Process simulation, optimisation and design

P.S.O.D.

ORGANIZATION ISSUES

Process simulation, optimization and design

Course objectives

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

The Model, what for?

A good model of the apparatus is needed to:– create a correct standalone apparatus design– create a correct process, consists of many

apparatus: » simulation» optimization» design

The tools...

pen and piece of paper (supported by basic calculation hardware) usually enough for the standalone apparatus design

even quite simple process optimization problem needs to involve the computer to complete the mission in reasonable time.

Ammonia synthesis plant

13 streams8 params per stream20 params of equip.means 124 variables!

e.g. 39 params defined by designerleaves 85 equations to solve!!!

Model, how to use?

Manually– We need:

» Knowledge about 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 to use model created by someone else,

» PROGRAM» Skills in the program use

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.”

„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.”

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 process simulation (AspenOne, ProSIM, ChemCAD)

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 process simulation (AspenOne, ProSIM, ChemCAD)

MathCADMathCAD

The mathematical toolThe mathematical tool

Introduction User interface

– Writing cursor '+'– Math toolbars :

» Calculator – equation symbols» Graph – building the charts» Matrix – inserting matrix/vectors, matrices and vectoral

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 (ver. 2001)

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[:][=])

Numbers notation– Floating-point notation:

1.23·104

Multiplication symbol [*] Superscript (exponent) [^]

keystrokes : [1][.][2][3][*][1][0][^][4]

MathCAD intro Algebraic expressions

– +,-,/,*(not always needed), power [^]– Functions arguments "(...)"– Result (evaluation): [=]

Expression typing – standard mathematical notation:

554.103ln33

2 2

[2][/][3][+][3][^][2][][l][n][(][3][)][=]

To go back to basic level press spacebar or arrow right [2][/][3][+][3][^][2][space bar][l][n][(][3][)][=]

or

MathCAD intro

Variables notation– Latin and Greek alphabet ( [ctrl] + [g] after

typing Latin letter)– Case sensitivity: xX– Subscripts (not vector/matrix subscripts) [.]– Prim: x`, bis: x`` etc.

MathCAD intro Assigning values and expressions (similar to

Pascal programming language)– 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+3 keystrokes : [y][:][2][*][x][+][3]

Variable x has to be defined earlier

MathCAD introCorrect Incorrect

MathCAD intro Edition of the expressions

– To change the position of edited place press » space bar » navi arrows

Vertical line: shows place of insertion Horizontal: shows range will be inserted into function etc.

MathCAD functions Standard functions set Functions definition

– Syntax:FunctionName(arg1, arg2,...):= expression of arg1, arg2,....

– 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

local variables

MathCAD functions

Function of constant (number, scalar)

MathCAD functions

Function of variable

Local variable

Global variable

MathCAD functions

Range of arithmetic sequence

MathCAD functions

2D graphs: – Function of one variable f(x)

keystrokes : [f][(][x][)][shift]+[2][x]

MathCAD functions

Graphs: – Default independent values range: -10 ÷ 10– Can be edited

Graphs: – Several functions of one independent variable range: f(x), g(x)@x

keystrokes : [f][(][x][)][,] [g][(][x][)][shift]+[2][x]

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]

MathCAD functions

Graphs formatting:

MathCAD functions

Graphs formatting:

MathCAD functions

MathCAD functions

MathCAD functions

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