Hydraulic conductivity of rock fractures
Hydraulic conductivity of rock fractures
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DOI：
10.1007/bf00145263
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发表时间：
1996-04
影响因子：
2.7
通讯作者：
R. Zimmerman;G. Bodvarsson
中科院分区：
文献类型：
--
作者：
R. Zimmerman;G. Bodvarsson
在流体力学的范围内讨论了单相流体通过粗糙壁岩石裂缝的流动。“立方定律”的推导是作为光滑平行板之间流动的Navier-Stokes方程的解给出的-这是唯一适合精确处理的裂缝几何形状。各种几何和运动学的条件，是必要的，以Navier-Stokes方程被取代的更易处理的润滑或Hele-Shaw方程进行了研究和量化。通常，这需要足够低的流速，以及对孔轮廓的空间变化率的一些限制。各种分析和数值计算结果进行审查有关的问题有关的有效水力孔径的孔径分布的统计。这些研究都得出这样的结论，即有效水力孔径小于平均孔径，其系数取决于孔径的平均值与其标准差的比值。使用Hele-Shaw方程研究了岩石壁彼此接触的区域所引起的弯曲度效应，导致一个简单的校正因子，该因子取决于接触区域所占的面积分数。最后，预测的水力孔径进行比较，从文献中的孔径和电导率数据可在同一个裂缝的八个数据集的测量值。据发现，合理准确的预测水力传导率可以仅仅根据前两个时刻的孔径分布函数，和接触面积的比例。
The flow of a single-phase fluid through a rough-walled rock fracture is discussed within the context of fluid mechanics. The derivation of the ‘cubic law’ is given as the solution to the Navier-Stokes equations for flow between smooth, parallel plates - the only fracture geometry that is amenable to exact treatment. The various geometric and kinematic conditions that are necessary in order for the Navier-Stokes equations to be replaced by the more tractable lubrication or Hele-Shaw equations are studied and quantified. In general, this requires a sufficiently low flow rate, and some restrictions on the spatial rate of change of the aperture profile. Various analytical and numerical results are reviewed pertaining to the problem of relating the effective hydraulic aperture to the statistics of the aperture distribution. These studies all lead to the conclusion that the effective hydraulic aperture is less than the mean aperture, by a factor that depends on the ratio of the mean value of the aperture to its standard deviation. The tortuosity effect caused by regions where the rock walls are in contact with each other is studied using the Hele-Shaw equations, leading to a simple correction factor that depends on the area fraction occupied by the contact regions. Finally, the predicted hydraulic apertures are compared to measured values for eight data sets from the literature for which aperture and conductivity data were available on the same fracture. It is found that reasonably accurate predictions of hydraulic conductivity can be made based solely on the first two moments of the aperture distribution function, and the proportion of contact area.