National Technical University of Athens

The thermal conductivity of underground formations is particularly the measurement of their ability to heat transfer. Its determination is critical parameter in the design of several technical projects where heat transfer in soil takes place such as shallow geothermal systems, construction of buried pipes and high voltage cables in the ground.

Several researchers (De Vries, 1963, Tarnawski, 2000) have shown that thermal conductivity of soil, k, (W/(m.K)) depends on numerous parameters such as mineralogical composition, grain size of soil and physical properties as moisture content (w, %), dry density (pd, gr/cm3) and saturation (Sr, %). It is experimentally and theoretical shown that these parameters have an influence on the electrical resistivity (ρ, Ω.m) (Archie, 1942). The fact that both thermal conductivity and electrical resistivity depend on the same parameters, indicates the possibility of their interrelation.

The objective of our research is the investigation (qualitatively and quantitatively) of the influence of the soil physical parameters on thermal conductivity (k) and electrical resistivity (ρ) and thedevelopment of an expression that can be used to relate electrical resistivity tomography and geotechnical data to produce soil thermal conductivity profiles.

In order to achieve the abovementioned goal, a series of experiments have been performed during which k and ρ values of nine different soil types (of known mineralogical composition and grain size distribution) were measured while varying moisture and dry density. The experimental procedure and the results are presented in this study.

soil type /% mineralogy composition Kaol CSi SiL L SL LS Sf Sm Sc

Ca (Calcite) - 53 55 60 62 65 45 80 87Dol (Dolomite) 0 1 2 2 5 3

Qz (Quartz) 5 25 23 20 18 17 30 5 3Fd (Feldspar) 5 5 6 6 6 13 0 3

Mi- C (Ilites, Moscovian, Clorite, Kaolinite in case of

Kaol) 95 17 16 13 12 11 12 10 4Gs 2.53 2.64 2.64 2.65 2.66 2.66 2.66 2.67 2.67

Main Concept: Simultaneous measurement of thermal conductivity and electrical resistivity of model soil samples of known mineralogicalcomposition and grain size for different values of moisture [w%], dry density [pd gr/cm3] and, consequently, different Sr [%].

Four different grain size material-coarse, medium, fine sands and siltyclays- either plain or in predeterminedproportions - where used to generatethe soil samples.

Mixing and compaction different grain size soils, in varyingmoisture values according to the standard Proctor test (ASTM).The selected method ensures dimensions (diameter 10.1 cm height11.6cm) and homogeneity of samples suitable for the measurementof the thermal conductivity and electrical resistivity.[9 soil type – 79 soil samples]

1. Grain size distribution [diagram 1] (ASTM sieves, Stoke Methodfor estimating clay fraction)

2. Specific weight: density meter method3. Semi quantitative composition of soil (XRD, DTA, XRF) [table 1]4. Moisture and Dry Density measurement of samples

Table 1. Semi quantitative mineral composition and specific weight of each soil model.

[ Diagram 1. Grain size distribution curve ]

[ Diagram 2. Effect of electrodes length on electrical resistivity measurement ]

The measurement of resistance and consequently of resistivity is dependent on the distance ofelectrodes between each other and from the walls of the sample and on the depth of theelectrode in the soil (Bristow, 2001). In order to control this dependence an additional experimentwas performed. We firstly measure resistivity applying Wenner array in a small tank (30cmdiameter and 20cm height) with water of resistivity 11.6 Ω.m using various electrode distances (D= 2, 3, 4 and 5cm) and depths of electrodes in the water (h= 0, 0.5, 1, 1.5, 2 and 2.5cm). Then weput a plastic tube (10cm diameter and 20cm height) in the tank to simulate the dimensions of oursamples and inside the tube we measure resistivity applying Wenner array with electrodedistances (D = 1 and 2cm) and depths of electrodes in the water (h= 0, 0.5, 1, 1.5, 2 και 2.5cm).The effect of both the distance of electrodes between each other and their depth inside themedium are shown on Diagram 2. We decided to use electrode distance, D=2cm and depth of theelectrode in the soil, h=1cm. A correction factor F=0.98 in the output of eq. 1 was also applied.

Introduction

Material Soil Sample Generation Soil Sample’s Physical Properties measurements

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Thermal Conductivity Measurement:Based on the heat line source theory in infinite medium. Instrument: Anter QL 30 [ASTM D-5930 and D 5334]

Electrical Resistivity Measurement:Wenner electrode array with 4 equidistant copper electrodes. Instrument ABEM SAS300, 0.2mA current

• 72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010. Barcelona, Spain, 14 - 17 June 2010

Grain size distribution curve

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Thermal conductivity and electrical resistivitymeasurements cover a saturation rangebetween approximately zero value (dry soils) and92% (almost saturated soils). Greater saturationvalues could not be achieved under the chosencompaction method. The number of soilsamples was 79, representing nine soil type.

ReferencesDe-Vries. (1963). Thermal Properties of soil. In V. W. Wijk (Ed.), In Physics of Plant Enviroment. Amsterdam: North Holland Publishing Company, 210-235.

Tarnawski, V., Gori, F., Wagner, B., & Buchan, G. (2000). Modelling approaches to predicting thermal conductivtiy of soil at high temperature. International J Energy Res (24), 403-423.

Archie, G.E. (1942). The electrical resistivity log as an aid in determining some reservoir characteristics. Petroleum Transactions American Institute of Mining. Metallurgical, and Petroleum Engineers 146, 54–62.

Cook H. et al. (1980). Deep Sea drilling project. Initial Reports. University of California.

Bristow, K. L., Kluitenberg, G. J., Goding, C. J, Fitzgerald, T. S. (2001). A small multi-needle probe for measuring soil thermal properties, water content and electrical conductivity. Computers and Electronics in Agriculture, 265-280.

The maximum experimental values of thermal conductivity are asfollows: 2.19 W/m.K (loamy-sand-LS soil), 2.1 W/m.K (sandy-loam-SL), 1.91 W/m.K (kaolinite-Kaol), 1.83 W/m.K (loam-L), 1.77 W/m.K(sand-fine-Sf), 1.75 W/m.K, (sand-medium-Sm) , 1.6 W/m.K (sand-coarse-Sc), 1.46 W/m.K (silty-loam-SiL) and 1.34 W/m.K for theclay-silt (CSi) soil type. The above measurements are obtained atsaturations that correspond to the maximum accomplished drydensity values according to the experimental procedure.

Clay-silty soil sample provide the lower electricalresistivity value (8.35 Ω.m) under a saturation ofapproximately 80%. In the maximum saturation foreach type of soil the minimum resistivity values are:11.7 Ω.m for silty-loam (Si-L), 19.6 Ω.m for sandy-loam(SL), 23 Ω.m for loamy-sand (LS) and kaolinite (Kaol), 30Ω.m for Sand F and Sand M and 127 Ω.m for Sand C.

Thermal conductivity increases until a certain value of saturationthat differs with the granular range of the sample. The rate ofincrease is high until saturation values of 20-30% and then itbecomes lower up to a certain saturation where thermalconductivity values seem to be stabilized. As the grain sizedecreases, the value of saturation with the highest thermalconductivity increases. [Figure 1]

Generally we can observe a similarity among thermal and electrical conductivity (inverse of resistivity, ρ)with increasing saturation which can be interpreted by the increasing presence of water over the air in thepore space that facilitates thermal and current transportation.

Furthermore it was found that thermal conductivity of soil, has similar variation either versus saturation ordimensionless values of ρw/ρmeas [Figure 3]. Consequently, if the thermal conductivity can be expressed asfunction of saturation, it can be expressed as function of ρw/ρmeas as well.

According to the above observations a correlation between the variation of thermal conductivity andelectrical resistivity can be established.

A relation between electrical resistivity and thermalconductivity of soil was examined using thecorrelation between the dimensionless values ofexp[(kexp.ρw)/(ks.ρmeas)] and (ρw/ρmeas), where kexp is themeasured thermal conductivity of soil, ks is the thermalconductivity of solid minerals, ρw and ρmeas themeasured electrical resistivity of water and soilrespectively [Figure 4]. The values of thermalconductivity of solid minerals, ks, have been calculatedby using characteristic values ksi for each i mineral, asproposed by Tarnawski et al. (2000), as well as the semiquantitative mineral composition of soil, as representedon Table 1. All plots (Figure 3, Diagram 1,2,3) lead to ageneral semi-empirical correlation between kexp andρmeas for saturation greater than 15% [eq. 1], where αand b are constant parameters dependent onsize, shape and other physical properties of grainswhich are known for the type of soils we haveexamined.

At the present time, it is a subject of further research exploring various models of k and ρ, in order to refine the above relation for thedevelopment of robust model for the prediction of thermal conductivity of soils from electrical resistivity values.

• 72nd EAGE Conference & Exhibition incorporating SPE EUROPEC 2010. Barcelona, Spain, 14 - 17 June 2010

[Figure 4. Correlation of thermal conductivity and electrical resistivity of soils]

[Figure3. Variation of Thermal Conductivity of Loam vs Saturation (yellow line) and ρw/ρmeas (blue line) ]

[Figure 2. Variation of electrical resistivity of soils vs Saturation]

[ Figure 1. Variation of thermal conductivity of soils vs Saturation ]

1) 2) 3)

Comparing changes for Kaolinite and CSi, though the samples thathave similar granular composition and maximum thermalconductivity in the same saturation value, we observe differentvalues of k in the whole range of Sr

, mainly because of the differentmineral composition. [Figure 1- diagram 1]

The Figure 2 shows an inverse shape of the electrical resistivitycurves. The value of saturation where resistivity stabilizes is identicalto that of thermal conductivity and it also depends on soil type.

The stabilized resistivity in fine grains (C-Si, Si-L) becomes 8-11Ω.m[Fig 2- Diagram 1], in Kaol 23Ω.m, in mixed grains (SL, LS, L) 19-22Ω.m [Fig 2- Diagram 2], in sand fine and sand medium 30Ω.m and insand coarse >100 Ω.m [Fig 2- Diagram 3]

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Electrical Resistivity vs Saturation Electrical Resistivity vs Saturation Electrical Resistivity vs Saturation

Saturation [%] Saturation [%]Saturation [%]

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Thermal Conductivity vs Saturation Thermal Conductivity vs Saturation Thermal Conductivity vs Saturation