Approximation of intra-particle reaction/diffusion effects of immobilized enzyme system following reverse Michaelis–Menten (rMM) mechanism: third degree polynomial and Akbari–Ganji methods

Abstract

AbstractTwo approximate analytical expressions based on third degree polynomial and Akbari–Ganji’s method (AGM) were derived for the reaction/diffusion controlled kinetics of an immobilized enzyme ($$IE$$ IE ) systems. The approximation methods predict substrate concentration profile and effectiveness factor ($$\eta$$ η ) in a porous spherical particle. The reaction is assumed to follow reverse Michaelis–Menten ($$rMM$$ rMM ) kinetics. The approximate methods predictions were comparable to that of numerical solution (using the Matlab finite difference function, $$bvp4c$$ b v p 4 c ) at wide range of $${\phi }^{2}$$ ϕ 2 and $${y}_{o}$$ y o especially at low $${\phi }^{2}$$ ϕ 2 and high $${y}_{o}$$ y o (polynomial equation) and low $${\phi }^{2}$$ ϕ 2 and low $${y}_{o}$$ y o (AGM equation). Although the approximate solution was derived for $$rMM$$ rMM kinetics, the results can be used to describe other important enzymatic reaction kinetics such as simple Michaelis–Menten ($$MM)$$ M M ) kinetics and $$MM$$ MM with competitive product inhibition kinetics. A necessary design equation should be satisfied when using polynomial or AGM approximation for different enzyme kinetic equations. In this work, two examples of enzymatic reactions of industrial interest were studied, namely glucose-fructose isomerization follows $$rMM$$ rMM kinetics and hydrolysis of lactose follows Michaelis–Menten ($$MM$$ MM ) equation with competitive product (galactose) inhibition. Predictions of the developed third degree polynomial and AGM approximation equations agree with that of numerical solution, the percentage relative error for the effectiveness factor was less than 11 in comparison with the numerical solution. Good agreement between approximate and numerical estimations demonstrates the validity of these approximation methods.