Geomechanical constants of heterogeneous reservoirs: pore fluid effects on shear modulus

James G. Berryman

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 R (i.e., shear compliance changes over bulk compliance changes) is usually nonzero and can take a wide range of values, both above and below the value R = 4/15 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.