Annals of Nuclear Energy 94 (2016) 848–855
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Thermal conductivity of compacted bentonite as a buffer material for a high-level radioactive waste repository Jae Owan Lee ⇑, Heuijoo Choi, Jong Youl Lee Korea Atomic Energy Research Institute, 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-600, Republic of Korea
a r t i c l e
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Article history: Received 21 July 2015 Received in revised form 29 April 2016 Accepted 30 April 2016 Available online 7 May 2016 Keywords: Thermal conductivity Compacted bentonite Buffer High-level waste repository
a b s t r a c t Bentonite buffer is one of the major barrier components of a high-level radioactive waste (HLW) repository, and the thermal conductivity of the bentonite buffer is a key parameter for the thermal performance assessment of the HLW repository. This study measured the thermal conductivity of compacted bentonite as a buffer material and investigated its dependence upon various disposal conditions: the dry density, water content, anisotropic structure of the compacted bentonite, and temperature. The measurement results showed that the thermal conductivity was significantly influenced by the water content and dry density of the compacted bentonite, while there was not a significant variation with respect to the temperature. The anisotropy of the thermal conductivity had a negligible variation for an increasing dry density. The present study also proposed a geometric mean model of thermal conductivity which best fits the experimental data. Ó 2016 Elsevier Ltd. All rights reserved.
1. Introduction A high-level radioactive waste (HLW) repository in Korea will be constructed in bedrock several hundred meters below the ground surface. According the present design concept of the repository (Choi et al., 2008), it will be of a room-and-pillar design with vertical shafts extending from the ground surface to the access tunnels. The high-level waste, which is encapsulated in a canister, is deposited in an array of large-diameter boreholes (/ 2.24 m) drilled into the floors of the disposal rooms, and after emplacement of the container, the gap between the canister and the wall of the borehole is filled with a compacted bentonite. When all the boreholes in a disposal room are filled, then the room is backfilled with a compacted bentonite–sand mixture. One of the major functions of the bentonite buffer in the repository is to dissipate decay heat from the waste to the surrounding rock. The peak temperature in the buffer should not exceed the thermal design criterion adopted (100 °C) (SKBF/SKB, 1983; Cho et al., 1999), because this situation may lead to a mineralogical alteration (e.g., illitization, silicification etc.) of the bentonite used for the buffer and thereby compromise the required barrier performance of the buffer. The thermal environment of the buffer due to the decay heat may also have an influence on the hydraulic, mechanical and chemical behaviors of the bentonite buffer itself ⇑ Corresponding author. E-mail address: [email protected]
(J.O. Lee). http://dx.doi.org/10.1016/j.anucene.2016.04.053 0306-4549/Ó 2016 Elsevier Ltd. All rights reserved.
as well as the surrounding rock. Therefore, it is of essence to measure the thermal properties (e.g., thermal conductivity, specific heat capacity, and thermal expansion coefficient) of the bentonite buffer and to understand how they behave under disposal conditions, for the performance assessment of an HLW repository. Thermal conductivity is the quantity of heat that passes by the conduction in unit time and unit thickness through a plate of a particular area when its opposite face differs in temperature by one kelvin, and it primarily depends upon the constituent composition, density, pore-filling fluids, ambient temperature, and texture (Kukkonen and Suppala, 1999; Aurangzeb et al., 2007). The thermal conductivity of the bentonite buffer is a key parameter in the thermal analysis for the performance assessment of an HLW repository. A number of studies (Kahr and Müller-Vonmoos, 1982; Knutsson, 1983; Radhakrishna, 1984; Suzuki et al. 1992; Borgesson et al., 1994; Gangadhara and Singh, 1999; JNC, 2000; Ould-Lahoucine et al., 2002; Villar, 2002; Cote and Konrad, 2005; Kim et al., 2006; Tang and Cui, 2010; Ye et al., 2010; Cho et al., 2011) have been carried out to measure the thermal conductivity of the bentonite buffer, to investigate its dependence on experimental conditions, and also to develop relationships to estimate the thermal conductivity. The reported results of these studies imply that different bentonite buffer materials have been used for different countries that have their own disposal concept, and these bentonite buffer materials also has different thermal characteristics. These experimental results may have limitations to their application for the perfor-
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mance assessment and the design of buffers with different disposal concepts. Moreover, the dependence of the thermal conductivity upon the disposal conditions have been studied mainly on the dry density and water content of the compacted bentonite buffer, and in contrast to this, sufficient data have not been reported for the influence of temperature, the anisotropic structure of the compacted bentonite, and measurement methods on the thermal conductivity. The present study measures thermal conductivity for Kyeongju bentonite which is considered as a candidate buffer material of an HLW repository in Korea, and investigates the dependence of the thermal conductivity on various experimental conditions (dry density, water content, temperature, the anisotropic structure of the compacted bentonite). In addition, a constitutive model of thermal conductivity is proposed for the thermal analysis of the bentonite buffer of an HLW repository, based upon the experiment data obtained from the thermal conductivity measurements. 2. Materials and methods 2.1. Bentonite The bentonite used for this study was taken from Jinmyeong mine, Kyeongju, Korea (hereafter, referred to as Kyeongju bentonite). It was dried below 110 °C, pulverized, and then passed through No. 200 mesh American Society for Testing and Materials (ASTM) standard sieves. The Kyeongju bentonite contains montmorillonite (70%), feldspar (29%), and small amounts of quartz (1%) (Fig. 1). It was found to be Ca-type by Chun et al. (1998). Its chemical composition and particle size distribution are shown in Table 1 and Fig. 2, respectively. The Atterberg limit of the bentonite is as follows: a liquid limit of 244.5%, a plasticity of 46.1%, and a plasticity index of 198.4%. This study investigates compacted specimens of 100% bentonite. 2.2. Measurements of thermal conductivity Two types of measurement techniques based upon a transient method were employed: a thermal constant analyzer TPS 500 S
(Hot Disk AB, Sweden) for most measurements, and a quick thermal conductivity meter QTM-500 (Kyoto Electrics, Japan) for comparison with the results of the TPS 500 S as well as for investigation of anisotropy in thermal conductivity. The thermal constant analyzer TPS 500 S is a transient plane source method (Gustafsson, 1991). A measurement of the thermal conductivity was carried out using a sensor sheet and a sample holder, as shown in Fig. 3. The sensor sheet with a double spiral structure generates heat and measures the temperature change. The sample holder was designed for a good contact of the sensor sheet and bentonite specimen as well as no leakage of water vapor under high temperature conditions. The bentonite specimens were prepared by adjusting the water content of the powdered bentonite and then uniaxially compacting it to a target density in a stainless mold, which has an inside dimension of 0.03 m in diameter and 0.03 m in thickness, using a hydraulic press. The sensor sheet, for the measurement, is put between the two layers of compacted bentonite specimens, and they were then contacted and combined consistently with restrain rams. The thermal conductivity is computed using analytical data acquired from the sensor sheet. A quick thermal conductivity meter QTM-500 is a transient line source method. An impulse of thermal flow is supplied into a sample specimen with a heating hot wire installed in the measuring probe (PD-11). The probe is pressed on the evenly flattened surface of a sample specimen; the temperature rise is registered with a thermistor; and the thermal conductivity is computed from the test data acquired from the measuring probe. The compacted bentonite specimen for the QTM-500 measurement is a hexahedral block in shape. It is prepared using a stainless steel mold, which has an inside dimension of 0.15 0.06 0.02 m (Lee et al., 2013). The preparation procedure of a specimen with a hydraulic press is similar to that in the above-mentioned TPS 500 S. The measurement conditions for the thermal conductivity are combinations of the following variable values: a dry density of 1.5–1.8 Mg/m3, a water content of 0–17% in weight, and a temperature of 25–80 °C. The temperature is stepwise changed when controlled by a temperature-controlling dry oven. The measurement of the thermal conductivity in this study was done in triplicate for each experimental condition.
Fig. 1. X-ray pattern of the Kyeongju bentonite.
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Table 1 Chemical composition of the Kyeongju bentonite. Chemical constituent
Fig. 2. Particle size distribution of the Kyeongju bentonite.
Fig. 3. Sensor, sample holder, and measurement configuration for the TPS 500S.
3. Results and discussion 3.1. Comparison of thermal conductivities by TPS 500S and QTM 500 Fig. 4 compares thermal conductivities measured with the same bentonite samples using the PTS-500S and QTM-500 in order to evaluate the uncertainty of the thermal conductivity values due to the measurement methods. The present study did not observe a significant variation of the thermal conductivity with respect to the two measurement methods, as shown in the figure. However, for QTM-500, there was a difference of up to about 30% in the thermal conductivity for the same sample depending on the operators
even though the same measurement method was employed. This is supposed to be attributed to the difference in the skill level of the measurers. This is attributed to the degree of contact between the sample and sensor surfaces as well as the location of the sensor on the surface of the measurement sample. To reduce the uncertainty in the measurement of thermal conductivity, special care regarding these points is needed. 3.2. Influence of dry density on the thermal conductivity The influence of dry density on the thermal conductivity of compacted bentonite is shown in Fig. 5. The thermal conductivity
J.O. Lee et al. / Annals of Nuclear Energy 94 (2016) 848–855
k ¼ 1:35qd 1:11 for x ¼ 17% ðr 2 ¼ 0:98Þ k ¼ 1:09qd 1:00
k ¼ 0:87qd 0:88
k ¼ 0:58qd 0:59
Fig. 4. Comparison between the thermal conductivities obtained using different measurement methods.
for x ¼ 12% ðr 2 ¼ 0:95Þ
for x ¼ 5% ðr2 ¼ 0:99Þ
for x ¼ 0% ðr 2 ¼ 0:97Þ
where k is the thermal conductivity [W/m K], qd is the dry density of compacted bentonite [Mg/m3], x is the weight percentage of water (%), and r2 is the R-squared. Fig. 5 also shows that the rate of increase of thermal conductivity as a function of dry density has a greater value at a higher water content, which is probably attributed to the higher percentage of water with a higher thermal conductivity (0.58 W/m K) than air (0.024 W/m K) in the voids of the compacted bentonite. Literature reported thermal conductivities as a function of dry density for various bentonites (MX-80 (Kahr and MüllerVonmoos, 1982; Tang and Cui, 2010), FEBEX (Villar, 2002), Kunigel (Suzuki et al. 1992), GMZ (Ye et al., 2010)). Fig. 6 compares the thermal conductivities of this study with those in the literature when the dry density and water content are in the range of 1.5–1.8 Mg/m3, 0–17%, respectively. As shown in this figure, the plotted thermal conductivities ranged from a minimum of 0.30 W/m K to a maximum of 1.51 W/m K under the given experimental conditions. The thermal conductivity showed a higher value at higher water content. The thermal conductivity – dry density relation for each water content value had a similar trend for the Kyeongju bentonite to the reported bentonites. The thermal conductivity increased with an increase in the dry density. However, the value of the thermal conductivity and its rate of increase in the relationship were somewhat different depending on the different bentonite samples. This is probably because the thermal conductivity of the compacted bentonites is dependent on their mineral composition, texture, porosity, and pore-filling water (Kukkonen and Suppala, 1999; Aurangzeb et al., 2007). 3.3. Influence of water content on the thermal conductivity Fig. 7 shows the influence of water content on the thermal conductivity of the compacted bentonite for various dry densities (1.5 Mg/m3, 1.6 Mg/m3, 1.7 Mg/m3, 1.8 Mg/m3). As shown in this figure, the thermal conductivity increased with an increasing water content value for each dry density. The relation was almost linear up to less than 12% of water content, but beyond the value of water
Fig. 5. Therma conductivity as a function of dry density for the bentonite with various water contents.
is plotted as a function of the dry density for various water contents: 0%, 5%, 12%, and 17%. Under given experimental conditions, the thermal conductivity ranged from 0.301 W/m K to 1.337 W/m K and increased with increasing the dry density of the bentonite with a constant water content value. This is because, as the dry density of the compacted bentonite increases, the contact between the bentonite particles is improved, leading to a better heat conduction and an increase in its thermal conductivity. The relationship between the thermal conductivity and dry density is linear, and can be expressed:
Fig. 6. Comparison of the thermal conductivities of the present study with those of different bentonites reported in the literature.
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Fig. 7. Thermal conductivity as a function of water content for the bentonite with various dry densities.
content, there was somewhat higher increase rate of thermal conductivity. This increase of the thermal conductivity can be explained in two ways: one is that water with a higher thermal conductivity replaces the air in a void of the compacted bentonite as the water percentage of the bentonite increases, and thus it leads to an increase of the thermal conductivity; the other is that the bentonite swelling due to the water addition may make the voids of the compacted bentonite small and the bentonite approaches a saturated condition with increasing water content, resulting in an additional increase of the thermal conductivity. The relation of thermal conductivity versus water content which is non-linear particularly at lower or higher values of water content can be expressed by sigmoidal type equation. Villar (2002) and Wilson et al. (2011) used the following Eq. (2) to suggest empirical relations which fitted their experimental data.
A1 A2 þ A2 1 þ expððSr Sav Þ=BÞ
Fig. 8. Thermal conductivity (k) versus the degree of saturation (Sr) relation (symbols: experimental; lines: fitted).
Table 2 Fitting values determined for the parameters of the thermal conductivity (k)-degree of saturation (Sr) relationship, Eq. (2). Dry density (Mg/m3)
1.5 1.6 1.7 1.8
Coefficients of fitting A1
0.301 0.355 0.429 0.473
1.32 1.34 1.37 1.40
0.48 0.50 0.53 0.55
0.16 0.13 0.11 0.10
0.98 0.96 0.90 0.87
where A1 represents the value of k for Sr ¼ 0, A2 is the value of k for Sr ¼ 1, Sav is the degree of saturation for which thermal conductivity is the average of the two extreme values, and B is an empirical parameter. In the above Eq. (2), the degree of saturation (Sr Þ is related to the water content (x): Sr ¼ xqd =qw , where / and qw are the porosity and water density, respectively. Fig. 8 is a plot of the measured thermal conductivity as a function of the degree of saturation instead of the water content. The fitting results calculated using Eq. (2) were also included in the figure. The parameter values that best fit for each dry density are listed in Table 2. 3.4. Influence of temperature on the thermal conductivity Fig. 9 is a plot of the thermal conductivity of compacted bentonite as a function of temperature. This figure shows that a variation of the temperature does not make a significant influence on the thermal conductivity. The thermal conductivity was negligibly changed with an increasing temperature for the dry bentonite (water content = 0%), and for the compacted bentonite with a higher water content (water content = 12%), it displayed a little increase with increasing temperature, regardless of the dry density
Fig. 9. Thermal conductivity as a function of temperature.
of the compacted bentonite. This is probably attributable to the thermal conductivity of water and air increasing with an increasing temperature. Generally the thermal conductivity of non-metals
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such as clay minerals, which is primarily due to lattice vibration (phonons), decreases with increasing temperature (Clauser and Huenges, 1995; Horai, 1971; Ould-Lahoucine et al., 2002). On the other hand, the thermal conductivity of water and air increases with increasing temperature (Dean, 1992; Ramires et al., 1995). For the compacted bentonite used, it is supposed that its overall thermal conductivity is a combination of the thermal conductivities of solid phase substance, water and air; and a variation of thermal conductivity with increasing temperature for water and air is relatively larger than that for the solid phase substance, within the range of temperature evaluated in the present study. Literature (Radhakrishna, 1984; Suzuki et al., 1992; Wieczorek and Miehe, 2011) has reported that for the dry bentonite there is a negligible dependence of the thermal conductivity on the temperature at less than 100 °C, and there is a little change in the thermal conductivity with temperature for the bentonite at a given water content. However, changes of opposite trends were reported in two experiments. Suzuki et al. (1992) presented an increase of the thermal conductivity, while Wieczorek and Miehe (2011) looked at a decreasing thermal conductivity, when temperature increased. This difference, by the way, has not been explained by these papers. In summary, it follows that an increasing temperature does not influence significantly the thermal conductivity of the compacted bentonite in the ambient temperature range of less 100 °C. 3.5. Anisotropy of thermal conductivity in compacted bentonite The anisotropic structure of compacted bentonite by compaction influenced the physical properties of bentonite such as the swelling pressure, hydraulic conductivity, and ion diffusivity (Pusch, 1980, 1999; Lee et al., 2012). In the present study, to investigate the influence of the anisotropic structure on the thermal conductivity, the thermal conductivity on the two adjacent faces of the bentonite sample was measured, i.e., parallel (axial direction) and perpendicular (radial direction) to the compaction direction of the sample. Fig. 10 shows a comparison of the results measured for the compacted bentonite with the dry densities of 1.6 Mg/m3, 1.7 Mg/m3, and 1.8 Mg/m3. As shown in this figure, the thermal conductivity measured parallel to the compaction force direction was a maximum of 12% higher than the perpendicular thermal conductivity. This is likely attributed to the arranged aggregates of bentonite particles (micropeds) by the compaction.
The topography of the micropeds in the compacted bentonite would be somewhat uniformly parallel as compaction force increases (Pusch, 1980). However, the difference between the parallel and perpendicular thermal conductivities in Fig. 10 changed little with respect to an increasing dry density of the compacted bentonite. This implies that the influence of the structural anisotropy of the compacted bentonite on the thermal conductivity and thus the heat transfer across the buffer of a radioactive repository will be uniform. 3.6. Model of thermal conductivity for its application to thermal analysis In an HLW repository, the buffer is installed as highlycompacted bentonite blocks. The bentonite buffer, after its installation, is gradually saturated over time by ground water inflowing from the surrounding rock. In parallel to this, the decay heat from the radioactive waste is transferred through the buffer to the outside of the borehole. These processes result in hydraulic gradient and thermal gradient across the compacted bentonite buffer in the deposition borehole. Therefore, a constitutive model of thermal conductivity for thermal analysis should include its dependence on these factors affecting the thermal conductivity for the reliable performance assessment of the repository (Ikonen, 2008; Borgesson and Falth, 2006; Cho et al., 2010; Lee et al., 2014). Numerous models of thermal conductivity are presented in literature. Among them, the thermal conductivity models which are applicable for the bentonite buffer are grouped largely as follows: Kersten’s model (1949), Johansen’s model (1975), Sakashita and Kumada’s model (1998) and the geometric mean model (Woodside and Messmer, 1961; Sass et al., 1971; Cote and Konrad, 2005; Cho and Kwon, 2009). Kersten’s model is an empirical relationship between thermal conductivity, dry density, and water content for various types of soils. Johansen’s model considers the mineralogy of soils additionally. Sakashita and Kumada’s model accounts for the microstructure of compacted bentonites assuming that the intraparticle micropores and the interparticle macropores are of rectangular parallelepiped shape dispersed in a continuous solid phase. The geometric mean model, which was successfully used by Woodside and Messmer (1961) and Sass et al. (1971), is expressed based on the volumetric composition of sample-forming minerals:
n Y j
Fig. 10. Comparison between the thermal conductivities measured parallel and perpendicular to the compaction force direction.
n X /j ¼ 1;
Q where represents the product of the thermal conductivity of the constituting minerals kj raised to the power of their volumetric proportion /j , and the sum of the volumetric proportion of the minerals is equal to 1. The subscript j refers to the jth mineral, there being n minerals altogether. The present study, based on the above geometric mean model, proposes a new thermal conductivity model which best fits the experimental data obtained from the thermal conductivity measurements. The following assumptions are introduced in developing the model: (1) Bentonite is homogenous; (2) the void of the compacted bentonite is filled initially with air, and water replaces the air as the water fraction increases; (3) the effective thermal conductivity of the compacted bentonite is expressed by the weighted geometric mean of the mineral components’ thermal conductivities. The compacted bentonite is a porous medium with the void in the matrix. To describe the thermal conductivity of partially saturated compacted bentonite in terms of the dry density and degree of saturation converted from the corresponding water content, the above Eq. (3) is rewritten as:
J.O. Lee et al. / Annals of Nuclear Energy 94 (2016) 848–855 /
k ¼ kb b k/ww k/a a
with /b þ /w þ /a ¼ 1;
/b ¼ 1 / ¼ qd =qp /w ¼ ð1 /b ÞSr /a ¼ ð1 /b Þð1 Sr Þ where kb ; kw ; ka are the thermal conductivities of bentonite matrix, water and air, respectively. /b ; /w ; /a are the volumetric fraction of bentonite matrix, water, and air, respectively. / is the porosity of the compacted bentonite, qd is its dry density, qp is the particle density of bentonite, and Sr is the degree of saturation of the compacted bentonite. The compacted bentonite, in real situation, would not have tight contact among the bentonite particle, water and air, and it does not also have homogeneous distribution. Considering these facts, the above Eq. (2) can be modified as follows: mqd =qp
k ¼ kb
pð1qd =qp Þ
rÞ ðkSwr kð1S Þ a
where m and p are the exponents which take into account the unreality of the geometric mean model. When the arrangement of the compacted bentonite is an ideal configuration, the exponents m and p are equal to 1. The values of kw and ka are 0.58 W/m K and 0.024 W/m K at 25 °C. The thermal conductivity, kb of the bentonite matrix depends on the thermal conductivity of its constituent minerals. However, the mineral composition of the bentonite may differ from sample to sample, and thus the bentonite thermal conductivity, which is calculated from thermal conductivity of its constituent minerals, may involve a certain uncertainty. The present study, for this reason, determined the unknown values of kb ; m and p using the multivariate regression analysis based on the experimental data. As the results of the regression analysis, the modified geometric mean model and its calculated values of the parameters are as follows:
k ¼ 2:161mqd =qp ð0:58Sr 0:024ð1Sr Þ Þ m ¼ 1:506;
pð1qd =qp Þ
p ¼ 0:827
The R-squared of Eq. (6) was 0.94. The value of m is higher than 1, and on the other hand, p is lower than 1. This implies that the relative contribution of the volume fraction of bentonite to the effective thermal conductivity is larger than that of water and air. Fig. 11 represents the thermal conductivities calculated using the modified geometric mean model, Eq. (6) versus the measured values for the compacted bentonites with various dry densities and water contents. As shown in the figure, the model calculations of thermal conductivity underestimated a little the measurements, but most of the calculations fall in between the ±20% relative error lines. A larger discrepancy between the calculated and measured values occurs for the experimental data on the bentonite with the lower water content. Martin and Barcala (2005) presented in their large scale buffer material test that the water content at any point very close to the canister decreased at the early stage of disposal as the initial water moved outwards due to the thermal gradient (i.e., dry process) and, after the hydration by the inflow of the surrounding groundwater overcame the dry process, it slowly increased to a steady-state value. Considering such a decrease in the water content, there may be a certain uncertainty in the thermal conductivity at the early stage of disposal predicted using the proposed model, which implies that special attention is needed for practical use of the calculated results. The thermal conductivity model proposed in this study will be used as a constitutive input model in the thermal analysis of the bentonite buffer for an HLW repository in Korea.
Fig. 11. Comparison between the model calculations and measurements of the thermal conductivity for the compacted Kyeongju bentonite.
4. Conclusions This study measured the thermal conductivity of a bentonite buffer for an HLW repository, and investigated the influence of the dry density, water content, anisotropic structure of the compacted bentonite, and temperature on the thermal conductivity, as well as the uncertainty of the thermal conductivity value which may be induced owing to its measurement methods. The measurement results showed that the thermal conductivity was significantly influenced by the water content and dry density of the compacted bentonite. An increasing water content gave an increase in the thermal conductivity, as did an increase in the dry density. However, it was not significantly changed with an increase in temperature. The compacted bentonite showed anisotropy in the thermal conductivity: the thermal conductivity measured parallel to the compaction direction was a little higher than the perpendicularly measured conductivity. However, the anisotropy of the thermal conductivity had a negligible variation for an increasing dry density. The thermal conductivity might have a certain uncertainty depending on the measurer’s skill level, suggesting that special care is needed to obtain reliable measurement results. The present study also proposed a new geometric mean model of thermal conductivity which best fits the experimental data, which will be used as a constitutive input model in the thermal analysis of the bentonite buffer for an HLW repository in Korea. Acknowledgment This work was supported by Nuclear Research & Development Program of the National Research Foundation of Korea (NRF) Grant funded by the Ministry of Science, ICT and Future Planning (MSIP). References Aurangzeb, Khan, L.A., Maqsood, A., 2007. Prediction of effective thermal conductivity of porous consolidated media as a function of temperature: a test example of limestones. J. Phys. D Appl. Phys. 40, 4953–4958. Borgesson, L., Fredrikson, A., Johannesson, L., 1994. Heat conductivity of buffer materials. SKB Technical Report 94-29, SKB.
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