structural geology, propagation mechanics and - Stanford School of ...

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