Computer-Aided Modeling of Reactive Systems
This book introduces readers to powerful parameter estimation and computational methods for modeling complex chemical reactions and reaction processes. It presents useful mathematical models, numerical methods for solving them, and statistical methods for testing and discriminating candidate models with experimental data. Topics covered include:
Chemical reaction models
Chemical reactor models
Probability and statistics
Process modeling with single-response data
Process modeling with multi-response data
Computer software (Athena Visual Studio) is available via a related Web site http://www.athenavisual.com enabling readers to carry out parameter estimation based on their data and to carry out process modeling using these parameters. As an aid to the reader, an appendix of example problems and solutions is provided.
Computer-Aided Modeling of Reactive Systems is an ideal supplemental text for advanced undergraduates and graduate students in chemical engineering courses, while it also serves as a valuable resource for practitioners in industry who want to keep up to date on the most current tools and strategies available.
Chapter 2. Chemical Reaction Models.
2.1 Stoichiometry of Reaction Schemes.
2.2 Computability of Reaction Rates from Data.
2.3 Equilibria of Chemical Reactions.
2.4 Kinetics of Elementary Steps.
2.5 Properties of Reaction Networks.
2.6 Evidence for Reaction Steps.
Chapter 3. Chemical Reactor Models.
3.1 Macroscopic Conservation Equations.
3.2 Heat and Mass Transfer in Fixed Beds.
3.3 Interfacial States in Fixed-Bed Reactors.
3.4 Material Transport in Porous Catalysts.
3.4.1 Material Transport in a Cylindrical Pore Segment.
3.4.2 Material Transport in a Pore Network.
3.4.3 Working Models of Flow and Diffusion an Isotropic Media.
3.4.5 Transport and Reaction in Porous Catalysts.
3.5 Gas Properties at Low Pressures.
Chapter 4. Introduction to Probability and Statistics.
4.1 Strategy of Data-Based Investigation.
4.2 Basic Concepts in Probability Theory.
4.3 Distributions of Sums of Random Variables.
4.4 Multiresponse Normal Error Distributions.
4.5 Statistical Inference and Criticism.
Chapter 5. Introduction to Bayesian Estimation.
5.1 The Theorem.
5.2 Bayesian Estimation with Informative Priors.
5.3 Introduction to Noninformative Priors.
5.4 Jeffreys’ Prior for One-Parameter Models.
5.5 Jeffreys’ Prior for Multiparameter Models.
Chapter 6. Process Modeling With Single-Response Data.
6.1 The Objective Function S(_).
6.2 Weighting and Observation Forms98.
6.3 Parametric Sensitivities; Normal Equations.
6.4 Constrained Minimization Of S(_).
6.4.1 The Quadratic Programming Algorithm GRQP.
6.4.2 The Line Search Algorithm GRS1.
6.4.3 Final Expansions Around b_.
6.5 Testing the Residuals. 106.
6.6 Inferences from the Posterior Density.
6.6.1 Inferences for the Parameters.
6.6.2 Inferences for Predicted Functions.
6.6.3 Discrimination of Rival Models by Posterior Probability.
6.7 Sequential Planning Of Experiments.
6.7.1 Planning For Parameter Estimation.
6.7.2 Planning For Auxiliary Function Estimation.
6.7.3 Planning For Model Discrimination.
6.7.4 Combined Discrimination and Estimation.
6.7.5 Planning For Model Building.
Chapter 7. Process Modeling With Multiresponse Data.
7.1 Problem Types.
7.2 Objective Function.
7.2.1 Selection of Working Responses.
7.2.2 Derivatives of EQS. (7.2-1) and (7.2-3)150.
7.2.3 Quadratic Expansions; Normal Equations.
7.3 Constrained Minimization Of S(_.
7.3.1 Final Expansions Around b_.
7.4 Testing the Residual.
7.5 Posterior Probabilities and Regions.
7.5.1 Inferences Regarding Parameters.
7.5.2 Inferences Regarding Functions.
7.5.3 Discrimination among Rival Models.
7.6 Sequential Planning Of Experiments.
7.8 Process Investigations.
7.11 Proof of EQS. (7.1-16) and (7.1-17).
Appendix A. Solution of Linear Algebraic Equations.
A.1 Introductory Concepts and Operations.
A.2 Operations with Partitioned Matrices.
A.3 Gauss-Jordan Reduction.
A.4 Gaussian Elimination.
A.5 Lu Factorization.
Appendix B. Ddaplus Documentation.
B.1 What Ddaplus Does.
B.2 Object Code.
B.3 Calling Ddaplus.
B.4 Description of The Calling Arguments.
B.5 Exit Conditions and Continuation Calls.
B.6 The Subroutine fsub.
B.7 The Subroutine Esub.
B.8 The Subroutine Jac.
B.9 The Subroutine Bsub.
Appendix C. Gregplus Documentation.
C.1 Description Of Gregplus.
C.2 Levels of Gregplus.
C.3 Calling Gregplu.
C.4 Work Space Requirements for Gregplus.
C.5 Specifications For The User-Provided Model.
C.6 Single-Response Examples.
C.7 Multiresponse Examples.
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.