Study and Mathematical Modeling of the Production of Propionic Acid by Propionibacterium acidipropionici Immobilized in a Stirred Tank Fermentor

A mathematical model was developed that describes production of propionic acid by fermentation of sweet whey with Propionibacterium acidipropionici immobilized in calcium polygalacturonate beads in a fermentor-type stirred tank. This mathematical model is constituted by a partial differential equations system, which fits consumption, production, growth and internal diffusion rates in the support. Fermentation was experimentally studied with free cells and immobilized cells, effective diffusivities of lactose and propionic acid were estimated in the support, and typical parameters of the model were obtained by nonlinear regression of the experimental data. The variance analysis shows that the combination of ~max and Kd parameters is the source of variation most significative, also they were found to be the most sensitive parameters of the model. Finally, an effectiveness factor was calculated in order to assess the effect of mass transfer on the overall reaction rate observed.