A Fractal Model For Apparent Liquid Permeability Of Dual Wettability Shale Coupling Boundary Layer And Slip Effect

The apparent liquid permeability (ALP) of shale is challenging to be characterized due to complex wettability and nanopore size distribution. The nanopores in organic matter of shale are usually hydrophobic and the nanopores in inorganic matter are hydrophilic. The flow behaviors in these two different nanopores are quite different, and accurately predicting the ALP of shale is difficult. This paper proposes a fractal model for predicting the ALP of shale with dual wettability. The nonflowing boundary layer effect of water in inorganic pores and the slip effect in organic pores are considered, and the equations for describing the flow rate in single organic pore and inorganic pore are derived, respectively. With the assumption of the fractal distributions of organic pores and inorganic pores in shale, the analytical expression for predicting the ALP of shale is derived, and the key parameters influencing shale ALP are analyzed with sensitivity study. The research results show that the nonflowing boundary layer can reduce the ALP of inorganic pores, but slip effect will increase the ALP of organic pores. ALP of inorganic pores is affected by the thickness of nonflowing boundary layer, which is determined by the displacement pressure gradient, fluid viscosity, and pore size distribution. ALP of inorganic pores is more affected by contact angle and pore size distribution.