This paper concerns the modeling of vertical coaxial heat exchangers for Ground Source Heat Pump (GSHP) applications. Vertical coaxial borehole heat exchangers (CBHEs) can be buried at depths which are even higher than the conventional ones. In this case they are referred as Deep Borehole Heat Exchangers (DBHEs). As it is known, there is indeed a strong recent tendency, especially in the Scandinavian regions, to use high depth (500-1000 meters) underground heat exchangers for the GSHP applications. This study is aimed at the analysis of the BHE behaviour in the early period, say for Fourier numbers typical of the Thermal Response Test (TRT) measurements. The novelty of the present numerical results is related to the applicability of standard TRT methods when applied to DBHEs and different geothermal gradients can be found. To this aim a Fortran code has been developed for describing a 2D transient conduction and convection problem able to provide the fluid and ground temperature evolution as a function of a series of boundary conditions, including the initial and far field ground temperature distribution along the depth. The application of the present model is related to coaxial BHEs for the assessment of the effects of the undisturbed ground temperature profile and the direction of the carrier fluid on the ground thermal conductivity estimation in TRT experiments. It is here demonstrated that different BHE depths (ranging from 150 to 800m) and different undisturbed temperature profiles (including zero and positive geothermal gradients) can severely affect the TRT ground conductivity estimation (errors up to 25%) if the flow direction is based on the annular pipe or the central pipe inlets.

本文涉及用于地源热泵（GSHP）应用的垂直同轴热交换器的建模。垂直同轴钻孔热交换器（CBHE）的埋入深度甚至可以比传统埋入式热交换器高。在这种情况下，它们称为深孔热交换器（DBHE）。众所周知，特别是在斯堪的纳维亚地区，确实存在着将高深度（500-1000米）地下热交换器用于GSHP应用的强烈趋势。这项研究旨在分析早期的BHE行为，例如热响应测试（TRT）测量中典型的傅立叶数。当前数值结果的新颖性与标准TRT方法应用于DBHE的适用性有关，并且可以发现不同的地热梯度。为了这个目的，已经开发出用于描述二维瞬态传导和对流问题的Fortran代码，该二维瞬态传导和对流问题能够提供流体和地面温度随一系列边界条件而变的函数，包括沿深度的初始和远场地面温度分布。本模型的应用与同轴BHE有关，用于评估TRT实验中未扰动的地面温度曲线和载液方向对地面导热系数估算的影响。