Efficiency and selectivity of hydrogenating depolymerization of the coal extract benzene-insoluble part over the heterogeneous Co-Mo/Al2O3 catalyst were assessed using a mathematical model. The analytical equations of the mathematical model were generated based on material balance incorporating the physico-chemical phenomena (reaction and diffusion) both in the autoclave and the catalyst grain. The equations offer the possibility for predicting changes of the reactants in the autoclave during the process and for determining the distribution of reactant concentrations in the grain as a function of its radius. The analytical equations of the model serve as the basis of the algorithm for assessing the influence of restrictive diffusion on the effectiveness and selectivity of the catalyst, and also for defining the optimal radii of the catalyst's pores to enable free transport of reactants in the grain interior. (C) 2015 The Chemical Industry and Engineering Society of China, and Chemical Industry Press. All rights reserved.