NOVELTY - Method of determining optimum catalyst diameter from many potential catalyst diameters, comprises: expressing one or more mass transfer coefficients describing one or more mass transfers of the reactants from a bulk medium to the catalyst particles; determining many potential catalyst diameters over a desired range; determining reactor production rate of reaction products based on the mass transfer coefficients; and selecting an optimum diameter, where the optimum diameter is the potential catalyst diameter that produces the maximum reactor production rate of reaction products.    USE - The method is useful for determining optimum catalyst diameter for use in a reactor (slurry bubble column reactor), which is useful for producing methanol and other liquid hydrocarbon fuels from natural gas and synthesis gas (all claimed).    ADVANTAGE - The method permits accurate determination of the mass transfer coefficient in slurry bubble column reactor and other fluidized beds.    DETAILED DESCRIPTION - Method of determining an optimum catalyst diameter from many potential catalyst diameters for use in a reactor facilitating contact between reactants in a bulk medium and catalyst particles for the production of reaction products, where the bulk medium is one of gas, liquid or gas-liquid and where the bulk medium transfers kinetic energy to the catalyst particles and the reactor maintains reaction promoting conditions, comprises: expressing one or more mass transfer coefficients describing one or more mass transfers of the reactants from the bulk medium to the catalyst particles using, k(L) = ((D(L) theta one quarter ) divide by ( nu dp) one half )x Sc1/3, where, k(L) is one of the mass transfer coefficients, D(L) is diffusivity coefficient of the mass transfers from the bulk medium to the catalyst particles, nu is kinematic viscosity of the bulk medium and the catalyst particles, theta is catalyst particle granular temperature, Sc is Schmidt number ( nu divide by D(L)), dp is dimension of the each potential catalyst diameter; determining many potential catalyst diameters over a desired range; determining a reactor production rate of reaction products based on the mass transfer coefficients for each potential catalyst diameter in the many potential catalyst diameters, by utilizing a hydrodynamic model of the reactor, the bulk medium and the catalyst particle, where the hydrodynamic model determines a catalyst particle granular temperature and the hydrodynamic model determines the reactor production rate based on the mass transfer coefficients; and selecting an optimum diameter, where the optimum diameter is the one of the each potential catalyst diameter from the many potential catalyst diameters that produces the maximum reactor production rate of reaction products.