3 SO,3=2.10 gm -3 SNO,3=0.9gm
-1
-1
k L a 4= 0 d -5 -3 SO,4=2.10 gm -3 SNO,4= 0.1gm
-1
kLa5= 316 d -3 SO,5=0.9gm -3 SNO,5=8.6gm
k L a 6= 0 d -3 -3 SO,6=3.10 gm -3 SNO,6=2.6gm
-1
kLa7= 220 d -3 SO,7=0.6g m -3 SNO,7=7.9gm Qwaste = 299 3 -1 md
c. Modified UCT process configuration optimization (OC = 781 981 ) uECSD,3 = 194048 -1 gCODSs d
Qef = 18148 3 -1 md
ANOX -1
-1
kLa1= 0 d kLa2= 0 d -5 -3 -3 SO,2=0gm Qfresh,1 = SO,1=1.10 -2gm -3 -3 -3 SNO,2=2.10 gm 18446 SNO,1=3.10 gm 3 -1 3 -1 md Q r,ext,1 = 23806 m d
3 -1
Qr,int,7,3 = 0 m d -1
kLa3= 0 d -3 -3 SO,3=2.10 gm -3 SNO,3=0.8gm
-1
-1
kLa4= 0 d -5 -3 SO,4=1.10 gm -2 -3 SNO,4=8.10 gm
kLa5= 319 d -3 SO,5=0.9gm -3 SNO,5=8.8gm
-1
k L a 6= 0 d -3 -3 SO,6=3.10 gm -3 SNO,6=2.7gm
-1
kLa7= 218 d -3 SO,7=0.5gm -3 SNO,7=8.0gm Qwaste = 298 3 -1 md Qef = 18147 3 -1 md
d. 5 stages Bardenpho process configuration optimization (OC = 801 928) 3 -1
uECSD,3 = 377720 gCODSs d -1
Qr,int,5,3 = 0 m d
-1
-1 kLa1= 0 d kLa2= 0 d -3 -3 -5 -3 S =2.10 gm SO,2=1.10 gm Qfresh,1 = O,1 -3 -2 -3 SNO,1=0.7gm SNO,2=5.10 gm 18446 3 -1 3 -1 m d Qr,ext,1 = 20792 m d
-1
kLa3= 0 d -3 SO,3=0gm -3 -3 SNO,3=3.10 gm
-1
kLa4= 0 d -3 SO,4=0gm -4 -3 SNO,4=2.10 gm
-1
kLa5= 333d -3 SO,5=1.0gm -3 SNO,5=9.6gm
-1
kLa6= 0 d -3 -3 SO,6=3.10 gm -3 SNO,6=2.7gm
-1
kLa7= 217 d -3 SO,7=0.5gm -3 SNO,7=8.2gm
Qwaste = 299 3 -1 md
In the four configurations of Fig. 4, the internal -i.e. nitrate- recycle from the aerobic zone vanishes. Thus, the anaerobic “character” of the first zone “increases” and so do the P release. Optimal solutions for A2/O and 5-stages Bardenpho process configurations are the same (the differences observed are due to numerical aspects) since the internal recycles vanish: they present a zone (1st and 2nd reactors) with anoxic conditions followed by a zone (3rd and 4th reactors) with anaerobic conditions, and finally an alternate aerated zone. The external C source is added to the anaerobic zone (reactor 3). In VIP and modified UCT configurations the sludge recycle is directed to
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the 3rd reactor favoring anaerobic conditions in the 1st zone (reactors 1 and 2). The internal recycles coming from the anoxic zone could not be deleted since they are responsible for the biomass addition to the 1st zone. These recycle streams have a low SNO concentration. As a consequence, in these configurations, the readily biodegradable matter (SS) contained in the effluent and the external C can be use by XPAO (and be more efficiently used for SPO4 release) in the 1st anaerobic zone (reactors 1 and 2), increasing the P-removal efficiency. The models were implemented and solved using GAMS and CONOPT, respectively. Table 1. Costs and main variables optimal values Solution -1
OC (Euro year ) -1
EQef (kg PU d ) -1
Ea,ef (kWh d ) -1
Epump,ef (kWh d ) -1
uSLDGD,ef (kgSS d ) uECSD,ef (kgCODSs d-1) -3
SNH,ef (gN m ) -3
NTOT,ef (gN m )
Superstr.
A2/O
VIP
Mod. UCT
5 st. Bard.
762 678
801 929
779 166
781 981
801 928
7 121.22
6 904.80
6 855.87
6 870.22
6 910.02
6 630.72
6 970.10
6 692.08
6 723.81
6 970.36
963.46
846.11
1 540.15
1 476.92
843.64
2 793.95
2 929.63
2 816.55
2 829.37
2 929.56
65.90
379.55
176.49
194.05
377.72
4.00
4.00
4.00
4.00
4.00
13.96
13.37
13.18
13.23
13.39
-3
2.03
2.09
2.08
2.08
2.09
-3
BODef (gCOD m ) CODef (gCOD m )
46.53
46.58
46.89
46.83
46.57
Ptotef (gP m-3)
1.50
1.50
1.50
1.50
1.50
-3
16.17
16.12
16.52
16.45
16.11
XSS,ef (gSS m )
References N. Alasino, M. C. Mussati, N. Scenna, 2007, Wastewater treatment plant synthesis and design, Ind. Eng. Chem. Res., 46, 23, 7497. N. Alasino, M. C. Mussati, N. Scenna, 2006a, Synthesis of Activated Sludge Wastewater Treatment Plants for N Removal, XXII Interam. Chem. Eng. Congress- V CAIQ, 06C(505). N. Alasino, M. C. Mussati, N. Scenna, 2006 b, Optimization of the operation conditions for denitrifying wastewater treatment plants, EMSS06, 427. J Copp, 2002, The COST Simulation Benchmark: Description and Simulator Manual. Office for Official Publications of the European Community, Luxembourg. K.V. Gernaey and S.B. Jørgensen, 2004, Benchmarking combined biological phosphorus and nitrogen removal wastewater treatment processes. Contr. Eng. Pract., 12, 357. W. Gujer, M. Henze, T. Mino and M. van Loosdrecht, 1999, Activated Sludge Model No. 3, Wat. Sci. Techn., 39, 183. M. Mussati, K. Gernaey, R. Gani and S. Bay Jørgensen, 2002, Performance analysis of a denitrifying wastewater treatment plant. Clean Techn. & Env. Policies, 4, 171. L. Rieger , G. Koch ,M. Kuhni ,W. Gujer and H. Siegrist, 2001, The EAWAG Bio-P module for activated sludge model No. 3. Wat. Res., 35(16), 3887. I. Takács, G. Patry, and D. Nolasco, 1991, A Dynamic Model of the Clarification-Thickening Process. Wat. Res., 25, 1263. P.A. Vanrolleghem and S. Gillot, 2002, Robustness and economic measures as control benchmark performance criteria, Wat. Sci. Techn., 45(4-5), 117. Acknowledgements. The financial support from CONICET and ANPCyT is acknowledged.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A Systematic Procedure For Optimizing Crude Oil Distillation Systems Hasan Y. Alhammadi Chemical Engineering Department, University of Bahrain Isa Town, PO Box 32038 Kingdom of Bahrain
Abstract Nowadays, building new refinery units is very costly. Therefore, many retrofit projects to the existing crude oil distillation system are considered to increase the production capacity of the refinery by increasing the throughput. The objective of this research is to retrofit the atmospheric crude oil distillation column to reduce the vapor load through the column. Therefore, as the vapor load decreases, the throughput can be increased. Simultaneously, the heat exchanger network, furnace and pumps are considered both to identify any bottleneck associated with the retrofit procedure and to ensure an energy-efficient column design by reusing the available heat effectively. This retrofit design procedure will be explored by applying the suggested modifications on an existing case study by the use of a computer simulation and pinch analysis packages. Keywords: Crude oil distillation systems – Debottlenecking – Pinch analysis.
1. Introduction In any refinery, the atmospheric crude oil distillation column is the first processing unit. The atmospheric crude oil distillation fractionates the crude oil into products according to their boiling points. Therefore, the atmospheric column often forms the bottleneck in a refinery due to the large amount of crude oil introduced to the column to be processed. After that, each unit in the refinery processes a fraction of the feed taken as a single product from the atmospheric column [1]. In this paper, the proposed retrofit design procedure is presented and illustrated by using the case study of an atmospheric crude oil distillation column as shown in Figure 1. The bottlenecks in the existing system will be identified with respect to different points of view such as the vapour load, furnace duty, etc. Detailed information and graphs will not be presented in this paper due to the limitation in the number of pages. 1.1. Pinch Analysis of the Crude Oil Distillation Process Pinch analysis is applied to the crude oil distillation system to determine the minimum utility requirements and to find any applicable modifications to the process. The petroleum refining industry ranks third, after the chemical and the primary metal industry, in its energy consumption [2]. In addition, in any refinery, there is a wide range of temperatures where heat must be supplied or removed. Therefore, applying pinch analysis to the crude oil distillation system is necessary to reduce the energy consumption as far as possible.
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Figure 1: Base case configuration of the case study Pinch analysis is a thermodynamically based method for the design of heat and power systems. The method of pinch analysis groups the heat sources and sinks of the process streams into temperature intervals, where it is possible to transfer heat in each interval from heat sources to heat sinks [3]. The grand composite curve can be used to provide an interface between the distillation column and the utility system. If a number of different utilities are available, the grand composite curve can be used to determine the relative amount of each utility needed. If there are mismatches between the process streams profiles and the utility profile, then process modifications are needed to remove these mismatches as far as possible. Process modifications may change the heating or cooling requirements of the streams which will be reflected on the grand composite curve. The modifications, which increase the heat recovery, will increase energy savings. Pinch analysis, in particular the grand composite curve, provides valuable information about each modification to the crude oil distillation system with respect to the utility costs. The main objective of using pinch analysis is to maximize the use of the least expensive utilities and minimize the use of the most expensive utilities. 1.2. Decomposition of a Complex Column The atmospheric distillation column in a refinery is highly complex system because of the interactions between the main column with different side strippers and draw streams where the study of this complex system will be more difficult. However, the decomposition of the complex column into a series of simple columns ease and simplify its study. There are a number of advantages of decomposing a complex tower, namely: 1. It is easier to deal with a sequence of simple columns rather than a complex column with respect to understanding the process operations and the implications of design modifications to the process. 2. It is easier to formulate and converge a computer simulation for a sequence of simple columns than a complex column.
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3. To improve the stage distribution for each section in the crude tower, the tower is decomposed into a sequence of simple columns as a first step. After that, the ideal number of stages and the optimum feed stage for each simple column are found. Finally, the simple columns are merged back to the complex column with new numbers of stages for each section. 4. The available standard shortcut methods and distillation design procedures are not applicable to complex columns. However, they are for simple columns. For complex mixtures, e.g. crude oil, the standard shortcut methods are not accurate for designing the crude oil distillation column. However, these methods are used to get a starting estimation for designing the column. In essence, every complex column configuration can be decomposed into single columns and vice versa: every sequence of simple columns can be merged in to a more complex configuration. The decomposition of a complex column into a sequence of simple columns is used only for analysing and studying the system. Therefore, after analysing and modifying the sequence of the simple columns, they must be merged back into a complex column to be compared to the original one.
2. External Modifications The external modifications to retrofit the distillation system are considered as starting steps for the retrofit procedure. Simple modifications requiring little or no capital investment are implemented to improve the match between the heat exchanger networks (HEN) associated with the column and the available utilities. The external modifications do not change the column hardware and its internals [4]. 2.1. Removal of Inefficiencies In this level of retrofit, only simple modifications are implemented to remove any inefficiencies in the system and to improve the heat transfer efficiencies. In the base case study, there are some inefficiencies that are required to be removed as a starting point to increase the separation efficiencies and the energy savings. These inefficiencies are normally found in existing crude oil distillation towers because of their long working life. Through this long life, many modifications and developments are carried out for local improvements without considering the overall performance. During this long life, the crude oil distillation process is adjusted as the feed properties and the products specifications change with time. An inefficiency in the original configuration of the case study is shown where the product of the AGO side stripper is split into two streams one of is cooled and introduced again in the main column. This sub-cooled returned liquid performs the function of a pump around. This separation and remixing is clearly inefficient because of the higher amount of stripping steam required. One way to remove this inefficiency is done where the side draw from the main column is split first and returned as sub-cooled stream while the other stream is stripped in the side stripper. Therefore, the required stripping steam is reduced tremendously as the feed is reduced. The total savings in operating cost are $40,000/yr for this simple modification in the piping connections. Another example of inefficiency is mixing two vapour streams with a big difference in their composition causes this inefficiency. The returned vapour from the KE side stripper is mixed with the vapour inside the main column which resulting in mixing losses. This modification suggests that the vapour must be returned to the stage of the liquid side draw where the vapour composition of this stage is similar to the returned vapour from the side stripper. Due to the reduction in the reboiler duty of the KE side stripper,
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the absolute saving is another $30,000/yr for changing the location of the vapour return port on the column. Finally, the sequence of these simple columns is merged into a complex column with the new values of pump around and reboiler duties while the main column will not change. The fuel consumption (i.e. the furnace) is reduced by 4.2%. A reduction of 13% in the energy costs is achieved representing savings of $526,000/yr. Low investments are required for these external modifications to adjust the piping network to remove the inefficiencies and to install a new reboiler at the bottom of the LD side stripper. External modifications were considered first. This is because of the low investment that is required by these modifications. The throughput through the modified column could be increased by 39%. There are two options concerning the use of a reboiler or a combination of live steam and a reboiler at the KE side stripper. A trade-off exists between these two options where the use of a reboiler only is more beneficial with respect to the savings in the energy costs while the use of the combination of reboiler and steam save 16% in the furnace duty.
3. Internal Modifications The internal modifications to retrofit the distillation system consider the distillation column and its internals. In this level of retrofit, some changes are made in the internals or nozzles of the main column and the side strippers. Moreover, the reboilers and pump around loops are examined and adjusted as required. Therefore, more complex modifications are required at this level that lead to higher investments. The objective of these modifications is to find out the ideal distribution of stages for each section in the main column [4]. This ideal design is applied to the existing column by modifying its internal to the minimum extent to reduce the costs. 3.1. Redistribution of stages in the Column The main column is decomposed first into a sequence of six simple columns. After that, few iterations are done to find the ratio between the actual reflux to the minimum reflux where the total number of stages in the single columns equals the total in the original. After that, the sequence of the resulting column is merged into a complex column; the original tower has 25 stages in the main column while the ideal tower has 20 stages in the main column. As the total number of stages is the same, the difference in the stages in the main column is distributed among the side strippers. Obviously, it is expensive and impractical to rebuild the tower completely to match the ideal configuration. A compromise between the ideal and original design is required to reduce the modifications costs. Therefore, the original main column is kept unchanged as the ideal number of stages is less than the existed number. The complex column is broken into a sequence of simple columns. This sequence is initially set up with no thermal coupling and with the use of stripping steam instead of reboiling to have the best heat recovery potential. Then, the heat sinks are satisfied first followed by the relaxation of the excess heat sources. Finally, the sequences merged into a complex column. By applying the internal modifications, further reductions in the vapour load and the energy consumption compared to the external modifications are achieved. This is done by redistributing the stages of the column. After identifying the ideal distribution of stages, a compromise between the existing and the ideal columns is required to reduce the costs of these modifications. The throughput to the modified column could be increased by 48%. The maximum vapour load is shifted from the KE section (base case) to the vapour feed stage (after applying the internal modifications). When the vapour
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feed stage becomes the bottleneck, configurational modifications are required to be considered to reduce the vapour load through the main column.
4. Configurational Modifications This level of retrofit design of crude distillation systems is considered last. In this step, complex and costly modifications are investigated. The third level of modifications is the consideration of changes in the column configuration. This can be done by adding a pre-fractionator, a post-fractionator or a preflash train. The main column is changed as little as possible, keeping the same number of trays and position of nozzles to minimise the costs of modifying the main column. Because of the addition of a new column, the separation load, energy consumption and vapour load are reduced in the main column. Some difficulties could arise in this level of modifications due to specific limitations, such as space limits or the length of piping required. 4.1. Preflash Installation A preflash configuration is studied for this case study to reduce vapor load in the main column. The preflash is introduced to separate light products (overhead vapor, Distillate and Heavy Naphtha (HN)) outside the system. In the base case, the feed is heated from 24oC, where the vapor fraction is zero to 335oC to vaporize 76% of the feed. In the preflash configuration, the feed is preheated first from 24oC to 193oC to vaporize 30% of the feed. This preheated feed is flashed in a preflash tank to remove this light material. The vapor product of this preflash tank is processed in a separate column. This vapor product might contain a small amount of heavy materials as will as the liquid product might contain a small amount of light materials. These light materials could be recovered in the main column as overheated vapor. However, the specifications of the light products in the new column might not satisfy as a result of the existence of a high percentage of the heavy materials in the feed stream to the new column. Therefore, the percentage of heavy materials in the vapor product of the preflash should be monitored by adjusting the preheating to reduce the amount of heavy materials in the HN product. The specifications of the new column are estimated first by doing a shortcut simulation. The initial estimation of the pressure for the stages and the product specifications for this column are the same as for the HN section in the original tower. It is found that this column requires four trays and the feed tray is at stage 2. The liquid product of the preflash tank is repressurized and heated further in the furnace before it is flashed and introduced to the main column. 4.2. Rearrangement of Sections and Side Strippers In this step, the ideal number of stages and feed tray for each of the remaining sections are calculated. After removing the top section from the main column, the total number of sections in the main column is reduced from six to five. Therefore, in the initialization step, five columns are required to separate the remaining products. To redistribute the stages in the remaining sections, a shortcut simulation is used to find out the required number of trays, the feed tray location and the minimum reflux ratio for each column in the sequence. To make use of the existing column with the same number of trays (24 trays) iterations are required to adjust the sum of the rectifying sections in each column equal to 24 (number of trays in the main column). Finally, the sequence of the simple columns is merged into a complex column. The main column is not changed, but the side strippers and pump arounds need to be relocated or adjusted. The new configuration suggests increasing the bottom section by two stages which means moving the lowest side draw and pump around two stages up from the existing
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position. Fortunately, in this case study all other nozzles for the side strippers are not changed. However, the number of stages that is required for the side strippers changes. As the Heavy Naphtha (HN) side stripper is removed and since the AGO stripper requires two stages, rather than one, it is suggested that the AGO side stripper is replaced by the HN side stripper. The side stripper for the LD product will not change but the HD stripper requires one more stage. A new KE stripper with five stages is required. According to the pump arounds, only the top one needs to be moved. The original HN pump around can be moved from stage 5 and used as the AGO pump around at stage 21. A large reduction in the vapor load is shown where the maximum vapor flow, after the column is modified, is 52% of the maximum vapor flow of the base case. This implies that approximately 92% more feed can be processed by the modified column that the original column. The consumption of fuel for the whole system (including the new column) is reduced by 31%. The utility cost for the new configuration including the HN tower is reduced by 18%. This reduction represents an absolute saving of $720,000/yr. Configurational modifications are quite expensive due to the installation of a new column and pumps. However, the benefits from these modifications are much greater than for the simpler modifications discussed in the previous sections. The vapor load is reduced in the modified column by almost half which means the throughput can be almost doubled. In addition, the energy cost of the system is reduced by 18%. The options that are given for the location of the AGO side stripper give a trade-off. Which is the better option should be decided by design engineers for the specific case being investigated.
5. Conclusions The crude oil distillation system is a unit of major importance in every refinery. Any reduction in the vapor load through the distillation column will have an impact on the capacity of the refinery. The objectives of the retrofit studies are usually throughput increases or energy savings and are required to be met with the least capital spending. The proposed procedure divides the retrofit design procedure into three levels. At the first level, suggested external modifications to be applied where the original column does not change in order to remove inefficiencies from the system. Thereafter, reboiler and pump around duties are adjusted. The second level suggests internal modifications to find the best distribution of the stages in the column with the least investment. Therefore, a compromise between the original column and the ideal distribution of stages must be found. The third level of the retrofit modifications involves changing of the column configuration. This could be done by the installation of preflash units, pre-fractionators or post-fractionators units. For the presented case study, it has been shown that the throughput can be increased by 39% by applying the first level of modifications. For the second and third level, the throughput can be increased by 48% and 97% respectively.
References [1] Gary, J. and Handwerk, G., Petroleum Refining-Technology and Economics, Marcel Dekker Inc., New York, 1994. [2] Sittig, M., Petroleum Refining Industry-Energy Saving and Environmental Control, Noyes Data Corporation, New Jersey, 1978. [3] Smith, R., Chemical Process Design, Wiley, 2005. [4] Liebmann, K., Dhole, V. and Jobson, M., Integrated design of a conventional crude oil distillation tower using pinch analysis, Trans IChemE, 76, 1998.
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Evaluation of pervaporation process for recovering a key orange juice flavour compound: modeling and simulation Araujo W.A., Alvarez M.E.T., Moraes E.B., Wolf-Maciel M.R. Separation Processes Development Laboratory, School of Chemical Engineering, State University of Campinas (UNICAMP), P.O. Box 6066, Campinas-SP 13083-970,
[email protected], BRAZIL.
Abstract During fruit juice processing, characteristic flavour components are usually lost as consequence of the heating process. Membrane separation processes are considered as a promising alternative for this issue, e.g., in orange juice industry, an important agro industrial chain in Brazilian economy. Ethyl butyrate (EB) is one of the fresh orange flavour key contributors. Pervaporation is an attractive technology for processing thermal sensitive compounds. This membrane process is based on a selective transport of a liquid feed mixture through a selective polymeric or ceramic membrane. In this work, the pervaporation performance was simulated for recovering EB from a diluted binary aqueous mixture using a PDMS (poly(dimethylsiloxane)) hydrophobic membrane. Innovative preliminary process results obtained using predicted POMS (poly(octylmethylsiloxane)) properties are also presented. A FORTRAN simulator named PERVAP based on an essentially predictive mathematical model was applied in this work. Keywords: prediction, simulation, pervaporation, flavour, ethyl butyrate.
1. Introduction In 2005, Brazil and USA exported 89% of worldwide orange juice. Brazil produces 30% of worldwide orange, and regarding to juice, the number achieves 59% of the market (Neves and Jank, 2006). Esters and aldehydes are the primary contributors to fresh orange juice, although other components could also be important (NisperosCarriedo and Shaw, 1990). Conclusions related to chemical composition and sensory characteristics elaborated on basis on orange juice analyses pointed ethyl butyrate (EB) as the most important compound based on its level and on its sensory threshold (Burgard, 1995). An interesting applied research scenario involves the recovery of this key compound from single strength orange juice (SSOJ) prior to concentration (heating exposal) in evaporators or even from the evaporation effluents (water essence phases or water condensates). It is important to emphasize that EB content in SSOJ is around 0.5 ppm and in condensate streams probably ppb levels can be achieved (Nisperos-Carriedo and Shaw, 1990). Pervaporation have been considered an interesting alternative process for the current industrial options for aroma recovery, distillation, partial condensation, solvent extraction, adsorption, or a combination thereof. It is considered a basic unit operation with significant potential for the solution of various environmental and energetic processes (moderate temperatures). This separation process is based on a selective transport through a dense membrane (polymeric or ceramic) associated with a recovery of the permeate from the vapour phase. A feed liquid mixture contacts one side of a membrane; the permeate is removed as a vapour from the other side. Transport through
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the membrane is induced by the vapor pressure difference between the feed solution and the permeate vapor (vacuum). The most accepted mechanism transport model is the solution-diffusion model which can be described into three steps, (a) sorption into the membrane at the upstream side, (b) diffusion through the membrane, and (c) desorption into a vapour phase at the downstream side. More recently, pervaporation has been used to the extraction of compounds biotechnologically produced or recovered from perfumery wastes and PDMS (polydimethylsiloxane) was reported as the most used material in the available literature studies on flavour compounds recovery. POMS represents around 10% in this pervaporative application. This intense experimental PDMS studies provides a valuable experimental data library for performance directions compared to different materials and/or outputs of process simulators (Araujo et al., 2007; Baker, 2004; Baudot and Marin, 1997; Pereira et al., 2006; Zhang and Drioli, 1995). The aim of this work was to simulate organophilic pervaporation process (PDMS) for recovering EB from a diluted aqueous binary model solution. A simulator named PERVAP based on a predictive pervaporation modeling was applied (Alvarez et al., 2008). The PDMS preview results were presented in Araujo et al., 2007). Innovative preliminary evaluation of POMS hydrophobic membrane using predicted properties to estimate required parameters in PERVAP, is also one of the objectives of this paper. The model versatility and predictive improvement are challengeable tasks.
2. Material and Methods 2.1. Pervaporation model features and PERVAP software. The PERVAP simulator (tubular module) was developed by Alvarez (2005), using FORTRAN language (Compaq Visual Fortran Professional Edition 6.6.a). The mathematical model applied is based on the solution-diffusion mechanism. Activity coefficients of the components in the feed phase (γi) were determined using the m UNIFAC method (Magnussen et al., 1981). The prediction of diffusion coefficient (Di ) was carried out using the free-volume theory. The free-volume parameters were estimated from viscosity and temperature data of pure components and the binary interaction parameter between the component and the polymer was determined using the group-contribution lattice-fluid equation of state (GCLF-EOS) (Alvarez, 2005, Alvarez et al., 2008). The innovative application of zero shear viscosity predicted data was proposed in this work for POMS free-volume parameters, as an alternative when experimental polymeric membrane viscosity data are scarce or inexistent. 2.1.1. Prediction of diffusion in the membrane selective layer. m
The diffusion coefficient of component i (ethyl butyrate) in the membrane, (Di ), was predicted by the free-volume theory described by the equation (1) (Vrentas and Duda, 1977; 1979): Dim
§ ¨ ω1Vˆ1∗ + ξω2Vˆ2∗ §−E· ¨ = D0 (1 − φ1) (1 − 2χφ1) exp¨ ¸ exp − ¨ K K 11 © RT ¹ ω1 K21 − Tg1 + T + 12 ω2 K22 − Tg 2 + T ¨ γ γ © 2
(
)
(
)
· ¸ ¸ ¸ ¸ ¹
(1)
Evaluation of Pervaporation Process for Recovering a Key Orange Juice Flavour Compound: Modeling and Simulation
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2.1.2. Estimation of free-volume parameters for solvent and polymeric membranes Six parameters (three for each solvent and three for the polymer) were estimated using the following theories: (a) PDMS: (K22 – Tg2) and K22/γ were obtained in literature (Hong, 1995) using polymer viscosity and temperature data. This procedure is expressed in terms of the Williams-Landel-Ferry equation (Williams et al., 1955). The polymer’s free volume parameter was related to the Williams-Landel-Ferry constants as presented in equation (2). (b) The same approach was used to obtain (K22 – Tg2) and K22/γ for POMS (equation (2)), but zero shear viscosity data prediction was required prior to this step. (c) EB and Water: (K21 – Tg1) and K21/γ parameters were calculated for both components using pure component data of viscosity and temperature (Djojoputro and Ismadji, 2005). Hong (1995) presented equation (3) where free volume amount is related to viscosity. (d) Vˆ1∗ and Vˆ2∗ are critical volumes estimated as the specific volumes of the solvent and polymer at 0K using group contribution methods (Haward, 1970; Hong, 1995). ȗ and φ1 were calculated according to Vrentas and Duda concepts (1977, 1979). More details about all topics mentioned to estimate free-volume parameters are available in literature (Alvarez et al., 2008). § η (T ) ¨ log¨ 2 ¨ η 2 Tg 2 ©
( )
(
· − C WLF T − T 12 g2 ¸ ¸¸ = WLF ¹ C 22 − Tg 2 + T
ln η1 = ln A1 +
(γ Vˆ
∗ 1
K11
)
(2)
)
(3)
(K 21 − Tg1 ) + T
2.1.3. Zero shear viscosity (Ș0) prediction: POMS. The development of new polymeric structures for different technological applications usually requires knowledge about properties of this material. The prediction of properties using additive group contribution method is a valuable procedure adopted during the developments presented here. The group contribution method concept was applied to obtain viscosity data versus temperature, an intermediate step of the freevolume parameters estimation procedure (equation (2) inputs). Detailed concepts about prediction of polymer properties were studied and applied as presented in specific literature (Van Krevelen, 1992; Bicerano, 2002). Equations (4) and (5) are the key equations of the procedure to obtain zero shear viscosity predicted data. The references adopted in this section also allows to predict many others polymer properties. logη o = logη cr + 3.4 log(M w / M cr )
if Mw > Mcr
(4)
logη o = logη cr − log(M cr / M w )
if Mw < Mcr
(5)
2.1.4. Fundamental model equations of pervaporative process PERVAP simulator neglects mass transport in the boundary layer as assumption. Thus, equations (6) and (7) are assumed to calculate permeate fluxes for components i (EB) and j (water) (Alvarez et al., 2008). Ji =
xi ,a α p Dim §¨ x γ − m ¨ i ,a i ,a 1 + (α − 1) xi ,a Aγ i ©
· ¸ ¸ ¹
(6)
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Jj =
D mj §¨ x j ,a γ Aγ mj ¨©
j ,a
−
(1 − xi,a )pPisat ·¸ Pjsat [1 + (α − 1)xi ,a ] ¸¹
(7)
where, J is the permeate flux (mol/m2h), x is the mole fraction, Psat is the vapor pressure (kPa), p is the relative pressure, γ is the activity coefficient, Dm is the diffusion coefficient (m2/h) and α is the selectivity. 2.2. Inputs applied for simulating pervaporative process The PDMS and POMS membranes and process parameters were investigated using experimental studies for comparison (Sampranpiboon et al., 2000). The following operational conditions were applied for both membranes: temperature, 303.15 K; downstream pressure (permeate side), 0.3997 kPa; membrane thickness, 10 μm.
3. Results and Discussion The predicted and estimated free-volume parameters data used as inputs in PERVAP and diffusion coefficients results are presented in Table 1. The PDMS process performance is illustrated by Figures 1-3. Preview EB flux scenario using POMS is presented in Figure 4. For both membranes water permeate fluxes (Figures 1b and 4b) remained practically constant and did not present adjustments as satisfactory as the profile observed for EB (Figures 1a and 4a). Constant water fluxes are expected as mentioned in several studies, i.e., it is independent on the concentration of organic components for the case of diluted solutions (Pereira et al., 2006). The deviations presented for water (Figures 1b and 4b) were considered tolerable, since this kind of deviation was not observed by Alvarez et al. (2008), but it is important to emphasize that the study was not accomplished assuming a diluted feed stream, consequently, depletion layer impact was avoided considering a turbulent flow system. In diluted streams, this layer is a key issue related to diffusion and, consequently, separation performance. Figures 2a and 2b allow to observe pressure effect on the total permeation. It is possible to see as higher as vacuum better the total permeation, but separation capability is reduced as shown in Figure 2b and confirmed by selectivity profile in Figure 3a. A recovery (%) is presented in Figure 3b, concentration increases of the target compound in feed provides lower recovery results. This is an interesting graph for process set up definitions. Table 1. Inputs for PERVAP and Diffusivity output: PDMS and POMS. Component
Vˆ1∗
K11/γ (cm3/g⋅K)
K21-Tg1 (K)
D0 (cm2/s)
Ȥ
K22-Tg2 (K)
Dm (m2/h)
(cm3/g) PDMS - simulator inputs: Output -35.08 0.0380 EB 0.919 0.5×10-4 1.89×10-9 1.09×10-3 -81.00 -152.29 0.0029 H2O 1.071 8.5×10-4 2.11×10-16 2.18×10-3 POMS – simulator inputs: -35.08 0,0215 EB 0.919 0.5×10-4 2.63×10-8 1.09×10-3 -216.40 -3 -4 -152.29 0,0018 H2O 1.071 8.5×10 2.12×10-16 2.18×10 Note: E= zero (Araujo et al., 2007; Alvarez et al., 2008). K12/γ -PDMS =9.32×10-4 and POMS =3.45×10-3.
Evaluation of Pervaporation Process for Recovering a Key Orange Juice Flavour Compound: Modeling and Simulation
179
16.70
1.20 1.00
Experimental (Sampranpiboon et al., 2000) simulated
0,000110; 16,6000 Experimental
Experimental (Sampranpiboon et al., 2000) simulated
Jj (mol/m .h) - H2O
0.60
§3% variation
16.30
2
2
Ji (mol/m .h) - EB
16.50
0.80
0.40
16.10
0,00011; 16,1054 simulated data
0.20 0.00 0.0000
0.0001
0.0002
0.0003
0.0004
15.90 0.0000
0.0005
0.0001
mole fraction (x i )
0.0002
0.0003
0.0004
0.0005
mole fraction (x i )
1.0
14.0 1.5
18.0 16.0
0.0117
14.0
0.0116
12.0
0.0115
10.0
0.0114
12.0
8.0
2.0
6.0
0.0113
Ji
10.0
4.0
0.0112
Jj
2.0
8.0
0.0111
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0 0.0
0.0006
2
16.0
20.0
0.0118
2
0.5
0.0119
Ji (mol/m .h)- EB
18.0
(kPa)
0.1
Jj (mol/m .h)-H2O
20.0
Pressure
Total Permeate Flux: Ji+Jj (mol/m2.h)
(a) (b) Figure 1. General simulations of permeation fluxes: (a) H2O (b) EB
0.5
1.0
1.5
2.0
2.5
Permeate Pressure (kPa)
xi
(a) (b) Figure 2. (a) Downstream pressure effect in total permeate flow; (b) Pressure effect in partial permeate fluxes. 0.08
260.0
98.0
238.3 0.06
96.0
yi - Permeate
Selectivity
220.0 200.0 180.0 160.0
94.0 0.04 92.0 90.0
0.02
140.0
Mole Fraction EB - Permeate EB Recovery - Permeate
135.9
120.0
0.00
0.0
0.5
1.0
1.5
Permeate Pressure (kPa)
2.0
2.5
Recovery (%)
240.0
100.0
0
0.0001
0.0002
0.0003
0.0004
88.0 86.0 0.0005
x i - Feed
(a) (b) Figure 3. (a) Selectivity versus permeate pressure (PDMS) xi = 5.0·10-6; (b) EB recovery and permeate composition based on EB content in feed stream.
W.A. Araujo et al.
180 1.200
15.500 Experimental (Sampranpiboon et al., 2000)
0.00005; 15.217
Simulated
15.000
(a)
0.600 0.400
2
0.800
Jj (mol/m .h)- H2O
2
Ji (mol/m .h)- EB
1.000
§11% variation
14.500
(b)
14.000
13.500
0.00005; 13.568
0.200
13.000
0.000 0.0000
12.500 0.0000
Experimental (Sampranpiboon et al. 2000) simulated
0.0001
0.0002
0.0003
mole fraction - x
0.0004 i
0.0005
0.0001
0.0002
0.0003
mole fraction - x
0.0004
0.0005
i
Figure 4. Simulations of permeation: POMS - (a) EB (b) H2O
4. Conclusion Pervaporation is a very interesting process for recovering key compounds from diluted food industry streams (e.g., orange juice, evaporator condensates, etc.). The simulated results confirmed the satisfactory application of PDMS for EB recovery from diluted aqueous feed. The preliminary results using POMS allow to conclude that this membrane should be recommended as the ideal choice for this process. This membrane presented better permeation for EB, giving higher values of selectivity. The process simulations using predicted POMS properties presented promising results which encourages the topic continuity for consolidating this strategy. The simulator performance motivates the investigation of other binary mixtures. A friendly interface should be developed to improve the simulator applications by process engineers. Future PERVAP versions must consider the depletion layer modeling, which is a crucial topic to improve simulator applicability in diluted streams.
5. References Alvarez, M.E.T., 2005, PhD Thesis, State University of Campinas, Campinas, SP, Brazil. Alvarez, M.E.T., Moraes, E.B., Araujo, W.A., Maciel Filho, R., Wolf-Maciel, M.R., 2008. J. Appl. Polym. Sci., 107(4), 2256-2265. Araujo, W.A., Alvarez, M.E.T., Wolf-Maciel, M.R. 2007, In: Proceedings of European Congress of Chemical Engineering (ECCE6), Copenhagen. Baker, R., 2004. Membrane Technology and Applications, John Wiley & Sons Ltd., UK. Baudot, M., Marin, M., 1997. Trans IchemE. 75, 117-147. Bicerano, J., 2002. Prediction of polymer properties, New York: Marcel Dekker Inc. 784. Burgard, D.R., 1995. ACS Symp. Ser. 596, 21-32 Djojoputro, H., Ismadji, S., 2005. J. Chem. Eng. Data. 50, 727-731. Haward, R.N., 1970. J. Macromol. Sci. Rev. Macromol. Chem. C4 (2), 191-242. Hong, S.U., 1995. Ind. Eng. Chem Res. 34, 2536-2544. Magnussen, T., 1981. Ind. Eng. Chem. Process Des. Dev. 20, 331-339. Neves, M.F., Jank, M.S., 2006. São Paulo: PENSA-Agribusiness Intelligence Center, Report. Nisperos-Carriedo, M.O., Shaw, P.E., 1990. J. Agric. Food Chem. 38 (4), 1048-1052. Pereira, C.C., Ribeiro, A.C., Nobrega, R., Borges, C.P., 2006. J. Membr. Sci. 274, 1-23. Sampranpiboon, P., Jiraratananon, R., Feng, X., Huang, R.Y.M., 2000. J. Membr. Sci. 174, 55-65. Van Krevelen, D.W. 1992. Computacional modeling of polymers. New York: Marcel Dekker, 55. Vrentas, J.S., Duda, J.L., 1977. J. Polym. Sci. Part B: Polym. Phys. 15, 403-416. Vrentas, J.S., Duda, J.L., 1979. AICHE J. 25 (1), 1-24. Willians, M.L., Landel, R.F., Ferry, J.D., 1955. J. Am. Chem. Soc. 77, 3701-3707. Zhang, S., Drioli, E., 1995. Sep. Sci. Technol. 30 (1), 1-31.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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A Microeconomics-based approach to product design under uncertainty Craig Whitnack, Ashley Heller, Miguel J. Bagajewicza a
School of Chemical, Biological and Materials Engineering, University of Oklahoma, 100 E. Boyd St., Norman, OK 73019, US
Abstract In this paper, an existing methodology (Bagajewicz, 2007) for the development of consumer products is applied to winemaking. We use a price demand model that incorporates product quality and allows the determination of the most profitable product, which is not always the best product from the consumer’s perspective- a well known fact. The parameters of the model are however, uncertain, especially in the wine case. Thus, design under uncertainty needs to be performed. We present an analysis of profitable scenarios and their associated risk. The method allows vineyards to pick a specific wine quality, a production rate and bottle selling price based on their desired profitability and tolerable level of associated risk. Keywords: Product Design, Wine Production
1. Introduction Wine has long been considered an art form, where quality was held in the eyes of the producer. With the new information-rich consumer market, the consumer now holds the buying power. Because of this, wine producers must now cater more to the desires of their customers to not only obtain patronage, but loyalty as well. In order to accommodate these new demands, we apply a recently developed methodology (Bagajewicz, 2007) to winemaking which incorporates consumer satisfaction to pricing models. Consumer preferences are identified, allowing the data generated by market analysis to be related to wine properties. These wine properties are easily measured throughout the winemaking process and can be manipulated by the manufacturer at little cost. Modifiable processes include fermentation, clarification and stabilization, barrel toasting and aging (Cook et al., 1998). Finally after the consumer overall preferences are identified, the wine can be compared to the competitor and the selling price of the wine can be set by optimizing the producer’s return on investment. We first review briefly some of the consumer preference functions. We then compute a net present value as a function of price for different qualities as suggested by Bagajewicz (2007). Finally, we discuss the uncertainty associated to the model and suggest means to deal with uncertainty.
2. Pricing and Consumer Preference Models We use the same constant elasticity of substitution model as Bagajewicz (2007). This model is a small modification of the constant elasticity of substitution models found in literature (Hirshleifer and Hirshleifer, 1998; Varian, 1992) where hedonic theory is incorporated. This was extended to multiple competitors by Street et al. (2007). The final expression relating demand of new product to price is:
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C. Whitnack et al. ρ
p §α · d 1 = ¨¨ ¸¸ * 2 p1 β © ¹
§ Y − p1 d 1 · ¸¸ * ¨¨ p2 © ¹
1− ρ
* d1
ρ
(1)
where d1 is the demand of the new product, p1 its proposed price, p2 the average price of competitor wines, ρ a predetermined constant, Į a zero to one measure of the amount of knowledge the consumer has for the product of interest and, Y is the consumer budget, which satisfies (2) Y ≥ p1d1 + p 2 d 2 Finally, ȕ is a positive coefficient that relates how much more appealing the consumer will find the product of interest in comparison to the competing product. It is defined as the ratio of the consumer preference functions β = H 2 / H 1 . In turn, the consumer preference functions are related to product attribute scores (yi; in our case, taste, bitterness, sweetness, etc) as follows: (4) Hi = wi yi
¦
i
Each attribute is weighted based on the rank of importance (wi) to the consumer. Thus, the scores, or values of yi, can be manipulated by altering the production process.
3. Preference Functions Consumer preferences for each attribute (yi) and the weights (wi) can be identified through market research. The consumer preferences are determined using descriptive words for each characteristic (good as, bad as, more than, etc.) by comparing these characteristics to existing products (other wines in this case). These words can then be related to physical, measurable qualities. This level of preference is normalized on a scale ranging from 0 (minimum of 0% preference) to 1 (maximum of 100% preference). Once the utility of the consumer is identified, these characteristics are evaluated by their relation to physical attributes that can be manipulated. The wine attributes used here are: clarity, color, bouquet, acidity, sweetness, bitterness, body/texture, and finish/aftertaste. We now illustrate how this can be done for acidity and bouquet and leave all the rest of the attributes out for space reasons. Acidity can be broken down into different levels based on consumer descriptions. If the acidity is too high, it begins to taste tart or vinegary, whereas if it is too low, the wine can taste flabby and insipid. This presents a need for a balance in acidity, where consumer preference is at an optimum (100% preference). For example, consumers assign 0% preference to wine with tart/vinegary and flabby/insipid attributes, as these acidity levels are undesired. Thus a parabolic curve, with the apex associated with a “balanced” wine, is used to describe consumer preference relating to acidity levels (Figure 1-a). The correlation of tart/vinegary, balanced and flabby/insipid with pH is direct, so the connection is easily found. Typical table wines can range between a pH of 3.0 and 4.0. We consider that there is a linear relationship between consumer-described acidity and pH level (Figure 1-b). Therefore, increasing pH is accompanied by a constant decrease in acidity (Pandell, 1999). Once this correlation is established, the consumer utility can be plotted against the pH in order to find the optimum pH which returns 100% consumer preference for acidity (Figure 1-c). Later, the connection of pH with some wine ingredients or manipulated variables in the fermentation is easy.
A Microeconomics-Based Approach to Product Design Under Uncertainty Linear Relationship for Acidity
Preference Curve for Acidity
1
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Flabby/ Insipid
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y (% Preferenc)
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(a) 1 0.9 0.8
y (%Preference)
0.7 0.6
y = -4x2 + 28x - 48
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(c) Figure 1: (a) Consumer preference curve for acidity; (b) linear relationship for acidity descriptions and pH; (c) consumer preference curve as a function of pH. Bouquet was examined in detail to identify specific compounds which contributed to the consumer-identified aromas of the bouquet of wine stored in a toasted oak barrel. Important bouquets include butterscotch/caramel, clove, vanilla, and oak/coconut. Butterscotch/caramel bouquet is due to levels of furfural and 5-methylfurfural, with typical values ranging from 100 to 270 mg/kg of wine. A clove characteristic is due to the presence of small amounts of eugenol ranging between 5 to 25 ȝg/L. Vanilla levels in wine can be attributed to the amount of vanillin present. Typical values of vanillin in toasted wine range from 25 to 55 mg/kg of wine. Oak lactones are responsible for the oak/coconut presence in the bouquet, with typical values between 105-200 ȝg/L (Gutierrez, 2003). In our case, consumer preference reaches a maximum for high levels of vanilla and butterscotch/caramel, whereas for oak/coconut, consumer preference is at a maximum for the lowest levels of oak lactones. Consumer preference for clove, on the other hand, reaches a maximum for a moderate level of eugenol (Gawel, 2007). Just as is the case for the acidity, a parabolic curve is expected to describe the consumer preference in relation to the amount of eugenol (we skip the figures that illustrate then two step procedure and show the final one only). For all the bouquet characteristics, it is assumed that there is a direct, linear relationship between the amount of each compound and the strength of each characteristic. For example, a weak vanilla bouquet would be typical for low values of vanillin. Bouquet can now be obtained by exploring all the different options available for toasting the oak barrels. Toasting can be further categorized by different intensities from light to
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heavy toasts. Medium toasts offer the most potential for flavor, as heavy toasts tend to breakdown important compounds contributing toward the bouquet (Hale et al., 1999).
Figure 2: Consumer preference curve for clove bouquet as a function of eugenol.
4. Results Because of its versatile nature and softness (Waldner et al., 2007), pinot noir is thought to have great marketing potential and is used to demonstrate the proposed methodology. With Į and ȕ functions defined and integrated into the demand model, the selling price was varied at several different production rates to determine the optimum selling price based on the largest net present value calculated. Several variables were held constant, including the competition selling price p2, interest and inflation rate, rate of return, and working capital. The superiority function ȕ was chosen such that the “optimum” bottle of wine was being produced which maximized consumer utility for all wine attributes. Figure 3 displays the resulting range of net present values at each scenario. The graph shows a maximum net present value of approximately $180 million at a production rate of 2.5 million bottles per year and a selling price of $36.
NPW (Millions $)
200 180
3.5M
160 140
1.5M
4M
Production Rates
4.5M
1M
120
750K
5M
100
Optimum Curve 500K
80 60
250K
40 100K
20 0 20
30
40
50
60
70
80
90
100
110
120
130
Bottle Price ($) Figure 3: Net Present Value as a function of selling price at different production rates.
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Uncertainty was incorporated into the model, essentially allowing variations around a mean for the following main parameters: consumer preference (H2, H1), competitor price, consumer budget, and the interest rate. The resulting risk curve obtained for this optimum scenario (2.5M, $36) is shown in Figures 4 and 5 using dark large red rhombuses; The curve indicates that the probability of losing money with this product is around 16%. To explore other alternatives that could be less risky, 81 random scenarios were chosen that lie between $24 and $40 in Figure 3 and that are not necessarily on the curve of maximums. In other words, because of uncertainty, less risky propositions can come from a combination of price and production that is not on the envelope. Production rates between 1 million and 5 million bottles per year were subjected to each price range. Expected net present values and return on investments were documented and summarized along with opportunity values to display several different profitable decisions. Table 1 and Figure 4 summarize the top 10 best scenarios sorted by decreasing expected net present value and Figure 5 includes some of the most interesting ones, including one of very small risk.
Figure 4: Risk curves for scenarios in table 1. The large font curve (2M, $40) indicates the scenario with the largest ENPW.
Figure 5: Notable curves. The 1M, $34 curve shows very small risk, while the 4M, $30 curve has a large amount of risk.
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Table 1: Scenario summary sorted by decreasing ENPV K (mil) 2.0 2.0 2.5 2.5 2.0 2.5 2.5 1.5 3.0 1.5
p1 $40 $38 $38 $36 $36 $34 $40 $40 $34 $38
NPW ($M) $164.4809 $145.4147 $180.0475 $157.9517 $125.2131 $133.6295 $196.9221 $121.0204 $160.6865 $105.9404
ROI 174.4% 154.2% 153.0% 134.2% 132.8% 113.5% 167.3% 169.8% 114.3% 148.7%
ENPW ($M) $111.4790 $105.5204 $103.5408 $101.7105 $100.3082 $98.8314 $98.4923 $98.2411 $91.9723 $90.3933
EROI 117.0% 114.8% 89.3% 86.8% 104.5% 79.6% 85.0% 140.7% 66.1% 126.7%
=0 13.2% 10.8% 18.5% 16.1% 8.2% 10.4% 23.1% 7.7% 18.8% 5.8%
VAR ($M) $199.8601 $182.1242 $238.8682 $199.2029 $137.1119 $170.6370 $230.9303 $130.4865 $207.9432 $95.7308
OV ($M) $68.0365 $52.1656 $95.3255 $74.9491 $38.1458 $49.9637 $123.5832 $33.3729 $91.0473 $26.3069
The superiority beta (ȕ) function was further manipulated to examine the effects it had on associated risk. It was found that manufacturing a wine of lower consumer utility (higher beta) can, in some cases, reduce the risk at similar aspiration levels. A decrease in risk is always accompanied by a lower opportunity value. This delicate balance between associated risk and opportunity value is an important factor for decision making in economics.
5. Conclusions Each bottle of wine can be engineered to maximize the profit of the producer by use of the demand model. Incorporating uncertainty into the demand model can change the optimal product and allows manipulating financial risk. Altering the quality of the wine, or ȕ, can in some cases, lower the associated risk with that decision.
References M. Bagajewicz. (2007) On the role of Macroeconomics, Multi-scale Planning and Finances in Product Design. AIChE Journal, to appear. G. Cooke, J. Lapsley. Home Winemaking. The Regent of the University of California, Division of Agriculture and Natural Resources: 1998. R. Gawel, 2007, The Effect of Oak Type on Wine Aroma. Wine Education. http://www.aromadictionary.com/articles/oakandwinearoma_article.html. Retrieved February 21. A. Gutierrez. Sensory Descriptive Analysis of Red Wines Undergoing Malolactic Fermentation with Oak Chips. Journal of Food Science. Vol.68, Nr.3, 2003. M. Hale, K. McCafferty, E. Larmie, J. Newton, J. Swan. (1999). The Influence of Oak Seasoning and Toasting Parameters on the Composition and Quality of Wine. American Journal of Enology and Viticulture, Vol 50 No 4, pp 495-502. J. Hirshleifer J. and D. Hirshleifer (1998). Price Theory and Applications. Prentice hall, New Jersey. A. Pandell. The Acidity of Wine. (1999). Retrieved May 4, 2006. http://www.wineperspective.com/the_acidity_of_wine.htm. J. Street, J. Woody, J. Ardila and M. Bagajewicz. (2007) Product Design: A Case Study of Slow Release Carpet Deodorizers/Disinfectants. Industrial and Engineering Chemistry Research. To appear. H. Varian (1992) Microeconomic Analysis. W.W. Norton & Company. M. Waldner, J. Marais. (2006). Impact Aroma Components in South African Wines: A preliminary study. http://wynboer.co.za/recentarticles/1202impact.php3. Winetech. Retrieved February 20, 2007.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Model Predictive Control Based Planning in the Fruit Industry Aníbal Blanco,a Guillermo Masini,b Noemi Petracci,a Alberto Bandonia a
PLAPIQUI (UNS-CONICET), Camino La Carrindanga Km 7, Bahía Blanca (8000), Argentina b Mechanical Engineering Department, Engineering Faculty, Universidad Nacional del Comahue, Buenos Aires 14000, Neuquén (8300), Argentina
Abstract Typical Fruit Industry Supply Chains are highly interconnected networks conformed by farms, packaging plants, cold storage facilities and concentrated juice plants along with clients and third party raw material and services suppliers. The operational planning of such a chain should seek to respond to the before-the-season established product delivery commitments rather than to react in the face of “on-line” customer demand as in classic chains. In this contribution the operational planning of a typical fruit industry supply chain is addressed by means of a Model Predictive Control based scheme which is a model based control strategy that shows attractive features for multivariable, highly interacting, uncertain systems. This methodology naturally allows addressing the meaningful uncertainty in the system parameters and the possibility of supply chain disruption episodes. Keywords: Fruit Industry Supply Chain, Operational Planning, Model Predictive Control
1. Introduction Fruit Industry Supply Chains (FISC) are interconnected networks conformed by production nodes (farms), processing plants (fruit packaging and concentrated juice plants), and storage facilities, along with clients and third party raw material and services suppliers. Although Supply Chain optimization is a mature field, very few contributions on FISC modeling with management purposes have appeared so far in the open literature. In Masini et al. (2007) [1] a tactical multiperiod LP planning model for FISC management was proposed. For given processing and storage capacities and estimations of own fruit production (quantity and quality), the model returns the adequate allocation of packed fruit and concentrated juice along with the required third party raw material, storage and transportation to maximize profit in the following season. In Ortmann (2005) [2] models to optimize the fruit business with emphasis in foreign markets were proposed. The resulting single period LP models were designed to maximize the fruit flow and to minimize the transportation costs while identifying bottlenecks within the network, rather than to provide a planning tool for the system’s managers. The above-described contributions address the “tactical/strategic” levels of the decisionmaking process in centralized FISCs. However, such models are not appropriate as operational decision support tools, which need be able to capture the real dynamic behavior of the system to effectively aid in the operational instance of the FISC. FISCs possess particular operational features as compared with typical chains, that makes
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necessary to devise tailored tools for their management. For example, opposite to typical supply chains, which are commonly pull systems (demand driven), FISCs are push systems (seasonal raw material availability driven). Therefore, the major source of uncertainty is the amount and quality of the fruit entering the system each period, rather than the final product demand, since most products are pre-allocated before the season. Therefore, the operational planning of the FISC should seek to satisfy the already established product delivery commitments rather than to respond to “on-line” customer demand. A sound approach for operational optimization of supply chains is to conceptualize them as dynamic systems and to apply “classic” knowledge of control theory to operate them (Perea-Lopez et al., 2001 [3]). Among many approaches, Model Predictive Control (MPC) frameworks have been proposed for supply chain operational management (Bose and Pekny, 2000 [4], Perea Lopez et al., 2003 [5], Mestan et al., 2006 [6]). In the present contribution a MPC scheme is proposed for the operational management of a FISC, which naturally permits to deal with input uncertainty, as well as unexpected events, which can disrupt the system operations. This article is structured as follows. In section 2 a description of a typical FISC along with the required features of the corresponding operational planning model is provided. In section 3 the basics of the proposed MPC scheme are outlined. In section 4 experimental results for typical operative scenarios are discussed. A Conclusions and Future Work Section closes the article.
2. FISC System 2.1. FISC description A typical FISC (Fig. 1) is conformed by Own Farms (OF), Third Party Fruit Suppliers (TPS), Storage Facilities, Packaging Plants (PP), Concentrated Juice Plants (CJP) and clients, among other minor processing nodes. A very detailed description of the FISC infrastructure and business can be found in [1]. X14 RPFC
X1
OF
NPFS
X5
PP
X8
PFS
X10
PPFS
X12
OPFC
X15 X3
X7 X2
TPS
FRS
X6
CJP
X9
CJS
X4
X11
PCJS
X13
OCJC
X16
Fig. 1: FISC scheme
In farms, fruit of different varieties are grown and harvested according to particular harvests periods. Apples and pears are considered in this work. Each day of the harvesting period, OFs produce a certain amount of fruit of each variety. From the company’s point of view, the production of its farms can be processed in its own PPs (X1) and CJPs (X2). The production and quality distribution per variety in each farm
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can be described by average and standard deviation values based of historic industry data. A production cost per variety can be associated to each farm, which comprise growing and labor expenses. In PPs (Blanco et al., 2005 [7]) fresh fruit is received and stored (NPFS) previous washing, classification and packing. Each PP can also receive fresh fruit from TPS (X3). PPs produce waste fruit (damaged or too imperfect non-tradable fruit) devoted to juice production CJPs (X7), and packed fruit (X8), which is cold stored (PFS) previous delivery. PPs possess a maximum processing capacity and a related operating cost, which considers labor, energy and maintenance expenses. In CJPs, juice of the different types of fruit is produced. CJPs possess Fruit Reception Sites (FRS) where waste fruit is stored before processing. FRSs receive waste fruit from OFs (X2), TPSs (X4) and PPs (X7) The produced juice is stored in adequate storage facilities in the same plant (CJS) until delivery. CJPs possess a maximum processing capacity and a certain operating cost. For any FISC there exist two major markets for packed fruit: regional (RPFC) and overseas (OPFC). Concentrated juice only possesses the overseas market (OCJC). Two types of “demands” are considered. A “fixed” demand is conformed by the amounts of packed fruit and juice agreed with the different clients before the fruit season. For such compromises there is a specific time delivery schedule. An “eventual” demand represents the possibility of allocating the excess of goods at a lower price in any period (X15 and X16). Products are delivered by trucks to the regional market and by ship to the overseas market. Products to the overseas market can be stored in port storage facilities (PPFS and PCJS). Each product has a particular selling price in each market. The selling of the different products constitutes the main income of the system. Storage Facilities (NPFS, PFS, FRS, PPFS and PCJS) posses a maximum storage capacity and an associated cost related to the energy required to refrigerate the fruit. There exist significant transportation within the system. Fruit is transported by trucks between the different nodes of the chain. Transportation costs depend on the distances between the facilities and the type of transportation: refrigerated or not. 2.1. FISC model The complete mass balance model for the described network can be found in [1]. Since the model in [1] has “tactical” purposes, an LP approach with a weekly time discretization was adopted in that study. For the “operational” purposes of the present model, much more detail is required for meaningful decision-making. A daily discretization of the timeline is considered in order to take account of short-term uncertainty and potential disruption episodes. A major improvement regarding the model in [1] is the consideration of the “multi-product nature” of PPs and CJPs, meaning that either apples or pears can be processed in a particular period or that the plant is completely shutdown. The flows within the system are discretized since the transportation of goods between the nodes is done by trucks, which can perform a finite integer number of travels per day. Binary variables are introduced to model the integer decisions, leading to a MILP formulation. The overall purpose of an operational planning model is to maximize the net profit of the system in the face of uncertainty in fruit production, third party fruit availability and costs and potential chain disruption events such as unexpected out-of-service of processing plants and storage chambers, reduction in transportation capacity, etc. The total profit is defined as the total income per product sales minus the sum of fruit
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production and purchase costs, storage cost, transportation and operation costs and “client dissatisfaction” costs. This last term is a penalization for delivering less amount of product than agreed in the “fixed demand” schedule.
3. Model Predictive Strategy In order to address the above-described operating scenario, an MPC based scheme is adopted. MPC is a model based control strategy that shows attractive features for multivariable, highly interacting, nonlinear, uncertain systems. It was originally devised for chemical process control and later extended to many other areas due to intrinsic advantages regarding more classic control strategies. The MPC control implementation philosophy can be summarized as follows: for a given state and input variables (disturbances) in the present time, compute the profile of the manipulated variables along the considered time horizon in order to optimize the specified objective function while satisfying the system constraints. In order to do so, some estimation of the future values for the disturbances should be assumed. Since there exist a large degree of uncertainty in such estimations, it is not sound to implement the whole control profile. Rather, only the first element is actually implemented, and the whole control action is reevaluated in the next period with updated data. Such a “rolling horizon” control strategy permits to “walk through the timeline” [4] to predict how the system should evolve with the current and estimated future inputs and manipulations in order to achieve the desired objective. In order to implement a MPC strategy to optimize the operations of the FISC, the system has to be conceptualized as a dynamic entity in terms of states, input and outputs [5]. Some inputs will constitute “disturbances” to the model and some others “manipulated variables” for control purposes. A subset of the output variables will be “controlled outputs” whose values will be desired to follow some predefined trajectory or assume particular values in certain periods of the control horizon. For the FISC system, the state variables are the inventories of the different goods in the storage facilities: fresh fruit (NPFS), packed fruit (PFS, PPFS) and concentrated juice (CJS, PCJS). The manipulated variables are the flows of all the streams of the system (Fig. 1). The FISC is considered to be a “centralized” system [6]. For the MPC implementation, the overall profit of the business is maximized in each time period for a certain planning horizon, subject to the mass balance model of system.
4. Results and Discussion To demonstrate the performance of the proposed approach a FISC that comprehends one item of each instance in Fig. 1 is considered. Model data (plant and storage capacities, costs, distances, production averages and deviations, harvesting periods, etc.) can be found in [1]. Although several varieties of pears and apples exist, for the sake of simplicity, in the present model all varieties of each fruit are lumped into “apples” and “pears”. As well, although many different types of packed fruit are produced for the different markets, only “regional” and “overseas” packed fruit is considered in this model. In the MPC strategy, the described model is run in each day of the timeline for the whole planning horizon. Data is updated at every period since most of the parameters of the process are randomly generated from an average and a standard deviation value. A 100 days planning horizon was used. Results are reported for the first 25 runs of the predictive scheme. Within the planning horizon, five different scheduled delivery dates for the fixed demand were imposed, each with different agreed amounts of goods.
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Eventual sales (X15, X16) were allowed in any period of the horizon. A couple of scenarios were studied to illustrate a particular aspect of the system business. Scenario 1 In the first case it was considered that a rather large amount of third party fruit (X3 and X4) is available along the whole planning horizon. In order to maximize benefits, the company purchase fruit from TPS to produce packed fruit and concentrated juice (Fig 2a). Dissatisfied amounts of products (packed fruit and juice) for the fixed demand schedule are produced only in certain products in the scheduled delivery dates (Fig. 2b). Notice that within the first 25 periods reported there are only two scheduled delivery dates in days 15 and 20. In this scenario, large deliveries to the “eventual” market can be observed of both varieties of packed fruit (X15) in several days of the considered period (Fig 2c). Scenario 2 In the second scenario it was considered that TPS fruit availability is dramatically reduced (75%) from periods 30 to 70 of the planning horizon. It can be seen that the profiles of third party raw material purchase (Fig. 3a) and the dissatisfied fixed demand (Fig. 3b) present no meaningful discrepancies regarding the previous case for the first 25 periods. However a significant reduction in packed fruit eventual sales is observed, both in number and amount (Fig. 3c). Notoriously pear is not delivered at all to the eventual market. This is in fact an expected result since the model forsees the lack of fruit in the future and keep the available not selling it in the eventual maket to respond to scheduled deliveries far in the timeline which represent a better income.
5. Conclusions and Future Work In the present contribution a MPC scheme which implements a detailed MILP model was proposed to address the operational planning of a FISC. The approach was devised as a computer aided decision tool for the system manager to account for short-term uncertainty and disruption episodes of the system while including medium/large term forecasts of meaningful parametes such as raw material production, resources availability and costs. The analyzed case study suggests that very different decisions should be adopted regarding the particular foreseable scenario, which is a consequence of the high interconnection between the nodes and the restrictive constraints on the resources (raw material, storage and processing capacity, transportantion, etc.). For the studied instance (only one facility per node in Fig. 1) very large planning periods can be considered since the model is not very computationally expensive. For the case of the 100 days planning period adopted, only a few minutes of CPU time were required. Experiments indicate that even a “whole season” planning period model (365 days) can be solved in reasonable time. However, larger instances of the FISC (several OFs, PPs, CJPs, final products, etc.) will become rapidly intractable for such planning horizons. For such cases a different strategy should be adopted to produce detailed decision making advice for the present and immediate time periods while foreseeing delivery commitments far in the time line. Future work will address such scenario.
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Fig. 3: Scenario 2. a) third party purchase, b) dissatisfied fixed demand, c) packed fruit eventual sales.
References [1] G.L. Masini, A.M. Blanco, N.C Petracci and J.A. Bandoni, WILEY-VCH book "Supply Chain Optimization" Part II (Vol. 4), L. Papageorgiou and M. Georgiadis, editors (2007) [2] Ortmann F. G., Modeling the South African Fresh Fruit Export Supply Chain, MSc Thesis (2005). [3] E. Perea-Lopez, I. E. Grossmann, B. E. Ystie and T. Tahmassebi, Ind. Eng. Chem. Res. 40 (15) 3369 (2001) [4] S. Bose and J. F. Pekny, Comp. Chem. Eng. 24, 329 (2000) [5] E. Perea-Lopez, B. E. Ystie and I. E. Grossmann, Comp. Chem. Eng. 27, 1201 (2003) [6] E. Mestan, M. Turkay and Y. Arkun, Ind. Eng. Chem. Res. 45 (19) 6439 (2006) [7] A.M. Blanco,G.L. Masini, N.C Petracci and J.A. Bandoni, Journal Food Eng. 70, 299 (2005)
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Optimize process condensate reusing system for ammonia plant by the synthesis of MEN Li Chen,a,b Jian Du,a Zhihui Gao,a Pingjing Yao,a Warren D. Seider, c a
Institute of Chemical Process System Engineering, Dalian University of Technology, Dalian 116012, China b School of Environmental & Chemical Engineering, Dalian University, Dalian 116622, China c Chemical and Biomolecular Engineering Department, University of Pennsylvania, Philadelphia, PA 19104, USA
Abstract The process condensate from an ammonia plant contains many contaminants that can pollute the environment if emitted directly. Several techniques can be used to remove these pollutants, applied one at a time or together. To achieve a process design at minimum cost, a technique for mass exchange network (MEN) synthesis is used. Complications not encountered when synthesizing ordinary MEN are resolved using a simultaneous synthesis method involving the superstructure presented herein. The superstructure accounts for all feasible streams matched when targeting the minimum total annualized cost (TAC) of a network, with the minimum composition difference, İ, adjusted to trade off the operating cost and capital cost. In addition, the effects of the temperature and pressure in each mass exchanger on the phase equilibrium equations are considered. The mathematical formulation is a non-convex, nonlinear program solved using the adaptive, simulated-annealing, genetic algorithm (ASAGA) developed by our research group. Keywords: process condensate; synthesis of mass exchange network; multicomponents; total annualized cost.
1. Introduction In the production process of an ammonia plant, a lot of process condensate is produced everyday. Usually, this kind of process condensate contains many contaminants, such as ammonia, carbon dioxide, methanol etc, which can pollute the environment if emitted directly. However, several techniques have been developed to remove the pollutants, such as stripping with natural gas and medium pressure steam, which can be applied one at a time or together, so that the recovery condensate can be reused as boiler feed water or as water makeup for other process operating units. It is very important for the plant to design a process which can solve the problem with minimum cost. This is the work that can be solved by the synthesis of MEN. The concept of MEN was firstly introduced by El-Halwagi and Manousiouthakis[1-2]. The task of MEN is to transfer certain species (often pollutants) from a set of rich streams (contain contaminants to be removed) to a set of lean streams (often Mass Separating Agents, MSAs). By specifying a minimum composition difference, İ, the mass transfer pinch can be located, which is the thermodynamic bottleneck for mass transfer between process streams. The synthesis of MEN is one of the most important branches of process system engineering, which holds the dual benefits of improving the efficiency of resource and reducing the environmental pollution simultaneously. In the area of chemical industry, MENs are used to reduce the waste generated by a plant to an environmental acceptable level at the cheapest cost. It achieves the mass transfer by the composition gradient
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between rich and lean streams of each contaminant, so the study on the synthesis of MEN could not only reduces contaminant emission of a plant, but also improves resource utilization efficiency. Up to now many researches on improving the synthesis procedures of MEN have been done successfully [3-5]. However, we can still observe some weakness and limitations. First, most methods proposed specify a fixed minimum allowable composition difference instead of optimizing it; second, most research work are limited to the circumstance of transferring lower mass load, in which the input/output flow rates can be approximately regarded as constants; third, the researches on multi-component system are few and without regarding to the interactions of components. As a result, there are some challenges when deal process condensate reusing system with the synthesis methods for ordinary MEN directly. First, this is a non–ideal multicomponent system, in which the interactions of the components could not be omitted; second, the mass transfer loads between the rich and lean streams are relatively larger, which means that the inlet/outlet flow rates cannot be considered as constants as most ordinary MEN do; third, the effects of operating temperature and pressure in each unit on phase equilibrium equations cannot be omitted either. In order to synthesize an optimal process with minimum cost for process condensate reusing system of the ammonia plant, a simultaneous synthesis method based on the superstructure is presented in this paper. The superstructure can consider all the feasible stream matches, which can be used to handle both single-contaminant system and multi-contaminant system. And a nonconvex nonlinear programming (NLP) model of MEN can be established by targeting the minimum total annualized cost of network with the minimum composition difference İ as variables to trade off the operating cost and capital cost. And the effects of operating temperature and pressure in each equipment on the phase equilibrium equations are also considered, which can be obtained by linear fitting of thermodynamic data from simulation by Aspen Plus software. The equations are correlated to the operating temperature and pressure of the mass exchanger, the composition of each component, and composition differences between rich and lean streams.
2. Problem Description The process condensate data is derived from the process of a Synthetic Ammonia [7], in which 100,000 kg·hr-1 of process condensate is produced. All the related stream data are shown in Table 1 and Table 2. The condensate from the process consists of four contaminants mainly, which are to be removed away before reused by the boiler. There are several possible alternative processes to be selected, one is using natural gas to remove the contaminants, other is using medium pressure steam, and still others are employing both processes (in series or in parallel). It is desirable to design a process with minimum cost to realize zero effluents. This is a synthesis problem of multi-component MEN with a rich stream, one or two lean streams. This problem can be stated generally as follows: given are a set of rich process streams Ri (i=1, 2,…,NR), its flow rates, Gi, its supply inlet compositions yiin, p and its target outlet compositions y iout , p . Given also are a set of lean streams Sj (j=1, 2,…,NS), its maximal
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Table 1. Stream data for the case in Mass fraction yi , p / y iout ,p
Supply inlet composition Target outlet composition
NH3
0.995764
0.001848
0.001498
0.000574
-5
-4
-4
0.97446
4.0h10
CO2
Gin(kg·hr-1)
H2O
1.5h10
CH4O
3.4h10
CH4 0.0000
100000
0.025
Table 2. The price for streams and units water
Ammonia
Methanol
Item
Natural gas S1
Medium
Saturate tower
Stripping tower
pressure steam S2
with natural gas
with medium pressure steam
(̞·hr·kg-1·a-1) Price
49
27331
20148
438
(̞·stage-1·a-1) 1051
12000
14000
available flow rates, L j , its inlet and maximal outlet compositions, x inj , p and x out j, p . Different from most literatures, the changes of flow rates of the rich stream and lean stream passing through a unit are taken into consideration. So the synthesis task of MEN in this paper is to determine the inlet and outlet mass flow rates of each lean and in out rich stream per stage, Giin , Giout , L j and L j , their compositions and the optimal network targeting the minimal total annualized cost. In each mass exchanger, the phase equilibrium relation of each component is influenced by interactions of components in the system, and operating temperature and pressure. For a rich stream with composition of y i , p , the maximum theoretically attainable ∗ ∗ composition of the lean stream is x j , p , where x j , p = x j , p + İ i , j , p . The value of max
x ∗j , p depends on the phase equilibrium relations and the value of the composition
difference İi,j,p . Here, assume that in the range of compositions involved, the thermodynamically phase equilibrium relations between rich and lean streams are linear, and concern with the operating temperature T and pressure P, then we can obtain phase equilibrium equations as Eq. (1).
yi , p = a1, j , pTi. j + a2, j , p Pi , j + mi , j , p ( x j , p + İ i , j , p ) + bi , j , p (1) Where the coefficient of a1,j, , a2,j,p , mi,j,p , and bi,j,p are assumed to be constants and can be obtained by linearizing the phase equilibrium data of component p at different temperatures and pressures in a range of compositions.
3. Formulation of multi-stage superstructure and mathematical model 3.1. The multi-stage superstructure for multi-component MEN In order to consider all feasible matches in the network, a superstructure with stage-wise strategy is applied similar to the multi-stage superstructure proposed by Yee and Grossmann[6], where within each stage mass exchange can occur between each rich and lean stream. The number of stage required in the process relies on the number of rich
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in yin, p yk , p
out yout , k , p y , p
in yin, p y , k , p
out yout, k , p x , p
out xout , p x , k , p
xin, k , p xin, p
R1 R2
xin, k , p
xout, k , p
xout ,p
xin, p
S1 S2
Figure 1. Structure of stage-wise superstructure in stage k and lean streams, i.e., can be determined by Nk=max {NR, NS}. The proposed approach does not rely on the pinch and enables a simultaneous consideration for all the design factors. Fig. 1 shows the matching structure of stage-wise superstructure in each stage involving two rich and two lean streams. 3.2. Formation of mathematical model Based on above superstructure, the objective function of the optimal model in this paper is TAC of the MEN. The TAC involves the annualized operating cost and capital cost, as well as the recycle cost. In the mathematical model, the inlet and outlet flow rates and the compositions of rich and lean streams, together with the composition differences are taken as variables, which can be associated and calculated by the phase equilibrium equations and the corresponding constraints. Supposing the operating cost mainly lies on the flow rate of each lean stream and its unit price, and the capital cost depends mainly on the cost of tray number Ni,j,k and/or packing height Hi,j,k of each exchanger. The recycle cost relies on the quantity and unit price of the recycling components. Then, the objective function can be expressed as Eq. (2). min f TAC =
¦ c L + ¦¦¦ c j
j
j
i
'
''
j
' i , j ,k
k
× N i , j ,k +
¦¦¦ c i
j
k
'' i , j ,k
× H i , j ,k −
¦c p
''' pgp
(2)
' ''
Where, c j , ci , j , k , ci , j , k , c p denote the unit price of each stream or mass exchanger. The constraints of the optimal model involve: (1) Overall mass balances over the whole network; (2) Overall mass balance of component p over the whole network; (3) Overall mass balance in each mass exchange unit; (4) Mass balance of component p in each mass exchange unit; (5) Phase equilibrium constraints of component p in each mass exchange unit; (6) Outlet composition constraints of the component p for rich streams; (7) Maximal composition constraints of component p for lean streams; (8) Other thermodynamically, environmental feasibility constraints etc. At last, a NLP model is formed. Because there are a lot of variables and constraints in the model, it is very difficult to solve by a commercial software, so the optimal model is solved with ASAGA developed by our group.
4. Solution to case study Since the studying system is a little complicated, it is difficult for the components to get all the thermodynamic data. We obtain the data from Aspen Plus software. Then coefficients for the phase equilibrium relations of each component are correlated to the
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flow rate/ kg·hr-1 R
100000 31713
1
31375 68287
4798
93734 2
93734
95068
3
62359 4503
4503 10813
4905
4905
6316
S1 S2
Figure 2. The optimal structure of MEN for the case variables of temperature, pressure, the composition of each component in the rich and lean streams [8]. In order to solve the problem, firstly an initial two-stage superstructure network is constructed, and a NLP model is built based on the objective function and constraints that mentioned in the previous part of this paper, then the inlet and outlet flow rates of lean and rich streams in each unit, their compositions, and the set of composition differences are taken as variables, which can be optimized simultaneously by the ASAGA. The detailed optimal results for each stream are shown in the Fig. 2, Table 3 and Table 4. It is showed that this process condensate reusing system need three mass exchange units, one for natural gas stripping, two for medium pressure stripping. The process condensate first is divided into two streams, dealing with the natural gas and medium pressure steam respectively, and then the effluents are united and stripped with medium pressure steam again. Table 3. Results for the case
L1in
Item
L1out
L2in
L2out
N1
N2
N3
Number of plate
(kg·hr-1)
fc
fo
fTAC
(104̞·a-1)
Optimization with single stage[8]
9184
15342
6505
5200
15
8
-
127
1086
356
Optimization in this paper
4503
4798
6316
10813
28
12
6
256
861
236
Table 4. The outlet compositions of the reusing condensate out Mass fraction y i , p
H2O
NH3
Outlet composition by optimization
0.98270
3.2h10-5
0.1h10- 9
CO2
1.2h10- 4
CH4O
0.017
CH4
Target outlet composition
0.97446
4.0h10-5
1.5h10- 4
3.4h10- 4
0.025
The data on the Fig. 2 are flow rates of rich and lean streams passing through each unit. Although optimal structure of the network is a unit more than that of single stage, the TAC is 33.7% lower because the operating cost have been cut down considerably than that of single stage superstructure. The optimal operating temperatures and pressures of ° natural gas stripping tower and medium pressure steam stripping tower are 190.58 C, ° 37.18 MPa and 248.88 C , 36.07 MPa respectively. The data of table 4 show that all the outlet compositions of each component in the recovery condensate have satisfied the technical requirements, which implies that the proposed method can solve this kind of practical industry problem successfully.
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5. Conclusion The method presented in this paper can provide a better way to design the process condensate reusing system and reduce the total annualized cost of the network obviously while satisfying the requirements of process and environment. This is because all of the process variables, such as the flow rates, the set of composition differences, the operating temperatures and pressures and the network of mass exchange, can be optimized simultaneously. The results demonstrate that the suggested method is feasible, practicable, and effective for this case.
Nomenclature Symbols G flow rate of rich stream, kg·hr-1 f the annualized cost, ̞·a-1 g flow rate of recycle component, kg·hr-1 H the height of packed column, m L flow rate of lean stream, kg·hr-1 N number of stream or tray x the composition of component for each stage of lean stream, (mass fraction) y the composition of component for each stage of rich stream, (mass fraction) İ composition difference of component between rich and lean stream
Subscripts i j p k c o
rich stream number lean stream number the component number in stream stage number capital cost operating cost
References [1] M.M.El-Halwagi, V.Manousiothakis, Synthesis of mass exchanger network, AIChE Journal, No. 8 (1989) 1233. [2] M.M.El-Halwagi, V.Manousiothakis, Automatic Synthesis of Mass Exchange Networks with Single Component Targets, Chemical Engineering Science, No.9 (1990) 2813. [3] K.P. Papalexandri, E.N.Pistikopoulos, A. Floudas, Mass Exchange Networks for Waste Minimization: A Simultaneous Approach, Trans IChemE, 72 (Part A) (1994) 279. [4] N.Hallale, D. M.Fraser, Supertargeting for Mass Exchange Networks Part ĉ: Targeting and Design Techniques, Trans IChemE., 78 (Part A) (2000) 202. [5] C.L. Chen, P.S. Hung , Simultaneous synthesis of mass exchange networks for waste minimization, Computers and Chemical Engineering, No. 29 (2005) 1561. [6] T. F.Yee, I. E.Grossmann, Simultaneous optimization models for heat integration.Ċ.Heat exchanger network synthesis , Computers and Chemical Engineering, No. 14 (1990) 1165. [7] Y.Zhao, The reuse of the process condensed water in the ammonium synthesis, the bachelor dissertation of Dalian University of Technolygy, 2000. [8] L.Chen, Z.H.Gao, J.Du, P.J.Yao, PSE ASIA 2007, The 4th International Symposium on Design, Operation and Control of Chemical Processes, August 15-18, 2007, Xi’ an, China, pp.340.
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Entrainer-Based Reactive Distillation Versus Conventional Reactive Distillation For The Synthesis Of Fatty Acid Esters M.C. de Jonga, A.C.Dimianb, A.B. de Haana a
Process Systems Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands b HIMS, Faculty of Science, University of Amsterdam, Nieuwe Achtergracht 166, 1018 VW Amsterdam, The Netherlands
Abstract In this paper different reactive distillation configurations for the synthesis of isopropyl myristate were compared with the use of process models made in Aspen Plus©. It can be concluded that the configurations in which an entrainer is added are more capable to reach the required conversion of 99.0%: the required reactive section and energy amount is significantly smaller than in the configurations without entrainer. The differences in design and operating parameters of the different entrainer-based reactive distillation configurations are small. Only at higher pressures a two column set-up is favourable due to the reduced amount of entrainer. Keywords: Reactive Distillation, Entrainer, Modelling, Fatty Acids
1. Introduction Fatty acid esters are natural-based chemicals used among other things in cosmetics, plastics and surfactants. Nowadays the fatty esters are produced in batch reactors with use of strong acids like sulphuric acid. Their production processes involve costly separations, large energy consumption and polluting by-products. Because of equilibrium limitations high conversions can be only obtained by using a large excess of alcohol. For a more competitive process it is preferable to produce fatty esters in a continuous way, at higher yields, in multi-product equipment, using a heterogeneous catalyst. Reactive distillation is considered a promising technique because the integration of reaction and separation in one unit means significant savings in equipment and operation costs. Information on the esterification of long chain carboxylic acids such as fatty acids by reactive distillation is scarce. A few processes with various fatty esters and alcohols are described [1-3]. All refer to a homogeneous catalyst which causes pollution of the product. Steinigeweg and Gmehling [4] describe a process using a heterogeneous catalyst. They investigated the esterification of decanoic acid with methanol. The problem of all above processes is that the ester is not obtained in pure form such that further purification is necessary. Besides that, the alcohol, except for methanol, forms an azeotrope with water what is a disadvantage for realising higher yields. Omota et al. [5, 6] studied the feasibility of a single column process using a heterogeneous catalyst for the esterification of lauric acid with 2-ethyl-hexanol and methanol. They found that it is possible to obtain pure fatty acid ester in a single column process. Both esters can be produced in the same set-up, but under different operating conditions. However, problems can occur because of the product purity is highly
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sensitive to the reflux ratio. A promising way to improve this is by Entrainer-based Reactive Distillation (ERD) based on solid catalysts [7]. In ERD in situ separation is used to improve the yield of reaction whereas an entrainer feed is added to make the separation feasible by selectively increasing the relative volatility of one of the products. ERD promises to be advantageous for the synthesis of fatty acid esters. The entrainer increases the relative volatility of water (by-product) compared to the alcohol (reactant), such that during the reaction the water can be continuously removed by distillation. In this way the chemical equilibrium is shifted such that higher conversions can be obtained. In Figure 1 the flowsheet of the desired process is given, in which RS stands for Reactive Make – up Section and DS for Entrainer D Distillation Section. entrainer Water The conceptual feasibility DS of ERD for the synthesis of Fatty acid fatty acid esters is already R RS shown by Dimian et al. [7]. S Alcohol This work will concentrate on the gains that can be obtained using ERD with Fatty acid ester regarding to conventional RD. The objective of this Figure 1: Conceptual flowsheet for Entrainer-based Reactive work was to compare Distillation synthesis of fatty acid esters several possible process configurations from conventional RD to ERD for the synthesis of fatty acid esters: Conventional RD (one column), conventional RD (two column), conventional plus azeotropic RD (two column), ERD (one column) and ERD (two column). The comparison was done by process models made in Aspen Plus© for the esterification of myristic acid with isopropanol using a homogeneous catalyst. The models were constructed containing the necessary conditions (like capacity, conversion and purity) to be able to produce fatty acid esters. For these conditions, the processes are evaluated in ability to meet these requirements by comparing column size and energy consumption.
2. Modelling work 2.1. Process conditions and requirements All the configurations are designed such that a 99.0% conversion of myristic acid and a 99.9% product purity is obtained. The input parameters of the feed streams are based on a production of 1000 kg/hr (3697 mol/hr) isopropyl myristate and 99% conversion of the myristic acid. The ratio of myristic acid: ipa was fixed at 1:1.15. The operating pressures are 1, 5 and 10 bar and in simulations where an entrainer is used, this entrainer is cyclohexane. The kinetics of the reaction were experimentally determined. Because the reaction is very slow at atmospheric pressure a large hold-up is required to reach 99% conversion. For comparison the number of stages is set to 500 and the holdup per stage is varied. Results are obtain by Aspen Plus© simulations using the NRTL property model with the NRTL parameters taken from Aspen Plus©.
Entrainer-Based Reactive Distillation versus Conventional Reactive Distillation for the Synthesis of Fatty Acid Esters
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2.2. Process descriptions 2.2.1. Conventional Reactive Distillation (RD1)
B1
In conventional reactive distillation only one column is present in which the reaction takes places. The myristic acid is fed at the top of the column and the isopropanol at the bottom. Between those feed points the reaction takes place. The isopropyl myristate is collected at the bottom and the unreacted myristic acid and isopropanol will come out at the top together with the formed water. The reflux has a high water content because no water removal takes places. Therefore a conversion of 99% is not possible.
TOP
ACID
ALCOHOL
BOTTOM
Figure 2 Process scheme conventional reactive distillation
2.2.2. Conventional Reactive Distillation with water/alcohol separation (RD2)
B3 B2 3 TOP 2
B1 ACID 1
ALCOHOL
BOTTOM
Figure 3: Process scheme conventional reactive distillation with water/ alcohol separation
In this configuration the conventional reactive distillation column is taken but the top vapour is condensed and fed into a second column. In this column pure water is drawn off and an azeotropic mixture of water and isopropanol is recycled back to the reactive distillation column.
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2.2.3. Conventional Reactive Distillation combined with Azeotropic Distillation (RD3) In the conventional reactive distillation RECYCLE combined with azeotropic distillation an azeotropic distillation takes place in B3 2 the second column. An entrainer is fed in order to obtain pure isopropanol at ENTRAINE WATER B2 the bottom and a water/entrainer mixture at the top. The entrainer is chosen such that it forms an inmiscibility region with water and the TOP mixture can be separated by decantation. The entrainer phase can be B1 ACID recycled back in to the column and the isopropanol stream is recycled back to the reactive distillation column. ALCOHOL
BOTTOM 1
Figure 4 Process scheme conventional reactive distillation combined with azeotropic distillation
2.2.4. Entrainer-based Reactive Distillation (ERD1) RECYCLE
TOP
B1
B2
WATER
ENTRAINE
ACID
ALCOHOL
BOTTOM
The entrainer-based reactive distillation column consists of a reactive section with a distillation section placed on top, in where the entrainer is responsible for removing the water out of the reactive section. The top vapour, which consists of entrainer, water and isopropanol, is condensed and two phases are obtained through decantation: an aqueous phase and an entrainer rich phase which is refluxed back into the column.
Figure 5 Process scheme entrainer-based reactive distillation
2.2.5. Entrainer-based Reactive Distillation with entrainer/alcohol separation (ERD2) In this configuration the entrainer-based reactive distillation configuration is taken and the entrainer rich stream is separated in a second column into a pure entrainer stream and an alcohol stream.
Entrainer-Based Reactive Distillation versus Conventional Reactive Distillation for the Synthesis of Fatty Acid Esters
203
ENTR
B3
RECYCLE
ALC B2
WATER
B1 ENTRAINE
ACID
ALCOHOL
BOTTOM
Figure 6: Entrainer-based reactive distillation with entrainer/alcohol separation
2.3. Results and discussion In Table 1 the achieved conversion and product purity and the required design and operating parameters are summarized. In conventional reactive distillation the desired conversion can not be reached. However, because the unreacted acid will not end up in the bottom stream, it is possible to have a product purity of 99.9% which is not the case in the other configurations. When the conventional reactive distillation is combined with a water/alcohol separation, there are two extrema; a small reactive column and high amount of energy or a large reactive column and a low amount of energy. While the conventional reactive distillation was combined with azeotropic distillation it appeared that a pure alcohol recycle could only be obtained if the top stream of the reactive column has a low water content which means a low conversion. So the azeotropic distillation imposes a constraint on the conversion in the reactive column. However, a conversion of 99.0% is possible in this configuration but then it is not the matter of azeotropic distillation anymore. The entrainer ends up in the bottom stream of the second column and enters therefore the reactive column. Actually this is also a form of entrainer-based reactive distillation. Looking at this configuration, the entrainerbased reactive distillation and the entrainer-based reactive distillation combined with an entrainer/alcohol separation it can be seen that the differences in design and operating parameters are very small. It should be noted that the required hold-up per stage and the number of stages named in Table 1 are enormously large. Under these operating circumstances (kinetics, pressure) it is not possible to obtain 99.0% conversion in reasonable sized equipment. Table 1: Results overview 1 bar
Conversion [%] Product Purity [%] Hold- up reactive stage[l]1) Reboiler duty [kW] Condensor/decanter duty [kW] Nr of separation stages [-]
RD1
RD2a
RD2b
RD3
ERD1
ERD2
64 99.9 81 190 160 -
99 99.4 91 204 931 42)
99 99.0 178 140 58 22)
99 99.0 97 201 124 22)
99 99.0 96 203 118 13)
99 99.0 87 216 181 12)+63)
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Reboiler duty [kW] Entrainer amount [mol/hr] Total energy [kW]
350
813 1948
5 203
8 8100 333
7300 321
59 8900 456
1) hold-up per stage with a total of 500 reactive stages, 2) stages in separate distillation column, 3) stages in distillation section reactive distillation column
In Table 2 the results of the entrainer-based reactive distillation in two columns and in one column at different pressures can be found. The design and operating parameters do not differ significantly. Only at higher pressure the two column set-up is more efficient regarding the requirement entrainer amount. Table 2: Results overview different pressures
Conversion [%] Product Purity [%] Nr of reactive stages[-] Hold- up reactive stage[l]1) Reboiler duty [kW] Condensor/decanter duty [kW] Nr of separation stages [-] Reboiler duty [kW] Entrainer amount [mol/hr] Total energy [kW]
RD3 1 bar 99 99.0 500 97 201 124 22) 8 8100 333
ERD1 1 bar 99 99.0 500 96 203 118 13) 7300 321
RD3 5 bar 99 99.0 500 17 256 96 82) 5 4000 357
ERD1 5 bar 99 99.0 500 17 256 101 13) 4200 357
RD3 10 bar 99 99.0 380 10 287 87 52) 3 2500 377
ERD1 10 bar 99 99.0 380 10 285 111 13) 4600 397
1) hold-up per stage, 2) stages in separate distillation column, 3) stages in distillation section reactive distillation column
3. Conclusion In this paper different reactive distillation configurations for the synthesis of isopropyl myristate were compared with the use of process models made in Aspen Plus. It can be concluded that the configurations in which an entrainer is added are more capable of reaching the required conversion. However the product purity cannot be set higher than the conversion, they should be equal. The differences in design and operating parameters of those configurations are small. Only at higher pressures a two column setup is favourable due to the reduced amount of entrainer.
References 1. 2. 3. 4. 5. 6.
7.
Bock, H., G. Wozny, and B. Gutsche, Design and control of a reaction distillation column including the recovery system. Chem. Eng. Process., 1997. 36: p. 101-109. Jeromin, L.M., N. Bremus, and E. Peukert, Kontinuierliche veresterung in Reactionskolonnen. Fette, Seifen, Anstrichmittel, 1981. 83: p. 493-504. Schleper, B., et al., Einsatz eines eingachen simulationsmodells zur versuchsplanung fur eine gegenstrom-veresterungskolonne. Chem. Ing. Tech., 1990. 62: p. 226-227. Steinigeweg, S. and J. Gmehling, Esterification of a fatty acid by reactive distillation. Ind. Eng. Chem. Res., 2003. 42: p. 3612-3619. Omota, F., A.C. Dimian, and A. Bliek, Fatty acid esterification by reactive distillation. Part 1: equilibrium-based design. Chem. Eng. Sc., 2003. 58: p. 3159-3174. Omota, F., A.C. Dimian, and A. Bliek, Fatty acid esterification by reactive distillation. Part 2: kinetics-based design for sulphated zirconia catalysts. Chem. Eng. Sc., 2003. 58: p. 3175-3185. Dimian, A.C., F. Omota, and A. Bliek, Entrainer-enhanced reactive distillation. Chem. Eng. Process., 2004. 43: p. 411-420.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Supply chain optimization with homogenous product transport constraints Tivadar Farkasa, Zoltán Valentinyib, Endre Révc, Zoltán Lelkesd a
OptaSoft Kft.; permanent job at HAS-BUTE Materials Structure and Modeling Research Group, Szent Gellért tér 4., Budapest, H1111, Hungary b Provimi Pet Food (Pet Hungaria Kft.), Puskás Tivadar u. 12., Budaörs, H2040, Hungary c Budapest University of Technology and Economics, Department of Chemical and Environmental Process Engineering, MĦegyetem rkp. 3., Budapest, H1111, Hungary d OptaSoft Kft., BölcsĘ u. 5., Budapest, H1117, Hungary
Abstract Provimi Pet Food is the pet food division of Provimi, one of the world’s largest animal feed manufacturing and commercial companies. The dynamic growth of the company in the last years resulted in the necessity to optimize the supply chain. The supply chain problem has special characteristics such as special logical constraints of homogeneous transport, complex cost function, and large size. The developed mathematical model and computational experiences are presented here. Keywords: supply chain, transportation, MILP
1. Introduction The transportation problem is to minimize the total transportation costs and utilize all the supply of a set of sourcing units with respect to satisfying all the demands of a set of destinations. This task forms the basis of much more complicated problem classes such as supply chain allocation and distribution. No standardized model of supply chain allocation problems is accepted in the literature. According to Vidal and Goetschalckx (1997), the supply chain allocation problem involves determining (1) the number, location, capacity, and type of manufacturing plants and warehouses to use, (2) the set of suppliers to select, (3) the transportation channels to use, (4) the amount of raw materials and products to produce and ship among suppliers, plants, warehouses, and customers, and (5) the amount of raw materials, intermediate products, and finished goods to hold at various locations of inventory. Special constraints of particular cases such as complex cost functions or logical constraints are not involved in the general definition of supply chain. The case study of Provimi Pet Food, the pet food division of Provimi, one of the world’s largest animal feed manufacturing and commercial companies, is presented here in order to show the complexity and specialities of this problem, and the way it is solved. The main motives of why developing a supply chain model was necessary is first described, then the specialities of the supply chain of Provimi Pet Food are detailed with their mathematical formulation. Finally, computation results of optimizing different sizes of the problem using model versions of different complexity levels are presented.
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2. Motivation Provimi is one of the leading animal feed producers and distributors in the world, dealing with pet food, vitamins, special ready made and semi-finished products. The company developed its pet food division exponentially in the recent years, is present in 17 countries considering Europe only, has bought 20 other companies between 2002 and 2006, including 12 from Europe. Its shares have been doubled since 2001. The company intends continuing the expansion both globally and in Europe. The management is faced to new challenges because of the sudden increase in the number of European affiliated companies, and particularly the producing plants. The producing capacities distributed in factories of different pre-history in the countries should be coordinated to minimize the logistic and production costs, and to provide the company and the plants in time and reliably with the related information. Considering this situation, the European management decided introducing an optimizing software system to aid the supply chain. This project including the consultation work and developing the optimizer software system has taken approximately 5 months.
3. Problem characteristics As is expected in every particular application, the problem of Provimi Pet Food has specialities which call for special formulations and solution. Two main decision levels, the level of plants and the level of customers, are considered in the Provimi Pet Food supply chain problem. Customers have certain demands for products which can be produced in the plants. The production process is modeled as being consisted of two consecutive steps. Semi-products are produced in production lines. These semi-products are subsequently mixed and packaged in packaging lines. This packaged product is the final product of the plants, and is transported to the customers. The semi-products can be transported between plants, i.e. a packaging line can package semi-products produced in another plant. The level of suppliers is omitted from the model. The level of warehouses is considered merely in the transportation costs from plants to customers. If a product has to be stored in a warehouse during the transportation from a certain plant to a certain customer then the specific transportation cost of that route is increased with the cost of storage. Therefore, three levels are considered in the supply chain model of Provimi Pet Food: (1) production lines of plants, (2) packaging lines of plants, and (3) customers (see Fig. 1). The problem has four main special characteristics: (1) Complex cost functions, (2) Minimum constraints, (3) Homogenous transport constraints, (4) Large size.
Fig. 1. Supply chain model
Fig. 2. Stepwise constant cost function
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207
3.1. Complex cost functions The target is to minimize the sum of transportation costs, production costs, and packaging costs. The transportation costs are proportional to the amount of transported semi-products and products. Production and packaging costs consist of variable cost proportional to the amount of the products, and fix costs. Fix costs are given by stepwise constant functions, as is shown in Fig. 2. Intervals over which the fix costs are defined can be specified according to the working shifts, for example. 3.2. Minimum constraints 'Either / or' minimum constraints are considered at the production lines level, at the packaging lines level, at the semi-product transport, and at the product transport. In each case, existence of a minimum constraint means that the quantity of produced /packaged / transported semi-product / product either has to reach a defined minimum level or has to be zero. In each case this minimum constraint expresses the economical consideration that it is not worth to produce, package, or transport, below a minimum quantity (e.g. one truck, in the case of transportation). 3.3. Homogenous transport constraints Homogenous transport means that any amount of a given product is transported to a customer from a single, not a priori assigned, plant even if that product can be produced in several plants. Homogenous transport is specified in order to prevent the customer from receiving a mixture of different quality products that might occur because different raw materials and processing methods are applied at the different plants. 3.4. Large problem size The supply chain problem of Provimi Pet Food involves at least eight plants each containing one to three production and packaging lines, more than 80 customers, and more than 800 products. This large size and the above mentioned special constraints result in a very difficult and complex problem, and it renders developing and applying a well-formulated mathematical model necessary, as well as special preliminary procedures before commencing the optimization process.
4. Mathematical model The supply chain problem of Provimi Pet Food is first formulated as a Generalized Disjunctive Programming (GDP) model using continuous and logical variables, then it is transformed into a Mixed Integer Linear Programming (MILP) model using binary variables instead of the logical ones. The mathematical models incorporate mass balance equations, capacity constraints, the cost functions, and the special constraints mentioned in the previous section. The mass balance equations, the capacity constraints, and the variable cost functions, are all linear and need not be explained here. How the special constraints are formulated is explained below. 4.1. Complex cost functions The fix cost cl of production or packaging line l depends on its working hours tl. The range of variable tl is subdivided to a number of shifts s. The time moment borders of these shifts are given by the upper bound BTs of shift s. The constant fix cost of the line in shift s is given by parameter BCs. In the GDP representation, logical variables zsl,s are assigned to the shifts. If the value of the independent variable is in or above shift s then zsl,s=1, else zsl,s=0:
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º zsl ,s ª zsl ,0 º ª » « » « « BTl ,s −1 < t l ≤ BTl ,s » « tl = 0 » ⊕ s ≥1 » « cl = 0 » « cl = BCl ,s ¬ ¼ ¬ ¼
∀l, s
(1)
(Character ⊕ denotes the logical operation 'exclusive or' or XOR.) This logical equation is transformed into algebraic one using the method of Lelkes et al. (2005):
t l ≤ ¦ ( ysl ,s ⋅ DTl ,s )
∀l
(2)
cl ≥ ¦ ( ysl ,s ⋅ DCl ,s )
∀l
(3)
ysl ,s ≤ ysl ,s −1
∀l , s ≥ 2
(4)
s
s
where DTl,s is the length of shift s at line l, DCl,s is the fix cost increment of shift s of line l related to the fix cost of the previous shift s−1, and ysl,s is a binary variable. 4.2. Minimum constraints How these constraints are formulated is exemplified with the minimum product transport constraint. The qtp,c,pr transported quantity of product pr from plant p to customer c either has to be equal to zero or not smaller than a minimum transport quantity QTMINp,c,pr. In the GDP formulation of this constraint, logical variable ztp,c,pr ∈ {true, false} denotes whether there is product transport on the given route:
zt p ,c , pr ª ¬zt p ,c , pr º ª º ∨« «qt » » ¬ p ,c , pr = 0¼ ¬qt p ,c , pr ≥ QTMIN p ,c , pr ¼
∀p, c, pr
(5)
This logical constraint is transformed into algebraic form using binary variables ytp,c,pr ∈ {0, 1} instead of the logical ztp,c,pr ones:
qt p ,c , pr ≥ QTMIN p ,c , pr ⋅ yt p ,c , pr
∀p, c, pr
(6)
4.3. Homogenous transport constraints The homogenous transport of product pr to customer c can be defined as a logical constraint using logical variable zhp,c,pr. If zhp,c,pr is true, i.e. if product pr is transported only from plant p to customer c, then the transported quantity qtp,c,pr is equal to the demand Dc,pr of customer c for product pr, and the transported quantity from all the other p2p plants is zero.
ª zh p ,c , pr º ª ¬zh p 2≠ p ,c , pr º « »→« » «¬qt p ,c , pr = Dc , pr »¼ «¬qt p 2≠ p ,c , pr = 0»¼
∀p, c, pr
(7)
This logical constraint is transformed into algebraic form using the Convex Hull technique:
Supply Chain Optimization with Homogenous Product Transport Constraints
qt p ,c , pr = Dc , pr ⋅ yh p ,c , pr
¦ yh
p ,c , pr
=1
209
∀( p, c, pr )
(8)
∀( p, c, pr )
(9)
p
where yhp,c,pr is a binary variable.
5. The optimization method The solution of the problem is implemented in AIMMS modeling language (Bisschop and Roelofs, 1999) using CPLEX as MILP solver. AIMMS has been chosen by Provimi Pet Food because of its advanced graphical user interface, and because the most modern solvers can be attached, and the program can be easily extended and developed in case of changing requirements. In order to facilitate the optimization, preliminary procedures are developed which run before the optimization of the main model. First, the tightest bounds of the variables are computed using a Linear Programming (LP) model. Then a feasibility check is performed by solving a simplified LP problem generated from the main MILP model. If the problem is infeasible then the program provides the user with information about the possible reasons of infeasibility. If the problem is feasible then initial values are calculated by solving the relaxed LP model of the main MILP model. As a result of this initialization, the solution procedure of the main MILP model starts from a near optimal point, and thus the solution time is decreased. Finally, the main MILP model is solved. Solving the main MILP model takes no more than 15 seconds on a PC (2.6 MHz CPU, 512 Mb RAM), and solving the whole problem (including the generation of each mathematical model) takes no more than 5 minutes with relative optimality tolerance (gap) 10-13.
6. Computation results The developed MILP model is tested on three example data sets of different sizes. Main characteristics of the example data are shown in Table 1. Table 1. Characteristics of the example data sets Size
Nr. of prod. lines
Nr. of pack. lines
Nr. of customers
Nr. of products
Nr. of eqs.
Nr. of vars.
Nr. of bin. vars.
Small
3
5
19
201
4928
4659
1800
Medium
6
11
45
299
17365
19728
13608
13
21
83
856
88240
99707
79826
Large
The effect of including the special constraints (complex cost function equations minimum constraints, homogeneous transport constraints, and) are tested with different versions of the MILP model. Model 1 contains the material balances, the capacity constraints, and the cost functions only. Model 2 includes all the constraints of Model 1 and the minimum constraints as well. Model 3 includes all the constraints of Model 1 and the homogenous transport constraints as well. Model 4 contains all the above
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mentioned constraints. The solution time data (in CPU sec) at relative optimality tolerance (gap) 10-13 are collected in Table 2 and visualized in Fig. 3. Table 2. Computation time of model versions Size
Model 1
Model 2
Model 3
Model 4
Small
0.02
0.05
0.02
0.07
Medium
0.08
0.20
0.11
0.23
Large
1.06
4.58
1.23
6.47
Extending Model 1 with the minimum constraints (Model 2) increases the solution time at least with 150%. But including merely the homogenous transport constraints extension (Model 3) increases the solution time just slightly. Homogenous transport constraints are stricter constraints than minimum constraints but they probably cause smaller increase in solution time because (1) this extension means less number of constraints containing binary variables, and (2) their proper Convex Hull formulation results in smaller search space during the optimization. 7,00 6,00
CPU sec
5,00
Model 1
4,00
Model 2
3,00
Model 3 Model 4
2,00 1,00 0,00 Small
Medium
Large
Fig. 3. Computational times of model versions
7. Conclusions An MILP model has been developed for solving the supply chain problem of Provimi Pet Food. The model includes special logical constraints such as stepwise constant cost functions of production and packaging lines, minimum constraints for production, packaging and transportation, and the constraints of homogenous product transport. The solution procedure is developed in AIMMS modeling language.
References J. Bisschop, M. Roelofs, 1999, AIMMS The User’s Guide, Paragon Decision Technology B.V. Z. Lelkes, E. Rev, T. Farkas, Z. Fonyo, T. Kovacs, I. Jones, 2005, Multicommodity transportation and supply problem with stepwise constant cost function, European Symposium on Computer Aided Process Engineering 15, Elsevier, 1069-1074. C.J. Vidal, M. Goetschalckx, 1997, Strategic production-distribution models: A critical review with emphasis on global supply chain models, Eur. J. Op. Res. 98, 1-18.
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A sensitivity analysis on optimal solutions obtained for a reactive distillation column Rui M. Filipea, Steinar Hauanb, Henrique A. Matosc, Augusto Q. Novaisd a
DEQ-ISEL, R. Cons. Emídio Navarro, 1, 1959-007 Lisboa, Portugal DCE-CMU, Pittsburgh, PA 15213, USA c DEQB-IST, Av. Rovisco Pais, 1049-001 Lisboa, Portugal d DMS-INETI, Est.Paço do Lumiar, 1649-038 Lisboa, Portugal b
Abstract In previous work (Filipe et al. 2007) the multi-objective optimization of a distillation column was performed and the Pareto front relating the total number of stages, reactive holdup and cost, identified. In this work a study on how the Pareto optimal designs could be adapted for real implementation is presented. Different design details, such as reactive holdup and feed quality, are investigated and the sensitivity of the solutions assessed to quantify the effect on the column expected performance. Keywords: Reactive distillation, multi-objective optimization, sensitivity analysis.
1. Introduction The design and multi-objective optimization of complex reactive distillation columns can be addressed through a framework that combines the use of feasible regions and optimization techniques in order to assess the adequacy of this technology to reacting systems with variable degrees of relative volatilities (Filipe et al. 2006, 2007). In considering columns with distributed feeds, and given the specific nature of this intrinsically multi-objective problem, which leads to the generation of Pareto fronts, it was found that many solutions located in this front involved combining superheated and subcooled feeds. This combination provides a source or a sink of heat at specified trays of the columns which, while favorable to the reaction, tend to increase the internal flows in some sections of the column. In Filipe et al. (2006), a new optimization objective, a cost indicator, whose minimization was envisaged, was used to build the trade-off surface in association with the other objectives, reactive holdup and number of stages. Due to the large number of designs evaluated, a cost indicator based on the capacity values (Jobson et al. 1996) was preferred to a detailed cost calculation. The authors concluded that the designs using combined feeds had lower reactive holdups but higher cost indicator values. This work investigates some details related with the practical implementation of the Pareto optimal designs, through a number of sensitivity tests, with an emphasis being placed on catalyst usage and feed quality. The olefin metathesis system is used as the case study, wherein 2-pentene reacts to form 2-butene and 3-hexene, as a means to balance the light olefins obtained from cracking. This system is well suited for this analysis, since the vapor liquid equilibrium behavior is ideal and the reactant boiling point is intermediate to those of the two products, thus allowing for a wide range of feasible column designs.
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2. Methodology The Pareto fronts were generated using the design and optimization methodology previously described (Filipe et al. 2007). The main assumptions used at this step are: steady state operation, constant pressure, vapor-liquid equilibrium at every stage, kinetically controlled reaction occurring in the liquid phase, and negligible heat effects. The approach used determines the optimal locations for the catalyst, feeds and feed quality. Nevertheless, many of the reported designs tend to be operationally unrealistic as some trays may have too small amounts of catalyst or a very large number of feeds. To investigate how to translate these designs obtained from that simplified optimization model to a process simulator like Aspen Plus, a set of obtained solutions were used to initialize simulations in Aspen Plus, employing the RadFrac model and the Ideal property method. The number of stages, reboil ratio, distillate to feed ratio, location and quality of the feeds, as well as the reactive holdup distribution specifications, were taken from the former optimization results. The assumption of negligible heat effects made in the previous framework allows the decoupling of material and energy balance. The internal flows of the column will then change only due to inflows, outflows or reaction, this latter only if the number of moles change as a result of the reaction stoichiometry. However heat effects cannot be neglected in more detailed models such as those required for Aspen Plus, and simulations show that the internal flows change in trays without inlets or outlets, due to different heats of vaporization for the components inside the column. Setting reflux ratios instead of reboil ratios will then result in significantly lower values for the latter and, consequently, degradation in the purity of the outlet streams. Aspen Plus does not support the direct specification of the feed quality. To overcome this, a design specification was implemented: the feed temperature is adjusted to provide the required energy for the change in the internal liquid flow according to Ln = Ln+1 + q F where F is the feed flow, q the feed quality, and Ln+1 and Ln the liquid entering and leaving the tray, respectively. The cost indicator previously used (Filipe et al. 2006) is based on the size of internal flows, feeds and number of stages, providing an expedient method for the evaluation of a large number of solutions. In this work we analyze these solutions in more detail and employ energy demands and column diameters, with a view to compare the proposed designs, while looking at the accordance of the obtained results with capacity. The olefin metathesis system is used, with the physical properties and reaction kinetics being taken from the literature (Okasinski and Doherty 1998). The reaction is considered only to occur in the liquid phase with a negligible heat of reaction and ideal vapor-liquid equilibrium behavior at atmospheric pressure. The specifications for column operation are taken from Hoffmaster and Hauan (2006). The goal is to convert a pure pentene feed into product streams of butene and hexene with a purity of at least 98 mole percent using a feed flow of 2 kmol/h and a distillate to feed ratio of 0.5.
3. Results & discussion 3.1. Sensitivity to catalyst amount In this section a design case, designated as case A, located at the Pareto front obtained in the optimization step is used to investigate the sensitivity of the solution to changes in the total reactive holdup, i.e., the amount of catalyst required. This design has a reactive holdup (2.5 kmole) near the minimum achieved for the designated number of stages (14), which corresponds to a high capacity indicator value (65.23). It has 10 reactive stages (3 to 12), the feed is located on stage 8 and the feed quality is -0.4.
A Sensitivity Analysis on Optimal Solutions
213
Case A was implemented in Aspen Plus and a slight reduction in the product purity was observed when compared to GAMS results. Product streams show a purity of 97.64% mole fraction instead of 98.00%. As mentioned before, while the heat effects are neglected in the GAMS approach, now the effect of different molar vaporization enthalpies (2-butene < 2-pentene < 3-hexene) is reflected in the changes of the internal flow profile, as seen in Figure 1. The effect is more noticeable in the stages above the feed (1 to 7) where the concentration of 2-butene is higher and due to Figure 1. Internal vapor flows (case A) its lower vaporization enthalpy, the number of vaporized moles increases. In the stages below the feed stage the effect is less noticeable, and although still present, it cannot be perceived in the figure. To investigate the flexibility of the solution, an uniform distribution of the reactive holdup was tested. Redistributing the reactive holdup evenly by three, five and seven stages around the feed stage, led to a penalization of the purity up to 0.05%, while increasing the capacity cost indicator up to 0.15%. This is no longer an optimal design located at the Pareto front, but the increased flexibility offered by the redistribution of the reactive holdup without significant penalties, may be instrumental in improving the column operability. The effect of changing the total reactive holdup was also assessed. Figure 2 depicts the variation of the product purity, capacity and energy supplied to the column through reboiler and feed (Q), with the total reactive holdup (the reference case is indicated by the dashed line). The reactive holdup was changed proportionally in each tray and, as it can be seen, the conversion achieved is highly dependent on reaction availability. There is a noticeable decrease in purity if the reactive holdup is reduced, which is in accordance with the fact that this is a “near minimal” reactive holdup solution, as reported by GAMS. Capacity and energy follow a common trend which is expected, since the number of stages is kept constant and the column diameter was found to undergo only negligible changes. Internal flows and energy consumption are then closely related to each other.
Figure 2. Variation of the stream purity, capacity and energy versus the total reactive holdup
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In order to compare different solutions without explicitly calculating the cost, an objective function, OF, that considers product purity, catalyst amount and the sum of the energy supplied to the column in the reboiler and feed was defined, as follows: OF = 100
x RH Q − C1 − C2 xA RH A QA
(1)
where x is the purity of the stream (equal in both streams), RH the reactive holdup and Q the energy supplied as defined earlier. The subscript A designates case A which is used as the base case. The purity term is multiplied by a fixed value (100) to normalize the solutions and represents the profit obtainable by selling the product. C1 is related to the penalty of increasing the reactive holdup and can also be seen as the cost of catalyst. C2 is related to energy consumption in the reboiler and feed heater. The choice of values for the parameters in the function is not trivial as a large number of variables have been grouped into these coefficients, such as the market value of products and catalyst, catalyst specific activity and operating temperatures, amongst others. The analysis of the total reactive holdup influence was extended to analyze the sensitivity of the objective function parameters C1 and C2. Three different scenarios for each parameter were defined and the results are depicted in Figure 3. When C1 is increased, for a fixed C2, the shape of the function changes demonstrating the advantage of using the smallest reactive holdup that does not compromise product purity. Decreasing too much the reactive holdup would also reduce the objective function value due to the penalty on conversion. Varying C2, for a fixed C1, the observed changes are only on the relative position of the curve, not on its shape, which is due to energy consumption not being a variable of the process but an Aspen Plus result. 3.2. Sensitivity to feed quality In the optimization step, the feed quality q is allowed to take values between -2 and 2 (overheated vapor and subcooled liquid, respectively) and these values are usually selected, in particular, for solutions with low holdup. In fact, it was verified that the use of these feed qualities was responsible for the reduction of the total required holdup. Although interesting from the conceptual point of view and giving insight on how to overcome situations where conversion must exceed the limits imposed by the catalyst (e.g., catalyst deactivation or large volume being required), its practical implementation might be unrealistic. For example, for the particular system used in this section, the range -2 to 2 involves feed temperatures ranging between 689 and 92K.
Figure 3. Influence of C1 (left, for C2=50) and C2 (right, for C1=5) on the objective function
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215
The sensitivity to feed quality and the scope for the real implementation of designs involving extreme feed qualities is investigated in this section with case B. The details for this case are: 26 stages, 14 reactive stages (5-18), total reactive holdup equal to 1.1 kmole, two feeds (stages 9 and 20) with feed qualities of -2 and 2, respectively. The internal flows are increased in the trays located between feeds by using overheated vapor and subcooled liquid in the lower (F2) and upper (F1) feeds, respectively, as seen in Figure 4. As a result, the liquid flow passing through the lower part of the reactive section increases, increasing the total conversion. It is therefore apparent that by reducing the range of the feed qualities (q1 and q2), the product purity will also decrease as a result of reduction of the internal flows. Figure 5 depicts the effect of the variation of q1 and q2 on product purity and confirms this previous finding. As expected, purity is more sensitive to q2, since it is the actual “heat” feed, directly related to the energy supplied to the column. On the other hand, the temperature of F1 decreases as q1 increases, hence the available energy in the column is reduced, bringing about a degradation of the product purity. With a view to test the practical implementation of the design, a set of scenarios was devised (Table 1). We started with case B1 where the “cold” feed, F1, was suppressed. All the feed flow is now supplied through F2, which explains the high value for the energy demand Q. In B2 the feed condition was changed to saturated vapor (q2 = 0) which substantially reduces the energy supplied and, consequently, the product purity.
82
84
86
88
90
92
96
94
2 1.8 1.6 q1
84
86
88
90
92
94
96
1.4 1.2 86
-1
84
88
-1.5
90
92
94
96
1 -2
-0.5
q2
Figure 5. Variation of purity with the quality of the feeds
Figure 4. Internal liquid profiles
Table 1. Scenarios derived from case B Case
F1 (kmol/h)
F2 (kmol/h)
q1
q2
Reboil ratio
Purity (%)
Q (cal/s)
Capacity
B
1.0
1.0
+2
-2
1.7
96.96
8937
96.4
B1
0.0
2.0
-
-2
1.7
97.56
14797
160.5
B2
0.0
2.0
-
0
1.7
56.05
7077
77.5
B3
0.0
2.0
-
0
3.6
95.18
10713
128.5
B4
1.0
1.0
1
0
3.6
98.97
8986
116.8
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Case B3 was defined after case B2, by increasing the reboil ratio in such a way that the internal liquid flow at the feed stage was identical to case B. For B3, an increase in the reboil ratio has to be met also by an increase in the reboiler duty, implying a growth in the energy demand of up to 10713 cal/s. In case B4, combined feeds were used with qualities q set to 1 (liquid at boiling point) and 0 (saturated vapor), while still maintaining the internal flow at the second feed stage as already applied in case B3 (Figure 4). Again, the advantage of the combined feeds is demonstrated and the purity is seen to rise over the value obtained in case B, only with a small increase in the energy demand. The higher value of purity is due to the reactive trays located above F1, whose contribution now increases due to higher flows, by comparison with case B. Despite B4 being the best case, the total internal flow is found to be higher than in case B, which reflects directly in the capacity value. These tests also point out to alternatives for improving the capacity cost indicator: cases B and B4 have the same column diameter (0.2 m), practically the same energy requirement and still the capacity is higher in case B4. This suggests that the largest liquid and vapor flows in the column could be used in the cost indicator definition, rather than the actual individual stage flow values.
4. Conclusions This paper addresses an analysis of reactive distillation column designs obtained from optimization in GAMS with a view to their practical implementation. The sensitivity of the solutions to design variables, such as reactive holdup and feed quality are analyzed using an Aspen Plus model. It is found that some assumptions made at the optimization stage introduce deviations in the simulation results. Nevertheless, the optimized solutions are valuable starting points for further analysis and give important insights into the column design. Also, the selected range for the feed quality in the optimization stage was shown to be inappropriate for industrial practice, as it leads to unrealistic temperature ranges. However, it helped to confirm the advantage of using combined feeds, while emphasizing the need for a careful selection of the feed qualities. Finally, some insights have been gained in respect of potential improvements of the capacity cost indicator, which will be further explored in the future.
References Filipe, R. M., A. Q. Novais, et al. (2006). Multi-objective optimization of reactive distillation columns using feasible regions. 17th International Congress of Chemical and Process Engineering, Prague, Czech Republic. Filipe, R. M., S. Hauan, et al. (2007). Multi-Objective Design of Reactive Distillation. 17th European Symposium on Computer Aided Process Engineering. V. Plesu and P. S. AGACHI. 24, 407-412. Hoffmaster, W. R. and S. Hauan (2006). "Using feasible regions to design and optimize reactive distillation columns with ideal VLE." AIChE Journal 52, 5, 1744-1753. Jobson, M., D. Hildebrandt, et al. (1996). "Variables indicating the cost of vapour-liquid equilibrium separation processes." Chemical Engineering Science 51, 21, 4749-4757. Okasinski, M. J. and M. F. Doherty (1998). "Design Method for Kinetically Controlled, Staged Reactive Distillation Columns." Industrial & Engineering Chemistry Research 37, 7, 2821-2834.
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Synthesis of Zero Effluent Multipurpose Batch Processes Using Effective Scheduling Jacques F. Gouws a,b, Thokozani Majozia,c a
Department of Chemical Engineering, University of Pretoria, Lynnwood Rd, Pretoria, 0002, South Africa b Logistics and Quantative Methods, CSIR Built Environment, P. O. Box 395, Pretoria, 0001, South Africa c Department of Computer Science, University of Pannonia, Egyetem u. 10, Veszprém, H-8200, Hungary
Abstract Wastewater minimization in batch processes has gained much attention in the very recent past. Mainly 2 reasons lie behind this heightened interest. Firstly, batch operations are inherently flexible, which renders them ideal for volatile conditions that characterize today’s markets. Secondly, batch processes tend to produce highly toxic effluent streams, albeit in relatively small quantities in comparison to their continuous counterparts. The stringent environmental conditions militate against the latter characteristic of batch plants, hence the need to eliminate or minimize effluent. In most published literature, wastewater minimization is achieved through water reuse, water recycle, water regeneration reuse and water regeneration recycle. These concepts generally exclude the possibility of water being used as a key ingredient in the water using operations. However, some pharmaceutical and agrochemical operations, which traditionally operate in a batch mode, offer a unique opportunity to use recycle or reuse water as the main constituent of the final product. In some of these operations water constitutes more than 90% of the final product makeup. The problem addressed in this paper bears this feature, which consequently allows the batch processes to operate in a near-zero effluent mode. Moreover, the question of the number and size of the vessels used in a batch processing facility has always posed a problem. The incorrect approach to the synthesis of a batch plant can lead to the situation where processing vessels are over sized and even the possibility of idle processing vessels. This could pose a possible over capitalisation of an operation. In essence, an optimal design of a batch processing plant is determined by considering the scheduling of operations in the synthesis phase. The mathematically based method presented in this paper deals with the synthesis of a batch plant operating in the fashion mentioned above. The method determines the optimal size and number of processing vessels and wastewater storage vessels, while scheduling the operation in such a manner as to operate in a near-zero effluent fashion Keywords: effluent, minimization, process, batch.
1. Introduction Concern over the impact of industry on the environment is greater now than ever. Environmental legislation is becoming ever more stringent in an effort to reduce the
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negative impact industry has on the environment. Coupled with this is the fact that society is becoming ever more conscious of the state of the environment. Traditional end-of-pipe treatment methods are not always economically viable to meet stringent effluent targets. Therefore, process integration techniques are becoming ever more important in reducing the amount of effluent produced. Wastewater minimisation in batch processes has slowly gained some attention in the past few years. Past wastewater methodologies can roughly be divided into two main categories, namely, graphical techniques [1,2,3] and mathematical techniques [4,5,6,7]. Graphical techniques have their roots in graphical techniques developed for continuous processes, while mathematical techniques have their roots in mathematical programming. Past methodologies for wastewater minimisation in batch processes have been mainly focused on mass transfer based operations. In such operations water is consumed at the beginning of a unit operation and produced at the end. Reuse between different units is governed by availability of wastewater and the concentration of the contaminants present in the wastewater. Also, operations do exist where wastewater is produced as a result of a cleaning operation. If products produced from such operations require water as a raw material, it should be possible to reuse the wastewater as part of product formulation, since the wastewater is only contaminated with the residue in the previous batch of the same or another compatible product. The wastewater, when reused in this manner, is significantly reduced, hence the plant can operate in a near zero effluent fashion. Furthermore, the residue present in the wastewater is recovered, which could provide substantial economic benefits. A mathematical formulation for the synthesis of plants operating in a near zero effluent mode of operation has been developed. The formulation determines the number and size of processing vessels and storage vessels, while ensuring wastewater is reused as part of product. Since product integrity is of paramount importance, wastewater containing different contaminants is not allowed to mix. Hence, there is a dedicated storage vessel for each type of wastewater. Furthermore, the methodology is derived to take into account operations where the contaminant mass in the wastewater is negligible and where it is not negligible.
2. Problem Statement The problem addressed in this paper can be formally stated as follows. Given, i) required production over a given time horizon, ii) product recipe and production times, iii) maximum number of processing vessels and storage vessels, and iv) maximum and minimum capacity of processing vessels and storage vessels, determine the plant design that will minimise cost, i.e. the design with the optimal number and size of processing vessels and storage vessels as well as minimum effluent generation.
3. Mathematical Formulation The following sets, variables and parameters are used in the mathematical formulation
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Sets Sin,j = {sin,j | sin,j = input state into processing vessel j} J = {j | j = processing vessel} U = {u | u = storage vessel} P = {p | p = time point}
Variables fw(sin,j,p) fe(sin,j,p) vproc(j) vstor(u) eproc(j) y(sin,j,p)
mass of water used for a washout for state sin,j at time point p effluent water from processing vessel j at time point p capacity of processing vessel j capacity of storage vessel u existence binary variable for processing vessel j binary variable showing usage of state sin,j at time point p
Parameters Ȍwash Vmin Vmax Įproc ȕproc Įstor ȕstor Ce
factor relating the size of a processing vessel to the amount of washout water minimum capacity of a processing vessel maximum capacity of a processing vessel cost of a processing vessel cost of a processing vessel based on size cost of a storage vessel cost of a storage vessel based on size treatment cost of the effluent water
3.1. Mass balance constraints The first part of the mathematical formulation constitutes the mass balance constraints. Mass balances are done over a processing unit and a storage vessel. The mass balances over a processing vessel can be divided into two main groups. The first group comprises of all the constraints related to product generation and the second group, all the constraints related to a washout. The mass balances related to product include a raw material balance and a mass balance over a processing unit. The raw material balance ensures that the correct ratio of water and other raw materials is used for a product. Apart from the two balances there are also capacity constraints. The washout mass balances comprise of an inlet water balance and an outlet water balance. The amount of water used for a washout is dependent on the size of the processing vessel, and is determined using Equation (1), which is the inlet water balance. Equation (1) contains a non-linear term that is linearised using a Glover transformation[8].
f w (sin , j , p ) = Ψwash v proc ( j ) y (sin , j , p ), ∀ j ∈ J , sin , j ∈ S in , j
(1)
Mass balances over a storage vessel include a water balance and if necessary a contaminant balance. The formulation is capable of dealing with both the scenario where the contaminant mass in the washout water is negligible and not.
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3.2. Scheduling constraints Since the processes dealt with are batch processes the inherent discontinuous nature has to be taken into account. Scheduling constraints are formulated to ensure that the processing of raw material occurs after a washout has taken place, i.e. once a vessel has been cleaned, and after a previous batch has finished processing. Further constraints ensure a washout begins directly after the product has been removed from a processing vessel. Duration constraints are formulated for the production and washouts. Apart from the above constraints, the reuse of water in product also has to be scheduled. Constraints are formulated to ensure that water directly reused between two processing vessels occurs at the end of a wash from the source and the beginning of the processing of the sink. This is similar for indirect reuse, however, in this instance the timing of water moving to and from a storage vessel must coincide with the ending time of a washout and the beginning of product processing, respectively. The formulation also caters for a maximum storage time of washout water in a storage vessel. Constraints are formulated to ensure the difference between the inlet time and outlet time of water from a storage vessel is less than the maximum allowable storage time. 3.3. Design constraints The final constraints considered are the design constraints. The first of these are the existence constraints. An existence binary variable is defined for each processing vessel and each storage vessel. If a processing vessel processes material within the time horizon then the binary variable is set to one. This is similar for a storage vessel. The upper and lower bounds of a processing vessels size are defined using Equation (2) and similar constraint holds for a storage vessel.
e proc ( j )V min ≤ v proc ( j ) ≤ e proc ( j )V max ∀ j ∈ J
(2)
3.4. Objective function The objective function in the formulation is the minimisation of overall cost. In this instance the overall cost arises from the cost of the processing vessels, the cost of the storage vessels and the treatment costs of the effluent water. The objective function is given in Equation (3). The objective function is linear, as it was assumed that the cost of a processing vessel and storage vessel is a linear function of the size of the vessel.
min ¦ α proc e proc ( j ) + β proc v proc ( j ) + ¦ α stor e stor (u ) + β stor v stor (u ) j
+
¦ C f (s e
e
in. j
, p)
u
∀ j ∈ J , u ∈ U , s in , j ∈ S in , j , p ∈ P
(3)
sin , j p
4. Industrial Case Study The methodology was applied to an industrial case study stemming from a pharmaceuticals mixing facility. The industrial case study involves the design of a small mixing operation that produces three different products. Each product has a fixed ratio
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between the amount of water used in the product and other raw materials. For product 1 the ratio of water to other raw material is 80:20, for product 2 the ratio of water to other raw material is 82.5:17.5 and for product 3 the ratio is 90:10. 4000kg, 6000kg and 5000kg are required for products 1, 2 and 3 over a 24 hour time horizon respectively. The number and size of batches required to fulfill the production requirements is not known. A maximum of 4 mixing vessels can be used with a minimum capacity of 1000kg and a maximum capacity of 4000kg. Maximum reuse opportunities are ensured through the inclusion of the possibility of wastewater storage. Three distinct types of wastewater will be produced from the cleaning operation, due to the three different products mixed. Each type of wastewater has the possibility of being stored in a distinct storage vessel. The minimum and maximum capacity of each storage vessel is 500kg and 1500kg, respectively. The amount of water used for a washout was dependent on the size of the processing vessel. For every 1000kg increase in the mixers size the amount of water used for a washout would increase by 200kg. Therefore, Ȍwash has the value of 0.2. The constants used for the objective function are given in Table 1. Table 1. Cost data used in industrial case study Constant
Value
Įproc
400 (c.u./mixer)
ȕproc
0.8
Įstor
100 (c.u./storage vessel)
ȕstor
0.5
Ce
5 (c.u./kg wastewater)
The problem was formulated in GAMS and subsequently solved using CPLEX. The final design required 4 mixing vessels and no storage vessels for the wastewater. Mixing vessels 2, 3 and 4 each had a capacity of 1000kg and mixer 1 had a capacity of 3000kg. The total amount of effluent generated from the process was 600kg and the objective function had an optimal value of 9400 c.u. Effluent is generated, since there is no opportunity for further reuse of the wastewater at the end of the time horizon. The solution time was 7665 CPU seconds using a Pentium 4, 3.2 GHz processor. The problem had 423 binary variables and 2855 continuous variables. The Gannt chart showing the production schedule is given in Figure 1. The black striped boxes represent a production and the grey boxes represent a mixer being washed. The “P” in the striped boxes represents product and the number after the “P” represents the respective product number. The bold numbers represent the amount of water reused in product. From Figure 1 one can see that mixer 2 is dedicated to the production of product 2. This is similar for mixer 3, which is dedicated to the production of product 3. Mixers 1 and 4, however, produce batches of all three products. The size of the batches produced from each mixer is determined by the optimal size of the mixer, hence the size of the batches from mixers 2, 3 and 4 are 1000kg and from mixer 1 is 3000kg. Interesting to note is that mixer 3 does not produce any effluents throughout the time horizon.
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Effluent: 200
200
4
P3
P3
P1 200
200
Effluent: 200
200
Mixer
3
P3
P3
200
2
P3
P2
P2
P2
600
1
600
P1
P2
0
Effluent: 200
200
4
8
12
16
20
24
Time (hr)
Figure 1. Gannt chart representing the production schedule
5. Conclusions A methodology for the synthesis of batch plants incorporating the zero effluent mode of operation has been presented. In the zero effluent mode of operation, the wastewater generated in the operation is reused as a constituent in a batch of subsequent compatible product. The methodology determines the optimal size and number of processing vessels and wastewater storage vessels. The methodology has been applied to an industrial case study. The industrial case study involved the design of a pharmaceuticals mixing operation that produces three products. The resulting design for the industrial case study had 4 mixing vessels and no wastewater storage vessels. Three of the mixing vessels had a capacity of 1000kg and the remaining mixing vessel had a capacity of 3000kg.
References [1] Y. P. Wang and R. Smith, TransIChemE, 73(1995), 905. [2] D. C. Y. Foo, Z. A. Manan and Y. L. Tan, J. Clean. Prod., 13 (2005), 1381 [3] T. Majozi, C. J. Brouckaert and C. A. Buckley, J. Environ. Manage., 78 (2006), [4] R. Grau, M. Graells, J. Corominas, A. Espuña, and L. Puigjaner, L., Comp. Chem. Eng., 20 (1996), 853 [5] M. Almató, E. Sanmartí, A. EspuĔa, and L. Puigjaner, Comp. Chem. Eng., 21 (1997), s971 [6] J. K. Kim and R. Smith, Process Saf. Environ., 82 (2004), 238 [7] T. Majozi, Comp. Chem. Eng., 29 (2005), 1631 [8] F. Glover, Manage. Sci., 22 (1975), 455.
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Design Of A Syngas Infrastructure Paulien M. Herder, Rob M. Stikkelman, Gerard P.J. Dijkema, Aad F. Correljé Delft University of Technology; Department of Technology, Policy and Management, Jaffalaan 5, 2628 BX Delft, The Netherlands,
[email protected]
Abstract A cluster feeding on synthesis gas produced by gasification would create feedstock flexibility to existing petrochemical clusters, which is key to their continued prosperity in times of increasing uncertainty about global crude oil production and availability. This paper describes the design of such a syngas cluster and infrastructure where technical, economic and institutional requirements have been taken into consideration. A number of network topologies were explored. A double bus topology turned out to be the most attractive solution. Therein, users and suppliers can connect to a high volume, central ‘bus’ that comprises two pipelines for high and low quality syngas respectively. This topology allows for a major simplification of the methanol process, significantly reducing capital investment and operational cost. A “syngas market” is needed for the infrastructure to function properly. In it, syngas suppliers and users engage in transactions. For its design, two options were selected: bilateral contracts and trading on a syngas spot market. The latter provides flexibility and acts as a price determinate for low quality syngas. All low quality syngas is bought by a “transport services” company, which places it in a common pool from which users can buy the quantities they need. Keywords: systems engineering, infrastructures, system design, syngas.
1. Introduction The Port of Rotterdam, The Netherlands, has an important beneficial influence on the economy of the Netherlands as a centre of trade and industrial activity. Its large, stateof-the-art, petrochemical cluster converts imported crude oil into numerous end products. Its success, however, has also made the Rotterdam petrochemical cluster heavily dependent on crude oil and its continued supply. Since at present the cluster is quite inflexible in its need for crude oil as a feedstock, security of supply issues for crude oil threaten the operations of all cluster partners. In order to safeguard the continued competitiveness of the cluster, it is therefore important to reduce the dependency on crude oil by increasing the cluster’s feedstock flexibility. As a possible solution for increasing fuel diversification we identified the development of a synthesis gas -syngas- network. Syngas is a mixture of carbon monoxide (CO) and hydrogen (H2) and can be produced by gasification from any carbon-containing feedstock. A syngas network thus offers opportunities for feedstock diversification. A syngas mixture does not carry feedstock contaminants such as sulphur and heavy metals and thus forms an ideal basis for ‘designer fuels’ production, clean electric power generation and hydrogen manufacture. The advantages of syngas with respect to feedstock flexiblity and intermediate product standardization, combined with the expected increase in demand for designer fuels renders a syngas network in the port of Rotterdam very attractive.
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However, the design and implementation of a syngas infrastructure in an existing petrochemical cluster is a complicated task where multiple interests have to be catered for. Structural changes will be necessary for the energy and (petro-) chemical industry to allow successful introduction of a syngas network, not to mention the large capital investment required. The research reported in this paper focused on the design of a syngas cluster and infrastructure taking into account technical, economic and institutional requirements. The design approach was based upon an architecture paradigm [1]: “An adequate system architecture description must cover whatever aspects of cost, behavior, performance, organization, physical structure or other elements that need to be added to clarify the clients’ priorities.”
2. The petrochemical and energy cluster The current energy infrastructure in the Netherlands (see figure 1) can be characterised as rigid and inflexible. For decades, capital-intensive units such as power stations and oil refineries have converted one specific type of fossil resource into only a few products: most coal is converted into electric power, some 90% of crude oil is turned into transport fuels and natural gas is used to generate electric power and heat. At a short term a feedstock change cannot be realized for any of the facilities in this energy infrastructure. Long-term feedstock modification options are limited and often prohibitively expensive. Source 38% crude oil
Conversion Refinery
11% coal 0,8% biomass
Customer
Automotive Fuel
28% Transport
Petrochemicals Coal-fired IPP
0,4% residues 47% natural gas
Product
Gas/fuel oil Heat
Gas-fired IPP
27% Industry Gas
0% Water 0,3% Wind
Turbine
1,0% Uranium
Nuclear IPP
Electricity
45% services/ households
Figure 1. Overview of the current Dutch energy infrastructure (IPP = Independent Power Plant).
Meanwhile, it remains uncertain what the ideal or available energy resources mix for the Netherlands will be in 2020, in 2010, in 2008 or even next month. It may thus be strategically vital that this national energy infrastructure be made independent of specific feedstock. Rather than making a series of changes based upon the whims of the day, we suggest a long-term fundamental shift - to deliberately change our energy infrastructure so that it has feedstock flexibility in 2030 and 2050. This shift can be realised via a gradual transition, wherein over a period of 30-40 years the current oil
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refineries and power stations are replaced by a multi-fuel syngas cluster and infrastructure (see figure 2). This consists of a distribution network of: • Large, but flexible multi-fuel gasifiers that produce syngas of various qualities from various feedstock, • units to refine syngas to set specifications, and • industrial processes which convert syngas into useable products, electric power and heat. Source
Conversion
Product Design fuel
Crude oil Coal
Customer Transport
Petrochemicals
Biomass
Multi fuel gasifier Syngas complex
Residues
Heat
Natural gas
Industry Gas
Water Wind
Flexibility
Uranium
Turbine
Electricity
Services/ Households
Nuclear IPP Multi usability
Figure 2. The proposed Dutch energy infrastructure, 2040.
3. Technical Design One of the main degrees-of-freedom in the design of the syngas cluster and infrastructure is the network topology. In the design process, ring, star and bus network configurations were considered. The evaluation of options was underpinned by straightforward mass and energy balance calculations. The most attractive option turned out to be a ‘double bus’ network. Therein, one of the main syngas pipelines is reserved for syngas of “high quality” - syngas with low H2/CO ratio within a tight range. Such HQ syngas may originate from several gasifiers. The HQ pipeline syngas quality specification, the H2/CO ratio, must be sufficiently low to ensure that the users that require the highest quality syngas can be served. In this way, high CO content takes preference, which obviates the need for expensive decentralized cryogenic separation. Users that require syngas with a higher H2/CO ration could simply use the water gas shift reaction to increase H2 content. The most likely syngas consumers in the infrastructure are Fisher-Tropsch diesel processes, ammonia producers, methanol producers and the Direct Reduction of Iron (DRI) process. The H2/CO ratios required by these process range from >0.68–4.4. Assuming that syngas is produced using entrained flow reactors with reformers, preliminary economic evaluation revealed that the HQ pipeline should provide syngas in a ratio bandwidth of 0.9–1.1. In case several gasifiers are connected to the network, each may produce syngas of a different quality, as long as their joint product in the pipeline remains within the given
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bandwidth, which provideds leeway to cope with temporary maintenance shutdowns of individual gasifiers. A second pipeline network (LQ, Low Quality) must be developed to allow collection and transport of syngas generated in downstream production processes and to allow for flexibility of syngas quality at end-user point. The LQ pipeline network has a variable syngas quality, which is inadequate for some chemical processes but inconsequential or even beneficial for facilities such as electricity production and DRI [2]. The double bus infrastructure is illustrated in figure 3.
Figure 3. A double bus infrastructure
There are several reasons for building a second pipeline: first, valuable recycle flows can be efficiently transported to downstream users who would not mind the variable ratio and concentration of inert gases. Thereby, in upstream industrial processes the need for recycle equipment ceases to exist. The upstream producers could generate some income by selling their recycle flows. Secondly, in the upstream industrial processes one would not have to re-use flows they normally recycle. As a consequence, the design of such processes can be simplified. A methanol plant, for example, would fit perfectly in such an industrial cluster [3]. Currently, a methanol plant typically consists of a gasification section, a reactor section with a large recycle loop, and a distillation section (see figure 4a). When connected to a double bus syngas infrastructure, a methanol plant would be reduced to a reactor section and a (slightly adapted) distillation section, without the syngas recycle system, as illustrated in figure 4b. The elimination of the recycle equipment would lead to significant cost reductions in the investment and operational cost of the plant. Conversely, 40% of the raw syngas will be relegated to syngas with another ratio and can be sold to the LQ market (see next section).
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a) Conventional methanol process design (after Wesselingh et al., 1990) air furnace
CO2
CH4
CO / H2
Q CH4
reactor
reformer
H 2O
MeOH
condensator
distillation
H 2O b) Methanol process design in syngas infrastructure LQ Pipeline HQ Pipeline
CO / H2 CO / H2
reactor
condensator
MeOH distillation H 2O
Figure 4. Conventional (a) and new (b) methanol process design.
4. Market Design Presently, the institution “syngas market” does not exist. In the double-bus topology there are three dominant aspects in the design of such a market [4-6]: two types of transactions – trading high quality and low quality syngas respectively - and a network fee must be paid for transport services. As outlined in the technical design, in the double bus topology two pipeline networks operate adjacent to each other. Users of the high quality gas are allowed to feed their residue gas into the secondary network. In addition to these recycle flows from industries that use HQ syngas, LQ syngas is directly fed into the secondary network from gasification installations. To coordinate and balance the process of supply and demand over two networks a new organisation must be created, which role resembles the role of balancing organisations in the electricity and gas sectors. This organisation is responsible for balancing both networks through a market based balancing mechanism. Figure 5 presents the structure of the markets and transactions. As outlined in the technical design, the users of high quality syngas can eliminate their recycle stream to act as a supplier for the lower quality network. The HQ users have used the high COcontent syngas and deliver a mixture with a higher hydrogen concentration to the LQ network, and receive a price for their LQ syngas.
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Figure 5. Syngas market design
5. Conclusion An industrial infrastructure based on syngas is a viable answer to the increasing uncertainty in petrochemical and energy feedstock supply. It provides feedstock flexibility through a double-bus network that connects several gasification units. It provides syngas as a multi-functional building block for the downstream chemical and energy industries. The design of these industrial processes may be simplified to a large extent, provided that a syngas market is created similar to the natural gas and electricity markets to allow syngas trade and system load balancing.
Acknowledgements The authors would like to thank Diederik Apotheker, Dirk-Jan van der Elst, Marinda Gaillard, Marlies van den Heuvel, and Wouter van Lelyveld for their creative and hard work in exploring the syngas network topologies and market structures.
References 1. Maier, M.W., Rechting E. (2000), The Art of Systems Architecting, CRC Press, Inc. Boca Raton, FL, USA 2. Herder, P.M., Stikkelman R.M. (2004), Methanol-based Industrial cluster design: a study of the design options and design process, in Ind. Eng. Chem. Res, 43, p3879-3885 3. Energy solution centre (2007), Direct reduction: process description http://www.energysolutionscenter.org/HeatTreat/MetalsAdvisor/iron_and_steel/process_de scriptions/raw_metals_preparation/ironmaking/direct_reduction/ironmaking_direct_reducti on_process_desscription.htm (accessed 24/01/2007) 4. Koppenjan, J. & Groenewegen, J. (2005) ´Institutional design for complex technological systems´, Int. J. Technology, Policy and Management, Vol. 5,No. 3, pp. 240-257. 5. Joskow, P.L. (2003), Electricity sector restructuring and competition: Lessons learned, http://web.mit.edu/ceepr/www/2003-014.pdf (accessed 23/01/2007) 6. Bruin, H.de, Dicke W., (2006) Strategies for Safeguarding public values in liberalized utility sectors, in Public Administration, Vol. 84 No. 3.
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Implementation of a Reactive Dividing Wall Distillation Column in a Pilot Plant Rodrigo Sandoval-Vergaraa, Fabricio Omar Barroso-Muñoza, Héctor Hernández-Escotoa, Juan Gabriel Segovia-Hernándeza, Salvador Hernándeza, Vicente Rico-Ramírezb a
Facultad de Química, Universidad de Guanajuato, Noria Alta, s/n, Guanajuato, Gto., 36050, México b Instituto Tecnológico de Celaya, Depto. De Ingeniería Química, Av. Tecnológico y García Cubas s/n, Celaya, Gto., 38010, México
Abstract Based on the knowledge regarding steady state design, optimization and control obtained by using Aspen Plus and Aspen Dynamics process simulators, we have designed and implemented a reactive dividing wall distillation column (DWDC). The column can be used to carry out the equilibrium reaction between ethanol and acetic acid to produce ethyl acetate and water catalyzed by sulfuric acid. The reactive DWDC contains three packed sections and the middle section is the key part in order to minimize the energy consumption. That section contains a wall that can be moved to three positions to manipulate the split of the vapor stream, whereas the split of the liquid stream is achieved by using a side tank. The reactive DWDC contains a reflux valve used to control either the composition of the distillate or the temperature at some point in the first packed section. Also, a reboiler was implemented in the lower section, and the heat duty supplied to it is used to control either the composition of the bottoms product or the temperature in the reboiler. This design was proposed based on both steady and dynamic simulations. The minimum energy consumption was predicted in the steady state simulation; the dynamic simulations indicated that the minimum energy consumption can be achieved in practice by implementing two control loops of temperature (or composition), as described. Keywords: reactive distillation, thermally coupled distillation, pilot plant, control
1. Introduction Distillation is a unit operation widely used to separate multicomponent mixtures, in spite of its high energy consumption and low thermodynamic efficiency. As a result, engineers and researchers are interested in developing new configurations capable of reducing and improving the use of energy. It has been demonstrated that thermal linking can reduce energy demands between 30 and 50 percent depending on the composition of the mixture to be separated. The three thermally coupled distillation sequences (TCDS) that have been explored more in detail are the TCDS using a side rectifier, the TCDS involving a side stripper and the fully thermally coupled distillation sequence or Petlyuk system. Because of both the reduction in oil reserves and polices of reduction in Carbone Dioxide emissions (Kencse and Miszey, 2007), important research has been focused on design, optimization and control of the TCDS. Regarding the design of TCDS, Cristiansen et al. (1997) reported a design and optimization procedure for the Petlyuk distillation column that involves the search of the interconnecting
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streams of the system. Hernández and Jiménez (1999) presented a design method that minimizes the energy consumption for a given structure of the Petlyuk distillation column. Dunnebier and Pantelides (1999) reported a formal procedure based on mathematical programming for detecting the optimal design of integrated distillation columns. Also, dynamic studies have been reported for the TCDS; for instance, Jiménez et al. (2001) compared the theoretical control properties and closed-loop dynamic responses of conventional and thermally coupled distillation sequences, and they found that the TCDS schemes presented theoretical control properties and dynamic responses better that those of the conventional distillation sequences. In the same context, Serra et al. (2003) compared the controllability of different distillation arrangements and showed that some different operation conditions to those of the optimum energy consumption favored the operation of a dividing wall distillation column (DWDC). The Petlyuk system has been successfully implemented by using a dividing wall inside a distillation column, the resulting configuration is the dividing wall distillation column. Practical implementations of the DWDC have reported savings of up to 40% in both energy and capital costs (Becker et al., 2001; Schultz et al., 2002; Kaibel et al., 2006; Schultz et al., 2006). Because of polices in process intensification, we are interested in carrying out reactions in thermally coupled distillation sequences. Based on our experience regarding steady state design, optimization and control obtained by using simulations, we have designed and implemented a DWDC to carry out the equilibrium reaction between ethanol and acetic acid to produce ethyl acetate and water, using sulfuric acid as catalyst.
2. Base Case: Esterification Process The process used as base case for the design of the DWDC involves a reactor-column where ethanol and acetic acid are introduced to the reboiler, and the chemical reaction proceeds as catalyzed by sulfuric acid according the following reaction at equilibrium. 2 SO 4 ⎯ H⎯ ⎯→ C H 3 C O O H + C 2 H 5 O H ←⎯ ⎯⎯
H 2O + C H 3C O O C 2 H 5
(1)
The distillate is introduced into a decanter tank where two liquid phases are present. The organic phase is fed into the purification column of the reactor-column system to obtain a high purity ethyl acetate compound (99.5% weight at) whereas the separated aqueous phase is fed into a different conventional distillation column to recover the ethanol which is then returned to the reactor-column. It is important to highlight that two inconvenient aspects in the operation can be observed in this process: i) the chemical reaction yield is limited by the thermodynamic chemical equilibrium (presenting a limit to the ethyl acetate produced) and ii) the system shows the formation of two binary homogeneous azeotropes, one ternary homogeneous azeotrope and one heterogeneous binary azeotrope (Figure 1).
3. Steady State and Dynamic Simulation of the Reactive DWDC Previous to our practical implementation, the design and optimization methods reported in Hernández and Jiménez (1999) were implemented in a framework involving the Aspen Plus process simulator. Figure 2 presents the minimization of the energy consumption of the distillation column; notice that the energy consumption depends strongly on the values of the interconnecting streams. Appropriate values of the interconnecting streams are important to obtain the minimum energy consumption in the
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implemented reactive DWDC. Also, dynamic closed loops were designed for the reactive DWDC using the Aspen Dynamics process simulator. Two control loops of temperature were implemented, the first one in the first packed section and the second one in the reboiler. The reflux rate and reboiler heat duty were selected as manipulated variables for the first and second control loop, respectively. Figures 3 and 4 show that the reactive DWDC can achieve positive and negative set point changes in the control loops of temperature. Also, good dynamic closed responses were obtained for load rejection; for instance, changes in the feed composition. These results were considered for the design and implementation of the reactive DWDC.
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Figure 2 Energy optimization.
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Figure 1 Ternary map for the system.
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Figure 3. Dynamic responses for a positive change in the set point (1 °F) in the first control loops.
4. Implementation Issues and Operation of the Reactive DWDC Figure 5 depicts the DWDC implemented in a pilot plant using stainless steel 316L. We are interested in the control of the distillate composition, but this task is difficult to implement in industrial practice; hence, we control the temperature at some point in the packed section instead. Both of the control objectives require the manipulation of the
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reflux ratio in order to set the composition or temperature in their set points. As a result, a valve was implemented inside the column in order to manipulate the reflux to the distillation column (Figure 5, element 2).
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Figure 4. Dynamic responses for a negative change in the set point (1 °F) in the first control loops.
Several collector and distributor trays were placed in the three packed sections of the DWDC in order to guarantee homogeneous liquid distribution in the packed bed (Figure 5, elements 10 and 11). Special care needs to be taken between the first and second packed sections, because a collector tray (Figure 5, element 11) is needed in the bottom of the first packed bed in order to send the liquid to a side tank. This device plays an important role because during the steady state design and optimization, since it is fundamental to detect the optimal splits of liquid and vapor in the middle section of the DWDC to guarantee the optimal energy consumption in the reboiler. In practice, it is difficult to manipulate the splits of vapor; for that reason, the side tank (Figure 5, element 4) has been implemented to split the liquid to both sides of the wall in the middle section of the distillation column and to extract the water decanted. The DWDC contains three packed sections of Teflon rasching super-rings. In the middle section (Figure 5, elements 6 and 7) of the distillation column, a wall (Figure 5, element 5) was implemented so that it can be moved to three positions to manipulate the split of the vapor stream. This is the key packed section in the energy-performance of the DWDC, because the feed is introduced in one side (equivalent to the prefactionator in the Petlyuk system, Figure 5, element 7) and in the other one (Figure 5, element 6) a liquid side product is obtained (the side product stream in the main column of Petlyuk systems). As it can be seen, this section needs collector and distribution trays in the feed and side stream points. The first and third packed sections are similar to those of a conventional distillation column, and only distributor and support trays are required for the operation of the DWDC. A reboiler (Figure 5, element 9) that can be charged with the reacting mixture in the batch operation fashion was placed at the end of the third packed section. Finally, several thermocouples were implemented in the DWDC to register the temperature
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profiles. The future research work is focused on the experimental study of the hydraulics, steady state and closed-loop dynamics.
1 2 10 3 11 4
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Condenser Reflux valve First packed section Side tank splitter Dividing wall Second packed section (side product) Second packed section ( feed) Third packed section Reboiler Side product collector Side tanks for distillate Distributor tray Collector tray
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Figure 5 DWDC implemented in the pilot plant (patent in process).
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5. Conclusions We have designed and implemented a reactive divided wall distillation column for the production of ethyl acetate from acetic acid and ethanol. Important aspects derived from steady state simulation were considered; for instance, a side tank was implemented in order to split the liquid to both sides of the wall and a moving wall inside the column that allows to fix the split of the vapor stream. The dynamic simulations indicate that it is possible to control the composition of the top and bottoms products or two temperatures by manipulating the reflux rate and the heat duty supplied to the reboiler, respectively. The implementation of the reactive divided wall distillation columns takes into account important aspects like process intensification, minimum energy consumption and reduction in Carbon Dioxide emission to the atmosphere.
Acknowledgements We acknowledge the financial support provided by Universidad de Guanajuato, CONACyT and CONCyTEG (México).
References A.C. Christiansen, S. Skogestad, K. Lien, 1997, Complex Distillation Arrangements: Extending the Petlyuk Ideas. Comput. Chem. Engng., 21, S237. G. Dunnebier, C. Pantelides, 1999, Optimal Design of Thermally Coupled Distillation Columns. Ind. Eng. Chem. Res.,38, 162. H. Becker, S. Godorr, H. Kreis, 2001, Partitioned distillation columns –why, when and how, Chem. Eng. 108, 68. S. Hernández, A. Jiménez, 1999, Design of Energy-Efficient Petlyuk Systems. Comput. Chem. Eng., 23, 1005. A. Jiménez, S. Hernández, F. A. Montoy, M. Zavala-García, 2001, Analysis of Control Properties of Conventional and Nonconventional Distillation Sequences. Ind. Eng. Chem. Res., 40, 3757. M.A. Schultz, D.G. Stewart, J.M. Harris, S.P. Rosenblum, M.S. Shakur, D.E. O’Brien, 2002, Reduce costs with dividing-wall columns, Chem. Eng. Prog., 98, 64. B. Kaibel, H. Jansen, E. Zich, Z. Olujic, 2006, Unfixed Dividing Wall Technology for Packed and Tray Distillation Columns, In Distillation and Absorption ‘06, IChemeE Symp. Series No. 15, 252. H. Kencse, P. Mizsey, 2007, Comprehensive Process Investigation Methodology for EnergyIntegrated Distillation, In proceedings of 17th European Symposium on Computer Aided Process Engineering (ESCAPE), Elsevier, 24, 883. M.A. Schultz, D.E. O’Brien, R.K. Hoehn, C.P. Luebke, D.G. Stewart, 2006, Innovative Flowscheme using Dividing Wall Columns, In proceedings of 16th European Symposium on Computer Aided Process Engineering (ESCAPE) and 9th International Symposium on Process Systems Engineering (PSE), Elsevier, 21, 695. M. Serra, A. Espuña, L. Puigjaner, 2003, Controllability of different multicomponent distillation arrangements, Ind. Eng. Chem. Res., 42, 1773.
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Optimisation of a Bio-ethanol Purification Process Using Conceptual Design and Simulation Tools Patricia M. Hoch,a José Espinosa,b a
PLAPIQUI-UNS-CONICET, Camino La Carrindanga km 7-8000, Bahía Blanca, Argentina b INGAR-CONICET-UNL, Avellaneda 3657, S3002 GJC Santa Fe, Argentina
Abstract In this work, we propose an evolutionary optimisation procedure which intensively uses both conceptual and rigorous models for the design and simulation of unit operations involved in a bio-ethanol purification process. While conceptual models are used to determine initial values for design and operating variables of a given operation unit, rigorous simulation departing from initial estimates generated at conceptual design level enables to remove simplifying assumptions, interconnect equipments and calculate operating and investment costs. Once an initial design of the purification plant is obtained, opportunities of improvement are easily recognized and then tested by performing the design and simulation steps until a cost-effective bio-ethanol purification plant is achieved. Keywords: Bio-ethanol Purification Plant, Evolutionary Optimisation, Conceptual Design, Rigorous Simulation.
1. Introduction Optimisation of both design and operation variables of a bio-ethanol purification plant intended to produce fuel grade ethanol is a challenge to make the bio-fuel a realistic alternative in the energy market. Given the plant complexity and the high non-linearity of the corresponding models, we propose an evolutionary optimisation procedure which uses intensively both conceptual and rigorous models for the design and simulation of unit operations. It is quite difficult to obtain an initial estimation of the total number of trays of the main distillation column, placement of feed and side streams, and steam flow rate in the simulation environment, but this task is easily accomplished in the conceptual design environment. In addition, convergence of the rigorous model is enhanced by using initial estimates of internal profiles generated at the conceptual design level despite of the highly non-ideal behaviour of the multicomponent azeotropic mixture. Applying the same philosophy to estimate initial values for design and operating variables of the whole process, optimal values for a cost-effective bio-ethanol purification plant are reported. The methodology is applied to the purification process for a feed leaving the fermentation step of a conventional corn dry-grind processing facility producing 24 million liters/year of ethanol and 19 million kg/year distiller´s dry grains with solubles (DDGS). The feed to the purification plant (22170 kg/h) is mainly composed by ethanol (10.80 % w/w) and water (88.98 % w/w) with traces of methanol (0.0226 %) and fusel (0.2009 %). A simplified flow diagram is shown in Figure 1.
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Figure 1. Simplified flow diagram of a bioethanol purification plant.
2. Initial Design 2.1. Beer Column The vapour stream leaving the stripping column captures nearly all of the ethanol and components in traces produced during the fermentation step. The minimum energy demand of the process (i.e., minimum reboil ratio) is calculated through the lever arm rule by setting the bottom product as high purity water and the composition of the vapour stream as the corresponding to the vapour in equilibrium with hot wine. In other words, a pinch at the top of the stripping column is considered. In order to obtain a feasible design the following steps are performed: i) determine the maximum feasible separation and minimum energy demand (smin) by applying pinch theory. For this task, it is required an equilibrium calculation that can be performed in a conceptual model framework like DISTIL (Hyprotech, 1999); ii) calculate the reboil ratio s = 1.05 smin; iii) set a value for the number of stages N; iv) simulate a stripping column with reboiler first and then replace the reboiler with steam taking into account the reboiler duty and the latent heat of condensation of steam. This task can be done in a simulation framework like Hysys (Hyprotech, 1999). Few simulations were needed to achieve a quasi-optimal column design with 38 equilibrium stages, a column diameter of 0.9 m, a section pressure drop of 34.7 kPa and a steam flow rate of 3600 kg/h. The values obtained for the number of equilibrium stages and steam demand, together with the composition of ethanol in the outlet stream (51.52 % w/w) agree well with results presented in Kwiatkowski et al. (2006). 2.2. Hybrid Column As a multicomponent system formed by ethanol and water with traces of methanol and fusel is to be separated into a single column, a three steps conceptual design and rigorous simulation process is proposed. First, ethanol and methanol are lumped into one pseudo-component in order to obtain a first estimation of steam flow rate, number of stages necessary to separate an ethanol-rich stream from a fusel-rich stream, feed stage and side stream location (DISTIL). After rigorous simulation of the quaternary mixture in Hysys, separation between a methanol-rich stream and an ethanol-rich stream is considered by taking into account the distillation line departing from the composition of the distillate (DISTIL). Finally, both columns are integrated into a single one (Hysys). 2.2.1. Side-Stream Column In order to obtain a feasible design the following steps are performed: i) calculate smin(t) for the separation ethanol/water/1-pentanol (DISTIL), ii) estimate the number of
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equilibrium stages Nstages(t), feed stage Nfeed(t) and side stream location NSide Stream(t) for s(t) > smin(t) (DISTIL), iii) simulate the quaternary system (Hysys) for the design and operating variables obtained in step ii), iv) calculate the steam flow rate Vsteam(q) through the energy balance and simulate the column without reboiler (Hysys), v) simulate the system side-stream column plus decanter and water-rich phase recycle (Hysys). Table 1 presents the results of the conceptual design performed in DISTIL (steps i) and ii)) for the ternary mixture ethanol/water/1-pentanol, with the last component used to approximate the behaviour of a fusel component. Compositions of both ethanol and fusel in the bottom stream were selected taking into account the behaviour of the residue curve (DISTIL) corresponding to the liquid in equilibrium with the vapour feed in the neighbourhood of water vertex. As both for the ternary and quaternary mixture, the residue curve approaches the water vertex with compositions of ethanol above the mole fraction of fusel, the selected bottom composition reflects this behaviour. Figure 2(a) shows the corresponding composition profile in the composition simplex. The figure also shows a distillation boundary departing from the azeotrope ethanol-water and ending at the hetero-azeotrope water-fusel. The side stream is located inside the liquidliquid gap as this stream will be separated in a decanter into a fusel-rich phase (feed to the fusel plant) and a water-rich phase (recycle to column). Table 1. Results for the ternary system ethanol/water/1-pentanol (DISTIL).
Product Compositions, r, s and N Feed (vapor) Distillate Side Stream Bottom Rmin(t) / Smin(t) R(t) / S(t) Nstages(t) [including condenser and reboiler] Nfeed(t)/ NSide Stream(t)
[0.29798, 0.699132, 0.002888] [0.74144, 0.25850, 6.0 E-05] [0.05115, 0.91442, 0.03443] [9.6 E-06, 0.99999, 4.0 E-07] 2.839 / 1.00 2.839 / 1.00 17 [0 + 1-15 + 16] 4/11
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Figure 2. (a) Internal profile in the composition simplex corresponding to the base design with phase separator and water-rich phase recycle (Hysys); (b) Distillation lines corresponding to the distillate composition of the methanol column. System methanol/ethanol/water+1-pentanol at 101.3 kPa (DISTIL).
It is noteworthy that minimum reboil ratio for the given separation does not require an infinite number of stages. This behaviour can be explained in terms of bifurcation of adiabatic profiles and it will be subject of further analysis in a next contribution.
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2.2.2. Methanol Column and Hybrid Column The distillate stream of the side-stream column contains small amounts of methanol that must be separated from ethanol to agree with stringent quality standards (0.1 % V/V methanol in dehydrated ethanol at 20 oC). At a first glance, this separation could be performed in another distillation column. A different alternative would be to integrate this column with the side-stream column. The distillate line (DISTIL) corresponding to the distillate composition of the side-stream column shown in Figure 2(b) resembles the behaviour of the internal profile at total reflux and it can be considered as a good approximation to the actual operation of the methanol rectifying column, as the distillate flow rate of this column is low enough to produce a high reflux ratio. Therefore, it is possible to estimate the optimal number of stages in the rectifying section of the hybrid column as the number of trays necessary to separate the methanol in excess from the ethanol-rich stream. As shown in Figure 2(b), the methanol-rich distillate stream will also contain small amounts of ethanol and water due to the distillation line running from pure methanol to ethanol-water azeotrope. Figure 3 shows the internal profile in the composition tetrahedron after simulation of the hybrid column in Hysys. A loss of about 0.18 % w/w of ethanol in methanol-rich distillate occurs. The side streams are located near the maximum in ethanol (ethanolrich stream, 88.98 % w/w) and fusel (fusel-rich stream, 18.5 % w/w), respectively. The column has 35 equilibrium stages, a column diameter of 1.372 m, a section pressure drop of 11.8 kPa and a steam flow rate of 1800 kg/h. The vapour ethanol-rich stream is diverted to the first effect of the evaporation sector to provide heating while minimizing the steam demand of the plant. The condensed ethanol-rich stream is then fed to the pervaporation sector to remove the excess water. 250
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Figure 3. Internal profile in the composition tetrahedron corresponding to the hybrid column with phase separator, fusel plant and pervaporation sector.
Figure 4. Overall investment and operating costs for the two distillation columns and pervaporation sector versus ethanol mole fraction in the distillate of the hybrid column.
2.2.3. Fusel Plant and Pervaporation Sector The fusel-rich stream leaving the decanter is fed to the fusel sector where the stream is washed with water to recover about 96 % of the incoming ethanol. The resulting waterrich stream is recycled to the hybrid column. To do this, an overall amount of 363 kg/h wash-water and seven separation steps are necessary. The conceptual design of a crossflow operation is performed using DISTIL, while process simulation is done in Hysys. A conceptual design of pervaporation (PVA/PAN MOL 1140 membrane by GFT, Germany) following the model proposed by Vier (1995) and Bausa and Marquardt (2000) was implemented in Delphi environment (Borland, 1997) to determine pseudo
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optimal operating values for both maximum temperature (90 oC) and permeate pressure (2.026 kPa). The model was also implemented in Hysys as a user operation extension, which calculates the required membrane area areq as areq =1.25 amin (Bausa and Marquardt, 2000). Both heat and refrigeration duties are calculated in Hysys from the energy balance. Behaviour of trace components is taken into account by using wateralcohol separation factors. Approximate values were taken from D. Van Baelen et al. (2005). High purity bioethanol (99.5 % v/v) is obtained with an actual membrane area of 930 m2, while the water-rich permeate is recycled to the hybrid column. 2.2.4. DDGS Plant The coproduct plant is formed by a decanter centrifuge which separates the bottom stillage from the beer column in a wet cake (35 % solids, 2683 kg/h water) and a thin stillage (18443 kg water/h). Approximately 4626 kg water/h is recycled into the second step of the liquefaction process, while 13817 kg water/h is feed to a three-effect evaporator. The resulting syrup (35 % solids, 1287 kg water/h) is mixed with the wet cake coming from the centrifuge and sent to a rotary drum dryer. While the multiple effect evaporator is simulated in Hysys, only mass and energy balances for the dryer are incorporated in Hysys. The conceptual design of the dryer is performed according to the method presented in Ulrich and Vasudevan (2004) and data from National Corn-To Ethanol Research Center (2005-2007). Table 2 summarizes the investment and operation costs of the DDGS sector. The operation cost of 35.9 $/ton DDGS agrees well with the value reported by Batelle Memorial Institute (2005). Table 2. Operation ($/ton DDGS) and Investment ($) Cost corresponding to DDGS plant. [*] kg natural gas/ kg of water evaporated. [**] Overall operating costs = 34.55 $/ton DDGS Item
Characteristics
Rotary Dryer
D [m]= 1.664 L [m]= 13.31 IJ [min]= 19.6 rpm= 2.869 Qair [kg/h]= 39150 ȘNat. Gas = 0.048 [*] Areaoverall[m2]= 940 Pressure[kPa]= from 10-30 kPa Qsteam [kg/h]= 2700
Evaporator
Decanter Centrifuge
Invest./Op. Cost Ulrich & Vasudevan 1.39 E06/19.74
Invest./Op. Cost [**]; Batelle M. I. [***] 1.57 E06
1.523 E06/16.16
1.47 E06
1.07E06[***]/not calculated
1.07 E06
3. Evolutionary Optimisation Once an initial design is obtained, the following improvement opportunities were tested: i) design of the beer column in the neighbourhood of minimum energy demand (done from the very beginning of design process), ii) heat integration between the hybrid column and evaporation first effect (1270 kg/h of steam are saved), iii) heat recovery from the hot air leaving the dryer (saving 0.014 kg natural gas/kg water evaporated). Finally, a change in distillate composition of the hybrid column is proposed in order to capture the trade-offs between distillation and pervaporation costs. Resorting again to the conceptual design of the hybrid column for a set of distillate compositions, results
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shown in Figure 4 are obtained. The decrease of investment costs for distillate compositions richer in ethanol is related to a decrease in the membrane area needed to obtain dehydrated bioethanol (areq=848 m2). Table 3 shows both investment and operating costs of the quasi-optimal plant. All cases include improvements i), ii) and iii) mentioned above. Investment and operation costs are reduced by 6.64 % with respect to the base case and by 11.48 % with respect to the worst case analyzed. Cost coefficients used to obtain the reported values are Csteam=2.396E-2, Cwater=5.73E-3, Crefr=3.824E-2, Celectr=0.08 all in [$/kWh], Cnat gas=289 $/tn, C memb repl = 400 $/m2. Table 3. Overall costs for a bioethanol plant producing 24 million liters/year. The facility considers both the ethanol and co-product processing plants. DDGS Plant Separation Total
Investment, $ 3.985 E+06 3.768 E+06 7.753 E+06
Operating $/h 96.37 117.96 214.33
Investment, $/h 81.07 76.66 157.73
Total, $/h 177.44 194.62 372.06
4. Conclusions A cost effective design for a bio-ethanol separation plant using conceptual design followed by rigorous simulation is found. The minimum in the operation costs corresponds to a minimum in the steam flow rate of the hybrid column (1600 kg/h). The minimum in steam flow rate can be only explained by the presence of the fusel component, which influences both the energy demand and feasible products of the process. Therefore, designs based on the binary system ethanol-water do not represent the system behaviour in an accurate way.
5. Acknowledgements This work was supported by UNL, UNS, CONICET and ANPCyT from Argentina.
References Batelle Memorial Institute, Pacific Northwest Division, 2005, Quantifying Biomass Resources for Hydrothermal Processing II. Bausa, J. and W. Marquardt, 2000, Shortcut Design Methods for Hybrid Membrane/Distillation Processes for the Separation of Nonideal Multicomponent Mixtures, Ind. Eng. Chem. Res., 39, 1658-1672. Borland International Inc., 1997, Scotts Valley, USA, Delphi 3 User Manual. Hyprotech Ltd., 1999, Calgary, Canada, Hysys & Distil User Manuals. Kwiatowski, J. R; McAloon, A. J.; Taylor, F. and D. B. Johnston, 2006, Modeling the Process and Costs of Fuel Ethanol Production by the Corn Dry-Grind Process, Industrial Crops and Products, 23, 288-296. National Corn-To Ethanol Research Center, 2005-2007, Utilizing the National Corn-to-Ethanol Pilot Plant to Develop a Predictive Model for Distillers Dried Grain for the Fuel Ethanol and Animal Feed Industries. Ulrich, G. D. and P. T. Vasudevan, 2004, Chemical Engineering Process Design and Economics, A practical guide. 2nd ed., Process Publishing, Durham, New Hampshire. Van Baelen, D.; Van der Bruggen, B.; Van den Dungen, K.; Degreve, J. and C. Vandecasteele, 2005, Pervaporation of water-alcohol mixtures and acetic acid-water mixtures. Chemical Engineering Science, 60, 1583-1590. Vier, J.,1995, Pervaporation azeotroper wässriger und rein organischer StoffgemischeVerfahrensentwicklung und –integration, Ph. D. Thesis, Institut für Verfahrenstechnik, RWTH Aachen, Shaker Verlag, Aachen, Germany.
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Improvement of Operating Procedures through the Reconfiguration of a Plant Structure Satoshi Hoshino, Hiroya Seki, Tomoya Sugimoto, Yuji Naka Chemical Resources Laboratory, Process Systems Engineering Division, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku Yokohama 226-8503, Japan
Abstract In this paper, we aim to improve operating procedures through the reconfiguration of an existing chemical plant structure from the viewpoint of process safety and operability. For this purpose, we first structurize, i.e., decompose and modularize, the correspondence relation between the whole plant structure and the operating procedures with the use of a CGU (Control Group Unit) as the unit. Then, we manage information regarding the order relation of the operations among different CGUs by using a proposed CGU coordination. In this way, it is possible to improve the operating procedures by simply assessing and designing an operation or operating procedure within a CGU that needs to be modified. As an industrial example, we examine a startup procedure for an HDS (hydrodesulfurization) plant. Keywords: Process Design; Plant Reconfiguration; Operating Procedure; Improvement.
1. Introduction The structure of a chemical plant and process operating procedures at the plant have to be designed on the basis of careful assessment of the process safety and operability. Similarly, for an existing plant, from the viewpoint of the two criteria mentioned above, the plant structure or operating procedures have to be modified as necessary. To address this issue, we have proposed a plant structurization methodology based on the ANSI/ISA-88 standard (abbreviated as S88) [1] [2]. Furthermore, we have introduced the concept of a CGU (Control Group Unit) as the unit; finally, we have decomposed and modularized the correspondence relation between plant structure and process operating procedures [3] [4]. Here, the CGU is an inventory control unit that is defined as a plant area surrounded by control valves [4]. However, in the event that the process operations spread across different CGUs, to assess the process operating procedures from the viewpoint of safety and operability, we have to manage information regarding the order relation of the process operations as well as the structurization of the correspondence relation. To do so, in this paper, we provide a framework for the remedial design of the plant. As an industrial example, we examine a start-up procedure for an HDS (hydrodesulfurization) plant.
2. Related Studies So far, related studies, which have addressed the process operating procedures in a chemical plant, have mainly focused on the automatic generation of operating procedures. Rivas et al. have proposed a method to generate a procedure for valve operation by composing operation goals hierarchically [5]. Kinoshita et al. have solved the automatic generation of the operating procedures as the state transition problem [6]. Lakshmanan et al. have developed a program to generate the operating procedures with
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the use of a partial planner [7] [8]. Naka et al. have proposed a design methodology that automatically generates the operating procedures by changing the plant topology [9]. However, these related works have not focused on the generation of the process operating procedures in consideration of the correspondence relation with the plant structure. Furthermore, no study has taken into account the order relation among different CGUs. These are the challenges in this paper.
3. Framework for the Improvement of Operating Procedures 3.1. Approach In this paper, we propose and apply the CGU coordination to manage information regarding the order relation of the processes that spread across the different CGUs. By using the CGU coordination, it is possible to assess the process safety and operability in the CGUs. The detailed approach is described as follows: 1. Structurization of the correspondence relation between the plant structure and process operating procedures with the use of the CGU. 2. Careful assessment of each CGU from the viewpoint of process safety and operability. 3. Improvement of a process if necessary as a result of step 2. 4. Management of information regarding the order relation of the process operating procedures among different CGUs. 5. Integration of information and generation of the whole operating procedure. 3.2. CGU Coordination In designing chemical processes on the basis of the procedural control model with the use of the current PFC (Procedural Function Chart defined in the S88), we have to take into account the order relation of the processes among different CGUs. On the other hand, in our design framework, we simply consider the order relation of the operating procedures in each CGU by only using the CGU coordination. That is to say, plant designers are able to assess process safety and operability and design the operating procedures by focusing on a CGU unit only. In order to manage information regarding the order relation of the processes spread across the different CGUs, it is necessary to identify the following information, which is yielded by a conditional transition in a CGU: • end information of the operation in another CGU; and • similar information to the operation in another CGU. For the purpose described above, we have to distinguish the conditional transition from other conditional transitions. Moreover, CGU coordination requires having information. Therefore, in this paper, we contrive several symbols in addition to the conventional PFC. Figure 1(a) shows a symbol of the conditional transition. The operation and conditional transition indicated with the symbol shown in Fig. 1(a) are described in the CGU coordination as shown in Fig. 1(b) and Fig. 1(c). Figure 2 shows an example of the procedural control model, which consists of four CGUs in a continuous process described with the use of the contrived symbols. Thus, it is possible to identify the CGU, in which an operating procedure is executed by painting a color (light blue) on the CGUs that need to be operated. First off, the CGU coordination begins to execute operations from the start symbol; then, the end symbol is executed after all operations are done. As for the conditional transitions indicated by the symbol shown in Fig. 1(a), these conditions depend on the conditions in other CGUs. To manage information, the CGU coordination checks if the conditional transitions, which are depicted by Fig. 1(a), are met.
Improvement of Operating Procedures Through the Reconfiguration of a Plant Structure
(a)
(b)
243
(c)
Fig. 1 Further symbols described in the CGU coordination
Fig. 2 An example of a procedural control model and CGU coordination
3.3. Integration of Operation Procedures The integration process of the generated operating procedures for the CGU with the use of the CGU coordination is described as follows: Step 1. Integration of phases that are described with a tag, e.g., TRx, SAMEx, and IFx. Step 2. Checking of conditional transitions shown with an ellipse. Step 3. Indication of the executable phases in each CGU. Step 4. Connection of the indicated phases from the top to the bottom in sequence. Step 5. Execution of the end symbols as a parallel operation at the same time.
4. Case Study 4.1. HDS Plant As an industrial example, we examine a start-up procedure for an HDS (hydrodesulfurization) plant (see the detailed PDF (Process Flow Diagram) in [1] [2]). Figure 3 shows a simplified schematic of the HDS plant divided into four CGUs. Blended diesel oil which flows from the FSD (Feed Surge Drum) is mixed with H2-rich gas and heated by the RCF (Reactor Charge Furnace); after passing through the reactor, the reactor effluent is separated into gas and liquid at the HPS (High-Pressure
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Separator); H2S in the separated gas is absorbed in the amine scrubber, and the remaining H2 is recycled. The liquid is sent to the LPS (Low-Pressure Separator). Figure 4 shows the structurized process operating procedures for the existing operating procedures with the use of the proposed procedural control model. In Fig. 4, ‘Procedure,’ ‘Unit Procedure,’ and ‘Operation’ are shown.
Fig. 3 HDS plant decomposed and modularized by assigning the CGUs
4.2. Assessment of the Existing Operating Procedures For the design of operator-friendly operating procedures, it is necessary to simplify them. Furthermore, an operation should not be controlled in a CGU that is not directly involved. From the assessment result of Fig. 4, we conclude that the operations colored in gray, such as ‘gas circulation,’ ‘catalyst activation,’ and ‘rising temperature,’ present problems, as indicated in the following: • Gas circulation: although this is an operation that aims at the reactor circuit in the CGU 2, it is also included in CGU 4. • Catalyst activation: although this is an operation, which aims at the reactor in the CGU 2, it is also included in CGUs 1, 3, and 4. • Rising temperature: although this operation aims at the RCF in CGU 2, it is also included in CGU 4. 4.3. Improvement of the Operating Procedures For the problems mentioned in 4.2, we improve the operating procedures, i.e., CGUs and operations, as follows in consideration of process safety and operability. • Gas circulation: we remove the operation executed in CGU 4. For this purpose, we also remove the phase, ‘start the air cooler,’ in CGU 4. This phase has to be executed before the heated diesel oil in the RCF flows into CGU 4. • Catalyst activation: we remove the phases in CGU 1, ‘transfer the diesel oil to the reactor’ and ‘add the sulfide,’ the phase in CGU 3, ‘pressurize the LPS,’ and the phases in CGU 4, ‘pressurize the SOrec’ and ‘transfer the product diesel oil to the output tank.’ Moreover, as a new operation, we add the operation, ‘feed the diesel oil
Improvement of Operating Procedures Through the Reconfiguration of a Plant Structure
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to the reactor circuit,’ into CGU1. Then, the phase ‘add the sulfide’ in CGU 1 is moved into CGU 2. This modification results in the reconfiguration of a part of the plant structure002E The phases in CGUs 3 and 4, ‘pressurize the LPS’ and ‘pressurize the SOrec,’ are moved into the operation ‘initial charge’ in CGU 2. The operation, ‘catalyst activation,’ in CGU 3 is changed to ‘generation of the on-spec product’ through the LPS. • Rising temperature: we remove all operations executed in CGU 4. These operations are changed to the operation ‘generation of the on-spec product.’ The operation, ‘initial charge,’ in CGUs 3 and 4 is incorporated into the operation, ‘generation of the on-spec product.’ Figure 5 shows the improved operating procedures. Finally, this plant is able to be in a stable state after the operation ‘initial charge’ in CGUs 3 and 4 is executed. The operations shown in color are executed at the same time in each CGU.
Fig. 4 Structured description of the operating procedures of the HDS plant
5. Conclusions and Future Studies In this paper, for an existing chemical plant, we improved the operating procedures in terms of process safety and process operability. We structurized the correspondence relation between the whole plant structure and the operating procedures with the use of the CGU. After that, for the structurized correspondence relation between the plant structure and the operating procedures, we managed information regarding the order relation of the operations among different CGUs by using the proposed CGU coordination. As an industrial example, we examined a start-up procedure for the HDS plant, and, finally, we showed the improved operating procedures by simply assessing and designing an operating procedure within a CGU that needs to be modified.
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Fig. 5. Improved operating procedures (Procedure, Unit Procedure, and Operation)
References 1. 2.
3. 4.
5. 6.
7.
8.
9.
Instrumentation, Systems, and Automation Society, 1996, ANSI/ISA-88.01-1995 Batch Control Part 1: Models and Technology, ISA, Research Triangle Park, USA. Instrumentation, Systems, and Automation Society, 2001, ANSI/ISA-88.02-2001 Batch Control Part 1: Data Structures and Guidelines for Languages, ISA, Research Triangle Park, USA. H. Seki, S. Hoshino, T. Sugimoto, and Y. Naka, 2007, Structured Description of Operating Procedures for Continuous Chemical Processes, (submitted to PSE Asia, China). Y. Naka, H. Seki, S. Hoshino, and K. Kawamura, 2007, Information Model And Technological Information - Infrastructure For Plant Life Cycle Engineering, ICheaP-8 The eight International Conference on Chemical & Process Engineering. J. R. Rivas and D. F. Rudd, 1974, Synthesis of Failure-safe Operations, AIChE Journal, Vol, 20, No. 2, pp. 311-319. A. Kinoshita, T. Umeda, and E. OShima, 1982, An Approach for Determination of Operational Procedure of Chemical Plants, Proceedings of the International Symposium on Process Systems Engineering, pp. 114-120. R. Lakshmanan and G. Stephanopoulos, 1988, Synthesis of Operating Procedures for Complete Chemical Plants - I. Hierarchical, structured modeling for nonlinear planning, Computers and Chemical Engineering Vol. 12, No. 9/10, 985-1002. R. Lakshmanan and G. Stephanopoulos, 1990, Synthesis of Operating Procedures for Complete Chemical Plants - III. Planning in the presence of qualitative mixing constraints, Computers in Chemical Engineering, Vol. 14 No. 3, pp. 301-17. Y. Naka, M.L. Lu, H. Takiyama, 1977, Operational Design for Start-up of Chemical Processes, Computers Chem. Engng, Vol. 21, No. 9, pp. 997-1007.
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Graph-theoretic Approach to Optimal Synthesis of Supply Networks: Distribution of Gasoline from a Refinery Young Kim,a,b L.T. Fan,b Choamun Yun,a Seung Bin Park,a Sunwon Park, a,* Botond Bertok,c Ferenc Friedlerc a
Department of Chemical and Biomolecular Engineering, KAIST, Daejeon 305-701, Korea b Department of Chemical Engineering, Kansas State University, Manhattan, KS 66506, U. S. A. c Department of Computer Science, University of Pannonia, Egyetem u. 10, Veszprem, H-8200, Hungary
Abstract The synthesis of a supply network is profoundly convoluted because of its combinatorial complexity. Global or even near optimal solutions are, more often than not, unobtainable through the heuristic methods. On the other hand, the majority of the algorithmic methods, which mainly resort to mixed integer programming, in theory, can give rise to global optima; however, they are effective only for relatively minute networks. Obviously, it is highly desirable that a novel paradigm be established for optimally synthesizing supply networks; the adoption of the graph-theoretic method based on P-graphs (process graphs) is proposed herein for the synthesis of optimal supply networks. The proposed method is illustrated with examples. Each example has yielded simultaneously the optimal and near optimal structures of the supply network performing a specific task in the ranked order. The example reveals a unique feature of the method. Keywords: Supply network; graph-theoretic; P-graphs; optimal synthesis
1. Introduction The optimal design, i.e, synthesis, of a supply network tends to be profoundly convoluted because of its combinatorial complexities. Thus, excessive time and effort are often required for formulation and computation except for some cases [1]. As a result, a limited number of papers has been published on this subject [2, 3]. Furthermore, the majority, if not all, of the published papers adopts algorithmic methods to carry out the optimization of algebraic models via mixed integer programming (MIP). An approach proposed herein for the optimal synthesis of supply networks resorts to the unique graph-theoretic method based on process graphs (P-graphs) originally developed for process-network synthesis [4-8]. The approach is demonstrated by applying it to the optimal supply-network design for a fuel product, i.e., gasoline, from a refinery.
*
To whom correspondence should be addressed. E-Mail:
[email protected]
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Gasoline produced from crude oil is conveyed through a supply network to markets; obviously, gasoline is a material for which the law of mass conservation is universally valid. This material can be regarded as the raw material entering into the network or the final product exiting from the network. Any actions imposed on or disturbances affecting the material conveyed through the network will induce a change in one or more of its attributes, such as static pressure, flowrate, lot size, and/or locations, thereby transforming the material. Upon reaching the markets or retailers through a series of these transformations, the material can be regarded as the final product exiting from the network. Thus, operating, i.e., functional, units can be unequivocally identified at locations of such actions or disturbances. Naturally, the networks can be represented as P-graphs. One of the two cornerstones of the current graph-theoretic method for process-network synthesis is obviously the representations of the operating units with these P-graphs. The other is a set of 5 axioms of combinatorially feasible process networks [5, 6]. These 5 axioms give rise to 3 highly efficient algorithms for implementing the method. The profound efficacy of the proposed approach is demonstrated with two examples of gasoline manufactured at a refinery and supplied to retailers through distribution networks containing various terminals.
2. Methodology The present methodology comprises the following: (a) representing all the plausible operating units identified in terms of P-graphs; (b) composing the maximal structure from the P-graphs of the operating units via algorithm MSG (maximal structure generation); (c) generating exhaustively the combinatorially feasible network structures as solution-structures from the maximal structure via algorithm SSG (solution-structure generation); and (d) identifying all the feasible network structures among the combinatorially feasible network structures via MIP or, alternatively, determining only a limited number of the optimal and near optimal networks, in the ranked order of the objective function, directly from the maximal structure via algorithm ABB (accelerated branch and bound) [4-6, 9] 2.1. P-graph representations of operating units The structure of a supply network, visualized as a process network, is represented by Pgraphs, which are unique bipartite graphs. Unlike conventional bipartite graphs, or digraphs, the P-graphs are capable of capturing the syntactic and semantic contents of process networks. A P-graph comprises two types of vertices or nodes for representing materials and operating units; the former is symbolized by circles, and the latter, by horizontal bars. Table 1, to be elaborated later, illustrates the conventional as well as Pgraph representations of operating units. 2.2. Implementation of algorithms At the outset, the maximal structure of the gasoline-supply network, playing the role of process network, is composed via algorithm MSG with the P-graphs of all the operating units at its input. This algorithm totally excludes any combinatorially infeasible network structure in light of the five axioms in constituting a supply network. Thus, the maximal structure is the rigorous, minimally complex super-structure containing exclusively and exhaustively the combinatorially feasible network structures. Subsequent to the generation of the maximum structure, the combinatorially feasible network structures are exhaustively recovered as the solution-structures by resorting to algorithm SSG. Each solution-structure signifies a combinatorially feasible network of pathways linking the raw materials to the products. Nevertheless, not all the solutionstructures are necessarily feasible due to the violation of the mass balances in or around
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the network. The feasibility of an individual solution-structure, i.e., combinatorially feasible network structure, is assessed by optimizing the objective function via MIP subject to the mass-balance constraints. Naturally, this also gives rise to the optimality of the individual feasible network structures. In practice, only a limited number of optimal and near optimal structures would be of interest. Such network structures can be determined in the ranked order in terms of the objective function by means of algorithm ABB directly from the maximal structure. The objective function can be, profit, cost, sustainability, speed of supply, or any combination thereof.
3. Illustration The proposed approach is illustrated with a supply network to deliver gasoline from a refinery to one or two terminals through various routes by two means of transportation, i.e., pipelines and tanker-trucks. The optimal and near-optimal networks in the ranked order of cost are obtained for the two examples, one depicted in Figure 1 and the other depicted in Figure 2. Conventional and P-graph representations of an operating unit identified are provided in Table 1 as an example.
Figure 1 Gasoline supply from a refinery to a
Figure 2 Gasoline supply from a refinery to
terminal (Example 1).
two terminals (Example 2).
Table 1. Conventional and P-graph representations of an operating unit: gasoline loading on trucks Operating units No
Designation
Function
Streams
Diagrammatic representation Conventional
P-graph
Notation
S1-2 [G1]
Loading of gasoline on 4
DT1
trucks at distribution terminal 1
Description Gasoline supplied to DT1 Trucks
DT1([G1],[T]) =
S5-2 [T]
supplied to DT1
4
[G T]
Gasoline S4 [G4T]
loaded on trucks
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3.1. Example 1 Gasoline is transported from one refinery to a single terminal through a pipeline or by tanker-trucks; see Figure 1. The empty tanker-trucks are returned to the refinery to be reloaded for the succeeding delivery. The feasible network structures vary depending on the operating costs and capacity constraints of the pipeline and tanker-trucks. The resultant combinatorially feasible as well as feasible network structures are presented in Tables 2 and 3 for two sets of capacity constraints. Table 2. Combinatorially feasible and feasible networks for Example 1
N1* {1,2,3,6,f1}
Optimal value of objective function ($/month) 29
N2 {1,2,3,4,5,7,f1}
N2* {1,2,3,7,f1}
31
2
N3 {1,4,5,8,f1}
N3* {1,4,5,8,f1}
34
3
Combinatorially feasible networks {operating units} N1 {1,2,3,6,f1}
Feasible networks {operating units}
Rank 1
N4 {1,2,3,4,5,6,7,f1} N5 {1,2,3,4,5,6,8,f1} N6 {1,2,3,4,5,7,8,f1} N7 {1,2,3,4,5,6,7,8,f1} Table 3. Combinatorially feasible and feasible networks for Example 1 (Min. flowrate of S1-1 and S1-2 = 1)
Combinatorially feasible networks {operating units} N1 {1,2,3,6,f1} N2 {1,2,3,4,5,7,f1} N3 {1,4,5,8,f1}
N1* {1,2,3,6,f1}
Optimal value of objective function ($/month) 29
N2* {1,2,3,4,5,7,f1}
34
2
N3* {1,4,5,8,f1}
34
2
N5* {1,2,3,4,5,6,8,f1}
35
4
Feasible networks {operating units}
Rank 1
N4 {1,2,3,4,5,6,7,f1} N5 {1,2,3,4,5,6,8,f1} N6 {1,2,3,4,5,7,8,f1} N7 {1,2,3,4,5,6,7,8,f1} 3.2. Example 2 Unlike Example 1, two terminals are involved in this example; however, gasoline is supplied to the second terminal only by tanker-trucks as depicted in Figures 2 and 3. Empty tanker-trucks from the two terminals are considered to belong to the same materials in the network. They are returned to the refinery to be reloaded for the succeeding delivery; 72 combinatorially feasible network structures have been
Graph-Theoretic Approach to Optimal Synthesis of Supply Networks
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identified for this example, which, in turn, have yielded 4 feasible networks presented in Table 4.
Figure 3 Process flowsheet of Example 2. Table 4. Feasible networks for Example 2
Optimal value of Rank
objective function ($/day)
Feasible networks {operating units}
1
103
N1* {1,2,3,6,11,12,13,16,f1,f2}
2
105
N2* {1,2,3,6,9,10,11,14,f1,f2}
3
110
N3* {1,4,5,8,9,10,11,14,f1,f2}
4
120
N4* {1,4,5,8,11,12,13,16,f1,f2}
4. Discussion The efficacy of adopting the current graph-theoretic method based on P-graphs for systems, which are not traditionally regarded as process networks, such as supply networks, has been amply demonstrated by Halim and Srinivasan [10] in crafting the decision support system for waste minimization. The graph-theoretic method based on P-graphs definitely reveal the structural and operating features of supply networks in unquestionably more details than the conventional algorithmic method based on the MIP. Moreover, the superior computational efficiency of the former over the latter, especially for complex networks, has been unequivocally pointed out [8]. The efficacy of the proposed methodology is demonstrated with the two examples of a gasoline supply network. In Example 1, the combinatorially feasible solutions, i.e., networks, are identified via algorithms MSG and SSG [4~6]. The second columns of Tables 2 and 3 list the feasible networks determined via MIP for all combinatorially feasible networks contained in the first column of each table. Note that not all the combinatorally feasible networks are feasible; moreover, the number of feasible networks identified varies according to the mass constraints imposed as discernable in Tables 2 and 3. Specifically, Table 1 contains the results obtained without any mass flow constraint, and Table 2 contains the results obtained when the minimum mass
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flowrates of streams S1-1 and S1-2 are constrained to be 1. In Example 2, only a limited number of feasible networks satisfying the production requirements are recovered as the optimal or near-optimal networks in the ranked order via algorithms MSG and ABB without resorting to algorithm SSG and MIP [4~6, 9]. It is of utmost importance to simultaneously generate some near-optimal supply networks in the ranked order of the objective-function values along with the optimal one. These near-optimal networks serve as the stand-bys to immediately replace the optimal network in case of interruption arising from man-made catastrophes, e.g., warfare, or natural catastrophes, e.g., wild fires or storms. Such capabilities are totally absent from the MIP-based approaches.
5. Conclusion A highly efficient approach has been proposed for synthesizing, i.e., designing, a supply network for a fuel product. It has been unequivocally demonstrated that such a supply network is a process network, thereby rendering it possible to adopt the graph-theoretic method based on P-graphs (process graphs) for its synthesis. The method yields the optimal as well as near optimal networks simultaneously in the ranked order of a specific objective function, such as profit or cost. The profound efficacy of the proposed approach is amply demonstrated with two examples of supplying gasoline from a single refinery to one terminal in one example and two terminals in the other.
Acknowledgement This work was supported by the Brain Korea 21 project, Korea; and Department of Chemical Engineering and the Institute for Systems Design and Optimization, Kansas State University, U.S.A.
Literature Cited [1] C.H. Timpe and J. Kallrath, Eur. J. Oper. Res., Vol. 126 (2000) 422. [2] M.J. Meixell and V.B. Gargeya, Trans. Res. Part E., Vol. 41 (2005) 531. [3] A.G. Kok and S.C. Graves, Handbooks in operations research and management science, volume 11. Supply chain management: design, cooperation and operation, Elsevier, 2003. [4] F. Friedler, K. Tarjan, Y.W. Huang and L.T. Fan, Chem. Eng. Sci., Vol. 47 (1992a) 1973. [5] F. Friedler, K. Tarjan, Y.W. Huang and L.T. Fan., Comput. Chemeng., Vol. 16 (1992b) S313. [6] F. Friedler, L.T. Fan and B. Imreh, Networks, Vol. 28 (1998) 119. [7] M.S. Peters, K.D. Timmerhaus and R.E. West, Plant Design and Economics for Chemical Engineers, McGraw-Hill, New York, 2003. [8] R. Sargent, Comput. Chemeng., Vol. 29 (2005) 1237. [9] J. Liu, L.T. Fan, P. Seib, F. Friedler and B. Bertok, Ind. Eng. Chem. Res., Vol. 45 (2006) 4200. [10] I. Halim and R. Srinivasan, Ind. Eng. Chem. Res., Vol. 41 (2002) 196.
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Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications Mohamed T. Mahmuda, Iqbal M. Mujtabaa, Mansour Emtirb a School of Engineering, Design and Technology, University of Bradford, Bradford, West Yorkshire, BD7 1DP, United Kingdom. bLibyan Petroleum Institute, P.O.Box 6431Tripoli, Libyan Arab Jamahiriya
Abstract Unlike the past work, this work focuses on optimal design and operation of multivessel batch distillation column with fixed product demand and strict product specifications. Both the vapour load and number of stages in each column section are optimised to maximise a profit function. For a ternary mixture, the performance of the multivessel column is also evaluated against that of a conventional batch distillation column. Although the profitability and the annual capitalised cost (investment) of the multivessel column is within 2-3% compared to those of conventional column, the operating cost (an indirect measure of the energy cost and environmental impact) is more than 30% lower for multivessel column. Thus, for a given separation task, multivessel column is more environment friendly. Keywords: Multivessel Batch Distillation, Fixed Product Demand, Product Sequence, Optimisation.
1. Introduction Batch distillation is an important unit operation used in many chemical industries, and in particular in the manufacture of fine and specialty chemicals. While conventional batch distillation had received much attention, the research in multi-vessel batch distillation (MultiVBD) is handful (Furlonge et al., 1999; Low and Sorenson, 2003, 2005). Furlonge et al. (1999) considered the optimal operation problem for a fixed number of stages (total and in between the vessels). The objective was to minimise the mean rate of energy consumption required for producing products of specified purity while optimizing instantaneous heat input to the reboiler subject to product specifications (amount and purity). Various operating polices such as fixed vessel holdup, variable vessel holdup, etc. have been considered. Optimising the initial distribution of the feed among the vessels reduces the energy consumption by almost 15%. Low and Sorenson (2003) presented the optimal design and operation of MultiVBD column. A profit function based on revenue, capital cost and operating cost was maximized while optimising the number of stages in different column sections, reflux ratio, etc. They compared the performance of MultiVBD with that of conventional batch distillation column for a number of different mixtures and claimed that MultiVBD operation is more profitable. However, for all cases considered in their work, the products specifications and amounts were not matched exactly and therefore the
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conclusion is somewhat misleading. Also, reduced batch time in MultiVBD column was leading to additional production of products compared to that produced by the conventional column. Therefore, the additional profit can only be realised if there is a market demand i.e. if all the products which are produced are saleable. Low and Sorenson (2005) considered the optimal configuration, design and operation of batch distillation column based on overall profitability for a given separation duty. Using rigorous model, the mixed integer dynamic optimisation problem was solved using genetic algorithm. Again for a multicomponent separation case, MultiVBD configuration was chosen as optimum from among the conventional and inverted batch distillation columns. However, strict product specification was not maintained and the vapour load hit the upper bound to minimise the batch time and to maximize the profit. This work also led to unlimited production of products which was not sustainable and the profitability calculations were based on the assumption that all products produced are saleable. Contrary to these works, this research is focused on optimal design and operation of a MultiVBD column producing two desired products from a ternary mixture with fixed yearly product demand and strict product specifications. A profit function is maximised while optimising the number of stages in column sections of a MultiVBD and vapour load to the column. The results (profit, design and operation) are compared with those obtained using a conventional column. Simple process models are developed in gPROMS for both configurations and the optimisation problems are solved using the built in facilities within gPROMS.
2. Process Model Figure 1 shows the schematic of a MultiVBD Column. A dynamic model based on constant relative volatility, constant molar liquid holdup on the stages, total condenser and constant pressure is considered here and are shown in Figure 2. Note, the simple model for the conventional column is taken from Mujtaba (2004) and therefore is not presented here.
V, y
L, x j − 2
j −1
Stage j-1
V, yj
Condenser
V
L, x j −1 Stage j
V, y j +1
Vessel
L, x j Stage j+1
Plates
L
Vessel H f x fi L Reboiler
V
L
L
Fig.1 Multivessel Batch Distillation Column with Connection of Trays and Vessels
Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications
255
Condenser Component Balance:
dx1i V = ( y2i − x1i ) dt Hc
Internal plates, j=2 to (N-1); i = 1 to nc Component Balance:
Vapour Liquid Equilibrium:
dx ji dt
(
)
(
L V x j −1,i − x j ,i y j +1,i − y j ,i + Hj Hj
=
)
α i x j ,i
y j ,i =
nc
¦α x
k j ,k
k =1
Vessel Component Balance:
Hf
dx fi dt
(
= L f x ji − x fi
)
Reboiler Component Balance:
HN
dxN ,i dt
(
)
= L x N −1,i − x N ,i − V ( y N − x N ,i
)
The vapour liquid equilibrium relationship is same as in internal plates with j=N
Fig.2 Model Equations of Multivessel Batch Distillation System
3. Product Demands and Specifications A total of 2555 kmol/yr of Product A with 95% purity (molefraction) and 1214 kmol/yr of Product B with 95% purity (molefraction) are to be produced from 9790 kmol/yr of a ternary mixture (A, B, C) with composition <0.30, 0.20, 0.50> molefraction and relative volatility Į =<8.0, 4.0, 1.0>. Due to high purity demand of Product B, an intermediate off-cut is needed to be produced with no more than 60% purity in component A. Component C is not a valuable product. The maximum capacity of the MultiVBD column is 10 kmol and has 4 vessels including the reboiler and condenser holdup tank (3 column sections). Both conventional and the MultiVBD columns are available for a period of 8000 hrs/yr. The set up time for each batch of operation is 30 minutes. The total number of batches will therefore be 979 per year and the individual batch time would be 7.67 hr. For a batch with 10 kmol feed mixture (B0), the product profiles are calculated using steady state mass balance (Miladi and Mujtaba, 2006) as: Product A = 2.61 kmol/batch (D1); Product B = 1.24 kmol/batch (D2); Intermediate Off-Cut = 0.83 kmol/batch (R1) and Bottom Residue (in the reboiler) = 5.32 kmol/batch (Bf). In MultiVBD column, the products will be produced simultaneously while in the conventional column these will be produced sequentially as shown by State Task Network (STN) in Figure 3. Note, there is an extra middle vessel to produce an off-cut between D1 and D2.
4. Objective Function and Optimisation Problem Formulation The objective function (to maximise) is the profit per year and is defined (Mujtaba, 2004) as follows:
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Product
Feed
D1 T A S K
Bo Initial
R1 D2 Bf
t=0
t = tf
Multivessel Column R1
D1
Bo
Task 1
B1
D2
Task 2
Task 3
B2
Bf
Conventional Column Fig.3 STN for Multivessel and Conventional Column
Profit ($/yr) = P = ( C1 D1 + C2 D2 + C3 D3 − C4 R1 − C5 B0 − OCb ) × Nb − ACC Where, OCb = Operating cost ($/batch) = (K 3 V / A)× (t b − t s ) ACC = Annualised capital cost ($/year), K1 V
0.5
N
0.8
+ K2 V
0.65
(1) (2) (3)
with, K1 = 1,500; K2 = 9,500; K3 = 180; A = 8,000 N b = Number of batches / year = H / (t b + t s ) (4) tb = Batch time (hr); ts = Set-up time = 0.5 hr; H = Production horizon = 8000 h/year C1 = C2 = 20, C3, = C4, = 0 and C5 = 1 are the prices ($/kmol) of the desired products, bottom residue, off-cut, and raw material respectively (taken from Mujtaba, 2004; Mujtaba and Macchietto, 1993). The optimisation problem can be defined as: Given:
Optimise:
Maximise: Subject to:
The column configuration (MultiVBD or Conventional), fixed product demands with strict product specifications (purity), fixed batch time (tb) Number of stages (NS in different column sections for MultiVBD or N in Conventional column), the vapour load (V). In addition, the cut times (ti) and reflux ratio (ri) in each cut of conventional column The total profit (P) Any constraints (model equations, bounds on the variables, etc.)
Mathematically, the problem can be written as:
Max
N S (or N ),V (and ri ,ti )
Subject to:
P
Process Model Equations (Fig. 2) (Equality) Fixed product demands (Equality)
Optimal Design and Operation of Multivessel Batch Distillation Column with Fixed Product Demand and Strict Product Specifications
257
Product specifications (Equality) Bounds on N S (or N ), V , (and ri , ti ) (Inequality) Fixed batch time (Equality) Note, although Furlonge et al. (1999) reported that variable hold-ups in the vessels of MultiVBD reduces energy consumption, in this work, we distributed the feed in different vessels according to the product profiles calculated a priori. Also, for conventional column piecewise constant reflux ratio with two intervals were used for each cut. The above optimisation problem is solved using gPROMS software. Note, for CBD column, two reflux intervals were considered for each cut and the reflux ratio in each interval was assumed to be piecewise constant (Mujtaba, 2004).
5. Results and Discussions The results in terms of optimum number of stages, vapour load, reflux ratio, cut time, etc. are summarised in Table 1 for both columns. The results also show the operating cost per batch, annualised capital cost, profit per batch and per year. For MultiVBD column the total number of stages required is 40% more than that required for the conventional column (CBD). However, the vapour load for the MultiVBD column is about 25% lower compared to CBD and the operating cost (a measure of energy cost) is 30% lower. Finally, the overall profit realised by MultiVBD column is about 3% more that that by CBD column. The product demand and qualities (purities) of each main-cut and off-cut are achieved to the given specifications. Figure 4 shows the product quality at the end of the batch for MultiVBD column in each vessel. Table 1. Summary of the results Configuration
V
Nt
Kmol
OCb
ACC
P
P
$/b
$/yr
$/b
$/yr
CBD
3.0
10
0.55
35795
29.90
29270.8
MultiVBD
2.3
4, 6, 4
0.42
35111
30.72
30080.1
Reflux Ratio Profile for CBD: Main-Cut 1 ( D1) Reflux ratio Switching Time (hr)
Off-Cut ( R1)
Main-Cut 2 ( D2)
0.712
0.819
0.841
0.942
0.660
0.781
0.0-2.10
2.10-3.56
3.56-4.78
4.78-6.21
6.21-6.99
6.99-7.67
6. Conclusions Unlike previous work in MultiVBD column, in this work, the optimal design and operation of MultiVBD column is considered under fixed product demand and strict product quality specifications. Overall product demands, product quality and feed specifications allow calculation of product profiles (amount of each product) of each batch a priori using steady state mass balance calculations. For the given separation task, the MultiVBD column was found to be more profitable than the CBD column. Also the operating cost (an indirect measure of the energy cost
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and environmental impact) for MultiVBD column was more than 30% lower compared to that by CBD. In all cases, product demand and quality are met on specifications. Reflux drum (main cut-1)
Vessel - 1 (off cut-1) 0.7
Composition (mol fraction)
1
Compostion (mol fraction)
0. 9 0. 8 0. 7
x1
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x3
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0. 1
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Time (h)
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
Reboiler (bottom residue) Composition (mol fraction)
Composition (mol fraction)
Vessel - 2 (main-cut-2)
x2 x3 x1
0
2
4
6
Time (h)
8
10
1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0
x3
x1 x2 0
2
4
6
8
10
Time (h)
Fig.4 Composition Profiles of Each Vessel of MultiVBD Column
References H. Furlonge, C. Pantelides and E. Sorensen, 1999, Optimal Operation of Multivessel Batch Distillation, AIChE J, 45, 4, 781-801. gPROMS, (2005), Introductory User Guide, Process System Enterprise Ltd (PSE), http://www.psenterprise.com/gproms/ K. Low and E. Sorensen, 2003, Simultaneous Optimal Design and Operation of Multivessel Batch Distillation, AIChE J, 49, 10, 2564-2576. K. Low and E. Sorensen, 2005, Simultaneous Optimal Configuration, Design and Operation of Batch Distillation, AIChE J, 51, 1700-1713. M. Miladi and I.M. Mujtaba, 2006, Optimisation of design and operation parameters for ternary batch distillation with fixed product demand, Engineering Computations: International Journal for Computer-Aided Engineering and Software, 23, 7, 771-793. I.M. Mujtaba, 2004, Batch Distillation: Design and Operation, Imperial College Press, London. I.M. Mujtaba and S. Macchietto, 1993, Optimal operation of multicomponent batch distillationMultiperiod formulation and solution, Computers & Chemical Engineering, 17, 12, 11911207.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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An Integrated Framework for Operational Scheduling of a Real-World Pipeline Network Suelen Neves Boschetto,a Luiz Carlos Felizari,a Lia Yamamoto,a Leandro Magatão,a Sérgio Leandro Stebel,a Flávio Neves-Jr,a Lúcia Valéria Ramos de Arruda,a Ricardo Lüders,a Paulo César Ribas,b Luiz Fernando de Jesus Bernardob a
Federal University of Technology – Paraná (UTFPR/CPGEI), Av. Sete de Setembro, 3165, 80230-901 – Curitiba, PR, Brazil E-mail {suelen, felizari, lia}@cpgei.cefetpr.br {magatao, stebel, neves, lvrarruda, luders}@utfpr.edu.br b Logistic Division-Research and Development Centre, PETROBRAS-CENPES Rio de Janeiro/RJ, Brazil E-mail {paulo.ribas, lfjb}@petrobras.com.br
Abstract This paper addresses the problem of developing an optimisation structure to aid the operational decision-making of scheduling activities in a real-world pipeline network. During the scheduling horizon, many batches are pumped from (or passing through) different nodes (refineries, harbours or distribution terminals). Pipelines are shared resources operated and monitored 365 days a year, 24 hours per day. Scheduling details must be given, including pumping sequence in each node, volume of batches, tankage constraints, timing issues, while respecting a series of operational constraints. The balance between demand requirements and production campaigns, while satisfying inventory management issues and pipeline pumping procedures, is a difficult task. Based on key elements of scheduling, a decomposition approach is proposed using an implementation suitable for model increase. Operational insights have been derived from the obtained solutions, which are given in a reduced computational time for oil industrial-size scenarios. Keywords: Scheduling, Pipeline Network, MILP, Heuristics, Oil Industry. 1. Introduction Scheduling activities related to oil product distribution have received a growing interest in the last years. Distribution and transfer operations of such products can be carried out by road, railroad, vessels, or pipelines. Pipelines are one of the most important transportation modes for oil products in Brazil. Some papers
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have already addressed scheduling decisions for pipeline networks [1,2,3,4]. In this paper, the considered scenario is particularly complex due to the existence of many areas and pipes subject to particular operational constraints. The proposed approach compares to a previously developed work [5] in terms of complexity and computational performance. This paper is organized as follows. Section 2 presents some operational details of the considered pipeline network. The computational framework, including a global view of the optimisation structure, is given on Section 3. Section 4 shows the new implementation used for the optimisation structure, and Section 5 presents the obtained results with conclusions in Section 6. 2. The pipeline network The considered plant (Fig.1) involves 13 areas (nodes), including 4 refineries (nodes N1, N3, N9, and N11) and 2 harbours (N10 and N13), which receive or send products through 7 distribution terminals. In addition, it includes 29 multiproduct pipelines with particular volumes (e.g. pipe 1 has more than 42000 m3). Nodes are “connected” through pipes (e.g. pipes 3, 4, and 5 connect nodes N2 and N3). A product can take many hours to reach its final destination. A batch can remain in a pipe until another one pushes it. Many pipes can have their flow direction inverted due to operational procedures (e.g. pipes 5, 7, and 15). Each product has to be stored in a specific tankfarm within a node. More than 14 oil derivatives can be transported in this network. Adjacent products can share an undesirable interface, e.g. alcohol pumped just after diesel. In this case, it is necessary to pump another product between them (e.g. gasoline). Typical transfer tasks can involve pumping a batch through many areas. For instance, a batch can be pumped from node N3 to N7 through nodes N2, N5, and N8. In that case, the batch uses pipes 4, 8, 12, and 14. 3. The Computational Framework The computational burden to obtain a short-term scheduling for the considered scenario is a relevant issue. Therefore, a decomposition approach is proposed to address such real-world problem (Fig.2). This decomposition is based on the three key elements of scheduling: assignment of resources, sequencing of activities, and determination of resource timing used by these activities [6]. A Resource Allocation block (batch sequencing) takes into account production and consumption functions and typical volume of batches (lot sizes) in order to determine a set of candidate sequences of pumping. For instance, node N3 usually has a planning of diesel that can be (partially) stored within its limited tankage scenario. However, after some refining time, a batch must be sent, otherwise the diesel campaign has to be reduced due to lack of tankage. The Pre-Analysis gathers information provided by the Resource Allocation and calculates a series of temporal and volume parameters (bounds). Such bounds give a preliminary indication about scheduling feasibility. Then, the PreAnalysis pre-processed data are used by a continuous-time MILP model, which
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determines the operational short-term scheduling for the pipeline network. The MILP model considers, for instance, the pumping route (source or pumping origin, pipes, and destination), volume and flow rate for each product from a source. Particular attention is given to the fact that pipes have a considerable volume and they always operate fulfilled. Thus, they can “store” different products during pumping procedures. While a new product is sent from a source, previously “stored” products are pushed according to the new product flow rate. Moreover, stored products should be routed to their original destination. At each area, products arriving from pipes can be pumped to tanks or routed to other pipes. A set of tanks in each area can store different products. Inventory level can increase or decrease according to the volume and flow rate of each product pumping or due to “local” production and consumption. In addition, the MILP model considers the seasonal cost of electric energy and a series of operational requirements. Details of the obtained scheduling can be visualized by a series of graphical user interfaces (e.g. Fig.3).
Pre-Analysis Scenarios of Production, Consumption
MILP Model
Configuration of Routes, Areas Scenarios of Pipelines, Tanks
Data Base
Scheduling of Operational Activities
Operational Data Electric Energy Cost ...
Fig.1 – Pipeline Network
Resource Allocation (batch sequencing)
Fig.2 – Optimisation Structure
4. The Optimisation Structure 4.1. Pre-Analysis In this work, the continuous-time MILP model previously presented [5] was restructured, and a novel computational procedure (Pre-Analysis) is proposed. The Pre-Analysis uses information provided by the Resource Allocation (batch sequencing) unit. Based on the list of demanded batches supplied by this unit, the Pre-Analysis calculates a series of temporal and volume parameters (bounds). The underlying idea here is to provide structured sequences (not necessarily optimal) in a reasonable computation time. As an advantage of this approach, the computational burden to generate the minimum temporal blocks (pumping and receipt times) is removed from the MILP model. Furthermore, the complexity of the temporal constraints may vary from scenario to scenario,
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and the Pre-Analysis unit aids the description of these constraints included in the MILP optimisation model. During the scheduling horizon many batches may remain stopped within a pipeline, which causes different volumes of products to be effectively received and pumped at each operational area. As an output, the Pre-Analysis specifies the precise volumes to be pumped (volbomb,n,n',d) and received (volrecb,n,n',d) in a destination node. In addition, it establishes, for instance, the minimum time that a destination node could start to receive (tmin_irb,n,n',d) and could finish to receive (tmin_frb,n,n',d) a product (e.g. Eq.(1)). In Eq.(1), average flow rates are known (vzbi,n,n',d and vzbkir,n,n',d) as well as volume of pipes (vpd) and the number of necessary products for a batch to achieve a specific (intermediate) node (kir). Since the exact duration of activities involves pipeline stoppages and a series of operational constraints, these conditions should be addressed by the MILP model. kir 1 kir 1
tmin _ irb,n,n ',d
¦ i 1
volbombi ,n,n ',d vzbi ,n,n ',d
vpd
¦ volbom
bi ,n ,n ',d
i 1
(1)
vzbkir ,n,n ',d
4.2. MILP Model The model relies on MILP with a continuous-time approach. Variables were created in order to determine the exact time that a pumping procedure of a batch (b B) is started (ibb,n,n',d) and finished (fbb,n,n',d) from a node (n n' N) through a specific pipe (d D, where d connects n and nƍ). In a similar approach, other continuous variables determine the time that a destination node starts to receive (irb,n,n',d) and finishes to receive (frb,n,n',d) a product. In order to determine the value of these variables, the parameters tmin_irb,n,n',d and tmin_frb,n,n',d, previously calculated in the Pre-Analysis are used. In particular, the Pre-Analysis unit indicates the minimum pumping and receipt times of a batch. The formulation was extensively studied, and binary variables were used to enforce seasonality conditions of electric energy. Specific constraints were created in order to deal with inventory issues. So that, the MILP model tries to manage the operational scheduling in each node in order to minimize violations on time intervals. Each node has particular operational features, and the mathematical model has to address them. For instance, batches can be pumped from N8 by pipes 11, 14, and 20. At this node there exist a limited number of pumps and just one batch is allowed to be sent from N8 at a specific time. Thus, in a hypothetical case that various batches are to be sent from N8, the model must manage pumping start/finish times in order to respect this “local” characteristic. Another issue is that many pipes can have the flow direction reverted, according to operational convenience. A specific set of constraints was created to manage such operational condition. In the pipeline-scheduling literature (e.g. [3]) this has been proved to be a difficult issue. In addition, from node to node, a product typical flow rate can vary. For example, diesel is normally pumped from source N8 to final destination N1. At this case, the
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product “passes” through the intermediate node N4. The operation involves, respectively, pipes 11 and 6. From N8 to N4 by pipe 11 the average flow rate is 450 m3/h; from N4 to N1 by pipe 6 the average flow rate is 330 m3/h. 5. Results The decomposition framework has been extensively tested in typical operational scenarios. At these cases, the Resource Allocation block takes into account the planning of production/consumption of each product in each node during a month. Then, it determines candidate sequences of pumping. The pre-processed data are used by both the Pre-Analysis and the continuous-time MILP model. Typical instances yield large-scale MILPs. Such models have been solved to optimality in few CPU seconds using a commercial package [7]. To previously address the sequencing part has been a fundamental issue to reduce the computational burden. However, the final scheduling is influenced by the predetermined sequencing. Operational insights have been derived from the obtained solutions, and the proposed approach can aid the decision-making process. Fig.3 illustrates a Gantt chart of a real-world scenario involving approximately 70 batches pumped during a month. Information about scheduled batches can be derived from this chart. To determine such information used to be not trivial since the system operation was based on human experience without computational aid. As a consequence, operational losses were common. In particular, each batch has an identifying number, which remains as the batch passes through different pipes. One contribution of Pre-Analysis is highlighted in the Gantt. This module indicates the exact volume that is to be pumped along the product pumping route.
Fig.3 – Gantt Chart
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6. Conclusions A new optimisation structure (Fig.2) for the scheduling of operational activities in a real-world pipeline network (Fig.1) has been addressed in this paper. In addition, a new computational procedure was developed, the Pre-Analysis module. The real scenario could be addressed mostly due to Pre-Analysis scalability. The considered scenario is particularly complex and involves more nodes and pipes, compared to the one discussed in a previous work [5]. In order to address this scenario, a decomposition approach was used. This decomposition relied on a Resource Allocation block, which takes into account production/consumption functions and typical lot sizes to determine a set of candidate sequences of pumping. Furthermore, a Pre-Analysis block uses candidate sequences to determine temporal and volume parameters. These parameters were used in a continuous-time MILP model, which indeed determines the short-term scheduling of each batch in each node of the pipeline network. The implemented structure can be used, for instance, to identify system bottlenecks and to test new operational conditions. Computation time has remained at few CPU seconds. The proposed approach have allowed that a monthly planning of production and consumption be detailed in short-time scheduling operations within the considered pipeline network. Thus, operational insights can be derived from the obtained solutions. As an ongoing research, the Pre-Analysis would be used to determine other parameters for the MILP model. Acknowledgements The authors acknowledge financial support from ANP and FINEP (PRH-ANP / MCT PRH10 UTFPR) and CENPES (Under grant 0050.0017859.05.3). References 1. R. Rejowski Jr. and J.M. Pinto. A novel continuous time representation for the scheduling of pipeline systems with pumping yield rate constraints, Comp. and Chem. Eng. (2007), doi:10.1016/j.compchemeng.2007.06.021. 2. D.C. Cafaro and J. Cerdá. Dynamic scheduling of multiproduct pipelines with multiple delivery due dates, Comp. and Chem. Eng. (2007), doi:10.1016/j.compchemeng. 2007.03.002. 3. L. Magatão, L.V.R. Arruda and F. Neves-Jr. A mixed integer programming approach for scheduling commodities in a pipeline. Comp. and Chem. Eng., v.28 (2004) pp. 171-185. 4. S. Relvas, H.A Matos, APFD Barbosa-Póvoa, J. Fialho and A.S Pinheiro. Pipeline Scheduling and Inventory Management of a Multiproduct Distribution Oil System. Ind. and Eng. Chem. Res., v.45 (2007), pp. 7841-7855. 5. F. Neves-Jr, L. Magatão, S.L. Stebel, S.N. Boschetto, L.C. Felizari, D.I. Czaikowski, R. Rocha and P.C. Ribas. An Efficient Approach to the Operational Scheduling of a RealWord Pipeline Network. Proceedings of 17th European Symposium on Computer Aided Process Engineering, Elsevier Science, 2007. 6. G.V. Reklaitis. Overview of scheduling and planning of batch process operations. Proceedings of the NATO, Antalya, Turkey (1992) pp. 660-675. 7. ILOG OPL Studio 3.6.1 – User’s Manual. ILOG Corporation, France, 2002.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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An optimization framework of multibed pressure swing adsorption systems Dragan Nikolica, Michael C. Georgiadisb, Eustathios S. Kikkinidesa a
University of Western Macedonia, Department of Engineering and Management of Energy Resources, Sialvera & Bakola Str., 50100 Kozani, Greece,
[email protected],
[email protected] b University of Western Macedonia, Department of Engineering Informatics and Telecommunications, Agiou Dimitriou Park, 50100 Kozani, Greece,
[email protected]
Abstract Pressure Swing Adsorption (PSA) is an energy-efficient alternative to the traditional gas separation processes. This work presents a systematic optimization framework for complex PSA processes including multibed configurations and multilayered adsorbents. The effects of number of beds, PSA cycle configuration and various operating and design parameters on the separation quality and power requirements have been systematically optimized using recent advances on process optimization. The Unibed principle has been adopted relying on the simulation over time of only one bed while storage buffers have been used to model bed interactions. Two industrial multicomponent gas separations have been used to illustrate the applicability and potential of the proposed approach in terms of power consumption minimization and improvement of the product purity and recovery. Keywords: multibed PSA, dynamic optimization, hydrogen production
1. Introduction Separation of gas mixtures by PSA has become a common industrial practice in the area of small to medium scale air separation, small to large-scale gas drying, small to largescale hydrogen recovery from different petrochemical processes and trace impurity removal from contaminated gases. The theoretical modeling and optimization has accompanied the PSA technological development and few studies have been reported in the literature (Nilchan, and Pantelides, 1998, Jiang et al, 2003 and 2004, Cruz et al, 2003 and 2005). As it has been clearly shown the selection of optimal design and operating parameters is a difficult task due to several reasons: a large number of trade-offs between the key variables, large computational requirements to reach the Cyclic Steady State (CSS), and complicated models (large number of partial differential and algebraic necessary to describe multi-scale transport phenomena in adsorbent column and adsorbent particles). In this work, an optimization framework of multibed PSA systems is presented. A generic modeling framework previously presented by the authors (Nikolic et al, 2007) provides the basis for the development of the overall optimization approach.
2. The optimization framework A systematic optimization procedure, to determine the optimal design and operating conditions of a PSA system requires significant computational effort. In order to
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efficiently perform optimization studies, several changes in the existing modeling framework had to be made. The most important one is related to the reduction of the size of the underlying model as all beds are simultaneously simulated. Based on the work of Jiang et al (2004) the Unibed approach has been adopted. The Unibed approach assumes that all beds undergo identical steps so that only one bed is needed to simulate the multibed cycle. Information about the effluent streams (during pressure equalization steps) are stored in data buffers and linear interpolation is used to obtain information between two time points. To this end a gPROMSTM foreign object, VirtualBed, has been developed which imitates the behavior of the real adsorption column, records and restores pressure, enthalpy and composition of the streams. According to the Unibed approach whenever the real column undergoes the pressure equalization step it interacts with one of the VirtualBeds (depending how many pressure equalization steps exist in the PSA cycle).
3. Systematic analysis of the key optimization variables In this work, three different systems have been investigated: I) hydrogen recovery from steam methane reformer off-gas (SMROG) by using activated carbon, II) hydrogen separation from SMROG by using two layered columns (activated carbon and zeolite 5A), and III) nitrogen separation from air by using RS-10 molecular sieve. Due to the high process complexity, a systematic procedure has been followed to identify the most important process parameters and suitable case-dependent objective functions. The procedure relies on a parameter analysis to establish dependencies of input variables (design and operating) as well as their relative importance. To this end, results and important conclusions from several studies published in the literature (Shin and Knaebel, 1988, Nilchan and Pantelides, 1998, Waldron and Sircar, 2000, Jiang et al, 2003, Cruz et al, 2005 etc) have been used. The parameters studied include the particle size, column length and diameter, step times, feed and purge flowrates, distribution of adsorbents in multilayered adsorption columns, number of beds and PSA cycle design have been investigated. The base case parameters have been selected, only one variable at the time has been varied, and the effects analyzed. 3.1.1. Effect of particle size Particle size has a significant influence on the separation quality according to the well known linear driving force (LDF) equation. The LDF coefficient is inversely proportional to square of particle radius. On the other hand, a decrease in particle size increases pressure drop, which results in an earlier breakthrough and degradation of the performance. To tackle this problem Wankat, 1987 used the method of decreasing the adsorbent particle diameter while at the same time keeping the pressure drop constant (that is ratio Lbed/Rp2 = const since ¨P ~ Lbed/Rp2). Such technique resulted in fat, “pancake” column designs (very short columns with large diameter) which are capable to significantly reduce the dimensions of the column and amount of the adsorbent. In the systems under consideration in case studies I and II, a detailed analysis has shown that in the range of particle radius, bed length and diameter and velocities used, a smaller diameter has been always the preferable choice. However, in case study III, a trade-off has been revealed and particle radius was employed as the optimization decision variable. 3.1.2. Effect of column length and diameter Simulation results indicate that as the length-to-diameter ratio (L/D) increases, the product purity increases while recovery passes through the maximum.
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3.1.3. Effect of feed and purge gas pressures An increase in the feed pressure (for a constant amount of feed) imposes an increase in product purity and recovery due to the type of isotherm - adsorbent capacity increases as the pressure increases. On the other hand, an increase in the feed pressure leads to an increase in power needed for compression. To take advantage of potential opportunities (in terms of improving product purity and recovery) offered by complex cycle designs it is necessary to find the optimal feed pressure which ensures feasible pressure equalization steps and co-current depressurization with purge. In other words, to effectively use void gas in the column, the length of unused bed (LUB) has to be high enough to adsorb strong adsorptive components moving towards the end of column during co-current depressurization(s). This ensures that the product leaving the column is completely pure and can be used to repressurize and purge other columns. High LUB can be achieved by interrupting the adsorption step long before the concentration front reaches the end. This can be practically achieved by: (i) decreasing the feed flowrate (in the case of constant length), or (ii) extending the column length (in the case of constant feed flowrate) or (iii) increasing the adsorbent capacity by increasing the feed pressure. In this work, the adsorbent productivity has been kept constant, and the feed pressure is used to control the LUB (since the feed is available at the high pressures, up to 50bar, as the product of steam methane reforming). 3.1.4. Effect of feed flowrate A higher feed flowrate leads to a decrease in product purity and increase in product recovery. In system I both the product purity and recovery are not significantly affected by the feed flowrate mainly due to the high LUB. 3.1.5. Effect of purgeítoífeed ratio The Purge-to-feed ratio (that is purge gas flowrate) is one of the most important operating variables in PSA whose increase leads to an increase in purity and a significant decrease in recovery. It has been employed as an optimization variable in case studies I and III. 3.1.6. Effect of number of beds and cycle design The number of beds and cycle design are important decision parameters because well designed multibed PSA processes offer significant advantages in terms of continuous production and feed consumption, increased product recovery and energy savings. This can be achieved by using co-current depressurization steps (to repressurize and purge other columns), while simultaneously carrying out a number of certain operating steps. For instance, it is possible to repressurize the column by using high pressure product from the adsorption step thus reducing investments in additional equipment such as storage tanks or compressors. The effect of cycle design and number of beds has been analyzed in case study I due to the scale of the process – hydrogen production is a typical large-scale process where a large number of beds and complex configurations are typically employed. On the other hand, air separation is used for small to medium scale production. 3.1.7. Effect of step times In the range of parameters used in case studies I and II step times have negligible effects on product purity and recovery (due to the high LUB, as it is explained earlier). However, in case study III, the effect on process performance is significant. For instance, as the duration of pressurization (by using feed stream) increases, the purity decreases but recovery increases. This can be justified by the increased amount adsorbed during the prolonged step duration, which lowers the purity. The effect on
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product recovery is rather complicated since decrease in purity also decreases recovery but at the same time the product quantity increases in larger rates and the overall effect is an increase in recovery. In addition, longer pressurization s increases the power requirements. Regarding the duration of the adsorption step, longer adsorption times leads to an increase in purity and decrease in recovery. Purge and blowdown step times have similar effects: as the times increase, product purity increases but recovery decreases (longer time allows more impurities to desorb while at the same time more product is loss during the step). The power requirements slightly increase since larger quantities of feed are needed to repressurize the bed. 3.1.8. Effect of carbon to zeolite ratio The results of the analysis agree well with the literature studies (Park et al, 2000): the product recovery increases as the zeolite fraction increase while purity passes through a maximum. In addition, it is noticed that this effect is more important at lower pressures.
4. Case studies Based on the above analysis, three different case studies have been studied. The focus in case study I is on the effect of number of beds and PSA cycle design, in case study II on the effect of carbon-to-zeolite ratio while in case study III all operating variables and column design have been optimised. The general form of the optimization problems being solved is presented in Figure 1.
Figure 1. – The mathematical definition of the optimization problems
All process parameters (base case column geometry, process and adsorption isotherm parameters) have been adopted from the work of Park et al, 2000 (case studies I and II) and Shin and Knaebel, 1988 (case study III). Six different PSA cycle configurations with one, two, four, five, and eight beds have been selected and analyzed. Configuration C1 includes no pressure equalization steps, C2 and C4 include one, C5a and C5b two, and C8 three pressure equalization steps. Configurations C4 and C5b include one additional co-current depressurization step during which the product gas is used to purge other column (the limiting factor is that impurities are not allowed to breakthrough and contaminate purged column). Configurations C4, C5a, C5b, and C8 are properly designed to continuously produce hydrogen (and consume the feed) and to use the part of the pure product from adsorption step to finally counter-currently repressurize other columns (to the feed pressure). Feasible sequence of all operating steps has been automatically generated according our previous work (Nikolic et al 2006).
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The general optimization problems (presented in Figure 1) have been solved by using gPROMS implementation of reduced sequential quadratic programming algorithm and the orthogonal collocation on finite elements of 3rd order with 20 elements have been used to discretize the spatial domain. The typical size of the NLP problem was about 90,000 variables and the CPU time to reach the optimal solution varied from 13 to 50 hours depending on the complexity of the problem and the initial guesses used. 4.1.Case study I: Hydrogen recovery from SMROG The objective is to maximize product recovery for given minimum requirements in product purity (99.99%) while optimizing purge-to-feed ratio (0.5−2.5)*, feed pressure (15-30bar), L/D ratio (3-20) and gas valve constants (during blowdown and pressure equalization steps). All studies have been carried out keeping the cycle time, column volume, and adsorbent productivity constant. This way it was possible to analyze the separation quality for a given minimum purity and different process designs which process the same amount of feed in the same period of time. A comparison of the results between the base case (L/D ratio=5, purge-to-feed ratio=1, feed pressure=25bar, and base case gas valve constants) and the optimized case is presented in Figure 2.
Figure 2. – Optimization results (Case study I)
The results show that product recovery is improved by 7-38% of comparing to the base case design. An interesting result is that there are no significant differences in the process performance of configuration C4 compared to C5a, and C5b compared to C8. Although they include a lower number of beds and one pressure equalization step less, they employ a co-current depressurization step to purge other columns, which results in a significant effect of the process performance. In addition, the optimal feed pressure in C4 and C5b is higher compared to C5a and C8, respectively, due to the larger amount of gas needed to purge compared to the amount of gas spent in the last pressure equalization. This fact may be the limiting factor if the feed is not available at high enough pressure. However, these two effects are strongly depend on the system under consideration and it might not always possible to exploit them. *
the values in the parenthesis indicate upper and lower bounds in the optimization
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4.2. Case study II: Hydrogen recovery from SMROG (double layer) Two scenarios have been analyzed: a) maximization of product recovery for given minimum purity (99.99%) while optimizing carbon-to-zeolite ratio (0-1), and b) maximization of purity for given minimum recovery (30%) while optimizing carbonto-zeolite ratio (0-1). Two adsorbent layers and the same base case parameters as in the case study I (configuration C1) have been used. In case a) the maximal recovery is 40.38% and carbon-to-zeolite ratio 0.54. In case b) the maximal purity is 99.999%, recovery 41.29% and carbon-to-zeolite ratio 0.39. 4.3. Case study III: Nitrogen production from air The objective is to minimize power consumption for given minimum requirements in product purity and recovery while optimizing the feed pressure (300í600kPa); the feed flowrate (0.001í0.003m3STN); purge-to-feed ratio (0.5í2.0); step times for constant cycle time such blowdown (10í20s), adsorption (10í20s; particle radius (0.2í1.5mm); column length-to-diameter ratio (5í15) for constant column volume. ), It should be noted that purge time is calculated based on the total cycle time. Configuration C1 has been used and pressurization is done co-currently by using the feed stream. The optimization indicate a product purity of 99.99%, recovery of 5.06%, length-todiameter ratio 5, purge-to-feed ratio 0.85, feed pressure 3.5bar, feed flowrate 2.67E2m3STN/s, adsorption time 10.17s, blowdown time 15s and particle size 1.5mm.
5. Conclusions A systematic optimization framework for complex PSA systems has been developed. The results clearly indicate the benefits (in terms of product purity, recovery, and power requirements) that can be achieved by using the proposed approach. Future work will focus on applications in large-scale industrial processes involving complex multicomponent gas separations.
6.Acknowledgments Financial support from PRISM EU RTN (Contract number MRTN-CT-2004-512233) is gratefully acknowledged.
References P.C. Wankat, 1987, Intensification of sorption processes, Ind. Eng. Chem. Res., 26, 8, 1579. H.S. Shin, K.S. Knaebel, 1988, Pressure swing adsorption: An experimental study of diffusioninduced separation, AIChE J., 34, 9, 1409. S. Nilchan, C.C. Pantelides, 1998, On the optimisation of periodic adsorption processes, Adsorption, 4, 113. J.H. Park, J.N. Kim, S.H. Cho, 2000, Performance analysis of four-bed H2 process using layered beds, AIChE J., 46, 4, 790. W.E. Waldron, S. Sircar, 2000, Parametric study of a pressure swing adsorption process, Adsorption, 6, 179. L. Jiang, L.T. Biegler, V.G. Fox, 2003, Simulation and optimization of pressure-swing adsorption systems for air separation, AIChE J., 49, 5, 1140. L. Jiang, L.T. Biegler, V.G. Fox, 2004, Simulation and optimal design of multiple-bed pressure swing adsorption systems, AIChE J., 50, 5, 2904. P. Cruz, F.D. Magalhaes, A. Mendes, 2005, On the optimization of cyclic adsorption separation processes, AIChE J., 51, 5, 1377. D. Nikolic, M.C. Georgiadis, E.S. Kikkinides, 2006, Modelling of multi-bed pressure swing adsorption systems, 17th European symposium on computer aided process engineering, Computer-aided chemical engineering, 24, 159.
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Multi-Objective Design of Multipurpose Batch Facilities Using Economic Assessments Tânia Rute Pintoa, Ana Paula F. D. Barbósa-Póvoab and Augusto Q. Novaisa a b
Dep. de Modelação e Simulação, INETI, Lisboa, Portugal Centro de Estudos de Gestão do IST, IST, Lisboa, Portugal
Abstract This paper deals with the design of multipurpose batch facilities considering economic aspects. Like in almost facilities this type of problem involves the maximization of the total revenue as well as the minimization of the total cost. The best way to deal with these two goals simultaneously is either to combine them into a single criterion (e.g., profit) or to define the efficient frontier which offers the optimal solutions by multiobjective optimization. In this work the latter approach, while more elaborate, was adopted, since the exploration of this frontier enables the decision maker to evaluate different alternative solutions. In this paper the proposed model addresses this problem and presents the identification of a range of optimal plant topologies, facilities design and storage policies that minimize the total cost of the system, while maximizing the production, subject to total product demands and operational restrictions. An example is used to show the methodology application to the design of multipurpose batch facilities. Keywords: Design, Scheduling, Multipurpose, Multi-objective, RTN
1. Introduction In multipurpose batch facilities, a wide variety of products can be produced via different processing recipes by sharing all available resources, such as equipment, raw material, intermediates and utilities. Like most real-world problems, the design multipurpose batch facilities involves multiples objectives and most of the existing literature on the design problem, has been centred on a mono-criterion objective (Barbosa Povoa, 2007). However, some works have been appearing recently addressing such problem. Dedieu et al. (2003) developed a two-stage methodology for multi-objective batch plant design and retrofit, according to multiple criteria. A master problem characterized as a multiobjective genetic algorithm defines the problem design and proposes several plant structures. A sub-problem characterized as a discrete event simulator evaluates the technical feasibility of those configurations. Later on, Dietz et al. (2006) presented a multicriteria cost-environment design of multiproduct batch plants. The approach used consists in coupling a stochastic algorithm, defined as a genetic algorithm, with a discrete event simulator. A multi-objective genetic algorithm was developed with a Pareto optimal ranking method. The same author proposed the problem of the optimal design of batch plants with imprecise demands using fuzzy concepts (2008). The previous work of the same authors on multi-objective using genetic algorithms was extended to take into account simultaneously maximization of the net value and two performance criteria, i.e., the production delay/advance and flexibility. Also, Mosat et al. (2007) presented a novel approach for solving different design problems related to single products in multipurpose batch plant. A new concept of super equipment is used and requires an implicit definition of a superstructure. Essentially the optimization is
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made on the transfers between different equipment units in a design. The Pareto optimal solutions are generated by a Tabu search algorithm. Therefore, the multi-objective optimisation is still a modelling approach that requires further study when applied to the design of batch plants. In this way the resulting models would be able to act as potentially powerful decision making tools where different decisions are accounted for. Through the values of different objectives at the Pareto-optimum surface, decision makers will be able to select any solution depending on how much one objective is worth in relation to the other. In this work, the detailed design of multipurpose batch plants proposed by Pinto et al. (2003), where a RTN representation is used and a single mono-criterion objective was considered, is extended to include more than one economic objective. A multi-objective approach based on the H-constraint is explored. This method presents as an advantage the fact that it can be used for any arbitrary problem with either convex or non convex objective spaces. The final results allows the identification of a range of plant topologies, facilities design and storage policies associated with a scheduling operating mode that minimises the total cost of the system, while maximizing the production, subject to total product demands and operational restrictions. An example is solved to test the model applicability where different situations are evaluated.
2. Design Problem The optimal plant design can be obtained by solving the following problem: Given: x Process description, through a RTN representation; x The maximal amount of each type of resource available, its characteristics and unit cost; x Time horizon of planning; x Demand over the time horizon (production range); x Task and resources operating cost data; x Equipment and connection suitability; Determine: x The amount of each resource used; x The process scheduling; x The optimal plant topology as well as the associated design for all equipment and connectivity required. A non-periodic plant operating mode defined over a given time horizon is considered. Mixed storage policies, shared intermediated states, material recycles and multipurpose batch plant equipment units with continuous sizes, are allowed. Based on the above problem description a model was developed using the RTN representation and considering the discretization of time. N
¦c x
Maximize Z
j
j
j 1
N
s. t.
¦a
ij
x j d bi
i 1, 2,...M ;
j 1
xj t 0
j 1, 2,..., N
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3. Multi-objective optimization Generically the models considered have a clear, quantitative way to compare feasible solutions. That is, they have single objective functions. In many applications single objectives realistically model the true decision process. Decisions become much more confused when the problem arises in a complex engineering design, where more than one objective may be relevant. For such cases, as referred above, a multi-objective optimization model is required to capture all the possible perspectives. This is the case of the design of batch plants where two objectives are under consideration – one that maximizes the revenues (that is, production) and the other that minimizes the cost. The multi-objective optimization can be generically represented as: Maximize f m ( x)
m 1, 2,..., M ;
s. t. g j ( x) d 0 hk ( x) ( L) i
x
j 1, 2,...J ;
0
k
1, 2,..., K ;
(U ) i
i 1, 2,..., n.
d xi d x
where M defines the number of the objective function f(x) = (f1(x), f2(x),…,fm(x))T . Associated with the problem there are J inequalities and K equality constraints. A solution will be given by a vector x of n decision variables: X=(x1, x2 ,…, xn-1 , xn)T However, no solution vector X exists that maximizes all objective functions simultaneously. A feasible vector X is called an optimal solution if there is no other feasible vector that increases one objective function without causing a reduction in at least one of the other objective functions. It is up to the decision maker to select the best compromising solution among a number of optimal solutions in the efficient frontier. There are several methods to define this efficient frontier, but one of the most popular methods is the H-constraint, which is very useful since it overcomes duality gaps in convex sets. Using the H-constraint, the above formulation becomes: Maximize f u ( x) f m ( x) d H m m 1, 2,..., M and m z u
s. t.
g j ( x) d 0 hk ( x) ( L) i
x
where
Hm
j 1, 2,....; k
0
1, 2,..., K ;
(U ) i
d xi d x
represents an upper bound of the value of
f m . This technique suggests
handling one of the objectives and restricting the others within user-specified values. First the upper and lower bounds are determined by the maximization of the total revenue and minimization of the cost, respectively. Next, varying H, the optimization problem (maximization) is implemented with the objective function being the total revenue and the cost being a constraint varying between its lower and upper bounds.
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4. Example The presented method is applied to the design of a multipurpose batch plant that must produce [0; 170] tons of products S5, [0; 166] tons of S9 and S10, [0; 270] tons of products S6 and [0; 143] tons of products S11. Three raw materials, S1, S2 and S7, are used over the horizon of 24 h. The products S5 and S6 are both intermediate and final products. There are six main reactors (R1 to R6) available, and nine dedicated vessels. In terms of equipment suitability, only reactors R1 and R2 may carry out two processing tasks, T1 and T2, while each storage vessel and reactors R3, R4, R5 and R6 are only dedicated to a single state/task. Task T1 may process S1 during 2 hours in R1 or R2; task T2 may processes S2 during 2 hours in R1 or R2; task T3 may process during 4 hours in R3; T4 processes during 2 hours in R4; Task T5 may process S6 during 1 hour to produce the final product 0.3 of S11 and 0.7 of S8 in R5, and finally Task T6 processes during 1 hour S8 in reactor R6 to produce the final products S9 and S10. The connections capacity range from 0 to 200 [m.u./m2] at a fix/variable cost of 0.1/ 0.01 [103c.u.]. The capacity of R1, R2, R5 and R6 range from 0 to 150 [m.u./m2] while the others range from 0 to 200 [m.u./m2] (where m.u. and c.u. are, respectively, mass and currency units). The process resource-task-network representation is visible in figure 1.
Figure 1- The RTN process representation. 1800000 1600000
V2
V2
C
V1
E
B
V1
1400000 R1
Revenues
1200000
R1
R4
R3
V6 R3
1000000
V2
V1
E
V6
R4
D V5 R1
V2
A
D
800000
C
V2
V7
R4 V4
V6 R3
V1
R5
R6
V5
V9 V11 V10
600000
R1
R3 V5
B
V7 R1
400000
R4 R3
V6 V5
200000
R5
R6
V11
V10
V9
A 0 0
200
400
600
800
1000
1200
1400
1600
1800
2000
Costs
Figure 2- Efficient frontier for the optimal design of the multipurpose batch plant.
Multi-Objective Design of Multipurpose Batch Facilities Using Economic Assessments
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The problem described is solved and the efficient frontier obtained shown in figure 2. This forms the boundary of the feasibility region defined by the values of the two objectives. Every efficient point lies along the depicted boundary because no further progress is possible in one objective function without degrading the other. This is an alternative way to plot solutions of multi-objective models. For the case under study the objective value space is represented with axes for the cost and revenue objective functions. In the efficient frontier are visible some optimal plant topologies. The points A, B, C, D and E represent points where there is a topology change caused by the addition of one or more main equipment units to the previous topology. In figure 2 are shown these changes of topology and the respective final products. In table 1 are presented, for each point assigned, the final products and their quantity. In table 2 is presented the optimal design for the main equipment for each assigned point, in terms of capacities. For the point marked E, the optimal scheduling is shown in figure 3. It is visible the multi-task characteristics associated to equipment R1. This equipment performs not only T1 but also T2. All the other processing equipment units are single task dedicated. Table 1 – Quantities produced for each final product. A
B
C
D
E
S5
76.2
-
-
170
170
S6
-
155.5
258.6
270
270
S9
-
-
-
7.6
145.1
S10
-
-
-
7.6
145.1
S11
-
-
-
6.5
124.4
Table 2 – The optimal design for the main equipment. A
B
C
D
E
R1
76.2
93.3
103.4
141.2
120.3
R3
76.2
62.2
103.4
141.2
180.5
R4
-
155.5
129.3
140.5
159.1
R5
-
-
-
21.8
138.2
R6
-
-
-
15.3
96.8
V4
-
-
-
-
120.3
V5
76.2
-
51.72
170
170
V6
-
155.5
258.6
270
270
V9
-
-
-
7.6
145.1
V10
-
-
-
7.6
145.1
V11
-
-
-
6.5
124.4
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T6 T6 T6 R6 96.8 96.8 96.8
T5 T5 T5 R5 138.2138.2138.2
T4 159.1
R4 T3
R3 R1
0
2
4
T2
T2
T2
120.3
120.3
120.3
6
8
10
T4 159.1
T3
180.5 T1
180.5 T1 T1
95.5
12
T4 159.1
14
95.5
16
95.5
18
20
22
24
Figure 3 – The optimal scheduling for the plan topology assigned by E.
5. Conclusions The plant topology, equipment design, scheduling and storage policies of multipurpose batch plants are addressed in this paper, considering production maximization with costs minimization - a multi-objective optimization. The model was developed as a MILP model and the multi-objective method used in this work was the H-constraint. The efficient frontier obtained defined the optimal solutions allowing the identification of a range of plant topologies, facilities design and storage policies that minimize the total cost of the system, while maximizing production, subject to total product demands and operational restrictions. The proposed methodology allows the decision makers to evaluate the relationship between revenue and cost of given batch facilities, thus enabling them to develop an adequate business strategy.
References A.P.F.D. Barbosa-Póvoa, 2007, A Critical review on the design and retrofit of batch plants, Computers and Chemical Engineering, 31,833-855. A. Dietz, A. Aguilar-Lasserre, C. Azzaro-Pantel, L. Pibouleau, S. Domenech, 2008, A fuzzy multiobjective algorithm for multiproduct batch plant: Application to protein production, Comp. Chem, Eng, 32, 292-306. A. Dietz, C. Azzaro-Pantel, L. Pibouleau, S. Domenech, 2006, Multiobjective optimization for multiproduct batch plant design under economic and environmental considertions, Comp. Chem, Eng, 30, 599-613. S. Dedieu, L. Pibouleau, C. Azzaro-Pantel, S. Domenech, 2003, Design and retrofit of multiobjective batch plants via a multicriteria genetic algorithm, Comp. Chem, Eng, 27, 17231740. A. Mosat, L. Cavin, U. Fisher, K. Hungerbühler, 2007, Multiobjective optimization of multipurpose batch plants using superequipment class concept, Comp. Chem, Eng, article in press. T. Pinto, A.P.F.D. Barbosa-Póvoa, A.Q. Novais, 2003, Comparison Between STN, m-STN and RTN for the Design of Multipurpose Batch Plants, Computer Aided Chemical Engineering, Vol. 14, Editores A. Kraslawski e I. Turunen, Elsevier, 257-262.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Oil products pipeline scheduling with tank farm inventory management Susana Relvasa,c, Henrique A. Matosa, Ana Paula F.D. Barbosa-Póvoab, João Fialhoc a
CPQ-IST, DEQB, Av. Rovisco Pais 1049–001 Lisboa, Portugal CEG-IST, DEG, Av. Rovisco Pais 1049–001 Lisboa, Portugal c CLC, EN 366, km 18, 2050 Aveiras de Cima, Portugal b
Abstract The core component of the oil supply chain is the refinery, where the received oil batches are managed to feed the crude distillation units in proportions that give origin to the desired cuts and products. However, the oil supply and the oil products’ distribution have to answer in agreement to their predicted demands. For this reason, there is the need to build decision support tools to manage inventory distribution. This work focuses on the development of a MILP model that describes the oil products distribution through a pipeline that connects one refinery to one tank farm. In order to supply the local market, the model represents the interaction between the pipeline schedule and the internal restrictions at the tank farm. Real world data from CLC (a Portuguese company) validate the model formulation. Keywords: Oil products’ pipeline, inventory management, MILP, continuous time
1. Introduction Pipelines have widely been established as safe and efficient equipments to transport oil and oil products, either in short or long distances and in a cost effective way. However, the benefit will be higher if the relation between pipeline and tank farm is considered as a whole in a decision support tool to the oil products distribution. The works published so far in this area have a large focus on pipeline details and schedule, relying both in discrete (Rejwski and Pinto (2003), Magatão et al. (2004)) and continuous (Cafaro and Cerdá (2004, 2007) and Rejowski and Pinto (2007)) MILP formulations. Nevertheless, the storage availability for products reception at the tank farm, the inventory management issues and the clients’ satisfaction are important tasks that have impact on the optimal pipeline schedule. These issues have been previously addressed in the works by Relvas et al. (2006, 2007). Based on that work, this paper proposed a new MILP model that disaggregates the storage capacity of each product in physical tanks. Two parallel formulations for this problem are introduced and discussed, using as case study the real world scenario of CLC - Companhia Logística de Combustíveis. CLC distributes refinery’s products in the central region of Portugal.
2. Problem description and model representation Figure 1 resumes the operating system that comprises an oil products’ pipeline that pumps from a refinery to a tank farm. This distribution centre is located in a strategic local market. Each tank has a fixed product service and the clients are supplied at the distribution centre with the respective products.
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Pipeline
Tank Farm Refinery
Figure 1 – Problem’s operating system
The main given parameters are: a) the pipeline volume, b) maximum and minimum flowrates, c) the products to be pumped and matrix of possible sequences, d) the tanks’ capacity and product’s service, e) settling period by product; and as scenario data: f) the time horizon extent and number of days, g) the maximum number of batches to be pumped, h) the initial inventory by product and by tank, i) the state of each tank and the initial settling time of each tank (if applicable, otherwise set to zero), j) the daily clients’ demands and k) the planned pipeline stoppages, if any. The problem’s solution will comprise two parts: the pipeline schedule and the tanks’ inventory management. The pipeline schedule includes products’ sequence, pumping flowrates, batches’ volumes, timing issues and pipeline stoppages. The inventory management includes pipeline inputs, settling periods and outputs by product and tank. The problem’s objective is to optimize results under an operational objective function that combines several goals. Each is expressed by one dimensionless and normalized term (to comprise values between 0 and 1) and will be added to the function with a plus (if minimizing) or minus sign (if maximizing) and with a weight. The terms considered minimize the balance between the tank farm inputs and outputs (such that the flowrate is also minimized and imposing that this balance is positive), maximize the pipeline usage and maximize the product whose final inventory has the lowest value. The model formulation is based on the model proposed by Relvas et al. (2006, 2007), modified to account for individual tanks. The main characteristics of the model are: 1. Continuous time and volume scales – The model considers a single event to build the continuous time scale, which corresponds to the time when each batch has finished to be pumped to the pipeline. Additionally, this event is also used to update the batches’ volumetric position inside of the pipeline, referred to an axis with origin in the refinery and end in the tank farm. 2. Daily clients’ demands – The forecast of the demands is provided in a daily basis, which is also implemented in the model formulation. For this purpose, it is built a binary operator that transforms discrete time information in to continuous time. 3. Sequence of products – This is one of the main results of the pipeline schedule. However, it highly influences the model performance. For this reason, it has been approached as fixed or mixed sequences. These basically repeat a cycle unit of products. The main difference is that some products may be concurrent for some positions, which leads to mixed sequences or have fixed positions, fixed sequence.
3. Tanks’ Representation A tank farm is usually constituted by several tanks, which may have a fixed product’s service, i.e., they are always used for the same product, due to product quality conservation and tank’s calibration system, as well as other technical features.
Oil Products Pipeline Scheduling w ith Tank Farm Inventory Management
279
Additionally, the fact that the product has to settle after discharge from the pipeline and before being available for clients implies that at any moment there is at least one tank receiving product and another one available for clients. This will be part of a rotation scheme between tanks of the same product. The mathematical representation of this operational procedure has a main decision to take: either to represent the tanks in an aggregated manner or include each tank as a model instance and obtain additionally as model result the alternation schemes for all products. For the later, such detail level at the mathematical representation results in higher model size due to a new set, new variables (either continuous and binary, expanding the decision tree size) and higher number of equations. Three key aspects have to be considered when modeling individual tanks: i) the allocation of tanks to products, ii) the tanks’ operational cycle and iii) the initialization data. 3.1. Allocation of tanks to products This work will compare the model proposed by Relvas et al. (2006, 2007), which considers an aggregated tanks’ formulation, with a new formulation for the disaggregated representation. The first will be from now on referred as Aggregated Tanks’ Formulation (ATF), meanwhile the last will be referred as Disaggregated Tanks’ Formulation (DTF). For the DTF strategy a set of tanks (t) is defined such that each tank is referred as the tank t of product p. The variables defined on p are directly disaggregated in t. Therefore, the relation product-tank is implicit in the formulation. 3.2. Tanks’ operational cycle The major challenge in the model formulation is the representation strategy adopted for the tank cycle. Normal operation considers that each tank is filled up completely before settling. After the settling period, the tank is released for clients’ satisfaction, until it is totally empty. These procedures are usually related to the product quality, where it isn’t desired to mix products from several different batches. This implies that they are formulated four states for each tank: i) full, ii) delivering product to clients, iii) empty and iv) being filled up with product from the pipeline. Each one of the states has a corresponding state variable, related to tank inventory (ID), and has to be activated or deactivated whenever a boundary situation occurs (Eq. 1): the maximum (UB) and minimum (LB) capacities of the tank are met. For this purpose, the state variable (y, binary) will have to be activated whenever both inequalities (‘’ and ‘’) hold (Eq. 2):
y 1 o ID UB
(1)
y 1 o ID d UB ID t UB
(2)
These occurrences are formulated using big-M constraints, which require the definition of a tolerance to identify each state (within the given tolerance between the desired value and the variable value, the state variable is activated). Moreover, each variable that occurs in these constraints is now modeled as an integer variable (tank inventory, input and output volumes), enabling the definition of a tolerance lower than 1. The definition of a full or empty tank is applied for specific cases (tank inventory is at its limits). The remaining states are exclusive at any moment, i.e., each tanks is always either in a filling up cycle or in an emptying cycle (idle time intervals may occur in both cycles). Finally, whenever the tank is full and the corresponding state variable is activated, it also controls the settling period accomplishment.
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3.3. Initialization data A new set of data has now to be included in each model instance: the initial inventory of each tank and its current state. The initial state is crucial either in the model performance as well as on the optimal resources allocation. In a real world scenario, this data is provided by the prior time horizon.
4. Results The implementation will consider a real world example taken from CLC – Companhia Logística de Combustíveis, a Portuguese company operating in the distribution of oil products. This company transports six different products from a single refinery located in the south (P1 to P6), and distributes them in the central area of Portugal. The total number of tanks is 29 and they all have specific product service. The time horizon considered will cover 7 days of operation, taking as scenario the data from the first week of April 2006: initial inventories at each tank, initial contents of the pipeline and current state of each tank and, if settling, the current settling time. Additionally, they were considered the real clients’ demands occurred in that period. In order to compare the results obtained through the mathematical model with the real occurrences, it will be used the same sequence of products to pump that was verified within that period. The flowrate will be considered to vary between 450 and 650 vu/h (volumetric units/h). The model was implemented in GAMS 22.4 and solved with CPLEX 10.1, on a Pentium D820 with 2 GHz RAM. The stopping criteria were either the optimal solution or 2 hours of computation. CPLEX’s polishing option was used for 30 seconds. The disaggregated formulation was also run without specifying the initial states for tanks, leaving open their definition (DTFnoinit). Table 1 resumes the model performance for each strategy, as well as the value of the objective function obtained from the real occurrences at CLC. They are also indicated the relaxed solution and the amount of time that was spent to find the optimal solution, but without proving optimality. It can be observed the model size increase between a model with ATF and the corresponding DTF. The number of binary variables increased more than 400% for the same scenario. The model size has a large impact in CPU effort. Table 1 – Model performance for the proposed methodologies Formulation
“CLC”
ATF
DTF
DTFnoinit
# Continuous Variables
-
1736
2907
2994
# Binary Variables
-
414
2098
2156
# Equations
-
2889
6178
6178
# Nodes Explored
-
937
298784
1806494
# Iterations
-
6712
3464991
30364688
CPU time (s)
-
1.359
1096.578
7230.078
Time to find the optimal solution (s)
-
1.359
5.50
6482.00
Objective Function
-1.896985
-2.042726
-1.968652
-2.042726
Relaxed solution
-
-2.043577
-2.043577
-2.043577
Relative Gap (%)
-
0.00
0.00
0.04
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Regarding the optimal solutions obtained versus CPU effort, meanwhile in the ATF the optimal solution is found in less then 2 s, the DTF took about 18 min to prove optimality. However, the optimal solution was obtained relatively early in the search tree analysis (§ 5 s of computation), which means that the majority of the CPU effort is used to prove optimality. It should also be pointed out that the relaxed solution is equal between the three strategies, representing a good accuracy between formulations. Table 2 resumes the operational results. All solutions present a lower medium flowrate when compared to CLC’s occurrences. The DTF solution leads to a pipeline stop (without interfaces) and reducing pipeline usage. CLC verified both high flowrate and positive balance in inventory, increasing the final inventory. The results on minimum inventories are similar for all strategies, being P3 the product with lower levels. From the DTFnoinit results they were verified 8 different initial states. The reason why happens a pipeline stop in the DTF is due to P2 having all tanks satisfying clients at the moment when it is necessary to store a new batch. However, the initial state is given by CLC’s real occurrences, which were not provided by an optimization model. Table 2 – Model performance for the proposed methodologies Formulation
“CLC”
ATF
DTF
DTFnoinit
Medium flowrate (vu/h)
521.2
487.34
507.32
487.34
'Inventory (vu)
+5361
+31
+31
+31
Pipeline usage (%)
94.05
94.05
90.34
94.05
Final inventory level (%)
51.16
48.54
48.54
48.54
Minimum final inventory (%, product)
32.67 (P3)
32.53 (P3)
32.53 (P3)
32.53 (P3)
Minimum overall inventory (%, product)
32.67 (P3)
32.53 (P3)
30.54 (P6)
32.53 (P3)
-
-
0
-
# Interfaces during pipeline stops
The major benefit (balanced with the model complexity trade-off) from the DTF is the allocation of arriving batches to available tanks. At any moment it is known the state of a tank, defining precisely the available storage capacity and having impact in the volume and pumping rate of each batch on the pipeline schedule. If the results from the ATF are fed to the DTF, the model may turn infeasible, showing that the detail at the individual tank level is critical to define the pipeline schedule. This would be overcome using an iterative procedure where at each iteration an integer cut would be added to the DTF, eliminating infeasible solutions at the ATF level from the DTF search space. Figure 2 represents the inventory profiles for each product and strategy. It is visible the resemblance between reality and model formulations. The main differences are due to batches volumes transported and pumping rate, because both the sequence of products and outputs are equal between strategies.
5. Conclusions and Future Work This work presented a new model formulation that coordinates pipeline transportation with tank farm inventory management, including individual tanks’ details. The obtained model generates within the solution the rotation scheme for tanks that allows the verification of all required tank farm operations.
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S. Relvas et al. CLC
P1
ATF
DTF
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100%
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60% 40% 20%
0%
0% 0
24
48
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40%
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0%
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0%
0% 0
24
48
72 Time (h)
96
120
144
168
0
24
48
72 Time (h)
96
120
144
168
Figure 2 – Inventory profiles for each strategy and by product
The main achievement of the proposed model is to provide a detailed tank farm inventory management, looking into the sets of tanks of each product (rotation scheme). As future work it is proposed to improve the tanks’ cycle formulation and develop a set of examples to test the behavior of the Disaggregated Tanks Formulation. Additionally, it is proposed to develop a decomposition strategy to link subsequent time horizons.
6. Acknowledgments The authors gratefully acknowledge financial support from CLC and FCT, grant SFRH/BDE/15523/2004.
References R. Rejowski, Jr., J.M. Pinto, 2003, Comp. & Chem. Eng., 27, 1229 L. Magatão, L.V.R. Arruda, F. Neves, Jr, 2004, Comp. & Chem. Eng., 28, 171 D.C. Cafaro, J. Cerdá, 2004, Comp. & Chem. Eng., 28, 2053 S. Relvas, H.A. Matos, A.P.F.D. Barbosa-Póvoa, J. Fialho, A.S. Pinheiro, 2006, Ind. Eng. Chem. Res., 45, 7841 S. Relvas, H.A. Matos, A.P.F.D. Barbosa-Póvoa, J. Fialho, 2007, Ind. Eng. Chem. Res., 46, 5659 D.C. Cafaro, J. Cerdá, 2007, Comp. & Chem. Eng., doi:10.1016/j.compchemeng.2007.03.002 R. Rejowski Jr, J.M. Pinto, 2007, Comp. & Chem. Eng., doi:10.1016/j.compchemeng.2007.06.021
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Methodology of conceptual process synthesis for process intensification Ben-Guang Rong, Eero Kolehmainen, Ilkka Turunen Lappeeranta University of Technology, Fin-53851 Lappeenranta, Finland
Abstract A systematic method based on conceptual process synthesis for process intensification is presented. Starting from the analysis of relevant physical and chemical phenomena, the various possible concepts and principles for the processing tasks are investigated. This includes the introduction of the new concepts and principles through the variations and manipulations of the key process phenomena. The various partial solutions for process and equipment intensification are then generated through phenomena-based reasoning. Next, the feasible conceptual process alternatives are synthesized by combining the generated partial solutions. The example for the intensification of the peracetic acid production process was demonstrated, which particularly illustrated the intensification of the conventional batch process to the on-site microprocess through microreactor technology. Keywords: Methodology, Conceptual process synthesis, Process intensification, Process phenomena, Microstructured devices
1. Introduction Process Intensification (PI) is considered as one of the main current trends in process engineering. It is defined as a strategy for achieving dramatic reductions in the size of a chemical plant at a given production volume (Ramshaw C., 1983). As a consequence, one major approach of Process Intensification is pursuing the multifunctional and microstructured devices for the processing tasks, which are conventionally implemented in the traditional unit operations. Needless to say, to achieve the multifunctional and microstructured devices, we need new concepts and principles other than the traditional unit operations concepts for implementing the processing tasks. On the other hand, process synthesis and conceptual design, i.e. Conceptual Process Synthesis (CPS) has been established as a major discipline in Process Systems Engineering for the optimal design of process systems. Process Synthesis is usually based on the systematic methods for the generation of conceptual process alternatives. Numerous cases in process synthesis have shown that the true efficiency and performance of the manufacturing process are primarily determined by the decisions made at the conceptual design stage on the concepts, principles and mechanisms of the process systems. It is so that the true innovative and inventive designs very often come from the unique understandings and insights to the design problems concerning process concepts, principles and mechanisms. The innovative character of Process Intensification is in nice harmony with the objectives of Process Systems Engineering (Moulijn J.A. et al., 2006). It is so that Process Intensification needs the very front-end creativity for the generation of the novel concepts and principles for the processing tasks. Such novel concepts and principles are also the key elements in process synthesis for the generation of the innovative and inventive designs in terms of systems synthesis and equipment design.
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To this sense, conceptual process synthesis plays a key role and constitutes a major approach for process intensification to achieve the multifunctional and microstructured devices. In this work, a systematic methodology based on conceptual process synthesis for process intensification is presented.
2. The Methodology of conceptual process synthesis for PI The methodology of conceptual process synthesis for process intensification is focused on the generation of the novel concepts and techniques for the processing tasks. The methodology of conceptual process synthesis for process intensification is illustrated in Figure 1.
Process information
Step 1: Selection of main rate-determining and bottleneck processing steps and tasks
Step 2: Identification of the relevant process phenomena in key steps and tasks Step 3: Characterization and analysis of process phenomena Step 4a: Concepts for variation of the analysed process phenomena
Step 4b: Principles for manipulation of process phenomena
Step 5: Multiscale variations and manipulations of the phenomena
Step 6: Partial solutions for process and equipment intensification
Step 7: Combination of the partial solutions for process and equipment synthesis
Step 8a: Phenomena related tasks implemented in Microscale Step 9a: New intensified microstructured devices
Step 8b: Phenomena related tasks implemented in different scales Step 9b: New intensified hybrid devices
Step 8c: Phenomena related tasks implemented in Mesoscale Step 9c: New intensified Mesoscale process units
Step 10: Evaluation of technical feasibility
Figure 1.The methodology of conceptual process synthesis for process intensification
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For a chemical process, it is possible to identify a certain number of process phenomena which represent the key features and characteristics of the process. For example, chemistry and chemical reaction phenomena, materials phases and transport phenomena, phases behaviors and separation phenomena, etc. All these basic process phenomena concerning chemical reaction, mass transfer, heat transfer and fluid hydrodynamics are the fundamental information from which various processing concepts and principles (techniques) are generated for the processing tasks. These processing concepts and principles will principally determine the required process units and equipment for the manufacturing process. However, it must be indicated that for a specific phenomenon, there are very often several possible concepts or principles to deal with it. For example, different separation principles for a mixture separation. The feasible concepts and principles adopted will depend not only on the phenomenon itself, but also on the unique understanding and insights from the process engineers (designers). On the other hand, for a process or equipment intensification and design, it is unlikely that a single phenomenon is dealt with. The interactions and relationship among different phenomena are the real source for the generation of new concepts and principles for novel process and equipment. Moreover, to achieve novel process and equipment, the concepts and principles are concerned with various aspects of the process and equipment, may it be the catalyst or solvent employed, the internals of the equipment, the alternative energy form, the transfer mechanisms, the geometry of the equipment, etc. Therefore, a process phenomenon for process intensification must also consider various aspects of the process and equipment during the generation of the concepts and principles. Figure 2 illustrates the general characterization of a process phenomenon for PI which is concerned with the various aspects of the materials processing and the related elements for process and equipment intensification. Table 1 presents the associated attributes of each category for the characterization of a process phenomenon. Some commonly used principles for manipulation of process phenomena are presented in Table 2.(Rong et al., 2004).
Components and phases
Key variables
Energy sources
A Process Phenomenon for Process Intensification
Surface materials Operating modes
Flow patterns
Geometry
Facility medium
Figure 2. The characterization and related aspects of a process phenomenon for PI It is significant to notice that the concepts and principles to vary and manipulate any aspects of the phenomena will generate the corresponding partial solutions, from which the ultimate intensified process and equipment will be synthesized. Herein, the multiscale approach for variations and manipulations of the phenomena is emphasized. It means that the concepts and principles should be explored at all possible scales for the
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variations and manipulations of the phenomena. As a consequence, the generated partial solutions can be used to synthesize the intensified equipment in different scales. It can be expected that the combination of the partial solutions to synthesize the final process and equipment will not be straightforward; rather, there must be some conflicts and contradictions in the combination of the partial solutions. Therefore, at this stage, one needs some creative methods to remove or eliminate the encountered conflicts or contradictions. During the combination of the partial solutions, a major pivotal decision needs to be made is to determine at what scales to implement the processing tasks related phenomena. It can be microscale, or mesoscale or hybridscale (both microscale and mesoscale). Needless to say, it is the corresponding concepts and principles generated for the variations and manipulations of the processing tasks related phenomena that determine the scales of the intensified process and equipment. As a consequence, microscale, mesoscale or hybridscale devices and units are synthesized by the combination of the partial solutions. Thereby, the intensified microstructured devices, the intensified mesoscale process units, or the intensified hybridscale devices are obtained as the conceptual design alternatives from the conceptual process synthesis. The evaluation of PI results is often self-evident as long as the technical feasibility of the intensification concepts and principles can be verified. Nevertheless, once intensified process alternatives have been identified, the further detailed optimization can be performed. Table 1. The detail characterization to process phenomena for PI Phases+
Changes of variables Temperature Pressure Concentration Velocity Density Viscocity
Energy source
Geometry*
Surface material Metal Ceramic Plastics Chemical surface
L/G Gravity Geometry (1) L/S Centrifugal (Equipment) S/G Microwave Tank L Ultrasound Column G Electromagnetic Channel S Motor Tube S/L/G Heat transfer fluid Geometry (2) L1/L2 Magnetic field (Internals) L1/L2/G Reaction Geometry (3) L1/L2/S (Surfaces) + L-liquid, G-gas, S-solid, L1-Liquid phase 1, L2-Liquid phase 2 *Geometry (2): packings, plates, films, spray, uniform, specific structures, fiber Geometry (3): even, rough, porous, chemically/physically inert/active surface
Facility medium Catalyst Solvent Additive Membrane
Operate mode Static Rotating Moving Swing Spinning
Table 2. General principles for process phenomena manipulation. 1 2
Principles Enhance a favorable phenomenon
3
Attenuate an unfavorable phenomenon Eliminate a phenomenon
4
Combine several process phenomena
5
Separate phenomena
6
Mitigate the effect of a phenomenon by combing it with another Create a new phenomenon
7
Examples Enhance an oxidation reaction by using oxygen instead of air Decrease side-reactions by shortening residence time Eliminate an azeotropic behavior by adding a solvent in a distillation system Combine reaction and distillation into a reactive distillation External catalyst packages in reactive distillation Transfer reaction equilibrium limit by removing desired product immediately Create new phase interface for mass transfer
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3. Case study of peracetic acid process intensification Peracetic acid is the most widely used organic peroxy acid. It is a strong oxidizer, which could be used in disinfection and bleaching agent. Peracetic acid can be synthesized from acetic acid and hydrogen peroxide. The formation of peracetic acid takes place in the equilibrium reaction (1). In order to accelerate the reaction rate, acid catalyst is needed (Swern, D., 1970). Conventionally homogeneous sulphuric acid catalyst is used. The reaction scheme is shown in Eq. (1) CH3COOH + H2O2
H 2SO 4 m o CH3COOOH + H2O
(1)
Conventionally peracetic acid is produced in a tank reactor in the presence of homogeneous acid catalyst. In the process, sulfuric acid catalyst is first charged into the reactor, after which acetic acid and hydrogen peroxide are fed into the reactor. The mixture is heated up and equilibrium reaction (1) takes place. When homogeneous acid catalyst is used, separation of it from equilibrium mixture is carried out in a distillation column. When equilibrium is reached, sub-atmospheric pressure is drawn in the reactor. Vaporization of the reaction mixture begins. In the distillation column acetic acid, hydrogen peroxide and peracetic acid are separated from sulphuric acid catalyst (Swern, D., 1970). The simplified scheme of the conventional process is illustrated in Figure 3.
5
6
7 1 2 3
4
Figure 3. The scheme of the conventional process for producing peracetic acid. 1) Acetic acid, 2) Sulphuric acid, 3) Hydrogen peroxide, 4) Reactor, 5) Distillation column, 6) Distillate receiver, 7) Peracetic acid, acetic acid, hydrogen peroxide and water. In the conventional technology, the temperature range in production is 40 qC-60 qC due to safety reasons. Peracetic acid decomposes to oxygen and acetic acid in higher temperatures. However, higher temperature and higher initial concentrations of raw materials at optimal molar ratios increase the reaction rate and would lead to shortened residence time (Swern, D., 1970). Therefore, the major limits are identified for the conventional process in the reaction step, which is both rate-determining and equilibrium-limit. Moreover, it is also a bottleneck step in terms of inherent safety due to the exothermic reaction, the easier decomposition of peracetic acid and explosion. In order to carry out the reaction in higher temperatures and initial concentrations under controllable conditions, the continuously operated multi-channel reactor is taken into consideration. The continuous process contains a mixing step and a reaction step. Acetic acid and hydrogen peroxide are heated in heat exchangers and mixed in the mixing step. The equilibrium reaction takes place in the parallel reactor system. The scheme of the continuous process is depicted in Figure 4.
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Figure 4. Scheme of the continuous peracetic acid process with microreactors. In the parallel reactor system, the concept of a heterogeneous solid acid catalyst is applied. The phase of the catalyst is changed from liquid to solid. Using of heterogeneous catalyst to accelerate reaction rate enables the elimination of the distillation section described in the conventional process. The small-channel reactor is mechanically strong and it tolerates easily higher pressures than the conventional reactor. Furthermore, increased pressure eliminates the vaporization of the reaction mixture and therefore operation in higher temperatures and concentrations is safer than in conventional reactor. Heat transfer efficiency of the small channel reactor can be orders of magnitude higher than in conventional reactor. Since the reaction can not be considered as extremely fast, mixing step does not necessary require microscale application. However, in order to maximize the contact area between solid acid catalyst and the reacting mixture, microstructures in the catalyst section are beneficial. Variation and manipulation of phenomena result in the changes in phases (L ĺ L/S), process variables (TĹ, cĹ, pĹ) and geometry (tank, column ĺ multichannel, small scale channel, chemically active surface). The concept of the continuous reactor system offers potential to intensify the peracetic acid process.
4. Conclusions Process intensification needs the novel concepts and techniques for the processing tasks in the manufacturing process. At the same time, process intensification aims at the novel process and equipment to be synthesized based on the generated concepts and techniques. In this paper, a methodology of conceptual process synthesis for process intensification is presented. The methodology is focused on the generation of the novel concepts and techniques for the processing tasks by variations and manipulations of the identified key process phenomena. By doing so, various possible partial solutions for process intensification are obtained through varying and manipulating the process phenomena in a multiscale manner. Then, the conceptual process alternatives are synthesized by the combination of the generated partial solutions. A case study for the intensification of the peracetic acid process illustrated that the novel conceptual process alternative is achieved following the procedure in the methodology.
References J.A. Moulijn, A. Stankiewicz, J. Grievink, A. Gorak, 2006, Proceed. of ESCAPE16/PSE9, 29-37. C. Ramshaw, 1983, Chemical Engineer-London, 389, 13-14. B.-G. Rong, E. Kolehmainen, I. Turunen, M. Hurme, 2004, Proceed. of ESCAPE14, 481-486. D. Swern, 1970, Organic Peroxides, vol I, 61-64 and 337-484.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Process plant knowledge based simulation and design a
Jelenka B.Savkovic-Stevanovic, aSnezana B. Krstic, aMilan V.Milivojevic, b Mihailo B.Perunicic a
Department of Chemical Engineering, Faculty of Technology and Metallurgy, The University of Belgrade, Karnegijeva 4, 11000 Belgrade, Serbia, e-mai:savkovic@ tmf. bg.ac.yu,
[email protected],
[email protected] Faculty of Technology, The University of Novi Sad, Cara Lazara 1, 21000 Novi Sad, Serbia, e-mail:
[email protected]
Abstract A many number of modelling and simulation systems have been developed to aid in process and product engineering. In this paper the knowledge based process plant simulation model was developed. On the model development side, the issues of knowledge representation in the form of systematic component composition, ontology, and interconnections were illustrated. As a case study a plant for starch sweet syrup production was used. The system approach permits the evaluation of feasibility and global plant integration, and a predicted behavior of the reaction systems. The obtained results of the this paper have shown the variety quality of syrups simulation for different products. Keywords: Data base integration, Knowledge based operation, Optimizer, Product design.
1. Introduction Chemical and process engineering today is concerned with the understanding and development of systematic procedures for the design and optimal operation of chemical and process systems, ranging from micro-systems to industrial scale continuous and batch processes ( Mah, 1990; Thome, 1993; SavkovicStevanovic, 1995). It many years since process modelling become an advanced tool for design work in most companies. Process plant model objectives include to provide a comprehensive report of materials and energy streams, determine the correlation between process units, study the formation and separation of byproducts and impurities, support preventive maintain by tracking performance of key equipment over time and its relation to the buildup of impurities. In this paper the knowledge based simulation was developed for different products simulation.
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2. Knowledge based simulation The general framework presented here on the model development side, the issues of knowledge representation in the form of systematic composition, ontology, and quantity representaion was involved. On the model analysis side issues involving the automatic evaluation and presentation of simulation results. The plant simulation model should mirror the behaviour of a complex plant subject to constraints in feedstock, products, equipment capacities, operational parameters, and utilities consumptions. The life cycle concept may lead to a reliable and maintainable tool. One of the most widely used forms of simulation is that for operator training. So far operator training simulators have tended to use greatly simplified models in order to ensure real time performance and most effort has been invested in the development of user interface. A further aspect of the extended application of simulation for operator assistance could well be achieved in conjunction with expert systems. 3. Design In design, attention focuses on the main elements of material and heat balances, on equipment investment, and more generally, on process economics. While a deeper systems analysis of the plant would be worthwhile, considering that the basic design could be responsible for more than 80% of the cost of investment and operation, a detailed simulation and constrained, however, by the project schedule and lack of data. 4. Operation In operation, attention centres mainly on product flow rate and specifications, but also plant troubleshooting, controllability, and maintenance. The performance of reactors and separation systems impose the rules of the game. They are independent and time variable to some extent. Only a detailed plant simulation enables an understanding of these interdependencies and their quantitative evaluation. Thus, the exact knowledge of a detailed material and energy balance is by far more important in operations than in design. Even the flow rates of trace impurities are relevant, because they may impact equipment maintenance and environment protection. The material and energy balance as well as the operational characteristics of a plant are highly interconnected, and well suited for a system analysis. 5. Knowledge based process plant model development Using available flowsheeting software, it is possible to produce a computerized tool that will permit us to learn or even mirror the plant behaviour under different operating conditions or with different raw materials and product specifications. Such as tool is called the steady state plant simulation model. The steady state model, which is simpler to build, and has a wide variety of applications in its own right, it can be used directly in revamping and a wide variety of other engineering projects.
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Dynamic simulation is a process engineering tool that predicts how process and its controls respond to various upsets as a function of time. Dynamic simulation model leads benefits during plant start up. Process simulation and modelling techniques are very useful for optimizing design and operation. The outstanding advantage of the knowledge based simulator is its flexibility and semantic network. Developing such as model is a preliminary and necessary stage in achieving real time plant optimization which involves treating data reconciliation and rigorous simulation simultaneously by means of optimization techniques, whose objective is to maximize process profitability (Perunicic et.al.,2007). 6. Model of the sweet syrup production plant As a case study the starch converting plant was used. Summer wheat mills and starch converts into sugars after liquefaction, fermentation and conversion using corresponding enzymes. Partial starch hydrolysis is performed with α-amylase. The second phase deep hydrolysis is occurs at the present sweet enzymes. 6.1Biochemical reaction model
General kinetic model have involved Monod’s model. k1 k2 E + S ⎯⎯→ ES ⎯⎯→ P+E ←⎯ ⎯ k−1
(1)
dc ES = k1 ⋅ c E ⋅ c S − k −1 ⋅ c ES − k 2 ⋅ c ES dt
(2)
and product rate
dc P = k 2 ⋅ c ES dt
υ=
(3)
where E is enzyme, S is substrate, P is product, c is concentration and k is specific rate constant. 6.2 The steady state model
The starch plant for continuous sweet syrup production consists of a container for summer wheat, mill, fermentor, exchangers, bioreactors, and filter as individual process stages, or equipment items as shown in Fig.1(a),(b)and Fig.2. The overall mass balance NM
∑s ∂ F i
i
=0
i
(4)
i =1
Substream mass balance NSS NM
∑∑ s F f i
j =1 i =1
i
ij
=0
(5)
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Component mass balance NC NSS
NM
k =1 j ≠1
i ≠1
∑∑ ∑s F f i
i
ij
zi , j ,k = 0
(6)
and overall energy balance NM
NH
NW
i =1
i =1
i =1
∑ si ∂ i Fi hi + ∑ s j ∂ j H j + ∑ s k ∂ ki wk = RHS
(7)
equation i, where si = ,+1 for inlet streams and -1for outlet streams, ∂ i is stream scale factor, Fi mass flow stream i, fij is mass fraction of substream j in stream i, z ijk is mass fraction of component k in substream j of stream i, NM is number of inlet and outlet material streams, NH is number of inlet and outlet heat streams, NW is number of inlet and outlet work streams, NSS is number of substreams within material streams, NC-number of components specified on the components main or components group forms, hij is enthalpy of stream i, Hj is flow of heat stream j, wk is work of work stream k, RHS is right hand side of the energy balance equation. Additional material relationships can be specified which is very useful for reactive systems, NTi
∑C
ij
Fij = RHS i
(8)
j =1
where Cij coefficient term j in equation i, as determined by stream, substream and term, RGSi right hand side of mole/mass equation i, NTi is number of terms in mole/mass equation i. There are three elementary material balance according to stoichiometric description, and enthalpy balance which were formulated in this case study. The ability to describe the output composition of a reaction system for given reactor operating condition as function of variable input stream is the key feature that needs modelling of the chemical reactor in flowsheeting. 7. Optimization of plant design The input component data base and process parameters data base have developed as a relational data base system which linked with process models by simulation. SWEET SYRUP
GLUCOSABLE SYRUPS P11
P8
P5
P6
P5
P6 P8
Fig.1(a) Three reactors unit process
Fig.1(b) Four reactors unit process
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WHEAT
P1
P2
ENZYMES MIXTURE SWEET ENZYMES
WATER
P3
P5
P6
P8 SWEET SYRUP
P4 P7
P9
P10
P1-cointainer for summer wheat, P2-mill, P3-fermenter, P5-hydrolyser, P6-bioreactor for starch decomposition, P8- bioreactor, P4 and P9–heat exchangers, P7-cooler, P10-filter.
Fig. 2 The starch plant process simulation diagram A reactor simulation with detailed kinetics and a realistic flow model may be executed better with specialized software(Savkovic-Stevanovic.et.al.,2007). In fact, in flowsheeting only need an accurate description of the transformation linking the input the output of the reaction system. Optimization in design specification was achieved. This again highlights the differences between design and operations, in the design mode, the modelling of chemical reactors focuses on the main products rates. In this paper design mode was considered. For the examined starch plant in which starch converts into sugars after liquefaction, fermentation and conversion the main process units are shown in Fig.1(a) and (b). Using min-max principles and global optimization method the engineering economic objectives were provided. 8. Results and Discussion The use modelling for an actual automated equipped involved the continuous steady state nature of the processing units is starting from the crude streams and ending in the product streams as shown in Fig.2. Databases integration with process unit models is shown in Fig.3. Components and parameters data bases have made in Access program. The results are stored in a data base for further use. This is improving information processing.
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The results of starch converts in attending caustic soda and calcium chloride mass of sugar increases. Advantages of the employed technology to the acid hydrolysis are higher dextrin coefficient, less contents salt in the products, and no protein decomposition.
DbC
SIMULATION
DbP
D E S I G N DbC-component data base, DbP-parameters data base
Fig.3 Data bases integration with design structure 9. Conclusion The simulation flow diagram and optimization sequences of the process units for different products were examined. A relational data bases which including input component data base and process parameters data base as well as simulation results data base were developed. In this paper knowledge based process simulation and design of the starch plant were developed. The relational data bases system was linking with simulation models and simulation interface. The obtained results in this paper can be applied in the others domain. Acknowledgement. The authors wishes to express their gratitude to the Fund of Serbia for financial support.
References R.S.H.Mah,1990,Chemical Process Structures and Information Flow, Butterworths, Seyenoaks, U.K.. M..Perunicic, S. Krstic, M.Milivojevic, 2007, Process plant knowledge based simulation for design and manufacturing, Proceedings EUROSIM 2007-The 6th European Congress on Modelling and Simulation, 9-13, Sept., Ljubljana, 2007,pp.394. J.Savkovic-Stevanovic,1995, Process Modelling and Simulation, Faculty of Technology and Metallurgy, Belgrade. J.Savkovic-Stevanovic, T.Mosorinac, S.Krstic, R.Beric, 2007, Computer aided operation and design of the cationic surfactants production- Chapter, Chemical Engineering-24, Escape 17,Eds. V.Plesu and P.S.Agachi, Elsevier Science,p.195200. B.Thome,Ed.,1993, System Engineering-Principles and Practise of Computer Based Systems Engineering, John Wiley, New York.
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Study of Arrangements for Distillation of Quaternary Mixtures Using Less Than N-1 Columns Dulce María Méndez-Valenciaa, María Vázquez-Ojedaa, Juan Gabriel SegoviaHernándeza, Héctor Hernándeza, Adrián Bonilla-Petricioletb a
Universidad de Guanajuato, Facultad de Química, Noria Alta s/n, Guanajuato, Gto., 36050, México. b Instituto Tecnológico de Aguascalientes, Departamento de Ingeniería Química, Av. López Mateos 1801,20256, Aguascalientes, Ags. México
Abstract The design and dynamic properties of distillation sequences using side-stream columns with less than N-1 columns for separations of four-component mixtures are studied. Total annual cost and dynamic properties (using singular value decomposition) are used to compare the proposed arrangements with conventional cases. Quaternary feeds containing hydrocarbons were analyzed. For systems with low concentrations of one component in the feed, side-stream cascades often show significantly lower operating and capital costs and better dynamic properties compared to the base cases. Low purity requirements also favor side-stream cascades. Some rules are presented to predict which sequence will have the lowest capital cost and better dynamic properties. Keywords: Complex Distillation, energy consumption, dynamic properties.
1. Introduction Distillation columns consume a large portion of the total industrial heat consumption, so even small improvements which become widely used, can save important amounts of energy. To improve the energy efficiency of separation processes based on distillation, several strategies have been proposed. The optimal design and synthesis of multicomponent distillation systems remain as one of the most challenging problems in process systems engineering. When the number of products is three or four, the design and costing of all possible sequences can best determinate the most economical sequence. Often, however, unless the feed mixture has a wide distribution of component concentrations or a wide variation of relative volatilities may be based on operation factors. In that case, the direct sequence is often the choice. Otherwise, a number of heuristics and mathematical methods that have appeared in literature have proved to be useful for reducing the number of sequences for detailed examination (Seader and Westerberg, 1977; Modi and Westerberg, 1992; Brüggemann and Marquardt, 2003; Kossack et al., 2006). Most of the studies have focused on complete separation of N component mixtures using N-1 distillation columns with a reboiler at the bottom and a condenser at the top of each column. However, cascades that use less than N-1 columns for multicomponent distillation processes have not been extensively studied (Rooks et al, 1996; Kin and Wankat, 2004). In this paper, we present the design and control properties of eleven distillation arrangements with less than N-1 columns (Figure 1) for the separation of quaternary mixtures. The results are compared to five base cases with
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three columns each one (Figure 2). Some rules are presented to predict which sequence will have the lowest energy consumption, capital cost and better dynamic properties.
Figure 1. Schemes using less than N-1 columns for quaternary separations.
2. Design of Schemes In this work, we presented an energy-efficient design procedure for the design of complex arrangements. To overcome the complexity of the simultaneous solution of the tray arrangement and energy consumption within a formal optimization algorithm, we decoupled the design problem in two stages: (1) tray configuration; (2) optimal energy consumption. The first stage of our approach begins with the development of
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preliminary designs for the complex systems from the design aspects on conventional distillation columns. The conventional sequences (Figure 2) show six different tray sections.
Figure 2. Conventional schemes for quaternary separations.
These sections are used as a basis for the arrangement of the tray structure of the coupled schemes through a section analogy procedure. For instance, in the main column of the complex sequence of Figure 1a, the total number of trays is obtained by conceptually moving the stripper section from the third column to the bottom of first column of conventional sequence (Figure 2a). This situation generates an arrangement with less than N-1 columns to base cases with three columns. A similar procedure is applied to obtain the other complex schemes. After the tray arrangement for the arrangement with less than N-1 columns have been obtained, an optimization procedure is used to minimize the heat duty supplied to the reboilers of each complex scheme, taking into account the constraints imposed by the required purity of the four products streams. The optimization strategy can be summarized as: (a) A base design for the
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complex schemes is obtained. (b) Values for each side stream stage and flow were assumed. (c) A rigorous model for the simulation of complex schemes with the proposed tray arrangement is solved. In this work Aspen Plus was used for this purpose. If the product compositions are obtained, then the design is kept; otherwise, proper adjustments must be made. (d) One value of side stream flow is changed, going back to step (c) until a local minimum in energy consumption for the assumed value of side stream stage is detected.(e) The value of side stream stage is modified, going back to step (c) until the energy consumption is minimum. This result implies that an optimum value has been detected for the design of the complex scheme.
3. Control Properties One of the basic and most important tools of modern numerical analysis is the Singular value decomposition (SVD). One important use of the SVD is in the study of the theoretical control properties in chemical process. One definition of SVD is:
G = VΣ W H
(1)
In the case where the SVD is used for the study of the theoretical control properties, two parameters are of interest: the minimum singular value (σ∗), җthe maximum singular value (σ∗), and its ratio known as condition number (γ). The systems with higher minimum singular values and lower condition numbers are expected to show the best dynamic performance under feedback control (Klema and Laub, 1980). Also, it is important to note that a full SVD analysis should cover a wide range of frequencies.
4. Case of Study The case studies were selected to reflect different separation difficulties and different contents of the intermediate component of the quaternary mixtures. The mixtures considered are displayed in Tables 1 - 2. The mole fraction of 0.05 was shown to be a borderline value for use of side-stream columns for ternary separations (Tedder and Rudd, 1978). The total feed flowrate for all cases was 45.5 kmol/h. Since the feed involves a hydrocarbon mixture, the Chao-Seader correlation was used for the prediction of thermodynamic properties. The design pressure for each sequence was chosen such that all condensers could be operated with cooling water. Table 1. Examples with n-heptane.
Table 2. Examples with n-octane. Feed Composition (kmol/hr)
Feed Composition (kmol/hr) Component
M1
M2
M3
M4
M5
n-butane
A
2.56
30
5
5
30
n-pentane
B
25.64
3
45
25
40
n-hexane
C
41.03
55
45
40
25
n-heptane
D
30.77
12
5
30
5
Component
M6
M7
M8
n-butane
A
30
5
3
n-pentane
B
40
25
55
n-hexane
C
25
40
12
n-octane
E
5
30
30
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5. Results From the simulation results for the mixture M1 (Table 3) the system CS–III has the lowest TAC (and energy consumption). The base case shown in CS-IV is next and presents a significantly higher TAC. The purities of all products can be improved by adding more stages for both base cases. Table 3 displays the simulation results for example M1 for saturated liquid side-stream cascades (Figure 1a–1f) and for saturated vapor side-stream cascades (Figures 1g–1k). Since there is little component A in the feed, we expect the saturated liquid side-stream systems to be in general better than saturated vapor side streams. The TAC and energy consumption values confirm this conclusion (Schemes CC – I to CC – V have the lowest values in comparison with configurations CC- VI to CC – X). On the basis of the results, the configurations CC-II and CC-III are the best of the side-stream configurations (they have similar values of TAC and reboiler duty). They require similar heating than the best base cases, and TACs are similar to that of the best conventional sequence. However, the conventional sequences are more flexible if the concentration of A in the feed increases. In this case a more detailed dynamic behavior study would be justified. Similar conclusions can be shown for all mixtures. For this initial analysis of complex configurations, we simply estimated the SVD properties for each separation system at zero frequency. Such analysis give some preliminary indication on the control properties of each system around the nominal operating point. Table 4 gives the results for the SVD test for each sequence (case M1). In the case of conventional sequences, the CS- V has the best values. In the case of the complex sequences, the schemes CC-II and CC-III show the best results, which imply that those sequences are better conditioned to the effect of disturbances than the other complex systems. Those results show that the saturated liquid side-stream systems have better dynamic behavior. This situation is similar to the TAC values for the case M1, since there is little A in the feed. Similar results can be showed for the other mixtures in the case of the control properties. Based on the trends observed, we propose some heuristics for the use of complex sequences (best options in TAC values and dynamic behavior): (a) Use a complex scheme with a liquid side stream above the feed if there is a small amount (approximately 0.05 mole fraction or less) of the most volatile component in the feed. (b) A complex scheme with a vapor side stream below the feed can be used if there is a small amount (approximately 0.05 mole fraction) of the least volatile component in the feed to this column. (C) If a product is required at low purity side-stream configurations that withdraw this product as a side stream are often favored, but heuristic 1 must be satisfied. Table 3. Total annual cost (TAC, $ x 103/yr) of some representative cases of study.
CC - I CC - II CC - III CC - IV CC - V CC - VI CC - VII CC - VIII CC - IX CC - X CC - XI
M1
M2
M3
828 630 603 1879 1983 4191 2429 2497 2812 3521 4523
28905 1926 2394 512 1373 1522 1510 1038 3802 3843 2291
852 866 669 3092 3275 961 543 600 3000 3044 1053
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Table 4. Minimum singular value and condition number for each structure (M1). Sequence
σ*
γ*
CC - I CC - II CC - III CC - IV CC - V CC - VI CC - VII CC - VIII CC - IX CC - X CC - XI
1.4653 E-4 2.3106E-3 5.5807E-3 16101E-3 20189E-4 8.7115E-11 1.3788E-3 1.5073E-3 1.1245E-3 4.5061E-7 8.959E-4
20.714E3 487.7 552.7 95.91E2 121.387E3 43.860E8 42.35E2 64.29E2 18.43E2 14.924E6 59.70E2
6. Conclusions A general energy-efficient design procedure is developed for any type of the sidestreams designs with less than N-1 columns. The method is based on a section analogy procedure with respect to the characteristics of a conventional distillation sequence. The methodology provides a robust tool for the design of multicomponent side-streams designs. Some trends were observed for the use of complex sequences: the best option in TAC values and dynamic properties for complex schemes with a liquid side stream above the feed is when there is a small amount (approximately 0.05 mole fraction or less) of the most volatile component in the feed. In the case of complex scheme with a vapor side stream below the feed is when a small amount (approximately 0.05 mole fraction) of the least volatile component in the feed to this column. In the other cases, the best option is the conventional sequences. The heuristics can be considered useful because they were based on a detailed economic analysis.
7. Acknowledgment The authors acknowledge financial support received from CONCyTEG, CONACyT, Universidad de Guanajuato and Instituto Tecnológico de Aguascalientes, México.
8. References S. Brüggemann and W. Marquardt, 2003, Computer Aided Chemical Engineering, 15, 732. J.K. Kin and P.C. Wankat, 2004, Ind. Eng. Chem. Res., 43, 3838. V.C. Klema and A.J. Laub, 1980, IEEE Transactions on Automatic Control, 25, 164. S. Kossack, K. Kraemer and W. Marquardt, 2006, Ind. Eng. Chem. Res., 45, 8492. A.K. Modi and A.W. Westerberg, 1991, Ind. Eng. Chem. Res., 31, 839. R.E. Rooks, M.F. Malone and M.F. Doherty, 1996, Ind. Eng.Chem. Res., 35, 3653. J.D. Seader and A.W. Westerberg, 1977, AIChE J., 23, 951. D.W. Tedder and D.F. Rudd, 1978, AIChE J., 24, 303.
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A Hybrid Meta-heuristic Method for Logistics Optimization Associated with Production Planning Yoshiaki Shimizua, Yoshihiro Yamazakia, Takeshi Wadab a
Production Systems Engineering, Toyohashi University of Technology, Toyohashi, Aichi, 441-8580, Japan b Industrial Systems Engineering, Osaka Prefectural College of Technology, Neyagawa, Osaka, 572-8572 Japan
Abstract Associated with a strategic optimization of logistics network design to improve the business efficiency, we developed a method termed hybrid tabu search, and have applied it to various real-world problems through imposing proper conditions on the generic model. During a planning horizon for the design, however, there usually occur various changes assumed constant in such a strategic or static consideration. In this study, therefore, we have extended the previous method so that we can make a more reliable and operational decision by taking into account the dynamic circumstances and focusing on the role of inventory management of warehouse over planning horizon. Finally, numerical experiments revealed the significance of multi-term planning and the validity of the proposed method in comparison with the commercial software. Keywords: Multi-term logistics planning, Inventory management, Large-scale combinatorial optimization, Hybrid tabu search.
1. Introduction Logistic optimization has been acknowledged increasingly as a key issue of supply chain management to improve the business efficiency under global competition and agile manufacturing. Though many studies have been made in the operations research field associated with the combinatorial optimization (for example, Campbell, 1994), we need to make more elaborate efforts to cope with complex and complicated real world problems. From such aspect, we concerned various logistic optimization problems for strategic or static decision making. Associate with the production planning, however, it is necessary to notice the various deviations assumed constant in the strategic or static model. Taking into accounts such a dynamic circumstances, we can make a more reliable and operational decision making. In this study, therefore, we have extended our previous approach termed hybrid tabu search so as to deal with multi-term problem, and incorporate an inventory management of warehouse or distribution center (DC) into the logistic network design optimization. After presenting a general formulation and its algorithm, the validity of the proposed method is shown through numerical experiments.
2. Problem Formulation 2.1. Preliminary Statements Many studies in the area of operations research emphasize to develop new algorithms and compete their abilities through simple benchmarking and/or to prove theoretically the facts about how fast, how exactly and how large problem to be solvable. However,
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easy applications following these outcomes often cause a dramatic increase in problem size in real world problems, and accordingly such a difficulty that makes almost impossible to solve the resulting problem by any currently available software. Under such understanding, to cope with the specific problem in complex and complicated situation, we concerned various logistic optimization problems subject to the conditions such like a realistic discount of transportation cost, flexibility against demand deviations, multi-commodity delivery and so on (Shimizu & Wada, 2004; Wada, Shimizu & Yoo, 2005; Shimizu, Matsuda & Wada, 2006; Wada, Yamazaki & Shimizu, 2007). The hybrid tabu search used in those studies decomposes the original problem into upper-level and lower-level sub-problems, and applies a suitable method for each sub-problem. The upper level sub-problem decides the locations of DC by the sophisticated tabu search. Tabu search (TS; Glover, 1989) is a metaheuristic algorithm on a basis of local search technique with a memory structure. The TS repeats the local search iteratively to move from a current solution x to a possible and best solution x' in the neighbor of x. To avoid the cycling of the solution, the TS uses the tabu list that prohibits transition to any solutions for a while even if this will improve the current solution. On the other hand, the lower level sub-problem decides the network routes under the prescribed upper level decision. It refers to a linear program possible to be transformed into a minimum cost flow (MCF) problem. In practice, this transformation is carried out by adding virtual nodes and edges to the physical configuration as illustrated in Fig.1. Then the resulting MCF problem can be solved by the graph algorithm for which especially fast solution algorithm such as CS2 (Goldberg, 1997) is known. Now, by returning to the upper-level, neighbor locations are to be evaluated following the algorithm of the sophisticated tabu search. These procedures will be repeated until a certain convergence criterion has been satisfied. Figure 2 illustrates schematically this solution procedure. Selection probability of the local search operation summarized in Table 1 is decided based on the following ideas. It makes sense that the search types like “Add” and/or “Subtract” might be used often at the earlier stage of search while “Swap” is more suitable at the later stage where the number of open DCs attain almost at the optimum. Letting it be a basis to decide the probability, we further extended an idea to do it more effectively using the long-term memory or a history of so far search processes. That is, the probability of each operation is increased by a certain rate if it has brought about the update of solution. In contrast, these values are reset when the tentative solution is not improved by the prescribed consecutive duration and/or an feasible solution has not been obtained.
Fig.1 Transformation of network to MCF graph
Fig.2 Schematic procedure of hybrid tabu search
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Table 1 Employed neighborhood search operations Search type
Selection probability
Neighborhood operation
Add
padd
Let closed DC open.
Subtract
psubtract
Let open DC close.
Swap
pswap
Let closed DC open and open DC close.
2.2. Multiterm Model over Planning Horizon We have extended the static or single-term development to cope with the multi-term problem in a practical manner. By making use of the available stock of DC to the descendent periods (inventory management), we can expect to bring significant effects to the strategic decision making. After all, we have formulated mathematically the problem as a mixed-integer programming problem stated below. The objective function is composed of the total transportation cost between every facility, the total production cost at plant, and the total operational cost at each facility, the total holding cost at DC over the planning horizon, and the total fixed-charge for the open DCs. On the other hand, the constraints require to meet the demand of every customer every period; capacity constraint at each DC every period. The upper and lower bounds on the production ability of each plant every period, and the material balance at each DC every period. Additionally, non-negative conditions are imposed on the material flows and binary condition on the open/close selection. Finally, the model has the problem size such that: number of integer variables is J, continuous variables T (IJ+J2+JK+IK+J), and constraints T(2I+2J+K) where notation I, J, K and T denote number of plants, DCs, customers and terms, respectively.
3. The Hybrid Tabu Search for Multiterm Transport Under the multi-term condition, the lower level sub-problem of the hybrid tabu search needs to decide the network routes for every period. It refers to a linear program whose coefficient matrix becomes almost block diagonal per each period and expands rapidly with the number of terms as known from the foregoing statement.
(a)
(b) (b)
Fig.3 Transformation procedure to aggregate MCF graph for three-term problem: (a)Add edges for inventory, and (b) Final stage
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Table 2 Labeling on the edge Edge ID
Cost
Capacity
Description
#1
0
tЩTiЩI Pit
source㧙
#2
Cit
Pit - Pit
#3
t
Pi
t
Ci
t
source㧙plant i (period t) 㧙plant i (period t)
#4
Eij
#5
Hj
t
#6
Ejj't
DC j㧙DC j' (period t)
#7
Ejkt
DC j㧙customer k (period t)
#8
Eikt
plant i㧙customer k (period t)
D
Dkt
customer k㧙sink (period t)
stock at DC j (period t)
#9 #10
Kj
t
plant i㧙DC j (period t)
Uj
t
between doubled nodes representing DC
Noticing a special topological structure associated with the minimum cost flow problem, however, we can present a smart procedure to transform the bulk original problem into a compact form as follows: Step 1: Every period, place the nodes that stand for plant, DC (doubled), and customer. Next, virtual nodes termed source, , and sink are placed at the top and the bottom, respectively. Then connect the nodes between source and (#1), source and plant (#2), and plant (#3), up and down DC nodes (#5), and customer and sink (#9). This results in the graph as depicted in Fig.3 (a). Step 2: Letting z be the total amount of customer demand over planning horizon, z=t Щ Tk Щ K Dkt, flow this amount into the source, and flow out from the sink. Step 3: To constrain the amounts of flow, set the capacities on the edges identified by #1, #2, #3, #5 and #9 as each in “Capacity column” in Table 2. Apparently, there never induce any costs on edge #1 and #9 for the connections. Step 4: To allow the stock at DC, add the edges from down-DC node to up-DC node in the next period (#10) as shown in Fig.3 (a). For the labeling, see the “#10” row of the table. Step 5: Connect the edges between plant and DC (#4), DC and DC (#6), DC and customer (#7) and plant and customer (#8) every period. Step 6: Finally, place the appropriate label on each edge. From all of these, we have the final graph as shown in Fig.3 (b) that makes it possible to still apply the graph algorithm like CS2 (Goldberg, 1997). Consequently, we can solve the extensively expanded problem extremely fast compared with the linear programs.
4. Numerical Experiment 4.1. Preliminary Experiments In long term planning, instead of the dynamic model, a strategic or conceptual decision is often made based on the averaged values for the time being. This is equivalent to say that we attempt to obtain only a prospect from the static or single-term problem whose parameters fluctuate in reality over the planning horizon such as demand.
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To verify the advantage of considering the dynamic model that makes use of the stock at DC, first we compared the results between the (averaged) single-term model and the multi-term model using small size benchmark problems. In Table 3, we summarize the results taken place under the conditions of demand deviations. Thereat, we know that the dynamic model can derive the decisions with less total costs (the value of average model is represented as the rate to that of the multi-term model to be one hundred). Particularly, it is remarkable that the average model involve an infeasible solution against the demand deviations while the multi-period model always copes with the situation by virtue of the inventory management. For example, as shown in Fig.4, the appropriate production plan is carried out and the stocks at the DC are utilized to meet the customer demands changed beyond the production ability at plant.
Fig.4 Role of inventory in multi-term planning Table 4 Computation environment for numerical experiments Method
CPU type
Memory
OS
CPLEX
Pentium4 3.0 GHz
512 MB
Windows XP
This work
Pentium4 3.0 GHz
512 MB
Debian 3.0
4.2. Evaluation of the Proposed Algorithm From so far discussions, it is interesting to examine the effectiveness of the proposed method in terms of problem size. Every result of the proposed method is averaged over five trials. In Table 4, we summarize the computation environment for the present numerical experiments. Figure 5 compared the CPU times along the number of planning horizon between the proposed method and CPLEX 9.0 (parameters deciding problem size are set as I=2, J=25 and K=30, and a few problem sizes are shown there.). Thereat, we can observe the CPU time of the proposed method increases almost linearly while exponentially for the CPLEX. As shown in Table 5, the proposed method can derive the same results as the CPLEX (supposed optimal) with much shorter CPU times for every problem within the range where we can compare. For each, the gap between MIP and its LP relaxed problem stays almost at constant, say 8 㨪 10%, but the load (CPU time) rate increased considerably (but not so rapidly) with the term.
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Fig.5 Comparison of CPU time with commercial software
* Objective function value of Hybrid tabu/CPLEX
From these numerical experiments, the proposed method is expected to achieve the high approximation rate of optimality fast even for larger problems, and supposed to be promising for real world applications.
5. Conclusions This paper concerned a multi-term logistic optimization problem by extending a twolevel method termed hybrid tabu search developed by the authors previously. For this purpose, we have invented a systematic procedure to transform the mathematical programming model into a compact graph model manageable for inventory over the planning horizon. This enables us to solve the long-term logistic network optimization problem that any other methods never have dealt with. Numerical experiments revealed that such inventory control could bring about an economical effect and robustness against demand deviations. The validity of the proposed method was also shown in comparison with the commercial software.
References J. F. Campbell (1994). Integer programming formulations of discrete hub location problems, European Journal of Operational Research, 72, pp. 387-405 F. Glover (1989). Tabu search: Part I., ORSA Journal on Computing, 1, pp.190-206 A. V. Goldberg (1997). An Efficient Implementation of a Scaling Minimum-cost Flow Algorithm, J. Algorithm, 22, pp.1-29 Y. Shimizu and T. Wada (2004). Logistic Optimization for Site Location and Route Selection under Capacity Constraints Using Hybrid Tabu Search, Proc. 8th Int. Symp. on ComputerAided Process Systems Engineering, pp.612-617, Kunming, China Y. Shimizu, S. Matsuda and T. Wada (2006). A Flexible Design of Logistic Network against Uncertain Demands through Hybrid Meta-Heuristic Method, Proc. 16th Europe. Symp. on Computer-Aided Process Engineering, pp.2051-2056, Garmisch Partenkirchen, Germany T. Wada, Y. Shimizu, Jae-Kyu Yoo. (2005). Entire Supply Chain Optimization in Terms of Hybrid in Approach, Proc. 15th Europe. Symp. on Computer-Aided Process Engineering, pp.1591-1596, Barcelona, Spain T. Wada, Y. Yamazaki, Y. Shimizu (2007). Logistic Optimization Using Hybrid Meta-heuristic Approach, Transaction of the Japan Society of Mechanical Engineers, C-727, 73, pp.919-926
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Model-based investment planning model for stepwise capacity expansions of chemical plants Andreas Wiesnera, Martin Schlegelb, Jan Oldenburgb, Lynn Würtha, Ralf Hannemanna, Axel Poltb a
AVT-Lehrstuhl für Prozesstechnik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany b Corporate Engineering, BASF Aktiengesellschaft, Carl-Bosch-Str. 38, 67056 Ludwigshafen, Germany
Abstract In this contribution a novel investment planning model for the development of stepwise capacity expansion strategies for chemical plants is proposed. This method is implemented in a decision support tool that can be used during the early stage of plant engineering - a phase which is concerned with the conversion of a chemical process into a highly profitable plant. Based on a previous work by Oldenburg et al. [1], who proposed a method for a quick economic comparison of possible stepwise plant expansion scenarios versus building a full capacity plant, the approach presented in this paper is capable of identifying the optimal process-specific investment strategy on the level of unit operations. A mixed-integer linear programming model dedicated for stepwise capacity expansion strategies for chemical process plants forms the core of the tool. Keywords: Investment planning, Stepwise capacity expansion, Mixed-integer linear programming
1. Introduction One important decision to be taken in the course of investment projects for new chemical productions plants is the production capacity, for which the plant should be designed. In most cases, this decision is based on (often uncertain) marketing forecasts. From an economical point of view, it is paramount to meet the predicted sales amount with the plant capacity rather than having significant over- or under-capacities. Typically, the product demand is expected to grow in the future. However, the wider the time horizon is set for the forecast the less reliable the forecast becomes. In this context, it would be desirable to determine the optimal initial production capacity followed by an optimal sequence of future expansion steps in order to accommodate the product demand without unprofitable overcapacities. Such an approach is certainly more complex and requires taking future measures well into account during the planning phase. Even then, it is by no means certain, whether a stepwise expansion is economically more attractive. Due to those and several other reasons, it is common practice to install the largest possible capacity already at the beginning of the process life cycle, which we will term the “conventional strategy” in the following. To face the aforementioned challenge, Oldenburg et al. [1] proposed a method which enables a quick comparison of possible stepwise plant expansion scenarios versus building a full capacity plant. However, this method is not able to deliver a specific expansion strategy
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in detail, e.g. which piece of equipment has to be installed with which capacity at what time. For this purpose, an investment planning model for the identification of the economically most attractive investment strategy incorporating independent expansions of process units is addressed in this contribution. We propose an optimization approach using an investment planning model. It determines an optimal investment strategy by minimizing the investment costs including depreciation and discounting. The decision variables for the optimization are the dimensions of the installed equipment as well as the time points of installation and/or expansion. Due to the discrete-continuous nature of the problem, a linear mixed-integer formulation (MILP) is used for this purpose. The proposed method may be categorized as a multi-period investment model. The remainder of this paper is organized as follows: Section 2 relates our model to well known approaches based on multi-period investment models proposed in the literature. In Section 3, our investment planning model is introduced while in Section 4 the investment planning strategy of a generic process is presented as a case-study. Section 5 gives a discussion on the results of the case study. Finally, in Section 6 our findings are summarized.
2. Related Multi-Period Investment Models The proposed optimization approach falls into the category of multi-period investment models. Various related approaches can be found in the literature, (e.g. [2], [3]), including MILP optimization for long range investment planning. Some authors also consider stochastic elements to cover the potential uncertainties, which, however, is beyond the scope of this paper. The suggested investment model adopts the multiperiod MILP problem proposed by Sahinidis et al. (1989), which was originally intended to describe large sites consisting of many interconnecting processes producing many chemicals (cf. Fig. 1). For this reason, all process units employed in such a process are assumed to obey identical investment strategies. E
C
A
C
A
C
B A
C
Process 2
Process 1
D
A
A B
B
C
(3) Mixer
Process 3
Fig. 1: Schematic depiction of the multiperiod investment problem as proposed by Sahinidis et al. (1989)
A
A C
(1) Reactor
C
(2) Separation unit
Fig. 2: Schematic depiction of the investment planning model as proposed in this work
Our approach, in turn, can be considered as a process synthesis problem (simplified by linearization) with an additional time dimension, which, to the authors’ knowledge, has not yet been addressed on the level of detail down to unit operations and single pieces of equipment (cf. Fig. 2). Aiming at a stepwise capacity expansion, this is important though, since processes typically consist of a broad range of equipment with different operating ranges and size factors, requiring adapted expansions for different parts of the
Model-Based Investment Planning Model for Stepwise Capacity Expansions
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plant. The main issue of this contribution is the specific capacity expansion timing and sizing for each process unit in order to cope with particular investment strategies required for different chemical process units. Therefore, the MILP problem formulation of the investment planning model adds various additional constraints to fulfill the specific requirements as described in the subsequent section.
3. Investment Planning Model First of all, some requirements are stated: the specific problem that is addressed in this paper assumes that a network of process units and a set of chemicals are given. Ideally, this network is based on a stationary process flow diagram and thus all mass fluxes, design temperatures and design pressures are known. Also given are forecasts for the demands of products as well as the investment costs over a finite number of time periods within a long range planning horizon. Furthermore, it is assumed that the availability of raw materials and the demand of products are always fulfilled. In the following the investment planning model is described. The process units are connected by material streams, which include raw materials, intermediates and products. It is assumed that all required units in the process may be represented by one or more of the following three types of model units with respect to the mass balance (cf. Fig. 2): Type (1) represents the function of a reactor. This means that a different set of chemicals may enter and leave the unit due to a physico-chemical conversion. Moreover, it is assumed that material balances for raw materials and by-products can be expressed in terms of linear ratios to the production of the main product. Type (2) describes the function of a separation unit. By means of splitting factors, determined previously in the process simulation, a selective separation is modeled. The same set of incoming and outgoing chemicals is compulsory. Finally, type (3) represents the function of mixing, which is particularly of interest for recycle streams and the union of different partial processes. Again, the set of incoming and outgoing chemicals has to be identical. Either dedicated processes for single product or flexible processes can be modeled, which may operate in either a continuous or batch mode. Process flexibility is realized by a set of alternative production schemes producing different chemicals on identical process units. The process capacity for dedicated processes is determined by the set of process units that are required for a specific production scheme. For flexible processes, the capacity of a process unit has to accommodate for each production scheme. A capacity expansion can be accomplished by either adding parallel equipment or replacement of insufficient equipment. For flexible processes a capacity adaptation due to product change is guaranteed. Technical limitations are fulfilled by means of operating range constraints. Also, technical limits on capacity expansion timing and sizing as well as lead times for the installation can be specified. Generally, it is assumed that the process unit capacity can be expressed linearly depending on the sum of overall material flow leaving the process unit production scheme. Because plant extensions imply temporary shutdowns, constraints are added to guarantee a minimum of downtimes through combined capacity extensions. The objective function minimizes the investment costs over the given horizon and consists of the terms: 1) discounted linearized invest cost of all pieces of equipment, 2) additional costs, e.g. lack of production due to downtimes, and 3) cost savings due to depreciation related tax savings. Linear models are assumed for the mass balances. The cost relation during an early project phase can be nicely captured by a power function that is frequently applied for rough equipment cost estimations:
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C 2 § Q2 =¨ C1 ¨© Q1
· ¸¸ ¹
CEX
(1)
Based on a known cost C1 of an investment of capacity Q1 and so-called capacity exponent CEX, the cost C2 of a new capacity Q2 can be calculated using Eq. (1). Since the cost function is nonlinear, a piecewise linear approximation, e.g. the one proposed by Croxton et al. [4], of the cost function has to be applied leading to an overall linear model. The time horizon is divided into 1 year time periods.
4. Case Study The case study deals with a dedicated process, shown in Fig. 3, to which the investment planning model is applied. The process consists of ten process units including distillation and absorption columns, compressor, pump, heat exchanger and a reactor. Condenser Light ends column Reactant
Product column
Reactor Compressor
Raw material
Product
Vent Gas
By-product
Product Desorber
Heat exchanger
Pump By-product column
Product Absorber
Valuable by-product
Fig. 3: Example process considered for the stepwise capacity expansion
The catalytic reactions take place in the reactor assuming catalyst deactivation. The reaction states that the raw material and a reactant yield the main product. Additionally, a side reaction from raw material to an undesired by-product is considered by conversion of the reactant. Additionally, a second reaction involving the product and the absorbent in the product desorber is assumed to take place, which yields a valuable by-product. Each operation unit capacity is assumed to be designable within an upper and lower boundary to accommodate for any considered production rate. The product demand forecasts are given for a ten year horizon. The costs are represented by power functions which vary in terms of capacity exponents and hence different investment decisions for the process units are expected. The capacity exponents (c.f. Table 1) for the cost functions are taken from Peters and Timmerhaus [5]. For the piecewise linear approximation of the cost function, two time intervals are considered as default. Due to maximum capacity restrictions, the overall capacity of the reactor and the product absorption unit is achieved by an installation of at least three parallel reactors and two parallel absorption units comprising the same capacity. Equipment
Reactor
Column
Heat exchanger
Compressor Pump
Capacity exponent
0.65
0.6
0.44
0.69
0.34
Table 1: Values for capacity exponents for selected pieces of equipment
Due to technical/physical limitations, the range of operation of the compressor and the heat exchanger must be within 60%-100% and 80%-100% of the installed capacity,
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respectively. The capacity expansion can take place either in terms of a parallel installation of identical equipment, or a replacement of equipment accommodating the complete required capacity. In the case study only the compressor is assumed to be of the latter type. Furthermore, a lead time of two years is assumed for each expansion. Expansions of several pieces of equipment are integrated into one simultaneous expansion step. Due to the deactivation of the catalyst, a complete shut down of the process is assumed to take place every two years. The required capacity expansion can be carried out in the period of shut down to minimize the loss of production yield. Hence, any losses of production yields are neglected in this example process.
5. Results & Discussion
1,2
1
1
Fig. 4: Installed capacity sequence according to the conventional investment strategy
Product demand
Condenser
Pump
Compressor
By-product column
Heat exchanger
0
Product column
0,2
Reactor
0,4
L.E. column
0,6
Desorption column
0,8 Absorption column
Product demand
Pump
Condenser
Compressor
Heat exchanger
By-product column
0
L.E. column
0,2
Product column
0,4
Desorption column
0,6
Absorption column
0,8
standardized capacity
1,2
Reactor
standardized capacity
Based on the data mentioned in the previous section, the MILP model has been formulated. Due to the lack of space a thorough discussion of the model equation is impossible. The model has been solved applying the MILP solver SYMPHONY [6]. For the product demand an initial 35% of the total product demand achieved in the tenth year was assumed with a linear progression. This product demand forecast was used for the conventional alternative and the stepwise capacity expansion.
Fig. 5: Installed capacity sequence according to the stepwise capacity investment strategy
Fig. 4 and 5 show the result of the two investment alternatives. The sequence of the installed capacity over the given time horizon for the specific process units are each identified to the left of the diagram and the product demand forecast is located to the right of the respective diagram. Within the diagram one bar represents the investment sequence of one piece of equipment. The differences observed between the two alternatives may be summarized as follows: Equipment with a wide operational range, e.g. a column, is not affected by the stepwise capacity expansions at all, except for the units which were primarily intended on multiple unit installation with restricted capacities. However, for units which have a narrow operating range, the optimal investment strategy is achieved by stepwise capacity expansions. Hence, depending on the characteristics of the product demand a completely different optimal investment strategy for such equipment may arise. The overall discounted investment costs for the alternative are shown in Fig. 6. It demonstrates the significant reduction of investment costs, of about 7 % in total, when applying the stepwise capacity expansions. The major part of the cost reduction is achieved by the postponed installation of the third reactor and the second absorption unit. An experienced engineer may have achieved the obvious cost reduction by splitting the installation of the reactors and the absorption unit as well. However, there still exists a cost reduction due to the rigorous optimal timing and sizing which can be shown exemplarily for the heat exchanger and
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30000
7000
25000
6000
discounted investment cost (in T€)
discounted investment costs (in T€)
condenser capacity expansion. The comparison of cost resulting by either of the investment strategies for the heat exchanger and the condenser is given in Fig. 7. A total cost reduction of about 3.5 % in favor of the stepwise capacity expansion is achieved.
20000 15000 10000 5000
5000 4000 3000 2000 1000 0
0 1
3
5
7
9
total
year of investment conv. investment planning
stepw. investment planning
Fig. 6: Comparison of overall discounted investment costs
1
3
5
7
9
total
year of investment conv. investment planning
stepw. investment planning
Fig. 7: Comparison of heat exchanger and condenser investment cost
6. Conclusions A novel investment planning model for chemical plants has been proposed, which aims at stepwise capacity expansions. It provides the proper timing and sizing of the process units in order to minimize unprofitable overcapacities. That way, economically attractive alternatives compared to conventional investment planning can be offered already at an early stage of planning. Alternatively, it can be proven that the conventional planning, namely installing the full capacity at once, is the most attractive option for the considered case. The method is based on an extension of established multi-period investment models (MILP) and thus provides the minimal discounted investment costs for each process unit in the considered process. For our case study, it has been shown that the investment strategy of operation units with a wide operating range does not significantly vary for the conventional and the stepwise investment planning. However, for units with a narrow operation range, a significant investment cost reduction due to the proper timing and sizing of the unit installation was achieved.
References [1] J. Oldenburg and M. Schlegel and J. Ulrich and T.-L. Hong and B. Krepinsky and G.Grossmann and A. Polt and H. Terhorst and J.-W. Snoeck, A Method for quick evaluation of stepwise plant expansion scenarios in the chemical industry, in: V. Pleasu and P.S. Agachi (eds.) : 17th European Symposium on Computer Aided Process Engineering, Elsevier, 2007 [2] N.V. Sahinidis and I.E. Grossmann and R.E. Fornari and M. Chathrathi, Optimization model for long range planning in the chemical industry, Computers chem. Engng., 13, 9 (1989) 10491063. [3] L.C. Norton and I.E. Grossmann, Strategic planning model for complete process flexibility. IECRED, 33 (1994) 69-76. [4] K.L. Croxton and B. Gendron and T.L. Magnanti, A comparison of mixed-integer programming models for nonconvex piecewise linear cost minimization problems, Management Science, 49, 9 (2003) 1268-1273 [5] M.S. Peters and K.D. Timmerhaus, Plant Design and Economics for Chemical Engineers, McGraw-Hill, 4th Edition, 1991 [6] COIN-OR, SYMPHONY, 2006, online available at http://www.coin-or.org/projects.html, (accessed: 04. Oct. 2006)
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Divided Wall Distillation Column: Dynamic Modeling And Control Alexandru Woinaroschy, Raluca Isopescu UniversityPolitehnica of Bucharest, Polizu Str. 1-5, Bucharest 011061, Romania
Abstract The dynamic modeling of the dividing wall distillation column is used to determine optimal startup policies that minimise the time required to reach the imposed steady state operating values in terms of product compositions and flow rates. The problem is resolved by a convenient transformation of the dynamic model in a system of differential equations, avoiding algebraic calculations generally imposed by equilibrium solving, and by using iterative dynamic programming for the minimization of the startup time. An example referring to the separation of a ternary hydrocarbon mixture is presented. The variables that mostly influence the startup time were found to be the reflux ratio and side-stream flowrate. The optimal policies identified realise a considerable reduction of startup time, up to 70% compared to the startup operation at constant reflux ratio or constant side draw flowrate. Keywords: divided wall distillation column, dynamic modeling, optimal startup control
1. Introduction Despite its high energy consumption, distillation is the widest used separation technique in petrochemical and chemical plants. Thermally coupled distillation columns can lead to a significant energy reduction, up to 40% for the totally thermal integrated structure which is the Petlyuk column. The Petlyuk column built in a single shell is the divided wall distillation column (DWC) and is considered a very attractive solution for energy and capital cost savings in separation processes. Though its efficiency has been proved by numerous theoretical studies such as Triantafillou et al (1992), Sierra et al (2001) and also by some practical industrial applications, among which at least the 40 DWC implemented by BASF should be mentioned, the DWC is not yet a common solution. A reason for this can be a lack of understanding of the design and control of a DWC. Theoretical studies and experimental confrontations are still necessary to prove the big advantages of this solution and to find practical ways for a good design methodology and control strategies. The design and optimization of a divided wall column can be achieved by defining tray sections interconnected by liquid and vapor streams that represent the complex arrangement of a DWC. The structure used in the present paper lumps in four column-sections the trays of the DWC. These column sections represent the top of the DWC (trays above the dividing wall), the prefractionator (left side of the dividing wall) where the feed is located, the right side of divided wall where the side draw is located and the tray section below the dividing wall. The increased number of degrees of freedom (DOF) for a DWC imposes a thorough analysis of control variables to establish a convenient approach in modeling the process and establishing the control policy. Due to the increased number of DOF, both steady state and dynamic modeling of a DWC raises more problems than a simple column with a side draw and needs adequate solving algorithms. Halvorsen and Skogestad (2004) proved that the liquid and vapor splits have a great influence on the thermal efficiency
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of the DWC. More recently, Wang and Wong (2007) demonstrated that outside a given region defined by certain liquid and vapor split values, the composition control can compensate only for variation in feed characteristic, such as feed or composition, but not for internal flow changes. They proposed a temperature-composition cascade scheme to control a DWC. Temperature control strategies proved to be efficient also for complex schemes including heterogeneous azeotropic distillation and a DWC (Wang et al 2008). Startup policies must be considered as well when analysing the efficiency of a DWC. In order to promote the generalisation of DWC in industrial application it is necessary to provide reliable design methodologies and convenient start up strategies of the column. In order to promote the generalisation of DWC in industrial application it is necessary to provide reliable design methodologies, but it is also very important to define strategies for a convenient startup of the column. The present paper proposes a new dynamic model for a DWC and applies it to formulate the startup control.
2. Dynamic Distillation Model (DDM) The DDM proposed by Woinaroschy (1986, 2007) represents a good compromise between the degree of complexity and correctness. The advantage and originality of the selected model consist in the fact that the iterative algebraic equations are avoided. The core of the model consists in the following system of ordinary differential equations (with the usual notations for distillation field): Total mass balance around plate j:
dN j dt
= L j −1 + V j +1 − L j − V j ± FL , j ± FV , j
(1)
Component mass balance around plate j for component i:
d ( N j xi , j ) dt
= L j −1 xi , j −1 + V j +1 y i , j +1 − L j xi , j − V j yi , j ± FL , j x F ,i , j ± FV , j y F ,i , j (2)
Original equation for dynamic calculation of temperature on plate j: m
dT j dt
¦ =−
i =1
γ i , j Pi , j § pj m
¦ i =1
x dγ i , j ¨1 + i , j ¨ γ dx i, j i, j © xi , j γ i , j dPi , j pj
· dx i , j ¸ ¸ dt ¹
(3)
dT j
The state variables are Nj, j=1,2..n; xi,j, i=1,2..m-1, j=1,2..n; and Tj, j=1,2..n. The variation of total pressure during each time integration step is much smaller than the variations of composition and temperature. In order to simplify the procedure, the vapor pressure on each tray is considered constant along the time integration step, but it will be recomputed at the beginning of the new time step. The tray pressure drop is calculated on the base of hydraulic correlations, specific for the plate type. Vapor flow rate Vj is obtained from total energy balance and the vapor composition is calculated according to Murphree efficiency. Liquid flow rate Lj is computed on the base of Francis' correlation for the corresponding plate weir. The equilibrium,
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thermodynamic data, and other physical properties correlations are selected in function of the mixture nature. The system of differential equations was numerically integrated by fourth order Runge-Kutta-Gill method, the DDM being coded in FORTRAN.
3. Example A mixture of three components (60% benzene, 30% toluene and 10% ethylbenzene) is separated in a DWC with sieve plates and lateral downcomers. The vapor pressures Pi,j of components were calculated on the basis of Antoine equation, and the trays efficiency was set at value 1 (equilibrium trays). 3.1. Design of the divided wall column. The next column parameters were imposed as follows: feed specification: liquid at bubble point; feed flow rate: 0.0053 kmol s-1; side stream flow rate: 0.001455 kmol s-1; type of condenser: total; condenser pressure: 760 mm Hg; reflux ratio: 3; type of reboiler: total; reboiler heat duty: 417 kW; bottom liquid volume: 0.146 m3; tray surface (for top and bottom sections): 0.451 m2; tray surface (for right and left side of the dividing wall): 0.2255 m2; weir height: 0.025 m; hole diameter: 0.002 m. Using DDM (searching the values at final, stationary state) were established by several iterations the number of trays for the column sections, the location of the feed and side streams and the fraction of liquid flowing in the right hand side of the dividing wall. This iterative search was made in order to obtain the best separation of each component. The corresponding values are: Number of trays: top section: 6; left side: 15; right side: 15; bottom section: 13; Feed stream location: the 2nd from the top of the left side; Side stream location: the 3rd from the top of the right side; Fraction of liquid flowing in the right hand side of the dividing wall: 0.45. In these conditions the components’ mole fractions in the products are: 0.9564 benzene in the top product, 0.970 toluene in the side product and 0.9340 ethylbenzene in the bottom product. 3.2. Optimal startup control. Startup of distillation columns is a very challenging control and simulation problem due to both theoretical and practical aspects. A general sequence of actions which forms the basis for different startup procedures was formulated by Ruiz et al (1988). At the end of several preliminary actions all plates have enough liquid holdup, so that the liquid can start to fall down the downcomers. The downcomers are sealed and no vapor can go up through them. The liquid composition is the same on all plates, being equal with the feed composition. In the frame of present work these conditions define the initial state from which begins the effective startup transient operating regime procedure. Traditionally, the column is operated at constant values of control parameters. Usually, these are the prescribed values for the desired stationary regime. In an optimal transient regime procedure the column will be operated at prescribed time-distributed values of control parameters, in order to minimize the duration of the transient regime. In fact, optimal startup control consist in reaching a desired final state from a set of given initial condition in minimum time by an adequate control policy. That means minimization of the penalty performance index formulated as: ns
si (t f )
i =1
s si
¦ 1− I = tf + ω
ns
(4)
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where tf is the final time, Ȧ > 0 is a penalty coefficient, ssi are the desired final stationary state values, and the final values of state variables si (tf ), i = 1,2,…ns are calculated by integration of equations (1)-(3). Minimization of the penalty performance index is made through control variables ui subject to the bounds:
umini ≤ ui ≤ umaxi
i = 1, 2..., nu
(5)
A set of DDM simulations indicated that the more suitable control parameters for the optimal startup of the divided wall distillation columns are the reflux ratio and the sidestream flowrate. The task of optimal startup control of the DWC was solved using the algorithm proposed by Bojkov and Luus (1994), based on the iterative dynamic procedure given by Bojkov and Luus (1992, 1993) which employs randomly chose candidates for the admissible control. The algorithm was applied for 5 time stages. The grid points number for state-grid was 5, 9 for policy-grid, and 9 for piece time-grid. The region contraction factor was set at 0.8, and the total number of iterative dynamic procedure iterations was 10. The startup time for optimal reflux control is 120 min. and for side-stream flowrate control is 130 min. These results (for each case obtained after 44805 numerical integrations of the system (1)-(3) with 200 differential equations) are remarkable in comparison with operating at constant control parameters where the startup time is 380 min. For all these regimes the final stationary state corresponds to an average value of the normalized derivatives less than 10-6 (maximum integration step is 1 s.). In figures 1 and 2 are presented the optimal reflux control and the optimal side-stream flowrate control (subscript s indicates final, stationary value).
Figure 1. Optimal reflux control
Figure 2. Optimal side-stream flowrate control
The selected control variables (reflux or side-stream flowrate) can be easily manipulated in practical applications. In a DWC the reflux must be high enough to build-up the reflux on both sides of the dividing wall. The value of the reflux ratio strongly modifies the separation on both sides of the diving wall and hence it will affect the concentration profiles along the trays. Not only the distillate and bottom product will be influenced by the variation of reflux ratio, but also the side-stream which is desired to contain the intermediate component at very high concentration. This consideration can lead to the conclusion that a correct reflux policy will bring the DWC in stable operating condition in a reasonable time. The liquid split which is a means of controlling the side draw purity (Mutalib and Smith, 1998) was imposed at the value obtained in steady state as the feed composition did not vary in the present study. The influence of the liquid split
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variation along the startup period had an insignificant influence on the startup time. As regarding the vapor split it was left to adjust naturally according to the temperature distribution along the trays and pressure drop. In figures 3 and 4 are presented the evolutions of components’ mole fractions in the top and bottom products. In figure 3 the evolution of the benzene concentration in the top product at constant control parameters and at optimal side-flowrate control overlaps (for the entire time domain of optimal side-flowrate control, respectively 130 min.). It can be observed that the responses in the bottom concentrations are determinant for the values of startup time, as it was expected.
Figure 3. Evolution of benzene concentration in the top product for startup at constant control parameters and at optimal side-flowrate control ( ʊ ), and at optimal reflux control (---).
Figure 4. Evolution of ethylbenzene concentration in the bottom product for startup at constant control parameters (ʊ ), at optimal reflux control (---) and at optimal side-flowrate control (– · –).
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4. Discussion The selected value for the number of time stages to 5 seems to be too small. A higher value of this number increases drastically the CPU time, without a substantial improving of the performance index (Luus, 1989; Luus and Galli, 1991). In the case of side-stream flowrate control, the increase to 10 of the number of time stages have reduced the startup time only with one minute, but the corresponding control policy is more complicated. The attempt to find the optimal startup control of the divided wall column with other optimization techniques (Luus-Jaakola, Hooke-Jeeves) failed. As in the case of startup optimization of classical distillation columns (Woinaroschy, 2007) it is possible to avoid the undesirable secondary bang-bang effects of the piecewise constant control by replacing it with piecewise linear control.
5. Conclusions The dynamic model proposed proved to represent well the separation in a DWC of a ternary hydrocarbon mixture. The values of internal flows and temperature distributions along the trays reached at steady state were in good agreement with the simulations obtained in the frame of commercial simulators. The use as control variables the reflux ratio or the side-stream flowrate proved to enable a reduction of the startup time with about 70 % compared with classical startup procedures. The complex technique developed can be a useful tool in studying dynamic behavior and startup optimization for complex columns and can be easily extended to various mixtures.
References B. Bojkov, R. Luus, 1992, Use of Random Admissible Values for Control in Iterative Dynamic Programming, Ind. Eng. Chem. Res., vol. 31, p.1308 B. Bojkov, R. Luus, 1993, Evaluation of the Parameters Used in Iterative Dynamic Programming, Can. J. Chem. Eng., vol. 71. p. 451 B. Bojkov, R. Luus, 1994, Time-Optimal Control by Iterative Dynamic Programming, Ind. Eng. Chem. Res., vol. 33, p.1486 I. J. Halvorsen, S. Skogestad, 2004, Shortcut Analisys of Optimal Operation of Petliuk Distillation, Ind. Eng. Chem. Res., vol. 43, p.3994 R. Luus, 1989, Optimal Control by Dynamic Programming Using Accessible Grid Points and Region Reduction, Hung. J. Ind. Chem., vol. 17, p.523 R. Luus, M. Galli, 1991, Multiplicity of Solutions in using Dynamic Programming for Optimal Control, Hung. J. Ind. Chem., vol. 19, p. 55 M. I. A. Mutalib, R. Smith, 1998, Operation and Control of Dividing Wall Distillation Columns, Trans IchemE, vol. 76, part A, p. 318 C. A. Ruiz, I. T. Cameron, R. Gani, 1988, A Generalized Model for Distillation Columns III. Study of Startup Operations, Comput. Chem. Eng., vol. 12, p. 1 M. Serra, M. Perrier, A. Espuna, L. Puigjaner, 2000, Study of the Divided Wall Column Controlabillity: Influence of the Design and Operation, Comput. Chem. Eng., vol. 24, p. 901 C. Tryantafillou, R. Smith, 1992, The Design and Optimisation of Fully Thermally Coupled Distillation Columns, TransIChemE, part A, Chem. Eng. Res. Des., vol. 70(A5), p. 118 S. J. Wang, D. Wong, 2007, Controllability and energy efficiency of high purity divided wall column, Chem. Eng. Sci., vol. 62, p. 1010 S. J. Wang, C. J. Lee, S. S. Jang, S. S. Shien,2008, Plant-wide design and control of acetic acide dehydration system via heterogeneous azeotropic distillation and divided wall distillation, J. Process Control, vol. 18, p. 45 A. Woinaroschy, 1986, A New Model for the Dynamic Simulation of the Rectification Processes. I. Development of the Mathematical Model and Algorithm, Rev. Chim., vol. 37, p. 697 A. Woinaroschy, 2007, Time-Optimal Control of Distillation Columns by Iterative Dynamic Programming, Chem. Eng. Trans., vol. 11, p. 253
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimization of Preventive Maintenance Scheduling in Processing Plants DuyQuang Nguyen and Miguel Bagajewicz The University of Oklahoma, R. T-335 SEC, 100 E. Boyd, Norman, OK 73019, USA
Abstract A new methodology designed to optimize both the planning of preventive maintenance and the amount of resources needed to perform maintenance in a process plant is presented. The methodology is based on the use of a Montecarlo simulation to evaluate the expected cost of maintenance as well as the expected economic loss, an economical indicator for maintenance performance. The Montecarlo simulation describes different failure modes of equipment and uses the prioritization of maintenance supplied, the availability of labour and spare parts. A Genetic algorithm is used for optimisation. The well-known Tennessee Eastman Plant problem is used to illustrate the results. Keywords: Preventive maintenance, Maintenance optimization, Montecarlo simulation
1. Introduction Maintenance can be defined as all actions appropriate for retaining an item/part/equipment in, or restoring it to a given condition (Dhillon, 2002). More specifically, maintenance is used to repair broken equipment, preserve equipment conditions and prevent their failure, which ultimately reduces production loss and downtime as well as the environmental and the associated safety hazards. It is estimated that a typical refinery experiences about 10 days downtime per year due to equipment failures, with an estimated economic lost of $20,000-$30,000 per hour (Tan and Kramer, 1997). In the age of high competition and stringent environmental and safety regulations, the perception for maintenance has been shifted from a “necessary evil” to an effective tool to increase profit, from a supporting part to an integrated part of the production process. Effective and optimum maintenance has been the subject of research both in academy and in industry for a long time. There is a very large literature on maintenance methods, philosophies and strategies. In addition, there is a large number of Computerized Maintenance Management Systems (CMMS) software packages devoted to help managing / organizing the maintenance activities. Despite this abundance, the optimization of decision variables in maintenance planning like preventive maintenance frequency or spare parts inventory policy, is usually not discussed in textbooks nor included as a capability of the software packages. Nonetheless, it has been extensively studied in academic research: Many models were discussed and summarized in the excellent textbook by Wang and Pham (2006)] and various review papers, e.g. Wang (2002). Most of the models are deterministic models obtained by making use of simplified assumptions, which allow the use of mathematical programming techniques to solve. The most common optimization criterion is minimum cost and the constraints are requirements on system reliability measures: availability, average uptime or downtime. More complex maintenance models that consider simultaneously many decision variables like preventive maintenance (PM) time interval,
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labor workforce size, resources allocation are usually solved by Genetic algorithm (e.g. Sum and Gong, 2006; Saranga, 2004). Monte Carlo simulation is usually used to estimate reliability parameters in the model. Tan and Kramer (1997) utilized both Monte Carlo simulation and GA. None of preventive maintenance planning models considers constraints on resources available in process plants, which include labor and materials (spare parts). For example, the maintenance work force, which is usually limited, cannot perform scheduled PM tasks for some equipments at scheduled PM time because of the need to repair other failed equipments. Such dynamic situations can not be handled by deterministic maintenance planning models or are not considered in published maintenance planning models that use Monte Carlo simulation tools. To ameliorate all the aforementioned shortcomings, we developed a new maintenance model based on the use of Monte Carlo simulation. The model incorporates three practical issues that have not been considered in previous work: i) different failure modes of equipment, ii) ranking of equipments according to the consequences of failure, iii) labor resource constraints and material resource constraints. The maintenance model, which was developed by Nguyen et al. (2008) is integrated here with a GA optimization to optimize the PM frequency.
2. Monte Carlo simulation – based maintenance model 2.1. The objective value The objective value is the total maintenance cost plus economic loss (to be minimized). The economic loss is the loss caused by equipment failures that lead to reduced production rate or downtime. It is the economic indicator for maintenance performance, i.e. the better the maintenance plan the smaller the economic loss. Thus by minimizing the maintenance cost plus the economic loss, one simultaneously optimizes the cost and the performance of maintenance. The cost term includes four types of cost: the PM cost and CM cost, which are the costs associated with preventive maintenance and corrective maintenance activities, respectively, the Labor cost (the salary paid to employees) and the inventory cost (the cost associated with storing spare parts of equipments). The economic loss term includes two types of losses: i) economic loss associated with failed equipments that have not been repaired (for example, a fouled heat exchanger can continue operating but at reduced heat transfer rate, ii) economic loss due to unavailability of equipment during repair time. The economic loss is calculated as a loss rate ($ per day) multiplied by the duration of the period within which the loss is realized. To determine economic loss rates, an analysis is carried out on each piece of equipment to determine the economical effects of equipment failure, which include reduced production rate or even shutdown, the deterioration of product quality, etc. 2.2. Input data The following data are needed in the model: i) reliability data for equipment, ii) the time and the associated material cost to perform corrective maintenance (CM) and preventive maintenance, iii) economic data: labor paid rate, inventory cost rate and economic loss rate, iv) other data like the waiting time for an emergently ordered spare part to arrive.
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We assume that the failure distribution is exponential, thus, only one parameter is needed to describe the reliability of equipment: the mean time between failures (MTBF). Other distributions can be used but they require at least two parameters. 2.3. Ranking of repairs The equipments to be repaired are ranked according to the consequences of failures: 1 is emergent and 5 is affordable to go unrepaired. The maintenance of equipments with higher rank (higher priority) takes precedence over the lower ranked ones (Table 1). Table 1: Ranking of equipments for Maintenance purpose (following Tischuk, 2002) Consequence of Failure Probability of subsequent catastrophic Failure
High
Medium
Low
High
1
2
3
Medium
2
3
4
Low
3
4
5
2.4. Failure modes of equipments An equipment may have different failure modes involving different parts of the equipment. It can fail because of deterioration of mechanic parts (possible consequence is complete failure that requires equipment replacement) or electronic parts malfunction (partial failure that can be repaired). Different failure modes need different repair costs and repair times and induce different economic losses. The sampling of different failure modes of equipment is done as follows: i) assign a probability of occurrence for each type of failure mode using information on how common a failure mode is, ii) at the simulated failure time of the equipment, the type of failure mode that actually occurred is sampled in accordance with the failure modes’ probability of occurrence. 2.5. Decision variables Three decision variables are considered in the model: i) the PM time schedule that involves two parameters: the time to perform the first PM (called PM starting time) and the PM time interval, ii) the inventory policy, which is the decision whether to keep inventory for a specific spare part necessary for repairing a specific equipment, iii) the number of maintenance employees. The PM starting time and PM time interval are expressed as a fraction of MTBF (e.g. PM time interval = a*MTBF), the fraction a is to be optimized (for each equipment).
3. Monte Carlo simulation procedure Most of the material in this section is taken from a recent paper (Nguyen et al, 2008) that has explored the use of Monte Carlo simulation for evaluation purposes. 3.1. Maintenance rules - No delay in performing maintenance once the resources are available - If equipment has undergone corrective maintenance a predetermined period of time prior to the scheduled PM (current value = 7 days), the PM is suspended so that resources can be used elsewhere
D.Q. Nguyen and M. Bagajewicz
322
-
If, due to unavailability of resources, repair of an equipment has been delayed more than a predetermined threshold value (current value = 21 days), the priority for repair of that equipment is upgraded one level
3.2. Simulation details This technique is based on repeated sampling of the equipment failure and evaluation of the cost of maintenance activities as well as the economic losses associated to the failed states of equipments. The method continues sampling and computing an average until the average converges to a finite value. The sampling procedure is as follows: -
-
-
Failure times of equipments are sampled using reliability function (failure rate) of equipments At failure times of equipment, the type of failure modes that caused equipment failure is sampled in accordance with the probability of occurrence. The cost of corrective maintenance, the repair time and the economic losses are determined corresponding to the type of failure modes identified. Preventive maintenance requests for equipments are generated in accordance with the predetermined preventive maintenance schedule (predetermined PM policy) The planning time horizon is divided into time intervals of weeks. In each week: i) All the CM requests (when equipments failed) and all the scheduled PM requests are identified. ii) CM request and PM requests for equipment with highest priority will be fulfilled. Continuing with CM requests and PM requests for equipments with lower priority until the (labor and materials) resource available is used up. If resources are not available, the requested maintenance action has to be delayed until the resources become available again (e.g. the needed spare part is available through emergent purchasing). When a maintenance action is performed on an equipment at time t, that equipment is assumed to be as good as brand new and failure events for that equipment will be re-sampled (updated) starting from time t.
4. Genetic algorithm We used a standard binary GA whose detail can be found in various textbooks on GA. We describe only the step of coding from true values of decision variables into binary variables in the chromosome as follows: - The PM time frequency is given by a*MTBF (for each equipment). The fraction a, to be optimized by GA, is confined to take one of the following 16 values: [0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.2] (vector A). The value of a is indicated by the index i (the location) of the elements in vector A, e.g. if i = 2, then a = A[2] = 0.05 - A gene consisting of 4 binary variables klmn is used to represent the index i. - Genes for spare parts inventory and labor are similar (these variables are fixed in this paper). The GA parameters are as follows: population size = 20; fraction of population to keep = 0.5; mutation rate = 0.3; Roulette wheel selection and two point crossover method.
Optimization of Preventive Maintenance Scheduling in Processing Plants
323
5. Example The new framework for maintenance analysis and optimization is demonstrated using the well-known Tennessee Eastman (TE) plant. The description and the process flowsheet for the TE process can be found in the literature, e.g. in Ricker and Lee (1995). The list of equipments in the process is given in table 2. Table 2. List of equipment of the TE process Equipments
Quantity
MTBF (days)
Time for CM (hrs)
Time for PM (hrs)
Priority
Valves
11
1000
2-5
2
3
Compressors
1
381
12-18
6
1
Pumps
2
381
4-12
4
4
Heat Exchanger
2
1193
12-14
8
2
x
Flash drum
1
2208
24-72
12
1
x
Stripper
1
2582
48-96
12
1
x
Reactor
1
1660
12-72
12
1
x
PM interferes with production ?
The MTBFs for all equipments are obtained from Center for Chemical Process Safety (1989) and the maintenance time is obtained from Bloch and Geitner (2006) (for pumps, compressors, valves) or estimated if the information is not available (for other equipments). Our example shows the results when the PM time intervals are optimized. Other variables are fixed: ten employees, keeping inventory for all spare parts and reasonable numbers for the PM starting time. The maintenance model and the GA are implemented in Fortran running on a 2.8 GHz CPU, 1028 MB RAM PC. The final results for the fraction a (PM time interval = a*MTBF) are shown in table 3. Table 3. Optimal PM frequency Equipments
11 Valves
2 Compresors
2 Pumps
Flash drum
Fraction a
0.1 (6 valves) & 0.25 (5 valves)
0.1
0.2
1.2
Equipments
Heat Exchangers
Stripper
Reactor
Fraction a
1.2
1.0
1.0
These results are consistent with the results obtained by Nguyen et al.(2008): for the group of equipments whose PM does not interfere with production (e.g. valves & pumps), high PM frequency is obtained: fraction a ranges from 0.1 to 0.25 (Nguyen et al., 2008 obtained 0.1 by inspection). In turn, for group of equipments whose PM interferes with production (e.g. the reactor) such that PM causes economic loss during maintenance time, frequent use of PM is not recommended (fraction a = 1.0, 1.2). The evolution of the current best value of objective function is shown in figure 1, which shows that the objective value converges to a finite value only after 7 iterations. The computation time (after 57 iterations) is 1 hr 24 min.
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Obj. value (millions)
324
1.625 1.62 1.615 1.61 1.605 1.6 0
10
20
30
40
50
60
Iteration
Figure 1. Evolution of the current best objective value in GA iterations
6. Conclusions A new maintenance model based on the use of Monte Carlo simulation and integrated with GA optimization is presented in this article. The model incorporates three practical issues not considered in previous work and is capable of analyzing and optimizing complex maintenance operations.
References Bloch H.P and Geitner F.K. (2006). Maximizing Machinery Uptime, Elsevier, MA, USA. Center for Chemical Process Safety, AIChE (1989). Guidelines for Process Equipment Reliability Data with Data Tables, ISBN 0816904227 Dhillon B.S. 2002. Engineering Maintenance, CRC Press, Boca Raton, USA. Nguyen D.Q, C. Brammer and M. Bagajewicz. (2008). A New Tool for the Evaluation of the Scheduling of Preventive Maintenance for Chemical Process Plants. Industrial and Engineering Chemistry Research, To appear. Ricker N.L and Lee J.H. (1995). Nonlinear Modeling and State Estimation for the Tennessee Eastman Challenge Process. Comput. Chem. Eng., 19(9), 983-1005. Shum, Y.S and Gong, D.C. (2006). The Application of Genetic Algorithm in the Development of Preventive Maintenance Analytic Model. The International Journal of Advanced Manufacturing Technology. Vol. 32, pp.169-183. Saranga. H. (2004). Opportunistic Maintenance Using Genetic Algorithms. Journal of Quality in Maintenance Engineering, 10(1), pp. 66-74. Tan J.S. and Kramer M.A. (1997). A General Framework For Preventive Maintenance Optimization In Chemical Process Operations. Computers and Chemical Engineering, 21(12), pp. 1451-1469. Tischuk, John L. (2002). The Application of Risk Based Approaches to Inspection Planning. Tischuk Enterprises (UK). Wang H. and Pham H. (2006). Reliability and Optimal Maintenance, Springer Series in Reliability Engineering, Springer-Verlag, London. Wang H. (2002). A survey of maintenance policies of deteriorating systems. European Journal of Operational Research, 139(3), pp. 469-489.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Predictive Optimal Management Method for the control of polygeneration systems Andr´es Collazos, Fran¸cois Mar´echal ∗
´ Ecole Polytechnique F´ ed´ erale de Lausanne, LENI-STI, Bˆ at. ME A2, Station 9, CH-1015 Lausanne, Switzerland
Abstract A predictive optimal control system for micro-cogeneration in domestic applications has been developed. This system aims at integrating stochastic inhabitant behavior and meteorological conditions as well as modeling imprecisions, while defining operation strategies that maximize the efficiency of the system taking into account the performances, the storage capacities and the electricity market opportunities. Numerical data of an average single family house has been taken as case study. The predictive optimal controller uses mixed integer and linear programming where energy conversion and energy services models are defined as a set of linear constraints. Integer variables model start-up and shut down operations as well as the load dependent efficiency of the cogeneration unit. This control system has been validated using more complex building and technology models to asses model inaccuracies and typical demand profiles for stochastic factors. The system is evaluated in the perspective of its usage in Virtual Power Plants applications. Key words: predictive control, optimal management, polygeneration, microcogeneration
1. Introduction The integration of polygeneration systems in urban areas is seen as one of the promising routes for adressing CO2 mitigation needs. For example, decentralized combined heat and power production is foreseen in virtual power plant concepts [1]. The design of polygeneration systems in urban areas relies on the definition of the system management strategy that decides the operation of the energy conversion equipment (cogeneration ∗ Corresponding author. Email address:
[email protected] (Fran¸cois Mar´ echal). Preprint submitted to Elsevier
January 31, 2008
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A. Collazos and F. Maréchal
and heat pumping) and of the energy storage system in order to provide the energy services required at minimum cost. The design method is typically based on the definition of average days from which the ambient temperature and the demand profiles are taken as reference. One key component of this strategy is the energy storage equipment that is used to create a phase shift between the energy conversion and the demands allowing for equipment size reduction and better profitability. When the management strategy is based on optimization methods such as presented in Weber et al. [2], the design method relies on the definition of typical days during which the performances are computed assuming a perfect knowledge of the temperature profiles and energy demand. This assumption is, however, not acceptable when developing a management strategy for an existing system since these profiles are stochastic and are not perfectly predictable. The goal of this paper is to present a predictive control strategy for the optimal management of polygeneration systems in complex buildings. The method includes a predictive model of the energy demand of the building based on the prediction of the ambient temperature and an Auto Regressive model with eXternal inputs (arx) of the building heat losses, combined with a simplified simulation of the heat distribution system. The optimal management strategy uses a mixed integer linear programming model to decide the start up and shut down times of the equipment and decide the heat storage management. The optimal control system thus developed has been validated by connecting it with a detailed building simulation model that is assumed to represent the real non linear and stochastic behavior of the building in its environment. Finally, access to the electricity market price has been assumed. As targeted in virtual power plants concepts, it has been demonstrated that it is possible to use such systems for exploiting the energy storage systems – including the building structure – to increase the combined heat and power production, thus increasing the benefit of a globalized power production system. 2. Domestic energy system studied The system under study includes one cogeneration unit (a Stirling Engine) and a backup boiler, both fueled by natural gas. The system supplies heat to two heat storage tanks: one for the heating system, the other for the domestic hot water (dhw). The temperature in the heat distribution system (radiator system) is controlled by a 3-way valve and the temperature set point is determined as a function of the ambient and room temperatures using a heat loss model and heat distribution model. On Figure 1, Tdhw and Tsh are the temperatures of the water in the dhw tank and in the heat storage. Tin and Text are the room and outside temperatures of the building respectively. Tcg,out (t) is the temperature of the water exiting the cogeneraton unit, Tb,out (t) is the temperature of the water exiting the back-up boiler, Tdhw,in (t) is the temperature of the hot water going into the dhw tank, Tsh,in (t) is the temperature of the hot water going into the heat storage tank and Tr is the nominal return temperature ˙ b (t) are the mass flows entering the cogeneration unit and of the water. m ˙ cg (t) and m ˙ dhw (t) are the mass flows sent to the heat the back-up boiler respectively. m ˙ sh (t) and m storage and the dhw tank. E˙ cg is the electrical power output of the cogeneration unit, E˙ eg,out is the electrical power delivered by the electricity grid, E˙ eg,in is the power sold to the grid and E˙ h,in is the electrical power consumption in the building.
Predictive Optimal Management Method for the Control of Polygeneration Systems
The independent variables are the load charge of the cogeneration unit ucg (t) = the load charge of the storage heat output ush (t) = ˙
Qsh (t) , Qmax sh
327 ˙ cg (t) Q ˙ max , Q cg
the load charge of the back-up
Qsh (t) Qb (t) boiler ub (t) = Q ˙ b (t) . ˙ max , and the 3-way valve control uvlv (t) = Q ˙ cg (t)+Q b ˙ ˙ Here Qcg (t), Qsh (t) and Qb (t) are the heat outputs at time t of the cogeneration unit, the heat storage tank and the boiler respectively. The superscript max indicates the maximum allowed value for each variable. The sizes of the units in the system are calculated using a the Queuing Multi Objective Optimizer (qmoo) developed at the Energy Systems Laboratory at the EPFL (Leyland [3]) in combination with a linear programming problem as described by in Weber et al. [2]. The sizes of the units considered are shown on Table 1.
Table 1 ˙ ˙ Unit characteristics. Q=maximum heat output, η=efficiency, E=maximum electrical output, ηel =electrical efficiency, ηth =thermal efficiency, V =volume Boiler
Cogeneration Engine
Heat Stroage
dhw tank
˙ Q[kW ]
η[−]
˙ E[kW ]
ηel [−]
˙ Q[kW ]
ηth [−]
V [m3 ]
˙ Q[kW ]
V [m3 ]
2.17
0.8
2.25
0.2-0.25
6.83
0.7-0.75
0.45
10
0.12
The building characteristics correspond to the sia 380/1 target value single family home described by Dorer et al. [4]. The size of the cogeneration unit corresponds to an overall full load operating time of 3962 hours per year. The (variable) efficiencies used are based on the manufacturer’s technical data [5]. 3. The predictive controller The predictive control strategy calculates the optimal values of the controlled variables for t0 ≤ t ≤ t0 + ΔtM H , where t0 is the current instant and ΔtM H is the moving horizon length. The strategy is re-evaluated after every time step Δt. The optimal strategy is calculated by solving a Mixed Integer and Linear Programming (milp) model of the system. The objective of the milp is to minimize the sum of the operating costs as well as a penalty term that measures the total time during which the room temperature is outside the comfort range, for the given time horizon. In order to give a priority to comfort, a significant relative weight is assigned in the objective function to comfort violations. The operating costs are the sum of the gas consumption in the cogeneration unit and back-up boiler, added to the electricity consumption minus the electricity export. The back up boiler is modeled with a constant efficiency. The losses in the storage tanks are modeled using standard heat loss equations. The minimum required temperature for space heating water is calculated using the normalized equation from sia [6] applied to the nominal outlet temperature Text,0 and the nominal heating water supply temperature Tmin,0 [7]. The room temperature of the building is calculated by a second order arx model with the space heat delivered as input ΔTin (t + 2Δts ) + a1 ΔTin (t + Δts ) + a2 ΔTin (t) = b1 Q˙ h,in (t + Δts ) + b2 Q˙ h,in (t)
(1)
where ΔTin (t) = Tin (t) − 18 and Tin (t) is the room temperature. a1 , a2 , b1 and b2 are the coefficients of the model, Q˙ h,in (t) is the heat input and Δts = 14 Δt.
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A. Collazos and F. Maréchal
The control variable for the cogeneration unit is the heat output given by Q˙ cg (t) =ucg (t) · Q˙ max , cg
˙ ˙ max · cgon (t) + cgstart−up (t) · η start−up · Q˙ max . Q˙ min cg · cgon (t) ≤Qcg (t) ≤ Qcg cg,gas cg,th
(2) (3)
The electricity output of the cogeneration unit as a function of the heat output is given by the following piece-wise function start−up min E˙ cg (t) =cgon · E˙ cg + cgstart−up (t) · ηcg,el · Q˙ max cg,gas min min ˙ ˙ ˙ + Ecg + cgpw mel,1 Qcg (t) − Qcg (4) min + (1 − cgpw (t)) mel,2 Q˙ cg (t) − Q˙ cg,pw + mel,1 Q˙ cg,pw − Q˙ cg , The first term of the right hand side of Equation 4 corresponds to the minimal electricity output. cgon ∈ {0, 1} is the integer variable that indicates if the cogeneration unit is on or off. The second term corresponds to the electricity output when the unit is started. The variable cgstart−up (t) indicates whether the cogeneration unit has been started at time t; note that this is not an integer variable, but it can only take the values 0 and 1 because of its definition. The third and fourth terms of Equation 4 correspond to two piecewise linear components modeling the electrical output as a function of the heat output Q˙ cg (t). mel,1 and mel,2 are the linear slopes, cgpw ∈ {0, 1} is an integer variable that indicates which piece is used and Q˙ cg,pw is the breakpoint. A similar equation to Equation 4 is used for modeling the gas input as a function of the heat output. Finally, the cogeneration unit is constrained to stay on for at least nmin cg,on hours. In order to add the knowledge of the periodicity of one day to the next when calculating the strategies, a “cyclic” constraint is included A(t0 + 24 + 1) = A(t0 + 1)
(5)
where A is any state variable such as the room temperature, the energy stored in the heat storage tanks or the controlled variables. t0 is the time at which the strategy is being calculated. The cyclic constraint (Equation 5) is applied at time t0 + 1 in case the state at time t0 is not within the desired temperature range (in case of a large perturbation or a big discrepancy in the predictions). It is assumed that the system can move to a “good” state within an hour. 4. Validation In order to validate this control strategy a numerical model of the installation has been used. This consists of a Simulink model of the building’s thermal behavior adjusted to correspond to the sia 380/1 target value of a single family home [4], of the heat distribution system and a non linear cogeneration engine using the efficiency charts on [5]. The models described in Section 3 for the heat storage and dhw tank were used also for the simulation of these units. Standard and stochastic profiles of outside temperature, solar gains, internal free gains, electricity consumption and dhw consumption were used to simulate the environment and the inhabitants’ behavior. The temperature was predicted by its mean value from the past 30 days as described by [8]. The same approach was used to predict the solar gains, electricity consumption and dhw consumption. The gains from inhabitants and electrical appliances were considered as perturbations since they
Predictive Optimal Management Method for the Control of Polygeneration Systems
329
are not easily measured in a real implementation. The simulation is performed using the real values to validate the behavior of the control system when there are discrepancies between the predicted and real values. A correction is applied when the stored energy or the temperature of the storage tanks are outside the allowed range. This correction consists of adding some energy (positive or negative) in order to keep the allowed range.This extra energy gives an estimation of the reserve needed for the storage tanks. 5. Results
Management Unit
Tb,out
Tcg,out
Tr m cg
Grid Electricity (eg) consumer
Qcg Heat output Qb
Hot water
DHW tank (dhw)
Tdhw,in m dhw
h,in
Back-up boiler (b)
vlv
Tdhw
Tr Heat storage tank (hs)
Tr
Figure 1. Test case system
Tin Ths Thsmin
20 min req temp Resulting strategy Stategy at time 1128 Stategy at time 1139 Stategy at time 1151
18 16 1
ucg >ï@
Stirling engine (cg)
m hs
Eeg,out Ecg Eeg,in E
u b u vlv u sh
22
0.5 0
Text
Internal heat gains
1 ush >ï@
u cg
Electrical power
Tr m b
Tariff info
Temperature [ oC]
The milp optimization was performed using ampl-cplex. The calculation times were below 1 minute per strategy evaluation. The controller was applied during five days in spring. The operating costs for the system with the cogeneration unit are 13% lower than the operating costs when all the heat input to the system is delivered by a boiler and when all the elecricity is bought from the grid, with the same energy storage and distribution strategy. Figure 2 compares the room temperature Tin with its set-point and the temperature predicted by the controller for three non consecutive strategy reevaluation times. This picture shows that the controller reevaluates the strategy and adapts it at every time interval allowing it to compensate for the perturbations and for inaccuracies in the predictions. The Figure also shows that the predicted strategy differs from the final strategy for further times in the horizon (oscillations of ucg around 1160-1170), thus the necessity to re-evaluate the strategy more often than the actual horizon length.
0.5 0 1120
1130
1140 1150 1160 hour of the year [h]
1170
1180
Figure 2. Resulting and predicted strategies
Figure 3 shows the energy management with and without the cyclic constraint (Equation 5). The strategy that uses the cyclic constraint features a better management of the storage tanks, preventing a storage of heat in the tanks for longer periods and therefore reducing the storage losses. The operating costs for this strategy are around 2% lower with no extra penalty in the comfort or in the reserve energy required (Section 4). In the Virtual Power Plants perspective [1], the case where the electricity price is not constant has also been assessed to demonstrate the capabilities of the controller to adapt the strategy to take advantage of a time dependent electricity market price. Figure 4 compares the strategies with a varying electricity price and a constant electricity price. The varying price reduces the cost of energy supply by 5% with no additional comfort violation. The constant electricity price is the average of the varying electricity price over the 5 days considered.
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A. Collazos and F. Maréchal
2 1120
1140
1160 1180 1200 hour of the year [h]
1220
1240
Figure 3. Stored energy with and without the cyclic horizon approach
0.1 0.05 0 3 2 1 0
[kW]
Qdhw [kWh]
4
0 1100
1 0.5 0
electricity price [euro/kWh]
maximum heat storage capacity not cyclic cyclic
6
1 0.5 0
[kW]
0
[-]
ucg ub
5
E eg,out E eg,in
Qsh [kWh]
10
[-]
15
1 0.5 0
constant electricity price variating electricity price 1130
1135 1140 1145 hour of the year [h]
(
1150
Figure 4. Time dependent electricity price
6. Conclusions A model based predictive controller has been developed using a Mixed Linear and Integer Programming model to define the optimal management strategy of micro-cogeneration systems in building applications. The milp model takes into account starting and shutdown of the unit as well as the partial load efficiency using a piecewise formulation. The model includes the balance of the hot water storage tanks as well as the heat accumulation in the building envelope. The controller was validated with a numerical model of the system that is more detailed than the model used for the predictive controller. The predictions of temperature and solar gains as well as the consumption of domestic hot water and electricity are obtained. The cyclic horizon has proved to deliver a better performance than the “open” horizon. In the virtual power plants perspective, this controller shows an ability to adapt the strategy in order to profit from fluctuating price of the electricity. References [1] System-development, build, field installation and european demonstration of a virtual fuel cell power plant, consisting of residential micro-chps. [2] C. Weber, F. Mar´echal, D. Favrat, S. Kraines, Optimization of an SOFC-based decentralized polygeneration system for providing energy services in an office-building in Tokyo, Applied Thermal Engineering 26 (13) (2006) 1409–1419. [3] G. Leyland, Multi-objective optimisation applied to industrial energy problems, Ph.D. thesis, EPFL, Lausanne, Switzerland (2002). [4] V. Dorer, R. Weber, A. Weber, Performance assessment of fuel cell micro-cogeneration systems for residential buildings, Energy and Buildings 37 (2005) 1132–1146. [5] Solo stirling 161 combined power / heat (chp) module (2005). [6] Standard sia 384/2 (1988). [7] M. Zehnder, Efficient air-water heat pumps for high temperature lift residential heating, including ´ oil migration aspects, Ph.D. thesis, Ecole Polytechnique F´ed´ erale de Lausanne (2004). [8] G. Henze, D. Kalz, C. Felsman, G. Knabe, Impact of Forecasting Accuracy on Predictive Optimal Control of Active and Passive Building Thermal Storage Inventory, HVAC & R Research 10 (2) (2004) 153–178.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
331
Comparison of model predictive control strategies for the simulated moving bed Adrian Dietz, Jean-Pierre Corriou Laboratoire des Sciences du Génie Chimique (LSGC), Nancy Université, CNRS, 1, rue Grandville, BP 20451,F- 54001 Nancy Cedex
Abstract This work addresses the study of an efficient chromatographic separation unit operation control, the simulated moving bed (SMB). Linear model predictive control (MPC) is considered in this work. A comparison of two different sets of manipulated inputs is carried out: on one hand, the classical one often presented in the literature, which consists in manipulating directly different flow rates involved in the process and, on the other hand, an approach coming from other counter-current separation processes which consists in manipulating the ratios of flow rates of each SMB zone. The advantages and drawbacks of each control strategy are discussed. In all cases, results show clearly the interest of applying MPC to high complexity systems such as the SMB. Keywords: simulated moving bed, model predictive control.
1. Introduction Chromatographic techniques allow the separation of products with a high purity required in industrial fields such as fine chemistry, pharmaceutics, food. This unit operation is usually operated in batch mode and is well known for its high investment cost due to the adsorbent and large eluent consumption. In order to tackle this drawback, the continuous moving bed technology was first developed as the true moving bed (TMB) where the solid and the liquid flows move in countercurrent way. However, because of the solid flow, this process causes solid attrition, so that the SMB technology was then developed. In a SMB, the solid movement is simulated by simultaneous switching of the inlet and exit ports corresponding to feed, eluent, extract and raffinate, in direction of the fluid flow (Figure 1). Consequently, the continuous system corresponding to the TMB where a steady state can be obtained becomes a hybrid one resulting from a cyclic operation mode. Typical studies in the literature range from the design stage [1-5] to the operation [6], identification [7], parameter and state estimation [8-10], and control [11-16] of the SMB. Many different control techniques are mentioned including linear and non linear model predictive control and non linear geometric control. Several variants of this technology are also developed such as the Varicol process or the power feed operation. In this work, two different model predictive control strategies of a SMB differing by the choice of the manipulated inputs are compared. On one hand, the classical one often presented in the literature consists in directly manipulating different flow rates involved in the process and, on the other hand, the strategy mentioned by Couenne [17] consists in manipulating ratios of flow rates and is used for xylenes separation. The idea of using ratios of flow rates was already used in distillation control [18] where Skogestad consider the two-ratio configuration (L/D,V/B) as the best choice of manipulated inputs in case of dual control. In the same manner, the choice of flow rates ratios seems to be interesting for the SMB control because it reduces the high non-linearity of the process
332
A. Dietz and J.-P. Corriou
as the separation phenomena are directly related to flow rate ratios rather than to flow rates themselves. In the flow rate ratio control scheme [17], the two main outputs are the purity and yield of the products, two other outputs are respectively defined to guarantee a stable operation of the process and to optimize it. The manipulated inputs are the ratios of liquid flow rate in zone k divided by the equivalent solid flow rate. In the flow rate control scheme, the controlled outputs are the purities at the extract and raffinate outlets and the manipulated inputs are the eluent (solvent), extract, recycle and equivalent solid flow rates. Zone I Eluent
Raffinate
Zone II
Zone IV
Extract
Port switching direction
Feed
Zone III
Figure 1: Scheme of the Simulated Moving Bed.
A linear model predictive control law is retained in both cases because of its attracting characteristics such as its multivariable aspects and the possibility of taking into account “hard” constraints on inputs and inputs variations as well as “soft” constraints on outputs (constraint violation is authorized during a short period of time). To practise model predictive control, first a linear model of the process must be obtained off-line before applying the optimization strategy to calculate on-line the manipulated inputs. The model of the SMB is described in [8] with its parameters. It is based on the partial differential equation for the mass balance and a mass transfer equation between the liquid and the solid phase, plus an equilibrium law. The PDE equation is discretized as an equivalent system of mixers in series. A typical SMB is divided in four zones, each zone includes two columns and each column is composed of twenty mixers. A nonlinear Langmuir isotherm describes the binary equilibrium for each component between the adsorbent and the liquid phase.
1. Identification of the linear model The linear model for predictive control is based on the step responses of the process with respect to the various manipulated inputs. As mentioned previously, in a SMB, the solid flow is simulated by synchronous valve switching at given intervals. The switching period of the SMB is computed from the equivalent solid flow rate. A variable switching period induces a varying sampling period as the measurements are assumed to be performed only after each commutation and correspond to average concentrations over this switching period. 1.1. Linear model for flow rate control The step responses of the extract and raffinate purities, resp. y1 and y2, (Fig. 2) are obtained for 0.05% steps of respective eluent, recycle, extract and solid flow rates,resp. u1, u2, u3 and u4, used as manipulated inputs. The steps are performed after the process reaches a steady state purity of 95% for both products. Most of the responses are close to first order step responses and present similar time constants, which is suitable for further control. Only the step response of the extract purity with respect to the eluent
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flow rate (y1/u2) displays an inverse response, however it has a low order of magnitude like two other step responses (y1/u1, y1/u3).
Figure 2: Step response coefficients of the extract and raffinate purities with respect to the flow rates (from top to bottom: eluent, recycle, extract and solid ).
1.2. Linear model for ratio control The step responses for ratio control are obtained by varying successively the ratios uk of the liquid flow rates of the successive zones k over the equivalent solid flow rate (Fig. 3). The results show that several inverse responses are present; moreover different types of response dynamics exist. The liquid flow rates are calculated from the ratios in order to obtain a constant flow rate ratio in each zone of the SMB.
Figure 3: Step response coefficients of the extract and raffinate purities with respect to the flow rates ratios (from top to bottom: ratio in zone 1, zone 2, zone 3, zone 4 ).
The main remark is that the ratio step responses are very different from the simple flow rate step responses of Fig. 2. Second order responses are present (y1/u2, y1/u3), some step responses show low magnitudes (y1/u4, y2/u1, y2/u4). Also, some time constants are relatively different. When ratios are manipulated, several flow rates are simultaneously manipulated which makes the total character complex and unpredictable.
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2. Model predictive control The model predictive control used includes all features of Quadratic Dynamic Matrix Control [19], furthermore it is able to take into account soft output constraints as a non linear optimization. The programs are written in C++ with Fortran libraries. The manipulated inputs (shown in cm3/s) calculated by predictive control are imposed to the full nonlinear model of the SMB. The control simulations were made to study the tracking of both purities and the influence of disturbances of feed flow rate or feed composition. Only partial results are shown. 2.1. Flow rate control
Figure 4: Flow rate control in case of raffinate purity tracking. Left: controlled outputs. Right: manipulated inputs.
Figure 5: Flow rate control in case of feed flow rate disturbance rejection. Left: controlled outputs. Right: manipulated inputs.
Several points must be emphasized before discussing the results obtained. Being given that the sampling period depends on the solid flow rate, the dynamic matrix must be rebuilt at each computing step. In order to maintain the QL (optimization of quadratic criterion with linear constraints) nature of the optimization problem, the switching period for the future inputs is assumed to be identical to the first one calculated. The predicted outputs at different times are obtained by cubic spline interpolation. For a set point change of the raffinate purity from 0.95 to 0.96 and back to 0.95 (Fig. 4), the control of the raffinate purity is well ensured and the manipulated inputs undergo acceptable moves. The control of the extract purity would show similar characteristics. The disturbances of the feed flow rate of +10% and -10% applied at times 13000 and 19000s (Fig. 5) are well rejected and the manipulated flow rates are stabilized after a transient period corresponding to the disturbance effect.
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2.2. Ratio control As previously mentioned, the manipulated inputs are now the ratios of the liquid flow rates in each zone over the equivalent solid flow rate. However, in the Figures, the operating flow rates are shown. In the case of the SMB, the identification procedure presented some difficulties compared to the more classical flow rate identification and control. The control horizon was set to one for stability reasons, and higher prediction and model horizons were used. Fig. 6 is obtained for the same set point tracking as Fig. 4. The tracking is acceptable, more coupling is present for the extract purity and the manipulated inputs moves are less smooth. These results are slightly less satisfying than for flow rate control.
Figure 6: Ratio control in case of raffinate purity tracking. Left: controlled outputs. Right: operating flow rates.
Figure 7: Ratio control in case of feed concentration disturbance rejection. Left: controlled outputs. Right: operating flow rates.
The unmeasured feed concentration disturbance rejection posed more difficulties (Fig. 7). On the opposite, the measured feed flow rate disturbance is rejected without dynamic effects (Fig. 8) as the manipulated inputs are algebraically and linearly related to the disturbance value. Even if ratio control is globally less efficient that flow rate control, the capacity of ratio control to reject feed flow rate disturbances is attractive in some particular cases such as the pharmaceutical or the fine chemistry where the production is carried out by batches. Thus the set point remains constant because it is associated to the batch recipe resulting in a given final product concentration, and the main disturbance comes from the feed flow rate that can be modified by the pump operation or the operator.
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Figure 8: Ratio control in case of feed flow rate disturbance rejection. Left: controlled outputs. Right: operating flow rates.
4 Conclusions and Perspectives In this work, the influences of two different sets of manipulated inputs have been compared in the case of linear model predictive control of a simulated moving bed. The first one consisting in direct manipulation of flow rates of the SMB showed a very satisfactory behavior for set point tracking and feed disturbance rejection. The second one consists in manipulating the flow rates ratios over each SMB section. At the identification stage, this strategy proved to be more delicate as the step responses displayed important dynamic differences of the responses. However, when the disturbance concerns the feed flow rate, a better behavior is obtained whereas a feed concentration disturbance is more badly rejected. Other control studies, such as robustness and other control strategies, will be carried out in next works. Although the SMB control was carried out in simulation based on a realistic model of the process, the application of these control strategies to a real SMB for validation purposes should be done.
References [1] F. Charton and R.M. Nicoud, J. Chromatogr. A, 702 (1995), 97-112 [2] RM. Nicoud, LC-GC Int., 5 (1992), 43-47 [3] M. Mazzotti, G. Storti and M. Morbidelli, J. Chromatogr. A, 769 (1997), 3-24 [4] O. Ludemann-Hombourger and R.M. Nicoud, Sep. Sci. Technol. 35(12), (2000), 1829-1862 [5] C.B. Ching, K.H. Chu, K. Hidajat and M.S. Uddin, AIChE J., 38(11) (1992), 1744-1750 [6] M. Mazzotti, G. Storti and M. Morbidelli, J. Chhromatogr. A, 827 (1998), 161-173 [7] I.H. Song, S.B. Lee, H.K. Rhee and M. Mazotti, Chem. Eng. Sci., 61 (2006), 1973-1986 [8] M. Alamir, F. Ibrahim and J.P. Corriou, J. Process Cont., 16 (2006), 345-353 [9] E. Kloppenburg and E.D. Gilles, J. Process Cont., 1, (1999), 41-50 [10] M. Alamir, J.P. Corriou, J. Process Cont., 13, (2003), 517-523 [11] M. Alamir, F. Ibrahim and J.P. Corriou, J. Process Cont., 16 (2006), 333-344 [12] G. Erdem, S. Abel, M. Morari, M. Mazotti, M. Morbidelli and J.H. Lee, Ind. Eng. Chem. Res., 43 (2004), 405-421 [13] K.U. Klatt, F. Hanisch, G. Dünnebier, J. Process Cont., 12 (2002), 203-219 [14] M. Ben Thabet, M. Alamir, M. Bailly and J.P. Corriou, AIChE 97, Los Angeles, (1997), 1316-1321 [15] S. Natarajan and J.H. Lee, Comp. Chem. Engng., 24 (2000), 1127-1133 [16] A. Toumi and S. Engeel, Chem. Eng. Sci., 43(14), (2004) 3895-3907 [17] N. Couenne, G. Bornard, J. Chebassier and D. Humeau, in congress SIMO 2002, Toulouse, France, 10 (2002) [18] S. Skogestad, P. Lundstrom and E.W. Jacobsen, AIChE J, 36(5), (1990) 753-764 [19] C.E. Garcia and A.M. Morshedi, Chem. Eng. Comm., 46 (1986), 73-87
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Model Reduction Techniques for Dynamic Optimization of Chemical Plants Operation Bogdan Dorneanua, Costin Sorin Bildeaa,b, Johan Grievinka a b
Delft University of Technology, Julianalaan 136, Delft, 2628BL, The Netherlands Politehnica University of Bucharest, Polizu Street 1, Bucharest, 011061, Romania
Abstract The application of model reduction techniques in the context of dynamic optimization of chemical plants operation is investigated. The focus is on the derivation and use of reduced models for the design and implementation of optimal dynamic operation in large-scale chemical plants. The recommended procedure is to apply the model reduction to individual units or groups of units, followed by the coupling of these reduced models, to obtain the reduced model of the plant. The procedure is flexible and accurate and leads to a major reduction of the simulation time. Keywords: model reduction, dynamic optimization, alkylation
1. Introduction The strong competition in the industrial environment nowadays demands for economical operation of chemical plants. This goal can be achieved in two ways, which do not exclude each other. One approach is to continuously respond to the market conditions through dynamic operation. A second approach is to develop control systems that maintain the steady state or implement the optimal dynamic behaviour. For the first approach, the economical optimality is achieved through dynamic optimization. For the second approach, the development of the plantwide control structures to achieve stable operation is of paramount importance. However, both approaches presented above require dynamic models of the chemical plant. The quality of the model is crucial for achieving the objective: the model must represent the plant behaviour with good accuracy, but the complexity must be limited because both applications require repeated solution during limited time. Another requirement is that the model is easy to be maintained and adapted to future plant changes. The order-reduction of the process model could offer a solution. Several linear [1] and nonlinear techniques [2] have been developed and their application to different case studies reported. Although significant reduction of the number of equations is achieved, the benefit is often partial, because the structure of the problem is destroyed, the physical meaning of the model variables is lost and there is little or no decrease of the solution time [3]. In this contribution, the derivation of the optimal control profiles is realised by using a reduced model obtained through the model reduction with process knowledge approach. The procedure takes into account the inherent structure that exists in a chemical plant in the form of units or groups of units that are connected by material and energy streams. This decomposition mirrors the decentralization of the control problem. The recommended procedure is to apply model reduction to individual units, and then to couple together these reduced models. The technique will be applied to a case study: the iso-butane alkylation plant.
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2. Approaches to dynamic optimization The objective of the dynamic optimization is to determine, for a dynamic system, a set of decision variable time profiles (pressure, temperature, flowrate, heat duty etc.) that optimise a given performance criterion, subject to specified constraints (safety, environmental and operating constraints). The dynamic optimization problem of interest in this contribution can be stated as follows: tf min Obj ( x (t f ), u (t f ), y (t f ), t f , p ) = ∫ obj ( x (t ), u (t ), y (t ), t , p ) dt u (t ),t f 0
(1)
⋅
s.t.
f ( x(t ), x(t ), u (t ), z (t ), p ) = 0
(2)
g ( x (t ), u (t ), z (t ), p ) = 0
(3)
xmin ≤ x (t ) ≤ xmax
(4)
umin ≤ u (t ) ≤ u max
(5)
z min ≤ z (t ) ≤ z max
(6)
x (0) = x0
(7)
In this formulation, x (t ) are state (dependent) variables, u (t ) are control (independent) variables and z (t ) are algebraic variables, while p are time-independent parameters. The dynamic models of chemical processes are represented by differential-algebraic equations (DAEs). Equation (2) and (3) define such a system. Equations (4), (5) and (6) are the path constraints on the state variables, control variables and algebraic variables respectively, while equation (7) represents the initial condition of the state variables. Obj is a scalar objective function at final time, t f . The most common approach to DAE-based optimization problems is the transformation of the infinite-dimensional dynamic problem into a finite-dimensional nonlinear programming problem (NLP) [4]. Two main approaches have been developed in order to make this transformation. The first one is to decompose the dynamical system into the control and the state spaces. In the next step, only the control variables are discretized and remain as degrees of freedom for the NLP solver [5]. The method is called the sequential approach. The DAE system has to be solved at each NLP iteration. The disadvantages of the approach are: problems of handling path constraints on the state variables, since these variables are not included directly in the NLP solver [5]; the time needed to reach a solution can be very high in case the model of the dynamic system is too complex; difficulties may arise while handling unstable systems [4]. In the second approach, both the state and the control variables are discretized. In this way, a large-scale NLP problem is obtained, but the DAE system is solved only once, at
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the optimal point. In this way, the disadvantages of the sequential approach are eliminated, but there is still the issue of handling the problem size [4]. In the recent years, a new approach has been developed for eliminating this disadvantage [5]. This approach is called the quasi-sequential approach and takes the advantages of both the sequential and the simultaneous approaches: since both the control and the state variables are discretized, the path constraints for the state variables can be handled; the DAE system is integrated only once, so the computation becomes more efficient.
3. Model reduction for dynamic optimization As seen in the previous chapter, all the approaches used to solve the dynamic optimization problem integrate, at some point, the dynamical system of the chemical process. In order to obtain more efficiently the values of the optimum profile of the control variable, a suitable model of the system should be developed. That means that the complexity of the model should be limited, but, in the same time, the model should represent the plant behaviour with good accuracy. The best way to obtain such a model is by using the model reduction techniques. However, the use of a classical model reduction approach is not always able to lead to a solution [6]. And very often, the physical structure of the problem is destroyed. Thus, the procedure has to be performed taking into account the process knowledge (units, components, species etc.). In the following chapter, the application of the model reduction with process knowledge for the dynamic optimization will be presented. This will be done by means of a case study: the iso-butane alkylation plant. 3.1. The iso-butane alkylation plant The alkylation of iso-butane is a widely used method for producing high-octane blending component for gasoline. For the purpose of this study, the following reactions capture the overall chemistry: C4 H 8 + i − C4 H 10 → i − C8 H 18
(8)
C4 H 8 + i − C8 H 18 → C12 H 26
(9)
Figure 1. The iso-butane alkylation plant.
The reactions are exothermic and occur in liquid phase. The secondary reaction (9) has large activation energy, therefore high selectivity is favoured by low temperatures. The cooling is achieved in an external heat-exchanger. The second reaction is suppressed by keeping the concentration of butene low. Therefore, a large excess of iso-butane is fed to the reactor. From the reactor effluent, the light impurities, reactants, products and heavy products are separated by distillation and removed or recycled.
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The plantwide control structure (Figure 2) is the same as the one determined to have a stable behaviour in [6]: the flowrate of the fresh butene is specified, while the isobutane is introduced by inventory control. i – C4H10 F3
FB0 F1 LC
FC
FC
FA0 C4H8
F4
LC
Reaction section
Separation section F5
Figure 2. The proposed plantwide control structure for the iso-butane alkylation plant.
Local control is also present: the reactor is operated at constant volume and temperature, while for the distillation columns, the levels, pressure, and top and level compositions are controlled. The objective of the dynamic optimization problem should be stated before the model reduction is performed, in order to choose the right variables to be kept in the reduced model. The objective of the dynamic optimization problem will be stated as follows: Increase the plant production by 20% with minimal energy consumption in the distillation columns. It should be mentioned that this focus on energy may lead to a long transition period. 3.2. Reduced model The full nonlinear model is developed using Aspen Dynamics. For obtaining the reduced model, the same procedure presented in [6] is used. However, in this case the reduced model will be developed using gProms. First of all, the plant flowsheet is split into units / group of units. The splitting it is done in units to which local control is applied: the reactor (plus the heat exchangers around it), the distillation columns, mixing vessels, pumps. Since the mixers and the pumps are considered instantaneous (no dynamics) they are not interesting for the model reduction. Further, the units are individually reduced. Since the reactor has a strong nonlinear behaviour, the model simplification is used. A dynamic model is written using gProms, consisting of five component balances, and considering constant temperature and physical properties. For the distillation columns, linear model-order reduction will be used. The linear model is obtained in Aspen Dynamics. Some modifications to the previous study have been done to the linear models, in order to have the reboiler duty and the reflux ratio as input or output variables of the linear models. This is needed to have access to those variables in the reduced model, for the purpose of the dynamic optimization. A balanced realization of the linear models is performed in Matlab. The obtained balanced models are then reduced. The reduced models of the distillation columns are further implemented in gProms. When all the reduced models of the individual units are available, these models are further connected in order to obtain the full reduced model of the alkylation plant. The outcome of the model reduction procedure is presented in Table 1, together with some performances of the reduced model.
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Model Reduction Techniques for Dynamic Optimization Table 1. The model reduction of the iso-butane alkylation plant Unit
Model reduction technique
Full nonlinear model
Reduced model
CSTR
Model simplification
15 states
5 states
COL1
Model order-reduction
188 states
25 states
COL2
Model order-reduction
194 states
29 states
COL3
Model order-reduction
169 states
17 states
150 seconds
2 seconds
Simulation time
3.3. Dynamic optimization After the reduced model is obtained, the dynamic optimization problem (equations (1) – (7)) is implemented in gProms. The single shooting method is used. The objective function to be minimised is the sum of the reboiler duties in the distillation columns. Two control variables are considered: the flowrate of the fresh feed of butene ( FA0 ) and the flowrate of the first mixer’s outlet stream ( F1 ), which are also the variables on flow control in the plantwide control structure (Figure 2). After the 20% increase in the production is achieved, the optimizer is asked to ensure a new steady state is reached and the production is kept constant for a while. The two control variables are discretized into 25 time intervals. The size of the first 20 intervals is free, while for the last 5 it is fixed. A selectivity constraint is imposed, in order to maintain the formation of the secondary products at a low value. All the constraints are introduced as inequality type constraints. 46
930
43 40 37 34 5
10
15
Time / [hr]
20
870 810 750 Initial profile
a 0
Optimum profile
Optimum profile
F1 / [kmol/hr]
FA0 / [kmol/hr]
Initial profile
b
690 25
0
5
10
15
20
25
Time / [hr]
Figure 3. The optimum control profiles for: a) the component A fresh feed flowrate; b) the recycle flowrate.
The optimum profiles of the control variables (Figure 3) are obtained after several timeconsuming, trial-and-error iterations. The solution was obtained after a number of about 150 manual iterations, not taking into account the iterations performed by the solver. In each manual iteration, the initial profile was modified by the user, while the solver is trying to optimize this profile. The advantage of having a reduced model at this point is obvious. Further, the optimum profiles were implemented into Aspen Dynamics. The agreement between the responses of the nonlinear and reduced model is excellent (Figure 4). The difference between the reduced and the nonlinear model response is less than 2.3% at the end of the time span. However, the transition time is quite long, as expected when the objective was set. From an initial guess of 6 hours, the optimum solution led to a transition time of about 24 hours. To determine the cause of this behaviour, a study of the system’s time constant
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Production rate / [kmol/hr]
should be performed. This should be done before implementing the optimization, in order to get a better initial guess, and reduce the optimization time. 45 40 Full nonlinear model
35 Reduced model
30 25 20 0
5
10
15
20
25
Time / [hr]
Figure 4. Comparisons between the responses of the full and reduced model after the optimum control profiles are implemented.
4. Conclusions This paper proposes and demonstrates the advantage of exploiting the inherent structure that exists in a chemical plant for developing reduced models to be used during the dynamic optimization of chemical plants operation. The recommended procedure is to apply model reduction to individual units of the plant, and then to couple together these reduced models. The procedure is flexible, allowing different reduction techniques to be applied for different individual units, and the units to be chosen considering the future use of the reduced model. The solution time is significantly reduced, which makes the model easier to be applied for the purpose of our study. Another advantage of the procedure is the modularity of the reduced model, which can be very useful in the case of future plant changes, or even for when the reduced model is used for a different application. In these cases, instead of having to obtain a new reduced model of the whole plant, only the reduced model of the new unit would be changed. Acknowledgement: This project is carried out within the framework of MRTN-CT-2004-512233 (PRISMTowards Knowledge-Based Processing Systems). The financial support of the European Commission is gratefully acknowledged.
References 1. Antoulas, A.C., Sorensen, D.C., Approximation of Large-Scale Dynamical Systems: An Overview, Technical report, 2001, (http://www-ece.rice.edu/~aca/mtns00.pdf - last visited 31.10.2007). 2. Marquard, W, Nonlinear Model Reduction for Optimization Based Control of Transient Chemical Processes, Proceedings of the 6th International Conference of Chemical Process Control, AIChe Symp. Ser. 326, Vol. 98 (12), 2002. 3. Van Den Bergh, J., Model Reduction for Dynamic Real-Time Optimization of Chemical Processes, PhD Thesis, Delft University of Technology, The Netherlands, 2005. 4. Biegler, L.T., Grossmann, I.E., Retrospective on Optimization, Computers and Chemical Engineering 28 (1169), 2004. 5. Hong, W., Wang, S., Li, P., Wozny, G., Biegler, L.T., A Quasi-Sequential Approach to Large-Scale Dynamic Optimization Problems, AIChe Journal 52, No. 1 (255), 2006. 6. Dorneanu, B., Bildea, C.S., Grievink, J., On the Application of Model Reduction to Plantwide Control, 17th European Symposium on Computer Aided Process Engineering, Bucharest, Romania, 2007.
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A mathematical programming framework for optimal model selection/validation of process data Belmiro P. Duartea,c, Maria J. Mouraa, Filipe J.M. Nevesb, Nuno M.C. Oliveirac a
Department of Chemical Engineering, Instituto Superior de Engenharia de Coimbra, Rua Pedro Nunes, 3030-199 Coimbra, Portugal,
[email protected]. b CUF – Químicos Industriais, S.A., 3860 Estarreja, Portugal,
[email protected]. c GEPSI – PSE Group, CIEPQPF, Department of Chemical Engineering, University of Coimbra, R. Sílvio Lima – Pólo II, 3030-290 Coimbra, Portugal,
[email protected].
Abstract This work considers the use of information indices for optimal model selection and validation of process data. The approach followed assumes the existence of a set of fundamental process models associated with possible, although distinct, operating regions. A 2-phase mathematical programming algorithm for the assessment of structural changes and optimal fitting of local models in data series is proposed. This approach is used to determine the kinetic parameters of the gelation reaction of chitosan with genipin, employing dynamical elastic modulus data. Keywords: Model selection, Data validation, Information criteria, Mathematical Programming.
1. Introduction and Motivation We address the problem of efficiently using data relative to a chemical process or experiment for a set of activities associated to model validation, process monitoring and knowledge extraction. This problem has become progressively more and more common in the processing industry, with the incremental assembly of large networks of sensors, where extensive amounts of data are continuously produced as a result of a more careful monitoring, to improve the control and reduce the variability of the quality indexes. The approach followed assumes the existence of a set of fundamental process models associated with possible, although distinct, operating regions of the process. These models represent a priori knowledge that can be used to support the plant supervision, either by direct comparison of their predictions with the plant data or by regression of their parameters to particular subsets of the data. A fundamental question is then the determination of regions where some of the available models become applicable, and the selection of “appropriate” data sets for their regression. Related to this problem is also the question of identifying the points where the process changes, commonly referred as transition points. The determination of these transition points and the assessment of structural changes in data sets is traditionally performed by statisticallybased approaches. Two different methodologies can be found in the literature: 1. the use of estimators such as the Maximum Likelihood score [1], and supW [2] to locate iteratively the change points combined with asymptotic estimators or boostraping procedures to assess the confidence level of the original estimator; 2. the use of multivariate adaptive regression splines (MARS) [3], hinging hyperplanes (HH) [4] and adaptive logic networks (ALN) [5]. All these approaches have been considered for data mining purposes, but are not so efficient when a more careful model construction is
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required. Moreover, they often tend to overfit the data, even when cross validation or pruning procedures are employed to avoid that possibility. In this paper, we propose an algorithm based on a mathematical programming approach for the assessment of structural changes and optimal fitting of local models in data series. For simplicity, a system involving only one regressor and several inputs is considered, and maximum likelihood estimation (MLE) is employed in the objective function. This approach aims to reach the global optimal solution while avoiding hard enumeration-based algorithms [6].
2. Mathematical formulation We consider a system with one output Y ∈ ℜ and several inputs X ∈ ℜs . The data set D comprises the sequences {Yi ,1 ≤ i ≤ N } and {X i ,1 ≤ i ≤ N } of observations sampled at instants ti , where N is the total number of observations. We assume that the data is heteroskedastic with constant variance, and that the maximum number of possible underlying local models representing the process is known a priori, and designated by M . We denote by I ≡ {1," , N } the set of points considered, and by J ≡ {1," , M } the set of admissible local models, which are assumed to be linear in the coefficients. Here we consider that C j = ª¬ β 0 j , β1j ," , βsj º¼ characterizes the jth local model, relative to the regressors [1,X ] : T Yˆi = C j [1, X i ] , i ∈ I
(1)
The problem then consists on simultaneously determining the sets of consecutive points
{
S j = i jmin ," , i jmax i
min j
} that can be assigned as the region of validity of the jth model, with
standing for the first point in jth segment and i jmax for the last, and the respective
vectors of coefficients C j that maximize a global maximum-likelihood criteria. It is assumed that structural changes occur at the points where τ = {i : i ∈ S j i + 1 ∈ S j +1} , thus requiring the application of distinct models on each side of the transition points. Consequently, each model is assumed to be only valid in a region which is disjoint from all of the other regions identified in the data set D . Not all of the models in the set J need to be supported by the data used. Possible contamination of the data sets with outliers as well as the presence of points that do not fit any of the given models are also considered. Several related problems have been previously considered in the literature. In addition to the afore mentioned statistical approaches for structural change detection in data sets and their application for linear system identification [7], the joint problem of model structure determination and parameter estimation was addressed by [8-10]. A related approach was used by [11-13] in the context of data reconciliation. Additional aspects of model selection in chemical engineering are covered in [14]. Although the present problem shares common features with the all of the previous applications, it also presents unique characteristics that require a specific formulation. Since each data point needs to be (possibly) assigned to a specific model within J , binary variables wi , j are introduced to express this fact. The algorithm described is
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based on the use of the Bayesian Information Criterion (BIC) for the selection of the optimal model structure. Among other competing information criterion, this specific index was chosen because experience shows that it can provide an equilibrated balance between the discrimination ability towards simple-enough models, and the simplicity of its evaluation. To enlarge the domain of applicability of the present methodology within reasonable solution times, a two-phase approach is proposed. In the first step (problem P1) an approximate solution (number of models and approximate location of the boundaries) is obtained, through the simplification of the objective function considered. In this case a L1 norm is used, which originates a MINLP problem. The first phase of the algorithm can optionally be skipped, when a good initial solution is already available, e.g. through the previous application of one of the iterative strategies such as MARS, HH or ALN. Alternatively, the solution obtained in this step can be used for the identification of outliers in the data set [15-17]; these points are subsequently removed before the final solution phase. This is possible since the L1 norm is closer to the median, producing estimates which are less sensitive to the presence of outliers. In the second solution phase (problem P2) the minimization of the Bayesian Information Criterion (BIC) is directly considered, subject to model constraints, using a recursive estimation of the variance of the data [10]. The optimization problems solved in this case correspond to mixed integer quadratic programs (MIQP). The mathematical formulation of problem P1 can be succinctly expressed as: | ei , j | min ¦ −n j ln(2π ) − n j ln(σ j2 ) − ¦ 2 + p j ln(n j ) (2.a) w ,C ,σ
s.t.
j ∈J
i ∈I
σj
yi = C j [1, X i ] + ri , j , ∀j T
ri , j ≤ ei , j + (1 − wi , j )M max , M
¦w
i ,j
≤ 1, ∀i ,
j =1
wi −1, j ≥ wi , j , i > 1 ∧ j = 1 ,
(2.b)
ri , j ≥ ei , j − (1 − wi , j )M max N
(2.c)
≥ n min, j , ∀j
(2.d)
wi −1, j ≤ wi , j , i > 1 ∧ j = M
(2.e)
¦w
i ,j
i =1
wi −1, j + wi −1, j +1 ≥ w i , j +1 , i > 1 ∧ j < M
(2.f)
w1,1 = 1, w N ,M = 1 , wi , j ∈ {0,1}
(2.g)
Equation (2.a) presents the objective function, equation (2.b) corresponds to the underlying model structure, equations (2.c) formalize the assignment of the points to segments, where M max is a magnitude limit (constant), here set to M max = max (Yi ) + min (Yi ) , n j is the number of points assigned to jth local model, σ j the standard
deviation of the error and p j the number of parameters involved. Furthermore, equation (2.d) assigns each point to a single model, and implements the requirement that each structural model should include at least a pre-assigned minimum number of points. Equations (2.e-g) are employed to reduce the degeneracy of the optimization problem by setting an assignment order of the first points of the data set to the first local models. In many instances this problem can be solved approximately by considering the solution of a sequence of MILP problems that result from fixing both n j and σ j in each iteration; the estimates of these parameters are afterwards updated, and the solution of the MILP problem updated, sequentially. This is especially the case after careful
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initialization of the problem, when N is larger than M , due to the smaller sensitivity of n j and σ j to the exact delimitation of the regions. In the second phase, problem P2 can be formulated as: min
w ,C ,σ
¦ −n j ∈J
j
ln(2π ) − n j ln(σ j2 ) − ¦ i ∈I
ei2, j
σ j2
+ p j ln(n j )
(3.a)
s.t.
equations (2.b-2.g) (3.b) 1 σ j2 = ¦ei2, j (3.c) n i∈I As in the previous case, n j and σ j can often be estimated sequentially, after the solution of a series of MIQP problems. To speed up the solution of problem P2, a significant fraction of the binary variables included in this problem can be fixed to the values previously determined in P1. This is done by considering that possible changes in the assignment of points to different models only occur in the neighborhood of the transition points identified previously. In this case, the binary variables provided to the model are fixed for a set of points designated as S f , j ≡ {i : i ≥ i jmin + Δ ∧ i jmax − Δ} , ∀j with Δ denoting the number of points allowed to change in the vicinity of the structural changes location. The complementary set of S f , j , designated as S f , j contains all the points that are allowed to be reassigned to a different segment in this case. This definition makes the problem P2 much easier to solve, in practice.
3. Application This approach was employed to determine the kinetics of the gelation reaction of chitosan with genipin, employing dynamical elastic modulus data measured with a cone-and-plate rheometer. Chitosan is a biopolymer with large interest in biomedicine and therapeutic applications, due to its properties. Genipin is crosslinking agent employed to modulate the chitosan network properties achieved through the gelation. One of the techniques used to study the kinetics of polymerization reactions is based on monitoring the rheological properties of the mixture, particularly the elastic modulus, designated as rheokinetics [18]. This approach allows to establish a relation of the so called rheological degree of conversion with the fraction of liquid that turns into gel phase. The liquid-solid reactions are described by the Avrami model, here employed to represent the extent of gelation, designated as η (t ) , as a function of the time [19]:
η (t ) = exp ( −kt n )
(4)
where k and n are parameters dependent on the system. This equation can be linearized, defining R (t ) = ln ª¬ − ln (η (t ) ) º¼ = ln (k ) + n ln (t ) . Here
η (t ) =
G ' (t ) − G 0' G ∞' − G 0'
(5)
where G ' (t ) is the elastic modulus at time t , G 0' is its initial value and G ∞0 its maximal value. Several sources refer that the gelation mechanism of biopolymers, such as gelatine, follows a sequence of four phases [20]. The models representing the sol-gel transition are described by linear relations (Equation 5), with different parameters
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holding for different phases. The rheological monitoring of the gelation of the system chitosan-genipin reveals the occurrence of synerysis [21]. Therefore, the third and fourth phases of the gelation reaction are rheologically dominated by mechanical transformations, with the kinetic features extracted from data having no physical meaning. Morever, it was observed that due to the prevalence of the mechanical aspects, the behavior of the gel in phases 3 and 4 is indistinguishable, and three local models can be employed to represent the complete experiment. We used the dynamics of R (t ) resulting from an experiment lasting for about 12 hours (715 min) and the algorithm presented in Section 2 to determine: i. the kinetic parameters of the reaction rate for each of the gelation phases; ii. the points where change transitions occur. It is noteworthy to mention that the kinetic parameters fitted for the last two phases have no chemical significance due to the synerysis phenomenon. Therefore, in this situation, the total number of models could be fixed equal to 3. GAMS/CPLEX was used to solve both MILP and MIQP problems presented, using a relative tolerance of 10−3 . Table 1 presents the preliminary results for the parameters obtained from the solution of problems P1 and P2, with Δ =15, and N =715. We may see that the algorithm captures the dynamic transitions of the rheological behavior, and particularly the synerysis occurrence is located at the same instant by both norms. The transition from phase 1 to phase 2 is located at different instants. The local models determined in pre-processing phase denote a small difference relatively to the models arising from minimization due to the location of the first change point and because of the characteristics of both norms, L1 penalizing large deviations, and L2 penalizing the square of residuals. These features are well demonstrated by Figure 1.
Figure 1 – Experimental data and model fits obtained.
4. Conclusions A mathematical programming formulation for optimal model selection and validation of process data was considered in this paper. One important advantage of this methodology is its capability of reaching an optimal solution, while avoiding enumeration based algorithms. To reduce the total solution time and alleviate problems resulting from the presence of outliers in the data, a two-phase approach is suggested, where an approximated solution is first obtained and later refined by the direct solution of the BIC. While the numerical solution of the optimization problems involved can present
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some difficulties, some of the properties of the problem can be exploited to reduce these problems. The application of the methodology to the basic determination of kinetic parameters was considered and successfully performed in this work. Table 1 – Structural models for each of phases captured by monitoring the behavior. n Phase log(k ) Time interval (min) 1 2.557 -0.458 [0.00; 57.18] Pre-processing step 2 11.316 -2.616 ]57.18; 135.68] ( L1 minimization) 3 -0.686 0.162 ]135.68;714.68] 1 2.309 -0.383 [0.00; 50.18] Final step ( L2 2 10.981 -2.593 ]50.18; 127.18] minimization) 3 -0.292 0.098 ]127.18;714.68]
rheological CPU (s) 49.95
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References 1. 2. 3. 4. 5.
B.E. Hansen, J. Policy Modeling, 14 (1992) 514-533. D.W.K. Andrews, Econometrica, 61 (1993) 821-856. J.H. Friedman, Annals of Statistics, 19 (1991) 1-67. L. Breiman, IEEE Trans. Inf. Theory, 39 (1993) 999-1013. W.W. Armstrong, M.M. Thomas, Handbook of Neural Computation, Oxford University Press (1996). 6. J.A. Khan, S. Van Aelstb, R.H. Zamara, Comp. Stat. & Data Analysis, 52 (2007) 239-248. 7. J. Roll, A. Bemporadi, L. Ljung, Automatica (2004) 37-50. 8. Brink, T. Westerlund, Chemometrics & Intell. Lab. Systems, 29 (1995) 29-36. 9. H.Skrifvars, S. Leyffer, T. Westerlund, Comp. & Chem. Engng., 22 (1998) 18291835. 10. A.Vaia, N.V. Sahinidis, Comp. & Chem. Engng., 27 (2003) 763-779. 11. T.A. Soderstrom, D.M. Himmelblau, T.E. Edgar, Control Eng. Practice, 9 (2001) 869-876. 12. N. Arora, L. Biegler, Comp. & Chem. Engng., 25 (2001) 1585-1599. 13. C.L. Mei, H.Y. Su, J.Chu, J. Zhejiang Univ. Sci. A. 8 (2007) 904-909. 14. P.J.T. Verheijen, In: Dynamic Model Development, Methods, Theory and Applications, Series: Computer-Aided Chemical Engineering, Elsevier, 16 (2003), 85-104. 15. M.A. Fischler, R.C. Bolles, Comm. ACM, 24 (1981) 381-395. 16. S. Pynnonen, Proc. Univ. Vaasa, Discussion Papers 146 (1992). 17. K. Kadota, S.I. Nishimura, H. Bono, S. Nakamura, Y. Hayashizaki, Y. Okazaki, K.Takahashi, Physiol. Genomics 12 (2003) 251-259. 18. A.Y. Malkin, S.G. Kulichikin, Rheokinetics, Huethig & Wepf (1996). 19. M. Avrami. J. Chem. Phys., 7 (1939) 1103-1112. 20. V. Normand, S. Muller, J.-C. Ravey, A. Parker, Macromolecules, 33 (2000) 10631071. 21. G.V. Franks, B. Moss, D. Phelan, J. Biomat. Sci., 17 (2006) 1439-1450.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Towards on-line model-based design of experiments Federico Galvanin, Massimiliano Barolo and Fabrizio Bezzo* DIPIC – Dipartimento di Principi e Impianti di Ingegneria Chimica Università di Padova, via Marzolo 9, I-35131, Padova, Italy. * E-mail:
[email protected]
Abstract Model-based experiment design aims at detecting a set of experimental conditions yielding the most informative process data to be used for the estimation of the process model parameters. In this paper, a novel on-line strategy for the optimal model-based re-design of experiments is presented and discussed. The novel technique allows the dynamic update of the control variable profiles while an experiment is still running, and can embody a dynamic investigation of different directions of information through the adoption of modified design criteria. A case study illustrates the benefits of the new approach when compared to a conventional design. Keywords: model-based experiment design, parameter estimation.
1. Introduction Modern model-based experiment design techniques [1,2] allow the definition of the “best” experimental conditions to adopt in the experimentation in order to increase the informative content about a process being studied. Experimental data from designed experiments are essential in model identification both to assess the validity of a model structure (model discrimination), and to estimate the model parameters that allow the model to match the experimental data in the range of expected utilization. For parameter estimation purposes, a general procedure for the statistical assessment of dynamic process models described by a set of differential and algebraic equations (DAEs) can be defined through the following three steps [1]: 1. the design of a new set of experiments, basing on current knowledge (model structure and parameters, and prior statistics); 2. the execution of the designed experiments to collect new data; 3. the estimation of new model parameters and statistical assessment. The iteration of steps 1 to 3 provides a new information flux coming from planned experiments leading to a progressive reduction of uncertainty region (as demonstrated in several applications [3,4]). However, note that each experiment design step is performed at the initial values of model parameters, and the uncertainty of these values, as reported in the literature [5], can deeply affect the efficiency of the design procedure. In view of above, it would make sense to exploit while the experiment is running the increment of information acquired through the collection of new measurements, so as to perform a dynamic reduction of the uncertainty region of model parameters. In this paper, a new methodology based on the On-line Model-Based Re-design of the Experiment (OMBRE) is proposed and discussed. The basic idea of this novel technique is to update the manipulated input profiles of the running experiment performing one or more intermediate experiment designs (i.e., re-designs) before reaching the end of the experiment. Each re-design is performed adopting the current value of the parameters set, which is the value of estimated model parameters until that moment.
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2. The methodology It is assumed that the generic model is described by a set of DAEs in the form: f (x (t ), x(t ), u(t ), w,θ , t ) = 0 ® yˆ (t ) = g(x(t )) ¯
(1)
where x(t) is the Ns-dimensional vector of time dependent state variables, u(t) and w are, respectively, the model time dependent and time invariant control variables (inputs), θ is the set of Nθ unknown model parameters to be estimated, and t is the time. The symbol ^ is used to indicate the estimate of a variable (or a set of variables): y(t) is the M-dimensional vector of measured values of the outputs, while ǔ(t) is the vector of the corresponding values estimated by the model. Model-based experiment design procedures aim at decreasing the model parameter uncertainty region by acting on the experiment design vector ij: ϕ = [y 0 , u(t ), w , t sp , τ ] , T
(2)
where the vector tsp of sampling times of the y variables is a design variable itself; y0 is the set of initial conditions of the measured variables and IJ is the duration of the single experiment. In order to decrease the size of the inference regions of each of the parameters in a model, some measure ψ of the variance-covariance matrix Vθ of the parameters has to be minimised. This amounts to determining the optimal vector ϕ of experimental conditions required to maximise the expected information content from the measured data generated by one or more experiments. The choice of a proper design criteria (A-, D-, E-optimal [6] or SV-based [7]) deals with the choice of the measure function ψ of Vθ. If we take into account a number Nexp of experiments, the matrix Vθ is the inverse of the Nθ × Nθ dynamic information matrix Hθ (Zullo [8]): −1
ªN ªN M M −1 º −1 º Vș (ș, ϕ ) = « ¦ H *ș k (θ, ϕ k ) + (Ȉ ș ) » = « ¦¦¦ σ ij k QTi k Q j k + (Ȉ ș ) » = 1 = 1 = 1 = 1 k k i j ¬ ¼ ¬ ¼ exp
exp
−1
,
(3)
where H*θ |k is the information matrix of the k-th experiment (superscript * indicates that the information matrix refers to a single experiment), σij is the ij-th element of the inverse of the estimated variance-covariance matrix Σ of measurements errors, Σθ is the Nθ × Nθ prior variance-covariance matrix of model parameters, Qi is the matrix of the sensitivity coefficients the for i-th measured output calculated at each of the nsp sampling points. Prior information on the model parameter uncertainty region in terms of statistical distribution (for instance, a uniform or Gaussian distribution) can be included through the matrix Ȉș. Control vector parameterization techniques [9] allow for the discretisation of the control input profiles. Those profiles are approximated using piecewise constant, piecewise linear or polynomials functions over a pre-defined number of intervals. In the case of piecewise constant parameterization, the variables to be optimized are the switching times tsw (the vector of times at which each control variables change in value) and the switching levels of u (i.e the time invariant values of the control within each of the nsw switching intervals). Equation (3) is sufficiently general to be extended to define an on-line model based redesign of experiments. Through this strategy one seeks to update the current information by executing on-line, after a given “updating time” tup (either assigned or to be optimized), a parameter estimation session followed by a re-design of the remaining part of the experiment (and so adjusting the trajectories of control variables). One or more updates can be attained in the re-design, each one adding a new component (in the form of (2)) to the global ij vector of the experiment, so that it can be rewritten as:
Towards O n-line Model-Based Design of Experiments
[
]
ϕ = ϕ1 , ϕ 2 ,..., ϕ j ,..., ϕ nup +1 T
351
,
(4)
where nup is the number of control updates and ijj is the design vector after the (j-1)-th update. In a general fashion, each component ijj of ij could have a different dimension in terms of number of discretized control variables and/or sampling points (obviously ij1 will be the only component to enclose the initial values to be optimized). The amount of information gathered after the j-th re-design can be expressed in terms of the dynamic information matrix:
[
]
~ ~ ª j −1 ~ −1 º H ș , j (θ, ϕ ) = «¦ H *ș k (θ, ϕ k ) + H *ș (θ, ϕ j ) + (Ȉ ș ) » = H *ș (θ, ϕ j ) + K , ¬ k =1 ¼
(5)
where the sum of the prior information on model parameters (Ȉș-1) and the information acquired before the j-th re-design can be expressed as a constant term K. The symbol (~) indicates that the information content refers to a single updating interval. The efficiency of a design strategy deals with its capability to provide a satisfactory parameter estimation in terms of accuracy (i.e. closeness to “true” value) and precision (related to the dimension of the uncertainty region). As in practice the “true” values of model parameters are not known a-priori, only the precision is evaluated through two indicators: a global precision (ȍș) and a global t-factor (GTF) defined as: § ȍș = ¨ ¨ ©
−1
· ı ¸ , ¦ ¸ i =1 ¹ Nș
2 și
GTF =
1 Nș
NP
¦t i =1
−1 i
,
(6)
where the ti are the t-values statistics, depending by the diagonal elements of Vș and by the actual parameter estimate. For a reliable parameter estimation, each t-value must be greater than a computed reference value (given by the Student’s t distribution with N×M-Nș degrees of freedom).
3. Case study The OMBRE approach is applied to a biomass fermentation model [1], which, assuming Monod-type kinetics for biomass growth and substrate consumption, is described by the following DAEs set: dx rx șx dx1 = (r − u1 − ș 4 )x1 , 2 = − 1 + u1 (u 2 − x2 ) , r = 1 2 dt dt ș3 ș 2 + x2
,
(7)
where x1 is the biomass concentration (g/L), x2 is the substrate concentration (g/L), u1 is the dilution factor (h-1), and u2 is the substrate concentration in the feed (g/L). The model was demonstrated to be structurally identifiable with respect the parametric set ș. The conditions that characterise an experiment are the initial biomass concentration x10 (range 1-10 g/L), the dilution factor u1 (range 0.05-0.20 h-1), and the substrate concentration in the feed u2 (range 5-35 g/L). The initial substrate concentration x20 is set to 0 g/L and cannot be manipulated for experiment design purposes. The principal aim is to detect a proper design configuration allowing to estimate the parameter set ș in a satisfactory manner through a single experiment where both x1 and x2 are measured. It is assumed that the global experimental budget can be represented by a number of nsp = 24 sampling points and nsw = 12 switches to distribute on a maximum experimental horizon of IJmax = 72 h. The inputs u(t) can be manipulated and are represented as piecewise-constant profiles, and the output sampling times and the control variables switching times can be different. The elapsed time between any two
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sampling points is allowed to be between 0.01 h and IJi (the duration of the updating interval), and the duration of each control interval between 0.1 and 40 h. The model parameters are scaled to unity before performing each design step. A multiple shooting technique was used in order to reduce the possibility of incurring into local minima in the design step. However, note that the re-design strategy allows to split the nijdimensional optimisation problem into (nup+1) smaller optimizations, with great benefit for both robustness and quickness of the computation. Synthetic “experimental” data are obtained by simulation of model (7) with ș = [0.310 0.180 0.550 0.050]T as the “true” parameters set, and by adding normally distributed noise with a mean of zero (the vector of parameter units is [h-1, g/L, -, h-1]T) and ª0.5 0. º Ȉ=« » ¬ 0. 0.8¼
(8)
as the M×M variance-covariance matrix of measurements errors. This matrix assumes that the experimental equipment cannot deliver good quality data and that there is no dependence among different measurements. The initial guesses for the parameters are represented by the set θˆ 0 = [0.527 0.054 0.935 0.015]T, corresponding to a starting point that is quite far from the true value. 3.1. Proposed experiment design configurations and results A standard E-optimal experiment design was compared with the newly introduced OMBRE strategy at a variable number of updates of design variables. The following assumptions are made: 1. nsp/(nup+1) samples are acquired during each updating interval (i.e the time between two updating times), while the number of switches can vary; 2. the i-th re-design starts at the time in which the last optimized sample of each design phase (enclosed in iji-1) is acquired; 3. no delay time occurs between the key activities (design, experiment and parameter estimation phases) of the global design procedure; The following experiment design configurations are implemented: 1. STDE: standard E-optimal experiment design; 2. OMBRE-nup: on-line E-optimal re-design of the experiment with nup=1, 2, 3; 3. OMBRE-SV: on-line re-design with nup=3 including SV design criteria (based on the minimisation of the second maximum eigenvalue of Vθ) in the second updating interval. The results are compared in terms of a-posteriori statistics (Table 1) and global statistics (ȍș and GTF, Figure 1 (a) and (b)) obtained after the final parameter estimation session. Table 1 Comparison of different experiment design configurations. Apex * indicates t-values failing the t-test (the reference value is tref = 1.6802 and ș = [0.310 0.180 0.550 0.050]T ) Design STDE OMBRE-1 OMBRE-2 OMBRE-3 OMBRE-SV
Parameter Estimate șˆ [0.257 0.080 0.022]T [0.309 0.303 0.045]T [0.309 0.294 0.047]T [0.320 0.102 0.059]T [0.310 0.110 0.055]T
0.453 0.518 0.517 0.564 0.560
Conf. Interval (95%) [±0.0890 ±0.2963 ±0.0774 ±0.0882] [±0.0173 ±0.2308, ±0.0697 ±0.0156] [±0.0507 ±0.1009, ±0.0853 ±0.0319] [±0.0292 ±0.0984, ±0.0648 ±0.0276] [±0.0086 ±0.0623, ±0.0238 ±0.0072]
t-values [2.97 0.45* 2.02 0.41*] [11.01 1.32* 7.44 2.87] [6.10 1.12* 6.54 1.68*] [10.27 2.111 8.31 1.50*] [36.01 1.77 23.49 7.62]
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Global precision
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24 20 16 12
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8
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1
2
3
0
1
2
3
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nup
(a)
(b)
Figure 1 Global precision ȍș (a) and GTF (b) for selected re-design configurations at a variable number of updates (nup = 0 stands for a standard E-optimal experiment design).
30 u2 [g/l]
u2 [g/l]
The precision of the estimate can be assessed through the analysis of confidence intervals (95%) while the t-test allow to assess the accuracy of the designs. The results clearly show the benefits in adopting an OMBRE approach. Although the STDE design does not permit to reach satisfactory θˆ2 and θˆ4 , the insertion of a single update (OMBRE-1) provides a significant improvement in the precision of the estimate (see for instance the statistics for θˆ1 , θˆ3 and θˆ4 ). To improve the precision of θˆ2 the number of updates is increased. Although there is an increase in the global precision ȍș (Figure 1a), the advantages of using two or three updates are not so certain. In fact, the global tfactor exhibits an oscillatory behavior (Figure 1b). Note that OMBRE-2 provides a poor estimation of ș4 , and also θˆ2 is still statistically imprecise (although there is a reduction in interval of confidence with respect to OMBRE-1). An additional update provides a better precision in θˆ2 (see for instance the 95% confidence intervals), but θˆ4 is still inaccurate. It is interesting to note that by increasing the number of updates, one obtains a variation in capability of estimating different parameters, i.e. in the directionality of the design [7]. Therefore, it makes sense to assess the effect of an OMBRE-SV configuration in order to exploit the information related to the smaller eigenvalues of Vș. For the case being investigated, a standard E-optimal design acts mainly on the direction of variability of θˆ2 while a SV-based design tends to improve both θˆ1 and θˆ4 [7]. OMBRE-SV allows to estimate the entire ș set in a satisfactory manner increasing the global performance of OMBRE-3 estimation (see Figures 1a and 1b).
20
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Figure 2 Dilution factor (u1), substrate concentration in the feed (u2) and distribution of samples (tsp) as planned by OMBRE-3 (a) and OMBRE-SV (b). Black squares show the updating times.
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Figures 2a and 2b underline the differences between OMBRE-3 and OMBRE-SV configurations in terms of manipulated inputs and sampling times distribution. Note that the minimisation of the second largest eigenvalue determines the second redesign to be sensibly different from corresponding one in OMBRE-3. As a consequence, also the third re-designs are different from each other.
4. Final remarks A novel methodology of experiment design based on a on-line model based re-design of experiments (OMBRE) has been proposed and discussed. The new technique allows to embody in a model-based experiment design procedure the information content that is progressively acquired while an experiment is running. Results from an illustrative case study are encouraging and clearly demonstrate how the proper choice of a re-design configuration may guide the estimation to more precise and accurate patterns. It is also shown how OMBRE may incorporate different design techniques (e.g., the SV criterion) and thus take advantage of a more tailored directional approach in exploiting the content of the information matrix. Future work will assess the applicability of the OMBRE technique to larger systems and will develop a systematic procedure for the selection of the optimal re-design configuration.
Acknowledgements This research was carried out in the framework of the Progetto di Ateneo 2005 “Image analysis and advanced modelling techniques for product quality control in the process industry”.
References [1] S.P. Asprey, S. Macchietto, 2000, Statistical Tools for Optimal Dynamic Model Building, Comput. Chem. Engng., 24, 1261-1267. [2] I. Bauer, H.G. Bock, S. Körkel, J.P. Schlöder, 2000, Numerical Methods for Optimum Experimental Design in DAE Systems, J. Comput. Appl. Mathem., 120, 1-25. [3] G. Franceschini, S. Macchietto, 2007, Validation of a model for biodiesel production through model-based experiment design, Ind. Eng. Chem. Res., 46, 220-232. [4] C. Reverte, J.L. Dirion, M. Cabassud, 2007, Kinetic model identification and parameters estimation from TGA experiments, J. Anal. Appl. Pyrolysis, 79, 297-305. [5] S. Körkel, E. Kostina, H. G. Bock, J.P. Schlöder, 2004, Numerical methods for optimal control problems in design of robust optimal experiments for nonlinear dynamic processes, Opt. Methods and Software, 19, 327-338. [6] F. Pukelsheim, 1993, Optimal Design of Experiments, J. Wiley & Sons, New York, U.S.A. [7] F. Galvanin, S. Macchietto, F. Bezzo, 2007, Model-Based Design of Parallel Experiments, Ind. Chem. Res, 46, 871-882. [8] L. Zullo, 1991, Computer Aided Design of Experiments. An Engineering Approach, PhD Thesis, The University of London, U.K. [9] V.S. Vassiliadis, R. W. H. Sargent, C. C. Pantelides, 1994, Solution of a class of multistage dynamic optimizations problems. 1-Problems without path constraints, Ind. Eng. Chem. Res, 33, 2111-2122.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Sensor placement for fault detection and localization Carine Gerkens and Georges Heyen Laboratoire d’Analyse et de Synthèse des Systèmes Chimiques Department of Applied Chemistry, University of Liège Sart-Tilman B6A, B-4000 Liège (Belgium)
Tel: +32 4 366 35 23 Fax: +32 4 366 35 257 Email:
[email protected]
Abstract A general approach is proposed for designing the cheapest sensor network able to detect and locate a set of specified faults. The method is based on the sensitivity of process residuals with respect to faults. A genetic algorithm is used to select the sensors and their locations. Results are shown for two water networks. Keywords: sensor network, genetic algorithm, fault detection and isolation.
1. Introduction Nowadays, the interest for chemical process monitoring becomes more and more important. Indeed, environmental and safety rules must be satisfied and the required product quality must be achieved. Moreover, fluid leakages are expensive and must be detected as quickly as possible. Fault detection can only be done if a suitable sensor network is installed in the process. However, all measurements are corrupted by noise and the sensor precision has a great influence on the detectability and isolability of process fault. Therefore the sensor precision must be taken into account when a network is designed. In this study, a general method to design the cheapest sensor network able to detect and locate a list of faults in a given process is proposed. The method is based on the fault detection technique proposed by Ragot and Maquin [4]. Those authors use the notion of fault sensitivity to decide whether a residual is influenced or not by a specified process fault. As the problem is multimodal, not derivable and involves many binary variables, the sensor network optimization is done by means of a genetic algorithm (Goldberg [3]). Indeed, the efficiency of this optimization algorithm has been proved for similar problems, such as the design of efficient sensor networks for data reconciliation (Gerkens [2]). The method is illustrated for two water networks of different complexity. The detected faults are leakage in pipes and storage tanks, but other fault types could also be simulated and detected.
2. Fault detection and isolation The objective of fault detection is to determine whether the measurements remain in a normal range of values, as predicted by a process model for a given operating mode of the plant. If the difference between measurements and estimations is too large, a fault is detected. The fault detection and localization techniques are carried out in two steps: the
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estimation of the residuals and the decision. In order to make sure that all the faults that can occur in a process are detectable, the signature matrix must be analyzed. This matrix is the occurrence matrix of the potential fault variables in the model equations, expressed in residual form. As an example, let us consider the following system, characterized by four residuals and six variables at time t:
r1 ( t ) = f1 ( x1 ( t ) , x2 ( t ) , x5 ( t ) , x6 ( t ) )
r2 ( t ) = f 2 ( x1 ( t ) , x2 ( t ) , x3 ( t ) , x5 ( t ) , x6 ( t ) ) r3 ( t ) = f3 ( x3 ( t ) , x5 ( t ) , x6 ( t ) )
r4 ( t ) = f 4 ( x2 ( t ) , x4 ( t ) , x5 ( t ) ) The corresponding signature matrix has the form:
§X ¨ X Σ=¨ ¨0 ¨ ©0
X 0 0 X X· ¸ X X 0 X X¸ 0 X 0 X X¸ ¸ X 0 X X 0¹
A fault is detectable if the corresponding column in the signature matrix contains at least one non-zero element. A fault can be located if the corresponding column in the signature matrix is different from all other columns of the signature matrix. The fault localization consists of deducing what is the fault from the values of the residuals. For that purpose, fuzzy rules are elaborated from the signature matrix. They are linguistic “if-then” constructions of the general form “if A then B” where A are the premises and B the consequence of the rule. As noise influences the value of the residuals, some random perturbations in the measurements may be large enough to trigger a fault detection even when no fault occurs. Taking into account temporal persistence allows improving the detection procedure. For that purpose, instantaneous measurements are replaced by averages calculated over several time steps. The sensitivities of residuals to a given fault are different so that the magnitude of the residual deviations allows to characterize and isolate a fault. The isolability of faults can then be improved by using this difference of sensitivity. Let y be the measurement of a variable of the process. It is the sum of the true value x, the noise İ and the fault f:
y = x +ε + f
Since the true values satisfy the process model, they do not contribute to the residuals, which reflect two terms: the contribution of the noise rε and the contribution of the fault rf ; thus the effect of a fault can be masked by the effect of the noise according to their relative magnitudes. The noise contribution to the ith residual is defined as follows: n
rε ,i = ¦ mij ε j j =1
where mij are the elements of the matrix of the derivatives of the residuals with respect to the variables. If the errors are replaced by the precision of the sensors e j , one obtains the upper bound of the contribution of the noise on the ith residual:
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n
rε ,i = ¦ mij e j j =1
In the same way, the contribution of a unique fault f j affecting the ith residual is defined as follows:
rf j ,i = mij f j The lowest magnitude of the ith residual that allows distinguishing between the noise and the fault f j is defined by the bound: n
¦m
ij
τ ij =
ej
j =1
mij
So, the ith residual is sensitive to fault f j if the magnitude of that fault is higher than τ ij . Fault f j will be located if for all non-zero elements of the signature matrix, the absolute value of the corresponding residual is larger than the corresponding bound
τ ij
and for each zero element of the signature matrix, the absolute value of the corresponding residual is smaller than a fixed upper bound. For example, if one takes the derivative matrix of the process previously described:
§ 1 −0.5 ¨ 2 −4 Σ=¨ ¨0 0 ¨ 6 ©0
0 0 1 −2.5 · ¸ 2 0 3 1 ¸ 3 0 −2 −1 ¸ ¸ 0 −5 −4 0 ¹ T For the following error vector e = ( 0.5,1, 0.8, 0.4,1, 0.4 ) , the corresponding bounds matrix is given by:
∞ ∞ 3 1.2 · §3 6 ¨ ¸ ∞ 3.3 10 ¸ 5 2.5 5 τ =¨ ¨ ∞ ∞ 1.6 ∞ 2.4 4.8 ¸ ¨ ¸ ∞¹ © ∞ 2 ∞ 2.4 3 So, the third fault will be detected and located if the second residual has an absolute value larger than 5 and the third one an absolute value larger than 1.6.
3. Method description The design procedure allowing configuring the optimal sensor network able to detect and locate all the specified faults is carried out in four steps: - simulation of the process and of the faults that should be detected and located; - specification of the sensor database and the sensor requirements; - verification of the problem feasibility;
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optimization of the sensor network.
3.1. Simulation of the process and of the faults that should be detected and located The process is first simulated for typical operating conditions. Then, for each possible fault one decides the minimal magnitude of the fault that should be detected by the sensor network, for example a leakage of 1% of a stream flow rate. The faults are simulated one by one by increasing progressively the leakage until the minimal fault that should be detected is reached. The values of the variables at the beginning and at the end of each pipe obtained during the k last simulations are kept for each fault. No noise is added to the variables at this step because the noise depends on the precision of the measurement tools. The number of samples used to calculate the moving average of the variables depends on the frequency of the measurements and the speed at which the fault should be detected. If the number of measurement times is higher, the fault detection and location is slower but more reliable. If this number is too small, the noise influences more the magnitude of the residuals and the fault detection is more difficult. In the examples of paragraph 4, a value of 5 has been chosen. 3.2. Specification of the sensor database and the sensor requirements 3.2.1. The sensor database For each sensor type, the database contains the following information: - the name of the sensor; - the annualized cost of the sensor, i.e. the annualized sum of the purchase, installation and operating costs; - the type of variable that can be measured by the sensor; - the domain of validity of the measurement; - the accuracy of the sensor, as defined by the following equation:
σ j = ai + bi X j 3.2.2. The sensor requirements In this file, the sensors that exist and don’t have to be replaced are listed as well as the sensors that can not be placed at a particular location in the process. 3.3. Verification of the problem feasibility The problem feasibility check starts by enumerating all the sensors that can be placed in the plant. A binary gene is created for each sensor; its value is set to 1 when the sensor is selected and 0 otherwise. The set of genes forms a chromosome whose length is equal to the number of possible sensors. It may appear that a variable is measured by more than one sensor so that the precision of the most accurate one is taken into account for the bounds calculation. The residual bounds and the residuals are estimated for the initial sensor network: indeed, a noise bounded by the accuracy of the sensor is added to each variable for each measurement time before the mean of the variables and the residuals are calculated. The noise on the variables and then their values depend thus of the sensor network as well as the residual bounds. To ensure that the design problem accepts a solution, the initial sensor network has to be able to detect all the simulated faults. If it is not the case, new sensor types that are more precise should be added to the data base or the minimal magnitudes of the faults to be detected should be set higher. 3.4. Optimization of the sensor network When the existence of a solution has been verified, it can be optimized. The objective function to be minimized is evaluated this way:
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-
if all the faults can be detected and located, the objective function is the sum of the costs of all the sensor in the network; - if at least one fault can not be detected or located, the current solution is unfeasible and it is penalized by setting its merit function to a large value (twice the cost of all possible sensors). The goal function being generally multimodal, the problem being not derivable and containing only binary parameters, a genetic algorithm [2] has been used as the optimization method. The algorithm that has been used is based on the one developed by Caroll [1]. In this algorithm, the individuals are selected using tournament selection. A shuffling technique allows choosing randomly pairs for mating. A new population is generated by applying single-point cross-over and the jump mutation mechanisms. Individuals of the first population are chosen randomly, by activating randomly 80% of all each genes. The size of the population is set to 20 individuals. The probability of reproduction is fixed to 50%, the probability of single-point cross-over to 50% and the probability of jump mutation to 1%. The fitness function is evaluated for each individual of the new generation. The best one is then kept and duplicated in the case it would be subject to mutation in the following generation. The calculation is stopped when the objective function of the best individual remains unchanged during a specified number of generations.
4. Cases studies Two water networks have been studied. The first one is composed of five storage tanks and ten connection pipes (figure 1). The fifteen faults that should be detected and located are water leakages in the storage tanks or in the pipes. Each storage tanks can be fitted with a level meter, and the flow rate can be measured at both ends of each pipe, which means 25 possible sensors.
Figure 1
Figure 2
In the sensor database three level meters are available with different accuracies and prices, and 10 flow meters with different accuracies, prices and measurement domains. With this database, it is possible to place 135 sensors. That corresponds to a solution space of 2135 = 4.4*1040 solutions. This measurement system has a total cost of 11950 cost units.
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Obtaining the solution requires 14770 generations (295421 goal function evaluations) for a stop criterion of 6000 generations. The optimal sensor network is obtained after 301 seconds on a 1.6GHz computer. This optimal network costs 1860 units and counts 25 sensors, one for each possible sensor location. It allows detecting and locating all the 15 faults. The initial and most expensive network costs 3100 units (1240 cost units more than the optimal one). The second water network (figure 2) is composed of 14 storage tanks and 31 pipes so that there are 76 possible sensor locations. The sensor database contains three level meters with different accuracies and prices, and 15 flow meters with different accuracies, prices and measurement domains. The initial network counts 392 possible sensors. This corresponds to a solution space of 10118 solutions. This sensor network has a total cost of 34100 units. Obtaining the solution requires 26104 generations (522101 objective function evaluations) for a stop criterion of 6000 generations. The optimal sensor network is obtained after 5667 seconds on a 1.6GHz computer. This solution costs 6200 units and requires 76 sensors: one for each possible sensor location. It allows detecting and locating all the 45 faults. In order to detect and locate all the faults, one sensor is required at each location, but the network cost can be minimized by selecting the cheapest sensor that provides the required precision. The most expensive of those network costs this time 9000 costs units (2800 cost units more than the optimal one).
5. Conclusions The proposed design method allows building a sensor network that is able to detect and locate a specified list of tank and pipe leakages. This network is much cheaper than the initial one. The algorithm provides thus a practical solution, even if global optimality can not be demonstrated when using an evolutionary optimization algorithm. This method could be transposed for other types of faults such as the catalyst deactivation or the loss of efficiency in a compressor.
Acknowledgments The authors are grateful to the Walloon Region and the European Social Funds who cofinanced this research.
References 1. Caroll D.L., 21 August 2001, FORTRAN genetic algorithm driver version 1.7, Download from http://cuaerospace.com/caroll/ga.html, consulted on May 2004. 2. Gerkens C., Heyen G., 2005, Use of parallel computers in rational design of redundant sensor networks, Computers and Chemical Engineering 29, 1379-1387. 3. Goldberg D.E., 1989, Genetic algorithm in search, optimization and machine learning, Reading, MA, Addison-Wesley Publishing Company. 4. Ragot J., 2006, Fault measurement detection in an urban water supply network, Journal of Process Control 16, 887-902.
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Using kriging models for real-time process optimisation Marcos V.C. Gomes,a I. David L.Bogle,b Evaristo C. Biscaia Jr.,c Darci Odloakd a PETROBRAS S.A., Av. Horácio Macedo, 950, Rio de Janeiro RJ,Brazil 21941-915 b Chemical Engineering Department, University College London, London WC1E 7JE,UK c Programa de Engenharia Química – COPPE, Universidade Federal do Rio de Janeiro, P.O. Box 68502, Rio de Janeiro, 21945-970, Brazil d Departamento de Engenharia Química, Universidade de São Paulo, São Paulo 05508900 Brazil
Abstract Kriging models have been used in a number of engineering applications, to approximate rigorous models when those computer codes become too time-consuming to be used directly. In this context, they are called surrogate models or metamodels. The use of kriging models as metamodels for process optimisation was addressed in a previous paper [1] where a methodology for metamodel-based process optimisation was proposed, focusing on real-time applications. In this work, new developments were achieved through the use of new examples, one of which the optimisation of a real crude distillation unit involving 19 decision variables. The performance of the metamodel-based optimisation is compared with results obtained with the optimisation based on a first-principles model, embedded in a sequential-modular process simulator. It is shown that metamodel-based optimisation with adaptation of the metamodels during the optimisation procedure provides results with good accuracy and significant reduction of computational effort. The performance comparison between neural networks and kriging models for chemical processes is another contribution of this work.
Keywords: optimisation, crude distillation, kriging, neural network. 1. Introduction A metamodel is a reduced model that is fitted to approximate a complex model (usually a rigorous, first-principles mathematical model). The data used to fit the metamodel is obtained from several runs of the rigorous model, frequently called computer experiments. By analogy to physical experiments, experimental design techniques are used to define the sites where the data should be generated. Metamodels have been widely used in many fields of engineering, to replace rigorous mathematical models when they become too time-consuming or prone to numerical problems. One of the most typical uses of metamodels has been in optimal design where many design scenarios can be easily analysed by optimisation techniques. One of the most used families of reduced models that have been used as metamodels [2] are the kriging models. 1.1. Kriging models The kriging model structure presented here is the most frequently used in the literature (for more details, refer to [3]). Let the set of functions y(x,u) be a rigorous mathematical description of a process, where x are independent variables and u model parameters. The kriging models that approximate the rigorous one are built from a set of design
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points (X,Y) obtained from runs of the rigorous model for a set of parameters u0. They are composed by a linear regression model and a random function: yˆ i (x ) = ȕiT ⋅ f ( x ) + z i ( x ), i = 1! nY
(1 )
The first term is usually a low-order polynomial. The random functions zi have the following form: z i = riT ( x ) ⋅ R −1 ( Y − Fȕ i )
(2 )
where T
T
ª nX º ª nX º ri ( x) = «∏ ℜij (θij, X kj − x j )» and R im ( X m ) = «∏ ℜij (θij, X kj − X mj )» , ¬« j=1 ¼» ¬« j=1 ¼»
k, m = 1! nP
(3 )
The matrix F is obtained by computing the f(x) values for the design inputs X. ℜ are correlation models [4], usually built as functions of the distance between two sites. Therefore, Rim(Xm) is a matrix that contains the correlations between the design sites, and ri(x) is a vector that contains the correlations among a new site x and the design sites. 1.2. Applications on chemical processes Palmer and Realff [2] proposed the first work based on metamodels applied to chemical process design, using kriging models and polynomials. Later, Gomes et al.[1] proposed the use of metamodels for RTO applications. The alkylation process optimisation problem was used to validate the proposed methodology. Accurate solutions were reported with the metamodel approach with less than 30% of the required runs of the original model when compared to the solution based exclusively on the original model. As an extension of this work, it was attempted [5] to apply this methodology to two other examples, one of them a large real optimisation problem of a crude distillation unit (CDU). It was concluded that the previous proposed procedures should be improved, in order to allow their successful application to a wider class of problems. This improvement was accomplished by the introduction of a SAO algorithm. 1.3. Sequential Approximate Optimisation (SAO) SAO is a procedure used to solve optimisation problems when the model computation is time-consuming. The optimisation problem is decomposed into subproblems, confined to a fraction of the original search space, that are solved sequentially based on a trustregion strategy. The original problem functions are usually replaced by polynomials. The way by which the trust region is changed, the assessment of the model approximations and the termination criteria are important issues of the SAO algorithm. In this work, some aspects of a new methodology based on the use of metamodels for real-time process optimisation are presented. This methodology comprises the metamodel generation and its use along with a new SAO algorithm that contains automatic procedures for adaptation and assessment of metamodels. In this work, the highlights of the proposed methodology are presented, along with the results obtained with the optimisation of a real, industrial-scale crude distillation unit.
2. Example In order to validate the proposed methodologies, a real industrial problem has been addressed: the optimisation of the Crude Distillation Unit (CDU) and the Solvents Units of RECAP, a Brazilian refinery of PETROBRAS.
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2.1. Process description The crude oil is fed to the pre-flash column (N507) of the CDU, from which three streams are obtained. The top product is light naphtha which is sent to the solvents units. An intermediate stream constitutes extra-light diesel (DEL). The bottom stream is sent to the atmospheric column (N506), where it is split into the atmospheric residue (RAT), Kerosene, heavy diesel oil and heavy naphtha. The light and the heavy naphtha streams constitute the Solvents Units feed, where the high-valued products rubber solvent (SBO) and Paint diluent (DTI) are obtained after many separation operations. A third stream containing the heaviest remains of the feed is mixed to DEL, Kerosene and Heavy Diesel streams to generate the diesel oil stream. A recycle stream between column N751 and the solvents units feed tank is used to minimize losses of SBO.
Figure 1 – Scheme of the CDU and the Solvents Units of RECAP/PETROBRAS.
2.2. The process model The process model was built using PETROX, a proprietary sequential-modular process simulator from PETROBRAS. The simulation comprises 53 components and pseudocomponents and 64 unit operation modules, including 7 distillation columns and a recycle stream. All modules are built with rigorous, first-principles models. For optimization applications, PETROX was linked to NPSOL, an SQP optimisation algorithm. 2.3. The optimisation problem The optimisation problem takes the following form: min f [y (x ), x] x
(4 )
s.t. : h[y (x ), x] = 0 ; g[y (x ), x] ≤ 0 The set of functions y(x) in Equation (4) comprises all variables whose values are to be obtained from runs of the process simulator to compute the objective function and equality or inequality constraints. The objective function is the operational cost (ī): Γ=
nprods
¦ i =1
$ iprods ⋅ product i −
nutils
⋅ utility j −$ feed ⋅ feed ¦ $ utils j
(5 )
j=1
Table 1 presents the description of the decision variables and constraints of the problem.The problem inequality constraints (constraints 3-21) are related to product specifications and safety or performance limits. The equality constraints 1 and 2 were included to model the heat integration between the atmospheric column and the feed pre-heating train. Another 18 process variables take part of the objective function, as
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product flow rates or utilities. Table 1 - Decision variables and constraints of the optimisation problem 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
Decision variables (x) Crude flow rate Steam flow rate to N507 Steam flow rate to N506 Pumparound flow rate Atmospheric heater outlet temperature Kerosene flow rate Diesel reflux flow rate Heavy naphta molar flow rate DEL flow rate Temp. #2 N507 N701 feed flow rate N701 control temperature N703 control temperature N703 reflux flow rate N752 control temperature N753 reflux flow rate N506 pumparound outlet flow rate N753 top/feed ratio preheating train heat duty to N506
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
Constraints (h,g) Equality constraint #1 – heat integration Equality constraint #2 – heat integration Light naphta flow rate Diesel ASTMD86 85% temperature Naphta recycle flow rate DTI– Dry point DTI– Initial boiling point ASTMD86 N703 reboiler steam flow rate SBO– Dry point SBO– Initial boiling point ASTMD86 N753 control temperature N753 reboiler steam flow rate N753 bottom flow rate Temp #2 N506 N506 #10 – molar flow rate N506 #22 – molar flow rate N507 #10 – molar flow rate N701 #17 – molar flow rate N703 #3 – molar flow rate N752 #8 – molar flow rate N753 #14 – molar flow rate
3. Methodology: Metamodeling and SAO The methodology for the use of metamodels in RTO begins with the off-line generation of a base metamodel. All the following steps shall be performed during the optimisation procedure. The use of this metamodel in a real-time environment requires its adaptation to face not only changes in the process behaviour, but eventual mismatches between the metamodel and the rigorous model. A validation procedure is required to allow the assessment of the metamodel throughout the optimisation procedure, as well as a suitable set of termination criteria. A comprehensive description of the proposed methodology is presented in [5]. 3.1. Generation of the base metamodel The main aspects for metamodel generation are: (i) Generation of training data, through an experimental design strategy; (ii) Independent variable selection; (iii) Parameter estimation and (iv) Metamodel validation. The training data is generated based on the Latin Hypercube Design (LHD). A forward stepwise regression procedure is used to select the independent variables to be used by the metamodels of each dependent variable. For kriging models, the structure is defined by the set of independent variables selected – including quadratic terms – and the selection of the correlation model. The parameter estimation is performed by a maximum likelihood procedure. For neural nets, the activation function to be used is defined a priori. The structure is completed by the selection of the number of neurons in the hidden layer. A backpropagation procedure has been used for training. The procedure is presented in Figure 2. It starts with the training data, a set of candidate metamodel structures and a set of sets of initial estimates for the metamodel parameters. The best metamodel will be the one that provides the smaller prediction errors computed with a set of independent validation data. The best metamodel will be the one that provides the smaller prediction errors, computed with a set of independent validation data. 3.2. Sequential Approximate Optimisation (SAO) The SAO algorithm proposed in [6] was used as a basis of the algorithm proposed here (Figure 3). The key features of this algorithm are related to the way by which the base metamodel is adapted and assessed, the trust region updating procedure and the
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termination criteria for the optimisation procedure. CONFIGURATION
Training data Set of model structures {S1,…,Sk,…,SnS} Sets of parameter estimates {θ1,…, θj, …, θnθ}
Rigorous Model Base Metamodel SAO Parameters Problem configuration: Variables, , Limits, Initial estimates
Validationdata
Variable selection
Parameter Estimation
Compute prediction errors no
no
Rigorous Model
Metamodel Adaptation
Keep best metamodel
Optimisation k > nS ? yes
Update Trust Region
Check Termination Criteria
j > nθ? yes
NO
OK?
Best metamodel
YES
Figure 2 – The general procedure for metamodel generation
END
Figure 3 – SAO strategy applied to the metamodel-based optimisation.
4. Results Kriging models and neural nets were generated for each of the 39 dependent variables required for the computation of the objective function and the constraints. Table 2 presents the main characteristics of the metamodels (for more details, refer to [5]). To simulate a real-time operation, a set of case studies (Table 3) were proposed, where changes in the process behaviour were introduced by changing the model parameters. The objective was to verify if the adaptation procedure would be able to change the base metamodels in order to allow acceptable solutions to the optimisation problem. The selected model parameters were the feed composition (I and II), the global heat coefficient of the atmospheric column pumparound (UPPA – III and IV) and the global heat coefficient of the condenser of column N753 (UCOND - V). Table 2 - Main characteristics of the metamodels Size of training data set Size of validation data set Number of initial estimates kriging
186 399 10 Regression model
quadratic Gauss Spline Spherical
Correlation models
Neurons in the hidden layer Neural nets
Activation functions
2-5 Hidden layer
Log-sigmoid
Output layer
Linear
Table 3 – Cases for assessment of the SAO/metamodel procedure Case Base I II III IV V
CDU Feed, °API 33.0 32.5 33.5 33.0 33.0 33.0
UPPA 967 967 967 800 1300 967
UCOND 750 750 750 750 750 900
Two indexes were used to assess the proposed methodology, whose computation is described in Equation (6). The relative benefit shows the fraction of the profit obtained with the rigorous solution that could be attained with the metamodel/SAO procedure. x0
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is the initial state of the decision variables, xRIG is the rigorous solution and xSAO is the approximate solution. The relative effort shows the ratio between the number of simulation runs with the rigorous model required by the metamodel/SAO procedure and the correspondent number of simulations required by the rigorous solution. Benefit(%) = 100 ⋅
( ) ( ) (x ) − F (x )
Fobj x SAO − Fobj x 0 Fobj
RIG
0
Effort (%) = 100 ⋅
obj
NSIMSAO NSIM RIG
(6 )
Table 4 presents the obtained results. In most cases, a relative benefit above 85% was obtained, with a minimum value of 77%. The observed relative computational effort remained below 50% for 9 of the 12 cases studied, showing that good accuracy on the optimisation results was obtained with significant reduction of the computational effort. Table 4 - Attained benefit and relative computational effort with the SAO/metamodel procedure. Case Base I II III IV V
Kriging models Benefit, % Effort, % 94.0 35.8 78.7 42.5 89.0 22.4 85.2 21.1 97.9 87.0 90.2 29.7
Neural nets Benefit, % Effort, % 97.1 43.1 77.1 42.5 89.7 53.1 84.6 12.9 93.9 19.5 94.6 54.7
5. Conclusions A new strategy for Real-Time Optimisation combining metamodels and a Sequential Approximate Optimisation (SAO) procedure has been proposed. This methodology is based on automatic procedures, aiming its use in real-time applications. Kriging models and neural nets were used as metamodels. The methodology was tested with an example involving the optimisation of a crude distillation unit, using the first-principles models of a sequential-modular process simulator. The solution of the corresponding optimisation problem with this rigorous model required considerable computational effort. It is shown that the proposed methodology provides solutions with good accuracy and a significant reduction of computational effort. Another advantage of this approach is that the occurrence of numerical problems during the solution of the rigorous model does not result in the failure of the optimisation procedure. The reported results show that kriging models can be used to model chemical processes involving a large number of independent variables, and that they can perform as good as or better than neural nets.
References [1] M.V.C.Gomes, I.D.L.Bogle, D. Odloak, E.C.Biscaia Jr., An application of metamodels for process optimisation, Proceedings of the 16th European Symposium on Computer Aided Process Engineering, (2006) 1449. [2] K. Palmer, M. Realff, Trans IchemE, 80 (2002) Part A 760. [3] T.J. Santner, B.J. Williams, & W.I. Notz, Springer-Verlag New York, Inc. (eds.) The Design and Analysis of Computer Experiments. New York, 2002. [4] S.N. Lophaven, H.B. Nielsen, J. Sondergaard, DACE - A MATLAB Kriging Toolbox. Technical University of Denmark, Technical Report IMM-TR2002-12, 2002. [5] M.V.C.Gomes, Otimização Seqüencial por Aproximações – Uma aplicação em tempo real para o refino do petróleo, D.Sc. Thesis, (in portuguese), PEQ/COPPE/UFRJ, Rio de Janeiro, Brazil, 2007. [6] A.A.Giunta, M.S.Eldred, Proceedings of the 8th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimisation, Long Beach, USA, AIAA-2000-4935.
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Estimation Of A Class Of Stirred Tank Bioreactors With Discrete-Delayed Measurements Héctor Hernández-Escoto,a Ricardo Aguilar-López,b María Isabel NeriaGonzález,bAlma Rosa Domínguez-Bocanegrab a
Facultad de Química - Universidad de Guanajuato, Noria Alta s/n, Guanajuato, Gto., 36050, México b Departamento de Biotecnología e Ingeniería, Centro de Investigaciones y Estudios Avanzados – Instituto Politécnico Nacional, Av. 100 m, México D.F., 22222, México
Abstract This work addresses the problem of designing an on-line discrete-delayed measurement processor to estimate the state of a class of stirred tank bioreactors where the growth of sulfate reducing bacteria takes places. On the basis of the Monod-type model of the reactor, a geometric approach is straightforward applied to systematically construct and tune the data processor. The resulting estimator is tested on a continuous and a batch culture process, showing a robust convergence even in the presence of modeling errors. Keywords: discrete estimation, nonlinear estimation, bioreactor monitoring.
1. Introduction Sulfate reducing bacteria are anaerobic microorganisms that have become especially important in biotechnological processes (i.e. water treatment) due to its ability to degrade organic material and remove heavy metals [1]. Many processes of material degradation and heavy metal removal are carried on anaerobic bioreactors, which are large fermentation tanks provided with mechanical mixing, heating, gas collection, sludge addition and withdrawal ports, and supernatant outlets. The anaerobic digestion is affected by many factors including temperature, retention time, pH, and chemical composition of wastewater. In a practical framework, the reactor is operated on the basis of laboratory analysis of samples, usually taken out at periodic sampling times; nevertheless, the obtained information reflects the system status in the past depending on the sampling time interval. In view of the mentioned monitoring scheme, operation improvements imply more-frequent (or continuous) monitoring of the key variables; however, the lack of reliable, sterile and robust sensors obstacles this task [2]. This work focuses on the problem of predicting present-time key variables of a class of stirred tank bioreactors using discrete-delayed (DD) measurements; the class refers to the process of a sulfate-reducing bacterium growth. Related to model-based approaches, it is taken into account that, although the bioreactors can be considered as tank reactors for analysis purposes, their complex phenomena turns the conceptual and mathematical framework for model development large in place; moreover, the existing models are highly nonlinear. Then, a experimentally validated Monod-type kinetics model is considered in order to straightforward apply a state-feedback linearization approach that allows a systematic design of the estimator.
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2. The Bioreactor and its Estimation Problem It was considered a stirred tank reactor where the Desulfovibrio Alaskensis (DA) bacteria growth is carried out. The DA bacterium is a sulfate reducing bacteria used, in this case, to degrade some undesirable sulfate compounds to sulfides. It was previously determined that the Monod’s kinetic equation adequately describes our reactor [2], where its kinetics parameters were determined via standard methodology in a batch culture [3]. From mass balances and the kinetics Monod model, the reactor model is given by, .
X = – D X + μ(S) X := fX(.), . X S = D (SIN – S) – μ(S) Y := fS( .), S/X . X P = – D P + μ(S) Y := fP(.), P/X S μ(S) = μMAX k + S s
X(t0) = X0, S(t0) = S0,
(1a) yS(tk) = S(tk–1),
tD = tk+1 – tk. (1b)
P(t0) = P0,
(1c) (1d)
There are considered three states: substrate (sulfate compound) concentration (S), biomass (or DA) concentration (X), and sulfide concentration (P). The known exogenous inputs are: the dilution rate (D), and the substrate concentration (SIN) in the input flow (D). YS/X and YP/X are the sulfate and sulfide coefficient yields, respectively. μ( .) is the specific growth rate, and μMAX and ks are the maximum specific growth rate and the affinity constant, respectively. With suitable choices of D, the preceding model describes batch (D = 0), semibatch (D S = 0) and continuous (D ≠ 0) operations. In order to monitor the reactor, samples from the culture are taken anaerobically each hour. Sulphate concentration in the medium is measured by a fast and simple turbidimetric method based on the precipitation of barium [4]. Then, this is the only one measurement considered. The substrate concentration (yS) at the instant tk reflects the reactor state at the past instant tk–1; tD is the sampling-delay time period. Resorting to an estimation approach, the monitoring problem is translated to the one of designing an estimator that, on the basis of the bioreactor model, and driven by a sequence of DD-measurements {yS(t0), yS(t1), …, yS(tk)} each sampling time instant (tk) on-line yields estimates of the actual biomass (X(tk)), substrate (S(tk)) and sulfide (P(tk)) concentrations. Besides, X and P measurement could be eliminated, meaning a cost reduction due to additional on-line laboratory analysis.
3. Estimator Design By convenience, the reactor model is rewritten in compact vector notation: .
xS = fXS(xS, u, p), .
xS(t0) = xS0;
yS(tk) = δ xS(tk–1),
tD = tk – tk–1,
P = fP(x, u, p), P(t0) = P0, xS = [X, S,]’, x = [X, S, P]’, u = [D, SIN]’, p = [YS/X, YP/X, μMAX, ks]’, f = [fM, fS]’, f = [fM, fS, fP]’, δ = [0, 1],
(2a) (2b) (2c) (2d)
This form makes the cascade connection between the xS-states and the P-state marked. Also it is important to note that its time-varying solution describes a unique reactor motion x(t) determined by the initial conditions (x0), the inputs (u), and the parameters
Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements 369
(p), because of the continuous differentiability of f(.)(θS and θP are the transition maps of the differential equations 2a and 2b, respectively): P(t) = θP(t, t0, x0, u, p) xS(t) = θS(t, t0, xS0, u, p), θ = [θS, θP]’ or equivalently: x(t) = θ(t, t0, x0, u, p),
(3a) (3b)
On the basis of the reactor model (Eq. 1 or 2), the estimator is designed by a geometric non-linear approach [5]. The approach follows a detectability property evaluation of the reactor motion to underlie the construction, tuning and convergence conditions of the estimator. 3.1. Detectability Property For a moment, it is assumed that the S-measurement is continuous-instantaneous, in the understanding that this unrealistic assumption will be later removed. In a physical sense, the detectabilty property amounts to the solvability of the following differerential estimation problem: reconstruct the reactor motion x(t) provided the data: .
DS = {x0, yE(t), p},
yE = [yS, yS]’,
(4)
To solve this problem, the S-measurement equation (Eq. 2) is recalled in its continuousinstantaneous version (yS(t) = S(t)); later, a one time derivative is taken by replacing the resulting time-derivative of S (in the right-hand side) by the map fS(.); finally, the Pdynamics is recalled to obtain the following differential-algebraic system .
φ(xS, u, p) = yE,
P = fP(x, u, p),
P(t0) = P0;
φ(xS, p) := [S, fS(.)]’
(5)
It must be noticed the cascade interconnection between the algebraic and the differential items. At each time t, the two algebraic equations system admits a unique and robust solution for xS in any motion in which S ≠ 0 (the Jacobian matrix of φ is nonsingular for S ≠ 0). Feeding the solution into the differential equation, the following differential estimator, driven by the output yE, and the input signals u, is obtained: xS = σ(yE, p),
.
P = fP(yE, u, p),
P(t0) = P0,
(6)
On the framework of the detectability motion given in [5], the Jacobian matrix of φ is the observability matrix, and its non-singularity provides the robust partial observability of the reactor motion x(t), with observability index κ = 1; and the differential equation in Eq. 6 is the unobservable dynamics whose unique solution is the unobservable motion (Eq. 3a). 3.2. Estimator Construction Once the possibility of estimator construction was established, as mentioned above, the estimator construction followed a straightforward application of the construction procedure given in [5], but with one tenuous modification: the estimation sequence was delayed in one-step by replacing the discrete-instantaneous output estimation error
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{yS(tk) – S^ (tk)} by the DD one {yS(tk) – S^ (tk–1)} and considering the interval [tk–1, tk], instead of [tk, tk+1] as the work one. Then, the estimator is given by: x^ S(tk) = θS(tk, tk–1, x^ S(tk–1), u, p^ ) + G(x^ S(tk–1), u, p^ , tD, KP) (yS(tk) – δ x^ S(tk–1)) (7a) + H(x^ S(tk–1), u, p^ , tD) xI(tk–1), x^ S(t0) ≈ xS(t0), (7b) xI(tk) = xI(tk–1) + KI (yS(tk) – δ x^ S(tk–1)), xI(t0) = 0, ^ ^ ^ ^ P(tk) = θP(tk, tk–1, x(tk–1), u, p), P(t0) ≈ P(t0), (7c) where GP( .) = (∂Xsφ( .))–1 (Ω(tD))–1 KP, H( .) = (∂Xsφ( .))–1 (Ω(tD))–1 T(tD), tk = tk–1 + tD, P 2 1 0 1 º ª1 tDº, T(tD) = ª /2 tD º, KP = ª« k1 º», KI = kI. Ω(t ∂xsφ( .) = ª¬ . . , D) = ¬ ¬ tD ¼ 0 1¼ ∂XfS( )∂SfS( )¼ ¬ kP2 ¼ and z^ denotes the estimate of the variable z. θS and θP are the transition maps defined in Eq. (3). G(.) is a nonlinear gain constructed on the basis of the observability matrix ∂xsφ, which depends on the state xS, the sampling-delay time tD and the proportional gain KP. The estimator includes a sumatorial correction term (third term of Eq. 7a) to eliminate modeling error problems; xI is an extended state that accounts for the sumatorial output estimate error, and KI is the corresponding sumatorial gain. Ω(tD) is the transition matrix of model reactor in its state-feedback linearized (via the φ map) form; and the matrix T(tD) results from the transformation to original x-coordinates of the observer from its state-feedback linearized form. The estimator can be regarded as formed by two parts: the first (Eqs. 7a, b) is a closedloop observer that yield the estimate sequence {x^ S(tk)} (k = 0, 1, 2, …) convergent to the current sequence {xS(tk)}; and the second (Eq. 7c) is on open-loop observer driven by the xS-estimates that yields the estimate sequence {P^ (tk)} convergent to the current sequence {P(tk)}. 3.3. Estimator Tuning In order to choice the entries of the gain matrices KP and KI, the output estimation error dynamics in its state-feedback linearized form is recalled; this takes the following form: ε(tk+3) + (kP1 – 3) ε(tk+2) + (1/2 tD2 kI + tD k2P – 2 k1P + 3) ε(tk+1) + (1/2 tD2 kI – tD kP2 + k1P – 1) ε(tk) = qy,
ε = yS – δxS
(8)
The linear characteristics can be noticed on the left side of the equation; however in qy the inherent nonlinearities of the estimation error dynamics are enclosed. This means that, by suitable choices of the gains, the left side is stable, but qy is a potentially destabilizing factor of the dynamics. Except for qy, Eq. (8) establishes a clear relationship between the choice of the tuning parameters and the sampling-delay time value in front of the desired kind of estimation error response. Pole assignment into the unit circle was followed to make the linear-part of Eq. (8) stable. It was chosen a pole-pattern from a continuous framework (in the complex splane) as a reference departure point: λ1 = –ω,
λ2,3 = –ω (ξ ± (1 – ξ)1/2)
Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements 371
where ω and ξ corresponds to the characteristic frequency and the damping factor of a stable 3rd order linear dynamics of reference . These eigenvalues were map into the unit circle of the complex z-plane (the discrete framework) according to: γi = exp(λi tD),
i = 1, 2, 3.
Then, the characteristic polynomial of the pole set {γ1, γ2, γ3} was obtained in terms of the tuning parameters (ξ, ω) and the sampling-delay time (tD): (γ – γ1) (γ – γ2) (γ – γ3) = 0
γ3 + c1(tD, ξ, ω) γ2 + c2(tD, ξ, ω) γ + c3(tD, ξ, ω) = 0
Comparing the coefficients set of this characteristic polynomial of reference with those of the output estimation error dynamics (Eq. 8), the gains were obtained in well-defined terms of the sampling-delay time and the tuning parameters (tD, ξ, ω): kP1 = κ1(tD, ξ, ω),
k2P = κ2(tD, ξ, ω),
kI = κ3(tD, ξ, ω),
ω = s ωR.
It was introduced the parameter s, which is regarded as an accelerating factor of the dynamics with a certain time response of reference (ωR). Then, once the tD is defined, usually by practical considerations and ωR and ξ are fixed, s remains as the unique tuning parameter. In order to attain estimation convergence, the stable linear part of the error dynamics must dominate the non-linear one. In [5] it is implied that a value range of s (s ∈ (s*, s*) exists, whose wide directly depends on the magnitude of the modeling error (enclosed in qy) and on the sampling delay time (tD).
4. Simulation Results To show the performance of the estimator, a simulation study was realized. The model parameters for the DA bacteria are (YS/X, YP/X, μMAX, ks) = (0.25, 0.25/0.95, 0.035 h-1, 0.9 g L-1), which are the corresponding for the bioreactor considered as the actual plant. These parameters were obtained from a previous regression fitting over a set of experimental runs. For the estimator, a parametric error was introduced: k^ s = 0.8 instead of 0.9. Attending practical considerations, the sampling-delay time was set at tD = 1 h. 4.1. Continuous Operation For this operation the dilution rate was set at D = 0.025 h-1, and the substrate concentration in the flow input, at SIN = 5 g L-1. The initial conditions were: (i) Bioreactor: (X0, S0, P0) = (0.5, 5, 0), (ii) Estimator: (X^ 0, S^ 0, P^ 0) = (0.3, 6, 0). The tuning parameter were: (ωR, ξ, s) = (1/200, 10, 1). The behavior of the estimator is shown in Fig. 1a. The estimator adequately predicts the key variables at a time equivalent to ¼ of the bioreactor settling time (≈ 200 h); although, for the M and P variables, the presenttime prediction is faster.
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4.2. Batch Operation The initial conditions were: (i) Bioreactor: (X0, S0, P0) = (5, 12, 0), (ii) Estimator: (X^ 0, S^ ^ 0, P0) = (5.1, 11, 0). The tuning parameters were: (ωR, ξ, s) = (1/200, 10, 1). The behavior of the estimator is shown at Fig. 1b. Similar to the continuous operation, the estimator adequately predicts the key variables at a time equivalent to ¼ of the bioreactor settling time (≈ 20 h); but, the estimator must be off at a S-value close to zero, as suggested by the observability property. Biomass
Biomass
0.7
9
0.6
8 X (g/L)
X (g/L)
0.5
7
0.4
6
0.3 0.2 0
50
100
150 t(hr) Substrate
200
250
300
6
5 0
5
10
15 t(hr) Substrate
20
25
30
5
10
15 t(hr) Sulfide
20
25
30
15
5 S (g/L)
S (g/L)
10
4
5
3 2 0
50
100
150 t(hr) Sulfide
200
250
300
3
15 Bioreactor Estimator
10
P (g/L)
P (g/L)
2
1
0 0
0 0
Bioreactor Estimator
5
50
100
150 t(hr)
200
250
300
Fig. 1a. Performance of the estimator in a continuous operation.
0 0
5
10
15 t(hr)
20
25
30
Fig. 1b. Performance of the estimator in a batch operation
5. Conclusions In this work the design of a nonlinear estimator for a class of stirred tank bioreactor driven by discrete-delayed measurements has been presented. Based on a Monod-type kinetics model, the design included a systematic construction and tuning, and a convergence criterion. The design followed a geometric approach, and the tuning was done with a conventional pole-assignment technique. The performance of the estimator was shown in a simulated framework, that motivates the application of the estimator in a practical (laboratory or industrial level) framework.
References [1] [2]
Jorgensen, B. B., 1982, Mineralization of organic matter in a sea bed -the role of sulphate reduction-, Nature, 296, 643-645. Aguilar-López, R., Martínez-Guerra, R., Mendoza-Camargo, J. and M. I. NeriaGonzález, 2006, Monitoring of an industrial wastewater plant employing finite-time convergence observers, J. of Chemical Technology & Biotechnology, 81, 6, 851-857.
Estimation of a Class of Stirred Tank Bioreactors with Discrete-Delayed Measurements 373 [3] [4]
[5]
Bailey, J. E. and D. F. Ollis, 1986, Biochemical engineering fundamentals, Mc GrawHill, Singapore. Kolmert, A., Wikström, P. and K. Hallberg K, 2000, A fast and simple turbidimetric method for the determination of sulfate in sulfate-reducing bacterial cultures. J. Microbiol. Meth., 41, 179-184. Hernández, H. and J. Alvarez, 2003, Robust estimation of continuous nonlinear plants with discrete measurements, J. of Process Control, 13, 1, 69-89.
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18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimal Control of Batch Processes Using Particle Swam Optimisation with Stacked Neural Network Models Fernando Herrera, Jie Zhang School of Chemical Engineering and Advanced Materials, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K.
Abstract An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalise wide model prediction confidence bounds. PSO can cope with multiple local minima and could generally find the global minimum. Application to a simulated fedbatch process demonstrates that the proposed technique is very effective. Keywords: Batch processes, Neural networks, Particle swam optimisation, Reliability.
1. Introduction Batch or semi-batch processes are suitable for the responsive manufacturing of high value added products [1]. To maximise the profit from batch process manufacturing, optimal control should be applied to batch processes. The performance of optimal control depends on the accuracy of the process model. Developing detailed mechanistic models is usually very time consuming and may not be feasible for agile responsive manufacturing. Data based empirical models, such as neural network models [2] and nonlinear partial least square models [3], and hybrid models [4] have to be utilised. Stacked neural networks have been shown to possess better generalisation capability than single neural networks [5,6] and are used in this paper to model batch processes. An additional feature of stacked neural networks is that they can also provide prediction confidence bounds indicating the reliability of the corresponding model predictions [7]. Due to model-plant mismatches, the “optimal” control policy calculated from a neural network model may not be optimal when applied to the actual process [8]. Thus it is important that the calculated optimal control policy should be reliable. Conventional gradient base optimisation techniques are not effective to deal with objective functions with multiple local minima and can be trapped in local minima. Particle swam optimisation (PSO) is a recently developed optimisation technique that can cope with multiple local minima. This paper proposes using PSO and stacked neural networks to find the optimal control policy for batch processes. A standard PSO algorithm and three new PSO algorithms with local search were developed. In order to enhance the reliability of the obtained optimal control policy, an additional term is added to the optimisation objective function to penalise wide model prediction confidence bounds.
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2. Particle Swarm Optimisation PSO was first proposed by Kennedy and Eberhart [9]. The main principle behind this optimisation method is communication. In PSO there is a group of particles that look for the best solution within the search area. If a particle finds a better value for the objective function, the particle will communicate this result to the rest of the particles. All the particles in the PSO have “memory” and they modify these memorized values as the optimisation routine advances. The recorded values are: velocity (V), position (p), best previous performance (pbest) and best group performance (gbest). The velocity describes how fast a particle should move from its current position which contains the coordinates of the particle. The last two parameters are the recorded best values that have been found during the iterations. A simple PSO algorithm is expressed as [9]: V(k+1)=wV(k)+C1r(pbest(k)-p(k))+C2r(gbest(k)-p(k))
(1)
p(k+1) = p(k) + V(k+1)
(2)
where w is the halt parameter, C1 is the personal parameter, C2 is the group parameter and r is a random number between 0 and 1. The parameters w, C1 and C2 play important roles in PSO. The halt parameter (w) helps the particles to move around the search area. If it is too large the particles may miss the solution and if it is too small they may not reach it. Good values are usually slightly less than 1 [9]. The coefficients C1 and C2 indicate the preference of the particles for personal or communal results. If the value of C1 is larger than C2 then the particles will search for the best value within the best results obtained during its own search; they will not try to reach a communal best point. If vice versa, the particles will not perform individual searches, this will diminish the ability of the particles to perform “adventurous” searches. Kennedy and Eberhart [9] recommended that these values should be 2. This keeps a balance between the personal and communal search. Four PSO algorithms were developed here and they perform different ways to communicate search results within the community. The first one is the simplest code presented in [9], where the particles have the ability to communicate its result to all the members of the community. The other three are based on local searches performed within small groups formed in the community. In the second algorithm, the group is based on a circular community [10]. These small groups will only communicate with members of their own community. The expected result with this formation is that the particles will search more intensively the solution area. In the third algorithm, local search is presented as a cluster community. The difference with the circular community is the fact that only one particle will communicate and compare the results with members of other groups. The fourth algorithm performs a geographical search in that the particles will communicate with the particles that are close to them in the solution area. The expected results are that the local search algorithms explore more intensively the search area. The algorithms were then tested on the following two optimisation problems with multiple local minima or maxima:
max F =
1 2 i
2 § x §x · · 0.1 + ¨¨ ¦ − ∏ cos¨ i ¸ + 1¸¸ © i¹ ¹ © i =1 4000 i =1 2 2 min F = 20 + x1 + x2 − 50(cos 2πx1 + cos 2πx2 ) 2
(3)
(4)
Optimal Control of Batch Processes U sing Particle Swam Optimisation with Stacked Neural Network Models
377
All the four PSO algorithms can find the global optimal solutions whereas the gradient based optimisation algorithm from the MATLAB Optimisation Toolbox, fminunc, fails to find the global optimal solutions when the initial values are not close to the global optimal solutions.
3. Modelling of A Fed-Batch Process Using Neural Networks 3.1. A Fed-Batch Process The fed-batch reactor used in this work was taken from [11]. The batch reactor is based on the following reaction system: k1 A + B ⎯⎯→ C k2 B + B ⎯⎯→ D
This reaction is conducted in an isothermal semi-batch reactor. The desired product in this system is C. The objective is to convert as much as possible of reactant A by the controlled addition of reactant B, in a specified time tf = 120 min. It is not appropriate to add all B initially because the second reaction will take place, increasing the concentration of the undesired by-product D. Therefore, to keep a low concentration of product D and at the same time increase the concentration of product C, the reactant B has to be fed in a stream with concentration bfeed = 0.2. A mechanistic model for this process can be found in [11]. 3.2. Modelling the Fed-Batch Process Using Stacked Neural Networks Neural network models for the prediction of the amount of desired product CC(tf)V(tf) and the amount of undesired by-product CD(tf)V(tf) at the final batch time are of the form: (5) y1 = f1(U) (6) y2 = f2(U) where y1 = CC(tf)V(tf), y2 = CD(tf)V(tf), U = [u1 u2 … u10]T is a vector of the reactant feed rates during a batch, f1 and f2 are nonlinear functions represented by neural networks. For the development of neural network models simulated process operation data from 50 batches with different feeding profiles were generated using the mechanistic model of the process. In each batch, the batch duration is divided into 10 equal stages. Within each stage, the feed rate is kept constant. The control policy for a batch consists of the feed rates at these 10 stages. In the stacked neural network models several individual networks are trained using bootstrap re-sampling of the original data. The individual network outputs are combined to give the final model output. For each of the stacked neural network models, a group of thirty individual neural networks were developed. Each neural network contains in the hidden layer three nodes. The number of hidden nodes was selected based on the performance on the testing data. The nodes in the hidden layer use a hyperbolic tangent activation function while that in the output layer uses a linear activation function. The stacked neural network output is taken as the average of the individual network outputs. Fig. 1 and Fig. 2 show, respectively, the performance of individual networks and stacked networks for predicting the amount of desired product CC(tf)V(tf) on the training and unseen validation data sets. Fig. 1 indicates that in some networks the SSE on the training data is small but this is not the case on the unseen validation data. These results show that individual networks are not reliable. It can be seen from Fig. 2 that stacked networks give consistent performance on the training data and on the unseen validation data. The performance gradually improves when more networks are combined and approaches a stable level. This is observed on both the training and unseen validation
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SSE (validation)
SSE (training)
data. This result indicates that the stacked model for predicting the amount of desired product CC(tf)V(tf) is more reliable as the number of individual networks is increased. It does not matter if some networks do not have a good performance, what matters is the communal performance of the group.
Networks
SSE (validation)
SSE (training)
Figure 1. Performance of individual networks for predicting CC(tf)V(tf)
Networks
Figure 2. Performance of stacked networks for predicting CC(tf)V(tf)
4. Optimising Control Using PSO The objective of the optimisation is to maximise the amount of the final product while reducing the amount of the by-product. The optimisation problem solved in this work is:
min J = {α1[ D](t f ) − α 2 [C ](t f )}V (t f ) U
s.t.
0 ≤ ui ≤ 0.01, V (t f ) = 1
(i = 1, 2,", m)
where Į1 and Į2 are weighting parameters which were both set to 0.5 in this study, U is a vector of control actions (reactant feed rates), and V is the reaction volume. Table 1 lists the parameters used in global PSO (PSOG1 to PSOG4) and local PSO (PSOL1 to PSOL4) algorithms. For the local PSO algorithms, the sizes of the internal communities were kept the same in all the cases: 17 particles.
Optimal Control of Batch Processes U sing Particle Swam Optimisation with Stacked Neural Network Models
379
Table 1. Parameters used in PSO algorithms PSOG1
PSOG2
PSOG3
PSOG4
PSOL1
PSOL2
PSOL3
PSOL4
Particles
50
70
50
70
20
40
20
40
Halt
0.01
0.01
0.005
0.005
0.01
0.01
0.005
0.005
For the purpose of comparison, optimisation using a single neural network was first carried out. Table 2 shows the obtained results. As can be seen from the table, the values for the difference between the final amounts of product and by-product using the PSO codes were similar to the ones obtained using the MATLAB Optimisation Toolbox function, fmincon, in this fed-batch reactor. However, PSO can cope with multiple local minima in general as shown in Section 2. It can also be appreciated that an increment in the number of particles in the global version of the PSO code does not help the code to find a better solution for the optimization problem. This could indicate that the PSO code only needed a minimum number of particles and the inclusion of more particles will not be helpful. A different behaviour was encountered in the local version of the PSO. When more particles were used for the solution of the problem, then the code required less number of iterations to solve the problem. Changing the value of the halt did not show any improvement in the performance. As can be seen from the table, the results obtained using different halt values are similar. Another difference that could be seen between the two PSO codes is the fact that the local version can find a similar answer to the problem using fewer particles than the global version of the PSO code. Once the optimal feed rates were obtained, they were applied to the actual process (i.e. simulation by the mechanistic model of the process). Table 2 shows the difference between the amounts of the final product and by-product on neural network model and the actual process. It can be seen from Table 2 that the actual amounts of product and by-product under these “optimal” control policies are quite different from the neural network model predictions. This indicates that the single neural network based optimal control policies are only optimal on the neural network model and are not optimal on the real process. Hence, they are not reliable. This is mainly due to the model plant mismatches, which is unavoidable in data based modelling. A method to overcome the impact of model plant mismatch on optimisation performance was previously investigated by Zhang [8] where model prediction confidence bounds are incorporated as a penalty in the objective function. Therefore, the objective function can be modified as
min J = {α1[ D](t f ) − α 2 [C ](t f )}V (t f ) + α 3 ( stderr[C ] + stderr[ D]) U
s.t.
0 ≤ ui ≤ 0.01, V (t f ) = 1
(i = 1, 2,", m)
where stderr[C] and stderr[D] are the standard errors of the stacked models, Į3 is a weighting factor for model prediction confidence and was selected as 0.5 in this work. Table 2 shows the results obtained using the new objective function with stacked neural network models. It can be seen from Table 2 that the modified objective function with stacked neural network models leads to better performance on the actual process. It can be appreciated that the actual performance is very close to the ones calculated using the
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stacked neural network. This demonstrates that control policies obtained using stacked neural networks considering model prediction confidence bounds is much more reliable than those obtained using a single neural network model. Table 2. Values of ([C](tf) - [D](tf))V(tf) on neural network models and actual process Single neural network
Stacked neural network
Neural network
Process
Neural network
Process
fmincon
0.0411
0.0314
0.0304
0.0363
PSOG1
0.0400
0.0344
0.0296
0.0359
PSOG2
0.0405
0.0319
0.0297
0.0370
PSOG3
0.0399
0.0325
0.0302
0.0358
PSOG4
0.0396
0.0347
0.0300
0.0368
PSOL1
0.0377
0.0341
0.0298
0.0338
PSOL2
0.0407
0.0307
0.0298
0.0364
PSOL3
0.0394
0.0364
0.0297
0.0348
PSOL4
0.0397
0.0301
0.0297
0.0363
5. Conclusions The study demonstrates that particle swam optimisation is a powerful optimisation technique, especially when the objective function has several local minima. Conventional optimisation techniques could be trapped in local minima but PSO could in general find the global minimum. Stacked neural networks can not only given better prediction performance but also provide model prediction confidence bounds. In order to improve the reliability of neural network model based optimisation, an additional term is introduced in the optimisation objective to penalize wide model prediction confidence bound. The proposed technique is successfully demonstrated on a simulated fed-batch reactor.
References [1] D. Bonvin, J. Process Control, 8 (1998) 355-368. [2] J. Zhang, Trans. Inst. Meas. Control, 27, (2005) 391-410. [3] S. J. Zhao, J. Zhang, and Y. M. Xu, Ind. Eng. Chem. Res., 45, (2006) 3843-3852. [4] Y. Tian, J. Zhang, and A. J. Morris, Ind. Eng. Chem. Res., 40, (2001) 4525-4535. [5] D. V. Sridhar, R. C. Seagrave, and E. B. Bartlett, AIChE J., 42, (1996) 2529-2539. [6] J. Zhang, E. B. Martin, A. J. Morris, and C. Kiparissides, Comput. Chem. Eng., 21, (1997) s1025-s1030. [7] J. Zhang, Neurocomputing, 25, (1999) 93-113. [8] J. Zhang, Ind. Eng. Chem. Res., 43, (2004) 1030-1038. [9] J. Kennedy and R. Eberhart (1995). Particle Swarm Optimization. In Proceedings of the 1995 IEEE international conference on neural networks, Perth, Australia. Vol VI 1942 – 1948. [10] J. Kennedy and R. Mendes, IEEE Trans. Syst. Man Cybern. Part C-Appl. Rev., 36, (2006) 515-519. [11] P. Terwiesch, D. Ravemark, B. Schenker, and D. W. T. Rippin, Comput. Chem. Eng., 22, (1998) 201-213.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
381
Online LQG stabilization of unstable gas-lifted oil wells Esmaeel Jahanshahi, Karim Salahshoor, Riyaz Kharrat Petroleum University of Technology, South Khosro St., Sattarkhan Ave., Tehran 1453953153, Iran
Abstract The proposed strategies for stabilization of gas-lifted oil wells are offline methods which are unable to track online dynamic changes of the system. However, system parameters such as flow rate of injected gas and also noise characteristic are not constant with respect to time. An adaptive Linear Quadratic Gaussian (LQG) approach is presented in this paper in which the state estimation is performed using an Adaptive Unscented Kalman Filter (AUKF) to deal with unknown time-varying noise statistics. State-feedback gain is adaptively calculated based on Linear Quadratic Regulator (LQR). Finally, the proposed control scheme is evaluated on a simulation case study. Keywords: gas-lift; casing heading; state estimation; AUKF; LQR.
1. Introduction Gas-lift is a method for activation of low pressure oil wells. Figure 1 shows a typical diagram of a gas-lifted oil well [1]. In this method, gas is routed through surface gas injection choke (A) into the annulus (B) and then injected (C) deep into tubing (D) in order to be mixed with the fluid form reservoir (F). This reduces the density of oil column in tubing and lightens it to increase the production (E) rate from the low pressure reservoir. The oil production in the gas-lifted oil wells at their decline stages becomes unstable for low gas lift rates. This study focuses on the instability of gas-lifted wells due to casing heading phenomenon. Figure 2 demonstrates a typical example of the casing heading phenomenon simulated in OLGA®v5.0 [2]. The cyclic operation consists of three main phases [3] as follows: 1. The upstream pressure is smaller than Pti (tubing pressure at injection point), therefore no gas enters the tubing. The annulus pressure builds up until it reaches Pti. Then, injection into the tubing starts. 2. As gas mixes with oil in the tubing, the column lightens and the well starts producing. The gas injection rate does not fulfill the well’s need. Therefore, the pressure in the casing drops and production reaches a maximum. 3. Annulus pressure drops carrying along the injection gas rate wiv and the oil production. Less gas being injected, the oil column gets heavier and Pti exceeds the upstream pressure. Gas injection in the tubing stops. In order to suppress this oscillatory behaviour, the use of the automatic feedback control has been considered [4]. State space model and nonlinear full-state feedback have been used for stabilization of the system [5]. But, some of these state variables are not measurable, therefore, concept of state estimation from well-head measurements has been considered. A nonlinear observer is used for state estimation [6] which has shown satisfactory result in experiment [7]. As noted in [7], estimation is affected by noise. The standard Kalman filter has been used for state estimation and down-hole soft-
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sensing [8]. Advantage of Kalman Filtering (KF) compared to the nonlinear observer [7] is its capability of working in presence of noises [9]. But, the standard Kalman filter could be used only in a single operating point for a locally linearized dynamic of the system. To deal with this problem, extended Kalman Filter (EKF) has been used in [10] for down-hole soft sensing in gas-lifted oil wells.
Fig. 1. A gas lifted oil well
Fig. 2. Casing-heading phenomenon simulated with OLGAv5.0
EKF estimation accuracy may not be satisfactory to use estimated states for feedback control. Because, EKF uses a first-order approximation of nonlinear dynamics [9]. For state estimation of highly nonlinear systems, UKF is recommended [9]. However, for these methods, the measurement noise should be zero-mean Gaussian noise with known statistic characteristics. In this paper, an AUKF estimation approach has been proposed to increase the accuracy of state estimates despite the unknown time-varying statistic characteristics of measurement noise in online real world situations. The organization of this paper is as follows. In Section 2, the mathematical model of system is described. In Section 3, the AUKF algorithm is developed. In Section 4, an optimal control strategy will be introduced to stabilize the system. Simulation results are presented in Section 6. Finally, the results are summarized in Section 7.
2. Mathematical Model The gas-lift oil well operation can be described by the following state-space equations [7]: x1 = wgc − wiv °° ® x2 = wiv − w pc x2 /( x2 + x3 ) ° °¯ x3 = wr − w pc x3 /( x2 + x3 )
(1)
Where the state variables consist of x1 as the mass of gas in the annulus, x2 as the mass of gas in tubing, and x3 as the mass of oil in tubing. For more details, refer to [6, 7].
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3. AUKF State Estimation Algorithm In practice, down-hole measurements relating to tubing and annulus variables are not in general available. x1 can be measured and the remaining two states (x2 and x3) should be estimated. The available measurements are assumed to be y1(t)=x1 and y2(t)=Pt (tubing pressure at well head) [7]. The process dynamics and the measurement equations obey the following non-linear relationships: xk = f ( xk −1 , uk , k ) + wk −1
(2)
yk = h( xk , k ) + vk
(3)
Where f and h are known nonlinear functions. The random variables wk and vk represent the process and measurement noises, respectively. They are assumed to be independent, white noises with normal probability distributions; p(w)~N(0,Q) and p(v)~N(0,R). Julier and Uhlmann [11, 12] developed the UKF algorithm which does not require to linearize the foregoing general nonlinear system dynamics. The UKF algorithm uses a "deterministic sampling" approach to calculate the mean and covariance estimates of Gaussian random state variables (i.e., x) with a minimal set of 2L+1 sample points (L is the state dimension), called as sigma points [12, 13], through the actual nonlinear system dynamics without any linear approximations. Hence, this approach yields more accurate results compared to the KF and EKF. The results are accurate to the third order (Taylor series expansion) for Gaussian inputs for all the nonlinearities. For nonGaussian inputs, the results are accurate to at least the second order [12]. The UKF algorithm is well described in [9] and for sake of limited space we refer readers to this reference. Often, we do not know all parameters of the model or we want to reduce the complexity of modeling. Therefore, in real application, the exact value of R is not known a priori. If the actual process and measurement noises are not zero-mean white noises, the residual in the unscented Kalman filter will also not be a white noise. If this happened, the Kalman filter would diverge or at best converge to a large bound. To prevent the filter from divergence, we use adaptive version of UKF as follows. The innovation sequence is defined as η k = yk − h( xˆk− , k ) . Substituting the measurement model into ηk , gives η k = [h( xk , k ) − h( xˆk− , k )] + vk , with the fact that the difference between xk and xˆk− is a small divination, we could use a linear approximation for the term inside brackets, as η k = H k− [ xk − xˆk− ] + vv , where H k− = [∂h / ∂x]x = x− . Noting that we k
have ek− ≅ xk − xˆk− , Pk− = E[ek− ek−T ] and Rk = E[vk vk T ] . On the basis of assuming that wk and vk are uncorrelated white Gaussian noise sequences and the orthogonallity condition exists between observation error and state estimation error, the innovation covariance can be computed as E[ηkη kT ] = E[( H k− ek− )( H k− ek− )T ] + E[vk vkT ] . Combining the preceding equations, gives E[ηkηkT ] := Sk = H k− Pk− H T + Rk . When the innovation covariance E[ηkη kT ] is available, the covariance of the observation error Rk can be estimated directly from the preceding equation. Calculation of the residual covariance E[ηkηkT ] normally uses a limited number of samples of the innovation sequence:
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1 M
E[ηkη kT ] =
M −1
¦η m =0
η
(4)
− HPk− H T
(5)
T k −m k −m
As a result, Rak =
1 M
M −1
¦η m =0
η
T k −m k − m
In which M=100 represents the estimation window size. However, it is noted that (5) gives a valid result when the innovation sequence is stationary and ergodic over the M sample steps.
4. Adaptive LQR Control State feedback control is commonly used in control systems, due to its simple structure and powerful functions. Data-driven methods such as neural networks are useful only for situations with fully measured state variables. For this system in which state variables are not measurable and measurement function is nonlinear, we are dependant on system model for state estimation. On the other hand, as shown in figure 2, in openloop situations, system has limit cycle behavior and measurements do not give any information of system dynamics. Therefore, we use model-based approach. Parameters and variables that determine the system dynamic changes, such as ambient temperature, flow rate of well-head injected gas are measurable or a priori known as opening of production choke. Therefore, using these values, model can be adapted to the plant. To develop an adaptive controller, it is necessary to solve the related non-adaptive control problem when the parameters of the controlled plant are known. A crucial issue is the existence of an ideal (nominal) controller for a given control objective, which is equivalent to a set of matching conditions [14]. To calculate state feedback gain K[k], discrete linear-quadratic (LQ) regulator is used. The sate feedback law u[k ] = − K [k ]xˆ[k ] minimizes the quadratic cost function [15]: J (u[k ]) =
∞
¦ xˆ[k ]T Qxˆ + u[k ]T Ru[k ] + 2 xˆ[k ]T Nu[k ]
(6)
k =1
Where gain K[k] is calculated using following Riccati Equation: AT S + SA − ( SB + N ) R −1 ( BT S + N T ) + Q = 0
(7)
K[k] is derived from S by K [k ] = R −1 ( B[k ]T S + N T ) . Control scheme tracks values of variables and parameters that determine the operating point of systems and with any change in these parameters, a new linear controller gain is calculated based on the most recent operating point. It should be noted that computation time of every step for the combined state estimation and solving Riccati equation must be less that sampling time of the system.
5. Simulation Results Simulation of the model [6] and the proposed control scheme are implemented in MATLAB® with the nominal values of the case study described in [3]. For the sake of comparison, the same characteristics for process and measurement noises are considered
Online L Q G Stabilization of Unstable Gas-Lifted Oil Wells
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in all simulation runs. The initial values assumed for states and estimates have been considered similarly in all simulation runs. A Gaussian noise with constant variance of 0.03 is added to wgc as process noise. Variances of measurement noises for the first hour of simulation are considered to have constant values: 5 for y1(t) and 5000 for y2(t). From t=1 h to the end of simulation run, variances are increased linearly as unknown drifts, so that variances of measurement noises reach up to 50 and 80000 at the end of simulation time. Note that nonlinear observer [6, 7] also needs wpc (flow rate of production choke) as a third measurement that we do not consider any noise for it. First, we simulated the nonlinear observer proposed in previous works [6, 7]. As shown in figure 3, its estimation for the second state variable is very weak in presence of noises.
Fig. 3- The nonlinear observer estimates
Fig. 4- AUKF estimation for open-loop system
Figure 4 shows performance of the proposed AUKF for open-loop system. As described, it’s assumed that the induced drift in sensor noises are not known a priori to the filter and variances of measurement noises are estimated recursively by the adaptive estimation algorithm.
Fig. 5- Control signal and inputs to the system
Fig. 6- Outputs of the closed-loop system
To evaluate the proposed adaptive control performance, opening of production choke and flow rate of injected gas at the well-head are random pulses as command signals, as shown in figure 5. The opening value of the production choke upc also is the manipulated variable of the control strategy. Figure 6 shows noisy measurements and filtering outputs of closed-loop system, where variable variances of measurement noises are apparent. Note that wpc illustrated the stabilized behavior of closed-loop system. The state estimation also has been performed by Particle Filter [9] for comparison purposes. In this case, the algorithm was run with 1000 particle, so that the computation time could be affordable. Also, roughening factor of 0.1 is used. Similarly, the standard UKF algorithm has been simulated. In table 1, root mean square error values and computation times for different simulations are presented. Note that EKF and nonlinear
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observer estimate accuracies are not satisfactory and closing feedback with them can not stabilize the system. Algorithm Observer in [6, 7] EKF Standard UKF AUKF Particle Filter
RMSE Open-loop Close-loop 28.50, 28.43, 7.62 ----------19.13, 5.21, 100.8 ----------1.41, 0.83, 8.77 1.85, 0.52, 6.86 0.84, 0.25, 5.26 0.49, 0.18, 3.72 1.13, 0.42, 42.71 0.84, 0.32, 4.24
Computation time of the open-loop system 20 sec 122 sec 155 sec 188 sec 30400 sec
Table 1- Comparison of root mean square error and computation time of different algorithms.
6. Conclusions An adaptive UKF algorithm is presented to estimate the state variables in the face of unknown changes in characteristics of measurement noise. Accuracy of the proposed AUKF estimator is the best even compared with that of Particle Filter with much less computation time. The proposed LQG control scheme using this adaptive estimator can successfully stabilize the system despite of any system parameter and noise characteristic changes. Implementation of the proposed method in laboratory scale in the same way that is performed in [7] is recommended.
References [1] L. Sinegre, "Etude des instabilités dans les puits activés par gas-lift", in Spécialité “Mathématiques et Automatique”, Phd. thesis, Paris: Ecole des Mines de Paris, 2006. [2] Scandpower, OLGA Software Verion 5 User's Manual: Scandpower, 2006. [3] L. Sinegre, N. Petit, and P. Menegatti, "Predicting instabilities in gas-lifted wells simulation", American Control Conference, ACC, Minneapolis, Minnesota, USA, 2006. [4] B. Jansen, M. Dalsmo, L. Nøkleberg, K. Havre, V. Kristiansen, and P. Lemetayer, "Automatic Control of Unstable Gas Lifted Wells", SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 1999. [5] L. Imsland, B. A. Foss, and G. O. Eikrem, "State Feedback Control of A Class of Positive Systems: Application To Ggas Lift Stabilization," European Control Confrence, Cambridge, UK, 2003. [6] O. M. Aamo, G. O. Eikrem, H. Siahaan, and B. Foss, "Observer Design for Gas Lifted Oil Wells", American Control Conference, ACC, Boston, Massachusetts, USA, 2004. [7] O. M. Aamo, G. O. Eikrem, H. Siahaan, and B. Foss, "Observer design for multiphase flow in vertical pipes with gas-lift - theory and experiments", Journal of Process Control, vol. 15, pp. 247–257, 2005. [8] G. O. Eikrem, L. s. Imsland, and B. Foss, "Stabilization of Gas Lifted Wells Based on State Estimation," Intl. Symp. on Advanced Control of Chem. Processes, Hong Kong, China, 2004. [9] D. Simon, Optimal State Estimation, Kalman, H-inf and Nonlinear Approches. Hoboken, New Jersey: Wiley-Interscience, 2006. [10]H. H. J. Bloemen, S. P. C. Belfroid, and W. L. Sturm, "Soft Sensing for Gas-Lift Wells", SPE Annual Technical Conference and Exhibition, Houston, Texas, USA, 2004. [11]S. J. Julier and J. K. Uhlmann, "A New Extension of the Kalman Filter to Non-linear Systems," presented at AeroSense: The 11th Int. Symp. A.D.S.S.C., 1997. [12]S. J. Julier, J. K. Uhlmann, and H. Durrant-Whyte, "A new approach for filtering non-linear systems,", American Control Conference, ACC, Seattle, Washington, USA, 1995. [13]E. A.Wan and R. v. d. Merwe, "he Unscented Kalman Filter for Non-linear Estimatio," presented at IEEE Symposium 2000 (AS-SPCC), Lake Louise, Alberta, Canada, Oct. 2000. [14]G. Tao, Adaptive Control Design and Analysis. New york: Wiley-Interscience, 2003. [15]J. B. Burl, Linear Optimal Control: H-2 and H-inf Methods. Menlo Park, California: Addison Wesley Longman Inc., 1999.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Analysis of the Constraint Characteristics of a Sheet Forming Control Problem Using Interval Operability Concepts Fernando V. Lima a, Christos Georgakis a, Julie F. Smith b, Phillip D. Schnelle b a
Systems Research Institute & Department of Chemical and Biological Engineering, Tufts University, Medford, MA 02155, USA b DuPont Engineering Research and Technology, Brandywine 7304, 1007 Market Street, Wilmington, DE 19898, USA
Abstract An Interval Operability-based approach [1, 2] is applied to calculate operable output constraints for the Sheet Forming Control Problem (SFCP) from DuPont. The SFCP attempts to control the sheet thickness at 15 different points, which represent 15 output variables, using 9 manipulated variables in the presence of 3 disturbances. Thus, this problem represents a computationally complex, high-dimensional non-square system with more outputs than inputs. The SFCP is addressed here under two study cases: 1) a non-square, where all the 15 outputs are controlled independently of each other; 2) a square, where 6 outputs are combined in pairs, or zone variables, and controlled within their corresponding zone. Results show that significant reduction of the constrained region of process operation can be achieved for different output targets specified. Specifically, the hyper-volume ratio of the initial to the designed constrained regions range between 103 – 105. The calculated constraints are validated by running DMCplusTM (AspenTech) simulations for the extreme values of the disturbances. These constraints are intended for use online in model-based controllers (e.g., Model Predictive Control) to calculate the tightness with which each of the outputs can be controlled. Keywords: Operability, Sheet Forming Process, Non-square Systems, Model Predictive Control.
1. Introduction In recent years, chemical process designs have increased in complexity due to material and energy conservation requirements, integration of units, process optimization and stricter environmental regulations. Consequently, tools to systematically assess the capabilities of such designs and its integration with the process control structure have become increasingly important. These tools should identify a design’s ability to achieve the feasible region of operation around a steady-state in the presence of process disturbances. Specifically, it is important to determine the tightest feasible set of output constraints that can be achieved considering the constraint limitations of the input variables, which are design dependent [2]. The improper selection of these output constraints can make the controller infeasible when a disturbance moves the process outside its usual operating region. Hard constraints are enforced whenever feasible and softened whenever it is necessary to retain feasibility [3]. The Operability methodology originally introduced for square systems (Set-Point Operability [4]) and extended for non-square systems (Interval Operability [1, 2, 5, 6]) enables the systematic selection of
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such output constraints, so that they are as tight as possible and do not render the controller infeasible. Using the previously published Interval Operability concepts and algorithms, this paper aims to study the constraint characteristics of a Sheet Forming process from DuPont, which is characterized by a high-dimensional and non-square system. For such system, set-point control is not possible for all the outputs and interval control is necessary. This is done by analyzing two configurations of this problem, a 15 x 9 x 3 (outputs x inputs x disturbances) non-square system and a simplified 9 x 9 x 3 square sub-system. This simplified system is obtained by exploring the distributed characteristics of the SFCP by considering 6 zone variables. The presence of disturbances of high magnitude may preclude set-point control even for square systems. For such cases, the concept of Interval Operability may be equally applicable to calculate the tightest feasible output ranges.
2. Interval Operability Concepts The necessary sets to enable the Interval Operability assessment for an n x m x q (outputs x inputs x disturbances) system are defined in this section [5]. The Available Input Set (AIS) is the set of values that the process input variables can take based on the constraints of the process. The Desired Output Set (DOS) is given by the ranges of the outputs that are desired to be achieved and the Expected Disturbance Set (EDS) represents the expected steady-state values of the disturbances. These sets are mathematically represented by: AIS EDS
^u | u ^d | d
min i min i
` ; 1 d i d q`
d ui d uimax ; 1 d i d m ; DOS d d i d d imax
^y |
`
yimin d yi d yimax ; 1 d i d n ;
The Achievable Output Set for a specific disturbance value, AOS(d), is defined by the ranges of the outputs that can be achieved using the inputs inside the AIS: AOS(d)
^y |
y
Gu G d d ; u AIS, fixed d EDS`
(1)
where the matrices G and Gd represent the linear steady-state process and disturbance gain matrices, respectively. Finally, the Achievable Output Interval Set (AOIS) is defined as the tightest possible feasible set of output constraints that can be achieved, with the available range of the manipulated variables and when the disturbances remain within their expected values. The algorithm developed for the calculation of this important set is presented next.
3. Calculation of AOIS: Linear Programming Approach Two sets of output parameters are considered in the AOIS calculation: the steady-state target point (y0) and the relative output weights (w). The relative output weights represent the relative tightness with which each output will be controlled around its desired target and will affect the aspect ratio of the corresponding sides of the designed AOIS. For example, an aspect ratio of 1:10 between two outputs assures that one will be controlled 10 times more tightly, approximating set-point control. Several examples of AOIS calculations using different weights and output targets have been previously published [1, 2]. The set of points that characterize the vertices of the AOS can be easily calculated by directly mapping the vertices of the AIS and EDS using the linear steady-state process model (eq. 1). The calculation of AOIS in n is performed by
Analysis of the Constraint Characteristics of a Sheet Forming Control Problem
389
formulating the interval operability problem in a Linear Programming (LP) framework, where the AOS and the AOIS polytopes are described as a system of inequalities in the LP formulation. An overview of the algorithm for this calculation, presented in reference [6], is the following: 1) Define the relative weights w1, w2, ... wn that quantify the relative tightness within which each output needs to be controlled; 2) Select one of the extreme disturbance vectors d = di, i = 1, 2, …, k, which corresponds to one of the k = 2q vertices of EDS. Calculate AOS(di) (eq. 1) and the corresponding linear equalities and inequalities that define this set (see details in reference [6]); 3) Define a family of n-dimensional orthogonal parallelepipeds, P(Į), self-similar among them, centered at the target value of the outputs (y0), where the scalar Į affects each of their sizes by the following set of inequalities:
^y | b d y y 0 d b`
P (D )
(2)
where T
b
§ D D D · , ,, ¨ ¸ ; y0 w w w 2 n ¹ © 1
T
y01 , y02 ,, y0n
; and y
T
y1 , y2 ,, yn
4) Calculate the minimum value of Į, Įi, such that P(Įi) and AOS(di) have a single common point vi, by solving the LP problem below: Di
min D x
min f T x, x T
where f
¬ª 0 0 0n 1¼º ; and x
while y
vi P (Di ) AOS (di )
¬ª y1 y2 yn D ¼º
T
T
ª yT D º ; »¼ ¬«
(3)
5) Repeat steps 2 to 4 above for a total of k = 2q times to calculate the set of k points: v1, v2, … vk; 6) The final AOIS is the smallest orthogonal parallelepiped in n that includes all the k vi points from the LP solutions (AOIS = OP(v1, v2, v3, … vk)). This set defines the tightest set of output constraints that makes the process operable for the output target y0 and all the disturbance values inside the EDS.
4. Results: Sheet Forming Control Problem As briefly described above, the objective of the Sheet Forming Control Problem (SFCP) is to control the sheet thickness at 15 different points as uniformly as possible around different targets (y0). Thus, there are 15 controlled variables (CV’s), which correspond to the thicknesses in the cross-direction, with the same relative weight (w). Moreover, this process has 9 manipulated variables (MV’s) and 3 disturbance variables (DV’s). The steady-state gain model, the sets within which the input and output variables are constrained and the relative weights of the output variables are given in the following equations:
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F.V. Lima et al.
§ G y1 · ¨ ¸ ¨ G y2 ¸ ¨ G y3 ¸ ¨ ¸ ¨ G y4 ¸ ¨G y ¸ ¨ 5 ¸ ¨ G y6 ¸ ¨ ¸ ¨ G y7 ¸ ¨G y ¸ ¨ 8 ¸ ¨ G y9 ¸ ¨G y ¸ ¨ 10 ¸ ¨ G y11 ¸ ¨ ¸ ¨ G y12 ¸ ¨G y ¸ ¨ 13 ¸ ¨ G y14 ¸ ¨G y ¸ ©¨ 15 ¹¸
§ -2 ¨ ¨ -2 ¨ -2 ¨ ¨ -2 ¨ -2 ¨ ¨ -2 ¨ 0 ¨ ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨ 0 ¨ 0 ¨ ¨¨© 0
AIS EDS DOS w y ss u ss y0
0 -1.8
0
0
0 -0.00064
0
0 -1.6
0
0
0 -0.00035
0
0 -1.4 -2
0
0
0
0
0 0
0 -1.8 0 -1.6
0 0
0 0
0 0
-0.00036 -0.00064
0
0
0 -1.6
0
0
-0.00084
-2
0
0
-1.8
0
0
-0.00096
-2
0
0
-2
0
0
-0.001
-2
0
0
-1.8
0
0
-0.00096
-2
0
0
0
0
0
-0.00084
-2 -2
0 0
0 0
0 -1.8 0 -1.8
0 0
-0.00064 -0.00036
-2
0
0
0
-2
0
0
-2
0
0
0 -1.8
0
0
-2
0
0
0
0
0
0
0
0
0
§1.7 · ¨ ¸ ¨1.7 ¸ ¨1.7 ¸ 0 ¨ ¸ u G § · 0 1 ¨1.7 ¸ ¨ ¸ ¨ ¸ G u2 ¸ 1.7 0 ¨ ¨ ¸ 0 ¸ ¨ G u3 ¸ ¨ 0 ¨ ¸ ¨ 0 ¸ Gu 0 ¸¨ 4 ¸ ¨ ¸ ¨ G u5 ¸ ¨ 0 0 ¸ ¨ ¸¨ 0 ¸ ¨ G u6 ¸ ¨ 0 ¸ ¨G u ¸ ¨ 0 0 ¸¨ 7 ¸ ¨ 0 ¸ ¨ G u8 ¸ ¨ 0 ¸ ¨¨ G u ¸¸ ¨ 0 0 ¸© 9 ¹ ¨ 0 ¨ 0 ¸ ¨ 0 -0.00036 ¸¸ ¨ ¨¨© 0 -0.00064 ¸¸¹
0 0 0 0 1.7 1.7 1.7 1.7 1.7 0 0 0 0 0
0 · ¸ 0 ¸ 0 ¸ ¸ 0 ¸ 0 ¸ ¸ 0¸ 0 ¸ § G d1 · ¸¨ ¸ 0 ¸ ¨ G d2 ¸ ¸¨ 0 ¸ © G d3 ¸¹ 0¸ ¸ 1.7 ¸ 1.7 ¸ ¸ 1.7 ¸ 1.7 ¸¸ 1.7 ¸¸¹
(4)
u 9 | 210 d u1 d 230; 210 d u2 d 230; 220 d u3 d 235; ½ ° ° 220 u 235; 220 u 235; 220 u 235; d d d d d d ® ¾ 4 5 6 ° 2000 d u7 d 4000; 2000 d u8 d 4000; 2000 d u9 d 4000° ¯ ¿
^d ^y
3
`
| E d di d E ; for 1 d i d 3; and 0 d E d 12 ; d ss
15
0,
T
0, 0
`
|1.9 d yi d 2.3; for 1 d i d 15
T
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1 T T = 220, 220, 227.5, 227.5, 227.5, 227.5, 3000, 3000, 3000 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1, 2.1 T
where įy, įu and įd are deviation variables from the steady-state values for the outputs (yss), inputs (uss), and disturbances (dss), respectively. The scalar ȕ represents the magnitude of the disturbances, all three of which move in tandem. The design of the feasible set of output constraints will be performed here by considering the system above with its original dimensionality (section 4.1) and a 9 x 9 x 3 square approximation (4.2). 4.1. System with its Original Dimensionality To demonstrate the effectiveness of the proposed LP-based approach to handle highdimensional non-square systems, the SFCP (eq. 4) is addressed in its full dimensionality (15 x 9 x 3). The calculated minimum (ymin) and maximum (ymax) AOIS ranges for each controlled variable when ȕ = 12 are shown in the first two rows of Table 1. Because sheet-thickness uniformity is desirable, the following conservative set of output constraints, representing the widest thicknesses (y10, y11, y13), should be used: AOIS
^y
15
`
| 2.00 d yi d 2.20; 1 d i d 15
(5)
Analysis of the Constraint Characteristics of a Sheet Forming Control Problem
391
Thus, the hyper-volume ratio (HVR) [5] of the original (DOS) to the designed (AOIS) constrained regions is: HVR = (0.4/0.2)15 = 3.28 x 104. Hence, for the assumed disturbance values, this process could be feasibly operated within a constrained region that is significantly tighter than the one initially specified. These designed new limits were validated by running DMCplusTM (AspenTech) simulations for the extreme values of the disturbances, showing that the MPC controller does not violate these limits at the steady-state. Furthermore, the computational time for the AOIS calculation was only 0.18 seconds (Dell PC with a 3.0-GHz Intel Pentium 4 processor). If tighter control of the overall sheet thickness is intended, process modifications should be performed to enlarge the AIS, and thus shrink the AOIS, availing tighter control of y10, y11, and y13, at least. 4.2. Square Approximation Consider now a 9 x 9 x 3 square approximation of the SFCP, where the objective is to control each of the 9 outputs at ranges within the DOS using 9 inputs. In this case, it is assumed that the sheet thicknesses are controlled at specified zones, which are represented by the following set of zone variables (z): z1 z6
y4 y5 y6 y7 y1 y2 ; z2 y3 ; z3 ; z4 ; z5 y8 ; 2 2 2 y9 y10 y14 y15 y11 y12 ; z7 ; z8 y13 ; z9 ; 2 2 2
(6)
where y8 (z5) corresponds to the measurement at the center of the sheet. The zone variables have the same DOS limits, relative weights and the target values of the initial output variables. The solution of this approximated problem also provides an alternative way to calculate the achievable constraints for the output variables using the properties of this distributed process. The AOIS calculation is performed setting again ȕ = 12, which corresponds to its maximum value. The following AOIS ranges are obtained for this case: AOIS
^z
9
| 2.04 d zi d 2.16; 1 d i d 9, E
`
12
(7)
Here as well, the most conservative set of constraints is used, to guarantee feasibility and sheet uniformity, which corresponds to the limits of z5, z6, z7 and z8 (see Table 1). Observe that once again very tight control can be achieved, which is demonstrated by the high value of the ratio between the hyper-volumes of the original constrained region and the designed constrained region (HVR = 5.08 x 104). This implies that for the assumed disturbance values, the process could be operated feasibly within a constrained region 5.08 x 104 tighter than the region initially specified by the DOS. Because different targets for the sheet thickness are intended, the zone target will now be moved from its nominal value of 2.1 units to 2.0 units. For this target, the AOIS ranges for the zone variables obtained when the disturbance range is equal to -12 d1 12 (ȕ = 12) are the following: AOIS
^z
9
| 1.92 d zi d 2.08; 1 d i d 9, E
`
12
(8)
Thus, for the specified conditions, the original constrained region could be again significantly reduced (HVR = 3.81 x 103). As in the previous case, the results for this target of 2.0 units correspond to the conservative set of constraints, representing the widest calculated thicknesses among the zones.
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To conclude the analysis for this process example, the typical computational time for the AOIS calculations of all cases was 0.19 seconds. Here as well, simulations were performed using DMCplus to validate the results for all cases. Finally, observe that the simplification of a non-square system by a square one provides a less realistic calculation of the AOIS (eqs. 5 and 7). In fact, if the results obtained for the zone variables were used for the outputs within the corresponding zone, then infeasibilities would occur for some outputs. Table 1. Feasible output ranges (AOIS) calculated for the SFCP (ȕ = 12). The output variables for the original problem with 15 outputs, 9 inputs and 3 disturbance variables, are represented with y. The zone variables for the simplified square problem are represented with z. yi/zi
i=1
2,3
4
5,7
6
8
9
10,11,13
12
14
15
min
2.05
2.03
2.04
2.08
2.04
2.06
2.08
2.00
2.10
2.05
2.01
ymax
2.15
2.17
2.16
2.12
2.16
2.14
2.12
2.20
2.10
2.15
2.19
min
2.09
2.09
2.10
2.04
2.04
2.04
2.09
max
2.11
2.11
2.10
2.16
2.16
2.16
2.11
y
z z
5. Conclusions Interval Operability concepts were applied to calculate the tightest feasible set of output constraints for the Sheet Forming Control Problem (SFCP). By considering two different configurations of this problem, square and non-square, different sets of constraints were obtained. Results for both scenarios showed that significant constraint reduction can be achieved for the initial set of output constraints without rendering the control problem infeasible in the presence of process disturbances. Although the use of zone variables reduces the complexity of the problem, the results obtained using this configuration are less accurate than the ones calculated by addressing the problem in its full dimensionality. The square nature of the simplified problem provides tighter feasible ranges for the zone variables than the constraints calculated for the individual output variables when the non-square problem is solved. If the calculated ranges of the zone variables were to be used to define the ranges of all 15 measured outputs, in a 15 x 9 MPC (or DMC) controller, infeasibilities would occur. The minimal computational time required for the corresponding calculations enables the online adaptation of the controller constraints depending on the current state of the process.
Acknowledgments The authors gratefully acknowledge the financial support from PRF-ACS through grant # 45400-AC9. We also wish to acknowledge William M. Canney from AspenTech for providing the DMCplus software.
References [1] F. V. Lima and C. Georgakis, In Proceedings of the 2006 IFAC International Symposium on Advanced Control of Chemical Processes (ADCHEM) (2006) 989-994. [2] F. V. Lima and C. Georgakis, In Proceedings of the 2007 IFAC International Symposium on Dynamics and Control of Process Systems (DYCOPS) 3 (2007) 49-54. [3] J. B. Rawlings, IEEE Control Syst. Mag., 20 (2000) 38-52. [4] D. R. Vinson and C. Georgakis, J. Process Contr., 10 (2000) 185-194. [5] F. V. Lima and C. Georgakis, J. Process Contr., doi:10.1016/j.jprocont.2007.09.004 (2007). [6] F. V. Lima and C. Georgakis, Input-Output Operability of Control Systems, Automatica, submitted for publication (2007).
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Real-Time Optimization via Adaptation and Control of the Constraints Alejandro Marchetti, Benoît Chachuat, Dominique Bonvin Laboratoire d’Automatique, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Abstract In the framework of real-time optimization, measurements are used to compensate for effects of uncertainty. The main approach uses measurements to update the parameters of a process model. In contrast, the constraint-adaptation scheme uses the measurements to bias the constraints in the optimization problem. In this paper, an algorithm combining constraint adaptation with a constraint controller is presented. The former detects shifts in the set of active constraints and passes the set points of the active constraints to the latter. In order to avoid constraint violation, the set points are moved gradually during the iterative process. Moreover, the constraint controller manipulates linear combinations of the original input variables. The approach is illustrated for a simple case study. Keywords: Real-time optimization, constraint control, constraint adaptation.
1. Introduction Throughout the petroleum and chemicals industry, the control and optimization of many large-scale systems is organized in a hierarchical structure. At the real-time optimization level (RTO), decisions are made on a time scale of hours to a few days by a so-called real-time optimizer that determines the optimal operating point under changing conditions. The RTO is typically a nonlinear program (NLP) minimizing cost or maximizing economic productivity subject to constraints derived from steady-state mass and energy balances and physical relationships. At a lower level, the process control system implements the RTO results, including product qualities, production rates and active constraints (Marlin and Hrymak, 1997). Because accurate mathematical models are unavailable for most industrial applications, RTO classically proceeds by a two-step approach, namely an identification step followed by an optimization step. Variants of this two-step approach such as ISOPE (Roberts and Williams, 1981; Brdys and Tatjewski, 2005) have also been proposed for improving the synergy between the identification and optimization steps. Parameter identification is complicated by several factors: (i) the complexity of the models and the nonconvexity of the parameter estimation problems, and (ii) the need for the model parameters to be identifiable from the available measurements. Moreover, in the presence of structural plant-model mismatch, parameter identification does not necessarily lead to model improvement. In order to avoid the task of identifying a model on-line, fixed-model methods have been proposed. The idea therein is to utilize both the available measurements and a (possibly inaccurate) steady-state model to drive the process towards a desirable operating point. In constraint-adaptation schemes (Forbes and Marlin, 1994; Chachuat et al., 2007), for instance, the measurements are used to correct the constraint functions in the RTO problem, whereas a process model is used to
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estimate the gradients of the cost and constraint functions. This way, the iterates are guaranteed to reach a feasible, yet suboptimal, operating point upon convergence. Two types of transients can be distinguished in RTO systems: at the lower level, the dynamic response of the controlled plant between successive steady-state operating points generated by RTO; at the upper level, the transient produced by the iterates of the RTO algorithm. Most RTO algorithms do not ensure feasibility during these transient periods, thus resulting in conservative implementations with significant constraint backoffs and limited changes in operating point between successive RTO periods. Constraint violations during both types of transients can be avoided by controlling the active constraints that define optimal operation (Brdys and Tatjewski, 2005). The implementation of constraint control can significantly decrease the constraint backoffs required in the RTO optimization problem, resulting in increased cost. The set of active constraints might change due to process disturbances and changing operating conditions, thus resulting in different constraint-control schemes (Maarleveld and Rijnsdorp, 1970; Garcia and Morari, 1984). In this work, a constraint-adaptation scheme is combined with a constraint controller. Special emphasis is placed on selecting the set points and the manipulated variables used in the constraint controller at each RTO period. The effect of the constraint controller on the feasibility of intermediate operating points is studied, under the assumption of an ideal constraint controller. The paper is organized as follows. Section 2 formulates the optimization problem. The RTO scheme combining constraint adaptation and constraint control is presented in Section 3. The behavior of the proposed scheme, with and without the constraint controller, is illustrated for a simple quadratic programming (QP) problem in Section 4. Finally, Section 5 concludes the paper.
2. Problem Formulation The optimization problem for the plant can be formulated as follows:
min (u) := (u, y(u))
(1)
u
s.t. G(u) := g(u, y(u)) G max ,
(2) ny
where u denotes the vector of decision (or input) variables, and y is the n n vector of controlled (or output) variables; : u y is the scalar cost function ny nu to be minimized; and g i : , i = 1,..., ng , is the set of operating constraints. Throughout the paper, the notation ( . ) is used for the variables that are associated with the plant and (.) for those of the process model. The steady-state mapping of the plant, y(u), is assumed to be unknown, and only an n approximate model F(u, y, ) = 0 is available for it, where is the set of model parameters. Assuming that the model outputs y can be expressed explicitly as functions of u and , the cost function and the operating constraints predicted by the model can be written as (u, ) := (u, y(u, )) and G(u, ) := g(u, y(u, )), respectively. nu
3. Real-Time Optimization Scheme 3.1. Constraint Adaptation In the presence of uncertainty, the constraint values predicted by the model do not quite match those of the plant. The idea behind constraint adaptation is to modify the optimization problem by adding a correction term to the constraint functions. At each RTO iteration, a model-based optimization problem of the following form is solved:
Real-Time Optimization via Adaptation and Control of the Constraints
395
min (u k , ) uk
s.t. G(u k , ) + k G max ,
(3)
ng
where k denotes the vector of constraint correction factors. Under the assumption that measurements are available for every constrained quantity at the end of each RTO period, the correction factors can be updated recursively as:
k +1 = (I B) k + B[G(u k ) G(u k , )] ,
(4)
ng ng
where B is a diagonal gain matrix with diagonal elements in the interval (0,1] . An important property of the constraint-adaptation algorithm is that the iterates are guaranteed to reach a feasible, yet suboptimal, operating point upon convergence (Forbes and Marlin, 1994). However, the constraints can be violated during the iterations, which calls for using constraint backoffs and limiting operating point changes between successive RTO periods. Constraint adaptation (3-4) represents the “classical” constraint-adaptation scheme (Forbes and Marlin, 1994; Chachuat et al., 2007). In this paper, a novel way of adapting the constraints is proposed:
min (u k , )
(5)
s.t. G(u k , ) + k G max,k ,
(6)
uk
where the correction term k := G(u k 1 ) G(u k 1 , ) stands for the difference between the measured and predicted values at the previous RTO period. The maximum values G max,k for the constraints are calculated as:
G max,k = G(u k 1 ) + B[G max G(u k 1 )] .
(7)
For the combination with constraint control, constraint adaptation (6-7) is preferred because it gives the ability to vary the set points G max,k passed to the constraint controller. Upon convergence of this algorithm, the set points reach the original constraint bounds G max . Let u0 denote the optimal solution for the process model with = 0 in (3). It can be shown that the constraint-adaptation schemes (3-4) and (6-7) produce the same iterates when initialized with 0 and u0 , respectively, and the same diagonal gain matrix B is used, provided the set of active constraints does not change. At each RTO period, a set of optimal inputs, uk , and corresponding Lagrange na multipliers, k , are obtained from the numerical solution of (5-6). Let G ak k denote the vector of active constraints at u k . It is assumed that the Jacobian matrix of the na n a R k u , has full row rank at uk , i.e. the constraints satisfy a active constraints, G u,k regularity condition. It follows that the input space can be split into the nka -dimensional subspace of constraint-seeking directions and the (nu nka ) -dimensional subspace of sensitivity-seeking directions. These subspaces are spanned by the columns of the orthogonal matrices Vkc and Vks , respectively, as obtained from singular-value a decomposition (SVD) of G u,k : a = [U ck U sk ][ ck 0][Vkc Vks ]T . G u,k (8) 3.2. Combination with Constraint Control At the constraint-control level, the variables are considered as time-dependent signals. In this work, the constraint controller is designed so as to track the iteratively-updated active constraints by varying the process inputs along the constraint-seeking directions.
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More precisely, the manipulated variables (MVs) in the constraint controller correspond na to the corrections uck (t) k along the directions Vkc , from the model optimum uk . Observe that the MVs may change from RTO period to RTO period, e.g. when the active set of (5-6) changes. At each time instant, the inputs u k (t) are then reconstructed from the values of uck (t) , based on the knowledge of uk and Vkc , as:
(
)
u k (t) = U uk ,Vkc , uck (t) := uk + Vkc uck (t) .
(9)
The set points in the constraint controller correspond to the active constraints, na a G max,k k , determined at the RTO level. Finally, the controlled variables (CVs) are the active constraints G ak (t) := g a u k (t), y k (t) for the plant. At the initial time tk 1 of the k-th RTO period, the constraint controller is started from uck (tk 1 ) = VkcT u k 1 uk . At the terminal time tk of that period, the constraint controller yields a new steady-state operation, which corresponds to the set points a G max,k . The corresponding steady-state inputs u k are obtained from (9) as u k = U uk ,Vkc , uck (tk ) .
(
(
(
)
)
)
Figure 1. Scheme combining constraint adaptation and constraint control.
The overall optimization and control scheme is illustrated in Fig. 1, and the procedure can be summarized as follows: 1. Set k = 0. Initialize B. Start from a feasible (conservative) operating point u0 (without the constraint controller). 2. At steady state, measure G (u k ) and compute G max, k +1 from (7). Set k := k + 1 . 3. Calculate the solution uk of (5-6). 4. Determine the constraint-seeking directions Vkc from SVD of the Jacobian a matrix G u,k of active constraints at uk . 5. Formulate a square constraint-control problem where the MVs are the values of uck (t) , the CVs are the active constraints G ak (t) , and the set points are the a values G max,k of the active constraints identified in Step 3. 6. Apply the constraint controller to the plant and get the inputs u k corresponding to the new steady-state operation. Go to Step 2.
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3.3. Implementation Aspects The approach assumes that all the constrained variables can be measured or estimated on-line at a sampling period much smaller than the time constant of the controlled plant. Notice that the decision variables u in the RTO problem may very well be set points of feedback controllers acting directly on the plant manipulated variables. In this case, the constraint controller can be viewed as a primary controller in a cascade control configuration that corrects the set points produced at the RTO level. The constraint-control problem is a multivariable square control problem, and various controllers can be used, such as a discrete integral controller or a model predictive controller. In order to avoid overshoots, the set-point corrections can be implemented by ramps rather than steps. Also, small overshoots can usually be accommodated during the first a few iterations, i.e. when the set points G max,k are conservative with respect to the actual bounds G max .
4. Illustrative Example Consider the following QP problem:
min (u, ) := (u1 1)2 + (u2 1)2
s.t. G1 := 1 + 2 u1 u2 0,
(10)
G2 := 3 + 4 u1 + u2 0,
(11)
with two decision variables u = [u1 u2 ] , four model parameters = [1 ,..., 4 ] , and two uncertain constraints G1 and G2 . The parameter values for the model and the simulated reality are reported in Table 1. Note that the operating point determined from the model, without constraint adaptation, leads to constraint violation. T
T
Table 1. Values of the parameters for the model and the simulated reality.
1 2
3
4
Reality 0.4 0.8 -1.8 1.9 Model 0.9 0.4 -2.0 1.4
In this simple QP problem, an ideal constraint controller is assumed, i.e. the controller a determines uck (tk ) such that G a U uk ,Vkc , uck (tk ) = G max,k . The objective here is to illustrate the effect of constraint control on the feasibility of the steady-state intermediates. Both constraints are active at the optimum either for the reality or for the model. The constraint-adaptation algorithm is applied with and without constraint control, starting from u 0 = [0 1.4]T and with a diagonal gain matrix B = b I 22 with b (0,1] . The results obtained with b = 0.7 are shown in Fig. 2. It can be seen that, without constraint control, the iterates converge by following an infeasible path (left plot). In fact, the iterates can be shown to follow an infeasible path for any value of b (0,1] ; the constraint violation is reduced by decreasing the value of b, but this is at the expense of a slower convergence. With constraint control, on the other hand, the iterates converge without violating the constraints (right plot), irrespectively of the value of b. Both constraints are found to be active at the solution point of the optimization problem (5-6) for all iterations. Since the number of active constraints is equal to the number of decision variables, the constraint-seeking directions span the whole input space here.
(
)
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Figure 2. Illustration of the proposed algorithm for Problem (10-11). Left plot: Without constraint control; Right plot: With constraint control; Thick solid lines: constraint bounds for the simulated reality; Thick dash-dotted lines: constraint bounds predicted by the model without adaptation; Dotted lines: contours of the cost function; Light solid lines: iterates; Point R: optimum for the simulated reality; Point M: optimum for the model without adaptation.
5. Conclusions An optimization scheme combining constraint adaptation with constraint control has been proposed. This scheme presents two important features: (i) the constraint controller tracks the active constraint determined at the RTO level by adapting the inputs in the subspace of constraint-seeking directions, and (ii) the set points for the active constraints in the constraint controller are updated at each iteration and reach the actual constraint bounds upon convergence. In future work, this combined scheme will be compared to other existing approaches (e.g. Ying and Joseph, 1999). The combination of more involved RTO schemes with constraint control (e.g. Gao and Engell, 2005) will also be considered.
References M. A. Brdys and P. Tatjewski, 2005, Iterative algorithms for multilayer optimizing control. Imperial College Press, London, UK. B. Chachuat, A. Marchetti, and D. Bonvin, 2007, Process optimization via constraint adaptation, J. Process Contr., In press. J. F. Forbes and T. E. Marlin, 1994, Model accuracy for economic optimizing controllers: The bias update case, Ind. Eng. Chem. Res., 33, 1919-1929. W. Gao and S. Engell, 2005, Iterative set-point optimization of batch chromatography, Comp. Chem. Eng., 29, 1401-1409. C. E. Garcia and M. Morari, 1984, Optimal operation of integrated processing systems. Part II: Closed-loop on-line optimizing control, AIChE J., 30, 2, 226-234. A. Maarleveld and J. E. Rijnsdorp, 1970, Constraint control on distillation columns, Automatica, 6, 51-58. T. E. Marlin and A. N. Hrymak, 1997, Real-time operations optimization of continuous processes, AIChE Symp. Ser., 93, 156-164. P. D. Roberts and T. W. C. Williams, 1981, On an algorithm for combined system optimization and parameter estimation, Automatica, 17, 1, 199-209. C.-M. Ying and B. Joseph, 1999, Performance and stability analysis of LP-MPC and QP-MPC Cascade Control Systems, AIChE J., 45, 7, 1521-1534.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Integration of Engineering Process Control and Statistical Control in Pulp and Paper Industry Ana S. Matos, José G. Requeijo, Zulema L. Pereira Dept. Mec & Ind Eng and UNIDEMI, Faculty of Science and Tecnology, New University of Lisbon, 2829-516 Caparica, Portugal
Abstract The main goal of this article is to present a methodology and a framework that is able to bring together two important concepts: Engineering Process Control (EPC), which was developed by process engineers to achieve short time control, and Statistical Process Control (SPC), conceived and implemented by statisticians and quality managers for attaining medium and long term control. The integration of both concepts can represent a breakthrough in the final product performance, by creating the necessary conditions to decrease the variability of quality characteristics both in the short and long term. The integrated methodology was designed for the pulp and paper industry and was established in several phases. First, a mathematical model was developed to represent as much as possible the process dynamic behaviour. The transfer function obtained was then used to implement two components of the above mentioned concepts, namely controllers, based on the minimum variance criterion, and statistical control charts. At last, the two components were integrated into the process, which was submitted to several disturbances to ascertain the control achieved with the integration. The methodology was tested in a real industrial process of one of the most important pulp producers in the world and considered several scenarios. To illustrate the methodology, we present one of the scenarios that shows the benefits of EPC/SPC integration. Through the application of the developed methodology to real data, process engineers at the company are now able to use a valuable decision making tool when the production process is affected by certain disruptions, with obvious consequences on product quality, productivity and competitiveness. Keywords: Engineering Process Control, Statistical Process Control, Process Modelling.
1. Introduction Continuous improvement of any process requires reduction in the variability around the target value of its parameters. Traditionally, two different approaches have been used to accomplish this goal: Engineering Process Control (EPC) developed and employed by process and control engineers and Statistical Process Control (SPC), used by statisticians and quality engineers. Until recently, the main reason for keeping these two concepts separate was the different view each of them had about an industrial process. While SPC monitoring procedures seek to reduce the output variability by detecting and eliminating assignable causes of variation, EPC is usually applied to minimize the output variability by making online adjustments of one or more process inputs on a regular basis. The first attempts to integrate EPC and SPC appeared long ago, with the work of Barnard (1959). Using the machine-tool case study, the author demonstrated that automatic control and statistical control can be used in parallel.
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The first approach of integration presented to the statistical community was developed by MacGregor (1988), who suggested the use of control charts for monitoring the behaviour of a process under EPC. Inspired by the work of MacGregor (1988), several other authors became notorious in the field, leading to different approaches that reveal two great concerns associated with this type of integration: • Identification of the variables that must be monitored: if only output variables (quality characteristics), input variables (adjustable variables) or both of them; • Decision on whether to use automatic or manual controllers, the latter being or not constrained by statistical control; such decision would depend on adjustment costs and type of adjustment. The first approach that explicitly combines SPC with EPC was proposed by Vander Wiel et al. (1992) under the name of Algorithmic Statistical Process Control (ASPC). Following the same philosophy of ASPC, other reference studies emerged, such as Montgomery et al. (2000) and Huang and Lin (2002), among many others. An innovation introduced to the ASPC approach was the use of control charts applied to adjustable variables; the joint monitoring of input and output variables (using different control charts) was presented by Messina et al. (1996) and was followed by Tsung and Tsui (2003). Within a slightly different context, a third approach appears which considered the existence of adjustment costs. The implementation of control charts acting as a “supervisor” of the control actions was the way found by several authors to minimize adjustment costs (e.g. Box and Luceño, 1997 and Ruhhal et al., 2000). Recent years have witnessed the appearance of several research studies in this field. However, there have been scarce publications using real production data and demonstrating the practical application of the integration. This article tries to fill this gap, as it gives an example of integrated EPC/SPC applied to a real and complex continuous process. This new development was carried out in cooperation with a large paper and pulp production plant in Portugal, which is one of the most important producers in the world.
2. Development of an EPC/SPC Integration Methodology This article summarises an integrated EPC/SPC methodology developed by Matos (2006) as a doctoral research project. The main goal was the development of a methodology that could be tested and applied to a real case study. Additionally, it should also be adjustable to other industrial processes with similar technical requirements. Once the pulp production process is well understood, the first step is to characterize the methodological “hardware” and “software” elements that will be part of the integrated EPC/SPC. Within this work, the term hardware is used to describe the more physical elements, such as the mathematical model, the controllers and the control charts. On the other hand, the software is related to the rather intangible elements, namely the intervention criteria, the type of disturbances (for testing purposes) and the performance measures. The intervention criteria will constrain the rule to be applied by the controller and the control chart, as well as the way they interact in the integration. Altogether, the software elements allow the evaluation and comparison of different integration scenarios. As Figure 1 shows, the main stages of the proposed methodology are the preliminary data analysis, the identification of all process variables (outputs, inputs and disturbance variables), the transfer function model (i.e. the mathematical model that describes the
Integration of EPC and SPC in Pulp and Paper Industry
401
process behaviour), the controllers (based on the minimum variance criterion) and, finally, the univariate and multivariate control charts (designed to be applied to autocorrelated data).
Figure 1 – The main stages of the integrated EPC/SPC methodology
2.1. Case Study – Pulp and Paper Industry The case study presented here deals with a pulp and paper production process. The plant produces Bleached Eucalyptus Kraft Pulp, using the ECF process (Elemental Chlorine Free). The Kraft pulping process is performed in two different phases, which influence the final pulp quality: the cooking process of wood chips (eucalyptus globules) followed by the pulp bleaching. The cooking process is the phase that most contributes to the preservation of the main pulp characteristics, which, in turn, will ensure high quality paper. The viscosity of the bleached pulp, among other quality characteristics, constitutes one of the most important control parameters; the viscosity value depends, to a great extent, on the cooking process carried out in two continuous digesters working in parallel. After understanding the MO (modus operandis) of the bleached pulp process, the main input variables (which are measured in the digesters) were identified (Table 1). Table 1 – Input variables and symbols
Temperature Variables
Symbol
Concentration Variables Symbol Active-alkali AA Temperature in C4 zone TemC4 Sulphur index SI Temperature in C5 zone TemC5 Top black liquor TBL Temperature in C6 zone TemC6 White liquor C4 WLC4 Temperature in C8 zone TemC8 White liquor C8 WLC8 The present study considered four production periods with stabilized operational conditions (3 temporal data windows for estimation and 1 for validation). The samples were collected every 4 hours for both input (Table 1) and output (viscosity) variables. 2.2. Model Fitting After the preliminary data analysis, a satisfactory Box-Jenkins transfer function model was developed to describe, as much as possible, the dynamic behaviour of the bleached
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pulp process. The methodology used to obtain the transfer function model was carried out in three phases, as follows:
•
1st phase: fitting of several single-input single-output (SISO) transfer function models to identify possible relationships between input - output variables.
•
2nd phase: merging of the three data windows with the goal of obtaining a better profile of the bleached pulp process; the 1st phase was then repeated.
•
3rd phase: development of a multiple-input single-output (MISO) transfer function model using the results of the 2nd phase. The obtained model, which was developed using the Toolbox System Identification from MATLAB® software, explained 42% of the total data variation within the observation period: yt =
( −2,86 − 7, 46B ) WLC 8tD−12 + 5,90SI tD−12 − 4, 01WLC 4tD−22 − 5, 23TemC 4tD−21 − (1+0,99B )
− 2,90TemC 5tD−21 + 1, 66 AAtD− 22 +
1 ε (1 − 0,56B ) t
(1)
In the previous equation, yt is the deviation of viscosity from target at time t, εt is the white noise sequence and B defines the backshift operator. WLC8, SI, WLC4, TemC4, TemC5 and AA represent the variables of Table 1 in digester 1 (D1) and digester 2 (D2). The fitted model was successfully validated utilizing the data of the 4th window established for that purpose. Such mathematical model is the first “hardware” element and is the foundation of the complete methodology developed in the research. 2.3. Engineering Process Control and Statistical Process Control According to Figure 1, once the mathematical model has been defined, the study carries on with the definition of the other hardware components: controllers and control charts. The integrated control strategy used manual controllers constrained by the control chart decisions. The Ridge controller (del Castillo, 2002) based on a minimum variance criterion was found to have good characteristics to be adapted to the transfer function defined in (1). This controller has a tuning parameter that balances the variances of the output with the inputs. The development of an appropriate monitoring scheme through control charts leads to several questions, such as: which characteristics are to be monitored, where to apply the charts and which control charts are appropriate. To monitor the viscosity, three control charts were considered as good candidates, namely the EWMA with residuals, the CUSCORE chart and the EWMAST chart, since they revealed to be more effective in detecting changes of small magnitude than some other charts. It was considered equally important to apply multivariate control charts to monitor the input variables of the digesters. The multivariate study was performed using two control charts of the same type, but applied with different goals. The first one was applied directly to the digesters input variables, whereas the second one was applied to the difference between each input variable (real value) and the theoretical value shown by the controller. Given the large amount of variables and the auto-correlated structure exhibited by the data, the control charts were based on projection methods, namely the dynamic principal components analysis (DPCA), proposed by Ku et al. (1995). In both cases, i.e. controllers and control charts, the tuning parameters were obtained through simulation models developed on a MATLAB® platform.
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3. Results and Discussion of Integration Outputs After the definition of the three “hardware” elements previously described, one has to establish the “software” elements: intervention criterion, performance measures, type of disturbances and simulation conditions. The approach used in the research is somehow in between the second and the third approaches mentioned in the Introduction; on one hand, the integrated EPC/SPC focuses on control charts to monitor both the input and the output variables and, on the other, it uses a constrained manual controller. Therefore, the intervention criterion was established as a constrained action of the controllers by both control charts. The Asymptotic Mean Square Deviation (AMSD) was used as the performance measure to compare different scenarios, since it incorporates the deviations from the target and the variability (particularly useful when a process is submitted to a disturbance). Besides the use of AMSD, the Average Run Length (ARL) was applied to evaluate the performance of each control chart. Given the main characteristics of the pulp process, it was possible to list seven different types of disturbance that can affect the dynamic behaviour of the process: the input and output variables, the autoregressive parameter and the residuals of the model (φ, Nt). As regards the simulation conditions, the running of 10 000 cycles, with 248 observations each, was considered sufficiently credible. Since the proposed EPC/SPC was designed to be applied in sequential stages, the construction of the different scenarios starts with an open-loop process, followed by the incorporation of the control charts and then the manual controller. The scenarios are: 1)– open loop (system operating freely), 2)– entry of univariate control chart, 3)– entry of controllers (manual regime), 4)– entry of multivariate control chart applied to controllers, and 5)– entry of multivariate charts to control the input variables. Figure 2 compares the five scenarios when two disturbances were applied to the process. In the figure, δ is the size of the shift in the mean, measured in terms of the standard deviation (new mean = μ+δσ). Disturbance in noise component (N t(N ) t) Disturbance in noise component 3200
0
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Figure 2 – AMSD for the five scenarios with implementation of EWMAST chart
As can be seen in Figure 2, the scenarios present a different behaviour when the same control chart (EWMAST) was used. It is visible that the proposed methodology increased the process performance (scenarios 4 and 5), when compared with scenario 1 (no control) or with the tradicional approaches (scenarios 2 and 3).
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4. Conclusions The success inherent to an integrated methodology of this nature is closely associated with the ability of creating different scenarios and the skill in comparing them. Other requirements equally important are the quality of the mathematical model and the selection of both the controllers and the control charts. Although this study has used real production data to create the model, the employment of computational simulation revealed to be an essential tool in accomplishing the aim of the research. The developed simulation models were used for studying the sensitivity and robustness of controllers and control charts. Additionally, the simulation exercise is the only way of testing different scenarios when the process is submitted to several types of disturbance. As far as the literature review revealed, the pulp and paper industry has not applied integrated methodologies based on “black boxes”. According with the findings of present research, and once the best integrated scenario is obtained and appropriate interface software is developed, the process engineers can use the methodology as a decision making tool when the production process is affected by certain disruptions, with valuable consequences on quality, productivity and competitiveness. Consequently, one expects that the company where the research took place will, in the near future, benefit from the implementation of the proposed appoach. At last, it is also important to highlight the flexibility and adaptability of the methodology to any other type of production system when the production staff can use the available data to build a mathematical transfer function that models the dynamic behaviour of the process.
References Barnard, G. A., 1959, Control Charts and Stochastic Processes, Journal of the Royal Statistical Society B, 21(2), 239-271. Box, G. and Luceño, A., 1997, Statistical Control by Monitoring and Feedback Adjustment, John Wiley & Sons, NY. del Castillo, E., 2002, Statistical Process Adjustment for Quality Control, John Wiley & Sons, NY. Huang, B. and Lin, Y. L., 2002, Decision Rule of Assignable Causes Removal under an SPC-EPC Integration System, International Journal of Systems Science, 33(10), 855-867. Ku, W., Storer, R. H. and Georgakis, C., 1995, Disturbance Detection and Isolation by Dynamic Principal Component Analysis. Chemometrics and Intelligent Laboratory Systems, 30, 179-196. MacGregor, F., 1988, On-Line Statistical Process Control, Chemical Engineering Process, Oct: 21-31. Matos, A. S., 2006, Engenharia de Controlo do Processo e Controlo Estatístico da Qualidade: Metodologia de Integração Aplicada na Indústria da Pasta de Papel, PhD thesis, FCT/UNL, Lisboa, Portugal. Messina, W. S., Montgomery, D. C. and Keats, J. B., 1996, Strategies for Statistical Monitoring of Integral Control for the Continuous Process Industries, Statistical Applications in Process Control, New York, Marcel Dekker, 47, 193-214. Montgomery, D. C., Yatskievitch, M. and Messina, W. S., 2000, Integrating Statistical Process Monitoring with Feedforward Control, Quality and Reliability Engineering International, 16(6), 515-525. Ruhhal, N. H., Runger, G. C. and Dumitrescu, M., 2000, Control Charts and Feedback Adjustments for a Jump Disturbance Model. Journal of Quality Technology, 32(4), 379-394. Tsung, F. and Tsui, K. L., 2003, A Mean-Shift Pattern Study on Integration of SPC and APC for Process Monitoring, IIE Transactions, 35, 231-242. Vander Wiel, S. A., Tucker, W. T., Faltin, F. W. and Doganaksoy, N., 1992, Algorithmic Statistical Process Control: Concepts and an Application, Technometrics, 34(3), 286-297.
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A combined Balanced Truncation and MultiParametric Programming approach for Linear Model Predictive Control Diogo Narcisoa, Efstratios Pistikopoulosa a
Imperial College London, South Kensington Campus, Department of Chemical Engineering, SW7 2AZ, London, United Kingdom
Abstract We present a novel approach to Model Predictive Control problems, which combines a model reduction scheme coupled with parametric programming. Balanced Truncation is used to first reduce the size of the original Model Predictive Control formulation, while multi-parametric programming is employed to derive the parametric control laws offline. The theoretical developments are presented with an example problem. Keywords: MPC, Multi-Parametric Programming, Balanced Truncation.
1. Introduction Multi-parametric programming [1] has recently received a lot of attention in the open literature, especially because of its important applications in Model Predictive Control (MPC) [2]. In this context, a new class of controllers, the so-called parametric controllers has been invented [3] which allow for the off-line derivation, hardware implementation and installation of Model Predictive Control [4]. While the advantages of parametric controllers are well established, a key challenge for their wider applicability is the ability to derive parametric controllers from arbitrary large scale and complex mathematical models. In this context, Model Order Reduction [5] can be a useful tool, since it could lead to an approximate model of reduced size, and complexity and of sufficient accuracy. In this paper we present a Model Reduction technique incorporated with multiparametric programming and control, namely Balanced Truncation (BT). The use of Balanced Truncation eliminates a number of states of dynamic linear systems, while a bound on the maximum error obtained for the output vector can be established. This then allows for the derivation of (approximate) linear parametric controllers, which can be tested and validated (against the original high-fidelity model) off-line. These theoretical developments are presented next.
2. Balanced Truncation in Multi-parametric programming and control Balanced truncation is one model reduction technique, which is particularly suitable in the context of state-space dynamic models, linear Model Predictive Control and Multiparametric controller design, as discussed in the following. In Eq. (1) we present the mathematical formulation of the MPC problem we aim to solve. Given Eq. (1), we first seek to use balanced truncation to reduce the size of the model, and then solve the reduced control problem via our multi-parametric programming and control methodologies. The derived parametric controller can then be validated against the original, full space model.
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2.1. Balanced truncation in Multi-parametric programming and control We consider the following formulation in discrete time and linear form, already recast as a mp-QP problem (See [6]):
(1) Where the initial state x(t) corresponds to the vector of parameters in the multiparametric programming framework. Balanced truncation is then applied to Eq. (1). We work with the dynamic system (xt+k+1|t = Axt+k|t + But+k; yt+k|t = Cxt+k|t) and seek to find a transformation T such that the transformed system is balanced. Following the procedure as described in [5], we describe the dynamic system in an equivalent balanced form:
(2) -1
b
b
-1
b
For convenience, we write TAT as A , TB as T and CT as C . We incorporate (2) in (1) and hence convert into the transformed state x : for matrices K, P, Q and V in Eq. (1) we substitute x for T-1 x resulting in matrices Kb = KT-1, Pb = (T
−1 T
) PT-1, Qb =
(T −1 ) T QT-1 and Vb = T-1V, respectively (where superscript b denotes balanced realization of the corresponding matrices obtained after this step). For simplification, we rewrite Eq. (1) as follows:
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(3) Note that in Eq. (3) the parameter space has also been transformed. In the next step, we partition the vector x such that x = [ x1T , x 2T ]T, where x1 comprises the first p (the order of the reduced model) components of x . The matrices in Eq. (3) are also partitioned according to the partition of the state vector. The reduced order problem can then result from the deletion of the last n-p states, x 2 , and the corresponding matrix blocks, as follows:
(4) Note that Eq. (4) is not exactly equivalent to either Eq. (1) or Eq. (3): information on the dynamics is lost during the balanced truncation step. There is an “inherent” error in the calculation of the output vector y: even though a feasible solution may be obtained from the reduced problem, this may actually lead to constraint violations of the original problem. We consider here two ways to deal with this problem: (i) neglect the output bounds and keep only the input bounds; (ii) update the output bounds in order to ensure feasibility of all output solutions. These are presented next.
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2.1.1. Recasting option I: neglect output constraints Neglecting the output constraints will lead to a controller which is driven only by states stabilisation. In this case we keep only the constraints on the inputs as they are the same of the original problem. This type of control can be used whenever we do not have hard constraints. The main drawback of this is the loss of one of the most important features of MPC: the ability to deal with all types of constraints. 2.1.2. Recasting option II: update the output bound The second approach we consider here consists of updating accordingly the bounds of the outputs in order to ensure feasibility as follows. Given bounds on the output, ymin ≤ y ≤ ymax, these bounds are updated based on the output error according to the magnitude of the control input as follows [5]:
(5) Where σk corresponds to the singular values of the neglected states. Through Eq. (5) one can compute the maximum error, δ, on output y, as:
(6) We can then update the bounds on the outputs by further restricting the bounds on y as follows: (7) Eq. (7) will ensure that feasibility of the outputs is obtained regardless of the error on the outputs. 2.2. mp-QP formulation Using the state model (xt+k+1|t = Axt+k|t + But+k) we can proceed to convert Eq. (4) by updating the bounds on y (using either Eq. 7 or neglecting the output constraints), thereby recasting the MPC framework in a way that all future states are eliminated, as follows:
(8) T
ut+N_u-1T]T
Note that only inputs vector U = [ut , …, contain the optimisation variables where x1 provides the initial conditions for the states, which are the parameters in the multi-parametric programming framework. Finally, using the transformation of variables z = U + H-1FT x1 (t), Eq. (8) is converted into the mp-QP problem, as follows:
(9)
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The solution of Eq. (9) results in a set of parametric control laws valid in convex critical regions (the so called critical regions). An algorithm for the solution of Eq. (9) can be found in [1] or [7]. The algorithm has been implemented in MATLAB. A full example is presented next to simply illustrate its key steps and features. Detailed computational results and other examples are given elsewhere [8].
3. Example A random state-space system was generated in MATLAB. It consists of n = 10 states, m = 3 inputs and o = 3 outputs. We choose a small model for which the parametric controller can be derived for the original model; based on this solution we can then validate the solution of the controllers obtained from the reduced problems. Matrix A will not, in general represent a continuous stable system. Matrix A is stabilized and the model is then discretized, through the use of a time step (Δt = 1). In general, this step has to be as small as necessary to guarantee an accurate description. We perform a second discretization with Δt = 0.01 for simulation purposes, which we will use to test the performance of the obtained controllers. For the present control problem we considered the following bounds: (-2,-2,-2)T ≤ u ≤ (2,2,2)T; (-10,-10,-10)T ≤ y ≤ (10,10,10)T. We defined the parameter space so that: (-2, -2, …, -2) T ≤ x ≤ (2, 2, …, 2)T. The methodology was applied for p=10 (original size), p=6 and p=3. The first recasting option for the output bounds - deletion of the output constraints is presented here. We selected a time and control horizon with three steps. The parametric solutions, including both the set of critical regions and the associated parametric laws were obtained for each case. In order to test the performance of each controller, we simulated the behaviour of the system using the full descritized model with Δt = 0.01, starting from an initial perturbed state x = [1,1,… ,1]T. The aim of the controller is to drive the states to the origin. We simulated each of the controllers and the open loop responses for a total of 30 time steps. Fig. 1(A) shows the open loop response. 1.5
1.5
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−4
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Figure 1: Dynamic responses of the model used (A – open loop; B – controlled with p=10; C – controlled with p=6; D – controlled with p=3)
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In Fig. 1(B) one can observe that the parametric controller of order p = 10 improves the response when compared with the open loop response, as expected for this class of fullscale parametric controllers. For order p = 6 (Fig. 1(C)), there is an initial strong response from the controller which makes its performance of inferior quality by comparison to cases A and B. Nevertheless, it stabilizes the states. However, controller p=3 (Fig. 1(D)) shows a poor performance as a consequent of significant model reduction. While a controller based on reduced model of order p = 6 captures the significant dynamic information and enables stabilization of the perturbed state, in the case of reduced model of order p=3, important information is lost and the controller is not capable of stabilizing the states. Hence, the controller based on p=3 is rejected.
4. Concluding remarks We have presented a systematic procedure to derive parametric controllers based on (i) reduction of the original MPC model by the use of Balanced Truncation, and (ii) application of our multi-parametric programming and control toolbox [7]. Critical issues, which we have attempted to address in this paper and are subject of further developments at Imperial College include: • Controlling the error in the output constraints • Guarantee feasibility of all constraints for all parameter realization • Establishing equivalence between original and transformed problem • Identify the most suitable model reduction scheme for a wider class of models and applications
Acknowledgements Financial support from Marie Curie European Project PROMATCH (MRTN-CT-2004512441) is gratefully acknowledged.
References [1]. [2]. [3]. [4]. [5]. [6]. [7]. [8].
Pistikopoulos, E.N. et al., V., Multi-Parametric Programming, Wiley, Weinheim, 2007 Pistikopoulos, E.N. et al., Multi-Parametric Model-Based Control, Wiley, Weinheim, 2007 European Patent 1399784, ParOS, 2007 Dua, P. et al., Computers and Chemical Engineering, In Press (Available online 19 March 2007) Antoulas, A.C., Approximation of Large-Scale Dynamical Systems, SIAM, Philadelphia, 2005 Bemporad et al., Automatica 38, 2002 Dua, V. et al. , Computers and Chemical Engineering 26, 2002 Narciso, D. A. C. et al., Internal Report, CPSE – Imperial College, 2007
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Fault detection and isolation based on the modelbased approach : Application on chemical processes Nelly Olivier-Mageta, Gilles Hétreuxa, Jean-Marc Le Lanna, Marie-Véronique Le Lannb,c a
Laboratoire de Génie Chimique (CNRS - UMR 5503), INPT-ENSIACET 118, route de Narbonne F-31077 Toulouse Cedex 04, France b CNRS ; LAAS, 7, avenue du Colonel Roche, F-31077 Toulouse France c Université de Toulouse ; INSA ; LAAS ; 135, avenue de Rangueil ; F-31 077 Toulouse, France
Abstract In this paper, we present a method for the fault detection and isolation based on the residual generation. The main idea is to reconstruct the outputs of the system from the measurement using the extended Kalman filter. The estimations are compared to the values of the reference model and so, deviations are interpreted as possible faults. The reference model is simulated by the dynamic hybrid simulator, PrODHyS. The use of this method is illustrated through an application in the field of chemical process.
Keywords: Fault Detection and Isolation, Extended Kalman Filter, Dynamic Hybrid Simulation, Object Differential Petri nets, Distance.
1. Introduction In a very competitive economic context, the reliability of the production systems can be a decisive advantage. This is why, the fault detection and diagnosis are the purpose of a particular attention in the scientific and industrial community. The major idea is that the defect must not be undergone but must be controlled. Nowadays, these functions remain a large research field. The literature quotes as many fault detection and diagnosis methods as many domains of application (Venkatasubramanian, et al., 2003). A notable number of works has been devoted to fault detection and isolation, and the techniques are generally classified as: • Methods without models such as quantitative process history based methods (neural networks (Venkatasubramanian, et al., 2003), statistical classifiers (Anderson, 1984)), or qualitative process history based methods (expert systems (Venkatasubramanian, et al., 2003)), • And model-based methods which are composed of quantitative model-based methods (such as analytical redundancy (Chow and Willsky, 1984), parity space (Gertler and Singer, 1990), state estimation (Willsky, 1976), or fault detection filter (Franck, 1990)) and qualitative model-based methods (such as causal methods: digraphs (Shih and Lee, 1995), or fault tree (Venkatasubramanian, et al., 2003)). In this paper, the proposed approach to fault detection and isolation is a model-based approach. The first part of this communication focuses on the main fundamental concepts of the simulation library PrODHyS, which allows the simulation of the system reference model of a typical process example. Then, the proposed detection approach is presented. This exploits the extended Kalman Filter, in order to generate a fault indicator. In the last part, this approach is exploited through the simulation of the monitoring of a didactic example.
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2. PrODHyS environment The research works performed for several years within the PSE research department (LGC) on process modelling and simulation have led to the development of PrODHyS. This environment provides a library of classes dedicated to the dynamic hybrid simulation of processes. Based on object concepts, PrODHyS offers extensible and reusable software components allowing a rigorous and systematic modelling of processes. The primal contribution of these works consisted in determining and designing the foundation buildings classes. The last important evolution of PrODHyS is the integration of a dynamic hybrid simulation kernel (Perret et al., 2004 ; Olivier et al., 2006, 2007). Indeed, the nature of the studied phenomena involves a rigorous description of the continuous and discrete dynamic. The use of Differential and Algebraic Equations (DAE) systems seems obvious for the description of continuous aspects. Moreover the high sequential aspect of the considered systems justifies the use of Petri nets model. This is why the Object Differential Petri Nets (ODPN) formalism is used to describe the simulation model associated with each component. It combines in the same structure a set of DAE systems and high level Petri nets (defining the legal sequences of commutation between states) and has the ability to detect state and time events. More details about the formalism ODPN can be found in previous papers (Perret et al., 2004).
3. The supervision module Nowadays, for reasons of safety and performance, monitoring and supervision have an important role in process control. The complexity and the size of industrial systems induce an increasing number of process variables and make difficult the work of operators. In this context, a computer aided decision-making tool seems to be wise. Nevertheless the implementation of fault detection and diagnosis for stochastic system remains a challenging task. Various methods have been proposed in different industrial contexts (Venkatasubramanian et al., 2003). 3.1. Architecture Reference Model
– Residual Extended Kalman filter
Process
Signature
+
+
Rebuilt Incidence – Matrix
Generation of Fault Indicator
Decision : occurency of fault(s)
ON LINE OFF LINE
Adjustment of the Extended Kalman filter Process and/or Faulty simulated system Reference Model
+ –
Residual
Incidence matrix: Theoretical fault signatures
Experience return
Figure 1. Supervision Architecture For this purpose, the simulation model of PrODHyS is used as a reference model to implement the functions of detection and diagnosis. The supervision module must be able to detect the faults of the physical systems (leak, energy loss, etc.) and the faults of the control/command devices (actuators, sensors, etc.). As defined in (De Kleer et al.,
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1984), our approach is based on the hypothesis that the reference model is presumed to be correct. The global principle of this system is shown in Figure 1, where the sequence of the different operations is underlined. Moreover, a distinction between the on-line and off-line operations is made. Our approach is composed of three parts: the generation of the residuals, the generation of the signatures and the generation of the fault indicators. 3.2. The generation of the residuals The first part concerns the generation of the residuals (waved pattern in the Figure 1). In order to obtain an observer of the physical system, a real-time simulation is done in parallel. So, a complete state of the system will be available at any time. Thus, it is based on the comparison between the predicted behavior obtained thanks to the simulation of the reference model (values of state variables) and the real observed behavior (measurements from the process correlated thanks to the Extended Kalman Filter). The main idea is to reconstruct the outputs of the system from the measurement and to use the residuals for fault detection (Mehra and Peschon, 1971, Welch and Bishop, 1995, Simani and Fantuzzi, 2006). A description of the extended Kalman filter can be found in (Olivier-Maget et al., 2007). Besides the residual is defined according to the following equation: ˆ (t ) − X (t ) X i rir (t ) = i avec i ∈ {1, n} (Eqn. 1.) X i (t )
ˆ is the estimated state variable with the extended where Xi is the state variable, X i Kalman Filter and n is the number of state variables. Note that the generated residual rir (t ) is relative. As a matter of fact, this allows the comparison of a residual of a variable with a residual of an other one, since the residual become independent of the physical size of the variable. 3.3. The generation of the signatures The second part is the generation of the signatures (doted pattern in the Figure 1). This is the detection stage. It determinates the presence or not of a default. This is made by a simple threshold, ε i (t ) . The generated structure S rN i (t ) is denoted by the following equation: S rN i (t ) =
[ (r (t ) − ε' (t )); 0 ] ∑ Max [ (r (t ) − ε' (t )) ; 0 ] Max
n
k =1
r i
i
r k
avec i ∈ {1, n}
(Eqn. 2.)
k
ε (t ) , where ε i is the detection threshold. The value of ε i is chosen with ε' i (t ) = i X i (t ) according to the model error covariance matrix of the Extended Kalman Filter. 3.4. The generation of the fault indicators The last part deals with the diagnosis of the fault (hatched pattern in the Figure 1). The signature obtained in the previous part is compared with the theoretical fault signatures by means of distance. A theoretical signature T•,j of a particular default j is obtained by experience or in our case, by simulations of the process with different occurency dates of this fault. Then, a fault indicator is generated. For this, we define two distances: the
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relative Manhattan distance and the improved Manhattan distance. The first distance is denoted by the following expression: n
∑ SirN (t ) − Tij
i =1 D Mr j (t ) =
(Eqn. 3.) n The second distance, which allows the diagnosis of many simultaneous faults, is denoted by the following expression: n
∑ SirN (t ) × m ′ − Tij × n ′ ⋅Tij
i =1 D Ma j (t ) =
(Eqn. 4.)
n′
where n ′ is the number of non-zero elements of the theoretical default signature T•,j and m ′ is the number of non-zero elements of the default signature S rN (t ) .
4. Application: the adding-evaporation unit operation 4.1. Description FB
Treactor
Ulmax
Ulmin A+B
xB
Reactor
Material Feed
T (K)
298,15
298,15
P (atm)
1
1
xA=eau
0,6
0,01
xB=méthanol
0,4
0,99
Ul (mol)
300
-
Flow rate (mol/min)
-
5
Figure 2. The studied process Table 1. The operating conditions The process of adding-evaporation is generally used to change solvents. Its recipe describes a succession of evaporations and adding of the new solvent. This process is studied here (Figure 2). The operation conditions are listed in the Table 1. The values of the minimum and maximum holdups are respectively 200 and 800 moles. Before each adding of solvent, the reactor is cooled up to the temperature of 300,15K. The pressure is supposed to be constant during this operation. The goal of this process is to have a molar composition of methanol in the reactor at 0,95. 4.2. Results The behavior of this process is governed by thermal phenomena. A default of the reactor thermal system can damage the success of this operation. That is why, it is important to detect it as soon as possible. 4.2.1. Detection results We remind that the thresholds for the detection correspond to the model uncertainties obtained by the adjustment of the Extended Kalman filter. A default of the reactor heating energy feed is introduced at t = 20 min. This energy feed provides a heat quantity lower than the nominal one. Figure 3 shows the detection stage. It illustrates the evolution of the residuals linked to the liquid composition of water and methanol. From t = 80 min, the values of the both residuals underline the abnormal behavior of the process. The diagnosis is launched at t = 95 min.
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Residual xeau résidu xeau 0,06 0,04
Residual xméthanol résidu xméthanol
Max threshold
Min threshold
The detection date of the default
The occurency date of the default
Residual
0,02 0 0
20
40
60
80
100
120
140
-0,02 -0,04 -0,06 Time (min)
Figure 3. The evolutions of the composition residuals during the evaporation stage s1
0,0044098
s2
0,49367559
s3
0,50191462
s4
0
s5
0
s6
0
s7
0
Table 2. The instantaneous fault signature
4.2.2. Diagnosis results The residual is then estimated and we obtain the corresponding instantaneous default signature (Table 2). Notice that the exploited signature in this approach is non binary, in order to quantify the deviation due to the default. The construction of the theoretical fault signatures is based on numerous simulations, in which one of the defaults exposed in the Table 3 is generated. We compare the instantaneous fault signature (Table 2) with the theoretical fault signatures, by calculating the relative and improved Manhattan distances (Eqn. 3. and 4.). Then, the fault indicators are generated (Table 3). They correspond to the complement to 1 of these distances. Manhattan relative indicator
Manhattan improved indicator
Default 1
The up holdup sensor detects a value higher than the nominal value.
0,71428571
0,605
Default 2
The up holdup sensor detects a value lower than the nominal value.
0,71554566
0,7254961
Default 3
The temperature sensor detects a value higher than the nominal value.
0,71428571
0,64
Default 4
The temperature sensor detects a value lower than the nominal value.
0,71554566
0,7104961
Default 5
The material feed provides material with a degraded flow rate.
0,71714286
0,645
Default 6
The heating energy feed of the reactor has a temperature lower than the nominal one.
0,71428571
0,645
Default 7
The heating energy feed provides a heat quantity lower than the nominal value.
0,99819303
0,75330735
Default 8
The energy feed used for the cooling of the reactor has a temperature higher than the nominal one.
0,71554566
0,7104961
Default 9
The energy feed used to the cooling of the reactor provides a heat quantity lower than the nominal value.
0,71428571
0,585
Table 3. The default indicators of the example
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The relative Manhattan indicator detects the presence of the fault 7 with a probability of 99,8%. Nevertheless, any default is discriminated, since their indicators are higher than 0,68. 0,69 is the fixed criterion, which corresponds to the probability at the standard deviation according to the normal distribution. In the opposite, with the improved Manhattan indicator, the defaults 1, 3, 5,6 and 9 are eliminated, since their indicators are lower than 0,68. The four possibilities are these defaults 2, 4, 7 and 8. This example underlines the importance to the use of the both indicators to be able to conclude. So, by combining the results of the both indicators, we can rule on the presence of the default 7, since their indicators are the maximums. For this reason, this default is the most probable. So, the default is located on the energy feed of the reactor. Furthermore, it has been identified: the heating energy feed of the reactor provides a heat quantity lower than the nominal value.
5. Conclusion In this research work, the feasibility of using the simulation as a tool for fault detection and diagnosis is demonstrated. The method developed in this PhD rests on the hybrid dynamic simulator PrODHyS. This simulator is based on an object oriented approach. The fault detection and diagnosis approach, developed here, is a general method for the detection and isolation of the occurency of a fault. Besides, this approach allows the detection of numerous types of fault and has the ability to underline the simultaneous occurency of many faults. The works in progress aim at integrating this simulation model within a model-based supervision system. The goal is to define a recovery solution following the diagnosis of a default. For this, we exploit the results of signatures in order to generate qualitative information. For example, with these results, we have the ability to distinguish a simple degradation and a failure. Next, we combine our diagnosis approach with an other method, such as classification or case-based reasoning.
References Anderson T.W. (1984). An introduction to multivariate statistical analysis, New York: Wiley Chow E.Y. and A.S. Willsky (1984). IEEE Transactions on Automatic Control, Vol. 29 (7), pp. 603-614 De Kleer J. and B.C. Williams (1987). Artificial Intelligence, Vol. 32, pp. 97-130 Frank P.M. (1990). Automatica, Vol.26, pp. 459-474 Gertler J. and D. Singer (1990). Automatica, Vol. 26, pp.381-388 Mehra R.K. and J. Peschon (1971). Automatica, Vol.5, pp. 637-640 Olivier N., G. Hétreux and J.M. LeLann (2007). Fault detection using a hybrid dynamic simulator: Application to a hydraulic system CMS’07; Buenos Aires, Argentina Olivier N., G. Hétreux, J.M. LeLann and M.V. LeLann (2006). Use of an Object Oriented Dynamic Hybrid Simulator for the Monitoring of Industrial Processes, ADHS’06, Alghero, Italia Perret J., G. Hétreux and J.M. LeLann (2004). Control Engineering Practice, Vol. 12/10, pp. 1211-1223 Simani S. and C. Fantuzzi (2006). Mechatronics, Vol.16, pp. 341-363 Shih R. and L. Lee (1995). Industrial and Engineering Chemistry Research, Vol. 34 (5), pp. 16881717 Venkatasubramanian V., R. Rengaswamy, K. Yin and S. N. Kavuri (2003). Computers & Chemical Engineering, Vol. 27, pp. 293-346 Welch G. and G. Bishop (1995). An introduction to the Kalman filter, Technical Report TR 95041, University of North Carolina Willsky A.S. (1976). Automatica, Vol. 12, pp. 601 – 611
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Computer Aided Operation of Pipeless Plants Sabine Piana and Sebastian Engell Process Dynamics and Operations Group, Department of Biochemical and Chemical Engineering, Technische Universität Dortmund, 44221 Dortmund, Germany
Abstract Pipeless plants are a new production concept in which automated guided vehicles transport the substances in mobile vessels between processing stations. Since several batches are produced in parallel, decisions have to be made on the scheduling of the production, on the assignment of the equipment and on the routing of the vessels. This paper describes the combination of an evolutionary scheduling algorithm with a simulation-based schedule builder. The new algorithm yields up to 16 % better solutions than an as-soon-as-possible scheduling heuristic. Keywords: Pipeless plant, evolutionary algorithms, simulation, scheduling.
1. Pipeless Plants Pipeless plants are an alternative to traditional multiproduct plants with fixed piping. Their distinctive feature is that the processing steps are performed at fixed stations and the substances are moved around in mobile vessels by automated guided vehicles (AGVs). The recipes determine the order in which a vessel must visit the different stations. The cleaning of the vessels is carried out in separate cleaning stations and the stations are cleaned in place. Pipeless plants offer a high degree of flexibility, e. g. by enabling a change of the priorities of the orders or the bypassing of a blocked station. The reduction of fixed piping results in up to 20 % less time for cleaning and sterilizing when a product changeover occurs compared to conventional batch plants [1]. Under the simplifying assumption of fixed and known processing times for the steps of the recipes, the optimal scheduling of a pipeless plant can in principle be determined by mixed-integer linear programming. However, due to the presence of the spatial dimension of the problem (the movement of the vessels in the plant, collision avoidance of the AGVs, parking of vessels in different locations that lead to different travel times), an exact solution is currently infeasible for realistic problem sizes. The option which we pursue in this paper is to combine a detailed simulation with embedded heuristics and routing algorithms of a pipeless plant with an optimization algorithm that determines the optimal sequence of processing steps. As evolutionary algorithms (EAs) can embed simulations as black-box computations of cost function values, we use an EA for the optimization. The EA only handles a subset of the degrees of freedom (the sequencing decisions), and the simulation algorithm takes the role of a schedule builder that generates a full schedule using additional information and heuristics. The paper is structured as follows. The next section describes the inter-dependent decision variables that have to be determined during the operation of a pipeless plant. Section 3 motivates and describes the use of an EA for the scheduling of the steps of the recipes. Special attention is paid to the handling of infeasibilities by repair algorithms
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and the evaluation of the individuals by the schedule builder in Sections 4 and 5, respectively. The results of the algorithm for three example problems are described in Section 6 and the paper concludes with an outlook to further research.
2. Problem Statement and Previous Work The increased flexibility of a pipeless plant comes at the expense of a higher degree of complexity. Knowing the product demand, the number and size of the batches, the recipes and the plant layout, our objective is to find a schedule with minimum makespan that is feasible with respect to a set of constraints. 1. A schedule must guarantee that the steps are executed according to the sequence prescribed by the recipes. 2. Each recipe step must be assigned to a vessel, an AGV and a station. The chosen equipment must be available at the desired time and has to be able to perform the required operations, i.e. to possess the necessary technical functions. 3. After the assignment, the selected AGV must pick up the vessel and transport it to the selected station. The AGVs must not collide with each other during transports. The time that a recipe step needs for its execution at a station may depend on the initial state of the material in the vessel. The mass and the temperature of the content of a vessel are therefore included as state variables in the simulation model. The scheduling of the recipe steps is the most important decision. It has mostly been tackled by mixed-integer linear or nonlinear programming. These methods have been combined with other techniques, for example with a discrete event simulator [2], with a queuing approach [3], or with constraint programming [4], to find optimal schedules. The operation of a pipeless plant can be modeled using different degrees of accuracy. In [4] it is assumed that the vessels possess their own transportation device. Then the assignment of a vessel to an AGV is not necessary. Also fixed travel times and fixed paths of the AGVs are assumed. Furthermore, the durations of the processing steps are assumed to be deterministic. In contrast to [4], in [1] a modeling and simulation software that represents the pipeless plant and the chemical processes in a detailed fashion is described where the problems mentioned above are solved simultaneously by heuristic algorithms. Shortest paths for the AGVs are calculated using the A* algorithm, path conflicts are resolved by a first-come-first-serve (FCFS) scheme and a production schedule is determined by an as-soon-as-possible (ASAP) heuristic. In this paper, we continue the detailed model in [1] with an evolutionary optimization algorithm.
3. Evolutionary Scheduling Algorithm An EA works with a set of candidate solutions to the optimization problem. A solution is referred to as an individual and a set of μ solutions is called the population. Each individual has a fitness value which shows how good the solution is with respect to the objective function. Ȝ new individuals are added to the population by recombination and mutation of existing individuals. The idea is that the new individuals inherit good characteristics from the existing individuals. The Ȝ worst solutions are removed from the population. After several iterations, which are called generations, the algorithm provides a population that comprises good solutions. In our case, the EA generates individuals which represent a fully ordered sequence of the recipe steps of all batches. To evaluate the fitness of the candidate solutions, the assignment of the equipment, the routing of the AGVs and a calculation of the durations of the recipe steps are carried out by the simulation algorithm of [1]. The recipe steps are identified by their batch IDs to maintain precedence relations in the recipes when
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steps are exchanged during recombination and mutation. Fig. 1 shows the idea by means of a small example. The order of the sequence indicates the priority of the recipe steps. Each entry directs the simulator to schedule the first unscheduled step of the corresponding batch as soon as possible without delaying higher-priority steps. Schedule Encoded By Batch IDs
Recipe Steps
A Batch A
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B
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3 Schedule Encoded By Recipe Step IDs
Batch B
4
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Fig. 1: Representation of an Individual
Since each batch ID must occur a certain number of times (as often as the number of recipe steps of the batch), a recombination operator that preserves permutations is applied. The two best individuals out of a set of randomly chosen individuals are selected from the population. Then a random segment is copied from the first individual into a new individual. The missing elements are filled with the entries of the second individual. The newly generated individual is then subject to mutation with a probability p. By mutation, two randomly chosen entries are exchanged.
4. Handling of Infeasibility There are several reasons for infeasibility of new individuals. Precedence violation in a recipe is avoided by the chosen representation of an individual. However, it is possible that a recipe step cannot be scheduled at its position in the sequence because no suitable station or empty vessel are available. We could deal with this infeasibility inside the simulator by postponing the currently infeasible recipe step and continuing with the next recipe step in the sequence. Alternatively, the infeasibility can be removed before passing the individual to the simulator. This is done by a repair algorithm that employs problem-specific knowledge on recipes, vessels and stations. We chose the second option since the repair algorithm can be designed to maintain the priorities of the recipe steps to a larger degree than by postponing infeasible assignments. The repair algorithm for occupied stations is explained by the example individual in Fig. 2. Suppose that there are only two charging stations in the plant. After the fourth recipe step (charging batch 3) both charging stations are occupied by batch 2 and batch 3. Therefore it is impossible to execute the next step (charging batch 4). A charging station must be freed first. The first recipe step in the sequence that frees such a station is the seventh entry (heating batch 3). By inserting this step before the currently infeasible step, batch 3 is moved from the charging station to the heating station and batch 4 can be processed. It must, however, be checked that a heating station is available at this point. If not, another repair is needed. It may also happen that there is no free vessel available to start a new batch. The repair algorithm moves all recipe steps of the batch which can currently not be started to a position after a batch has been finished and thereby frees a vessel. Note, that entries of the batch which occur behind this position, are not moved forward as this would violate the specified order of the priorities.
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2 charging stations available
insert
n := number of occupied charging stations charge 1
heat 1
n=1
charge 2
n=0
charge 3
n=1
n=2
charge 4
heat 3
mix 1
n=3
Fig. 2: Repair Algorithm for Occupied Stations
5. Evaluation of Individuals The software PPSiM (Pipeless Plant Simulation [1]) provides an environment to model a pipeless plant in a fast and intuitive manner and to perform simulation studies to compare design alternatives. The routing of the mobile vessels as well as variable durations of the processing steps are taken into account during the simulation. The program generates a production schedule according to a simple ASAP heuristic in which the recipe steps are scheduled in a chronological order according to their earliest possible start times. The solutions can be visualized as Gantt charts. The EA is embedded into PPSiM to perform an optimization of the decision variables. It interacts with the simulator in two ways. First, the simulator computes the ASAP solution. The initial population of the EA consists of multiple copies of this solution and other random solutions. Secondly, the simulator maps the sequence of recipe steps proposed by the EA into a feasible schedule and evaluates its fitness. The framework is shown in Fig. 3 where it can be seen which tasks are accomplished by the graphical interface, the simulator and the optimizer.
Problem Definition
Heuristic Solution
Initial Population
Visualization
Schedule Building
Check & Repair
Variation No
Best Solution
Evaluation & Penalty Graphical Interface PPSiM
SIMULATOR
Yes
Stop?
Selection
OPTIMIZER
Fig. 3: Simulation Optimization with an Evolutionary Scheduling Algorithm
6. Experimental Results This section reports on the experimental results that were obtained with the proposed approach on three case studies: a small problem, an industrial problem and a problem from the literature. In the small problem, two batches of a first product and two batches of a second product have to be produced. There are two AGVs, three vessels and one station for each of the technical functions required by the recipes. The problem is simple
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since neither timing constraints such as different starting times or deadlines nor much potential for routing conflicts are present. The second case study is an industrial problem. The plant under consideration produces a set of consumer care products. 7 batches of the same product and of the same sizes have to be produced. All batches can start at the same time. The underlying process is a mixing process in which various substances are charged and the material is mixed, heated and cooled. The production recipe defines 12 steps and has a linear structure. After the production process, all products have to be stored to determine the product quality by a laboratory analysis. Then the content is discharged (packed) and the vessel is cleaned. The plant area is divided into a production area, an intermediate storage and parking area, a discharging area, and a cleaning area. The production stations are arranged in a clockwise order to minimize the probability of collisions during the execution of the recipes. Finally a plant with a herringbone layout taken from [4] is treated. The authors of [4] assume that the recipe steps have fixed processing durations and that the AGVs move on specified paths with fixed transfer times. Thus, a detailed simulation of the processing steps and the routing of the AGVs are unnecessary. A difference to our simulation model is that the authors assign buffers to the stations at which AGVs can wait. It is possible to use these buffers as parking positions for empty and for clean vessels. We modeled the example without these buffers and instead defined parking positions at the side of the plant layout. To be able to compare the results, we subtract the time needed for these additional transfers from the makespan. This corresponds to 18 minutes per batch. Table 1 shows the relative improvement obtained by the proposed EA on the initial ASAP solution. The parameters of the EA were set to ȝ=10 and Ȝ=2. The probability of a mutation was 80 %. The results are reported for a set of five runs with a time limit of 60 seconds. It can be seen that the improvement for the simple problem is larger than for the industrial problem. The best solutions for the simple problem do not run many batches simultaneously. It is a weakness of the ASAP solution to start too many batches at once. Thereby vessels are blocking each other and stations can be occupied only later in time. For the industrial problem, however, it seems that the ASAP solution is already a good schedule so that the EA cannot improve it much. We suppose that this is due to the plant layout which minimizes the probability of collisions. Table 1. Improvement obtained by the Scheduling EA within 60 seconds Best run
Worst run
Median run
Simple
-16.3 %
-15.4 %
-16.1 %
Industrial
-2.4 %
-0.0 %
-1.0 %
Herringbone
-4.8 %
-3.9 %
-4.5 %
For the third example, our algorithm is compared to the results of the authors of [4] who solve the scheduling and sequencing problem by constraint programming (CP). It can be seen in Table 2 that it takes slightly more time to compute the heuristic ASAP solution than to find the first feasible solution by CP, but that the ASAP solution has a significantly smaller makespan. The EA improves the initial solution in less than half a minute to a solution which is very close to the optimum.
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1
CP Makespan
CPU time
2
Makespan
First solution
1.97 sec
46680 sec
0.1 sec
63720 sec
Best solution (Best run)
25.5 sec
44444 sec
722.6 sec
44280 sec
Best solution (Worst run)
10.5 sec
44844 sec
1: Pentium 4, 3 GHz, 512 MB RAM
2: P3500 MHz
7. Conclusion and Outlook Pipeless plants are an interesting alternative to standard multiproduct plants due to their flexibility and the potential to decrease the makespan of a production plan significantly. The optimization of a pipeless plant is treated in a hierarchical way. An EA schedules the production steps and a simulator with heuristics for the assignment of the equipment and for the routing of the AGVs is used as the schedule builder. In examples, the new scheduling procedure decreased the makespan by up to 16 % compared to a heuristic solution. For a problem from the literature we found a good first solution and the EA quickly returned a solution that is very close to the optimum. Our approach is therefore suitable for online applications where the fast computation of a good feasible solution is of prime concern. The simulation of the transfers is the most time consuming step in our approach. Many AGV paths have to be generated and eventually to be modified. In the future we plan to work with approximations to decrease the calculation time and to steer the algorithm more efficiently to good solutions. This can be done by evaluating the individuals exactly only after several generations of the algorithm. This may, however, result in infeasible individuals whose fitness is overestimated. An approach that circumvents this problem was proposed by [5] where the authors advise to evaluate the individuals first by an approximated simulation. Only promising individuals are then evaluated by the exact simulation. Individuals that are estimated to be of low quality are directly eliminated. Both schemes cause an uncertainty in the cost function of the EA. The tradeoff between the precision of the evaluation of the cost function and the computation times will be investigated in future work. In addition, it will be investigated whether the assignment of the equipment to the steps of the recipe can also be improved with reasonable computing times by using a second embedded EA for this task.
References 1. A. Liefeldt, 2008. Logistic Simulation of Pipeless Plants. In: S. Engell (Edt.), Logistics of Chemical Production Processes, 1st edn, Wiley VCH Verlag GmbH. 2. R. Gonzalez and M. Realff, 1998. Operation of pipeless batch plants – I. MILP schedules. Computers & Chemical Engineering 22 (7-8), 841 – 855. 3. D. Yoo, I.B. Lee and J. Jung, 2005. Design of Pipeless Chemical Batch Plants with Queueing Networks. Industrial & Engineering Chemistry Research 44, 5630 – 5644. 4. W. Huang and P. Chung, 2005. Integrating routing and scheduling for pipeless plants in different layouts. Computers & Chemical Engineering 29, 1069 – 1081. 5. J. April, F. Glover and M. Laguna, 2003. Practical Introduction to Simulation Optimization. Proceedings of the 2003 Winter Simulation Conference.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Off-line design of PAT* systems for on-line applications Ravendra Singha, Krist V. Gernaeyb, Rafiqul Gani †a a
CAPEC, bBioEng, Department of Chemical and Biochemical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark
Abstract In the manufacturing industry, for example, the pharmaceutical industry, a thorough understanding of the process is necessary in addition to a properly designed monitoring and analysis system (PAT system) to consistently obtain the desired end-product properties. A model-based computer-aided framework including the methods and tools through which the design of monitoring and analysis systems for product quality control can be generated, analyzed and/or validated, has been developed. Two important supporting tools within the framework are a knowledge base and a model library. The knowledge base provides the necessary information/data during the design of the PAT system and the model library generates additional or missing data needed for design. Optimization of the PAT system design can be achieved in terms of product data analysis time and/or cost of monitoring equipment subject to the maintenance of the desired product quality. Keywords: monitoring, quality control, process analytical technology, modelling
1. Introduction Today a significant opportunity exists to improve the product quality and to optimize the production process through the implementation of innovative system solutions for on-line monitoring, analysis and system control. Application of PAT systems (FDA/CDER, 2005) in manufacturing paves the way for continuous process and product improvements through improved process supervision based on knowledgebased data analysis, ‘Quality by design’ concepts, and through feedback control (Gnoth et al., 2007). Currently, one of the main difficulties in implementing PAT systems on a manufacturing process is the unavailability of methods and tools through which a PAT system can be designed in a systematic way. In this manuscript a model-based computer-aided framework is presented, including the methods and tools through which the design of monitoring and analysis systems (i.e., the PAT systems) for product quality monitoring and control can be generated, analyzed and/or validated.
2. Design Framework The design of a process monitoring and analysis system (note, from here on we will use the term ‘PAT system’ to refer to such a system) is a step-wise procedure involving the selection of critical process variables, followed by the selection and placement of suitable monitoring and analysis equipments, and finally, the coupling of the monitoring and analysis tools to a control system to ensure that the selected critical process * PAT: Process Analytical Technology † Corresponding author (
[email protected])
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variables can be controlled. As shown in fig. 1, the starting point for the design methodology is the problem definition in terms of process specifications and product quality specifications that can be provided either by the manufacturer or the PAT system designer. A model library and a knowledge base have been developed, and act as the supporting tools for the design of a PAT system. The ICAS-MoT modeling tool (Sales-Cruz, 2006) is used for simulation of process operational models and the systematic procedure proposed by Gani (Gani et al., 2006) is used for model analysis. As shown in fig.1, the developed design algorithm relates the available product and process specifications to the available supporting tools, and subsequently generates the PAT system. If the obtained PAT system satisfies the requirements then it is selected as the designed PAT system. The validation of the obtained PAT system is achieved by comparing the simulated process performance with known process specifications. If the process performance does not comply with the process specifications then the corresponding design steps are repeated until a satisfactory design is obtained.
Figure 1. Framework overview 2.1. Supporting Tools 2.1.1. Knowledge base The knowledge base contains useful information needed for design of PAT systems. It has been built through an extensive literature and industrial survey. It covers a wide range of industrial processes such as fermentation, crystallization and tablet manufacturing. It contains information for typical unit processes in terms of the type of operation they perform, the process variables involved, the corresponding manipulating variables (actuators), the equipments typically used for on-line measurement of data (type of equipment, accuracy, precision, operating range, response time, resolution, drift, cost etc.). 2.1.2. Model library The model library contains a set of mathematical models for different types of unit processes, sensors and controllers. Similar to the knowledge base, it covers a wide range of industrial processes (fermentation, crystallization, tablet manufacturing). These models support process analysis and help to generate additional or missing data needed to obtain the design of a PAT system. For example, the models can be applied for the prediction of process variables which are not measurable but required for the final design. Simulations with the models can also be used for performing a sensitivity analysis through which the effect of process variables on the final product properties can be analyzed and critical process variables can be identified. The simulation models
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fermentation. Analyzing the effect of process variables on the fermentation operation shows that the pH violates the lower and upper limit of the optimal pH range in open loop (see fig. 4), indicating thereby that it needs to be controlled throughout the fermentation process. Repeating this procedure for all process variables yields the following critical variables: temperature, pH, DO, dissolved CO2, homogeneity in the fermentor and temperature in sterilizer and homogeneity in the mixing tank. 0.16
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Figure 3. Profile of operational objective
Figure 4. Critical process variable (pH)
DO(%change)
3.5. Interdependency analysis Interdependency analysis is performed for each critical process variable to select the actuator. For example, the dependency of the DO concentration (response variable) on the air flow rate & stirrer speed (sensitivity parameters) is shown in fig 5. The air flow rate is more sensitive compared to the Interdependency analysis 12 stirrer speed and thus the air flow rate is Air flow rate selected as an actuator for DO control. 10 Stirrer speed Repeating the procedure for all critical 8 control variables yields actuators as M ore sensitive 6 follows: coolant flow rate for temperature, Less 4 ammonia flow rate for pH, air flow rate sensitive for DO and dissolved CO2, stirrer speed 2 for homogeneity control in the fermentor, 0 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 steam flow rate for heat sterilization Parameter (% change) temperature control and stirring duration Figure 5. A ctuator selection for D O for homogeneity in the mixing tank. 3.6. Performance analysis of monitoring tools The performance of available monitoring tools (obtained from the knowledge base) for each measured variable is compared and monitoring tools are selected as follows: Thermocouple for temperature, electrochemical sensor for pH, optical sensor for DO and dissolved CO2, and NIR for homogeneity. 3.7. Proposed process monitoring and analysis system A feasible alternative of the process monitoring and analysis system is shown in fig. 6. Within the fermentor, the DO concentration, pH, temperature and homogeneity need to be monitored and controlled. Temperature in the heat sterilizer and homogeneity in mixing tank also need monitoring and control. The aeration intensity used for DO control also influenced the dissolved CO2 concentration so it is not needed to control this variable explicitly. The critical process variables, corresponding monitoring tools and actuators are shown in fig. 6. The response time of the selected monitoring tools is
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selected control variable. In this analysis the effect of process parameters on the individual selected critical process variable is compared. A special feature (Sales-Cruz and Gani, 2006) of ICAS-MoT can be used for this analysis. First, the response variable and the sensitivity parameters are selected. Then these parameters are perturbed and the effect of each parameter on the response variable is analyzed. The process parameter which has the most significant effect on the considered critical process variable (response variable) is selected as the actuator for that variable. At the moment only SISO control is considered in the design methodology. The possibility to also select more advanced multivariable control systems in the PAT system design will be included in the future. 2.2.4. Performance analysis of monitoring tools The performance analysis of the process monitoring tools is performed to select the appropriate monitoring tools for each measurable critical process variable. The measurement equipment for each measured critical process variable is selected from the knowledge base, where one is able to list all the available sensors included in the knowledge base for that variable. The performance of different types of measurement equipment can be compared. The monitoring tool is then selected on the basis of one or more of the following performance criteria: accuracy, precision and resolution, sensor drift, response time and cost and operating range. The type of performance criterion selected is application specific.
3. Case study: Fermentation process - Design of PAT system The process flow sheet is adopted from the literature (Petrides et al., 1995) (see fig. 6). 3.1. Product property specifications The desired product from the fermentation process is E. coli cells. At the end of the fermentation process, the assumed E. coli cell concentration is 30 g/liter (dry cell weight) in which the protein content is assumed to be 20% of the dry cell mass. The composition (mass basis) of the outlet stream from the fermentor comprises 2.95% biomass, 4.00% glucose, 0.58% salts, and 92.46% water. 3.2. Process specifications The basic raw materials required include: starting culture (E. coli cells), nutrients (glucose and salts), tryptophan, water, ammonia and air. The process equipment includes: fermentor, mixing tank, continuous heat sterilizer, centrifugal compressor, air filter and storage tank. 3.3. Process analysis The process analysis provides the following list of process variables: temperature in the fermentor, pH in fermentor, dissolved oxygen (DO) in the fermentor, dissolved CO2 in the fermentor, coolant flow rate, coolant temperature, ammonia flow rate, stirrer speed in the fermentor, stirrer speed and stirring duration in the mixing tank, air flow rate to the fermentor, heat sterilization temperature, steam flow rate in sterilizer, stirrer speed in the mixing tank and stirring duration, cell growth rate, heat of reaction, substrate concentration, biomass concentration in the fermentor, homogeneity in the fermentor, homogeneity in the mixing tank 3.4. Sensitivity analysis The operational objective for the fermentation step is to maximise the specific cell growth rate. Open loop simulations (fig. 3) show that the value of the specific growth rate is considerably lower than the maximum specific growth rate throughout the batch
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fermentation. Analyzing the effect of process variables on the fermentation operation shows that the pH violates the lower and upper limit of the optimal pH range in open loop (see fig. 4), indicating thereby that it needs to be controlled throughout the fermentation process. Repeating this procedure for all process variables yields the following critical variables: temperature, pH, DO, dissolved CO2, homogeneity in the fermentor and temperature in sterilizer and homogeneity in the mixing tank. 0.16
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Figure 4. Critical process variable (pH)
DO(%change)
3.5. Interdependency analysis Interdependency analysis is performed for each critical process variable to select the actuator. For example, the dependency of the DO concentration (response variable) on the air flow rate & stirrer speed (sensitivity parameters) is shown in fig 5. The air flow rate is more sensitive compared to the Interdependency analysis 12 stirrer speed and thus the air flow rate is Air flow rate selected as an actuator for DO control. 10 Stirrer speed Repeating the procedure for all critical 8 control variables yields actuators as M ore sensitive 6 follows: coolant flow rate for temperature, Less 4 ammonia flow rate for pH, air flow rate sensitive for DO and dissolved CO2, stirrer speed 2 for homogeneity control in the fermentor, 0 -18 -15 -12 -9 -6 -3 0 3 6 9 12 15 18 steam flow rate for heat sterilization Parameter (% change) temperature control and stirring duration Figure 5. A ctuator selection for D O for homogeneity in the mixing tank. 3.6. Performance analysis of monitoring tools The performance of available monitoring tools (obtained from the knowledge base) for each measured variable is compared and monitoring tools are selected as follows: Thermocouple for temperature, electrochemical sensor for pH, optical sensor for DO and dissolved CO2, and NIR for homogeneity. 3.7. Proposed process monitoring and analysis system A feasible alternative of the process monitoring and analysis system is shown in fig. 6. Within the fermentor, the DO concentration, pH, temperature and homogeneity need to be monitored and controlled. Temperature in the heat sterilizer and homogeneity in mixing tank also need monitoring and control. The aeration intensity used for DO control also influenced the dissolved CO2 concentration so it is not needed to control this variable explicitly. The critical process variables, corresponding monitoring tools and actuators are shown in fig. 6. The response time of the selected monitoring tools is
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also shown in the figure, which shows that the selected monitoring tools are robust enough to allow for successful implementation of the control system.
Figure 6. Fermentation process flow sheet with designed PAT system. c: controller, R: response time, T90: time for 90% response, NIR: near infrared, [ ]: indicates the reference number in the knowledge base‡
4. Conclusions A well-designed PAT system is essential to obtain the desired product quality consistently. In this work we proposed a model-based computer aided framework including the methods and tools for systematic design of PAT systems. The application of the developed framework and methodology was demonstrated through a fermentation process case study. The developed framework and methodology are generic: the proposed systematic approach to the design of a PAT system is complimentary to traditional process design, and should thus have a broad application range in chemical and biological processes.
References FDA/CDER, 2005, PAT, Process Analytical Technology (PAT) Initiative, U.S. Food and Drug Administration, Center for Drug Evaluation and Research, http://www.fda.gov/Cder/OPS/PAT.htm Gani, R., Muro-Suñé, N., Sales-Cruz, M., Leibovici, C., & Connell, J. P. O. (2006). Fluid Phase Equilibria, 250, 1-32. Gnoth, S., Jenzsch, M., Simutis, R., & Lübbert, A. (2007). Journal of Biotechnology, 132 (2), 180-186. Petrides, D., Sapidou, E., & Calandranis, J. (1995). Biotechnology and Bioengineering, 48 (5), 529-541. Sales-Cruz, M. (2006). Development of a Computer Aided Modelling System for Bio and Chemical Process and Product Design. PhD. Thesis, CAPEC, Department of Chemical Engineering, Technical University of Denmark. Sales-Cruz, M., & Gani, R. (2006). ChERD, 84 (A7), 583-594. ‡
[9]http://www.rmprocesscontrol.co.uk/Electrochemical-sensors/pHPLUS-Electrodes.htm [50] http://www.in-situ.com/In-Situ/Products/TROLL9500/TROLL9500_RDO.html [60] http://195.173.150.81/Process_16_2.pdf, [107] http://www.smartsensors.com/spectherm.pdf
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
New Method for Sensor Network Design and Upgrade for Optimal Process Monitoring Miguel J. Bagajewicz, DuyQuang Nguyen and Sanjay Kumar Sugumar School of Chemical, Biological and Materials Engineering, University of Oklahoma, Norman, OK 73069
Abstract Previous methods on nonlinear sensor network design minimize cost subject to a variety of constraints linked to the network performance: precision, residual precision, error detectability and resilience. In recent work, the use of accuracy as an attribute of a network that can replace precision, error detectability and resilience more effectively has been considered. In this paper, we propose a sensor network design methodology based on accuracy thresholds. Keywords: Software Accuracy, Sensor Networks, Instrumentation Network Design.
1. Introduction In contrast with the use of objective functions such as observability or reliability that had been used, Bagajewicz (1997, 2000) formulated a mixed integer nonlinear programming to obtain sensor networks satisfying the constraints of residual precision, resilience, error detectability at minimal cost. A tree enumeration was proposed where at each node the optimization problem of the different characteristics are solved. To reduce the computational time Gala and Bagajewicz (2006a), proposed the tree enumeration approach based on branch and bounding, using cutsets. To make the computation more effective, especially for large scale problems, Bagajewicz and Gala (2000b), proposed a decomposition procedure where the process flow diagrams are decomposed to reduce the number of cutsets used for the enumeration. Non linear networks have been discussed by Nguyen and Bagajewicz (2007), where they resort to an equation based approach using bipartite graph as opposed to regular directed graphs and show that the concept of cutsets needs further modification. They explore the use of variable enumeration in an inverted order that is removing sensors from a fully instrumented network, as opposed to adding sensors to a sensor-empty network. This strategy proved efficient for networks with stringent requirements of precision, error detectability and resilience. All the above work focused on minimizing network cost using precision, residual precision, error detectability and resilience constraints. In this work we also minimize network cost, but we use software accuracy (as defined by Bagajewicz, 2005), which replaces all the above network attributes, as a constraint. We first review accuracy and we then discuss issues of the methodology involved to calculate accuracy at each node. We finish with an example.
2. Software Accuracy Accuracy has been conventionally defined as the sum of absolute value of the systematic error and the standard deviation of the meter (Miller, 1996). Since in the absence of hardware or software redundancy the systematic errors cannot be detected, this conventional definition is not practical. Bagajewicz, (2005) defined accuracy with
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respect to the gross error detection scheme used to identify gross errors, thus differentiating software accuracy from hardware accuracy. Specifically, Bagajewicz (2005) considered that the presence of gross systematic errors δ induces biases in all streams through the use of data reconciliation. These induced biases are given by
δˆ = [I − SW ]δ
(1)
where, W = A T (ASA T )−1 A , matrix A is the incidence matrix and matrix S is the variance-covariance matrix of measurements. The case considered is the linear case. He then defines accuracy as the sum of precision and the maximum undetected aforementioned induced bias.
aˆ i = σˆ i + δ i∗ where aˆ i
δ i∗
(2)
and σˆ i are the accuracy, the maximum undetected induced bias and the
precision (square root of variance , Sˆ ii ) of the estimator, respectively. Next, he proposed to calculate the maximum undetected induced bias under the assumption that the maximum power test would be used in a serial elimination procedure. Thus, the maximum induced bias that will be undetected is given by (Bagajewicz, 2005):
( p) ( p) δˆi( p ,1) = Max δˆcrit ,i , s = Z crit Max ∀s
[(I − SW )is ]
∀s
(3)
Wss
In the presence of nT gross errors in positions given by a set T, the corresponding induced bias in variable i is ( p) ]i = δ crit( p),i − ¦ (SW ) is δ crit( p),s δˆi( p ) = [[I − SW ]δ crit
(4)
s∈T
where
( p) is the vector containing a critical value of the gross error size in the selected δ crit
positions corresponding to the set T at the confidence level p. In order to find the maximum possible undetected induced bias, one has to explore all possible values of gross errors in the set. Thus for each set ‘T,’ he proposed to define a binary vector ‘qT’ to indicate the location of gross errors and obtain the maximum induced and undetected bias by solving the following problem: ½½ δˆi( p ) (T ) = Max ®δ crit ,i qT ,i − ¦ ( SW )is δ crit , s qT , s ¾° ∀s ¯ ¿° ° s.t (5) ° ¾ Wks ( p) ° ∀k δ crit , s qT , s ≤ Z crit ¦ ° W ∀s kk ° ° ∀k qT ,k δ crit ,k ≥ 0 ¿
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The absolute value constraint can be replaced by two inequalities, one for the negative sign and one for the positive one. The problem becomes a linear one. Thus for nT=2, the feasible region has a form of a rhombus, as in Figure 1. The rhombus is composed of positive and negative constraints of the problem that arise from the absolute value. We recognize that the solution lies in one of the four corners, which depends on how the two gross errors in question contribute to the induced bias
Both θ1 & θ2 are detected
θ2
Only θ2 is detected δ2
−δ1 = −
ξ
Both θ1 & θ2 are detected
ξ Wi 2i 2
ξ
Z2 = ξ
W 'i1i1
Wi1i1
No gross error - δ1
δ1
is detected
Only θ1 is detected
Z1 = ξ - δ2
Both θ1 & θ2 are detected
−δ 2 =
−ξ
Only θ2 is detected
W "i 2i 2
θ1 Only θ1 is detected Both θ1 & θ2 are detected
Figure 1. Different regions when two gross errors are present in the system (From Nguyen et al, 2006) Worth noticing, in some cases the above set of equations can be linearly dependant. This happens when the set of gross errors proposed in an equivalent set (Jiang and Bagajewicz, 1998). We illustrate this for the system of Figure 2. S2
S1
S3 Figure 2. Equivalency of gross errors Assume that one wants to compute the induced bias in stream S1 by considering two biases in S2 and S3. This leads to two parallel lines, as it is illustrated in Figure 3. θ2
Undetected region θ1
Figure 3. Graphical consequence of biases equivalency
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It can be inferred from figure 2 and clearly shown in figure 3 that if the bias in stream S2 and bias in stream S3 are equal but in opposite side (such that the balance S1 = S2 + S3 is still valid), then those biases cannot be detected no matter how big they are.
3. Calculation of Software Accuracy at each node of the search tree In this work, we use the tree enumeration method using list of fundamental units, which can be variables (Bagajewicz, 1997) or cutsets (Gala and Bagajewicz, 2006a, b) or equations (Nguyen and Bagajewicz, 2007). At each node, software accuracy needs to be evaluated based on two inputs: 1. 2.
The positions of the sensors (given by a binary vector q). We assume there are n sensors. The maximum number of gross errors (nT) the user is willing to consider in the definition of accuracy.
Thus, if nT >n, the maximum number of gross errors is assumed to be n, that is nT=n. When n=nT , only one system of equations needs to be solved, and if nT
4. Example We consider the process illustrated in Bagajewicz, (2005) (Figure 4) that has 7 streams and 4 nodes. F4 F1
F2
F3
F5
F7
F6 Figure 4. Flowsheet for example
We assume we need accuracy of 3% in stream 1 and 2% in stream 2 allowing only one gross error (nT=1). The sensor precisions, flowrates and sensor costs are given table 1. Table1. Precision, Flow rates, Sensor Cost of Example 1
Stream S1 S2 S3 S4 S5 S6 S7
Sensor Precision (ıi) 1 0.447 1 1 1 1 1
Flow Rates (Fi) 100 140 140 20 120 20 100
Sensor Cost 20 25 20 15 20 10 30
The above problem was solved by using the tree enumeration algorithm to find the accuracy values at each node and compare with the desired accuracy. It is found that the
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optimal solution is obtained only when all the streams but S7 and S2 are measured. The network cost is 85. It is also of interest to study the way accuracy changes as sensors are added. This is shown in Table 2 and Figure 5. This would correspond to the first branch of the enumeration tree (no branching criteria used). Table 2. Accuracy and Cost as a function of the number of sensors
Streams measured 1 1,2 1, 2, 3 1, 2, 3, 4 1, 2, 3, 4, 5 1, 2, 3, 4, 5, 6 1, 2, 3, 4, 5, 6, 7 Optimal Solution 1, 3, 4, 5, 6
Accuracy (ai) % S1= 1223.69 S2= 979.46 S1= 531.09 S2= 385.93 S1= 531.09 S2= 1.56 S1= 385.38 S2= 1.57 S1= 385.39 S2= 1.28 S1= 2.67 S2= 1.24 S1= 1.55 S2= 1.23 S1= 2.79 S2= 1.99
Cost of the network 20 45 65 80 100 110 140 85
Figure 5. Accuracy vs. Number of Streams Measured
We consider now the case of two gross errors in the system (nT=2). In this case, several equivalencies of gross errors can appear and therefore many combinations of errors lead to unbounded accuracy. Table 3 shows only the nodes of the tree that do not show unbounded results. Clearly, in this problem, one needs to measure all streams if accuracy is to be below 2.8 and 2.0 for streams S1 and S2. Only one node with 6 streams qualifies for a requirement of accuracy below 3.3 and 2.5 for streams S1 and S2 respectively. All other bounded nodes exhibit accuracies that are unacceptable. This is
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something that error detectability used together with precision constraints cannot capture. Situations with 3 or more gross errors will be discussed in future work. Table 3. Accuracy and Cost as a function of the number of sensors (nT=2) Streams measured Cost Accuracy (ai) % Any 2 measurements Any 3 measurements (1,2,5) 4 Measurements (1,2,3,5) 4 Measurements (1,2,5,7) or (1,3,5,7) 5 Measurements (1,2,3,6,7) 6 Measurements (1,2,3,4,5,7) 6 Measurements (1,2,3,4,6,7) 6 Measurements (1,2,3,5,6,7) All measurements
65 85 95 105 130 120 125 140
S1= unbounded S2= unbounded S1= 797.07 S2= 557.53 S1= 770.07 S2= 283.01 S1= 396.71 S2= 557.92 S1= 391.32 S2= 284.15 S1= 396.71 S2= 2.198 S1= 3.264 S2= 2.446 S1= 3.136 S2= 283.149 S1= 2.748 S2= 1.98
5. Conclusions A method incorporating software accuracy to design sensor networks was presented. We highlighted the importance of gross error equivalency (Bagajewicz and Jiang, 1998) in determining accuracy. Thus, we conclude that networks prone to have more than one bias need to be heavily instrumented if all reasonable biases are to be detected so that software accuracy is reasonable. Acknowledgement: Support from a Grant from the Petroleum Research Fund PRF # 45603-AC9 is acknowledged.
References M. Bagajewicz, 1997, “Design and Retrofit of Sensor Networks in Process Plants”, AIChE Journal, Vol. 43, No. 9 M. Bagajewicz, 2000, “Process Plant Instrumentation: Design and Upgrade”, Technomic Publishing Company, Inc, Lancaster, PA. M. Bagajewicz, 2005, “On the definion of Software Accuracy in Redundant Measurement Systems”, AIChE Journal, Vol. 51, No. 4. M. Bagajewicz, M. Gala, 2006a, “Efficient Procedure for the design and Upgrade of Sensor Networks using Cutsets and Rigorous Decomposition”, Ind. Eng. Chem. Res., Vol. 45, No. 20. M. Bagajewicz, M. Gala, 2006b, “Rigorous Methodology for the Design and Upgrade of Sensor Networks using Cutsets”, Ind. Eng. Chem. Res., Vol. 45, No. 20. M. Bagajewicz and Q. Jiang, 1998, “Gross Error Modeling and Detection in Plant Linear Dynamic Reconciliation” Comput. Chem. Eng., 22, 12, 1789-1810. M. Bagajewicz, D. Nguyen, 2007, submitted for publishing, “Design of Nonlinear Sensor Networks for Process Plants”. R. W. Miller, 1996. Flow Measurement Engineering Handbook, McGraw-Hill, New York. S. Narasimhan and C. Jordache, 2000, Data Reconcialiation & Gross Error Detection: An Intelligent Use of Process Data”, Gulf Publishing Company, Houston, TX. D. Nguyen Thanh, K. Siemanond, and M. Bagajewicz, 2006. On the determination of downside financial loss of instrumentation networks in the presence of gross errors. AIChE Journal. Vol 52, No 11, pp. 3825-3841.
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A Novel Proactive-Reactive Scheduling Approach In Chemical Multiproduct Batch Plants Elisabet Capón, Georgios M. Kopanos, Anna Bonfill, Antonio Espuña and Luis Puigjaner Chemical Engineering Department, Univesitat Politècnica de Catalunya, Av. Diagonal 647, E08028, Barcelona, Spain. Email:
[email protected]
Abstract This work addresses the challenge of combining the proactive and reactive scheduling approaches for enhanced management of chemical multiproduct batch plants under uncertainty. First, a reactive MILP continuous-time scheduling model is adopted from previous contributions [1]. Afterwards, in order to make feasible the comparison between reactive and proactive approaches, the former model is appropriately reformulated into an equivalent proactive scheduling model. Both approaches are compared through several case studies in order to shed light on their specific features by using a performance criterion that provides quantitative measures of their respective efficiency. From this comparison originates the development of a new scheduling approach which aims to take advantage of the major assets of these two different scheduling approaches dealing with uncertainty. The resulting scheme endeavors to tackle unforeseen events more efficiently and to improve the decision-making process in the scheduling of chemical multiproduct batch industries. Future work will focus on validation and further improvement of the proposed strategy. Keywords: reactive scheduling, proactive scheduling, multiproduct batch plants, uncertainty, MILP model
1. Introduction Scheduling is a critical decision-making procedure in chemical process industries. Its vital role in the performance of the whole supply chain network is strongly emphasized by a large number of authors. Chemical process industries are dynamic in nature and, therefore, different kinds of unexpected events, such as equipments breakdowns, changes in processing and/or setup times, inadequacy of raw materials, due date modifications, order cancellations and price changes, occur quite frequently. Underestimating uncertainty and its impact can lead to decisions that neither safeguard a company against threats, nor take advantage of eventual opportunities that higher levels of uncertainty may provide [2]. Therefore, deterministic studies considering nominal plant operating conditions and production capacity during the whole time horizon are not the most appropriate to deal with the real scenario. Nowadays, two approaches are mainly used to deal with uncertainty in process industry environments: proactive and reactive scheduling. Proactive scheduling allows to fully exploit the flexibility of the process and, consequently to meet production goals to a
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higher degree. However, it requires information to characterize the uncertainty and incorporate it into the scheduling process. Additionally, it disregards the possibility to react to new information in the future, thus reducing the optimization capabilities [3]. As a result, if the revealed uncertainty is not taken into account in the initial representation then significant disturbances and infeasibilities may appear in scheduling process thus affecting the performance and the effectiveness of the whole supply chain entity. On the other hand, reactive scheduling modifies the predictive schedule to adjust it to changes to production environment. Uncertainty is dealt on-line and scheduling decision-making is based on updated plant information; however, this is not always possible. In some cases, operations are not flexible enough to adapt the process to the proposed changes. Moreover, it entails an additional computing cost, and the use of sophisticated optimization methods which are still limited. Most of the literature considers only one of the aforementioned approaches at a time, and little research is focused on their integration. Therefore, combining reactive scheduling and an approach that accounts for uncertainty can be a promising direction [4]. The aim of this work is to encompass both methods and compare their effectiveness to deal with uncertainty thus suggesting a hybrid proactive-reactive approach. This work proceeds as follows. First, a reactive model is derived from that proposed by Méndez and Cerdá [1]. Secondly, the proactive equivalent formulation is generated. Next, a more realistic new evaluation criterion is defined. Then, two case studies are presented and their results analyzed. Finally, the proposed solution approach considering the integration of both reactive and proactive models is described and evaluated.
2. Reactive MILP model In this section, the reactive scheduling model used in this work is presented. This model represents a modified version of the MILP continuous-time formulation previously published [1]. Unit reallocation and resequencing of orders are both permitted. The assignment constraints Eq.(1) must be posed for those orders that can be reassigned (IA). Moreover, timing constraints Eq.(2) to Eq.(5), must be met by orders that can be either reassigned (IA) or resequenced (IS). In addition, sequencing constraints among the different kind of orders must be established: Eq.(6) to Eq.(12). Finally, the objective function is defined by Eq.(13).
¦Y
ij
1 i IA
(1)
j JRi
i IS, j J iold
Tsi t max ª¬ ru j ,roi º¼
i IS, j Jiold
Tfi t Tsi +ptij +suij Tsi t
¦ max ª¬ru
j
j JRi
Tfi t Tsi
,roi º¼ ·Yij
¦ pt +su ·Y ij
j JRi
ij
ij
(2) (3)
i IA
(4)
i IA
(5)
A Novel Proactive-Reactive Scheduling Approach in Chemical Multiproduct Batch Plants
Tfi sudii ' j d Tsi ' M 1 X ii '
i IS, i ' ISi ' i , i i ', j Jiold , j Jiold '
Tfi ' sudi ' ij d Tsi MX ii ' Tfi sudii ' j d Tsi '
i IS, i ' ISi ' i , i i ', j Jiold , j Jiold '
old i ISi ' i , i ' IS, i i ', j Jiold , j Jiold Riold ' , Ri '
437
(6) (7) (8)
Tfi sud ii ' j d Tsi ' M 1 X ii ' +M 1 Yi ' j i IS, i ' IA, i i ', j J iold JRi (9) Tfi ' sud i ' ij d Tsi MX ii ' +M 1 Yi ' j
i IS, i ' IA, i i ', j J iold , j JRi
(10)
Tfi ' sud i ' ij d Tsi MX ii ' +M 2 Yi ' j Yij
i , i ' IA, i i ', j JIi , j JIi '
(11)
Tfi sud ii ' j d Tsi ' M 1 X ii ' +M 2 Yi ' j Yij
i , i ' IA, i i ', j JIi , j JIi '
(12)
Ti t Tfi Di
i ;
Ei t Di - Tfi
min D i E i E iTi
i ;
(13)
3. Proactive MILP model This section contains the proposed proactive MILP scheduling model equivalent to the already presented reactive model. Uncertain processing times, unit set-up times and breakdown time points and durations are taken into account. This is a two-stage scenario-based model, whose first-stage variables belong to allocation and sequencing, and second-stage are processing times. Moreover, an additional second-stage binary variable, Vbis, is introduced, in order to consider those orders to be processed after a breakdown occurs. Assignment constraints and timing constraints are given by Eq.(14) and Eq.(15), respectively. The finishing times constraints are given by Eq.(16) and Eq.(17); the same pair of constraints, here omitted due to space limitations, should be applied for starting times as well. Finally, Eqns.(18) and (19) are sequencing constraints. The considered objective function is the same as in the previous model.
¦Y
ij
1 i
(14)
j JIi
Tfis Tsis t
¦ max ª¬ru
,roi º¼ pt ij suij ·Yij
i , s
(15)
Tfis t Tb js Tb rep i , j JB, s js MVbis M 1 Yij
(16)
Tfis d Tb js Tb rep i , j JB, s js M 1 Vbis M 1 Yij
(17)
j JIi
j
Tfis sud ii ' j d Tsi ' s M 1 X ii ' M 2 Yij Yi ' j i JIi , i ' JIi ' , i i ', j ,s
(18)
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Tfi ' s sud i ' ij d Tsis MX ii ' M 2 Yij Yi ' j i JIi , i ' JIi ' , i i ', j ,s
(19)
4. Evaluation criterion Proactive and reactive scheduling approaches are two different strategies aimed at dealing with unexpected events in the plant. In this work, an evaluation criterion is established in order to make feasible the aforementioned comparison. The proposed metric consists of a combination of the already stated objective function, OF, plus a rescheduling cost, weighted by the plant operational cost. Therefore, the evaluation criterion metric is given by Eq.(20).
OF DTs RC ·Costoper
CReval
(20)
The total starting time deviation of all batches from the original schedule, which was first considered as a schedule stability measure by Wu et al [5], is given in Eq.(21). DTs
¦ Ts i
' i
(21)
Ts i
The reallocation cost is defined as the product of the number of reallocated orders and a weighting fraction, Ȗ, of the OF value. RC Nreal ·J ·OF (22)
5. Case studies An example taken from Pinto and Grossmann [6] is used as the case study. A total of 15 single-stage orders and 4 processing units are considered. Regarding the proactive approach, a total of 45 scenarios taken by Monte Carlo sampling, with the same probability of occurrence, with 5 different processing times, 3 set-up times, and 3 breakdown time points, Tb, of different duration, Trb, in a given unit are considered. The mathematical models have been implemented in GAMS 22.3, CPLEX (9.0). It is assumed that an unexpected event unveils along the time horizon. If the proactive schedule results infeasible, the right-shifting policy is applied to it. This schedule is compared with the reactive one for the nominal scenario. Both schedules are compared in terms of the proposed evaluation criterion, Eq.(20) excluding operational costs for the sake of simplicity. Two main cases are presented. Firstly, the unveiled uncertainty is considered in the scenarios of the proactive approach (Table 1); secondly, uncertainty unveils partially out of the considered range (Table 2). Scheduling Approach
Tb = 12+3
Tb = 19+4
Tb = 22+2
OF DTs RC CReval (%) OF DTs RC CReval (%) OF DTs RC CReval (%)
Proactive + 4.1 5.1 Rightshifting 3.7 5.3 0.4 Reactive
9.2 9.4
-2.0
28.5 8.1
-
36.6
27.2 10.4 5.4 43.0
-14.9
36.5 9.6
-
46.1
28.7 10.1 5.7 44.5
Table 1. Example with unveiled uncertainty considered in the proactive scenarios.
3.7
A Novel Proactive-Reactive Scheduling Approach in Chemical Multiproduct Batch Plants
Scheduling Approach
Tb = 11+6
Tb = 20+5
439
Tb = 25+4
OF DTs RC CReval (%) OF DTs RC CReval (%) OF DTs RC CReval (%)
Proactive + 4.1 6.7 - 10.8 48.5 12.1 - 60.6 14.2 Rightshifting 3.7 5.3 0.4 9.4 37.2 12.3 7.4 57.0 Reactive
6.3
28.5 5.3
-
33.9
67.5
13.6 3.9 2.7 20.2
Table 2. Example with unveiled uncertainty beyond the range of the proactive scenarios.
Results for the first case are shown in Table 1. The reactive model objective function has a lower value than that obtained from the proactive approach. This stems from the fact that unit reallocation is allowed in the reactive model; which permits further improvement in the objective function. In case the uncertainty unveils in the time range of the proactive model scenarios, it seems that the closer to the beginning of the time horizon the uncertainty unveils, the better evaluation criterion values in the proactive approach. However, the closer to the end of the time horizon, the better the reactive model schedules performs. If uncertainty is not in the range of the proactive model scenarios (Table 2), the reactive approach gives better evaluation criterion values in all cases. The last scenario in Table 2 is an extreme case and demonstrates the superiority of the reactive model (a 67,5% better) if the uncertainty takes place very close to the end of time horizon (Fig. 1).
Figure 1. Unveiled uncertainty at time point 25 days.
6. Proactive-Reactive control scheme In order to combine the proactive and reactive scheduling approaches, a proactivereactive control scheme is proposed in Fig. 2, based on the results obtained in the previous sections. The aforementioned scheme aims to encompass the advantages of both approaches. It has been assumed that only one unexpected event takes place in the whole time horizon. The algorithm starts by solving the proactive model and applying the resulting schedule into the plant. Then it performs the schedule and, along the time horizon, it checks if an uncertainty unveils. If not, the algorithm ends; otherwise, it checks whether the uncertainty is contained into the proactive model scenarios. If so and the current schedule is feasible, it goes on performing the initial schedule. In case that the current schedule is unfeasible, right-shifting is applied and the result is sent to the plant. If the
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unveiled uncertainty is not considered in any proactive model scenario, then the reactive model is solved using as objective function the evaluation criteria previously proposed. Therefore, the reactive approach results are closer to the reality because they take into account the cost of deviation from initial times and the cost of reallocation. The obtained schedule is sent to the plant, and simultaneously, the proactive model with the new objective function is solved again for a time period TPR ahead of the time point where the reactive schedule is applied. This TPR is selected according to the complexity of the problem. The proactive model excludes the orders that have already begun processing according to the already implemented reactive schedule. Finally, the reactive and the new proactive schedules are compared, and the best model is chosen according to the decision-making procedure of keeping the reactive model or changing it with the new proactive one.
7. Conclusions In this work, a comparison between proactive and reactive approaches has been carried out in terms of a new proposed evaluation criterion that considers earliness and tardiness, as well as rescheduling costs. This cost takes into account the total deviation from initial starting times and a batch reallocation cost which is proportional to the objective function. According to the presented case studies, the further from initially considered values uncertainty unveils, the better the reactive schedule performs according to the evaluation criterion. On the contrary, if uncertainty unveils as forecasted, and early in the time horizon, the best choice is the proactive approach. Future work will be focused on the validation and further improvement of the proactive-reactive control scheme.
Acknowledgements
Figure 2. Proactive-reactive scheme
Financial support received from Ministerio de Educación y Ciencia (FPU-grants) is fully appreciated.
References [1] C. Méndez, J. Cerdá, Comps Chem. Eng., 27 (2003) 1247 [2] A. Gupta, C. Maranas, Comps Chem. Eng., 27 (2003) 1219 [3] S. Engell, A. Market, G. Sand, R. Schultz, C. Schulz, Ch. Onl. Opt. Lar. Sca. Sys., (2001) 649 [4] Z. Li, M. Ierapetritou, Comps Chem. Eng., (2007) (In press) [5] S. Wu, R. Storer, P.C. Chang, Comps Oper. Res., 20 (1993) 1 [6] J.M. Pinto, I. Grossmann, Ind. Eng. Chem. Res., 34 (1995) 3037
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Model Predictive Control of the Waste Water Treatment Plant Based on the Benchmark Simulation Model No.1-BSM1 Vasile-Mircea Cristea, Cristian Pop, Paul Serban Agachi Babes-Bolyai University, 11 Arany Janos Street, 400028 Cluj-Napoca, Romania
Abstract Control of the WWTP is not a trivial task since the unit is nonlinear, features large time constants and delays, and interaction between variables is important. Model Predictive Control algorithm is a good candidate for such demanding task. The paper presents the results for controlling the WWTP using MPC. The Benchmark Simulation Model No.1BSM1 has been used as a standard for performance assessment and evaluation of the control strategy. Control of the Dissolved Oxygen in the aerated reactors and nitrate level in the anoxic compartments has been performed using the MPC control strategy. Air flow rate in the aerated reactors and internal recycle flow have been chosen as manipulated variables. The obtained results show the incentives of MPC over classical PI control with respect to overshoot and time response. A combined feedbackfeedforward MPC scheme is also proposed for disturbance rejection and its incentives are shown. Keywords: MPC, WWTP, BSM1.
1. Introduction As the public awareness of environmental problems increases and the environmental legislation gets stricter, the Waste Water Treatment Plant (WWTP) operating requirements are becoming more and more demanding. WWTPs protect local ecosystems against increased load of waste products and waste disposal, preventing waste accumulation in lakes, rivers or underground waters. Degradation of organic material present in wastewaters consumes the oxygen inventory and the lack of oxygen may affect the living organisms. Even if most of the organic components are removed prior to accumulation in receivers, there are other chemical species, such as phosphorous and nitrogen, that are still present and may produce eutrophication, which is also a source of the oxygen consumption. Consequently, the WWTP has to remove the organic components and the suspended solids but also to reduce the nitrogen and phosphorous to an acceptable content. Usually, a WWTP consists in a mechanical treatment step where filters remove larger objects and particles, followed by the chemical-biological treatment steps where chemicals and microorganisms remove organic matter and reduce the nitrogen and phosphorous content from wastewaters. The most widespread biological treatment process is the activated sludge process, where microorganisms (bacteria, fungi, protozoa, and rotifers) are used for oxidizing organic material and nitrogen removal. A wide range of municipalities and industries that treat wastewater containing organic chemicals, petroleum refining wastes, textile wastes, and municipal sewage uses the activated sludge process. The active sludge process converts dissolved and colloidal organic contaminants into biological sludge, further removed by settling. For nitrogen
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removal the activated sludge process consists in both aerated and non-aerated (anoxic) reactors. In the aerated reactors the bacteria oxidize ammonium to nitrate by the socalled nitrification process. In the anoxic reactors bacteria change nitrate into nitrogen, using oxygen present in the nitrate ions. This transformation is denoted as the denitrification process. The demanding operating requirements may be only obtained, especially for large wastewater treatment units, by appropriate control techniques intended to keep the operation of the unit at the most efficient working regime. Model Predictive Control (MPC) is a good candidate for these challenging control tasks.
2. Model description and model predictive control approach The Benchmark Simulation Model No.1-BSM1 has been used as a standard model [1], based on the most popular Activated Sludge Model No.1 (ASM1) developed by the International Association on Water Pollution Research and Control, for modelling and for performance assessment and evaluation of the control strategy [2]. The schematic representation of the WWTP is presented in Fig.1.
Figure 1: WWTP activated sludge process with predenitrification.
As presented in Fig.1 the nitrogen removal is achieved using a first denitrification step performed in the anoxic tanks, placed before the aerated basins where the nitrification step is carried out. The unit consists in five biological reactor tanks connected in series. The first two anoxic tanks are assumed perfectly mixed and have a volume of 1000 m3 each. The rest of the three aerated tanks have a volume of 1333 m3 each. They are all modelled according to the ASM1 model. Eight different processes are modelled, involving thirteen state variables. An internal recycle from the last tank to the first one is used to supply the denitrification step with nitrate. The last tank has to reduce the Dissolved Oxygen (DO) concentration before the recycled water is fed back to the first anoxic tank. For the secondary settler the one-dimensional ten-layer system implementing the double exponential settling velocity model has been used [3]. In order to investigate the control performance for disturbance rejection a set of three different weather conditions, i.e. dry weather, stormy weather and rainy weather, have been considered in special designed disturbance influent input files. The dynamic model succeeds to capture the main dynamic features of the biological wastewater treatment unit, needed for the control investigations. Model Predictive Control, also referred as moving or receding horizon control, has become an attractive control strategy especially for linear but also for nonlinear systems subject to input, state or output constraints [4]. MPC determines the control action based
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on the prediction of future dynamics of the system, allowing early control action to be taken in order to accomplish the control performance based on the expected future behaviour. The incentives of MPC algorithm, compared to traditional control algorithms, are associated to the need the system usually has for satisfying input, state or output constraints. These constraints put limitations on the achievable control performance, but this task is systematically managed by the MPC optimisation objective (with associated constraints), compared to the ad-hoc solutions frequently used in conventional control. The MPC algorithm used for the control of the wastewater treatment unit uses the combination of feedback and feedforward control design in order to reduce the effects of the large time constants shown by the process.
3. Results of the MPC and PID control approach Control of the WWTP is difficult because the unit is nonlinear, features large time constants and pure delays, and interaction between variables is important [5]. The lack of feasible measuring instrumentation and the strong disturbances acting on the unit during changing weather conditions result in influent composition and flow rate upsets that make the control of the WWTP even more challenging. Advanced control strategies, such as Model Predictive Control, are needed to obtain good control performance. Available manipulated variables for the nitrogen removal are: air inlet flow rate in the aerated compartments, internal recycle flow rate, sludge recycle flow rate and eventually, the external carbon dosage. The first two of them will be used in the present study. In the traditional decentralized control approach the air flow rate is employed for the control of the DO concentration in the aerated reactors, since the autotrophic nitrification bacteria development may be directly affected. The internal recycle flow rate influences the supply of nitrate for the denitrification process but also the DO concentration in the anoxic reactors, since DO may be also transported from the aerated reactors. It becomes obvious that, due to interactions, a multivariable control strategy would bring better performance, compared to the classical decentralized PID approach. For the beginning, the decentralized approach has been implemented with two PI control loops in order to have a reference to which the MPC performance may be compared. The two control loops are: control of the DO level in the last aerated reactor to a setpoint value of 2 g/m3 by manipulating the air inlet flow rate of the same reactor (in fact, the oxygen transfer coefficient KLa, constrained to a maximum value of 10 h-1) and control of the nitrate level in the second anoxic reactor to a setpoint value of 1 g/m3 by manipulating the internal recycle flow rate (constrained to a maximum value of 92230 m3/day). The tuning parameters of the two PI controllers are those recommended in the Cost Simulation Benchmark [1]. Control results of the PI decentralised approach will be further presented together with the MPC results, for the case of the dry weather input disturbance scenario. The dynamic simulator and the control simulations have been implemented on the Matlab/SimulinkTM platform. The second investigated control approach is based on the MPC algorithm, aimed to control the same output variables (nitrate and DO concentrations) by manipulating the same (air and internal recycle) flow rates. The control set-up is presented in Fig.2.
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Figure 2: MPC feedback control scheme.
Comparison between the PI decentralized control and MPC control of the nitrate and DO concentration is presented in Fig. 3 and Fig. 4. Nitrate concentration [g/cubic meter]
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MPC control PI control
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0
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Figure 3: Comparison between MPC and PI control of the nitrate concentration. 4.5
MPC control PI control
DO concentration [g/cubic meter]
4 3.5 3 2.5 2 1.5 1 0.5 0
0
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4
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Figure 4: Comparison between MPC and PI control of the DO concentration.
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The WWTP control results presented in Fig.3 and Fig.4 show the superiority of the MPC nitrate concentration control compared to the PI control. Although the MPC DO concentration control is less effective, compared to PI control, it may be assessed that the overall MPC control performance for disturbance rejection is superior to the case of the PI control approach. This conclusion may be drawn on the basis of the relative small offset introduced by the MPC of DO concentration compared to the important reduction of the offset brought by MPC of the nitrate concentration. For the MPC multivariable controller a sampling time of T=5 min has been used. The prediction horizon has been of p=200 and the control horizon of m=10. The appropriate MPC controller tuning has been achieved by simulation. For further improvement of the control performance the MPC feedforward-feedback control structure is proposed. The nitrate and DO concentrations in the inlet flow of the first anoxic reactor are measured and used for feedforward control, while the nitrate concentration in the second anoxic reactor together with the DO concentration in the last aerated rector are used for feedback control. The combined feedforward-feedback MPC is presented in Fig.5.
Figure 5: MPC feedforward-feedback control scheme.
Results of the MPC feedforward-feedback MPC are presented in Fig.6 and Fig.7. A detailed representation, extracted from the 14 days simulation of the WWTP control, is shown for revealing incentives of the proposed control approach. 1.06 Feedforward-feedback MPC Feedback MPC
2.1 DO concentration [g/cubic meter]
Nitrate concentration [g/cubic meter]
Feedforward-feedback MPC Feedback MPC
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2.05 2 1.95 1.9 1.85 1.8 1.75
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Figure 6: Nitrate feedforward-feedback MPC.
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Figure 7: DO feedforward-feedback MPC.
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Results presented in Fig.6 and Fig.7 show an improvement of the nitrate concentration control for the case of the feedforward-feedback MPC, compared to feedback MPC resulting in diminished overshoot, smaller offset and shorter settling time. For the DO concentration the improvement is not important. The feedforward-feedback MPC controller has been used with the same tuning parameter values as for the feedback MPC case. MPC control approach shows its incentives over the classical decentralized PI control due to the intrinsic capability of counteracting interactions between controlled variables, the use of future process behaviour predictions for computing the control actions, the straightforward implementation of the combined feedforward-fedback control setup, the capability of systematic constraints handling and its optimal feature, all as a result of directly involving the process model in the MPC control law.
4. Conclusions The presented MPC control performance of the nitrate concentration in the second anoxic reactor and the DO concentration control in the last aerated reactor of the predenitrification WWTP have shown improved results compared to the traditional decentralised PI control. The multivariable feedback MPC controller provides an effective improvement of the WWTP operation aimed to organic and ammonium pollutants removal, proved in the presence of the dry weather disturbance programme of the Cost Benchmark WWTP BSM1. Although the feedback MPC control approach presents favourable performance, the combined feedback-feedforward MPC control approach succeeds to accomplish superior control performance, shown by its short setting time and reduced overshoot and small offset. Further development of the feedforward-feedback MPC approach for controlling a larger number of the WWTP variables is straightforward. As MPC control may successfully work in the presence of constraints, for both manipulated and controlled variables, the proposed control design outperforms the traditional control approach and reveals incentives for its practical implementation.
Acknowledgements Funding from grants CEEX 112 and PN 71-006 is gratefully acknowledged.
References [1] J.B Copp (Ed.), 2002, The COST Simulation Benchmark-Description and Simulation Manual, Luxembourg: Office for Official Publications of the European Communities. [2] H. Henze, C.P.L. Jr. Grady, W. Gujer, G.V.R. Marais, 1987, T. Matsuo, A general model for single-sludge Wastewater Treatmant systems, 1987, Wat. Res., 21(5), 505-515. [3] I. Takaks, G.G. Patry, D. Nolasco, 1991, A dynamic model of the clarification thickening process, Wat. Res., 25(10), 1263-1271. [4] M.V. Cristea, S.P. Agachi, V. Marinoiu, 2003, Simulation and Model Predictive Control of a UOP Fluid Catalytic Cracking Unit, Chem. Eng. and Proc., 42, 67-91. [5] M. Yong, P. Yongzhen, U. Jeppsson, 2006, Dynamic evaluation of integrated control strategies for enhanced nitrogen removal in activated sludge process, Contrl. Eng. Prac., 14, 1269-1278.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Load balancing control system of a furnace from atmospheric distillation unit Cristian Pătrăúcioiua, Sanda Mihalachea a
Petroleum Gas University of Ploiesti, 100680, Bd. Bucuresti, Romania
Abstract The furnace from the atmospheric distillation unit represents an example of heat transfer equipment with big capacity, with two parallel passes. Because of constructive imperfections and non-uniformly heat transfer, the difference between the two passes becomes significant. This paper presents the results of research in studying, modeling and simulating the control systems for load balancing. The paper is structured in four parts. The first part presents the main issues regarding load balancing control for multiple parallel passes. The second part is dedicated to the proposed structure design of the load balancing control system for the furnace from atmospheric distillation unit. The third part contains the developing of a specific control algorithm. The fourth part contains the tests made by the authors for tuning the designed controller using the control system model and simulations and presents the implementation of the structure design of the load balancing control system for the furnace from atmospheric distillation unit.
Keywords: tubular furnaces, load balancing control, dynamic simulations.
1. Operating issues of tubular furnaces with multiple parallel passes The process specifications on raw material speed through furnaces coils imposed the use of two or four parallel passes, e.g. the furnaces from the atmospheric distillation unit, vacuum distillation unit, catalytic reforming unit, coker unit, catalytic cracking unit. The conventional control structure of radiant section for a typical tubular furnace from the atmospheric distillation unit (output capacity 3.5 Mt/year) is presented in figure 1 [1]. Because the conventional temperature control system only controls one outlet temperature or in the best case the temperature of the mixing point, in current operations there are several situations [1, 2, 3]: 1. One of the outlet temperatures is bigger than the setpoint for the associated pass. This situation leads to a growing coking and cracking phenomena on this coil. Under conditions, the vaporized fraction diminishes, affecting the light oils efficiency. 2. One of the outlet temperatures is smaller than the setpoint for the associated pass, this leads to a reduction of the vaporized percent from the raw material, reducing the plant efficiency. World-wide there were developed and implemented control structures that solve particular problems of load balancing control [4, 5, 6]. This paper presents the results of research in studying, modeling, simulating and implementing the control systems for load balancing.
2. Proposed control system structure The structure of a load balancing control system mainly depends on the particularities of the constructive furnace [7, 8]. The literature study and also the research in the Romanian refineries over the last 15 years have led to the following stages in designing the control system: a) designing the control structure; b) generating control algorithm;
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Fig. 1. The conventional control structure of a furnace from the atmospheric distillation unit.
c) mathematical modeling of the control system; d) digital simulating and tuning of the controllers; e) industrial testing of the proposed control system. In figure 2 there is presented the proposed control system structure for load balancing control for two parallel passes furnaces. The control system for load balancing in the atmospheric distillation unit furnace must accomplish the following functions: − control the throughput of the furnace; − load balancing of the two parallel passes. The throughput control function is accomplished by B1, B2, S1, S2, S3 and S4 blocks. The throughput controller has as setpoint the total flowrate M i . The total flowrate processed within furnace is computed with sum S2, the error ¨Md is computed in S1 sum, and B2 block equally divides the throughput variation for the two parallel passes. The load balancing function is achieved by S3, S4, S5, S6 and B3 modules. The S6 comparator computes the temperature difference from the two passes, and the B3 block computes the setpoint for the first pass, m1i . The flowrate setpoint for the second pass is calculated by S5 sum. The S3 and S4 sums are intended to form the flowrate setpoints for the two parallel passes. For each pass, the flowrate setpoint is formed by two components: one generated by the load balancing control system and the other generated by the throughput control system. The measured process variables are: T1, T2 – passes temperatures; m1, m2 – volume flowrates of the two passes.
3. The control algorithm The control algorithm consist in two parts: the first part is dedicated to temperature balancing for parallel multiple passes and the second part is for total flowrate control. 3.1. The load balancing control algorithm This algorithm is based on eliminating the effect of error, defined as e = T1 − T2 ≡ ΔT ,
(1)
where T1,T2 represent parallel passes temperatures at the output of the radiant section. The elimination of the effect of the error is achieved with a PI control algorithm. The command u of the PI controller is the flowrate setpoint of the first pass of furnace, u = m1i , and the second flowrate setpoint is computed with relationship m2i = M − m1i .
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Fig. 2. The proposed control system structure.
3.2. The total flowrate control algorithm The total flowrate M, processed in furnace is computed as the sum of the measured flowrates m1 and m2, M = m1 + m2 , and controlled with the two flowrate control systems on each pass. The setpoint of the total flowrate controller, i = M i , is applied in a temporized manner such as
M
di
1 t i ° M dt , t < τ = ®τ 0³ °M i , t ≥τ ¯
(2)
The setpoint variation ΔM d = M di − M , makes the corrections of the total flowrate. This action is equally divided between the two parallel passes.
4. The control system model and simulation The control system is composed of the process subsystem (tubular furnace) and the control equipment. The control system model is obtained from each subsystem model. 4.1. The process model The process model is represented by the heat transfer and the mixing process of the two heated parallel passes (figure 3). The input variables of the process are: the thermal duties on the two parallel passes, QTi , i = 1, 2 , and the associated volume flowrates, mi , i = 1, 2 . The mathematical model of the furnace is composed of the model associated to each coil and the model of the mixing node with temperature Te: ap
QT dTi + Ti = i , i = 1,2 ; dt cmi
[°C]
(3)
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Fig. 3. The block scheme of the mathematical model of the tubular furnace.
Te =
m1T1 + m2T2 , m1 + m2
[°C]
(4)
where ap is the time constant of the transfer process, c – the thermal coefficient. 4.2. The control equipment model The control equipment model is composed of three temperature transducers models and two control valves models, each model defined by a
dy + y = bx , dt
(5)
where a is the specific time constant, y – the output variables, b – the gain factor, x – the input variables. The control equipment model is completed by the pass balancing controller model and the temperature controller model. 4.3. The control system simulation In order to simulate the mathematical model of the control system there is required that the model constants and the initial conditions of the control system are specified. The disturbances applied to the control system consist in de-balancing the temperatures of the two parallel passes. In this way, the thermal duty of the first parallel pass is bigger than the second pass duty so that the total thermal duty remains unchanged and the mixing node temperature as well. The settling time of control system is presented in figure 4. The control system response is damped oscillating, being characterized by the following qualitative parameters: the maximum dynamic error, ΔTmax = max T1 (t ) − T2 (t ) , and the oscillations damping period, τ amort , corresponding to an error ΔT (t ) ≤ 2 °C .
4.4. The controller tuning The PI controller, dedicated to the load balancing and throughput control, has two tuning parameters: the proportional gain Kp and integral time Ti. A proper functioning of the control system requires a good tuning of the software controller. According to the simulated results, the quasi-optimum tuning parameters of the controller are: K p = 2.5 and Ti = 1 min. These values ensure a maximum dynamic error of oscillation damping period of 2.7 min.
5°C and an
5. Implementing the control system The proposed control system is applied to the atmospheric distillation unit furnace. In figure 5 there is presented the proposed solution for implementing the control system.
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Fig. 4. The damped oscillations response to the changes of disturbances.
The authors have implemented and tested the proposed control system in a Romanian petroleum refinery. In figure 6 there is presented the capture of an industrial test. The difference between the temperatures of the two passes is over 20°C in the case of no load balancing control. At the moment when the control system is activated, this difference drops bellow 4°C, which is the resolution of the diagram from figure 6. As shown in figure 6, the test was done with the main temperature control system (of the heated product) on manual mode. Compared to some existing multivariable control packages the proposed method uses a controller design procedure that does not need high level of expertise. Completing the control structure with total outlet temperature loop, the results proved the efficiency of proposed method that can be extended to larger number of passes.
6. Conclusions An industrial furnace with multiple parallel passes and multiple burners is commonly used in petroleum refineries to heat the preprocessed oil to a specific temperature.
Fig. 5. The implementing the load balancing control system for the furnace from the atmospheric distillation unit: BC – the balancing controller.
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Fig. 6. The results of the industrial test. In order to maintain the furnace running in a safe, stable, and high-efficiency state it is necessary to control the outlet temperatures of the multiple passes to be the same. Traditional control methods usually have difficulties in controlling these temperatures, and some advanced control methods are too complex for a convenient use. In this paper, a control technique is proposed to distribute the inlet flowrates so that the outlet temperatures are as identical as possible. The principle of the proposed method is firstly explained and demonstrated, then the system analysis, the controller design, and the simulation experiments are presented, and finally the results of application to an industrial refinery furnace are reported. This technique has the following advantages: it does not need complicated design procedures, the controller structure is simple, it is easy to apply and it can be extended to furnaces with different number of passes.
References [1] C. Pătrăúcioiu, Automatic optimization of fuel combustion in tubular furnaces (in Romanian), PhD Thesis, Petroleum-Gas University of Ploiesti, Romania (1994). [2] X. Wang, D.Z.Zheng, Load balancing control of furnace with multiple parallel passes, Control Engineering Practice, Volume 15, Issue 5 (2007). [3] M.E. Masoumi, S.M. Sadrameli, J. Towfighi, A. Niaei. Simulation, optimization and control of a thermal cracking furnace, Energy Volume 31, Issue 4 (2006). [4] * * * Advanced Process Control Handbook 2, Hydrocarbon Processing, March (1987). [5] * * * Advanced Process Control Handbook 3, Hydrocarbon Processing, March (1988). [6] * * * Advanced Process Control Handbook 4, Hydrocarbon Processing, March (1989). [7] S. Frâncu (Mihalache), Modern control of a balancing furnace system. Proceedings of 2-nd Technical & Scientifical Session, Universities from România & Moldova, Ploieúti, Romania (1999). [8] Del Vale El Cid J. L. Bessere Automatisierung mit neuen Systemen, Regelungstechniche Praxis, Jahrgang, (1981).
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Optimal operation of sublimation time of the freeze drying process by predictive control: Application of the MPC@CB Software N. Daraoui, P. Dufour, H. Hammouri, A. Hottot Université de Lyon, F-69000,, Lyon, France; Université Lyon 1, F-69622, Lyon, France CNRS, UMR 5007, LAGEP (Laboratory of Process Control and Chemical Engineering), 43 bd du 11 novembre,F- 69622 Villeurbanne, France
[email protected]
Abstract This paper presents the application of a model based predictive control strategy for the primary stage of the freeze drying process, which has not been tackled until now. A model predictive control framework is provided to minimize the sublimation time. The problem is directly addressed for the non linear distributed parameters system that describes the dynamic of the process. The mathematical model takes in account the main phenomena, including the heat and mass transfer in both the dried and frozen layers, and the moving sublimation front. The obtained results show the efficiency of the control software developed (MPC@CB) under Matlab. The MPC@CB based on a modified levenberg-marquardt algorithm allows to control a continuous process in the open or closed loop and to find the optimal constrained control. Keywords: Freeze drying, moving boundary, non linear distributed parameter systems, model based predictive control, internal model control.
1. Introduction Freeze drying is a separation process in biotechnology, food and pharmaceutical industries, frequently used to stabilize and preserve the products [1-2]. Compared with conventional drying techniques, freeze drying is generally considered to produce highest quality dried products. In freeze drying, major costs being apportioned are: the energy for sublimation of frozen solvent during the primary drying stage, the energy for the removal (desorption) of bound (unfrozen) solvent during the primary and secondary drying stages, the energy to support vacuum and labor, and overhead costs which are all a function of the drying time. Moreover, one very important parameter in the study of freeze drying is the temperature of the product which must carefully be controlled during the primary and the secondary stages of freeze drying. A number of freeze-drying models have been published in the literature to describe the freeze-drying process. The model of Liapis and Litchfield [3] was seen to be more accurate than the model of King [4]. The sublimation model was then improved upon [5] by including the removal of bound water in equations. This model is commonly known as the "sorption-sublimation model". Various numerical methods can be used to solve the governing equations. Liapis and co-workers used a one-dimensional method which the method of orthogonal collocation [6] was applied to solve the equations. Ferguson et al. [7] used the finite element method to solve the governing equations.
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Very few papers deal with the on-line optimal control of freeze drying. The optimal control of the primary and secondary drying stages of bulk solution freeze drying in trays was formulated and solved by [8]. The contribution of this paper is therefore to provide a model predictive control (MPC) framework, as applied in [9], to minimize under constraints the drying time during the primary stage of the freeze drying process of Bovin Serum Albumin (BSA) solution, a formulation whose physical data are available and freeze drying were already carried out. To satisfy this purpose, a control software (MPC@CB) is used, allowing solving any other constrained optimal control problems for any processes. The dynamics of the moving sublimation ice front and the temperature profiles of the product are presented here.
2. Freeze drying process Freeze-Drying is a drying process where the solution is first frozen, thereby converting most of the water to ice, and the ice is removed by sublimation at low temperature and low pressure during the primary drying stage of the process. Since freeze drying is the most complex and expensive technique of drying, its use is usually restricted to delicate heat sensitive products. In the pharmaceutical industry, the solution is normally filled into glass vials, the vials are placed on temperature controlled shelves in a large vacuum chamber, and the shelf temperature is lowered to freeze the product. After complete solidification, the pressure in the chamber is lowered to initiate rapid sublimation. To carry out the objective of this paper, we consider a one-dimensional freeze drying model based on the work of Liapis and Sadikoglu [8]. During the primary drying, the vial contains two regions: a dry layer, in which the majority of water was sublimated and a frozen layer. These two areas are separated by a moving interface called the sublimation front. In this work, it is assumed that [5]: • One dimensional heat and mass transfer. • The sublimation front is planar and parallel to the horizontal section of the vial. • The gas phase inside the pores of the dry layer is composed only of pure water vapor, i.e. the effect of inert gas is negligible because the amount of inert gas in the drying chamber is much smaller than that of water vapor. • The value of the partial pressure of water vapor at the top of the dry layer is equal to the total pressure in the sublimation chamber. • The frozen region is considered to be homogeneous with uniform thermal conductivity, density and specific heat. The mathematical model consists of the unsteady state energy balance in the dried and frozen regions: ∂T1 c pg ∂ ( N wT1 ) ΔH v ρ1 k ∂ 2T1 = 1e − − , t > 0 , 0 < z < H (t ) k C ° 2 ∂z ρ1e c p1 ∂z ρ1e c p1 ρ1e c p1 d sw ° ∂t ° 2 ° ∂T2 = α ∂ T2 , t > 0 , H (t ) < z < L 2 ° ∂t ∂z 2 ® 1 ° dH ° dt = − ρ − ρ N w , t > 0 , z = H (t ) 2 1 ° ° ∂Csw = − k d Csw t > 0 , 0 < z < H (t ) ° ¯ ∂t
(1)
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Where T1 is the dried layer temperature, T2 is the frozen layer temperature, Nw is the mass transfer flux of the water vapour, Csw is the bound water and H is the sublimation interface. The different parameters of the model are presented in [12]. In this work, we use a simplified equation to describe the dynamic of the mass flux based on the diffusion equations of Evans. The equation is given by the following expression:
Nw =
−Mwk1 ( pH − p0 ), t > 0 RigT1H
(2)
Where p0 and pH is the partial pressures of water vapor at z=0 and z=H(t) respectively. The pressure boundary condition at the top surface of the material being dried is defined as a constant pressure inside the drying chamber, and the vapor pressure at the sublimation interface is defined as an equilibrium vapor pressure according to the temperature of the interface. The initial conditions for the equation (1) are given by:
T1(z, t) = T2 (z, t) = T o °° + ®H(t) = 0 ° 0 °¯Csw (z, t) =Csw
for 0 ≤ z ≤ L , t = 0 for t = 0
(3)
for 0 ≤ z ≤ L , t = 0
The boundary conditions for the equations (1) are as follows: ∂ T1 ° − k1e ∂ z = q1 , t > 0, z = 0 ° °° ρ 2 c p 2T2 − ρ1c p1T1 ∂ T1 ∂ T2 § = − k2 + ¨ −Δ H s + ® − k1e ¨ ∂z ∂z ρ 2 − ρ1 ° © ° ° − k 2 ∂ T2 = q 2 t > 0, z = L , ∂z ¯°
· ¸¸ N w , ¹
t > 0, z = H ( t )
(4)
Where Tlp(t), Tup(t) are respectively the temperatures of the lower and upper heating plates. For general freeze dryers, the temperature of the upper and lower heating plates are the same, i.e. Tlp(t)=Tup(t). The important objective of the on-line control is to decrease the drying time under constraints, while maintaining the quality of the product. Furthermore, an important constraint for primary drying is that one must never allow the product temperature to exceed its glass transition temperature. This constraint can be expressed by:
T2 ( z , t ) ≤ Tg ,
H (t ) < z < L , ∀t > 0
(5)
The output variable of the process considered in our control problem corresponds to the measured temperature at the bottom of the vial. In the sequel, it is assumed that only the process output is constrained to satisfy the inequality (5). The second constraints during the primary drying stage of the freeze drying process dealing with the heat flux at the top and bottom surfaces and respectively. Their magnitudes depend respectively on the value of the temperature of the heating plate at the upper surface of the vials, and the temperature of the heating plate at the bottom surface of the vials. These temperatures are assumed to be the same and the manipulated variable u(t) is subjected to the constraints in the following form:
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Tmin ≤ u (t ) = Tlp (t ) = Tup (t ) ≤ Tmax , ∀t > 0
(6)
3. Simulation results In this study, we are interested to find the optimal on-line tuning of the manipulated variable for the constrained optimization of the sublimation time. To realize the MPC under constraints of the freeze drying process, we used the MPC@CB software 1 developed with Matlab. Control Software: main features of MPC@CB The codes of the MPC@CB software have been written to run with Matlab. It allows realizing the MPC under constraints of the specified continuous process. The originality of these codes is first the easy use for any continuous SISO process (Single Input Single Output), through the user files (where model equations have to be specified), synchronized by few main standards files (where the user has to make few (or no) changes. The original feature of the software is the straightforward resolution of various model based control problems through different choices: 1. Open or closed loop control. 2. MPC for a trajectory tracking problem, with or without the output constraint. 3. MPC to solve an operating time minimization problem, with or without the output constraint. The other originality is the method used to develop the codes : it is very easy to introduce new parts in the code, such as : 1. MPC with an user defined control problem. 2. Handle SIMO, MISO or MIMO model . 3. Introduce a software sensor (observer). 4. Apply the software for a real time application [11]. For more the details about the MPC@CB software and the operations conditions, the reader can refer to [12]. The optimal minimization of the drying time under constraints may be equivalent to define the performance index as the maximization of the velocity of the sublimation interface. Since MPC@CB solves a minimization problem, the objective function is: min u J (u ) =
1
¦ ϑ + V ( j)
Np
2
∀j ∈ J1
j
(7)
accounting for the magnitude constraints for the manipulated variable and the output process. The velocity V is given by V=dH/dt and ϑ >0 is a small positive parameter, introduced to avoid the division by zero in (7). In Figure 1, the dynamics of the moving sublimation ice front H(t) and its velocity are presented. The optimization procedure based on the MPC@CB software is iterated until the position H(t) reaches the length L, which means the end of the primary drying stage.
1
© University Claude Bernard Lyon 1 - EZUS. In order to use MPC@CB, please contact the author :
[email protected]
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The profile of the bottom surface temperature of the materiel being dried, the heating plate temperature, as well as the glass transition temperature are presented in Figure 2. In order to satisfy the output constraint, the temperature is then kept near this constraint value for the rest of the time of the primary drying stage by reducing iteratively the heat flux input. The efficiency of the IMC-MPC strategy over open loop control can be seen: The drying time obtained for the primary drying stage using the MPC@CB software is equal 18 hours, while the required time for the sublimation step is about 24.11 hours in open loop.
4. Conclusion This study tackled the model based predictive control of the primary stage of the freeze drying process. Using the mathematical model of Liapis et al., in which the dynamic of the mass flux was simplified, the model based predictive control of the freeze drying is studied. Taking into account of the non linear partial differential equation model of the process, the idea was to combine the IMC structure and the MPC framework. The resulting IMC-MPC chart corrected the modelling errors introduced in the model based on line optimizer. Constraints on the manipulated variable and controlled variables are handled. This framework was used to optimize the drying time during the primary drying stage of the freeze drying process. The simulations results of the minimization problem were established using the MPC@CB code developed in Matlab. The difficulty related to this problem was the choice of the trajectory given by u0 . Since the measured temperature is at the bottom surface of the vial, one may design an observer that estimates the temperatures at different z.
References [1] A.I. Liapis, M.J. Pikal, R. Bruttini 1996 Research and development needs and opportunities in freeze drying. Drying Technology, 14, 1265-1300. [2] A.I. Liapis, R. Bruttini 1994 A theory for the primary and secondary drying stages of the freeze drying of pharmaceutical crystalline and amorphous solutes ; comparison between experimental data and theory, Separation Technology, 4, 144155. [3] A.I. Liapis, R.J. Litcheld 1979 Optimal control of a freeze dryer-I: theoretical development and quasi-steady state analysis Chemical Engineering Science, 34, 975-981. [4] CJ. King CJ 1971 Freeze drying Foods CRC Press, Cleveland, OH, 1-54. [5] R.J. Litcheld, A.I. Liapis 1979 An adsorption-sublimation model for a freeze dryer. Chemical Engineering Science, 34:1085. [6] A.I. Liapis, L.J. Litcheld 1979 Numerical solution of moving boundary transport problems in finite media by orthogonal collocation. Computers and Chemical Engineering, 3: 615-621. [7] Ferguson, RW. Lewis, L. Tomosy 1993 A finite element analysis of freeze-drying of a coffee sample Computers Methods Applications Mechanical Engineering 1993, 108: 341-352. [8] H. Sadikoglu, A.I. Liapis 1997 Mathematical Modelling of the Primary and Secondary Drying Stages of Bulk Solution Freeze-Drying in Trays: Parameter stimation and Model Discrimination by Comparison of Theoretical Results with Experimental Data, Drying Technology, 15: 791-810
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[9] P. Dufour P, F. Couenne, Y. Touré 2003 Model predictive control of a catalytic reverse flow reactor. Control of industrial spatially distributed parameter processes, Special issue of IEEE Transactions on Control System Technology, 11(5) : 705-714. [10] N. Daraoui, P. Dufour, H. Hammouri 2007 Model predictive control of the primary drying stage of a freeze drying of solutions in vials : a application of the MPC@CB software (part 1). The 5th Asia-Pacific Drying Conference, Hong Kong, China, 2 : 883-888. [11] K. Abid, P. Dufour, I. Bombard, P. Laurent 2007 Model predictive control of a powder coating process : an application of the MPC@CB software. IEEE Chinese Control Conference, Zhangjiajie, China, 2 : 630-634. [12] N. Daraoui, P. Dufour, H. Hammouri, A. Hottot 2007 On line constrained optimization of the primary drying stage of lyophilization, American Institute of Chemical Engineers (AIChE) Journal, submitted, ref. AIChE-07-10884.
FIG. 1: Optimization of drying time : time variation of the moving interface H(t)(bottom) and its velocity (top) during the primary drying stage
FIG. 2: Optimization of drying time : time variation of the bottom surface and heating plate temperatures during the primary drying stage
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Improving Steady-State Identification Galo A. C. Le Roux,a Bruno Faccini Santoro,a Francisco F. Sotelo,a Mathieu Teissier,b Xavier Joulia,b a
LSCP, Departamento de Engenharia Química, Escola Politécnica da USP, Av. Prof. Luciano Gualberto 580, Tr3, São Paulo, SP zip code 05508-900, Brazil bEcole Nationale Supérieure des Ingénieurs en Arts Chimiques et Technologiques 118 Route de Narbonne 31077 TOULOUSE Cedex 04, France
Abstract The use of online data together with steady-state models, as in Real Time Optimization applications, requires the identification of steady-state regimes in a process and the detection of the presence of gross errors. In this paper a method is proposed which makes use of polynomial interpolation on time windows. The method is simple because the parameters in which it is based are easy to tune as they are rather intuitive. In order to assess the performance of the method, a comparison based on Monte-Carlo simulations was performed, comparing the proposed method to three methods extracted from literature, for different noise to signal ratios and autocorrelations. The comparison was extended to real data corresponding to 197 variables of the atmospheric distillation unit of an important Brazilian refinery. A hierarchical approach was applied in order to manage the dimension of the problem. The studies showed that the method proposed is robust and that its performance is better than others. Keywords: Steady-State, Savitzky-Golay, Simulation, Non-Parametric Tests, Refining
1.
Introduction
Petroleum shortage is an important issue. Improving the efficiency of refineries by optimising their operation is one of the measures that must be implemented. In order to do so using computational tools available, like Real Time Optimization (RTO), it is mandatory to use data obtained in steady-state operation. This justifies the need for steady-state detection procedures, because the adaptation of process models to data obtained exclusively in steady state operation leads to better solutions (Bhat & Saraf, 2004). The analysis of real data is non-trivial because they include a stochastic component and statistical methods must be employed in order to perform the task. In this work an original usage of Savitzky-Golay filter is proposed. An estimate for the local derivative is obtained from the interpolation process, which is used in a test that allows the discrimination of steady-states. In this contribution, first, a short review of the steady-state identification methods most used is presented. Then, a comparison of the behavior of these methods based on benchmark data is performed in order to develop and calibrate the methodologies that are further applied to a case study based on real data from a crude distillation unit.
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Steady-State Identification
Steady-State identification is the first step for data processing in RTO (Bhat and Saraf, 2004) that also includes gross error detection and data reconciliation. In this work we present a review of the techniques used for steady-state identification. But, as literature reports experiences exclusively with parametric methods, we propose the study of some non-parametric techniques. 2.1. Modified F Test Cao & Rhinehart (1995) proposed an F-like test applied to the ratio (R) of two different estimates of the variance of the system noise. Each of these estimates is calculated using an exponential moving-average filter. The data are also filtered using a moving-average filter. One parameter, varying from 0 to 1, must be chosen for each of the filters (λ1, λ2 and λ3). The values of these parameters are set based on the relevance of the actual values in comparison to the past ones, and could be interpreted as forgetting factors and express something analog to a window size. If the statistic R, which is evaluated at each time step, is close to one, then the data can be considered in steady state. The maximum acceptable variability is defined by means of a critical value Rcrit. Cao & Rhinehart (1995) proposed that the parameters of the method be tuned empirically and present some guidelines for the procedure. 2.2. Reverse Arrangements Test (RAT) A non-parametric test is the Reverse Arrangements Test, in which a statistic, called A, is calculated in order to assess the trend of a time series. The exact procedure of calculation as well as tables containing confidence intervals is described in Bendat & Piersol (2000). If A is too big or too small compared to these standard values could mean there is a significant trend in the data, therefore the process should not be considered in steady state. The test is applied sequentially to data windows of a given size. 2.3. Rank von Neumann Test The rank modification of von Neumann testing for data independence as described in Madansky (1988) and Bartels (1982) is applied. Although steady-state identification is not the original goal of this technique, it indicates if a time series has no time correlation and can thus be used to infer that there is only random noise added to a stationary behavior. In this test a ratio v is calculated from the time series, whose distribution is expected to be normal with known mean and standard deviation, in order to confirm the stationarity of a specific set of points. 2.4. Polynomial Interpolation Test (PIT) Savitzky & Golay (1964) developed the algorithm for a filter to treat data measured in noisy processes, as spectroscopy. An experimental measurement series is filtered first by choosing a window size, n (which must be an odd number). Each window is interpolated using a polynomial of degree p, with p < n. Information obtained from the interpolated polynomial is less noisy. Thus, the first derivative of each polynomial at the central points is calculated and the value is used as a statistic for assessing the stationarity of the point. The parameters of the filter are the window size, n, and the polynomial degree, p.
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Benchmark Data
To analyze the advantages and drawbacks of each test comparatively, two sets of calibration functions were created. The first one is derived from four functions, representing different levels of stationarity. In each of these cases, three levels of random white noise are added with different amplitudes corresponding to 1, 5 and 10% standard deviations, of the original data. This set of functions is presented in Fig. 1.
Figure 1. Set of calibration functions: (A) original and (B) with first level of noise
The second one is based on two intervals: a ramp and a constant segment. For the ramp segment, three different slopes are tested: 1, 0.5, and 0.1. As previously, random noise with different amplitudes was added. A Monte-Carlo study was carried out in order to estimate the performance of each test. The methodology for assessing the performance is as follows: random noise is generated and each test for stationarity is applied to the central point of the positive slope segment and also at the central point of the constant piece. The number of times where the test succeeds or fails are recorded and a new random noise is generated. After some iterations (typically 1000) it is possible to find an approximate distribution for the probability of success and also for the type I (the process is considered nonstationary while it is in fact) and II errors. This procedure is applied for each test and for different parameters, thus portraying the sensitivity of the probability distribution as a function of the parameter values. Even for non-parametric tests, such sensitivity can be studied with respect to the size of the window, for instance.
4.
Results and Discussion
4.1. Benchmark Set 4.1.1. Polynomial Interpolation Test The degree of the polynomials is kept constant and equal to 2. This choice is justified by the fact that results depend more on the window size than on the degree of the polynomial.
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When applied to the first set of functions, the estimations of the first derivative are quite close to the intuitive expected values. In order to quantify its efficiency, the second set of functions is used in the Monte-Carlo study described above. For a given noise level, the average accuracy is calculated as the mean of accuracies for the 3 different slopes. The major difficulty in tuning this test is not that of choosing n but that of finding which should be the threshold for the derivative for a process is considered as stationary. This is the most important parameter and must be chosen according to the expected tolerance to variations. In Fig. 2, the dependence of the quality of the results on this treshold value is apparent.
Figure 2. Performance of Polynomial Interpolation Test for window size=51 and first level of noise
The existence of a region where fractions of errors type I and II are simultaneously small indicates that for some data series this test is able to clearly identify a stationary from a non-stationary point. However, for the case with several simultaneous variables that is analyzed later this is not necessarily true. 4.1.2. Modified F Test For the first set, it was possible to observe that this test works adequately (there is a significant trend in the analyzed data) and the values of R obtained were much larger than Rcrit. However, as noise level increases, the test does not perform properly and all the functions are considered stationary. It is possible to verify this fact from the Monte Carlo analysis results (Table 1) and to notice that its efficiency is similar to PIT for the first level of noise, which is the closer to real data. It is found that Ȝi parameters have little influence over the final result. 4.1.3. Reverse Arrangements Test Standard values of A are only tabulated for a few data sizes. As a consequence it is more difficult to choose a length for the window that would be neither too small nor too large.
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One reasonable choice was to consider 30 data points. But, for this, only the means of 3 successive points could be analyzed because the resulting time series has to be only 10 values long, which is the smallest value presented in tables. Unfortunately, averaging reduces the influence of noise. As for the other tests, this test behaves adequately for the first data set. From Monte Carlo analysis it was observed that the results are worst than for the Polynomial Interpolation Test but better than the techniques described in literature. 4.1.4. Rank von Neumann Test 30-points data windows were analyzed in order to make the comparison with the previous tests similar. The performance is adequate for the first data set, but type I errors get too large if the noise is too intense. The same behavior arises when testing the second set (Table 1). Table 1. Results of Steady-State identification on benchmark set (MF = Modified F test, RAT = Reverse Arrangements test, RVN = Rank von Neumann test) Noise Level
1
2
3
RAT
RVN
MF
RAT
RVN
MFa
RAT
RVN
Correct Answers 78,52
87,58
84,75
50,77
72,42
63,92
50,52
59,67
53,45
Type I Error
41,88
13,17
26,40
97,46
44,50
68,13
97,92
69,75
89,13
Type II Error
1,08
11,67
4,10
1,0
10,67
4,03
1,04
10,92
3,97
Test
a
a
MF
a
Ȝ1 = 0.2, Ȝ2 = 0.1, Ȝ3 = 0.1
4.2. Case study: crude oil atmospheric distillation unit Data from a Brazilian Refinery corresponding to the units comprehended from the desalinization to the separation into LPG, naphtha, kerosene, diesel and gasoil were analyzed. 197 relevant variables were retained and data measurements concerning 5 months of operation (one measurement every ten minutes) were available. Among the variables, 27 were considered to be key to the process, based on engineering considerations. The stationarity test is applied only to this smaller set. The whole system is considered to be at steady state if and only if all these 27 variables are stationary. As RAT appeared to be the most reliable test among the non-parametric ones, it was used to designate some steady-state windows from the huge database. According to RAT there are not many of these windows. Even so, one can choose some of them and verify the agreement between any other given test and RAT. If the accuracy of both parametric tests was not so different in the benchmark set, the situation changes dramatically towards PIT performance. This might be explained by, what can be termed “lack of noise” in the real data. In fact, for a time series to be considered stationary by the F-like test, it must have some level of noise. Cao & Rhinehart (1995) recommend the introduction of a white noise before analyzing data,
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but this procedure could lead to inconsistent results, for enough noise makes any time series “stationary “.
Figure 3. Steady-state identification for real data and for its first derivative (window size=51 and limit of derivative =0.1)
In Fig. 3 an example of the steady-state identification using PIT for real temperature data (left side) is presented. For illustrative purposes only five variables were used. The analysis of the first derivative (right side) is an auxiliary tool in order to analyze the behavior of the system.
5.
Conclusions
It was shown that for simulated data PIT performs better than the other tests studied. In addition, this test is the one that agrees better with RAT in the real case study. Its most important parameter, the window size, can be adjusted in order to deal with situations where the process could be more sensitive to small changes. PIT is very simple and intuitive: for its implementation, a plot of the derivatives can be used in order to help in the selection of the steady states.
References Savitzky, M. Golay, 1964, Smoothing and Differentiation of Data by Simplified Least Squares Procedures, Anal. Chem., Vol 36, pp. 1627-163 S. Cao, R. Russell, 1995, An efficient method for on-line identification of steady state, J. Proc. Cont. Vol 5, No. 6, pp. 363-374 S.A. Bhat, D.N. Saraf, 2004, Steady-state identification, gross error detection, and data reconciliation for industrial process units, Ind. Eng. Chem. Res. Vol 43, pp. 4323-4336 J. Bendat, A. Piersol, 2000, Random data : analysis and measurements procedures, John Wiley & Sons Madansky, J. 1988, Prescriptions for working statisticians, Springer - Verlag New York R. Bartels, 1982, The Rank Version of von Neumann’s Ratio Test for Randomness, Journal of the American Statistical Association, Vol. 77, No. 377, pp. 40-46
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Application of adaptive neurofuzzy control using soft sensors to continuous distillation Javier Fernandez de Canete, Pablo del Saz-Orozco, Salvador Gonzalez-Perez System Engineering Dpt. , Plaza El Ejido s/n, Malaga, 29013, SPAIN
Abstract Recent years have seen a rapidly growing number of hybrid neurofuzzy based applications in the process engineering field, covering estimation, modeling and control among others. In fact, proper operation of a distillation column requires knowledge of products compositions during the entire duration of the operation. The use of inferential composition estimators (soft sensors) has long been suggested to assist the monitoring and control of continuous distillation columns. In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to the composition dual control of the distillation column. Genetic algorithms are used to automatically selection of the optimum control signal based on an ANFIS model of the plant. The performance of the developed ANFIS estimator is further tested by observing the performance of the dual control system for both set point tracking and disturbance rejection cases. Keywords: distillation control, neurofuzzy networks, soft sensors, genetic algorithms
1. Introduction Neural and fuzzy applications have been successfully applied to the chemical engineering processes [1], and several control strategies have been reported in literature for the distillation plant modeling and control tasks [2]. Recent years have seen a rapidly growing number of neurofuzzy control applications [3]. Beside this, several software products are currently available to help with neurofuzzy problems. Basically, a fuzzy controller is composed of a rule base containing fuzzy if-then rules. A database with membership functions of the fuzzy sets, an inference engine and two fuzzification and defuzzification interfaces to convert crisp inputs into degrees of match with linguistic values and vice versa. An ANFIS system (Adaptive Neuro Fuzzy Inference System) [4] is a kind of adaptive network in which each node performs a particular function of the incoming signals, with parameters updated according to given training data and a gradient-descent learning procedure. This hybrid architecture has been applied mostly to the control of nonlinear single input single output (SISO) nonlinear systems [5], while application to general multiple inputs multiple outputs (MIMO) control problems rely both on decoupling control to produce a set of SISO controllers or else designing a direct multivariable controller . Proper operation of a distillation column requires knowledge of products compositions during the entire duration of the operation. Although product composition can be
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measured on-line, it is well known that on-line analyzers are complex pieces of equipment that are expensive and difficult to maintain. They also entail significant measurement delays, which can be detrimental from the control point of view [6]. Therefore, to circumvent these disadvantages, it is possible to estimate the product composition on-line, rather than measuring it. The use of such inferential composition estimators (or soft sensors) has long been suggested to assist the monitoring and control of continuous distillation columns [7]. Genetic algorithms (GA) are model machine learning methodologies, which derive their behaviour from a metaphor of the processes of evolution in nature and are able to overcome complex non-linear optimization tasks like non-convex problems, noncontinuous objective functions, etc. [8]. They are based on an initial random population of solutions and an iterative procedure, which improves the characteristics of the population and produces solutions that are closer to the global optimum. This is achieved by applying a number of genetic operators to the population, in order to produce the next generation of solutions. GAs have been used successfully in combinations with neural and fuzzy systems. Particularly in neurofuzzy control, GAs have been utilized extensively to tune the neurofuzzy controller parameters and acquire the fuzzy rules [9]. In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to train an ANFIS model so that a GA performs the searching for the optimal dual control law applied to the distillation column. The performance of the developed ANFIS estimator is further tested by observing the performance of the ANFIS based control system for both set point tracking and disturbance rejection cases.
2. Process Description The distillation column used in this study is designed to separate a binary mixture of methanol and water, which enters as a feed stream with flow rate Fvol and composition XF between the rectifying and the stripping section, obtaining both a distillate product stream Dvol with composition XD and a bottom product stream Bvol with composition XB. The column consists of 40 bubble cap trays. The overhead vapor is totally condensed in a water cooled condenser (tray 41) which is open at atmospheric pressure. The process inputs that are available for control purposes are the heat input to the boiler Q and the reflux flow rate Lvol. Liquid heights in the column bottom and the receiver drum (tray 1) dynamics are not considered for control since flow dynamics are significantly faster than composition dynamics and pressure control is not necessary since the condenser is opened to atmospheric pressure. The model of the distillation column used throughout the paper is developed by [10], composed by the mass, component mass and enthalpy balance equations used as basis to implement a SIMULINK model (figure 1) which describes the nonlinear column dynamics as a 2 inputs (Q , Lvol ) and 2 output (XD , XB ). Implementations details for the overall column dynamics are given in [11].
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Figure 1. Schematic of the SIMULINK model of the distillation
3. ANFIS Estimator An ANFIS system is a kind of adaptive network in which each node performs a particular function of the incoming signals, with parameters updated according to given training data and a gradient-descent learning procedure. This hybrid architecture has been applied to the modeling and control of multiple-input single-output (MISO) systems [4].
Figure 2. Architecture of the ANFIS structure
The architecture of the ANFIS is constituted by several layers (fig. 2). If we consider for simplicity two inputs x and y and two outputs f1 and f2 for a first-order Sugeno fuzzy model, with Ai and Bj being the linguistic label associated with x and y respectively, every node in layer 1 represents a bell-shaped membership function μ Ai (x) or μ B ( y ) i with variable membership parameters. Usually we choose the bell-shaped functions. Nodes of layer 2 output the firing strength defined as the product ω ji = μ A ( x) × μ B ( y ) , i i where the set of nodes in this layer are grouped for each output j. A normalization process is computed in layer 3 giving the normalized ω ji , and the Sugeno-type consequent of each rule with variable parameters pi, qi and ri is implemented in layer 4 yielding fj as the output of the single summation node f i = ω ji ( pi x + qi y + ri ) and finally the single node of layer 5 computes de overall outputi as a summation of all incoming signals.
¦
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The learning procedure consists of two stages. In the forward pass training input data go forward the ANFIS architecture, and in the backward pass the error rates propagate backward, being the both the consequent and the membership parameters updated by gradient descent.
4. ANFIS-GA Controller The complete ANFIS based estimation and control system is described below (figure 3). yˆ[ k ]
T [k ] ANFIS ESTIMATOR
~ y [k ]
TDL ANFIS MODEL
+ -
u[k ] e[k ]
GA CONTROLLER DISTILLATION COLUMN
y d [ k + 1] TDL : Tapped Delay Line Figure 3.Estimation and Control ANFIS based structure
4.1. ANFIS estimator of the composition (ANFIS ESTIMATOR block) In order to infer the composition from temperature an ANFIS net is used. Previously, a sensitivity study is performed in order to choose the correct set of temperatures to infer top and bottom compositions (figure 4). The sensitivity index proposed is defined as the partial derivative of each available primary variable (product composition) with respect to changes in each secondary variable (tray temperature). dependency 41 36 31 tray
26 21 16 11 6 1 0
0,01
0,02
0,03
0,04
0,05
0,06
normalized derivate
Figure 4.Composition-temperature dependencies.
A three temperature vector T[k] = [T41[k],T21[k],T1[k]] is selected as input to the ANFIS predictor which output the predicted values of composition vector
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yˆ[k ] = [ Xˆ D [k ], Xˆ B [k ]] . After a trial-error process we have selected 5 membership
functions per input as a compromise solution between computation time and precision. Normally, in a plant operation, both real values are measured off-line in the laboratory. In this study, the ANFIS parameter update is made accepting the simulation results as same with the actual plant data. Training set is generated by selecting 1200 temperature data points obtained by during column open loop operation with range for LVol (0-5E-06 m3/h) and heat flow Q (0-2000 J/s) for fixed feed rate conditions FVol = 1 E-06 m3/h, XF = 0.3. An additional temperature data set consisting of 150 data points was used to test the ANFIS predictor afterwards. The error in the training phase is under 0.00025% and 0.0015% in the validation phase. For training pattern generation we assume an initial steady state for the column after a start-up process. 4.2. ANFIS modeling of the distillation column (ANFIS MODEL block) Prior to the design of the controller, an ANFIS network has been used as an identification model of the distillation column dynamics. To obtain representative training data, varying feed flows, initial liquid composition values both in the column, boiler and condenser along with input values for the control actions were imposed on the model. The identification model has been carried out using an ANFIS network given by ~ y[k ] = f ( yˆ[k ], yˆ[k − 1], yˆ[k − 2], u[k ]) after selecting the best structure among possible ones, with u[k] = [LVol[k],Q[k]] and yˆ[k ] regularly spaced covering the same range as defined in section 4.2. As the model’s dynamic will be modified with unknown perturbations, this ANFIS model will be updated with the real plant response. 4.3. Genetic Algorithm Controller (GA CONTROLLER block ) As the estimation of the composition vector ~ y[k ] in the next simulation step according the present and previous states of yˆ[k ] and the input to the system u[k] can be achieved using the ANFIS model net, the control problem can be implemented as an optimization problem in which the function to minimize is the difference between the desired output yd [k ] and the estimated one ~y[k ] in the next step. As a result, the optimum control law u[k] is elicited for the distillation control problem. This control approach enables the searching of an optimum control signal for each point in the operating range of the nonlinear distillation plant. In order to search for the optimum for the highly non-linear function a genetic algorithm is used with 75 members fixed population, 75 generations and random mutation. If an error under 0.01% is achieved, the algorithm is stopped in order to accelerate the simulations.
5. Results The aim in the design of the composition ANFIS estimator is to use together with ANFIS-GA for dual composition control of the distillation column. Therefore, the composition estimator is tested by using the SIMULINK model before it is used for control. The performance of the control structure is checked for set-point and disturbance rejections, as is shown in figure 5.
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Figure 5. Performance of the ANFIS-GA for a pulse change in top (bottom) product purity from 96% to 98% (4% to 2%) in t = 2000 s and change in XF from 40% to 30% in t = 4450 s.
6. Conclusions and Future Works We have proposed a hybrid neurofuzzy design methodology to dual composition control in a MIMO binary distillation column. An ANFIS structure has been employed both for prediction of composition profiles from temperatures and design of optimum control law using a GA search technique, by using an ANFIS model based fitness function. The results obtained point to the potential use of this control strategy in areas of design related to operability and control in process engineering. Future works are directed towards the application of the proposed methodology to a real small scale pilot plant.
References [1] A. Bulsari. Neural networks for chemical engineers. Elsevier, Amsterdam, 1995. [2] M.A. Hussain, M. A. “Review of the applications of neural networks in chemical process control. Simulation and on-line implementations”, Artificial Int. in Eng, Vol. 13 (1999) pp. 55-68. [3] J. Engin, J. Kuvulmaz and E. Omurlu. “Fuzzy control of an ANFIS model representing a nonlinear liquid level system”. Neural Computing and Appl., Vol. 13, n. 3 (2004) pp. 202-210. [4] R. Jang and C. Sun. Neuro-fuzzy modeling and control. Proceedings of the IEEE 1995, Vol. 83 n. 3 (1995) pp. 378-405. [5] M. Denai, F. Palis and A. Zeghbib. “ANFIS based modeling and control of nonlinear systems: A tutorial”, Proceedings of the IEEE Conference on SMC (2004), pp. 3433-3438. [6] H. Leegwater. Industrial experience with double quality control. In W. L. Luyben (Ed.), Practical distillation control. New York, USA: Van Nostrand Reinhold, 1992. [7] S. Park and C. Han. “ A non-linear soft sensor based on multivariate smoothing procedure for quality estimation in distillation columns”, Comp. and Chem. Eng. Vol. 24 (2000), pp. 871-877. [8] Z. Michalewitz, Genetic Algorithms + Data Structures = Evolution Programs, Springer, Berlin, Germany, 1992. [9] P. Fleming and R. Purshouse – Evolutionary algorithms in control systems engineering: a survey. Control Engineering Practice, Vol. 10 (2002) pp. 1223–1241. [10] M. Diehl, I. Uslun and R. Findeisen.”Real-time optimization for large scale processes: Nonlinear predictive control of a high purity distillation column”, On Line Optimization of Large Scale System: State of the Art, Springer-Verlag, 2001. [11] J. Fernandez de Canete, S. Gonzalez-Perez and P. del Saz Orozco. “A development of tools for monitoring and control of multivariable neurocontrolled systems with application to distillation columns”, Proc. EANN 2007 Int. Conf., Thesaloniki, Greece, (2007), pp. 296-305.
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Correlation-Based Just-In-Time Modeling for SoftSensor Design Koichi Fujiwara, Manabu Kano, Shinji Hasebe Kyoto University, Nishikyo-ku, Kyoto, 615-8510, Japan
Abstract Soft-sensors are widely used for estimating product quality or other key variables when on-line analyzers are not available. However their estimation performance deteriorates when the process characteristics change. To cope with such changes and update the model, recursive methods such as recursive PLS and Just-In-Time (JIT) modeling have been developed. When process characteristics change abruptly, however, they do not always function well. In the present work, a new method for constructing soft-sensors based on a JIT modeling technique is proposed. In the proposed method, referred to as correlation-based JIT modeling, the samples used for local modeling are selected on the basis of the correlation among variables instead of or together with distance. The proposed method can adapt a model to changes in process characteristics and also cope with process nonlinearity. The superiority of the proposed method over the conventional methods is demonstrated through a case study of a CSTR process in which catalyst deactivation and recovery are considered as changes in process characteristics. Keywords: soft-sensor, Just-In-Time modeling, recursive partial least squares regression, principal component analysis, estimation
1. Introduction A soft-sensor, or a virtual sensor, is a key technology for estimating product quality or other important variables when online analyzers are not available (Kano and Nakagawa, 2008). In chemical industry, partial least squares (PLS) regression has been widely used for developing soft-sensors (Mejdell and Skogestad, 1991; Kano et al., 2000; Kamohara et al., 2004). However, their estimation performance deteriorates when process characteristics change. For example, equipment characteristics are changed by catalyst deactivation or scale adhesion. Such a situation may bring to decline product quality. Therefore, soft-sensors should be updated as the process characteristics change. To cope with such changes and update statistical models, recursive methods such as recursive PLS were developed (Qin, 1998). However, when a process is operated within a narrow range for a certain period of time, the model will adapt excessively and will not function within a sufficiently wide range of operation. On the other hand, Just-In-Time (JIT) modeling, which was proposed to cope with the changes in process characteristics and the process nonlinearity (Bontempi et al., 1999), generates a local model from past data around a query point only when an estimated value is requested. JIT modeling is useful when global modeling does not function well. However, its estimation performance is not always high because the samples used for local modeling are selected on the basis of the distance from the query point and the correlation among variables is not taken into account. In the present work, a new method for soft-sensor design is proposed. In the proposed method, referred to as correlation-based JIT (C-JIT) modeling, the samples used for local modeling are selected on the basis of the correlation instead of or together
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with the distance. The C-JIT modeling can cope with abrupt changes of process characteristics that conventional method cannot. The usefulness of the proposed method is demonstrated through a case study of a CSTR process in which catalyst deactivation and recovery are investigated as the changes in process characteristics.
2. Conventional methods In this section, conventional soft-sensor design methods are briefly explained. 2.1. Dynamic PLS PLS has been widely used for building a soft-sensor because it can cope with a colinearity problem. Here X ∈ ℜ N × M and Y ∈ ℜ N × L are matrices whose ith rows are the ith measurements of inputs xi and outputs yi, respectively. The columns of these matrices are mean-centered and scaled appropriately. In PLS, X and Y are decomposed as follows: X =TP T + E , Y = TQ T + F (1) where T ∈ ℜ N × R is the latent variable matrix, P ∈ ℜ M × R and Q ∈ ℜ L× R are the loading matrices of X and Y , respectively. R denotes the number of latent variables. E and F are the error matrices. The estimation performance of soft-sensors can be improved by taking into account process dynamics. For this purpose, the past information is used as inputs in addition to the present information. This method is referred to as Dynamic PLS (Ricker, 1993; Kano et al., 2000). 2.2. Recursive PLS The estimation performance of a statistical model will deteriorate when process characteristics change. Therefore, soft-sensors should be updated as process characteristics change. However, redesign of them is very laborious and it is difficult to determine when they should be updated. To cope with these problems, recursive PLS was proposed (Qin, 1998). Whenever both new input and output variables, x new and y new , are measured, the recursive PLS updates the model by using ª βP T º ª βQ T º X new = « T » Ynew = « T » , 0 < β ≤ 1 ¬ x new ¼ ¬ y new ¼ where β is the forgetting factor.
(2)
2.3. Just-In-Time modeling In general, a global linear model cannot function well when a process has strong nonlinearity in its operation range, and it is difficult to construct a nonlinear model that is applicable to a wide operation range since a huge amount of samples are required. Therefore, methods that divide a process operation region into small multiple regions and build a local model in each small region have been proposed. An example is a piecewise affine (PWA) model (Ferrari-Trecate et al., 2003). However, in the PWA model, the optimal division of the operation region is not always clear and the interpolation between the local models is complicated. Another method for developing local models is JIT modeling, which has the following features: • When new input and output data are available, they are stored into a database. • Only when estimation is required, a local model is constructed from samples located in a neighbor region around the query point and output variables are estimated. • The constructed local model is discarded after its use for estimation.
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In JIT modeling, samples for local modeling should be selected appropriately and online computational load becomes large.
3. Correlation based Just-In-Time modeling Conventional JIT modeling uses a distance to define a neighbor region around the query point regardless of the correlation among variables. In the present work, a new JIT modeling method that takes account of the correlation is proposed. In the proposed C-JIT modeling method, the data set that has the correlation best fit to the query sample is selected for local modeling. 3.1. Evaluation of correlation similarity Although several indices of similarity between data sets have been proposed (Kano et al., 2001; Kano et al, 2002), the Q statistic is used in C-JIT modeling. The Q statistic is derived from principal component analysis (PCA), which is a tool for data compression and information extraction (Jackson and Mudholkar, 1979). P
¦ (x
Q=
p
− xˆ p ) 2
(3)
p =1
where xˆ p is the prediction of the pth input variable by PCA. The Q statistic is a
distance between the sample and the subspace spanned by principal components. That is, the Q statistic is a measure of dissimilarity between the sample and the modeling data from the viewpoint of the correlation among variables. In addition, to avoid extrapolation, Hotelling's T 2 statistic can be used. R t r2 T2 = (4) 2
¦σ r =1
tr
where σ t2 denotes the variance of the rth score t r . r
The T 2 statistic expresses
normalized distance from the origin in the subspace spanned by principal components. To improve the model reliability, Q and T 2 can be integrated into a single index for the data set selection as proposed by Raich and Cinar (1994) for a different purpose: J = λT 2 + (1 − λ )Q, 0 ≤ λ ≤ 1 (5) 3.2. Correlation-based Just-In-Time modeling In the proposed C-JIT modeling, samples stored in the database are divided into several data sets. Although the method of generating data sets is arbitrary, each data set is generated so that it consists of successive samples included in a certain period of time in this work, because the correlation among variables in such a data set is expected to be very similar. To build a local model, the index J in Eq. (5) is calculated for each data set, and the data set that minimizes J is selected as the modeling data set. Figure 1 shows the difference of sample selection for local modeling between JIT modeling and C-JIT modeling. The samples consist of two groups that have different correlation. In conventional JIT modeling, samples are selected regardless of the correlation, since a neighbor region around the query point is defined by distance. On the other hand, C-JIT modeling can select samples whose correlation is similar to that of the query point by using the Q statistic. Assume that S samples are stored in the database and z i = [ x iT , y iT ]T . To cope with process dynamics, measurements at different sampling points can be included in z i . The procedure of C-JIT modeling is as follows:
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1. Newly measured input and output measurements z S +1 are stored in the database. 2. The index J is calculated from z S +1 and a data set z {S } that was used for building the previous local model f {S } . J I = J . 3. If J I ≤ J I , then f {S +1} = f {S } and Z {S +1} = Z {S } . f {S +1} is used for estimation until the next input and output measurements z S + 2 are available. When z S + 2 is available, return to step 1. If J I > J I , go to the next step. Here J I is the threshold. 4. k = 1 . 5. The kth data set Z k = [ z k , " , z k +W −1 ]T ∈ ℜ ( M + L )×W is extracted from the database, where W is the window size. 6. The index J of the kth data set, J k , is calculated from Z k and z S +1 . 7. k = k + d . If k ≤ S − W + 1 , then return to step 5. If k > S − W + 1 , then go to the next step. Here d is the window moving width. 8. The data set Z k that minimizes J k is selected, and it is defined as Z {S +1} . 9. A new local model f {S +1} whose input is X {S +1} = [ x K , ! x K +W −1 ]T and output is Y {S +1} = [ y K , ! , y K +W −1 ]T is built.
10. The updated model f {S +1} is used for estimation until the next input and output measurements z S + 2 are available. When z S + 2 is available, return to step 1. Principal component regression (PCR) is used in the proposed C-JIT modeling because scores are calculated in step 6. In addition, steps 2 and 3 control the model update frequency.
Fig. 1: Sample selection for local modeling in JIT modeling (left) and C-JIT modeling (right).
4. Case Study In this section, the estimation performance of the proposed C-JIT modeling is compared with that of recursive PLS and conventional JIT modeling through their applications to product composition estimation for a CSTR process. 4.1. Problem Settings A schematic diagram of the CSTR process is shown in Fig. 2 (Johannesmeyer and Seborg, 1999). In this process, an irreversible reaction A → B takes place. The set point of reactor temperature is changed between ± 2K every ten days. Measurements of five variables, reactor temperature T, reactor level h, reactor exit flow rate Q, coolant flow rate QC, and reactor feed flow rate QF, are used for the analysis and their sampling interval is one minute. In addition, reactant concentration CA is measured in a
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laboratory once a day. A soft-sensor that can estimate CA accurately in real time needs to be developed. In this case study, to consider catalyst deactivation as the changes in process characteristics, the frequency factor k0 is assumed to decrease with time. In addition, the catalyst is recovered every half year (180 days). Figure 3 shows the deterioration and recovery of the frequency factor. The operation data for the past 540 days were stored in the database. While newly measured data are stored, the soft-sensor is updated in the next 180 days. 4.2. Estimation by Recursive PLS and Just-In-Time modeling Soft-sensors are constructed by using recursive PLS with the forgetting factor β = 0.97 and JIT modeling. In recursive PLS, the model is updated every 24 hours when CA is measured. To take into account process dynamics, the inputs consist of the samples at present and one minute before. The number of latent variables is four, which is determined by trial and error. On the other hand, in JIT modeling, linear local models are built by using Euclid distance as the measure of selecting samples used for local modeling. Matlab Lazy Learning Toolbox was used (http://iridia.ulb.ac.be/~lazy). The estimation results are shown in Table 1. In this table, r denotes the correlation coefficient between measurements and estimates, and RMSE is the root mean square error. The results show that neither recursive PLS nor JIT modeling functions well. In general, recursive PLS is suitable only for slow changes in process characteristics. On the other hand, the reason for the poor performance of JIT modeling seems that JIT modeling does not take account of correlation among variables when a local model is built.
Fig2: Schematic diagram of CSTR.
Fig. 3: Change of a frequency factor.
Table 1: Estimation performance of recursive PLS, JIT modeling, and C-JIT modeling
r RMSE
recursive PLS 0.88 2.07
JIT modeling 0.82 2.43
C-JIT modeling 0.99 0.54
Fig. 4: Estimation result of CA by C-JIT modeling with λ = 0.01 (Window Size: 10 day).
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4.3. Estimation by Correlation-based Just-In-Time modeling The criterion for selecting a data set is to minimize the index J in Eq. (5) with λ = 0.01 . The local model is updated every 24 hours when CA is measured, W=10, and d=1, which are determined by trial and error. The estimation results are shown in Fig. 4 and Table 1. The left figure shows the estimation result for 180 days. The right figure shows the enlarged result for two months before and after the catalyst recovery. In this figure, PCs is the number of principal components. The results show that the estimation performance of C-JIT modeling is significantly higher than that of the conventional methods. With the proposed C-JIT modeling, RMSE is improved by about 78% and 74% in comparison with recursive PLS and JIT modeling, respectively.
5. Conclusion In the present work, to develop a soft-sensor that can cope with the changes in process characteristics, a new correlation-based JIT modeling method is proposed. The superiority of the proposed C-JIT modeling over the conventional methods is demonstrated through a case study of a CSTR process in which catalyst deactivation and recovery are investigated. In recursive PLS and conventional JIT modeling, it is difficult to adapt models when the process characteristics change abruptly. On the other hand, the C-JIT modeling can cope with the abrupt changes in process characteristics.
References G. Bontempi, M. Birattari and H. Bersini, 1999, Lazy Learing for Local Modelling and Control Design, Int. J. Cont., Vol. 72, No. 7/8, 643 G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, 2003, A Clustring Technique for the Identification of Piecewise Affine System, Automatica, Vol. 39, Issue 2, 205 J. E. Jackson, and G. S. Mudholkar, 1979, Control Procedures for Residuals Associated with Principal Component Analysis, Technometrics, Vol. 21, Issue 3, 341 M. Johannesmeyer and D. E. Sebog, 1995, Abnormal Situation Anaylsis Using Pattern Recognition Techniques and Histrical Data, AIChE Annual meeting, Dallas, Oct.31-Nov. 5 H. Kamohara, A. Takinami, M. Takeda, M. Kano, S. Hasebe and I. Hashimoto, 2004, Product Quality Estimation and Operating Condition Monitoring for Industrial Ethylene Fractionator, J. Chem. Eng. Japan, Vol.. 37, No.3, 422 M. Kano, S. Hasebe, I. Hashimoto and H. Ohno, 2002, Statistical Process Monitoring Based on Dissimilarity of Process Data, AIChE J., Vol. 48, No.6, 1231 M. Kano and Y. Nakagawa ,2008, Data-Based Process Monitoring, Process Control, and Quality Improvement: Recent Developments and Applications in Steel Industry, Comput. Chem. Engng., Vol. 32, 12 M. Kano, H. Ohno, S. Hasebe, and I. Hashimoto, 2001, A New Multivariate Statistical Process Monitoring Method Using Principal Component Analysis, Comput. Chem. Engng., Vol. 25, No.7-8, 1103 M. Kasper and W. H. Ray, 1993, Partial Least Squares Modeling as Successive Singular Value Decomposition, Comput. Chem. Engng., Vol. 17, Issue 10, 985 T. Mejdell and S. Skogestad, 1991, Estimation of Distillation Compositions from Multiple Temperature Measurements Using Partial-Least-Squares Regression, Ind. Eng. Chem. Res., Vol. 30, Issue 12, 2543 S. J. Qin, 1998, Recursive PLS Algorithms for Adaptive Data Modeling, Comput. Chem. Engng., Vol. 22, No. 4/5, 503 A. Raich and A. Cinar, 1994, Statistical Process Monitoring and Disturbance Diagnosis in Multivariable Continuous Processes, AIChE J., Vol. 42, Issue 1,995 N. L. Ricker, 1988, Use of Biased Least-Squares Estimators for Parameters in Discrete-Time Pulse Response Models, Ind. Eng. Chem. Res., Vol. 27, Issue 2, 343
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
Integrating strategic, tactical and operational supply chain decision levels in a model predictive control framework José Miguel Laínez, Georgios M. Kopanos, Mariana Badell, Antonio Espuña, Luis Puigjaner Universitat Politècnica de Catalunya, Av. Diagonal 647, E-08028, Barcelona, Spain
Abstract In this work an MILP model which achieves the integration of all three Supply Chain (SC) decision levels is developed. Then, the stochastic version of this integrated model is applied as the predictive model in a Model Predictive Control (MPC) framework in order to incorporate and tackle unforeseen events in the SC planning problem in chemical process industries. Afterwards, the validation of the proposed approach is justified and the resulting potential benefits are highlighted through a case study. The results obtained of this particular case study are analyzed and criticized towards future work. Keywords: supply chain optimization, decision levels, MILP, model predictive control.
1. Introduction Although the Process Systems Engineering community (PSE) faces an increasing number of challenging problems, enterprise and SC remain subjects of major interest offering multiple opportunities. It is believed that further progress in this area will mean a unique opportunity demonstrating the PSE potential to enhance company’s “value preservation”. One of the key components in supply chain management (SCM) and enterprise wide optimization (EWO) is the decision making coordination and integration at all levels. Recent work offers models to separately tackle problems arising in the three standard SC hierarchical decision levels: strategic (long-term: network design), tactical (medium-term: aggregated planning) and operational (short- term: scheduling). These models, because of their nature and purpose, have very different timescales. It becomes evident the challenge of solving large size multi-scale optimization problems when considering the integration of decision levels. Since scheduling is also a basic building block in the more general area of EWO1, it is indispensable its incorporation into the already existed design-planning models. Furthermore, it is noteworthy that SC planning is not a one time event, but a dynamic activity. Firms are in the need of a closed-loop planning approach in order to preserve competitiveness. This approach should be capable of revising planned activities, updating uncertain parameters (e.g., lead times, market demand and interest rates) and considering the effects of incidences; so that future plans are adapted to enhance SC performance under the current highly dynamic business environment. A MPC framework can be used as an appropriate approach to continuously improve the SC planning. The MPC framework attempts to optimize a performance criterion that is a function of the future control variables. By solving the optimization problem all
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elements of the control signal are defined. However, only a portion of the control signal is applied to the SC system. Next, as new control input information and disturbance forecasts are collected, the whole procedure is repeated, which produces a feed-forward effect and enables the SC system to follow-up the dynamic business environment.
2. Problem statement A novel stochastic multi-period design/planning/scheduling MILP model of a multiechelon SC with financial considerations is used as a predictive model in this work. The model assumes that different technological equipment is available to be installed in potential sites and assists in their selection. Furthermore, the model allows the expansion of plant equipment capacities, not only in the first planning period. Regarding the financial area, the mathematical program endeavors to evaluate the shareholder value.
3. Control Strategy In Fig.1, a general schematic of the proposed MPC framework for SCM is shown. It follows a brief description of the control strategy. When the SC process is disturbed, data required to describe the current SC state are captured and sent to the controller. Next, scenarios are calculated by the forecasting module. As it is indicated there, the control signal that is implemented in the SC processes only comprises the first stage variables resulting from the stochastic optimization problem. In fact, first stage variables are associated to next period decisions that are made prior to uncertainty realization. Disturbances (i.e. demand, prices, interest rates)
SC Planners & executives
Control variables: capacity increases, facilities production and distribution rates
Supply chain processes
1st Stage control signal
Process output
Control algorithm Integrated SC model Strategic (Design) Tactical (Planning)
Forecasting module
Finances
Time series analysis: Mean and forecast error caracterization
Operational (Scheduling)
SC design/planning model Stochastic MILP
1st stage Here and now variables (Frozen stage)
Sampling tool
Recourse stages Wait and see variables (Flexible stage)
Output: Parameters estimation, Scenarios
Optimizer
Predictive and optimal controller
Figure 1. Control strategy
Sensors (data collecters)
Control input: current demand, capacity and materials availability, stocks, capacity pitfalls …
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Integrating SC Decision Levels in a MPC Framework
3.1. The control algorithm The predictive model within the control algorithm consists in a multistage stochastic MILP. A scenario based approach is applied. Refer to Puigjaner and Laínez 2 for scenario tree description and stochastic formulation indices details (l; ~l). 3.1.1. Process operations formulation Design-Planning formulation. The stochastic design-planning approach presented in this work is inspired from the STN formulation3. The presented approach relies on the flexible echelons concept. The connectivity between echelons is not imposed; consequently, a facility may play the role of either a processing or a distribution site. Material flows among facilities are allowed. Moreover, the proposed design-planning formulation simplifies the representation of batch and/or continuous process into the same framework, which facilitates its integration with scheduling models. The basic equations are next presented. Eq.(1) is the mass balance equation for each echelon f and material s. The design decisions are modeled through Eqns.(2)-(3). Eq.(4) forces the production to be within installed capacity and a minimum utilization factor. Eqs.(5)-(6) force materials flow from suppliers and to markets to be lower than an upper bound given by their capacity limitations. l Ssft~ = l
XX f0
X
l ®sij Pijf 0 f t~ ¡ l
f0
i2Ts j2(Ji \Jf 0 ) l¤ +Ssf t¡1~l¤
XX
X
i2T¹s j2(Ji \Jf )
l ® ¹sij Pijf f 0 t~l
(1)
8s; f; ~l ; t 2 Tl ; l¤ 2 L¤t¡1 ; ~l¤ 2 AH l¤ ~l
¤
l l l Fjft~ = Fjf t¡1~l¤ ¡1 + F Ejf t~l¡1 l¡1
8f; j 2 Jf ; l; ~l¡1 ; t 2 Tl ; l¤ 2 L¤t¡1 ; ~l¤ ¡1 2 AH l¤ ¡1;~l¡1 l L l l U Vjf t~l¡1 F Ejf t · F SEjft~l¡1 · Vjf t~l¡1 F Ejf t l ¯jf Fjf t~l¡1 ·
XX
8f; j 2 Jf ; l; ~l¡1 ; t 2 Tl
(2) (3)
l l ijff 0 Pijf f 0 t~l · Fjf t~l¡1
f 0 i2Ij
(4)
8f; j 2 Jf ; l; ~l ; t 2 Tl ; ~l¡1 2 AH l¡1;~l
X X X f0
l l Pijf 0 f t~ · Demsft~ l l
8s 2 f p; f 2 m; l; ~l ; t 2 Tl
(5)
i2ITs j2Ji
X X X
l Pijf f 0 t~l · Asft
8f 2 e; s 2 rmf ; l; ~l ; t 2 Tl
(6)
f 0 i2ITs j2Ji
Scheduling formulation. The scheduling formulation is an extension of STN representation 2 permitting scheduling in multiple facilities. Eqns.(7)-(8) are used for mass balances and assignment decisions, respectively. 0
¡pti +1 X ts =tsX i2Ji
t0s =ts
Wijf t0s · 1 8f; j 2 (Jbatch \ Jf ); ts
(7)
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J.M. Laínez et al.
Sschedsfts ¡ Sschedsf ts ¡1 = XX
XX
®sij Bijf ts ¡pti ¡
i2Ts j2Ji
® ¹ sij Bijfts + RMsf ts
8s; f; ts
(8)
i2T¹s j2Ji
Integration of decision levels. The integration between the models for design-planning and scheduling is carried out through Eqns.(9)-(11). Eq.(9) states that production allocated in equipment j is identical in both models. In Eq.(10) the availability of raw material is computed from received materials according to the planning formulation. Raw material availability is then included in the scheduling mass balance of Eq.(8). Scheduling equations may be applied in more than one planning period. The appropriate equations for incorporating scheduling in first planning period (t = 1) are next presented. l Pijff t~l =
X
Bijf ts
8f; j 2 (Jbatch \ Jf ); i 2 Ij ; t = 1; l 2 Lt ; ~l
(9)
ts
RMsf ts =
X XX f 0 6=f i2T¹s j2Ji
l ® ¹ sij Pijf 0 f t~ l
8s; f; ts = 1; t = 1; l 2 Lt ; ~l
(10)
Eq.(11) is included to rectify capacity availability in the planning model. This correction is done based on the scheduling model task assignment (Wijts). Eq.(11) should be merely applied to those equipments which are production bottlenecks. Additionally, it is worth to mention that it must be checked that market demand is not actually the bottleneck process in the planning period, where scheduling is performed. X
l ijf f Pijff t~l ·
XX
Wijfts pti
8f; j 2 (Jbottle \ Jf ); t > 1; l 2 Lt ; ~l
i2Ij ts
i2Ij
(11)
As it can be noticed, Eqs.(7)-(11) can be easily unplugged from the whole model in case the decision maker decides not to consider scheduling issues. 3.1.2. Financial formulation and objective function The financial side of the problem is tackled through the inclusion of a set of constraints that characterize economical issues, such as payments to providers, short and long term borrowing, pledging decisions, buying/selling of securities, fixed assets acquisition. Furthermore, the expected corporate value (E[CV]), which is calculated using the discounted-free-cash-flow method (DFCF) as described by Eqns.(12)-(13), is the objective function used in this work. The complete set of financial constraints as well as the equations that permit the integration between finances and process operations models can be found in the work of Puigjaner and Laínez 2.
E[CV ] =
X ~L
L
P~
L
³
L
L
DF CF~ ¡ N etDebtT ~ L
L
´ (12)
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Integrating SC Decision Levels in a MPC Framework
L
DF CFT ~
L
0 XX =@ t
X
¡
l2Lt ~l 2ADl~
L
+
l F CFt~ l l 1 + W ACCt~ l
SV~LL L
(1 + W ACCT ~ )
1 ¢t A
(13) 8~L
T
L
4. Illustrative example The special characteristics of the proposed approach are highlighted by solving the design-planning of a SC comprising three potential facility locations that can act as distribution and/or processing sites. A set of potential equipment technologies are assumed to be available for the processing sites. Five products (P1-P5) can be manufactured into seven different equipments types (TA to TG); final products can be transferred to three markets (M1-M3) even without passing through distribution centers. Batch products P4 and P5, which are produced in batch equipments TD-TG, follow the STN example presented in Kondili et al2. A time horizon of five years is considered. It is composed of twelve planning periods with a length of one month each. In this example, market demand, prices of final products and interest rates are regarded as uncertain factors which unfold every year. A scenario tree which contains 32 leaf nodes (scenarios) is considered. It takes 27,970 CPU seconds to reach a solution for the design problem with a 5% integrality gap on an Intel Core Duo 2 computer using the MIP solver of CPLEX. 1 0.9 0.8
Financial Risk (Ω)
0.7 0.6 0.5 0.4 0.3 0.2
Stochastic Integrated Approach Deterministic Sequential Approach
0.1 0 0.5
1
1.5
2
CV (m.u.)
2.5
3 8
x 10
Figure 2. Financial risk curve of Corporate Value
The two stage shrinking horizon approximation presented in the work of Balasubramanian and Grossmann4 was used to solve the multistage stochastic problem. In the first step of the control strategy, a design problem is solved. For the first month the scheduling model is taken into consideration. The problem has been also solved using a sequential manner (bi-level optimization) in order to compare it with the proposed approach. In this sequential manner the scheduling is not included when dealing with the design of the SC network. As shown in Fig. 2, the E[CV] and financial risk for the traditional approach seem to yield to better values. It should be noted that differences may arise when executing detailed scheduling in the sequential approach. Obviously, this fact occurs because of the aggregated capacity overestimation.
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Recalling this fact, the MPC algorithm has been repeated during 10 planning month periods. Here, the uncertainty is assumed to unveil every month. The results are shown in Fig. 3. It can be noticed that the proposed integrated approach gives higher accumulated free cash flows (which are a key element in corporate value calculation) than the sequential one after the implementation of scheduling. An improvement of 12.33% is achieved. 6
Accumulated value
15
x 10
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10
5
0
−5
1
2
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4 5 6 7 Periods (month)
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Figure 3. Accumulated value for both approaches
5. Final considerations and future work A means of integrating the three standard SC decision levels is presented. Moreover, a novel SC design-planning model that permits a simple integration with scheduling models is proposed. The results show that significant improvements can be gained when all of these decision levels are incorporated into a single model. Moreover, the absence of scheduling can lead to apparently better corporate value which does not correspond to real scenario; resulting in myopic decision making. A drawback of the proposed approach is the computational burden that is required to solve the stochastic integrated monolithic model. Future work will be focused on applying decomposition strategies for tackling the aforementioned problem.
Acknowledgments Financial support received from the "Generalitat de Catalunya" (FI grants) and Ministerio de Educación y Ciencia (FPU grants). European Community (projects PRISM-MRTN-CT-2004-512233) is fully appreciated. Besides, financial support from Xartap (I0898) and ToleranT (DPI2006-05673) projects is gratefully acknowledged.
References 1. I.E. Grossmann, 2005, Enterprise-wide optimization: A new frontier in process systems engineering. AICHE J., 28, 260-275 2. L. Puigjaner, J.M. Laínez, 2007, Capturing dynamics in integrated supply chain management, Comput. Chem. Eng. ,doi:10.1016/j.compchemeng.2007.10.003. 3. E. Kondili, C. Pantelides, R. Sargent, 1993, A general algorithm for short-term scheduling of batch operations-I: MILP formulation, Comput. Chem. Eng., 17, 211-227. 4. J. Balasubramanian, I.E. Grossmann, 2004, Approximation to multistage stochastic optimization in multiperiod batch plant scheduling under demand uncertainty. Ind. Eng. Chem. Res., 43, 3695-3713.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Hybrid strategy for real time optimization with feasibility driven for a large scale three-phase catalytic slurry reactor Delba N.C. Meloa, Adriano P. Marianoa, Eduardo C. Vasco de Toledob, Caliane B. B. Costaa and Rubens Maciel Filhoa a
Laboratory of Optimization, Design and Advanced Control (LOPCA).Faculty of Chemical Engineering; State University of Campinas (Unicamp). P.O. Box 6066 13081-970, Campinas, SP, Brazil.
[email protected] b Petrobras SA, Paulínia Refinery (REPLAN),Rodovia SP 332 - KM 132, P.O. Box 1, CP: 13140-000. Paulínia, SP- Brazil.
Abstract In this work it is proposed a suitable hybrid optimization algorithm built up with the association of global and local optimization methods. The adopted computer assisted approach is driven by the need for a global optimization method characterized by efficiency in terms of reduced computational time and efforts whereas being robust. The basic idea is to join the fast convergence properties of gradient-based optimization methods with the wide exploration ability of population-based ones, which makes the developed algorithm a useful tool in real-time applications. Since unavoidable disturbances are present during process operation, efficient optimization algorithms must be available to deal in an on-line fashion with high dimensional and non-linear processes. In the developed code, a Genetic Algorithm (GA) is designed to provide an estimate of the global optimum. Then, a local method of search (the Sequential Quadratic Programming, SQP) is used to improve this candidate solution. As case study, the optimization of a three-phase catalytic slurry hydrogenation reactor is considered. The optimization algorithm determines, in real time, the optimal operating condition, defined in terms of maximization of profit. This condition should then be used in an advanced control layer. The results of the hybrid approach are compared with those obtained only considering the micro-GA. The latter approach was able to, alone, solve the optimization problem, but using a large number of generations and, consequently, with higher computational time. The advantage of the hybrid algorithm are that fewer number of generations is employed prior to the SQP utilization. Thus, the new GA-SQP code was able to determine the final solution considerably faster than the isolated GA, reducing the number of functions evaluations for solutions when compared to the number required for the GA to stop the evolution. The hybrid algorithm drives to feasible solution translated into higher profits at reasonable computational costs, being identified as a robust optimization code, useful in real time optimization applications. Keywords: Real-time Optimization, Genetic Algorithm, Sequential Quadratic Programming, Hybrid Algorithms, Hydrogenation Reactors.
1. Introduction On-line optimization must cope with the variability of the process conditions, originated by disturbances that significantly affect the process economy.
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The present work introduces a hybrid optimization algorithm, GA-SQP, which joins an initial genetic search to a deterministic optimization algorithm (Sequential Quadratic Programming, SQP). This sort of hybrid algorithm is demanded for efficient online optimization of high dimensional and non-linear processes, in which purely deterministic optimization algorithms normally fail to drive the process to the global optimum. In order to illustrate the application of the developed hybrid algorithm, the optimization of a three-phase hydrogenation catalytic slurry reactor is considered. The study aims to determine the optimal operating conditions that lead to maximization of profit. Some researchers have combined various optimization algorithms to improve the search efficiency and computational effort, including evolutionary algorithms (EA), simulated annealing (SA), particle swarm optimization (PSO), ant colony optimization (ACO), hybrid PSO-SQP, hybrid GA-ACO. Nevertheless, the combination of the GA and SQP algorithms is reported only in a few works [1,2].
2. Case Study- Three-phase hydrogenation catalytic slurry reactor In order to show the efficiency and applicability of the hybrid optimization algorithm, the three-phase catalytic reactor, in which the hydrogenation of o-cresol to 2-methylcyclohexanol takes place, is considered. This process was modeled by Mariano et al. [3]. The resistances to mass and heat transfers at the gas–liquid and liquid–solid interfaces, the heat exchange with the coolant fluid and the consideration of the physicochemical properties variation, which impacts on the mass and heat-transfer coefficients, were considered. The rigorous model also included a multi-component flash to consider the effect of the phase change of the reacting medium on the reactor dynamic behavior, as well as an appropriate procedure of correction of the global heattransfer coefficient to represent the phase change of the refrigerant fluid. The model developed by Mariano et al. [3] is therefore here used as internal process model for the optimization routine, which seeks the optimal process conditions that drive the reactor to maximization of profit.
3. Proposed Hybrid Optimization The proposed hybrid optimization algorithm is built up with the association of global and local optimization methods. The basic idea is to join the fast convergence properties of gradient-based optimization methods with the well-known ability of populationbased ones, which makes the developed algorithm a useful tool in real-time applications. In the developed code, a Genetic Algorithm (GA) is designed to provide an estimate of the global optimum. Then, a local method of search (Sequential Quadratic Programming, SQP) is used to improve this candidate solution. Figure 1 illustrates the basic idea of the hybrid algorithm. The hybrid optimization starts with the GA, which executes all subroutines until the specified number generations; the algorithm then shifts to the SQP, which is a faster method.
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Figure 1. Flowchart of the GA-SQP Hybrid Optimization Algorithm.
4. Optimization Problem Applied to the Case Study 4.1. Selection of the decision variables The decision variables used for the optimization of the reactor must be selected among the operating ones. After considering industry requirements, the effect of each of the operating variables on the objective function and the easiness of how these variables can be changed in the plant, the feed flow rate of hydrogen (FAo) and the reactor feed temperature (Tfo) were chosen as the decision ones. Thus the optimization routine searches for the values of FAo and Tfo that, with the current value of o-cresol flow rate, lead to maximal reactor profit. 4.2. Selection of objective function The optimization of any industrial process aims the profit maximization. Thus, the profit function is a natural choice as an objective function. The profit function, as outlined by Xiong and Jutan [4] and Sequeira et al. [5], can be calculated based on the selling price of the products and on the costs of raw materials, operation and energy. Then, in this work, the objective function, adapted to the multiphase reactor, is as follows: Profit = a*(FC) – b*(FAo-FA) – c*(FBo-FB)
(1)
where a is the selling price of the reaction product and b and c are the costs of raw materials; FA, FB and FC are the molar stationary flow rates of hydrogen, o-cresol and 2-methyl-cyclohexanol at the reactor exit, respectively and FAo and FBo are the flow rate of hydrogen and o-cresol in the feed. In Eq. (1), it is considered that there is a recycle of unreacted hydrogen and o-cresol. Since the remaining operating costs are fixed (salaries and others) and the energy cost related to the utilities can be considered negligible (the excess heat generated by the chemical reaction can be removed without significant cost [6]), the terms related to operating and energy costs do not appear in Eq. (1). It is important to stress that this work considers just the reactor itself in the hydrogenation plant and, therefore, the higher the o-cresol conversion, the greater the profit is expected to be. In this way, separation costs are not considered and, consequently, the profit here maximized is referred only to the reactor operation. Obviously, upstream and downstream operations have their own costs, which would decrease the calculated profits of Section 5.
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4.3. Optimization Problem The optimization problem considered is expressed by Eq. (2). Maximize Eq.(1) (FAo, Tfo) subject to model equations
(2)
In order to search for the optimum, the relations between variables must be given to an optimization algorithm. This is here provided by the model equations developed by Mariano et al. [3]. The model calculates all mass and heat transfers, besides the hydrogenation reaction rate. Since there are three phases (the catalysts is solid, the hydrogen is a gas and the o-cresol is liquid), both reactants must come to the solid pores, where the reaction takes place, and the unreacted reactants and the reaction product must then leave the catalyst particle. All these phenomena are accounted for by partial differential equations for mass and energy balances for each component in each phase. Since the feed flow rate of hydrogen and the reactants temperature are searched for, the upper and lower bounds stipulated for these variables in the optimization algorithms were selected according to the hydrogenation reaction stoichiometry and practical possible temperatures. For the optimizations here accomplished, the o-cresol feed rate was considered to be 1.29 kmol/h. In this way, Table 1 shows the lower and upper bounds of the considered decision variables. Table 1. Lower and upper bounds of the decision variables Variable
Lower bound 1.07 450.0
FAo (kmol/h) Tfo (K)
Upper bound 6.44 650.0
5. Results and Discussion 5.1. Optimization by Genetic Algorithm (GA) A binary micro genetic algorithm (GA) code was run for 50 generations with 5 individuals, totalizing 250 evaluations of the objective function. A maximum number of generations were used as stopping criterion in the genetic programming. The values for the crossover, the jump mutation and creep mutation probabilities (the genetic algorithm parameters) were previously optimized and the best ones were 0.5, 0.02 and 0.02, respectively. These values were the ones used in all optimization trials using the GA in this work. Table 2 brings the characteristics of the optimal operating point found solely by a micro-GA for the 50 generations, as well as the computational time demanded for the search (on a 2.8 GHz 768 Mb RAM AMD Athlon processor). Table 2. Optimal response found by micro-GA Optimal point and run characteristic
Profit (US$/h) o-cresol conversion (%) FAo (kmol/h) Tfo (K) Computational time (min)
Value 467.02 94.37 1.16 649.2 184
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Figure 2 shows the profit evolution for the best individual in each generation. This Figure shows how the solutions evolve in the 50 generations. Clearly the profit increases rapidly in the beginning of the search, but, after some generations, the rate of improvement gradually ceases, until almost no gain in the objective function is achieved in the last generations.
Figure 2. Evolution of the profit for each generation in a solely micro-GA optimization run
5.2. Hybrid optimization As it was observed in item 5.1, the GA was able to solve the problem after a large number of generations, consuming around 3h of CPU time, although it was also observed that the best fitness value does not change after a number of generations. In this way, a hybrid approach has been used, which couples GA with SQP. The GA procedure is used in the first stage to find a solution (i.e. an individual) within the attraction domain of the supposed global optimum. This solution is then used as initial guess for the SQP algorithm. The GA-SQP hybrid algorithm was built in order to run a micro-GA with the same code parameters as in section 5.1, except by the maximal number of generations, which was stipulated to 5. Afterwards, a SQP algorithm is used to improve the best individual found by the GA. Table 3 brings the optimal characteristics found by the hybrid algorithm, as well as the computational time the code demanded for the search. Table 3. Optimal response found by GA-SQP Optimal point and run characteristic
Profit (US$/h) o-cresol conversion (%) FAo (kmol/h) Tfo (K) Computational time (min)
Value 467.90 94.54 1.07 650.0 13
The hybrid structure was proved to be of high efficiency. First of all, it is easy to see, from Tables 2 and 3 that the profit and conversion are slightly greater for the optimal point found by the GA-SQP algorithm. Secondly, and very importantly, the computational time was significant lower for the hybrid algorithm, with scales compatible with real time applications for a supervisory control.
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The time demanded for an optimization algorithm to solve the problem is a consequence of the number of function evaluations it uses to come to the response. The micro-GA (section 5.1) evaluated the profit 250 times, each one for each individual of each generation. The GA-SQP, however, demanded just 31 function evaluations and, even so, achieved a better objective function value than the isolated micro-GA. The evolution of both algorithms (isolated GA and GA-SQP) during the search, as a function of objective function evaluations, is shown in Figure 3.
Figure 3. Trajectory of GA and GA-SQP methods towards the optimum point
6. Conclusions A hybrid optimization algorithm was developed joining a genetic search (GA) to the Sequential Quadratic Programming (SQP) algorithm. The developed code had its efficacy tested in the maximization of a hydrogenation reactor profit. Although no proof of convergence is available for GA-based codes in literature, the hybrid algorithm was able to solve the optimization problem, achieving a better optimal point within only 7% of the time demanded by a rigorous GA search. The computational time the GA-SQP algorithm solves the problem makes it a useful tool for real-time applications in a supervisory control structure.
Acknowledgements The authors acknowledge FAPESP (Fundação de Amparo à Pesquisa do Estado de São Paulo) for the financial support given to this work.
References [1] B. Mansoornejad, N. Mostoufi and F. Jalali-Farahani, Chem. Eng., in Press (2007). [2] R. Faber, H. Arellano-Garcia and G. Wozny, 2007. A Hybrid Optimization Approach to parameter Estimation. In: V. Plesu and P. S. Agachi (Eds.), Proceedings of the 17th European Symposium on Computer Aided Process Engineering (ESCAPE 17), Bucharest, Romania. [3] A. P. Mariano, E. C.Vasco de Toledo, J. M. F. Silva, M. R. Wolf-Maciel and R. Maciel Filho, Comp. Chem. Eng., 29 (2005), 1369. [4] Q. Xiong, A. Jutan, Chem. Eng. Sci., 58 (2003), 3817. [5] S. E. Sequeira, M. Herrera, M. Graells and L. Puigjaner, Comp. Chem. Eng., 28 (2004), 661. [6] J. F. Forbes, T. E. Marlin and J. F. MacGregor, Comp. Chem. Eng., 18(6) (1994), 497.
18th European Symposium on Computer Aided Process Engineering – ESCAPE 18 Bertrand Braunschweig and Xavier Joulia (Editors) © 2008 Elsevier B.V. All rights reserved.
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Adaptive Control of the Simultaneous Saccharification - Fermentation Process from Starch to Ethanol Silvia Ochoaa, Velislava Lyubenovab, Jens-Uwe Repkea, Maya Ignatovab and Günter Woznya. a
Department of Process Dynamics and Operation, Technical University of Berlin, Sekr. KWT 9, Strasse 17. Juni 135, Berlin 10623, Germany. b Institute of Control and System Research, Bulgarian Academy of Sciences, Sofia, Bulgaria.
Abstract In this paper, a new adaptive control strategy for the fed-batch Simultaneous Saccharification - Fermentation Process from Starch to Ethanol (SSFSE) process is proposed in order to maintain the glucose concentration at a quasi-equilibrium state by feeding starch into the process only when the glucose production rate is lower than its consumption rate. By maintaining the equilibrium state for the glucose, it is possible to reach higher values for the ethanol production rate for a longer time; and therefore to increase the ethanol concentration along the process. As the adaptive controller requires online information about the glucose production and consumption rates, software sensors for them are developed. The difference between the estimated values for the consumption and production rates is considered as a control marker, which is used for determining the feeding profile of starch into the fermentor. Keywords: Adaptive Control, Soft sensors, Ethanol, Fed batch process.
1. Introduction During the past years, the demand for the production of bio-fuels has increased rapidly, especially in the bioethanol case, which currently is produced mostly from sugar cane and starch - containing raw materials. Traditionally, ethanol production from starchy materials is done in a sequential two-step process which includes two main stages: i) the enzymatic hydrolysis of starch to glucose (by means of the enzymes α- amylase and glucoamylase) and ii) the fermentation of glucose to ethanol (mostly by the action of yeast). A crucial drawback of the sequential (two-step) process is the slow hydrolysis rate (usually hours) due to the reduction of the enzymatic activity caused by an inhibitory effect when high sugar concentrations are present. A challenging perspective to overcome this problem and at the same time to increase the yield of the ethanol production process is to conduct the process in a one-step mode doing the simultaneous saccharification and fermentation of starch to ethanol (SSFSE) by means of recombinant strains (Altintas et al., 2002.). In this way, the ethanol production process from starch is more efficient not only in terms of saving overall production time but also in terms of reducing equipment costs. Due to these reasons, the SSFSE process seems to be a suitable alternative for bio-ethanol production at an industrial level. It is important to notice that as have been stated by Nakamura et al. (1997), by means of a fed-batch
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SSFSE process, the ethanol production can be enhanced when compared to a batch process. For all these reasons, in this work a novel adaptive control scheme for a fedbatch SSFSE process is proposed, which due to its simplicity is suitable for industrial applications.
2. Soft Sensors Development 2.1. Model for Control According to the well known General Dynamical Model Approach by Bastin and Dochain (1990), a model for the control of the process can be derived on the basis of a process reaction scheme. For the bio-ethanol production from starch by Saccharomyces cerevisiae, the reaction scheme can be assumed as shown in Figure 1. ϕ1 S ⎯⎯→ G
ϕ2 G ⎯⎯→ X + Enz
ϕ3 G ⎯⎯→ E
Figure 1. Reaction scheme for the bio-ethanol process.
The model for control for the fed batch process is given by (Lyubenova et al; 2007): dS F = −ϕ1 + [S − Sin ] V dt
(1)
dG F = k1ϕ1 − k2ϕ 2 − k3ϕ 3 − G V dt
(2)
dX F = ϕ2 − X V dt
(3)
dE F = ϕ3 − E V dt
(4)
dEnz F = k4ϕ 2 − Enz V dt
(5)
dV =F dt
(6)
Where S, G, X, E and Enz are respectively the starch, glucose, cells, ethanol and enzyme concentrations inside the reactor, Sin is the starch concentration on the feed, F is the feed flow rate, V is the volume of liquid in the fermentor and ϕ1, ϕ2, ϕ3 represent the reaction rates for starch degradation, cells growth and ethanol production, respectively. The unstructured model presented in (Ochoa et al., 2007) is used here as the “real” plant. The ki (for i=1 to 4) kinetic parameters of the model for control were identified by an optimization procedure given in Mazouni et al. (2004), using as error index the mean square error between the state variables of the unstructured model and the model for control. 2.2. Soft Sensors of Glucose Production and Consumption rates: As the main purpose of this paper is to implement an adaptive control strategy for controlling the SSFSE process by means of starch feeding only when the glucose consumption rate is higher than its production rate; it is necessary to follow these two rates on line. Unfortunately, such kind of sensors are not available and therefore, soft
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sensors must be developed. For that purpose, in the following it is assumed that on-line starch and glucose concentrations measurements are available. 2.2.1. Soft sensor of glucose production rate The software sensor for ϕ1 is an observer-based estimator with the following structure:
(
dSˆ F F = −ϕˆ1 − S m + Sin + C1 Sm − Sˆ V V dt
(
dϕˆ1 = C2 S m − Sˆ dt
)
(7)
)
(8)
where C1 and C2 are tuning parameters and Sm is the measurement value for the starch considering white noise (ε). Glucose production rate θ1 is estimated using the first term of the right hand side of equation (2), that is: ∧
∧
θ1 = k1 ϕ1
(9)
2.2.2. Soft sensor of glucose consumption rate By observing equation (2), it can be seen that glucose consumption rate θ2 is given by: (10)
θ 2 = k2ϕ2 + k3ϕ3
Where an estimator of θ2 can be obtained by:
(
dGˆ ∧ ∧ F = θ1 − θ 2 − Gm + C3 Gm − Gˆ V dt ∧
(
d θ2 = C4 Gm − Gˆ dt
)
(11)
)
(12)
where C3 and C4 are tuning parameters and Gm is the measurement value for the glucose considering white noise. The four tuning parameters are found using the procedure described in Ignatova et al. (2007). For the present case, the expressions shown in Figure 2 are applied. C1 = 2ξ
C3 = 2ξ
2
m11s 2m21s
C2 =
C1 4ξ 2
m11g
C4 =
C3 4ξ 2
2m21g
2
Figure 2. Tuning Parameters for the Estimators (Ignatova et al. 2007) ∧
∧
where m11s and m21s are the upper bounds of d ϕ1/ dt and d θ 2 / dt ; m21s and m21g are the upper bounds of additive noise for starch and glucose measurements respectively, and ξ is a damping coefficient taken as an usual value of 0.99 (Bastin and Dochain, 1990). The white noise signals, ε , simulate measurement noises at standard deviation of 5% of the mean of S and G concentrations. The optimal values for the tuning parameters Ci are C1=1.23, C2=0.386, C3=4.427, C4=5; using m11s=0.35, m21s=1.3, m11g=0.45, and m21g=0.1. In Figure 3, the glucose consumption and production rates soft sensors are compared to the values obtained in the real plant (unstructured model); it can be seen that the observers track adequately the behavior of the true values.
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Glucose Production /Comsumption Rates (g/lh)
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Figure 3. Soft Sensors Vs Real Plant (Unstructured Model)
3. Adaptive Controller Usually it is claimed that a fed-batch process (when compared to a batch) offers the main advantage of having a dilution ratio that is used as a degree of freedom for control purposes. However, it is not straightforward to calculate a suitable dilution rate (or a feeding profile), because when this is too high, the concentration of the metabolite of interest can be decreased due to the dilution effect. Additionally, when the dilution rate is too low, it is possible that the substrate fed into the process be not enough to fulfill the requirements for cell growth, cells maintenance and product formation. Therefore, in this paper, it is proposed to calculate the dilution rate as a function of the glucose production and consumption rates; in order to keep a balance between them. Besides, we propose to feed starch into the process only when the process really needs it, that is, when the glucose production rate is lower than its consumption rate. For that purpose, in this work a marker is used as a switch to decide between batch (without feeding) or fed batch operation. The marker, used in the adaptive control scheme proposed in Figure 4, is defined as follows: ∧
∧
Δ = θ1− θ 2
(13)
The marker is the difference between the glucose production and consumption rates, ∧
∧
where θ1 ,θ 2 are the corresponding values predicted by the software sensors presented in section 2. As mentioned by Kapadi and Gudi (2004), usually it is considered that the feeding stream to the process contains not only starch but also glucose (∼15% of the starch concentration), due to the previous autoclaving of the starch. Therefore, the mass balance for the glucose should consider this term as follows: d (GV ) = g input + g produced − g depleted dt
(14)
dG F (Gin − G ) = +Δ dt V
(15)
Where g represent the glucose mass flow rates (fed into the process, produced or consumed) and Gin is the glucose concentration on the feed stream. Assuming that after an initial batch period, the glucose concentration in the fermentor reaches an equilibrium state, we have:
Adaptive Control of the SSFSE Process
F =−
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Δ ⋅V Gin − G
(16)
Furthermore, after the initial batch period Gin>>G; therefore, the control law for calculating the feeding rate of starch into the fermentor is given by: F ≈−
Δ ⋅V = − KVΔ Gin
(17)
Equation 17 shows the control law that should be applied for maintaining the glucose concentration in an equilibrium state reaching a balance between the glucose production and consumption rates. By analyzing equation 17, it is possible to see that the dilution rate will be calculated by means of a proportional feedback controller in which the feedback error is taken as the deviation between both rates. Of course, control law (17) will present offset due to the fact that an integral action is not taken into account as part of the control calculations, but as the idea of this paper is to present a simple and easy way to implement the control law, we decided to allow the offset error. In Figure 4 it is shown the adaptive control scheme proposed in this work for controlling the SSFSE process. S F
Control Algorithm Adaptive Controller
Δ
Process (unstructured model)
-θ2
θ1
Estimators
+ε +ε
G
Sm Gm
Figure 4. Adaptive control scheme of the SSFSE process
It is important to remark that the control scheme proposed in Figure 4 is catalogued as adaptive (according to the definition by Bastin and Dochain (1990)), because it has the potential to adapt itself (due to the online estimations given by the soft sensors) to variations in the kinetics of the process.
4. Example: Adaptive Control of the SSFSE process The control scheme shown in Figure 4 was applied to the SSFSE process using the fed batch version of the unstructured model proposed in Ochoa et al. (2007) as the object for control. Simulations of starch and glucose concentrations are corrupted by additive noise ε. These white noise signals, simulate measurement noises at 5% of the standard deviation for the mean values of both S and G concentrations. As stated before, the control law (17) will be applied only when the marker is negative; therefore, the control algorithm block is expressed as follows: if Δ ≥ 0 0 F =® ¯− KVΔ if Δ < 0
(18)
In Figure 5 are shown the simulation results for the ethanol concentration and the ethanol growth rate for the fed batch SSFSE process using a starch input concentration of 50g/l (containing 7.5g/l of glucose available due to autoclaving), applying the adaptive control scheme (Figure 4). Besides, the fed batch results are compared to those for the batch process, which was open loop simulated using the model given in Ochoa et al. (2007). It can be seen that the ethanol concentration (and therefore the productivity) for the controlled fed batch process is higher than the ethanol concentration reached
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under batch operation. Furthermore, it is important to remark that the ethanol production rate in the fed batch process can be kept at higher values than for the batch, assuring a more productive process. 18
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Figure 5. Ethanol concentration (left side) and ethanol production rate (right side): controlled Fed batch vs. Batch.
5. Conclusions In this paper, an adaptive control strategy for the fed-batch SSFSE process was proposed, convergence and stability will be analyzed in a future work. The process is monitored by means of software sensors for glucose consumption and production rates. The difference between the estimated values for the consumption and production rates is considered as a control marker, which is used for i) switching from the batch to the fed-batch phase automatically, and ii) for determining the magnitude of the input flow required to maintain the desired value for the glucose. By maintaining that quasiequilibrium state, it was possible to avoid a fast decrease in the ethanol production rate, and therefore to continue producing ethanol for a longer time, improving the productivity of the process.
References M. Altintas, B. Kirdar, Z. I. Önsan and K. Ülgen. 2002, Cybernetic Modelling of growth and ethanol production in a recombinant Saccharomyces cerevisiae strain secreting a bifunctional fusion protein, Process Biochem., 37, 1439-1445. G. Bastin and D. Dochain. 1990. On-line estimation and adaptive control of bioreactors. M. Ignatova, V. Lyubenova, M.R. García and C. Vilas. 2007, Indirect adaptive linearizing control of a class of bioprocesses – Estimator tuning procedure, Journal of Process Control, In Press. M Kapadi and R Gudi. 2004. Optimal Control of Fed-batch Fermentation Involving Multiple Feeds using Differential Evolution. Process Biochemistry 39, 1709-1721. V. Lyubenova, S. Ochoa, J-U. Repke, M. Ignatova and G. Wozny. 2007, Control of one Stage Bio Ethanol Production by Recombinant Strain, Biotechnol. & Biotechnol. Eq. D. Mazouni, M. Ignatova, and J. Harmand. 2004, A simple mass balance model for biological sequencing batch reactors used for carbon and nitrogen removal, Proceedings of the International IFAC Workshop Decom-TT’2004 Automatic Systems for Building the Infrastructure in Developing Countries Regional and Global Aspects, 283–288. Y. Nakamura, F. Kobayashi, M. Ohnaga and T. Sawada. 1997. Alcohol Fermentation of Starch by a Genetic Recombinant Yeast Having Glucoamylase Activity. Biotechnology and Bioengineering, 53, 21–25. S. Ochoa, A. Yoo, J-U. Repke, G. Wozny and D.R. Yang. 2007, Modeling and Parameter Identification of the Simultaneous Saccharification-Fermentation Process for Ethanol Production, Biotechnol. Prog., 23, 1454-1462.
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Advanced Control Monitoring in Petrobras’ Refineries: Quantifying Economic Gains on a RealTime Basis Rafael Pinotti,a Antonio Carlos Zanin,a Lincoln Fernando Lautenschlager Moroa a
Petrobras, Refining Technology, Optimization,Av. República do Chile, 65, Sala 2102, Centro, Rio de Janeiro - 20031-912 - Brazil Abstract In this paper we describe how Petrobras’ engineers have been using information from real-time databases in order to continuously monitor the performance of advanced control applications, including the calculation of economic gains. The monitoring uses formulas that take into account feed flow rates, targets calculated by the optimization layer of multivariable control, controlled variables upper and lower limits and other parameters. The economic benefits are based on the degrees of freedom and the active constraints at the steady state predicted by the linear model embedded in the controller. In order to improve the current monitoring, parameters dealing with process variability will be incorporated in the formulas. By doing this, it will be also possible to quantify external disturbances that affect the performance of the advanced control systems and identify regulatory control problems.
Keywords: advanced control monitoring, industrial automation, refining industry, online optimization
1. Introduction The Advanced Control Monitoring in Petrobras’ refineries serves a twofold objective: to evaluate the efficiency of the installed applications, and to manage the engineering staff aiming at the improvement of this efficiency, which can be translated through adequate formulas into economic gains. The fact that Solomon’s 2006 Worldwide Refining APC/ Automation Performance Analysis placed Petrobras in the second quartile, and one particular refinery in the first quartile, shows us not only that we have managed well the applications and the several systems that support them, such as DCS and data banks, but also that there is still room for improvement. Advanced Control applications are part of the broader context of Industrial Automation, a multidisciplinary activity which has evolved for more than twenty years in our refineries, so it seems fit to start with a brief history of Industrial Automation in the Downstream area of the company. This is dealt with in section 2. Section 3 explores the details of the monitoring process and the plans to develop a more comprehensive approach by adding measures of
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process variability. Section 4 shows the results obtained by the management of advanced control applications, and section 5 summarizes the main conclusions. 2. Industrial Automation in Downstream Nowadays every Brazilian oil refinery has at least one operating advanced control application. This is the result of many years of investment in hardware, software and the development of human resources. Additionally, real time optimization systems are being successfully implemented in many units. Industrial Automation history in the Petrobras’ Downstream area can be traced back to 1986, when the company decided to replace old analog instrumentation by digital control systems (DCS), which, given the sheer size of the refining park, with 10 oil refineries, demanded a considerable investment. A second stage was initiated in 1989, with the issue of a general plan, focusing on the rate of return of investments in industrial automation. It was acknowledged then that this return would only be fully realized through the implementation of systems aiming the real time optimization of process units. This situation prompted a significant investment in: • An array of technical training to the technical staff, ranging from specialization to doctoral work, in order to provide the company with high level human resources; • Development of Multivariable Predictive Control (MPC) algorithms [1] and inferences, through a gradual absorption of technology; • Widespread installation of automation systems, including advanced control, real time optimization, blending, etc. A third stage has been initiated around the year 2000, focusing on the effectiveness of the installed applications. In order to guarantee such effectiveness a series of actions has been planned and executed: • Development of a benefits evaluation methodology for each kind of optimization application [2]; • Rigorous monitoring of the actual results; • Technical assistance to solve problems that negatively impact the applications performance; • Continuous improvement of the technology and software; • High level training to improve the technical skills of users and developers; • An extensive optimization program, involving the mathematical modeling of all process units and the use of these models to define the operating targets. 3. Advanced Control Monitoring The main benefits that can be obtained from advanced control are:
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• • • • • •
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Improvement in product quality; Increased yields of the most valuable products; Increase in unit feed flow rate; Energy savings; Improved operational stability; Increased unit operational factor by protecting the process from violating operational constraints.
It is usually assumed that an advanced control application will reduce the standard deviation of controlled variables by at least 50%. This allows the controller to move the controlled variables closer to the constraints, without increasing the probability of off-spec production, as illustrated in figure 1. Cutler and Perry [3] state that available benefits for on-line optimization plus advanced control can amount to 6-10% of the added value of a given process. The basis for the monitoring methodology is the fact that the economic benefits from the advanced control are directly associated with the activation of process constraints within the operating region, that is, a good control system pushes as many as possible controlled variables to their limits, although it is not always true due to the nonlinearities involved. Thus, each control application calculates an index, defined as:
PCAT =
Nactcontr × 100 Nman
Figure 1 – Illustration of Advanced Control Benefits
Where PCAT stands for Percent of Active Controlled Variables, while Nactcontr is the number of active controlled variables and Nman is the total number of manipulated variables. However, this formula has to be corrected with a factor PCATopt (Optimum PCAT) due to the fact that not every manipulated variable
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corresponds to a degree of freedom and that disturbances in the unit prevent the controller from operating continuously at constraints. So, the economic benefits from the application are calculated as follows:
$CAV = $ Benefit ×
PCAT PCATopt
Where $CAV is the economic benefit obtained and $Benefit is the standard benefit for the unit, drawn from literature or from process data before and after advanced control implementation. Both have units of dollars per unit feed flow rate. The Optimum PCAT is defined as:
PCATopt =
fd × PNactcontr × 100 Nman
Where fd is a factor (smaller than 1) used to compensate for unit disturbances, and PNactcontr is the potential number of active controlled variables, which is defined according to the optimization objectives and the controller potential for effective action upon these variables. 4. Results The Advanced Control Performance Index for each application is defined by the fraction PCAT/PCATopt [2], where PCATopt is defined caseby-case. The Performance Index for a whole refinery is calculated as a weighted average of the application indexes, with each weight corresponding to the application economic benefit. Although the Performance Index has oscillated substantially for some refineries, the general average has been fairly stable above 80%, with a slight tendency for increase. This methodology can pinpoint applications that demand technical assistance, but a thorough performance assessment requires a more detailed analysis. More specifically, the current methodology has the following disadvantages: it offers only a macroscopic analysis of the applications; it does not give a statistical distribution of the active variables, which is of great value for the improvement of the operating systems; it does not assess the operational stability of the process. So, a computational solution has been developed to provide valuable information on the statistical distribution of active variables, both controlled and manipulated. It consists, as shown in figure 2, of a Visual Basic tool, which gets data from the process historian and from the MPC configuration database. The tool can generate reports in Excel format. Figure 3 shows a a general view of the controlled (CV) and manipulated (MV) variables. Figure 4
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shows a VB display for the end point of gasoline, a very important product quality parameter and an advanced control controlled variable as well. As for the operational stability of the process, Petrobras has recently developed another VB tool, which also generates excel reports. The mathematical basis for the measurement of operational stability is focused on the standard deviation of process variables related to product quality (mainly product draw temperatures from fractionators). Petrobras joined the group of oil companies that participated in Solomon’s 2006 Worldwide Refining APC/ Automation Performance Analysis, and the final report ranked Petrobras, in the second quartile, with one particular refinery in the first quartile.
Figure 2 – Computational Tools for Advanced Control Monitoring
Figure 3 – VB display of a general view of the variables
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5. Conclusions The advanced control applications installed in Petrobras’ refineries are part of an Industrial Automation effort that goes back more than twenty years. The recent focus on the monitoring of these applications in order to guarantee the realization of their full economic benefit has prompted the development of a useful methodology, which shows that we are now reaping more than 80% of the potential benefits, on average. However, this methodology has a macroscopic nature.
Figure 4 – VB display of the gasoline ASTM end point New tools have been recently developed allowing a thorough analysis of each application in terms of statistical distribution of active variables and of process variability. The last Solomon APC Study has evidenced the fact that the company has a good position among the leading oil companies with respect of advanced process control and automation performance in general. References 1. L. F. L. Moro, D. Odloak, 1995, “Constrained multivariable control of fluid catalytic cracking converters”. Journal of Process Control, v.5, n.1, p.29-39. 2. A. C. Zanin, L. F. L. Moro, 2004, “Gestão da Automação Industrial no Refino”. Rio Oil & Gas Expo and Conference. 3. C. R. Cutler, R. T. Perry, 1983, “Real time optimization with multivariable control is required to maximize profits”. Computers and Chemical Engineering, v.7, n.5, p.663-667.
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Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation Diego Martinez Prata, José Carlos Pinto, Enrique Luis Lima Programa de Engenharia Química/COPPE/UFRJ, Cidade Universitária, Rio de Janeiro - CP 68502, CEP 21945-970, Brasil.
Abstract This paper presents a comparative performance analysis of various robust estimators used for nonlinear dynamic data reconciliation process subject to gross errors. Robust estimators based on cost functions derived from robust probability theory reduce the effect of gross errors on the reconciled data, avoiding the traditional iterative requirement procedures. The following robust probability functions were compared in this paper: Cauchy, Fair, Hampel, Logistic, Lorentzian, Normal Contaminated and Welsch. As a benchmark for this study it was adopted a nonlinear CSTR frequently reported in the process data reconciliation literature. The comparative analysis was based on the ability of the reconciliation approaches for reducing gross errors effect. Although the presence of constant biases has represented a problem for all the analyzed estimators, Welsch and Lorentzian cost functions, in this order, have shown better global performance. Keywords: Nonlinear dynamic data reconciliation, robust estimation and gross error.
1. Introduction Nowadays, data reconciliation (DR) represents an important step for many engineering activities in chemical processes as for example real time optimization and control implementations. It adjusts the measurement data, usually assumed associated to normally distributed random errors, to satisfy process constraints. However, to obtain satisfactory estimates, the negative influence of less frequently gross errors should be eliminated. This class of errors can be considered measurements that do not follow the statistical distribution of the bulk of the data. Gross errors can be divided in two classes: outliers and bias. The first class may be considered to include some abnormal behavior of measurement values as for example process leaks or malfunctioning instruments. The second class refers to the situation in which the measurement values are systematically too high or too low. A number of approaches have been proposed to deal with gross errors, mainly related to their detection and elimination. The traditional methods include serial elimination, compensation, and combinatorial ones, however these approaches are based on the assumption that the measurements are normally (Gaussian) distributed in which case Corresponding author:
[email protected]
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Weighted Least Squares (WLS) is the maximum likelihood estimator. As gross errors do not satisfy this ideal assumption an iterative sequential procedure is necessary for gross error detection and elimination, increasing computational effort. Tjoa and Biegler (1991) proved that using the Contaminated Normal estimator instead of the WLS one, any outlier present in the measurements could be replaced with reconciled values, without requiring iterative detection and elimination procedures. Johnston and Kramer (1995) reported the feasibility and better performance of robust estimators when used to cope with DR problems in the presence of gross errors. Subsequently, different types of robust estimators and their performance on DR were reported (Table 1). These studies have shown the potential of robust statistics to perform DR in the presence of gross errors, resulting in robust estimators that are insensitive to deviations from ideal assumptions, tending to look at the bulk of the measured data and ignoring atypical values. Table 1 Examples of Robust Estimators used for Data Reconciliation
Author (Year) Tjoa and Biegler (1991) Johnston and Kramer (1995) Zhang et al. (1995)R Albuquerque and Biegler (1996) D Chen et al. (1998)R Bourouis et al. (1998) R Arora and Biegler (2001) D Özyurt and Pike (2004) R Wongrat et al. (2005) Zhou et al. (2006) R
Estimator Applied Normal Contaminated Normal Contaminated and Lorenzian Normal Contaminated Normal Contaminated and Fair Fair and Lorenzian Normal Contaminated Hampel Normal Contaminated, Cauchy, Fair, Logistic, Lorenzian and Hampel Hampel Huber
Works applied on real plant data (steady state conditions).
D
Works applied in NDDR.
In our knowledge robust estimators have not been applied in nonlinear dynamic real plant data yet. The first comparative study among some robust estimators in DR has been presented by Özyurt and Pike (2004). They conclude that the estimators based on Cauchy and Hampel distributions give promising results, however did not consider dynamic systems. Other earlier studied has been accomplished by Basu and Paliwal (1989) in autoregressive parameter robust estimation issues, showing that for their case the Welsch estimator produced the best results. This work presents a comparative performance analysis among some robust estimators (all estimators reported by Özyurt and Pike, 2004, and Welsch estimator) for nonlinear dynamic data reconciliation (NDDR in the presence of gross errors.
Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation 503
2. Problem formulation The most important robust estimators for data reconciliation belong to the class of M-estimators, which are generalizations of the maximum likelihood estimator. Assuming uncorrelated measurement data their covariance matrix becomes diagonal and the generalized DR problem has the form, § z yi min ¦ U ¨ i i © Vi s. t. ª dy t º , y t » f« ¬ dt ¼
b ¬ª y t ¼º
· ¸ min ¦ U ([i ) i ¹
(01)
0 (02)
0
g ª¬ y t º¼ t 0 where ȡ is any reasonable monotone function used for DR formulation, ıi and ȟi are, respectively, the standard deviation and the standard error of the discrete measured variable zi, y is the vector of estimated functions yi (reconciled measurements, model parameters and non-measured variables), f is a vector of dynamic constraints, h and g are, respectively, vectors of equality and inequality algebraic constraints. As an example, using the generalized formulation the ȡ functions for the weighted least squares and Welsh estimators take the following forms, WLS
UWLS ([ )
1 2 [i 2
Welsch
UW ([ , cW )
cW2 2
° ª § [ · 2 º ½° « ¨ i ¸ » ¾ 1 exp ® «¬ © cW ¹ »¼ ¿° °¯
(03)
(04)
where cW is a tuning parameter related to asymptotic efficiency (Rey,1988). Methods used to measure the robustness of an estimator involve an influence function (IF) that can be summarized by the effect of an observation on the estimates obtained (Arora and Biegler, 2001). The Welsch M-estimator introduced by Dennis and Welsch (1976) is a soft redescending estimator that, as the Cauchy estimator, presents an IF asymptotically approaching zero for large |ȟ|. The 95% asymptotic efficiency on the standard normal distribution is obtained with the tuning constant cW = 2.9846. Figures 1 and 2 show, respectively, the effect of the standard error on the standardized ȡ functions and influence functions for the WLS and Welsch
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estimators. It can be observed in both figures that the robust estimator is much less influenced by large errors. 50
4
40 Influence Functions
ȡ functions
3 30
20
2
1 10
0 -10
0 -5
0
5
Standard Error
Fig. 1. ȡ: WLS (---) and Welsch (ņ).
10
0
5
10
15
20
Standard Error
Fig. 2. IF: WLS (---) and Welsch (ņ).
Several strategies have been proposed to solve constrained nonlinear dynamic programming problems (Biegler and Grossman, 2004). In this work a sequential strategy is applied to a time moving window (size = 5). For every sample time the differential equations of the dynamic constraints and the nonlinear programming optimization problem are solved sequentially using the measured data over the window until convergence is reached. The optimization problem is solved using the Gauss-Newton based solver ESTIMA (Noronha et al., 1993). 3. Illustration example
The performance of the robust estimators has been tested on the same CSTR used by Liebman et al. (1992) where the four variables in the system were assumed to be measured. The two input variables are the feed concentration and temperature while the two state variables are the output concentration and temperature. Measurements for both state and input variables were simulated at time steps of 1 (scaled time value corresponding to 2.5 s) adding Gaussian noise with a standard deviation of 5% of the reference values (see Liebman et al., 1992) to the “true” values obtained from the numerical integration of the reactor dynamic model. Same outliers and a bias were added to the simulated measurements. The simulation was initialized at a scaled steady state operation point (feed concentration = 6.5, feed temperature = 3.5, output concentration = 0.1531 and output temperature = 4.6091). At time step 30 the feed concentration was stepped to 7.5. Due to space limitations, only results of output concentration and temperature for the WLS and Welsch estimators are presented in Figures 3, 4, 5 and 6. The symbols (ņ), (ż) and (Ɣ) represent the “true”, simulated and reconciled data, respectively. The output temperatures plotted have been magnified to emphasize the effect of the bias on their estimates.
Comparative Analysis of Robust Estimators on Nonlinear Dynamic Data Reconciliation 505
5.20
0.17
Output Temperature (scaled)
Output Concentration (scaled)
0.19
Bias
0.15 0.13 0.11 0.09 0.07 Outlier
0.05 0.03
5.10 5.00 4.90 4.80 4.70 4.60 4.50 4.40
0
20
40 60 Sampling Instant (scaled)
80
100
70
80 85 90 Sampling Instant (sacled)
95
100
Fig. 4. WLS: Output Temperature.
Fig. 3. WLS: Output Concentration. 5.20
0.19 0.17
Output temperature (Scaled)
Output Concentration (scaled)
75
Bias
0.15 0.13 0.11 0.09 0.07 Outlier
0.05
5.10 5.00 4.90 4.80 4.70 4.60 4.50 4.40
0.03 0
20
40 60 Sampling Instant (scaled)
80
Fig. 5. Welsch: Output Concentration.
100
70
75
80 85 90 Sampling Instant (scaled)
95
100
Fig. 6. Welsch: Output Temperature.
Comparing Figures 3 and 5 it can be seen that in the presence of an outlier in sampling time 25 the reconciled output concentrations using the robust Welsch estimator are better that the ones using the WLS estimator, which presents smearing values around this sampling time. However, even a robust estimator can result in biased estimates in the presence of a bias as can be seen around sampling times 80-82. In this work the time varying window always corresponds to measured values. However if the time varying window is built with the measured values at the current sample time and the already reconciled values at past sample times the effect of a bias will be minimized. Figures 4 and 6 show the effect of bias measurements in the reconciled values of the output temperature, and again the WLS estimator results in worst estimates. Looking for a fair comparison among the estimators it was used the TER (Total Error Reduction) criteria proposed by Serth et al. (1987) that can be applicable when the “true” values are known. Table 2 summarizes the results obtained and shows best results for the Welsch and Lorentzian estimators. Table 2. TER analysis results for the estimators studied.
Estimator Applied WLS Normal Contaminated Cauchy Fair Hampel Logistic Lorentzian Welsch
Output Concentration 0.2040 0.2885 0.3667 0.4072 0.3953 0.3633 0.4290 0.4724
Output Temperature 0.9501 0.9635 0.9631 0.9632 0.9622 0.9628 0.9655 0.9657
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4. Conclusions
In this work a comparative analysis of the capacity of robust estimators to reduce the negative effect of gross errors on nonlinear dynamic data reconciliation was accomplished. The results obtained have shown that among the studied cases the Welsch and Lorentzian robust estimators produced better reconciled values, but they also have shown that, although the robust estimators were more efficient in reducing the effect of biases, this problem still deserves more investigation. References Albuquerque, J. S., Biegler, L. T., 1996. Data Reconciliation and Gross-Error Detection for Dynamic Systems. AIChE J. 42, 2841. Arora, N., Biegler, L. T., 2001. Redescending estimators for Data Reconciliation and Parameter Estimation. Comput. Chem. Eng. 25, 1585. Basu, A., Paliwal, K. K., 1989. Robust M-Estimates and Generalized M-estimates for Autoregressive Parameter Estimation. TENCON 89, 4th IEEE region 10 Int. conf., Bombay. Biegler, L. T., Grossmann, I. E., 2004. Retrospective on optimization. Comput. Chem. Eng., 28, 1169. Bourouis, M., Pibouleau, L., Floquet, P., et al., 1998. Simulation and data validation in multistage flash desalination plants. Desalination. 115, 1. Chen, X., Pike, R. W., Hertwing, T. A., Hopper, J. R., 1998. Optimal Implementation of On-Line Optimization. Comput. Chem. Eng. 22, S435. Dennis, J. E., Welsch, R. E., 1976. Techniques for Nonlinear Least Squares and Robust Regression. Proc. Amer. Statist. Ass. 83-87. Johnson, L. P. M., Kramer, M. A., 1995. Maximum Likelihood Data Rectification: Steady-State Systems. AIChE J. 41, 2415. Liebman, M. J., Edgar, T. F., Lasdon, L. S., 1992. Efficient Data Reconciliation and Estimation for Dynamic Processes Using Nonlinear Programming Techniques. Comput. Chem. Eng. 16, 963. Noronha, F.B., Pinto, J.C., Monteiro, J.L., et al.. 1993. Um Pacote Computacional para Estimação de Parâmetros e Projeto de Experimentos, Technical Report, PEQ/COPPE/UFRJ. Özyurt, D. B., Pike, R. W., 2004. Theory and practice of simultaneous data reconciliation and gross error detection for chemical process. Comput. Chem. Eng. 28, 381. Rey, W. J. J., 1983. Introduction to Robust and Quasi-Robust Statistical Methods. SpringerVerlang, Berlin/ new York. Serth, R. W., Valero, C. M., Heenan, W. A., 1987. Detection of gross errors in nonlinearly constrained data: a case study. Chem. Eng. Commun. 51, 89. Tjoa, I. B., Biegler, L. T., 1991. Simultaneous Strategy for Data Reconciliation and Gross Error Detection of Nonlinear Systems. Comput. Chem. Eng. 15, 679. Wongrat, M., Srinophakun, T. Srinophakun, P., 2005. Modified genetic algorithm for nonlinear data reconciliation. Comput. Chem. Eng. 29, 1059. Zhang, Z., Pike, R.W., Herting, T., 1995. Source reduction from chemical plants using on-line optimization. Waste Management. 15, 183. Zhou, L., Su, H., Chu, J., 2006. A new method to solve robust data reconciliation in nonlinear process. Chinese J. Chem. Eng. 14, 357.
Acknowledgements The authors would like to thank CNPq and CAPES for financial support.
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State estimation for dynamic prediction of hydrate formation in oil and gas production systems J. Rodriguez Perez, C.S. Adjiman, C.D. Immanuel Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K.
Abstract Since oil and gas production is moving to deeper waters, subsea pipelines are being subjected to higher pressures and lower temperatures. Under such conditions, the formation of hydrates is promoted. Hydrates are solid, non-flowing compounds of gas and water whose formation can cause line blockages, with the consequent economical losses and safety risks. The increasing hydrate formation propensity suggests the necessity to predict the possibility of hydrate formation in on-line operation so as to take preventive control actions and thereby provide flow assurance. Although a detailed dynamic model will enable the prediction of the possibility of hydrate formation, model inaccuracies and process disturbances will make this prediction less accurate. The usage of key available measurements will enable to address these disadvantages. The aim of this paper is to develop a combined state and parameter estimator for this process, by combining a dynamic model with available measurements. Keywords: hydrate formation, state estimation, moving horizon, particle filtering.
1. Introduction As the readily accessible oil and gas reserves are becoming exhausted, it is necessary to be able to consider oil fields prone to more severe conditions and from more remote locations. This includes oil fields previously considered to be uneconomical, like those in deep ocean environments, which are subjected to high pressures and low temperatures. Such extreme conditions promote the formation of a solid nonstoichiometric compound of gas and water – the so-called clathrate of natural gas, or more commonly known as gas hydrates [1]. When hydrates form, they block transmission lines, causing important economic losses due to the production stoppage. It would be ideal to operate the pipeline outside the hydrate formation envelop. However, as mentioned above, the high pressures and low temperatures associated to less accessible reserves leave the pipelines within the hydrate formation region [2]. Therefore, the ability to predict formation of hydrates in the field will play a vital role in exploiting these reserves. The aim of this study is to develop a combined state and parameter estimator for this process as a means for the prediction of hydrate formation towards preventive feedforward control. The present focus is on the gas-liquid flow riser. The model used is a complex nonlinear infinite-dimensional system accounting for momentum, mass and energy balances [3], and the measurements available include temperature and pressure at different locations along the riser. Since the problem being tackled is of distributed parameter nature, location where such measurements are taken, along with its type, is crucial for estimator performance. Moving horizon estimation (MHE) is well suited as it facilitates the sensor structure selection (both in a dynamic and static sense). MHE is proven to outperform
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the Kalman classic approach with greater robustness to both bad initial state guess and poor tuning parameters [4, 5]. Besides, MHE framework naturally handles most of the challenges of state estimation as applied to real systems, such as constraints and nonlinearities [4, 5]. However, solving the optimisation that underlies the MHE formulation at each sampling interval becomes too expensive in such a complex system, making it necessary to reduce the computational requirements. Particle filtering (PF) is a fairly new and promising class of state estimator that provides a recursive Bayesian approach to dynamic estimation in nonlinear systems, based on sequential Monte Carlo techniques. Although very fast and easy to implement, their ability to converge under poor priors (initially-specified regime of the uncertain states and parameters) is unproven. Thus, it becomes advantageous to combine the robustness of MHE with regard to good initial guesses and a convenient sensor structure on the one hand, and the speed of PF on the other hand to solve the combined state and parameter estimation problem [6, 7]. The MHE and PF frameworks will be demonstrated separately for a simpler problem involving the Van der Vusse reactor, before tackling the hydrate formation problem in the complete oil and gas production system. Future work will consider the individual and the hybrid frameworks for the hydrate prediction problem.
2. Methodology The state estimation problem is to determine an estimate of the state x(T) given the chosen model structure and a sequence of observations (measurements) of the system Y(T) = { y(0),…, y(T)}. 2.1. Moving horizon estimation Moving horizon estimation is a practical strategy for designing state estimators by means of online optimization, which allows one to include constraints and nonlinearities in the state estimation [8]. In order to improve the estimation procedure, imperfect models can be augmented with other physical information, such as constraints on states variables, process disturbances or model parameters. Many process uncertainties are bounded, as well as state variables, which are also almost always positive. Unlike the process uncertainties, constraints on state variables are implicitly enforced by the model of the process, but it is not rare to face approximate models where this implicit enforcement may fail. Then, the inclusion of constraints is needed also on the state variables so as to reconcile the approximate model with the process measurements. The online solution of this constrained estimation problem, known as full information estimator because we consider all the available measurements, is formulated as an optimization problem – typically posed as a least squares mathematical programsubject to the model constraints and inequality constraints that represents bounds on variables or equations. Although online optimization allows constraints on estimates as part of the problem formulation, formulating a state estimation problem with inequality constraints prevents recursive solutions as Kalman filter, and therefore, the estimation problem grows with time as more measurements become available. The computational complexity scales at least linearly with time, and consequently, the online solution is impractical due to the
State Estimation for Dynamic Prediction of Hydrate Formation
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increasing computational load, necessitating bounds on the size of the mathematical program. To make the problem tractable, the strategy adopted is to reformulate the problem using a moving, fixed-size estimation window by breaking the time interval into two pieces. Thus, in moving horizon estimation we account explicitly only for the second part of the time interval, while the remaining process measurements are compactly summarized using a function named arrival cost, responsible for transforming the unbounded mathematical problem into an equivalent fixed-dimension mathematical program [8, 9]. Assuming the discrete model is readily available, the following is a simple mathematical formulation of the problem T −1
min
xT
− N
,{ w
k
} Tk
−1 =T − n
¦
Lk (w
k
,vk ) + Z
k =T − N
T − N
(z)
s.t.
x k + 1 = f ( x k , u k ) + Gw
k
yk = h(xk ) + vk Where xk are state variables, wk and vk are the model and process disturbances, respectively, Lk is a stage cost function and ZT-N (z) is the arrival cost function. A discrete-time model is adopted in the above formulation for illustrative purposes. A continuous-time model can also be used. 2.2. Particle Filtering From a Bayesian interpretation, MHE and the extended Kalman filter assume normal or uniform distributions for the prior and the likelihood. Unfortunately, these assumptions are easily violated by nonlinear dynamic systems in which the conditional density is generally asymmetric, potentially multimodal and can vary significantly with time. Unlike other nonlinear estimation methods, particle filtering (PF) allows to solve the online estimation problems without any assumption about the dynamics and shape of the conditional density. Bayes’ rule provides the theoretical background to integrate the past information or prior, with the current information or likelihood. The core idea is to represent the required conditional density of the states as a set of random samples (particles), rather than as a function over state space. The algorithm starts with a randomly generated set of samples at the first point, and propagates these samples to produce future distributions. Samples representing the prior are generated as the prediction of the state passing samples from the posterior at the previous step through the state equation. Hence, this prediction step utilises information about process dynamics and model accuracy without making any assumption about any characteristics of the distributions. Alike, once the measurement is available, the posterior is obtained as the correction of the state using the updated prior and the measurement (likelihood) itself. Therefore, this correction step utilises the measurement model and information about the measurement error, again without requiring any assumptions about the distributions. At this stage, solving the estimation problem is simply a matter of
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selecting a representative sample such as a mean, mode or median from the samples representing the posterior [6, 7]. 2.3. Combination of MHE and PF Solving the optimisation that underlies the MHE formulation at each sampling interval becomes too expensive in a complex system, making it necessary to reduce the computational requirements. Particle filtering (PF) is a fairly new and promising class of state estimator that provides a recursive Bayesian solution to estimation in nonlinear systems based on sequential Monte Carlo techniques. Although very fast and easy to implement, PF is more sensitive to poor initial guesses, because it means that there is little overlap between the particles representing the initial prior and the likelihood obtained from the measurements. Due to the limited number of particles, the posterior distribution is often less accurate than that obtained by methods that rely on an approximate but continuous prior distribution. Thus, it becomes advantageous to combine the robustness of MHE with regard to good initial guesses and a convenient sensor structure on the one hand, and the speed of PF on the other hand to solve the combined state and parameter estimation problem. This promising combined strategy will be explored in the future [7].
3. Case study The MHE and PF frameworks will be demonstrated separately for a simpler problem involving the well studied nonlinear benchmark problem of the Van der Vusse scheme [10]: a feed stream of feedstock A enters a reactor and reacts to form the desired product, B. The model assumes a first order reaction for the conversion of A into B, with two competing reactions BĺC and 2AĺD. Temperature-dependent Arrhenius reaction rates are assumed. The model has four states: concentration of A, concentration of B, reactor temperature, and cooling jacket temperature. 3.1. Moving horizon estimation For this case of study, it is supposed that the four states are directly measurable. The estimation problem is posed as a least squares objective function subject to the model nonlinear differential equations as constraints, restricting the mathematical program to the size of the moving window, and therefore ignoring the data outside such window. A model-process mismatch is introduced by using a E/R value in the Arrhenius Law of the first order (A ĺ B) reaction of -9658.3 K instead of the nominal value (-9758.3 K). The initial state is x0 =[2.14; 1.09; 387.15; 385.15] and the estimator is implemented with a window length of 50 samples (measurements are taken every 10 seconds) and the prior guess x =[2.34; 1.29; 392.15; 390.15]. Noise is added to the measurements with mean zero and variance 0.5 for the temperatures and 0.01 for the concentrations. Figure 1 shows the model prediction, the actual values (measurements) and the MHE prediction for the four states. 3.2. Particle filtering The particle filter is implemented with 100 particles at the same conditions used for the MHE. Figure 2 shows the model prediction, the actual values (measurements) and the PF prediction for the four states.
State Estimation for Dynamic Prediction of Hydrate Formation
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As can be seen from the two figures, the moving horizon estimator recovers much faster than the particle filter from the bad prior guess. The price of this higher robustness is the greater computational expense required to solve the MHE optimisation.
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