A mathematical model was developed to describe a dialysis process for the continuous fermentation of whey lactose to lactic acid, with neutralization to a constant pH by ammonia. In the process, whey of a relatively high concentration is fed into the fermentor circuit at a relatively low rate so that the residual concentration of lactose is low. The fermentor effluent contains ammonium lactate, bacterial cells, and residual whey solids and could be used as a nitrogen-enriched feedstuff for ruminant animals. Only water is fed into the dialysate circuit at a relatively high rate. The dialysate effluent contains purified ammonium lactate and could be converted to lactic acid and ammonium sulfate for industry. The fermentation was specifically modeled as a set of equations representing material balances and rate relationships in the two circuits. Dialysis continuous fermentations, in general, were modeled by combining these equations and by using dimensionless parameters. The generalized model was then solved for the steady state and used to simulate the specific fermentation on a digital computer. The results showed the effects of various material and operational and kinetic parameters on the process and predicted that it could be operated efficiently.
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