Mathematical Modeling of Biofilm Thickness in a Membrane Aerated Biofilm Reactor

This research presents a mathematical model for biofilm development in a Membrane-Aerated Biofilm Reactor (MABR). MABR is a novel configuration in wastewater treatment, in which hollow-fiber membranes are used to provide oxygen and serve as substratum to the biofilm, while wastewater provides substrate from the opposite direction.;The mathematical model was developed to describe (1) biofilm development, (2) concentration profiles of substrate, biomass and oxygen in biofilm and (3) biofilm thickness in a MABR. The model was investigated to predict these phenomena in a MABR over 0 to 10 day periods. The function 'pdepe' in MATLAB was used for the mass transfer and utilization of oxygen and organic substrate in a MABR while simultaneously evaluating microbial growth in the biofilm.;The model in this study can predict biofilm development over time. The simulation results for the concentration profiles of substrate and microorganisms in biofilm of MABR using the model are reasonable compared to other studies reported in the literature (Pavasant et al. 1996 and Casey et al. 1999a, 2000a and 2000b);Comparison of biofilm thickness with 3 different influent concentrations of the substrate (= acetate) was investigated. This study showed that the three biofilm thicknesses were 1.45 mm, 2.12 mm and 2.56 mm, and average growth rates of biofilm were 0.14 mm d-1, 0.20 mm d-1 and 0.25 mm d-1, when influent concentrations of acetate were 100 mg L-1, 200 mg L-1 and 300 mg L-1, respectively.;The changes in maximum concentration of biomass in biofilm were also investigated. The concentrations of maximum biomass increased continuously until they reached steady-state values of 35 mg L-1, 74.6 mg L-1 and 115 mg L-1, when influent concentrations of acetate were 100 mg L-1, 200 mg L-1 and 300 mg L-1, respectively. The concentration of maximum biomass at steady-state increased in direct proportion to influent concentration of acetate.;Further improvement of the model is necessary to achieve more accurate simulation in a biofilm of MABR. First, the equations for the detachment of biofilm should be added to the model. Next, the main partial differential equations of substrate and biomass should be further developed for more accurate representation of the interaction with the partial differential equations of oxygen.;In conclusion, the mathematical model showed the possibility of predicting the trends in system variables through simulations of biofilm development and biofilm thickness, microbial growth and reduction of substrate in biofilm of a MABR.