CSTR and PFR in Series

For the specified final conversion Xaj, the conversion Xai achieved in the PFR is calculated such that the space times for both the reactors are equal, that is. 

For a first-order irreversible reaction A-PFR connected in series, show that the overall conversion is independent of which reactor precedes when the reactor volumes are equal. 

Graphical method for calculation of x ffor CSTR followed by PFR. 

Consider the PFR followed by the CSTR, the rate equation for the first-order reaction is 

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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. 

The order of a CSTR and PFR in series is investigated for a third-order reaction. [2nd ed. PI3-10]... 

Figure 13-19 Real reaclor modeled as a CSTR and PFR in series.

C) Using the two preceding simulations, link them to form a new reactor consisting of a CSTR and PFR in series. To integrate the PFR equation initial conditions are needed at the inlet. Let each initial condition needed for the PFR concentrations be given as the exit concentrations from the CSTR. 

Step 5 A PFR trajectory is drawn from the position where the mixing line meets the CSTR trajectory. When this PFR trajectory is convex, it extends the previous AR to form an expanded candidate AR. Return to Step 2. Otherwise, repeat the procedure from Step 3. As shown in Figure 6.12, the PFR trajectory (line 7) leads to a convex attainable region. The boundaries of the region are (a) the linear arc (line 5) from A to C, which represents a CSTR with a bypass stream (b) the point C, which represents a CSTR and line 7 from C to B, which represents a CSTR followed by a PFR in series. Note that the maximum composition of CO is obtained at point D, using a CSTR and PFR in series. The maximum selectivity, defined by the ratio of CO/CH4, is also achieved at point D, where the ratio is 0.47, as compared to point C, where the ratio is only 0.30. ... 

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. 

The schemes (a) and (b) involving CSTR and PFR in series are used when it is required to increase the final conversion. Note that the reaction rate is an important parameter in this analysis. In case (a) PFR + CSTR, first consider the PFR. As the conversion increases, the reaction rate decreases along the PFR. Therefore, it would take a long time to achieve the desired high conversion. Therefore, a CSTR is connected in series to complete this reaction. In case (b) CSTR + PFR, first consider the CSTR. Only a limited conversion may be obtained at the outlet of the CSTR and of course this is dependent on the space velocity of the reactor. In this case, a PFR is then connected in series to achieve higher conversions. 

The final sequences we shall consider are combinations of CSTRs and PFRs in series. An industrial example of reactors in series is shown in the photo in Figure 2-9. This. sequence is used to dimerize propylene (A) into isohexanes (B), e.g.. 

When a brand-new reactor system is being designed, it is tmcommon (but not impossible) to encounter a situation that calls for using CSTRs and PFRs in series. However, if existing equipment is being used to satisfy an interim need, to establish production quickly, or to expand an existing plant, there may be good reason to consider such combinations. 

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. 

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