Experimental and Numerical Analyses of Apparent Gas Diffusion Coefficient in Gas Shales

A unified model of apparent gas diffusion coefficient in gas shales has been developed by considering the combined effects of Knudsen diffusion, Fick diffusion, and surface diffusion. Results showed that the model predictions matched the measured apparent gas diffusion coefficient in Longmaxi black shale reasonably well when the correction factor for real surface diffusion was approximately equal to 0.01. Results of sensitivity analyses revealed that Knudsen diffusion and Fick diffusion control the bulk of the methane diffusion in shale nanopores. The governing mechanism of methane molecules transport through shale nanopores varied depending on the overburden pressure, pore pressure, and resultant effective stress (i.e., contributions of Fick diffusion and Knudsen diffusion to the apparent gas diffusion coefficient varied depending on the level of pore pressure and effective stress). The apparent methane diffusion coefficient also varied depending on the size of the pore space. The effective radius of pores in a formation with a relatively high effective stress is smaller than that of the one with a relatively low effective stress. Greater apparent methane diffusion coefficient is, therefore, observed in a relatively lower effective stress formation because of the increasing contributions of Fick and Knudsen diffusion. Considering the combined effects of pore pressure and effective stress, we have found that the overall impact of gas production from shale formations (i.e. the decreasing pore pressure and the corresponding increase in effective stress) was to increase apparent methane diffusion coefficient, which would result into further stimulation of the gas production from shale reservoirs.