Chapter 4, Problem 4.11E

Interpretation Introduction

(a)

Interpretation:

The dynamic model of the given process is to be developed and the degree of freedom analysis is to be performed.

Concept introduction:

For chemical processes, dynamic models consisting of ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

In the steady-state process, the accumulation in the process is taken as zero.

The degree of freedom analysis of a process model ensures that its model equations are solvable. The expression to calculate the degree of freedom is:

$N_F=N_V-N_E$   ..... (1)

Here, $N_F$ is the number of degree of freedom for the process model, $N_V$ is the total number of process variables, and $N_E$ is the total number of independent equations written for the process model.

Interpretation Introduction

(b)

Interpretation:

The model to characterize the transfer function $\frac{{W^{\prime }}_3\left(s\right)}{{P^{\prime }}_c\left(s\right)}$ is to be developed. Also, the orders of denominator and numerator of the transfer function are to be identified. It is to be stated if the gain of the function be unity or not.

Concept introduction:

For chemical processes, dynamic models consisting ordinary differential equations are derived through unsteady-state conservation laws. These laws generally include mass and energy balances.

The process models generally include algebraic relationships which commence from thermodynamics, transport phenomena, chemical kinetics, and physical properties of the processes.

The difference in the actual variable $\left(y\right)$ and the original variable $\left(\overline{y}\right)$ is known as deviation variable $\left(y^{\prime }\right)$. It is generally used while modelling a process. Mathematically it is defined as:

$y^{\prime }=y-\overline{y}$

In steady-state process, the accumulation in the process is taken as zero.