Gas diffusivity in coal is an important parameter in estimating the recovery rate of coal seam gas. It is well recognized that the diffusivity is not a constant and gas pressure dependent. Previous studies reported contradicting results: some laboratory results showed that diffusivity is positively correlated with pore pressure while others indicated that diffusivity decreases with pore pressure. The goal of this study is to resolve this discrepancy. In this study, a fully coupled finite element (FE) model of coal deformation (gas sorption induced swelling or shrinking), gas flow in fractures and gas diffusion in coal matrix is developed to quantify the role of gas diffusion in coal matrix. In this model, the gas diffusivity is defined as a function of the effective stress in the matrix. The effective stress in the coal matrix is related to the total stress, the matrix gas pressure, and the fracture gas pressure. This definition itself can resolve the observed contradiction: there are two gas pressures, one is for the matrix while the other for the fractures; the gas diffusivity is directly proportional to the matrix gas pressure, and inversely proportional to the fracture gas pressure. We applied the coupled model to simulate the evolution of gas diffusivity during the extraction of coal seam gas. Simulation results are consistent with our novel definition of gas diffusivity.

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