Empirical and Analytical Correlation of the Reaction Kinetics Parameters of Cuttle Bone Powder Immobilized Lipase Catalyzed Ethyl Ferulate Synthesis

Abstract

A mathematical modeling, which depicts the cuttlebone immobilized lipase catalyzed ethyl ferulate production by esterification of ferulic acid and ethanol has been developed for the first time based on various kinetic parameters determined experimentally in the present study. This model describes the concentration profiles of substrates and product inside the immobilized catalyst taking into account of non-steady state diffusion reaction conditions. The system of non-linear partial differential equations involved in this model has been solved analytically using new approach to the homotopy perturbation method. The obtained analytical results were compared with experimental results and a satisfactory agreement is noted. In an experimental study, the lipase from Bacillus subtilis AKL13 was produced and immobilized on cuttlebone powder of Sepia officinalis. The adsorption and thermodynamic parameters demonstrated that the cuttlebone powder could offer more surface coverage for enzyme binding (129.1 mg g−1) and improvement in the thermal stability. Esterification reaction was conducted at optimized conditions and 96% of ester conversion was achieved with in 24 h. Various diffusion and reaction kinetic parameters such as Thiele modulus, effectiveness factor, reaction velocity and Michaelis–Menten constants were determined experimentally and used for mathematical modeling.