Part II Process Dynamics

Process model types

1. Mathematical model

2. Fundamental and empirical model

3. Steady-state and dynamic model

4. Lumped (ODE) and distributed (PDE) model

Chapter 3 Modelling principles

Example 3.1

(1) Overall material balance

(2) Component material balance

(3) Energy balance

Example 3.2 Isothermal CSTR

Example 3.3 Two isothermal CSTR

※ Linearization

Which is used to approximate the nonlinear system with linear differential equations.

(1) Enthalpy H

(2) Equilibrium vapor mole fraction y

(3) Reaction rate

Linear approximation

＊ Linearization for one variable

Ex. 3.4 linearization of Arrhenius equation

Sol.:

＊ Linearization for more variables

Ex. 3.5 Linear approximation of density of an ideal gas

Sol.:

＊ Linearization for differential equations

S1. The first-order differential eqn

S2. The steady state values as initials

S3. Linearization

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

where CA, F, CAi, are derivative variables, and

S2. Standard form

where

Ex. 3.7 Linearization of an isothermal CSTR

To determine steady state values

The derivation variable is introduced as

(S1) The standard form is arranged as

(S2) Dynamic responses

Ex. 3.8 (Complex) nonisothermal CSTR

Homework#1 Simulation of CSTR system (limited to up 20 reports) (see, appendix C)