Modeling of Enzymes Reaction-Diffusion in Immobilized Biocatalysts Using Homotopy Perturbation, Third Approximation and Numerical Methods

Document Type : Research Article

Authors

1 Department of Chemical Engineering, Faculty of Engineering, Ferdowsi University of Mashhad, Mashhad, I.R. IRAN

2 Department of Chemical Engineering, Abadan School of Petroleum Engineering, Abadan University of Petroleum Industry, Abadan, I.R. IRAN

3 Department of Chemical Engineering, Faculty of Chemical Engineering, Shiraz University, Shiraz, I.R. IRAN

Abstract

In this research, the concentration of the enzyme in a spherical immobilized biocatalyst through
the reaction-diffusion equation has been investigated. The Michaelis-Menten type was utilized for the kinetic mechanism of enzyme reaction. The obtained equation is a second-order nonlinear ordinary differential equation (ODE) with variable coefficients. So, the Homotopy Perturbation Method (HPM) and Third Approximation Method were utilized as semi-analytical methods to solve the reaction-diffusion equation. Besides, the obtained ordinary differential equation is also solved by numerical method. The profiles of dimensionless substrate concentration and effectiveness factor versus dimensionless distance of biocatalyst for different values of Michaelis-Menten constant and Thiele Modulus were obtained. Then, the amount of deviation from numerical solution for each approximation method has been analyzed. The results show that the Third Approximation Method only in high values of Michaelis-Menten constant and low values of Thiele modulus has good agreement with the numerical method, while the HPM has a great match with the numerical method in all values of Michaelis-Menten constant and Thiele Modulus. Moreover, the effectiveness factor has been analyzed by HPM and it has been found that appropriate conditions for a high-value effectiveness factor are and. The HPM and Third Approximation Method results on two types of real and laboratory catalysts have also been compared with real data, the results show that HPM has more accurate and better results than the Third Approximation Method. Finally, the HPM has been used for analyzing dimensionless substrate concentration of different geometries of biocatalysts including spherical, cylindrical, and slab catalysts.

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References

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