Computational Methods in Chemical Engineering الطرق الحسابية في الهندسة الكيميائية

..Computational Methods in Chemical Engineering        الطرق الحسابية في الهندسة الكيميائية

Instructor: Prof. Ibrahim S. Al-Mutaz,   Room 2B57,   Phone [phone]

 
Class Hours: 1 3 @ 10:00-11:50, 1@ 13:00-14:50, http://faculty.ksu.edu.sa/Almutaz/ 
 Description of the Course:

a. Purpose, Structure
Application of computational techniques for solving numerical problems that arise in chemical‎engineering problems. Using high-level programming languages such as Fortran or MATLAB. ‎Topics include solving systems of linear and nonlinear algebraic equations, ordinary ‎differential equations (initial and boundary value problem) and curve fitting.‎ Basic principles of optimization of linear constrained and nonlinear unconstrained problems are also introduced.
Students expected to practice of using computer programming (e.g. Fortran, IMSL, MATLAB) to apply various numerical methods for solving problems.

b. Topics to be covered

Introduction
(Basic definitions, various types of process models and the corresponding type of resulting equations, Computational errors, conditioning and stability of algorithms, General process modeling, Modeling examples of lumped parameter and distributed parameter systems. Non-dimensionalization of model equations, Introduction to Fortran, IMSL and MATLAB programming.)
 Linear Algebraic Equations

• Matrix Inversion / Gauss Elimination (Introduction to Matrices)
• LU decomposition (product of a lower and an upper triangular matrix)
• Jacobi and Gauss-Seidel methods (the Liebmann method or the method of successive displacement, an iterative method used to solve a linear system of equations)
• Computer-based solutions

o      LSARG subroutine (Fortran IMSL subroutine that solves a real general system of linear equations with iterative refinement) (example_Fortran-code).
o      MATLAB solution of system of linear equations (backslash operator \ , left division, rref function)
 Non-Linear Algebraic Equations
(Single variable and multi-variable systems, Roots of polynomials) ... solution of Algebraic Eq's.

• Bisection method
• Newton-Raphson method
• Secant method
• Computer-based solutions

o      NEQNF subroutine (Fortran IMSL subroutine that Solves a system of nonlinear equation using a modified Powell hybrid algorithm and a finite-difference approximation to the Jacobian)... Example of using NEQNF.
o      MATLAB solution of system of non-linear equations (fzero, roots functions)

Ordinary Differential Equations-Initial Value Problem    ... Introduction to ODE's

• Taylor’s series method
• Euler method
• Runge Kutta method
• Computer-based solutions

o      IVPAG subroutine (Fortran IMSL subroutine that Solves an initial-value problem for ordinary differential equations using either Adams-Moulton’s or Gear’s BDF method)...Example of using IVPAG.
o      MATLAB solution of initial value problems for ordinary differential equations (ode23, ode45, ode113, ode15s, ode23s, ode23t, ode23tb)... ode matlab document. 

Ordinary Differential Equations-Boundary Value Problem    ... Introduction to ODE's

• Finite-difference method (Sect. 3-1 of Riggs' text), Useful Finite Difference Approximation
• shooting method
• Runge Kutta method
• Computer-based solutions

o      BVPFD subroutine (Fortran IMSL subroutine that Solves a (parameterized) system of differential equations with boundary conditions at two points, using a variable order, variable step size finite difference method with deferred corrections) ...Example of using BVPFD.
o      MATLAB solution of boundary value problems for ordinary differential equations (bvp4c) ...bvp4c matlab document. (Matlab codes for BVP in zip format)

Optimization   ... Chapter-6: Optimization_Rigss-Text

• Introduction to optimization methods
• uni-dimensional problems
• multi -dimensional problems
• linear programming technique
• Computer-based solutions

o      NCONF subroutine (Fortran IMSL subroutine solves the optimization problem based on the successive quadratic programming algorithm and a finite difference gradient)... Example of using NCONF.
o      minFunc is a Matlab function for unconstrained optimization of differentiable real-valued multivariate functions using line-search methods.
     Also Matlab Optimization Toolbox function fminunc.
o      minConf is a set of Matlab functions for optimization of differentiable real-valued multivariate functions subject to simple constraints on the parameters.
     Also Matlab Optimization Toolbox function fmincon. 
Function approximation, Curve fitting, Linear regression, Polynomial regression, Multiple linear regression Linear transformation
Useful link: MIT opencourse_ 10.34 Numerical Methods Applied to Chemical Engineering
Downloaded Materials on Fortran:

• Metcalf, M. and Reid, J. Fortran 90/95 Explained, Oxford University Press, 1996. (download part1, part2).
• W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes in Fortran 90: The Art of Parallel Scientific Computing, Volume 2 of Fortran Numerical Recipes, Second Edition (New York: Cambridge University Press,1996)
• Chapter 1: Numerical Computation from: A. Kayode Coker, "FORTRAN Programs for Chemical Process Design, Analysis, and Simulation", Elsevier Science and Technology Books, 1995.

Downloaded Materials on Matlab:

• Introduction to Matlab, Chapter 1 of "Numerical Computing with MATLAB" by Cleve Moler.
• Introduction to Matlab by Nicolas Hudon Chemical Engineering, Queen’s University, January 17, 2006. 
• Chapter_3-Matlab-and-Problem-Solving_muya.
• Matlab-Reference-Tables.

Downloaded Materials on Matrices:
Matrices-and-Linear-Equations , Chapter 2 of Serge Lang, "Introduction to Linear Algebra", Second Ed, Springer, New York,2000.
c. Texts
-          J. B. Riggs, An Introduction to Numerical Methods for Chemical Engineers, 2nd Edition, Texas Tech University Press, 1994.(Riggs-Fortran codes, in zip format)
     Essential Reading:
o      A. Constantinides and N. Mostoufi, Numerical Methods for Chemical Engineers with MATLAB applications, Prentice Hall, 1999.
o      J. B. Riggs, An Introduction to Numerical Methods for Chemical Engineers, 2nd Edition, Texas Tech University Press, 1994.
o      M. B. Cutlip and M. Shacham, Problem Solving in Chemical Engineering with Numerical Methods, Prentice Hall, 1999.
o      O. T. Hanna and O. C. Sandall, Computational Methods in Chemical Engineering, Prentice Hall, 1995.
o    S. C. Chapra and R. P. Canale, Numerical Methods for Engineers, with Software and programming ‎Applications, 4th Edition, McGraw-Hill,2002 ‎
o      S. K. Gupta, Numerical Methods for Engineers, New Age International Publishers Limited-Wiley Eastern Limited, New Delhi, 1995.
o      W. F. Ramirez, Computational Methods for Process Simulation, 2nd Edition, Butterworth, 1997.
 d. Prerequisite
   ChE 302‎: Computerized material and energy balances.    
    GE 204: Computer application in engineering.    
    GE 209: Programming in FORTRAN.

e. Requirements:
    homework, midterm(s), paper and final exam.

..