PFR Alone

General spelll Possible spelling error new symbol name CApfr is similar to existing symbol CApfro . 

---

To summarize these last examples, we have seen that in the design of reactors that are to be operated at conditions (e.g.. temperature and initial concentration) identical to those at which the reaction rate data were obtained, we can size determine the reactor volume) both CSTRs and PFRs alone or in various combinations. In principle, it may be possible to scale up a laboratory-bench or pilot-plant reaction system solely from knowledge of as a function of X or Q. However, for most reactor systems in industry, a, scale-up proce.s.s cannot be achieved in this manner because knowledge of solely as a function of X is seldom, if ever, available under identical conditions. In Chapter 3. we shall see how we can obtain = yfX) from information obtained either in the laboratory or from the literature. This relationship will be developed in a two-step process. In Step 1, we will find the rate law that gives the rate as a function of concentration and in Step 2, we will find the concentrations as a function of conversion. Combining Steps 1 and 2 in Chapter 3. we obtain -/-.v =JiX). We can then use the method.s developed in this chapter along with integral and numerical methods to size reactors. 

Note that the auto-thermal PFR reactor (preheat of inlet reactant by the outlet reaction mixture) exhibits similar behaviour with CSTR. Even if the PFR alone is stable, the positive feedback of heat through the recovery heat exchanger makes the system unstable. The stabilisation can be obtained by introducing a heat source that keeps constant the feed reactor temperature (see also the Chapter 13). 

A reactor type constraint In this scenario, the construction of the AR is carried out by using PFRs alone. This approach is similar to that discussed in Chapters 2 and 3. This is done because situations might arise when only access or knowledge to a specific reactor type is available. We will be interested in how this constraint impacts construction of the AR, and ultimately how this influences what states are achieved. 

Different reactor networks can give rise to the same residence time distribution function. For example, a CSTR characterized by a space time Tj followed by a PFR characterized by a space time t2 has an F(t) curve that is identical to that of these two reactors operated in the reverse order. Consequently, the F(t) curve alone is not sufficient, in general, to permit one to determine the conversion in a nonideal reactor. As a result, several mathematical models of reactor performance have been developed to provide estimates of the conversion levels in nonideal reactors. These models vary in their degree of complexity and range of applicability. In this textbook we will confine the discussion to models in which a single parameter is used to characterize the nonideal flow pattern. Multiparameter models have been developed for handling more complex situations (e.g., that which prevails in a fluidized bed reactor), but these are beyond the scope of this textbook. [See Levenspiel (2) and Himmelblau and Bischoff (4).]... 

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... 

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... 

Reactant A decomposes according to a second order reaction. Two streams are to be processed, the first with Ca0 = 1 and = 1 the other with Ca0 = 2 and Vg = 2. For the first stream alone in a PFR the volume needed for 75% conversion is Vrl. What arrangement of streams and reactors will require the least total volume for conversion down to Ca = 0.25 ... 

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. 

So far we have been considering temperature ramping only, with flow rates held constant. In this section we consider the possibility of varying the flow rate during a run. The TS-CSTR turns out to be very simple to deal with, with marvelous possibilities for interactive control. The TS-PFR, as usual, requires much more careful consideration. In both the plug flow and CSTR reactors, flow scanning can be used alone or in combination with temperature scanning. 

Interestingly enough, this negative set of parameters fits one of the TS-PFR experiments from die cited work quite well. The data at a reactant composition where C0/02 = 0.06/0.04 is well fitted, as judged by the SSR, by the abnormal parameters of Chapter 9. At the same time, it was impossible to fit this set of parameters to all four TS-PFR experiments with anywhere near the sum of squares of residuals obtained using set 1. Even for the C0/02 = 0.06/0.04 data alone, a plot of error vs. rate clearly shows a systematic deviation of the calculated values from the experiment. Such distribution-of-errar plots are seldom reported in the literature. They should be, but the available data from a testing program, or even from a more fundamental study, is rarely adequate for this kind of consideration. Nonetheless, it must be understood that ... 

The heat of reaction developed by an exothermal reaction in an adiabatic reactor can save energy by means of a feed-effiuent-heat exchanger (FEME) device, as in the case of the HDA process. Even if PFR is stable as stand-alone unit, it may become unstable in such energy recovery loop. This problem will be analysed in Chapter 13 as an example of interaction between reactor design, energy saving and control. 

Another remarkable example is the recycle of energy developed in an adiabatic PFR for reactants preheating. Although the stand-alone PFR reactor is stable, in recycle it may become unstable. Consequently, control is needed to stabilise it. Moreover, the stabilisation depends on the design of the units involved in recycle. Section 13.6 develops more this issue. 

Such a feasibility constraint, characteristic to recycle systems, does not appear for stand-alone reactors. It can be explained by simple material balance reasons. The separation section does not allow the reactant to leave the process. Therefore, for a given a reactant input (Fa) either large reactor volume V) or fast kinetics ( CTref)) are necessary to consume entirely the reactant fed and avoid accumulation. These three variables are conveniently grouped in the plant Damkdhler number. The factor Zj accounts for the degradation of reactor performance due to impure reactant recycle. We note that a similar feasibility conditions also holds when the concentration of the reactant in the product stream is nonzero. Moreover, systems containing a purge stream of fixed flow rate have the same qualitative behaviour as the simple system described here. Finally, we remark that the condition 13.17 applies also to the system PFR -Separator - Recycle. 

The tubular reactor is so named because the physical configuration of the reactor is normally such that the reaction takes place within a tube or length of pipe. The idealized model of this type of reactor is based on the assumption that an entering fluid element moves through the reactor as a differentially thin plug of material that fills the reactor cross section completely. Thus, the terms piston flow or plug flow reactor (PFR) are often employed to describe the idealized model. The contents of a specific differential plug are presumed to be uniform in temperature and composition. This model may be used to treat both the case where the tube is packed with a solid catalyst (see Section 12.1) and the case where the fluid phase alone is present. 

When reaction and mixing are the only two processes available within a system, the AR may be constructed via combinations of CSTRs, PFRs, DSRs and mixing alone. No other reactor types are required to form the AR. 

Figure 6.6 shows an illustrative example of the AR boundary for three-dimensional Van de Vusse kinetics. The boundary structures have been exaggerated slightly to help emphasize certain characteristics for the discussions below." Elements of the AR boundary are composed of surfaces that are initiated from either mixing or reaction surfaces. Reaction surfaces themselves must produce extreme points (specifically protrusions) that result from PFR solution trajectories alone. Determination of the AR boundary structures is simplified greatly as a result we know that the final approach to any exposed point on the true AR boundary... 

Theorem 2 describes how the manifold of PFR trajectories, considered in theorem 1, may be accessed using these two reactors alone. In order for connectors to service the PFR manifold, they must also travel on the AR boundary. Furthermore, feed points to either these special CSTRs or DSRs must be taken from a point already situated on the AR boundary. 

Models of BCR can be developed on the basis of various view points. The mathematical structure of the model equations is mainly determined by the residence time distribution of the phases, the reaction kinetics, the number of reactive species involved in the process, and the absorption-reaction regime (slow or fast reaction in comparison to mass transfer rate). One can anticipate that the gas phase as well as the liquid phase can be either completely backmixed (CSTR), partially mixed, as described by the axial dispersion model (ADM), or unmixed (PFR). Thus, it is possible to construct a model matrix as shown in Fig. 3. This matrix refers only to the gaseous key reactant (A) which is subjected to interphase mass transfer and undergoes chemical reaction in the liquid phase. The mass balances of the gaseous reactant A are the starting point of the model development. By solving the mass balances for A alone, it is often possible to calculate conversions and space-time-yields of the other reactive species which are only present in the liquid phase. Heat effects can be estimated, as well. It is, however, assumed that the temperature is constant throughout the reactor volume. Hence, isothermal models can be applied. 

---