Abstract Investigation of seepage law of fluid flow through a self-affine, rough fracture has attracted broad attention because of its fundamental importance for complex hydrodynamic problems. Although it is natural to assume that permeability value depends on aperture size, it is hard to determine which is the appropriate relationship between them because of the large number of parameters related to the multi-scale geometries and mismatched behaviors in internal surfaces. Moreover, those parameters are hard to obtain by field observation or laboratory tests. For these, we focused on synthesising mismatched composite topography of natural fractures and numerical simulation of fluid flow through them at pore scale. Firstly, the control mechanism of self-affine property was clarified, and a novel Weierstrass-Mandelbrot (W-M) function was proposed to model self-affine profile as per fractal topography theory. Afterwards, a weighting algorithm was developed to construct the composite topography of fractures accounting for the mismatched behavior. Finally, the effects of mismatched behavior, hydraulic and surface tortuosities on fracture flow were systematically analyzed by numerical simulations using Lattice Boltzmann methods (LBM) at pore scale. Our investigation indicates that the aperture distribution is dominated by the mismatched range between internal surfaces, however the hydraulic and surface tortuosity effects are approximately scaled by 2 ( H − 1 ) (H is the Hurst exponent) with the mean aperture despite of its distribution. Moreover, it was found that the local surface roughness factor, accounting for effects from surface geometries with size smaller than the value of mean aperture, is stationary at long range and inversely proportional to fracture permeability. Based on above discussions, the validity of triple-effect model for permeability prediction of mismatched self-affine fractures was established.

中文翻译：

---

错配自仿射裂缝中流体流动三效模型的有效性

摘要 流体通过自仿射粗糙裂缝的渗流规律研究因其对复杂流体动力学问题的根本重要性而受到广泛关注。尽管假设渗透率值取决于孔径大小是很自然的，但由于与多尺度几何形状和内表面不匹配行为相关的大量参数，很难确定它们之间的适当关系。此外，这些参数很难通过现场观察或实验室测试获得。对于这些，我们专注于合成不匹配的天然裂缝复合地形以及在孔隙尺度上通过它们的流体流动的数值模拟。首先明确了自仿射属性的控制机制，并提出了一种新的 Weierstrass-Mandelbrot (WM) 函数来根据分形地形理论对自仿射剖面进行建模。之后，开发了一种加权算法来构建考虑不匹配行为的裂缝复合地形。最后，使用格子玻尔兹曼方法 (LBM) 在孔隙尺度上通过数值模拟系统地分析了失配行为、水力和表面曲折对裂缝流动的影响。我们的调查表明，孔径分布主要由内表面之间的不匹配范围决定，然而，尽管其分布不同，但水力和表面曲折效应大约按 2 ( H - 1 )（H 是赫斯特指数）缩放。此外，发现局部表面粗糙度因子，考虑到尺寸小于平均孔径值的表面几何形状的影响，在长距离上是静止的，并且与裂缝渗透率成反比。基于以上讨论，建立了错配自仿射裂缝渗透率预测三效模型的有效性。