Analysis of Relaxation Time of Temperature in Thermal Response Test for Design of Borehole Size

Abstract

A new practical method for thermal response test (TRT) is proposed herein to estimate the groundwater velocity and effective thermal conductivity of geological zones. The relaxation time of temperature (RTT) is applied to determine the depths of the zones. The RTT is the moment when the temperature in the borehole recovers to a certain level compared with that when the heating is stopped. The heat exchange rates of the zones are calculated from the vertical temperature profile measured by the optical-fiber distributed temperature sensors located in the supply and return sides of a U-tube. Finally, the temperature increments at the end time of the TRT are calculated according to the groundwater velocities and the effective thermal conductivity using the moving line source theory applied to the calculated heat exchange rates. These results are compared with the average temperature increment data measured from each zone, and the best-fitting value yields the groundwater velocities for each zone. Results show that the groundwater velocities for each zone are 2750, 58, and 0 m/y, whereas the effective thermal conductivities are 2.4, 2.4, and 2.1 W/(m∙K), respectively. The proposed methodology is evaluated by comparing it with the realistic long-term operation data of a ground source heat pump (GSHP) system in Kazuno City, Japan. The temperature error between the calculated results and measured data is 6.4% for two years. Therefore, the proposed methodology is effective for estimating the long-term performance analysis of GSHP systems.

Keywords

• relaxation time of temperature
• thermal response test
• groundwater velocity
• moving line source theory
• optical fiber distributed temperature sensor