00 Computer-Aided Computation for Chemical Engineers.pdf

8/11/2019 00 Computer-Aided Computation for Chemical Engineers.pdf

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Computer-Aided Computation

for Chemical Engineers

Cheng-Liang ChenPSELABORATORY

Department of Chemical EngineeringNational TAIWAN University


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Chen CL 1


for Chemical EngineersCourse Objectives

This course emphasizes the derivation of a variety of numerical

methods and their application to the solution of chemical

engineering problems. The first objectiveof 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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Chen CL 2



Course ObjectivesRecently, MATLAB has been widely recognized as ahigh-performance language for technical computing. It integrates

computation, visualization, and programming in an easy-to-use

environment. The second objectiveof this course is to enable

students to solve the resultant models using MATLAB and

Simulink.


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Chen CL 3



Course ObjectivesNote: We are not going to train you as a programmerorsoftwareengineer. 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 propersolution;

4. Use computer program for solving the problem.


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Chen CL 4

Computer-Aided Computationfor Chemical Engineers

Outline

Simulink and MATLAB

Materials Illustrative Applications

Simulation with Simulink

Simulink solution of ODEs, some linear

and nonlinear functions

Simulink simulation examples:a gas process

a stirred-tank heater

a batch bioreactor

Computing with MATLAB

Plotting tips

Programming techniques

Problem solving steps

Some simple engineering problems

C C


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Chen CL 5


Outline

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

Newton-Raphson method

Solution of the Colebrook Equations

Solution of the Soave-Redlich-KwongEquation

Solution ofnth-Degree Polynomials andTransfer Functions

Newtons method for simultaneous

nonlinear equations

Solution of Nonlinear Equations in

Chemical Equilibrium

Ch CL 6


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Chen CL 6


Outline

Numerical Solution of Simultaneous Linear Algebraic Equations


Cramers rule

Gauss elimination method

Gauss-Jordan reduction methodGauss-Seidel substitution method

Jacobi method

Heat transfer in a pipe

Solution of a steam distribution

problemSolution of chemical reaction andmaterial balance equations

Ch CL 7


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Chen CL 7


Outline

Finite Difference Methods and Interpolation


Finite Differences (FDs):Backward-Forward-Central

Difference equations and their solutionsInterpolating polynomials

Interpolation of equally spaced pts

Gregory-Newton method

Stirlings method

Interpolation of unequally spaced pts

Lagrange polynomials

Spline interpolation

Equally spaced data: Gregory-Newtonmethod

The Lagrange polynomials and cubicsplines

Ch CL 8


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Chen CL 8


Outline

Numerical Differentiation and Integration


Differentiation by FDs:Backward-Forward-Central

Spline differentiation

Mass transfer flux from an open vessel

Derivative of vectors of equally spaced

ptsNewton-Cotes formulas of integration

Gauss quadrature

Spline integration

Multiple integrals

Integration formula:trapezoidal and Simpsons 1/3 rules

Integration formulas:Gauss-Legendre quadrature


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Chen CL 10


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Chen CL 10


Outline

Numerical Solution of Partial Differential Equations


Solution of PDEs using finitedifferences

Elliptic PDEsParabolic PDEs

Hyperbolic PDEs

Solution of the Laplace and Poissonequations

Solution of parabolic PDEs for diffusionSolution of parabolic PDEs for heattransfer

Chen CL 11


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Chen CL 11


Outline

Linear and Nonlinear Regression Analysis


Review of statistical terminologies

Linear regression analysis

The least squares methodProperties of estimated par.s

Nonlinear regression analysis

The method of steepest descent

The Gauss-Newton method

Newtons method

The Marquardt method

Multiple nonlinear regressions

Analysis of variance

Nonlinear regression using theMarquart method

Chen CL 12


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Chen CL 12


Outline

Process Optimization


Linear programming

Nonlinear programming with and

without constraintsMixed-integer linear programming

Mixed-integer nonlinear programming

Refinery process

Synthesis of water networks

Synthesis of cooling-water networks

Synthesis of heat-exchanger networks

Chen CL 13


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Chen CL 13

Computer-Aided Computationfor Chemical EngineersText 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 7for Engineers,

McGraw-Hill, New York, 2005.


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Chen CL 15


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Chen CL 15

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 Common Lisp Object System

COBOL USA (1959) Business data processing COmmon Business-Oriented Language

BASIC (1965) Simple on PC Beginners All Purpose Symbolic Instruction Code

C Bell (1972) Systems programming Predecessor language was named B

PROLOG (1972) Symbolic computation (AI) PROgramming LOGic (Frence)

Ada USA (1980) Real-time distributed systems Ada Augusta Byron collaborated with nineteenth-

century computer pioneer Charles Babbage

Smalltalk (1980) Graphical user interfaces; Object-oriented programming

Objects talk to one another via messages

C++ Supports objects and objected-

oriented programming

Incremental modification of C (++ is the C

increment operator)

JAVA SUN (1995) Supports Web programming Originally named Oak

Chen CL 16


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Chen CL 16

Progress of Programming Languages

1955

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Year


(Machine Language) (Assembly Language)

01011010 ADD

Chen CL 17


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(Machine Language) (Assembly Language)FORTRAN

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

AVE=(X+Y)/2.0

PRINT *, X,Y,AVE

7 CONTINUE

END

Chen CL 18


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Chen CL 18


1955

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Year



COBOL

01 EMPLOYEERECORD 05 EMPLOYEENUMBER PIC 9(5)

05 EMPLOYEENAME PIC X(30)

05 BIRTHDATE

10 BIRTHMONTH PIC 99

10 FILLER PIC X

10 BIRTHDAY PIC 99

05 DATEHIRED

10 MONTHHIRED PIC 99

10 FILLER PIC X

10 DAYHIRED PIC 99

Chen CL 19


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Chen CL 19


1955

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Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG(defun length (x) (cond ((null x) 0)

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

(length (I Love Computers))

3

Chen CL 20


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1955

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Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG

BASIC

VISUAL

BASIC

Dim i, sum

sum = 0

For i = 1 to 10

sum = sum + 1

Next i

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Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG

BASIC

VISUAL

BASIC

ALGOL60

PASCAL

MODULA2

MODULA3

if (i > 0) then

x := 10

else

y := 5

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1955

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Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG

BASIC

VISUAL

BASIC

ALGOL60

PASCAL

MODULA2

MODULA3

CPL

C

if (i > 0)

x = 10;

else

y = 5;

Chen CL 23


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1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG

BASIC

VISUAL

BASIC

ALGOL60

PASCAL

MODULA2

MODULA3

CPL

C

SIMULA

SMALLTALK

C++

C++Standard

Chen CL 24


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1955

1960

1965

1970

1975

1980

1985

1990

1995

2000

Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG

BASIC

VISUAL

BASIC

ALGOL60

PASCAL

MODULA2

MODULA3

CPL

C

SIMULA

SMALLTALK

C++

C++Standard

ADA

JAVA

Chen CL 25


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1955

1960

1965

1970

1975

1980

1985

1990

1995

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Year



COBOLLISP

SCHEME

COMMON

LISP

CLOS

PROLOG

BASIC

VISUAL

BASIC

ALGOL60

PASCAL

MODULA2

MODULA3

CPL

C

SIMULA

SMALLTALK

C++

C++Standard

ADA

JAVA

MATLAB

Chen CL 26


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MATLAB ?

MATrixLAB

oratory

In 1978, Professor Cleve Moler (New Mexico University, USA)

usedFORTRANto write the MATLABfor applications involvingmatrices, 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 toolboxesrun under the core MATLABprogram

Chen CL 28


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SimulinkGraphical Dynamic Simulation

built on top of

MATrixLABoratory

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Thank You for Your AttentionQuestions Are Welcome

00 Computer-Aided Computation for Chemical Engineers.pdf

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