Reactor Scale Balance and Species Continuity

1 Reactor Scale Balance and Species Continuity Equations 

Determination of the spatial dependence of the (one-point joint velocity-composition) micro-PDF, f, or its moments is often difficult, and in many cases only the distribution of properties (pA in the entire volume, that is, at the reactor scale, is desired. The volume integral or macro-average of (12.4.1-11) for statistically stationary flow is  

The volume averaged distribution function or macro-PDF, I, also called the internal distribution function, is given by  

The statistical description of the macro-scale behavior (12.6.1-2) involves averaging over all macro-scales, noted, and implies spatial sampling over the entire reactor volume V. This is different from the averaging introduced in Sections 12.4 and 12.5 which sampled only over all micro-scales. As a consequence, the macro-PDF, I, is not local, i.e., does not depend on the spatial coordinates z, in contrast to the micro-PDF. Hence, extracting local information on mixing from a RTD is not possible. The first term on the left-hand side of (12.6.1-1) represents any flow into or out of the macroscopic volume. The derivation is similar to that used in Chapter 7 and is given in Himmelblau and Bischoff [1968]. 

By sampling over all micro- and macro-scales, the averages or integrals in (12.6.1-1) and (12.6.1-2) account for the combined effects of micro- and macro-mixing on the reactor-scale behavior. Only in particular cases, specific information on micro- or macro-mixing can be associated with or extracted from / (see Example 12.6.1.A). This will be shown to be of importance for the applicability of RTD to cases in which both flow and reaction occur (see Section 12.6.4). The solution of (12.6.1-1) requires closure models for /,  

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