Optimal feed rates strategies with operating constraints for the penicillin production process

Abstract

This work presents a deterministic non-structured model of the penicillin production process. For the model development were considered Contois growth type model, yield coefficients among growth, substrate and oxygen uptake, production specific rates, endogenous and maintenance metabolism, substrate excess product inibition and hydrolyse from penicillin to peniciloic acid. Volumetric oxygen transfer coefficient was estimated through Reynolds and Power numbers, and apparent viscosity as a cell concentration function, and gasefied fluid power. The operation mode was feed-batch, and the parameters were obtained from the literature. The resulting model was solved by a forth-order Runge-Kutta algorithm. Process productivity optimization was initially made with relation to cell initial concentration, fed-batch flow rate and substrate fed-batch concentration. To carried out this procedure, it was necessary to consider process operating constraints as the bioreactor final volume, dissolved oxygen, cell and substrate concentrations. These operating constraints were computed in relation to productivity through the concept of the penalty functions. Using this procedure, it was possible to obtain the state variables leading to the best productivity and taking into account the constraints, through an optimization algorithm based on the modified simplex method. With fixed optimal values of the cell and substrate feed-batch concentrations, feed-batch flow rate strategies of two types were performed: (1) first, second, and third order polinomial functions with six hours samples were used, and (2) with independent values with six and twelve hours samples. The optimization algorithm was the same as above mentioned. With the proposed methodology it was possible to obtain the operating variables so that the best productivity with state constraints can be achieved for the production phase of the penicillin process.