Nonideal flow

In this chapter, we consider nonideal flow, as distinct from ideal flow (Chapter 13), of which BMF, PF, and LF are examples. By its nature, nonideal flow cannot be described exactly, but the statistical methods introduced in Chapter 13, particularly for residence time distribution (RTD), provide useful approximations both to characterize the flow and ultimately to help assess the performance of a reactor. We focus on the former here, and defer the latter to Chapter 20. However, even at this stage, it is important to realize that ignorance of the details of nonideal flow and inability to predict accurately its effect on reactor performance are major reasons for having to do physical scale-up (bench — pilot plant - semi-works - commercial scale) in the design of a new reactor. This is in contrast to most other types of process equipment. 

We first describe features of nonideal flow qualitatively, and then in terms of mixing aspects. For the rest of the chapter, we concentrate on its characterization in terms of RTD. This involves (1) description of the experimental measurement of RTD functions (.E, F, IF), and development of techniques for characterizing nonideal flow and (2) introduction of two simple models for nonideal flow that can account for departures from ideal flow. 

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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).]... 

These two types of deviations occur simultaneously in actual reactors, but the mathematical models we will develop 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... 

ILLUSTRATION 11.6 USE OF THE DISPERSION MODEL TO DETERMINE THE CONVERSION LEVEL OBTAINED IN A NONIDEAL FLOW REACTOR... 

A stirred-tank flow reactor may be single-stage or multistage. As an ideal backmix flow reactor, it is referred to as a CSTR or multistage CSTR this is treated in Chapter 14. Nonideal flow effects are discussed in Chapter 20. 

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). 

In general, each form of ideal flow can be characterized exactly mathematically, as can the consequences of its occurrence in a chemical reactor (some of these are explored in Chapter 2). This is in contrast to nonideal flow, a feature which presents one of the major difficulties in assessing the design and performance of actual reactors, particularly in scale-up from small experimental reactors. This assessment, however, may be helped by statistical approaches, such as provided by residence-time distributions. It... 

The characterization of flow by statistical age-distribution functions applies whether the flow is ideal or nonideal. Thus, the discussion in this section applies both in Section 13.4 below for ideal flow, and in Chapter 19 for nonideal flow. 

Figure 13.2 Exit-age distribution function E(t) for arbitrary (nonideal) flow showing significance of area under the E(t) curve...

Figure 13.3 Typical form of F for arbitrary (nonideal) flow...

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. 

Figure 19.1 Examples of nonideal flow in stirred-tank and packed-bed vessels...

Figure 19.2 Effect of some features of nonideal flow on E(t)...

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