 Research
 Open access
 Published:
Evaluating an enhanced thermal response test (ETRT) with high groundwater flow
Geothermal Energy volume 12, Article number: 1 (2024)
Abstract
Enhanced thermal response tests (ETRT) enable the evaluation of depthspecific effective thermal conductivities. Groundwater flow can significantly influence the interpretation of ETRT results. Hence, this study aims to critically evaluate an ETRT with high groundwater flow (> 0.2 m d^{−1}). Different approaches in determining the specific heat load of an ETRT are compared. The results show that assuming constant electrical resistance of the heating cable with time can account for an inaccuracy of 12% in the determination of effective thermal conductivities. Adjusting the specific heat loads along the borehole heat exchanger (BHE) depth, the specific heat loads vary within 3%. Applying the infinite line source model (ILS) and Péclet number analysis, a depth–average hydraulic conductivity is estimated to be 3.1 × 10^{–3} m s^{−1}, thereby, confirming the results of a pumping test of a previous study. For high Darcy velocities (> 0.6 m d^{−1}), the uncertainty is higher due to experimental limitations in ensuring a sufficient temperature increase for the evaluation (ΔT > 0.6 K). In these depths, the convergence criterion of Δλ_{eff}/λ_{eff} < 0.05/20 h for the ILS sequential forward evaluation cannot be achieved. Thus, it can be concluded that timeaveraging of the heat load by monitoring voltage and current during ETRT is essential. Therefore, the specific heat load adjustment along the heating cable is recommended. To improve the estimation of depthspecific effective conductivities with high groundwater flow and to reduce the sensitivity towards temperature fluctuations (ΔT ~ 0.1 K), measures for applying higher specific heat loads during the ETRT are essential, such as actions against overheating of the cable outside the BHE.
Introduction
For the dimensioning of ground source heat pump (GSHP) systems, knowledge of the thermal properties of the subsurface is crucial. Not only the effective thermal conductivity λ_{eff} of the subsurface but also the consideration of groundwater flow is important, since advection can significantly improve the heat transport and, therefore, the efficiency of borehole heat exchangers (BHE) (Stauffer et al. 2014). The thermal response test (TRT) is an established method to determine insitu effective thermal conductivities (Spitler and Gehlin 2015). In a conventional TRT, a defined heat load is injected into or extracted from the ground by circulating the heat transfer fluid of the BHE, and the temperature development is measured at the inlet and outlet of the pipes with temperature probes (Verein Deutscher Ingenieure 2020). Using analytical solutions of the heat source equation, e.g., the infinite line source model (ILS), an integral value of the effective thermal conductivity can be derived (Carslaw and Jaeger 1959; Gehlin 2002; Verein Deutscher Ingenieure 2020). Elevated groundwater flow (> 0.1 m day^{−1}) can influence the interpretation of TRT results (Chiasson et al. 2000; Signorelli et al. 2007). The system adjusts fast to the applied heat disturbance when advection is present and significant. If the ILS is applied, higher values of the effective thermal conductivity λ_{eff} will be evaluated due to the groundwater flow and the results will show sensitivity towards evaluation time (Sanner et al. 2005; Angelotti et al. 2018; Katsura et al. 2006). Other evaluation models such as the moving infinite line source model (MILS) are, therefore, recommended if groundwater flow is present (Diao et al. 2004; MolinaGiraldo et al. 2011; Wagner et al. 2013).
In the last years, the TRT setup was further developed (Wilke et al. 2020; Zhang et al. 2021). One development was the application of optic fibre distributed temperature sensing (DTS) for quasicontinuous temperature profile measurement, the socalled distributed TRT (DTRT) with the advantage of determining depthspecific effective thermal conductivities (Fujii et al. 2006; Acuña 2013). Another development was the use of heating cables as a heat source. With heating cables, a more controlled heat load can be applied to the subsurface with less metrological effort (Raymond et al. 2010). With an enhanced TRT (ETRT) (Wilke et al. 2020), also described as actively heated fibre optic TRT (ATRT) (Zhang et al. 2021), fibre optic cables are used along with heating cables. Thus, the advantages of both implementations are combined. Most ETRT studies were conducted with a hybrid cable, a composite cable of fibre optic and heating cables (Huber 2013; Lehr and Sass 2014; Vieira et al. 2017; Galgaro et al. 2018; Maldaner et al. 2019; Dalla Santa et al. 2022; Hakala et al. 2022; Simon and Bour 2022). Hence, temperature measurement and heating were located at the same location. However, some studies used separate heating cable and fibre optic cable in different shanks of the BHE pipe (Vélez Márquez et al. 2018). Thereby, adding the distance between both cables as an additional parameter of uncertainty. Hakala et al. (2022) used an additional reference fibre optic cable to measure the temperature in the subsurface apart from the elevated temperature at the heating cable.
Applying a TRT, the correct determination of the effective thermal conductivity is proportionally linked to the correct calculation of the applied heat load Q. In an ETRT, the heat load is induced by an electrical shortcut of the conductor material of the heating cable. The electrical resistance of the conductor material depends on temperature (Hacker and Sumereder 2020). During an ETRT, the cable temperature increases when the cable is heated. Thereby, its electrical resistance also changes. If the heat load is calculated with a resistance value that is determined before or at the start of an ETRT, the temperature dependence of the resistance is not considered (Luo et al. 2015). In contrast, other studies accounted for this by logging not only the voltage but also the current during the ETRT and then calculating the average heat load for the entire heating time (Huber 2013; Vélez Márquez et al. 2018; Dalla Santa et al. 2022). Raymond et al. (2010) addressed the problem of temperaturedependent resistance by calibrating their heating cable in a circulation bath under varying temperatures before use. In some studies, the use of a power controller was recommended ensuring a constant heat load over time (Lehr and Sass 2014; Hakala et al. 2022). For several studies, the determination approach for the heat load was not mentioned specifically (Freifeld et al. 2008; Heske et al. 2011; Riegger et al. 2012; Bussmann et al. 2015; Vieira et al. 2017; Galgaro et al. 2018; Zhang et al. 2020). Summarising, no distinction between the different ways to calculate the specific heat load is currently made in the ETRT literature. The overall assumption is that the specific heat load does not vary along the length of the heating cable (Lehr and Sass 2014; Maldaner et al. 2019; Dalla Santa et al. 2022; Hakala et al. 2022). However, as implied by Wilke et al. (2020), during an ETRT the temperature increase in the cable varies along the depth depending on the contact material of the cable (air, unsaturated soil, saturated soil, groundwater influence) and, therefore, its electrical resistance. For the application of soil water content determination, Sayde et al. (2014) addressed this by performing an adjustment of the electrical resistance along the cable length using fibre optic temperature measurements.
Of the TRT studies applying heating cables, only a limited amount is conducted in environments with enhanced groundwater flow. For example, Lehr and Sass (2014) analysed ETRT data from a study site with groundwater velocities of > 0.4 m d^{−1} in various depths. They used Péclet number analysis to derive Darcy velocities from ILS results. Antelmi et al. (2020) applied the MILS to evaluate temperature data (from wireless probes) at a study site with depthspecific groundwater velocities ranging between 0.001 m d^{−1} and 0.26 m d^{−1}. However, the principle of ETRT is analogously applied in hydrogeology as active distributed temperature sensing (ADTS) focusing mainly on the determination of groundwater flow velocity (Banks et al. 2014; Read et al. 2014; Coleman et al. 2015; Bense et al. 2016). Instead of a hybrid cable, most often the steel case of the fibre optic cable is used as the heating element (Ciocca et al. 2012; Read et al. 2014; Sayde et al. 2014; Del Val et al. 2021; Simon and Bour 2022). Des Tombe et al. (2019) and Bakker et al. (2015) applied the MILS to evaluate groundwater velocity from their ADTS results. Del Val et al. (2021) placed the fibre optic cable between the well casing and the aquifer. They analysed the temperature data regarding groundwater flow by separating it into different heating phases. The application of ETRT for the identification of depths with enhanced groundwater flow is promising. However, due to the limited amount of studies, further experience and understanding regarding the experimental issues of ETRT are necessary.
The objective of this study is to critically evaluate an ETRT with high groundwater flow. Hence, the results of a case study in Biberach an der Riß (Germany) are presented. The evaluation of depthspecific effective thermal conductivities is conducted by applying the ILS with iterative forward modelling. Furthermore, the hydraulic conductivity is evaluated with Péclet number analysis and compared to the results applying the MILS as well as to the results of a pumping test. In addition, different methods for specific heat load calculations, which are used in the literature, are compared. Thus, for the first time, the specific heat load during the ETRT is adjusted along the heating cable using the theory of temperaturedependent resistances. The models are critically discussed and their suitability is evaluated. Finally, lessons learned are presented from applying an ETRT with high groundwater flow. Although mainly sitespecific results are discussed, this study provides useful information for the planning and evaluation of future ETRT.
Materials and methods
Experiment
Study site
The study site is located at the Biberach University of Applied Sciences in Biberach an der Riß, Germany (Fig. 1a). This area is part of the Molasse basin. The borehole has a depth of 24 m below ground level (bgl) and penetrates the entire upper quaternary aquifer, which is characterised by alternating gravel and sand layers (Fig. 1). The thermal conductivities were measured in the laboratory from bucket samples collected during drilling (Reuß et al. 2012). They were measured with the hot wire method (Isomet 2104, Applied Precision Ltd.) and range between 1.5 and 2.8 W m^{−1} K^{−1} (Reuß et al. 2012). Table 1 gives a summary of the thermal conductivity values. In a previous study, the unconfined groundwater level was identified at a depth of about 5.6 m bgl (Reuß et al. 2012). The hydraulic gradient was measured to be i = 0.002 (Reuß et al. 2012). The mean hydraulic conductivity of the aquifer was measured by a pumping test to be k = 3.1 × 10^{–3} m s^{−1} (Reuß et al. 2012). From 23.4 m bgl, the aquifer is limited by tertiary sediments of the Upper Freshwater Molasse, predominantly marlstones.
Materials
Figure 1b, c presents the experimental setup. The BHE consists of a double Upipe with a pipe diameter of 0.025 m. The borehole has a radius of 0.089 m and is grouted with an enhanced backfill material (ThermoCem® PLUS, HeidelbergCement, λ_{grout} = 2.0 W m^{−1} K^{−1}). In addition to 21 resistance temperature sensors (Pt100), the BHE is equipped with a hybrid cable (Fig. 1d) with an optic fibre for temperature measurements and three copper conductors as heating element (Helukom® ADSQ(ZN)B2Y, 1 × 4 G 50/125 + Cu 3 × 0.5 mm^{2}, length = 69.1 m). The measuring technique was preassembled at the outside of one Upipe.
Enhanced thermal response test (ETRT)
The ETRT started on 28th June 2021. The heating time was about 170 h. A constant voltage of about 75 V was applied to the heating cable with a DCpower supply (Power Ten Inc., R86 D200100; 200V/100A). The voltage and the resulting current were logged for the entire heating time. The voltage was measured with a multimeter (Ahlborn, ALMEMO® 2590, measurement uncertainty ± 0.4 V). The current was indirectly measured by measuring the voltage at a shunt (Ahlborn, ALMEMO® 2590, measurement uncertainty ± 0.5 mV). The temperature was measured using DTS (Agilent, AP Sensing, N4386B, dual end measurement, measurement uncertainty manufacturer value ± 0.2 K). The temperature was measured every 60 s over the entire length of the hybrid cable with a spatial resolution of 0.5 m and a measurement interval of 1 m. The calibration of the DTS measurement was conducted by adjusting the offset to the resistance thermometers when determining the undisturbed ground temperature T_{0}. At the beginning, from minutes 19 to 46, there was a break in heating. For the effective thermal conductivity evaluation using the ILS model, this is not expected to influence, since the first hours of temperature data are excluded from the analysis.
Evaluation
Calculation of the specific heat load
For the calculation of the heat load, the electrical power P_{el.} [W] is assumed to be equal to the heat load Q [W]:
With Joule’s Law, the heat load is calculated as the product of voltage U [V] and current I [A] (Meschede 2015):
The specific heat load q [W m^{−1}] is then the heat load per meter length l of the heating cable:
To compare different approaches applied in ETRT studies, Eqs. 2 and 3 are calculated with a single measurement at the beginning of the ETRT, therefore, assuming a constant electrical resistance of the heating cable by time. This value is further referred to as q_{R=fix}. In addition, the arithmetic mean of the specific heat load over the entire heating time is calculated to an average specific heat load q_{ave}.
Spatial adjustment of the specific heat load
According to Ohm’s Law, the measured current is related to the electrical resistance R [Ω] of the cable. Electrical resistance is dependent on temperature, as stated in Eq. 4 (Meschede 2015). The resistance at a defined temperature R_{T} is calculated using the temperature difference to a reference temperature T_{20} and the materialspecific temperature coefficient of the resistance (TCR) α_{T20}:
The reference resistance R_{T20} is calculated using the literature value of the resistivity ρ_{T20} and the length l and cross section A of the heating cable (Meschede 2015):
Values for α_{T20} and ρ_{T20} are taken from Kuchling (2014). Applying Ohm’s law, the specific heat load can be calculated using the following equation:
The optic fibre provides temperature values averaged over the measuring time of 60 s for every 0.5 m. Considering the heating cable as a serial connection of resistances, it applies \({R}_{{\text{total}}}= \sum {R}_{i}\) and \({I}_{{\text{total}}}={I}_{i}\). Thus, the specific heat load can be individually determined for every length interval of the hybrid cable. The depthspecific heat load is the sum of the specific heat loads applied to both shanks of the Upipe. Hence, applying the principle of temperaturedependent resistances using the depthdifferentiated temperature measurement of the DTS, the specific heat load is spatially adjusted along the heating cable. This value is further referred to as the adjusted specific heat load q_{adj}.
Evaluation of depthspecific effective thermal conductivities
As the hybrid cable is installed in a loop next to an Upipe of the BHE (Fig. 1d), the temperature data of two corresponding length intervals of the DTS cable are averaged for each depth interval. In a preliminary data processing step, a moving average of every 20 measurement values of the fibre optic data is applied to reduce the noise. Then, the effective thermal conductivity λ_{eff} is evaluated using the ILS model as given in Eqs. 7 and 8 (Carslaw and Jaeger 1959; Gehlin 2002):
T(r,t) is the temperature at a defined distance r from the heat source and a specific time t. T_{0} is the undisturbed subsurface temperature at time t = 0. E_{i} is the exponential integral, α is the thermal diffusivity calculated:
and assuming a volumetric heat capacity of the subsurface ρc_{p} of 2.5 MJ m^{−1} K^{−1} (Verein Deutscher Ingenieure 2010), r_{b} is the borehole radius, R_{th} is the thermal borehole resistance, γ is Euler’s constant and m is the slope of the linear regression line. The evaluation time is determined by applying the following theoretical starting criterion (Gehlin 2002):
A model error of 5% is accepted by setting P = 10. Based on the German technical guideline VDI 46405 (Verein Deutscher Ingenieure 2020), the data are evaluated iteratively with the sequential forward evaluation. The convergence criterion for an effective thermal conductivity constancy of Δλ_{eff}/λ_{eff} < 0.05/20 h is applied. For q, the values for the different specific heat load calculations are inserted into Eq. 8 (see Sects. "Calculation of the specific heat load" and "Spatial adjustment of the specific heat load"). The ILS is only valid for transient heat transport. For the ideal case of constant unique groundwater flow with equal groundwater temperatures, the temperature approaches a constant value at steadystate conditions. If advection is present and significant, these conditions can occur during a TRT. Thus, for the evaluation of effective thermal conductivities, the data are evaluated up to the time when the temperature increase starts to stagnate. Thus, the point, when the effective thermal conductivity starts to approach infinity, is identified. The degree of determination R^{2} and the convergence criterion are additionally considered. Measurement uncertainties of the results are considered according to the study by Witte (2013).
Evaluation of hydraulic conductivities with Péclet number analysis
As a simple way to estimate Darcy velocities from TRT results, some studies applied the Péclet analysis (Lehr and Sass 2014; Pambou et al. 2019). This method assumes a simple linear relationship between the advective heat flow component and the difference between effective thermal conductivity λ_{eff} and thermal conductivity by conduction only λ, as stated in Eqs. 11 and 12. Péclet number analysis is applied for depth intervals below the groundwater level of 5.6 m:
The thermal conductivity λ is taken from laboratory measurements (Sect. "Calculation of the specific heat load"). To attribute the laboratory values to the depth intervals evaluated with DTS, weighted arithmetic mean values of corresponding thermal conductivities are calculated.
v_{f} is the Darcy velocity, l_{c} = r_{b} is the characteristic length based on similar studies (Ferguson 2015) and ρc_{p,w} is the volumetric heat capacity of water.
Assuming a constant hydraulic gradient of i = 0.002 (see Sect. "Calculation of the specific heat load"), a value for the hydraulic conductivity k can be derived:
Evaluation of hydraulic conductivities with the MILS
With significant groundwater flow, the evaluation of TRT with the MILS is recommended (Diao et al. 2004; MolinaGiraldo et al. 2011; Wagner et al. 2013). Hence, the data set is additionally evaluated by applying the following MILS (Eq. 14):
ϑ is the angle to the groundwater flow direction. Considering the observation point r as the borehole radius r_{b}, the average temperature at the borehole wall is calculated as the integral average in all spatial directions (Diao et al. 2004), which can be approximated at ϑ = π/2. The variable v_{th} is the effective heat transport velocity and u is the integration variable. The thermal conductivity λ is taken from laboratory measurements (see Sect. "Calculation of the specific heat load"). Since the MILS also applies for steadystate conditions, in contrast to the ILS the later time data can be also evaluated. The parameter estimation problem is solved by minimising the root mean squared error (RMSE) by fitting R_{th} and v_{th} with the NelderMead algorithm.
The Darcy velocity v_{f} can be calculated using the effective heat transport velocity (v_{th}) as follows (Zubair and Chaudhry 1996; Diao et al. 2004):
ρc_{s} is the volumetric heat capacity of the soil.
Results and discussion
Averaging the specific heat load
The specific heat load, calculated using Eq. 3, is plotted in Fig. 2 about the heating time.
At the start of the heating, the specific heat load equals 22.8 W m^{−1}. This value is representative of the specific heat load assuming constant electrical resistance of the heating cable with time q_{R=fix} (Table 2). Within the first minutes of heating, the specific heat load shows a strong decrease of nearly 10%. Then, the specific heat load varies between 20.5 W m^{−1} and 21.4 W m^{−1} with a timeaveraged specific heat load of q_{ave} = 20.8 W m^{−1} (Table 2). Hence, the results show that although a constant voltage is applied to the heating cables, the specific heat load shows some variations during the ETRT, which are most significant at the start of the test. Thus, assuming constant electrical resistance can account for an inaccuracy in the determination of the specific heat load. An average specific heat load is more representative of the heat load applied during the ETRT.
The change in the specific heat load during the ETRT can be explained by a change in the electrical resistance of the heating cable. The electrical current is a direct indicator of the electrical resistance as an integral value for the total cable length (Fig. 2). The change in the electrical resistance is a consequence of the change in the cable temperature. In Fig. 2, the average subsurface temperature T_{sub} and the average surface temperature T_{sur} are plotted complementary by calculating the arithmetic mean of the respective cable lengths. The temperature change and thus the change of the specific heat load is most distinct within the first minutes of the ETRT. The temperatures increase by around 11 K in the subsurface and by around 28 K at the surface. This first heating phase is attributed to the cable material, mainly the cable isolation (Fig. 1d). The variation of the specific heat load for the rest of the heating time can be attributed mainly to the part of the cable outside the borehole. At the surface, high diurnal temperature variations can be observed during the test. In the subsurface, these variations are considerably smaller. Hence, a depthspecific assessment of the specific heat load is suggested (Sect. "Spatial adjustment of the specific heat load").
Summarised, the assumption of constant electrical resistance is inappropriate for the calculation of the specific heat load. Prior knowledge of the cable's electrical resistance is insufficient to derive the heat load from the applied voltage. Further measurements of the heat load during the experiment are, therefore, necessary. Then, an average value can be calculated for the entire heating time. At the same time, the model assumption of constant heat load during the ETRT for effective thermal conductivity estimation can be confirmed. The average specific heat load is more representative of the heat load applied during the ETRT.
Spatial adjustment of the specific heat load
The theory of temperaturedependent resistances for adjusting the specific heat load along the depth of the BHE (Eq. 6) is applied. The results are plotted in Fig. 3. The specific heat loads along the entire length of the heating cable range between 20.2 W m^{−1} and 23.0 W m^{−1} (Fig. 3b). Higher specific heat loads can be found at the surface, whereas lower specific heat loads are calculated for the installed cable in the ground. According to the theory (Eq. 6), these differences are associated with the differences in the temperature increase along the cable. The different temperature increases along the cable are associated with varying heat transport along the length of the cable.
Along the heating cable, three representative areas are identified: (1) The upper part of the heating cable is installed above the surface. Here, heat transfer is mainly characterised by the surrounding air and is expected to be low. Thus, the cable significantly heats up. Due to the diurnal temperature changes, high variations of the specific heat load during the heating time can be observed (Fig. 3a), which can also be seen in Fig. 2. (2). The lower part of the heating cable is installed below the groundwater level. Here, the heat transfer is characterised by conductive and convective transport and is expected to be quite good. Hence, the cable shows a lowtemperature increase only due to the applied heat load. Compared to the upper part of the heating cable, only a marginal time dependency of the specific heat load is apparent. (3) Above the groundwater level, the heating cable is installed some meters in the vadose zone. Heat transfer is predominantly characterised by conduction. Moisture content and seepage can have an influence. Effectively, only the part of the heating cable installed inside the BHE can inject heat into the subsurface. Along the length of the heating cable inside the BHE, the heat load only varies within 3% between 20.2 and 20.6 W m^{−1}. Calculating the average of the adjusted specific heat loads for this part provides an average adjusted specific heat load of 20.2 W m^{−1} (Table 2). Figure 3b compares this value with the other approaches for heat load calculation (see Sect. "Averaging the specific heat load": q_{R=fix} and q_{adj,ave}). The deviations between q_{R=fix} and q_{adj,ave} is 12% and only 3% between q_{ave} and q_{adj,ave}.
In this study, the variations along the depth of the BHE are minor. Overall, the variations of the specific heat along the cable length mainly depend on the following aspects: (1) It is influenced by the material of the heating cable. The dependence of the electrical resistance and, therefore, of the specific heat load on the temperature is proportional to the temperature coefficient of resistance (TCR) of the material (Eq. 4). (2) The influence of the surface depends on the ambient conditions as well as the percentage of the heating cable above the surface, which is most often determined by the sitespecific conditions. In this study, the ETRT was conducted in summertime with ambient temperatures above 28 °C during the day. The hybrid cable was exposed to the subsurface with a length of 24 m, which corresponds to 35% of the total cable length. (3) The heat transport in the subsurface determines the variation of the specific heat load along the depth of the BHE. When the thermal properties of the subsurface are very different along the depth, e.g., at a study site, where alternating layers of aquifers and aquitards are present, the temperature increase during the ETRT can vary considerably (> 30 K) with depth. This can account for a significant difference (> 8%) in the heat load at the different depths. Further information on the thermal properties of the subsurface in this study can be found in the following section.
Figure 3b emphasises that by adjusting the heat loads with the DTS measurements, the variation of the specific heat loads along the heating cable can be calculated. This method can be easily integrated into the evaluation procedure and is, therefore, highly recommended for the evaluation of future ETRTs. However, the application of this adjustment is limited to ETRT using hybrid cables or cables, where the fibre optic is in direct contact with the heating cable. Only then, the DTS temperature measurements can be used representatively for the temperature of the heating cable.
Depthspecific effective thermal conductivity evaluation
Table 2 summarises the depthaveraged results for the effective thermal conductivities, Darcy velocities and hydraulic conductivities applying different specific heat loads. The deviation in the effective thermal conductivity is proportional to the deviation in the specific heat load (Eq. 8). Thus, the errors of 3% and 12%, respectively, can also be found in this comparison. Referring to the results of Sects. "Averaging the specific heat load" and "Spatial adjustment of the specific heat load", the further discussion of the results focuses solely on the evaluation of applying the adjusted specific heat load.
With the ILS, the depthaveraged effective thermal conductivity is evaluated to 4.5 W m^{−1} K^{−1}. With Péclet number analysis, an average Darcy velocity of 0.53 m d^{−1} is evaluated. Applying a hydraulic gradient of i = 0.002, an average hydraulic conductivity of 3.1 × 10^{–3} m s^{−1} is calculated. With the MILS an average Darcy velocity of 0.23 m d^{−1} is evaluated. The average hydraulic conductivity value analysed with the MILS is estimated to be 1.4 × 10^{–3} m s^{−1}. Thereby, both hydraulic conductivity values are within the same order of magnitude as derived with the pumping test (k_{pt}) with 3.1 × 10^{–3} m s^{−1} (Reuß et al. 2012). Thus, the comparison between the different methods indicates that the evaluation of the ETRT regarding average Darcy velocity and hydraulic conductivity is successfully conducted (Table 2).
Over the entire depth of the BHE, heterogeneous thermal properties of the subsurface can be observed (Fig. 4).
The effective thermal conductivities vary between 1.9 and 9.3 W m^{−1} K^{−1} (Fig. 4b). Lower effective thermal conductivities are evaluated for the upper part of the borehole and between 15.5 and 18 m. High effective thermal conductivities with values above 6 W m^{−1} K^{−1} are evaluated for depths around 9.5, 12.5 and 22 m. According to the results of the Péclet number analysis, these high effective thermal conductivities can be attributed to high Darcy velocities in the order of about > 0.6 m d^{−1} and, therefore, to high hydraulic conductivities. The MILS results confirm areas of higher Darcy velocity (Fig. 4c), however, also indicate that high Darcy velocities are slightly overestimated with Péclet number analysis. Comparing the results with the borehole profile (Fig. 4d), elevated effective thermal conductivities and Darcy velocities correlate with zones of coarser sediments. In addition, the evaluated hydraulic conductivities are between 1.1 × 10^{–4} and 8.8 × 10^{–3} m s^{−1}, which are in the range of typical sand and gravel aquifers (Domenico and Schwartz 1990).
Discussion
In the following paragraph limitations of this study are discussed. Figure 5 shows the evaluation procedure for effective thermal conductivity for two representative depth intervals (5 m and 12.5 m). Complementary, the evaluation of all 45 analysed depth intervals can be found in the supporting information (Additional file 1: Figs. S1–S45).
The depth interval at 5 m represents a conductiondominated depth interval. The entire time data shows a transient temperature increase. Applying forward modelling, the effective thermal conductivity results converge to a stable value within the convergence criterion of Δλ_{eff}/λ_{eff} < 0.05 within 20 h. Contrary, the depth interval at 12.5 m is advectiondominated. The iterative evaluation indicates strong groundwater influences showing an increase in effective thermal conductivities with evaluation time. The later temperature–time data approaches a steady state value and is not evaluated with ILS. Hence, no convergence is obtained. In Fig. 4, the areas, where convergence of the effective thermal conductivity result cannot be achieved are highlighted. Convergence cannot be achieved for 33% of the evaluated depth intervals, which are associated with high advective heat transport. In depth intervals with high groundwater flow, the system quickly approaches steadystate conditions, which reduces the evaluation time. For these depth intervals, nearsteadystate conditions are achieved within 2–3 days. Hence, fewer data points can be used for linear regression. The degree of determination R^{2} is lower (< 0.85, for z = 12 m and 12.5 m < 0.7). Summarised, even though the ILS evaluation is conducted for all depth intervals, the assumptions of the ILS are invalid for some areas of high Darcy velocities. This is indicated by the convergence criterion and the overestimation of the Darcy velocities in comparison with the MILS.
In addition, the Péclet number analysis to estimate Darcy velocities from ILS results has to be examined critically. Applying the Péclet number analysis, several assumptions are made that contribute to the uncertainty of the estimate. (1) The method defines the advective heat flow component by the difference between effective thermal conductivity λ_{eff} and thermal conductivity by conduction only λ. However, whereas thermal conductivity λ increases linearly with the specific heat load (Eq. 7), the effective thermal conductivity at groundwaterinfluenced conditions increases nonlinearly (Eq. 14). (2) The characteristic length is an ambiguous number. It depends on the experiment time and the heat transfer properties of the medium. By defining the characteristic length as a fixed value equal to the borehole radius, the estimated Darcy velocities are assumed to be defined mainly by the properties of the borehole. Thereby, a conservative calculation approach is chosen, which can result in an overestimation of higher Darcy velocities. Instead of the borehole radius, the radius of temperature influence would be a more suitable value. However, the determination of this value is challenging. (3) Thermal conductivity values of the subsurface have to be known. In this study, thermal conductivities from laboratory measurements of disturbed samples are used. Thus, there are uncertainties, e.g., whether the depthspecific laboratory values actually represent the thermal conductivities at insitu conditions or whether these values represent the considered soil volume influenced by the TRT. Alternatively, thermal conductivities can be defined from ETRT results influenced by conduction only, thereby, defining one single value of thermal conductivity for the entire depth of the BHE. As indicated in Fig. 4b, average deviations of 14% between the thermal conductivities from laboratory measurements and ETRT results can be observed (depth interval 2.5 to 5.5 m). Regarding these uncertainties, the Péclet analysis can only be used to give a rough estimate. For a more precise determination of Darcy velocities from ETRT results the MILS has to be applied. Nevertheless, with the ILS, valid estimates of the average values and qualitative identification of areas of enhanced heat transport are analysed. Despite a higher uncertainty of the results, the lower computational effort justifies the application of the ILS.
In depth intervals with high groundwater flow, the heat is transported fast away from the BHE. Thus, the temperature increase, that can be used for evaluation, is low (< 0.6 K, Fig. 4a). Overall, temperature fluctuations within the DTS data in the order of ΔT ~ 0.1 K are observed. Thus, for depth intervals with a lowtemperature increase, the uncertainty of the calculation increases, too. The applied specific heat load of 20 W m^{−1} for this highly advective aquifer does not generate a sufficient temperature increase to evaluate for all depths (Fig. 4a), however, is in the typical range of specific heat loads applied in TRT studies using heating cables between 6.1 to 48 W m^{−1} with an average of about 25 W m^{−1} (Freifeld et al. 2008; Raymond et al. 2010; Huber 2013; Lehr and Sass 2014; Vieira et al. 2017; Galgaro et al. 2018; Vélez Márquez et al. 2018; Maldaner et al. 2019; Zhang et al. 2020; Minchio et al. 2020; Antelmi et al. 2020; Giordano et al. 2021; Dalla Santa et al. 2022; Hakala et al. 2022; Simon and Bour 2022).
The duration of the ETRT within this study was about 170 h, which is quite long for a TRT. Concerning the evaluation of a TRT, the longer the testing time, the bigger the sample volume of the subsurface. Hence, the effect of the grouting material decreases with time, as well as the influence of inhomogeneity of the subsurface. Thus, a more representative evaluation of the subsurface conditions can be conducted, especially by combining it with the sequential forward modelling (Sect. "Evaluation of depthspecific effective thermal conductivities"). However, regarding the practical application of ETRT, a shorter test duration is required. From Additional file 1: Figs. S1–S45, a testing time of about 80 to 90 h can be recommended that allows for a clear identification of the turning point, when effective thermal conductivity values start to increase and, therefore, to evaluate the groundwater effect. Nevertheless, the required testing time depends on sitespecific conditions, such as the subsurface conditions, the grouting material and the borehole radius.
Figure 6 shows the relation between Darcy velocities and effective thermal conductivities as evaluated in this study and compared to reported values from other studies dealing with the determination of groundwater flow velocities from TRT data from TRT data (Angelotti et al. 2018, Antelmi et al. 2020, Huber 2013, Huber et al. 2014, Lehr and Sass 2014, Sakata et al. 2021).
It contains data from different aquifer types with varying properties. In addition, different TRT methods and evaluation procedures were applied. The data collection highlights that with increasing Darcy velocities, effective thermal conductivities also increase. In Fig. 6b, the correlation between these two properties is separately fitted for three distinct data sets, including the two data sets from this study and the data set from Huber (2013), where Darcy velocities were experimentally set in sandbox experiments. The power function in the form of \(y={\text{a}} {x}^{{\text{b}}}+{\text{c}}\) is fitted to the data. If the exponent b becomes 1.0 the power function will take the form of a linear equation. Thus, comparison of linear and exponentiating relationship between the Darcy velocity and effective thermal conductivities is made easier. The parameter c corresponds to the thermal conductivity λ without groundwater flow. Thus, it depends highly on the geologic conditions of the study site. The average thermal conductivity of this study determined in the laboratory is 2.5 W m^{−1} K^{−1}. The deviations of c from this value also indicate the difficulty in distinguishing between the heat transport mechanism of conduction and advection at low flow conditions. The relationship in Fig. 6b shows that effective thermal conductivity is not significantly affected by groundwater flow up to a Darcy flow of about 0.2 to 0.3 m d^{−1}. With increasing Darcy velocities, the effective thermal conductivity increases significantly. The highest degree of determination is achieved for the results of the Péclet number analysis. This is expected, as the Darcy velocities are directly derived from the effective thermal conductivities based on a linear relationship (Eq. 12). The deviation from the perfect correlation is mainly due to the variance in thermal conductivity derived from laboratory measurements. However, the assumptions made for the evaluation with the Péclet number analysis result in high uncertainties in the estimation of Darcy velocities with this method, as discussed before in detail. The data set with the lowest degree of determination is the data set from Huber (2013), which can be easily explained. On one hand, different measurement methods were applied. The effective thermal conductivities are evaluated from temperature–time data, whereas the Darcy velocities are measured with flowmeters. On the other hand, results from several tests are combined in one data set. The fit calculated for the data set by Huber (2013) agrees well with the fit for the Péclet number analysis, which supports the assumptions made for the Péclet number analysis. However, it does not prove that the Péclet number analysis is the recommended analysis method for this specific case study.
The MILS fit significantly deviates from the best fit of the other two data sets. The plotted MILS data set includes the results of both evaluation methods (ILS and MILS) based on the same experimental data (Fig. 6). Although, the chosen convergence criterion was acceptable for evaluation using the ILS. The latter is not the recommended model for the evaluation of groundwaterinfluenced TRT. However, uncertainties, therefore, still remain, which could result in an overestimation of the derived effective thermal conductivities especially for higher Darcy velocities. To address these uncertainties during the evaluation of ETRTs, we recommend performing field experiments under controlled groundwater flow velocities combined with numerical heat transport models.
For the conduct of future ETRTs with high groundwater influence, the knowledge derived from this study can provide valuable insights. Ensuring a sufficient temperature increase for the evaluation of all depth intervals is crucial for the reliable determination of effective thermal conductivities and groundwater velocities. This could reduce the sensitivity of the data towards temperature noise and at the same time improve the estimation of the regression (Fig. 6) and, therefore, of the depthspecific effective thermal conductivities. Nevertheless, increasing the specific heat load for ETRT is not trivial. Depending on the experimental setup and conduct, different aspects have to be considered. In principle, it applies, that the higher the heat load, the higher the temperature increase. However, the highest possible heat load is defined by cable specifications. Typically, the maximum temperature allowed for such cables is 60 to 80 °C. Especially in the upper part of the heating cable, when the cable is in contact with air, there is a high risk of overheating at high specific heat loads (Fig. 2). Hence, to increase the heat load during the ETRT, the heat transfer in the surface area has to be improved. Thus, actions against overheating are necessary, e.g., burying the cable or placing waterfilled tubes on it. In the study by Hakala et al. (2022), they used an air fan to cool the cable. However, practical issues and site characteristics, such as the duration of the experiment, the available space to bury the cable, and the necessary length of the cable above the surface have to be considered. Apart from that, improvements in the material of the heating cable towards the application at elevated temperatures are desirable. A compromise between decreasing the thermal resistance of the heating cable, and at the same time maintaining sufficient electrical isolation when working with current in a wet environment have to be made. In addition, the fibre optics have to be protected against moisture. Otherwise, the temperature measurement becomes inaccurate. Further issues applying a higher heat load have to be considered. For ETRTs in open boreholes or with the heating cable installed inside the heat exchanger pipe induced convection can occur. Regarding this, Hakala et al. (2022) recommended a maximum specific heat load of 20 W m^{−1}. However, a grouted cable is used in this study indicating a minor influence. There are only a few studies, which compare the influence of the heat load on the results of TRTs. Huber (2013), for example, compared in his ETRT study different specific heat loads at the same BHE ranging from 6 to 46 W m^{−1}. He observed that less variation in depthspecific thermal conductivities was resolved by applying a higher specific heat load. Partly, this could be explained by a lower influence on the accuracy of the temperature measurement due to a higher temperature increase. In addition to increase the heat load, the uncertainty of the slope can be reduced using temperature measurements with better accuracy than DTS. This includes placing additional punctual temperature sensors or combining DTS data with temperature profiles from wireless measurement tools (Schüppler et al. 2021).
Conclusion
In this study, an ETRT is evaluated with significant groundwater flow (> 0.2 m d^{−1}). Different approaches for the determination of the specific heat load of the ETRT are discussed. Evaluations of effective thermal conductivities and Darcy velocities are conducted by applying the ILS combined with the Péclet number analysis and the MILS. Depthaveraged effective thermal conductivity and hydraulic conductivity are evaluated to be 4.5 W m^{−1} K^{−1} and 3.1 × 10^{–3} m s^{−1}, respectively. Considering the results of this study, the following conclusions can be made:

(1)
Assuming constant electrical resistance of the heating cable can account for an inaccuracy of 12% in the determination of depthspecific effective thermal conductivities. Thus, this method is inappropriate for the calculation of the specific heat load. Hence, timeaveraging of the heat load by logging voltage and current during the ETRT is recommended.

(2)
Applying the theory of temperaturedependent resistances, the variation of the specific heat loads along the length of the heating cable can be adjusted. In this study, variations within 3% were observed along the BHE. For hydrogeological conditions with varying groundwater flow (i.e., at a study site with alternating layers of aquifers and aquitards), the variations are expected to be more significant. The adjustment of the specific heat loads can be easily integrated into the evaluation procedure and is, therefore, also recommended.

(3)
For high Darcy velocities, experimental issues ensuring a sufficient temperature increase (ΔT > 0.6 K) are shown to increase the uncertainty of the evaluation. To reduce the sensitivity towards temperature fluctuations, measures applying a higher specific heat load are desirable. This includes actions against overheating of the cable outside the borehole heat exchanger and improvements of the material of the heating cable towards the application at elevated temperatures (> 60 °C). In 33% of the analysed depth intervals, due to a fast adjustment of the system to the applied heat load, the convergence criterion of Δλ_{eff}/λ_{eff} < 0.05/20 h of the ILS sequential forward evaluation cannot be achieved. Temperature measurements with better accuracy (adding punctual sensors, in combination with profiles from wireless measurement tools) are expected to also improve the evaluation of ETRT.
Finally, to address the uncertainties during the evaluation of ETRTs with high groundwater flow, we recommend performing field experiments under controlled groundwater flow velocities combined with numerical heat transport models.
Availability of data and materials
The data sets used and/or analysed during the current study are available from the corresponding author upon reasonable request.
Abbreviations
 A :

Crosssectional area [m^{2}]
 ADTS:

Active distributed temperature sensing
 ATRT:

Actively heated fibre optic thermal response test
 bgl:

Below ground level
 BHE:

Borehole heat exchanger
 DTRT:

Distributed thermal response test
 DTS:

Distributed temperature sensing
 E _{i} :

Exponential integral
 ETRT:

Enhanced thermal response test
 GSHP:

Ground source heat pump
 i :

Hydraulic gradient
 I :

Current [A]
 ILS:

Infinite line source model
 k :

Hydraulic conductivity [m s^{−}^{1}]
 l :

Cable length [m]
 l _{c} :

Characteristic length [m]
 m :

Slope [K ln(s)^{−}^{1}]
 MILS:

Moving infinite line source model
 Pe :

Péclet number
 PE:

Polyethylene
 P _{el} :

Electrical power [W]
 Q :

Heat load [W]
 q :

Specific heat load [W m^{−}^{1}]
 q _{adj} :

Adjusted specific heat load [W m^{−}^{1}]
 q _{ave} :

Average specific heat load [W m^{−}^{1}]
 q _{R} _{=fix} :

Specific heat load assuming constant electrical resistance [W m^{−}^{1}]
 R :

Electrical resistance [Ω]
 R^{2} :

Degree of determination
 r :

Distance [m]
 r _{b} :

Borehole radius [m]
 R _{T} :

Electrical resistance at a defined temperature [Ω]
 R _{T20} :

Reference electrical resistance [Ω]
 R _{th} :

Thermal borehole resistance [m K W^{−}^{1}]
 T :

Temperature [°C]
 T _{sub} :

Subsurface temperature [°C]
 T _{sur} :

Surface temperature [°C]
 t :

Time [s]
 T _{0} :

Reference temperature [°C]
 TCR:

Temperature coefficient of resistance
 TRT:

Thermal response test
 u :

Integration variable
 U :

Voltage [V]
 VDI:

Verein Deutscher Ingenieure
 v _{f} :

Darcy velocity [m d^{−}^{1}]
 v _{th} :

Effective heat transport velocity [m s^{−}^{1}]
 z :

Depth [m
 α :

Thermal diffusivity [m^{2} s^{−}^{1}]
 α _{T20} :

Temperature coefficient of resistance [K^{−}^{1}]
 γ :

Euler’s constant
 ϑ :

Angle to the groundwater flow direction
 λ :

Thermal conductivity [W m^{−}^{1} K^{−}^{1}]
 λ _{eff} :

Effective thermal conductivity [W m^{−}^{1} K^{−}^{1}]
 ρc _{s} :

Volumetric heat capacity of the soil [J m^{−}^{3} K^{−}^{1}]
 ρc _{w} :

Volumetric heat capacity of water [J m^{−}^{3} K^{−}^{1}]
 ρ _{T20} :

Reference resistivity [Ω mm^{2} m^{−}^{1}]
References
Acuña J. Distributed thermal response tests—new insights on Upipe and Coaxial heat exchangers in groundwaterfilled boreholes [Dissertation]. Stockholm: KTH Royal Institute of Technology; 2013.
Angelotti A, Ly F, Zille A. On the applicability of the moving line source theory to thermal response test under groundwater flow: considerations from real case studies. Geothermal Energy. 2018. https://doi.org/10.1186/s405170180098z.
Antelmi M, Alberti L, Angelotti A, Curnis S, Zille A, Colombo L. Thermal and hydrogeological aquifers characterization by coupling depthresolved thermal response test with moving line source analysis. Energy Convers Manage. 2020. https://doi.org/10.1016/j.enconman.2020.113400.
Bakker M, Caljé R, Schaars F, van der Made KJ, de Haas S. An active heat tracer experiment to determine groundwater velocities using fiber optic cables installed with direct push equipment. Water Resour Res. 2015;51(4):2760–72. https://doi.org/10.1002/2014WR016632.
Banks EW, Shanafield MA, Cook PG. Induced temperature gradients to examine groundwater flowpaths in open boreholes. Groundwater. 2014;52(6):943–51. https://doi.org/10.1111/gwat.12157.
Bense VF, Read T, Bour O, Le Borgne T, Coleman T, Krause S, et al. Distributed temperature sensing as a downhole tool in hydrogeology. Water Resour Res. 2016;52(12):9259–73. https://doi.org/10.1002/2016WR018869.
Bussmann G, Bracke R, Eicker T, Wittig V, Tuente H, Gueldenhaupt J, et al. GeoStar—a scalable borehole heat exchanger plant for growing district heating systems and restricted urban areas. In: World Geothermal Congress; 19–25 April; Melbourne, Australia; 2015.
Carslaw HS, Jaeger JC. Conduction of heat in solids. 2nd ed. Oxford: Oxford Science Publications; 1959.
Chiasson A, Rees SJ, Spitler JD. A preliminary assessment of the effects of groundwater flow on closedloop groundsource heat pump systems. ASHRAE Trans. 2000;106:380–93.
Ciocca F, Lunati I, van de Giesen N, Parlange MB. Heated optical fiber for distributed soilmoisture measurements: a lysimeter experiment. Vadose Zone J. 2012. https://doi.org/10.2136/vzj2011.0199.
Coleman TI, Parker BL, Maldaner CH, Mondanos MJ. Groundwater flow characterization in a fractured bedrock aquifer using active DTS tests in sealed boreholes. J Hydrol. 2015;528:449–62. https://doi.org/10.1016/j.jhydrol.2015.06.061.
Dalla Santa G, Pasquier P, Schenato L, Galgaro A. Repeated ETRTs in a complex stratified geological setting: highresolution thermal conductivity identification by multiple linear regression. J Geotech Geoenviron Eng. 2022. https://doi.org/10.1061/(ASCE)GT.19435606.0002724.
Del Val L, Carrera J, Pool M, Martínez L, Casanovas C, Bour O, Folch A. Heat dissipation test with fiberoptic distributed temperature sensing to estimate groundwater flux. Water Resour Res. 2021. https://doi.org/10.1029/2020WR027228.
Des Tombe BF, Bakker M, Smits F, Schaars F, van der Made KJ. Estimation of the variation in specific discharge over large depth using distributed temperature sensing (DTS) measurements of the heat pulse response. Water Resour Res. 2019;55(1):811–26. https://doi.org/10.1029/2018WR024171.
Diao N, Li Q, Fang Z. Heat transfer in ground heat exchangers with groundwater advection. Int J Therm Sci. 2004;43(12):1203–11. https://doi.org/10.1016/j.ijthermalsci.2004.04.009.
Domenico PA, Schwartz FW. Physical and chemical hydrogeology. Hoboken: John Wiley & Sons, Inc.; 1990.
Ferguson G. Screening for heat transport by groundwater in closed geothermal systems. Groundwater. 2015;53(3):503–6. https://doi.org/10.1111/gwat.12162.
Freifeld BM, Finsterle S, Onstott TC, Toole P, Pratt LM. Ground surface temperature reconstructions: using in situ estimates for thermal conductivity acquired with a fiberoptic distributed thermal perturbation sensor. Geophys Res Lett. 2008. https://doi.org/10.1029/2008GL034762.
Fujii H, Okubo H, Itoi R. Thermal response tests using optical fiber thermometers. GRC Trans. 2006;30:559–63.
Galgaro A, Pasquier P, Schenato L, Cultrera M, Santa GD. Soil thermal conductivity from early TRT logs using an active hybrid optic fibre system. 2018:1–9. https://doi.org/10.22488/okstate.18.000023.
Gehlin S. Thermal response test: method development and evaluation [Dissertation]. Luleå: Luleå University of Technology; 2002.
Giordano N, Lamarche L, Raymond J. Evaluation of subsurface heat capacity through oscillatory thermal response tests. Energies. 2021;14(18):5791. https://doi.org/10.3390/en14185791.
Hacker V, Sumereder C. Electrical engineering: fundamentals. München, Wien: De Gruyter Oldenbourg; 2020.
Hakala P, Vallin S, Arola T, Martinkauppi I. Novel use of the enhanced thermal response test in crystalline bedrock. Renew Energy. 2022. https://doi.org/10.1016/j.renene.2021.10.020.
Heske C, Kohlsch O, Dornstädter J, Heidinger P. Der EnhancedGeothermalResponseTest als Auslegungsgrundlage und Optimierungstool. bbr Sonderheft. 2011.
Huber H. Experimentelle und numerische Untersuchungen zum Wärmetransportverhalten oberflächennaher, durchströmter Böden [Dissertation]. Darmstadt: Technical University of Darmstadt; 2013.
Huber H, Arslan U, Sass I. Zum Einfluss der Filtergeschwindigkeit des Grundwassers auf die effektive Wärmeleitfähigkeit. Grundwasser. 2014;19(3):173–9. https://doi.org/10.1007/s0076701402637.
Katsura T, Nagano K, Takeda S, Shimakura K. Heat transfer experiment in the ground with groundwater advection. In: The IEA 10th Energy Conservation Thermal Energy Storage Conference. New Jersey, USA; 2006.
Kuchling H. Taschenbuch der Physik. 21st ed. München: Carl Hanser verlag GmbH & Co. KG; 2014.
Lehr C, Sass I. Thermooptical parameter acquisition and characterization of geologic properties: a 400m deep BHE in a karstic alpine marble aquifer. Environ Earth Sci. 2014;72(5):1403–19. https://doi.org/10.1007/s126650143310x.
Luo J, Rohn J, Xiang W, Bayer M, Priess A, Wilkmann L, et al. Experimental investigation of a borehole field by enhanced geothermal response test and numerical analysis of performance of the borehole heat exchangers. Energy. 2015;84:473–84. https://doi.org/10.1016/j.energy.2015.03.013.
Maldaner CH, Munn JD, Coleman TI, Molson JW, Parker BL. Groundwater flow quantification in fractured rock boreholes using active distributed temperature sensing under natural gradient conditions. Water Resour Res. 2019;55(4):3285–306. https://doi.org/10.1029/2018WR024319.
Meschede D. Gerthsen Physik. 25th ed. Berlin, Heidelberg: Springer Spektrum; 2015.
Minchio F, Cesari G, Pastore C, Fossa M. Experimental hydration temperature increase in borehole heat exchangers during thermal response tests for geothermal heat pump design. Energies. 2020;13(13):3461. https://doi.org/10.3390/en13133461.
MolinaGiraldo N, Bayer P, Blum P. Evaluating the influence of thermal dispersion on temperature plumes from geothermal systems using analytical solutions. Int J Therm Sci. 2011;50(7):1223–31. https://doi.org/10.1016/j.ijthermalsci.2011.02.004.
Pambou CHK, Raymond J, Lamarche L. Improving thermal response tests with wireline temperature logs to evaluate ground thermal conductivity profiles and groundwater fluxes. Heat Mass Transfer. 2019;55(6):1829–43. https://doi.org/10.1007/s002310182532y.
Raymond J, Robert G, Therrien R, Gosselin L. A novel thermal response test using heating cables. In: World Geothermal Congress; 25–29 April; Bali, Indonesia; 2010.
Read T, Bour O, Selker JS, Bense VF, Le Borgne T, Hochreutener R, Lavenant N. Activedistributed temperature sensing to continuously quantify vertical flow in boreholes. Water Resour Res. 2014;50(5):3706–13. https://doi.org/10.1002/2014WR015273.
Reuß M, Koenigsdorff R, Zorn R, Kuckelkorn J, Steger H, Pröll M, Feuerstein P. Qualitätssicherung bei Erdwärmesonden und Erdreichkollektoren, Final report, Federal Ministry for Economic Affairs and Technology (FKZ: 0327453A). 2012.
Riegger M, Heidinger P, Lorinser B, Stober I. Auswerteverfahren zur Kontrolle der Verfüllqualität in Erdwärmesonden mit faseroptischen Temperaturmessungen. Grundwasser. 2012;17(2):91–103. https://doi.org/10.1007/s0076701201922.
Sakata Y, Katsura T, Serageldin AA, Nagano K, Ooe M. Evaluating variability of ground thermal conductivity within a steep site by history matching underground distributed temperatures from thermal response tests. Energies. 2021;14(7):1872. https://doi.org/10.3390/en14071872.
Sanner B, Hellström G, Spitler J, Gehlin S. Thermal response test—current status and worldwide application. In: World Geothermal Congress; 24–29 April; Antalya, Turkey; 2005.
Sayde C, Buelga JB, RodriguezSinobas L, El Khoury L, English M, van de Giesen N, Selker JS. Mapping variability of soil water content and flux across 1–1000 m scales using the Actively Heated Fiber Optic method. Water Resour Res. 2014;50(9):7302–17. https://doi.org/10.1002/2013WR014983.
Schüppler S, Zorn R, Steger H, Blum P. Uncertainty analysis of wireless temperature measurement (WTM) in borehole heat exchangers. Geothermics. 2021;90:102019. https://doi.org/10.1016/j.geothermics.2020.102019.
Signorelli S, Bassetti S, Pahud D, Kohl T. Numerical evaluation of thermal response tests. Geothermics. 2007;36(2):141–66. https://doi.org/10.1016/j.geothermics.2006.10.006.
Simon N, Bour O. An ADTS toolbox for automatically interpreting active distributed temperature sensing measurements. Ground Water. 2022. https://doi.org/10.1111/gwat.13172.
Spitler JD, Gehlin SE. Thermal response testing for ground source heat pump systems—an historical review. Renew Sustain Energy Rev. 2015;50:1125–37. https://doi.org/10.1016/j.rser.2015.05.061.
Stauffer F, Bayer P, Blum P, Giraldo NM, Kinzelbach W. Thermal use of shallow groundwater. Boca Raton: CRC Press; 2014.
Vélez Márquez M, Raymond J, Blessent D, Philippe M, Simon N, Bour O, Lamarche L. Distributed thermal response tests using a heating cable and fiber optic temperature sensing. Energies. 2018;11(11):3059. https://doi.org/10.3390/en11113059.
Verein Deutscher Ingenieure. VDI 4640 part 1, Thermal use of the underground, Fundamentals, approvals, environmental aspects. 2010.
Verein Deutscher Ingenieure. VDI 4640 part 5, Thermal use of the underground, Thermal response test (TRT). 2020.
Vieira A, AlberdiPagola M, Christodoulides P, Javed S, Loveridge F, Nguyen F, et al. Characterisation of ground thermal and thermomechanical behaviour for shallow geothermal energy applications. Energies. 2017;10(12):2044. https://doi.org/10.3390/en10122044.
Wagner V, Blum P, Kübert M, Bayer P. Analytical approach to groundwaterinfluenced thermal response tests of grouted borehole heat exchangers. Geothermics. 2013;46:22–31. https://doi.org/10.1016/j.geothermics.2012.10.005.
Wilke S, Menberg K, Steger H, Blum P. Advanced thermal response tests: a review. Renew Sustain Energy Rev. 2020;119:109575. https://doi.org/10.1016/j.rser.2019.109575.
Witte HJ. Error analysis of thermal response tests. Appl Energy. 2013;109:302–11. https://doi.org/10.1016/j.apenergy.2012.11.060.
Zhang B, Gu K, Shi B, Liu C, Bayer P, Wei G, et al. Actively heated fiber optics based thermal response test: a field demonstration. Renew Sustain Energy Rev. 2020;134:110336. https://doi.org/10.1016/j.rser.2020.110336.
Zhang X, Han Z, Ji Q, Zhang H, Li X. Thermal response tests for the identification of soil thermal parameters: a review. Renew Energy. 2021;173:1123–35. https://doi.org/10.1016/j.renene.2020.12.028.
Zubair SM, Chaudhry MA. Temperature solutions due to timedependent movinglineheat sources. Heat Mass Transf. 1996;31(3):185–9. https://doi.org/10.1007/s002310050044.
Acknowledgements
The authors would like to thank Andreas Köhler of the Biberach University of Applied Sciences for his help with the ETRT measurements and provision of the Pt100 temperature data. The helpful comments of the two reviewers are also gratefully acknowledged.
Funding
Open Access funding enabled and organized by Projekt DEAL. This study was funded by the funding programme QEWSplus (Grant Number 03EE4020B, 03EE4020E, https://www.qewsplus.de/) by the Federal Ministry for Economic Affairs and Climate Action.
Author information
Authors and Affiliations
Contributions
AA, HS and PB developed the methodology and designed the study. AA, HS and RZ carried out the TRT. AA executed the data analysis and prepared the draft of the manuscript. All authors read and approved the final manuscript.
Corresponding author
Ethics declarations
Competing interests
The authors declare that they have no competing interests.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Information
Additional file 1.
Evaluation of effective thermal conductivities with the infinite line source model for all evaluated depthintervals.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Albers, A., Steger, H., Zorn, R. et al. Evaluating an enhanced thermal response test (ETRT) with high groundwater flow. Geotherm Energy 12, 1 (2024). https://doi.org/10.1186/s4051702300278y
Received:
Accepted:
Published:
DOI: https://doi.org/10.1186/s4051702300278y