A Numerical Primer for the Chemical Engineer, Second Edition

Designed as an introduction to numerical methods for students, this book combines mathematical correctness with numerical performance, and concentrates on numerical methods and problem solving. It applies actual numerical solution strategies to formulated process models to help identify and solve chemical engineering problems. Second edition comes with additional chapter on numerical integration and section on boundary value problems in the relevant chapter. Additional material on general modelling principles, mass/energy balances and separate section on DAE’s is also included. Case study section has been extended with additional examples. Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Dedication 6 Contents 8 Introduction 14 Preface 16 1. The role of models in chemical engineering 18 1.1 Introduction 18 1.2 The idea of a model 19 1.3 Model building 20 1.4 Model analysis 21 1.5 Model solution strategies 22 1.6 The seven-step modeling procedure 23 1.7 Ingredients of process models 27 1.8 Summary 27 1.9 Exercises 28 2. Errors in computer simulations 30 2.1 Introduction 30 2.2 Significant digits 30 2.3 Round-off and truncation errors 31 2.4 Break errors 33 2.5 Loss of digits 33 2.6 Ill-conditioned problems 34 2.7 (Un-)stable methods 36 2.8 Summary 37 2.9 Exercises 37 3. Linear equations 38 3.1 Introduction 38 3.2 MATLAB 38 3.3 Linear systems 38 3.4 The inverse of a matrix 39 3.5 The determinant of a matrix 40 3.6 Useful properties 41 3.7 Matrix ranking 42 3.8 Eigenvalues and eigenvectors 43 3.9 Spectral decomposition 44 3.10 Summary 46 3.11 Exercises 46 4. Elimination methods 48 4.1 Introduction 48 4.2 MATLAB 48 4.3 Gaussian elimination 48 4.4 LU factorization 53 4.5 Summary 56 4.6 Exercises 56 5. Iterative methods 58 5.1 Introduction 58 5.2 Laplace's equation 58 5.3 LU factorization 61 5.4 Iterative methods 62 5.5 The Jacobi method 63 5.6 Example for the Jacobi method 66 5.7 Summary 68 5.8 Exercises 68 6. Nonlinear equations 70 6.1 Introduction 70 6.2 Newton method 1D 70 6.3 Newton method 2D 72 6.4 Reduced Newton step method 73 6.5 Quasi-Newton method 76 6.6 Summary 77 6.7 Exercises 77 7. Ordinary differential equations 80 7.1 Introduction 80 7.2 Euler's method 80 7.3 Accuracy and stability of Euler's method 82 7.4 The implicit Euler method 84 7.5 Stability of the implicit Euler method 84 7.6 Systems of ODEs 85 7.7 Stability of ODE systems 86 7.8 Stiffness of ODE systems 88 7.9 Higher-order methods 88 7.10 Boundary value problems 91 7.11 Summary 95 7.12 Exercises 95 8. Numerical integration 98 8.1 Introduction 98 8.2 Euler's method 98 8.3 The trapezoid method 102 8.4 Simpson's method 103 8.5 Estimation of errors using numerical integration 104 8.6 The Richardson correction 105 8.7 Summary 106 8.8 Exercises 107 9. Partial differential equations 1 108 9.1 Introduction 108 9.2 Types of PDEs 108 9.3 The method of lines 109 9.4 Stability 113 9.5 Summary 114 9.6 Exercises 114 10. Partial differential equations 2 116 10.1 Introduction 116 10.2 Transport PDEs 116 10.3 Finite volumes 117 10.4 Discretizing the control volumes 118 10.5 Transfer of heat to fluid in a pipe 119 10.6 Simulation of the heat PDE 122 10.7 Summary 124 10.8 Exercises 124 11. Data regression and curve fitting 126 11.1 Introduction 126 11.2 The least squares method 126 11.3 Residual analysis 129 11.4 ANOVA analysis 131 11.5 Confidence limits 131 11.6 Summary 131 11.7 Exercises 132 12. Optimization 134 12.1 Introduction 134 12.2 Linear programming 135 12.3 Nonlinear programming 137 12.4 Integer programming 139 12.5 Summary 141 12.6 Exercises 142 13. Basics of MATLAB 146 13.1 Introduction 146 13.2 The MATLAB user interface 146 13.3 The array structure 147 13.4 Basic calculations 148 13.5 Plotting 150 13.6 Reading and writing data 151 13.7 Functions and m-files 151 13.8 Repetitive operations 152 14. Numerical methods in Excel 154 14.1 Introduction 154 14.2 Basic functions in Excel 154 14.3 The Excel solver 154 14.4 Solving nonlinear equations in Excel 156 14.5 Differentiation in Excel 158 14.6 Curve fitting in Excel 158 15. Case studies 162 15.1 Introduction 162 15.2 Modeling a separation system 162 15.3 Modeling a chemical reactor system 163 15.4 PVT behavior of pure substances 165 15.5 Dynamic modeling of a distillation column 168 15.6 Dynamic modeling of an extraction cascade (ODEs) 170 15.7 Distributed parameter models for a tubular reactor 176 15.8 Modeling of an extraction column 178 15.9 Fitting of kinetic data 182 15.10 Fitting of NRTL model parameters 184 15.11 Optimizing a crude oil refinery 188 15.12 Planning in a manufacturing line 190 Bibliography 194 Index 198 1 The role of models in chemical engineering 1.1 Introduction 1.2 The idea of a model 1.4 Model analysis 1.5 Model solution strategies 1.6 Summary 1.7 Exercises 2 Errors in computer simulations 2.1 Introduction 2.2 Significant digits 2.3 Round-off and truncation errors 2.4 Break errors 2.5 Loss of digits 2.6 Ill-conditioned problems 2.7 (Un-)stable methods 2.8 Summary 2.9 Exercises 3 Linear equations 3.1 Introduction 3.2 MATLAB 3.3 Linear systems 3.4 The inverse of a matrix 3.5 The determinant of a matrix 3.6 Useful properties 3.7 Matrix ranking 3.8 Eigenvalues and eigenvectors 3.9 Spectral decomposition 3.10 Summary 3.11 Exercises 4 Elimination methods 4.1 Introduction 4.2 MATLAB 4.3 Gaussian elimination 4.4 LU factorization 4.5 Summary 4.6 Exercises 5 Iterative methods 5.1 Introduction 5.2 Laplace's equation 5.3 LU factorization 5.5 The Jacobi method 5.6 Example for the Jacobi method 5.7 Summary 5.8 Exercises 6 Nonlinear equations 6.1 Introduction 6.2 Newton method 1D 6.3 Newton method 2D 6.4 Reduced Newton step method 6.5 Quasi-Newton method 6.6 Summary 6.7 Exercises 7 Ordinary differential equations 7.1 Introduction 7.2 Euler's method 7.3 Accuracy and stability of Euler's method 7.4 The implicit Euler method 7.5 Stability of the implicit Euler method 7.6 Systems of ODEs 7.7 Stability of ODE systems 7.8 Stiffness of ODE systems 7.9 Higher-order methods 7.10 Summary 7.11 Exercises 8 Numerical integration 8.1 Introduction 8.2 Euler's method 8.3 The trapezoid method 8.4 Simpson's method 8.5 Estimation of errors using numerical integration 8.6 The Richardson correction 8.7 Summary 8.8 Exercises 9 Partial differential equations 9.1 Introduction 9.2 Transport PDEs 9.3 Finite volumes 9.4 Discretizing the control volumes 9.5 Transfer of heat to fluid in a pipe 9.6 Simulation of the heat PDE 9.7 Summary 9.8 Exercises 10 Data regression and curve fitting 10.1 Introduction 10.2 The least squares method 10.3 Residual analysis 10.4 ANOVA analysis 10.5 Confidence limits 10.6 Summary 10.7 Exercises 11 Optimization 11.1 Introduction 11.2 Linear programming 11.3 Nonlinear programming 11.4 Integer programming 11.5 Summary 11.6 Exercises 12 Basics of MATLAB 12.1 Introduction 12.2 The MATLAB user interface 12.3 The array structure 12.4 Basic calculations 12.5 Plotting 12.6 Reading and writing data 12.7 Functions and m-files 12.8 Repetitive operations 13 Numerical methods in Excel 13.1 Introduction 13.2 Basic functions in Excel 13.3 The Excel solver 13.4 Solving nonlinear equations in Excel 13.5 Differentiation in Excel 13.6 Curve fitting in Excel 14 Case studies 14.1 Introduction 14.2 Modeling a separation system 14.3 Modeling a chemical reactor system 14.4 PVT behavior of pure substances 14.5 Dynamic modeling of a distillation column 14.6 Dynamic modeling of an extraction cascade (ODEs) 14.7 Distributed parameter models for a tubular reactor 14.8 Modeling of an extraction column 14.9 Fitting of kinetic data 14.10 Fitting of NRTL model parameters 14.11 Optimizing a crude oil refinery 14.12 Planning in a manufacturing line Bibliography Index "This book emphasizes the deriviation and use of a variety of numerical methods for solving chemical engineering problems. The algorithms are used to solve linear equations, nonlinear equations, ordinary differential equations and partial differential equations. It also includes chapters on linear- and nonlinear regression and ond optimizaiton. MATLAB is adopted as the programming environment throughout the book. MATLAB is a high performance computing program. An introductory chapter on MATLAB basics has been added and Excel users can find a chapter on the implementation of numerical methods in Excel. Another chapter with worked out exaples are given in the Case study chapter to demonstrate the numerical techniques. Most of the examples were written in MATLAB and are compatible with the latest versions of MATLAB. It is important to mention that the main purpose of this book is to give the students a flavor of numerical methods and problem solving, rather than to be an in depth guide to numerical analysis. The chapters end with small exercises that students can use to familiarize them selves with the numerical methods. The material in this book has been used in undergraduate and graduate courses in the chemical engineering department of Eindhoven University of Technology. To aid lecturers and students course materials have also been made available on the web at http://webpage.com. The author would finally thank everybody who has been helpful and supportive in the creation of this book, especially some of the Ph.D. students at Eindhoven University that have assisted during lectures and directly influenced the content of this book: Juan Pablo Gutierrez, Esayas Barega and Arend Dubbelboer"-- Provided by publisher This book applies actual numerical solution strategies to formulated process models to help identify and solve chemical engineering problems. Second edition comes with chapter on numerical integration and sections on boundary value problems, general modelling principles, mass/energy balances and separate section on DAE’s.