A Reactor Model

In this exercise we are going to look at how a dynamic model can be produced which will predict the outlet concentrations from a simple continuous stirred tank reactor (CSTR). The reactor arrangement is shown in the diagram. To simplify things, I'm making the following assumptions (in real modelling situations, you'd need to be very careful in making some of these assumptions!): Perfect mixing Perfect level control Constant and equal densities across all streams Perfect temperature control. This assumption means the reactor is held at a constant temperature. If this assumptions isn’t made we’d need to include temperature dependant reaction rates, and would also need to do an energy balance to model the temperature dynamics.

In the reactor it is assumed that a simple, irreversible, isomerisation of A to B occurs. The rate of destruction of A is given by:

In this model, we don’t need to do a total mass balance because of the assumptions we’ve made (perfect level control and constant density give a constant total mass balance). The first thing we need to do therefore is to produce a component balance for A. Have a go at this yourself - ‘A’ enters and leaves the reactor in the flows and is also destroyed (watch the sign in the ‘generation’ term) in the reactor.

Now, let’s continue with the model, by working out the component balance for the product, B. Have a go at writing the balance yourself. Remember that no B enters the reactor, but some leaves in the exit stream, and that B is produced directly from the destruction of A.

You can see that the B balance is dependant on the reactor concentration of A - this means that the B balance has to be solved simultaneously with the A balance.