Modeling of Gas Desorption and Diffusion Kinetics in a Coal Seam Combined with a Free Gas Density Gradient Concept

Gas diffusion in a coal seam plays an essential role in the efficient and effective exploitation of underground coalbed methane (CBM). Based on the concept of free gas density gradient-driven flow, in this work, we formulated and validated a theoretical model to quantify gas desorption and diffusion kinetics in a coal seam at different temperatures. Once the governing equations are formulated and non-dimensionalized, they are numerically solved with the finite difference method and then validated with the experimental measurements on gas desorption at different temperatures. The mechanism of temperature affecting gas diffusion kinetics was elaborately explored. Also, the advantages of the proposed free gas density gradient model (FGDGM) compared to the traditional unipore diffusion model (UDM) were well evaluated and discussed. It is found that the FGDGM simulations are basically consistent with the experimental data, but the UDM prediction deviates significantly from the experimental measurements at different temperatures. By introducing a new dimensionless temperature variable and performing sensitivity analysis, the dimensionless gas desorption is found to increase with temperature, while the incremental gas desorption varies across the entire temperature range. With the temperature increasing from 293 to 313 K, both the gas desorption increment and gas yield enhancement are found to be the largest. In addition, there exists a linear relationship between diffusivity and temperature because a high temperature increases the gas molecules' activity and accelerates the pore expansion. It is clearly found that temperature has a considerable contribution to the gas diffusion kinetics in a coal seam, and appropriately boosting the coal temperature to enhance CBM recovery is feasible and valuable.