Apparent Permeability of Clayey Shale Gas Reservoirs: Simultaneous Effects of Stress and Slippage

Abstract

Shale is a fine-grained sedimentary rock comprising various clay minerals and nanoscale pores. The internal nanoporous structure not only results in shale having ultralow permeability but also leads to a significant slip flow (non-Darcy) phenomenon. The slip effect can be described by the Klinkenberg equation, but recent studies have found deviations in ultralow permeability media. To deeply explore the gas slippage effect of shale with different orders of magnitude of permeability based on the plate flow model, an absolute permeability model considering the effects of poroelasticity (stress-dependent permeability behavior), gas absorption, and fluid dynamics (slippage effect) is established in this study. Furthermore, first-and second-order corrections are made to the absolute permeability to establish an apparent permeability model. Finally, the applicable conditions of the two modified models are verified and compared. The results show the following: (1) When the confining pressure is constant, there is a critical pressure point in which the apparent permeability (k g ) is the lowest. When the effective stress is constant, the apparent permeability continues to decrease with the increase of the pore pressure. (2) When 0 < k g < 5 mD or 0 < k g < 0.5 mD, the first-order slip coefficient is an order of magnitude larger than the secondorder slip coefficient. When 0 < k g < 0.01 mD or 0 < k g < 0.005 mD, the contribution of the second-order slip coefficient is greater than that of the first-order slip coefficient. (3) The clay content is negatively correlated with permeability and positively correlated with the stress dependence of the permeability. Notably, this conclusion is valid only when the permeability is of a similar order of magnitude. These results may increase our understanding of slip flow within the nanopores of low-permeability reservoirs, which is necessary to accurately predict k g of unconventional reservoirs.