Section 3.7.2: Process Case Study

You should first look at some revision material on material balances in section 1.2.1.

We describe here a simple recycle chemical process which will be used in a case study to illustrate a number of aspects of steady-state modelling and algebraic equation solving.

Process Description

The process is to make product C from reactants A and B by the reaction

A + B -> C

It is fed with a mixture of A and excess B containing none of the product material C.

The conversion in the reactor is R based on A.

Following the reactor all unreacted A and B are recovered in the overheads of a distillation column and recycled. The product C is not fully separated, a fraction S of that fed to the separator remains in the overheads.

To avoid the buildup of unreacted B, a fraction P of the overhead stream is removed as a purge.

Simple Process Model

The parameters of the model are:

The fractional conversion R in the reactor, typically 0.8
The fractional recovery S of C in the column overheads, typically 0.1
The fraction P of the overhead stream which is purged, typically 0.05

18 variables x₁ to x₁₈ can be associated with the 3 molar flows of each of the species A, B and C in the 6 unknown process streams as shown in the flowsheet above. Here x₁ is the flowrate of A entering the reactor, x₂ that of B, and x₃ that of C. Similarly x₄ is the flowrate of A out of the reactor, and so forth.

The operations are all described by linear equations, as discussed in section 1.2.1. hence the whole process amy be described by a set of 18 linear equations as shown below.

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