Semi-analytical and numerical modeling of U-bend deep borehole heat exchanger

Abstract

U-bend deep borehole heat exchanger (DBHE) is a new promising kind of ground heat exchanger, but nowadays there are lack of accurate efficient models to simulate U-bend DBHE. This paper has developed a semi-analytical model of U-bend DBHE, which considers the unsteady heat transfer of borehole, heterogenous soil thermal properties and geothermal gradient. A 2D numerical model and an analytical model based on infinite line-source theory are also developed, and the three models are compared with experimental data for different boundary conditions. Based on the soil thermal properties estimated by logging data and rock identification, the three models have large errors when compared with experimental data. Based on a soil thermal conductivity λs estimated by matching experimental data, the three models match better with experimental data, and it is inferred that λs should be measured by thermal response test instead of rock identification. The semi-analytical model and 2D numerical model match very well for all the time, but the analytical model has large differences with 2D numerical model, which is because the analytical model ignores borehole heat capacity and time-varying heat flows at the borehole wall. This paper could provide a cost-effective semi-analytical model and some advices for U-bend DBHE.