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

A mechanistic model of organic substrate biodegradation in membrane-attache d biofilms growing in extractive membrane bioreactors is presented and anal ysed to establish the rate-limiting steps. The model accounts for counterdi ffusion and reaction of oxygen and organic substrate within the biofilm, an d predicts detailed substrate concentration profiles and the evolution over time of biofilm thickness. Good agreement was found between model predicti ons and organic substrate flux and biofilm thickness measured experimentall y 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 co nstitutes a small fraction of the entire biofilm volume. This allows a cons iderable simplification of biofilm modelling. A simple diffusion model was formulated as an alternative to the more complex full diffusion-reaction mo del for the calculation of organic substrate flux. This simple model is bas ed on the insight that the organic compound flux is limited primarily by th e 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 f ull mechanistic model, the biofilm thickness and organic substrate flux. (C ) 1999 Elsevier Science Ltd. All rights reserved.