Mathematical Modeling of 6-APA Production by Enzymatic Hydrolysis of Penicillin G in a Batch Reactor

Abstract 6-Aminopenicillanic acid (6-APA) is a β-lactam intermediate of major industrial relevance and a key precursor for producing semisynthetic antibiotics. This study presents the development and analysis of a mathematical model describing 6-APA production via heterogeneous enzymatic hydrolysis of penicillin G in a batch reactor catalyzed by penicillin G acylase (PGA) immobilized on spherical supports. The model is formulated using coupled mass balances in the liquid and solid phases, explicitly considering diffusive and convective transport effects on the reaction kinetics. The resulting system of differential equations is solved using three independent approaches: the method of lines (MOL), adopted as the reference solution with explicit spatial dependence, the classical approximation, and the coupled integral equation approach with H1,1 approximation, the latter two being considered approximate solutions. A convergence analysis defines the spatial discretization required for the MOL solution. Comparison among the three methodologies shows excellent agreement, demonstrating the consistency of the solutions obtained. The results indicate that the mass Biot number (Bim) plays a critical role in reactor performance, with complete conversion being achieved at reduced reaction times for Bim equal to 10. The results demonstrate the validity of the proposed model and the effectiveness of the solution methods used, contributing to the analysis and optimization of heterogeneous enzymatic processes at the industrial scale.