Effects of temperature, test duration and heat flux in thermal conductivity measurements under transient conditions in dry and fully saturated states

. In shallow geothermal energy systems (SGES) thermal conduction can be considered the dominant process in the heat transfer between the primary circuit (borehole heat exchanger or thermoactive geostructure) and the surrounding ground. Thus, a proper characterization of soil thermal properties, namely of its thermal conductivity, is mandatory for evaluating this energy exchange. There are difficulties associated to the assessment of soil thermal conductivity by laboratory methods related, among other factors, to the samples’ quality and to the measuring method itself. The purpose of this work is to analyse the effect of changing test control parameters in thermal conductivity measurements in transient conditions by means of a high accuracy thermal probe in both dry and fully saturated states. In order to eliminate potential measurements’ deviations and errors due to sample variability the same reconstituted samples were used several times. In each condition the sand samples were systematically tested under different ambient temperatures (10ºC, 20ºC, and 40ºC) controlled by means of a climatic chamber. The effects of changing the tests heating time and imposed thermal fluxes were also analysed.


Introduction
With the inflation of global population and consequently the increase in energy demand, local low-enthalpy geothermal energy sources are becoming a crucial matter of interest [1] for building acclimatization. Shallow geothermal energy systems (SGES), which are commonly known as Ground Source Heat Pump systems (GSHP), use the nearly steady temperature of the ground surface layers as an energy source and/or an energy sink in both heating and cooling modes [2]. Such systems have shown to be sustainable alternatives for buildings acclimatization when compared with conventional airconditioning systems [3].
SGES energy efficiency is highly dependent on the thermal energy transfer between the surface soil layers and the energy geostructure embedded within it. This heat transfer process is led by conduction due to an imposed temperature gradient occurring between soil and the geostructure (primary circuit of the GSHP) [4]. Hence, the evaluation of soil thermal properties, namely its thermal conductivity, is of major importance in analysing the heat transfer process [5].
Thermal conductivity, Ȝ (W/(m.K)), is a physical property that measures the material capability to conduct heat [6]. According to Fourier´s law of heat conduction (Eq. 1), the heat flow rate vector (W/m 2 ) for a given temperature gradient ߘܶ in (ºC/m) is directly proportional to Ȝ [7]: Soil is a three-phase system consisting of solid particles and voids containing water and/or air. Its global thermal conductivity depends on thermal conductivity of each phase (solid, liquid and gas), as well as on its corresponding volumetric fraction and spatial arrangement [8].
Grain size distribution, mineralogy, relative density and moisture content, among others, are important factors affecting the thermal conductivity [9]. Several studies [e.g. 10 -12] have shown the major influence of soil water content on thermal conductivity, and consequently on the heat transfer on the primary circuit.
Thermal conductivity Ȝ can be measured in the laboratory by means of several techniques, which can be divided into two large groups; (i) steady-state methods and (ii) transient methods [6]. In steady-state methods thermal properties are measured by establishing a temperature gradient across the sample that does not change over time, while in transient methods the timedependent heat dissipation is monitored. Steady-state E3S Web of Conferences 195, 04007 (2020) E-UNSAT 2020 https://doi.org/10.1051/e3sconf/202019504007 methods tend to be more accurate, how soils, there is a relatively little e assumption. Transient methods tend to and rapid when compared with stead avoiding water migration in the sampl measured value. Whereas, steady-stat longer measurement durations allow a temperature gradient in the soil samp repeatable values [13]. Nevertheless, d between different methods requires analysing undisturbed soil samples co same place under the same conditions ( density, soil composition, soil structure All these factors make therm measurement and comparison by techniques in a challenging process.
This paper presents part of a prelim the study of the factors affecting Ȝ me transient conditions. For this purp determinations of thermal conductivi samples were carried out in both dry an situations and under different tempe conditions, ranging between 10ºC a values were considered the threshold the primary circuit of a SGES locate Aveiro, Portugal. The impact of the a was also tested, as well as the effect o the test heating time, which has varied b 1000s.
The hot line source transient method experiments. With this method a therma inserted in the soil sample.

Transient test method
The needle probe method is based assumption of a radial heat flow of a l of infinite length and infinitesimal isotropic and homogeneous medium. W current of constant intensity passes th probe (heat source or hot wire), the ther of the sample can be derived fro temperature change at a certain distan wire over a specific time interval.
Hence, the analytical solution (line of soil thermal conductivity obtained b flux ܳ (W/m) during a heating time ‫ݐ‬ (s with radius ‫ݎ‬ (m) can be expressed i temperature gradient οܶ (ºC/m) occu sample as follows [14]: temperature rises , respectively.

Testing device
The equipment used in this TPSYS02 system supplied equipment can measure therm of a thermal probe. TP02 t length and 1.5mm diameter. I of ߣ within the range of 0 accuracy (±0.02 W/mK). A scheme of the thermal pro where: (1) reference temper wire; (3) hot joint where T_ joint measuring T_cold; (5) p needle with the MCU; (6) 10 the sensor is located.  The sample with higher vo compacted) was also tested un ߣ measurements were car samples, allowing a direct conductivities in dry and sat same test conditions. By usin same solid particles structure effect of the test variables.
ASTM D 5334 -08 standa a minimum diameter of the re s study to measure Ȝ is by Hukseflux [15]. This mal conductivity by means thermal probe, is 150mm t enables the measurement .1-6 W/(m.K)] with high obe is shown in Figure 1, rature sensor, (2) heating _hot is measured; (4) cold plastic wire connecting the 0mm base diameter, where ents [15] and fully saturated) cted to perform systematic ements. This reference soil ch grain-size distribution is imum (17.20 kN/m 3 ) and volumetric weights were D 4253-00 standard [16]. sample of 51 mm was used. The equipment recommends that the sampl should not be less than 15 times the nee which is equivalent to 22.5mm, for t (1.5mm of diameter). Therefore, a me 50mm diameter was selected. The leng recipient should permit the insertion of in the soil sample, which in this case im 200 ±30 mm. Hence, a 210mm heig selected.
Each soil sample was tested under s ambient temperature conditions. These applied by means of a climatic cham Experiments performed in dry and satur were carried out under three amb conditions: 10, 20 and 40ºC. The selection was based on the anticipated S temperatures. Before the heat injection the therm was inserted in the centre of the samp was placed inside the climatic ch prescribed ambient temperature. T monitored until its temperature, registe thermocouples, equalized the one m climatic chamber. At that instant the so thermal equilibrium with the interior chamber.

Test measurement series
Thermal conductivity measurements we the two specimens of Fontainebleau above. By testing systematically the tw controlled temperature and satura uncertainties related to heterogeneities a minimized.
For each sample, a series of th executed. For each series several tests changing control parameters as describe The effect of ambient temper condition was tested by applying tempe and 40ºC. This condition was control before, by a climatic chamber. For temperature a new thermal equilibrium climatic chamber was attained after som minimum). The time elapsed to achi equilibrium depended on the specimen More time was required in the s particularly for the highest temperatur manual of the e recipient radius edle probe radius, the case of TP02 etal recipient with gth (height) of the f the entire needle mplies a length of ght recipient was strictly controlled e conditions were mber (Figure 3

Effect of heating temperature
The first variables analysed w boundary (ambient) temperat were analysed for the two se dry conditions. Thereby the ef was also accounted for.
An initial test series w reconstituted sand sample w 15.35 kN/m 3   ll the variables affect the conductivity. It is clearly with increasing ambient n. It is also noted that it ter a limited period of time. The effect of the relative density is, as expected, significant. Obviously, the reduction of the sample voids, results in higher conductivity. Thermal conductivity ɉ varied 20%, for e=0.85, and 27%, for e=0.70, taking as reference value the minimum ɉ.

Effect of heating time, ambient temperature and heat flux (dry sample, intermediate density)
For the dry sample with intermediate density the effect of changing the magnitude of the heat flux was also tested. Therefore, for the same sample a new series of tests was performed for the same values of the test duration and ambient temperature. In Figure 5 are shown ߣ measurements for the three test variables considered (t, T, Q). For the same test conditions, an increase in the applied heat flux resulted in higher thermal conductivity values. Additionally, under a heat flux of Q=2.49 W/m, in the same sand sample, the same trends as the ones described previously, were observed, namely: an increase of ߣ with the heating time (100, 250, 500, and 1000s) and with the climatic chamber temperature (10, 20, and 40ºC).
The thermal conductivity values ranged in dry state between 0.22W/(m.K) for variables (t, T, Q): (100s, 10ºC, 0.85 W/m) and 0.29W/(m.K) for (1000s, 40ºC, 2.49 W/m). This increase in the measured value of ߣ has reached a relative difference of 31,8%. The relation obtained between thermal conductivity and heating time tends to be a logarithmic regression with R-squared values ranging between 0.944 and 0.968.

Effect of heating time and ambient temperature (dry and fully saturated sample, intermediate density)
The dry sample of intermediate density (e=0.7) was immersed in water until achieving fully saturated conditions. Thermal conductivity measurements were performed in the fully saturated state, changing the tests ambient temperature and heat duration time, for the same values as in the previous series. As the same sample was used a direct comparison between dry and saturated states is allowed. Figure 6 shows the values of thermal conductivity measurements at both dry and saturated states. As expected, the differences are very significant, reaching an increase of more than 10 times in the thermal conductivity of the same sample under the same temperature boundary condition.
Globally the same trends were observed in the saturated sample, i.e., under an increase in temperature and in the test time duration, a higher thermal conductivity estimate is obtained by this method.

Conclusions
This preliminary study has presented thermal conductivity measurements using a non-steady-state method by means of a thermal probe. The experiments carried out in Fontainebleau sand samples in both dry and fully saturated conditions have shown a clear dependence of Ȝ on the sample state and test variables considered in this study.
Experiments have been performed under three temperature ambient controlled conditions similar to the ones anticipated in the ground where a SGES is embedded. By testing systematically the same sample, the effect of heterogeneity is eliminated and the differences obtained are a direct result of the change in test control parameters. The main conclusions of the performed tested series, are that ߣ increaseds with increasing test temperature and heat flux under both saturation states. The effect of the test heating time was also significant. The major differences were obtained under fully saturated conditions, where the ߣ measured relative to the minimum value have varied as much as 39%. Those differences in thermal conductivity values could be due to air or water convection in the soil voids and/or to the underlying theoretical model approximation.