Constitutive Modeling of Hydromechanical Coupling in Double Porosity Media Based on Mixture Coupling Theory

Modeling of fluids in deformable geoformation media has gained much attention in the past decades due to significant applications such as groundwater prediction, and shale gas and carbon capture and storage. However, considerable research has been focused on the porous media concept, and dual network (fracture and pores) multiphysics coupled modeling has remained a challenge due to the lack of a systemic theory to bridge the physical deformation of the media (e.g., rocks) and the interaction of water flow in pores and fractures. This paper adopts the nonequilibrium thermodynamics-based approach, the mixture coupling theory, to develop a thermodynamics consistency constitutive model for the fully coupled hydromechanical behavior in double porosity formation. The energy dispassion due to fluid flow in matrix pore and fracture is given through nonequilibrium thermodynamics, and the relationship between the solid and fluid is linked through the Helmholtz free energy. The dynamic evolution of stress, porosity change of the matrix pores, and fracture are derived with respect to mechanical strain, pore pressure, and fracture pressure to account for the flow–deformation interaction. The developed constitutive equations are then solved numerically to show the hydraulic and mechanical behavior of double porosity formation, as well as their sensitivity to parameters.