Vertical temperature profiles and borehole resistance in a U-tube borehole heat exchanger

The design of ground source heat pump systems requires values for the ground thermal conductivity and the borehole thermal resistance. In situ thermal response tests (TRT) are often performed on vertical boreholes to determine these parameters. Most TRT analysis methods apply the mean of the inlet and outlet temperatures of the circulating fluid along the entire borehole length. This assumption is convenient but not rigorous. To provide a more general approach, this paper develops an analytical model of the vertical temperature profile in the borehole during the late-time period of the in situ test. The model also includes the vertical temperature profile of the undisturbed ground. The model is verified with distributed temperature measurements along a vertical borehole using fiber optic cables inside a U-tube for the circulating fluid. The borehole thermal resistance is calculated without the need for the mean temperature approximation. In the studied borehole, the mean temperature approximation overestimates the borehole resistance by more than 20%.