A mathematical model is developed that accounts for internal fouling of membranes due to soluble microbial products during subcritical flux operation, and for supercritical flux fouling due to cake formation and compression.. The model takes into account the filtration effect generated
by the cake. A set of differential equations is derived and solved numerically to obtain a description of cake formation and growth, removal of substrate due to cake-membrane behavior, change in membrane permeability over time, increase in cake headloss over time, removal of soluble microbial
products by the cake, and change of transmembrane pressure over time. The model allows operational changes of membrane operation such as modifications of permeate fluxes e.g. membrane relaxation, modification of aeration rates, backflushing and changes in water quality variables during one
run. The model adequately describes several commonly observed effects such as: exponential increase in transmembrane pressure due to high mixed liquor suspended solids, reduced fouling rates at increased aeration intensities, subcritical operation fouling, and effect of increased particle
size on the filterability of the microbial suspension.
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