Effect of depth and fluid flow rate on estimate for borehole thermal resistance of single U-pipe borehole heat exchanger

Abstract Accurate estimates for ground thermal parameters and borehole thermal resistance are important to improve the design of borehole heat exchangers (BHEs) in ground-coupled heat pump systems(GCHPs). In order to improve the estimating accuracy of borehole thermal resistance, this paper presents a simple analytical method for evaluating the actual averaged –over-the –depth mean fluid temperature (MFT) in the U-pipe of BHE to calculate borehole thermal resistance . Furthermore, the effects of borehole depth and volumetric flow rate on the calculating RMSE distribution between borehole thermal resistance and effective borehole thermal resistance are investigated. The conclusion shows that the relative deviation between the two borehole thermal resistances corresponding to the volumetric flow rate 1.5e-4m3/s increases from 4.2% to 29.7% when borehole depth changes from 50m to 200m. Finally, the borehole depths corresponding to different volumetric flow rate are optimized to find the boundary line where are nearly equal to in the operating time, and the impacts of grout thermal conductivity and heat rate per unit depth of BHE on the boundary line are quantitatively analyzed. Volumetric flow rate has more effect on with the higher grout thermal conductivity, the relative error between the two corresponding to V=1.5e-4m3/s and V=3e-4m3/s is 10.8% for =2.3W/(m.°C). The effect of heat rate per unit depth of BHE on is very limited, the relative error between the two corresponding to W/m and W/m is 5.4% under V=1.5e-4m3/s, and it is only 3.7% under V=3e-4m3/s.