EQE038 – Simulação e Otimização
de Processos Químicos
– Aula 2 –
Concepts of modeling and simulation. Object-oriented modeling in EMSO.
Argimiro R. Secchi
EQ/UFRJ
30 de agosto de 2013
1
Applications of Process Modeling
applications
tools
2
Some questions that could be answered with these applications
• Market: if the price of a product increases, what will be the reduction of demand and
what should be the new scheduling of production?
• Production planning: having several sources of raw material and several
manufacturing plants, how to distribute the raw material among these plants and what
products each plant has to produce?
• Synthesis: what process should be used for manufacturing a given product?
• Design: what type and size of equipment are necessary to produce a given product?
• Operation: what operating condition will maximize the production of a product?
• Control: how a process input can be manipulated to keep a measured process output
at its desired value?
• Safety: if an equipment failure occur, what will be the impact over the operators and
other equipments?
• Environment: how long will take to biodegrade a contaminated soil by dangerous
waste?
3
Difficulties in Dynamic Simulation
• Reliable models
• High-Index DAE systems
• Large-Scale systems
• Model consistency:
- Degree of Freedom (DoF)
- Dynamic Degree of Freedom (DDoF)
- Units of measurement
- Structural non-singularity
- Consistent initial condition
4
Concepts of Modeling and Simulation
Modeling in Latin: modus = a measure, a small representation of a
designed or existing object.
from dictionary: a mathematical or physical system, obeying certain
specified conditions, whose behavior is used for understanding a
physical, biological or social system, with analogy in some aspects.
Is only an approximate representation of a real system.
Process model: a set a equations and specifications that allows to
predict the behavior of a process.
first principles or
mechanistic model
empirical relations
5
Model Building
 A mathematical model has:
• A set of model parameters (reaction order, valve constant, etc.)
• A set of variables (temperatures, pressures, flow rates, etc.)
• A set of equations (algebraic and differential) relating the variables
 Problems in model building:
• Number of equations and variables do not match (DoF  0)
• Equations of the model are inconsistent (linear dependence, UOM, etc.)
• The number of initial conditions and DDoF do not match
6
Modeling Tools
The available tools for process modeling may be classified into:
• Block-Oriented
focus on the flowsheet topology using standardized unit models and
streams to link these unit models
• Equation-Oriented
rely purely on mathematical rather than phenomena-based
descriptions, making difficult to customize and reuse existing models
• Object-Oriented
Models are recursively decomposed into a hierarchy of sub-models and
inheritance concepts are used to refine previously defined models into
new models
(Bogusch and Marquardt, 1997)
7
Object-Oriented Modeling
A process flowsheet model can be hierarchically decomposed:
Plant
Column
Linked Trays
Reaction
System
Separation
System
Condenser
Tray
Splitter
Linked
Trays
Pump
Tray
Pretreat.
System
Tray
Feed Tray
Separation
System
Column 3
Column 2
Column 1
Tray
Linked
Trays
Rebolier
8
energy balance
thermodynamic equilibrium
mol fraction normalization
liquid flow model
vapor flow model
concrete model (real tray)
mass balance
concrete model (ideal tray)
Tray
abstract model
Object-Oriented Modeling
efficiency model
9
Object-Oriented Modeling
Model types
Abstract models: are models that embody coherent and
cohesive, but incomplete concepts, and in turn, make these
characteristics available to their specializations via
inheritance. While we would never create instances (devices)
of abstract models, we most certainly would make their
individual characteristics available to more specialized models
via inheritance.
Concrete models: are complete models, usually derived from
abstract models, ready to be instantiated, i.e., we can create
devices (e.g., equipments) of concrete models.
10
Object-Oriented Modeling
OOM main concepts
Inheritance: is the process whereby one object acquires
(gets, receives) characteristics from one or more other objects.
Aggregation: is the process of creating a new object from two
or more other objects, or an object that is composed of two or
more other objects.
Condenser
Splitter
Linked
Trays
Pump
Feed Tray
Column model =
Condenser + Splitter +
Pump + Linked Trays +
Feed Tray + Reboiler
Linked
Trays
Rebolier
11
Object-Oriented Modeling
Examples of general-purpose object-oriented modeling languages:
• ABACUSS II (Barton, 1999)
• ASCEND (Piela, 1989)
• Dymola (Elmqvist, 1978)
• EcosimPro (EA Int. & ESA, 1999)
• EMSO (Soares and Secchi, 2003)
• gPROMS/Speedup (Barton and Pantelides, 1994)
• Modelica (Modelica Association, 1996)
• ModKit (Bogusch et al., 2001)
• MPROSIM (Rao et al., 2004)
• Omola (Andersson, 1994)
• ProMoT (Tränkle et al., 1997)
12
Object-Oriented Modeling
A simpler example
source
sink
Level Tank
>>>
>>>
Streams
Inlet
Material stream feeding the tank
Outlet Material stream leaving the tank
Parameters
k
Valve constant
D
Hydraulic diameter of the tank
Variables
A
Tank cross section area
V
Tank volume
h
Tank level
Devices: source, tank, sink
Available model of the tank
Model with circular cross section
Model with square cross section
13
Object-Oriented Modeling
Inheritance
Model equations
mass balance: Fin  Fout 
Fin
dV
dt
valve equation: Fout  k h
liquid volume: V  A h
Fin
Fin
Fout
Fout
Fout
14
Object-Oriented Modeling
EMSO:
Abstract model
using "types";
Model Tank_Basic
Fin
PARAMETERS
k as Real (Brief=“Valve constant", Unit=’m^2.5/h’, Default = 12);
D as length (Brief=“Tank hydraulic diameter", Default = 4);
VARIABLES
in Fin as flow_vol (Brief=“Feed flow rate");
out Fout as flow_vol (Brief =“Output flow rate");
A as area (Brief=“Cross section area");
Fout
V as volume (Brief=“Liquid volume");
mass balance: Fin  Fout
dV

dt
valve equation: Fout  k h
liquid volume: V  A h
h as length (Brief=“Tank level");
EQUATIONS
“Mass balance“ Fin - Fout = diff(V);
“Valve equation“ Fout = k * sqrt(h);
“Liquid volume“ V = A * h;
end
15
Object-Oriented Modeling
Concrete models
Fin
Fin
Fout
Fout
Inheritance
Model Tank_Circular as Tank_Basic
Model Tank_Square as Tank_Basic
PARAMETERS
Pi as Real (Default = 3.1416);
EQUATIONS
“Cross section area" A = (Pi * D^2) / 4;
EMSO
EQUATIONS
“Cross section area“ A = D^2;
end
end
16
Object-Oriented Modeling
Flowsheet
source
Fin
Fout
Fout
sink
EMSO:
using "tank_oom";
FlowSheet Tanks
DEVICES
source as Feed;
T_c as Tank_Circular;
T_sq as Tank_Square;
sink as Sink;
CONNECTIONS
source.F to T_c.Fin;
T_c.Fout to T_sq.Fin;
T_sq.Fout to sink.F;
SET
T_c.D = 3 * ’m’;
T_sq.D = 3 * ’m’;
SPECIFY
source.F = 20 * ’m^3/h’;
INITIAL
T_c.h = 1 * ’m’;
T_sq.h = 2 * ’m’;
OPTIONS
TimeStart = 0;
TimeEnd = 20;
TimeStep = 0.5;
TimeUnit = ’h’;
end
17
Object-Oriented Modeling
Model switching
Model Tank_Section as Tank_Basic
PARAMETERS
Pi as Real (Default = 3.1416);
Section as Switcher (Valid = ["Circular", "Square"],
Default = "Circular");
EQUATIONS
switch Section
case "Circular":
“Cross section area" A = (Pi * D^2)/4;
case "Square":
“Cross section area" A = D^2;
end
end
using "tank_oom";
FlowSheet Tanks2
DEVICES
source as Feed;
T_c as Tank_Section;
T_sq as Tank_Section;
sink as Sink;
CONNECTIONS
source.F to T_c.Fin;
T_c.Fout to T_sq.Fin;
T_sq.Fout to sink.F;
SET
T_c.D = 3 * ’m’;
T_sq.D = 3 * ’m’;
T_c.Section = ”Circular”;
T_sq.Section = ”Square”;
SPECIFY
source.F = 20 * ’m^3/h’;
INITIAL
T_c.h = 1 * ’m’;
T_sq.h = 2 * ’m’;
OPTIONS
TimeStart = 0;
TimeEnd = 20;
TimeStep = 0.5;
TimeUnit = ’h’;
end
18
Object-Oriented Modeling
Aggregation
source
Tank model
mass balance: Fin  Fout 
P0
dV
dt
liquid volume: V  A h
P0
P
sink
Level Tank
outlet pressure: P  P0   g h
Valve model
mass balance:
Fin  Fout
valve equation: Fout  k
pressure drop:
P
g
P  Pin  Pout
19
Object-Oriented Modeling
Tank model with valve
using "types";
Model Tank_Basic
PARAMETERS
D as length (Brief=“Tank hydraulic diameter", Default = 4);
rg as Real (Brief=“rho * g", Unit =’kg/(m*s)^2’, Default = 1e4);
Valve model
using "types";
Model Valve
PARAMETERS
k as Real (Brief=“Valve constant",
Unit=’m^2.5/h’, Default = 12);
VARIABLES
in Sin as stream (Brief=“Inlet stream");
rg as Real (Brief=“rho * g",
out Sout as stream (Brief =“Outlet stream");
A as area (Brief=“Cross section area");
V as volume (Brief=“Liquid volume");
h as length (Brief=“Tank level");
valve as Valve (Brief=“Valve model");
CONNECTIONS
Sout to valve.Sin;
EQUATIONS
“Mass balance“ Sin.F – Sout.F = diff(V);
“Liquid volume“ V = A * h;
“Outlet pressure“ Sout.P = Sin.P + rg * h;
end
Unit =’kg/(m*s)^2’, Default = 1e4);
VARIABLES
in Sin as stream (Brief=“Inlet stream");
out Sout as stream (Brief =“Outlet stream");
DP as press_delta (Brief=“Pressure drop");
EQUATIONS
“Mass balance“ Sin.F = Sout.F;
“Valve equation“ Sout.F = k * sqrt(DP/rg);
“Pressure drop“ DP = Sin.P – Sout.P;
end
20
Object-Oriented Modeling
Flowsheet
using "tank_valve_oom";
FlowSheet Tanks
DEVICES
source as Feed;
T_c as Tank_Circular;
T_sq as Tank_Square;
sink as Sink;
CONNECTIONS
source.Sout to T_c.Sin;
T_c.valve.Sout to T_sq.Sin;
T_sq.valve.Sout to sink.Sin;
SET
T_c.D = 3 * ’m’; T_sq.D = 3 * ’m’;
SPECIFY
source.Sout.F = 20 * ’m^3/h’;
source.Sout.P = 1 * ’atm’;
T_c.valve.Sout.P = 1 * ’atm’;
sink.Sin.P = 1 * ’atm’;
INITIAL
T_c.h = 1 * ’m’; T_sq.h = 2 * ’m’;
OPTIONS
TimeStart = 0;
TimeEnd = 20;
TimeStep = 0.5;
TimeUnit = ’h’;
end
21
Modeling workshop
Model equations
mass balance: Fin  Fout 
Fin
dV
dt
valve equation: Fout  k h
Fin
Fin
Fout
liquid volume:
V  Ah
A =  h (D  h)
Fout
Fout
Fin
D h
V h   
 2 3
2
h
Fout
22
Modeling workshop
Flowsheet
source
Fi = 20 m3/h
n
D=3m
h(0) = 1 m
Fout
D=3m
h(0) = 2 m
Fout
D=3m
h(0) = 2.5 m
h
Fout
Fo
ut
sink
23
Elementos Básicos na Modelagem
1. Descrição do processo e definição do problema
Definir o Modelo
Construir o Modelo
2. Teoria e aplicação das leis fundamentais
3. Hipóteses e considerações simplificadoras
4. Equacionamento
5. Análise de Consistência
6. Solução desejada
Validar o Modelo
7. Matemática e computação
8. Solução e validação
24
Modeling
1. Process Description and Problem Definition
• Process Description
– Process objectives
– Process flowsheet
– Process operation
• unit operations and control
• Problem Definition
– Simulation objectives
– Simulation applications
25
Modeling
Process Description
Example: level tank
Fin
V
h
Fout
A liquid flows in and out of a tank due to gravitational forces.
We wish to analyze the volume, height and flowrate variations in
the tank (system response) as function of feed disturbances.
26
Modeling
2. Fundamental Laws: Theory and Applications
• Bases to be used in the modeling
- mass conservation

  ( .  v )
t
- momentum conservation
( v)

t
[. v v]
P
[.]
 g
advection
pressure forces
viscous forces
gravitational forces
- energy conservation

t
  ˆ 1 2 
  U  2 v   

 

1 

  . v  Uˆ  v 2  
2 


(.q )
  g .v 
(.P v)
(.[.v])
advection
conduction
gravit. forces work
pressure forces work
viscous forces work
27
Modeling Levels
28
Modeling Levels
Modelo Microscópico
Modelo de Gradientes Múltiplos
Modelo de Máximo Gradiente
Modelo de Macroscópico
29
Modeling
3. Simplifying Assumptions
• Establish the assumptions and simplifications
• Define the model limitations
- constant specific mass
- isothermal
- perfect mixture
- Fout  k h
30
Modeling
4. Mathematical Model
• Data mining for simulation
– Collect data and information of the studied system
– Identify the engineering unit of measurements
– Specify operating procedures
– Specify the operating regions of the variables
• Memory of Calculation
– Mathematical model
– Define unit of measurements of variables and parameters
– Define and specify free variables
– Define and determine values of parameters
– Define and establish initial conditions
31
Mathematical Model
Conservation laws
First Principles
Models
Hybrid Models
dV
F
dt
dX 
F
 μ  X
dt 
V
dT F
UA
 (Te  T) 
(T  Tc )
dt V
ρVCp
Parametric
A(q) y(t) 
B(q)
C(q)
u(t) 
e(t)
F(q)
D(q)
Neural Nets
Empirical Models
Fuzzy Logic
32
Modeling
Mathematical Model
In the simulator
• Build process equipment models
– Identify and create abstract and concrete models
– Declare variables and parameters
– Write model equations
– Compose the equipment model via inheritance and aggregation
• Build process flowsheet
– Declare flowsheet devices
– Define process connections
– Set process parameters values
– Specify process free variables
– Establish initial conditions
– Establish simulation options
33
Mathematical Model
mass balance: Fin  Fout 
Fin
dV
dt
valve equation: Fout  k h
liquid volume: V  A h
(1)
(2)
(3)
Fin
Fin
Fout
(4)
Fout
Fout
34
Modeling
5. Consistency Analysis
• Model consistency analysis for unit of measurements (UOM)
• Degree of freedom analysis
• Dynamic degree of freedom analysis
variable
Fin, Fout
V
A
h, D
k
t
UOM
m3 h-1
m3
m2
m
m2.5 h-1
h
equations
(1): [m3 h-1] – [m3 h-1] = [m3] / [h]
(2): [m3 h-1] = [m2.5 h-1] ([h])0.5
(3): [m3] = [m2] [m]
(4): [m2] = ([m])2
35
Modeling
Consistency Analysis
variables: Fin, Fout, V, A, h, D, k, t  8
constants: k, D  2
specifications: t  1
driving forces: Fin  1
unknown variables: V, h, A, Fout  4
equations: 4
Degree of Freedom = variables – constants – specification – driving forces –
equations = unknown variables – equations = 8 – 2 – 1 – 1 – 4 = 0
Dynamic Degree of freedom (index < 2) = differential equations = 1
Needs 1 initial condition: h(0)  1
36
Modeling
6. Desired Solution
• Plan case studies
• Define:
– Objectives of the study
– Problems to be solved
– Evaluation criteria
For the given example and initial condition (h0 or V0), we
wish to analyze h(Fin), V(Fin) and Fout(Fin).
37
Modeling
7. Computation
• Define the desired accuracy
• Specify the simulation time and reporting interval
• Verify the necessity of specialized solvers (high-index problems)
38
Modeling
8. Solution and Validation
• Analyze simulation results
• Analyze state variables dynamics
• Test model fitting with plant data
hexp
– Compare simulation x plant
hcalc
39
Modeling
Solution and Validation
• Check output sensitivity to input disturbances
• Carry out parametric sensitivity analysis
• Analyze output data with statistical techniques
• Verify results coherence
• Document obtained results
40
Modeling
Remarks
• Start with a simple model and gradually increase complexity when
necessary;
• The model should have sufficient details to capture the essence of
the studied system;
• It is not necessary to reproduce each element of the system;
• Models with excessive details are expensive, difficult to implement
and to solve;
• Interact with people that operate the equipment;
• Deeply understand the process behavior.
41
– A simple in EMSO –
Starting EMSO
42
43
Model
44
Model
Language – Equation-based system
Equations
The order the equations
appear in the model do not
matter
Equivalent Equations
Can be written in any
user desired form
45
Model
Language – Object-Oriented Modeling
The modeling and simulation of
complex systems is facilitated by
the use of the Object-Oriented
concept
Equipment
Component
System
The system can be decomposed in
several components, each one
described separately using its
constitutive equations
The components of the
system exchange information
through the connecting ports
46
Model Components
Including submodels and types
Automatic model
documentation
Symbol of variable in
LaTeX command for
documentation
Basic sections
to create a
math. model
Port location to draw a
flowsheet connection
Input and output
connections
47
Basic Variable Types in a Model
Parameters and variables are declared within their
valid domains and units using types created based on
the built-in types: Real, Integer, Switcher, Plugin
48
Building a Model: A simple example – level tank
Streams
Inlet
Material stream feeding the tank
Outlet Material stream leaving the tank
Parameters
k
Valve constant
D
Hydraulic diameter of the tank
Variables
A
Tank cross section area
V
Tank volume
h
Tank level
Devices: source, tank, sink
>>>
>>>
Available model of the tank
Model with circular cross section
Model with square cross section
49
Material Stream Modeling
The material stream carries the
information entering and leaving the
equipment
VARIABLES
F
T
P
volumetric flowrate
temperature
pressure
Source - component that has a feed
material stream.
It has an output connection
Source
Sink
Sink - component that receives an
output material stream.
It has an input connection
50
Level Tank Modeling
Mass balance
dV
 Fin  Fout
dt
Valve equation
Fout  k h
Inlet
Feed material stream to the tank
Fin inlet volumetric flowrate
Tin inlet temperature
Pin inlet pressure
Outlet Output material stream from the tank
Fout outlet volumetric flowrate
Tout outlet temperature
Pout outlet pressure
Thermal equilibrium
Tin  Tout
Mechanical equilibrium
Pin  Pout
Area
 D2

A 4
 D2

if circular
if square
51
Level Tank: Inheritance
Fin
Basic tank
Fin
Fin
Fout
Fout
Circular tank
Fout
Square tank
52
Creating a MSO file for Model
Menu
New
Model
Destination
File
Name
53
Creating a Model using the template
using
including references to other files.
Model a new model is declared with the keyword Model
and its name.
a model contains a few basic sections:
PARAMETERS
section which defines the parameters of the
model.
VARIABLES
section which defines the variables of the model.
EQUATIONS
section which describes the model equations.
54
Creating a Material Stream Model
Including predefined types of
EMSO
Symbol of
variable
are LaTeX
commands
Model
Documentation
Using the types defined
in the file “types.mso”
selecting the
desired unit of
measure
55
Creating a Source Stream Model
Using the
same file
Model
Documentation
Output
Connection
56
Creating a Sink Stream Model
Using the
same file
Model
Documentation
Input
Connection
57
Creating a Basic Tank Model
Reference
Creating new
UOM
Model
Ports
EMSO Built-In Function
EMSOquickRef.pdf
58
Creating the Circular Tank Model
Using the
same file
Inheritance
Model inherits all the
attributes of the class
from which it derives
Equation
Writing the particular
equations model
SET
Defining
values ​for
parameters
59
Creating the Square Tank Model
Using the
same file
Inheritance
Model inherits all the
attributes of the class
from which it derives
Equation
Writing the particular
equations model
60
FlowSheet
61
Process Diagram – FlowSheet
The equipment are
called DEVICES
In EMSO the user
can manipulate
various
FlowSheets at
same time
A FlowSheet
consists of a series
of unit operations or
equipment connected
to each other
62
FlowSheet
Language – Component-based system
streamPH
The system modeling is made by the
use, configuration and connection of
pre-existing components
63
FlowSheet Components
Parameters of
DEVICES
Degree of Freedom
Simulation
options
Dynamic Degree of
Freedom
64
Creating a MSO file for FlowSheet
Menu
New
FlowSheet
File
Name
Destination
65
Creating a FlowSheet using the template
using
including references to other files.
FlowSheet
A process diagram is declared with the keyword FlowSheet and
its name.
A FlowSheet contains some basic sections:
PARAMETERS
DEVICES
CONNECTIONS
SET
SPECIFY
INITIAL
OPTIONS
...
66
FlowSheet for the Level Tank
Parameters of
DEVICES
Degree of Freedom
Simulation
options
Dynamic Degree of
Freedom
67
Consistency Analysis of the Process
EMSO analyzes
the consistency
of the system
created in the
FlowSheet
68
Simulation of the Level Tank Process
Simulation
details
69
Level Tank Results
double-click
Horizontal axis is always the
independent variable (usually time)
70
Series of Level Tanks
Building a system consisting of three
tanks connected in series
71
Series of Level Tanks - FlowSheet
Degrees of freedom
increases
72
Series of Level Tanks - Results
73
Building a more interesting Model: CSTR with Van der Vusse
reaction
Variables
V
Reactor volume
r1, r2, r3 Reaction rates
Ca, Cb,
Cc, Cd
Molar concentrations
h
Reactor level
tau
Residence time
Streams
Inlet
Feed material stream with molar concentration
Outlet Output material stream with molar concentration
Parameters
Cv
Valve constant
k1
Constant of reaction rate 1
k2
Constant of reaction rate 2
k3
Constant of reaction rate 3
A
Cross-section area
74
Van der Vusse Reactor – Modeling
Overall mass balance
dV
 Fin  Fout
dt
Valve equation
Fout  CV
Component mass balances
h
Thermal equilibrium
Tin  Tout
Mechanical equilibrium
Pin  Pout
Volume
V  Ah
Reaction rates
Residence time
Perfect mixing
75
Van der Vusse Reactor – Stream Model
Adding molar
concentration in the
material stream
76
Van der Vusse Reactor – Attributes
77
Van der Vusse Reactor Model
78
Van der Vusse Reactor – Model Equations
79
Van der Vusse Reactor – FlowSheet
80
Van der Vusse Reactor – Results
81
Exercises
1) Simulate the CSTR example for different values of the valve
constant ​to find the one that maximizes the concentration of
component B at the outlet of the reactor at steady state.
Comment the results;
2) Modify the reactor model by adding an opening fraction on the
outlet valve: Fs  xCv h and make this fraction vary
sinusoidally x = (1 + sin (t)) / 2, where t is given in hours. Use a
Cv value of 20 m2,5/h. Comment the results for a 20 h simulation;
3) Build a block diagram to simulate the CSTR process.
82
References
• Himmelblau, D. M. & Bischoff, K. B., "Process Analysis and Simulation - Deterministic Systems", John Wiley &
Sons, 1968.
• Felder, R. M. & Rousseau, R. W., "Elementary Principles of Chemical Processes", John Wiley & Sons, 1978.
• Denn, M., "Process Modeling", Longman, New York, 1986.
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Special thanks to
Prof. Rafael de Pelegrini Soares, D.Sc.
Eng. Gerson Balbueno Bicca, M.Sc.
Eng. Euclides Almeida Neto, D.Sc.
Eng. Eduardo Moreira de Lemos, D.Sc.
Eng. Marco Antônio Müller
For helping in the preparation of this material
For supporting the ALSOC Project.
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EP 2013
... thank you for your attention!
http://www.enq.ufrgs.br/alsoc
Solutions for Process Control and Optimization
Process Modeling, Simulation and Control Lab
• Prof. Argimiro Resende Secchi, D.Sc.
• Phone: +55-21-2562-8307
• E-mail: arge@peq.coppe.ufrj.br
•
http://www.peq.coppe.ufrj.br/Areas/Modelagem_e_simulacao.html
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