A novel exit boundary condition for the axial dispersion model

Abstract

A new modification of the Danckwerts' exit boundary condition for the axial dispersion model is proposed. According to the novel boundary condition, the concentration gradient at the reactor exit is a fraction of the gradient predicted by the plug flow model. The fraction is a function of the Peclet number. A family of suitable function expressions has been derived. The exit boundary condition provides a smooth transition from the complete back-mixing model with a zero concentration gradient to the plug flow model with a finite concentration gradient. The boundary condition is illustrated via two examples: a first-order reaction and an autocatalytic reaction. The correct asymptotics for the boundary condition have been demonstrated by an analytical solution of the first-order reaction model. Numerical solution of the autocatalytic kinetics with global orthogonal collocation indicates that the use of the modified boundary condition improves the performance of the numerical algorithm compared to the performance obtained using the classical Danckwerts' boundary condition.