Abstract: 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.

摘要： 本文按多孔催化剂内多组分分子扩散及努森扩散联合过程的特性,导出了描述等温球形催化剂内单一反应的反应物和产物浓度分布的二阶非线性常微分方程组.微分方程中各个反应组分的浓度梯度强烈相互耦合.在计算机上用打靶法求解此常微分方程组提出的两点边值问题,即可求得各个反应组分的浓度分布和催化剂效率因子的数值解.由于反应组分的有效扩散系数间的差异,催化剂内反应组分的组成变化之间的关系不再符合反应的化学计量关系.当内扩散过程的阻滞作用严重时,催化剂颗粒内会出现“死区”,死区内反应组分的浓度趋近于平衡浓度,实际上不再继续进行反应.存在死区时,使用此数学模型及解题方法可求出死区的半径及此情况下催化剂的效率因子.工业上常用的圆柱状催化剂按照相等比外表面积的球体处理.