Combinations of CSTRs and PFRs in Series

In this series arrangemem, is evaluated at X2 for the second CSTR. 

Starting with the differential form of the PFR design equation 

The curves we have been using in the previous examples are typical of 

Example 2-5 An Adiabatic IJquid-Phase homerizt an The isomerization of butane 

Calculate the volume of each of the reactors for an entering molar flow rate of n-butane of SO kmol/hr. 

The final sequences we shall consider are combinations of CSTRs and PFRs I series.. Kn industrial example of reactors in series is. shown in the photo in Fi ure 2-9. Thi.s sequence is used to dimerize propylene into isohexanes, e.g.. 

Fitjure 2-9 Dimersol G tan orjiunorTKiallit catalyst) unit (two CSTR.s and one lubuhr reactor in series) to dimerize propylene into isolteaanes. Institut Fran aj.s du Pi trule process. [Photo courtesy ol Eduions Techntp (Institut Franyais du Pdirolc).] 

Id ibis series amn emeni -r evaluated at X for the second CSTR. 

The volumes of the first two CSTRs in series (see Example 2-5) are Reactor 1 

---

Real reactors deviate more or less from these ideal behaviors. Deviations may be detected with re.sidence time distributions (RTD) obtained with the aid of tracer tests. In other cases a mechanism may be postulated and its parameters checked against test data. The commonest models are combinations of CSTRs and PFRs in series and/or parallel. Thus, a stirred tank may be assumed completely mixed in the vicinity of the impeller and in plug flow near the outlet. 

This generalization applies to any combination of CSTRs and PFRs in series and parallel, for normal kinetics. 

Figure 10-12 shows the shape of the E(t) curves for various combinations of CSTRs and PFRs in series. The conunents beside each figure show how the information required to quantify the model and to calculate reactor performance can be extracted. 

Structures (c) and (e) are both similar, as both structures involve combinations of a CSTR and PFR in series. It is known that the final approach to the extreme points of the AR take place as a result of the union of PFR trajectories, and thus we should expect that final fundamental reactor type of any optimal reactor structure on the AR boundary is a PFR. We may conclude that structure (e) does not produce an effluent concentration that is an exposed point on the AR boundary (although the effluent concentration may still lie on the AR boundary, the point will not be exposed). The CSTR feeding the PFR in (c) must therefore produce a concentration that is a point on the AR boundary. 

Understanding Reactor Flow Patterns As discussed above, a RTD obtained using a nonreactive tracer may not uniquely represent the flow behavior within a reactor. For diagnostic and simulation purposes, however, tracer results may be explained by combining the expected tracer responses of ideal reactors combined in series, in parallel, or both, to provide an RTD that matches the observed reactor response. The most commonly used ideal models for matching an actual RTD are PRF and CSTR models. Figure 19-9 illustrates the responses of CSTRs and PFRs to impulse or step inputs of tracers. 

Simple combinations of reactor elements can be solved direc tly. Figure 23-8, for instance, shows two CSTRs in series and with recycle through a PFR. The material balances with an /i-order reaction / = /cC are... 

Consider the series combination of PFR and CSTR s shown in Figure 8.19. In terms of the fundamental design equations for these idealized... 

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. 

A particular vessel behavior sometimes can be modelled as a series or parallel arrangement of simpler elements, for example, some combination of a PFR and a CSTR. Such elements can be combined mathematically through their transfer functions which relate the Laplace transforms of input and output signals. In the simplest case the transfer function is obtained by transforming the linear differential equation of the process. The transfer function relation is... 

Erlang with time delay expC-t Vd + t2s/n)n The last item is of a PFR and an n-stage CSTR in series. More complex combinations are the subject of problems P5.01.33, P5.03.10, P5.03.02 and... 

Gibilaro [49] has considered a recycle model of the form of eqn. (60) where Gj (s) and G2(s) are general series combinations of PFR and equal size CSTR reactors and he gives sixteen references to published work involving more restricted forms of Gj (s) and G2 is). With an infinite choice over the forms of G (s) and G2(s) and the magnitude of R, the recycle model is seen to be the most flexible of all flow-mixing models. The performance of each specific form of Gj (s) as a potential reactor must be investigated individually in practice, the model is often reduced to a pure PFR element... 

In addition to the one-parameter models of tanks-in-series and dispersion, many other one-parameter models exist when a combination of ideal reactors is to model the real reactor. For example, if the real reactor were modeled as a PFR and CSTR in series, the parameter would be the fi action,/, of the total reactor volume that behaves as a CSTR Another one-parameter model would be the fi action of fluid that bypasses the ideal reactor. We can dream up many other situations which would alter the behavior of ideal reactors in a way that adequately describes a real reactor. However, it m be that one parameter is not sufficient to yield an adequate comparison between theoiy... 

To demonstrate these ideas, let us consider three different schemes of reactors in series two CSTRs, two PFRs, and then a combination of PFRs and CSTRs in series. To size these reactors, we shall use laboratory data that gives the reaction rate at different conversions. 

Now consider two CSTR reactors in series. The hatched area ABEE is proportional to the volume of the first one, while the area from BDCF to the second reactor. These volumes are distinct and their sum differs from that equivalent to a single CSTR that reaches the same final conversion, which is proportional to the area ACDF . Therefore, the combination of two CSTR reactors in series results in a reduction in total reactor volume, when targeting the same final conversion. There will be different average residence times in each reactor, increasing the final yield. Note that the combination of multiple CSTR reactors in series tends to approach a single PFR reactor. 

When a steady stream of fluid flows through a vessel, different elements of the fluid spend different times within it. The time spent by each fluid element can be identified by an inert tracer experiment, where a pulse or a step input of a tracer is injected into the flow stream, and the concentration of the pulse in the effluent is detected. As the reader may quickly infer, the tracer must leave the PFR undisturbed. On the other hand, a step pulse may give rise to an exponential distribution in a CSTR. In the beginning of this chapter, we already demonstrated that PFR behavior approaches that of a CSTR under infinite recycle. It follows that infinite CSTRs in series behave like a PFR. Thus, we conclude that any nonideal reactor can be represented as a combination of the PFR and MFR to a certain degree. First, let us show a representative pulse response curve for each of the ideal reactors in Figure 3.5. As seen in the figure, the response to a step input of tracer in a PFR is identical to the input function, whereas the response in a CSTR exhibits an exponential decay. The response curves as shown in Figure 3.5 are called washout functions. The input function of the inert tracer concentration [/] can be mathematically expressed as... 

Figure 10-12 The exit-age distribution for various combinations of PFRs and CSTRs in series.

---