CSTR and PFR

In the following example, we compare the sizes of a CSTR and a PFR required to achieve the same conversion. This is for normal kinetics. 

Calculate the ratio of the volumes of a CSTR and a PFR ( Vst pf) required to achieve, for a given feed rate in each reactor, a fractional conversion (/A) of (i) 0.5 and (ii) 0.99 for the reactant A, if the liquid-phase reaction A - products is (a) first-order, and (b) second-order with respect to A. What conclusions can be drawn Assume the PFR operates isothermally at the same T as that in the CSTR. 

This example can be solved using the E-Z Solve software (file exl7-2.msp) or as follows. The volumes for a CSTR and a PFR are determined from the material-balance equations  

In accordance with the discussion in Section 17.1.1, this is the same result as for Vst/Vbr given by equation 17.1-4 with a = 0 (i.e., with no down-time). 

The conclusions illustrated in Table 17.1 are (1) for a given order, n, the ratio increases as /a increases, and (2) for a given /A, the ratio increases as order increases. In any case, for normal kinetics, ST Vpp, since the CSTR operates entirely at the lowest value of CA, the exit value. (Levenspiel, 1972, p. 332, gives a more detailed graphical comparison for five values of n. This can also be obtained from the E-Z Solve software.) 

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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. 

Figure 23-7 illustrates the responses of CSTRs and PFRs to impmse or step inputs of tracers. 

The Module tunctionstorthe CSTR and PFR withthesespeciesandkineticsarewrittenin whattollowsas"cstrABD" and"pfrABD."... 

When a reactor is operating at steady state, the rate of energy release by chemical reaction must be equal to the sum of the rates of energy loss by convective flow and heat transfer to the surroundings. This statement was expressed in algebraic form in equations 10.3.4 and 10.4.6 for the CSTR and PFR, respectively. It will serve as the physical basis that we will use to examine the stability of various operating points. 

In the case of an LFR, it is important to distinguish between its use as a model and its occurrence in any actual case. As a model, the LFR can be treated exactly as far as the consequences for performance are concerned, but there are not many cases in which the model serves as a close approximation. In contrast, the CSTR and PFR models serve as useful and close approximations in many actual situations. 

We focus attention in this chapter on simple, isothermal reacting systems, and on the four types BR, CSTR, PFR, and LFR for single-vessel comparisons, and on CSTR and PFR models for multiple-vessel configurations in flow systems. We use residence-time-distribution (RTD) analysis in some of the multiple-vessel situations, to illustrate some aspects of both performance and mixing. 

Comparison of the CSTR and PFR models shows that the latter gives better performance. 

Since the values fj of the open end configuration do not fall within the yields of the CSTR and PFR, that boundary condition is not valid. The PFR and CSTR profiles are compared on the figure with the closed end result at Pe = 2. 

Figure 4.28 Effect of reactor type on the concentrations of Sj and A in the basic system. The reactor types are indicated at the top of each section. Data for fed-batch, CSTR, and PFR are taken from Figures 4.4, 4.14, and 4.16, respectively.

Thus, for known kinetics and a specified residence time distribution, we can predict the fractional conversion of reactant which the system of Fig. 9 would achieve. Recall, however, that this performance is also expected from any other system with the same E(t) no matter what detailed mixing process gave rise to that RTD. Equation (34) therefore applies to all reactor systems when first-order reactions take place therein. In the following example, we apply this equation to the design of the ideal CSTR and PFR reactors discussed in Chap. 2. The predicted conversion is, of course, identical to that which would be derived from conventional mass balance equations. 

The model is seen to be a series sequence of N equal sized CSTRs which have a total volume V and through which there is a constant flowrate Q. From the physical standpoint, it is natural to restrict N, the number of tanks, to integer values but, mathematically, this need not be the case. When N is considered as a continuous variable which lies between one and infinity, a model results which can be used to interpolate continuously between the bounds of mixing associated with the CSTR and PFR. For N less than unity, the model represents systems with partial bypassing [41]. For integral values of N eqn. (43) may be inverted directly (see Table 9, Appendix 1) to give... 

Determine the reactor volumes of CSTR and PFR required to attain a fractional conversion of A, = 0.95. 

Calculate the fractional conversions of A in the output stream from the CSTR and PFR. 

Material and energy balances for batch, CSTR and PFR are in Tables... 

Remark 4 The representation of the reactor units is based on CSTRs and PFRs which represent the two different extremes in reactor behavior. Note, however, that reactors with various distribution functions can be incorporated. 

Remark 1 The reactor network consists of ideal CSTRs and PFRs interconnected in all possible ways (see superstructure of reactor network). The PFRs are approximated as a cascade of equal volume CSTRs. The reactors operate under isothermal conditions. 

If pore diffusion is unimportant, i.e., if the effectiveness factor r is equal to 1, then with constant conversion policy both CSTR and PFR yield half-lives identical to Eq. (5.74) with arbitrary kinetics. With constant flow rate policy, the measured half-life is identical to that obtained through Eq. (5.74) only if the enzyme is saturated, i.e., [S] fCM, and the reaction is zeroth order. 

The building block of the superstructure representation is the generic reactor unit, which follows the shadow reactor concept (32). This generic unit is illustrated in Figure 4. Each generic unit consists of reactor compartments in each phase of the system, and each processes the reaction. The shadow reactor compartment assumes a state from the set of homogeneous reactors. The default units in the set include CSTRs and PFRs with side streams. The interface between a given pair of... 

Figure 2 Comparison of reactant exit concentration of a CSTR and PFR of the same residence time...

For complex catalytic reactions requiring numerical analyses, it is useful to write the material balance equations for flow reactors in terms of molecular flow rates per active site (/ /, = Fi/Sr), which are denoted as molecular site velocities. For batch reactors, the number of gaseous molecules per active site (Ns,i = Ni /.SR) is used. (These normalized quantities are typically of the order of unity.) The batch reactor, CSTR, and PFR material balance equations become the following ... 

Reactor Selection Ideal CSTR and PFR models are extreme cases of complete axial dispersion (De = oo) and no axial dispersion (De = 0), respectively. As discussed earlier, staged ideal CSTRs may be used to represent intermediate axial dispersion. Alternatively, within the context of a PFR, the dispersion (or a PFR with recycle) model may be used to represent increased dispersion. Real reactors inevitably have a level of dispersion in between that for a PFR or an ideal CSTR. The level of dispersion may depend on fluid properties (e.g., is the fluid newtonian),... 

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. 

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