Thermal response tests on deep borehole heat exchangers with geothermal gradient

Vertical borehole heat exchangers are often coupled to heat pumps to transfer heat between the ground and the inside of a building. A transient heat transfer model has been developed for a coaxial borehole while taking into account the geothermal gradient found in deep boreholes. The analytical solution is obtained by applying Laplace transform methods followed by a numerical inversion to real time. The model is verified through comparisons with measured vertical temperature profiles in a borehole, as well as temperature profiles from previous numerical simulations. Sensitivity studies on simulated thermal response tests (TRT) under heat extraction demonstrate that applying a uniform temperature profile instead of the actual undisturbed ground temperature profile causes an underestimation of ground thermal conductivity. This simplification in a 2D model causes an additional estimation error as large as 9% for the cases studied. For a conventional 1D radial model the additional errors in the estimated ground thermal conductivity are as large as 28%. These errors are in addition to propagated errors from the uncertainties of the input parameters. Ignoring the geothermal gradient also affects the estimated effective borehole resistance.