Modeling and simulation of chemical process systems

519 Pages·2019·105.73 MB·English

by  Ghasem, Nayef

Modeling and Simulation of
Chemical Process Systems

Modeling and Simulation of
Chemical Process Systems
Nayef Ghasem
MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with permission. The
MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or
discussion of MATLAB® and Simulink® software or related products does not constitute endorsement or
sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB®
and Simulink® software.
CRC Press
Taylor & Francis Group
6000 Broken Sound Parkway NW, Suite 300
Boca Raton, FL 33487-2742
© 2019 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
No claim to original U.S. Government works
Printed on acid-free paper
International Standard Book Number-13: 978-1-1385-6851-8 (Hardback)
International Standard Book Number-13: 978-0-2037-0508-7 (eBook)
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers
have attempted to trace the copyright holders of all material reproduced in this publication and apologize
to copyright holders if permission to publish in this form has not been obtained. If any copyright material
has not been acknowledged please write and let us know so we may rectify in any future reprint.
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter
invented, including photocopying, microfilming, and recording, or in any information storage or retrieval
system, without written permission from the publishers.
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and
registration for a variety of users. For organizations that have been granted a photocopy license by the
CCC, a separate system of payment has been arranged.
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
used only for identification and explanation without intent to infringe.
Library of Congress Cataloging‑in‑Publication Data
Names: Ghasem, Nayef, author.
Title: Modeling and simulation of chemical process systems / Nayef Mohamed Ghasem.
Description: Boca Raton, FL : CRC Press/Taylor & Francis Group, 2018. |
Includes bibliographical references and index.
Identifiers: LCCN 2018025236 | ISBN 9781138568518 (hardback : acid-free paper)
| ISBN 9780203705087 (ebook)
Subjects: LCSH: Chemical processes--Computer simulation. | Chemical
engineering--Data processing.
Classification: LCC TP184 .G483 2018 | DDC 660/.28--dc23
LC record available at https://lccn.loc.gov/2018025236
Visit the Taylor & Francis Web site at
http://www.taylorandfrancis.com
and the CRC Press Web site at
http://www.crcpress.com
MATLAB® and Simulink® are trademarks of The MathWorks, Inc. and are used with permission. The
MathWorks does not warrant the accuracy of the text or exercises in this book. This book’s use or Contents
discussion of MATLAB® and Simulink® software or related products does not constitute endorsement or
sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB®
and Simulink® software.
Preface ......................................................................................................................xi
CRC Press
Taylor & Francis Group Acknowledgments ..............................................................................................xiii
6000 Broken Sound Parkway NW, Suite 300 Author .....................................................................................................................xv
Boca Raton, FL 33487-2742
© 2019 by Taylor & Francis Group, LLC
CRC Press is an imprint of Taylor & Francis Group, an Informa business
1. Introduction .....................................................................................................1
No claim to original U.S. Government works 1.1 Background ..........................................................................................1
1.2 Mathematical Models .........................................................................2
Printed on acid-free paper
1.3 Why Study Process Modeling and Simulation? .............................3
International Standard Book Number-13: 978-1-138-56851-8 (Hardback)
1.4 Terminology of Process Modeling and Simulation ........................4
International Standard Book Number-13: 978-0-2037-0508-7 (eBook)
1.4.1 State Variables and State Equations ..................................4
This book contains information obtained from authentic and highly regarded sources. Reasonable efforts
1.4.2 Steady State and Transient ..................................................4
have been made to publish reliable data and information, but the author and publisher cannot assume
responsibility for the validity of all materials or the consequences of their use. The authors and publishers 1.4.3 Lumped versus Distributed Parameters...........................5
have attempted to trace the copyright holders of all material reproduced in this publication and apologize 1.4.4 Model Verification ................................................................5
to copyright holders if permission to publish in this form has not been obtained. If any copyright material
1.4.5 Model Validation ..................................................................6
has not been acknowledged please write and let us know so we may rectify in any future reprint.
1.5 The Steps for Building a Mathematical Model ...............................6
Except as permitted under U.S. Copyright Law, no part of this book may be reprinted, reproduced, 1.6 Fundamental Balance Equations ......................................................6
transmitted, or utilized in any form by any electronic, mechanical, or other means, now known or hereafter
1.6.1 Material Balance ...................................................................7
invented, including photocopying, microfilming, and recording, or in any information storage or retrieval
system, without written permission from the publishers. 1.6.2 Total and Component Balances ..........................................8
1.6.3 Material Balance on Individual Components ..................9
For permission to photocopy or use material electronically from this work, please access www.copyright.
com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood 1.6.4 Energy Balance ...................................................................10
Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and 1.6.5 Momentum Balance ...........................................................11
registration for a variety of users. For organizations that have been granted a photocopy license by the
1.7 Process Classification ........................................................................12
CCC, a separate system of payment has been arranged.
1.7.1 Continuous Process ...........................................................13
Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are
1.7.2 Batch Process ......................................................................13
used only for identification and explanation without intent to infringe.
1.7.3 Semibatch Process ..............................................................14
1.8 Types of Balances ..............................................................................14
Library of Congress Cataloging‑in‑Publication Data
1.9 Procedure of Mass Balance ..............................................................14
Names: Ghasem, Nayef, author.
1.9.1 Microscopic Balance ..........................................................15
Title: Modeling and simulation of chemical process systems / Nayef Mohamed Ghasem.
Description: Boca Raton, FL : CRC Press/Taylor & Francis Group, 2018. | 1.9.2 Macroscopic Balance ..........................................................16
Includes bibliographical references and index. 1.10 Transport Rates ..................................................................................16
Identifiers: LCCN 2018025236 | ISBN 9781138568518 (hardback : acid-free paper)
1.10.1 Mass Transport ...................................................................17
| ISBN 9780203705087 (ebook)
Subjects: LCSH: Chemical processes--Computer simulation. | Chemical 1.10.2 Momentum Transport .......................................................18
engineering--Data processing. 1.10.3 Energy Transport ................................................................20
Classification: LCC TP184 .G483 2018 | DDC 660/.28--dc23
1.11 Thermodynamic Relations ...............................................................22
LC record available at https://lccn.loc.gov/2018025236
1.12 Phase Equilibrium .............................................................................23
1.12.1 Flash Calculations ..............................................................25
Visit the Taylor & Francis Web site at
1.13 Chemical Kinetics ..............................................................................26
http://www.taylorandfrancis.com
1.14 Process Control ..................................................................................27
and the CRC Press Web site at
1.15 Number of Degrees of Freedom......................................................28
http://www.crcpress.com
v
K43602_Discl.indd 1 08/24/18 10:10:03 AM
vi Contents
1.16 Model Solution ..................................................................................30
1.17 Model Evaluation ..............................................................................32
Problems ..........................................................................................................35
References .......................................................................................................38
2. Lumped Parameter Systems .......................................................................39
2.1 Introduction .......................................................................................39
2.2 Model Encountered in Material Balances Only ............................40
2.2.1 Material Balance Without Reactions .................................40
2.2.1.1 Degree of Freedom Analysis ...............................41
2.2.2 Material Balance for Chemical Reactors ...........................46
2.2.3 Gas Phase Reaction in a Pressurized Reactor ..................58
2.2.4 Reaction with Mass Transfer ..............................................60
2.2.4.1 Assumptions .........................................................60
2.2.4.2 Liquid Phase ..........................................................61
2.2.4.3 Vapor Phase ...........................................................61
2.2.4.4 Degrees of Freedom Analysis .............................62
2.3 Energy Balance ..................................................................................62
Problems ........................................................................................................100
References .....................................................................................................105
3. Theory and Applications of Distributed Systems ................................107
3.1 Introduction .....................................................................................107
3.2 Mass Transport ................................................................................108
3.2.1 Mass Transfer in Cartesian Coordinate ..........................109
3.2.2 Component Continuity Equation ....................................111
3.2.2.1 Component Mass Continuity Equation ..........111
3.2.2.2 Component Molar Continuity Equation .........113
3.3 Fluid Dynamics ...............................................................................114
3.4 Energy Transport .............................................................................118
3.4.1 Energy Transport in Cartesian Coordinates ...................119
3.4.2 Conversion Between the Coordinates .............................121
3.5 Introduction of Equations of Change ...........................................121
3.5.1 Equations of Change in Cartesian Coordinates .............122
3.5.2 Equations of Change in Cylindrical Coordinates ..........123
3.5.3 Equations of Change in Spherical Coordinates .............124
3.6 Applications of the Equations of Change ....................................126
Problems ........................................................................................................151
References .....................................................................................................153
4. Computational Fluid Dynamics ...............................................................155
4.1 Introduction .....................................................................................155
4.2 Equations of Motion .......................................................................156
4.2.1 Cartesian Coordinate .........................................................156
4.2.2 Cylindrical Coordinates ....................................................156
Contents vii
4.2.3 Spherical Coordinates .......................................................157
4.2.4 Solving Procedure ..............................................................157
4.3 Fluid Dynamic Systems ....................................................................158
4.3.1 Velocity Profile in a Triangular Duct .................................158
4.3.2 Fluid Flow in a Nuzzle ........................................................159
4.3.3 Fluid Flow Past a Stationary Sphere .................................159
4.3.3.1 COMSOL Simulation ...........................................160
4.3.4 Incompressible Fluid Flows Past a Solid Flat Plate.........160
4.3.4.1 COMSOL Solution ................................................163
4.4 Application to Fluid Dynamics .......................................................164
Problems ........................................................................................................218
References .....................................................................................................221
5. Mass Transport of Distributed Systems .................................................223
5.1 Introduction .......................................................................................223
5.2 Diffusion of Gas through a Membrane Tube ................................224
5.3 Mass Transfer with Chemical Reaction ..........................................227
5.4 Plug Flow Reactor .............................................................................230
5.5 Diffusion of Gas in Solid ..................................................................232
5.5.1 Assumptions .........................................................................233
5.6 Diffusion with Chemical Reaction ..................................................235
5.7 Leaching of Solute from Solid Particles .........................................238
5.8 Applied Examples .............................................................................239
Problems ........................................................................................................269
References .....................................................................................................272
6. Heat Transfer Distributed Parameter Systems ......................................273
6.1 Introduction .......................................................................................273
6.1.1 Equations of Energy ............................................................274
6.2 Heat Transfer from a Fin ..................................................................275
6.3 Radial Temperature Gradients in an Annular Chemical
Reactor ................................................................................................277
6.4 Heat Transfer in a Nonisothermal Plug-Flow Reactor ................280
6.5 Temperature Profile across a Composite Plane Wall ...................281
6.5.1 Energy Balance on Wall 1 ....................................................283
6.5.2 Energy Balance on Wall 2 ....................................................284
6.6 Applied Examples .............................................................................285
Problems ........................................................................................................358
References .....................................................................................................361
7. Case Studies .................................................................................................363
7.1 Membrane Reactors ..........................................................................363
7.1.1 Equilibrium Conversion .....................................................365
7.1.2 Numerical Solution of Equilibrium Conversion .............367
7.1.3 Numerical Solution in Case of Hydrogen Permeation ...368
viii Contents
7.1.4 Variable Feed Concentration ..............................................371
7.1.5 Effect of Membrane Thickness ...........................................373
7.2 Absorption of Carbon Dioxide from Flue Gas ..............................374
7.2.1 Capture of Carbon Dioxide Using Fresh Water ...............374
7.2.1.1 Model Equations ..................................................375
7.2.1.2 COMSOL Simulation ...........................................376
7.2.2 Capture of CO Using Aqueous Sodium Hydroxide ......380
2
7.2.2.1 Model Equations ..................................................380
7.2.2.2 COMSOL Simulation ...........................................381
7.3 Packed Bed Reactors .........................................................................385
7.3.1 Isothermal Packed Bed Reactor .........................................386
7.3.1.1 Model Development ............................................386
7.3.1.2 COMSOL Simulation ...........................................389
7.3.2 Adiabatic Packed Bed Reactor ...........................................394
7.4 Fluid Flow of Two Immiscible Liquids ..........................................396
7.4.1 Model Development ............................................................396
7.4.2 COMSOL Simulation ...........................................................396
7.5 Production of Propylene Glycol in Adiabatic Tubular
Reactor ................................................................................................399
7.5.1 Model Development ............................................................400
7.5.1.1 Boundary Conditions ..........................................402
7.5.2 COMSOL Simulation ...........................................................403
7.6 Coupling of Fluid and Heat Transfer (Multiphysics) ..................407
7.7 Unsteady Diffusion of Contaminated Source from the Skin
of a Pipe Line .....................................................................................411
7.8 Maxwell-Stefan Diffusion ................................................................414
7.8.1 Hydrogen Production .........................................................415
References .....................................................................................................420
8. Computing Solutions of Ordinary Differential Equations ................421
8.1 Introduction .......................................................................................421
8.2 Numerical Solution of Single Ordinary Equation ........................423
8.2.1 Euler Method ........................................................................424
8.2.2 Modified Euler Method.......................................................429
8.2.3 Midpoint Method .................................................................433
8.2.4 Heun Predictor-Corrector Method ....................................438
8.2.5 Runge-Kutta Method ...........................................................440
8.2.5.1 Second-Order Runge-Kutta (RK2) .....................440
8.2.5.2 Third-Order Runge-Kutta (RK3) ........................441
8.2.5.3 Fourth-Order Runge-Kutta .................................442
8.3 Simultaneous Systems of First-Order Differential Equations.....456
8.4 Summary ............................................................................................459
Problems ........................................................................................................459
References .....................................................................................................462
Contents ix
9. Higher-Order Differential Equations .....................................................463
9.1 Introduction .......................................................................................463
9.2 Initial and Boundary Value Problems ............................................469
9.3 Shooting Method ...............................................................................470
9.4 Simultaneous Ordinary Differential Equation ..............................479
9.5 Solving High-Order Differential Equations Using COMSOL ....480
Problems ........................................................................................................492
References .....................................................................................................496
Index .....................................................................................................................497