A model has been developed that predicts the physical changes that coal and biomass char particles undergo during conversion to gaseous products at both low and high temperatures. The model takes into account the diffusion of oxygen from the ambient gas to the external surface of the particle and for the combined effects of diffusion and reaction in the particle's pores. Pore diffusion effects are described using equations for the combined effects of bulk and Knudsen diffusion, and a three-step heterogeneous reaction mechanism is used to describe oxygen adsorption and CO and CO2 desorption at the particle surface. A surface area sub-model is used that takes into account pore growth and coalescence as solid material is gasified.

The particle is divided into a number of concentric annular volume elements. The mass loss rate, the specific surface area, and apparent density in each volume element depends upon the local particle conditions, which vary as a consequence of the adsorbed oxygen and gas-phase oxygen concentration gradients inside the particle. The model predicts in time, the rate of burning, the char particle temperature, and the changes in the particle diameter, apparent density and specific surface area as combustion proceeds, given conditions in the ambient gas and the initial char properties.

The predicted variations in particle size and apparent density with mass loss for burning under various combustion regimes are used to evaluate mode of burning sub-models. Of particular interest is the prediction of the particle's effectiveness factor during conversion under conditions when the burning rate is limited by the combined effects of pore diffusion and the intrinsic chemical reactivity of the particle material. A Thiele modulus-effectiveness factor relation is developed that is applicable over the lifetime of the particle while burning in any combustion regime.