Brown and Korringa constants for heterogeneous thinly layered poroelastic media

Abstract

Macromechanical characterization of a layered poroelastic package treated as a homogeneous (upscaled) medium is presented. The characterization is based on the knowledge of the poroelastic properties of the package's constituents. Specifically, we provide closed-form expressions for the sum of the fourth-order average elastic compliances tensor S′ijkk of the solid frame and pore space compressibility 1/Kϕ, previously defined in Brown and Korringa's extended formulation of the Gassmann's fluid substitution equations. These constants allow, thus, to perform fluid substitution on an upscaled composite consisting of poroelastic layers. Each layer within the layered package is assumed to have isotropic symmetry, uniform porosity, and single pore-filling fluid and composed of several homogeneously distributed mineral phases such that each layer is approximately Gassmann consistent; however, the fluid and mineral phases as well as the porosity may vary from one layer to the next along the package. In addition, we obtain insights into the sensitivity of S′ijkk and 1/Kϕ when an approximate fluid substitution operation is used. Moreover, it is shown that the S′ijklof the upscaled medium can have transverse isotropy symmetry. The degree of anisotropy is controlled by the volume fractions of individual layers and the contrast of elastic properties between the layers. The results for S′ijkk and 1/Kϕ are compared to those obtained by Berryman and Milton (BM) for a two-phase isotropic composite. At a limiting case of an effectively isotropic medium, this paper's results coincide with those of BM.