DEVIATIONS FROM IDEAL REACTOR PERFORMANCE

CHAPTER 6 DEVIATIONS FROM IDEAL REACTOR PERFORMANCE 

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We shall consider three methods of estimating deviations from ideal reactor performance. The first method is to determine the actual RTD from experimental response data and then calculate the conversion by assuming the flow to be wholly segregated (Sec. 6-8). This model should be a good approximation, for example, for a tubular-flow reactor, where the flow is streamline. It would not describe a nearly ideal stirred-tank reactor, for here the fluid is nearly completely mixed when it enters the reactor. In this case no error is introduced by an approximation of the RTD, since the actual... 

Fig. 3-4 Deviations from ideal tubular-flow performance (a) longitudinal mixing due to vortices and turbulence, (b) laminar-flow (poor radial mixing), (c) bypassing in fixed-bed catalytic reactor...

The other two methods are subject to both these errors, since both the form ofi the RTD and the extent of micromixing are assumed. Their advantage is that they permit analytical solution for the conversion. In the axial-dispersion model the reactor is represented by allowing for axial diffusion in an otherwise ideal tubular-flow reactor. In this case the RTD for the actual reactor is used to calculate the best axial dififusivity for the model (Sec. 6-5), and this diffusivity is then employed to predict the conversion (Sec. 6-9). This is a good approximation for most tubular reactors with turbulent flow, since the deviations from plug-flow performance are small. In the third model the reactor is represented by a series of ideal stirred tanks of equal volume. Response data from the actual reactor are used to determine the number of tanks in series (Sec. 6-6). Then the conversion can be evaluated by the method for multiple stirred tanks in series (Sec. 6-10). 

Denbigh has provided useful guidelines for deciding when deviations (in conversion) from ideal tubular-flow performance are significant. In laminar flow, molecular diffusion in the axial direction causes little deviation if the reactor is reasonably long with respect to its diameter. Molecular diffusion in the radial direction may be important, particularly for gases, but it serves to offset the deviation from ideal performance caused by the velocity distribution. That is, radial diffusion tends to make the reactor... 

Aside from these large-scale, macroscopic deviations from ideal flow patterns, nonideal F t) responses can arise from diffusion within the reactor, from velocity profiles in tubular reactors that deviate from the plug-flow pattern, or from combinations of the two effects. It is the sum combination of all such processes that constitute what we have called mixing effects on chemical reactor performance In what follows, we will first attempt to develop a model adequate for the types of F t) and C t) behavior illustrated in Figures 4.3(b) and 4.4(b), then attempt to extend these ideas to modeling some of the more pathological behavior illustrated in Figure 5.1. 

Diagnosing the non-ideality does not stop with finding out if the reaction vessel is ideal or non-ideal. On knowing that the reactor is non-ideal, it is necessary to predict the impact of non-ideality on the reactor performance, which is the conversion achievable in the reactor. For this, the non-ideality has to be quantified first. Quantification of non-ideality involves assigning some kind of metric or measure for the extent of deviation from ideality. By comparing the RTD of the reaction vessel with the RTD of ideal reactors, one can get a qualitative idea about the gap or deviation between the real and the ideal reactors. Fiowever, one has to come up with an appropriate quantification of this gap in such a manner that this quantification will be useful for predicting the conversion achievable in the reactor. 

For a basic understanding of chemical reactor design, start with Sections 4.10.1 and 4.10.2, where different ideal and isothermal reactor types are introduced and the respective performance equations are derived. You should then study the behavior of real reactors (non-ideal flow and residence time distribution, Section 4.10.4) and the simplest model to account for deviations of real systems from ideal reactors, the tanks-in-series model (Section 4.10.5). 

The important fact for the practicing engineer to remember is that deviations from ideal behavior negatively impacts the performance of a reactor. Every attempt should be made to minimize or eliminate this effect. 

In formulating and using nonideal reactor models one should keep in mind our overall objective which is to build and operate an ideal reactor. Only ideal reactors are scaleable and their performance predictable. The nonideal flow models and experimental RTD curves are needed to assess deviations from ideality. When these deviations are small, a successful one-or-two parameter model can be constructed to interpret them. When deviations are large, one should concentrate on finding ways to diminish them rather than to interpret them. Multiparameter models are difficult to use and have very little value in scaleup. The exceptions are situations when the variations of some model parameters can be predicted independently based on first principles or based on accumulated experimental evidence. 

In the previous section we indicated how various mathematical models may be used to simulate the performance of a reactor in which the flow patterns do not fit the ideal CSTR or PFR conditions. The models treated represent only a small fraction of the large number that have been proposed by various authors. However, they are among the simplest and most widely used models, and they permit one to bracket the expected performance of an isothermal reactor. However, small variations in temperature can lead to much more significant changes in the reactor performance than do reasonably large deviations inflow patterns from idealized conditions. Because the rate constant depends exponentially on temperature, uncertainties in this parameter can lead to design uncertainties that will make any quantitative analysis of performance in terms of the residence time distribution function little more than an academic exercise. Nonetheless, there are many situations where such analyses are useful. 

The available models mostly refer to ideal reactors, STR, CSTR, continuous PFR. The extension of these models to real reactors should take into account the hydrodynamics of the vessel, expressed in terms of residence time distribution and mixing state. The deviation of the real behavior from the ideal reactors may strongly affect the performance of the process. Liquid bypass - which is likely to occur in fluidized beds or unevenly packed beds - and reactor dead zones - due to local clogging or non-uniform liquid distribution - may be responsible for the drastic reduction of the expected conversion. The reader may refer to chemical reactor engineering textbooks [51, 57] for additional details. 

We particularly like these three flow or reacting patterns because they are easy to treat (it is simple to find their performance equations) and because one of them often is the best pattern possible (it will give the most of whatever it is we want). Later we will consider recycle reactors, staged reactors, and other flow pattern combinations, as well as deviations of real reactors from these ideals. 

Deviation from the two ideal flow patterns can be caused by channeling of fluid, by recycling of fluid, or by creation of stagnant regions in the vessel. Figure 11.1 shows this behavior. In all types of process equipment, such as heat exchangers, packed columns, and reactors, this type of flow should be avoided since it always lowers the performance of the unit. 

The reactors treated in the book thus far—the perfectly mixed batch, the plug-flow tubular, and the perfectly mixed continuous tank reactors—have been modeled as ideal reactors. Unfortunately, in the real world we often observe behavior very different from that expected from the exemplar this behavior is tme of students, engineers, college professors, and chemical reactors. Just as we must learn to work with people who are not perfect, so the reactor analyst must learn to diagnose and handle chemical reactors whose performance deviates from the ideal. Nonideal reactors and the principles behind their analysis form the subject of this chapter and the next. 

In practice, especially in large-scale reactors, plug-flow or complete mixing are rarely achieved, and it is desirable to quantify the deviation from those idealized flow conditions. Also, when a chemical reactor does not perform at the expected level, it is necessary to identify the reason. A diagnostic method that is applied in such situations is based on measuring the residence time distribution (RTD) in the reactor. An inert tracer is injected at the reactor inlet, and its concentration at the reactor outlet is measured with time. By comparing the outlet concentration curve to the inlet concentration curve, the RTD curve of the reacting fluid in the reactor can be constructed [1,7,10,43]. 

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