Optimal sequences of stirred tank reactors

In this section we shall study in detail the optimal choice of holding time and temperature in a sequence of stirred tanks in which a single exothermic reversible reaction is taking place. As soon as the word optimal is used the question must be asked, In what sense is the design to be optimal Here we shall only treat the simplest of optimization problems, but their interplay is instructive. 

however, let us introduce a notation which may look a little perverse at first sight but which helps to clarify the problem. It is to number the stages from the last to the first as shown in Fig. 7.25. Thus the feed to reactor n is from reactor n + 1 

We could set up three basic optimal problems. First, suppose the feed 

A third problem could be arranged in which a very crude cost estimate would be set up. If is the price of a mole of A, the cost of the feed stream is 4- while the value of the product stream is q 2 

More complicated and realistic problems could be devised in which we 

---