Semi-analytical modeling and multi-objective optimization of horizontal-well deep borehole heat exchangers

This study develops a high-efficiency semi-analytical model to predict the long-term thermal behavior of horizontal-well deep borehole heat exchangers (DBHEs). Model accuracy was validated against experimental data and 3-D numerical simulations. A Monte-Carlo uncertainty-propagation scheme combined with Pearson correlation analysis reveals that solid-phase thermal conductivities main dominate thermal performance. Systematic parametric analysis identifies key drivers: reducing flow from 1000 to 200 m 3 /day reduces the 120-day outlet temperature by 57.4 %; extending the horizontal well from 100 to 1000 m adds 29 °C; increasing seepage velocity and widening the annulus outperforms enlarging the inner pipe. Based on these insights, a particle swarm optimization (PSO) algorithm simultaneously explores pipe radius, horizontal-well length, working fluid flow rate and groundwater seepage velocity to maximize the objective function—the working fluid outlet temperature and minimize system costs. The optimal configuration comprises outer and inner pipe inner radius of 0.10m and 0.02m, respectively; a horizontal length of 433.5m; a working fluid flow rate of 5.0×10 -5 m 3 /s; and a groundwater seepage velocity of 1.0×10 -5 m/s, yielding a predicted outlet temperature of 338K. The integrated framework of rapid semi-analytical modeling, rigorous sensitivity quantification and multi-objective optimization and identifies key drivers to boost heat-extraction efficiency and economic viability.