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 process simulation

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

7. Introduction

8. All the simulation related issues requires THE MODEL

9. A 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 for: • Apparatus design • 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 computer

11. Model, how to calculate? • Manually • We need: • Knowledge • Paper and pen • Log tables, slide rule, calculator • Computer supported calculation • We need: • Knowledge • 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 (MathLab, MathCAD) • 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":=" (keys [:][=])

18. Numbers notation • Floating-point notation: 1.23·104 Multiplication symbol [*] Superscript (exponent) [^] Key sequence: [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 • Variables notation • 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 (Pascal like) • One value assigned to one variable: x:=5keys: [x][:][5] • Range of arithmetic progression assigned to variable • Default step: x:=0..3 (means numbers 0, 1, 2, 3)keys [x][:][0][;][3] • Defined step: x:=0,2..6 (means numbers 0, 2, 4, 6) keys [x][:][0][,][2][;][6] • Expression to variable:y:=2·x+3keys: [y][:][2][*][x][+][3] 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 • Standard functions set • Functions definition • Syntax:FunctionName(arg1, arg2,...):= expression • E.g. f(x,y)=x·ykeys: [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 (or vector)

28. MathCAD functions • Graphs: • Function of one variable f(x)keys: [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)@xkeys: [f][(][x][)][,] [g][(][x][)][shift]+[2][x]

31. MathCAD functions • Graphs: • Several functions of several different independent variable range: f(x), g(z)@x, zkeys: [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

36. MathCAD – vectors and matrix • Matrix variable definition • vector – one column matrix

37. MathCAD – vectors and matrix

38. MathCAD – vectors and matrix • Matrix operations • Multiply by constant • Matrix transpose [ctrl]+[1] • Inverse [^][-][1] • Matrix multiplying • Determinant

39. MathCAD – vectors and matrix • To read the matrix elements Ar, k: key [[] r- row nr, k – column nr • e.g. element A1,1 keys: [A][[][1][,][1][=] • To chose matrix column • First column A( A<0>):keys [A][ctrl]+[6][0] • Default first column number is 0, (to change : Math/Options/Array Origin)

40. MathCAD – vectors and matrix • Calculations of dot product and cross product of vectors

41. MathCAD – vectors and matrix • Special definition of matrix elements as a function of row-column number Mi,j=f(i,j) • E.g. Value of element is equal to product of column and row number

42. MathCAD 3D graphs • 3D graphs of function on the base of matrix : [ctrl]+[2][M] • M – matrix defined earlier RESTICTION: function arguments have to bee integer type

43. MathCAD 3D graphs • 3D Graphs of function of real type arguments • Using procedure: CreateMesh(function, lb_v1, ub_v1, lb_v2, ub_v2, v1grid, v2grid) • Assign result to variable • Plot of the variable like plot of matrix ([ctrl]+[2]) Boundariescan be the real type numbers. (def. –5,5) Grids have to be integer type numbers (def. 20)

44. MathCAD 3D graphs

45. MathCAD 3D graphs - formating

46. MathCAD 3D graphs – formatting: fill options

47. MathCAD 3D graphs – formatting: fill options Contours colour filled

48. MathCAD 3D graphs – formatting: line options

49. MathCAD 3D graphs – formatting: Lighting

50. MathCAD 3D graphs – formatting: Fog and perspective