Effective Permeability of Media with a Dense Network of Long and Micro Fractures
Effective Permeability of Media with a Dense Network of Long and Micro Fractures
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DOI：
10.1007/s11242-008-9241-9
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发表时间：
2009-01-01
影响因子：
2.7
通讯作者：
Barthelemy, J. -F.
中科院分区：
文献类型：
--
作者：
Barthelemy, J. -F.
本文提出了一种估算任意各向异性随机裂缝介质有效渗透率的新方法，该介质中既有微裂缝，也有大量长裂缝横切代表性体积元。裂缝被虚构的可渗透材料所取代，其切向渗透率由泊泽维尔流推断出来。提出了一种推导宏观渗透率的自洽格式。一方面，长裂缝对有效渗透率的贡献表现为裂缝切向渗透率的简单叠加。另一方面，微裂缝的贡献需要求助于与嵌入在各向异性矩阵中的椭球体相关的二阶Hill（或Eshelby）张量计算的辅助问题，这是一个完整的程序。在改造方案中充分体现了微裂缝正常渗透率的影响，并对其进行了分析。特别是，它表明，它必须选择足够大，以允许家庭之间的联系。最后开发了实例，并与二维情况下的数值模拟进行了比较。
This article presents a new methodology to estimate the effective permeability of random fractured media of any anisotropy containing both microfractures and a large number of long fractures crosscutting the representative volume element. The fractures are replaced by fictitious permeable materials for which the tangential permeability is deduced from a Poiseuille flow. A self-consistent scheme is proposed to derive the macroscopic permeability. On the one hand, the contribution of long fractures to the effective permeability writes by simple superposition of the fracture tangential permeabilities. On the other hand, the contribution of microfractures needs to resort to auxiliary problems requiring the computation of second-order Hill (or Eshelby) tensors related to ellipsoids embedded in an anisotropic matrix, for which a complete procedure is detailed. The effect of the microfracture normal permeability is put in evidence in the upscaling scheme and analyzed. In particular, it is shown that it must be chosen large enough to allow the connections between families. Examples are finally developed and compared to numerical simulations in the 2D case.