The elastic coefficients of double‐porosity models for fluid transport in jointed rock

Abstract

Phenomenological equations (with coefficients to be determined by specified experiments) for the poroelastic behavior of a dual porosity medium are formulated, and the coefficients in these linear equations are identified. The generalization from the single‐porosity case increases the number of independent coefficients for volume deformation from three to six for an isotropic applied stress. The physical interpretations are based upon considerations of different temporal and spatial scales. For very short times, both matrix and fractures behave in an undrained fashion. For very long times, the double‐porosity medium behaves like an equivalent single‐porosity medium. At the macroscopic spatial level, the pertinent parameters (such as the total compressibility) may be determined by appropriate field tests. At an intermediate or mesoscopic scale, pertinent parameters of the rock matrix can be determined directly through laboratory measurements on core, and the compressibility can be measured for a single fracture. All six coefficients are determined from the three poroelastic matrix coefficients and the fracture compressibility from the single assumption that the solid grain modulus of the composite is approximately the same as that of the matrix for a small fracture porosity. Under this assumption, the total compressibility and three‐dimensional storage coefficient of the composite are the volume averages of the matrix and fracture contributions.