This book addresses the applications of MATLAB€ and Simulink in the solution of chemical engineering problems. By classifying the problems into seven different categories, the author organizes this book as follows: Chapter One - Solution of a System of Linear Equations Chapter Two - Solution of Nonlinear Equations Chapter Three - Interpolation, Differentiation and Integration Chapter Four- Numerical Solution of Ordinary Differential Equations Chapter Five - Numerical solution of Partial Differential Equations Chapter Six - Process Optimization Chapter Seven - Parameter Estimation Each chapter is arranged in four major parts. In the first part, the basic problem patterns that can be solved with MATLAB€ are presented. The second part describes how to apply MATLAB€ commands to solve the formulated problems in the field of chemical engineering. In the third and the fourth parts, exercises and summary of MATLAB€ instructions are provided, respectively. The description of the chemical engineering example follows the sequence of problem formulation, model analysis, MATLAB€ program design, execution results, and discussion. In this way, learners are first aware of the basic problem patterns and the underlying chemical engineering principles, followed by further familiarizing themselves with the relevant MATLAB€ instructions and programming skills. Readers are encouraged to do exercises to practice their problem-solving skills and deepen the fundamental knowledge of chemical engineering and relevant application problems.

2. Author Biography
Current Position: Vice President, National Quemoy
University, Taiwan (Aug. 2014 - )
Education: Ph.D. in Chemical Engineering, National
Cheng Kung University, Taiwan (May 1990)
Experiences:
Vice President, National Quemoy University, Taiwan
(Aug. 2014 - )
Life-long Distinguished Professor, National Quemoy Univeristy, Taiwan (Aug. 2021-)
Distinguished Professor, National Quemoy Univeristy, Taiwan (Aug. 2017- July 2021 )
Professor of the Center for General Education, National Quemoy Univeristy, Taiwan (Aug. 2014- )
Visiting Scholar at the Massachusetts Institute of Technology (MIT), USA (Aug. 2010-July 2011)
Dean of the FCU Extension, Feng Chia University, Taiwan (Aug. 2007-July 2009)
Dean of the College of Continuing Eduation, Feng Chia University, Taiwan (Aug. 2005-July 2007)
Associate Dean of the College of Engineering, Feng Chia University, Taiwan (Aug. 2003-July 2005)
Chairman of the Chemical Engineering Department, Feng Chia University, Taiwan (Aug. 2001-July
2003)
Visiting Professor at the University of California, Santa Barbara, USA (Jan. 2000-Aug. 2000)
Professor of the Chemical Engineering Department, Feng Chia University, Taiwan (Aug. 1997-July
2014)
Associate Professor of the Chemical Engineering Department, Feng Chia University, Taiwan (Aug.
1992-July 1997)
Honors:
Teaching Excellence Award granted by National Quemoy Univeristy, Taiwan (2017)
Associate Editor of the Journal of the Taiwan Institute of Chemical Engineers (2012-2015)
Chairman of the Accreditation Group, Institute of Engineering Education Taiwan (2006-2014)
Teaching Excellence Award granted by Feng Chia University, Taiwan (2006)
Honorary member of the Phil Tau Phil Academic Society, Taiwan (1998)
A–Level Research Awards from the National Science Council of Taiwan (1997-2000)
Research fields:
Process control
Process design, simulation and optimization
Artificial intelligent technologies and applications
Publications:
Over 150 refereed journal and conference papers
Over 20 technical reports
Author of 4 books about the applications of MATLAB in reltated engineering fields.
Chen, Chyi-Tsong 陳奇中
Scan to download
MATLAB programs of this book.

3. v
Table of Contents
Chapter 1: Solution of a System of Linear Equations .......................... 1
1.1 Properties of linear equation systems and the relevant
MATLAB commands ............................................................................. 1
1.1.1 A simple example: the liquid blending problem ..................................... 1
1.1.2 Relevant properties of linear equation systems ....................................... 3
1.1.3 Relevant MATLAB commands .............................................................. 5
1.2 Chemical engineering examples .......................................................... 10
Example 1-2-1 Composition analysis of a distillation column system .................... 10
Example 1-2-2 Temperature analysis of an insulated stainless steel pipeline ......... 14
Example 1-2-3 Composition analysis of a set of CSTRs ........................................ 18
Example 1-2-4 Independent reactions in a reaction system .................................... 21
Example 1-2-5 Composition distributions in a distillation column ......................... 24
Example 1-2-6 Steady-state analysis of a batch reaction system ............................ 36
1.3 Exercises ................................................................................................ 43
1.4 Summary of the MATLAB commands related to this chapter ......... 48
Chapter 2: Solution of Nonlinear Equations .................................... 51
2.1 Relevant MATLAB commands and the Simulink solution interface 51
2.1.1 Nonlinear equation of a single variable ................................................ 51
2.1.2 Solution of a system of nonlinear equations ......................................... 61
2.2 Chemical engineering examples .......................................................... 70
Example 2-2-1 Boiling point of an ideal solution ................................................... 70
Example 2-2-2 Equilibrium concentrations in a reaction system ..............................74
Example 2-2-3 Analysis of a pipeline network ....................................................... 78
Example 2-2-4 A drying process through heat conduction and forced convection 82
Example 2-2-5 Simulation of a multistage binary distillation ................................. 86
Example 2-2-6 Analysis of a set of three CSTRs in series .................................... 100
2.3 Exercises .............................................................................................. 103
2.4 Summary of MATLAB commands related to this chapter ............. 122
Chapter 3: Interpolation, Differentiation, and Integration .............. 125
3.1 Interpolation commands in MATLAB .............................................. 125
3.1.1 One-dimensional interpolation ........................................................... 125
3.1.2 Two-dimensional interpolation ........................................................... 129

4. vi | MATLAB® Applications in Chemical Engineering
3.2 Numerical differentiation ................................................................... 131
3.2.1 The application of the MATLAB diff command in numerical
differentiation ................................................................................... 132
3.2.2 Polynomial fitting and its application to the calculation of
derivatives of a data set ....................................................................... 134
3.2.3 Higher-order derivatives of a data set ................................................. 135
3.2.4 The derivatives calculation of a known function ................................ 146
3.2.5 A method for calculating numerical gradients .................................... 151
3.3 Numerical integration ........................................................................ 153
3.3.1 Integral of numerical data ................................................................... 153
3.3.2 Integral of a known function ............................................................... 154
3.3.3 Double integral ................................................................................... 156
3.4 Chemical engineering examples ........................................................ 157
Example 3-4-1 Preparation of a water solution with a required viscosity .......... 157
Example 3-4-2 Interpolation of diffusivity coefficients ..................................... 159
Example 3-4-3 Reaction rate equation of a batch reactor ................................... 161
Example 3-4-4 Volume fraction of solid particles in a gas-solid fluidized bed .. 167
Example 3-4-5 Average residence time calculation based on a tracer response . 170
Example 3-4-6 Design of an absorption tower ................................................... 173
Example 3-4-7 Reaction time of an adiabatic batch reactor ............................... 176
Example 3-4-8 Breakthrough time determination for an absorption tower ........ 179
3.5 Exercises .............................................................................................. 183
3.6 Summary of the MATLAB commands related to this chapter ....... 195
Chapter 4: Numerical Solution of Ordinary Differential Equations 197
4.1 Initial value problems for ordinary differential equations ............. 197
4.1.1 The standard problems ........................................................................ 197
4.1.2 The MATLAB ODE solvers ............................................................... 198
4.1.3 Solving ODEs with MATLAB Simulink ............................................ 205
4.1.4 The DEE solution interface ................................................................. 218
4.2 Higher-order ordinary differential equations .................................. 222
4.3 Stiff differential equations ................................................................. 227
4.4 Differential-algebraic equation system ............................................. 232
4.5 Boundary-valued ordinary differential equations ........................... 236
4.5.1 Problem patterns ................................................................................. 236
4.5.2 MATLAB commands for solving two-point boundary value problems 238
4.5.3 Multipoint BVP ................................................................................... 248
4.6 Chemical engineering examples ........................................................ 254
Example 4-6-1 Temperature and conversion distributions in a catalyzed tubular

5. Table of Contents | vii
reactor ....................................................................................... 254
Example 4-6-2 Temperature and conversion distribution in a plug-flow reactor . 260
Example 4-6-3 Biochemical process dynamics in a batch reactor ........................ 265
Example 4-6-4 Temperature distribution on a flat panel with heat conduction and
radiation ...................................................................................... 268
Example 4-6-5 Flow dynamics of a non-Newtonian fluid .................................. 271
Example 4-6-6 Optimal operation temperature for penicillin fermentation ....... 277
4.7 Exercises .............................................................................................. 285
4.8 Summary of the MATLAB commands related to this chapter ....... 308
Chapter 5: Numerical Solution of Partial Differential Equations . 311
5.1 Classifications of PDEs......................................................................... 311
5.1.1 The order of a PDE ............................................................................. 311
5.1.2 Nonlinearity of a PDE ........................................................................ 312
5.1.3 Categories of initial conditions and boundary conditions ................... 313
5.2 The MATLAB PDE toolbox ............................................................... 316
5.2.1 The MATLAB PDE solver ................................................................. 316
5.2.2 The PDE graphical interface toolbox .................................................. 331
5.2.2.1 The solvable PDE problem patterns ......................................................... 333
5.2.2.2 Solution of PDE problems with the pdetool interface .............................. 335
5.3 Chemical engineering examples ........................................................ 341
Example 5-3-1 Temperature and reaction rate distributions in a catalyzed reactor 341
Example 5-3-2 Concentration distribution in a diffusive reaction system .......... 350
Example 5-3-3 Rapid cooling of a hot solid object ............................................ 358
Example 5-3-4 Two-dimensional heat transfer ................................................... 362
Example 5-3-5 The permeation of gaseous solute into a liquid film .................. 373
Example 5-3-6 Concentration distribution of ethanol in a tube .......................... 378
Example 5-3-7 Heat conduction of a long rod .................................................... 380
Example 5-3-8 Unsteady-state heat conduction in a flat panel ........................... 384
5.4 Exercises .............................................................................................. 388
5.5 Summary of the MATLAB commands related to this chapter ....... 397
Chapter 6: Process Optimization ..................................................... 399
6.1 The optimization problem and the relevant MATLAB commands 399
6.1.1 Optimization problems of a single decision variable .......................... 399
6.1.2 Multivariate optimization problems without constraints .................... 401
6.1.3 Linear programming problems ........................................................... 404
6.1.4 Quadratic programming problem ........................................................ 406

6. viii | MATLAB® Applications in Chemical Engineering
6.1.5 The constrained nonlinear optimization problems .............................. 409
6.1.6 The multi-objective goal attainment problem ..................................... 413
6.1.7 Semi-infinitely constrained optimization problem ............................. 418
6.1.8 The minimax problem ......................................................................... 426
6.1.9 Binary integer programming problem ................................................ 430
6.1.10 A real-coded genetic algorithm for optimization ................................ 432
6.1.10.1 Fundamental principles of the real-coded genetic algorithm ................... 432
6.1.10.2 Application of the RCGA algorithm to solve optimization problems ........ 436
6.2 Chemical engineering examples ........................................................ 448
Example 6-2-1 Maximizing the profit of a production system ........................... 448
Example 6-2-2 The optimal photoresist film thickness in a wafer
production process ....................................................................... 452
Example 6-2-3 Minimal energy of a chemical equilibrium system .................... 453
Example 6-2-4 Maximal profit of an alkylation process .................................... 456
Example 6-2-5 Maximum separation efficiency in a single-effect distillatory ... 463
Example 6-2-6 Dynamic optimization of an ammonia synthesis process .......... 467
Example 6-2-7 Optimal operating temperature for a tubular reactor .................. 474
6.3 Exercises .............................................................................................. 481
6.4 Summary of the MATLAB commands related to this chapter ....... 501
Chapter 7: Parameter Estimation ................................................... 503
7.1 Parameter estimation using the least-squares method .................... 503
7.1.1 Linear least-squares method ............................................................... 503
7.1.2 Nonlinear least-squares methods ........................................................ 510
7.1.3 The confidence interval of parameter estimation ................................ 514
7.2 Chemical engineering examples ........................................................ 517
Example 7-2-1 The solubility model of sulfur dioxide .........................................517
Example 7-2-2 The rate equation of a catalyzed reaction system ....................... 520
Example 7-2-3 Isothermal adsorption model for activated carbon ..................... 524
Example 7-2-4 Transfer function of a heating process ....................................... 527
Example 7-2-5 Estimation of the reaction rate constants for a fermentation process 530
Example 7-2-6 Parameter estimation for a packed bed reactor described
by a partial differential equation model ....................................... 536
Example 7-2-7 Parameter estimation using D-optimal experimental design method
....................................................................................................... 545
7.3 Exercises .............................................................................................. 549
7.4 Summary of the MATLAB commands related to this chapter ....... 560
References .......................................................................................... 563
Index ................................................................................................... 569