A mathematical model to describe the hydrodynamics of the slurry bubble-column reactor (SBCR) for converting synthesis gas into liquid fuels has been developed. This model includes the complete granular temperature balance based on the kinetic theory of granular flow. The kinetic theory model and the computer code(1) were extended to include the effect of the mass-transfer coefficient between the liquid and gas and the water gas shift reaction in the Air Products/DOE LaPorte SBCR. In this model, the mass-transfer coefficient is an input. It was estimated from a relationship between the fundamental equations of the boundary layers and the turbulent kinetic energy of particles (granular temperature) computed by the hydrodynamic model with no reaction. We have varied the particle size from 20 to 100 mu m and discovered a maximum in the granular temperature. For the particles over this range, the mass-transfer coefficient has the highest values. With reaction, this model was used to predict the slurry height, gas holdup, and rate of methanol production of the Air Products/DOE LaPorte SBCR. The computed granular temperature was around 30 cm(2)/s(2), and the computed catalyst viscosity was close to 1.0 cP, as shown by Wu and Gidaspow (Chem. Eng. Sci. 2000, 55, 573). The estimated volumetric mass-transfer coefficient has a good agreement with experimental values shown in the literature. A critical issue in the SBCR that has not been addressed in the literature is that of optimum particle size. The optimum size was determined for maximum methanol production in a SBCR. The size was about 60-70 mu m, which was found for maximum granular temperature in the model with no reaction.