The Effect of Residence Time Distribution on the Rate of Advancement of the Reaction

Abstract

In any form of continuous reactor the different reagent molecules spend different residence times in the reacting zone. The degree to which a reaction advances after a lapse of nominal residence time may be somewhat different from that expected from classical (micro) kinetics and the known order of the reaction.

If the reaction mixture passes laminarly through a reasonably large cylindrical reactor-one in which intermolecular diffusion is negligible-the effective measure of the advancement of the reaction in terms of the residual concentration of the reagent - measured (i) as an actual distributed system C and (ii) as an idealized system in which all molecules spend an equal tlme of residence C_m. may be expressed by the equation:

Equation (29)

where n is order of reaction, S=k_nC₀^n-1τ₀, and τ₀ is the minimal time of residence (time for the central core).

Equation (29) becomes meaningless when n=1 and is replaced by

Equation (30)

The ratio C/C_m increases as S increases; the increase, however, is the less pronounced the higher the value of n.

If the mixture passes through a mixed tank reactor advancement of the degree of the reaction is measured by a function given by Metzner and Pigford. For a second order of reaction a correct treatment can only be carried out if a distinction is made between the square on the mean concentration and the mean of the square concentration.