REACTOR PERFORMANCE WITH NONIDEAL FLOW

The TIS and DPF models, introduced in Chapter 19 to describe the residence time distribution (RTD) for nonideal flow, can be adapted as reactor models, once the single parameters of the models, N and Pe, (or DL), respectively, are known. As such, these are macromixing models and are unable to account for nonideal mixing behavior at the microscopic level. For example, the TIS model is based on the assumption that complete backmixing occurs within each tank. If this is not the case, as, perhaps, in a polymerization reaction that produces a viscous product, the model is incomplete. 

In addition to these two macromixing reactor models, in this chapter, we also consider two micromixing reactor models for evaluating the performance of a reactor the segregated flow model (SFM), introduced in Chapters 13 to 16, and the maximum-mixedness model (MMM). These latter two models also require knowledge of the kinetics and of the global or macromixing behavior, as reflected in the RTD. 

As a preliminary consideration for these two micromixing models, we may associate three time quantities with each element of fluid at any point in the reactor (Zwietering, 1959) its residence time, t, its age, ta, and its life expectancy in the reactor (i.e., time to reach the exit), te  

At the inlet of a reactor, ta = 0, and te = V, at the outlet, te = 0, and ta = t. In the SFM, fluid elements are grouped by age, and mixing of elements of various ages does not occur within the vessel, but only at the outlet ta s t. In the MMM Model, on the other hand, fluid elements are grouped by life expectancy, such that te = f. This important consideration is reflected in the detailed development of each model. 

In the following sections, we first develop the two macromixing models, TIS and DPF, and then the two micromixing models, SFM and MMM. 

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Chapter 20 Reactor Performance with Nonideal Flow... 

In this section, we apply the axial dispersion flow model (or DPF model) of Section 19.4.2 to design or assess the performance of a reactor with nonideal flow. We consider, for example, the effect of axial dispersion on the concentration profile of a species, or its fractional conversion at the reactor outlet. For simplicity, we assume steady-state, isothermal operation for a simple system of constant density reacting according to A - products. 

In this chapter, the Navier-Stokes equations have been solved in the actual 3D geometry of the reactor, thereby exploiting the full potential of the new approach, and detailed surface kinetics (Visconti et al., 2013) was implemented in the model with two main implications. On a more fundamental level, it demonstrates the power of the CAT-PP approach proposed here, which allows us to perform simulations of complex catalytic reactors characterized by nonideal flow fields, in which multistep reactions take place. On a more applied level, it allows us to assess the extent of the nonidealities of the simulated operando FTIR reaction cell, which is commercially available and is used by many research groups worldwide. This is extremely relevant especially for researchers who ivant to use the cell to collect quantitative information, since it will allow the verification of whether the cell is an ideal reactor or not. This latter hypothesis has been exploited, for example, by Visconti et al. (2013) to develop the first comprehensive and physically consistent spectrokinetic model for NOx storage... 

Equation 13.5-2 is the segregated-flow model (SFM) with a continuous RTD, E(t). To what extent does it give valid results for the performance of a reactor To answer this question, we apply it first to ideal-reactor models (Chapters 14 to 16), for which we have derived the exact form of E(t), and for which exact performance results can be compared with those obtained independently by material balances. The utility of the SFM lies eventually in its potential use in situations involving nonideal flow, wheic results cannot be predicted a priori, in conjunction with an experimentally measured RTD (Chapters 19 and 20) in this case, confirmation must be done by comparison with experimental results. 

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. 

At some point in most processes, a detailed model of performance is needed to evaluate the effects of changing feedstocks, added capacity needs, changing costs of materials and operations, etc. For this, we need to solve the complete equations with detailed chemistry and reactor flow patterns. This is a problem of solving the R simultaneous equations for S chemical species, as we have discussed. However, the real process is seldom isothermal, and the flow pattern involves partial mixing. Therefore, in formulating a complete simulation, we need to add many additional complexities to the ideas developed thus far. We will consider each of these complexities in successive chapters temperature variations in Chapters 5 and 6, catalytic processes in Chapter 7, and nonideal flow patterns in Chapter 8. In Chapter 8 we will return to the issue of detailed modeling of chemical reactors, which include all these effects. 

However, external mass transfer of hydrogen might play a role. An important conclusion was that the liquid distribution over the individual channels was not uniform. Of course, in the regular monolithic structure an initial maldistribution will be preserved throughout the reactor. Consequently, the conditions at the inlet of the reactor are critical. In this case nonuniform wetting of the channels was concluded to be the reason for the increase of process rate with increasing flow rate. In spite of this nonideality, the reactor performed satisfactorily Rates and selectivities were comparable to or higher than those reported... 

The reader may very well wonder what happened to the chemical reaction, since we have mostly discussed mixing models in this chapter without reference to reaction. In review of the various approaches to modeling nonideal flow effects on reactor performance, however, we find that in fact a number of these have already been treated, although perhaps with different applications in mind. The classes of reactor models we have treated are... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we discuss assume that the residence-time distribution function may be attributed to one or the other of these flow situations. The first class of nonideal flow conditions leads to the segregated flow model of reactor performance. This model may be used with the residence-time distribution function to predict conversion levels accurately for first-order reactions that occur isothermally (see Section 11.2.1). The second... 

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. 

Classical reactor analysis and design usually assume one of two idealized flow patterns plug flow or completely backmixed flow. Real reactors may approach one of these however, it is often the nonidealities and their interaction with chemical kinetics that lead to poor reactor design and performance (Levenspiel, 1998). Nonidealities include channeling, bypassing, and dead zones, among others. 

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