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Model Reduction in Chemical Engineering Case Studies Applied to Process Analysis Design and Operation Model Reduction in Chemical Engineering Case studies applied to process analysis design and operation Cover design by JM&BD Model Reduction in Chemical Engineering Case studies applied to process analysis design and operation Proefschrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft, op gezag van de Rector Magnificus, prof. ir. K.C.A.M. Luyben, voorzitter van het College voor Promoties in het openbaar te verdedigen op maandag 4 juli 2010 om 15:00 uur door Bogdan DORNEANU Inginer diplomat (Universitatea Politehnica din Bucureşti, Roemenië) geboren te Medgidia (Roemenië) Dit proefschrift is goedgekeurd door de promotor: Prof. ir. J. Grievink Samenstelling promotiecommissie: Rector Magnificus Voorzitter Prof. ir. J. Grievink Technische Universiteit Delft, promotor Dr. ir. C.S. Bildea University Politehnica of Bucharest, copromotor Prof. dr. ir. P.M.J. van den Hof Technische Universiteit Delft Prof. dr. F. Kapteijn Technische Universiteit Delft Dr. ir. H.J.M. Kramer Technische Universiteit Delft Prof. dr. ir. P.M.M. Bongers Technische Universiteit Eindhoven / Unilever Prof. dr. P.D. Iedema Universiteit van Amsterdam Dr. ir. P.J.T. Verheijen Technische Universiteit Delft, reservelid Keywords: model reduction, process modelling, plantwide control, dynamic optimization, alkylation, ice cream freezing An electronic version of this thesis is available from http://www.library.tudelft.nl ISBN 978-90-8570-771-4 Copyright ©2011 by Bogdan Dorneanu All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without the prior written permission from the author. Printed in The Netherlands by CPI Wöhrmann Print Service Motto “It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” A. Einstein A significant part of the research was carried out within the framework of MRTN-CT-2004-512233 (PRISM – Towards Knowledge-Based Processing Systems). The financial support of the European Commission and Unilever R&D Vlaardingen is gratefully acknowledged. Table of contents Summary ............................................................................................................................................... i Samenvatting ....................................................................................................................................... v Rezumat............................................................................................................................................... ix Chapter 1 – Introduction .................................................................................................................... 1 1. Role of modelling in chemical engineering ................................................................................... 2 1.1. Model applications and benefits ....................................................................................... 2 1.2. Efforts and cost factors for model development and application ...................................... 5 2. Requirements for model use in chemical engineering ................................................................... 5 3. Process models and modelling ....................................................................................................... 6 3.1. Process models ................................................................................................................. 6 3.2. Model classification ......................................................................................................... 8 3.3. Model development steps ................................................................................................. 9 3.4. Dual way of modelling: decomposition and aggregation over detail levels.................... 13 4. Motivation and formulation of the research problem ................................................................... 15 5. Research approach and outline of the thesis ................................................................................ 18 6. References ................................................................................................................................... 20 Chapter 2 – Process modelling and model reduction ..................................................................... 25 1. Introduction ................................................................................................................................. 26 2. A design view on process modelling ........................................................................................... 27 2.1. Levels of decomposition in the modelling procedure ..................................................... 28 3. Contextual and structure levels of decomposition ....................................................................... 30 3.1. Contextual level .............................................................................................................. 30 3.2. Structure level ................................................................................................................ 31 3.2.1. Process decomposition and physical structure of the model ........................................... 31 3.2.2. Behavioural structure of the model ................................................................................. 36 3.2.3. Model connectivity ......................................................................................................... 37 4. Mathematical, numerical and software implementation levels .................................................... 39 4.1. Mathematical level: behavioural models of nodes .......................................................... 40 4.1.1. Coordinates ..................................................................................................................... 40 4.1.2. Classification of quantities .............................................................................................. 41 4.1.3. Classification of equations .............................................................................................. 42 4.1.4. Validity and applicability conditions (knowledge constraints) ....................................... 46 4.1.5. Types of operations in model equations .......................................................................... 46 4.1.6. Model classification ........................................................................................................ 46 4.2. Mathematical level: Connectivity ................................................................................... 47 4.3. Mathematical level: Aggregation at system level ........................................................... 49 4.4. Relationship between the structure and the complexity of the model ............................. 51 4.4.1. Number of equations ....................................................................................................... 52 4.4.2. Number of terms in the model equations ........................................................................ 52 4.4.3. Connectivity of the model equations ............................................................................... 53 4.5. Numerical level .............................................................................................................. 53 4.6. Software implementation level ....................................................................................... 54 5. Existent model reduction techniques ........................................................................................... 55 5.1. Approaches to model reduction of process models ........................................................ 55 5.2. Contextual level .............................................................................................................. 55 5.3. Structure level ................................................................................................................ 56 5.3.1. Model reduction at physical structure level ..................................................................... 56 5.3.2. Model reduction at behavioural structure level ............................................................... 58 5.4. Mathematical level ......................................................................................................... 59 5.4.1. Model simplification techniques ..................................................................................... 60 5.4.2. Model order-reduction techniques ................................................................................... 61 5.5. System level ................................................................................................................... 62 5.6. Numerical level .............................................................................................................. 62 6. Model reduction for chemical engineering applications .............................................................. 63 7. Selected research problems in model reduction ........................................................................... 64 8. Conclusions ................................................................................................................................
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