The Biot coefficient for a low permeability heterogeneous limestone

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Abstract

This paper presents the experimental and theoretical developments used to estimate the Biot coefficient for the heterogeneous Cobourg Limestone, which is characterized by its very low permeability. The coefficient forms an important component of the Biot poroelastic model that is used to examine coupled hydro-mechanical and thermo-hydro-mechanical processes in the fluid-saturated Cobourg Limestone. The constraints imposed by both the heterogeneous fabric and its extremely low intact permeability [\(K \in (10^{-23},10^{-20})~\hbox {m}^{2}\)] require the development of alternative approaches to estimate the Biot coefficient. Large specimen bench-scale triaxial tests (150 mm diameter and 300 mm long) that account for the scale of the heterogeneous fabric are complemented by results for the volume fraction-based mineralogical composition derived from XRD measurements. The compressibility of the solid phase is based on theoretical developments proposed in the mechanics of multi-phasic elastic materials. An appeal to the theory of multi-phasic elastic solids is the only feasible approach for examining the compressibility of the solid phase. The presence of a number of mineral species necessitates the use of the theories of Voigt, Reuss and Hill along with the theories proposed by Hashin and Shtrikman for developing bounds for the compressibility of the multi-phasic geologic material composing the skeletal fabric. The analytical estimates for the Biot coefficient for the Cobourg Limestone are compared with results for similar low permeability rocks reported in the literature.

Keywords

Biot coefficient Skeletal compressibility Solid material compressibility Voigt-Reuss-Hill estimates Hashin-Rosen estimates Cobourg limestone 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Civil Engineering and Applied MechanicsMcGill UniversityMontréalCanada

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