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The methods presented have been successfully applied to determine
geomechanical parameters for one reservoir model assuming Weber
sandstone is the host rock. Although the details differ, the general ideas used above
for elastic and poroelastic constants can also be used to obtain
bounds and estimates of electrical formation factor and fluid permeability
for the same random polycrystal of porous laminates model.
Analysis of permeability and fluid flow for this model (and especially
memory effects) requires some extra care, and so I defer
this part of the work to another contribution.
The present work has concentrated on an examination of the very low frequency
(quasi-static, drained behavior) and very high frequency (undrained
behavior) results for the double-porosity model using composites
theory as the main analysis tool. This approach is justified in part
because it is well-known (using one pertinent example) in the analysis
of viscoelastic media (Hashin, 1966; 1983; Vinogradov and Milton, 2005)
that the low and high frequency viscoelastic limits can both be treated using
the methods of quasi-static composites analysis, since the complex moduli
become real in these limits. The corresponding result is certainly
pertinent for the full double-porosity reservoir analysis as well.
Further work is needed of course to determine the behavior for all
the intermediate frequencies, but this harder part
of the work will necessarily be both partly analytical [for example:
Pride *et al.* (2004)]
and partly computational [for example: Lewallen and Wang (1998)]
in nature, and will therefore be presented
in future publications.

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** Up:** Berryman: Geomechanical analysis with
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Stanford Exploration Project

10/31/2005