Approximation methods to evaluate the effect of axial dispersion in isothermal flow reactors

TLDR: In this paper, two quasi-analytical methods are given for the approximate solution of the nonlinear differential equation governing the effect of longitudinal dispersion on the concentration profile in an isothermal flow reactor with reaction orders other than zero or first.

Abstract: Two quasi-analytical methods are given for the approximate solution of the nonlinear differential equation governing the effect of longitudinal dispersion on the concentration profile in an isothermal flow reactor with reaction orders other than zero or first. The first method converts the nonlinear differential equation and its boundary conditions into a nonlinear integral equation which is solved by iteration, while the second method generates approximate solutions by considering axial dispersion as a perturbation on the reaction kinetics. By using the perturbation method a dimensionless group has been generated that is characteristic of the interaction between axial diffusion and reaction kinetics. It is also demonstrated that an axial dispersion coefficient characteristic of Taylor diffusion can be applied in the presence of a reaction of any order and that the effect of depletion of concentration by chemical reaction is to aid in the reduction of radial concentration gradients. Deux methodes quasi-analytiques sont donnees pour la solution approchee de l'equation differentielle non-lineaire relative a la dispersion longitudinale du profil des concentrations pour les reactions autres que celles du premier degre dans un reacteur a ecoulement isothermique. La premiere methode consiste dans la conversion de l'equation differentielle non-lineaire et de ses conditions limites en une equation integrate non-lineaire qui est resolue par iteration. La seconde methode consiste a creer des solutions approximatives en considerant la dispersion axiale comme perturbation de la cinetique de la reaction. En utilisant cette methode de perturbation un groupe sans dimensions, caracteristique de l'interaction entre la diffusion axiale et la cinetique de la reaction, a ete genere. II est aussi demontre qu'un coefficient de dispersion axiale, caracteeristique de la diffusion Taylor, peut-ětre applique en presence d'une reaction de tout degre et que l'effet d'amoindrir la concentration par reaction chimique est d'attenuer les gradients de concentration radiale.