Variational phase-field fracture approach for non-isothermal CO₂-water two-phase flow in deformable porous media

When CO2 is injected to induce fracture in rock, the fracture tends to propagate in a more complex pattern and at a lower critical pressure compared to water injection. This study presents a fracture propagation model under CO2-water two-phase flow, based on the variational thermo-hydro-mechanical phase-field approach. For each constituent (water and CO2), the mass balance equation is derived while accounting for the capillary effect and the respective equations of state. Meanwhile, the equivalent pressure from two fluids modifies the potential energy description in thermo-poro-elastic media, following our previous micromechanics based model. The proposed model has been verified against the analytical solutions for one-dimensional incompressible, immiscible two-phase flow, and plane strain hydraulic fracture propagation, known as the KGD fracture. Our numerical experiments indicate that fractures propagate at lower breakdown pressures under supercritical CO2 injection, and their paths are more influenced more by pre-existing weak interfaces due to low viscosity of CO2.