Fractured rocks are often modeled as multiscale populations of interconnected discrete fractures (discrete fracture network, DFN). Graph representations of DFNs reduce their complexity to their connectivity structure by forming an assembly of nodes connected by links (edges) to which physical properties, like a conductance, can be assigned. In this study, we address the issue of using graphs to predict flow as a fast and relevant substitute to classical DFNs. We consider two types of graphs, whether the nodes represent the fractures (fracture graph) or the intersections between fractures (intersection graph). We introduce an edge conductance expression that accounts for both the portion of the fracture surface that carries flow and fracture transmissivity. We find that including the fracture size in the expression improves the prediction of flow compared to expressions used in previous studies that did not. The two graph types yield very different results. The fracture graph systematically underestimates local flow values. In contrast, the intersection graph overestimates the flow in each fracture because of the connectivity redundancy in fractures with multiple intersections. We address the latter issue by introducing a correction factor into the conductances based on the number of intersections on each fracture. We test the robustness of the proposed conductance model by comparing flow properties of the graph with high-fidelity DFN simulations over a wide range of network types. The good agreement found between the intersection graph and test suite indicates that this representation could be useful for predictive purposes.

中文翻译：

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基于图的流建模方法适用于多尺度离散裂缝网络模型

断裂岩石通常被建模为相互连接的离散裂缝（离散裂缝网络，DFN）的多尺度种群。DFN的图形表示形式通过形成由链接（边）连接的节点的集合来降低其连接结构的复杂性，可以将物理特性（如电导）分配给这些链接（边）。在这项研究中，我们解决了使用图形预测流量作为传统DFN的快速且相关的替代品的问题。我们考虑两种类型的图，即节点代表裂缝（裂缝图）还是裂缝之间的交点（相交图）。我们引入了一个边缘电导表达式，该表达式既可以解释裂缝面的流动部分，又可以解释裂缝的透射率。我们发现，与以前的研究中没有使用的表达式相比，在表达式中包括裂缝大小可以改善对流动的预测。两种图形类型产生非常不同的结果。裂缝图系统地低估了局部流量值。相反，由于具有多个相交的裂缝中的连通性冗余，相交图高估了每个裂缝中的流动。我们通过基于每个裂缝上的相交数将校正因子引入电导来解决后一个问题。通过将图形的流动特性与各种网络类型的高保真DFN仿真进行比较，我们测试了所建议电导模型的鲁棒性。