Multiscale modeling of a membrane bioreactor for the treatment of oil and grease rendering wastewaters

Membrane bioreactors represent an attractive alternative for food industries wastewater treatment. This type of reactors comprise an aerobic tank (where the biochemical reactions take place) and a membrane tank (where the final filtration process occurs). Mathematical modeling of these systems is a practical tool for the design, control and optimization of wastewater treatment plants. Among the modeling approaches, there is no mathematical model that is specifically designed for membrane bioreactors, and that captures the hierarchical nature of these systems. In the present work, new mathematical models for mass and momentum transport are derived from the fundamental equations at the continuum level. With the use of the volume averaging method, effective medium models for both the aerobic and membrane tanks were developed. This modeling approach has the advantage that the coefficients involved in the model can be predicted from closure schemes, without representing a demanding computational effort. This deterministic model allows predicting the most favorable design and operating conditions. Additionally, numerical simulations of these models give rise to a better understanding of the involved mass transport mechanisms in the membrane tank, this is achieved through the prediction of the fluid velocity, and the dynamics of the total mass flux and the concentration at each point in the tank. The models derived here are valuable because they allow analyzing the effect of each (operational and/or design) parameter over the dynamics of long-chain fatty acids and oxygen concentrations.