Prediction and parametric analysis of 3D borehole and total internal thermal resistance of single U-tube borehole heat exchanger for ground source heat pumps

Abstract

The borehole and total internal thermal resistance are both significant parameters in evaluating the thermal performance of the ground source heat pump. This study aimed to obtain the accurate correlation of the 3D borehole and total internal thermal resistance (Rb,3D and Ra,3D) and analyze the impacts of parameters on the Rb,3D and Ra,3D. Firstly, eight parameters affecting the Rb,3D and Ra,3D, including the borehole diameter, pipe diameter, pipe-pipe distance, borehole depth, soil thermal conductivity, grout thermal conductivity, pipe thermal conductivity, and fluid velocity inside the pipe, were considered and an L-54 design matrix was generated. Then, the 3D numerical model, coupling with the four-resistance model, was proposed to calculate Rb,3D and Ra,3D for each case. After that, the response surface methodology was employed to obtain and verify the correlation of Rb,3D and Ra,3D, which were compared with the existing resistance calculation methods. Lastly, analysis of variance was carried out to reveal parameters that have statistically significant impacts on the Rb,3D and Ra,3D. Results show that the rationality and accuracy of the correlation of Rb,3D and Ra,3D can be verified by the determination coefficient and P value of regression model, as well as the P value of lack-of-fit. The existing resistance calculation methods are more or less inaccurate and the discrepancies in some cases can be up to 86.74% and 111.35% for the borehole and total internal thermal resistance. The pipe and grout thermal conductivity, pipe and borehole diameter, and the pipe-pipe distance can be seen as the significant contributory factors to the variation of Rb,3D and Ra,3D.