An efficient hybrid model for thermal analysis of deep borehole heat exchangers

Abstract

The deep borehole heat exchanger (DBHE) shows great potential in seasonal thermal energy storage and its high performance efficiency with smaller land occupancy attracts increasing attention as a promising geothermal energy exploitation technique. With respect to a vertical BHE with extremely long length pipes buried underground, thermal analysis of the unsteady heat transfer process of the system is quite complicated. Due to the high temperature underground, the deeper part of BHE can extract more heat from the rock, which leads to a higher heat extraction rate. The heterogeneous distribution of heat flux density and geothermal gradient cannot be described properly by the existing analytical models. Although a full 3D numerical solution can reflect these features, it always requires high computational resources and presents numerical instabilities. In this paper, we propose a hybrid modeling method with high efficiency to simulate the temperature evolution inside the DBHE, and the heat propagation front in the surrounding rock mass. The temperature evolution inside the DBHE is solved by finite difference schemes, while the heat propagation in the surrounding rock is determined by an analytical formulation of thermal impacted radius. The coupling is achieved via source/sink term by incorporating the heat flux between the DBHE and the surrounding rock. Furthermore, an innovative analytical formulation describing the heat flux density is also presented, which accounts for the key parameters affecting the thermal performance of the DBHE system. Our proposed model is further verified against results with full 3D numerical solution under the same configurations. It is demonstrated that the proposed model can capture the key physical process of the heat transfer problem, while maintaining the calculation accuracy required by the engineering application. Regarding the calculation speed, the model results are around 30 times faster when compared to the full 3D numerical solution.