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ONKALO POSE Experiment – Determination of In Situ Thermal Properties of Rocks in Drillholes ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411 POSIVA OY Olkiluoto FI-27160 EURAJOKI, FINLAND Phone (02) 8372 31 (nat.), (+358-2-) 8372 31 (int.) Fax (02) 8372 3809 (nat.), (+358-2-) 8372 3809 (int.) December 2014 Working Report 2014-41 Arto Korpisalo, Ilkka Suppala Ilmo Kukkonen Teemu Koskinen
Transcript of ONKALO POSE Experiment – Determination of In Situ Thermal ... · ONKALO POSE EXPERIMENT –...
ONKALO POSE Experiment –Determination of In Situ Thermal Properties
of Rocks in Drillholes ONK-PP340, ONK-PP346,ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411
POSIVA OY
Olki luoto
FI-27160 EURAJOKI, F INLAND
Phone (02) 8372 31 (nat. ) , (+358-2-) 8372 31 ( int. )
Fax (02) 8372 3809 (nat. ) , (+358-2-) 8372 3809 ( int. )
December 2014
Working Report 2014-41
Arto Korpisalo, I lkka Suppala
I lmo Kukkonen
Teemu Koskinen
December 2014
Working Reports contain information on work in progress
or pending completion.
Arto Korpisalo, I lkka Suppala
Geological Survey of F inland
I lmo Kukkonen
University of Helsinki
Teemu Koskinen
Stips Oy
Working Report 2014-41
ONKALO POSE Experiment –Determination of In Situ Thermal Properties
of Rocks in Drillholes ONK-PP340, ONK-PP346,ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411
ONKALO POSE EXPERIMENT – DETERMINATION OF IN SITU THERMAL PROPERTIES OF ROCKS IN DRILLHOLES ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411
ABSTRACT
The thermal drillhole device TERO76 (for Ø76 mm drillholes) used in this study for determining thermal properties of rocks in situ was developed at the Geological Survey of Finland for Posiva in the early 2000’s. The measurement method is based on monitoring the temperature variation of a cylindrical heating source in a drillhole. The measured data can be interpreted with full numerical 3D codes as well as with an analytical infinite line source method, a ‘rapid interpretation tool’, which makes it possible to calculate the first estimates of thermal properties already in the field. Both methods were applied in this study. Because of the unique measurement geometry, only the thermal conductivities can accurately be estimated using the late times of heating periods (accuracy 2%). The cylindrical source method cannot directly give the thermal diffusivity or volumetric heat capacity at a sufficient accuracy. Thermal diffusivities are estimated by using the average specific heat capacities and densities of the rock type at the measurement point, or the laboratory results on the general diffusivity-conductivity relationship for different Olkiluoto rock types. The latter technique was applied in this study. Thermal properties were determined in four shallow drillholes (ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411) located in the ONKALO investigation niche 3 (ONK-TKU-3620) at the access tunnel chainage of 3620 m. The measurement positions (17) were strictly selected on the grounds that approximately an equal number of in situ results would be available in both veined gneiss (VGN) and pegmatitic granite (PGR). The results from the drillholes ONK-PP340 and ONK-PP346 measured in a previous project are also presented in this report. In veined gneiss, the average conductivity determined with numerical model of the present measurements is 3.49 (2.83) Wm-1K-1 and diffusivity 1.8910-6 (1.3710-6) m2s-1. The laboratory values of Olkiluoto rocks types are represented in the parentheses. The corresponding values determined with the analytical line source method are 3.33 Wm-1K-1 and 1.7710-6 m2s-1. In pegmatitic granite, the average numerical conductivity is 3.76 (3.20) Wm-1K-1 and diffusivity 2.0110-6 (1.7510-6) m2s-1. The analytical conductivity and diffusivity values of pegmatitic granite are 3.59 Wm-1K-1 and 1.9110-6 m2s-1, respectively. The results agree well with the previous TERO results at Olkiluoto and in the ONKALO. The analytically determined values are on the average about 5% lower (always within <10%) than the numerically determined values. When comparing with the laboratory values, the analytical results are, on the other hand, higher than the laboratory values (~10%). The difference may be attributed to the anisotropy of thermal conductivity controlled by the orientation of gneissic foliation, to the drillholes intersecting the foliation at abrupt angles and to the fact that the TERO measurements represent conductivity (diffusivity) values in the radial direction from the drillhole. Reasons for the difference between the numerical and analytical results can be generated, for instance, by the numerical model inaccuracies, poorly known thermal
bulk properties of the probe due to problems in calibrating a long probe, approximations included in the analytical method, or using different time intervals of the heating period. Keywords: Thermal conductivity, specific heat capacity, thermal diffusivity, nuclear, waste disposal, Olkiluoto, TERO, drillhole.
KALLION IN SITU TERMISTEN MÄÄRITYS KAIRANREI'ISSÄ ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411 TIIVISTELMÄ
Tässä työssä käytetty kallion termisten ominaisuuksien in situ mittaamiseen tarkoitettu TERO- laitteisto (reikäkoko Ø76 mm) kehitettiin ja rakennettiin GTK:ssa yhteistyönä Posiva Oy:n kanssa 2000 luvun alussa. Mittausmenetelmä perustuu sylinterimäisten lähteiden hyväksikäyttöön kairanrei'ssä. Mittausdata tulkitaan numeerisella 3D-ohjelmalla ja analyyttisellä äärettömän viivalähteen menetelmällä, "rapid interpretation tool", joka mahdollistaa termisten ominaisuuksien estimaattien laskemisen jo kentällä. Tässä työssä tulokset on laskettu molemmalla menetelmällä. Mittausgeometrian takia vain lämmönjohtavuus voidaan arvioida (2 %) suoraan käyttämällä hyväksi lämmityskäyrien loppuosia. Menetelmällä ei saada arvioitua kallion diffusiviteettia tai lämpökapasiteettia tilavuusyksikköä kohti riittävän tarkasti. Diffusiviteetti voidaan arvioida kivityypin keskimääräisen ominaislämpökapasiteetin ja tiheyden avulla ja/tai lämmönjohtavuuden ja diffusiviteetin korrelaation avulla. Tässä työssä käytettiin hyväksi jälkimmäistä tekniikkaa.
TERO mittaukset tehtiin ja kallion lämpöominaisuudet määrättiin neljässä uudessa kairanreiässä (ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411) ONKALOn POSE tutkimustilassa +345 m tasolla. Seitsemäntoista uutta mittauspistettä valittiin siten, että in situ tuloksia olisi yhtä monta sekä suonigneissistä (VGN) että pegma-tiittisestä graniitista (PGR). Kairanreiät ONK-PP340 ja ONK-PP346 oli mitattu edellisessä projektissa, ja tulokset on esitetty myös tässä raportissa. Tutkimuksen tuloksena suonigneissin keskimääräinen numeerinen lämmönjohtavuus on 3,49 (2,83) Wm-1K-1 ja diffusiviteetti 1,8910-6 (1,3710-6) m2s-1 sekä analyyttinen johtavuus 3,33 Wm-1K-1 ja diffusiviteetti 1,7710-6 m2s-1. Olkiluodon kivien laboratoriomittausten keskimääräiset johtavuudet ja diffusiviteetit on esitetty suluissa. Pegmatiittisen graniitin keskimääräinen numeerinen lämmönjohtavuus on 3,76 (3,20) Wm-1K-1 ja diffusiviteetti 2,0110-6 (1,7510-6) m2s-1 sekä analyyttinen lämmönjohtavuus 3,59 Wm-1K-1 ja diffusiviteetti 1,9110-6 m2s-1. Tulokset sopivat hyvin yhteen aiempien TERO -tulosten kanssa Olkiluodossa ja ONKALOssa. Analyyttiset tulokset ovat keskimäärin <5 % pienemmät kuin numeeriset ja aina <10 % pienemmät. Toisaalta, analyyttiset arvot ovat <10 % suuremmat kuin laboratorioarvot. Ero johtunee kivilajien lämmönjohtavuuden ansiotrooppisuudesta, joka riippuu gneissin liuskeisuudesta, reikien ja liuskeisuuden välisestä kulmasta, ja siitä että TERO -tulokset edustavat lämmönjohtavuutta kairanreiän radiaalisuunnassa. Numeeristen ja analyyttisten tulosten erot voivat johtua esimerkiksi numeerisen mallin epätarkkuudesta, lämpölähteen heikosti tunnetuista lämpöominaisuuksista, analyytti-sessä menetelmässä tehdyistä oletuksista, tai lämmityskäyrän erilaisesta hyväksi-käytöstä. Avainsanat: Lämmönjohtavuus, ominaislämpökapasiteetti, terminen diffusiviteetti, ydinjätteiden loppusijoitus, Olkiluoto, ONKALO, TERO, kairanreikä.
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TABLE OF CONTENTS ABSTRACT TIIVISTELMÄ
PREFACE ....................................................................................................................... 3
1 INTRODUCTION .................................................................................................... 5
2 DRILLHOLE LOGGING DEVICE TERO ................................................................. 7
3 MEASUREMENT PRINCIPLES ............................................................................ 11
3.1 Principles of measuring rock thermal properties in a drillhole ....................... 11
3.2 Practical approach ........................................................................................ 11
4 MEASUREMENTS WITH TERO IN SITU LOGGING DEVICE ............................ 13
4.1 TERO76 measurements in drillholes ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405 and ONK-PP411 ................................................ 13
4.2 Laboratory measurements of drillcores of Olkiluoto type rocks .................... 16
4.3 Estimates of thermal properties in situ .......................................................... 16
5 SUMMARY OF RESULTS .................................................................................... 25
6 DISCUSSION AND CONCLUSIONS .................................................................... 35
REFERENCES ............................................................................................................. 37
APPENDIX A ................................................................................................................ 39
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3
PREFACE
The study has been carried out at the Geological Survey of Finland (GTK) on contract for Posiva Oy. On behalf of the orderer, the supervising of the work was done by Topias Siren and Johanna Savunen (Posiva Oy) and Erik Johansson (Saanio & Riekkola Oy). The report was previewed by Prof. John Hudson (REC, UK). The geophysical design, equipment, construction, measurements, software development, interpretation and reporting were done by Arto Korpisalo and Ilkka Suppala (GTK), Ilmo Kukkonen (Helsinki University) and Teemu Koskinen (Stips Oy).
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5
1 INTRODUCTION
Thermal parameters of rocks are necessary data in planning a final repository for spent nuclear fuel in deep bedrock. The thermal properties of rocks can be determined from laboratory measurements of core samples, theoretical calculations from mineral composition and data on properties of the constituent minerals, and with in situ measurements in drillholes. Laboratory measurements and theoretical calculations on thermal properties of rocks at Olkiluoto and other previous disposal candidate sites in Finland have been presented previously by Kjørholt (1992), Kukkonen Lindberg (1998, 1995), Kukkonen et al. (2011) and Kukkonen (2000). A comparison between different laboratory measurements applied in site studies in Finland and Sweden has been given by Sundberg et al. (2003). In situ measurements have been under development in Posiva since 1999. Kukkonen and Suppala (1999) summarized the literature data on various in situ techniques and carried out theoretical simulations of in situ measurements. At the beginning of the 2000’s, two devices were developed and constructed for determining thermal properties of rocks in situ under projects with Posiva. The first version, TERO56, was usable in Ø56 mm diameter drillholes (Kukkonen et al. 2005) but, after drilling of new and larger 76 mm diameter drillholes, a new 76 mm device TERO76 was designed and constructed (Kukkonen et al. 2007). In 2010, the renovation of the TERO76 device was accomplished with some new features (Kukkonen et al. 2014).
The numerical estimations of thermal properties are based on fitting measured temperature data to forward modelling of conductive heat transfer from a cylindrical heating source with finite length (Kukkonen et al. 2011). An analytical rapid slope interpretation tool was designed to estimate the thermal conductivity quickly immediately after a measurement session has been finished in the field. The slope method is based on fitting measured temperatures as a function of time to asymptotic functions of an infinite line model to yield the value of the thermal conductivity from the slope of the fitted line during the heating period (Korpisalo et al. 2012). The diffusivities are simply estimated using the laboratory results on the diffusivity-conductivity relationship of different Olkiluoto rock types (Kukkonen et al. 2011). With the developed software the thermal conductivity and diffusivity profiles of the measurement range in a drill hole are available when the last measurement has been taken. On the other hand, the first estimates of the rapid slope method can serve as starting points or seeds for the numerical and more sophisticated inversion procedures.
The present study reports results from TERO76 measurements in six shallow drillholes (ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411) located in the ONKALO investigation niche 3 (ONK-TKU-3620) at the access tunnel chainage 3620 m.
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7
2 DRILLHOLE LOGGING DEVICE TERO
TERO probes (TERO56 and TERO76) are used with the same winch and cables (Kukkonen et al. 2014, 2007; Suppala et al. 2004). The complete logging device comprises the drillhole tool, logging cable and winch, together with the computer and current source located at the ground surface. The winch and steel armoured cable were purchased from the German company LogIn GmbH, and they represent standard geophysical logging instrumentation of the day. The cable is a 700 m long, steel armoured, 4-conductor, logging cable. The motorized winch is controlled from a separate control panel. In principle, the winch system has an option for automated operation, but this is not included in the present TERO devices.
A computer collects the depth data from the winch and, with the aid of the control unit, also measured resistances from temperature sensors, heating current and voltage, as well as the resistances of the single point resistance sensor.
The main components of the TERO devices are shown in Figure 1. The system at the Geological Survey of Finland (GTK) in Espoo is depicted in Figure 2.
Figure 1. The components of the TERO logging devices (not to scale) (Kukkonen et al. 2005).
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Figure 2. TERO logging device at GTK, Espoo (Kukkonen et al. 2005).
The basic properties of the TERO devices are as follows: determination of thermal conductivity and diffusivity in situ in 56/76 mm diameter
water-filled drillholes the measurement principle: thermal response of a heated cylinder length of cable is 700 m, motorized winch the outer diameter of the probe is 50/70 mm length of the heated part of the probe is 1.64 m heating power is 1050 W monitoring of heating power is carried out from the probe and cable at surface heating takes place with heating foils installed at the inner surface of the probe tube flow of water along the measurement section is prevented with soft packers made of
silicon rubber number of NTC temperature sensors is 28/4, located on the inner surface of
aluminium tube, resolution 0.5 mK, range 430ºC a galvanic single point sensor is included in the tool for the precise determination of
logging depth a common control box for the electronics of TERO and SinglePoint measurements
(Figure 3a) a power source (UPS) to assure continuous measurements also during possible
disturbances in the common power network (Figure 3b)
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a)
b)
Figure 3. a) TERO control box. b) New power source (UPS). Photo: Korpisalo 2013.
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3 MEASUREMENT PRINCIPLES
3.1 Principles of measuring rock thermal properties in a drillhole
The measurement principle of TERO devices is monitoring the temperature of a heated finite length cylinder in a drill hole (Kukkonen et al. 2014, 2007, 2004, 2001; Suppala et al. 2004). Let us assume a situation where the in situ probe (the cylinder) is initially in a drillhole under thermal stationary conditions. When the probe is heated, its temperature, as a function of time, depends on the applied heating power, heat capacity of the probe, heat losses into rock, thermal properties of the surrounding rock and the thickness of the water layer between the probe and drillhole wall. Temperatures are also dependent on the internal structure of the probe and its material properties. In the present numerical study, the probe properties are taken into account as solid parameters in the time-dependent heat conduction model. The remaining parameters, which need to be estimated, are the thermal properties of the surrounding medium. In a drillhole, the probe is (mostly) immersed in water, and the thickness of the water layer varies with varying hole calliper. In the interpretation, when in situ diffusivities (alternatively volumetric heat capacity) of the rock must be estimated, the water layer, acting as a heat capacitor and resistance, must be taken into account. Thus, when heating is turned on, the rapid rise in temperature is dependent mainly on the thermal properties of the probe and the thermal resistance between the probe and surroundings, and a temperature gradient is generated between probe and rock. As the heating power is constant, the temperature rise reaches an asymptotic behaviour, showing a constant increase as a function of the logarithm of time (at late heating times). At the asymptotic phase, the temperature rise depends on the thermal conductivity of the surrounding rock. After heating is turned off, a rapid temperature drop is followed by a slower decrease of the temperature due to continued dissemination of the heat into the rock.
The linear equation of conduction of heat determines the temperature (r,t) distribution (Carslaw Jaeger 1959; Jager & Charles-Edwards 1968). When numerical model studies are undertaken, the model (probe and the surroundings) must be discretized in high detail to ensure acceptable results. It is possible to approach the problem using simplified analytical models, e.g. an infinite line-source or infinite long hollow probe model. A short mathematical analysis of conduction equation and the main mathematical principles of the simplified models are given in Appendix A.
3.2 Practical approach
An infinite line-source and an infinite hollow probe model are analytical cylinder models. When late times of heating period are concerned, the temperature rise of both models can be simplified to the asymptotic functions Eq. 6 and Eq. 9 (Appendix A). Thus, the rock conductivity can be obtained from the slopes of the temperature curves against the natural logarithm of time. Such an approach of estimating conductivity with the model c1*log(t)+c2 is entirely appropriate if one discards the data from small times and uses only data for times when there is a linear relationship between temperature and log(t). This approach is widely used in many disciplines with considerable success (see e.g. Kukkonen and Suppala 1999). The approach works because the properties of the probe (e.g. diameter, construction) are not important at late times when the temperature curve exhibits log-linear behaviour. However, the confident use of this technique should
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contain a thorough exploration when the time has been elapsed before the (1/t)-term becomes sufficiently small so that they can be ignored and what could be the value of contact resistance H between the probe and the environment.
The Rapid Interpretation Tool (slope method) for conductivity and diffusivity determinations in rocks is implemented in MATLAB® software (Figure 4). The infinite line model allows the usage of late heating and late cooling periods in conductivity estimations. Adding a correction term into Eq. 6 (Appendix A) is supposed to take into account, e.g. a contact resistance and the deviations of the Ei-function from the logarithm function (Vries 1952). Thus, there are three available models to be used in the GUI to interpret TERO measurements: infinite line model, infinite line model with correction term, and Blackwell’s hollow tube model. In the last model, only the late heating period can be used for calculations. After the rock conductivity has been determined, the diffusivity can be estimated simply (Korpisalo et al. 2012).
Figure 4. Rapid Interpretation Tool for TERO data (Korpisalo et al. 2012).
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4 MEASUREMENTS WITH TERO IN SITU LOGGING DEVICE
4.1 TERO76 measurements in drillholes ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405 and ONK-PP411
The TERO76 measurement series was continued in four shallow drillholes (ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411) located in the ONKALO investigation niche 3 (ONK-TKU-3620) at the access tunnel chainage 3620 m in March 2014 (Figures 5 and 6). The drillholes ONK-PP340 and ONK-PP346 were measured during a previous measurement project (March 2012) and the results are also be presented in this report (Valli et al. 2014). The drillholes intersected mostly veined gneiss (VGN) and pegmatitic granite (PGR) thus, being the same rock type where the spent nuclear fuel canisters are going to be disposed. The measurement points (17) were strictly selected so that approximately an equal number of values would be available in both VGN and PGR.
New timing settings of the measurements adapted in the previous projects were utilized. When the probe is centralized in a measurement point where the four thermistors are precisely at the level of the measurement depth, a stabilization period of ~56 hours is taken. The actual measurement is done by using a heating period of 6 hours and a short cooling period (1020 min) followed by removal of the probe to the next measurement position.
Figure 5. The detailed layout of the investigation niche 3 (ONK-TKU-3620) (left) and the location of niche at the access tunnel chainage 3620 in the ONKALO (right).
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Figure 6. The locations of the measured shallow drillholes in the ONKALO investigation niche 3 (ONK-TKU-3620) are marked by red circles and ONK-EH3 (ONK-PP259) by a blue circle (Valli et al. 2014). See the location of ONK-EH3 in Figure 5 above.
The ONKALO measurements were performed in March 2014 (between March 20 and 30, 2014). The drillholes were shallow with depths of <10 m. Thus, the measurements deviated from the usual conditions at the surface. The additional weights could not be used and the probe was manhandled downwards by hand using a firm steel pole but pulling upwards could be done by the winch. The measurement points were strictly selected based on the rock type (Figure 7).
Figure 7. Rock type analysis of drillholes in the POSE niche (Toropainen 2014, 2012). Approximate measurement points are schematically presented by black arrows (not to scale).
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In addition, the point in a particular rock type (VGN/PGR) was selected so that at least the whole heating part of the probe was in that rock type. The points were carefully marked on the winch cable to lower the probe precisely to the same depths. The measurement programme was conducted starting from the lowest point (6.95 m) of drillhole ONK-PP398 and continuing to the third lowest point (5.4 m) to avoid and minimize the thermal disturbance from the previous measurement point. The next position was the uppermost (1.80 m) after which the probe was lowered to the second lowest position (6.20 m), and so on. Thus, there was always room enough between the adjacent positions to avoid any disturbance from the previous measurement (Figure 8).
Figure 8. TERO measurement ongoing in the investigation niche 3 (ONK-TKU-3620) drillhole ONK-PP398. Drillhole ONK-EH3 (ONK-PP259) is secured with a yellow metal frame. Photo: Korpisalo 2014.
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4.2 Laboratory measurements of drillcores of Olkiluoto type rocks
In the report by Kukkonen et al. (2011), the results of laboratory measurements of Olkiluoto rock types carried out at the Geological Survey of Finland during 19942010 are summarized. The average thermal conductivity (25°C) of samples is 2.91 Wm-1K-1, and the averages of the main rock types fall within 2.663.20 Wm-1K-1. The highest average conductivities are related to pegmatitic granite and the lowest to mica gneiss. The average specific heat capacity (at 25°C) of all samples is 712 Jkg-1K-1. The highest specific heat capacity averages were observed for veined gneiss and mica gneiss, and the lowest for pegmatitic granite. Diffusivity was calculated from measured values of conductivity, specific heat capacity and density. Average diffusivity is 1.4710-6 m2s-1, and the averages of rock types are within 1.341.7510-6 m2s-1. The highest values are related to pegmatitic granite, and the lowest values to mica gneiss (Table 1).
Table 1. Summary of rock thermal properties in Olkiluoto (Kukkonen et al. 2011).
Rock type
Conductivity Wm-1K-1
Std N Specific heat
capacity Jkg-1K-1
Std N Diffusivity 10-6m2s-1
Std N Density kgm-3
Std N
VGN 2.83 0.53 216 725 33 149 1.37 0.25 147 2741 43 218
TGG 2.78 0.39 56 696 19 22 1.35 0.12 21 2700 29 54
DGN 2.95 0.64 20 708 28 17 1.53 0.34 17 2742 51 20
MGN 2.66 0.49 6 724 41 6 1.34 0.28 6 2742 33 6
PGR 3.20 0.41 89 689 17 61 1.75 0.18 61 2635 38 89
KFP 2.78 n.a. 1 687 n.a. 1 1.48 n.a. 1 2729 n.a. 1
QGN 2.49 n.a. 2 714 n.a. 1 1.01 n.a. 1 2766 n.a. 2
All samples
2.91 0.51 390 712 32 257 1.47 0.29 254 2711 59 389
Values are given at room temperature; Std = standard deviation; N = number of samples; Rock types: VGN, veined gneiss; TGG, tonalitic-granodioritic-granitic gneiss; DGN, diatexitic gneiss; MGN, mica gneiss; PGR, pegmatitic granite; KFP, potassium-feldspar porphyry; QGN, quartzitic gneiss.
4.3 Estimates of thermal properties in situ
In the following, we present the results of the thermal properties from the TERO measurements in six drillholes (ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405, ONK-PP411) using both the numerical estimation (Kukkonen et al. 2014, 2007, 2005) and rapid analytical methods (Korpisalo et al. 2012). In addition, we present a simple conductivity prediction for VGN based on the dependence of conductivity on core angle of rock foliation (Figure 43 in Kukkonen et al. 2011). For PGR the average of previous laboratory measurements (Table 1 in Kukkonen et al. 2011) is applied as a prediction. The numerical estimation from TERO76 data was handled as a non-linear least squares problem. The analytical parameter estimation is based on fitting the measured temperatures to simplified functions of infinite line source yielding asymptotically a straight line as a function of logarithm of time whose slope can be used in the estimation of the thermal conductivity directly. The estimates of thermal parameters of the drillholes have been displayed in Tables 27. The rock type analysis of the drillholes is presented in Figure 7 (Toropainen 2014, 2012) where the approximate measurements positions are also marked by black arrows.
Tab
le 2
. T
herm
al c
ondu
ctiv
itie
s
(Wm
-1K
-1)
and
diff
usiv
itie
s s
(10-6
ms-2
) of
roc
k in
dri
llho
le O
NK
-PP
346
from
the
ana
lyti
cal
(upp
er
valu
es)
and
num
eric
al (
low
er v
alue
s) m
etho
ds (
aver
age
valu
es o
f th
erm
isto
rs)
usin
g th
e w
hole
len
gth
of t
he a
lum
iniu
m t
ube
(164
1 m
m)
as
a th
erm
al s
ourc
e.
ON
K-P
P346
Dep
th
(m)
Roc
k ty
pe
Fol
iatio
n co
re
angl
e D
epth
(m
) /A
ngle
(°)
Con
duct
ivity
pre
dict
ion
from
fol
iatio
n an
d/or
ro
ck ty
pe1
1.N
TC
2.N
TC
3.N
TC
4.N
TC
s
s
s
s
3.00
P
GR
3.
31/5
0 3.
20
3.56
3.
97
1.89
2.03
3.
54
1.89
3.
60
1.92
3.
62
1.93
4.25
P
GR
3.20
3.
39
3.55
1.
80
1.89
3.
40
1.81
3.
41
1.81
3.
40
1.81
5.50
P
GR
3.20
3.
48
3.61
1.
85
1.92
3.
45
1.83
3.
49
1.85
3.
49
1.85
6.75
V
GN
n.
a.
3.
15
3.30
1.
66
1.74
3.
14
1.66
3.
14
1.66
3.
14
1.65
8.00
V
GN
8.
30/1
5 3.
30
3.01
3.
08
1.58
1.62
3.
00
1.57
3.
01
1.58
3.
01
1.58
The
roc
k ty
pes
of th
e m
easu
rem
ent p
oint
s: V
GN
v
eine
d gn
eiss
; PG
R
peg
mat
itic
gra
nite
. NT
C
neg
ativ
e te
mpe
ratu
re c
oeff
icie
nt th
emis
tor.
1 Pre
dict
ion
of c
ondu
ctiv
ity b
ased
on
aver
age
valu
es o
f pr
evio
us l
abor
ator
y m
easu
rem
ents
(T
able
1 i
n K
ukko
nen
et a
l. 20
11)
for
PG
R a
nd d
epen
denc
e of
con
duct
ivity
on
cor
e an
gle
of f
olia
tion
(-0.
0129
x (
90 -
cor
e an
gle)
+ 3
.492
7) f
or V
GN
(F
igur
e 43
in K
ukko
nen
et a
l. 20
11).
17
Tab
le 3
. T
herm
al c
ondu
ctiv
itie
s
(Wm
-1K
-1)
and
diff
usiv
itie
s s
(10-6
ms-2
) of
roc
k in
dri
llho
le O
NK
-PP
340
from
the
ana
lyti
cal
(upp
er
valu
es)
and
num
eric
al (
low
er v
alue
s) m
etho
ds (
aver
age
valu
es o
f th
erm
isto
rs)
usin
g th
e w
hole
len
gth
of t
he a
lum
iniu
m t
ube
(164
1 m
m)
as
a th
erm
al s
ourc
e.
ON
K-P
P340
Dep
th
(m)
Roc
k ty
pe
Fol
iatio
n co
re
angl
e D
epth
(m
) /A
ngle
(°)
Con
duct
ivity
pr
edic
tion
from
fo
liatio
n an
d/or
roc
k ty
pe1
1.N
TC
2.N
TC
3.N
TC
4.N
TC
s
s
s
s
3.00
P
GR
3.60
/60
3.20
3.
48
3.68
1.
85
1.96
3.
48
1.85
3.
49
1.85
3.
49
1.85
4.25
V
GN
n.
a.
3.
34
3.53
1.
77
1.87
3.
32
1.76
3.
34
1.77
3.
34
1.77
5.50
V
GN
5.
40/6
0 3.
11
3.09
3.
30
1.63
1.74
3.
08
1.62
3.
10
1.63
3.
09
1.63
6.75
D
GN
n.
a.
3.
29
3.46
1.
74
1.83
3.
27
1.73
3.
26
1.72
3.
25
1.72
8.00
D
GN
7.
40/5
5 3.
04
3.18
3.
38
1.68
1.79
3.
18
1.68
3.
19
1.68
3.
19
1.68
The
roc
k ty
pes
of t
he m
easu
rem
ent
poin
ts:
VG
N
vei
ned
gnei
ss;
PG
R
peg
mat
itic
gra
nite
; D
GN
d
iate
xitic
gne
iss.
NT
C
neg
ativ
e te
mpe
ratu
re c
oeff
icie
nt
ther
mis
tor.
1 Pre
dict
ion
of c
ondu
ctiv
ity b
ased
on
aver
age
valu
es o
f pr
evio
us l
abor
ator
y m
easu
rem
ents
(T
able
1 i
n K
ukko
nen
et a
l. 20
11)
for
PG
R a
nd d
epen
denc
e of
con
duct
ivity
on
cor
e an
gle
(-0.
0129
x (
90 -
cor
e an
gle)
+ 3
.492
7) f
or V
GN
(F
igur
e 43
in K
ukko
nen
et a
l. 20
11).
18
Tab
le 4
. T
herm
al c
ondu
ctiv
itie
s
(Wm
-1K
-1)
and
diff
usiv
itie
s s
(10-6
ms-2
) of
roc
k in
dri
llho
le O
NK
-PP
398
from
the
ana
lyti
cal
(upp
er
valu
es)
and
num
eric
al (
low
er v
alue
s) m
etho
ds (
aver
age
valu
es o
f th
erm
isto
rs).
The
who
le l
engt
h of
the
alu
min
ium
tub
e (1
641
mm
) ha
s be
en u
sed
as a
ther
mal
sou
rce
in th
e an
alyt
ical
cal
cula
tion
s.
ON
K-P
P398
Dep
th
(m)
Roc
k ty
pe
Fol
iatio
n co
re
angl
e D
epth
(m
) /A
ngle
(°)
Con
duct
ivity
pr
edic
tion
from
fo
liatio
n an
d/or
ro
ck ty
pe1
1. N
TC
2.
NT
C
3.
N
TC
4.
NT
C
s
s
s
s
1.80
P
GR
3.20
3.
72
3.92
1.
99
2.10
3.
76
2.
01
3.
76
2.
01
3.
73
2.
00
2.20
P
GR
3.20
3.
78
3.97
2.
02
2.13
3.
75
2.
00
3.
76
2.
01
3.
81
2.
04
2.60
P
GR
3.20
3.
62
3.74
1.
93
2.00
3.
67
1.
96
3.
60
1.
92
3.
61
1.
93
5.40
V
GN
n.
a.
3.
57
3.75
1.
90
2.00
3.
56
1.
89
3.
57
1.
90
3.
58
1.
91
6.20
V
GN
n.
a.
3.
60
3.64
1.
92
1.94
3.
56
1.
89
3.
56
1.
90
3.
57
1.
90
6.95
V
GN
n.
a.
3.
37
3.52
1.
79
1.87
3.
40
1.
81
3.
45
1.
83
3.
36
1.
78
The
roc
k ty
pes
of th
e m
easu
rem
ent p
oint
s: V
GN
v
eine
d gn
eiss
; PG
R
peg
mat
itic
gra
nite
. NT
C
neg
ativ
e te
mpe
ratu
re c
oeff
icie
nt th
erm
isto
r.
1 Pre
dict
ion
of c
ondu
ctiv
ity b
ased
on
aver
age
valu
es o
f pr
evio
us l
abor
ator
y m
easu
rem
ents
(T
able
1 i
n K
ukko
nen
et a
l. 20
11)
for
PG
R a
nd d
epen
denc
e of
con
duct
ivity
on
cor
e an
gle
of f
olia
tion
(-0.
0129
x (
90 -
cor
e an
gle)
+ 3
.492
7) f
or V
GN
(F
igur
e 43
in K
ukko
nen
et a
l. 20
11).
19
Tab
le 5
. T
herm
al c
ondu
ctiv
itie
s
(Wm
-1K
-1)
and
diff
usiv
itie
s s
(10-6
ms-2
) of
roc
k in
dri
llho
le O
NK
-PP
399
from
the
ana
lyti
cal
(upp
er
valu
es)
and
num
eric
al (
low
er v
alue
s) m
etho
ds (
aver
age
valu
es o
f th
erm
isto
rs).
The
who
le l
engt
h of
the
alu
min
ium
tub
e (1
641
mm
) ha
s be
en u
sed
as a
ther
mal
sou
rce
in th
e an
alyt
ical
cal
cula
tion
s.
ON
K-P
P399
Dep
th
(m)
Roc
k ty
pe
Fol
iatio
n co
re
angl
e D
epth
(m
) /A
ngle
(°)
Con
duct
ivity
pr
edic
tion
from
fo
liatio
n an
d/or
ro
ck ty
pe1
1. N
TC
2. N
TC
3. N
TC
4. N
TC
s
s
s
s
3.10
P
GR
3.20
3.
61
3.81
1.
922.
04
3.65
1.95
3.59
1.91
3.61
1.92
5.70
V
GN
n.
a.
3.
62
3.76
1.
932.
01
3.64
1.94
3.62
1.93
3.60
1.92
6.95
V
GN
n.
a.
3.
43
5.70
* 1.
823.
13*
3.45
1.83
3.42
1.81
3.41
1.81
The
roc
k ty
pes
of th
e m
easu
rem
ent p
oint
s: V
GN
v
eine
d gn
eiss
. * s
puri
ous
valu
es g
ener
ated
by
data
pro
blem
. NT
C
neg
ativ
e te
mpe
ratu
re c
oeff
icie
nt th
erm
isto
r.
1 Pre
dict
ion
of c
ondu
ctiv
ity b
ased
on
aver
age
valu
es o
f pr
evio
us l
abor
ator
y m
easu
rem
ents
(T
able
1 i
n K
ukko
nen
et a
l. 20
11)
for
PG
R a
nd d
epen
denc
e of
con
duct
ivity
on
cor
e an
gle
of f
olia
tion
(-0.
0129
x (
90 -
cor
e an
gle)
+ 3
.492
7) f
or V
GN
(F
igur
e 43
in K
ukko
nen
et a
l. 20
11).
20
Tab
le 6
. T
herm
al c
ondu
ctiv
itie
s
(Wm
-1K
-1)
and
diff
usiv
itie
s s
(10-6
ms-2
) of
roc
k in
dri
llho
les
ON
K-P
P40
5 fr
om t
he a
naly
tica
l (u
pper
va
lues
) an
d nu
mer
ical
(lo
wer
val
ues)
met
hods
(av
erag
e va
lues
of
1st
and
4th
ther
mis
tors
). T
he w
hole
len
gth
of t
he a
lum
iniu
m t
ube
(164
1 m
m)
has
been
use
d as
a th
erm
al s
ourc
e in
the
anal
ytic
al c
alcu
lati
ons.
ON
K-P
P405
Dep
th
(m)
Roc
k ty
pe
Fol
iatio
n co
re
angl
e D
epth
(m
) /A
ngle
(°)
Con
duct
ivity
pre
dict
ion
from
fol
iatio
n an
d/or
ro
ck ty
pe1
1. N
TC
2. N
TC
3. N
TC
4. N
TC
s
s
s
s
1.80
P
GR
3.20
3.
55
3.69
1.
89
1.97
3.
57
1.
89
3.
57
1.
87
3.
53
1.
88
2.20
P
GR
3.20
3.
67
3.80
1.
96
2.03
3.
68
1.
97 3.
65
1.
95 3.
66
1.
95
2.60
P
GR
3.20
3.
69
3.82
1.
97
2.05
3.
72
1.
99
3.
70
1.
97
3.
68
1.
97
5.40
V
GN
5.
15/7
5 3.
20
3.60
3.
83
1.95
2.05
3.
70
1.
97
3.
61
1.
93
3.
64
1.
94
6.20
V
GN
n.
a.
3.
47
3.54
1.
84
1.88
3.
51
1.
87
3.
48
1.
85
3.
46
1.
84
6.95
V
GN
7.
35/4
0 2.
84
3.17
3.
35
1.87
1.77
3.
21
1.
70
3.
22
1.
70
3.
17
1.
67
The
roc
k ty
pes
of th
e m
easu
rem
ent p
oint
s: V
GN
v
eine
d gn
eiss
; PG
R
peg
mat
itic
gra
nite
. NT
C
neg
ativ
e te
mpe
ratu
re c
oeff
icie
nt th
erm
isto
r.
1 Pre
dict
ion
of c
ondu
ctiv
ity b
ased
on
aver
age
valu
es o
f pr
evio
us l
abor
ator
y m
easu
rem
ents
(T
able
1 i
n K
ukko
nen
et a
l. 20
11)
for
PG
R a
nd d
epen
denc
e of
con
duct
ivity
on
cor
e an
gle
of f
olia
tion
(-0.
0129
x (
90 -
cor
e an
gle)
+ 3
.492
7) f
or V
GN
(F
igur
e 43
in K
ukko
nen
et a
l. 20
11).
21
Tab
le 7
. T
herm
al c
ondu
ctiv
itie
s
(Wm
-1K
-1)
and
diff
usiv
itie
s s
(10-6
ms-2
) of
roc
k in
dri
llho
le O
NK
-PP
411
from
the
ana
lyti
cal
(upp
er
valu
es)
and
num
eric
al (
low
er v
alue
s) m
etho
ds (
aver
age
valu
es o
f 1s
t an
d 4t
h th
erm
isto
rs).
The
who
le l
engt
h of
the
alu
min
ium
tub
e (1
641
mm
) ha
s be
en u
sed
as a
ther
mal
sou
rce
in th
e an
alyt
ical
cal
cula
tion
s.
ON
K-P
P411
Dep
th
(m)
Roc
k ty
pe
Fol
iatio
n co
re
angl
e D
epth
(m
) /A
ngle
(°)
Con
duct
ivity
pre
dict
ion
from
fol
iatio
n an
d/or
ro
ck ty
pe1
1. N
TC
2. N
TC
3. N
TC
4.N
TC
s
s
s
s
3.50
V
GN
3.
65/5
0 4.
42/5
5 2.
97
3.04
3.
25
3.45
1.
72
1.83
3.
24
1.
71
3.
24
1.
71
3.
26
1.
72
7.50
V
GN
7.
55/5
0 2.
97
3.16
3.
30
1.66
1.75
3.
16
1.
66 3.
17
1.
67 3.
14
1.
65
The
roc
k ty
pes
of th
e m
easu
rem
ent p
oint
s: V
GN
v
eine
d gn
eiss
. NT
C
neg
ativ
e te
mpe
ratu
re c
oeff
icie
nt th
erm
isto
r.
1 Pre
dict
ion
of c
ondu
ctiv
ity b
ased
on
aver
age
valu
es o
f pr
evio
us l
abor
ator
y m
easu
rem
ents
(T
able
1 i
n K
ukko
nen
et a
l. 20
11)
for
PG
R a
nd d
epen
denc
e of
con
duct
ivity
on
cor
e an
gle
of f
olia
tion
(-0.
0129
x (
90 -
cor
e an
gle)
+ 3
.492
7) f
or V
GN
(F
igur
e 43
in K
ukko
nen
et a
l. 20
11).
22
23
In total 27 in situ measurements has now been made in six POSE drillholes: 11 in pegmatitic granite, 14 in veined gneiss and 2 in diatexitic gneiss. The common conclusion about the estimated thermal conductivities is that the analytical values are lower (< 10%) than the numerical values but higher than the laboratory values (~ 10%) (see Tables 17). As in the previous projects, the diffusivities are calculated using the conductivitydiffusivity relation of Olkiluoto type rocks s = 0.5754-0.153 (Kukkonen et al. 2011). In drillhole ONK-PP399 (6.95 m), the numerical estimation of thermal conductivity and diffusivity suffer from data fitting problem due to the used numerical model generating anomalous high veined gneiss conductivity and diffusivity values of 5.7 Wm-1K-1 and 3.1310-6 m2s-1. On the contrary, the analytical results are at normal values 3.43 Wm-1K-1 and 1.8210-6 m2s-1.
24
25
5 SUMMARY OF RESULTS
The measurement series of thermal properties of rocks continued in four shallow drillholes in the ONKALO investigation niche 3 (ONK-TKU-3620). The results were calculated using both the analytical and numerical methods (Korpisalo et al. 2012; Kukkonen et al. 2014, 2007, 2005). Figures 922 present the results from the drillholes using the different interpretation methods (see also Tables 27).
Figure 9. Thermal conductivities in drillhole ONK-PP346. The numerical results are plotted as blue symbols, analytical as red (mean value of thermistors). The laboratory values are shown as green symbols, respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2012).
26
Figure 10. Thermal diffusivities in drillhole ONK-PP346. The numerical results are plotted as blue symbols, analytical as red (mean value of thermistors). The laboratory values are shown as green symbols, respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2012).
Figure 11. Thermal conductivities in drillhole ONK-PP340. The numerical results are plotted as blue symbols, analytical as red (mean value of thermistors). The laboratory values are shown as green symbols, respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2012).
27
Figure 12. Thermal diffusivities in drillhole ONK-PP340. The numerical results are plotted as blue symbols, analytical as red (mean value of thermistors). The laboratory values are shown green symbols, respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2012).
Figure 13. Thermal conductivities in drillhole ONK-PP398. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on The PGR section is not homogeneous but there is two sections of VGN at 2.692.88 m and 3.143.41 m Toropainen (2014).
28
Figure 14. Thermal diffusivities in drillhole ONK-PP398. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014).
Figure 15. Thermal conductivities in drillhole ONK-PP399. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014). A possible data fitting error within the numerical method at 6.95 m.
29
Figure 16. Thermal diffusivities in drillhole ONK-PP399. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014). A possible data fitting error within the numerical method at 6.95 m.
Figure 17. Thermal conductivities in drillhole ONK-PP405. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014).
30
Figure 18. Thermal diffusivities in drillhole ONK-PP405. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014).
Figure 19. Thermal conductivities in drillhole ONK-PP411. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014).
31
Figure 20. Thermal diffusivities in drillhole ONK-PP411. The numerical results are plotted as blue and analytical as red symbols (mean values of thermistors), respectively. The rock types of drillhole are plotted in the horizontal pillar below based on Toropainen (2014).
The results are gathered in two data diagrams consisting of the drillhole rock types and the estimated thermal parameters. The analytical conductivities and diffusivities are represented in Figure 21 and the numerical values in Figure 22, respectively.
32
Figure 21. The combined data window for the analytical results. Drillhole rock types are represented according to Figure 7. The conductivities (W/mK) are plotted on the right side of the drillhole pillar and the diffusivities (10-6m2/s) on the left side. The value points correspond to the depths where the four thermistors are approximately centralized.
Figure 22. The combined data window for the numerical results. Drillhole rock types are represented according to Figure 7. The conductivities (W/mK) are plotted on the right side of the drillhole pillar and the diffusivities (10-6m2/s) on the left side. The value points correspond to the depths where the four thermistors are approximately centralized.
33
The correspondence between the numerical and analytical conductivity and diffusivity estimates is good, although, the numerical method produces slightly (on the average 5% higher conductivity values than the analytical method. In extreme cases the difference may amount up to 10%. However, the variation of conductivity values from both methods follows each other suggesting a minor systematic difference between the methods. The same behaviour was also recognized in the previous project (Korpisalo et al. 2014). The difference may be attributed, for instance, to basic differences between models, to numerical model inaccuracies (e.g. heat capacity of the probe is poorly known), to using different time intervals of the heating period in data fitting procedures, or to deviations between the assumed infinite source length vs. real 3D conditions. The difference is, however, quite small. As thermal conductivity of a specific rock type is a function of its mineral content, porosity, pore fluid, anisotropy, and temperature, variation in conductivity and diffusivity values may take place due to geological heterogeneity, e.g. due to the natural variation of rock's mineral content and orientation of foliation within the rock type (Kukkonen et al. 2011). In Figures 922, the color pillars represent the main rock types at the measured depth levels. The sections are not necessarily homogeneous as is the case in drillhole ONK-PP398 where two thinner VGN sections are discovered at 2.692.88 m and 3.143.41 m within the PGR section. Thus, heterogeneity in the local main rock type may be one reason for the abrupt changes in the conductivities (Figures 13) (Toropainen 2014). The thermal conductivities were directly estimated using the late times of heating periods. In the analytical solutions, the choice of measurement time used in inversion affects the estimated parameters but there are also many other possible factors that can generate biases in the estimates (Korpisalo et al. 2012). In addition, according to Kukkonen et al. (2014, 2007), the thermal parameters contribute differently to the TERO response in different time periods of the measurement. The thermal conductivity of metamorphic rocks, such as the migmatitic gneisses at Olkiluoto, is often strongly anisotropic. Therefore, information on anisotropy is necessary and laboratory measurements are required in different directions of foliation. Only small differences are seen in the conductivity estimates between numerical and analytical methods (Figures 9, 11, 13, 15, 17, 19). The diffusivities were simply estimated using the laboratory results on diffusivity-conductivity relationship (Kukkonen et al. 2011) of different Olkiluoto rock types (Figures 10, 12, 14, 16, 18, 20). The only perceptibly large difference between the numerical and analytical solution happens at the depth of 6.95 m in drillhole ONK-PP399 where the numerical conductivity estimate is 5.7 Wm-1K-1 and the analytical 3.43 Wm-1K-1. It was generated data fitting problem due to the used numerical mode. The model should be remodelled to cancel the behaviour but it was not reasonable due to a single point. Anisotropy of thermal conductivity is the main factor explaining the differences between laboratory measurements and in situ measurements. TERO76 results indicate the thermal conductivity in the radial direction from drill hole, whereas laboratory samples represent conductivity in the direction of the drill hole axis, unless especially prepared otherwise (see e.g., Kukkonen et al. 2005). In Tables 27 the TERO76
34
measurements are supported by a prediction of conductivity based on anisotropy data of VGN (Figure 43 in Kukkonen et al. 2011). The predictions are on the average within 11% of the numerical estimates and within 6% of the analytical estimates. The result can be considered relatively good taking into account the fact that the foliation data are point-like observations from the drill core and not necessarily representative of the complete section measured with TERO76. A similar prediction result based on foliation was reported for OL-KR56 and OL-KR46 in Korpisalo et al. (2014). For the PGR which is assumed to be isotropic, the prediction was based on the average value obtained in previous laboratory measurements (Kukkonen et al. 2011). The predictions for PGR are on the average within 15% of the numerical estimates and within 10% of the analytical result. Most of them fall within ± 1 standard deviation of the previous PGR conductivity average, but systematically below the average. It may imply that the PGR conductivity varies within the Olkiluoto site. Laboratory measurements of PGR conductivity is also affected by the coarse grain size, and geological heterogeneity effects may creep into to laboratory data on PGR. In the reports (Kukkonen et al. 2014, 2007, 2005), it is emphasized that even with a detailed finite numerical model, the more precise estimation of rock thermal diffusivity in situ is difficult and needs highly accurate temperature measurements and the accurate knowledge of heat capacity of the TERO device. When comparing the thermal estimates from in situ measurements with the results from core samples of Olkiluoto type rocks, the estimates are slightly higher.
35
6 DISCUSSION AND CONCLUSIONS
Thermal conductivities may vary by a factor of two for different rock types. This is due to the variation of rock's mineral content and to several physical factors. Porosity is not significant for thermal properties in the intact Olkiluoto rocks, which have porosities well below 1%. In plutonic and metamorphic rocks the main factor is the dominant mineral phase. The feldspar in plutonic rocks and quartz content in metamorphic rocks control effectively thermal conductivity. A high content of feldspar means low conductivities and high quartz content means high conductivity. Both for plutonic and metamorphic rocks, the decrease in thermal conductivity with temperature depends on their dominant mineral content (Kukkonen et al. 2011; Clauser & Huenges 1995).
In the new TERO76 device, the current and voltage in the heater are monitored during the measurements, thus the heating power is accurately determined and more reliable estimates of thermal conductivity can be produced. Both the analytical and numerical method has its own error sources (Kukkonen et al. 2014, 2007, 2005; Korpisalo et al. 2012). Banaszkiewicz et al. (1997) reported the results of linear line source method suggesting that the error of the thermal conductivity amounts to a few percent (< 5%) but the corresponding error of thermal diffusivity is about 15%. Highly accurate temperature data is needed to achieve a better accuracy. Kukkonen et al. (2014) and Kekäläinen (2013) concluded that the thermal conductivity can be determined reliably (within 2% of the correct value) from the TERO measurements. When the temperature data are ideally accurate and unbiased with a maximum error of 0.03 K, diffusivity can be determined with an accuracy of 5% (Kukkonen et al. 2014).
Diffusivity is a very cumbersome parameter to estimate from TERO data, mostly due to the unknown diffusivity-contact resistance relationship. Therefore, an unbiased diffusivity estimate is provided using the petrophysical relationship between conductivity and diffusivity (Kukkonen et al. 2011). This method was applied in the present study.
The thermal properties of rock around six shallow drillholes (ONK-PP340, ONK-PP346, ONK-PP398, ONK-PP399, ONK-PP405 and ONK-PP411) were determined with the TERO measurements in March 2014 and 2012. Seventeen new measurements were made in four new drillholes in total. The estimated results from the present measurements are represented in Figures 922. The specific conductivities and diffusivities of each drillholes are given in Figures 920 and all the results are gathered in Figures 2122. The drillhole surroundings are comprised of two main rock types: pegmatitic granite and veined gneiss. Diatexitic gneiss occurs in the lower part of drillhole ONK-PP340 (Figure 21). Thus, the measurement points correspond to the same rock types where the spent nuclear fuel canisters are going to be disposed. Kukkonen et al. (2011) investigated and reported the thermal laboratory properties of Olkiluoto type rocks. According to their results, in pegmatitic granite (PGR) the average thermal conductivity and diffusivity are 3.20 Wm-1K-1 and 1.7510-6 m2s-1. The corresponding average numerical values from the present in situ measurements are 3.76 Wm-1K-1 and 2.0110-6 m2s-1 and the analytical 3.59 Wm-1K-1 and 1.9110-6 m2s-1. In veined gneiss (VGN), the average laboratory thermal values are 2.83 Wm-1K-1 and 1.3710-6 m2s-1. The average numerical values of the present in situ measurements are
36
3.49 Wm-1K-1 and 1.8910-6 m2s-1 and analytical 3.33 Wm-1K-1 and 1.7710-6 m2s-1. The average laboratory thermal properties of diatexitic gneiss (DGN) are 2.95 Wm-1K-1 and 1.5310-6 m2s-1. The average numerical values from the present in situ measurements are 3.42 Wm-1K-1 and 1.8110-6 m2s-1 and 3.23 Wm-1K-1 and 1.7010-6 m2s-1 for the analytical method.
The behaviour of conductivities and diffusivities agree well with the previous TERO results at the Olkiluoto site and in the ONKALO (Korpisalo et al. 2014). The analytical values are lower (<10%) than the numerical values. When comparing with the laboratory values, the analytical results are on the other hand higher than the laboratory values (~10%). The difference may be attributed to the anisotropy of thermal conductivity, to the drillholes intersecting the foliation at abrupt angles and to the fact that the TERO measurements represent conductivity (diffusivity) values in the radial direction from the drillhole. The predictions of VGN conductivity from foliation orientation data in the drillholes shows relatively good agreement with TERO results on the average within 11% of the numerical and within 6% of the analytical estimates, and indicates the importance of thermal anisotropy in interpreting laboratory and in situ measurements. The reported average factor of anisotropy is ~1.4 (min/max) in the Olkiluoto rock types in general (Kukkonen et al. 2011) and must be taken into account in interpreting TERO data.
Previous laboratory measurements showed a clear dependence of conductivity on orientation of foliation for veined gneiss (VGN), although with a scatter of about ±1 Wm-1K-1 around the regression line (Kukkonen et al. 2011). On the other hand, no dependence of thermal conductivity on orientation of foliation for diatexitic gneiss (DGN) was observed. The data set for DGN was, however, small (16), and the result would benefit of revision with new laboratory measurements.
The difference between the numerical and analytical results which on the average is less than 5% in conductivity can be considered relatively small. Anyway, the analytical results are systematically lower than the numerical estimates. The difference may be attributed, for instance, to basic differences between models, to numerical model inaccuracies (e.g. heat capacity of the probe is poorly known), to using different time intervals of the heating period in data fitting procedures, or to deviations between the assumed infinite source length vs. real 3D conditions. Further checking of these issues is needed.
In this study we have developed and successfully implemented practical procedures for dense in situ measurements in shallow drillholes. The determined thermal conductivity and diffusivity values in situ are considered to be accurate within a few (< 5%) percent of the correct values.
37
REFERENCES
Banaszkiewicz, M., Seiferlin, K., Spohn, T., Kargl, G. & Kömle, H. 1997. A new method for the determination of thermal conductivity and thermal diffusivity from linear heat source measurements. Re. Sci. Instrum. 68(11), November 1997.
Blackwell, J. H. 1954. A Transient-Flow Method for determining of Thermal Constants of Insulating Materials in Bulk. Journal of Applied Physics, Part I: Theory, February 1954, p. 137144.
Carslaw, H. S. & Jaeger, J. C. 1959. Conduction of heat in solids. Oxford University Press, Oxford, 510 p.
Clauser, C. & Huenges, E. 1995. Thermal Conductivities of Rocks and Minerals in Rock Physics and Phase Relations: A handbook of Physical Constants. AGU Reference Shelf, vol. 3, p. 105126.
Jager, J. M. & Charles-Edwards, J. 1968, Thermal Conductivity Probe for Soil-moisture Determinations. Journal of Experimental Botany, Vol. 20, No. 62, p. 4651.
Kekäläinen, P. 2013. Mathematical Modelling and Evaluation of TERO Measurements. Posiva Oy, Working Report 201310, 19 p.
Kjørholt, H. 1992. Thermal properties of rocks. Teollisuuden Voima Oy, TVO/Site investigations, work report 9256, 13 p.
Korpisalo, A, Kukkonen, I., Suppala, I. & Koskinen, T. 2014. Thermal Conductivities and Diffusivities of Rocks in Four Shallow ONKALO Holes and Drillholes OL-KR46 and OL-KR56. Posiva Oy, Working Report 201336, 31 p.
Korpisalo, A, Kukkonen, I., Suppala, I. & Koskinen, T. 2012. Determination of thermal conductivity and thermal diffusivity of rocks from transient in-situ measurements using rapid slope method. Posiva Oy, Working Report 201257, 55 p.
Kukkonen, I., Korpisalo, A., Suppala, I. & Koskinen, T. 2014. In situ determination of thermal properties of rocks in crystalline rock drill holes with TERO56 and TERO76 devices. Posiva Oy, Posiva Report 201306, 56 p.
Kukkonen, I., Kivekäs, L., Vuorinen, S. & Kääriä, M. 2011. Thermal properties of rocks in Olkiluoto: Results of laboratory measurements 1994-2010. Posiva Oy, Working Report 201117, 96 p.
Kukkonen, I., Suppala, I., Korpisalo, A. & Koskinen, T. 2007. Drill hole device TERO76 for determining of rock thermal properties. Posiva Oy, Working Report 200701, 39 p.
Kukkonen, I., Suppala, I., Korpisalo, A. & Koskinen, T. 2005. TERO borehole logging device and test measurements of rock thermal properties in Olkiluoto. Posiva Oy, Posiva Report 200509, 96 p.
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Kukkonen, I. 2000. Thermal properties of the Olkiluoto mica gneiss: Results of laboratory measurements. Posiva Oy, Working Report 200040, 28 p.
Kukkonen I., Suppala I. & Koskinen T. 2001. Measurement of rock thermal properties in situ: numerical models of borehole measurements and development of calibration techniques. Posiva Oy, Working Report 200123, 47 p.
Kukkonen, I. & Suppala, I. 1999. Measurement of thermal conductivity and diffusivity in situ: Literature survey and theoretical modelling of measurements. Posiva Oy, Posiva Report 991, 69 p.
Kukkonen, I. & Lindberg, A. 1998. Thermal properties of rocks at the investigation sites: measured and calculated thermal conductivity, specific heat capacity and thermal diffusivity. Posiva Oy, Working Report 9809e, 29 p.
Kukkonen, I. & Lindberg, A. 1995. Thermal conductivity of rocks at the TVO investigation sites Olkiluoto, Romuvaara and Kivetty. Nuclear Waste Commission of Finnish Power Companies, Report YJT9808, 29 p.
Sundberg, J., Kukkonen, I. & Hälldahl, L. 2003. Comparison of thermal properties measured by different methods. Swedish Nuclear Fuel and Waste Management Co, Report SKB R0318, 37 p.
Suppala, I., Kukkonen, I. & Koskinen, T. 2004. Kallion termisten ominaisuuksien reikäluotauslaitteisto TERO (Drill hole tool ”TERO” for measuring thermal conductivity and diffusivity in situ). Posiva Oy, Working Report 200420, 43 p. (in Finnish).
Toropainen, V. 2014. Pose Experiment - Core Drilling Of Drillholes ONK-PP398...405 and ONK-PP410...413 in ONKALO at Olkiluoto 2013. Working Report 2014-26.
Toropainen, V. 2012. ONKALO POSE Experiment–Core Drilling of Drillholes ONK-PP340347 in ONKALO at Olkiluoto 2012. Posiva Oy. Working Report 201237, 66 p.
Toropainen, V. 2010. ONKALO Pose Experiment – Core Drilling of Drillholes ONK-PP223...226, ONK-PP253...261and ONK-PP268...272 in ONKALO at Olkiluoto 2009–2010. Posiva Oy. Working Report 201086, 66 p.
Valli, J., Hakala, M., Wanne, T., Kantia, P. & Siren, T. 2014. ONKALO POSE experiment – Phase 3: Execution and monitoring. Posiva Oy, Working Report 2013-41.
de Vries, D. A. 1952. A nonstationary method for determining thermal conductivity of soil in-situ. Soil Science, 73, 1952, no:2, p. 8389.
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APPENDIX A
The linear equation of conduction of heat giving the temperature (r,t), dependent on the location r (location vector in a Cartesian coordinate system) and on time t, is (Carslaw Jaeger 1959; Jager & Charles-Edwards 1968):
),()),()((),(
)( trgtrrKt
trrcρ
(1)
The heat equation above states that the temperature within a body depends upon the rate of its internally-generated heat g(r,t), its capacity to store some of this heat c(r), and its rate of thermal conduction. When conductivity is constant or not a function of r, Eq. 1 can be written as
),(112 trgKts
(2)
In Eq. 1, K is thermal conductivity, which is a tensor variable (Wm-1K-1), ρc is volumetric heat capacity (densityspecific heat capacity in Jm-3K-1) and g is heating power (Wm-3). Thermal diffusivity is the ratio of thermal conductivity and heat capacity s = K/ρc. Dividing both sides of Eq. 1 by K, shows that the problem can be also described in terms of thermal diffusivity and heat conduction (Eq. 2). When numerical model studies are undertaken, the model (probe and the surroundings) is discretized in detail according to Eq. 1. However, it is a complicated and time-consuming way to handle the heat transfer problem and there might be situations where quick solutions are needed. It is possible to approach the problem by simplified models and we present two possible solutions in this report. The first model is an infinite line-source model and the second model an infinite long hollow probe model.
The first model has an infinitely long heat source with a vanishing radius. Heat input is constant and only the radial heat flow is provided. Contact resistance is absent in this model. According to Carslaw Jaeger (1959), the solution for a line-source with infinite length embedded in a homogeneous medium of thermal conductivity K, can be written as
at
rEi
K
qtr
44,
2
(3)
where q is amount of heat produced in source, a is thermal diffusivity of the environment and t is the time. The exponential integral Ei is defined as
dxxx
xEi
x
)exp(1
)(
(4)
40
For 0x1, the exponential integral can be expanded into a power series
...!22!11
)log(2
xx
xEi (5)
where is Euler's constant. For very small values of at
rx
4
2
, the series can be reduced
by truncating the higher order terms and Eq. 3 can be simplified in the form
ctK
qt log
4 (6)
Thus, Eq. 6 indicates that, if the temperature at ro is plotted as a function of the logarithm of time, a linear response curve will be obtained, and the thermal conductivity of the environment is simply
curve of slope/42 q
K (7)
It is interesting to see that one doesn't need the knowledge of the thermal diffusivity of the material and the location ro where temperature is measured.
An infinite length probe model which includes the thermal resistance at the interface and which has a finite radius was reported by Blackwell (1954). Constant input power is assumed. Furthermore, material surrounding the probe is continuous, homogeneous and isotropic. The probe's thermal conductivity is infinite. Basic equations and boundary conditions after Blackwell are
trbtarrr
; 11 2
22
22
22
0 ;021 tTT
0 ; 212
tbrHr
K
0 t; 2 111
2
brt
cMQbr
K (8)
where 1, M1, c1 are temperature, mass/unit length and specific heat of the probe, 2, K, a2
2 are temperature, thermal conductivity and diffusivity of external material, r is the radial coordinate, b is the external radius of the probe, t is time, H is the interface resistance at surface r=b, Q=heat supplied/unit probe length/unit time.
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Eq. 8 can be solved using the Laplace transformation yielding an integral equation whose asymptotic behaviour during large-times of the heating period can be written as
2
2222
1
124log14log
2
124log
2 TO
bH
KT
bK
aT
TbH
KT
K
Qbt (9)
where is Euler's constant, bQQ 2/ , bcM 2/11 and 222 / btaT . The O-term can be
ignored because, when the time t increases, this term becomes negligible.
Thus, the rise in probe temperature as a function of time simplifies to
BtADtCt
BtAt )log()log(1
)log()(1 (10)
where K
GbA
2
,
Hb
Kba
K
GbB
2)4ln()ln(2)ln(
22
2 , b is the external radius of the
probe, a and K are the diffusivity and conductivity of rock, is Euler's constant and H is the contact resistance between the probe and the environment. G is heating power (W/m). Furthermore, after a long time, the C and D terms can also be ignored, since again these terms become small compared with the A and B terms. Thus, a fit of TERO data to Eq. 10 will yield the value of K from the constant A. Using the constant B, it could be possible to evaluate also the diffusivity under certain conditions (very good contact is needed to keep the last term negligibly small or otherwise the H term should be known accurately).
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