Process simulation, optimisation and design

1. Process simulation, optimisation and design

2. P.S.O.D. ORGANIZATION ISSUES

3. Course scope • Introduction • MathCAD • Introduction to CAPE • Simple simulation of heat exchange process using common software • ChemCAD (by dr Robert Kubica)

4. Process simulation, optimisation and design Course objectives

5. Provide the students with: • using specialized software for mathematical problems solution • clear understanding of what is a process simulation, a process optimization and process design • using commonly available software to solve simulation problems • using specialized software for steady state process simulation • using specialized software for dynamic process simulation

6. Lectures are available on the web address www.chemia.polsl.pl/~jkocurek/Studenci.html

7. Introduction

8. All the issues related to simulation requires.... THE MODEL

9. The Model,what is it? • A model is a representation of some aspects of real world objects by: • other parameters easier to measure • scaled down objects • equations and numbers – mathematical models

10. The Model,what for? • A good model of the apparatus is needed to: • create a correct apparatus design • create a correct process: • simulation • optimization • design • apparatus design can be done with pen and piece of paper but even quite simple process optimization problem needs to involve the computerto complete the mission in reasonable time.

11. Model, how to calculate? • Manually • We need: • Knowledgeabout the process to create the model • Paper and pen • Log tables, slide rule, calculator • Mathematical skills • Computer supported calculation • We need: • Knowledge about the process to create the model or how to use model created by someone else, • PROGRAM • Skill of how to use a program

12. COMPUTER PROGRAM DEFINITION „Set of instructions in a logical sequence interpreted and executed by a computer enabling the computer to perform a required function; also called software. Programs are the "thought processes" of computers, without which they cannot operate. Programs are written in various languages, to conform with the operating system of particular computers.”

13. Computer supported calculation • PROGRAM • Written by user, using programming language: • Low level (assembler) • High level (C, Pascal, Fortran, Basic) • Written by user, using common applications for calculation • Spreadsheets (Excel, Calc) • Mathematical tools (MathCAD, MathLab, Mathematica) • Specialized software for modeling and process simulation (AspenOne, ProSIM, ChemCAD)

14. MathCAD The mathematical tool

15. Introduction • User interface • Writing cursor '+' • Toolbars • Calculator – equation symbols • Graph – building the charts • Matrix – inserting matrix/vectors, matrics operation • Calculus – derivatives, integrals, limits, summation, iterated product • Symbolic • Evaluation • Boolean –logical operation • Programming • Greek – inserting Greek letters • Turn of the Resource center at startup View/Preferences/Startup Options

17. Basic operations • Typing: • "normal" – text • Forced by: [shift]+["] • Automatically: after space insertion • "variable" – interpreted by program • Default • The typing modes are identified by style: • Normal – Font is Arial (by default) • Variable – Font is Times (by default) • Assign symbol":=" (keystrokes[:][=])

18. Numbers notation • Floating-point notation: 1.23·104 Multiplication symbol [*] Superscript (exponent) [^] keystrokes : [1][.][2][3][*][1][0][^][4]

19. MathCAD intro • Algebraic expressions • +,-,/,*(not always needed), power [^] • Functions arguments "(...)" • Result (evaluation): [=] • Expression typing – standard mathematical notation: [2][/][3][+][3][^][2][][l][n][(][3][)][=] or [2][/][3][+][3][^][2][space bar][l][n][(][3][)][=] To go back to basic level press spacebar or right arrow

20. MathCAD intro • Variablesnotation • Latin and Greek alphabet ( [ctrl] + [g] after typing Latin letter) • Case sensitivity: xX • Subscripts (not vector/matrix subscripts) [.] • Prim: x`, bis: x`` etc.

21. MathCAD intro • Assigning values and expressions (Pascalprogramming languagelike) • One value assigned to one variable:x:=5keystrokes: [x][:][5] • Range of arithmetic progression assigned to variable • Default step: x:=0..3 (means numbers 0, 1, 2, 3)keystrokes[x][:][0][;][3] • Defined step: x:=0,0.2..1 (means numbers 0, 0.2, 0.4, 0.6, 0.8, 1) keystrokes[x][:][0][,][0][.][2][;][1] • Expression to variable:y:=2·x+3keystrokes : [y][:][2][*][x][+][3] Variable x has to be defined earlier

22. MathCAD intro Correct Incorrect

23.  MathCAD intro • The expressions edition • To change the position of edited place press space bar Vertical line: shows place of insertion of a sign Horizontal: shows range will be inserted into function etc.

24. MathCAD functions local variables • Standard functions set • Functions definition • Syntax:FunctionName(arg1, arg2,...):= expression • E.g. f(x,y):=x·y keystrokes : [f][(][x][y][)][:][x][*][y] • Calculations with use of defined (or predefined) functions: • Evaluation for constants • Evaluation for defined variables • Evaluation for range of constants (vectors)

25. MathCAD functions • Function of constant (scalar)

26. MathCAD functions • Function of variable Global variable Local variable

27. MathCAD functions • Range of arithmetic sequence

28. MathCAD functions • 2D graphs: • Function of one variable f(x) keystrokes : [f][(][x][)][shift]+[2][x]

29. MathCAD functions • Graphs: • Default independent values range: -10 ÷ 10 • Can be edited

30. MathCAD functions • Graphs: • Several functions of one independent variable range: f(x), g(x)@x keystrokes : [f][(][x][)][,] [g][(][x][)][shift]+[2][x]

31. MathCAD functions • Graphs: • Several functions of several different independent variable range: f(x), g(z)@x, z keystrokes : [f][(][x][)][,] [g][(][z][)][shift]+[2][x][,][z]

32. MathCAD functions • Graphs formatting:

33. MathCAD functions • Graphs formatting:

34. MathCAD functions

35. MathCAD functions Show markers enabled