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 C A. S1. Linear approximation

where C A, F, C Ai, 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)