A data-driven modeling-based multi-objective optimization approach for medium-deep coaxial borehole heat exchanger

Efficient operation of medium-deep borehole heat exchanger relies on structural and operational optimization. Global optimization requires evaluating system behavior across various design parameters, but high experimental investment and computational time costs hinder efficient multi-objective optimization of such systems. To address this, a statistical modeling-based multi-objective optimization method for coaxial borehole heat exchanger is proposed. First, a thermal-hydraulic coupled numerical model is developed and validated using field test data. Second, to enable fast assessment of heat extraction of BHE, statistical regression prediction model is constructed using the response surface methodology, with its generalization capability verified through analysis of variance. Finally, dual-objective genetic algorithm optimization is performed to maximize both heat output and coefficient of performance under cost constraints, yielding a Pareto optimal set. The optimized results of a single-well BHE geothermal heating system in the porous aquifer of Henan Province, China reveal a trade-off between thermal output and energy efficiency, requiring parameter optimization based on specific goals. Compared to the design scheme in field test, the compromise solution selected from the Pareto optimal solution set can increase heat extraction by 8.2% and improve coefficient of performance by 7.9%. The prediction model based on response surface methodology can effectively replace complex numerical simulations, greatly reducing computational cost for medium-to-deep geothermal system optimization.