Plug-flow reactor nonideal

Another phenomenon of highly nonlinear systems is parametric sensitivity. We illustrated this behavior for the temperature profile in the plug-flow reactor. Nonideal distillation systems can also show this sensitivity. For example, in Fig. 6.5 a small change in the feed composition or organic reflux flow can dramatically change the composition ( and t emperature) profile in the column. Instead of a vinyl acetate-rich profile in the top section, a water-rich profile can be present. 

The asymptotic mean size is 59A reached at 0.5 m, assuming that the reactor is an ideal plug flow reactor where all the particles are the same size. To further this anal3 is, we can add dispersion into this reactor analysis and correct for the nonideal nature of this reactor. The dispersion analysis allows the prediction of the geometric standard deviation of the partice size distribution due to variations in the residence time distribution. 

In a large incinerator operating at high Reynolds number, about 1 % of the gas flows in the laminar boundary layer near the wall, where the average velocity and temperature are mueh lower than the midstream values. The conversion in the boundary layer is decreased, because the temperature effect is more important than the increase in residenee time. The predicted effect of boundary-layer flow on toluene destruction in a large incinerator is shown in Figure 6.9 [26]. There is little effect at 99% conversion, but for X > 0.999, the nonideal reactor requires more than twice the residence time of an ideal plug-flow reactor. 

The reactors with recycle are continuous and may be tanks or tubes. Their main feature is increasing productivity by returning part of unconverted reactants to the entrance of the reactor. For this reason, the reactant conversion increases successively and also the productivity with respect to the desired products. The recycle may also be applied in reactors in series or representing models of nonideal reactors, in which the recycle parameter indicates the deviation from ideal behavior. As limiting cases, we have ideal tank and tubular reactors representing perfect mixture when the recycle is too large, or plug flow reactor(PFR) when there is no recycle. 

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. 

Nonideal Plug-Flow Reactor via Transfer Matrix... 

As we shall see in Section 5.1.1.1, reactors can be classified as batch and continuous reactors, which in turn can be idealized as stirred-tank and plug-flow reactors. We shall not consider any nonideality of fluid flow behavior, since most industrial reactors exhibit only small deviations from ideality. One object of reactor design and operation is to ensure this. 

Experimental kinetic data always should be taken in a reactor that behaves as one of tiie tiiree ideal reactors. It is relatively straightforward to analyze the data from an ideal batch reactor, an ideal plug-flow reactor, or an ideal stirred-tank reactor. This is not the case if the reactor is nonideal, e.g., somewhere between a PFR and a CSTR. Characterizing the behavior of nonideal reactors is difficult and imprecise, as we shall see in Chapter 10. This can lead to major uncertainties in the analysis of data taken in nonideal reactors. 

Ideal flow is introduced in Chapter 2 in connection with the investigation of kinetics in certain types of ideal reactor models, and in Chapter 11 in connection with chemical reactors as a contrast to nonideal flow. As its name implies, ideal flow is a model of flow which, in one of its various forms, may be closely approached, but is not actually achieved. In Chapter 2, three forms are described backmix flow (BMF), plug flow (PF), and laminar flow (LF). 

Our treatment of Chemical Reaction Engineering begins in Chapters 1 and 2 and continues in Chapters 11-24. After an introduction (Chapter 11) surveying the field, the next five Chapters (12-16) are devoted to performance and design characteristics of four ideal reactor models (batch, CSTR, plug-flow, and laminar-flow), and to the characteristics of various types of ideal flow involved in continuous-flow reactors. Chapter 17 deals with comparisons and combinations of ideal reactors. Chapter 18 deals with ideal reactors for complex (multireaction) systems. Chapters 19 and 20 treat nonideal flow and reactor considerations taking this into account. Chapters 21-24 provide an introduction to reactors for multiphase systems, including fixed-bed catalytic reactors, fluidized-bed reactors, and reactors for gas-solid and gas-liquid reactions. 

The classic analysis of reactors involves two idealized flow patterns— plug flow and mixed flow. Though real reactors never fully follow these flow patterns, in many cases, a number of designs approximate these ideals with negligible error. However, deviation from ideality can be considerable. Typically, in a reaction vessel, we can have several immediate cases closer to plug or mixed flow. Of course, nonideal flow concerns all types of reactors used in heterogeneous processes, i.e. fixed beds, fluidized beds, continuous-flow tank reactors, and batch reactors. However, we will focus on fixed beds and batch reactors, which are the common cases. 

The mass balances [Eqs. (Al) and (A2)] assume plug-flow behavior for both the gas/vapor and liquid phases. However, real flow behavior is much more complex and constitutes a fundamental issue in multiphase reactor design. It has a strong influence on the reactor performance, for example, due to back-mixing of both phases, which is responsible for significant effects on the reaction rates and product selectivity. Possible development of stagnant zones results in secondary undesired reactions. To ensure an optimum model development for CD processes, experimental studies on the nonideal flow behavior in the catalytic packing MULTIPAK are performed (168). 

In earlier chapters, tubular reactors of several forms have been described (e.g., laminar flow, plug flow, nonideal flow). One of the most widely used industrial reactors is a tubular reactor that is packed with a solid catalyst. This type of reactor is called fixed-bed reactor since the solid catalyst comprises a bed that is in a fixed position. Later in this chapter, reactors that have moving, solid catalysts will be discussed. 

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 actual practice, a truly plug-flow or completely mixed-flow regime in a reactor is not attained because of longitudinal dispersion and nonideal mixing conditions. The equations reported here approximate the actual conditions in the held. 

The flows in PFR and MFR can be precisely deflned by simple mathematical eqnations, and the batch reactor is simply the batch version of the PFR. A reactor is now considered where the flow is between plug and fnlly mixed, i.e., a nonideal reactor. Two common examples of such partially mixed reactors are the recycle reactor and the tanks-in-series reactor. In the recycle reactor, part of the outlet from a reactor is recycled at the inlet, thns establishing some mixing between the downstream and the upstream fluids. In the tanks-in-series reactor, several mixed-flow reactors are operated in series. A single MFR is fully mixed, whereas an inflnite nnmber of MFRs (or a... 

In an ideal fixed-bed reactor, plug flow of gas is assumed. This is, however, not a good assumption for reactive solids, because the bed properties vary with position, mainly due to changing pellet properties (and dimensions in most cases), and hence the use of nonideal models is often necessary. The dispersion model, with all its limitations, is still the most practical one. The equations involved are cumbersome, but their asymptotic solutions are simple, particularly for systems... 

Yet another approach is based on the following simple notion. The characteristic C i) curve of Figure 4.4(b) for responses intermediate to the ideal limits is broader and more diffuse than that of the pulse input response for the plug-flow limit. This suggests that some type of diffusion or dispersion term might be incorporated into the basic plug-flow model to represent the effects of nonideal flows on reactor performance. 

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. 

It is shown that these deviations do not become large until n approaches, say, 2 to 4. From Figure 5.3 it is clear that for = 20 there are significant differences already between the residence-time and exit-age distributions of the nonideal reactor and the plug-flow case, yet the deficit in conversion is only 1.5%. The reason for this is a... 

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