Most theoretical models for the unsteady -->thermal response of geothermal boreholes include a network of thermal resistances that provides the heat injection rates per unit pipe length of the different pipes inside the borehole in terms of the fluid temperatures in those pipes and of the thermal response of the ground surrounding the borehole. That network presents certain symmetries that are well known in the research field. However, when the thermal inertias of the grout and of the ground located close to the borehole are taken into account, for example through the enhanced multipole method recently developed by the authors, some of these symmetries break down. The present work provides mathematical proofs for this break down as well as for other symmetries and asymmetries present in the network of thermal resistances and for which no proofs exist in the prevailing literature.

地热井眼的非稳态->热响应的大多数理论模型都包括一个热阻网络，该热阻网络提供了井眼内不同管道的单位管道长度的热注入率，以这些管道中的流体温度和热量为依据。井眼周围地面的响应。该网络呈现出在研究领域中众所周知的某些对称性。但是，当考虑灌浆和靠近钻孔的地面的热惯性时，例如，通过作者最近开发的增强型多极方法，这些对称性中的一些就会分解。