Thermal response test for shallow geothermal applications: a probabilistic analysis approach

Background: Thermal Response Test (TRT) is an onsite test used to characterize the thermal properties of shallow underground, when used as heat storage volume for shallow geothermal application. It is applied by injecting/extracting heat into geothermal closed-loop circuits inserted into the ground. The most common types of closed loop are the borehole heat exchangers (BHE), horizontal ground collectors (HGC), and energy piles (EP). The interpretation method of TRT data is generally based on a regression technique and on the calculation of thermal properties through different models, specific for each closed loop and test conditions. Methods: A typical TRT record is a graph joining a series of experimental temperatures of the thermal carrier fluid. The proposed geostatistical approach considers the temperature as a random function non-stationary in time, with a given trend, therefore the record is considered as a ‘realization’, one of the possible results; the random nature of the test results is transferred to the fluctuations and a variogram modeling can be applied, which may give many information on the TRT behavior. Results: In this paper, a nested probabilistic approach for TRT output interpretation is proposed, which can be applied for interpreting TRT data, independently of the different methodologies and technologies adopted. In the paper, for the sake of simplicity, the probabilistic approach is applied to the ‘infinite line source’ (ILS) methodology, which is the most commonly used for BHE. Conclusions: The probabilistic approach, based on variogram modeling of temperature residuals, is useful for identifying with robust accuracy the time boundaries (initial time t0 and the final time tf) inside which makes temperature regression analysis possible. Moreover, variograms are used into the analysis itself to increase estimation precision of thermal parameter calculation (ground conductivity λg, ground capacity cg, borehole resistance Rb). Finally, the probabilistic approach helps keep under control the effect of any cause of result variability. Typical behaviors of power, flows, and temperatures and of their interaction with the specific closed-loop circuit and geo-hydrological system are deepened by variogram analysis of fluctuations.