Sequences of adiabatic stirred tanks

We shall not discuss such problems in full detail, but an elementary one is worth considering. Suppose that the extent is fixed and so is the feed temperature 7 , which we will now denote by 7 i since it is the feed to the first reactor. We ask how much reaction in the first stage and how much cooling between stages should take place if the total holding time is to be least. The temperature at the exit of the first reactor is Tfi + Jf, and the feed temperature of the second reactor will be chosen to be Tf + J, so that 

The two choices to be made are of fi and Tfi- Now the choice of Zy, only affects the second term on the right of Eq. (8.3.1), and we know from problem B of Sec. 8.2 that, in this case, the state (f, should be on Since 2 has been specified, this fixes as JTo find we notice that 

Another way to achieve cooling between stages is to mix the product of the first stage with cold unreacted feed before passing to the next stage. This has the merit of simplicity and may avoid excessive interchanger equipment. It is shown for two stages in Fig. 8.6. A fraction Xq of the feed is heated 

This is represented by point C on line F5, where by similar triangles FC XFB. The adiabatic path for the second reactor would go through the point (0, Tyr,) where 

In the second reactor the change in state is represented by segment CD in the lower part of Fig. 8.6. The full equations are thus 

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