Segregated and Maximum Mixed Flows

In some important cases, limiting models for chemical conversion are the segregated flow model represented by the equation 

Numerical integration of the equation is sufficiently accurate by starting at (x , — 4) and proceeding to t, = 0 at which time the 

With a given RID the two models may correspond to upper and lower limits of conversion or reactor sizes for simple rate equations thus 

The data also can be rearranged to show the conversion limits for a reactor of a given size. 

When the rate equation is complex, the values predicted by the two models are not necessarily limiting. Complexities can arise from multiple reactions, variation of density or pressure or temperature, incomplete mixing of feed streams, minimax rate behavior as in autocatalytic processes, and possibly other behaviors. Sensitivity of the reaction to the mixing pattern can be estabhshed in such cases, but the nature of the conversion limits will not be ascertained. Some other, possibly more realistic models wiU have to be devised to represent the reaction behavior. The hterature has many examples of models but not really any correlations (Naumann and Bufiham, 1983 Wen and Fan Westerterp et al., 1984). 

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Relative sizes of vessels with segregated and maximum mixed flows of the same variance are derived over a range of parameters in some of the problems, particularly P5.07.06. 

The mixing pattern in an n-stage CSTR battery is intermediate between segregated and maximum mixed flow and is characterized by residence time distribution with variance o2 = 1/n. Conversion in the CSTR battery is found by solving n successive equations... 

Nonideal Flow Patterns 556 Residence Time Distribution 556 Conversion in Segregated and Maximum Mixed... 

Figure 8.16 Alternate represeritation of completely segregated flow (A), maximum mixed flow(B), and an intermediate mixing pattern (C).

The residence time distribution measures features of ideal or nonideal flows associated with the bulk flow patterns or macromixing in a reactor or other process vessel. The term micromixing, as used in this chapter, applies to spatial mixing at the molecular scale that is bounded but not determined uniquely by the residence time distribution. The bounds are extreme conditions known as complete segregation and maximum mixedness. They represent, respectively, the least and most molecular-level mixing that is possible for a given residence time distribution. 

Figure 17.2. Relative volumes of maximum-mixed and segregated flow reactors with the same RTDs identified by n = 1 /< , as a function of conversion for second- and half-order reactions. For first-order reactions the ratio is unity throughout.

In contrast to segregated flow, in which the mixing occurs only after each side stream leaves the vessel, under maximum mixedness flow, mixing of all molecules having a certain life expectancy occurs at the time of introduction of fresh material. These two mixing extremes—as late as possible and as soon as possible, both having the same RTD— correspond to extremes of reactor performance. 

FIG. 23-14 Comparison of maximum mixed, segregated, and plug flows, (a) Relative volumes as functions of variance or n, for several reaction orders. Q ) Second-order reaction with n = 2 or 3. (c) Second-order, n = 2. d) Second-order, n = 5. 

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