By James Wei (Ed.)
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Extra resources for Advances in Chemical Engineering, Vol. 24
Some tentative steps in that direction have been taken (Allen, 1991; Frenklach, 1985;Froment, 1987; Vynckler and Froment, 1991), and perhaps a rigorous mathematical structure within which such problems should be couched can be found in a series of extremely interesting papers by Feinberg (1980, 1987, 1988, 1989, 1991a,b). A very concise review of some of the contents of these papers is given in Appendix C; further discussion of the Feinberg approach is given in the next section. ’* Krambeck (1994b) has observed that the McCoy reversible polymerization kinetics are rather artificial, and that they do not satisfy detailed balance.
An important consideration about exact lumping is the following one, which is due to Coxson and Bischoff (1987a). If one considers reactor types other than a batch (or, equivalently, a plug flow) reactor, exact lumping carries over. In other words, the dynamics of the reduced system behave as if they were representative of true intrinsic kinetics. ) A somewhat similar result was proved by Wei and Kuo (1 969) for the case of reactions with diffusion, such as occurs in porous catalysts. The constraints required for exact lumping are invariably very strict, and it is only natural that works have been published where the concept of “approximate” lumping is introduced.
However, Eq. (102) can also describe reversible kinetics. Let c*(x) be the equilibrium concentration distribution that will eventually be attained from the initial dishbution c(x,O), and let F[c*(z)] = 0, so that the (reversible) equilibrium condition is satisfied at some nonzero c*(x). Equation (102), however, can only describe a special form of approach to equilibrium. In fact, suppose that F[c(z,O)] is positive (or negative). Equation (102) now implies that the concentration of all reactants decreases (or increases) until c(x, t ) becomes equal to c*(x).