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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