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) 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.

立式井眼热交换器通常与热泵相连，以在地面和建筑物内部之间传递热量。考虑到深孔中的地热梯度，已经为同轴孔开发了瞬态传热模型。解析解决方案是通过应用Laplace变换方法，然后将数值反演为实时来获得的。通过与井眼中测得的垂直温度曲线以及先前数值模拟的温度曲线进行比较，验证了该模型。对模拟热响应测试（TRT）的敏感性研究表明，应用统一的温度曲线而不是实际的不受干扰的地面温度曲线会导致对地面导热系数的低估。在2D模型中的这种简化导致所研究案例的额外估计误差高达9％。对于常规的一维径向模型，估计的地面导热系数的附加误差高达28％。这些误差是由于输入参数不确定性造成的传播误差之外的补充。忽略地热梯度也会影响估计的有效井眼阻力。