A Numerical Primer for the Chemical Engineer, Second Edition

✍ Scribed by Edwin Zondervan

• Publisher: CRC Press
• Year: 2019
• Tongue: English
• Leaves: 209
• Edition: 2
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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