Design of Reactor-Separator Processes

Using the BATCHFRAC simulator, the results are as follows, where Distil, and Accum. refer to the instantaneous distillate and product accumulator, respectively  

As can be seen, the total batch time is nearly 8 hr, the amounts of 99.9 mol% methanol and 99.98 mol% propylene glycol products are 29.88 Ibmol and 33.03 Ibmol, respectively. Note that after step 4 the methanol product accumulator contains 0.999 X 29.88 = 29.85 Ibmol methanol. The remainder, 33.33 - 29.85 = 3.48 Ibmol methanol is recovered initially in the water product accumulator during step 6. Hence, the water product accumulator contains a slop cut of water. Nearly all of the propylene glycol is recovered in the still. These results can be reproduced using the BATCHHiAC file, EXAM 12-3. bkp, on the multimedia CD-ROM.  

In this section, an approach to solving the optimal control problem is introduced for reactor-separator processes. The approach involves the simultaneous determination of the batch times and size factors for both of the process units. Furthermore, the interplay between the two units involves trade-offs between them that are adjusted in the optimization. It should be noted that simpler models, than in normal practice, are used here to demonstrate the concept and, in the first example, provide an analytical solution that is obtained with relative ease. 

For the first-order reaction, it can be shown (Exercise 12.4) that  

To locate the maximum, substitute the equations above and differentiate  

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