Process simulation, optimisation
and design
P.S.O.D.
ORGANIZATION ISSUES
Course scope
Introduction
 MathCAD
 Introduction to CAPE

– Simple simulation of liquid flow and heat
transfer process

ChemCAD (by dr Robert Kubica)
Process simulation, optimisation
and design
Course objectives

Provide the students with:
– using specialized software for mathematical
problems solution, modeling and engineering
– clear understanding of what is
» a process simulation,
» a process optimization
» process design
– using a mathematical software to solve simulation
problem
– using specialized software for steady state process
simulation
– using specialized software for dynamic process
simulation
Lectures are available on the web
address
www.chemia.polsl.pl/~jkocurek/Studenci.html
Introduction
All the issues related to
simulation requires....
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 streams
8 params per stream
20 params of equip.
means 124 variables!
e.g. 39 params defined
by designer
leaves 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.”
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)
MathCAD
The 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:
2 2
 3 ln 3  10.554
3
[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 arrow right
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.
MathCAD intro

Assigning values and expressions (similar to
Pascal programming language)
– One value assigned to one variable:
x:=5
keystrokes: [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 intro
Correct
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
local variables
– 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
MathCAD functions

Function of constant (number, scalar)
MathCAD functions

Function of variable
Global variable
Local 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
MathCAD functions

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
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