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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where kmax <strong>and</strong> kmin are the maximum <strong>and</strong> minimum principal effective permeability<br />
values, kp is the permeability parallel to the b<strong>and</strong>s when θ=0°, kn is the permeability<br />
normal to the b<strong>and</strong>s when θ =0°, <strong>and</strong> k+ is the isotropic permeability when half <strong>of</strong> the<br />
b<strong>and</strong>s are set orthogonal to the other half (θ =90°). Since the analytical solution for k+<br />
only holds for low percentages <strong>of</strong> DBs, we use k+ as calculated by our numerical method<br />
in the equations above to find the maximum <strong>and</strong> minimum effective permeability values<br />
as functions <strong>of</strong> wb/W, θ <strong>and</strong> kb/km.<br />
Figure 6.11 shows the results for kb/km=10 -2 over the entire range <strong>of</strong> wb/W for<br />
intersection angles <strong>of</strong> θ =15°, 30°, 60°<strong>and</strong> 90°. Both principal effective permeability<br />
values decrease as wb/W increases, with the reduction in kmin being most pronounced. The<br />
degree <strong>of</strong> this permeability anisotropy also decreases as θ increases, with an isotropic<br />
permeability drop attained at θ =90°. For kb/km=10 -3 , the anisotropy introduced is even<br />
more pronounced, approaching 2 orders <strong>of</strong> magnitude as θ approaches 0° <strong>and</strong> the pattern<br />
becomes essentially parallel. For the generally high intersection angles (~80) <strong>and</strong> low<br />
volume percents (~10%) exhibited for cross-hatch DB patterns in the Aztec, relatively<br />
isotropic permeability reductions ranging from about 0.7 to1.5 orders <strong>of</strong> magnitude<br />
would be expected.<br />
6.3. Anastomosing<br />
No analytical solutions exist for the systematic, but irregular anastomosing pattern, so<br />
the purely numerical method was used to calculate effective permeability tensors for a<br />
finely discretized version <strong>of</strong> a real, 12 x 15 m DB outcrop pattern mapped in the Aztec on<br />
a low altitude balloon photograph (Figure 6.12). Not surprisingly, the maximum effective<br />
permeability is oriented roughly parallel to the mean trend <strong>of</strong> the b<strong>and</strong>s, while minimum<br />
permeability is directed roughly perpendicular. We also compared the effective<br />
permeability <strong>of</strong> this real anastomosing pattern to an idealized parallel pattern using the<br />
same average spacing <strong>and</strong> wb/W ratio <strong>of</strong> 15%. As expected, effective b<strong>and</strong>-parallel<br />
*<br />
p<br />
permeability (k ) was somewhat lower for the anastomosing pattern—0.79 versus 0.85 at<br />
kb/km=10<br />
-2 —due presumably to b<strong>and</strong> connectivity <strong>and</strong> associated compartmentalization<br />
*<br />
along trend. On the other h<strong>and</strong>, effective b<strong>and</strong>-normal permeability ( k ) was significantly<br />
higher for the anastomosing pattern—0.26 versus 0.06 at kb/km=10<br />
-2 —due presumably to<br />
163<br />
n