Abstract Permeability significantly affects the production of shale oil and shale gas, and shale microstructures characterized by pore and fracture spaces innately affect the permeability. However, the quantitative characterization of permeability related to pore and facture spaces is not fully understood. This work aims to propose 3D spatial fracture-pore fractal dimensions to predict shale permeability and their effects on fluid flow behaviors. First, triaxial compressive stress and X-ray CT imaging tests are conducted on shale samples to establish fractural models. The digital surface roughness segmentation (DSRS) method is then proposed to obtain the fracture-pore microstructures. Next, spatial fractal dimensions of self-similarity microstructures are proposed to predict the microstructural permeability. Finally, two-phase fluid flows are simulated to study the hydrocarbon flow behaviors in fractural microstructures using the level set method. The results show that the average relative errors between the microstructural spatial dimensions and theoretical fractal dimensions are all less than 3%, highlighting the accuracy of the proposed method. The numerical results for permeability are very close to the analytical solutions, in which fracture permeability is almost 100 times the order of magnitude of the pore structure permeability in the nanoscale pore shale, and the facture and pore structure permeabilities both increase with increasing spatial fractal dimension. The changes of fluid flow behaviors are similar to the permeability variations, and the fluid phase fraction increases with increasing fractal dimension.

中文翻译：

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纳米级孔隙页岩分形维数的数字评估以及对页岩渗透率的微观结构洞察

摘要 渗透率显着影响页岩油和页岩气的产量，以孔缝空间为特征的页岩微观结构对渗透率有先天影响。然而，与孔隙和裂缝空间相关的渗透率的定量表征尚未完全了解。这项工作旨在提出 3D 空间裂缝 - 孔隙分形维数，以预测页岩渗透率及其对流体流动行为的影响。首先，对页岩样品进行三轴压应力和X射线CT成像测试，建立压裂模型。然后提出了数字表面粗糙度分割（DSRS）方法来获得裂缝孔隙微观结构。接下来，提出了自相似微结构的空间分形维数来预测微结构渗透率。最后，使用水平集方法模拟两相流体流动以研究裂缝微观结构中的烃类流动行为。结果表明，微观结构空间维数与理论分形维数的平均相对误差均小于3%，突出了所提方法的准确性。渗透率的数值结果与解析解非常接近，其中裂缝渗透率几乎是纳米级孔隙页岩孔隙结构渗透率的100倍数量级，裂缝和孔隙结构渗透率均随着空间分形维数的增加而增加. 流体流动行为的变化类似于渗透率变化，流体相分数随着分形维数的增加而增加。