A new formulation of apparent permeability for gas transport in shale

Recently, a few apparent permeability formulations have been proposed for gas transport in tight formations aiming of correcting flow deviation caused by slip flow and Knudsen diffusion. However, the effect of surface diffusion has always been neglected. Surface diffusion happens when gas molecules adsorb on the solid surface. Considering significant proportion of adsorbed gas (20%-80%) in shale, surface diffusion could play an important role during gas transport. In this paper, we presented a new apparent permeability formulation, which takes surface diffusion into account, for gas transport in shale. The parametric study of the presented formulation shows apparent permeability is sensitive to pressure, temperature, pore radius and surface roughness. The permeability caused by surface diffusion can be several times larger than shale intrinsic permeability at low pressure. Neglecting surface diffusion in the formulation would underestimate gas flux by 25%.