Estimation of groundwater flow rates based on the thermal-hydro response of energy pile: A multi-stage inversion framework with optimisation algorithm

The groundwater flow field significantly influences the operational performance and long-term thermal behaviour of energy pile systems. However, accurately estimating groundwater flow dynamics around energy piles throughout their operational periods remains challenging. A novel theoretical model was developed to interpret the full-cycle thermal response (heating/cooling and recovery stages) of the energy pile-groundwater system (FC-EPG). A segmented multi-stage inversion framework integrated with optimisation algorithm was proposed to precisely estimate groundwater flow rates across different stages. A laboratory-scale energy pile platform with a controllable, homogeneous seepage field was constructed to verify the inversion framework. Results show that the proposed framework achieves excellent curve-fitting performance (R2 > 0.95) and high flow estimation accuracy, with errors below 5 % during heating/cooling and below 15 % during recovery. Analysis indicates that the pile's “barrier effect” results in lower flow rates downstream than actual values. The thermal energy stored within the pile was quantitatively calculated, revealing that “thermal storage effect” causes underestimation of flow rates during recovery stages. Sensitivity analysis demonstrates that the framework maintains robust performance under noisy measurement data. The proposed inversion framework realises high-accuracy quantitative groundwater flow field estimation, providing a theoretical basis for daily-scale and adaptive regulation of energy pile systems.