A Novel Apparent Permeability Model in Shale Gas Reservoirs

Abstract

A novel apparent permeability model of shale gas is derived considering the stress dependence, the thickness of adsorbed layer, slip flow, Knudsen diffusion and surface diffusion. The thickness of the adsorbed layer is derived according to the porosity occupied by the adsorbed phase in the capillary model. Consequently, the impact of the adsorbed layer and its change with the pressure on apparent permeability can be clearly revealed in the novel model in ultramicropores, or micropores, or mesopores, or macropores. With the stress dependence and the thickness of adsorbed layer considered simultaneously, the effective hole radius is substantiated to be smaller than the original hole radius to a certain degree. On account of this, the ratio of apparent permeability to the intrinsic permeability computed by the novel model is a lot distinct from the existing models. As the pressure increases, the ratio in the novel model declines from above 1 to below 1, followed by a slight upward trend. However, the ratio in other models drops all the way and yet remains above 1 as the pressure rises. Finally, the impact factors of permeability, including stress dependence coefficient, hole radius, reservoir pressure, Langmuir volume and Langmuir pressure, are analyzed. The contribution of slip flow, Knudsen diffusion and surface diffusion to apparent permeability is also illustrated.