Applied Maths and Modeling for Chemical Engineers

8/6/2019 Applied Maths and Modeling for Chemical Engineers

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Applied Mathematicsand Modeling forChemical Engineers

Richard G. RiceLouisiana State University

Duong D. DoUniversity of QueenslandSt. Lucia, Queensland, Australia

John Wiley &Sons, Inc.New York Chichester Brisbane Toronto Singapore

Copyright 1995 John Wiley & Sons Retrieved from: www knovel com


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Acquisitions Editor Cliff RobichaudMarketing Manager Susan J. ElbeSenior Production Editor Savoula AmanatidisDesigner Pedro A. NoaCover Designer Ben ArringtonManufacturing Manager Lori BulwinIllustration Coordinator Eugene P. AielloThis book was typeset in Times Roman by Science Typographers, Inc. and printed and boundby Hamilton Printing Company. The cover was printed by Phoenix Color Corp.

Recognizing the importance of preserving what has been written, it is a policy ofJohn Wiley & Sons, Inc. to have books of enduring value published in the United Statesprinted on acid-free paper, and we exert our best efforts to that end.

Copyright 1995 by John Wiley & Sons, Inc.All rights reserved. Published simultaneously in Canada.Reproduction or translation of any part of this work beyond that permitted by Sections 107and 108 of the 1976 United States Copyright Act without the permission of the copyright owneris unlawful. Requests for permission or further information should be addressed to the PermissionsDepartment, John Wiley & Sons, Inc.Library of CongressCataloging-in-Publication DataRice, Richard G.Applied mathematics and modeling for chemical engineers / RichardG. Rice. Duong D. Do.

p. cm.(Wiley series in chemical engineering)Includes bibliographical references and index.ISBN 0-471-30377-11. Differential equations. 2. Chemical processesM athematicalmodels. 3. Chemical engineeringM athematics. I. Duong, D. Do.II . Title. III. Series.QA371.R37 1994660'.2842'015118dc20 94-5245CIP

Printed in the United States of America.10 9 8 7 6 5



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To Judy, Toddy Andrea, and William,for making it all worthwhile,RGR

To An and Binh, for m akingmy life fullDDD



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The revolution created in 1960 by the publication and widespread adoptionof the textbook Transport Phenomena by Bird et al. ushered in a new era forchemical engineering. This book has nurtured several generations on theimportance of problem formulation by elementary differential balances. Model-ing (or idealization) of processes has now become standard operating proce-dure, but, unfortunately, the sophistication of the modeling exercise has notbeen matched by textbooks on the solution of such models in quantitativemathematical terms. Moreover, the widespread availability of computer soft-ware packages has weakened the generational skills in classical analysis.The purpose of this book is to attempt to bridge the gap between classicalanalysis and modern applications. Thus, emphasis is directed in Chapter 1 tothe proper representation of a physicochemical situation into correct mathemat-ical language. It is important to recognize that if a problem is incorrectly posedin the first instance, then any solution will do. The thought process of "idealiz-ing," or approximating an actual situation, is now commonly called "modeling."Such models of natural and man-made processes can only be fully accepted ifthey fit the reality of experiment. We try to give emphasis to this well-knowntruth by selecting literature examples, which sustain experimental verification.Following the model building stage, we introduce classical methods in Chap-ters 2 and 3 for solving ordinary differential equations (O DE), adding newmaterial in Chapter 6 on approximate solution methods, which include pertur-bation techniques and elementary numerical solutions. This seems altogetherappropriate, since most models are approximate in the first instance. Finally,because of the propensity of staged processing in chemical engineering, weintroduce analytical m ethods to deal with important classes of finite-differenceequations in Chapter 5.In Chapters 7 to 12 we deal with numerical solution methods, and partialdifferential equations (PDE) are presented. Classical techniques, such as combi-nation of variables and separation of variables, are covered in detail. This isfollowed by Chapter 11 on PDE transform methods, culminating in the general-ized Sturm-Liouville transform. This allows sets of PDEs to be solved ashandily as algebraic sets. Approximate and numerical methods close out thetreatment of PDEs in Chapter 12.

Preface



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This book is designed for teaching. It meets the needs of a modern under-graduate curriculum, but it can also be used for first year graduate students.The homework problems are ranked by numerical subscript or an asterisk.Thus, subscript 1 denotes mainly com putational problems, whereas subscripts 2and 3 require more synthesis and analysis. Problems with an asterisk are themost difficult and are suited for graduate students. Chapters 1 through 6comprise a suitable package for a one-semester, junior level course (3 credithours). Chapters 7 to 12 can be taught as a one-semester course for advancedsenior or graduate level students.Academics find increasingly less time to write textbooks, owing to demandson the research front. RGR is most grateful for the generous support fromthe faculty of the Technical University of Denmark (Lyngby), notably Aa.Fredenslund and K. Ostergaard, for their efforts in making sabbatical leavethere in 1991 so successful, and extends a special note of thanks to M.Michelson for his thoughtful reviews of the manuscript and for critical discus-sions on the subject matter. He also acknowledges the influence of colleaguesat all the universities where he took residence for short and lengthy periodsincluding: University of Calgary, Canada; University of Queensland, Australia;University of Missouri, Columbia; University of Wisconsin, Madison; and ofcourse Louisiana State University, Baton Rouge.

Richard G. RiceLouisiana State UniversitySeptember 1994Duong D. DoUniversity of QueenslandSeptember 1994

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Applied Maths and Modeling for Chemical Engineers