Optimal temperature control in a batch bioreactor with parallel deactivation of enzyme

Abstract

A biotransformation process with parallel deactivation of biocatalyst running in a batch reactor has been analyzed. A non-linear deactivation model suggested by Do and Weiland has been taken into account. Based on variational calculus analytical 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. Solutions for a stationary process and that carried out at the active upper and lower temperature limitations have been presented. Furthermore, an analysis of the course of the process under isothermal conditions as those indispensable for the appropriate choice of the optimal conditions has been presented. Based on an example of hydrogen peroxide decomposition process in the presence of the native catalase of yeast Saccharomyces cerevisae (CSC) the obtained solution has been described. In addition an influence of the quotient of energy of deactivation and reaction processes, initial and final biocatalyst activity and conversion on the course of the optimal temperature profiles have been considered. It has been proved that a decrease in the activation energy quotient and the final biocatalyst activity as well as an increase in conversion results in an increase of the overall process duration time. Also a comparison of the course of the stationary temperature profiles at different ranges of substrate concentration and the effect of the latter on the analyzed objective function has been made. It has been revealed that in case of processes which run at any range of the substrate concentrations, in order to achieve the shortest duration time of their course, it is appropriate to conduct them at possibly the lowest concentration range.