The Elastic Coeecients of Double-porosity Models for Fluid Transport in Jointed Rock

Phenomenological equations (with coeecients to be determined by speciied experiments) for the poroelastic behavior of a dual porosity medium are formulated and the coeecients in these linear equations are identiied. The generalization from the single porosity case increases the number of independent coeecients for volume deformation from three to six for an isotropic applied stress. The physical interpretations are based upon considerations of diierent 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 eld 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 coeecients are determined from the three poroelastic matrix coeecients 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 coeecient of the composite are the volume averages of the matrix and fracture contributions. 3