Prediction of transmembrane pressure build-up in constant flux microfiltration of compressible materials in the absence and presence of shear

Constant flux filtration is a common mode of operation for submerged membrane filters and membrane bioreactors. A model was developed to describe the pressure rise as a function of time or processed volume taking into account both the cake formation and cake consolidation stage. The approach described here is based on the Nelder Mead optimisation method to calculate best solution for key parameters. These include the consolidation time constants and compressibility parameter that can be used to describe the filtration over a wider range of conditions. The consolidation time constant calculated for flocculated yeast shows a power law relationship with flux over a range of conditions. Furthermore, the concept is extended to sheared systems. A shear-dependent model for constant flux filtration is presented over a narrow range of shear rates constrained by the minimum shear required to distribute cake evenly and the maximum shear permissible before cake erosion/lift is induced. Additional work is required to model the cake behaviour above the point at which cake lift occurs.