Estimating Thermal Response Test Coefficients: Choosing Coordinate Space of The Random Function

Shallow Geothermal Systems (SGS) are widely used to provide low-cost heating and cooling of residential and commercial buildings. SGS can be an economically-viable solution even for commercial buildings, where controlled temperature is fundamental for the production processes. To assess the thermal resistance of the soil and the performance of a SGS, Thermal Response Tests (TRT) must be performed. TRT machines are today designed mainly for short term monitoring, for relatively deep SGS (up to 200 m) and for being used by expert operators. Lightweight, low-cost machines for both fast and long term, reliable and unattended TRT for very Shallow Geothermal Systems (vSGS) are not available today. This paper describes the design of a micro-TRT machine (mTRT) for vSGS, which is gaining interest in the civil engineering, environmental, energy and food chain sectors. The paper describes the features of the wireless monitoring system, the design choices to achieve the required accuracy and the software developed for adding remote control capability. Experimental validation in a real test field demonstrates the quality of measurements collected for analysing the TRT data.

Thermal Response Tests (TRT) are conducted to determine the equivalent thermal conductivity and, in some cases, the volumetric heat capacity of the subsurface, which are essential for designing low-temperature geothermal systems. During TRTs, heated water is circulated through a ground heat exchanger (GHE), while the temperature variations at the borehole's inlet and outlet are monitored over time (Pasquier et al., 2016). Generally, TRT interpretation yields averaged thermal properties along the entire GHE, overlooking variations in geological materials that can affect heat transfer efficiency. Acquiring detailed thermal and hydraulic property data at varying depths allows for the optimization of GHE design to enhance overall performance. Furthermore, traditional TRTs primarily rely on water temperature measurements, providing limited information into the spatial distribution of temperature changes in the surrounding geological environment.Geophysical methods, such as electrical resistivity monitoring, can provide complementary measurements using the sensitivity of electrical resistivity to temperature changes.  In this study, we investigate the use of geoelectrical monitoring during TRTs to image temperature variations in the geological environment to improve the recovery of localized thermal properties. A geoelectrical cable is placed inside the borehole during the TRT, with an electric current injected through surface and borehole electrodes. Another set of surface and borehole electrodes measures the resulting potential differences. Varying electrode spacing allows to measure apparent resistivity changes at different radial distances from the borehole. This means that electrical measurements are sensitive to temperature changes at various depths in the geological environment and could image heat transfer during the TRT. We conducted two proof-of-concept studies on standing column wells (SCW) in Varennes and Saint-Anne-des-Plaines in Québec, Canada, to test electrical monitoring during a TRT. The SCWs were subjected to heating, bleeding and recovery phases, while time-lapse electrical measurements were taken using a geoelectrical cable installed in the SCWs.Field data shows a strong correlation between apparent electrical resistivity and temperature variations during heating and recovery cycles. Geoelectrical data is compared with infinite and cylindrical line source models to simulate temperature-induced resistivity changes around the SCW. Preliminary results indicate varying sensitivity of apparent resistivity variations to SCW water temperatures, as well as to the subsurface's thermal conductivity and heat capacity. Building on these findings, the study aims to derive localized thermal parameters from the geoelectrical data. This approach highlights the potential of geophysical monitoring to enhance the accuracy of thermal characterization in TRTs.Pasquier, P., Nguyen, A., Eppner, F., Marcotte, D., & Baudron, P. (2016). Standing column wells. Advances in Ground-Source Heat Pump Systems (pp. 269–294). Elsevier. http://dx.doi.org/10.1016/B978-0-08-100311-4.00010-8

Knowledge of ground thermal properties is most important for the proper design of large BHE(borehole heat exchanger) systems. Thermal response tests with mobile measurement devices were first introduced in Sweden and USA in 1995. Thermal response tests have so far been used primarily for in insitu determination of design data for BHE systems, but also for evaluation of grout material, heat exchanger types and ground water effects. The main purpose has been to determine insitu values of effective ground thermal conductivity, including the effect of ground-water flow and natural convection in the boreholes. Test rig is set up on a small trailer, and contains a circulation pump, a heater, temperature sensors and a data logger for recording the temperature data. A constant heat power is injected into the borehole through the pipe system of test rig and the resulting temperature change in the borehole is recorded. The recorded temperature data are analysed with a line-source model, which gives the effective insitu values of rock thermal conductivity and borehole thermal resistance.

Shallow closed-loop geothermal systems are worldwide applied providing economical and environmental benefits. This paper presents an in-situ study of four Borehole Heat Exchangers of 100 m long, installed in an heterogeneous bedrock in the campus of the University of Liege (Liege, Belgium). A Thermal Response Test (TRT) of a heating phase of 7 months was conducted in one of the boreholes. During this test, temperature was measured at the pipe inlet and outlet, as well as along the four boreholes by the fiber optics. To further investigate the measured data, the test was simulated by 3D numerical modeling. The comparison of the measured data with the numerical results allowed to detect the critical parameters for the behavior of the BHE and for the temperature evolution in the surrounding rock mass. In this case study, the behavior of the BHE could be predicted based on the results of a typical-duration TRT (of a few days), considering the ground an homogenous and isotropic material. However, the thermal plume in the surrounding ground seems to be influenced by several factors, such as the bedrock heterogeneity, the distance to the heating source, air temperature variations and thermal effects at the borehole bottom end.

Thermal response test (TRT) is a common procedure for characterization of ground and borehole thermal properties needed for the design of a shallow geothermal heat pump system. In order to investigate and to develop more accurate and robust procedures for TRT control, modelling, and evaluation in semi-permeable soils with large water content, a pilot borehole heat exchanger was built in the main campus of the Universitat Politècnica de València. The present work shows the results of the experiments performed at the site, analysing the improvements that have been introduced both in the control of the heat injected during TRTs and in the methods to infer the ground thermal parameter. Three models are compared: two based on the infinite-line source theory and one based on the finite-line source scheme. The models were tested under two possible configurations of the equipment, i.e., with and without strict control of injected heat. Our results show the importance of heat injection control for a robust parameter assessment and the existence of additional heat transfer processes that the used models cannot completely characterize and that are related to the presence of significant groundwater flow at the site. In addition, our experience with the current installation and the knowledge about its strengths and weaknesses have allowed us to design a new and more complete test-site to help in the analysis and validation of new ground heat exchanger geometries.

The United Kingdom is experiencing a period of rapid growth in the use of ground source heat pump systems. Most installations in the United Kingdom use vertical ‘borehole’ heat-exchanger arrays, the design of which depends on four parameters: formation thermal conductivity, formation heat capacity, heat-exchanger resistance and heat-exchanger grout material heat capacity. Conventionally, two of these parameters (conductivity and resistance) are obtained from a thermal response test carried out on a trial heat exchanger at the site of interest by fitting thermal response data to classical line-source heat conduction theory. This test method gives no information on the heat capacities of the formation and grout material and requires an assumption about the former to enable the heat-exchanger resistance parameter to be extracted. In this work, a new method is developed for extracting all four parameters using a trust-region search algorithm in conjunction with a detailed numerical model of the test heat exchanger. Results give excellent agreement between the fitted-model predictions of heat-exchanger outlet water temperature and measured outlet water temperature for 13 test cases. A further advantage of the method developed here is that it can be used with data sets that contain disturbances and discontinuities. Practical applications: Most of the ground source heat pump installations in the United Kingdom use vertical ‘borehole’ heat-exchanger arrays. The design of these arrays requires information about the rock formation thermal conductivity and volume specific heat capacity and the borehole heat-exchanger thermal resistance and grout material volume specific heat capacity. These design parameters are usually obtained from a thermal response test carried out on a trial heat exchanger at the site of interest. In this work, thermal response test results from 13 UK sites are presented and a new method for obtaining the four design parameters is developed and proposed.

Thermal response tests (TRTs) are performed on borehole heat exchangers in order to evaluate ground and borehole thermal properties, which are needed in the design of ground-source heat-pump systems. When parameter estimation techniques are applied to evaluate the ground thermal conductivity and borehole thermal resistance, the map of the root mean square error (RMSE) sometimes shows a shallow descent to the global minimum. This study obtains a steeper descent by estimating the component of borehole resistance without heat capacity as a separate parameter. A temperature derivative curve is introduced to identify the boundaries between three distinct periods of a TRT, which are borehole-dominated, transition, and steady heat-flux periods. The effective borehole resistance and ground thermal conductivity can be evaluated independently from each other during the borehole-dominated and steady heat-flux periods, respectively. Meaningful estimates of the ground volumetric heat capacity can be obtained from the TRTs in this study in only limited cases. The best chance is when the grout and ground thermal conductivities are nearly equal and the borehole thermal resistance is small.

Energy tunnel is a new type of geothermal exchanger in ground source heat pump systems due to their technical and cost improvements over traditional borehole geothermal exchangers. The main reason that the factors affecting the heat exchange capacity of energy tunnel are unclear makes its development be restricted. An in-situ full-scale study using the thermal response tests (TRT) and thermal performance tests (TPT) is performed to investigate the factors affecting the heat exchange capacity in Badaling Energy Tunnel of Beijing-Zhangjiakou High-speed Railway. This paper analyzes the influences of constant heating power, inlet water temperature, air temperature in tunnel, circulating water flow velocity, operation mode, and pipe connection on the heat exchange capacity of the energy tunnel. The test results reveal that (1) the heat exchange rate of the energy tunnel decreases with the increasing constant heating power, (2) the heat exchange rate of the energy tunnel is positively proportional to the inlet water temperature, (3) the heat exchange rate of the energy tunnel at a circulating water flow velocity of 1.1 m3/h is larger than that at 0.5 m3/h, it is smaller than that at 0.8 m3/h, (4) the air temperature in tunnel has a great effect on the heat exchange rate of the energy tunnel, and the pipes connected in parallel or connected in series have a slight effect on the heat exchange rate of the energy tunnel, (5) the average heat exchange rate in an intermittent operation mode is approximately 18.5% larger than that in a continuous operation mode. The test results can be used for the thermal design of energy tunnels.

Borehole thermal resistance and ground thermal properties (thermal conductivity and heat capacity) are the key parameters to implement the ground source heat pump (GSHP), usually obtained by thermal response test. In this study, a novel sequential parameters estimation method for the above three parameters is proposed, and the sensitivity analysis by using a special correlation method is performed to decide the best estimation sequences. At first, the Spearman partial rank correlation coefficient was used to represent the correlation between the estimated thermal properties and fluid temperature for the line source model (ILS), then the estimation sequence for the three parameters could be determined by the correlation results. Lastly, with the estimation step, Monte Carlo method was adopted to determine the parameters replacing conventional iterative algorithms. In addition, the effect of value bounds and initial inputs as well as random samples was investigated. The results showed that compared to the other estimation steps, the estimation sequence following borehole resistance firstly, then thermal conductivity, heat capacity lastly could get the best precision with 4.5%, 0.4%, 1% respectively. Specially, the estimation precision for ground heat capacity could be promoted by the sequential estimation. Also, the effect of value bounds on estimation precision was nearly eliminated by the proposed method.

Accurate estimation of the thermal properties of soil and concrete piles is critical for designing energy piles. This paper proposes an algorithm that can simultaneously estimate the thermal conductivities and diffusivities of soil (ks and as , respectively) and concrete piles (kb and ab, respectively) using data from thermal response tests (TRTs). The outstanding feature of the algorithm is its use of a composite-medium cylindrical-surface heat source solution. The proposed algorithm is a theoretically complete short-term solution that considers the heat capacity of the concrete pile and the difference in thermal properties between the soil and concrete pile. Sensitivity analysis shows that the data of early-time TRTs reduce the linear dependence of the parameters, thereby allowing the simultaneous estimation of ks, as, kb , and ab . The new algorithm is validated using the reported TRT data. Results show that the four parameters could be estimated with high accuracy by using the data sampled between 10 and 50 h. Moreover, ks and kb have relative errors of 11.05% and 24.47%, respectively. In conclusion, the proposed algorithm is easy to implement and computationally more efficient compared with algorithms using numerical models. Thus, the use of this algorithm may potentially reduce the time and cost of TRTs.

Effects of groundwater flow on thermal response test of deep borehole heat exchanger

The use of renewable energies, and of geothermal energy in particular, is increasingly being applied in Germany and Europe for the development of new residential districts. The use of geothermal borehole heat exchangers (BHE), in combination with ground-source heat pumps (GSHP), represents an important part of shallow geothermal systems, which are used, among other systems, in urban areas due to their small space requirements. Over the course of planning BHE systems, performance must be determined via the parameters of thermal conductivity, thermal capacity, undisturbed ground temperature, and borehole thermal resistance. These can be identified by the experimental approach known as thermal response testing (TRT). The thermal parameters change due to the influences of the seasonal temperature fluctuations that take place in the ground. In this paper, a pilot double-U BHE heat exchanger field with a depth of 120 m was investigated from this perspective. TRT was carried out using monthly measurements taken over the period of one year using an electrically powered mobile TRT device. The evaluation of the individual tests was carried out using the line-source, moving-line-source, and cylinder-source theories. Our results show that the season in which TRT was implemented had an influence on the determined thermal parameters, with better thermal conditions being obtained in winter months. This is especially visible for thermal conductivity, with monthly deviations of 0.1 W/(m∙K), independent of the evaluation approaches used.

Error analysis of thermal response tests

Adapted composite two-region line source methods for evaluation of borehole heat exchangers with advanced materials

A thermal response test (TRT) analysis for a cylindrical energy pile (CEP) was carried out in order to determine the thermal properties of the materials in different regions of the system being modelled. Sample test data were generated by using a three-dimensional numerical model of the CEP. Various combinations of the materials inside and outside the CEP were investigated. It was found that the thermal properties of both the CEP and the surrounding soil could be determined with sufficient accuracy. This was important as the effective thermal properties of the CEP depended on the design of the CEP which could be very difficult to determine by other means. Another study was made to explore the possibility of assuming a homogeneous material outside the pipes with the adoption of equivalent thermal properties determined from the TRT analysis so that an analytical modeling approach could be employed. A comparison of the simulation results was made for the CEP based on the specified thermal properties of the various regions with those for the case in which the equivalent thermal properties was used. By applying a cooling-dominated annual periodic load profile, it was found that the simulated temperature of the fluid leaving the CEP could differ substantially. This meant that the assumption of a homogeneous material outside the pipes could lead to erroneous results.