PFRs in Parallel

Now let s consider two PFRs in parallel. This case is not quite as obvious. We learned previously that operating two PFRs in series gives the same performance as a single PFR operating at the same space time. Here we will analyze the case where both of the parallel PFRs have the same feedrate, feed composition, and temperature. Again, normal kinetics will be assumed. The situation is shown in the following figure. 

Let reactor 1 be the smaller of the two reactors, i.e., Vi V l. Since both reactors have the same molar inlet flow rate of A, and the same feed composition and the same 

The shaded area on the left, with diagonals running from lower left to upper right, is equal to 2 (V ao) — (Fi/Faq) - This area is proportional to (F — Vi), the volume savings associated with the smaller reactor, operating at a conversion xa,i, relative to a reactor with a volume of V, with the same feed rate (Fao/2), operating at a higher conversion x. 

Clearly, the shaded area on the right is larger than the shaded area on the left, so that. 

For two PFRs in parallel, with the same feed to each reactor, the required total volume is greater if the reactors have different volumes and operate at different conversions than if they have the same volume and operate at the same conversion. This is the same result that we obtained for two CSTRs in parallel. 

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Figure 23-8 develops the overall transform of a process with a PFR in parallel with two CSTRs in series. C(t) is found from C(.s) by inversion of the output transform. 

FIGURE 15.12 An arbitrary residence time distribution modeled as PFRs in parallel. 

Figure 14-14 Combinations of ideal reactors used to model real PFRs. (a) two PFRs in parallel (b) PFR and CSTR in parallel.

Find the conversion for a first-order reaction in a composite system that consists of a perfect mixer and a PFR in parallel. 

The completely segregated stirred tank can be modeled as a set of PFRs in parallel, with the lengths of the individual piston flow elements being distributed exponentially. Any RTD can be modeled as piston flow elements in parallel. Simply divide the flow evenly between the elements and then cut the tubes so that they match the shape of the washout function. See Figure 15.12. A reactor modeled in this way is said to be completely segregated. Its outlet concentration is found by averaging the concentrations of the individual PFRs ... 

Two PFRs in parallel one operated at Xj and the other operated at X2, with a combined mixture of both exit streams forming X3. 

Figure 6.7 Different proposed optimal reactor structures, (a) PFRs in parallel, (b) CSTR with feed bypass, (c) CSTR-PFR, (d) DSR-PFR with feed bypass (e) PFR-CSTR, and (f) DSR-PFR.

The scheme (g) combining CSTR and PFR in parallel is unusual. This combination also requires equal conversions at the outlet of each reactor. Note, however, that the volumes are different from one another. 

The examples in the preceding sections were quite specific and were constructed to facilitate analysis. With either CSTRs or PFRs in parallel, it was best to have both reactors operating at the same conversion x. The performance of parallel reactors operating at different conversions that averaged to x was infimor. 

Despite the last generalization, there are occasions where it is necessary or desirable to use PFRs in parallel. For example, exothermic reactions sometimes are run in reactors that resemble shell-and-tube heat exchangers. A single reactor may have hundreds of tubes in... 

Figure 10-11 shows the shape of the E(t) curves that result from various combinations of CSTRs and PFRs in parallel. The conunents beside each figure indicate how the values of Ti and T2 that are required to quantify the model and to calculate reactor performance can be extracted from the E(t) curves. 

Figure 10-11 The exit-age distribution for various combinations of CSTRs and PFRs in parallel.

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