On the symmetry properties of the network of thermal resistances representing the thermal response of slender geothermal boreholes

Abstract

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.