Estimation of closure of a fracture under normal stress based on aperture data
Estimation of closure of a fracture under normal stress based on aperture data
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DOI：
10.1016/j.ijrmms.2007.04.009
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发表时间：
2008-02
影响因子：
7.2
通讯作者：
K. Matsuki;E. Wang;A. Giwelli;K. Sakaguchi
中科院分区：
文献类型：
--
作者：
K. Matsuki;E. Wang;A. Giwelli;K. Sakaguchi
根据Brown和Scholz提出的公式并根据初始孔径的测量数据，估算了加载和弹性闭合（卸载）中正常应力下41 mm水力裂缝的闭合。通过引入有效/无效初始孔径的概念，并假设初始孔径的高斯和χ 2概率密度函数（PDF），由初始孔径的标准差（SD）和谱矩以及平均有效初始孔径与初始孔径SD的比值确定正应力-闭合曲线。结果表明，对于加载和弹性闭合，初始孔径的χ 2 PDF比Gaussian PDF能更好地再现大法向应力下法向应力-闭合曲线的非线性。此外，基于平均有效初始孔径与确定的水力裂缝的初始孔径的SD的比率，对于1 m的拉伸裂缝中的裂缝区域，估计了尺寸对正应力-闭合曲线的影响。结果表明，裂缝的闭合随裂缝面积的增大而增大，裂缝面积对裂缝闭合的影响取决于初始孔径的SD。
The closure of 41-mm hydraulic fractures under normal stress in both loading and elastic closure (unloading) was estimated according to the formula proposed by Brown and Scholz and based on data measured for the initial aperture. By introducing the concept of an effective/ineffective initial aperture and by assuming Gaussian and χ2probability density functions (PDFs) of the initial aperture, the normal stress versus closure curve was determined from the standard deviation (SD) and the spectral moments of the initial aperture and the ratio of the mean effective initial aperture to the SD of the initial aperture. The results showed that the non-linearity in the normal stress versus closure curve at large normal stresses was reproduced better by the χ2PDF of the initial aperture than the Gaussian PDF for both loading and elastic closure. Furthermore, based on the ratio of the mean effective initial aperture to the SD of the initial aperture determined for the hydraulic fractures, the effect of size on the normal stress versus closure curve was estimated for fracture areas in a tensile fracture of 1m. The results showed that closure increases with the size of the fracture area, and that the effect of size on the closure of the fracture is governed by the SD of the initial aperture.