According to the behavior of the combined process of multicomponent molecular diffusion and Knudson diffusion in porous catalysts

a set of second order nonlinear ordinary differential equations describing the concentrationprofiles of reactants and products for a single reaction in an isothermal spherical catalyst has been developed in this paper. In these differential equations

the concentration gradients of different reaction components are strongly coupled together. By using shooting method to solve the two-point boundary value problem posed by this set of equations

the concentration profile of each reaction component and the numerical solution of effectiveness factor can he obtained. Because of the differences between the effective diffusion coefficients of the reaction species

the relations between the changes of their compositions in catalyst no longer obey the stoichiometric relations of the reaction. When the intraparticle diffusion restriction is serious

in the catalyst it may appear a "dead zone"

in which the concentrations of the reaction components are asymptotic to the equilibrium concentrations and the chemical reaction practically does not proceed. As the "dead zone" exists

applying this mathematical model and the solution procedure

the radius of "dead zone" and the effectiveness factor under this condition can be solved. The cylindrical sh.ape catalysts commonly used in industry are treated as spheres of equal specific external surface.