Simulation of supercritical CO<sub>2</sub> fracturing based on the cohesive phase-field method

Considering the heat transfer between the fracturing fluid and the rock, a thermo-hydro-mechanical coupled cohesive phase-field model is proposed to address the dynamic fracture propagation problem in supercritical CO₂ fracturing. The failure mode of the rock is assumed to be dynamic quasi-brittle fracture, facilitated by the introduction of an inertial term and the traction-separation law. CO₂ property parameters under varying temperature and pressure conditions are obtained using REFPROP software and integrated with the governing equations for fluid flow and heat transfer through interpolation functions. A two-dimensional numerical model for supercritical CO₂ fracturing was established to investigate the fracture propagation behavior under different injection rates, viscosities, reservoir horizontal stress differentials, and initial temperatures. The results indicate that: (1) There exists an optimal displacement for supercritical CO₂ fracturing, maximizing both fracture length and stimulated area; (2) Provided that the wellhead pressure does not exceed the limit, increasing the viscosity of the supercritical CO₂ fracturing fluid can reduce leak-off and enhance the stimulated reservoir area; (3) The magnitude of the horizontal stress differential has minimal impact on temperature and pressure changes within the formation, yet it significantly influences fracture morphology; (4) The initial temperature of the reservoir primarily affects rock fracture through thermal stress; higher initial temperatures lead to more complex fracture morphologies. By examining the branching patterns of fractures and their fluid pressure responses, the fracturing effects of supercritical CO₂ under various engineering and geological parameters are elucidated, providing valuable guidance for the design of field supercritical CO₂ fracturing operations.