Gas diffusion coefficient estimation of coal: A dimensionless numerical method and its experimental validation

The diffusion coefficient is one of the key parameters to control gas desorption and transport kinetics in coal with pressure evolution. Accurate estimation of diffusion coefficient of coal is of great significance for coalbed methane production planning and coal mine gas control management. However, the most commonly used analytical method was found to underestimate the gas diffusion coefficient due the assumption of constant surface concentration in solving the Fick diffusion model. This study conducted a series of experiments to measure the gas adsorption and diffusion using the volumetric method. The Fick diffusion model was solved by both analytical method and the numerical method to estimate the gas diffusion coefficient based on the experimental data. We compared estimated diffusion coefficients from both the analytical and numerical approaches. It is found that the diffusion coefficient is a pressure dependent parameter and it negatively correlates with the pressure. The gas diffusivity in coal is also a gas type-dependent property. As observed, the CO₂ diffusion coefficients were found to be higher than of CH₄. It suggests CO₂ molecules diffuse faster than CH₄ molecules through the same porous coal matrix. This may be attributed to CO₂ molecules own relative smaller kinetic diameter than CH₄ molecules. The analytical method will underestimate the gas diffusion coefficient because it assumes a constant gas concentration boundary condition. The numerical method is a better representation of the real gas diffusion process and we recommend to using the numerical method for the diffusion coefficient estimation if possible.