A coal gasification mathematical model that can predict temperature, converted fraction and particle size distribution for solids have been developed for a high pressure fluidized bed. For gases in both emulsion and bubble phase, it can predict temperature profiles, gas composition, velocities and other fluid-dynamic parameters. In the feed zone, it could be considered a Gaussian distribution or any other distribution for the solid particle size. Experimental data from literature have been used to validate the model. Finally, the model can be used to optimize the gasification process changing several parameters, such as excess of air, particle size distribution, coal type and reactor geometry. (C) 2010 Elsevier Ltd. All rights reserved.