Studies on discrete fracture network models have recently shown progress by incorporating aperture heterogeneity to individual fracture elements for more accurate description of flow-related processes in subsurface fractured rocks. Compared to a more realistic account of fracture-scale void heterogeneity, the standard Reynolds equation (RE) is mostly adopted as the flow governing equation despite its inaccuracy described in many previous studies. To find effective models for flow in rock fractures under realistic subsurface stresses with proper knowledge of the associated uncertainties, we test four conceptual flow models with incorporation of five local-scale approximations in rock fractures with varying stress-induced void heterogeneity. From the analysis, we show that the parallel-planar plate local-scale approximation in the standard RE can lead to both overestimation and underestimation of the local flow due to the defect of the aperture-averaging approach. In general, higher local deviations are observed for slow-flow regions in the fracture void for all tested local-scale approximations, whereas the faster-flow regions are responsible for the overall deviation of the predicted fracture transmissivity. Among the tested local-scale approximations, two of them are found to evidently improve the standard RE in terms of describing the local velocity field and estimating the overall fracture transmissivity, with absolute mean deviations of ∼11% and ∼7%, respectively. The results from this work further confirm improved flow estimation for subsurface stressed rock fractures by incorporating more accurate local-scale approximations.

中文翻译：

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局部尺度近似对描述具有应力引起的空隙异质性的岩石裂缝中的流体流动的意义

最近对离散裂缝网络模型的研究表明，通过将孔径非均质性结合到单个裂缝元素中，可以更准确地描述地下裂缝岩石中与流动相关的过程。与对裂缝尺度空隙异质性的更现实的描述相比，标准雷诺方程 (RE) 主要被用作流动控制方程，尽管其在许多先前的研究中描述的不准确。为了在正确了解相关不确定性的情况下，在实际地下应力下找到有效的岩石裂缝流动模型，我们测试了四个概念流动模型，并结合了具有不同应力引起的空隙异质性的岩石裂缝中的五个局部尺度近似值。从分析来看，我们表明，由于孔径平均方法的缺陷，标准 RE 中的平行平面板局部尺度近似会导致局部流动的高估和低估。一般来说，对于所有测试的局部尺度近似，裂缝空隙中的慢速流动区域观察到较高的局部偏差，而快速流动区域是导致预测裂缝透射率的总体偏差的原因。在测试的局部尺度近似中，发现其中两个在描述局部速度场和估计整体裂缝透射率方面明显提高了标准 RE，绝对平均偏差分别为 ~11% 和 ~7%。