Inclusion-based effective medium models for the permeability of a 3D fractured rock mass
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Accepted version
Published version
Author(s)
Ebigbo, AOD
Lang, PS
Paluszny, A
Zimmerman, RW
Type
Journal Article
Abstract
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, αα , and the ratio between matrix and fracture permeability, κκ . Two different regimes can be identified, corresponding to α/κ<1α/κ<1 and α/κ>1α/κ>1 . The lower the value of α/κα/κ , 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 α/κ≫1α/κ≫1 , a distinct percolation threshold is observed, whereas for α/κ≪1α/κ≪1 , 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.
Date Issued
2016-04-15
Date Acceptance
2016-04-03
Citation
Transport in Porous Media, 2016, 113 (1), pp.137-158
ISSN
1573-1634
Publisher
Springer
Start Page
137
End Page
158
Journal / Book Title
Transport in Porous Media
Volume
113
Issue
1
Copyright Statement
© The Author(s) 2016. This article is published with open access at Springerlink.com
License URL
Sponsor
Commission of the European Communities
Natural Environment Research Council (NERC)
Grant Number
309067
NE/L000660/1
Subjects
Science & Technology
Technology
Engineering, Chemical
Engineering
Fracture networks
Permeability
Effective medium models
HYDRAULIC CONDUCTIVITY
CONNECTIVITY
SYSTEMS
SCHEME
TENSOR
FLOW
Environmental Engineering
0904 Chemical Engineering
0905 Civil Engineering
0102 Applied Mathematics
Publication Status
Published