Time- and Pressure-Independent Gas Transport Behavior in a Coal Matrix: Model Development and Improvement

In research on coalbed methane, there is no accurate and reasonable description of the gas transport behavior in a coal matrix over the entire time and pressure scale. The classical Fick diffusion model is inadequate to describe the transport behavior of methane in a coal matrix. It is also very controversial to use the Darcy flow model to simulate the gas migration in a coal matrix. In this study, experiments involving methane desorption in coal particles were conducted under variable-pressure boundary conditions. Based on previous research, a new theoretical model of free gas density gradient (FGDG) is proposed in which the mass flux of the gas is proportional to the FGDG, and the key parameter is defined as the microchannel diffusion coefficient (D-m). Based on this new theoretical model, a mathematical model for the gas desorption flow in a coal matrix is developed, and the numerical solution is obtained by the dimensionless finite-difference method. It is shown that the simulation results for methane desorption based on the FGDG model and the Darcy flow model are consistent with the experimental data on the entire desorption time scale. The permeability coefficient of the Darcy flow model is independent of time but dependent on pressure, while the microchannel diffusion coefficient in the FGDG model can eliminate its dependence on time and pressure, which makes the modeling and solution of methane desorption easier and more convenient. A comprehensive investigation shows that the newly proposed FGDG model is more reasonable than the Fick diffusion model and the Darcy flow model and can be used preferentially to describe the gas transport in a coal matrix. These findings can provide a theoretical basis for further simulating and predicting coal production and gas transport behavior.