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.
Membrane bioreactors (MBRs) for wastewater treatment are becoming increasingly popular across the world due to the high quality of their treated effluent, relative simplicity, and increased reliability. The cost of membranes has been steadily reducing over the last decade and the operation of the systems has simplified. At the same time, the operational expenditures have reduced as the energy requirements for operation and the membrane cleaning and replacement costs continue to decrease.
The most widely applied commercial technologies are all based on the concept of submerged membranes. The membranes are usually located in a separate membrane tank placed after the biological tank in the same location as the final clarifier in an activated sludge tank. Continuous recirculation of the mixed liquor takes place between the biological tank and the membrane tank. Suction is applied to the inside of the membrane to create a transmembrane pressure that drives the treated water from the outside of the membrane to the inside and then out of the system. The permeate is the treated water, consistently of very high quality. The biological flocs, colloidal particles, and some soluble compounds are retained on the outside of the membrane. The flow of water towards the membranes convectively transports all of these substances to the membrane surface. The membranes are continuously aerated to induce turbulence and movement which controls deposition of substances on the membrane surface.These substances can foul the surface, thus compromising the operation of the whole plant. Understanding membrane fouling in MBRs is, therefore, critical for the successful application of the technology.
There have been numerous advances in the understanding of membrane fouling in MBRs. The interrelation between the operational conditions of the biological process and the fouling potential of the mixed liquor is now better understood. The role of soluble microbial products, SMPs, colloidal particles and biological flocs has also been better elucidated. Finally, the effects of aeration intensity and the rate of fouling has been recently clearly described.
There are some mathematical models of membrane fouling that can account for internal fouling of the membranes (Weisner and Apel, 1996) but their application is usually limited to laboratory conditions with constant flux or differential pressure. On the other hand, there is a significant body of knowledge on the description of cake filtration in several different disciplines. In environmental engineering, cake filtration theory is usually applied for understanding dewatering operations and consolidation of soils (Lee and Chang, 2000). To the knowledge of the authors, there is not any existing model of submerged membrane fouling that dynamically couples internal and external-cake membrane fouling, including cake filtration effects and compressibility. The objective of this contribution is to present such model, to test the applicability of the model with published data, and to establish future directions for model development.