Residence cascade CSTR

The physical situation in a fluidized bed reactor is obviously too complicated to be modeled by an ideal plug flow reactor or an ideal stirred tank reactor although, under certain conditions, either of these ideal models may provide a fair representation of the behavior of a fluidized bed reactor. In other cases, the behavior of the system can be characterized as plug flow modified by longitudinal dispersion, and the unidimensional pseudo homogeneous model (Section 12.7.2.1) can be employed to describe the fluidized bed reactor. As an alternative, a cascade of CSTR s (Section 11.1.3.2) may be used to model the fluidized bed reactor. Unfortunately, none of these models provides an adequate representation of reaction behavior in fluidized beds, particularly when there is appreciable bubble formation within the bed. This situation arises mainly because a knowledge of the residence time distribution of the gas in the bed is insuf-... 

The polymerization time in continuous processes depends on the time the reactants spend in the reactor. The contents of a batch reactor will all have the same residence time, since they are introduced and removed from the vessel at the same times. The continuous flow tubular reactor has the next narrowest residence time distribution, if flow in the reactor is truly plug-like (i.e., not laminar). These two reactors are best adapted for achieving high conversions, while a CSTR cannot provide high conversion, by definition of its operation. The residence time distribution of the CSTR contents is broader than those of the former types. A cascade of CSTR s will approach the behavior of a plug flow continuous reactor. 

Consider a reactor network that consists of a cascade of two weU-stirred reactors that differ in size but behave as ideal CSTRs. Prior to initiation of a trial designed to determine the average residence time for the cascade, the reactors are operating at steady state at a volumetric flow rate V. The volumes of the first and second CSTRs are and respectively. 

N, of units in a series (NCSTR). As with the CSTR mode of operation, the concentration profile in each tank is uniform in both space and time. However, over the entire length of the cascade, the space/concentration profile will show a typical step function curve. It is not difficult to see that this spatial behavior approximates that of a CPFR. As a rule, a cascade with N > 5 can actually be used as a process engineering substitute for a CPFR (see residence time distribution. Sect. 3.3.1). 

In Case B, the total residence time of the cascade of reactors is kept constant. Let us distribute this total over our reactors (see Fig. 8.3, Case B). For the CSTR, the residence time of every reactor is t/A, so Dajv = Da/A, where r and Da relate to the residence time and Damkohler number of the cascade of reactors/zones and Da / is the Damkohler number for reactor/zone A. Hence, in the second column of Table 8.1, Da is replaced with Da/A. Then,... 

The tanks-in-series model considers the actual reactor as a system of N identical CSTRs with the same total volume as the actual reactor. The Pg and Eg functions of a cascade are shown in Figure 4.10.49 and are given by (with the dimensionless time 0=t/r and the mean residence time T = Vr/V = NVtanit/T) ... 

It follows from calculations in the proceeding section that the necessa reactor volume of a continuous stirred tank reactor (CSTR) needed to obtain a high degree of conversion is relatively large. A so-called "cascade of CSTR s (a number of CSTR s in series) can be a practical alternative. Let us assume that we replace one CSTR with volume V by a series of n equal CSTR s that have the same total volume. The mean residence time in each reactor is then x/n. We can calculate the relative degree of conversion in each consecutive reactor, for any reaction order, with eq. (3.49), where X is replaced by x/n. We find then for... 

The relation between the degree of conversion of a first order reaction, the number of CSTR s in a cascade, and the total mean residence time is shown in figure 3.8. We see that particularly for high desired degrees of conversion a cascade of several CSTR s appears attractive. 

Assume that a certain first order reaction (constant density) requires a mean residence time in one CSTR of 3 hours (10,800 s) to reach a degree of conversion of 0.99. If we would use three CSTR s in series, we find from equations (3.38) and (3.51) that the total mean residence time of the cascade to reach 0.99 conversion is only 1193 s, or approximately 20 min. This means that the total reactor volume needed to obtain the desired conversion is in this case 9 times smaller This ratio increases as the desired degree of conversion is higher. 

Axial mixing in reactors with predominant axial flow can also be modelled by a cascade of a large number of perfectly mixed CSTR s, as described in section 7.1.3. It appears that the residence time distribution (RTD) of a tubular reactor with axial mixing can approach the RTD of a cascade of N perfectly mixed CSTR s when the following condition applies... 

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