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2nd Edition

# A Numerical Primer for the Chemical Engineer, Second Edition

By

## Edwin Zondervan

ISBN 9781138315389
Published August 27, 2019 by CRC Press
192 Pages - 64 B/W Illustrations

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## Book 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.

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
12.7 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

...

## Author(s)

### Biography

Edwin Zondervan was born and raised in Leeuwarden, the Netherlands. After finishing his bachelor with a specialization in process automation in Leeuwarden he continued in Groningen with a M.Sc. in chemical engineering. Then he moved To Enschede and pursued a Ph.D. on modeling, optimization and control of dead-end membrane filtration of surface water. He defended his doctorate at Groningen in 2007. He worked from 2007 to 2015 at Eindhoven University of Technology. He has been working as associate researcher at the laboratories of Technical University of Catalonia, Carnegie Mellon University, Denmark Technical University and Imperial College . Besides research Edwin Zondervan has been very active in the educational gremials where he trained many generations of students in process design, process control and numerical methods. For the latter one Edwin published a textbook that was released in 2014: “A numerical primer for the chemical engineer”. Recently Edwin Zondervan joined the Institute for environmental science and Technology of Bremen University, where he obtained a professorship in “Process Systems Engineering”. The newly established Laboratory of Process Systems Engineering (PSE) at Bremen University (which was established within Bremen’s Excellence Initiative) will conduct research in the field of sustainable and flexible system design of energy networks. The main objective of the laboratory of PSE is to develop network modeling techniques and dynamic optimization tools and to apply them to the design and operation of complex energy/process systems. The PSE group distinguishes two working areas: i) Novel energy technologies and devices and ii) Energy Efficient production. Where the challenges lie in 1) decisionmaking under uncertainty, 2) sustainable design and 3) managing complexity. In addition the PSE group will be active in the development of an Energy Systems Institute at Bremen University and setup a specialized course program in this field.

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