On the Evaluation of the Exit Boundary Condition for the Axial Dispersion Bioreactor System

Abstract

Employment of the axial dispersion theory to model chemical or biochemical processes often results in coupled parabolic partial differential equations (PDEs). The classical Danckwerts boundary conditions have been widely used to solve these PDEs despite the fact that artificial suppression of the exit concentration gradient to zero may be physically unrealistic and may cause numerical instability. In this study, a recently developed exit boundary condition is shown to be inapplicable to model processes which demonstrate significant differences in the dynamics of components ± typically found in biochemical processes. Using an activated sludge process and a pilot-scale subsurface flow (SSF) constructed wetland as case studies, we demonstrated in this study that a time-dependent exit boundary condition is more appropriate for use with the Danckwerts inlet boundary condition and the axial dispersion theory to model a biological system operating at near-plug flow conditions. Instead of using steady-state results we found that evaluation of alternative exit boundary condition using dynamic simulation results is more realistic.

Residence time distributions of gas flowing through rotating drum bioreactors

“…This downstream boundary condition (open flow) has been used to simplify the analysis. Recent work by Lee and Newell (1998) suggests that a time-dependent exit boundary condition is more correct. However, for low dispersion, which is expected in these systems, there is negligible difference between this boundary condition and the closedflow boundary condition.…”