A semi-analytical model for heat transfer in coaxial borehole heat exchangers

Heat transfer model is important for the design of coaxial borehole heat exchanger (CBHE). However, the existing models have some disadvantages, such as costing too much computation time, ignoring the geothermal gradient and concerning the borehole heat capacity as a whole. In this paper, a semi-analytical model is developed by considering the geothermal gradient and the heat capacities of different parts of the borehole: 1D radial heat transfer in the grout and the soil is analyzed based on an analytical solution; temperature distributions of the internal fluid and the annular fluid are calculated numerically. To verify the feasibility of the proposed model, it is compared with another model and experimental data, and it is compared with OGS simulation data of a deep CBHE. Compared with another model, the fluid temperature distributions calculated by the proposed model match better with experimental data especially at the early time of heat injection. The fluid temperature distributions calculated by the proposed model match well with OGS simulation data except during the early several days, noting that the OGS simulation data are not accurate at the early time. The results show that the proposed model is feasible and efficient.

Automated summary

In this study, a semi-analytical model is developed for evaluating heat transfer in coaxial borehole heat exchangers, taking into account geothermal gradient and heat capacities of different borehole components. The proposed model demonstrates better agreement with experimental data and OGS simulation results compared to existing models, particularly in capturing fluid temperature distributions during early stages of heat injection. Overall, the results validate the feasibility and efficiency of the proposed model.