Fluid flow through rock media is highly significant in underground water management, the geothermal recovery process, and various underground engineering applications. Fractures have a critical effect on the fluid flow through low-permeability rocks since they serve as the major flow channels in the rock formation. Consequently, the evaluation of fracture permeability is crucial to many engineering applications, such as the geothermal recovery process, exploitation of hydrocarbon resources, and various underground engineering applications. However, fluid flow through rough fractures is complex under the effects of rough profiles and variable apertures. The variation of fracture apertures causes the nonlinear distribution of the pressure along the fracture and thus intensifies the difficulties of studying the flow in fractures. In this study, variable-aperture fractures were simplified as axisymmetric fractures using the Weierstrass–Mandelbrot function. To address the nonlinear distribution of pressure caused by aperture variations, a method is proposed to segment fractures with variable lengths by considering the weights of fracture apertures. With the segmented results, we evaluated the permeability of rough fractures using a modified local law. The evaluation results aligned with the lattice Boltzmann simulation results. Finally, combining the analytical solution of flow through asymmetric fractures with sinusoidal profiles, the proposed methods were thereby validated.

中文翻译：

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可变孔径的粗壁裂缝单相流的定量表征

通过岩石介质的流体流在地下水管理，地热回收过程以及各种地下工程应用中具有重要意义。裂缝对通过低渗透率岩石的流体流动具有至关重要的影响，因为它们是岩层中的主要流动通道。因此，裂缝渗透率的评估对于许多工程应用至关重要，例如地热采收过程，油气资源的开采以及各种地下工程应用。但是，在粗糙轮廓和可变孔径的作用下，流经粗糙裂缝的流体很复杂。裂缝孔径的变化导致压力沿裂缝的非线性分布，从而加大了研究裂缝流动的难度。在这个研究中，使用Weierstrass–Mandelbrot函数将可变孔径的骨折简化为轴对称骨折。为了解决由孔径变化引起的压力的非线性分布，提出了一种通过考虑裂缝孔径的权重来分割长度可变的裂缝的方法。通过分段结果，我们使用修正的局部定律评估了粗糙裂缝的渗透率。评估结果与格子Boltzmann模拟结果一致。最后，结合非对称裂缝流动的解析解和正弦曲线，对所提出的方法进行了验证。提出了一种通过考虑裂缝孔的权重来分割长度可变的裂缝的方法。通过分段结果，我们使用修正的局部定律评估了粗糙裂缝的渗透率。评估结果与格子Boltzmann模拟结果一致。最后，结合非对称裂缝流的解析解和正弦曲线，对所提出的方法进行了验证。提出了一种通过考虑裂缝孔的权重来分割长度可变的裂缝的方法。通过分段结果，我们使用修正的局部定律评估了粗糙裂缝的渗透率。评估结果与格子Boltzmann模拟结果一致。最后，结合非对称裂缝流的解析解和正弦曲线，对所提出的方法进行了验证。