Astarita’s uniform kinetics

The incorporation of Astarita s uniform kinetics into the separable form of a doubly-distributed reaction is now possible. The specification of g(y) in u(jc, y, 0) = f(x)g(y), together with K and R, defines the kinetics G that will then be distributed by x, g, k, and R also define [Pg.200]

Besides having the capital property of being able to imitate any kinetics—see Eq. 61—Astarita s uniform kinetics are often patient of a mechanistic derivation. Thus, for what Astarita and Ocone call uniform generalized Langmuir isotherm kinetic mechanism (UGLIKM), we might take 6(x) dx to be the fraction of catalytic surface occupied by the species A(x) with index in... 

The simplest model of a bubbling fluidized bed, with uniform bubbles exchanging matter with a dense phase of catalytic particles which promote a continuum of parallel first order reactions is considered. It is shown that the system behaves like a stirred tank with two feeds the one, direct at the inlet the other, distributed from the bubble train. The basic results can be extended to cases of catalyst replacement for a single reactant and to Astarita s uniform kinetics for the continuous mixture. 

THE FLUID BED WITH ASTARITA S UNIFORM KINETICS, 113 ACKNOWLEDGMENTS, 115 NOTATION, 115 REFERENCES, 116... 

Astarita and Ocone s uniform kinetics (1988) may be used for the background kinetics (with distribution parameter y). It will be recalled that they showed that kinetics of the form... 

On this view of the reactor it is not surprising to find Astarita and Occone s methods for uniform kinetics work for the bubbling fluid bed. Replacing kcp by kcp x, t) F[/ K(y)cp(y)dy]. Thus the balance over the dense phase is... 

Here c(x, t)dx is the concentration of material with index in the slice (x, x + dx) whose rate constant is k(x) K(x, z) describes the interaction of the species. The authors obtain some striking results for uniform systems, as they call those for which K is independent of x (Astarita and Ocone, 1988 Astarita, 1989). Their second-order reaction would imply that each slice reacted with every other, K being a stoichiometric coefficient function. Only if K = S(z -x) would we have a continuum of independent parallel second-order reactions. In spite of the physical objections, the mathematical challenge of setting this up properly remains. Ho and Aris (1987) have shown how not to do it. Astarita and Ocone have shown how to do something a little different and probably more sensible physically. We shall see that it can be done quite generally by having a double-indexed mixture with parallel first-order reactions. The first-order kinetics ensures the individuality of the reactions and the distribution... 

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