Mathematical Modeling of Membrane Fouling in Submerged Membrane Bioreactors Effect of Colloids

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. Critical flux equations based on limiting behavior balancing massic transport to and from the membrane accurately predict observed critical flux determinations. Massic flux from the membrane, backtransport, exhibits a maximum value that produces a maximum limit to scouring efficiency. The need for inclusion of cake compression effects to accurately predict observed fouling resistance is confirmed. Critical fluxes for colloidal particles defined operationally for particles with sizes between 1.5 and 0.04 um are significantly lower than critical fluxes for larger biological floc particles. This is in accordance with previously reported observations. The higher specific resistance and lower fluxes make colloidal particles the likely most important contributor to overall fouling in MBRs under practical operational conditions. Soluble microbial products due to the smaller size are significant for long term pore plugging fouling more than cake based fouling.