Pet food wastewaters contain considerable amounts of oils and greases, which make them difficult to treat. Membrane bioreactors represent an attractive alternative for food industries' wastewater treatment. Mathematical modeling of this type of system 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

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... ture of these systems. In the present work, new mathematical models are developed, from the fundamental equations for mass and momentum transport at the level of the continuum. With the use of the volume averaging method, effective medium models for both the aerobic and membrane tanks, which are the most important components of the system, were developed. Among the characteristics of the modeling approach used here, it has the advantage that its coefficients can be predicted from closure schemes, without representing a demanding computational effort. The membrane bioreactor models deduced here are deterministic and predict the most favorable design and operating conditions through numerical simulation, making them useful as a tool for analyzing the effect of each parameter over the LCFA and oxygen concentrations. 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