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| Titel |
Inclusion-based effective medium models for the field-scale permeability of 3D fractured rock masses |
| VerfasserIn |
Anozie Ebigbo, Philipp S. Lang, Adriana Paluszny, Robert W. Zimmerman |
| Konferenz |
EGU General Assembly 2016
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| Medientyp |
Artikel
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| Sprache |
en
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 18 (2016) |
| Datensatznummer |
250132198
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| Publikation (Nr.) |
 EGU/EGU2016-12681.pdf |
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| Zusammenfassung |
| Fractures that are more permeable than their host rock can act as preferential, or at least
additional, pathways for fluid to flow through the rock. The additional transmissivity
contributed by these fractures will be of great relevance in several areas of earth science and
engineering, such as radioactive waste disposal in crystalline rock, exploitation of fractured
hydrocarbon and geothermal reservoirs, or hydraulic fracturing. In describing or predicting
flow through fractured rock, the effective permeability of the rock mass, comprising both the
rock matrix and a network of fractures, is a crucial parameter, and will depend on several
geometric properties of the fractures/networks, such as lateral extent, aperture, orientation,
and fracture density.
This study investigates the ability of classical inclusion-based effective medium models
(following the work of Sævik et al., Transp. Porous Media, 2013) to predict this permeability.
In these models, the fractures are represented as thin, spheroidal inclusions, the interiors of
which are treated as porous media having a high (but finite) permeability. The predictions of
various effective medium models, such as the symmetric and asymmetric self-consistent
schemes, the differential scheme, and Maxwell’s method, are tested against the results of
explicit numerical simulations of mono- and polydisperse isotropic fracture networks
embedded in a permeable rock matrix. Comparisons are also made with the Hashin-Shrikman
bounds, Snow’s model, and Mourzenko’s heuristic model (Mourzenko et al., Phys. Rev. E,
2011).
This problem is characterised mathematically by two small parameters, the aspect ratio of
the spheroidal fractures, α, and the ratio between matrix and fracture permeability, κ. Two
different regimes can be identified, corresponding to α∕κ < 1 and α∕κ > 1. The lower the
value of α∕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 > 1, a distinct percolation threshold is observed, whereas for
α∕κ < 1, the matrix is sufficiently transmissive that a percolation-like 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 also found
to be very accurate, particularly for monodisperse networks. Finally, it is shown
that Snow’s model essentially coincides with the Hashin-Shtrikman upper bound. |
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