CONCLUSIONS

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.