P1: / P2: May 10, 2002 17:36 Foley Foley-FM An Introduction to Chemical Engineering Analysis Using Mathematica P1: / P2: May 10, 2002 17:36 Foley Foley-FM P1: / P2: May 10, 2002 17:36 Foley Foley-FM 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 P1: / P2: May 10, 2002 17:36 Foley Foley-FM ∞ 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 Harcourt Place, 32 Jamestown Road, London NWI 7BY, UK http://www.academicpress.com 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 MV987654321 P1: / P2: May 10, 2002 17:36 Foley Foley-FM 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 P1: / P2: May 10, 2002 17:36 Foley Foley-FM 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 xiii [...]... complex and the analyses tougher By learning to program in the Mathematica environment, with its very low barriers to entry and true sophistication, one can carry over this ordered thinking and the methodologies it enables into other programming languages and approaches In fact, it can be done nearly automatically for any piece of code written in Mathematica and which needs to be translated into C or... longer assigned to the list of values: In[12]:= ls1 = ls1 Out[13]= ls1 We may also have occasion to want to generate the vector of values and to assign these values to a list name, but we may not want to see all of them For example, suppose we wanted all the values for x x from between 1 and 100 This can be done and the list can be named, but we may not want this sent to the screen To suppress it we... to have a life-partner, my spouse Karin, who knows and understands what I am about and what I really need to do and get done For her support and that of my daughters, Erica and Laura, who often strolled into my home office to find me hunched over the computer and to ask how my book was coming along, I offer my sincerest and deepest thanks The book represents a way to teach a first course in chemical engineering. .. quantitatively This section also shows some of the powerful objects that preexist in the Mathematica and which can be used creatively to solve problems and illustrate concepts At this point, the question that arises is whether to cover kinetics — batch, continuous stirred tank reactor (CSTR) and plug flow reactor (PFR) — next, and then to cover some prob­ lems in mass transfer later, or to do mass transfer... mass transfer and to have the former in place before doing chemical kinetics, since one can then do interfacial kinetics with the proper physical foundation Chapters 7, 8, and 9 deal with chemical kinetics and idealized reactors It should be quite familiar territory Here as in previous chapters the focus is upon the interplay between analysis and experiment Classical topics such as reaction stoichiometry... steadystate algebraic equations I also never fail to mention Boudart’s point that it is easy to measure rates of chemical reaction with an experiment operated in a well-mixed stirred tank-type reactor This another good time to teach the linkage between analysis and experiment with a system that is both quite easy to visualize and conceptualize It is surprising to many of the better students that something... papers in longhand and then either give it to someone else to “type into the computer,” or if younger and lower in some ranking system do it themselves The PC plus printer (first dot matrix, then laser) was used as an electronic combination of typewriter and mimeograph machine It took at least another few years before most of us had made the transition to using the computer as a computer and not as a... system and that it will “say” what you want it to “say.” We rarely take the time in engineering to develop topics from an historical perspective — which is too bad Our history is every bit as rich and the characters involved as interesting as any of those our colleagues in the humanities discuss Why not talk about Fourier in Egypt with Napoleon for a little while when dealing with heat transport, or Newton’s... toss up as to which to do first based on fundamentals Hence Chapters 5 and 6 deal with mass transfer and then adsorption and both come before chemical kinetics and reactors Adsorption is interest­ ing to cover separately because one can get to a more molecular level and bring in physical chemistry concepts, as well as more complex rate expressions without chemical reaction It is also very nice to distinguish... reach an asymptote equal to that which we can derive from the PFR equation and that for simple kinetics the conversion is larger than it would be for the same volume relegated to one well-mixed CSTR This approach turns out to be fun to teach, seemingly interesting and P1: / P2: May 10, 2002 17:36 Foley Foley-FM xx Preface for an Instructor actually useful, because the student begins to understand how . Foley-FM An Introduction to Chemical Engineering Analysis Using Mathematica P1: / P2: May 10, 2002 17:36 Foley Foley-FM P1: / P2: May 10, 2002 17:36 Foley Foley-FM An Introduction to Chemical Engineering. 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 P1: / P2: May. into other programming languages and approaches. In fact, it can be done nearly automatically for any piece of code written in Mathematica and which needs to be translated into C or Fortran