Interface model between the bioreactor and the membrane in a membrane bioreactor for wastewater treatment.

This paper proposes a structure of an integrated mathematical model of a membrane bioreactor (MBR) and describes the links between two main parts of a MBR model: the bioreactor and the membrane. In case of an immersed MBR three types of links are considered: a relationship between specific cake resistance (SCR) and extracellular polymeric substances (EPS) in the bioreactor, a relationship between air scour rate and shear stresses on the membrane surface, and a relationship between concentration of soluble microbial products (SMP) in the bioreactor and rate of pore constriction. While SMP concentration features directly in the equations of pore constriction, EPS are assumed to affect SCR which in turn has an effect on cake filtration. The relationship between EPS and SCR is described with a linear algebraic equation. Shear stresses on the membrane surface are calculated as a function of air scour rate with a one- imensional slug flow model.