Substrate counterdiffusion and reaction in membrane-attached biofilms: mathematical analysis of rate limiting mechanisms

Abstract

A mechanistic model of organic substrate biodegradation in membrane-attached biofilms growing in extractive membrane bioreactors is presented and analysed to establish the rate-limiting steps. The model accounts for counterdiffusion and reaction of oxygen and organic substrate within the biofilm, and predicts detailed substrate concentration profiles and the evolution over time of biofilm thickness. Good agreement was found between model predictions and organic substrate flux and biofilm thickness measured experimentally in a lab-scale single-tube extractive membrane bioreactor. Analysis using this model showed that, due to oxygen diffusion limitations, the reaction zone within the biofilm is located at the biofilm/biomedium boundary and constitutes a small fraction of the entire biofilm volume. This allows a considerable simplification of biofilm modelling. A simple diffusion model was formulated as an alternative to the more complex full diffusion–reaction model for the calculation of organic substrate flux. This simple model is based on the insight that the organic compound flux is limited primarily by the biofilm diffusion resistance. The diffusion model was combined to a yield-based expression for biofilm accumulation to give the evolution over time of biofilm thickness. The simplified model predicts, as accurately as the full mechanistic model, the biofilm thickness and organic substrate flux.