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Working Report 98-09e Thermal properties of rocks at the investigation sites: measured and calculated thermal conductivity, specific heat capacity and thermal diffusivity Ilmo Kukkonen Antero Lindberg March 1998 POSIVA OY Mikonkatu 15 A, FIN-001 00 HELSINKI, FINLAND Tel. +358-9-2280 30 Fax +358-9-2280 3719 Working Report 98-09e Thermal properties of rocks at the investigation sites: measured and calculated thermal conductivity, specific heat capacity and thermal diffusivity Ilmo Kukkonen Antero Lindberg March 1998 AUTHOR ORGANIZATION: Geological Survey of Finland P.O. Box 96 FIN-02151 Espoo Finland ORDERER: Posiva Oy Mikonkatu 15 A FIN -00100 Helsinki Finland NUMBER OF THE ORDER: 9798/971AJH tlh'vnJ 1/w~~. CONTACT PERSON OF THE ORDERER: Aimo Hautajärvi CONTACT PERSON OF THE AUTHOR ORGANIZATION: Ilmo Kukkonen WORKING REPORT 98-09e THERMAL PROPERTIES OF ROCKS IN THE POSIVA INVESTIGATION SITES: MEASURED AND CALCULATED THERMAL CONDUCTIVITY, SPECIFIC HEAT CAPACITY AND THERMAL DIFFUSIVITY ·-:=2o~.~~,_._ ~,L__A NAMES OF THE AUTHORS: EXAMINER OF THE AUTHOR ORGANIZATION: Ilmo Kukkonen and Antero Lindberg Dr. Tech. M.Sc. L(~~ Lauri Eskola Research Professor Research & Development, Geophysics 7 Working Report 98-09e Thermal properties of rocks at the investigation sites: measured and calculated thermal conductivity, specific heat capacity and thermal diffusivity Ilmo Kukkonen Antero Lindberg Geological Survey of Finland March 1998 Working Reports contain information on work in progress or pending completion. The conclusions and viewpoints presented in the report are those of author(s) and do not necessarily coincide with those of Posiva. 2 KIVILAJIEN TERMISET OMINAISUUDET TUTKIMUSALUEILLA: MITATTU JA LASKETTU LÄMMÖNJOHTAVUUS, OMINAISLÄMPÖKAPASITEETTI JA TERMINEN DIFFUSIVITEETTI TIIVISTELMÄ Tässä raportissa esitetään tuloksia Posiva Oy:n tutkimuspaikkojen kivilajien termisten ominaisuuksien tutkimuksista. Tutkimuksessa käytettiin kivilajinäytteitä, jotka otettiin Posiva Oy:n eri tutkimuspaikkojen syväkairausrei'istä. Näytteitä oli kaikkiaan 35 kpl, ja niistä mitattiin lämmönjohtavuus, ominaislämpökapasiteetti ja terminen diffusiviteetti. Näytteiden petrografisesti määritettyjen kvantitatiivisten mineraalikoostumusten avulla laskettiin lämmönjohtavuus käyttäen erilaisia numeerisia estimaattoreita. Diffusiviteetti laskettiin myös käyttäen lämmönjohtavuutta, ominaislämpökapasitettia ja tiheyttä, joka mitattiin vesi-ilmapunnituksen avulla. Aikaisemmin on raportoitu Olkiluodon, Romuvaaran ja Kivetyn lämmönjohtavuustutkimusten tuloksia. Tässä työssä lämmönjohtavuuden mittaukset ja mineraalikoostumukseen perustuvat laskennalliset lämmönjohtavuuden määritykset laajennettiin koskemaan myös Hästholmenin kivilajinäytteitä. Hästholmenin pyterliittisten graniittien lämmönjohtavuus on hieman 1 alhaisempi (2.3-2.8 W m- K- 1) kuin tasarakeisten ja porfyyriittisten graniittien (3.4-3.5 W m- 1 K- 1). Posivan tutkimusalueiden kivilajinäytteiden ominaislämpökapasiteetti on välillä 770-830 J kg- 1 K- 1, ja keskiarvot kullekin alueelle ovat: Olkiluoto 798 ± 20 (std) J kg- 1 K- 1, Romuvaara 824 ± 15 J kg-1 K- 1, Kivetty 809 ± 16 J kg- 1 K- 1 ja Hästholmen 807 ± 11 J kg-1 K-1. Terminen diffusiviteetti (laskettuna mitatun lämmönjohtavuuden, ominaislämpökapasiteetin ja tiheyden avulla) on eri alueilla vastaavasti: Olkiluoto 1.42 ± 0.38 ·106 m2 s-\ Romuvaara 1.19 ± 0.16 ·10-6 m2 s- 1, Kivetty 1.25 ± 0.25 ·10-6 m 2 s-1 ja Hästholmen 1.42 ± 0.22 ·10-6 m2 s- 1 • Avainsanat: Lämmönjohtavuus, ominaislämpökapasiteetti, terminen diffusiviteetti, mineraalikoostumus 3 THERMAL PROPERTIES OF ROCKS AT THE INVESTIGATION SITES: :MEASURED AND CALCULATED THERMAL CONDUCTIVITY, SPECIFIC HEAT CAPACITY AND THERMAL DIFFUSIVITY ABSTRACT Thermal properties of rock samples taken from drill cores from the investigation sites of the Posiva Oy were investigated. Thermal conductivity, specific heat capacity, thermal diffusivity, density and mineral composition of 35 rock samples were measured. Thermal conductivity was measured with steady-state laboratory method (divided bar instrument), specific heat capacity was determined with a calorimetric method, and diffusivity was measured with a transient heat conduction instrument. Thermal conductivity was calculated from quantitative mineral composition data detennined petrographically using thin sections. Diffusivity was also determined indirectly from measured thermal conductivity, specific heat capacity and rock bulk density which was measured as well. Special attention is paid here to heat capacity measurements as thermal conductivity has been discussed already earlier in detail for Olkiluoto, Romuvaara and Kivetty investigation sites. Thermal conductivity of the Hästholmen samples are smaller for the pyterlitic granites (2.3-2.8 W m- 1 K- 1) than in the even grained or porhyritic granites (3.4-3.5 W m- 1 K-1). Specific heat capacities of the Posiva rocks range from 770 to 830 J kg- 1 K- 1, with the following mean values for each site: Olkiluoto 798 ± 20 (std) J kg- 1 K- 1 , Romuvaara 824 ± 15 J kg- 1 K-\ Kivetty 809 ± 16 J kg- 1 K- 1 and Hästholmen 807 ± 11 J kg- 1 K- 1• Thermal diffusivity (calculated from measured conductivity, heat capacity and density) values are correspondingly: Olkiluoto 1.42 6 2 1 ·10- m s- , Kivetty 1.25 ± 0.25 ± 0.38 ·10-6 m2 s- 1, Romuvaara 1.19 ·10-6 m2 s- 1 and Hästholmen 1.42 ± 0.22 ± 0.16 ·10-6 m2 s- 1 • Key words: thermal conductivity, specific heat capacity, thermal diffusivity, mineral composition 4 Preface The study has been carried out at the Geological Survey of Finland on contract for Posiva Oy. Ilmo Kukkonen was responsible for coordination of the project, thermal conductivity analysis and report compilation and Antero Lindberg for mineral composition analysis and geological consultation. The work has been supervised by Aimo Hautajärvi at Posiva and Erik Johansson at Saanio & Riekkola Consulting Engineers. 5 Table of contents 1 INTRODUCTION 6 2 SAMPLING 6 3 LABORATORYMEASUREMENTS 7 3 .1 Thermal conductivity 7 3. 2 Specific heat capacity 8 3. 3 Thermal diffusivity 10 3. 4 Calculation of thermal conductivity and diffusivity 10 4 MINERALOGICAL COMPOSITION OF THE SAMPLES 11 5 SPECIFIC HEAT CAPACITIES OF ROCK-FORMING MINERALS AND ROCKS 14 6 RESULTS 17 7 RELATIONSHIPS BETWEEN THERMAL PROPERTIES, QUARTZ CONTENT AND DENSITY 21 8 DISCUSSION AND CONCLUSIONS 25 9 REFERENCES 26 APPENDIX 28 6 1 INTRODUCTION Thermal properties (conductivity, specific heat capacity and diffusivity) are necessary parameters needed in planning of a final repository for spent nuclear fuel in deep bedrock. Bedrock temperatures are expected to increase in the immediate vicinity of the repository after the final disposal due to radiogenic heat production of the spent fuel. Depending on the thermal properties of the rock matrix considerable differences in bedrock temperatures may arise, which must be taken into account in the repository planning. Recently, the present authors investigated the thermal conductivity of 27 seIeeted rock samples from the Posiva Oy investigation sites Olkiluoto, Romuvaara and Kivetty (Kukkonen and Lindberg, 1995). Both measured conductivity and values calculated from mineral composition determined from thin sections with point counting technique were discussed. In the present study, the same samples were used again but ten new samples from the Hästholmen, Loviisa, area were added. In addition to thermal conductivity, also specific heat capacity, density, and thermal diffusivity were determined experimentally in the laboratory. Theoretical multi-component models and the data on mineral composition were used for estimating thermal conductivity, and thermal diffusivity was determined also indirectly using measured conductivity, specific heat capacity and density. 2 SAMPLING The samples used in this study were partly the same as in Kukkonen and Lindberg ( 1995). Ten new samples were provided by Posiva from the Hästholmen drill holes HH-KR1, KR2 and KR3 (Table 1). In addition to this, repeated sampling was performed for nine earlier samples from Olkiluoto, Romuvaara and Kivetty, necessary for the direct measurement of thermal diffusivity (Table 1). 7 Table 1. Samples from the Hästholmen drill holes (HH) and the repeated sampling from the Olkiluoto (OL), Romuvaara (RO) and Kivetty (KJ) drill holes. Hole Depth (m) No. Preliminary rock type classification HH-KR1 500.26-500.50 26 Pyterlite HH-KR1 508.49-508.71 27 Pyterlite HH-KR1 515.50-515.74 28 Pyterlite HH-KR2 404.41-404.68 29 Pyterlite HH-KR2 416.68-416.94 30 Pyterlite HH-KR3 485.69-485. 89 31 Even grained rapakivi granite HH-KR3 494.36-494.57 32 Even grained rapakivi granite HH-KR3 504.71-404.92 33 Even grained rapakivi granite HH-KR3 527.73-527.95 34 Even grained rapakivi granite HH-KR3 531.19-531.44 35 Even grained rapakivi granite OL-KR1 402.91-403.03 3 Mica gneiss OL-KR1 423.95-424.10 4 Mica gneiss OL-KR2 502.87-502.97 9 Mica gneiss RO-KR1 450.95-451.20 10 Tonalite gneiss RO-KR1 500.75-501.00 11 Tonalite gneiss RO-KR1 602.10-602.20 12 Tonalite gneiss KI-KR3 467.99-468.10 20 Porphyritic granodiorite KI-KR3 KI-KRS 445.09-445.20 401.28-401. 38 21 24 Granite Porphyritic granodiorite Legend: No. refers to the sample numbering used in Table 5. 3 LABORATORY MEASUREMENTS 3.1 Thermal conductivity Thermal conductivity was measured with the steady-state divided bar method using apparatus built at the GSF (Fig. 1). The method is described in detail by Kukkonen and Lindberg 8 ( 1995). The samples used in the instrument are 7 mm thick disks cut perpendicularly from the drill core, and they are measured in a water-saturated state after two days in a water bath in normal room temperature and pressure. Inaccuracies in thermal conductivity values are considered to be smaller than 5 %. r-)--~ • ' • -------1 WARM :_ _ WATER_ __ (r-~r.~~~ !.....,__\~.J T1 Quartz Temperature sensors T2 ~~.~-=~·:~~~-~~·:_~. ·:~.#-(G_~·::\ /~ Sample ~,:. F.-~~~~-.·;~~~-~-~~~~~~.~~~ .(;,: ~:?; : h5 a Quartz Fig. 1. Schematic representation of the divided bar method (Kukkonen and Lindberg, 1995). 3.2 Specific heat capacity Specific heat capacity was measured using the same samples as in the conductivity measurements. The measurement method is the calorimetric method, and the sample is first heated to a known temperature, then placed into a calorimeter including a weighed amount of water, and the fmal temperature reached by the calorimeter-water-sample system is measured (Fig. 2). Specific heat capacity (J kg·• K- 1) is derived as follows: (1) where m 1 is the mass of the sample (kg), CK is the heat capacity of the calorimeter (70 9 J K- 1), Cp 1 is the specific heat capacity of water (4180 J kg- K- 1 ), mF is the mass of water in the calorimeter (kg), and v1 is the initial temperature of the sample, v2 is the initial temperature of the water and calorimeter and vM is the final temperature reached in the calorimeter ( o C). The heating of the sample is performed by placing it in a vessel with boiling water. The temperature (v 1) of the water is measured immediately before transporting the sample into the calorimeter. Temperature in the calorimeter is monitored with a temperature sensor (element Analog Device AD 590) having a nominal resolution of 0.002 K. ' "'/ (!J/) .. -- .......... ' '\ Hg-thermometer 1 ~~.=:=----.-.-t-- T-sensor ..__...ioiooiioio~.... - ...~- Sample Computer Calorimeter Hoth bath Fig. 2. Schematic representation ofthe calorimetric method usedfordetermining specific heat capacity. The measurement of specific heat capacity is simple in principle, but the practicallaboratory operations must be done carefully to achieve accurate results. This means that heat losses from and into the calorimeter, cooling of the sample during transport from the hot water bath to the calorimeter, as well as hot water contamination brought with the sample must all be investigated. The tests based on measuring samples of pure copper and bismuth indicate the present system can obtain an inaccuracy of about 5 % or less, and a repeatability of about 3 %. 10 3.3 Thermal diffusivity Direct measurement of thermal diffusivity was done with a commercial instrument ISOMET 104, manufactured by Applied Precision Ltd., Slovakia. The instrument appiies transient heat transfer with a contact probe, which is placed in contact with the cut and slightly polished surface of a drill core (Fig. 3). A transient heating signal is transmitted to the sample, its decay is monitored by the probe and thermal diffusivity is obtained from the decay curve. According to the manufacturer, the measured diffusivity is obtained with an uncertainty of less than 15 %. --- To computer ISOMET surface probe Heat source and - - - - - r - temperature L-.,--_ _ _ _ _ _Lr-..,-----l Drill core sensor Smooth rock surface Fig. 3. Schematic representation of the direct measurement of thermal diffusivity using the ISOMET 104 apparatus. 3.4 Calculation of thermal conductivity and diffusivity In addition to measured data thermal conductivity was also calculated from the mineral composition as in Kukkonen and Lindberg ( 1995) including the arithmetic, harmonic and geometric mean estimators. Further, thermal diffusivity was calculated from measured conductivity, specific heat capacity and density: s = k/(d c) (2) 1 where s is diffusivity (m2 s- 1), k is thermal conductivity (W m- Km-3) and c is specific heat capacity (J kg- 1 K- 1 ). 1 ), d is density (kg 11 4 MINERALOGICAL COMPOSITION OF THE SAMPLES The mineralogical composition of the samples was determined with the point counting technique using thin sections prepared from the counterpart of the conductivity sample as described in Kukkonen and Lindberg (1995). This ensures the minimal effects from geological 'noise', i.e. variations in mineral composition. The earlier data was adapted from Kukkonen and Lindberg (1995), and the new Hästholmen samples were measured accordingly. The results with a short geological description are given in Table 2. Table 2. The mineralogical composition (vol.- %) of thin sections from the Hästholmen investigation site. Cafeulated by point counting method, 1000 points/thin section. HH-KR1 HH-KR1 HH-KR1 HH-KR2 HH-KR2 no 1 no 2 no 3 no 4 no 5 500.26 508.49 515.50 404.41 416.68 plagioclase 18.7 23.3 9.7 12.3 27.8 K-feldspar 43.3 45.2 77.2 63.9 38.8 quartz 25.2 20.4 7.8 17.0 22.3 biotite 2.5 4.1 0.4 2.2 2.3 homblende 6.2 3.6 2.3 2.6 4.7 muscovite/ 2.0 1.2 1.7 0.7 1.4 0.1 + 0.1 + + 0.1 Mineral sericite epidote carbonate 0.1 apatite 0.4 0.5 0.2 0.2 0.1 chlorite 0.7 0.8 + 0.6 1.1 fluorite 0.1 + + 0.2 0.4 0.2 + + 0.9 0.4 0.1 1.1 100.0 100.0 100.0 100.0 30 27 33 30 PYT PYT zircon opaques Total 0.8 100.0 Anorthite-% 35 Rock type PYT PYT 12 Table 2 (cont.) Legend HH-KR1 = Hästholmen drill hole 1 500. 26 = core length (m) at sampling point + = observed optically PIT = pyterlite, EG GR = even grained granite, P GR = porphyritic granite 1) Pyterlite with medium grained (3 - 5 mm) groundmass and K-feldspar phenocrysts from 10 to 15 mm in diameter. Alteration ofplagioclase to sericite is slight, hornblende has partly altered to biotite and opaques, biotite to chlorite. K-feldspar is quite clear. 2) Pyterlite containing K-feldspar grains up to 22 mm in diameter and also one plagioclase grain reaching 12 mm. Alteration of all minerals is more intensive as in sample 1. 3) Thin section contains only one K-feldspar phenocryst in which the other minerals are as inclusions. 4) Pyterlite where goundmass is from medium to coarse grained as in samples 1 and 2 with K-feldspar phenocrysts up to 17 mm. Several plagioclase grains are heavily sericitized; also hornblende and biotite are more altered (than in samples 1 and 2), mainly to chlorite. 5) Pyterlite as above. Sericitization of K-feldspar is stronger than in samples above. 13 Table 2, continues. HH-KR3 HH-KR3 no 7 HH-KR3 no 8 no 9 no 10 494.36 504.71 527.73 531.19 plagioclase 23.4 22.1 18.4 22.1 20.8 K-feldspar 36.2 40.6 43.3 35.5 37.6 34.1 quartz 2.9 biotite homblende muscovite/ 0.9 sericite 0.1 epidote 30.9 3.3 33.5 2.7 34.8 4.3 35.1 3.6 Mineral HH-KR3 HH-KR3 no 6 485.69 0.1 0.3 0.9 0.5 1.0 0.6 0.4 0.1 0.5 0.1 + 0.1 apatite + + + + chlorite 1.1 0.7 0.7 1.1 0.8 fluorite 0.7 0.8 0.3 0.4 0.7 zircon + (+) + + + 0.6 0.3 0.4 0.3 0.3 carbonate opaques Total 100.0 Anorthite-% 28 100.0 100.0 100.0 100.0 30 30 29 Rock type EGGR EG/P GR 35 PGR EG/P GR EGGR 6) Even grained granite samples 6 -J 0 contain some coarser quartz and K-feldspar grains so that the texture seems to be also slightly porphyritic. Sample no 6 contains only one K-feldspar phenocryst (JO mm) infine grained (0.5 -J.5 mm) groundmass. Plagioclase has moderately sericitized, K-feldspar weakly. Biotite has altered to chlorite (JO- 25 %). Quartz grains are clear but several of them are undulating. 7) Even grained (1. 0 -J. 5 mm) groundmass contains two large (about 5 mm in diameter) quartz grains. Alteration of minerals as above. 8) Porphyritic granite where several quartz grains are from 3 to 7 mm in diameter and one K-feldspar is reaching J5 mm. The groundmass is even grained (0.5- J.O mm). 14 Table 2 (cont.) 9) Even and fine grained groundmass (0. 5 -1. 5 mm) with some quartz phenocrysts up to 6 mm in diameter. Plagioclase has thoroughly altered to sericite. 10) Even grained granite with grain size appr. 0. 5-1.5 mm. Some quartz and biotite grains are slightly coarser (2 - 3 mm). Plagioclase is moderately sericitized and JO- 20 % of biotite has altered to chlorite. According to the petrographical study, the Hästholmen samples are either pyterlitic rapakivi granites or even grained or porphyritic granites. Their major minerals are potassium feldspar, plagioclase, quartz, biotite, homblende and muscovite, and accessory minerals include epidote, carbonate, apatite, chlorite, fluorite, apatite, zircon and opaques. 5 SPECIFIC HEAT CAPACITIES OF ROCK-FORMING MINERALS AND ROCKS Data on specific heat capacities of minerals is provided by Schön (1983) and Cermak and Rybach (1982) who have compiled summaries from several sources. An overview of the specific heat capacities of typical rock-forming minerals is given in Table 3. In comparison to thermal conductivity of minerals (see Kukkonen and Lindberg, 1995 for a table of values) there is much less relative variation in the specific heat capacities of minerals. Normal major minerals of acid and intermediate rocks (feldspars, quartz, pyroxenes, amphiboles mica) have values ranging from 650 to 800 J kg-• K- 1 • Mafic minerals have slightly higher values than felsic minerals. The variation is higher among typical accessory minerals. Carbonates and fluorite may reach and exceed 900 J kg-• K- 1, whereas opaque oxides are close to the values of typical silicates, but sulphide minerals have low values ranging from about 200 to 550 J kg-• K- 1 • The specific heat capacity of minerals is temperature dependent. Data on quartz and olivine (Cermak and Rybach, 1982) suggest that specific heat capacity increases about 10-15 % between 25 and 1oooc. The specific heat capacity of crystalline low-porosity rocks is controlled by the specific heat capacities of the individual minerals and their relative amounts in the rock. The data in Table 3 suggests, thatrocks consisting mainly of quartz, feldspars, mica and amphiboles should have specific heat capacities in the range of 700-750 J kg-• K- 1 at temperatures 15 0-27°C. Measured values of rock samples have much higher variation, and globalliterature 1 data ranges from about 700 to as high as 1200 J kg-• K- (Cermak and Rybach, 1982). However, it has not been possible here to investigate, whether this could be attributed to temperature dependence, the applied measurement methods, or poorly controlled measurements. Also Schön (1983) reports crystalline rock values in the range of 6701300 J kg-• K- 1 • Similar to minerals, the specific heat capacity of rocks is temperature dependent and increases with increasing temperature. A curve fitted for data on several rock types (granite, granodiorite, diorite, granulite and basalt) suggests an increase of about 12 % between 25 and 100°C (England, 1978). Measurements of specific heat capacities of rock samples from the Posiva investigation sites (Kjerholt, 1992) suggested an increase of 8-20 % for specific heat capacity between 10 and 60°C. 16 Table 3. Specific heat of typical rock-forming minerals. Numerical data adopted from the compilations by Schön (1983) and Cermak and Rybach (1982). Schön (1983) (17-27°C) Cermak and Rybach (1982) (0°C) 711-837 700-709 albite 710-750 709 Olicoclase Ab89Anll 837 744 (at 25°C) Mineral Plagioclase Labrador Ab46 Afls4 Anorthite Ab4 A~6 Potassium feldspar 700 711 700 Microcline 670-690 680 Orthoclase 628-650 610 Quartz c. 750 698 Biotite 770 Muscovite 760 Amphiboles Hornblende 650-750 Antophy liite 740 Pyroxenes Enstatite Diopside 800 (60°C) 700-750 690 980 790 (36°C) 840 800-880 550 780-930 740 (pyrope at 58°C) Fluorite 900 Sillimanite Zircon Pyrite 500-520 850 743 610 (at 60°C) 500 Olivine Forsterite Fayalite Carbonates Gamet Chalcopyrite 540 (at 50°C) Sphalerite 450 Galena 207 Magnetite 600 Hematite 620-628 610 17 6 RESULTS The calculated thermal conductivities with measured values are given in Table 4. The data is presented for all the 35 samples, but the data on samples from Olkiluoto, Romuvaara, Kivetty and Syyry were discussed in detail already in Kukkonen and Lindberg ( 1995). Calculated thermal conductivities of the Hästholmen samples are highest when the arithmetic mean estimator is used, and lowest when the harmonic mean estimator is applied. Values calculated with the geometric mean estimator fall between these two. The measured data of the pyterlites are best approximated by the harmonic mean values, whereas the even grained rapakivi granites are best simulated by the geometric mean. For the even grained granites the differences between the measured values and calculated geometric mean are smaller than 0.1 W m- 1K- 1 • The calculated values of thermal conductivity differ most from the measured values in the pyterlitic rapakivis. This can be attributed to the coarse grain size of the pyterlites, and the textural variation is too big to be mitigated in the sample size. Particularly this appiies to the sample HH1-515.50, which is very coarse grained, and practically consists of a single large feldspar grain with plagioclase and quartz as inclusions. The measured thermal conductivity (2.28 W m- 1 K- 1) is close tothevalue of alkali feldspar (2.31-2.49 W m- 1 K- 1; Kukkonen and Lindberg, 1995) and plagioclase (1.68-2.34 W m- 1 K- 1). The generally higher thermal conductivity of the even grained granites can be attributed to their higher quartz contents in comparison to the pyterlites (Table 2). The results of heat capacity and diffusivity studies are summarized in Table 5. Specific heat capacities of the rocks range from about 770 to 830 J kg- 1 K- 1• The values are comparable to literature data measured on similar rock types (Schön, 1983). Typical rock forming minerals have specific heat capacities between 690 and 830 (Cermak and Rybach, 1982; Schön, 1983). However, it must be here taken into account that specific heat capacity of rocks is strongly temperature dependent and the values of quartz and olivine increase by about 12 percent from 25°C to 100°C (Cermak and Rybach, 1982). Increase of specific heat capacity of 8-20 % between 10 and 60°C was also reported by Kjerholt (1992) in laboratory measurements of rock samples from the Posiva investigation sites. Our measurements are representative of the specific heat capacity at a temperature of about 99°C which is the temperature of the hot bath. The final temperature in the calorimeter was usually 24-25°C. Thus the values in Table 4 could be reduced accordingly. 18 Table 4. Thermal conductivity calculated from mineralogical composition using the arithmetic, harmonic and geometric mean values and the measured thermal conductivity. Sample Rock type k(ar) k(har) k(geo) k(meas) OL1-402.79 MGN 4.19 2.86 3.40 3.21 OL1-418.40 OL1-420.71 MGN GR 4.26 3.49 3.06 6.05 2.96 4.16 5.15 4.68 OL1-423.86 MGN 3.85 2.69 3.13 2.38 OL1-450.52 OL2-342.76 GR GRDR 3.57 3.75 2.76 3.06 3.77 2.70 3.11 2.55 OL2-354.58 GRDR 3.61 2.79 3.12 2.76 OL2-486.41 OL2-502.81 MGN MGN GRGN 4.15 4.17 2.89 2.89 3.39 3.41 2.50 2.74 3.82 2.70 3.13 2.69 TGN GRGN 4.12 2.82 3.34 3.11 2.53 2.81 2.48 2.87 2.83 2.51 R01-451.30 R01-500.57 R01-602.35 R01-700.62 TGN 3.45 3.43 R01-762.87 MGN 4.15 2.81 3.35 2.89 R01-782.74 R03-397.31 MGN MGN 3.74 3.25 2.60 2.50 3.03 2.77 2.38 2.28 R03-398.78 MGN 3.30 2.56 2.83 2.07 KI1-652.82 GR 2.69 GRDR 2.58 3.01 2.91 2.76 KI2-495.80 3.53 3.49 2.52 KI3-415.15 Kl3-445.24 KI3-468.13 K14-500.80 KI5-401.50 15/SY6-267 .00 HH1-500.26 GR GR GR GR DR PYT 4.13 4.45 3.22 3.32 3.28 2.41 3.73 2.94 3.13 2.52 2.58 2.53 2.22 2.80 3.42 3.69 2.77 2.85 2.80 2.29 3.16 3.32 3.36 2.63 2.72 2.44 2.23 2.68 HH1-508.49 PYT 3.44 2.65 2.95 2.84 HH1-515.50 PYT 2.81 2.49 2.60 2.28 HH2-404.41 PYT 3.29 2.65 2.88 2.71 HH2-416.68 PYT 3.58 2.71 3.04 2.67 HH3-485.69 EGGR 4.21 2.99 3.49 3.42 GR 19 Table 4 (cont.) Sample Rock type k(ar) k(har) k(geo) k(meas) HH3-494.36 EG/P GR 4.02 2.90 3.35 3.41 HH3-504.71 HH3-527.73 PGR 4.14 2.98 3.45 3.49 EG/P GR EGGR 4.21 2.99 3.01 3.49 3.40 3.52 3.47 HH3-531.19 4.24 = mica gneiss, GR = granite, GRDR = granodiorite, TGN = tonalite gneiss, DR = diorite, PYI' = pyterlite, EG GR = even grained granite, EGIP GR = even grainedlporphyritic granite, P GR = porphyritic granite. Legend: Rock types, MGN One of our samples (15/SY6-267 .9) was included in the laboratory measurements of Kjerholt (1992) at the Norwegianlnstitute ofTechnology. The measured values ofthermal conductivity are very similar (NTH: 2.24- 2.25 W m- 1 K- 1, GSF: 2.23 W m- 1 K- 1). Specific heat capacity values measured at NTH are 716 (10°C), 733 (35°C) and 769 J kg- 1 K- 1 (60°C). If the data is extrapolated to 99°C the specific heat capacity would be about 790 1 1 J kt K- , which is very close to the present results at GSF (799 J kg- 1 K- 1) and within our estimated error of determination (5 %) . The thermal diffusivity calculated from measured density, conductivity and specific heat capacity range from 0.9·10-6 to 1.6·10-6 m2 s- 1 (one sample 2.2·10-6 m2 s- 1). The values measured with the Isomet 104 apparatus are somewhat lower and range from 1.1 ·1 G6 to 1.4·10-6 m2 s- 1 • There is a trend of increasing diffusivity with increasing conductivity, which can be attributed to the effect of quartz which has high conductivity and diffusivity. 20 Table 5. Measured thermal conductivity, specific heat capacity, diffusivity and density. s(1) d s(2) Sample No. c k OL-KR1-420. 71 1 772 4.68 2.22E-06 2726 1.12E-6 OL-KR1-450.52 2 784 3.77 1.82E-06 2639 1.24E-6 OL-KR1-402. 79 3 796 3.21 1.48E-06 2725 OL-KR1-423. 86 4 831 2.38 1.04E-06 2748 OL-KR1-418 .40 5 785 3.06 1.42E-06 2733 OL-KR2-342. 76 6 793 2.55 1.17E-06 2742 OL-KR2-354.58 7 800 2.76 1.29E-06 2659 OL-KR2-486.41 8 823 2.50 1.09E-06 2774 OL-KR2-502.81 9 819 2.74 1.22E-06 2727 1.17E-6 RO-KR1-451. 30 10 816 2.69 1.23E-06 2678 1.13E-6 RO-KR1-500.57 11 829 3.11 1.40E-06 2674 1.30E-6 RO-KR1-602.35 12 810 2.81 1.30E-06 2649 1.35E-6 RO-KR1-700.62 13 826 2.51 1.12E-06 2703 RO-KR1-762.87 14 814 2.89 1.28E-06 2754 RO-KR1-782.74 15 818 2.38 1.05E-06 2767 RO-KR3-397 .31 16 854 2.28 9.38E-07 2846 KI-KR1-398. 78 17 832 2.07 8.58E-07 2899 KI-KR2-652. 82 18 829 2.76 1.23E-06 2701 KI-KR3-495. 80 19 819 2.52 1.14E-06 2699 KI-KR3-468.13 20 798 2.63 1.22E-06 2693 1.12E-6 KI-KR3-445. 24 21 788 3.36 1.62E-06 2632 1.28E-6 KI-KR4-415.15 22 796 3.32 1.57E-06 2647 KI-KR4-500.80 23 812 2.72 1.23E-06 2719 KI-KR5-401.50 24 800 2.44 1.11E-06 2741 1.08E-6 15/SY6-267. 9 25 799 2.23 9.80E-07 2847 HH-KR1-500.26 26 795 2.68 1.26E-06 2674 HH-KR1-508.49 27 816 2.84 1.29E-06 2686 HH-KR1-515.50 28 827 2.28 1.05E-06 2618 HH-KR2-404.41 29 809 2.71 1.27E-06 2632 HH-KR2-416.68 30 810 2.67 1.22E-06 2689 1.23E-6 21 Table 5 (cont.) c k HH-KR2-485.69 31 801 3.42 1.62E-06 2625 HH-KR3-494.36 32 799 3.41 1.62E-06 2629 1.26E-6 HH-KR3-504. 71 33 788 3.49 1.67E-06 2650 HH-KR3-527. 73 34 810 3.40 1.59E-06 2629 HH-KR3-531.19 35 811 3.47 1.62E-06 2634 1.40E-6 Sample No. s(1) d s(2) Legend c specific heat capacity (J/(kg K)); calorimeter apparatus GSF k thermal conductivity (WI (mK)); divided bar instrument GSF s (1) calculated diffusivity (m21s) s(2) measured diffusivity (/SOMET 104 apparatus) d density; water-air weighing, GSF 7 RELATIONSHIPS BETWEEN THERMAL PROPERTIES, QUARTZ CONTENT AND DENSITY The compiled measurement data on petrophysical properties and mineralogical composition was also used for investigating relationships between different properties. Thermal conductivity is linearly correlated (r = 0. 71) with quartz content of rocks (Fig. 4). This result allows indirect estimation of thermal conductivity from quartz content data with an uncertainty of about ±0.5 W m- 1 K- 1 which is the typical range of data point scattering around the regression Iine in Fig. 4. Thermal diffusivity (calculated from measured values of conductivity, specific heat capacity and density) is linearly correlated with measured conductivity (Fig. 5). This is not unexpected, since the conductivity values were used in calculating the diffusivity values (eq. 2), and therefore the cross-plotted variables are not fully independent. If the temperature dependence of specific heat capacity is taken into account, the diffusivity values in Fig. 5 increase accordingly. As the temperature dependence is not specifically known for the studied rocks only an estimate of this effect can be given, and the broken Iine in Fig. 5 was calculated assuming a 12 % increase in specific heat capacity between 25 and 99 o C. 22 Directly measured diffusivity (s(2) values in Table 5) and measured thermal conductivity are also positively correlated but the coefficient of correlation and slope of the regression Iine are smaller (Fig. 6). This can be attributed to the small number of samples, the fact that the measurements do not represent exactly the same piece of rock due to different requirements on sample preparation ofthe applied instruments, and the contact resistance effects of the ISOMET transient instrument. If thermal diffusivity is to be estimated indirectly with the aid of conductivity, the regression Iine in Fig. 5 is recommended for this purpose in the investigation sites. Rock density and thermal conductivity are weakly (r = -0.51) correlated (Fig. 7). This can be attributed to the effect of quartz content on these parameters. Quartz has a low density (2630 kg m-3) but high thermal conductivity (7. 7 W m- 1 K- 1), and as a result increasing quartz content of rock increases thermal conductivity but decreases density. A similar trend was reported for Finnish rocks in general by Kukkonen and Peltoniemi (1998). -- 1 ~ - • Measured conductivity vs. quartz content Samples from Posiva investigation sites, N • 35 4 1 E 3: >- 3 •• • • • 1-- > 1-- • 2 () = 0.04 qu :::> + 1.83 0 z 0 () 0 10 20 30 40 50 QUARTZ-% Fig. 4. Relationship between measured thermal conductivity and quartz content of the samples. 23 -1 en Diffusivity vs. conductivity Samples from Posiva investigation sites N 35 = 2.5 C\1 E CD 1 ~ 2.0 >- 1- > 1.5 U) ::::> u.. u.. 1.0 r = 0.53 k (meas) - 0.20 0.99 0 2 2.5 3.0 3.5 4.0 4.5 5 Fig. 5. Relationship between thermal diffusivity (calculatedfrom measured conductivity, specific heat capacity and density) and measured thermal conductivity. The broken Iine indicates the relationship after modifying the specific heat capacity values (measured at 99°C) to room temperature values according to an assumed temperature increase of 12 % in specific heat capacity between 25 and 100 o C. 2.5 Measured diffusivity vs. conductivity -- Samples from Posiva investigation sites. N • 12 1 en C\1 E CD 2.0 1 0 ,.... >- 1.5 1- > en ::::> 1.0 u.. u.. s 0 r = 0.53 = 0.14 k(meas) + 0.81 0.5 2 2.5 3.0 3.5 4.0 4.5 5 Fig. 6. Relationship between directly measured thermal diffusivity and thermal conductivity. 24 3200 Density vs. conductivity Samples from Posiva investigation sites, N • 35 - 3000 C"') 1 E ........ 2800 0) ~ >en z 1-- .... .... 2600 w 0 d r 2400 = -65.70 = -0.51 k(meas) + 2892 2.5 2 3.0 3.5 4.0 5 4.5 CONDUCTIVITY (Wm- 1K- 1} Fig. 7. Relationship between rock density and thermal conductivity. 5.5 Conductivity vs. specitic heat capacity 1 5.0 1 4.5 -E ~ 3: 4.0 >- 3.5 1-- > 1-- u :::> k(meas) = -0.02 c + 19.31 = -0.65 r 1 • 3.0 2.5 0 2.0 u • • 0 z Samples from Posiva investigation sites, N • 35 1.5 • • • ;-.,...-.--oor--,--~r---lr---T---T--r---r"-r--.,----.---T--..--~....,..._-,---+. 700 750 800 850 900 SPECIFIC HEAT CAPACITY (J kg- 1K- 1) Fig. 8. Relationship between speciftc heat capacity and thermal conductivity. 25 A weak negative correlation (r = -0.65) was observed between specific heat capacity and measured thermal conductivity, but the scatter of data points is considerable (Fig. 8). The correlation can be attributed to the effects of variations in the contents of quartz and other felsic major minerals which have slightly smaller specific heat capacity values than mafic minerals (Table 3). 8 DISCUSSION AND CONCLUSIONS The present results indicate the typical values of thermal properties of the rock types in the Posiva investigation sites. Thermal conductivity can be estimated with the aid of simple estimators and quantitative data on mineralogical composition. Particularly, geometric mean seems to be a good estimator for isotropic, fine or medium-grained rocks. Thermal conductivities of very coarse-grained rocks are more difficult to determine, because typical samples and thin sections represent too small volumes in comparison to the texture of the rocks. This problem could be overcome either by increasing the sample size, but in the case of pyterlitic textures reasonable laboratory samples prepared from drill cores are probably never sufficiently big. lnstead, in situ techniques should be developed for measurements in boreholes. The mineral composition of rocks should also be determined with altemative methods, as thin sections cannot be prepared nor investigated under the microscope in a size which would be essentially larger than the present size (40 mm in diameter). For instance, chemical silicate analysis of the mineral composition could be tested as an altemative. In this study, thermal diffusivity was measured in two ways, both indirectly through conductivity, density and calorimetric measurement of specific heat capacity, as well as through direct measurement. Both techniques have their advantages and disadvantages. The method based on specific heat is influenced by the temperature dependence of thermal properties, if the all measurements are not representative of the same temperature. The temperature effect could be corrected for, given that specific heat of the rock is known as a function of temperature. The increase of specific heat capacity of typical rocks is about 12 % between 25 and 100°C. lt would increase the calculated diffusivity values correspondingly ifmodified to room temperature (Fig.5). This, however, cannot be done very accurately as the temperature dependencies of conductivity and specific heat capacity are not known specifically of these samples. 26 The direct measurements of thermal diffusivity are rapid to make with the instrument applied in this study, but the measurements suffer from the contact resistance problems, and the surface preparation, applied loading or possible fluid in the contact have essential effects on the results. The present results are based on measurements on a dry slightly polished (powder 180) surface. Further, the small size of the drill cores in respect to the surface probe is problematic, too, and may create a deviation from the assumed halfspace condition. Thus, we consider the direct measurements only as estimates of the order of magnitude of diffusivity. The investigated relationships between measured petrophysical and compositional data suggest that thermal diffusivity can be estimated indirectly with the relationship between conductivity and diffusivity (Fig. 5). As a frrst approximation, such an estimate can substitute the measurement of specific heat capacity and density for the determination of diffusivity. Measurements of thermal conductivity could be substituted with an estimate based on the relationship between quartz content and conductivity (Fig. 4), but the obtained estimation accuracy (±0.5 W m- 1 K- 1) is inferior to that of measurements of samples (about ±0.2 W m- 1 K- 1). Thermal conductivity of the Hästholmen samples are smaller for the pyterlitic granites (2.3-2.8 W m- 1 K- 1) than in the even grained or porhyric granites (3.4-3.5 W m- 1 K- 1) reflecting their different quartz contents. Specific heat capacities of the Posiva rocks range from 770 to 830 J kg- 1 K- 1, with the following mean values for each area: Olkiluoto 798 ± 20 (std) J kg- 1 K- 1 , Romuvaara 824 ± 15 J kg- 1 K- 1 , Kivetty 809 ± 16 J kt 1 K- 1 and Hästholmen 807 ± 11 J kg- 1 K-1. Thermal diffusivity (calculated from measured conductivity, heat capacity and density) values are correspondingly: Olkiluoto 1.42 ± 0.38 ·10-6 m2 s-t, Romuvaara 1.19 ± 0.16 ·10-6 m 2 s- 1 , Kivetty 1.25 ± 0.25 ·10-6 m 2 s- 1 and Hästholmen 1.42 ± 0.22 ·10-6 m 2 s- 1 • 9 REFERENCES Cermåk, V. and Rybach, L., 1982. Thermal conductivity and specific heat of minerals and rocks. In: G. Angenheister (Editor), Landolt-Börnstein: Numerical Data and Functional Relationships in Science and Technology, New Series, Group V (Geophysics and Space 27 Research), Voi. 1a (Physical Properties of Rocks). Springer, Berlin, p. 305-343. England, P. C. , 1978. Some thermal considerations of the Alpine metamorphism - past, present and future. Tectonophysics, 46, 21-40. Kukkonen, 1. and Lindberg, A., 1995. Thermal conductivity of rocks at the TVO investigation sites Olkiluoto, Romuvaara and Kivetty. Nuclear Waste Commission of Finnish Power Companies, Report YJT-95-08, 29 pp. Kukkonen, I.T. and Peltoniemi, S., 1998. Relationships between thermal and other petrophysical properties of rocks in Finland. Physics and Chemistry of the Earth (in press). Kjerholt, H., 1992. Thermal properties of rocks. Teollisuuden Voima Oy, TVO/Site investigations, work report 92-56, 13 pp. Schön, J., 1983. Petrophysik. Ferdinand Enke, Stuttgart, 405 pp. 28 APPENDIX PHOTOGRAPHS OF THE THERMAL CONDUCTIVITY SAMPLES FROM THE HÄSTHOLMEN DRILL HOLES Sample identification: Number in photo Sample 1 HH-KR1-500.26 2 HH-KR1-508.49 3 HH-KR1-515.50 4 HH-KR2-404.41 5 HH-KR2-416.68 6 HH-KR2-485.69 7 HH-KR3-494.36 8 HH-KR3-504. 71 9 HH-KR3-527. 73 10 HH-KR3-531.19 29 1 2 4 5 7 8 3 9 0 2 4 CM