Long-term heat transfer analysis of deep coaxial borehole heat exchangers via an improved analytical model

The heat transfer calculation of deep coaxial borehole heat exchangers (DCBHE) involves complex geological conditions, mainly including geothermal gradient, layered ground profile, non-uniform heat transfer along depth, and fluid–solid coupled heat transfer. However, no analytical model can fully consider all of these factors currently. In this study, an improved analytical model for DCBHE based on the moving finite line source (MFLS) model is proposed to fully analyze the heat transfer performance. By comparing with the experimental data of an in-situ test of a 2500 m DCBHE, it is shown that the proposed model has higher accuracy compared with other analytical models. To analyze the heat transfer sustainability of the DCBHE in the in-situ test, the degrees of reduction in local heat flux and heat extraction power are calculated from the aspects of the single heat-extraction season and periodic operations. The results show that the local sustainability of the strata between 0 m and 1510 m is worse than the average value and pulls down the sustainability of whole DCBHE. After 30 years of operation, the reductions of heat extraction power at the transient stage and stable stage of the extraction season are 11.8% and 9.6%, respectively. Moreover, the groundwater flow can make the reduction in local heat flux smaller (only 4%~6%) and more constant with years, but the effect of groundwater flow is not significant within one season. The research findings can potentially guide the structural design and optimization of DCBHE and serve the long-period operations of DCBHE.