thermal properties of rocks at the investigation sites: measured and

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




Ilmo Kukkonen

Antero Lindberg

March 1998

AUTHOR ORGANIZATION:

ORDERER:

NUMBER OF THE ORDER:

CONTACT PERSON OF THE ORDERER:

CONTACT PERSON OF THE AUTHOR ORGANIZATION:

Geological Survey of Finland P.O. Box 96 FIN -02151 Espoo Finland

Posiva Oy Mikonkatu 15 A FIN -00100 Helsinki Finland

9798/971 AJH

tlh'vnJ 1/w~~. Aimo Hautajärvi

Ilmo Kukkonen

WORKING REPORT 98-09e

THERMAL PROPERTIES OF ROCKS IN THE POSIV A INVESTIGATION SITES: MEASURED AND CALCULATED THERMAL CONDUCTIVITY, SPECIFIC HEAT CAP ACITY AND THERMAL DIFFUSIVITY

NAMES OF THE AUTHORS:

EXAMINER OF THE AUTHOR ORGANIZATION:

·-:=2o~.~~,_._ ~,L__A Ilmo Kukkonen and Antero Lindberg 7 Dr. Tech. M.Sc.

L(~~ Lauri Eskola Research Professor Research & Development, Geophysics




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 LÄMMÖNJOHTA VUUS, 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

alhaisempi (2.3-2.8 W m-1 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 m2 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 ± 0.38 ·10-6 m2 s-1, Romuvaara 1.19 ± 0.16

·10-6 m2 s-1, Kivetty 1.25 ± 0.25 ·10-6 m2 s-1 and Hästholmen 1.42 ± 0.22 ·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 se Ieeted 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




OL-KR1 402.91-403.03 3 Mica gneiss



RO-KR1 450.95-451.20 10 Tonalite gneiss



KI-KR3 467.99-468.10 20 Porphyritic granodiorite

KI-KR3 445.09-445.20 21 Granite

KI-KRS 401.28-401. 38 24 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 % .

• -------1 r-)--~ WARM (r-~r.~~~

• ' : _ _ WATER _ __ ! .....,__\~.J T1

Temperature T 2 sensors

Quartz

~~.~-=~·:~~~-~~·:_~ .. ·:~.#-(G_~·::\ /~ Sample ~,:. : h5 a

F.-~~~~-.·;~~~-~-~~~~~~.~~~ .(;,: ~:?; 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 m1 is the mass of the sample (kg), CK is the heat capacity of the calorimeter (70

9

J K-1), Cp is the specific heat capacity of water (4180 J kg-1 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 (v1) 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.

Computer

' - - .......... .. "'/ ' (!J/) '\ Hg-thermometer

1

~~.=:=----.-.-t-- T -sensor ..__...ioiooiioio~ .... - ... ~- Sample

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 sensor

Drill core

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)

where s is diffusivity (m2 s-1), k is thermal conductivity (W m-1 K-1

), d is density (kg

m-3) and c is specific heat capacity (J kg-1 K-1

).

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.

Mineral 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

sericite

epidote 0.1 + 0.1 + 0.1

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

zircon + + + opaques 0.8 0.9 0.4 0.1 1.1

Total 100.0 100.0 100.0 100.0 100.0

Anorthite-% 35 30 27 33 30

Rock type PYT PYT PYT PYT

Table 2 (cont.)

Legend

HH-KR1 = Hästholmen drill hole 1

12

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 of plagioclase 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.

Mineral HH-KR3 HH-KR3 HH-KR3 HH-KR3 HH-KR3

no 6 no 7 no 8 no 9 no 10

485.69 494.36 504.71 527.73 531.19

plagioclase 23.4 22.1 18.4 22.1 20.8

K-feldspar 36.2 40.6 43.3 35.5 37.6

quartz 34.1 30.9 33.5 34.8 35.1

biotite 2.9 3.3 2.7 4.3 3.6

homblende 0.1 0.3

muscovite/ 0.9 0.9 0.5 1.0 0.6

sericite

epidote 0.1 0.4 0.1 0.5 0.1

carbonate + apatite + + + + 0.1

chlorite 1.1 0.7 0.7 1.1 0.8

fluorite 0.7 0.8 0.3 0.4 0.7

zircon + (+) + + + opaques 0.6 0.3 0.4 0.3 0.3

Total 100.0 100.0 100.0 100.0 100.0

Anorthite-% 28 30 35 30 29

Rock type EGGR EG/P GR 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.

1 0) 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 CAP ACITIES 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 1 oooc.

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

data ranges from about 700 to as high as 1200 J kg-• K-1 (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 670-

1300 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).

Mineral Schön (1983) Cermak and Rybach (1982)

(17-27°C) (0°C)

Plagioclase 711-837 700-709

albite 710-750 709

Olicoclase Ab89Anll 837 744 (at 25°C)

Labrador Ab46Afls4 700

Anorthite Ab4A~6 711 700

Potassium feldspar

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 800 (60°C)

Diopside 700-750 690

Olivine

Forsterite 980 790 (36°C)

Fayalite 840 550

Carbonates 800-880 780-930

Gamet 740 (pyrope at 58°C)

Fluorite 900 850

Sillimanite 743

Zircon 610 (at 60°C)

Pyri te 500-520 500

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 MGN 4.26 2.96 3.49 3.06

OL1-420.71 GR 6.05 4.16 5.15 4.68

OL1-423.86 MGN 3.85 2.69 3.13 2.38

OL1-450.52 GR 3.57 2.76 3.06 3.77

OL2-342.76 GRDR 3.75 2.70 3.11 2.55

OL2-354.58 GRDR 3.61 2.79 3.12 2.76

OL2-486.41 MGN 4.15 2.89 3.39 2.50

OL2-502.81 MGN 4.17 2.89 3.41 2.74

R01-451.30 GRGN 3.82 2.70 3.13 2.69

R01-500.57 TGN 4.12 2.82 3.34 3.11

R01-602.35 GRGN 3.45 2.53 2.87 2.81

R01-700.62 TGN 3.43 2.48 2.83 2.51

R01-762.87 MGN 4.15 2.81 3.35 2.89

R01-782.74 MGN 3.74 2.60 3.03 2.38

R03-397.31 MGN 3.25 2.50 2.77 2.28

R03-398.78 MGN 3.30 2.56 2.83 2.07

KI1-652.82 GR 3.53 2.69 3.01 2.76

KI2-495.80 GRDR 3.49 2.58 2.91 2.52

KI3-415.15 GR 4.13 2.94 3.42 3.32

Kl3-445.24 GR 4.45 3.13 3.69 3.36 KI3-468.13 GR 3.22 2.52 2.77 2.63 K14-500.80 GR 3.32 2.58 2.85 2.72

KI5-401.50 GR 3.28 2.53 2.80 2.44

15/SY6-267 .00 DR 2.41 2.22 2.29 2.23

HH1-500.26 PYT 3.73 2.80 3.16 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

Table 4 ( cont.)

Sample

HH3-494.36

HH3-504.71

HH3-527.73

HH3-531.19

Rock type

EG/P GR

PGR

EG/P GR

EGGR

k(ar)

4.02

4.14

4.21

4.24

19

k(har)

2.90

2.98

2.99

3.01

k(geo)

3.35

3.45

3.49

3.52

k(meas)

3.41

3.49

3.40

3.47

Legend: Rock types, MGN = 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.

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

J kt1 K-1, 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.

Sample No. c k s(1) d s(2)

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.)

Sample No. c k s(1) d s(2)

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

Legend

c specific heat capacity (J/(kg K)); calorimeter apparatus GSF

k thermal conductivity (WI (mK)); divided bar instrument GSF

s (1) calculated diffusivity (m21 s)

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 ~ -1

E 3:

>-1-->

4

3

1-- 2 () :::> 0 z 0 ()

0

Measured conductivity vs. quartz content

Samples from Posiva investigation sites, N • 35

• •

•

= 0.04 qu + 1.83

10 20 30

QUARTZ-%

• • •

•

40 50

Fig. 4. Relationship between measured thermal conductivity and quartz content of the

samples.

--1en 2.5 C\1

E CD 1

~ 2.0

>-1-> 1.5 U) ::::> u.. u.. 1.0 0

2

23

Diffusivity vs. conductivity Samples from Posiva investigation sites N = 35

0.53 k (meas) - 0.20 r = 0.99

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

--1 en

C\1 2.0 E CD 1 0 ,....

>- 1.5 1-> en ::::> 1.0 u.. u.. 0

0.5 2

Measured diffusivity vs. conductivity

Samples from Posiva investigation sites. N • 12

2.5

s = 0.14 k(meas) + 0.81 r = 0.53

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


3000 -C"')

1 E ........

0) 2800 ~ ....

>-1-- 2600

....

en z w -65.70 k(meas) + 2892 0 d =

2400 r = -0.51

2 2.5 3.0 3.5 4.0 4.5 5

CONDUCTIVITY (Wm- 1K- 1}

Fig. 7. Relationship between rock density and thermal conductivity.

1 ~ -1 E

3:

>-1--> 1--u :::> 0 z 0 u

5.5

5.0

4.5

4.0

3.5

3.0

2.5

2.0

Conductivity vs. specitic heat capacity


• k(meas) = -0.02 c + 19.31 r = -0.65

• 1

•

• •

•

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 half

space 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 kt1 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 m2 s-1, Kivetty 1.25 ± 0.25 ·10-6 m2 s-1 and Hästholmen 1.42 ± 0.22 ·10-6 m2 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 3

4 5

7 8 9

0 2 4 CM

thermal properties of rocks at the investigation sites: measured and

Documents