A dynamic model of apparent permeability for micro fractures in shale gas reservoirs

The object of this paper is to study the coupled impacts of medium deformation and slippage effect on variation of apparent permeability for micro fractures, and to investigate the mechanism of effective stress condition and pore structure parameters on gas flow in shale gas reservoirs. A dynamic apparent permeability model for micro fractures is presented, which accounts for the coupled effects of medium deformation and gas slippage simultaneously based on the smooth plate model and combined with the fractal theory, as well as microscopic gas flow mechanism. Then the reliability verification and sensitivity analysis of the established model are performed. The results show that: The apparent permeability decreases firstly and then increases slowly as pore pressure reduces, and the critical pressure is about 5 MPa. The huge difference between the two coupled mechanism (medium deformation and slippage effect), resulting in the variation of apparent permeability curve with different effective stress states, which also explained the variation of stress sensitivity for shale with different loading modes in testing from microscopic perspective. The deeper "groove" of the apparent permeability curve when the maximum aperture is smaller. In addition, the higher the porosity and fractal dimension of the aperture, and the lower the tortuosity fractal dimension, the greater the apparent permeability is.