Comprehensive laboratory investigation and model fitting of Klinkenberg Effect and its role on apparent permeability in various U.S. shale formations

摘要

Hydraulic fracturing in shales is challenging because of the complicated stress status. The confining pressure imposed on a shale formation has a tremendous impact on the permeability of the rock. The correlation between confining pressure and rock permeability is complicated and might be nonlinear. Gas flow in low-permeability shales differs significantly from liquid flow because of the Klinkenberg effect, especially when the pore pressure is relatively low. The Klinkenberg effect results from gas molecule slip at the solid walls inside the nanopores, where the collision between gas molecules and solid surfaces is more frequent than the collision between gas molecules. This effect causes the increase of apparent permeability (i.e., the measured permeability). In this study, the simple effective stress law and the effective stress coefficient law were used to study the relationship between permeability and effective stress. In the simple effective stress law, the effective stress is calculated as the difference between confining pressure and pore pressure. The Klinkenberg coefficient and the effective mean pore radius can then be calculated. In the effective stress coefficient law, there is an effective stress coefficient (i.e., the Biot coefficient) which controls the influence of pore pressure on the effective stress. In this study, the effective stress coefficient was obtained by analyzing a large number of laboratory data measured under varying pore pressures and confining pressures. Specifically, the permeabilities of core samples extracted from four U.S. shale formations were measured using a pulse decay permeameter under varying combinations of confining and pore pressures. The samples were cored in the directions parallel to and perpendicular to the shale bedding planes, in order to test the role of bedding plane direction on the measured permeability. Laboratory results demonstrate that the permeabilities of all core samples fell in the range between 10~(-2