Thermodynamically consistent anisotropic constitutive relations for a poroelastic material saturated by two immiscible fluids

This paper presents thermodynamically consistent, fully anisotropic linear poroelastic constitutive equations for porous material saturated by two immiscible fluids formulated with measurable material coefficients. General formulations of fully anisotropic constitutive equations were derived from results of the existing thermodynamic framework. Presented formulations are independent with the averaged pore pressure approach or any assumptions on the relation between Bishop's effective stress coefficient and the saturation of the wetting phase fluid. Series of thought experiments are conducted to reformulate the derived equations into those expressed by measurable material coefficients under the assumption of homogeneous solid constituent. As a result, all the material coefficients were found to be described by porosity, drained elastic constants and the Biot–Willis coefficient tensor, which are common to saturated poroelasticity and Bishop's effective stress coefficient.