Inclusion-Based Effective Medium Models for the Permeability of a 3D Fractured Rock Mass
Inclusion-Based Effective Medium Models for the Permeability of a 3D Fractured Rock Mass
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DOI：
10.1007/s11242-016-0685-z
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发表时间：
2015-12
影响因子：
2.7
通讯作者：
A. Ebigbo;P. Lang;A. Paluszny;R. Zimmerman
中科院分区：
文献类型：
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作者：
A. Ebigbo;P. Lang;A. Paluszny;R. Zimmerman
有效渗透率是描述流体在裂隙岩体中流动的基本参数。本研究考察了经典的基于包含性的有效介质模型的能力(遵循S等人的工作)。摘自《运输多孔介质》100(1)：115-142,2013。DOI：10.1007/s11242-0130208-0)来预测这种渗透率，这取决于裂缝/网络的几个几何性质。这是通过比较各种有效介质模型，如对称和非对称自洽格式、差分格式和麦克斯韦方法，以及嵌入渗透性岩石基质中的单色和多色散各向同性裂缝网络的显式数值模拟结果来实现的。还与Snow的模型和Mourzenko的启发式模型(Mourzenko等人)的Hashin-Shtrikman界限进行了比较。在Phys Revv E 84：036-307,2011年。DOI：10.1103/PhysRevE.84.036307)。这个问题的特点是两个小参数，即球状裂缝的纵横比和基质与裂缝渗透率的比值。可以确定两种不同的制度，对应于和。的值越低，流经矩阵的意义就越大。由于两种流型的不同，有效渗透率对裂缝密度的依赖关系在两种流型下也不同。当，观察到明显的渗流阈值，而对于，矩阵是足够的透射性，这样的转变不被观察到。自洽有效介质方法对单弥散各向同性裂隙网络和多弥散各向同性裂隙网络均表现出较好的精度。Mourzenko方程是非常精确的，特别是对于单分散网络。结果表明，斯诺模型与Hashin-Shtrikman上界基本一致。
Effective permeability is an essential parameter for describing fluid flow through fractured rock masses. This study investigates the ability of classical inclusion-based effective medium models (following the work of Sævik et al. in Transp Porous Media 100(1):115–142, 2013. doi: 10.1007/s11242-013-0208-0 ) to predict this permeability, which depends on several geometric properties of the fractures/networks. This is achieved by comparison of various effective medium models, such as the symmetric and asymmetric self-consistent schemes, the differential scheme, and Maxwell’s method, with the results of explicit numerical simulations of mono- and poly-disperse isotropic fracture networks embedded in a permeable rock matrix. Comparisons are also made with the Hashin–Shtrikman bounds, Snow’s model, and Mourzenko’s heuristic model (Mourzenko et al. in Phys Rev E 84:036–307, 2011. doi: 10.1103/PhysRevE.84.036307 ). This problem is characterised by two small parameters, the aspect ratio of the spheroidal fractures,, and the ratio between matrix and fracture permeability,. Two different regimes can be identified, corresponding toand. The lower the value of, the more significant is flow through the matrix. Due to differing flow patterns, the dependence of effective permeability on fracture density differs in the two regimes. When, a distinct percolation threshold is observed, whereas for, the matrix is sufficiently transmissive that such a transition is not observed. The self-consistent effective medium methods show good accuracy for both mono- and polydisperse isotropic fracture networks. Mourzenko’s equation is very accurate, particularly for monodisperse networks. Finally, it is shown that Snow’s model essentially coincides with the Hashin–Shtrikman upper bound.