Thermal interaction of geothermal boreholes with groundwater flows at peclet numbers of order unity

Abstract

The presence of aquifers significantly affects the thermal response of geothermal boreholes. Consequently, theoretical models used in the design and sizing of geothermal heat exchangers must account for their presence. Existing models in the literature are effective for creeping groundwater flows, where heat convection close to the borehole is weak compared to heat conduction and the resulting Peclet number is small compared to unity. But strong groundwater flows, with Peclet numbers of order unity and beyond, are also present in real-world applications, such as in high-permeability soils or when energy piles are involved. In these cases, current models fail to correctly account for the flow field in the vicinity of the boreholes, leading to unsatisfactory results or the need of empirical tuning parameters. By using asymptotic expansion techniques, a new theoretical model for the thermal interaction of geothermal boreholes with strong groundwater flows has been developed. It is physically sound, mathematically rigorous, and free of tuning parameters. Comparisons with detailed numerical simulations demonstrate the models’ promising performance and accuracy. Furthermore, the developed model is applicable to other heat transfer problems involving circular cylinders and potential or Darcy flows, thereby extending its relevance beyond the field of low-temperature geothermal energy.