TUM Library

1 The role of models in chemical engineering1.1 Introduction1.2 The idea of a model1.4 Model analysis1.5 Model solution strategies1.6 Summary1.7 Exercises 2 Errors in computer simulations2.1 Introduction2.2 Significant digits2.3 Round-off and truncation errors2.4 Break errors2.5 Loss of digits2.6 Ill-conditioned problems2.7 (Un-)stable methods2.8 Summary2.9 Exercises 3 Linear equations3.1 Introduction3.2 MATLAB3.3 Linear systems3.4 The inverse of a matrix3.5 The determinant of a matrix3.6 Useful properties3.7 Matrix ranking3.8 Eigenvalues and eigenvectors3.9 Spectral decomposition3.10 Summary3.11 Exercises 4 Elimination methods4.1 Introduction4.2 MATLAB4.3 Gaussian elimination4.4 LU factorization4.5 Summary4.6 Exercises 5 Iterative methods5.1 Introduction5.2 Laplace's equation5.3 LU factorization5.5 The Jacobi method5.6 Example for the Jacobi method5.7 Summary5.8 Exercises 6 Nonlinear equations6.1 Introduction6.2 Newton method 1D6.3 Newton method 2D6.4 Reduced Newton step method6.5 Quasi-Newton method6.6 Summary6.7 Exercises 7 Ordinary differential equations7.1 Introduction7.2 Euler's method7.3 Accuracy and stability of Euler's method7.4 The implicit Euler method7.5 Stability of the implicit Euler method7.6 Systems of ODEs7.7 Stability of ODE systems7.8 Stiffness of ODE systems7.9 Higher-order methods7.10 Summary7.11 Exercises 8 Numerical integration8.1 Introduction8.2 Euler's method8.3 The trapezoid method8.4 Simpson's method8.5 Estimation of errors using numerical integration8.6 The Richardson correction8.7 Summary8.8 Exercises 9 Partial differential equations 9.1 Introduction9.2 Transport PDEs9.3 Finite volumes9.4 Discretizing the control volumes9.5 Transfer of heat to fluid in a pipe9.6 Simulation of the heat PDE9.7 Summary9.8 Exercises 10 Data regression and curve fitting10.1 Introduction10.2 The least squares method 10.3 Residual analysis10.4 ANOVA analysis10.5 Confidence limits10.6 Summary10.7 Exercises 11 Optimization11.1 Introduction11.2 Linear programming11.3 Nonlinear programming11.4 Integer programming11.5 Summary11.6 Exercises 12 Basics of MATLAB12.1 Introduction12.2 The MATLAB user interface12.3 The array structure12.4 Basic calculations12.5 Plotting12.6 Reading and writing data12.7 Functions and m-files12.8 Repetitive operations 13 Numerical methods in Excel13.1 Introduction13.2 Basic functions in Excel13.3 The Excel solver13.4 Solving nonlinear equations in Excel13.5 Differentiation in Excel13.6 Curve fitting in Excel 14 Case studies 14.1 Introduction14.2 Modeling a separation system14.3 Modeling a chemical reactor system14.4 PVT behavior of pure substances14.5 Dynamic modeling of a distillation column14.6 Dynamic modeling of an extraction cascade (ODEs)14.7 Distributed parameter models for a tubular reactor14.8 Modeling of an extraction column14.9 Fitting of kinetic data14.10 Fitting of NRTL model parameters14.11 Optimizing a crude oil refinery14.12 Planning in a manufacturing line BibliographyIndex

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.

"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.

OCLC-licensed vendor bibliographic record.