An analytical heat transfer model for the mid-deep U-shaped borehole heat exchanger considering groundwater seepage

Ground source heat pump systems consisting of deep boreholes and heat pumps can be used for heating buildings. It is known as an effective way to utilize geothermal resources, however, there is a problem with high development costs. Therefore, it is important to establish a precise heat transfer model to develop a high-efficiency geothermal heat exchanger to reduce the development cost of mid-deep geothermal energy. Most of the existing heat transfer models for deeply buried pipes only consider thermal conductivity and treat the geotechnical soil as a homogeneous me-dium, or do not consider the stratification and groundwater seepage phenomena, which make the models inaccurate. This study established an analytical heat transfer model considering geotechnical stratification and seepage developed for the U-shaped deep borehole heat exchanger (U-DBHE), and the analytical solution for temperature response is obtained. Using the developed analytical model, we plotted the trends that reveal the relationship between the thermal per-formance of U-DBHE and various parameters and explored the influence of seepage phenomena on heat extraction performance. The model can also serve as a reference for the development of heat transfer models for buried pipe heat exchangers with groundwater seepage. Given that the proposed analytical model is time-consuming and stable, and can be an efficient tool for U-DBHE design and optimization.