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Part II Process Dynamics
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Process model types
1. Mathematical model
2. Fundamental and empirical model
3. Steady-state and dynamic model
4. Lumped (ODE) and distributed (PDE) model
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Chapter 3 Modelling principles
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Example 3.1
(1) Overall material balance
(2) Component material balance
(3) Energy balance
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Example 3.2 Isothermal CSTR
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Example 3.3 Two isothermal CSTR
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※ Linearization
Which is used to approximate the nonlinear system with linear differential equations.
(1) Enthalpy H
(2) Equilibrium vapor mole fraction y
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(3) Reaction rate
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Linear approximation
* Linearization for one variable
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Ex. 3.4 linearization of Arrhenius equation
Sol.:
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* Linearization for more variables
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Ex. 3.5 Linear approximation of density of an ideal gas
Sol.:
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* Linearization for differential equations
S1. The first-order differential eqn
S2. The steady state values as initials
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S3. Linearization
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Ex. 3.6 A differential eqn. from a CSTR system
Where
Find the time constant and gains of transfer function of CA.
S1. Linear approximation
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where CA, F, CAi, are derivative variables, and
S2. Standard form
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where
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Ex. 3.7 Linearization of an isothermal CSTR
To determine steady state values
The derivation variable is introduced as
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(S1) The standard form is arranged as
(S2) Dynamic responses
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Ex. 3.8 (Complex) nonisothermal CSTR
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Homework#1 Simulation of CSTR system (limited to up 20 reports) (see, appendix C)