Multiple CSTR

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... 

It is possible to extend this treatment to the case of multiple CSTR s operating in series by adapting the procedure outlined by Denbigh and Turner (2). Let (ACA)U (ACA)2, and (ACA)h represent the changes in the concentration of species A that take place in tanks one, two, and i, respectively. 

With the feed divided as in equation (17.2-1), the two tanks act together the same as one tank of volume V= Vj + V2. There is thus no inherent performance advantage of multiple CSTRs in parallel, but there may be increased operating flexibility. 

Packed beds usually deviate substantially from plug flow behavior. The dispersion model and some combinations of PFRs and CSTRs or of multiple CSTRs in series may approximate their behavior. 

These steady-state design results indicate that dynamic controllability of a multiple-CSTR process could be poor if the reactions are irreversible and exothermic. 

Multiple CSTRs in Series with Different Temperatures... 

Multiple CSTRs with Reversible Exothermic Reactions... 

As an alternative to multiple CSTRs we might consider the use of a single CSTR followed by a distillation column. The per-pass conversion of reactant can be low, giving a reactor effluent with considerable reactant. Then this mixture is separated in a distillation column that recycles the unreacted component back to the reactor. 

The reactor in the reactor-stripper process is larger than the first reactor in the 3-CSTR process and therefore has more heat transfer area. However, all the conversion occurs in this one reactor, so we would expect the heat transfer rate to be high. In fact, it is not high but is even lower than the heat transfer rate in the 1-CSTR process (1.78 x 106 kJ/s, as shown in Fig. 2.21). The reason for this unexpected result is the large recycle stream in the reactor-stripper process. We assume that its temperature is 322 K. The total flow into the reactor is 0.1591 krnol/s (the sum of the recycle 0.1241 kmol/s and the fresh feed is 0.03506 kmol/s), while the flow into the first reactor of the 3-CSTR process is just the fresh feed. Thus the larger sensible heat of the larger stream reduces the heat than must be transferred in the reactor. Note that the total heat of reaction for a 98% conversion is 2.395 x 106 kJ/s. The sensible heat of the large feed stream to the reactor in the reactor-stripper process is 1.398 x 106 kJ/s. In the 3-CSTR process (and in all the multiple CSTR processes) the sensible-heat term in the first reactor is only 0.616 x 106 kJ/s because the flowrate is smaller. 

The reaction studied in Section 2.2 has two reactants and therefore offers the possibility of adjusting the compositions of the reactants in the reactor to achieve some economic or control objective. In this section we first find the cost of operating single and multiple CSTR processes to achieve a specified conversion. Then we design an alternative process consisting of a reactor and a distillation column that separates product C from the unreacted A and B in the reactor effluent and recycles them back to the reactor. 

Design Of Multiple CSTR Systems The reaction and the overall reaction rate are given below ... 

Let us return to the comparison we made in Chapter 2 of multiple CSTRs in series. In Section 2.6.1 the steady-state designs of 1-, 2-, and 3-CSTR processes were developed, and in Section 2.9.1 the capital costs of the three alternative processes were determined. The steady-state calculations indicate control problems in the first reactor of the 2-CSTR and 3-CSTR processes because the jacket temperatures are getting closer to the supply cooling water temperature. 

The first step is to calculate limits for the reaction volume. One CSTR will give the maximum volume and a plug-flow reactor will give the minimum volume. The total reaction voliune for multiple CSTRs will lie somewhere between these two limits. After calculating the reaction volume, calculate the required heat transfer and the heat-transfer area. Then, either select a jacket, a coil, jacket plus a coil, or an external heat exchanger. 

For preliminary design purposes, the estimate from Eq. (52) is an adequate predictor of achievable PI performance when all tanks are tightly controlled. If control on one tank of a multiple CSTR system is rendered ineffective—due to uncertainty, high delay compared to the minimum delay, or simply the absence of a controller—the predicted disturbance attenuation should be increased by 50%. An exception to this is the case of variation in the sensitivity of pH to concentration on the final CSTR. In this case, no degradation of performance from that obtained with the minimum buffering (maximum titration curve slope) will occur as the performance required in terms of concentration deviations relaxes along with the controller performance. 

Taking the multiple CSTR concept to its logical extreme, a very large number of small tank reactors connected in series can be likened to carrying out the same process in a very long, narrow-bore tube, referred to as a tubular flow, or pipe reactor. By placing sections or all of this tube in externally heated... 

Typical reactor type Mechanically agitated reactor with a heating jacket or condenser Mechanically agitated reactor with a heating jacket or condenser CSTR, tubular reactor, multiple CSTRs, fluidized bed reactor, loop reactor... 

Multiple CSTRs with a pre-reactor such as a small CSTR, a single-pass tube or a spiral-flow cylinder ... 

Nucleation rates, copolymer compositions and growth rates for different size particles can be measured under fixed conditions in a steady-state CSTR. The influence of changes in important parameters can be studied by multiple CSTR runs with different reaction envEonments. The modelling of particle growth kinetics is one phenomenon for which the CSTR is particularly well suited. 

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