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.

Geomechanical analysis with rigorous error estimates for a double-porosity reservoir model

“…These results also show how the constituent properties K d , α, B up-scale at the macrolevel for a two-constituent composite [10,12]. We find …”

“…This is natural for a 12 and a 22 because the storage material contains no fractures, and therefore is not sensitive to fracture compliance, whereas those mechanical effects on the overall reservoir response can be very large. The behavior of a 23 also shows little dispersion as this value is always quite close to zero [10,12] Table 1. For each coefficient, three curves are shown, depending on which estimate of the overall bulk modulus is used: lower bound (dot-dash line), self-consistent (solid line), or upper bound (dashed line).…”

A New Coal-Permeability Model: Internal Swelling Stress and Fracture–Matrix Interaction

“…Because coal matrix and fractures (cleats) have dramatically different mechanical properties, this interaction can have a significant effect on permeability changes under certain conditions, as will be demonstrated in this study. Although considerable effort has also been made with respect to modeling mechanical deformation processes and their coupling with flow processes in dual-continuum systems (fractured rock) (e.g., Wilson and Aifantis 1982;Bai et al 1993;Berryman and Wang 1995), these studies have focused on developing governing equations for coupled liquid flow and mechanical processes, rather than determining relationships between permeability and other related properties. Second, the previously discussed permeability models also generally assume that a change in the length of a matrix block (resulting from swelling or shrinkage) causes an equal but opposite change in the fracture aperture.…”

Two-Dimensional Fractional Order Generalized Thermoelastic Porous Material

“…A short list of papers pertinent to the present study includes Biot(1941Biot( , 1956, Gassmann (1951), Biot and Willis (1957), Biot (1962), Deresiewicz and Skalak (1963), Mandl (1964), Nur and Byerlee (1971), Brown and Korringa (1975), Rice and Cleary (1976), Burridge and Keller (1981), Zimmerman et al (1986Zimmerman et al ( ,1994, Berryman and Milton (1991), Thompson and Willis (1991)], Pride et al (1992), Berryman and Wang (1995), Tuncay and Corapcioglu (1995), Alexander and Cheng (1991), Charlez, P. A., and Heugas, O. (1992), Abousleiman et al (1998), Ghassemi and Diek (2002), Tod (2003).…”