Plug flow approaches

Having pointed out the modifications to be made to a design based upon the plug flow approach, it is salutary to note that axial dispersion is seldom of importance in fixed bed tubular reactors. This point is illustrated in Example 3.8. 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

Cyclohexane. The LPO of cyclohexane [110-82-7] suppUes much of the raw materials needed for nylon-6 and nylon-6,6 production. Cyclohexanol (A) and cyclohexanone (K) maybe produced selectively by using alow conversion process with multiple stages (228—232). The reasons for low conversion and multiple stages (an approach to plug-flow operation) are apparent from Eigure 2. Several catalysts have been reported. The selectivity to A as well as the overall process efficiency can be improved by using boric acid (2,232,233). K/A mixtures are usually oxidized by nitric acid in a second step to adipic acid (233) (see Cyclohexanol and cyclohexanone). 

The smaller reactor approaches plug-flow behavior and exhibits a large temperature gradient. In this case, external recycle provides the same degree of back-mixing as is provided by internal circulation in the larger diameter reactor. 

Fig. 8. Theoretical residence time distributions A, combustor style approach to plug flow B, turbulent bed (100% backmixed).

Example 5 Percent Approach to Equilibrium For a reversible reaction with rate equation r = L[A — (1 — A)Vl6], the size function kV,./V of a plug flow reactor will be found in terms of percent approach to equilibrium ... 

Often, complete mixing cannot be approached for economic reasons. Inactive or dead zones, bypassing, and limitations of energy input are common causes. Packed beds are usually predominantly used in plug flow reactors, but they may also have small mixing zones... 

The Colburn equation is based on complete mixing on the plate. For incomplete mixing, e.g., liquid approaching plug flow on the plate, Rahman and Lockett [I. Chem. E. Symp. Sei No. 61, 111 (1981)] and Lockett et al. [Chem. Eng. ScL, 38, 661 (1983)] have provided corrections for Eq. 14-44. Figure 14-26 and Eq. 14-94 may be used to evaluate the effects of entrainment on efficiency. 

The distribution of residence times of reactants or tracers in a flow vessel, the RTD, is a key datum for determining reactor performance, either the expected conversion or the range in which the conversion must fall. In this section it is shown how tracer tests may be used to estabhsh how nearly a particular vessel approaches some standard ideal behavior, or what its efficiency is. The most useful comparisons are with complete mixing and with plug flow. A glossary of special terms is given in Table 23-3, and major relations of tracer response functions are shown in Table 23-4. 

Plug flow is approached at low values of the dispersion coefficient or hi values or Peclet number. A criterion developed by Mears (Chem. Eng. Sci., 26, 1361 [1971]) is that conversion will be within 5 percent of that predicted by phig flow when... 

For conversions under about 95% of equilibrium, the performance of a five-stage CSTR battery approaches plug flow. 

Eigure 8-25 shows the RTD of different numbers of tanks in series. As the number increases, the behavior of the system approaches that of a plug flow reactor. 

A practical method of predicting the molecular behavior within the flow system involves the RTD. A common experiment to test nonuniformities is the stimulus response experiment. A typical stimulus is a step-change in the concentration of some tracer material. The step-response is an instantaneous jump of a concentration to some new value, which is then maintained for an indefinite period. The tracer should be detectable and must not change or decompose as it passes through the mixer. Studies have shown that the flow characteristics of static mixers approach those of an ideal plug flow system. Figures 8-41 and 8-42, respectively, indicate the exit residence time distributions of the Kenics static mixer in comparison with other flow systems. 

The yield that can be attained by a semibatch process is generally higher because the semibatch run starts from scratch, with maximum values of both variables Cg (o) = Cg and k] (o) = k . However, the yield from a continuous run in which t equals the batch time is governed by the product of Cg (t) and kj (t), so > and k (t) = k °. Because neither of these conditions is likely to be fulfilled completely, a continuous polymerization in a backmix reactor will probably always fail to attain the Y attainable by a semibatch reactor at the same t. However, several backmix reactors in series will approach the behavior of a plug flow continuous reactor, which is equivalent to a semibatch reactor. 

In our calculation we assume that the gas mixture approaches equilibrium under conditions where the pressure is constant. This situation corresponds, for instance, to a volume of gas moving through a plug flow reactor with a negligible pressure drop. (Note that if the ammonia synthesis were carried out in a closed system, the pressure would decrease with increasing conversion.)... 

A system has been constructed which allows combined studies of reaction kinetics and catalyst surface properties. Key elements of the system are a computer-controlled pilot plant with a plug flow reactor coupled In series to a minireactor which Is connected, via a high vacuum sample transfer system, to a surface analysis Instrument equipped with XFS, AES, SAM, and SIMS. When Interesting kinetic data are observed, the reaction Is stopped and the test sample Is transferred from the mlnlreactor to the surface analysis chamber. Unique features and problem areas of this new approach will be discussed. The power of the system will be Illustrated with a study of surface chemical changes of a Cu0/Zn0/Al203 catalyst during activation and methanol synthesis. Metallic Cu was Identified by XFS as the only Cu surface site during methanol synthesis. 

If the process is carried out in a stirred batch reactor (SBR) or in a plug-flow reactor (PFR) the final product will always be the mixture of both products, i.e. the selectivity will be less than one. Contrary to this, the selectivity in a continuous stirred-tank reactor (CSTR) can approach one. A selectivity equal to one, however, can only be achieved in an infinite time. In order to reach a high selectivity the mean residence time must be very long, and, consequently, the productivity of the reactor will be very low. A compromise must be made between selectivity and productivity. This is always a choice based upon economics. 

In special cases, the departure from ideal single stirred-tank mixing behaviour is intended, e.g., when a series of stirred tanks are used to approach that of plug-flow, as shown in Fig. 3.26. 

Note that as Pe becomes large, the conditions approach plug flow, and as Pe approaches zero conditions approach perfect mixing. 

---