Abstract
The purpose of the present work was to determine the thermal performance of borehole heat exchangers, considering the influences of their geometric configurations and the thermophysical properties of the soil, grout and pipe wall material. A three-dimensional model was developed for the heat and mass transfer in soil (a porous medium) and grout, together with one-dimensional conductive heat transfer through the pipe walls and one-dimensional convective heat transfer of the heat transfer fluid circulating in the pipes. An algorithm was developed to solve the mathematical equations of the model. The COMSOL Multiphysics software was used to implement the algorithm and perform the numerical simulations. An apparatus was designed, installed and tested to implement the thermal response test (TRT) method. Two wells of depth 50 m were drilled in the Almaty region in Kazakhstan. Gravel and till/loam were mainly found, which are in accordance with the stratigraphic map of the local geological data. In each well, two borehole heat exchangers were installed, which were an integral part of the ground source heat pump. The TRT measurements were conducted using one borehole heat exchanger in one well and the data were obtained. The present TRT data were found to be in good agreement with those available in literature. The numerical results of the model agreed well with the present TRT data, with the root-mean-square-deviation within 0.184 °C. The TRT data, together with the predictions of the line-source analytical model, were utilized to determine the soil thermal conductivity (λg = 2.35 W/m K) and the thermal resistance of the borehole heat exchanger from the heat transfer fluid to the soil (Rb = 0.20 m K/W). The model was then used to predict the efficiencies of the borehole heat exchangers with various geometric configurations and dimensions. The simulation results show that the spiral borehole heat exchanger extracts the highest amount of heat, followed by the multi-tube, double U-type parallel, double U-type cross and single U-type. It is also found that the spiral configuration can save 34.6% drilling depth compared with the conventional single U-type one, suggesting that the spiral configuration is the best one in terms of the depth and the maximum heat extracted. The simulation results showed that (i) more heat was extracted with a higher thermal conductivity of grout material, in the range of 0.5−3.3 W/m K; (ii) the extracted heat remained unchanged for a thermal conductivity of pipe material higher than 2.0 W/m K (experiments in the range of 0.24−0.42 W/m K); (iii) the extracted heat remained unchanged for a volumetric flow rate of water higher than 1.0 m3/h (experimental flow rate 0.6 m3/h); and (iv) the heat extracted by the borehole heat exchanger increased with an increase in the thermal conductivity of the soil (experiments in the range of 0.4−6.0 W/m K). The numerical tool developed, the TRT data and simulation results obtained from the present work are of great value for design and optimization of borehole heat exchangers as well as studying other important factors such as the heat transfer performance during charging/discharging, freezing factor and thermal interference.