Numerical Solution of the Mathematical Model for Constant Pressure Gas Desorption in a Coal Matrix

An in-depth understanding of gas diffusion behavior in a coal matrix is essential for the prevention of gas hazards and the prediction of coalbed methane (CBM) recovery. There is still no consensus on the mechanism of coal matrix gas diffusion and further research is needed. In this paper, a mathematical model of coal matrix gas desorption and diffusion driven by the free-gas density gradient (FGDG) was proposed and developed, solved by finite-difference numerical methods, and validated with experiment data regarding gas desorption under a constant pressure condition. The dependence of key coefficients (permeability coefficient and microchannel diffusion coefficient) on pressure was analyzed, and the accuracy and rationality of Fick's model, Darcy's model, and the FGDG model were analyzed. The accuracy and rationality of the Fick, Darcy, and FGDG models were discussed. The results show that the predicted results of FGDG and Darcy models are consistent with the experimental data, and the permeability and microchannel diffusion coefficients do not vary with time. However, when the diffusion coefficient in the Fick model is a constant value, the simulated results are not consistent with the experimental data in the whole desorption time. The permeability coefficient shows a negative exponential decrease with the initial gas pressure, while the microchannel diffusion coefficient is subject to very limited fluctuation with gas pressure. Therefore, the gas desorption diffusion flow process in the coal matrix is more consistent with the free-gas density gradient-driven mechanism, which is an upgraded version of the Fick and Darcy models. This paper enriches the research ideas and thoughts of a gas diffusion model in a coal matrix.