Process Model

A process model is a set of equations, including the necessary input data to solve the equations, that allow us to predict the behavior of a chemical process system.

1. Fundamental Model: Derived from • Material and energy balances

• Physical and Chemical Properties

2. Empirical Model: Obtained by “fitting” data • Numerical Methods

• Statistical Analysis

Example 1

The following liquid-phase, isothermal first order reaction, with rate constant k, is occurring in a batch reactor.

A ⟶ B

How does the concentration of species A change with time if the initial concentration is C_{A0}?

Fundamental Model

\begin{aligned}\frac{dC_{A}}{dt} & = & −kC_{A} \\ C_{A}(0) & = & C_{A0} \end{aligned}

Integrating:

C_{A} = C_{A0}e^{−kt}

If k is known a priori, the above expression tells us how C_{A} changes with time.

Empirical Model

• Measure C_{A} with t and plot the data.

• Find an equation that “best fits” the data.

Types of Process Models

1. Steady state models.

2. Dynamic models. In this course, we will develop:

• dynamic models from first principles.

• approximate models of chemical processes.

Reasons for Developing Process Models

1. Operator training

2. Process design

3. Safety

4. Control system design

Developing Dynamic Process Models

• Step 1: Problem statement

• Step 2: Assembly of information – Sketch

– System and Notation

– Axiomatic laws

– Rate laws and Constitutive relations – Assumptions

• Step 3: Combine information

• Step 4: Boundary conditions/Constraints • Step 5: Simplify equations

Example 2

A typical liquid storage process is shown in the figure below. How does the height change with time ?

Example 3

Two tanks-in-series are shown in the figure below. How do the heights of the liquid in the two tanks change with time ?

Example 4

A mixing process is shown in the figure below. How does the outlet concentration change with time ?

Example 5

A series reaction is taking place in a CSTR. The first reaction is second order w.r.t. A and the second reaction is first order w.r.t. B. How do the outlet concentrations of species A, B, and C change with time ?