Abstract Initial water content and subsequent fracturing fluid injection lead to gas-water flow in shale nanopores, especially the water-wet pores. But there is few research and experiment to introduce relative permeability curves governing multiphase transport behaviors in shale nanopores. With the consideration of water true slippage and gas slippage, an analytical model illustrating gas-water relative permeability curve in fractal-like tree pore structures has been constructed, aiming to explain gas-water two phase flow behaviors and further evaluate the effects of pore size distributions and water films on gas-water transport. Sensitivity analysis verifies that smaller pore radius, more branching levels and less branching number tend to increase the gas relative flow capacity. Also, ignoring the existence of high-viscosity water molecules has been discovered to reduce water flow resistance. But if the high-viscosity water film loses its mobility, water relative permeability drops slightly. In contrast, mobile bulk water molecules are mainly conducive to increase the gas molecules relative movements. Besides, the analysis of pore size distribution confirms that the fractal-like tree network possesses a more significant gas dominancy compared with log-normal pore network.

中文翻译：

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页岩气水相对渗透率曲线的分形模型

摘要 初始含水量和随后的压裂液注入导致页岩纳米孔隙，特别是水湿孔隙中的气水流动。但很少有研究和实验介绍控制页岩纳米孔中多相输运行为的相对渗透率曲线。考虑水真滑移和气滑移，构建了分形树状孔隙结构气水相对渗透率曲线的解析模型，旨在解释气水两相流动行为，进一步评价孔隙大小的影响气水输送的分布和水膜。灵敏度分析证实，较小的孔半径、更多的支化水平和更少的支化数往往会增加气体的相对流动能力。还，已发现忽略高粘度水分子的存在会降低水流阻力。但如果高粘度水膜失去流动性，水的相对渗透率会略有下降。相比之下，流动的本体水分子主要有利于增加气体分子的相对运动。此外，孔径分布分析证实，与对数正态孔隙网络相比，分形树状网络具有更显着的气体优势。