Definition of a thermal conductivity map for geothermal purposes

Abstract

The use of geothermal energy is spreading globally due to its many advantages, especially for heating and cooling. The correct design of a geothermal system requires knowledge of the parameters of the subsoil rocks, and particularly the thermal conductivity (k), which is the intrinsic ability of a material to transfer thermal energy as a result of a temperature gradient. A thermal conductivity map of the geological formations is time-consuming to produce, but can be of great help when selecting the location of a low-enthalpy geothermal installation, resulting in significant savings and an increase in the efficiency of that installation. The preferred option for determining k is an in situ thermal response test, but laboratory methods may be an alternative if it is not available or affordable. In this work, the needle thermal probe method has been used to measure the k of representative outcropping rocks in Oviedo (NW Spain), since it allows to obtain a rapid determination, its cost is comparatively low and it can be implemented in a portable device. 162 measurements have been carried out on a total of 27 samples, ranging from 0.2 (clay) to 5.4 W m⁻¹ K⁻¹ (quartzite). A relationship has been found between the k of the rocks and their characteristics, such as mineralogy, anisotropy or geological age and a thermal conductivity map was created.

Introduction

The thermal conductivity (k) is a measure of the ability of a certain material to conduct heat and it can be defined as the amount of heat per unit time that passes through a unit area with a temperature gradient in the direction of flow. It is used in Fourier’s heat conduction equation for homogeneous solids. A higher thermal conductivity of a material implies a better conduction of heat. The determination of the thermal conductivity of rocks is relevant in mining, civil engineering and geothermal applications. It can be useful for all kinds of heat flow calculations, geodynamic studies, heat transfer simulations for geological repositories such as radioactive waste, mining ventilation studies, recovery from heavy oil reservoirs, underground storage of energy or fuel, underground structures such as tunnels or subway stations, buried high-voltage power cables, oil and gas pipelines, ground modification employing heating and freezing, etc. Rocks with a higher thermal conductivity are more efficient at transferring heat energy, so the accuracy of rock thermal conductivity determination affects the design of these workings. Nevertheless, this work focuses on geothermal uses as the main application of the knowledge of this parameter (Wang et al. 2021; Álvarez et al. 2019; Popov et al. 2016).

Recently, renewable energy sources have gained importance, in order to accomplish the guidelines set in the Paris Agreement of 2015, to reach the zero-carbon emissions goal. It is estimated that world energy demand will increase by 62% before 2050 (International Energy Agency 2020), so a rise in renewables is expected, first in Europe and then in the rest of the world, in order to replace conventional fossil resources and reduce greenhouse gas emissions (Álvarez et al. 2021; International Energy Agency 2020). In fact, the new European Energy Efficiency Directive (EU) 2023/1791 (European Parliament, 2023) requires Member States to migrate their urban heating and cooling systems to 100% renewable energy, waste heat or a combination of both by 2050. Among the renewable geological resources, geothermal ones are the most notable, being used for the production of electricity (high enthalpy resources), direct applications of heat such as balneotherapy or certain industrial and agricultural processes and space and district heating/cooling by means of a heat pump (low and very low enthalpy resources). Geothermal energy direct use involves drawing heat from the ground around a borehole, e.g., after injecting fluid through the borehole or simply extracting groundwater or mine water (Menéndez et al. 2020), but is not considered a direct use if a heat pump is operated. Geothermal energy is considered one of the cleanest forms of energy on earth and according to the U.S. Environmental Protection Agency (EPA), geothermal heat pumps are the most energy-efficient and cost-effective systems for heating and cooling buildings (EIA 2020; Menéndez et al. 2019). The utilization of geothermal energy is increasing rapidly worldwide, reaching a total installed thermal power of 108 GWt, and the largest use of thermal energy (around 60%) is for geothermal heat pumps (Lund and Toth 2021). The latter is also the most widely implemented geothermal use in Spain, although this type of energy still lacks much development in the country.

The sustainable exploitation of these type of resources is essential to guarantee their future conservation that allows their long-term use, while respecting the environment. Thus, a complete characterization of the geothermal system must be undertaken before starting the resource exploitation (Huenges 2010; Rybach 2003). The sustainability of a geological system for the use of geothermal energy means that it has the capacity to maintain the level of production for a long time and, among other factors, that extractable energy depends on the characteristics of the rock matrix (Rybach and Mongillo 2006). Numerical simulation is a useful tool for the design of a geothermal exploitation system, which allows evaluating its response after a certain number of years under different exploitation conditions/scenarios. The reliability of the modeling results depends on the precision of the input data, especially the boundary conditions and the assignment and calibration of the thermophysical parameters (Andrés et al. 2017). The model will be much more accurate if the geological properties of the rocks, such as porosity, density, permeability or thermal conductivity are known (Franco and Vaccaro 2014). The thermal properties of the rocks are critical parameters for predicting the lifetime performance of geothermal systems. In particular, the thermal conductivity of the local rocks is an essential parameter to design a system to use low-enthalpy geothermal resources. The following sections explain how to determine this parameter in order to create a thermal conductivity map.

As previous studies, it is worth highlighting the study by Sáez et al. (2017), who drew up a map of thermal conductivities of the province of Ávila (central Spain). Sixty representative samples of the geological formations of this province (1 sample per 134 km²) were measured with an equipment similar to that used in this work. Stylianou et al. (2016) mapped the thermal conductivities in Cyprus from 135 representative samples of the different formations (1 sample per 68 km²), using the thermal needle method.

Determination of thermal conductivity of rocks

Thermal conductivity represents the numerical relationship between heat flow and temperature differences (Fig. 1). It is an intensive property, i.e., it does not depend on mass. Considering a cube of homogeneous material of side Δz with a temperature difference of ΔT between two opposite faces, the heat flow (q) through the cube from the face with the highest temperature to the coldest one is proportional to the quotient between the temperature difference and the distance between the faces (ΔT/Δz). The constant of proportionality is the thermal conductivity (k, in W m⁻¹ K⁻¹) (Chekhonin et al. 2012). Although the thermal conductivity varies considerably from one material to another, in the case of rocks there is usually not great variability; it usually ranges between 0.5 to 7 W m⁻¹ K⁻¹. The variability of thermal conductivity values in rocks and sediments depends on many factors, the three most important being: (i) mineralogical composition (i.e., silica content, so k is higher in rocks such as quartzites and quartz-arenites); (ii) porosity/density (related to age and depth); and (iii) degree of saturation (because k of water in the pores is higher than that of air).

Fig. 1

Definition of thermal conductivity (mod. Chekhonin et al. 2012)

Thermal rock properties are not easy to measure. Laboratory methods work with small samples, faster and with higher resolution than in situ methods, where thermal properties are measured along a borehole, showing more heterogeneity. Steady-state and transient methods can be used to measure thermal conductivity both in the laboratory and in situ (Thermal Response Test (TRT)). Optical scanning can be also employed to quantify thermal properties.

As far as laboratory methods are concerned, the divided-bar steady-state method is the standard technique for measuring rock samples. It obtains the thermal conductivity of a disc-shaped sample by placing it under pressure between two cylindrical metal plates held at a constant temperature. Discs of a reference material whose thermal conductivity is known flank the sample. When steady state is reached, the conductivity of the sample is obtained by comparing the temperature drop across its length with the drop across the reference material. This determination takes time to reach thermal equilibrium and it is particularly difficult to cut and polish the sample to ensure good contact between the bars, especially in poorly consolidated rocks (Chekhonin et al. 2012; Beck 1957). In laboratory transient methods, a heat pulse is applied to the sample, usually with a needle-shaped probe, recording the temperature response of the sample (typically with a sensor at the midpoint of the thin probe) as a function of time. The thermal conductivity is calculated from a theoretical model that predicts how the material should respond in that configuration. This type of method allows the determination of directional dependence, as the needle can be repositioned to change the direction of the measurement. Compared to steady-state methods, transient methods are faster and require less sample volume and lower temperature gradients. Optical scanning methods use remote optical thermal sensors to scan the sample surface for the thermal signature of a focused heat source (e.g., a laser light), which moves, together with the sensors, along the sample. The thermal conductivity below the scan line is calculated according to a theoretical model that predicts the temperature as a function of time or by comparing the temperature rise in the sample with that of a standard material of known conductivity, which is placed close to the scan line (Chekhonin et al. 2012). Finally, the thermal conductivity of a rock can also be determined as a function of its mineralogical composition, taking into account its porosity/density, organic matter content and degree of saturation. The conductivity of the matrix of a sample is estimated from the tabulated thermal conductivities of its mineralogical components, whose proportion can be determined, e.g., by optical microscopy. The effect of porosity and the pore-filling fluid must be taken into account (Andrés et al. 2016).

The TRT consists of introducing heat throughout a geothermal borehole for 48 to 72 h, in order to know the capacity of the ground to store and transmit the heat. Heating elements are generally used to produce thermal energy for the heat exchanger fluid, which is circulated in a heat exchanger pipe. Throughout this test, constant monitoring of the inlet and outlet temperatures to the geothermal exchanger, flow rate and power supplied over time, is maintained. The effective/weighted average thermal conductivity of the bedrock is obtained from these data as a function of depth, so it is feasible to size correctly the geothermal system according to the required demands. Compared to laboratory methods, TRT determination of the thermal conductivity is more expensive but more precise because it takes into account all the influencing factors along the length of the geothermal borehole, such as the different materials traversed, the filling material, the water table, etc. Notwithstanding, the determination of the thermal conductivity of the rock itself is affected by the effect of pore water and water advection on the efficiency of heat transfer, which can be relevant in fractured/permeable bedrocks (Hakala et al. 2022; GEOTER 2021).

In this work, the transient thermal needle probe method is applied to rock samples. The temperature variation is measured after applying a constant electrical current for a certain time to a metallic needle that is heated, embedded in the sample in a pre-drilled hole, and impregnated with thermal grease to reduce the contact resistance. The temperature variation is measured by means of a thermocouple, which is inside the needle, together with the heat source. The heating phase is followed by a cooling phase that lasts the same time. This method is used when conductivities are in the range of 0.01 to 6 W m⁻¹ K⁻¹, and temperatures usually between − 0 and 50 ºC. Among the advantages of the method is its speed, its relatively low cost and that it can be implemented using a portable device (Assael et al. 2010).

Area of study

Asturias is a traditionally industrial and mining region in NW Spain. It has no potential of geothermal medium–high enthalpy resources. However, shallow geothermal energy can be exploited by both vertical closed loop exchange systems in boreholes and open loop exchange systems using groundwater as an energy source, given the abundance of shallow aquifers (García de la Noceda 2020). This region has more than 10 MW of installed thermal capacity with about 300 geothermal installations (GEOPLAT 2021). The use of geothermal energy allows to give a second life to coal mines and to achieve the energy transition objectives, favoring the social-economic development of the region (Loredo et al. 2016, 2017). Domestic applications of geothermal energy are being developed in central Asturias, the most populated area, and in particular in the council of Oviedo, the capital of the region, with 220,000 inhabitants (21% of the regional population) and a surface area of 187 km². Although a map of surficial thermal potential (in W m⁻¹) is available for the whole region of Asturias (scale 1:200,000), which was deduced from the lithology of outcrops of geological materials (IDAE 2011), a thermal conductivity map has not been published yet.

Geology

The study area is located in the Cantabrian Zone, the outermost part of the Variscan orogenic mountain range. Figure 2 shows a geological map of the municipality of Oviedo, elaborated from the continuous digital map of Spain (GEODE 2023), indicating the outcropping lithostratigraphic units (from oldest to youngest) within its boundary. Three sets of sedimentary rocks can be distinguished, separated from each other by two unconformities. The basement, constituted by pre-Permian Palaeozoic rocks—occupies most of the municipality in surface extent—outcrops on the N, SE and SW edges. In the northern sector, the series comprising the Middle-Upper Devonian (Moniello limestones and Naranco Fe-rich sandstones), the Lower and Middle Carboniferous (Alba, Barcaliente and Valdeteja limestones) and the Upper Carboniferous (Folgueras and Carriles Groups, sets of shales, siltstones and sandstones with thin coal seams at the top) can be found. They are strongly folded, forming a synclinal structure that corresponds to the highest elevations (450–630 m a.s.l.) in the studied area. The SW sector is constituted by three folds (syncline–anticline–syncline SW–NE trending): synclines show the Carboniferous record, while the anticline is composed by the whole Devonian set (Rañeces Group—limestones, dolostones and marls and the above cited Moniello and Naranco Formations). Silurian and Ordovician rocks appear in a small area in the core of the anticline. Finally, the SE border combines a new syncline with the limestones of the Barcaliente Formation in the core and ample outcrops of the Devonian series in the limbs. This fold overlaps by means of a thrust the Westphalian sediments constituted by conglomerates (Olloniego) and microconglomeratic sandstones (Canales). Between the two unconformities, the Cretaceous series (green colors in the map) can be found. This period is represented by slightly less than 200 m of detrital sediments not completely lithified, among which are some limestone levels are interbedded, more frequently in the upper part. The Tertiary succession is formed by up to 200 m of alluvial and lacustrine facies (mostly clays and limestones, respectively), accumulated in a graben during the Paleogene. Quaternary age materials have been restricted to the alluvial deposits (flood plains) of the two main rivers: Nalón and Nora.

Fig. 2

Geological map and location of the 22 samples taken in the lithostratigraphic units of Oviedo (the 4 asterisked numbers designate samples taken in the indicated formation but outside the municipality of Oviedo)

Materials and methods

The lithostratigraphic units of Oviedo were sampled by selecting a representative sampling point where the formation was accessible and its location was recorded using a hand-held GPS (Fig. 2). Notwithstanding, four samples (#1, 2, 7 and 14) were taken in the corresponding formation but outside the boundary of the municipality of Oviedo, for accessibility reasons. The direction of stratification (S₀) was identified in the field. A total of 22 geological units were sampled, but in some cases (#5, 10, 15 and 26), two facies were sampled for each formation, which means a total of 26 samples (more than one sample per 10 km²). Unweathered rock samples of at least 20 cm × 20 cm × 20 cm were selected and taken to the laboratory at the University of Oviedo facilities. For non-cohesive Tertiary and Quaternary materials, measurements were performed in situ.

Transient line-heat source methods have been used to measure the thermal conductivity of porous materials for more than 60 years. Their limitations are related to the fragility of the probes, the variability of the ambient temperature, the relevance of the moist of the samples and the contact resistance between the probe and the material (e.g., the hole made for the probe often disturbs the surrounding material). To mitigate this, METER sensors are relatively large and robust, they keep heating times as short as possible (i.e., one minute) and limit the heat input. Short heating times and low heating rates requires high resolution temperature measurements (± 0.001 °C). The rate of temperature drift is determined (monitoring the probe temperature for 30 s) prior to the measurement to correct the reading for drift. The start temperature and the drift are then subtracted from the measurements (METER 2020).

The transient thermal needle probe method was applied to the samples using a TEMPOS thermal property analyser (METER). The probe consists of a needle with a heater and a temperature sensor inside. A constant electric current pass through the heater for 60 s and the sensor temperature is monitored over time (every second) during heating and cooling. The analysis of the time dependence of the temperature of the sensor, when the probe is in the material under test, determines the k. The TEMPOS controller can read different sensors. The RK-3 sensor, a single thick needle (60 mm long and 3.9 mm in diameter), measures thermal conductivity and thermal resistivity and is designed specifically for use in hard materials such as rock or cured concrete, where a 4 mm (5/32 in.) hammer bit can be used to drill a hole in the material. Before inserting the RK-3 sensor, which was impregnated with thermal grease Artic Silver 5 of high k, to ensure good thermal contact with the rock, any remaining dust or drill cuttings were blown out of the hole with compressed air. This sensor was used in most of the samples. Only in non-cohesive materials the sensor TR-3 (100 mm long, 2.4 mm in diameter), designed for soil and other granular or porous materials, was used (Fig. 3). This device conforms to the specifications for the Lab Probe called out by the IEEE 442-1981 (Guide for Soil Thermal Resistivity Measurements; IEEE 1981) and ASTM D5334 (Standard Test Method for Determination of Thermal Conductivity of Soiled and Soft Rock by Thermal Needle Probe Procedure; ASTM 2014) (METER 2020).

Fig. 3

Measurement of thermal conductivity by means of a Tempos thermal needle probe device on a boulder sample using a rock sensor (RK-3) and thermal grease (left) and on clayey alluvial sediments using a soil sensor (TR-3) in situ (right)

Two holes (60 mm long and 4 mm in diameter) were drilled manually in rock samples in the directions parallel and perpendicular to the stratification, leaving a security distance higher than 1.5 cm from all sides to avoid errors (METER 2020). Since the thermal conductivity of rocks (k) is a function of the nature of fluids filling the interstitial pores and fractures, rock samples were oven dried at 105 ºC for at least 24 h prior to the measurement of the thermal conductivity in homogeneous dry conditions. Water thermal conductivity is around 0.6 W m⁻¹ K⁻¹, whereas in the rocks it ranges from 0.5 to 6.5 W m⁻¹ K⁻¹, approximately (Chekhonin et al. 2012). The differences between measures in dry and saturated samples must be taken into account, particularly in those with high porosity. Stylianou et al. (2016) found that the k in saturated samples are higher or equal to that of the same samples when they are dry. Since void space, or air, has essentially zero thermal conductivity, saturated samples will have higher k than dry samples and it increases with the degree of saturation.

The temperature data obtained from probes were traditionally converted to thermal properties using an approximation to the solution for the infinite line-heat source equations, but this has not always worked well (Meng et al. 2023). Blackwell (1954) provided an exact solution for a finite diameter heated probe with contact resistance and Knight et al. (2012) implemented a method that transforms Blackwell’s solution to the time domain. This has been extensively used to produce improved algorithms for equipment like that used in this work, which is described below.

Considering the needle as a line-heat source, the simplified Eq. 1 could be used to predict its temperature for short heating times (60 s). This is the equation used in the ASTM/IEEE mode (ASTM 2014; IEEE 1981):

$$\Delta T= \left[\frac{q}{4\pi k}\right]{\text{ln}}\left(t+{t}_{0}\right)+C,$$

(1)

where $\Delta T$ is the temperature rise at the needle (°C), q is the heat input at the needle (W m⁻¹), k is the thermal conductivity (W m⁻¹ K⁻¹), t is time (s), and t₀ is a time offset (s).

The starting temperature and drift are subtracted from the temperatures giving the $\Delta T$ values. Since the values of q and t are known, the values of k, t₀ and C are determined by least squares or by a different iterative method, so t₀ is the one that minimizes the standard error of estimate. Conductivity is proportional to the inverse of the slope when temperature is plotted versus ln t (METER 2020).

The analyser provides the standard error (Syx) of the estimate, as a measure of goodness-of-fit used in a least squares analysis. It is an error term that quantifies how well the regression line fits the data. Syx does not indicate how close the result is to the real value, because this is unknown, but it indicates how close a theoretical heating curve can be matched to the measured heating curve (a lower Syx is a closer match). Syx therefore gives an idea of the degree of confidence of the answer, although even if Syx is higher, the result may still be accurate.

Three measurements were made on each hole (a total of 6 in each sample), leaving at least 15 min between measurements, to ensure cooling of the needle. The relative standard deviation (RSD) was calculated in all cases. The k in each of the two directions (parallel and perpendicular to the stratification) was obtained as the arithmetic mean of the three measurements and the global value of k as the mean of the previously obtained values in both directions. In the case of the existence of two different facies for the same formation, we proceeded in the same way with each of the samples and the global k was obtained as a weighted average with the relative abundance of each of the facies with respect to the total.

Finally, using a Geographic Information System (GIS), the calculated mean values of thermal conductivity for each geological formation were plotted to create a map.

Results and discussion

Compared to previous studies, this work stands out for its higher density of sampling points and for the original fact of making measurements in two directions with respect to the stratification of the rocks, which allows the influence of anisotropy to be assessed, as well as for including the comparison with TRT data. Table 1 shows the coordinates and the formation of each sample, as well as the mean thermal conductivity obtained for each direction and the global values assigned to the corresponding formation. The lowest thermal conductivities in the council of Oviedo are in the order of 0.2 W m⁻¹ K⁻¹ in formations such as the Nora River alluvial (Quaternary) and the Tertiary of Oviedo and the highest values reach a maximum of 5.35 W m⁻¹ K⁻¹ (Barrios quartzite), followed by the sandstone of the Paquete Canales (4.98 W m⁻¹ K⁻¹). During the measurements, the average applied power was 5.02 W m⁻¹ and the mean heating velocity was 1.27 °C min⁻¹. The measured resistivity ranged from 18 (quartzite) to 866 (clay) Rho (°C cm W⁻¹) and the S_yx error varied from 0.01 to 0.73%, with an average of 0.16% (70.4% of the measurements have a S_yx < 0.2%). The RSD of the measurements made on the same sample is below 2.2% in all cases and 67% of the cases have a RSD of less than 1%, indicating a high repeatability, considering the accuracy of the equipment (10%).

Table 1 Final values of thermal conductivity obtained for each sample

Lithology

Figure 4 shows three groups of samples, according to their lithology. The most common lithology (52% of the samples) are the limestones and their thermal conductivity vary between 1.14 and 2.95 W m⁻¹ K⁻¹, with an average of 2.25 W m⁻¹ K⁻¹. Fine-grained rocks, such as clays and shales, have a lower thermal conductivity, averaging 0.85 W m⁻¹ K⁻¹. The highest values are recorded in rocks with higher silica content, such as sandstones and quartzites that exceed 5 W m⁻¹ K⁻¹, although they show a higher variability (average of 3.61 W m⁻¹ K⁻¹). Within this group, 2 subgroups are separated: (i) quartz-arenites (samples 1, 3, 6 and 12), with the highest conductivities, and (ii) alternating sequences of conglomerates, sandstones, graywackes and siltstones (samples 10a, 11, 13 and 14), in which the silty horizons and matrix tend to generally decrease the conductivity value. It must be noted the high content of Fe₂O₃ in samples 3 (oolitic texture) and 6 (haematitic cement), that might exert some positive influence on the k values.

Fig. 4

Grouping of thermal conductivity values of samples according to their lithology

Age

Stylianou et al. (2016) studied the possible relationship between thermal conductivity and the geological age of rocks, analyzing samples of the same lithology but of different ages, and concluded that this property increases with the geological age of the formation. In this work, among the limestones, sample 20b from the Tertiary of Oviedo, has the lowest thermal conductivity and is also the youngest in age, whereas sample 8, from the Barcaliente Formation, has the highest k. This formation is one of the oldest, as well as the Alba and the Valdeteja Formations (samples 7 and 9, respectively), which also have a high thermal conductivity. Regarding the fine-grained lithology, the Quaternary clay of the alluvial of the Nora River (21) and the Tertiary clays of Oviedo (20a) are the formations with the lowest thermal conductivity of the whole series. These are the youngest of those sampled, together with the alluvial sediments of the Nalón River (22), but this presents conglomeratic facies and thus a higher k. The maximum is reached in sample 2 from the Formigoso Formation (the oldest rock of this group) with a thermal conductivity of 1.6 W m⁻¹ K⁻¹. With respect to quartz-rich clastic rocks, sample 1 from the Barrios Formation, of Ordovician age (the oldest of this group and the whole series) has the highest conductivity. Samples 3 (Silurian) and 6 (Devonian) are the following in age and they also have high k, whereas samples 10a, 11 (Upper Carboniferous) and 14 (Cretaceous) show lower values. Although it is not a fixed rule, some relationship can be inferred between the thermal conductivity of rocks and their geological age, since for similar lithologies, older formations tend to have a higher thermal conductivity than younger ones, probably because with the age, sediments become more dense and less porous (generally due to a greater burial under sediments) so this evolution increases the thermal conductivity.

Anisotropy

Thermal conductivity of rocks is closely related to their texture, structure and mineral composition, so it shows anisotropy in space (heat flows preferentially in certain directions). This property of the rocks varies according to their difference in abundance and spatial arrangement of minerals, the laminated structure or stratification (sedimentary rocks) and the fracturing or planar fabric due to compression (igneous and metamorphic rocks), etc. (Wang et al. 2021). Although in some studies and numerical simulations the thermal conductivity of rocks is considered to be isotropic for simplicity (Zhang et al. 2019), it must be noted that this hypothesis might not fully reflect the actual heat transfer processes in the rock mass (Wang et al. 2021). The most common type of thermal anisotropy in rocks is observed when they have a layered/stratified structure: the thermal conductivity in the direction perpendicular to the bedding is generally lower than the conductivity in any direction parallel to it. In finely layered rocks, the value in the direction perpendicular to the layers is usually 5 to 30% (up to 50% in some cases) lower than its value in directions parallel to them (Chekhonin et al. 2012). It should be taken into account that when the determination is made with a needle inside a hole in the rock, the thermal conductivity in the direction parallel to the stratification is obtained by measuring in a hole perpendicular to it and vice versa (Fig. 5).

Fig. 5

Propagation of heat from the thermal needle probe in the rock, in relation to stratification

In this case, comparing the pairs of conductivities measured in both directions for each sample, it is observed that the average tendency is for the thermal conductivity to be quite similar in both, although in general slightly higher when measured in the direction parallel to the stratification. This could be due to the fact that in the perpendicular direction the bedding planes (weak and less dense zones) exert some resistance to the passage of heat, thus decreasing the thermal conductivity of the samples, as indicated in Fig. 5. The thermal conductivity in the direction parallel to the stratification of the rocks is—on average—16% higher than the thermal conductivity in the direction perpendicular to it. The quotient of the k in the direction parallel to the stratification k and that measured in the direction perpendicular varies between 0.95 (limestone from Otero-Las Tercias Formation) and 1.83 (Nora River alluvial) (Fig. 6).

Fig. 6

Relation between the k measured in the direction of stratification and the k measured in the direction perpendicular to the stratification

Comparison to TRT

According to Sáez et al. (2017), there is a high correlation between shallow and deep materials, so the results obtained in outcropping samples are useful to be considered, e.g., for a geothermal well, although less accurate than those obtained with a TRT. The thermal conductivity data from the TRT performed in four vertical geothermal boreholes were provided by the geothermal companies INGEO and GEOKI. Two of these boreholes are located in Oviedo and the other two in other councils, but the materials traversed in them are equivalent (in lithology and age) to the formations measured in Oviedo (Table 2). When performing a TRT the thermal conductivity of the entire series crossed is measured by a single value, so for comparative purposes the materials crossed by each of the boreholes must be known. Assigning to each section the values determined in this work and calculating weighted averages with the mentioned thicknesses, the average thermal conductivities are obtained for every well (Table 2). These values are lower than those obtained experimentally with the TRT and there are several reasons that may explain this mismatch. First, there may be deficiencies in the knowledge of the actual column traversed in each borehole and differences between the outcropping and the deep rocks, e.g., there are lateral facies changes in the Tertiary, which becomes more marly at depth. But the most notable differences are due to the effect of the annular space filling of the borehole prior to TRT and the effect of the saturation of the materials in situ. The TRT is carried out after the borehole has been drilled and conditioned for the future geothermal installation, which means that the annular space between the probe and the ground is filled with siliceous gravel/geothermal mortar about 20 cm thick; given the high conductivity of this fill, it is expected to record an average thermal conductivity higher than that of the ground without such fill. On the other hand, the water inside pores or fractures (degree of saturation) might cause the same effect. The thermal conductivity of the traversed rocks on a drilled well can be measured experimentally, e.g., from core samples taken during drilling, but this does not provide information on bedrock faults or water-saturated layers, so the k is usually higher during a TRT due to the advection of water. The enhanced TRT (fiber optic method combined with TRT) might provide an indication of how much thermal conductivity is increased by water advection in fractures (Hakala et al. 2022). In addition, in loose sediments, when a sample is extracted from the ground, its real density is modified. Unfortunately, TRT in Asturias is not often performed and few data are available. Access to more TRT data from deep wells would be desirable in order to compare them with the measured values, but it should not be forgotten that the thermal conductivity values obtained in this work correspond to outcrop and dry samples, so they are not easily extrapolable at depth (precise determinations of porosity and saturation conditions at depth would be necessary). However, they are very useful for establishing surface values and comparing the different formations.

Table 2 Comparison of the average k values obtained in situ by TRT and those calculated as a weighted average of the k values of the materials traversed

As mentioned above, a meticulous design of a geothermal system requires careful consideration, a key factor being the thermal conductivity of the ground at the intended installation site. Accurate determination of this parameter is achieved by means of a TRT, but performing this test significantly increases the implementation costs of geothermal projects, which is affordable for large-scale projects, but could make smaller installations financially unfeasible. When a TRT is not carried out, it is common to assume the worst case scenario, where the thermal conductivity of the rock is often considered at its minimum value according to theoretical tables, thus unnecessarily inflating the capacities of the heat pumps and consequently the project budget (Sáez et al. 2017). This circumstance, together with the lack of information about this technology, may be the reason why geothermal installations are not carried out more frequently and on a large scale in Spain and particularly in Asturias. In that sense, local maps of thermal conductivity might be very useful.

Thermal conductivity map

The thermal properties of each type of rock may vary according to their place of origin, and generalizations cannot be made based on specific measured values from a particular area (Stylianou et al. 2016). Therefore, it would be desirable for those responsible for implementing geothermal systems to have access to site-specific maps of thermal conductivity as a starting point to assist them in their decision-making process. A thermal conductivity map of Oviedo was created using QGIS (Fig. 7). As mentioned above, this map is a valuable tool for the selection of the most favorable location of a very low temperature geothermal installation. It becomes a good starting point in the knowledge of the terrain, as well as a significant reduction in the installation budget and an improvement in the efficiency of the installation if a TRT is not performed, so it should be publicly available. As it was previously stated, the values represented correspond to outcrop samples. In the same way that a geological map shows the lithologies at surface, but a geological section is necessary to know their arrangement in the subsurface, the extrapolation of thermal conductivity values at depth (e.g., in a geothermal borehole) requires knowledge of the stratigraphic column traversed by the borehole. Knowing the formations traversed and their thicknesses, as well as the moisture content (since saturation of the materials can significantly increase the thermal conductivity), a conservative average estimate of the borehole thermal conductivity could be made, avoiding the need to perform a costly TRT. However, this test, performed in situ, will always be the most reliable tool to determine the thermal conductivity of a geothermal borehole.

Fig. 7

Thermal conductivity map of the outcropping geological formations in the municipality of Oviedo

Figure 7 shows that the center of the city of Oviedo (mostly Tertiary), marked with a circle in Fig. 2, is not the ideal location for a geothermal installation, since the Tertiary has very low k and it is not an aquifer but an aquitard. For example, thanks to the urban alluvial aquifer in Zaragoza (Spain), the city center shows an outstanding development of shallow geothermal energy systems (García et al. 2022), but this is not the case in Oviedo. Thus, in terms of thermal conductivity of the rocks, it seems preferable to select the areas located to the N or the SW of the city (Devonian), as well as the SE (Carboniferous), with a higher thermal conductivity.

Conclusions

The adequate exploitation of low-enthalpy geothermal resources requires knowledge of the thermal properties of the ground, such as thermal conductivity. For achieving this, the best option is to carry out a thermal response test (TRT) in situ. However, this test involves high costs associated with borehole drilling, etc., and it is not rare that for small projects, standardized values of this property are usually taken by default. This assumption might imply an inadequate design and oversizing of the installation, often unnecessarily increasing costs, since the specific values for the particular geological formation are unknown. Therefore, tools such as a map of thermal conductivities would favor decision-making within a geothermal project.

In this work, the transient thermal needle probe method was applied to samples of the lithostratigraphic units of Oviedo, and an average value of 2.4 W m⁻¹ K⁻¹ was obtained for these rocks, ranging from 0.2 (clays) to 5.4 W m⁻¹ K⁻¹ (quartzites), since the thermal conductivity follows the following order according to lithology: siliciclastic rocks > limestones > fine-grained detrital rocks. It seems that there is a relationship between the thermal conductivity of the rocks and their geological age, since in general, for the same lithology, the rocks with the lowest conductivity are the youngest and those of older age are more conductive. Notwithstanding the features that influence most are the mineralogy and the texture. The thermal conductivity in the direction parallel to the bedding of the rock is generally slightly higher than the conductivity in a direction perpendicular to it (anisotropy), because heat conduction is favored in the directions of the stratification planes.

From the average values obtained for each formation, a thermal conductivity map of Oviedo has been made. This map provides valuable information, not available until now, useful for the preliminary design of a very low enthalpy geothermal installation in this area.