Analytical model of heat transfer of U-shaped borehole heat exchanger under convolution theory and its optimal heat extraction analysis

Middle deep borehole heat exchanger (DBHE) has become widely known as one of the main ways of geothermal energy development and utilization, and the use of middle DBHE system for heating buildings has received much attention. More accurate analytical models for a coaxial borehole heat exchanger (CBHE) have been built using the convolution theorem, however, a U-shaped deep borehole heat exchanger (U-DBHE) has not been reported. Therefore, in this paper, to obtain more accurate fluid temperature distribution, an analytical model of middle DBHE considering geological stratification phenomenon is developed by using convolution theorem. The relative error of the analytical model is verified within 5% by numerical simulation. At the same time, the interaction between the three factors was analyzed and studied by response surface method: mass flow, inlet temperature and geothermal gradient on heat extraction and heat loss rate. The results reveal that for thermal extraction, the significance levels of the three factors are from large to small: geothermal gradient > inlet temperature > mass flow, for heat loss rate, the two factors of flow rate and inlet temperature are significant, and the impact of geothermal gradient is not significant. In this engineering project, when the inlet water temperature is 10 °C, the flow rate is 26.65 kg/s and the geothermal gradient is 4.5 °C/hm, there is a maximum heat extraction of 2424.16 kW.