Time-dependent dynamic diffusion processes in coal: Model development and analysis

Abstract

Gas diffusion, a critical process during underground gas drainage and coalbed methane recovery, is viewed as the bridge connecting the coal matrix and fractures. Study on gas diffusion is of great significance to the understanding of gas migration in coal seams and the prediction of gas production. Gas diffusivity is one of the most important parameters characterizing the diffusion process. In previous studies, diffusivity was generally viewed as a constant, but the experimental results show that it is strongly dependent on diffusion time. In order to fill the gap between the existing theories and experimental results, this paper proposes a physical model for gas diffusion in coal matrix, based on which a time-dependent diffusivity model is developed from the perspective of fluid dynamics. In this model, the diffusivity of coal particles is divided into two parts, namely time-dependent diffusivity and residual diffusivity. With the continuation of the diffusion process, the diffusivity exponentially decreases with the time. Based on the time-dependent diffusivity and the classical unipore diffusion model, a time-dependent diffusion model is established. To indicate the rationality and superiority of the newly developed model, both the unipore diffusion model and time-dependent diffusion model are used to fit the experimental data, and the results show that the fitting effect of time-dependent diffusion model is obviously better than that of the unipore diffusion model. Finally, the physical nature of the time dependence of the diffusivity is discussed, and it is believed that the change of the pore pressure and its resultant alteration of the pore structure are the main reasons for the variation of diffusivity with time.