A fractal model based on a new governing equation of fluid flow in fractures for characterizing hydraulic properties of rock fracture networks
A fractal model based on a new governing equation of fluid flow in fractures for characterizing hydraulic properties of rock fracture networks
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DOI：
10.1016/j.compgeo.2016.01.025
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发表时间：
2016-05
影响因子：
5.3
通讯作者：
Ri-cheng Liu;Bo Li;Yujing Jiang
中科院分区：
文献类型：
--
作者：
Ri-cheng Liu;Bo Li;Yujing Jiang
提出了一种离散裂隙网络(DFN)中裂缝的分维长度分布模型，该模型采用了一个表示裂隙几何分布特征的分维Df和一个表示DFN中单个裂隙表面粗糙度引起的流体流动曲折程度的分维Dt。在该模型中引入了基于立方定律的单裂缝渗流控制方程。模拟了具有不同裂缝几何特征和边长的1290个DFN中的流体流动，计算了它们的等效渗透率。结果表明，用该模型计算得到的裂隙尺寸分布的幂指数a与前人报道的结果基本一致。DFN的流量与e6-DT成比例变化，其中e是孔径，这与文献中报道的现场测量结果更符合，而不是经典立方定律(E3)的预测。DFN的等效渗透率对用来产生裂缝长度的随机数比用来产生裂缝方位和中心点的随机数更敏感。随着Df的增加，代表基元体积(Rev)的大小减小。当DFN的尺寸大于REV时，随机数引起的等效磁导率的变化保持不变。当Df<；1.5时，DFN中的流体流动主要是长度小于DFN边长的相对较小的裂缝。随着Df的增加，流体流动更多地被较长的裂缝所主导，特别是那些穿过模型的裂缝。
This study presents a fractal length distribution model of fractures in discrete fracture networks (DFNs), adopting a fractal dimension D f that represents the geometric distribution characteristics of fractures and another fractal dimension D T that represents the tortuosity of fluid flow induced by surface roughness of single fractures in DFNs. A new governing equation for fluid flow in single fractures based on the cubic law was incorporated into this fractal model. Fluid flow in 1290 DFNs with different geometric characteristics of fractures and side lengths was simulated and their equivalent permeability was calculated. The results show that the values of a, which is the power law exponent of the fracture size distribution, calculated by the proposed fractal model are consistent with those reported in similar previous studies. The flow rate of a DFN changes proportionally with e 6-D T where e is the aperture, which agrees better with the in-situ measurements reported in literature than the prediction of classical cubic law (e 3). The equivalent permeability of DFNs is more sensitive to the random number utilized to generate the fracture length than the ones used to generate the orientation and center point of fractures. With the increment of D f, the size of the representative elementary volume (REV) decreases. When the size of a DFN is larger than the REV, the variation of equivalent permeability induced by the random number holds constant. When D f< 1.5, fluid flow in a DFN is dominated by the relatively small fractures with their lengths shorter than the side length of the DFN. With increasing D f, fluid flow becomes more dominated by the longer fractures, especially the ones cutting through the models.