The principal purpose of this section is the estimation of the thermal conductivity of the borehole column described above. To that end, different methods and procedures implemented in previous author’s researches are considered here to finally compare them with the results of a TRT. The following subsections contain the description of each of the mentioned thermal conductivity estimator techniques.
2.2.1. KD2 Pro Measurements
In a previous research work, the thermal conductivity map of the province of Ávila (study area of this research) was created from experimental measurements on the principal geological formations of the region. Representative rocky samples were collected and taken to the laboratory, where the thermal conductivity parameter was measured.
After systematic sample processing—drilling and carving obtaining samples with a specific size, removal of excess material—KD2 Pro equipment was used to measure the thermal conductivity of each geological formation. Before its use, a hole of 6 cm length and 3.9 mm in diameter was made on each rocky sample in order to introduce the RK-1 sensor of KD2 Pro device. More information about the specific measuring methodology is provided in the full published version of the manuscript [
21].
As a result of the KD2 Pro measurement, the mentioned research provides the thermal conductivity of the rocky and soil formations. According to the borehole column in
Figure 2, the volume of ground under study is constituted by different layers of materials. In order to obtain a representative thermal conductivity value of the whole column well, the thermal conductivity of each layer and its thickness must be considered. Based on the results offered in the research, thermal conductivities of the borehole materials were deduced. All this information is included in
Table 2. Thermal conductivity values presented in
Table 2 correspond to the average values registered for each geological formation in the manuscript considered here. However, for the last layer of altered adamellites, the lowest values of the mentioned study were selected due to the presence of loose materials and the altered state of granite rocks in that level.
Finally, the thermal conductivity representative of the whole studied borehole can be obtained from the application of Equation (1) and the information previously attached in
Table 2.
where:
kT = Global thermal conductivity of the whole borehole column.
k1 = Thermal conductivity of the geological formation of layer 1.
k2 = Thermal conductivity of the geological formation of layer 2.
k3 = Thermal conductivity of the geological formation of layer 3.
k4 = Thermal conductivity of the geological formation of layer 4.
T1 = Thickness of layer 1 expressed as a percentage of the total well thickness.
T2 = Thickness of layer 2 expressed as a percentage of the total well thickness.
T3 = Thickness of layer 3 expressed as a percentage of the total well thickness.
T4 = Thickness of layer 4 expressed as a percentage of the total well thickness.
2.2.2. Geophysics
Geophysical prospecting has been used in previous works as a ground thermal conductivity estimator. The principal basis of these studies is the correlation of a geophysical parameter and thermal conductivity measurements (using KD2 Pro device) to finally predict the thermal behavior of the ground in depth. A more detailed description of these methods and their implementation in the area of the present research is included in the following subsections.
(1) Seismic data:
The first geophysical method makes reference to the implementation of seismic prospecting tests. In a previous research work, the mentioned tests were implemented on three different geological formations (schists, medium grain and coarse-grained adamellites) using MASW and seismic refraction techniques in order to register P and S waves velocities. At the same time, thermal conductivity of each formation was measured by the use of KD2 Pro equipment. These tests were made on the most and least decomposed samples of each geological environment to find the lowest and highest conductivity values. Finally, this published research correlates the propagation velocities of P and S waves and the thermal conductivity of samples from the same material [
22].
The ultimate result of this work is to predict the thermal behavior of the geological formations included in the study. By identifying the propagation velocities of the seismic waves in a certain area, the evolution of the thermal conductivity of the ground in that area can be evaluated. Thus, 2D thermal conductivity sections provided in the mentioned research allow estimation of the evolution of ground thermal conductivity in depth for each specific formation.
In order to ensure application of this methodology, seismic refraction tests were conducted on the area where the borehole of study is located. The results of these tests are provided in
Figure 3.
After the distribution of the P wave velocity was identified in depth, different thermal conductivity measurements were taken in order to identify the most and least thermal conductive samples, meaning those with the highest and lowest compaction levels. These values correspond to the minimum thermal conductivity of anthropogenic fills and the maximum thermal conductivity for the altered adamellite; they are presented in
Table 3. It should be noted that altered adamellites were extracted from the drilling process at depths where they were identified. These samples were then used in thermal conductivity characterization.
By measuring P wave velocity and thermal conductivities in the study area, the correlation between both parameters was obtained (graphically presented in
Figure 4). This is based on pairing the lowest thermal conductivity value with the lowest p wave velocity (in the same area) and the highest thermal conductivity with the highest p wave velocity. More information on this method is provided in the mentioned published research.
From the above correlation and by following the instructions of the mentioned research, the distribution of the thermal conductivity parameter in the area considered here is displayed in the 2D section of
Figure 5.
According to
Figure 5, the volume of ground included under the borehole is constituted by a set of layers with different thermal conductivity values. This information can be observed in
Table 4.
Finally, the global thermal conductivity of the borehole column is deduced from the application of the above data (
Table 4) in Equation (1).
(2) Electrical resistivity:
In this case, electrical resistivity data were collected to finally create a 3D thermal conductivity map of the area of interest. The fundamentals of this method are similar to the one explained before; electrical resistivity results are correlated with thermal conductivity measurements and a relation between both parameters is obtained for a certain geological formation. The research work, including this methodology, was focused on granite rocks (adamellites), and the electrical resistivity was obtained using the Electrical Resistivity Tomography (ERT) technique. Thermal conductivity measurements were, in turn, taken using KD2 Pro equipment following the same operational procedure (tests were made on the most and least decomposed rocky samples) [
23].
The results of this research disclose a certain relation between thermal conductivity and electrical resistivity. This relation can be observed in Equation (2).
where:
To apply Equation (2), the electrical resistivity of the materials in the study area must be known. To this end, an ERT test was conducted around the mentioned area, obtaining a 2D electrical resistivity section (presented in
Figure 6).
On interpretation of the above 2D electrical resistivity section, the borehole considered in this study is constituted by a series of layers with different thickness and characterized by variable electrical resistivity values. All these data are included in
Table 5; the thermal conductivity of each layer is obtained by application of Equation (2).
As in the previous cases, Equation (1). must be used to finally define the global thermal conductivity of the borehole column from partial thermal conductivity values and thickness of each layer.
2.2.3. Thermal Response Test
The last procedure implemented in this research is the realization of a Thermal Response Test in the borehole. These tests are routinely used to estimate borehole thermal properties with regard to the mentioned thermal conductivity. The conventional TRT consists of circulating heated fluid (usually water) in a closed loop. During the test, fluid temperatures are measured at the ground heat exchanger inlet and outlet, along with the flow rate. Theses measured values are then analyzed by analytical or numerical models with the aim of calculating thermal conductivity and borehole thermal resistance [
3,
24].
(1) Test implementation
First, the borehole was geothermally prepared for the test by installing a polyethylene single-U tube heat exchanger of 32 mm with spacers located one meter apart. Taking advantage of the high groundwater level in the area, grouting material was not used [
25,
26]. The working fluid was water (during the test, low ambient temperatures were not expected) and the connection of the inlet and outlet heat exchangers and the TRT device was made with polyethylene tubes that were externally insulated. In order to set the initial condition of this test, a temperature register (PCE-T recorder) was used to measure the base temperature of the ground, obtaining a constant value of 14.6 °C at a depth of 40 m.
In this research, TRT was done according to UNE-EN ISO 17628:2017 regulations [
27]. The TRT device implemented here constituted of a heat injection system, a circulating pump, and electrical resistance as heat source. The resistance allows three different heating levels, corresponding to the injection of 3 kW (stage 1), 6 kW (stage 2), and 9 kW (stage 3). The TRT equipment also included a Kamstrup energy meter (to register a large number of parameters), commercially known as MULTICAL 801.
Once the borehole was properly equipped, the sequence of events was as follows:
- -
Circuit filling and establishment of the appropriate working pressure.
- -
Activation of the circulating TRT pump and starting of the first heating stage (3 kW).
- -
General system operation during a certain period of time.
- -
Downloading and data management from the Kamstrup register.
- -
Calculation of the global thermal conductivity parameter.
The TRT duration is a controversial subject—while reducing TRT duration could help reduce costs, the accuracy of results could be affected. Following the regulation mentioned before [
27], the minimum duration of the TRT can be estimated by Equation (3).
where:
By applying Equation (3) and estimating thermal conductivity of 1.80 W/mK and volumetric thermal capacity of 2.16 × 10
6 J/m
3/K [
28], the minimum duration required for the thermal response test in the studied borehole would be:
Despite this value, the real duration of the test was 43 h, which sought to guarantee total stabilization of the system. Additionally,
Figure 7 shows the TRT device and some sequences of the test.
(2) Thermal conductivity calculation
In a borehole heat exchanger of sufficient length in comparison with its radius, the analytical solution of Kelvin’s Line Source can be applied to solve the heat equation and analyze TRT data. According to the infinite line-source model (use as a laboratory method since 1905), the thermal conductivity parameter can be obtained from the constant power rate and the slope of the temperature variation in time [
29,
30]. The interpretation of TRT results relies on a first-order approximation to linearize the mentioned infinite line-source model, neglecting the early measurements.
where:
Q = heat flux (kW/min)
b = slope (min)
H = borehole length (m)