Integrating the geothermal gradient in models for distributed thermal response test analysis on U-tube boreholes

A Distributed Thermal Response Test on a vertical borehole estimates important parameters required for the design of Ground-Source Heat Pump systems. As the borehole depth increases, the effects of the geothermal gradient increase, but these effects are neglected by analytical models based on the typical delta thermal resistance network of a U-tube borehole. This study demonstrates that measured vertical temperature profiles at the end of the fluid circulation of a Distributed Thermal Response Test often sufficiently capture the natural heating effects of the geothermal gradient. Through a new time superposition procedure, these measured profiles integrate the effects of the geothermal gradient into a suitable analytical borehole model of the subsequent heat injection/extraction period. In applications to test data sets, the modified model estimates the ground thermal conductivity as well as borehole and internal thermal resistances. The study verifies these modified analytical models by using numerically simulated data sets and evaluates how the inclusion of the geothermal gradient affects parameter estimation. Additionally, the study provides guidelines on the applicability of the original and modified models using key dimensionless groups, which also indicate ranges of the accuracy and uncertainty of estimated parameters.