CSTR cascades

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

Size Comparisons Between Cascades of Ideal Continuous Stirred Tank Reactors and Plug Flow Reactors. In this section the size requirements for CSTR cascades containing different numbers of identical reactors are compared with that for a plug flow reactor used to effect the same change in composition. 

CSTR cascade and a PFR reactor. Note how rapidly PFR behavior is approached as N increases. Levenspiel has also included lines of constant kx on this figure, and these lines may be useful in solving certain types of design problems, as we will see in Illustration 8.10. 

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... 

This equation is the CSTR cascade analog of equation 9.1.11 for a PFR. It indicates that the overall yield is a summation over the instantaneous yields weighted by the fraction of the concentration change that takes place in each tank. 

The reactor temperature controller (loop 2) is the primary controller, whereas the jacket temperature controller (loop 3) is the secondary controller. The advantage of the cascade control is that the reactor temperature control quickly reacts by the cascade system to disturbances in cooling fluid inlet conditions. The d3mamics of the transfer function G32 is faster than that of G 22-In the CSTR cascade control there are two control loops using two different measurements temperatures T and Tj, but only one manipulated variable Fj. The transfer function of the primary controller is the following ... 

A continuous reactor such as the CSTR cascade behaves like a batch reactor at start up. 

Around the same time, Glasser et al. (17) retrieved and extended the insightful methods of Horn (18) and presented graphical procedures known as the attainable region (AR) method. Their approach requires the graphical construction of the convex hull of the problem and helps to exemplify the need for a systematic and general methodology. In principle, the reactor network with maximum performance in terms of yield, selectivity, or conversion can be located on the boundary of the AR in the form of DSR and CSTR cascades with... 

Equations (8.3.26) and (8.3.27) are generally applicable to all types of CSTR cascades. If one recognizes that the use of such cascades is almost invariably restricted to liquid systems and that in such systems density changes caused by reaction or thermal effects are usually quite small, then additional relations or simplifications can be developed from these starting equations. In particular, this situation implies that at steady state the volumetric flow rate between stages is substantially constant. It also implies that for each reactor, 7, = t,, and that the following relation between concentration and fraction conversion is appropriate ... 

Figure 8.14 is in essence a plot of this ratio versus the fraction conversion for various values of N, the number of identical CSTRs employed. The larger the value of N, the smaller the discrepancy in reactor volume requirements between the CSTR cascade and a PFR reactor. Note... 

A Analysis of CSTR Cascades Under Non-Steady-State Conditions... 

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