Advances in Chemical Engineering, Vol. 24 by James Wei (Ed.)

By James Wei (Ed.)

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Since the ^ system is of lower order, there must exist couples of different m’s, m l and m2, which result in the same m^, say, = . Such couples will be called L-equivalent, and indicated with the notation m l = m2. Now one may want to impose another constraint, namely, that each of the original N species appears in only one of the N ^ species; hence, every column of L has to be a unit vector of the type 0, 0, . , 1, . , 0. This is called “proper” lumping. Lumping that is not proper, however, is possible; see Section I1,C.

In Section III,B, Eq. ] The matrix K must satisfy several constraints, which are best illustrated by considering a simple three-component system. The rate of formation of compo- MULTICOMPONENT MIXTURES 31 + nent 1 from components 2 and 3 is k21rn2 kslms, where the k’s are true kinetic constants; hence for the off-diagonal elements of K one has the constraint K,, = -kIJ I0 (off-diagonal). r, where the sum is intended over J different from I. Given Eq. (80), one sees that the entries in each column of K sum to zero, so that Eq.

Furthermore, we begin by considering the simple case where the intrinsic kinetics are linear. Let c,(x, t ) and cB(x,t ) be the concentration distribution of the initial reactants of type A, and of the desired products of type B. ] Let CA(t) = and CB(t) = be the corresponding overall concentrations [with, again, Cc(t) = 1 - CA(t) cB(t)]. For the sequential case (which in the context of a discrete description was discussed in 1974 by Golikeri and Luss), let x be normalized so that it is proportional to the kinetic constant of the first step.

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