Chapter 2
Developing Models for
Optimization
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Everything should be made as simple
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TERMINOLOGY OF MATHEMATICAL MODELS
There are many additional ways to classify mathematical models besides those used in Chapter 2. For our
purposes it is most satisfactory to first consider grouping the models into opposite pairs:
deterministic vs. probabilistic linear vs. nonlinear
steady state vs. nonsteady state
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Common Sense in Modeling
What simplifications can be made? How are they justified?
Types of Simplifications
(1)Omitting Interactions (2)Aggregating Variables (3)Eliminating Variables
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Precautions in Model Building
(1) Limits on availability of data and accuracy of data Examples: Kinetic coefficients
Mass transfer coefficients
(2) Unknown factors present or not present in scale up Examples: Impurities in plant streams
Wall effects
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(4) Models used for one purpose used improperly for another purpose
Example: Invalidity of kinetic models
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2. Empirical Models
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Semi-empirical Model Fitting
s t f
Heat exchanger data, p. 54
Quadratic Curve Fitting
2 2
1 2 3 1 2 1 3
y =
β + β x + β x (x =1, x = x x = x )
Least squares analysis leads to 3 linear equations in 3 unknowns (n data points)
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