A semi-analytical heat transfer model for deep borehole heat exchanger considering groundwater seepage

Abstract

Groundwater seepage has important effect on the deep borehole heat exchanger (DBHE, having a depth of about 1000–3000 m) performance, but there is lack of efficient analytical or semi-analytical heat transfer model of DBHE considering groundwater seepage. By combing the temperature response functions (G-functions) of moving infinite line source (MILS) model, steady-state MILS model and steady-state moving infinite cylindrical source (MICS) model, a composite G-function is developed to analyze the MICS problem in the DBHE with groundwater seepage. Subsequently a semi-analytical model of DBHE is proposed based on the composite G-function to analyze the DBHE performance with groundwater seepage. The composite G-function and semi-analytical model are verified by comparison with numerical, analytical and experimental results. The composite G-function matches well with the G-function of numerical MICS model for different Péclet numbers (Pe) except during short time, and has higher precision than the G-function of MILS model. The proposed semi-analytical model using the composite G-function matches well with a 3D numerical model for different Darcy velocities at the infinite distance (u∞) and borehole radii (rb), and has higher precision than that using the G-function of MILS model. The proposed semi-analytical model is also applied to a field test of DBHE, and the result shows that the proposed semi-analytical model matches well with experimental data. The results indicate that the proposed semi-analytical model using the composite G-function is efficient to predict the DBHE performance in wide ranges.