Effect of stress, concentration and temperature on gas diffusion coefficient of coal measured through a direct method and its model application

• Diffusion coefficients of coal were directly measured with stable concentration gradient. • The influence of stress on diffusion coefficient is much smaller than seepage. • The influence trend of gas pressure/concentration is different between adsorptive gas and non-adsorptive gas. • The diffusion model with variable diffusion coefficient is established, and the predicted result is consistent with the measured result. Diffusion in coal is a key process of gas migration in coal seams. Usually, the gas diffusion coefficient is inferred from desorption data indirectly. In this paper, a directly steady-state method based on Fick's law, was applied to get diffusion coefficients under various conditions of stress, concentration gradient, temperature and gas type. It is found that the gas diffusion coefficient is in a negatively linear relationship with the stress, but this correlation is weak. The diffusion coefficient of methane decreases in a power function with the increase of concentration gradient, while the diffusion coefficient of non-adsorptive gas (helium) decreases first and then increases. The gas diffusion coefficient in coal is positively correlated with temperature, satisfying Arrhenius formula. Based on the measured relationships and Fick's law, a model considering diffusion coefficient variation for coal particles was established and used to predict the gas desorption characteristics of coal with the varying temperature. The predicted result is consistent with the measured result, indicating the reliability of the direct measurement method of diffusion coefficient. It can provide a new way for the prediction of gas diffusion behavior in coal under changing conditions.