Poroelastic coefficients for anisotropic single and double porosity media

Abstract

Closed-form expressions for poroelastic coefficients are derived for anisotropic materials exhibiting single and double porosity. A novel feature of the formulation is the use of the principle of superposition to derive the governing mass conservation equations from which analytical expressions for the Biot tensor and Biot moduli, among others, are derived. For single-porosity media, the mass conservation equation derived from the principle of superposition is shown to be identical to the one derived from continuum principle of thermodynamics, thus confirming the veracity of both formulations and suggesting that this conservation equation can be derived in more than one way. To provide further insight into the theory, numerical values of the poroelastic coefficients are calculated for granite and sandstone that are consistent with the material parameters reported by prominent authors. In this way, modelers are guided on how to determine these coefficients in the event that they use the theory for full-scale modeling and simulations.