Complicated gas–water transport behaviors in nanoporous shale media are known to be influenced by multiple transport mechanisms and pore structure characteristics. More accurate characterization of the fluid transport in shale reservoirs is essential to macroscale modeling for production prediction. This paper develops the analytical relative permeability models for gas–water two-phase in both organic and inorganic matter (OM and IM) of nanoporous shale using the fractal theory. Heterogeneous pore size distribution (PSD) of the shale media is considered instead of the tortuous capillaries with uniform diameters. The gas–water transport models for OM and IM are established, incorporating gas slippage described by second-order slip condition, water film thickness in IM, surface diffusion in OM, and the total organic carbon. Then, the presented model is validated by experimental results. After that, sensitivity analysis of gas–water transport behaviors based on pore structure properties of the shale sample is conducted, and the influence factors of fluid transport behaviors are discussed. The results show that the gas relative permeability is larger than 1 at the low pore pressure and water saturation. The larger pore pressure causes slight effect of gas slippage and surface diffusion on the gas relative permeability. The larger PSD fractal dimension of IM results in larger gas relative permeability and smaller water relative permeability. Besides, the large tortuosity fractal dimension will decrease the gas flux at the same water saturation, and the surface diffusion decreases with the increase of tortuosity fractal dimension of OM and pore pressure. The proposed models can provide an approach for macroscale modeling of the development of shale gas reservoirs.

中文翻译：

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考虑润湿特性的页岩多孔介质中气水传输的分形模型

已知纳米多孔页岩介质中复杂的气水传输行为受多种传输机制和孔隙结构特征的影响。更准确地描述页岩储层中的流体输送对于生产预测的宏观建模至关重要。本文利用分形理论建立了纳米多孔页岩有机质和无机质（OM 和 IM）中气水两相的相对渗透率分析模型。考虑页岩介质的非均质孔径分布（PSD）而不是具有均匀直径的曲折毛细管。建立了 OM 和 IM 的气-水输运模型, 包括由二级滑移条件描述的气体滑脱、IM 中的水膜厚度、OM 中的表面扩散和总有机碳。然后，所提出的模型由实验结果验证。之后，基于页岩样品的孔隙结构特性进行了气水运移行为敏感性分析，并讨论了流体运移行为的影响因素。结果表明，在低孔隙压力和含水饱和度下，气体相对渗透率大于1。较大的孔隙压力导致气体滑脱和表面扩散对气体相对渗透率的影响较小。IM的PSD分形维数越大，气体相对渗透率越大，水相对渗透率越小。此外，在相同含水饱和度下，较大的曲折分形维数会降低气体通量，而随着OM曲折分维数和孔隙压力的增加，地表扩散会减小。