The influence of geometrical factors on the efficiency of diffusion-controlled reactive processes that take place on the surface of a porous catalyst particle is studied using the theory of finite Markov processes. The reaction efficiency is monitored by calculating the mean walklength [n] of a randomly diffusing atom/molecule before it undergoes an irreversible reaction at a specific site (reaction center) on the surface. The three cases (geometries) considered are as follows. First, we assume that the surface is free of defects and model the system as a Cartesian shell (Euler characteristic, Omega = 2) of integral dimension d = 2 and uniform site valency v(i) = 4. Then, we consider processes in which the diffusing reactant confronts areal defects (excluded regions on the surface); in this case, both cl and Omega remain unchanged, but there is a constriction of the reaction space, and the site valencies v(i) are no longer uniform. Finally, the case of a catalyst with an internal pore structure is studied by modeling the system as a fractal solid, viz. the Menger sponge with fractal dimension cl = 2.73. The sensitivity of the reaction efficiency to the dimensionality of the reaction spare (integer vs fractal), to the local symmetry at the reaction center las defined by the site valency v(i)), and to the size of the catalyst particle las specified by the number N of lattice sites defining the system) is quantified by comparing the numerically exact values of [n] calculated in each case.