A stochastic axial dispersion model for tubular flow reactors

Abstract

The continuous limit of a general random walk gives rise to the stochastic or Kolmogorov diffusion form of an axial dispersion model for tubular flow reactors. The resultant equation is different from the Kolmogorov diffusion equations available in the literature, in that it includes a term to account for the chemical reaction occurring in the reactor. A comparison has been made between the axial dispersion model for tubular flow reactors of the Kolmogorov diffusion form and that of the Fickian diffusion form. While the drift and dispersion or diffusion coefficients in the former are derived quantities having explicit physical significance, the dispersion or diffusion coefficient in the latter, strictly speaking, is a proportionality constant that needs to be determined empirically. The appropriate initial and boundary conditions are presented and discussed. Under the assumption that thermal energy is totally transported by flowing molecules or particles, the results obtained in this work may be applicable to thermal transport through the reactor operated adiabatically.