Much work has been carried out on adsorption capacity of coals. Diffusive transport processes within the coal matrix blocks could be the rate-limiting step for adsorption during gas injection and production operations. Identifying these processes and determining their contributions to overall mass transport is a complex and time consuming procedure. The paper presents numerical diffusion models in varying coal particles and investigates transport mechanisms. For this purpose, the coal particle is represented as a microporous solid penetrated by a network of larger interconnected macropores. The solid adsorbs the bulk of the gas. A simple relationship between the apparent and intrinsic Fickian diffusion coefficients is derived in the case of single-component (methane) transport and Langmuir-type adsorption. Mass transport in the bidisperse coal particle is significantly influenced by the adsorption in the microporous solid. The investigation is then extended to study concentration dependence of the microporous solid diffusion for binary (methane-CO2) mixtures using the Maxwell-Stefan formulation. It is found that co-diffusion of the gas molecules enhances the gas mass transport in the solid in the presence of competitive sorption dynamics, while counter-diffusion may diminish the gas mass transport. The influence of lateral interactions among the adsorbed molecules in the solid phase is discussed. The work finds application in modelling CBM and CO2-ECBM processes.