With an extension of the geological entropy concept in porous media, the approach called directional entrogram is applied to link hydraulic behavior to the anisotropy of the 3D fracture networks. A metric called directional entropic scale is used to measure the anisotropy of spatial order in different directions. Compared with the traditional connectivity indexes based on the statistics of fracture geometry, the directional entropic scale is capable to quantify the anisotropy of connectivity and hydraulic conductivity in heterogeneous 3D fracture networks. According to the numerical analysis of directional entrogram and fluid flow in a number of the 3D fracture networks, the hydraulic conductivities and entropic scales in different directions both increase with spatial order (i.e., trace length decreasing and spacing increasing) and are independent of the dip angle. As a result, the nonlinear correlation between the hydraulic conductivities and entropic scales from different directions can be unified as quadratic polynomial function, which can shed light on the anisotropic effect of spatial order and global entropy on the heterogeneous hydraulic behaviors.

中文翻译：

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使用方向地质熵通过 3D 裂缝网络估计导水率的各向异性

随着地质熵概念在多孔介质中的扩展，称为定向熵图的方法被应用于将水力行为与 3D 裂缝网络的各向异性联系起来。一种称为方向熵尺度的度量用于测量不同方向上空间顺序的各向异性。与基于裂缝几何统计的传统连通性指标相比，方向熵尺度能够量化非均质3D裂缝网络中连通性和导水率的各向异性。根据对多个3D裂缝网络中的定向熵图和流体流动的数值分析，不同方向的导水率和熵尺度均随着空间顺序（即迹线长度减小和间距增大）而增大，并且与倾角无关角度。因此，不同方向的水力电导率和熵尺度之间的非线性相关性可以统一为二次多项式函数，这可以揭示空间秩序和全局熵对非均质水力行为的各向异性影响。