00 Computer-Aided Computation for Chemical Engineers.pdf

Computer-Aided Computation for Chemical Engineers

Cheng-Liang Chen

PSE

LABORATORY

Department of Chemical Engineering National TAIWAN University

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Computer-Aided Computation for Chemical Engineers Course Objectives This course emphasizes the derivation of a variety of numerical methods and their application to the solution of chemical engineering problems. The first objective of of the course is to enable the students to formulate chemical engineering problems as mathematical models belonging to one of the following categories: 1. Complex consecutive calculations, 2. Linear and nonlinear algebraic equations, 3. Ordinary differential equations, 4. Partial differential equations, and 5. Multiple linear and polynomial regressions.

Chen CL

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Computer-Aided Computation for Chemical Engineers Course Objectives This course emphasizes the derivation of a variety of numerical methods and their application to the solution of chemical engineering problems. The first objective of of the course is to enable the students to formulate chemical engineering problems as mathematical models belonging to one of the following categories: 1. Complex consecutive calculations, 2. Linear and nonlinear algebraic equations, 3. Ordinary differential equations, 4. Partial differential equations, and 5. Multiple linear and polynomial regressions.

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Computer-Aided Computation for Chemical Engineers Course Objectives Recently, MATLAB has been widely recognized as a high-performance language for technical computing. It integrates computation, visualization, and programming in an easy-to-use environment. The second objective of of this course is to enable students to solve the resultant models using MATLAB and Simulink.

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Computer-Aided Computation for Chemical Engineers Course Objectives Note: We are not going to train you as a programmer or software engineer . The main learning objectives in this course include:

1. To use computational tool(s) for solving engineering problems effectively; 2. Understand and analyze the problem and formulate the model accurately; 3. Use analytical methods or numerical techniques to find proper solution; 4. Use computer program for solving the problem.

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Computer-Aided Computation for Chemical Engineers Outline

Simulink and MATLAB Materials

Illustrative Applications Simulink solution of ODEs, some linear

Simulation with Simulink

Computing with MATLAB Plotting tips Programming techniques Problem solving steps

and nonlinear functions Simulink simulation examples: a gas process a stirred-tank heater a batch bioreactor

Some simple engineering problems

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Numerical Solution of Nonlinear Equations Numerical Methods

Illustrative Applications

Types of roots and their approximation Methods of successive substitution Methods of linear interpolation Wegstein method

Solution of the Colebrook Equations Solution of the Soave-Redlich-Kwong Equation

Newton-Raphson method

Solution of nth-Degree Polynomials and Transfer Functions

Newton’s method for simultaneous nonlinear equations

Solution of Nonlinear Equations in Chemical Equilibrium

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Numerical Solution of Simultaneous Linear Algebraic Equations Numerical Methods

Cramer’s rule Gauss elimination method Gauss-Jordan reduction method Gauss-Seidel substitution method Jacobi method


Heat transfer in a pipe Solution of a steam distribution problem Solution of chemical reaction and material balance equations

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Finite Difference Methods and Interpolation Numerical Methods


Finite Differences (FDs): Backward-Forward-Central Difference equations and their solutions Interpolating polynomials Interpolation of equally spaced pts Gregory-Newton method Stirling’s method Interpolation of unequally spaced pts Lagrange polynomials Spline interpolation

Equally spaced data: Gregory-Newton method The Lagrange polynomials and cubic splines

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Numerical Differentiation and Integration Numerical Methods

Differentiation by FDs: Backward-Forward-Central Spline differentiation Newton-Cotes formulas of integration Gauss quadrature Spline integration Multiple integrals


Mass transfer flux from an open vessel Derivative of vectors of equally spaced pts Integration formula: trapezoidal and Simpson’s 1/3 rules Integration formulas: Gauss-Legendre quadrature

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Numerical Solution of Ordinary Differential Equations Numerical Methods


Linear ODEs

Solution of a Chemical reaction system

Nonlinear ODEs: initial-value problems Euler and modified Euler methods Runge-Kutta methods Adams-Moulton methods Simultaneous DEs Nonlinear problems

ODEs:

Solution of non-isothermal plug-flow reactor

boundary-value

The shooting method The finite difference method Collocation methods Step-size control and Stiff DEs

Flow of a non-Newtonian fluid Optimal temperature profile penicilline fermentation

for

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Numerical Solution of Partial Differential Equations Numerical Methods

Solution of differences

PDEs

Elliptic PDEs Parabolic PDEs Hyperbolic PDEs


using

finite

Solution of the Laplace and Poisson equations Solution of parabolic PDEs for diffusion Solution of parabolic PDEs for heat transfer

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Linear and Nonlinear Regression Analysis Numerical Methods


Review of statistical terminologies Linear regression analysis The least squares method Properties of estimated par.s Nonlinear regression analysis The method of steepest descent The Gauss-Newton method Newton’s method The Marquardt method Multiple nonlinear regressions Analysis of variance

Nonlinear regression Marquart method

using

the

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Process Optimization Numerical Methods

Linear programming Nonlinear programming with and without constraints Mixed-integer linear programming Mixed-integer nonlinear programming


Refinery process Synthesis of water networks Synthesis of cooling-water networks Synthesis of heat-exchanger networks

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Computer-Aided Computation for Chemical Engineers Text Book and References



Constantinides, A. and N. Mostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications, Prentice

Hall, Upper Saddle River, NJ, 1999. 

Cutlip, M. B., and M. Shacham, Problem Solving in Chemical Engineering with Numerical Methods, Prentice Hall, Upper Saddle

River, NJ, 2nd Ed., 2007. 

William J. Palm III , Introduction to MATLAB 7 for Engineers,

McGraw-Hill, New York, 2005.

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Some Notes 

Computer room: lecture, in-class practice and exercise Tuesday 2 : 10 Thursday 1 : 20 

∼

∼

3 : 20 2 : 40

(50%)

Prepare one document file for each exercise:

D93524013 2007 03 08 1.doc

D93524013 2007 03 08   



registration no

date

1 . doc

  version

doc file

Document file should include problem description , main results and discussion , relevant figures and tables , and m-files for each problem.  E-mail your report file immediately to teaching assistant (Ciou Y.J. [email protected] ) BEFORE you leave computer room  You can modify your report and e-mail it again to teaching assistant after the class. However, you have to use another file name: D93524013 2007 03 14 2.doc 

Two examinations: mid-term and final

(25% + 25%)

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Some High-level Programming Languages Language

Key Data

Application Area

Origin of Names

FORTRAN

IBM (1957)

Scientific programming

FORmula TRANslation language

LISP

MIT (1958)

Symbolic computation (AI)

LISp Processing

COBOL

USA (1959)

Business data processing

COmmon Business-Oriented Language

Simple on PC

Beginner’s All Purpose Symbolic Instruction Code

Systems programming

Predecessor language was named B

Symbolic computation (AI)

PROgramming LOGic (Frence)

Real-time distributed systems

Ada Augusta Byron collaborated with nineteenthcentury computer pioneer Charles Babbage

Graphical user interfaces; Objectoriented programming

Objects ”talk” to one another via messages

Supports objects and objectedoriented programming

Incremental modification of C increment operator)

Supports Web programming

Originally named ”Oak”

BASIC C PROLOG Ada Smalltalk

(1965) Bell (1972) (1972) USA (1980) (1980)

C++ JAVA

SUN (1995)

→

Common Lisp Object System

(++ is the C

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Progress of Programming Languages Progress of Programming Languages 1955

(Machine Language)

(Assembly Language)

1960 1965 1970 r 1975 a e Y

1980 1985 1990 1995 2000

01011010

ADD

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(Machine Language)

FORTRAN

1960 1965 1970

DO 7, LOOP = 1,5 READ *, X, Y

r 1975 a e Y

1980 1985 1990 1995 2000

AVE=(X+Y)/2.0 PRINT *, X,Y,AVE 7 CONTINUE END

(Assembly Language)

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Progress of Programming Languages Progress of Programming Languages 1955 1960

(Machine Language)

FORTRAN COBOL

1965 1970

01 EMPLOYEE−RECORD 05 EMPLOYEE−NUMBER PIC 9(5)

r 1975 a e Y

1980

05 EMPLOYEE−NAME 05 BIRTH−DATE 10 BIRTH−MONTH 10 FILLER 10 BIRTH−DAY

1985

1995 2000

PIC 99

PIC X PIC 99

05 DATE−HIRED 10 MONTH−HIRED 10 FILLER

1990

PIC X(30)

10 DAY−HIRED

PIC 99

PIC X PIC 99

(Assembly Language)

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(Machine Language) LISP

FORTRAN

(Assembly Language)

COBOL

1960 1965 1970

(defun length (x) PROLOG

r 1975 a e Y

(t(+1 (length (cdr x)))))) SCHEME

1990 1995 2000

(length ’(I Love Computers)’) 3

1980 1985

(cond ((null x) 0)

COMMON LISP

CLOS

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(Machine Language)

LISP

FORTRAN

(Assembly Language)

COBOL

1960

BASIC

1965 1970 PROLOG

r 1975 a e Y

SCHEME

Dim i, sum sum = 0 For i = 1 to 10

1980

sum = sum + 1 Next i

1985 1990

COMMON LISP

CLOS VISUAL

1995 2000

BASIC

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FORTRAN

(Assembly Language)

COBOL

1960

ALGOL60

BASIC

1965 1970

PASCAL

PROLOG

r 1975 a e Y

SCHEME

1980 1985

MODULA−2 COMMON LISP

if (i > 0) then x := 10 else

1990

CLOS

MODULA−3

y := 5 VISUAL

1995 2000

BASIC

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FORTRAN

(Assembly Language)

COBOL

1960

ALGOL60 CPL

BASIC

1965 1970 r 1975 a e Y

PASCAL

C

PROLOG SCHEME

1980 1985

MODULA−2 COMMON LISP

if (i > 0) x = 10; else

1990

CLOS

MODULA−3

y = 5; VISUAL

1995 2000

BASIC

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(Machine Language)

LISP

FORTRAN

(Assembly Language)

COBOL

1960

ALGOL60 CPL

BASIC

1965 SIMULA

1970 PROLOG

r 1975 a e Y

SCHEME SMALLTALK

1980 1985 1990

PASCAL

C

COMMON LISP

MODULA−2

C++

MODULA−3 CLOS VISUAL

1995

C++

Standard

2000

BASIC

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(Machine Language)

LISP

FORTRAN

(Assembly Language)

COBOL

1960

ALGOL60 CPL

BASIC

1965 SIMULA

1970 r 1975 a e Y

SCHEME SMALLTALK

1980 1985 1990

PASCAL

C

PROLOG

ADA

C++

COMMON LISP


1995 2000

MODULA−2

JAVA

C++

Standard

BASIC

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(Machine Language)

LISP

FORTRAN

(Assembly Language)

COBOL

1960

ALGOL60 CPL

BASIC

1965 SIMULA

1970 r 1975 a e Y

SCHEME SMALLTALK

1980 1985 1990

PASCAL

C

PROLOG

MATLAB ADA

C++

COMMON LISP


1995 2000

MODULA−2

JAVA

C++

Standard

BASIC

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MATLAB ?

MATrix LABoratory 

In 1978, Professor Cleve Moler (New Mexico University, USA) used FORTRAN to write the MATLAB for applications involving matrices , linear algebra , and numerical analysis



In 1984, Jack Little (Stanford University) used C to rewrite and to commercialize the MATLAB software (MathWorks Company)



MATLAB is both a computer programming language and an interactive software environment for using that language

effectively

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Why MATLAB ? Outstanding Features 

Significantly simpler programming



Continuity (no distinction) among integer, real, and complex values (any variable can take any type of number without special declaration)



Extended range of numbers and their accuracy (all in double precision)



Extensive graphic tools including graphic user interface functions



A comprehensive mathematical library



Capability of linking with traditional programming languages



Transportability of MATLAB programs



MATLAB has a number of add-on software modules, called toolboxes, that perform more specialized computations. All toolboxes run under the core MATLAB program

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Simulink Graphical Dynamic Simulation built on top of

MATrix LABoratory

00 Computer-Aided Computation for Chemical Engineers.pdf

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