Prediction of Thermal Breakthrough and Parameter Optimization in Geothermal Reinjection Systems Based on Deep Neural Networks: A Case Study of the Qihe Geothermal Field

Predicting thermal breakthrough and optimizing injection-production parameters are essential for sustainable geothermal development. Traditional hydrothermal coupled simulations in porous media entail substantial computational costs, which limits their use in dense multi-parameter screening. This study develops a physics-constrained surrogate workflow for the Qihe geothermal doublet system by using COMSOL to generate hydrothermal simulation data and a deep neural network (DNN) to emulate the simulator response within a predefined operating domain. The DNN was trained on physics-driven synthetic outputs rather than independent field observations, and a 2.0 °C decrease in production temperature was used as the thermal breakthrough criterion. Under scenario-wise validation, the surrogate model achieved a test-set R2 of 0.9995 and an RMSE of 0.0351 °C, indicating accurate approximation of the deterministic simulator response within the bounded parameter space. The surrogate-based global scan identified a favorable operating region near a well spacing of 462 m, a reinjection temperature of 20 °C, and a reinjection rate of 150 m3/h. To evaluate whether this result was affected by sparse well-spacing sampling, additional COMSOL simulations were performed at 430, 440, 450, 460, 462, 470, 480, 490, and 500 m under the same reinjection temperature and rate. These simulator-based validation cases showed a continuous thermal response with increasing well spacing. The 2.0 °C thermal breakthrough time increased from 46 yr at 430 m to 61 yr at 500 m, while the 50-year cumulative heat extraction increased from 6594.2 to 6722.9 TJ. The 430 and 440 m cases experienced thermal breakthrough before the 50-year design life, whereas the 450 m case was close to the design boundary. The 460 and 462 m cases did not reach the 2.0 °C decline threshold within the 50-year design life and retained relatively high heat-extraction efficiency per unit well spacing. Therefore, the engineering recommendation is revised from a single precise optimum to a locally validated spacing interval of approximately 460–462 m under the present equivalent-porous-medium assumption. The proposed workflow does not replace hydrothermal simulation; instead, it provides a rapid screening tool that narrows the design space before targeted simulator verification and field calibration.