Example Optimal Reactor Structure for Minimum Residence Time

5 Example Optimal Reactor Structure for Minimum Residence Time 

I Reaction and Feed Specification All of the examples described in this chapter possess equivalent versions involving residence time as well. If it is desired to retain the same components as before, and also include residence time in the state vector, then the resulting AR must be of one dimension higher than that originally posed— two-dimensional problems in concentration space are thus three-dimensional problems if residence time is considered as well. With this in mind, consider now the single autocatalytic reaction involving components A and B 

We wish to determine the optimal reactor structure corresponding to the lowest possible residence time achieved by the system. 

Component A reacts in the presence of component B to form more B, and therefore one mole of A is reacted for every mole of B that is formed overall. It is assumed that B is the desirable component. The associated rate expression for component A is assumed to follow 

2 Concentration and Rate Vectors Since the objective in this example is to determine the reactor structure corresponding to lowest residence time, the state vector for which the AR will be built from must reflect this perspective accordingly. Seeing as component B may be determined by stoichiometry and the value of c, one need to only include either component A or B for the other may then be found by mass balance. Hence a two-dimensional state vector may be formed containing the concentration of A and the system residence time. This is given simply as follows  

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