Pore Fluid Effects on Shear Modulus in a Model of Heterogeneous Rocks, Reservoirs, and Granular Media

Journal Article · Wed Mar 23 04:00:00 EST 2005 · Journal of Geophysical Research

DOI:https://doi.org/10.1029/2004JB003576· OSTI ID:862376

Berryman, J G

To provide quantitative measures of the importance of fluid effects on shear waves in 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. 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 all space, 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 range of behavior to be expected. In particular we compare and contrast these results to 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 the shear modulus demonstrate that the ratio of compliance differences R (i.e., shear compliance changes over bulk compliance changes when going from drained to undrained behavior, or vice versa) is usually nonzero and can take a wide range of values, both above and below the value R = 4/15 valid for low porosity, very low aspect ratio flat cracks. Results show the overall shear modulus in this model can depend relatively strongly on mechanical properties of the pore fluids, sometimes (but rarely) more strongly than the dependence of the overall bulk modulus on the fluids.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA
• Sponsoring Organization: USDOE
• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 862376
• Report Number(s): UCRL-JRNL-210754
• Journal Information: Journal of Geophysical Research, Journal Name: Journal of Geophysical Research Journal Issue: B7 Vol. 110; ISSN JGREA2; ISSN 0148-0227
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
42 ENGINEERING
54 ENVIRONMENTAL SCIENCES
58 GEOSCIENCES
ASPECT RATIO
COMPLIANCE
MECHANICAL PROPERTIES
MICROSTRUCTURE
POLYCRYSTALS
POROSITY
SHEAR