Computer-Aided Modeling of Reactive Systems

by Stewart, Warren E.; Caracotsios, Michael

• ISBN13: 9780470274958
• ISBN10: 0470274956
• Edition: 1st
• Format: Hardcover
• Copyright: 2008-04-11
• Publisher: Wiley-AIChE

Summary

This book will acquaint the reader with some of the important tools and strategies now available for investigating chemical processes and systems on personal computers. It presents useful mathematical models, numerical methods for solving them, and statistical methods for testing and discriminating candidate models with experimental data. The book includes instruction on Chemical Reaction Models, Chemical Reactor Models, Probability and Statistics, Bayesian Estimation, Process Modeling with Single-Response Data, Process Modeling with Multiresponse Data, along with an appendix of worked problems and solutions. Software is also available for academic adopters via Athena Visual Studio, downloadable at www.AthenaVisual.com, The software enables readers to do these computations and view the results on their personal computer screens, print them and transmit them. Familiarity withMicrosoft Windows (1998 or later) is required, but little knowledge of Fortran,since Athena converts equation statements directly into Fortran code as described in the Athena tutorial on your computer's desktop.

Author Biography

The Late Warren E. Stewart, PhD, was a professor of chemical engineeringat the University of Wisconsin–Madison, published numerous research articles, coauthored the landmark textbook Transport Phenomena, and was the recipient of many awards from AIChE, ACS, ASEE, and the University of Wisconsin. He was a fellow of the American Institute of Chemical Engineers and a member of the National Academy of Engineering.

Michael Caracotsios, PhD, is a Senior Modeling and Optimization Specialist in research and development at UOP LLC, a company that has been delivering cutting-edge technology to the petroleum refining, gas processing, petrochemical production, and other major manufacturing industries for over ninety years. He is also an Adjunct Professor of Chemical Engineering at the Northwestern University.

Table of Contents

Overview	p. 1
References and Further Reading	p. 2
Chemical Reaction Models	p. 3
Stoichiometry of Reaction Schemes	p. 3
Computability of Reaction Rates from Data	p. 6
Equilibria of Chemical Reactions	p. 7
Kinetics of Elementary Steps	p. 11
Properties of Reaction Networks	p. 15
Evidence for Reaction Steps	p. 25
Problems	p. 28
References and Further Reading	p. 29
Chemical Reactor Models	p. 39
Macroscopic Conservation Equations	p. 39
Material Balances	p. 39
Total Energy Balance	p. 41
Momentum Balance	p. 41
Mechanical Energy Balance	p. 42
Heat and Mass Transfer in Fixed Beds	p. 47
Interfacial States in Fixed-Bed Reactors	p. 48
Material Transport in Porous Catalysts	p. 54
Material Transport in a Cylindrical Pore Segment	p. 55
Material Transport in a Pore Network	p. 56
Working Models of Flow and Diffusion in Isotropic Media	p. 57
Discussion	p. 58
Transport and Reaction in Porous Catalysts	p. 58
Gas Properties at Low Pressures	p. 59
Notation	p. 60
References and Further Reading	p. 62
Introduction to Probability and Statistics	p. 65
Strategy of Data-Based Investigation	p. 65
Basic Concepts in Probability Theory	p. 66
Distributions of Sums of Random Variables	p. 69
Multiresponse Normal Error Distributions	p. 72
Statistical Inference and Criticism	p. 73
Problems	p. 75
References and Further Reading	p. 76
Introduction to Bayesian Estimation	p. 77
The Theorem	p. 77
Bayesian Estimation with Informative Priors	p. 80
Introduction to Noninformative Priors	p. 84
Jeffreys Prior for One-Parameter Models	p. 86
Jeffreys Prior for Multiparameter Models	p. 88
Summary	p. 91
Problems	p. 91
References and Further Reading	p. 92
Process Modeling with Single-Response Data	p. 95
The Objective Function S([theta])	p. 96
Weighting and Observation Forms	p. 98
Parametric Sensitivities; Normal Equations	p. 99
Constrained Minimization of S([theat])	p. 102
The Quadratic Programming Algorithm GRQP	p. 102
The Line Search Algorithm GRS1	p. 104
Final Expansions Around [theat]	p. 105
Testing the Residuals	p. 106
Inferences from the Posterior Density	p. 107
Inferences for the Parameters	p. 108
Inferences for Predicted Functions	p. 110
Discrimination of Rival Models by Posterior Probability	p. 112
Sequential Planning of Experiments	p. 115
Planning for Parameter Estimation	p. 115
Planning for Auxiliary Function Estimation	p. 116
Planning for Model Discrimination	p. 116
Combined Discrimination and Estimation	p. 118
Planning for Model Building	p. 119
Examples	p. 119
Summary	p. 122
Notation	p. 125
Problems	p. 127
References and Further Reading	p. 133
Process Modeling with Multiresponse Data	p. 141
Problem Types	p. 142
Objective Function	p. 148
Selection of Working Responses	p. 149
Derivatives of Eqs. (7.2-1) and (7.2-3)	p. 150
Quadratic Expansions; Normal Equations	p. 151
Constrained Minimization of S([theta])	p. 152
Final Expansions Around [theat]	p. 153
Testing the Residuals	p. 153
Posterior Probabilities and Regions	p. 154
Inferences Regarding Parameters	p. 154
Inferences Regarding Functions	p. 156
Discrimination Among Rival Models	p. 156
Sequential Planning of Experiments	p. 158
Examples	p. 159
Process Investigations	p. 161
Conclusion	p. 165
Notation	p. 166
Addendum: Proof of Eqs. (7.1-16) and (7.1-17)	p. 168
Problems	p. 169
References and Further Reading	p. 172
Solution of Linear Algebraic Equations	p. 177
Introductory Concepts and Operations	p. 177
Operations with Partitioned Matrices	p. 180
Gauss-Jordan Reduction	p. 182
Gaussian Elimination	p. 184
Lu Factorization	p. 186
Software	p. 187
Problems	p. 187
References and Further Reading	p. 188
DDAPLUS Documentation	p. 189
What DDAPLUS Does	p. 189
Object Code	p. 191
Calling DDAPLUS	p. 191
Description of the Calling Arguments	p. 191
Exit Conditions and Continuation Calls	p. 200
The Subroutine fsub	p. 203
The Subroutine Esub	p. 203
The Subroutine Jac	p. 205
The Subroutine Bsub	p. 206
Numerical Examples	p. 208
References and Further Reading	p. 216
GREGPLUS Documentation	p. 217
Description of GREGPLUS	p. 217
Levels of GREGPLUS	p. 219
Calling GREGPLUS	p. 219
Work Space Requirements for GREGPLUS	p. 226
Specifications for the User-Provided Model	p. 226
Single-Response Examples	p. 228
Multiresponse Examples	p. 244
References and Further Reading	p. 257
Author Index	p. 259
Subject Index	p. 265
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