In this investigation, a mathematical model for HDS of diesel fuel in a slurry bubble column reactor was developed. The model is based on the axial dispersion of the heterogeneous gas flow regime, which includes two various bubble classes: large (20 +/- 70 mm) and small (1 +/- 10 mm). By assuming only large or large plus small bubbles in the column, single- and two-bubble class mode equations are developed. The developed models to solving the mass and enthalpy balances from which the sulfur conversion was obtained that undertaken. The chemical kinetics over NiMoS/gamma Al2O3 catalyst were undertaken for the reaction rate of the involved reactions. The reactor operating conditions including pressure of 50 bar at a temperature of 350 degrees C, inlet superficial gas velocity of 0.1 m s(-1), and liquid velocity of 0.005 ms(-1) were chosen. The obtained modeling results revealed 99.53% and 98.95% of sulfur removal for single- and two- bubble classes, respectively. Furthermore, the results of the two models compared satisfactorily with experimental data from open literature, and a collation utilizing empirical data between the two hydrodynamic models demonstrated that the two-bubble model was more compatible with the empirical data than the single-bubble model. The results of modeling including temperature variations, other reactor characteristics and conversion of desired product were discussed throughout in this research in detail. (C) 2015 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.