Assessment on the thermal efficiency of deep borehole heat exchangers under rock and soil heterogeneity

Abstract

To improve the prediction accuracy of heat gain in deep coaxial well heat exchanger (DCBHE), a fast calculation method based on the Proper Orthogonal Decomposition (POD) is proposed. This method analyzes the thermal conductivity distribution and temperature variations across different rock and soil layers. However, this algorithm only extracts the feature information from the original data, potentially introducing errors by not retaining all the data. To address this issue, a modification scheme is proposed. After modification, the relative error decreases from 3.5 % to 0.5 %, while the calculation speed increases by 3.7 %. The temperature distribution in layered rock and soil is then analyzed. It is found that the dimensionless temperature in layered conditions is higher than in uniform conditions, particularly near the heat source, with the maximum deviation ranging from 0.08596 to 0.56375. The modified POD method is 51.8 times faster than the Finite Difference Method (FDM) and provides higher accuracy, with a relative error of about 1.81 %. The study also examines the impact of rock and soil stratification on heat transfer. It finds that increased thermal conductivity inhomogeneity reduces heat transfer capacity, whereas a higher temperature gradient improves heat transfer efficiency, with a maximum increase of 15.25 %. While the inlet fluid temperature has a minimal effect on local heat removal capacity, it significantly enhances overall heat removal efficiency. Finally, by optimizing and predicting the fluid temperature at the borehole outlet, the optimal solution is achieved when the correlation coefficient (R² ≥ 0.99). The predicted range of soil thermal conductivity is 3.26 to 3.38 W/(m·K). This rapid prediction method offers a valuable reference for engineering design and optimization of heat exchangers, enhancing their application efficiency.