The multiphase flow behavior in shale porous media is known to be affected by multiscale pore size, dual surface wettability, and nanoscale transport mechanisms. However, it has not been fully understood so far. In this study, fractal model of gas–water relative permeabilities (RP) in dual-wettability shale porous media for both injected water spontaneous imbibition and the flow back process are proposed using fractal geometry. The shale pore structure is described as tortuous with different pore sizes and morphologies including slit pore, equilateral triangle, circular pore and square pore. The proportion of each pore morphology can be obtained from SEM/FIB-SEM pore structure characterization results. Injected water spontaneous imbibition after hydraulic fracturing is modeled as the capillary force dominated process and injected water flow back is modeled as a non-wetting gas phase drainage process in inorganic matter. The organic pores are deemed to be not accessible by injected water. The boundary slip of water and free gas flow in the inorganic matrix are considered while both free gas flow and adsorbed gas flow are modeled in organic matter. The proposed gas–water RP fractal model is verified via comparisons with the available experimental data and is discussed in detail. Study results reveal that gas phase RP increases with increasing pore fractal dimensions and tortuosity fractal dimensions, whereas it decreases with increasing Total Organic Carbon (TOC) volumes. Water phase RP decreases with increasing of pore fractal dimensions and tortuosity fractal dimensions, whereas it increases with increasing TOC volumes.

中文翻译：

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注水自吸回流过程中双润湿性多尺度页岩多孔介质气水相对渗透率分形模型

众所周知，页岩多孔介质中的多相流动行为受到多尺度孔径、双表面润湿性和纳米级传输机制的影响。但是，到目前为止还没有完全理解。在这项研究中，使用分形几何提出了注入水自吸和回流过程的双润湿性页岩多孔介质中气水相对渗透率（RP）的分形模型。页岩孔隙结构曲折，具有不同的孔径和形态，包括狭缝孔、等边三角形、圆形孔和方形孔。从SEM/FIB-SEM孔结构表征结果可以得到每种孔形态的比例。将水力压裂后的注入水自吸过程建模为毛管力主导过程，将注入水回流建模为无机物中的非润湿气相排水过程。有机孔被认为不能被注入水进入。考虑了无机基质中水和自由气体流动的边界滑移，而有机物质中的自由气体流动和吸附气体流动均被建模。通过与现有实验数据的比较验证了所提出的气-水 RP 分形模型，并进行了详细讨论。研究结果表明，气相RP随着孔隙分形维数和曲折分形维数的增加而增加，而随着总有机碳（TOC）体积的增加而减小。