berryman@sep.stanford.edu

## ABSTRACT
To provide quantitative measures of the importance of
fluid effects on shear waves in the heterogeneous reservoirs,
a model material called a ``random polycrystal of porous laminates''
is introduced. This model
poroelastic material has constituent grains that are layered (or
laminated), and each layer is an isotropic, microhomogeneous porous
medium. All grains are composed of exactly the same porous
constituents, and have the same relative volume fractions. But the order of
lamination is not important because the up-scaling method used to
determine the transversely isotropic (hexagonal) properties of the grains
is Backus averaging, which - for quasi-static or long-wavelength
behavior - depends only on the volume fractions and layer properties.
Grains are then jumbled together totally at random, filling the reservoir,
and producing an overall isotropic poroelastic medium. The
poroelastic behavior of this medium is then analyzed using the
Peselnick-Meister-Watt bounds (of Hashin-Shtrikman type). We study
the dependence of the shear modulus on pore fluid
properties and determine the expected range of behavior. In
particular we compare and contrast these results with those anticipated
from Gassmann's fluid substitution formulas, and to the predictions of
Mavko and Jizba for very low porosity rocks with flat cracks.
This approach also permits
the study of arbitrary numbers of constituents, but for simplicity the
numerical examples are restricted here to just two constituents. This
restriction also permits the use of some special exact results
available for computing the overall effective stress coefficient
in any two-component porous medium.
The bounds making use of polycrystalline microstructure are very tight.
Results for shear modulus demonstrate that the ratio of compliance
differences |

- INTRODUCTION
- ELASTICITY OF LAYERED MATERIALS
- BOUNDS ON ELASTIC CONSTANTS FOR RANDOM POLYCRYSTALS
- POROELASTICITY ESTIMATES AND BOUNDS
- FOUR SCENARIOS
- CONCLUSIONS
- Appendix A: Effective Stress Coefficient and Partial Saturation
- Appendix B: Hill's Equation and Heterogeneous Porous Media
- : REFERENCES
- About this document ...

5/3/2005