Optimal insulation backfill depth analysis of coaxial deep borehole heat exchanger based on multi-factor orthogonal experiments

Coaxial deep borehole heat exchanger (DBHE) coupled with ground source heat pump (GSHP) system has been widely applied in building heating. Insulation backfill is essential for the heat transfer performance of DBHE in colder regions. However, few studies focus on the combined influence of multi-factors on the optimal insulation backfill depth. In this paper, an orthogonal experiment was designed to explore the influence of multi-factors on the optimal insulation backfill depth of DBHE by using a numerical heat transfer model. Sensitivity analysis concluded that heat transfer factors such as inlet flow rate (A), inner pipe thermal conductivity (B), inlet temperature (C), geothermal gradient (D), and pipe depth (E) all affected insulation backfill depth of DBHE, and the comparison order of significance are C > D > B > A > E. An optimal insulation backfill depth exists for different DBHE heat transfer conditions. Compared with no insulation backfill, the average heat extraction of buried pipe under optimal insulation backfill conditions increased by 6.09 kW, with an average growth rate of 8.78 %. In addition, multiple linear regression analysis was utilized to examine the relationship between affecting factors and the optimal insulation backfill depth, based on the findings of orthogonal tests. The outcomes revealed that inlet temperature, inner pipe thermal conductivity, and pipe depth were positively correlated, with the highest standardized positive correlation value of 0.755 for inlet temperature. In contrast, inlet flow and geothermal gradient were negatively correlated, with the highest standardized negative correlation coefficient of −0.420 for the geothermal gradient. The linear regression equation could predict the magnitude of optimal insulation backfill depth with diverse input parameters. The relative error between the predicted and simulated values of the equation was less than 5 %. The findings of this research can guide the popularization and application of the GSHP coupled with the DBHE system in colder regions.