Multiple CSTR cascade

CONTROL AND STARTUP OF A 3-STAGE CSTR CASCADE MULTIPLE OPERATING STATES AND COUNTERCURRENT COOLING... 

Analysis of CSTR Cascades under Nonsteady-State Conditions. In Section 8.3.1.4 the equations relevant to the analysis of the transient behavior of an individual CSTR were developed and discussed. It is relatively simple to extend the most general of these relations to the case of multiple CSTR s in series. For example, equations 8.3.15 to 8.3.21 may all be applied to any individual reactor in the cascade of stirred tank reactors, and these relations may be used to analyze the cascade in stepwise fashion. The difference in the analysis for the cascade, however, arises from the fact that more of the terms in the basic relations are likely to be time variant when applied to reactors beyond the first. For example, even though the feed to the first reactor may be time invariant during a period of nonsteady-state behavior in the cascade, the feed to the second reactor will vary with time as the first reactor strives to reach its steady-state condition. Similar considerations apply further downstream. However, since there is no effect of variations downstream on the performance of upstream CSTR s, one may start at the reactor where the disturbance is introduced and work downstream from that point. In our generalized notation, equation 8.3.20 becomes... 

Let us turn now to the second of the problems mentioned earlier—determination of the combination of CSTRs that is best suited to achieving a specified conversion level. We begin by considering the case of a cascade of two arbitrarily sized ideal CSTRs operating under isothermal conditions and then briefly treat the problem of using multiple identical CSTRs in series. Consider the two cascade configurations shown in Figure 8.12. For the first reactor, equation... 

For cascades of multiple equal-sized CSTRs, the problem of determining the reactor sizes necessary to achieve a specified degree of conversion can be solved by a trial-and-error procednre. In this case the lines in figures analogous to Figure 8.11 will aU be parallel to one another. Consequently, one draws a number of parallel lines equal to the number of CSTRs that he or she intends to use, with the first line passing through the inlet composition. When the slope used provides the necessary match with the final effluent composition specified, this slope may be used to determine the necessary reactor volume. Illustration 8.7 indicates the use of this technique. 

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