A Borehole Thermal Resistance Correlation for a Single Vertical DX U-Tube in Geothermal Energy Application

Abstract

The ground source coupled heat pump is considered as one of the most important technologies utilized in the field of sustainable energy. The borehole thermal resistance has a great impact on the total thermal resistance between the fluid that flows inside the buried U-tube and ground. This issue is related directly to the heat transfer efficiency of the ground part of the heat pump and the effective coefficient of performance of the heat pump system. The capability of the ground heat exchanger to dissipate or absorb energy to or from the ground determines the size and geometry configuration of these heat exchangers. The present research represents a model for the prediction of the borehole thermal resistance of a ground heat exchanger. The U-tube heat source or sink was replaced by a single equivalent concentric tube in the borehole possessing equal thermal resistance as that of the original U-tube heat exchanger. The model was applied for four different U-tube/borehole configurations, the test U-tubes were (9.52) mm, (12.7) mm, (15.88) mm, and (19.05) mm for a borehole to U-tube diameter ratios range of (3.94) to (7.88). The correlation showed a nonlinear dependency for the equivalent tube diameter and hence the thermal resistance of the filling on the U-tube diameter. It has also shown that for the same U-tube/borehole configuration, increasing of the U-tube legs spacing reduces the thermal resistance and approaching a minimum as the tube legs are located close to the borehole wall. Further, for the same borehole size, the thermal resistance exhibited a decrease as the U-tube size was increased and vice versa. At a borehole size of (75) mm, shank spacing to tube diameter ratio of (2), and a grout thermal conductivity of (0.78) W/m.K, the borehole total thermal resistance of the (9.52) mm U-tube size was higher than that of the (19.05) mm by (74)%. The model revealed that the grout thermal conductivity plays an important role in the thermal resistance assessment; the latter showed a decrease as the thermal conductivity increases to the highest test value of 1.9 W/m.K. The predicted thermal resistance was compared with other available correlations in the open literature and found to be consistent in the data trend and magnitudes with acceptable margin.