By James Wei (Ed.)
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Extra resources for Advances in Chemical Engineering, Vol. 24
A semilog plot of cI (I = 1,2) versus time (see Fig. 1) would be linear for both reactants. However, suppose that for some reason one is able to measure only the overall concentration c1 c2;this is also plotted in Fig. 1. the curve is nonlinear, and it seems to indicate an overall kinetics of order larger than unit. This shows that the overall behavior of the mixture is qualitatively different + time FIG. 1. Time behavior of single reactant and overall concentrations. MULTICOMPONENT MIXTURES 35 from the behavior of individual reactants: Experiments with model compounds (say, with only A , ) do not give information on the overall behavior; conversely, overall experiments (where one measures c1 c 2 )may well mask the actual intrinsic behavior of individual reactants.
IV. Kinetics A. EXACT AND APPROXIMATE LUMPING As discussed in Section III,C, the concept of “lumping” is related to the idea that it might be possible, in analyzing the kinetic behavior of a multicomponent mixture, to substitute for the real system (which involves a very large, possibly infinitely large number of chemical reactions) a lower order system with a finite number of pseudocomponents which, in some sense to be made precise, behaves either exactly or approximately in the same way as the original system.
One then normalizes the time scale as well by defining the dimensionless time t as k*r. The “overall” concentration C(t) is defined with a weighting function that is identical to unity, C(t)=
Advances in Chemical Engineering, Vol. 24 by James Wei (Ed.)