Intraparticle convection, diffusion and Michaelis-Menten kinetics in porous slab catalysts

Diffusion-reaction model for a porous catalyst has been widely studies for the past three decades or so. However, intraparticle convection has not been accounted for in the majority of reaction-diffusion studies in porous catalysts till recently. Though it has been reported in some early works that the intraparticle convection plays significant role in enhancing the substrate transport inside the porous solid especially for the case of large pores (Nir and Pismen, 1977; Rodrigues and Orfao, 1984; Stephanopoulos and Tsiveriotis; 1989), but later studies have largely neglected this important effect. The forced intraparticle flow can contribute significantly to the total intraparticle nutrient transport rate in general. This becomes more significant especially in the case of immobilized biocatalysts applications with limited reactant solubility, such as oxygen in aqueous phase, typically encountered in aerobic fermentation and biodegradation. The earlier studies on the intraparticle convection have focused on zero and first order kinetics as cited above. However, a host of biological recations are represented by Michaelis-Menten kinetics, which is the focus of the present study. A theoretical study was made of the effect of the intraparticle convection on the reaction rate in a slab biocatalyst with large pores containing immobilized enzyme or cells. Zero order, first order and Michaelis-Menten kinetics were studied. The main focus in this research is to investigate the effect of intraparticle convection on the nutrient transport in a porous solid catalyst for the case of Michaelis-Menten kinetics. The convection effect is represented in term of intraparticle Peclet Number in the differential equation obtained as a result of mass balance for the nutrient transport inside the catalyst solid. The effect of intraparticle flow on the intrapraticle nutrient transport is studied by solving the resulting differential equation for the concentration profile inside the solid which in turn is used to calculate the effectiveness factor of the catalyst. The convection-diffusion model for the Michaelis-Menten kinetics is solved numerically using an explicit finite difference scheme. Zero order and first order kinetics cases are revisited and solved analytically. The exact solutions for the first and zero order reactions is later used to validate our numerical code before it is implemented for the case of Michaelis-Menten kinetics. There appears close conformity between the exact solution and the numericalsolution for first and zero orders kinetics. The results for the Michaelis-Menten kinetics show that convection enhances the rate of nutrients transport inside the porous solid. With increasing value of Intraparticle Peclet Number, higher concentration of the substrate with increasing depth inside the solid is observed. Comparing the results for the Michaelis-Menten with zero and first order kinetics, it is observed that the effect of convection is more pronounced for the zero and first order reactions than the Michaelis-Menten kinetics. This is apparent from the concentration profiles for these cases. References: Nir A and Pismen L M , Chem. Eng. Sci, 1976 Rodrigues A E , Orfao J M and Zoulalian A , Chem. Eng. Commun., 1983 Stephanopoulos G and Tsiveriotis K , Chem. Eng. Sci.,