A new semi-analytical model for studying the performance of deep U-shaped borehole heat exchangers

In deep geothermal exploitations, the U-shaped borehole heat exchanger (UBHE) has a longer fluid retention time and a larger contact area with the formation. In order to improve the utilization efficiency of geothermal energy, it is becoming increasingly important to accurately evaluate the performance of the deep UBHEs. In this study, the authors develop a new semi-analytical model for characterizing the heat transfer behavior of the deep UBHE geothermal system. In this developed model, the temperature change within the wellbore is numerically simulated by the finite difference method, whereas the temperature change between the formation and the wellbore is analytically simulated by the Green's-function. Besides, the non-uniform heat flux distribution along the horizontal section is considered to characterize three-dimensional heat transfer behaviors. By means of this model, the influences of developing strategies and well configurations on the outlet temperature and total thermal power are investigated. The calculation results indicate that the traditional assumption of uniform temperature along the horizontal section can induce significant errors in evaluating the performance of the UBHE geothermal systems; the horizontal section length is more conducive to improving the extraction performance in a shallower geothermal formation, and a longer horizontal section leads to a higher outlet fluid temperature, together with a larger total thermal power; a higher injection rate, as well as a lower injection fluid temperature, is more favorable for improving the total thermal power; an insulation casing with a length equaling the depth of injection point can lead to the maximum thermal power of the UBHE geothermal system.