By James Wei (Ed.)
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Extra info for Advances in Chemical Engineering, Vol. 24
MULTICOMPONENT MIXTURES 33 For further details on the Wei and Kuo analysis of exact lumping, and for alternate mathematical descriptions of the same problem, the reader is referred to the original literature. We move here to a brief discussion of an extension due to Bailey (1972), who considered the case where the original system is a continuous one, so that Eq. (79) is written as dm(x)/dt = -
It is in the area of approximate lumping that the distinction between the meaning of lumping, as used in this article, and of overall kinetics, possibly becomes a fuzzy one. For instance, the analysis of many parallel irreversible first-order reactions, to be briefly discussed in the next section, has been called lumping in the literature, though it is not in any sense an exact (Wei-Kuo) lumping, nor an approximate one: One chooses to consider only one lump, as given later by Eq. ASTARITA original system (except when the latter consists in fact of only one species).
98) is (a+ l ) / a ;that is, it is always larger than the intrinsic order of unity, except when a approaches infinity. When the intrinsic kinetics are linear (first order) the apparent overall order of reaction is larger than the intrinsic one; this, as will be seen, is not necessarily the case when the intrinsic kinetics are nonlinear. Physically, the point is easily understood by considering that, as time goes by, the components with the largest kinetic constants disappear first, and hence that the average kinetic constant of the mixture [which is proportional to the first moment
Advances in Chemical Engineering, Vol. 24 by James Wei (Ed.)