Introduction - Sahand University of Technology
Transcript of Introduction - Sahand University of Technology
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Introduction
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Contents:
1- Design, Modeling, Simulation, Optimization,
Their Applications and Relations
1-1- Design (Determination of equipment size, …)
(Cost, Capability, Maintenance, Safety)
Steps:
Conceptual Design
Basic Design
Detail Design
1-2- Modeling
Definition
Programming
Using software
1-3- Simulation
1-4- Optimization
1-5- Applications and Relations
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Contents (continue):2- Modeling and Engineering Problem solving
2-1- Physical Model2-2- Mathematical Model2-3- Numerical Model2-4- Modeling Using Software
3- Types of Modeling 3-1- Steady State3-2- Pseudo Steady State3-3- Unsteady State
4- Modeling procedure
5- Programming and Using of Software
Lumped model
1 D Model
2 D Model
3 D Model
4 D Model
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-1- Design (Determination of equipment size, …)
(Cost, Capability, Maintenance, Safety)
Design Steps:
Conceptual Design
Basic Design
Detail Design
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-1- Design (Determination of equipment size, …)
(Cost, Capability, Maintenance, Safety)
Design Steps:
Conceptual Design
Basic Design
Detail Design
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-2- Modeling
Modeling is a fundamental and quantitative way to understand complex systems and phenomena.
A model is an imitation of reality.
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Model:
“A model (M) for a system (S)
and an experiment (E) is
anything to which E can
be applied in order to answer questions
(P) about S”
“A Processes Engineering Model is
typically a mathematical representation (M)
of a physical system (S) for a specific
purpose (P) and experiment (E)”
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Model
The Process Modeling
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations1-3- Simulation
Process simulation is used for the design, development, analysis, and optimization of technical processes
Simulation is also used for scientific modeling of natural systems or human systems in order to gain insight into their functioning
Simulation can be used to show the eventual real effects of alternative conditions and courses of action. Simulation is also used when the real system cannot be engaged, because it may not be accessible, or it may be dangerous or unacceptable to engage, or it is being designed but not yet built, or it may simply not exist
It is mainly applied to
Chemical plants Chemical processes
Safety engineering Testing
Training (Flight Simulators) Education
video games (war Games) power stations
and similar technical facilities.
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-3- Simulation
Simulation Steps:
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-4- Optimization
In mathematics, computer science and economics, optimization, or mathematical programming, refers to choosing the best element from some set of available alternatives.
In the simplest case, this means solving problems in which one seeks to minimize or maximize a real function by systematically choosing the values of real or integer variables from within an allowed set. This formulation, using a scalar, real-valued objective function, is probably the simplest example; the generalization of optimization theory and techniques to other formulations comprises a large area of applied mathematics. More generally, it means finding "best available" values of some objective function given a defined domain, including a variety of different types of objective functions and different types of domains.
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-4- Optimization
optimization techniquesOptimization methods are crudely divided into two groups:SVO - Single-variable optimizationMVO - Multi-variable optimization
For twice-differentiable functions, unconstrained problems can be solved by finding the points where the gradient of the objective function is zero (that is, the stationary points) and using the Hessian matrix to classify the type of each point. If the Hessian is positive definite, the point is a local minimum, if negative definite, a local maximum, and if indefinite it is some kind of saddle point.The existence of derivatives is not always assumed and many methods were devised for specific situations. The basic classes of methods, based on smoothness of the objective function, are:Combinatorial methodsDerivative-free methodsFirst-order methodsSecond-order methods
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1- Design, Modeling, Simulation, Optimization, Their
Applications and Relations
1-5- Applications and
Relations
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2- Engineering Problem solving and Modeling
2-1- Engineering Problem Solving
2-2- Physical Model
2-3- Mathematical Model
2-4- Numerical Model and Programming
2-5- Modeling Using Software
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2-1- The Engineering Skills:
1) How to represent a design problem
2) How to generate possible ideas for designs
3) How to effectively conduct a search for a
solution
4) How to plan and schedule activities
5) How to make efficient use of resources
6) How to organize the components and activities
of a team design project
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2-1-1- Problem Solving Steps:
The strategy has eight steps- seven working steps and
one motivational step- listed below:
1) I can (positive attitude)
Try to view each problem as a challenge, and don’t give up too easily.
2) Define
Identify the “Knowns”, Identify the “Unknowns”, State in simpler terms,
Develop a diagram, schematic, or visual representation for the problem
3) Explore (pre-planning and we double-check that we understand the
problem)
You think about what the problem is actually asking you to solve, what
additional information you might need, and general strategies that might
be applicable
Dose the problem makes sense?
Assumptions
What are the key concepts and possible approaches
What level of understanding is tested?
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2-1-1- Problem Solving Steps (cont.):
4) Plan
Main goal (unknown), subgoals (Unknown), Initial Values (Known) and
assumptions
5) Implement
Solve the equations
6) Check
7) Generalize
some questions:
What specific facts have you learned about the content?
Could this problem have been solved more efficiently?
Could you have applied something you learned in solving this problem
to another problem that you’d seen in the past?
Were there any problems or bugs that you encountered that you
should remember, in case you run into them again?
8) Present the results
Show your work
Give good directions
Be neat
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2-1-2- Problem Solving Steps (Example):
How much CO2 does a typical passenger car produce per year? (p:113)
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2-2- Physical Model
A physical model (most commonly referred
to simply as a model, however in this sense it
is distinguished from a conceptual model) is
a smaller or larger physical copy of an
object. The object being modeled may be
small (for example, an atom) or large (for
example, the Solar System).
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2-3- Mathematical Model
A mathematical model is a description of a system using mathematical language.
The process of developing a mathematical model is termed mathematical
modeling (also written modeling).
Mathematical models are used not only in the natural sciences (such as physics,
biology, earth science, meteorology) and engineering disciplines, but also in the
social sciences (such as economics, psychology, sociology and political science);
physicists, engineers, statisticians, operations research analysts and economists
use mathematical models most extensively.
Mathematical models can take many forms, including but not limited to
dynamical systems, statistical models, differential equations, or game theoretic
models.
These and other types of models can overlap, with a given model involving a
variety of abstract structures.
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2-4- Numerical Model and Programming
- Drive Required Equations in General Form
-Consider Boundary and Initial Conditions
- Prepare Flowchart of Program
- Write Program
- Get Results
- Compare with Available Data (*)
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2-5- Modeling Using Software
-Select a proper and User Friendly Software
- Find Its Tutorial Help and Examples
- Run Simple Models or Programs
- Run Your Program or Model
-Get Results
- Compare with Available Data
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3- Types of Modeling
Steady State
Pseudo Steady State
Unsteady State
Lumped model
1 D Model
2 D Model
3 D Model
4 D Model
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4- Modeling procedure
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The Process System A Process Model
4-1- Model
SISO: Simulation interoperability Standards Organization
MIMO: multiple-input and multiple-output
SS: steady state
m: model
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4-2- Goals for Process Modeling
Flow Sheeting
Design
Optimization
Process Control
Prediction
Regulation
Identification
Diagnosis
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4-3- Model Building White-box modeling
A white-box model (also called glass box or clear box) is a system where all necessary information is available.
Black-box modeling
A black-box model is a system of which there is no a priori information available.
Grey-box modeling
Real process systems
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4-4- Systematic Modeling Procedure
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1. Problem Definition
Clear description of system
input/output
spatial distribution
time characteristics
etc
Statement of modeling intention
intended goal or use
acceptable error
anticipated inputs/disturbances
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1. Problem Definition (cont.)
CSTR descriptiondetails
lumped ?
dynamic
Goal (intent)inlet change range
± 10% accuracy
control design
Definition Example (Step 1)
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2. Controlling Factors / Mechanisms
Chemical reaction
Mass transfer
convective, evaporative, ...
Heat transfer
radiative, conductive, …
Momentum transfer
ASSUMPTIONS
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2. Controlling Factors / Mechanisms
Mechanisms - CSTR (step 2)
Chemical reaction A P
Perfect mixing
No heat loss (adiabatic)
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3. Data for the problem
Physico-chemical data
Reaction kinetics
Equipment parametersV
Plant data
RHEK ,,0
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4. Model construction
Assumptions
Boundaries and balance
Volumes
Characterizing Variables
Conservation equationsmass
energy
momentum
Constitutive equations reaction rates
transfer rates property relations
balance volume relations
control relations &
equipment constraints
Conditions (ICs, BCs)
Parameters
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4. Model construction (cont.)
Assumptions A1: perfect mixing
A2: first order reaction
A3: adiabatic operation
A4: equal inflow, outflow
A5: constant properties
CSTR Model (step 4)
Equations conservation
constitutive
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4. Model construction (cont.)
Initial Conditions
Parameters and inputs
10% accuracy
30% - 50% accuracy
CSTR Model (step 4)
• Industrial measured data is
± 10 to 30%
• Estimated parameters from
laboratory or pilot plant data is
±5 to 20%
• Reaction kinetic data is
± 10 to 50 % (if nothing else is specified)
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5. Model solutionWhat variables must be chosen in the model to satisfy the
degrees of freedom?
Is the model solvable?
What numerical (or analytic) solution technique should be
used?
Can the structure of the problem be exploited to improve the
solution speed or robustness?
What form of representation should be used to disp1ay the
results (2D graphs, 3D visualization)?
How sensitive will the solution output be to variations in the
system parameters or inputs?
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5. Model solution (cont.)
Mechanistic
Empirical
Stochastic
Deterministic
Lumped parameter
Distributed parameter
Linear
Nonlinear
Continuous
Discrete
Hybrid
Based on mechanisms/underlying phenomena
Based on input-output data, trials or experiments
Contains model elements that are probabilistic in nature model
Based on cause-effect analysis
Dependent variables not a function of spatial position
Dependent variables are a function of spatial position
Superposition principle applies
Superposition principle does not apply
Dependent variables defined over continuous space-time
Only defined for discrete values of time and/or space
Containing continuous and discrete behavior
Type of model Criterion of classification
Model Classification
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5. Model solution (cont.)
Algebraic systems
Ordinary differential equations
Differential-algebraic equations
Partial differential equations
Integro-differential equations
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5. Model solution (cont.)Type of model Equation
Steady-state
problem
types
Dynamic problem
Deterministic
Stochastic
Lumped parameter
Distributed
parameter
Linear
Nonlinear
Continuous
Discrete
Nonlinear algebraic
Algebraic/difference
equations
Algebraic equations
EPDEs
Linear algebraic equations
Nonlinear algebraic
equations
Algebraic equations
Difference equations
ODEs/PDEs
Stochastic ODEs or difference
equations
ODEs
PPDEs
Linear ODEs
Nonlinear ODEs
ODEs
Difference equations
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6. Model verification
Model Verification
Model Validation
Reality
Conceptual Model Computerised Model
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6. Model verification (cont.)
Verification is determining whether the model is behaving correctly.Is it coded correctly and giving you the answer you intended? This is not the same as model validation where we check the model against reality.You need to check carefully that the model is correctly implemented. Structured programming using top-down algorithm design can help here as well as the use of modular code which has been tested thoroughly.This is particularly important for large-scale models.
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6. Model verification (cont.)
Structured programming approach
Modular code
Testing of separate modules
Exercise all code logic
conditions
constraints
Verification is determining whether the model is behaving correctly. Is it coded correctly and giving you the answer you intended? This is not the same as model validation where we check the model against reality. You need to check carefully that the model is correctly implemented. Structured programming using top-down algorithm design can help here as well as the use of modular code which has been tested thoroughly. This is particularly important for large-scale models.
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7. Model calibration/validation
Generate plant data
Analyze plant data for quality
Parameter or structure estimation
Independent hypothesis testing for validation
Revise the model until suitable for purpose
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For Discussion (1)
Open tank system
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For Discussion (2)
Closed tank system
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5- Programming and Using of Software
5-1 ProgrammingSelect Proper Language and Learn It
5-2 Using Software
Select Proper and User Friendly Software
Find Tutorial Help and Examples