optimization, batch bioreactor, optimal temperature control, biocatalyst deactivation, variational calculus
A batch biotransformation process running in the presence of microorganisms cells revealing a specified enzyme activity has been considered. A non-linear deactivation model suggested by Do and Weiland has been taken into account for modeling of the process. Based on variational calculus computations aimed at finding an optimal selection of temperature conditions that ensure obtaining maximum conversion or minimum duration time necessary for its attaining have been carried out. The solutions were given and discussed for the stationary process, and for the active upper and lower temperature limitations. It has been proved that an application of microorganisms cells results in slowing down the reaction rate and shifting the initial temperature of the stationary profile to higher values. They are more pronounced the lower the permeability of the cell membrane is. In consequence, an extension of the process duration time is observed along the sections of the optimal profile while the lower temperature constraint usually becomes inactive.