Uses of a PFR

The PFR model is frequently used for a reactor in which the reacting system (gas or liquid) flows at relatively high velocity (high Re, to approach PF) through an otherwise empty vessel or one that may be packed with solid particles. There is no device, such as a stirrer, to promote backmixing. The reactor may be used in large-scale operation 

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In Table 18.1, values of RcBmax are given for K - 0, K = 1 and For this type of network, with normal kinetics, the performance of a CSTR cannot surpass that of a PFR that is, use of a PFR leads to a greater cB max at a smaller However, if the CSTR is staged, its performance can be closer to that of a PFR. 

Macro- and miniemulsion polymerization in a PFR/CSTR train was modeled by Samer and Schork [64]. Since particle nucleation and growth are coupled for macroemulsion polymerization in a CSTR, the number of particles formed in a CSTR only is a fraction of the number of particles generated in a batch reactor. For this reason, their results showed that a PFR upstream of a CSTR has a dramatic effect on the number of particles and the rate of polymerization in the CSTR. In fact, the CSTR was found to produce only 20% of the number of particles generated in a PFR/CSTR train with the same total residence time as the CSTR alone. By contrast, since miniemulsions are dominated by droplet nucleation, the use of a PFR prereactor had a negligible effect on the rate of polymerization in the CSTR. The number of particles generated in the CSTR was 100% of the number of particles generated in a PFR/CSTR train with the same total residence time as the CSTR alone. 

Thus, for Michaelis-Menten kinetics, a PFR type reactor, predominantly a packed-bed reactor (PBR, Figure 9.1b) is preferred to the continuous stirred-tank reactor (CSTR, Figure 9.1a), since it requires less biocatalyst to reach the same level of conversion. In this case, ideal reactors are those with high space time/yield to increase the efficiency of the transformation. PBRs with immobilized catalyst have a clear advantage in that voidage is low 34% compared to over 80-90% for CSTR [35]. However, if pH control is required, the use of a PFR is not advised. In case of substrate inhibition, a CSTR (Figure 9.1a) operated at high conversion is to be preferred. On the other hand, when product inhibition is pronounced, a... 

The performance of the laminar flow reactor is appreciably worse than that of a PFR, but remains better than that of a CSTR (which gives T=0.5 for kt= 1). The computed value of 0.4432 may be useful in validating more complicated codes that include diffusion. 

To characterize the performance of a PFR subject to an axial gradient in temperature, the material and energy balances must be solved simultaneously. This may require numerical integration using a software package such as E-Z Solve. Example 15-4 illustrates the development of equations and the resulting profile for fA with respect to... 

In a chemical process, the use of recycle, that is, the return of a portion of an outlet stream to an inlet to join with fresh feed, may have the following purposes (1) to conserve feedstock when it is not completely converted to desired products, and/or (2) to improve the performance of a piece of equipment such as a reactor. It is the latter purpose that we consider here for a PFR (the former purpose usually involves a separation process downstream from a reactor). For a CSTR, solution of problem 14-26 shows that recycling alone has no effect on its performance, and hence is not used. However, it provides a clue as to the anticipated effect for a PFR. The recycle serves to back-mix the product stream with the feed stream. The effect of backmixing is to make the performance of a PFR become closer to that of a CSTR. The degree of backmixing, and... 

For an autocatalytic reaction, Example 15-10 shows that a recycle PFR operating with an optimal value of R requires the smallest volume for the three reactor possibilities posed. (In the case of a PFR without recycle, the size disadvantage can be offset at the expense of maintaining a sufficient value of cBo (in the feed), but this introduces an alternative disadvantage.) A fourth possibility exists for an even smaller volume. This can be realized from Figure 15.8 (although not shown explicitly), if the favorable characteristics of both normal and abnormal kinetics are used to advantage. Since this involves a combination of reactor types, we defer consideration to Chapter 17. 

For a relatively small amount of dispersion, what value of Pei would result in a 10% increase in volume (V) relative to that of a PFR (Vpf) for the same conversion (/a) and throughput (q) Assume the reaction, A - products, is first-order, and isothermal, steady-state, constant-density operation and the reaction number, Mai = at, is 2.5. For this purpose, first show, using equation 20.2-10, for the axial-dispersion model with relatively large Per, that the % increase s 100(V - V pfWpf = 100MAi/Pei. 

The specific rate is k = 5.2 1 iter/gmol-hr at 82 C. Equal molal quantities the reactants are to be used. They are supplied as aqueous solutions, bicarbonate as 15 wt% and the chlorhydrin as 30 wt%. Production of glycol to be 20 kg/hr at 95% conversion. Specific gravity of the feed mixture 1.02. Find the required reactor volumes of a PFR and of a CSTR. 

Not always is the PFR a side undesired reaction in polymers. In some cases, it has been used for practical purposes like selective image development [248], Another important use of the PFR is the photostabilization of polymers [249]. Aromatic esters and polyesters are sometimes mixed with other polymers in order to protect them from light. This delays aging of the polymer because the light is... 

CSTRs in series. The latter is often normalised by dividing by the volume of an ideal PFR required to perform the same duty. Different charts are required for each reaction rate expression. Figure 12 refers specifically to first-order kinetics, but other charts are available in, for instance refs. 17, 18 and 26. Figure 12 re-emphasises many of the points we have made already. In particular, the performance of the N CSTRs in series tends to that of a PFR of the same total volume as N becomes large and the PFR volume required to achieve a certain conversion for a first-order reaction is always smaller than the total volume of any array of CSTRs which perform the same duty. Charts in the form of Fig. 12 are particularly useful when performing approximate design calculations. 

Imagine a first-order reaction taking place in such a system under conditions where rk, i.e. VkjQ, is 10 and R is 5. Using the technique previously adopted in Sect. 5.1 and outlined in Appendix 2, we can readily calculate that this system would achieve 96.3% conversion of reactant. Under these conditions, the recycle reactor volume turns out to be 3.03 times that of an ideal PFR required for the same duty. This type of calculation allows Fig. 14 to be constructed this is similar in form to Fig. 12, but lines of constant for the tanks-in-series model have been replaced by lines of constant recycle ratio for the recycle model. From a size consideration alone, the choice of a PFR recycle reactor is not particularly... 

Using the approximation of a PFR with a cascade of equal volume CSTRs in series, we allow for all feed streams (i.e., fresh feeds, streams from the outlets of other reactors) to be distributed to any of the CSTRs that approximate the PFR unit. In addition, potential by-passes around each CSTR that approximates the PFR unit are introduced so as to include cases in which full utilization of these CSTRs is not desirable. 

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),... 

As discussed in Fig. 19-2, for a given conversion, the reactor residence time (or reactor volume required) for a positive order reaction with dispersion will be greater than that of a PFR. This need for a longer residence time is illustrated for a first-order isothermal reaction in a PFR versus an ideal CSTR using Eqs. (19-13) and (19-19). 

Next use this polynomial and an ODE solver to plot fte conversion down Uie length (i.e., volume) of a PFR and find the CSTR volume for 80% converison for an entering molar flow rate of 5 mol/s. 

Note that some might interpret the statement of this part to mean the use of one PFR and one CSTR of equal, but unspecified, volumes, to reach the original goal of 95 % conversion. The result for this case is a volume of 3.3 m for each reactor. 

From Figure 2-6. wc note a very important observation The total volume to achieve 80% conversion for five CSTRs of equal volume in series is roughly the same as the volume of a PFR, As wc make the volume of each CSTR smaller and increase the number of CSTRs, the total volume of the CSTRs in series and the volume of the PFR will become identical. That is, we can model a PFR with a large number of CSTRs in series. This concept of using many CSTRs in series to model a PFR will be used later in a number of situations, such as modeling catalyst decay in packed-bed reactors or transient heat effects in PFRs. 

As we can see, the selectivity reaches a maximum at a concentration Cv Because the concentration changes down the length of a PFR. we cannot operate at this maximum. Consequently, we will use a CSTR and design it to operate at this maximum. To find the maximum. C, we differentiaie Sb y wn C, set the derivative to zero, and solve for C. That is. 

Use scaleable heat transfer The feed flow rate scales as S and a cold-feed stream removes heat from the reaction in direct proportion to the flow rate. If the energy needed to heat the feed from Tin to Tout can absorb the reaction exotherm, the heat balance for the reactor can be scaled indefinitely. Cooling costs may be an issue, but there are large-volume industrial processes that have Tin -40°C and Tout 200°C. Obviously, cold feed to a PFR will not work since the reaction will not start at low temperatures. Injection of cold reactants at intermediate points along the length of a PFR is a possibility but lowers conversion. In the limiting case of many injections, this will reduce reactor performance to that of a CSTR. See Section 3.5 on transpired-wall reactors. 

Finite difference methods are implemented in gPROMS (2001). Aspen Dynamics uses the third approach. Care should be paid to a convenient description of a PFR. A number of ten CSTR s is sufficient, but when the temperature variation is highly nonlinear, the use of several PFR reactors in series is recommended. 

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