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Brown and Korringa constants for heterogeneous thinly layered poroelastic media
Author(s) -
Wollner Uri,
Mavko Gary
Publication year - 2017
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2016jb013672
Subject(s) - poromechanics , isotropy , anisotropy , materials science , porosity , compressibility , symmetry (geometry) , composite number , tensor (intrinsic definition) , porous medium , composite material , geometry , mechanics , optics , physics , mathematics
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 tensorS ijkk ′of the solid frame and pore space compressibility 1/ K ϕ , 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 ofS ijkk ′and 1/ K ϕ when an approximate fluid substitution operation is used. Moreover, it is shown that theS ijkl ′of 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 forS ijkk ′and 1/ K ϕ 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.