Introduction to Chemical Engineering Analysis Using Mathematica

531 Pages·2002·9.267 MB·English

by  Henry C. Foley

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An Introduction to Chemical
Engineering Analysis Using
Mathematica
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An Introduction to
Chemical Engineering
Analysis Using
Mathematica
Henry C. Foley
The Pennsylvania State University
University Park, PA
San Diego San Francisco New York Boston
London Sydney Toronto Tokyo
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This book is printed on acid-free paper. �∞
Copyright 2002, Elsevier Science (USA)
All rights reserved.
No part of this publication may be reproduced or transmitted in any form or by any means, electronic
or mechanical, including photocopy, recording, or any information storage and retrieval system,
without permission in writing from the publisher.
Requests for permission to make copies of any part of the work should be mailed to: Permissions
Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887-6777.
Academic Press
An imprint of Elsevier Science
525 B Street, Suit 1900, San Diego, California 92101-4495, USA
http://www.academicpress.com
Academic Press
An imprint of Elsevier Science
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Library of Congress Catalog Card Number: 00-2001096535
International Standard Book Number: 0-12-261912-9
PRINTED IN THE UNITED STATES OF AMERICA
02 03 04 05 06 MV 9 8 7 6 5 4 3 2 1
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For Karin, Erica, and Laura
1 A Primer of Mathematica ........................................... 1
1.1 Getting Started in Mathematica.......................................... 1
1.2 Basics of the Language...................................................... 1
1.3 Simple Commands ............................................................. 2
1.4 Table, Plot, Map, and Plot3D.............................................. 3
1.5 Lists and ListPlot, Fit, and Show......................................... 30
1.6 Solve and NSolve............................................................... 39
1.7 Differentiate and Integrate .................................................. 43
1.8 DSolve ................................................................................ 46
1.9 NDSolve.............................................................................. 52
1.10 Units Interconversion........................................................ 56
1.11 Summary .......................................................................... 58
2 Elementary Single- Component Systems ................ 59
2.1 The Conservation of Mass Principle and the Concept of
a Control Volume...................................................................... 59
2.2 Geometry and the Left-Hand Side of the Mass Balance
Equation.................................................................................... 87
2.3 Summary ............................................................................ 112
3 The Draining Tank and Related Systems................. 113
3.1 The Right-Hand Side of the Mass Balance Equation ......... 113
3.2 Mechnaism of Water Flow from Tank - Torricelli’s Law,
A Constitutive Relationship....................................................... 114
3.3 Experiment and the Constitutive Equation.......................... 116
3.4 Solving for Level as a Function of Time.............................. 124
3.5 Mass Input, Output, and Control......................................... 125
3.6 Control ................................................................................ 143
3.7 Summary ............................................................................ 150
4 Multiple-Component Systems................................... 151
4.1 The Concept of the Component Balance............................ 151
4.2 Concentration versus Density............................................. 153
4.3 The Well-Mixed System...................................................... 154
4.4 Multicomponent Systems.................................................... 154
4.5 Liquid and Soluble Solid ..................................................... 163
4.6 Washing a Salt Solution from a Vessel............................... 175
4.7 The Pulse Input Tracer Experiment and Analysis............... 180
4.8 Mixing ................................................................................. 187
4.9 Summary ............................................................................ 203
5 Multiple Phases-Mass Transfer................................. 205
5.1 Mass Transfer versus Diffusion.......................................... 206
5.2 Salt Dissolution................................................................... 207
5.3 Batch................................................................................... 209
5.4 Fit to the Batch Data........................................................... 214
5.5 Semicontinuous: Pseudo Steady State .............................. 218
5.6 Full Solution........................................................................ 220
5.7 Liquid-Liquid System .......................................................... 225
5.8 Summary ............................................................................ 248
6 Adsorption and Permeation ...................................... 249
6.1 Adsorption........................................................................... 249
6.2 Permeation ......................................................................... 263
6.3 Permeation-Adsorption and Diffusion................................. 263
6.4 Expanding Cell.................................................................... 282
6.5 Summary ............................................................................ 296
7 Reacting Systems-Kinetics and Batch Reactors .... 297
7.1 How Chemical Reactions Take Place................................. 298
7.2 No-Flow/Batch System....................................................... 301
7.3 Simple Irreversible Reactions - Zeroth to Nth Order........... 303
7.4 Reversible Reactions - Chemical Equilibrium..................... 317
7.5 Complex Reactions............................................................. 328
7.6 Summary ............................................................................ 360
8 Semi-Continuous Flow Reactors.............................. 363
8.1 Introduction to Flow Reactors............................................. 363
8.2 Semicontinuous Systems ................................................... 365
8.3 Negligible Volume Change................................................. 366
8.4 Large Volume Change........................................................ 373
8.5 Pseudo-Steady State.......................................................... 379
8.6 Summary ............................................................................ 382
9 Continuous Stirred Tank and the Plug Flow
Reactors ......................................................................... 383
9.1 Continuous Flow-Stirred Tank Reactor............................... 383
9.2 Steady-State CSTR with Higher-Order, Reversible
Kinetics ..................................................................................... 387
9.3 Time Dependence - The Transient Approach to
Steady-State and Saturation Kinetics ....................................... 392
9.4 The Design of an Optimal CSTR........................................ 401
9.5 Plug Flow Reactor .............................................................. 407
9.6 Solution of the Steady-State PFR....................................... 410
9.7 Mixing Effects on Selectivities - Series and
Series-Parallel with CSTR and PFR ......................................... 418
9.8 PFR as a Series of CSTRs................................................. 424
9.9 Residence Time Distribution............................................... 435
9.10 Time-Dependent PFR-Complete and Numerical
Solutions ................................................................................... 451
9.11 Transient PFR................................................................... 452
9.12 Equations, Initial Conditions, and Boundary Conditions... 452
9.13 Summary .......................................................................... 457
10 Worked Problems..................................................... 459
10.1 The Level-Controlled Tank ............................................... 459
10.2 Batch Competitive Adsorption .......................................... 467
10.3 A Problem in Complex Kinetics ........................................ 474
10.4 Transient CSTR................................................................ 478
10.5 CSTR-PFR - A Problem in Comparison and Synthesis.... 482
10.6 Membrane Reactor - Overcoming Equilibrium with
Simultaneous Separation.......................................................... 488
10.7 Microbial Population Dynamics......................................... 496
Index ............................................................................... 505
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Preface for an Instructor
This book is an experiment. To be precise, the book is not an experiment, but the approach
of introducing and employing new concepts of chemical engineering analysis, concurrently
with new concepts in computing, as is presented within this book, is experimental. Usually,
the student of a first course in chemical engineering is presented with material that builds
systematically upon engineering concepts and the student works within this linear space to
“master” the material. In fact, however, the process is never so linear. For example, mathe­
matics, in the form of geometry, algebra, calculus and differential equations, is either dredged
back up from the student’s past learning to be employed practically in the solution of material
and energy balance problems or new math methods are taught along the way for this purpose.
In fact a good deal of “engineering math” is taught to students by this means and not just at
this introductory level — as it should be.
Therefore the critic might suggest that teaching computing simultaneously with introduc­
tory engineering concepts is not new, and instead simply adds, from the students’ perspective,
to the list of apparently “extra items” we already teach in a course and subject such as this
one. That would be a fair criticism, if that were how this book had been designed. Fortunately,
this book is intentionally not designed that way, but is instead designed with engineering
and computing fully integrated — that is, they are introduced concurrently. I have purposely
sought to avoid the simple addition of yet another set of apparently non-core learnings on top
of the already long list of core learnings, by carefully staging the introduction of new com­
puting methods with those of new types of engineering problems as they are needed. In this
way the computing level rises with the engineering level in order to match the requirements
of the problem at hand. Furthermore, the computing is not relegated to “gray boxes” or just to
certain problems at the end of the chapter, but is integrated into the very text. By proceeding
this way one actually leads the student and reader through a two-space of engineering and
computing concepts and their application, both of which then reinforce one another and grow
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