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| Titel |
A new method for calculating the mean aperture of fractures in rocks: The dual mean |
| VerfasserIn |
P. W. J. Glover, S. R. Ogilvie, E. Isakov |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250019305
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| Zusammenfassung |
| The intrinsic permeability or hydraulic aperture of single fractures can be determined with the
Local Cubic Law, LCL, F(x,y) = -∇P where, F is the vector of the flow flux,
H is the separation distance or local aperture of the fracture, ∇P is the local pressure
gradient applied to the fluid and μ is the dynamic viscosity of the fluid. Fracture wall
roughness should cause an overestimation of this permeability if it is of the same order of
magnitude as fracture aperture variation. However, in laminar flow systems (to which the
majority of subsurface flow belongs), roughness will not affect the mean flow velocity or flux
as viscous drag near the fracture walls dampens the effect of roughness (Reynolds Number <
1). Predictions of the LCL worsen as the fracture surfaces are brought together due
to an increase in in-plane toruosity. Overestimations of fracture permeability are
often due to inappropriate averaging of the separation between fracture walls, the
mechanical aperture, H. All mean values depend upon the mean surface heights of
the two surfaces used to define the fracture aperture. However, it is common to
quote the mean aperture for the scenario where the relative mean surface heights
of the two surfaces used to define the fracture aperture are such that the fracture
surfaces just touch. The simple arithmetic mean aperture, Ha, is well defined, but of
little practical use for fluid flow calculations. The geometric mean aperture, Hg,
is well defined if the surfaces do not touch, but collapses to zero if the surfaces
touch at one or more points even if the rest of the aperture is patent to flow. The
harmonic mean aperture, Hh, is also well defined but again it collapses to zero if the
surfaces touch. To overcome the problem, we define the dual mean, Hdm. This is the
arithmetic mean of the geometric mean apertures along all fracture profiles in the
direction of presumed fluid flow through the fracture. It has a physical basis, and is
sensitive to anisotropy in the plane of the fracture, i.e., it has different values in
different directions through the fracture. We use the dual mean in the two cartesian
directions in the plane of the fracture x and y. For the x-direction this is defined as,
Hdmx = ∑
j=1Nyexp, where Nx, Ny are the dimensions of
the measurement grid in the xand ydirections, respectively, Aij is the value of the fracture
aperture at the grid point with indexes (i,j), and Hdmx is the dual mean aperture computed
with respect to x-direction (of the flow). We have tested the dual mean by finite
element modelling and applied it to five rough fractures for which the physical and
hydraulic aperture are known. The dual means in both directions across the fracture
apertures show a much better correlation to the modelled hydraulic apertures than
standard arithmetic mean apertures. We conclude that this is a pragmatic approach to
calculating the mean aperture of a fracture where the surfaces touch at at least one point. |
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