Dimensionless numbers for the analysis of air sparging aimed to reduce fouling in tubular membranes of a membrane bioreactor

Membrane bioreactors (MBR) combine conventional wastewater treatment and membrane filtration to create a system that uses very efficient, specialized microbes, produces a high quality effluent, and leaves small footprint. Fouling remains the major drawback of membrane processes, including MBR systems. Recently, one of the more frequent strategies employed to combat fouling and its consequent reduction in production is air sparging, in which injecting gas bubbles to the membrane generates high shear stress and scours cake layers from the membrane surface. This study mainly focused on permeate flux enhancement by air sparging. The results showed that air sparging over several weeks significantly increased permeate flux. In interpreting the findings, the dimensionless fouling and shear stress numbers are utilized. The fouling number is the ratio of the Peclet number for mass transfer and the Sherwood number. It was found that fouling resistance significantly decreased with air injection ratios between 0.4 and 0.5. This paper introduces a new approach: dividing the fouling number by the Reynolds number, which basically corresponds to the ratio of the Schmidt and Sherwood numbers. That dimensionless number, subsequently called the viscous fouling number shows qualitatively the same graph as the fouling number if viscosity remains constant. If viscosity changes during the filtration process, the fouling number and the viscous fouling number diverge from each other. Using the viscous fouling number instead of the fouling number may be especially useful for processes where fluctuations in viscosity are significant, as they are in MBR.