Revisiting Thermal Performance of Shallow Ground-Heat Exchangers Based on Response Factor Methods and Dimension Reduction Algorithms

Geothermal energy assumes an increasingly crucial role in advancing carbon neutrality. However, heat transfer calculations for shallow ground-heat exchangers (GHE) face challenges, including large computational loads for pipe arrays and insufficient long-term operational analysis. This study proposes two key innovations: first, the introduction of the Response Factor Method (RFM), which accelerates long-term heat-transfer calculations by constructing a coefficient matrix library; second, a dimension-reduction algorithm for large-scale pipe arrays (LADR), balancing simulation speed and accuracy. The simulation model is developed and validated experimentally, with the simulated outlet temperature showing a 0.2% average relative error compared to measured values, with a 20-times speed-up of simulation time compared to the original method. Moreover, the LADR can realize a reduction in calculation load into only two or three boreholes while the neglectable errors do not affect numerical results. The study found that heat extraction increases linearly with borehole depth, but with diminishing returns. Increasing pipe diameter and spacing enhances heat extraction, while overloading reduces reliability. Intermittent operation significantly boosts the load-bearing capacity of individual pipes. The thermal effect radius during the transitional period is larger than that during the heating/cooling periods. We observed and explained the ground heat accumulation in a thermally balanced system for the first time. Additionally, there are differences in thermal performance at different borehole locations within the array, along with a load transfer effect. This research provides valuable insights for optimizing shallow GSHPs.