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1
EQE038 – Simulação e Otimização de Processos Químicos
Argimiro R. Secchi
– Aula 2 –
Concepts of modeling and simulation. Object-oriented modeling in EMSO.
EQ/UFRJ
30 de agosto de 2013
3
• 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?
Some questions that could be answered with these applications
Some questions that could be answered with these applications
4
Difficulties in Dynamic SimulationDifficulties 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
5
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.
empirical relationsfirst principles or mechanistic model
Concepts of Modeling and SimulationConcepts of Modeling and Simulation
6
Model BuildingModel 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
7
Modeling ToolsModeling 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)
8
Object-Oriented ModelingObject-Oriented ModelingA process flowsheet model can be hierarchically decomposed:
Plant
Sep
arat
ion
Sys
tem
Pretreat. System
Reaction System
Separation System
Co
lum
n 1
Co
lum
n 2
Co
lum
n 3
Column
Feed Tray
Linked Trays
Linked Trays
Condenser
Splitter
Pump
Rebolier
Linked Trays
Tray
Tray
Tray
Tray
9
Object-Oriented ModelingObject-Oriented Modeling
Tray
mass balance
energy balance
thermodynamic equilibrium
mol fraction normalizationabs
tra
ct m
ode
l
liquid flow model
vapor flow model con
cret
e m
ode
l (id
ea
l tra
y)
efficiency model
con
cret
e m
ode
l (re
al tr
ay)
10
Object-Oriented ModelingObject-Oriented Modeling
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.
Model types
11
Object-Oriented ModelingObject-Oriented Modeling
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.
OOM main concepts
Feed Tray
Linked Trays
Linked Trays
Condenser
Splitter
Pump
Rebolier
Column model = Condenser + Splitter + Pump + Linked Trays + Feed Tray + Reboiler
12
Object-Oriented ModelingObject-Oriented Modeling
• 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)
Examples of general-purpose object-oriented modeling languages:
13
StreamsInlet Material stream feeding the tankOutlet Material stream leaving the tankParametersk Valve constantD Hydraulic diameter of the tankVariablesA Tank cross section areaV Tank volumeh Tank levelDevices: source, tank, sink
Available model of the tank>>> Model with circular cross section>>> Model with square cross section
Object-Oriented ModelingObject-Oriented Modeling
A simpler example
Level Tank
source
sink
14
Object-Oriented ModelingObject-Oriented Modeling
Model equations
Fin
Fin
Fin
Fout
Fout
Fout
in out
dVF F
dt mass balance:
outF k hvalve equation:
V A hliquid volume:
Inheritance
15
Object-Oriented ModelingObject-Oriented Modeling
using "types";
Model Tank_Basic
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");
V as volume (Brief=“Liquid volume");
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
EMSO:
Fin
Fout
Abstract model
in out
dVF F
dt mass balance:
outF k hvalve equation:
V A hliquid volume:
16
Object-Oriented ModelingObject-Oriented Modeling
Model Tank_Square as Tank_Basic
EQUATIONS
“Cross section area“ A = D^2;
end
EMSO
Concrete models
Model Tank_Circular as Tank_Basic
PARAMETERS
Pi as Real (Default = 3.1416);
EQUATIONS
“Cross section area" A = (Pi * D^2) / 4;
end
Inheritance
FinFin
FoutFout
17
Object-Oriented ModelingObject-Oriented Modeling
using "tank_oom";FlowSheet TanksDEVICES 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
Fout
Fin
Fout
source
sink
Flowsheet EMSO:
18
Object-Oriented ModelingObject-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 Tanks2DEVICES 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
19
Object-Oriented ModelingObject-Oriented Modeling
Aggregation
Level Tank
source
sink
P0
P0
P
Tank model
in out
dVF F
dt mass balance:
V A hliquid volume:
0P P g h outlet pressure:
out
PF k
g
valve equation:
Valve model
in outP P P
in outF Fmass balance:
pressure drop:
20
Object-Oriented ModelingObject-Oriented Modeling
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);
VARIABLES
in Sin as stream (Brief=“Inlet stream");
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
Tank model with valve Valve modelusing "types";
Model Valve
PARAMETERS
k as Real (Brief=“Valve constant",
Unit=’m^2.5/h’, Default = 12);
rg as Real (Brief=“rho * g",
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
21
Object-Oriented ModelingObject-Oriented Modeling
using "tank_valve_oom";FlowSheet TanksDEVICES 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
Flowsheet
22
Modeling workshopModeling workshop
Model equations
in out
dVF F
dt mass balance:
outF k hvalve equation:
Fin
Fout
h
A = h (D h)
2
2 3
D hV h
liquid volume:
V A h
Fin
Fin
Fin
Fout
Fout
Fout
23
Flowsheet
Modeling workshopModeling workshop
Fi
n
Fout
source
Fout
Fout
h
Fo
ut
sink
= 20 m3/h
D = 3 m
h(0) = 1 m
D = 3 m
h(0) = 2 m
D = 3 m
h(0) = 2.5 m
24
Elementos Básicos na ModelagemElementos Básicos na Modelagem
1.Descrição do processo e definição do
problema
2.Teoria e aplicação das leis fundamentais
3.Hipóteses e considerações simplificadoras
4.Equacionamento
5.Análise de Consistência
6.Solução desejada
7.Matemática e computação
8.Solução e validação
Definir o Modelo
Construir o Modelo
Validar o Modelo
25
1. Process Description and Problem Definition1. Process Description and Problem Definition
• Process Description– Process objectives– Process flowsheet– Process operation
• unit operations and control
• Problem Definition– Simulation objectives– Simulation applications
ModelingModeling
26
Process DescriptionProcess DescriptionExample: level tank
h
Fout
Fin
V
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.
ModelingModeling
27
2. Fundamental Laws: Theory and Applications2. Fundamental Laws: Theory and Applications
t
v ( . )
advection pressure forces viscous forces gravitational forces
( )[ . ] [ . ]
vv v P g
t
2 2
advection conduction gravit. forces work pressure forces work viscous forces work
1 1ˆ ˆ. ( . ) . ( . ) ( .[ . ])2 2
U v v U v q g v Pv vt
- mass conservation
- momentum conservation
- energy conservation
• Bases to be used in the modeling
ModelingModeling
29
Modelo Microscópico
Modelo de Gradientes Múltiplos
Modelo de Máximo Gradiente
Modelo de Macroscópico
Modeling Levels
30
3. Simplifying Assumptions3. Simplifying Assumptions
- constant specific mass
- isothermal
- perfect mixture
- outF k h
• Establish the assumptions and simplifications
• Define the model limitations
ModelingModeling
31
4. Mathematical Model4. 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
ModelingModeling
32
Mathematical ModelMathematical Model
First Principles
Models
Conservation laws
XV
Fμ
dt
dX
Fdt
dV
)T(TρVC
UAT)(T
V
F
dt
dTc
pe
Empirical Models
Neural Nets
Fuzzy Logic
Parametric
e(t)D(q)
C(q)u(t)
F(q)
B(q)y(t)A(q)
Hybrid Models
33
• 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
Mathematical ModelMathematical Model
In the simulator
ModelingModeling
34
Fin
Fin
Fin
Fout
Fout
Fout
in out
dVF F
dt mass balance:
outF k hvalve equation:
V A hliquid volume:
Mathematical ModelMathematical Model
(1)
(2)
(3)
(4)
35
5. Consistency Analysis5. Consistency Analysis
• Model consistency analysis for unit of measurements (UOM)
• Degree of freedom analysis
• Dynamic degree of freedom analysis
variable UOM
Fin, Fout m3 h-1
V m3
A m2
h, D m
k m2.5 h-1
t 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
ModelingModeling
36
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
Consistency AnalysisConsistency Analysis
ModelingModeling
37
For the given example and initial condition (h0 or V0), we wish to analyze h(Fin), V(Fin) and Fout(Fin).
6. Desired Solution6. Desired Solution
• Plan case studies• Define:
– Objectives of the study– Problems to be solved– Evaluation criteria
ModelingModeling
38
7. Computation7. Computation
• Define the desired accuracy
• Specify the simulation time and reporting interval
• Verify the necessity of specialized solvers (high-index problems)
ModelingModeling
39
• Analyze simulation results
• Analyze state variables dynamics
• Test model fitting with plant data
– Compare simulation x plant
hexp
hcalc
8. Solution and Validation8. Solution and Validation
ModelingModeling
40
• Check output sensitivity to input disturbances
• Carry out parametric sensitivity analysis
• Analyze output data with statistical techniques
• Verify results coherence
• Document obtained results
Solution and ValidationSolution and Validation
ModelingModeling
41
• 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.
RemarksRemarks
ModelingModeling
45
EquationsEquationsThe order the equations The order the equations
appear in the model do not appear in the model do not mattermatter
Equivalent EquationsEquivalent EquationsCan be written in any Can be written in any
user desired formuser desired form
ModelLanguage – Equation-based system
ModelLanguage – Equation-based system
46
The modeling and simulation of complex systems is facilitated by the use of the Object-Oriented
concept
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
SystemSystem
EquipmentEquipment
ComponentComponent
ModelLanguage – Object-Oriented Modeling
ModelLanguage – Object-Oriented Modeling
47
Model ComponentsModel Components
Including sub- models and types
Automatic model documentation
Symbol of variable in LaTeX command for
documentation
Basic sections to create a
math. modelPort location to draw a flowsheet connection
Input and output connections
48
Parameters and variables are declared within their valid domains and units using types created based on the built-in types: Real, Integer, Switcher, PluginReal, Integer, Switcher, Plugin
Basic Variable Types in a ModelBasic Variable Types in a Model
49
Building a Model: A simple example – level tank
StreamsInlet Material stream feeding the tankOutlet Material stream leaving the tankParametersk Valve constantD Hydraulic diameter of the tankVariablesA Tank cross section areaV Tank volumeh Tank levelDevices: source, tank, sink
Available model of the tank>>> Model with circular cross section>>> Model with square cross section
50
Material Stream Modeling
The material stream carries the information entering and leaving the
equipment
VARIABLESF volumetric flowrateT temperatureP pressure
Source Source - component that has a feed material stream.It has an output connectionoutput connection
SinkSink - component that receives an output material stream. It has an input connectioninput connection
SourceSource
SinkSink
51
Inlet Feed material stream to the tankFin inlet volumetric flowrateTin inlet temperaturePin inlet pressure
Outlet Output material stream from the tankFout outlet volumetric flowrateTout outlet temperaturePout outlet pressure
Level Tank Modeling
2
2
Mass balance
Valve equation
Thermal equilibrium
Mechanical equilibrium
Area
if circular4
if square
in out
out
in out
in out
dVF F
dt
F k h
T T
P P
DA
D
54
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:
PARAMETERSsection which defines the
parameters of the model.VARIABLES
section which defines the variables of the model.EQUATIONS
section which describes the model equations.
Creating a Model using the template
55
Including Including pre-defined pre-defined
types of types of EMSOEMSO
Model Model DocumentationDocumentation
selecting the selecting the desired unit of desired unit of
measure measure
Symbol of Symbol of variable variable
are LaTeX are LaTeX commandscommands
Using the types defined Using the types defined in the file “types.mso”in the file “types.mso”
Creating a Material Stream Model
56
Using the Using the same filesame file
Output Output ConnectionConnection
Creating a Source Stream Model
Model Model DocumentationDocumentation
57
Creating a Sink Stream Model
Using the Using the same filesame file
Input Input ConnectionConnection
Model Model DocumentationDocumentation
58
ReferenceReference
Model Model PortsPorts
Creating new Creating new UOMUOM
EMSO Built-In FunctionEMSO Built-In FunctionEMSOquickRef.pdf
Creating a Basic Tank Model
59
InheritanceInheritanceModel inherits all the Model inherits all the attributes of the class attributes of the class from which it derivesfrom which it derives
SETSETDefining Defining values for values for parametersparameters
EquationEquationWriting the particular Writing the particular
equations modelequations model
Creating the Circular Tank Model
Using the Using the same filesame file
60
Creating the Square Tank Model
Using the Using the same filesame file
InheritanceInheritanceModel inherits all the Model inherits all the attributes of the class attributes of the class from which it derivesfrom which it derives
EquationEquationWriting the particular Writing the particular
equations modelequations model
62
In EMSOEMSO the user can manipulate
various FlowSheetsFlowSheets at
same time
The equipment are called DEVICESDEVICES
A FlowSheetFlowSheet consists of a series
of unit operations or equipment
connected to each other
Process Diagram – FlowSheet
63
streamPH
The system modeling is made by the The system modeling is made by the use, configuration and connection of use, configuration and connection of
pre-existing componentspre-existing components
FlowSheetLanguage – Component-based system
FlowSheetLanguage – Component-based system
64
FlowSheet ComponentsFlowSheet Components
Degree of Freedom
Dynamic Degree of Freedom
Simulation options
Parameters of DEVICES
66
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:
PARAMETERSDEVICESCONNECTIONSSETSPECIFYINITIALOPTIONS. . .
Creating a FlowSheet using the template
67
Degree of Freedom
Dynamic Degree of Freedom
Simulation options
Parameters of DEVICES
FlowSheet for the Level Tank
68
EMSO analyzes the consistency of the system created in the
FlowSheet
Consistency Analysis of the Process
70
Horizontal axis is always the independent variable (usually time)
double-click
Level Tank Results
71
Building a system consisting of three Building a system consisting of three tanks connected in seriestanks connected in series
Series of Level Tanks
74
Building a more interesting Model: CSTR with Van der Vusse reaction
StreamsInlet Feed material stream with molar concentrationOutlet Output material stream with molar concentrationParametersCv Valve constantk1 Constant of reaction rate 1 k2 Constant of reaction rate 2 k3 Constant of reaction rate 3 A Cross-section area
VariablesV Reactor volumer1, r2, r3 Reaction rates Ca, Cb,Cc, Cd Molar concentrations h Reactor level tau Residence time
75
Overall mass balance
Valve equation
Thermal equilibrium
Mechanical equilibrium
Volume
in out
out V
in out
in out
dVF F
dt
F C h
T T
P P
V Ah
Van der Vusse Reactor – Modeling
Component mass balances
Reaction rates
Residence timePerfect mixing
76
Adding molar Adding molar concentration in the concentration in the
material streammaterial stream
Van der Vusse Reactor – Stream Model
82
ExercisesExercises
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: 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.
sF xCv h
83
ReferencesReferences• 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.• Luyben, W. L., "Process Modeling, Simulation, and Control for Chemical Engineers", McGraw-Hill, 1990.• Silebi, C.A. & Schiesser, W.E., “Dynamic Modeling of Transport Process Systems”, Academic Press, Inc., 1992.• Ogunnaike, B.A. & Ray, W.H., “Process Dynamics, Modeling, and Control”, Oxford Univ. Press, New York, 1994.• Rice, R.G. & Do, D.D., “Applied Mathematics and Modeling for Chemical Engineers”, John Wiley & Sons, 1995.• Bequette, B.W., “Process Dynamics: Modeling, Analysis, and Simulation”, Prentice Hall, 1998.• Engell, S. E Klatt, K.-U. Nonlinear Control of a Non-Minimum-Phase CSTR, Proc. of American Control Conference, Los Angeles, 2041 – 2045 (1993).• Rodrigues, R., R.P. Soares and A.R Secchi. Teaching Chemical Reaction Engineering Using EMSO Simulator. Computer Applications in Engineering Education, Wiley (2008).• Soares, R.P. and A.R. Secchi. EMSO: A New Environment for Modeling, Simulation and Optimization. ESCAPE 13, Lappeenranta, Finlândia, 947 – 952 (2003).
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For helping in the preparation of this material
Special thanks to
For supporting the ALSOC Project.
Prof. Rafael de Pelegrini Soares, D.Sc.Prof. Rafael de Pelegrini Soares, D.Sc.Eng. Gerson Balbueno Bicca, M.Sc.Eng. Gerson Balbueno Bicca, M.Sc.Eng. Euclides Almeida Neto, D.Sc.Eng. Euclides Almeida Neto, D.Sc.Eng. Eduardo Moreira de Lemos, D.Sc.Eng. Eduardo Moreira de Lemos, D.Sc.Eng. Marco Antônio MüllerEng. Marco Antônio Müller
85
... thank you for your attention!
Process Modeling, Simulation and Process Modeling, Simulation and Control LabControl Lab
• Prof. Argimiro Resende Secchi, D.Sc.Prof. Argimiro Resende Secchi, D.Sc.
• Phone: +55-21-2562-8307Phone: +55-21-2562-8307
• E-mail: [email protected]: [email protected]• http://www.peq.coppe.ufrj.br/Areas/Modelagem_e_simulacao.htmlhttp://www.peq.coppe.ufrj.br/Areas/Modelagem_e_simulacao.html
http://www.enq.ufrgs.br/alsoc
EP 2013
Solutions for Process Control and OptimizationSolutions for Process Control and Optimization