Material Behavior and Computational Validation of Deep CO₂ Closed-Loop Geothermal Systems in Carbonate Reservoirs

Closed-loop geothermal systems (CLGSs) avoid groundwater production and offer stable deep heat supply, but their long-term performance hinges on reliable coupling between the wellbore, the near-well interface and the surrounding formation. Using the D22 well in the Xiongan New Area (deep carbonate reservoir), we built a three-domain thermo-hydraulic framework that updates CO₂ properties with temperature and pressure and explicitly accounts for wellbore-formation thermal resistance. Two geometries (U-tube and single-well coaxial) and two working fluids (CO₂ and water) were compared and optimized under field constraints. With the coaxial configuration, CO₂ delivers an average thermal power of 186.3 kW, exceeding that of water by 44.9%, while the fraction of wellbore heat loss drops by 3-5%. Under field-matched conditions, the predicted outlet temperature (76.8 °C) agrees with the measured value (77.2 °C) within 0.52%, confirming the value of field calibration for parameter transferability. Long-term simulations indicate that after 30 years of continuous operation the outlet temperature decline remains <8 °C for CO₂, outperforming water and implying better reservoir utilization and supply stability. Sensitivity and Pareto analyses identify a practical operating window, i.e., flow velocity of 0.9-1.1 m s^-1 and depth of 3000-3500 m, favoring the single-well coaxial + CO₂ scheme. These results show how field-calibrated modeling narrows uncertainty and yields implementable guidance on geometry, operating conditions, and wellbore insulation strategy. This study provides quantitative evidence that CO₂-CLGSs in deep carbonate formations can simultaneously increase thermal output and limit long-term decline, supporting near-term engineering deployment.