Analytical Solution of Gas Flow in Rough-Walled Microfracture at In Situ Conditions

The development of the unconventional gas and CO2 sequestration is moving to deep formations. Because of the small flow pathways in the matrix, the Knudsen number might be high even though the gas is dense. In fact, due to the relatively high pressure at in situ conditions, gas flow in microfractures usually manifests a strong slip and nonideal gas effects. Therefore, understanding the coupling mechanism of these two on gas flow in rough-walled microfractures is required to accurately model subsurface flow behavior. In this study, pressure-driven gas flow in rough-walled microfracture is analyzed in depth. Starting from the local governing equations for gas flow, a local flow model that includes gas slip and nonideal gas effects is derived by solving the Stokes equation with a first-order slip boundary condition. Focusing at the representative elementary volume scale, the upscaled solutions to gas flow in a fracture with sinusoidal surface are derived to obtain the apparent permeability. The impact of nonideal gas effects, fracture roughness and aperture, and the tangential momentum accommodation coefficient on CH4 and CO2 flow is analyzed. The results show that fracture roughness introduces a high degree of heterogeneity in gas flow. At in situ conditions effects of gas slip, fracture roughness and tangential momentum accommodation coefficient on gas flow are reduced. The ideal gas law is capable of estimating CH4 flow to some extent. However, it fails to estimate CO2 flow in microfractures.