A fast analytical solution for formation temperature prediction and regional suitability of BHE arrays

Ground-source heat pump systems using borehole heat exchanger (BHE) arrays are widely used for building heating and cooling. However, long-term thermal imbalance may cause subsurface heat accumulation or depletion, reducing system performance. Existing numerical models can effectively capture the transient thermal behavior of system, but they are computationally intensive and unsuitable for rapid evaluation. This study develops a fast analytical solution for predicting the dynamic thermal response of BHE arrays under time-varying loads by coupling a single-borehole analytical model with a thermal-load redistribution method to account for inter-borehole interference. The proposed model shows good agreement with numerical simulations, with deviations within 5%. In addition, a dynamic exergy efficiency ratio is further introduced to evaluate regional suitability and long-term operational performance. Case studies for three representative cities-Guangzhou, Tianjin, and Harbin, reveal significant heat accumulation (∼10 °C) in Guangzhou, cold accumulation (∼–12 °C) in Harbin, and near thermal balance in Tianjin. Under non-compensated operation conditions, the exergy efficiency ratio (ε) approaches zero or becomes negative during peak seasons, whereas thermal compensation significantly improves long-term performance. The proposed analytical framework provides an efficient and practical tool for rapid system design and regional suitability assessment of shallow geothermal applications.