A new approach to estimating temperature fields around a group of vertical ground heat exchangers in two-dimensional analyses

Vertical ground heat exchangers (VHEs), in the form of either Borehole Heat Exchanger (BHE) or thermo-active piles, are increasingly being deployed to provide low cost and sustainable heating and cooling to buildings. These are often installed within densely built urban environments, where adjacent foundation systems and underground structures can be affected by soil temperature changes induced by the heat exchangers. Therefore, they need to be considered in the geotechnical design of such structures, which typically involves carrying out two dimensional finite element plane strain analyses in order to assess their stability and performance. In such a scenario, it is common to model a line of heat exchangers as a planar source with one infinite dimension and a heat flux rate calculated by dividing the design extraction rate of a single heat exchanger by their spacing in the out-of-plane direction. This study shows that this approach largely overestimates the generated temperature field and proposes a simplified but accurate procedure to estimate the required heat flux to be applied to the planar heat sources in a 2D analysis. For this purpose, a correction factor, T∗, is introduced which is shown to depend on geometric parameters and thermal ground properties.