Model of biomass concentration in membrane filtration recycling systems subject to single substrate-limited growth kinetics

Membrane filtration has the ability to limit microbiological growth in metalworking fluids (MWFs). To appropriately design and size a membrane filtration system for this application, the rate of microbia removal must be assessed relative to microbial population (biomass) growth This research utilizes the Monod Equation describing biomass growth limited by a single substrate to evaluate if biomass levels can be maintained below a prescribed level in a perfectly mixed MWF system. The model for predicting biomass in the MWF system is obtained by numerical solution of a system of coupled non-linear differential equations. The model solution permits membrane filtration design and sizing decisions based on microbial growth data specific to MWF chemistries, microbial species, and manufacturing facilities. It is revealed that the ratio of the filtration rate to the MWF volume must exceed the maximum specific growth rate of microorganisms to control biomass concentrations in the system under arbitrary initial substrate and contamination levels. The control of microbial growth in the system also requires that appropriate cleaning intervals be selected for the membrane filtration process tank. The microbial rejection coefficient, which is characteristic to a given membrane, has a dominant impact on the required cleaning interval.