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 micro(max) and K(d) 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.
In this work we have optimized a batch distillation column as an optimal control policy problem. We used the optimal constant reflux policy for the process, and the objective function is to maximize the thermodynamic efficiency for a fixed time given a product concentration. The simulation model of the column considers its complete dynamics, and it has been formulated as a nonlinear programming problem for the solution of the thermodynamic efficiency. We use a SQP based dynamic optimization technique in this work. The procedure is shown for the separation of a binary mixture Benzene + Toluene. The achieved accumulated thermodynamic efficiency was close to 80%. Also we have compared with the optimal control problem of the maximum distillate for the same separation above, and we can observe that in the problem we proposed, less reflux is required, and even when thermodynamic efficiency in the problems is quite close, the energetic requirement in the problem we propose herein is smaller.
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