A systematic approach has been developed to estimate the relationship between the permeability and connectivity of two-dimensional fracture networks, in which the network connectivity is evaluated with the concept of geological entropy as informative index of spatial disorder. The geological entropy is quantified by the entropic scale, a metric developed by Bianchi and Pedretti (2018), which is here applied to integrate multiple properties of two-dimensional fracture networks, including aperture, spacing, length, orientation. Through the comparisons among several existing connectivity indicators including the entropic scale in an illustrative example, only the entropic scale is positively correlated with the permeability concerning aperture and can be successfully used to quantify the network connectivity. In order to understand connectivity characteristics dependence of the permeability, a computational method combining fracture network generation and steady-state flow simulation is developed. Based on the results of detailed numerical simulations considering hydraulic behavior and connectivity characteristic in various fracture networks, the entropic scale and permeability are simultaneously inversely proportional to length and proportional to spacing with the same global entropy, but exhibit weak dependence on the orientation variation. A simple closed-form empirical expression in terms of quadratic polynomial model between the permeability and entropic scale is proposed. The results indicated that geological entropy is valid and appropriate to quantify the connectivity and predict the permeability of two-dimensional fracture networks.

中文翻译：

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利用地质熵评价二维裂缝网络渗透性的连通性特征

已经开发了一种系统方法来估计二维裂缝网络的渗透率和连通性之间的关系，其中网络连通性以地质熵的概念作为空间无序的信息指标进行评估。地质熵通过熵标度进行量化，熵标度是 Bianchi 和 Pedretti (2018) 开发的一种度量标准，这里应用于整合二维裂缝网络的多个属性，包括孔径、间距、长度、方向。通过一个示例中包括熵尺度在内的几个现有连通性指标的比较，只有熵尺度与孔隙渗透率正相关，可以成功地用于量化网络连通性。为了理解渗透率的连通性特征依赖性，开发了一种结合裂缝网络生成和稳态流动模拟的计算方法。基于考虑各种裂缝网络中水力行为和连通性特征的详细数值模拟结果，熵尺度和渗透率同时与长度成反比，与间距成反比，具有相同的全局熵，但对方向变化的依赖性较弱。提出了渗透率和熵尺度之间的二次多项式模型的简单闭式经验表达式。结果表明，地质熵对于量化二维裂缝网络的连通性和预测渗透率是有效和适当的。