Fluid transport in shales is complex due to the various storage spaces and multiple transport mechanisms, especially for multiphase transport during flowback and early stage of production. This study proposes a gas-water relative permeability fractal model during a gas displacing water process in shale gas reservoirs, with incorporations of (1) real gas transport controlled by Knudsen Number (Kn) and second-order slip boundary, (2) slip length for water phase transport, (3) a mobile water film with varying thickness due to rock–fluid interaction and (4) stress-dependence. Specially, the varying thickness of water film is determined according to the extended Derjaguin–Landau–Verwey–Overbeek (DLVO) theory through van der Waals, electrostatic and structural force during a drainage process. Moreover, the organic matter (OM) and inorganic matter (IOM) pore structures are considered with individual pore/tortuosity fractal dimensions. The proposed model is verified by comparing with an analytical model and experimental data. Results show that the decreasing pore pressure during depressurization brings a decline in gas relative permeability, while the decreasing pore pressure has little impact on water relative permeability. The impact of pore and tortuosity fractal dimensions of OM can be ignored compared with that of IOM. Furthermore, neglecting the mobile water film with varying thickness during a gas drainage process leads to an overestimation of gas relative permeability, especially at smaller pore sizes. This work presents a comprehensive model to determine gas-water relative permeability in shales by considering fluids/reservoir properties and rock–fluid interaction in full, which reveals multiphase transport mechanisms in the unconventional reservoirs.

中文翻译：

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具有多种传输机制和岩液相互作用的页岩多孔介质中的分形多相传输模型

页岩中的流体运移复杂，储集空间多样，运移机制多样，尤其是返排和生产初期的多相运移。本研究提出了页岩气储层气驱水过程中的气水相对渗透率分形模型，包括（1）由克努森数（Kn）和二级滑动边界控制的实际气体输送，（2）滑动长度对于水相传输，（3）由于岩石 - 流体相互作用和（4）应力依赖性而具有不同厚度的流动水膜。特别地，水膜的变化厚度是根据扩展的 Derjaguin-Landau-Verwey-Overbeek (DLVO) 理论通过范德华力、静电力和排水过程中的结构力确定的。而且，有机物 (OM) 和无机物 (IOM) 孔隙结构被考虑为具有单独的孔隙/曲折分形维数。通过与分析模型和实验数据的比较来验证所提出的模型。结果表明，降压过程中孔隙压力的降​​低会导致气体相对渗透率的下降，而孔隙压力的降​​低对水的相对渗透率影响不大。与IOM相比，OM的孔隙和曲折分形维数的影响可以忽略不计。此外，在瓦斯抽采过程中忽略不同厚度的流动水膜会导致气体相对渗透率的高估，特别是在较小的孔径下。