Part II Process Dynamics. Process model types 1.Mathematical model 2.Fundamental and empirical...

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Part II Process Dynamics

Transcript of Part II Process Dynamics. Process model types 1.Mathematical model 2.Fundamental and empirical...

Page 1: Part II Process Dynamics.  Process model types 1.Mathematical model 2.Fundamental and empirical model 3.Steady-state and dynamic model 4.Lumped (ODE)

Part II Process Dynamics

Page 2: Part II Process Dynamics.  Process model types 1.Mathematical model 2.Fundamental and empirical model 3.Steady-state and dynamic model 4.Lumped (ODE)

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)