structural geology, propagation mechanics and - Stanford School of ...
structural geology, propagation mechanics and - Stanford School of ...
structural geology, propagation mechanics and - Stanford School of ...
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effective permeability represents an average bulk or “upscaled” permeability for the host<br />
rock <strong>and</strong> small-scale heterogeneities taken together.<br />
A variety <strong>of</strong> numerical techniques have been developed to compute effective<br />
permeability for use in coarse scale modeling. Extensive discussion <strong>of</strong> these can be found<br />
in the reviews <strong>of</strong> Wen <strong>and</strong> Gomez-Hern<strong>and</strong>ez (1996) <strong>and</strong> Renard <strong>and</strong> de Marsily (1997).<br />
Many <strong>of</strong> the techniques also have been used to quantify the effects <strong>of</strong> fine scale features<br />
on large scale permeability. For example, several researchers have computed effective<br />
permeability values for finely interbedded s<strong>and</strong>-shale sequences, finding that shale streak<br />
volume fraction (Vsh ) is the key controlling parameter. Desbarats (1987) modeled<br />
s<strong>and</strong>/shale sequences composed <strong>of</strong> homogeneous, isotropic s<strong>and</strong>stone (permeability=kss)<br />
<strong>and</strong> homogeneous, isotropic shale lenses (permeability=ksh). For ksh/kss=10 -4 , he found the<br />
effective vertical permeability to be an order <strong>of</strong> magnitude less than kss for Vsh ≈30%, <strong>and</strong><br />
2 orders <strong>of</strong> magnitude less for Vsh ≈65%. He found the effective horizontal permeability<br />
to be reduced by an order <strong>of</strong> magnitude for Vsh ≈70%. Deutsch (1989) determined that for<br />
a relative shale/s<strong>and</strong>stone permeability <strong>of</strong> ksh/kss=10 -5 , effective isotropic permeability<br />
drops by an order <strong>of</strong> magnitude for Vsh ≈50% <strong>and</strong> 2 orders <strong>of</strong> magnitude for Vsh ≈65%.<br />
These results suggest that for Vsh greater than 65%, effective horizontal <strong>and</strong> vertical<br />
permeability drop by about 1 <strong>and</strong> 2 orders <strong>of</strong> magnitude, respectively, thus inducing an<br />
order-<strong>of</strong>-magnitude permeability anisotropy.<br />
Previous studies also have demonstrated that other types <strong>of</strong> small scale sedimentary<br />
<strong>and</strong> <strong>structural</strong> heterogeneities can exert substantial permeability effects in pure s<strong>and</strong>stone.<br />
Durl<strong>of</strong>sky (1992) showed that cross bedding in æolian s<strong>and</strong>stones can reduce effective<br />
permeability by an order <strong>of</strong> magnitude <strong>and</strong> induce an anisotropy <strong>of</strong> maximum to<br />
minimum permeability (kmax/kmin) greater than 5. Similarly, it has been shown that the<br />
presence <strong>of</strong> open joints can increase effective permeability by 2 or more orders <strong>of</strong><br />
magnitude, <strong>and</strong> that the presence <strong>of</strong> low porosity deformation b<strong>and</strong>s (DBs) can reduce<br />
effective permeability by 2 or more orders <strong>of</strong> magnitude (Antonellini <strong>and</strong> Aydin, 1994;<br />
Lothe et al., 2002; Taylor <strong>and</strong> Pollard, 2000; Taylor et al., 1999). As a natural<br />
consequence <strong>of</strong> their dominant tabular/planar geometry, both joints <strong>and</strong> DBs also can be<br />
expected to induce permeability anisotropy (Antonellini <strong>and</strong> Aydin, 1995).<br />
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