Nonideal reactors

Various types of industrial reactors may occur in different phases as applications and desired properties of the final product, for example, the fixed bed, fluidized bed, slurry bed, and bed phase reactors. In fluidized bed reactors as in slurry bed, the solid (catalyst) is composed of very small particles and moving along the reactor. The fluid flow over these reactors is complex. In these systems, the flow of the fluid phase is not homogeneous and there are large deviations from the ideal behavior of a CSTR or plug flow reactor (PFR), characterizing them in nonideal reactors. 

On the other hand, there are exceptional advantages in these reactors, such as improved heat and mass transfer, increased contact between the reactants, and mainly lower contact time reaction. 

As in ideal reactors, the kinetics and reaction conditions are similar. However, the distribution of products is quite different and to correlate them with the experiments, it requires a more detailed study of the conditions of nonideality, for example, interfacial and surface phenomena, heat and mass transfer, and flows types. These phenomena characterize the axial and radial dispersion, caused by diffusion and convection. 

The flows in catalyst beds are different from those presented in the fixed bed, fluidized bed, or slurry. The flows are random they depend on empty spaces within a fixed bed, through which the gases or fluids flowing, and to the apparent velocity of the solid within a fluidized bed/slurry. These phenomena are characteristic of the nonideal reactors. 

There are two ways that allow us to characterize the nonideal reactors  

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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).]... 

Note if K=0, the program generates a tracer step-response curve for the nonideal reactor. 

We win develop mass balances in terms of mixing in the reactor. In one limit the reactor is stirred sufficiently to mix the fluid completely, and in the other limit the fluid is completely unmtxed. In any other situation the fluid is partially mixed, and one cannot specify the composition without a detailed description of the fluid mechanics. We wiU consider these nonideal reactors in Chapter 8, but until then all reactors wiU be assumed to be either completely mixed or completely unmixed. 

We will not attempt to solve the preceding equations except in a few simple cases. Instead, we consider nonideal reactors using several simple models that have analytical solutions. For this it is convenient to consider the residence time distribution (RTD), or the probability of a molecule residing in the reactor for a time f. 

Figure S-13 Residence time dstiibutions for the nonideal reactors considered in titis chapter.

The next level of sophistication is to use the nonideal reactor models developed in this chapter. These are fairly simple to calculate, and the results tell us how serious these nonideaUties might be. 

For any more complex flow pattern we must solve the fluid mechanics to describe the fluid flow in each phase, along with the mass balances. The cases where we can still attempt to find descriptions are the nonideal reactor models considered previously in Chapter 8, where laminar flow, a series of CSTRs, a recycle TR, and dispersion in a TR allow us to modify the ideal mass-balance equations. 

The age of a fluid element is defined as the time it has resided within the reactor. The concept of a fluid element being a small volume relative to the size of the reactor yet sufficiently large to exhibit continuous properties such as density and concentration was first put forth by Danckwerts in 1953. Consider the following experiment a tracer (could be a particular chemical or radioactive species) is injected into a reactor, and the outlet stream is monitored as a function of time. The results of these experiments for an ideal PFR and CSTR are illustrated in Figure 8.2.1. If an impulse is injected into a PFR, an impulse will appear in the outlet because there is no fluid mixing. The pulse will appear at a time ti = to + t, where t is the space time (r = V/v). However, with the CSTR, the pulse emerges as an exponential decay in tracer concentration, since there is an exponential distribution in residence times [see Equation (3.3.11)]. For all nonideal reactors, the results must lie between these two limiting cases. 

Concentrations of tracer species using an impulse input, (a) PFR (ti = t(, + t). (b) CSTR. (c) Nonideal reactor. 

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. 

The basic ideas or concepts used to characterize and model nonideal reactors are really few in munber. Before proceeding further, a few selected examples of nonideal mixing and modeling from the author s experiences will be presented. 

Three concepts used to describe nonideal reactors appear in the examples the distribution of residence times in the system, die quality of mixing, and the model used to describe die system. All three of these concepts are considered when describing deviations from the mixing patterns assumed in ideal reactors. The three concepts can be regarded as characteristics of the mixing in nonideal reactors. 

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