We performed a set of numerical simulations to characterize the interplay of fracture network topology, upscaling, and mesh refinement on flow and transport properties in fractured porous media. We generated a set of generic three-dimensional discrete fracture networks at various densities, where the radii of the fractures were sampled from a truncated power-law distribution, and whose parameters were loosely based on field site characterizations. We also considered five network densities, which were defined using a dimensionless version of density based on percolation theory. Once the networks were generated, we upscaled them into a single continuum model using the upscaled discrete fracture matrix model presented by Sweeney et al. We considered steady, isothermal pressure-driven flow through each domain and then simulated conservative, decaying, and adsorbing tracers using a pulse injection into the domain. For each simulation, we calculated the effective permeability and solute breakthrough curves as quantities of interest to compare between network realizations. We found that selecting a mesh resolution such that the global topology of the upscaled mesh matches the fracture network is essential. If the upscaled mesh has a connected pathway of fracture (higher permeability) cells but the fracture network does not, then the estimates for effective permeability and solute breakthrough will be incorrect. False connections cannot be eliminated entirely, but they can be managed by choosing appropriate mesh resolution and refinement for a given network. Adopting octree meshing to obtain sufficient levels of refinement leads to fewer computational cells (up to a 90% reduction in overall cell count) when compared to using a uniform resolution grid and can result in a more accurate continuum representation of the true fracture network.

翻译：我们开展了一系列数值模拟，以刻画裂隙多孔介质中裂隙网络拓扑、尺度升级和网格细化对流动与输运特性的相互作用。我们生成了不同密度下的一组通用三维离散裂隙网络，其中裂隙半径从截断幂律分布中采样，其参数大致基于现场场地表征。我们还考虑了五种网络密度，这些密度基于逾渗理论采用无量纲密度定义。生成网络后，我们采用Sweeney等人提出的升级离散裂隙矩阵模型，将其升级为单一连续体模型。我们考虑了每个域内稳态等温压力驱动流，然后通过脉冲注入模拟了保守、衰减和吸附示踪剂的输运。对于每次模拟，我们计算了有效渗透率和溶质穿透曲线作为关注量，以比较网络实现之间的差异。我们发现，选择网格分辨率使升级网格的整体拓扑与裂隙网络相匹配至关重要。若升级网格具有裂隙（高渗透率）单元连接的路径，而裂隙网络本身没有，则有效渗透率和溶质穿透的估计将不正确。虚假连接无法完全消除，但可通过针对给定网络选择合适的网格分辨率和细化来管理。采用八叉树网格划分以获得足够细化水平时，与使用均匀分辨率网格相比，计算单元更少（总体单元数减少高达90%），并能更准确地连续体表示真实裂隙网络。