Borehole temperature evolution during thermal response tests
Introduction
Thermal response tests (TRTs) are routinely used to determine subsurface and borehole thermal properties, which are needed to size ground heat exchangers for commercial or institutional ground-coupled heat pump systems. The conventional TRT, also referred to as a borehole thermal conductivity test, consists in circulating heated water in a closed loop, which mimics heat transfer occurring in a ground heat exchanger (ASHRAE, 2007, Sanner et al., 2005). Water temperature variations are measured at the ground heat exchanger inlet and outlet during the test, along with flow rate. Measured temperatures and flow rates are then analyzed with analytical or numerical models (Gehlin and Hellström, 2003) to determine the subsurface thermal conductivity and the borehole thermal resistance.
In addition to measuring water temperatures at the inlet and outlet of the heat exchanger, it has been recently proposed to also measure temperature variations inside the borehole during a TRT to determine the thermal properties as a function of depth (Fujii et al., 2006, Fujii et al., 2009). As shown by Fujii et al., 2006, Fujii et al., 2009, measuring the temperature inside the borehole makes it possible to determine the vertical distribution of subsurface thermal conductivity when the distribution of geological units along the borehole is known. In a variation of the conventional TRT (Raymond et al., 2010), temperature was measured at different depths in the borehole, while heat was injected by inducing an electric current through heating cables installed inside the pipes of the ground heat exchanger. This modified TRT is easier to perform than the standard TRT because it uses lighter equipment and does not require water circulation. The temperature recorded inside a ground heat exchanger, however, depends on the location of the temperature sensor inside the borehole. That location is difficult to determine because sensors and pipes can move when lowered in the borehole. Because the temperature inside the borehole can be variable, the location of the temperature sensors can influence the analysis of a test and consequently affect the estimation of thermal properties by curve fitting.
The primary objective of this work is to quantify the temperature variation inside a ground heat exchanger made with a single U-pipe during a thermal response test (Fig. 1) and determine the influence of that variation on the estimation of subsurface and borehole thermal properties. The methodology consists of simulating TRTs using a two-dimensional numerical model for heat transfer in the subsurface and in the borehole. The simulations investigate the impact of sensor locations on temperature measurements in the borehole for the conventional TRTs and modified TRTs that use heating cables. The simulated borehole temperatures are also used to determine the most appropriate approach for estimating the borehole thermal resistance. Determination of the axial variation of both the subsurface thermal conductivity and the borehole thermal resistance provides additional information for the design of large ground-coupled heat pump systems.
Section snippets
Theoretical background
The subsurface thermal conductivity and borehole thermal resistance are typically estimated by matching with the line source model temperatures measured during a TRT (Gehlin and Hellström, 2003). The line-source model is derived from Kelvin's analytical solution for transient heat conduction from an infinite linear heat source embedded in a homogenous medium, with constant temperature at an infinite radial distance (Carslaw, 1945, Ingersoll et al., 1954). For variable heat injection rates, the
Development of the numerical model
To compute conductive heat transfer in a borehole and the subsurface during a TRT, a two-dimensional model is used; it is assumed that heat transfer from the ground heat exchanger pipes is predominantly radial at a given depth, which is reasonable when the subsurface geothermal gradient is small. The thermal properties of the different materials representing the borehole and the subsurface are assumed to be homogenous, isotropic, and independent of temperature. The energy input resulting from
Verification examples
Simulations are initially conducted with a simplified geometry to verify the numerical model results because transient models with the proposed boundary conditions are first used here to evaluate thermal resistance across the borehole. The ground heat exchanger, illustrated in Fig. 3, contains a single pipe located at the borehole center. This simplified geometry is chosen because the combined grout and pipe thermal resistance can be determined exactly with the relation used to calculate the
Results
Simulations conducted to reproduce TRTs with conventional and heating cable equipments are carried out using parameters for the base case scenario given in Table 1. The model results shown in Fig. 5 illustrate the borehole temperature at the end of heat injection and five hours after stopping heat injection. The temperature distribution inside the borehole varies significantly during heat injection, but homogenizes during recovery. Fig. 6 shows the temporal variation of temperature at various
Discussion
Numerical simulations of TRTs with conventional and heating cable equipments indicate the temperature inside the borehole varies significantly according to measurement location during heat injection, but not during late recovery. The borehole temperature homogenizes rapidly after heat injection is stopped. It is therefore recommended to install sensors inside the U-pipe during conventional TRTs, or to monitor temperature recovery for both the conventional and the modified TRT, to minimize
Conclusion
Simulations of temperature evolution in a 2D slice of borehole during thermal response tests (TRTs) indicate that the monitoring and analysis of temperature recovery can minimize the test uncertainty when measurements are recorded inside the borehole, because temperature is not influenced by the sensor location during late recovery. Numerical model results also suggest that the borehole thermal resistance is best evaluated in the field during a conventional TRT using a combination of heating
Acknowledgements
Funding for this research was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC). Additional funding in the form of student scholarships from NSERC, the Fonds québécois de la recherche sur la nature et les technologies (FQRNT), the Canadian Foundation for Geotechnique (CFG), and the Canadian Institute of Mining-Thetford Mines Branch (CIM-TM) is also acknowledged. The first author is particularly grateful for the generous support from these organizations. The
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