Batch reactor performance for the enzymatic synthesis of cephalexin: influence of catalyst enzyme loading and particle size

A mathematical model is presented for the kinetically controlled synthesis of cephalexin that describes the heterogeneous reaction–diffusion process involved in a batch reactor with glyoxyl-agarose immobilized penicillin acylase. The model is based on equations considering reaction and diffusion components. Reaction kinetics was considered according to the mechanism proposed by Schroën, while diffusion of the reacting species was described according to Fick's law. Intrinsic kinetic and diffusion parameters were experimentally determined in independent experiments. It was found that from the four kinetic constants, the one corresponding to the acyl-enzyme complex hydrolysis step had the greatest value, as previously reported by other authors. The effective diffusion coefficients of all substances were about 5 × 10−10 m2/s, being 10% lower than free diffusion coefficients and therefore agreed with the highly porous structure of glyoxyl-agarose particles. Simulations made from the reaction–diffusion model equations were used to evaluate and analyze the impact of internal diffusional restrictions in function of catalyst enzyme loading and particle size. Increasing internal diffusional restrictions decreases the Cex synthesis/hydrolysis ratio, the conversion yield and the specific productivity. A nonlinear relationship between catalyst enzyme loading and specific productivity of Cex was obtained with the implication that an increase in catalyst enzyme loading will not increase the volumetric productivity by the same magnitude as it occurs with the free enzyme. Optimization of catalyst and reactor design should be done considering catalyst enzyme loading and particle size as the most important variables. The approach presented can be extended to other processes catalyzed by immobilized enzymes.