By James Wei (Ed.)
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Additional info for Advances in Chemical Engineering, Vol. 24
Another possible steady state is c(x,t) = 6(x), which is everything of nothing. ” e. Conclusions on Reaction Networks. The preceding discussion shows that a few simple cases where the topology of the reaction network is nontrivial can be analyzed, and formal solutions are (within bounds) possible. It also shows that as soon as some structure is assigned to the topology, the mathematics become quite complex, and therefore one concludes that there is little hope of dealing with complex topologies other than numerically.
111) is intended in the limiting sense CA(t)= -In t when a = 00 (single component). For the sequential case (Aris, 1989), let u(x) be the (dimensionless) kinetic constant for the second step. One obtains cB(x,t) = +(a,x)(e-"' - e-""")/(a(x) - 1). In the particularly simple case where u(x) = u (a constant), one obtains (Aris, 1989): (a - l)cB(t) = (1 f t/a)-" - (1 + Ut/a)-" (113) which satisfies the SCI. The term Ce(t) always goes through a maximum at some value oft, and hence a selectivity problem [a value o f t for which CB(t)is maximized] exists both for the single component and for the mixture cases.
It is also of interest that the apparent overall order of reaction given by Eq. (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.)