A Numerical Primer for the Chemical Engineer, Second Edition

Description

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 Half Title Title Page Copyright Page Dedication Contents Introduction Preface 1. The role of models in chemical engineering 1.1 Introduction 1.2 The idea of a model 1.3 Model building 1.4 Model analysis 1.5 Model solution strategies 1.6 The seven-step modeling procedure 1.7 Ingredients of process models 1.8 Summary 1.9 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 5.4 Iterative methods 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 Boundary value problems 7.11 Summary 7.12 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 1 9.1 Introduction 9.2 Types of PDEs 9.3 The method of lines 9.4 Stability 9.5 Summary 9.6 Exercises 10. Partial differential equations 2 10.1 Introduction 10.2 Transport PDEs 10.3 Finite volumes 10.4 Discretizing the control volumes 10.5 Transfer of heat to fluid in a pipe 10.6 Simulation of the heat PDE 10.7 Summary 10.8 Exercises 11. Data regression and curve fitting 11.1 Introduction 11.2 The least squares method 11.3 Residual analysis 11.4 ANOVA analysis 11.5 Confidence limits 11.6 Summary 11.7 Exercises 12. Optimization 12.1 Introduction 12.2 Linear programming 12.3 Nonlinear programming 12.4 Integer programming 12.5 Summary 12.6 Exercises 13. Basics of MATLAB 13.1 Introduction 13.2 The MATLAB user interface 13.3 The array structure 13.4 Basic calculations 13.5 Plotting 13.6 Reading and writing data 13.7 Functions and m-files 13.8 Repetitive operations 14. Numerical methods in Excel 14.1 Introduction 14.2 Basic functions in Excel 14.3 The Excel solver 14.4 Solving nonlinear equations in Excel 14.5 Differentiation in Excel 14.6 Curve fitting in Excel 15. Case studies 15.1 Introduction 15.2 Modeling a separation system 15.3 Modeling a chemical reactor system 15.4 PVT behavior of pure substances 15.5 Dynamic modeling of a distillation column 15.6 Dynamic modeling of an extraction cascade (ODEs) 15.7 Distributed parameter models for a tubular reactor 15.8 Modeling of an extraction column 15.9 Fitting of kinetic data 15.10 Fitting of NRTL model parameters 15.11 Optimizing a crude oil refinery 15.12 Planning in a manufacturing line Bibliography Index