Segregated flow

Example 12 Segregated Flow The pilot unit of Fig. 23-11 with n = 9.3 has... 

Segregated flow Occurs when all molecules that enter together also leave together. A state of aggregation is associated with every RTD. Each aggregate of molecules reacts independently of every other aggregate thus, as an individual batch reactor. 

Conversion in segregated flow is less than in plug flow and somewhat greater than in a CSTR battery with the same variance of the RTD. 

In contrast to segregated flow, in which the mixing occurs only after each sidestream leaves the vessel, under maximum mixedness mixing of all molecules having a certain period remaining in the vessel (the life expectation) occurs at the time of introduction of fresh material. These two mixing extremes—as late as possible and as soon as possible, both consistent with the same RTD—correspond to performance extremes of the vessel as a chemical reactor. 

FIG. 23-13 The two limiting flow patterns with the same RTD. a) Segregated flow, in which all molecules of any exit stream have the same residence time, (h) Maximum mixed flow, in which all molecules of an external stream with a certain life expectation are mixed with all molecules of the internal stream that have the same life expectation. 

Numerical solutions of the maximum mixedness and segregated flow equations for the Erlang model have been obtained by Novosad and Thyn (Coll Czech. Chem. Comm., 31,3,710-3,720 [1966]). A few comparisons are made in Fig. 23-14. In some ranges of the parameters n or fte ihe differences in conversion or reaclor sizes for the same conversions are substantial. On the basis of only an RTD for the flow pattern, perhaps only an average of the two calculated extreme performances is justifiable. 

Consider a segregated flow system as illustrated in Figure 9-2, with a known RTD, in whieh a reaetion A —> produets. The disappearanee rate of A is... 

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... 

In the segregated flow model the contents of the volume elements of the fluid do not mix with one another as they move through the reactor. Each element may be considered as a small closed system that moves through the reactor. The different systems spend varying amounts of time in the reactor, giving rise to the measured residence time distribution func-... 

To illustrate the nature of the limits that the segregated flow and mixing models place on the expected conversion level, it is useful to examine what happens to two elements of fluid that have the same volume V, but that contain different reactant concentrations C1 and C2. We may imagine two extreme limits on the amount of mixing that may occur. 

The basic premise of the segregated flow model is that the various fluid elements move through the reactor at different speeds without mixing with one another. Consequently, each little fluid element will behave as if it were a batch reactor operating at constant pressure. The conversions attained within the various fluid elements will be equal to those in batch reactors with holding times equal to the residence times of the different fluid elements. The average conversion level in the effluent is then given by... 

ILLUSTRATION 11.5 USE OF THE SEGREGATED FLOW MODEL TO DETERMINE THE CONVERSION LEVEL OBTAINED IN A NON-IDEAL FLOW REACTOR... 

Use the F(t) curve generated in Illustration 11.1 to determine the fraction conversion that will be achieved in the reactor if it is used to carry out a first-order reaction with a rate constant equal to 3.33 x 10 3 sec-1. Base the calculations on the segregated flow model. 

This result compares to a value of 0.666 predicted on the basis of the segregated flow model. Excellent agreement should be obtained for the first-order case if the dispersion parameter gives a good fit of the experimental F(t) curve. Agreement for reaction orders other than unity will not be nearly as good. 

All these values are close to those predicted by the segregated flow and dispersion models. 

Use the F(t) curve for two identical CSTR s in series and the segregated flow model to predict the conversion achieved for a first-order reaction with k = 0.4 ksec-1. The space time for an individual reactor is 0.9 ksec. Check your results using an analysis for two CSTR s in series. 

Segregated flow with reactive gas residence time curve. 

Quantitative molecular-property relationship Segregated-flow model Reduced folate carrier protein... 

K. S., A new physiologically based, segregated-flow model to explain route-dependent intestinal metabolism, Drug. Metab. Dispos. 2000, 28, 224-235. 

In this chapter, we focus on the characteristics of the ideal-flow models themselves, without regard to the type of process equipment in which they occur, whether a chemical reactor, a heat exchanger, a packed tower, or some other type. In the following five chapters, we consider the design and performance of reactors in which ideal flow occurs. In addition, in this chapter, we introduce the segregated-flow model for a reactor as one application of the flow characteristics developed. 

The chapter begins with a reiteration and extension of terms used, and the types of ideal flow considered. It continues with the characterization of flow in general by age-distribution functions, of which residence-time distributions are one type, and with derivations of these distribution functions for the three types of ideal flow introduced in Chapter 2. It concludes with the development of the segregated-flow model for use in subsequent chapters. 

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