TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Method: The step of determining the reactor production rate includes the effect of a water-gas shift reaction. Determining a reactor production rate of reaction products for each potential catalyst diameter in the many potential catalyst diameters includes selecting many particle concentrations, where the particle concentration is defined as the quantity of particles per unit volume of the bulk medium, and determining the reactor production rate of reaction products for the each potential catalyst diameter at each particle concentration in many particle concentrations. Determining the reactor production rate further includes correlating the catalyst particle granular temperature to the one or more mass transfer coefficients. Preferred Components: The granular temperature is substantially in the form of turbulence kinetic energy. The potential catalyst diameter in the many potential catalyst diameters is an effective catalyst particle diameter based upon the relationship between catalyst particle concentration and a coagulation coefficient for the catalyst particles. The bulk medium is an inert liquid and the catalyst particles are in the form of a powder and the inert liquid and the powder form a slurry. The optimum catalyst diameter for reactor production of methanol and other liquid hydrocarbon fuels in the slurry bubble column reactor is 60-70 mu m. The optimum catalyst diameter is 20-120 mu m. The slurry bubble column reactor is a Fischer-Tropsch reactor producing hydrocarbon fuels form synthesis gas, and the catalyst particles are comprised of a Fischer-Tropsch catalyst.    TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The reactor is a gas-solid, liquid-solid or gas-liquid-solid fluidized bed reactor, preferably a slurry bubble column reactor for producing methanol and other liquid hydrocarbon fuels from natural gas. The hydrodynamic model utilizes multi-phase computational fluid dynamics with the kinematic viscosity of the bulk medium as input and the hydrodynamic model is capable of computing hold-up and flow patterns for gas-liquid flow and gas-liquid-solids flow.