An Analytical Investigation of the Heat-Transfer Performance of a Deep U-Shaped Borehole Heat-Exchangers System in Porous Media

Compared with previous analytical designs for deep UBHE, the present study is new in three aspects: (1) a segmented FLS model combined with the virtual heat source method is applied to the full U-shaped path (injection, horizontal, and production wells) in a unified formulation; (2) equivalent thermal conductivity is introduced to account for groundwater seepage in porous media, avoiding the need for separate CFD or coupled numerical solvers; (3) the relationship between production well depth and the maximum effective insulation length is quantified and discussed. Deep U-shaped borehole heat-exchangers (UBHE) systems boast high heat-exchange efficiency, yet most analytical models are too simplistic, causing inaccuracies. This study proposes a segmented finite line source (FLS) model for UBHE using the virtual heat source method. Introducing equivalent thermal conductivity (kequ), it treats rock-soil as a groundwater-saturated porous medium, coupling seepage’s dynamic heat-transfer impact. By comparing the simulation results of the same type of research within 720 h, the average temperature difference between the models was found to be 1.31 °C, with an error rate of 5.31%, which is 40.87 percentage points lower than the existing achievements, thereby demonstrating the accuracy of this model. In addition, based on this model, the influence trends of five main factors such as seepage velocity and geothermal gradient on the system’s heat exchange were drawn and analyzed. Among them, the laying length of the insulation layer was analyzed in detail. The results show that its maximum laying length should be in line with the depth node where reverse heat exchange occurs with the production well. Under the set conditions of this study, when the depth of the production well is 2500 m, the maximum laying length of the insulation layer is 1900 m.