Physics-informed neural network for modeling coupled fluid flow and heat transport in a geothermal doublet system

Geothermal energy is an important renewable energy resource, and geothermal doublet systems are widely used for its sustainable exploitation. Accurate simulation of coupled fluid-flow and heat-transfer processes in geothermal doublet systems provides an important basis for assessing thermal-breakthrough risk and optimizing production and reinjection schemes. The proliferation of machine learning techniques provides new approaches to improving geothermal simulation, but challenges remain in maintaining agreement with governing physical laws, adapting to varying conditions, and ensuring prediction reliability. This study develops a physics-informed neural network (PINN) framework for simulating transient hydro-thermal processes in a geothermal doublet system. The model incorporates the governing equations of transient fluid flow and heat transport into the loss function and adopts a dual-network architecture to represent hydraulic and thermal fields separately. The proposed framework is first validated against analytical solutions for one-dimensional heat conduction and radial groundwater flow problems. It is then applied to a geothermal doublet case based on the Xianxian geothermal field. A data-driven deep neural network (DNN) is introduced as a baseline to investigate the contribution of physical constraints under different training data conditions. Staged training and sampling refinement strategies are combined to improve the predictive performance of the PINN. The results show that the PINN achieves lower prediction errors and smaller PDE residuals than the DNN under limited training data conditions. The final optimized model reproduces the spatiotemporal evolution of hydraulic head and temperature in both global and local regions, while maintaining relatively small prediction errors and overall agreement with the governing equations throughout the investigated simulation period. Adaptability analysis demonstrates that the proposed framework can be effectively adapted to different physical and operational scenarios through scenario-specific retraining while maintaining comparable predictive performance. The study demonstrates that PINNs can serve as a physics-constrained surrogate modeling framework for geothermal doublet systems and provide a complementary approach to conventional numerical methods for simulating coupled subsurface processes.