Turbulence level significance of the coalescence-dispersion rate parameter

Abstract

The random coalescence-and-dispersion (C–D) models for non-ideal mixing in reactors involve a rate parameter, I, which is the frequency of the coalescence and dispersion events divided by the available number of coalescence sites per unit residence time, where residence time is a measure of reactor size. An approximate relationship between I and hydrodynamic parameters has been found by carefully comparing C–D computations, where I varies with location, with actual measurements of the turbulent energy dissipation rate, ε, and the turbulence length scale, L s, in a tubular reactor. At each location I was determined such that the calculated conversion of a second-order reaction matched the measured conversion. The relationship found was: I≈ 1333(ε/ L s 2) 1 3 ( −τ/ N) where L s, is the length scale of segregation, ε has dimensions of velocity squared per unit time, and ( −τ N) is the residence time divided by the number of coalescence sites. The relationship above was applied to the C–D modeling of a semi-batch reactor with a consecutive-competitive reaction. The resulting yields and selectivities under the various conditions of the experimental data were very close to experimental results.