On the network of thermal resistances embodying the response of geothermal boreholes to creeping groundwater flows

Aquifers are known to enhance the heat exchange between geothermal boreholes and the ground. To accurately assess this enhancement, theoretical models for the thermal interaction of geothermal boreholes with groundwater flows are necessary. Such models already exist in the literature but rely on ideas and methodologies intended for purely conductive grounds. Despite their satisfactory performance, the lack of mathematical rigor limits their capabilities and future development. The present work aims to overcome these limitations by deriving a mathematically rigorous and physically sound model for the case of creeping groundwater flows. This allows to evaluate, for the first time, the conceptual merits and limitations of the current state of the art and to envision ways of improving it.