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.

中文翻译：

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双润湿性页岩耦合边界层和滑移效应的表观液体渗透率分形模型

由于复杂的润湿性和纳米孔径分布，页岩的表观液体渗透率 (ALP) 难以表征。页岩有机质中的纳米孔通常是疏水性的，无机质中的纳米孔是亲水性的。这两种不同纳米孔的流动行为差异很大，准确预测页岩的ALP是很困难的。本文提出了一种用于预测具有双重润湿性的页岩 ALP 的分形模型。考虑了水在无机孔隙中的非流动边界层效应和有机孔隙中的滑移效应，分别推导出了描述单个有机孔隙和无机孔隙中流速的方程。假设页岩有机孔和无机孔分形分布，推导了预测页岩ALP的解析表达式，并对影响页岩ALP的关键参数进行了敏感性研究。研究结果表明，非流动边界层可以降低无机孔隙的ALP，但滑移效应会增加有机孔隙的ALP。无机孔隙的 ALP 受非流动边界层厚度的影响，该厚度由驱替压力梯度、流体粘度和孔径分布决定。无机孔的 ALP 受接触角和孔径分布的影响较大。无机孔隙的 ALP 受非流动边界层厚度的影响，该厚度由驱替压力梯度、流体粘度和孔径分布决定。无机孔的 ALP 受接触角和孔径分布的影响较大。无机孔隙的 ALP 受非流动边界层厚度的影响，该厚度由驱替压力梯度、流体粘度和孔径分布决定。无机孔的 ALP 受接触角和孔径分布的影响较大。