Thermal response testing (TRT) is a widely used in situ method for the characterisation of ground thermal properties for shallow geothermal energy applications, in particular for borehole and pile heat exchangers. The most common application of thermal response testing involves the measurement of undisturbed ground temperature, ground thermal conductivity, and thermal resistance of the ground heat exchanger [85
], which are critical design parameters for the design and analysis of borehole and pile heat exchangers. Undisturbed ground temperature is a key thermo-geological parameter needed for the assessment of the geothermal potential of an area. The temperature difference between the undisturbed ground temperature and the mean heat carrier fluid temperature circulating in the heat exchanger leads directly to the heat transfer between the ground heat exchanger and the surrounding ground. Ground with higher thermal conductivity not only yields larger heat transfer rates but also recuperates more rapidly from thermal depletions and thermal build-ups. Thermal resistance of the ground heat exchanger, Rb
), is the effective thermal resistance between the heat carrier fluid in the ground heat exchanger and the surrounding ground. A lower value of thermal resistance leads to better system performance, a smaller ground heat exchanger size, and a lower installation cost.
4.1. Undisturbed Ground Temperature
For SGE applications, the ground temperature is characterised by three different ground zones: surface, shallow, and relatively-deep. Temperature profiles of the surface ground zone (i.e., top few centimetres) and the shallow ground zone (i.e., from the surface zone to a few meters down) vary with the diurnal and seasonal changes of ambient air temperature, respectively. Underground temperature of the relatively-deep zone (i.e., from the shallow zone to few hundred meters down) increases slowly with depth due to the geothermal gradient.
In most practical cases, especially concerning vertical borehole applications, a single value of average ground temperature, generally referred to as the undisturbed ground temperature, is used as a design parameter. Several studies, including References [92
], have underlined the significance of undisturbed ground temperature, and have shown its effect on factors including sizing of the ground heat exchanger, extracted thermal power, and performance of the heat pump, among others.
The undisturbed ground temperature is determined, in situ, by mainly two methods, i.e., downhole temperature logging, and the fluid circulation method [88
]. In the downhole temperature logging method, the temperature distribution along the borehole depth is measured by means of a downhole temperature sensing system. A simple or weighted average of the measured temperature values is then used to approximate the undisturbed ground temperature. Various downhole temperature measurements systems, including wired temperature sensors, submersible wireless probes, and fiber optics, among others, are used in practice. This method is relatively easy to apply to groundwater-filled boreholes, where the temperature measurements can generally be taken by lowering the downhole sensors in the spacing between the heat exchanger pipes and the borehole outer wall. The downhole sensing system is generally retracted after performing the measurements. In grouted boreholes, the application of downhole temperature logging is slightly more complicated. Measurements in the spacing between the heat exchanger pipes and the borehole wall can only be taken if a permanent downhole temperature sensing system has been installed before grouting the borehole. Otherwise, the temperature can only be measured inside the heat exchanger pipes. It is important that the heat carrier fluid is kept in the pipes long enough to reach thermal equilibrium with the surrounding ground. It is also important to submerse the sensing element slowly to prevent any disturbance of the fluid in the pipes.
The fluid circulation method involves circulating the heat carrier fluid through the undisturbed borehole without injecting or extracting any heat. Firstly, the fluid is kept long enough in the heat exchanger pipes to reach equilibrium with the surrounding ground. Then, the undisturbed ground temperature is estimated from the fluid temperature exiting the ground heat exchanger. The most common approach is to circulate the fluid in the ground heat exchanger until temperature variations peter out, and the circulating fluid temperature stabilises. The stabilised fluid temperature is then taken as an approximation of the undisturbed ground temperature. A second approach [99
] is to use the minimum temperature value of the heat carrier fluid exiting the ground heat exchanger during the first circulation cycle as an estimation of the undisturbed ground temperature. A third approach is to take the average temperature of the fluid exiting the ground heat exchanger during the first circulation cycle as an estimate of the undisturbed ground temperature.
When using the fluid circulation measurement method, several factors, including fluid temperature outside the ground loop, heat gains from the circulation pump, ambient coupling, and fluid residence time in the heat exchanger, may affect the undisturbed ground temperature measurements. This is particularly relevant if the fluid is circulated through the ground heat exchanger more than one time. Javed and Fahlén [100
] and Gehlin and Nordell [101
] compared various approaches to measure undisturbed ground temperatures on a multi-borehole field and a single borehole, respectively. The results of both these studies suggest that the average temperature of the fluid exiting the ground heat exchanger during the first circulation cycle provides the best estimate of the undisturbed ground temperature. On the contrary, the stabilised fluid temperature and the minimum fluid temperature approaches are both shown to have serious shortcomings. The undisturbed ground temperature value could be greatly influenced by ambient coupling and heat gains from the circulation pump when using the stabilised fluid temperature approach. Similarly, the minimum recorded temperature approach could result in strongly underestimated undisturbed ground temperature value, especially with low ambient temperatures during the measurement.
When measuring the undisturbed ground temperature, it is necessary to pay attention to the effects of urbanisation and other anthropogenic activities on the measured temperature values [102
]. Elevated ground temperatures and zero or negative ground temperature gradients should be expected and allowed in the design of shallow geothermal systems in close proximity to existing facilities including buildings and structures, or in urban areas.
4.2. Thermal Response Testing
A thermal response test consists of measuring the temperature evolution of a ground heat exchanger under a prescribed thermal load. Several variations of the test procedure exist e.g., References [86
The thermal response test variants differ based upon their operation mode (i.e., heating or cooling), boundary conditions (constant heat flux or constant input temperature), analysis period (active phase or recovery phase), and measurement system (standard, distributed, or enhanced sensing), among others. However, the common principle upon which all variants of thermal response tests are based is capturing the thermal response of the ground to a known thermal excitation, and evaluating ground and borehole thermal properties using a suitable heat transfer model.
Despite all its variants and recent developments, the conventional approach to thermal response testing remains the most prevalent and universal approach, and is the preferred testing method for estimating ground and borehole thermal properties. This is due to the simplicity of design, implementation, control, and evaluation of the conventional approach. When performed in the conventional way, the standard methodology of thermal response testing begins with measuring undisturbed ground temperature, followed by constant power heat injection or extraction for a period of 2–3 days. Most often the testing is performed in heat injection mode to minimise the influence of external factors affecting the measurements. An electric resistance heater is typically used to heat the heat carrier fluid at a constant power rate q
of 50–80 W·m−1
. The temperature of the heat carrier fluid entering and leaving the borehole is measured, together with the flow rate, ambient temperature, and input power to the electric heater and the circulation pump. Measurements are taken at regular intervals of 1–10 min. Finally, measurements are analysed using a mathematical heat transfer model, most commonly the infinite line source approximation, to evaluate ground thermal conductivity and borehole thermal resistance values. Figure 9
and Figure 10
, respectively, show schematic diagrams of a typical thermal response test setup, and the most typical measurements taken during a standard thermal response test.
Evaluation of thermal response tests can be carried out using direct or parameter estimation methods. Direct evaluation methods are based on simplified approximations of infinite line source [115
] and infinite cylindrical-source [116
] solutions. To use the direct methods, thermal power injected to the borehole or extracted from it should remain almost constant over the whole test duration. The standard deviation of the input power should be less than ±1.5% of the mean input power, and the maximum variation should be smaller than ±10% [117
Of the direct methods, the infinite line source approximation method is easiest to implement and is widely used because of its simplicity and strong intuitive appeal. The method involves plotting experimentally measured mean temperatures of heat carrier fluid entering and exiting the borehole heat exchanger against logarithmic time, and using a straight line to fit the experimental measurements. The line source approximation is mostly recommended for times larger than 20 rb2
, which generally accounts to 10–20 h for a typical borehole. This is due to the limitation of the infinite line source approximation to match the original model at smaller times—the error of the approximation for time 5 rb2
is 10% and for time 20 rb2
/α is less than 2.5%. The slope and intercept of the straight line are used to calculate ground thermal conductivity [86
] and borehole thermal resistance [118
Parameter estimation methods allow the analysis of thermal response tests with power variations higher than those deemed acceptable with direct evaluation methods. Parameter estimation methods account for variations in input power by considering stepwise-constant heat pulses rather than an overall constant input power. These methods initially use estimated values of ground conductivity and borehole resistance to simulate the heat carrier fluid temperature. The estimated values are then optimised by minimising the error between simulated and experimentally measured fluid temperatures. Parameter estimation methods for evaluating thermal response tests are based on both analytical as well as numerical models. Several parameter estimation methods have been implemented in high-level programming languages and are available as standalone computer programs. These include, among others, Geothermal Properties Measurement (GPM) [119
], Vertical Borehole Analysis and Parameter Estimation Program [120
], and TRT Evaluation Program (TEP) [121
]. Software tools GPM and Vertical Borehole Analysis and Parameter Estimation Program are, respectively, based on one-dimensional finite-difference and two-dimensional finite-volume models, whereas software tool TEP is based on the analytical method proposed by Reference [122
]. Parameter estimation methods based on infinite line source and infinite cylindrical-source approximations have also been implemented by individual users in spreadsheets and mathematical analysis software [94
One important factor when analysing thermal response tests is that there could exist more than one combination of the ground thermal conductivity and borehole thermal resistance values that can match the experimentally measured temperature curve [123
]. However, as noted by Reference [124
], the two parameters have counterbalancing effects on the design, and using the experimentally determined values of both parameters mitigates some of the error that would occur if only the ground conductivity value estimated from the test is used for the design. It is still, however, recommended to separately calculate the borehole thermal resistance value to counter-check the experimentally determined value. Several methods to calculate borehole thermal resistance have been presented and compared in References [125
]. A lower value of borehole thermal resistance improves the performance of the system and lowers the total required borehole length. A key factor is this regard is the choice of the grouting material between heat exchanger pipes and the surrounding ground [8
Thermal response tests are subjected to possible errors caused by uncertainties in measurements, in (input) design parameters, and in the analysis method. Uncertainties in measurements arise from factors such as imprecise location, calibration, or limitations of the measuring instruments and fluctuations in the test environment. Air trapped in the pipes can also cause severe measurement inaccuracies concerning water flow rate and can negatively affect the heat transfer to the ground. Uncertainties in design parameters are caused by inaccessible, incomplete, or inaccurate data on material properties (e.g., densities and heat capacities of heat carrier fluid), geometrical dimensions (e.g., diameter and depth of borehole), and boundary and input conditions (e.g., undisturbed ground temperature). Uncertainties in the analysis method are attributable to the inherent limitations of mathematical models used to determine ground conductivity and borehole resistance values as well as the duration of thermal response tests. In References [100
], detailed uncertainty analyses of thermal response tests were presented. The overall uncertainty for each of these studies, when determined by adding all of the individual uncertainties in quadrature, are approximately ±5–10% for ground thermal conductivity and ±10–15% for borehole thermal resistance. Taking a somewhat different approach, Javed [129
] evaluated nine boreholes in close proximity using the commonly-used infinite line source approximation method, and found overall experimental uncertainties of ±7% in ground conductivity value and 20% in borehole thermal resistance value.
Thermal response test results have been shown to be highly sensitive to several factors, which include climatic conditions, groundwater flow, input power variations, test duration, and analysis method. Climatic conditions cause undesired heat exchange to or from the thermal response test setup. It has been demonstrated that ground conductivity estimations inferred from thermal response testing can be affected by a factor of one third if energy losses outside the borehole are neglected [130
]. Figure 11
shows an example of a thermal response test that has been strongly affected by ambient weather conditions. When performing a thermal response test, pipe connections between the test rig and the borehole, and other components of test rig including accumulator tank, circulation pump, etc., must be thermally insulated to prevent, as far as possible, the transfer of heat between the heat carrier fluid and the ambient air. A few methods to assess and eliminate the effects of ambient conditions on thermal response tests are also available [99
Thermal response test measurements may also be affected by hydrogeological conditions. In the presence of significant groundwater flow, ground thermal properties evaluated by the commonly-used infinite line source approximation are invalidated. Figure 12
shows the evolution of heat carrier fluid temperatures, simulated for two cases, one with and one without groundwater flow. It can be clearly observed that due to the enhanced heat transfer between the heat carrier fluid and the ground, the evolution of heat carrier fluid temperature over time is inhibited by the presence of groundwater flow. When evaluating a test with significant groundwater flow, the enhanced heat transfer translates into a higher but inaccurate estimation of ground thermal conductivity, which continuously increases with the analysis time. It is recommended to always perform a sequential analysis [131
] when evaluating a thermal response test to explore the effect of groundwater flow on the test results. Groundwater flow-influenced thermal response tests can alternatively be evaluated using a moving line source or other advection-based analytical or numerical methods, including those suggested by References [132
The accuracy of thermal response test results also depends on power variations during the test. Direct evaluation methods, including the infinite line source approximation, assume constant heat injection or extraction rates. When these methods are used for the evaluation of thermal response tests, fluctuations in supply power can lead to inaccurate results. In case of significant power variations, either effects of variable heat rates should be removed from the test [136
], or parameter estimation methods should be used for evaluating the tests [94
The duration of a thermal response test greatly influences the accuracy of the estimated results. A longer test duration yields more accurate and reliable evaluation of ground and borehole thermal properties. This is because longer test durations allow borehole heat transfer to reach quasi-steady state, while simultaneously reducing statistical errors due to power and thermal fluctuations. The American Society of Heating, Refrigerating and Air-Conditioning Engineers [117
] h. However, in References [139
], minimum test durations of 50 and 60 h were emphasised, respectively. Long-duration thermal response tests (>100 h) were performed in References [120
] to study the effects of different test lengths on the estimated properties. Their findings suggest that ground conductivity and borehole resistance estimates converge for test durations longer than 100 h. For test durations between 50 and 100 h, the estimated results have a maximum absolute deviation of approximately 5% of the converged values. For test durations shorter than 50 h, the errors in estimated ground conductivity and borehole resistance values are much larger. In Reference [118
], a method to calculate the minimum test duration necessary to estimate ground thermal conductivity within 10% of the converged value from a long TRT was developed.
4.3. Distributed and Enhanced Thermal Response Testing
Conventional thermal response tests give average values of ground conductivity over the entire length of the borehole heat exchanger. It is not possible to measure thermal conductivity for different geological layers with a conventional test. Identifying vertical contrasts in thermal conductivity along the borehole depth may allow for the optimisation of borehole designs with respect to their placement, size, and depth.
Distributed and Enhanced Thermal Response Tests (DTRTs and ETRTs) are testing methods that measure variations in ground thermal conductivity along the entire length of the borehole heat exchangers. Both methods rely on temperature measurements taken at multiple depths along the borehole, using downhole sensors placed in the grout, or inside or outside the ground heat exchanger pipes. A distributed thermal response test [107
] is very similar to a standard thermal response test. It consists in injecting heat to, or extracting heat from, the borehole heat exchanger at constant power and measuring thermal response of the ground at multiple instances along the borehole depth. The measurements are obtained by means of temperature sensors (e.g., thermocouples, thermistors, resistance temperature detectors) or fiber optic cables. Figure 13
shows examples of downhole installation of temperature sensing and fiber optic elements used for distributed thermal response testing in practice.
An enhanced thermal response test [113
] involves injecting heat into the ground by means of one or more copper heating cables and measuring the vertical ground temperature distribution with an optical fiber cable. Generally, the copper and optical fiber cables are integrated in one single ‘hybrid cable’. The hybrid cable is shaped and sized after the ground heat exchanger, and is placed on the outside of the heat exchanger. Figure 14
shows component and installation details of hybrid cables used for enhanced thermal response testing.
The main reason for using fiber optics for distributed and enhanced thermal response testing is the acquisition of a high-resolution temperature distribution along the borehole depth. Each fiber is connected to a Distributed Temperature Sensing (DTS) equipment, which injects laser light. The signal is scattered and reemitted from the observed point. The backscattered signal consists of light scattered by a variety of mechanisms. Among these, the anti-Stokes Raman backscatter signal is sensitive to temperature and is used to measure the temperature profile along the fiber length. The position of the temperature reading is determined by the arrival time of the reemitted light pulse. The use of DTS in thermal response testing allows measurements of high spatial, temporal, and temperature resolution. Tests with spatial resolution of 0.2–5 m, temporal resolution of 1–10 min, and temperature resolution of 0.1–0.5 K are considered state-of-the-art today.
The analysis of distributed and enhanced thermal response tests is also quite similar to that of a conventional thermal response test, but with a few modifications. When analysing a distributed or an enhanced thermal response test, the borehole is divided into several smaller zones, each of 0.5 m or larger. For each zone, mean fluid temperature and difference between inlet and outlet temperature values are obtained from the vertical temperature measurements taken along the borehole (see Figure 15
). Thermal power to each zone is determined as a multiple of the mass flowrate of the heat carrier fluid times the difference between zone inlet and outlet temperatures. For an enhanced thermal response test, the injected power is constant for the entire borehole length and can be directly calculated from the electric power supplied to the heating cable. The analysis is performed separately for each zone, and corresponding estimations of thermal conductivity and borehole resistance are obtained. The analysis can be performed using any of the evaluation methods described earlier, though infinite line source approximation is mostly used. For better accuracy, it is common to carry out the analysis in the recovery phase, especially for enhanced thermal response tests.
Several recent studies have demonstrated the advantages of distributed and enhanced thermal response tests over conventional tests. These tests have been successfully used to identify and characterise hydraulic fractures (e.g., [144
]) and ground layers (e.g., [141
]). An example is also presented here to demonstrate the advantages of a distributed temperature sensing-based thermal response test over a conventional test. Figure 16
shows the thermal characterisation of the subsurface based on two nearby boreholes in Limelette, Belgium. The boreholes are 74 and 120 m deep, and are separated by about 6 m. Conventional and enhanced thermal response tests were carried out on both boreholes. The test parameters and results are summarised in Table 1
. The ground conductivity estimations obtained from the conventional thermal response test and the average values obtained from the enhanced thermal response tests are very similar. There is a maximum difference of about 0.3 W·m−1
in the ground conductivity estimations from the two methods. However, as demonstrated in Figure 16
, the enhanced thermal response test provides comprehensive breakdown of thermal conductivity values along the borehole.
In Figure 17
, average ground thermal conductivity estimates from distributed and enhanced thermal response tests are compared to conventional test-based estimates, as reported in the literature. In all cases, results from the distributed and enhanced tests are in quite good agreement with the corresponding TRT estimates, with differences less than 10%. The results of the enhanced thermal response tests presented in this paper also displayed a similar tendency, as shown in Table 1
There are also considerations and constraints when using distributed and enhanced thermal response tests. One significant aspect that needs to be considered when using distributed temperature sensing is that, unlike other temperature sensors, fiber optic measurements require continuous in situ calibration. This is because any change in the operating conditions of the optical fiber and the DTS equipment (e.g., ambient temperature), alters the calibration parameters [145
]. It is, hence, necessary to place a section of the optical fiber into a known-temperature environment, e.g., water or ice bath, during the whole testing procedure for offset calibration. Moreover, longer fiber lengths also need to be adjusted for slope losses, thus requiring calibration measurements at two different sections of the fiber optic. Furthermore, when evaluating distributed or enhanced thermal response tests, it is often assumed that there is no heat transfer between different zones, like those shown in Figure 15
. However, this assumption is void if different geological layers with significantly different ground thermal conductivities are present, which can significantly affect the test results [150
]. Also, the distributed temperature measurements depend on the location of the fiber in the heat exchanger, and the relative position of the heat exchanger pipes to each other. As these positions are unknown, and may also vary along the borehole depth, there are certain intrinsic errors in calculating the average fluid temperature for each zone. Due to these and other potential problems and limitations in applying distributed and enhanced thermal response tests, there exist certain uncertainties in ground properties estimated from these approaches, an example of which can also be seen in Figure 16
for two enhanced thermal response tests performed on two nearby boreholes.
4.4. Thermal Response Testing of Foundation Pile Heat Exchangers
Energy piles are energy geostructures that utilise reinforced concrete foundation piles as heat exchangers. Pile heat exchangers are less slender than borehole heat exchangers, being shorter and wider than the latter, hence yielding lower aspect ratios (length/diameter). Borehole heat exchanger aspect ratios range from 100 to 1500, whereas energy pile aspect ratios are typically smaller than 50. Energy piles consist of reinforced concrete (instead of grout) and their structural integrity is prioritised over thermal performance for obvious reasons. Energy piles vary in length, typically between 10 to 50 m with a diameter from 0.3 to 1.5 m, utilising different types of design geometries [151
] (see Table A2
in the Appendix
However, due to the underlying similarities between the borehole and pile heat exchangers, attempts have been made to adapt the thermal response testing practice and interpretation methods to energy piles [152
]. Longer duration thermal response tests are usually needed for pile heat exchangers due to their larger diameter—and, hence, thermal mass—in comparison to traditional borehole heat exchangers. The testing procedure remains similar to that for borehole testing. However, there is a lack of scientifically supported guidelines for the interpretation of energy pile thermal response test data. International guidelines limit the practicability of field testing energy piles to diameters up to 0.3 m because of time and cost restrictions [153
]. Table A2
provides a summary of studies where strict use of the thermal response testing method has been adopted for pile heat exchangers to determine the soil thermal conductivity.
When analysing energy pile thermal response test data, models that have been developed for vertical borehole heat exchangers, such as the infinite line source [116
], are generally applied. However, large diameter and short aspect ratio heat exchangers deviate from traditional, generally assumed line source behaviour. When using the line source model to evaluate thermal response tests, the thermal response after a few hours is assumed to be log-linear with respect to time. For low aspect ratio piles, this linear behaviour never truly occurs as three-dimensional effects (i.e., surface boundary conditions and end effects), causing the actual thermal response of piles to diverge from that of line source solutions [154
]. The axial effects imply that the measured temperatures always fall below the line source modelled temperatures, which further implies that the line source-based interpretation will systematically overestimate the thermal conductivity.
In the dimensioning of borehole heat exchanger fields, the borehole thermal resistance is considered constant, as it is assumed that the borehole heat exchanger reaches a steady-state condition after a few hours of operation. However, piles can take days or even months to reach a steady-state condition and the assumption of constant pile thermal resistance neglects the thermal inertia related to large diameter piles [154
To appropriately interpret thermal response test data from pile heat exchangers, a number of alternatives exist (Table A2
), either in the form of analytical solutions, (semi)empirical functions, or 2- or 3D numerical models. The first category includes analytical solutions such as the line and cylindrical source finite solutions suggested by References [116
] and [115
], the finite line source solution presented by Reference [155
], the composite cylindrical model to account for the contrasting thermal properties of the pile and the soil reported in References [156
], the infinite solid cylindrical heat source model described in References [91
], and semi analytical models such as those described in Reference [159
]. The second category includes temperature response empirical functions (so-called G-functions), e.g., see Reference [154
], which are developed for specific ranges of pile heat exchanger geometries and provide temperature solutions for different pile aspects ratios (shown in Figure 18
). The final category potentially constitutes the most accurate means to back-analyse thermal response tests and estimate thermal parameters. However, the computational effort of a full 3D numerical model-based interpretation is potentially too burdensome for routine thermal design.
Zarrella et al. [160
] recently back-analysed a thermal response test on a 20-m-long, double U-tube 0.6m diameter energy pile near Venice (Italy). The geological setting includes alternating layers of clay and silty sand. The inversion of measured temperatures utilises a detailed numerical forward model based on an electrical analogy, making use of lumped thermal capacities and resistances [161
]. Comparing this interpretation with the traditional line heat source approach, the authors found that the latter approach led to ground conductivity estimates roughly twice the numerical model-based estimate. This suggests that the choice of interpretation method can cause significant errors in the dimensioning of the overall system. Thus, the authors recommend the use of an interpretation method that accounts for 3D effects and the actual geometry of the pile. Similar conclusions are drawn in Reference [162
], where synthetic data from a 3D finite element model of a 1m diameter pile was used to find an upper bound of 50% for the error in estimating thermal conductivity when using the line source model. In Reference [163
], a 3D numerical finite element model was employed to simulate short-term TRTs on prototype 0.4 m diameter precast energy piles placed in partially saturated weathered granite in Korea. Similar to the findings of Reference [162
], the numerical assessment of thermal conductivity resulted in values of about half of those estimated by conventional 1D analysis.
An analogous fully 3D numerical approach was also employed in References [164
], where the experimental results of a multi-stage, one-month-long TRT of a 0.3 m diameter test pile installed in London clay were reproduced. The same data were analysed in Reference [166
]. Soil thermal conductivity was estimated with a numerical method, the infinite line source, and the pile G-functions proposed by Loveridge and Powrie (2013) [154
]. The line source method overestimated the ground thermal conductivity values by up to 20% compared to the numerical method. The values estimated from empirical methods such as G-functions were closer to those from the 3D numerical model, with a maximum difference of 10%.
Based on the above studies and similar outcomes from other authors (e.g., [157
]), it is demonstrated that the use of numerical methods to back-analyse TRT data on energy piles is a more accurate way to estimate soil and concrete thermal parameters. These methods are preferred over traditional 1D methods, especially when referring to short duration TRT data, and/or analysing large diameter, multiple U-tube, low conductivity concrete, or otherwise less conventional energy piles. One possible shortcoming of numerical methods is their computational expense, and the characterisation they require, which is generally greater than other methods and can make them unsuitable for routine practical usage. In this respect, the use of (semi)empirical methods such as as G-functions can be an advantage, as they represent a compromise between reliability and ease of use/computation time.