Computation of Mathematical Models for Complex Industrial Processes (Advances in Process Systems Engineering)

Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes. Thus, they provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios. Readership: Students, academics and practitioners in the field of chemical engineering, numerical analysis and computational mathematics. Contents 10 Preface 6 List of Figures 14 List of Tables 16 1. Introduction 18 1.1 Background 19 1.2 Motivation 22 1.3 Process Modelling 24 1.4 Model Approximation 25 1.5 Algorithm Design and Setup 25 1.6 Interpretation of Verification of Computing Results 26 1.7 Book Outline 27 2. Fundamentals of Process Modelling and Model Computation 30 2.1 Building Mathematical Models 30 2.2 General ODE and PDE Models for Industrial Processes 33 2.3 Examples of ODE and PDE Process Models 35 2.3.1 ODE Model for Enzyme Reaction 35 2.3.2 PDE Model for Population Balance 35 2.3.3 PDE Model for Transonic Flow 36 2.4 Solutions of Process Models 36 2.4.1 Solution of an Initial Value Problem of ODE 37 2.4.2 Solution of a Boundary Value Problem of ODE 37 2.4.3 Solution of a PDE 37 2.5 The Runge-Kutta Methods 38 2.6 Finite Difference Methods 39 2.7 Wavelets-Based Methods 43 2.7.1 Multiresolution Analysis 43 2.7.2 Basis Functions of Daubechies’ Wavelets 45 2.7.3 Computation of the Connection Coefficients 47 2.8 High Resolution Methods 49 2.8.1 Koren’s High-Resolution Scheme 50 2.8.2 Solving PDEs with Dirichlet Boundary Conditions 51 2.8.3 Solving PDEs with Cauchy Boundary Conditions 52 2.8.4 Solving PDEs with Neumann Boundary Conditions 53 3. Finite Difference Methods for Ordinary Differential Equation Models 56 3.1 Fermentation Processes 56 3.2 Biology of Lysine Synthesis 57 3.3 Model Construction 58 3.4 Numerical Approximations of Fermentation Models 60 3.5 Simulation for Batch Fermentation 63 3.6 Simulation for Fed-Batch Fermentation 64 4. Finite Difference Methods for Partial Differential Equation Models 68 4.1 Continuous Galvanizing Processes 68 4.2 Development of a PDE Model 72 4.3 Discrete State Space Model 74 4.4 Stability Analysis and Parameter Settings of the Model 78 4.5 Identification of Model Parameters 79 4.6 Least-Square Algorithms for System Identification 82 4.7 Simplification of System Identification Algorithms 83 4.8 Simulations and Industrial Applications 85 5. Wavelets-Based Methods 90 5.1 Process Modelling for Chemical Reactions 91 5.1.1 Chemical Reactions 91 5.1.2 Model Development 92 5.2 Three Versions of Wavelet Collocation Methods 94 5.2.1 Basic Wavelet Collocation Method 94 5.2.2 Improved Wavelet Collocation Method I 94 5.2.3 Improved Wavelet Collocation Method II 95 5.3 Wavelet Collocation Method for Reaction Processes 96 5.4 Model Development for Crystallization Processes 98 5.5 Wavelet Galerkin Method for PDEs 100 5.6 Solution Based on Wavelet Galerkin Method 101 6. High Resolution Methods 104 6.1 Column Chromatographic Separation Processes 104 6.2 Model Development for Column Chromatography 106 6.2.1 Mechanism and Assumptions for Process Modelling 106 6.2.2 Basic Model 107 6.2.3 Adsorption Isotherm Model 108 6.2.4 Complete Process Model 109 6.3 Analytical Solution for Linear Equilibrium Case 110 6.4 Model Discretization Using High Resolution Methods 113 6.5 The Alexander Method for Time Integration 115 6.6 Solutions to the Chromatographic Process Model 117 6.7 Crystallization and Population Balance Equations 120 6.7.1 Motivations for Modelling of Crystallization 121 6.7.2 Development of Population Balance Equation Model 121 6.8 Crystallization with Pure Size-Independent Growth 123 6.8.1 Upwinding Scheme for Approximating ni+1/2 123 6.8.2 Approximating ni+1/2 via κ-flux Interpolation 124 6.8.3 Optimized 1/3-flux Interpolation for Approximating ni+1/2 125 6.9 Process with Size-Independent Growth and Nucleation 126 7. Comparative Studies of Numerical Methods for SMB Chromatographic Processes 130 7.1 Chromatographic Separation Processes 131 7.1.1 Fixed Bed Chromatography 131 7.1.2 Moving Bed Chromatography 132 7.1.3 Simulated Moving Bed Chromatography 133 7.1.4 Economical Advantages of SMBC Operation 135 7.1.5 Challenges in Solving SMBC Process Models 136 7.2 Dynamic Modelling of SMBC Processes 137 7.2.1 Column Model for Chromatography 138 7.2.2 Node Model for an SMB System 139 7.3 Numerical Computation 140 7.3.1 Upwind-1 Finite Difference Discretization 141 7.3.2 Wavelet Collocation Discretization 142 7.3.3 Discretization using High Resolution Method 143 7.3.4 Settings for Numerical Computation 144 7.4 Case Study I: Fructose-Glucose Separation 144 7.5 Case Study II: Bi-naphthol Enantiomers Separation 149 7.6 Concluding Remarks 154 8. Conclusion 158 Bibliography 162 Designed for undergraduate and postgraduate students, academic researchers and industrial practitioners, this book provides comprehensive case studies on numerical computing of industrial processes and step-by-step procedures for conducting industrial computing. It assumes minimal knowledge in numerical computing and computer programming, making it easy to read, understand and follow. Topics discussed include fundamentals of industrial computing, finite difference methods, the Wavelet-Collocation Method, the Wavelet-Galerkin Method, High Resolution Methods, and comparative studies of various methods. These are discussed using examples of carefully selected models from real processes of industrial significance. The step-by-step procedures in all these case studies can be easily applied to other industrial processes without a need for major changes and thus provide readers with useful frameworks for the applications of engineering computing in fundamental research problems and practical development scenarios