determination of thermal conductivity and thermal diffusivity of … · 2013-08-19 ·...

June 2013

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.

Arto Korpisalo, I lmo Kukkonen

I lkka Suppala

Geological Survey of F inland

Teemu Koskinen

Stips Oy

Working Report 2012-57

Determination of Thermal Conductivity andThermal Diffusivity of Rocks from Transient

In-Situ Measurements Using Rapid Slope Method

DETERMINATION OF THERMAL CONDUCTIVITY AND THERMAL DIFFUSIVITY OF ROCKS FROM TRANSIENT IN-SITU MEASUREMENTS USING RAPID SLOPE METHOD

ABSTRACT The thermal drillhole devices (Ø56 mm and Ø76 mm drillholes) for determining thermal properties of rocks in-situ in drillholes was developed and constructed under TERO projects in Geological Survey of Finland with Posiva in early 2000’s (Kukkonen et al. 2005; Kukkonen et al. 2007). Today, in addition to the numerical inversion technique a rapid interpretation tool has been developed based on simple cylindrical models. Measurements in drillholes OL-KR2 and OL-KR14 were re-interpreted using the solution of infinite line model and/or an approximate solution of the hollow tube model (Blackwell's large time solution, Blackwell, 1954). Results evaluated using both methods have been gathered and compared in this paper. The numerically optimized estimates of thermal properties in OL-KR2 and OL-KR14 were based on least square methods and results have been published in our previous papers (Kukkonen et al. 2005; Kukkonen et al. 2007). Parallel to the numerical approaches of interpretation evaluation methods were developed towards a more user-friendly direction and after the implementation of the infinite line source and the hollow tube models, thermal conductivity may be estimated from the late heating period under certain conditions. The introduced analytical methods cannot be used to estimate the thermal diffusivity or the volumetric heat capacity directly from the heating or cooling periods but diffusivity may be calculated simply using measured laboratory values of specific heat capacity and density of Olkiluoto rock types (Kukkonen et al. 2011). The conductivities determined by means of a numerical model in OL-KR2 were between 3.31 and 4.54 Wm-1K-1 and the analytical model conductivities from 2.40 to 4.46 Wm-1K-1 with the slope method. Numerically estimated diffusivities are in the range between 1.3510-6 and 2.0410-6 m2s-1. The slope method estimates are in the range between 1.3110-6 and 2.2810-6 m2s-1. Results determined from OL-KR14 by numerical estimation provides conductivity values 2.95-3.78 Wm-1K-1 with corresponding slope method estimates 3.03-3.92 Wm-1K-1. Numerically estimated diffusivity values are in the range between 1.7110-6 and 2.1210-6 m2s-1. Corresponding values for slope method are ranging from 1.5410-6 to 1.9510-6 m2s-1. Estimation of diffusivity and specific heat capacity is more problematic due to the strong correlation of the contact resistance effects and diffusivity, as well as the poorly known drillhole calliper. The temperature measurements at the heat source make the diffusivity estimations very inaccurate. Thus, additional measurements of rock heat capacity and density, i.e. volumetric heat capacity, values are needed for improved parameter estimation in thermal modelling of a repository.

Keywords: Thermal conductivity, specific heat capacity, thermal diffusivity, nuclear waste disposal, Olkiluoto, gneiss, in-situ measurement, TERO.

KALLION LÄMMÖNJOHTAVUUDEN JA DIFFUSIVITEETIN MÄÄRITTÄMINEN IN-SITU MITTAUKSISTA RAPID SLOPE-MENETELMÄLLÄ TIIVISTELMÄ Tässä työssä käytetty kallion termisten ominaisuuksien in-situ mittaamiseen tarkoitetut TERO -laitteistot (reikäkoot Ø56 mm ja Ø76 mm) kehitettiin ja rakennettiin GTK:ssa yhteistyönä Posiva Oy:n kanssa 2000 luvun alussa (Kukkonen et al. 2005; Kukkonen et al. 2007). Numeerisen menetelmän rinnalle kehitettiin nopean tulkinnan työkalu ja kahden Olkiluodon tutkimusreiän (OL-KR2 ja OL-KR14) mittaukset tulkittiin uudes-taan käyttämällä hyväksi äärettömän viivalähteen ratkaisua ja/tai äärettömän onton sylinterin likimääräistä malliratkaisua. Menetelmien tulokset on koottu yhteen, ja ne esitetään tässä raportissa. Kallion termiset ominaisuudet OL-KR2 ja OL-KR14 mittauksista on laskettu optimoimalla numeerisen mallin parametrit ja tulokset on julkaistu raporteissa (Kukkonen et al. 2005; Kukkonen et al. 2007). Tässä työssä on kehitetty nopean tulkinnan menetelmää kenttätyön aikana tehtävän tulosten analysoinnin helpottamiseksi. Äärettömän viivalähteen ja onton sylinterin malleilla voidaan arvioida kallion lämmönjohtavuus suoraan lämmityskäyrän loppuosalta, jossa anturin lämpeneminen on saavuttanut asymptoottisen käyttäytymisen eli vakiokasvun ajan logaritmin funktiona. Menetelmällä ei saada arvioitua kallion diffusiviteettia tai lämpökapasiteettia tilavuusyksikköä kohti riittävän tarkasti. Diffusiviteetti voidaan laskea kivityypin lämpökapasiteetin ja tiheyden avulla tai lämmönjohtavuuden ja diffusiviteetin korrelaation avulla (Kukkonen et al. 2011). Numeerisella mallilla lasketut lämmönjohtavuusarvot OL-KR2 in-situ mittauksista ovat välillä 3,31-4,54 Wm-1K-1. Vastaavat nopean tulkinnan arvot ovat 2,40-4,46 Wm-1K-1. Numeerisesti lasketut diffusiviteetit ovat välillä 1,35-2,0410-6 m2s-1. Nopean tulkinnan diffusiviteetit ovat välillä 1,31-2,2810-6 m2s-1. Numeerisella mallilla ratkaistut johta-vuudet OL-KR14 mittauksista ovat välillä 2,95-3,78 Wm-1K-1 ja nopean tulkinnan mukaiset välillä 3,03-3,92 Wm-1K-1. Numeerisen mallin termiset diffusiviteetit ovat välillä 1,71-2,1210-6 m2s-1 ja vastaavat nopean tulkinnan termiset diffusiviteetit välillä 1,54-1,9510-6 m2s-1. Termisen diffusiviteetin (ja lämpökapasiteetin) arvioiminen reikämittauksesta on ongel-mallisempaa, mikä johtuu kontaktiresistanssi-ilmiöiden ja diffusiviteetin voimakkaasta korrelaatiosta lämmönsiirtoyhtälöissä, mutta myös huonosti tunnetun reikähalkaisijan vuoksi. Lämpötilojen mittaaminen anturissa, missä myös lämmitys tapahtuu, tekee diffusiviteetin arvioimisen suoraan lämpökäyrältä hyvin vaikeaksi ja epätarkaksi. Loppusijoitustilan lämpökehityksen mallintamiseen tarvitaan tietoa lämmön diffu-siviteetista ja lämpökapasiteetista tilavuusyksikköä kohti. Erillisiä mittauksia tarvitaan siis ominaislämpökapasiteetin ja tiheyden tarkemmaksi määrittämiseksi. Avainsanat: Lämmönjohtavuus, ominaislämpökapasiteetti, terminen diffusiviteetti, ydinjätteiden loppusijoitus, gneissi, Olkiluoto, TERO

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TABLE OF CONTENTS ABSTRACT TIIVISTELMÄ

PREFACE ................................................................................................................... 3

1 INTRODUCTION ................................................................................................. 5

2 DRILL HOLE LOGGING DEVICE TERO ............................................................ 7

3 MEASUREMENT PRINCIPLES .......................................................................... 9

3.1 Principles of measuring rock thermal properties in a drillhole ..................... 9

3.2 TERO Graphical Interface ......................................................................... 13

4 RAPID INTERPRETATION TOOL .................................................................... 15

4.1 Graphical Interface .................................................................................... 15 4.1.1 Rapid interpretation ............................................................................... 16 4.1.2 Simulation and interpretation studies – finite line model ....................... 22 4.1.3 Simulation and interpretation studies – infinite hollow tube model ........ 26

5 MEASUREMENTS WITH TERO IN-SITU LOGGING DEVICES ...................... 29

5.1 Drillhole OL-KR2 with TERO56 probe ....................................................... 29

5.2 Drillhole OL-KR14 with TERO76 probe ..................................................... 29

5.3 Laboratory measurements of drill cores .................................................... 30

5.4 Interpretation and comparison with laboratory measurements .................. 31 5.4.1 Numerical estimates and laboratory values in OL-KR2 ......................... 31 5.4.2 Rapid slope method estimates in OL-KR2 ............................................ 33 5.4.3 Numerical estimates and laboratory values in OL-KR14 ....................... 40 5.4.4 Rapid estimates in OL-KR14 ................................................................. 41

6 SUMMARY OF RESULTS ................................................................................ 47

7 DISCUSSION AND CONCLUSIONS ................................................................ 51

REFERENCES .......................................................................................................... 53

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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 Kimmo Kemppainen, Jere Lahdenperä, Topias Siren and Aimo Hautojärvi (Posiva Oy) and Erik Johansson (Saanio & Riekkola Oy). The geophysical design, equipment, construction, measurements, software development, interpretation and reporting were done by Arto Korpisalo, Ilmo Kukkonen, Ilkka Suppala (GTK) and Teemu Koskinen (Stips Oy).

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1 INTRODUCTION Thermal parameters of rocks are necessary data in planning final repository for spent nuclear fuel in deep bedrock. The thermal properties of rocks can be determined with laboratory measurements of core samples, theoretical calculations from mineral composition and data on properties of the constituent minerals, and with in-situ measurements in drill holes. 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 1995, 1998) and (Kukkonen 2000; Kukkonen et al. 2011). 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 done 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. In the beginning of 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). The numerical thermal property estimations are based on fitting measured temperature data to forward modelling of conductive heat transfer from cylinder sources with finite length with good results. However, the numerical and sophisticated inversion procedure is laboured and quite demanding to execute, so a new and a rapid interpretation tool was needed to estimate thermal properties of rocks quickly and reliably 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 and an infinite hollow tube model to yield the value of the thermal conductivity K2 from the slope of the fitted line under certain conditions. Rapid results of diffusivities are calculated trivially using the known values of specific heat capacity and density of Olkiluoto rock types (Kukkonen et al. 2011). Thus, the thermal conductivity and diffusivity profiles of the measurement range are ready 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 procedure. This paper provides the user with a user manual of the Rapid Interpretation Tool. It is a comprehensive documentation of the GUI: its structure, usage and the results provided. In addition, previous results of numerical inversions in two drillholes OL-KR2 and OL-KR14 are compared with results of the new rapid method.

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2 DRILL HOLE LOGGING DEVICE TERO TERO probes (TERO56 and TERO76) are used with the same winch and cables (Suppala et al. 2004). The complete logging device comprises the drill hole tool, logging cable and winch together with the computer and current source located at the earth 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 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 of automated operation, but it is not included at the present TERO devices. A computer collects the depth data from the winch and with the aid of the control unit 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 GTK in Espoo is depicted in Figure 2.

Figure 1. The components of the TERO logging devices (not in scale).

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Figure 2. TERO logging device at GTK, Espoo. The basic properties of the TERO devices are as follows: determination of thermal conductivity and diffusivity in-situ in 56/76 mm water-

filled drill holes the measurement principle: Thermal response of a heated cylinder length of cable is 700 m, motorized winch the outer diameter of probe is 50/70 mm length of the heated part of the probe is 1.5 m heating power is 22/49 W at maximum 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, located around the probe along four

axial lines, resolution 0.5 mK, range 4-30 ºC a galvanic single point sensor is included in the tool for precise determination of

logging depth with the aid of fracture anomalies determination of tool orientation is done with the magnetic field (3-component

flux gate sensors) and inclination (acceleration) sensors.

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3 MEASUREMENT PRINCIPLES

3.1 Principles of measuring rock thermal properties in a drillhole The measurement principle of both TERO devices is similar (Suppala et al. 2004; Kukkonen et al. 2005; Kukkonen et al. 2007). Let us assume a situation where the in- situ probe is initially in a drill hole 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, and the thickness of the water layer between the probe and drill hole 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 thermal properties of the surrounding medium. In a drill hole, the probe is (mostly) immersed in water, and the thickness of the water layer varies with varying hole calliper. In the interpretation the water layer, acting as a heat capacitor and resistance, must be taken into account. Thus, when heating is turned on rapid rise in temperature is dependent mainly on the thermal properties of the probe and the thermal resistance between the probe and surroundings and temperature gradient is generated between probe and rock. Because the output power is constant the temperature rise reaches an asymptotic behaviour, constant increase as a function of the logarithm of time (late heating period). At that asymptotic phase the temperature rise depends on the thermal conductivity of surrounding rock. After heating is turned off a rapid temperature drop is followed by a slower decrease of the temperature due to continued spreading of the heat into the rock 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):

),()),()((),(

)( 2 tgtKt

tcρ rrr

rr

(3.1)

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. 3.1 can be written as

),(11

2

2 trgKts

(3.2)

In Eq. 3.1 K2 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 = K2/ ρc. Dividing both sides of Eq. 3.1 by K2 shows that the problem can be also described in terms of thermal diffusivity and heat conduction (Eq. 3.2). When

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numerical model studies are done, the model (probe and the surroundings) is discretized in detail according to Eq. 3.1. 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 paper. 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 (Carslaw Jaeger 1959), the solution for a line-source with infinite length embedded in a homogeneous medium of thermal conductivity K2, can be written as

at

rEi

K

qtr

44,

2

2 (3.3)

where q is amount of heat produced in source, a is thermal diffusivity of the environment and t is the time. Exponential integral Ei is defined as

dxxx

xEi

x

)exp(1

)(

(3.4)

For 0x1, the exponential integral can be expanded into a power series

...!22!11

)log(2

xx

xEi (3.5)

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. 3.3 can be simplified in the form

ctK

qt log

4 2 (3.6)

Thus, Eq. 3.6 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 simple

curve of slope/42 q

K (3.7)

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 is arbitrary.

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An infinite length probe model which includes the thermal resistance at the interface and which has a finite radius was reported by Blackwell (Blackwell, 1954). Constant input power is assumed. Furthermore, material surrounding the probe is homogeneous and isotropic. The probe's thermal conductivity is infinite. Basic equations and boundary conditions after Blackwell are

0 t; 2

0 ;

0 ;0

0 ; 11

111

22

212

2

21

222

22

22

brt

cMQbr

K

tbrHr

K

tTT

trbtarrr

(3.8)

where 1, M1, c1 temperature, mass/unit length and specific heat of the probe, 2, K2, a2

2 are temperature, thermal conductivity and diffusivity of external material, r is radial coordinate, b is external radius of the probe, t is time, H is interface conductivity at surface r=b, Q=heat supplied/unit probe length/unit time.

Eq. 3.8 can be solved using Laplace transformation yielding an integral equation whose asymptotic behaviour during large-times of heating period can be written as

22

2

222

21

124log14log

2

124log

2 TO

bH

KT

bK

aT

TbH

KT

K

Qbt

(3.9)

where is Euler's constant, bQQ 2/ , bcM 2/11 and 222 / btaT . 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 (3.10)

where 22 K

GbA

,

Hb

Kba

K

GbB 22

2

2)4ln()ln(*2)ln(

2 2 , b is the

external radius of the probe, a and K2 are the diffusivity and conductivity of rock, is Euler's constant and H is the contact conductivity between the probe and the environment. G is heating power (W/m). Furthermore, after a long time C and D terms can also be ignored, since again these terms become small compared with A and B terms. Thus, a fit of TERO data to Eq. 3.10 will yield the value of K2 from the

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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 it should be known). As a summary, an infinite line-source and an infinite hollow probe model are cylinder models. When late times of heating period are concerned the temperature rise of both models can be simplified to asymptotic functions Eq. 3.6 and Eq. 3.9. Thus, rock’s 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. 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 contain a thorough exploration when the time has been elapsed before (1/t)-term becomes sufficiently small so that they can be ignored and what could be the value of contact conductance 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 3). Infinite line model allows the usage of late heating and late cooling periods in conductivity estimations. Adding a correction term into Eq. 3.6 is supposed to take into account e.g. a contact resistance and the deviations of 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 rock’s conductivity has been determined the diffusivity can be estimated trivially.

Figure 3. Rapid Interpretation Tool for TERO data.

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3.2 TERO Graphical Interface As a part of the system development a graphical interface system (Figure 4) was designed and constructed for the TERO56 device (Kukkonen et al. 2005). The same interface is applied with the TERO76 probe. TERO Graphical Interface (TGI) is a versatile analysis and interpretation toolbox, which is developed in MATLAB environment. The development work is done under Windows XP Operating System but XP is not a strict demand. To use the whole power of the TGI there should be at least 1 GB ROM memory (2 GB is recommended). In the case that MATLAB 6.5.1 or earlier versions must be installed, Java exception errors will be generated by the system. The system works best in the latest version of MATLAB. In addition, the TGI system requires the latest version of FEMLAB. Further details and instructions of the TGI system can be found in the User's guide (Korpisalo 2005).

Figure 4. View of the TERO Graphical Interface.

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4 RAPID INTERPRETATION TOOL The interface can be used both for modelling studies and interpretation of TERO data collected by different versions of TERO device. Two types of thermal heat sources are available for simulations: an infinite line and an infinite hollow tube source. Both are cylindrical models. Line models have infinite lengths with infinitesimal or finite radius. The tube model has an infinite conductivity and an infinite length and an inner and an outer radius. A finite heat capacity can be related to the tube model. In addition, the hollow tube model takes into account the contact conductance between the tube and the environment. Rapid interpretations are based on a series expansion of the infinite line source model and a long-term approximation of the infinite hollow tube model. The implementation is done in MATLAB® software. Thus, MATLAB must be installed before using this tool. GUI doesn’t need any special installation but copying the appropriate m-files. After path settings, GUI can be invoked by typing TERO in command line and the main panel is displayed on screen. 4.1 Graphical Interface

Main panel of interface contains all the tools that are needed in model simulations and to input binary TERO data to be interpreted. Thus, type TERO and the main window will appear as shown in Figure 5.

The main panel is divided into many subpanels and a window for graphics. To proceed with TERO data interpretation the main subpanel is called TERO (Figure 6). It contains all necessary buttons and options to handle a rapid interpretation (except Submit-button which is common for many other actions, too).

Figure 5. The TERO interface (main panel) as it appears when starting a session.

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4.1.1 Rapid interpretation

Figure 6. TERO–subpanel to handle binary data and make rapid interpretations based on slope methods. Preliminary steps During TERO’s short history there has been several versions of TERO devices and different devices has been used in different situations. Thus, the first task is to decide which drillhole data is going to be handled (Figure 7).

As a default is the new 4-thermistor model – New 76 mm Kr46. Only Kr46 data is available. Old 76 mm option is not usable. The first 76 mm model was used in Kr14 and continued with next generation model in Kr30 and Kr31. TERO project was started with the 56 mm probe which was used successfully in Kr2. Normally, a temperature measurement contains a long enough stabilization period which is followed by a several hours heating period. Thus, the whole measurement may consist of monitored temperatures over 20 hours. To assure accurate timing marks for different periods, user may have to generate an accurate current file (text-file) which must be loaded using Read Current-option. Using Browser user locates the corresponding current file and system loads current-time values. It is highly recommend that user generates current files in every case.

Figure 7. Selection of TERO data position and device version.

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Figure 8. Load binary data and calibrate. As a next step the proper binary data file must be loaded by pressing Load and calibrate–button (Figure 8) which is continued by the selection of the corresponding calibration file. Binary data files (names) have a format of TERO_date_time (Figure 9a). Calibration files (e.g. calibfile56) are collected in the corresponding folders (Figure 9b). The last selection is to find the current file – currentdate_depth (Figure 9c). After these selections the system is ready to display measured values. After data is loaded, the system gives user a hint about environment’s conductivity displaying temperature vs. power numbers. Higher numbers refer (<< 1.0) to lower environment’s conductivity (Figure 10).

a) b) c) Figure 9. a) Binary data file collection. b) Calibration. c) Current-file collection. Before displaying measured values, user has to select a rock type in the listbox below (Figure 10).

Figure 10. Temperature rise vs. power value. After a rock type is selected, the associated heat capacity and density values are gathered to Rock-panel (VGN-type selected with heat capacity 725 Jkg-1K-1 and density 2741 kgm-3, Kukkonen et al. 2011).

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The construction of older versions of TERO-devices contained 28+4 thermistors contrary to a new device where only 4 thermistors exist. In older devices thermistors were arranged in four lines (7 thermistors in each) and lines were separated by 90 degrees. Only the central thermistors (4, 11, 18, 25) are used in interpretations. Thermistors are renumbered as 1, 2, 3, 4 in this report. At this stage heating and cooling period durations are plotted both in TERO-panel and Time step-panel. In addition, measurement depth (Depth = 325) is displayed in TERO-panel (Figure 11). Notice that when you want to make simulations with different heat sources, you can use these time steps in calculations. Default step size is set as 10 s, which may be too rough when final results are needed. Thus, decrease the value and find its effect on theoretical curves.

Figure 11. TERO-data is ready for further process. After these preliminary steps, go to Curves-panel to display temperature profiles and you are ready for interpretations. However, temperature profiles may contain disturbing peaks which must be cleaned before interpretation (Figure 12).

Figure 12. Peaks which may disturb interpretation. Use Pan and Zoom-tools to locate the peak in the middle of screen and then use Delete peak-option in TERO-panel.

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Delete peak–option is a simple linear mean to delete peaks or user can fit a straight line to data with two mouse button clicks. After all peaks are cleaned the profile is ready to be interpreted (Figure 13).

Figure 13. Cleaned TERO temperature profile. Interpretation steps When you prepare to make interpretations, all needed options are under TERO interpretation-option (Figure 14). Click checkbox (TERO interpretation) to proceed.

Figure 14. TERO interpretation-options. As stated earlier (chapter 3.1), if fitting a straight line to data when lin(T)-log(t) – condition is assumed to be valid (later times in heating period), it is possible to use the slope of the line to get the first estimate for rock’s conductivity. Three approximate models are selectable. Using infinite line source solution (default), you may use both heating and cooling period or you have to select Cooling or Heating in Heating or cooling-panel (Figure 15). Two other models allow only heating period to be used and system does it automatically.

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Figure 15. Heating and cooling period-selections. After one model is finished you have to click TERO interpretation–checkbox again. Related to every model the fitting results are plotted on the screen at Display all- or Display fitting result–modes. Display all- mode is the default. When changing from one mode to another, user has to use first Curve-panel options (Figure 11) to restore the whole curve on screen after which other mode selection is possible. Fitting results of different modes (Figure 16).

Figure 16. Fitting results of different modes. As a default time ranges have fixed lengths (No use-option) but user may also change the time range (Use data selection-option) when needed (Figure 17).

Figure 17. Time range selection.

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Click both Use data selection-option and Select TERO-data interval-option active. Move cursor on plotting area and define time range (Figure 18). Repeat interpretation selections.

Figure 18. New time range selection. Periodical use of this option is possible only with the actual period (heating or cooling) and curve selected. When moving to another curve or another period, click No use-option first and repeat interpretation selections after which user is allowed to use DATA selection again. Go through all models and have corresponding conductivity values written (Figure 19) on screen.

Figure 19. All calculations are finished with corresponding results. Thermal diffusivity is another valuable parameter and it is calculated automatically using the rock type definitions or the relation Kukkonen expressed (Kukkonen et al. 2011). User’s choice for rock type with corresponding specific heat capacity and density are used (Figure 10). To proceed to following measurement point, repeat loading procedures or at first select both device and drillhole options and Read current –options. And finish interpretation just like above. User may define the heat capacity by determining both the specific heat capacity and/or density values and the corresponding diffusivity is modified according to the changes. In addition, the conductivity value can be determined freely by user in Rock-panel (Figure 10).

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4.1.2 Simulation and interpretation studies – finite line model Simulations based on analytical solutions are important and quick mean to investigate how different thermal properties of rock influence over temporal temperature profiles. The present version of this interface includes two cylindrical models: the finite line source (Kluitenberg 1993) and the infinite hollow tube model (Blackwell 1954; Goodhew & Griffiths 2004). The hollow tube model allows additional parameters to be attached to heat source. Namely, a finite inner and outer radius, a finite heat capacity and a contact resistance between the tube and the environment. Heat profiles may be calculated at a finite distance from the source using both models. In addition, the hollow tube model allows temperatures to be calculated on outer surface of the tube. Preliminary steps At the first step select the model or activate Pulsed finite- or Pulsed hollow cylinder–option (hollow tube is the default option). Let’s start with the pulsed finite line source by clicking the corresponding checkbox (Figure 20).

Figure 20. Pulsed finite line source model subpanel. In addition to checkbox subpanel contains the half length of line source (default value 0.75m is the half length of TERO-heater dimension). Heating-panel has minimum and

maximum F-factor values ( 2/4 rat ) and starting and ending points of the heating period. The cooling period has corresponding values. Boxes are filled during calculations. Timing figures are displayed in Time steps-panel (Figure 21). It is also possible that user loads TERO-data and gets the timing marks from there.

Figure 21. Timing of an analytical solution.

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By using a listbox in TERO-panel, user can determine the thermal properties (Figure 10). Do it by selecting VGN and corresponding thermal values are displayed on screen (heat capacity 725 Jkg-1K-1 and density 2741 kgm-3). Conductivity is set as 3.5 Wm-1K-1 and calculation point as 0.01 m from the line surface (they are default values and user can make his own selections). Before making any calculations, have a look at Device-panel, where the heater resistance and the current are set as 64.7 /m and 0.49 A. Values are actual values of the TERO heater (Figure 22).

Figure 22. Heater properties. Simulation and interpretation steps Normal action is to proceed with forward calculations with Forward-option but user may also invert the calculated values back to thermal parameter values to test inversion accuracy (Figure 23).

Figure 23. Forward-option is the default setting when analytical solutions are used. But user can also invert the solution back to thermal parameters by selecting Inversion- option. To proceed with forward calculations (Forward-option selected), just click Submit-button. Calculation takes some seconds after which the temperature curve is displayed on screen (Figure 24).

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Figure 24. Temperature curve of a finite line source model. Rock type VGN. Conductivity 3.5 Wm-1K-1. Radius 0.01m from line source. User can freely change values in Rock- and Device-panels to examine the effects on profiles. In Figure 25 rock’s thermal conductivity has been first decreased from a value of 3.5 Wm-1K-1(red) to a value of 3.0 Wm-1K-1 (blue) and then increased to a value of 4.0 Wm-1K-1(green). In addition, heating period has been reduced to 11000 seconds (black). Hold on and Hold off-options are used (Figure 17) to leave former curve on screen.

Figure 25. Temperature curves corresponding to conductivity values 3.0 (red), 3.5 (blue), 4.0 Wm-1K-1 (green). One more calculation has been done by reducing heating period to 11000 seconds (black). For testing purposes, the inversion of thermal properties from analytical temperature curves is possible, just make Inversion-option active and select Heating or Cooling (Figure 26) and the corresponding conductivity and diffusivity values are displayed on screen after clicking Submit-button. Data selection options are usable.

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Figure 26. User can also invert the forward solutions back to thermal parameters by selecting Inversion option. VGN rock type is used with conductivity of 3.5 Wm-1K-1 (Figure 10). Both heating and cooling period results are printed. In Figure 27 the fitting result of heating period is displayed in Display All-mode and the cooling period result in Display fitting result–mode.

Figure 27. Different display modes used for the heating period (Display all) and the cooling period (Display fitting result). These were short instructions to simulate the finite line source model and invert thermal properties of rock which were used in simulation.

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4.1.3 Simulation and interpretation studies – infinite hollow tube model Another model which can be used in simulations is the infinite hollow tube model (Blackwell 1954; Goodhew Griffiths 2004). The hollow tube model allows additional parameters to be attached to the heat source. Namely, inner and outer radius, heat capacity and contact resistance between the tube and the environment. Temperatures may be calculated at various distances from the source and in addition on the outer surface of the tube. Preliminary steps All buttons and selections needed are situated in Hollow cylinder–panel (Figure 28). As can be seen this model is the default model or Pulsed hollow cylinder–option is active.

Figure 28. Hollow cylinder–panel (default values).The default Contact factor is calculated using a value of 0.6 Wm-1K-1 for water conductivity and a value of 0.003 m for water layer dimension. As with the finite line source model user can make simulations (Interpretation off is active) and interpretations (in Interpretation-panel Blackwell log-function-option is on). Simulation and interpretation steps.

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Let’s start with simulations. As a first step, use listbox options in TERO-panel to select a rock type. Then user has two choices: he can use either Kluitenberg’s analytical solution which is precise in the whole time period or Blackwell’s original solution which can be used only partly (very early and late times during heating period but not usable or accurate at intermediate times). Thus, Kluitenberg is the default option. In addition, the default calculation position is tube’s surface (Probe surface is active) and no interpretation is done (Interpretation off is active). After rock type selection user can have probe’s heat capacity per unit length as the corresponding rock value or define tube’s heat capacity per unit length precisely. But starting with default values user can get familiar easier with the model and changing parameter values step by step feel and see the responses in temperature curves (Figure 29). Rock type was selected as VGN and as a value of tube’s heat capacity was used the corresponding rock’s heat capacity values (2800 Jm-1K-1).

Figure 29. Hollow tube model. Red profile plotted with Default values (Figure 28). The power may deviate depending on the used TERO data. After changing contact conductance from 200 Wm-2K-1 to 50 Wm-2K-1 temperature curve is plotted as blue line. Changing rock’s conductivity from 3.5 Wm-1K-1 to 3.0 Wm-1K-1, curve is plotted as green. The black temperature curve corresponds to a situation where the contact conductance was restored to the default value (50 Wm-2K-1) keeping the rock's conductivity at the value of 3.0 Wm-1K-1. Model behaves logically and changes in curves are as they should be. Thus, decreasing a contact conductance between the probe and environment, tube’s temperature should increase, as it happens. When decreasing rock’s conductivity temperature values should increase and so it is in Figure 29. Restoring contact conductance to its default value of 200 Wm-2K-1 increases temperature values effectively because of the decreased conductivity value of rock 3.0 Wm-1K-1. The Hollow cylinder –panel contains many additional parameters which are explained thoroughly by Blackwell (1954). Interpretation steps are started with setting Blackwell log-function–option active in Interpretation-panel. Inversion results are plotted in the box (Figure 30).

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Figure 30. Hollow type interpretation options and a result. As with finite line model, the result can be plotted both as lin-lin scale and lin-log –scale (Figure 31).

Figure 31. Fitting result of Blackwell’s hollow tube model using lin-lin-scale.

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5 MEASUREMENTS WITH TERO IN-SITU LOGGING DEVICES 5.1 Drillhole OL-KR2 with TERO56 probe Drillhole OL-KR2 was selected as a first target for full scale test measurements with the TERO56 device. The hole has a nominal diameter of 56 mm, and it intersects mostly migmatitic gneiss, granite and granitic pegmatite. The main focus of the in- situ measurements was to determine the properties of gneiss, which is the prevailing rock type at Olkiluoto. A measurement program was designed with an aim to locate both homogeneous and less homogeneous sections of the gneiss, and also of the granitoid rocks. The same sections were later sampled for laboratory measurements for comparison. Twenty two 1.5 m long sections of the drillhole were chosen for measurements. In this, we used the video images of the drillhole as well as previous single point logs. For repeatability reasons we wanted to have good control of the logging depths and hydraulically conductive and active fractures possibly disturbing the thermally conductive regime. In addition, the hydraulic transmissivities were also checked for high hydraulic conductivities. Most of the sections had very low transmissivities (Kukkonen et al. 2005; Pöllänen Rouhiainen, 2002). The loggings were carried out in two stages, between May 19 and June 5, 2004 and between September 17 and 28, 2004. Excluding a problem with pressure sealing of the cable head, and replacement of certain electronic circuit boards, the TERO56 device was observed to be functional and it worked well. The logging program is summarized in report by Kukkonen (Kukkonen et al. 2005). 5.2 Drillhole OL-KR14 with TERO76 probe TERO56 probe was developed for slim 56 mm drillholes. However, new drillholes drilled in the area were 76 mm drillholes, thus new TERO76 equipment was developed and manufactured. Drill hole OL-KR14 was selected as a target for full-scale test measurements with the new TERO76 device. The hole has a nominal diameter of 76 mm, a dip of 70º and it intersects mostly migmatitic gneiss, granite and tonalite (Niinimäki 2001). The main focus of the in-situ measurements was to demonstrate the technical functioning of the new TERO76 probe and to determine the properties of gneiss and granitoid rocks at a number of selected depths. The logging program is summarized in our previous paper (Kukkonen et al. 2007). Seven 1.5 m long sections of the drill hole were chosen for measurements at depths between 394 and 465 m. In this, we used the video images of the drill hole as well as previous single point logs. For repeatability reasons we wanted to have good control of the logging depths and to avoid hydraulically conductive and active fractures possibly disturbing the thermally conductive regime. The sections were selected using the reports on rock types and fractures of the OL-KR14 drill core (Niinimäki 2001) and the flow difference measurements in the hole (Pöllänen Rouhiainen 2002).

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The loggings were carried out in March 2006. The TERO76 probe was observed to be functional and it worked well. The friction of the probe packers was found to be considerable, and lowering of the probe in the drill hole was very slow. During measurements, the temperature records were disturbed by high frequency noise (“spikes”). 5.3 Laboratory measurements of drill cores Because all previous determinations of thermal properties at the Olkiluoto investigation site had been based on laboratory measurements of drill core samples (Kukkonen and Lindberg 1995, 1998; Kukkonen 2000), it was also necessary to measure the drill cores corresponding to the in-situ measurement intervals of drillhole OL-KR2. Three pieces of drill core samples were selected systematically from the in- situ measurement sections in such a way that the central sample was taken from the centre of the in-situ interval and two others were taken at 50 cm above and beneath the central point of the 1.5 m long interval. The sampling however, was locally complicated by the lack of core at the investigated sections because core had been already consumed for other purposes (Kukkonen et al. 2005). In OL-KR14 corresponding drill core measurements have not been carried out. In report by Kukkonen (Kukkonen et al. 2011) they present summarized laboratory results of Olkiluoto rock types carried out at Geological Survey of Finland during 1994-2010. The complete data set comprises 392 drill core samples from 12 drill holes representing the planned repository volume at depths of about 400-500 m. The majority of the samples represent veined gneiss, pegmatitic granite, tonalitic-granodioritic-granitic gneiss (56-216 samples/rock type), whereas diatexitic gneiss, mica gneiss, K-feldspar porphyry and quartzitic gneiss are in minority (1-20 samples/rock type). The average thermal conductivity (at 25 °C) of all samples is 2.91 Wm-1K-1, and the averages of main rock types (veined gneiss, tonalitic-granodioritic-granitic gneiss, diatexitic gneiss, mica gneiss and pegmatitic granite) fall within 2.66-3.20 Wm-1K-1. The standard deviations of conductivity are 0.4-0.6 Wm-1K-1, and the histograms of main rock types overlap. The overlapping, as well as the values of standard deviations reflects geological variability in the migmatitic formation. Highest average conductivities are related to pegmatitic granite and lowest to mica gneiss. The average specific heat capacity (at 25 °C) of all samples is 712 Jkg-1K-1. Highest specific heat capacity averages were observed for veined gneiss and mica gneiss, and lowest for pegmatitic granite, respectively. The standard deviations are relatively small in the range of 19-41 Jkg-1K-1. 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 1.34-1.7510-6 m2s-1. The highest values are related to pegmatitic granite, and the lowest values to mica gneiss. The standard deviations are in the range of 0.1–0.310-6 m2s-1.

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However, one has to be careful because in-situ thermal properties may deviate significantly from laboratory values, even if the effect of temperature, pressure and pore-fluid is accounted for. It is always a question about a certain scale dependence in which different factors are involved: in-situ measurements represent an average over a much larger rock volume than laboratory measurements performed on small samples. On the other hand, small-scale variations may thus be lost in in-situ measurements. A summary table is given in Table 1 (Kukkonen et al. 2011). Table 1. Summary of rock’s thermal properties in Olkiluoto (Kukkonen et al. 2011). Rock type

Conduc-

tivity

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. 5.4 Interpretation and comparison with laboratory measurements In the following we present the comparison of the thermal properties from in-situ measurements in OL-KR2 and OL-KR14 drillholes with laboratory results. The numerical estimation was handled as a nonlinear least squares problem. Misfit between the time dependent measured and modelled temperatures is minimized by applying the Levenberg-Marquardt method (Dennis & Schnabel 1996; Madsen et al. 2004). This damped Gauss-Newton method locally approximates the given nonlinear problem with linear least squares problem. Numerical estimates were published and concerned thoroughly in reports (Kukkonen et al. 2005; Kukkonen et al. 2007). The rapid parameter estimation is based on fitting the measured temperatures to simplified functions of infinite line and hollow tube model (Eq. 3.6, 3.9) yielding a straight line whose slope can be used in the estimation of the thermal conductivity directly. 5.4.1 Numerical estimates and laboratory values in OL-KR2 Laboratory results of OL-KR2 drill cores and numerical estimates of thermal parameters have been displayed in Table 2. Thermal conductivities of the gneiss samples are in a

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good agreement with previous results. In the sampled sections the gneiss foliation is in most cases approximately perpendicular to the drill core axis. Therefore, the standard samples represent mostly the minimum conductivity with a mean of 2.85±0.23 Wm-1K-1. The samples drilled in the direction perpendicular to the core axis, which in gneiss samples corresponds to the plane of schistosity, yielded systematically higher conductivities, with a mean of 3.42±0.16 Wm-1K-1. The average factor of anisotropy is 1.25±0.25 but individual values range from 0.83 to 2.00. The existence of a systematic anisotropy, particularly in the gneiss, is an important factor influencing the interpretation of the in-situ measurements, which are particularly sensitive for the thermal conductivity in the radial direction from the drillhole axis.

Table 2. Summary of in-situ and laboratory measurements of thermal conductivity and diffusivity (drillhole OL-KR2).

Depth (m)

Rock type

λH sH λa λp sa sp F λ

326.0-327.5 TGG 3.31 1.48 2.72 3.28 1.37 1.65 1.20 335.0-336.5 TGG 3.61 1.62 2.75 3.25 1.63 1.39 1.24

340.0 – 341.5 VGN 3.29 1.48 2.97 3.04 1.51 1.53 1.24 345.5 – 347.0 TGG 3.22 1.45 2.45 2.98 1.24 1.52 1.31 350.0 – 351.5 TGG 3.25 1.49 2.62 2.99 1.32 1.49 1.07 354.5 – 356.0 TGG 3.34 1.35 2.70 3.24 1.36 1.64 1.24 365.0 – 366.5 TGG 3.41 1.53 3.12 3.40 1.60 1.72 1.09 377.0 – 378.5 TGG 3.27 1.45 2.49 2.77 1.25 1.39 1.17 379.9 – 381.4 TGG 3.32 1.51 2.80 3.13 1.41 1.57 1.08 386.0 – 387.5 TGG 3.31 1.47 2.57 3.25 1.33 1.64 1.21 388.9 – 390.4 TGG - - 2.51 3.10 1.26 1.58 1.20 446.5 – 448.0 PGR 4.04 1.76 3.42 4.33 1.77 2.22 1.20 467.0 – 468.5 VGN 4.35 1.88 3.08 4.29 1.39 2.08 1.39

470.85– 472.35 VGN 4.22 2.04 3.00 - 1.49 - - 476.0 – 477.5 VGN 4.23 1.87 3.43 4.18 1.70 2.09 1.17 481.0 – 482.5 PGR 3.87 1.72 3.34 2.77 1.72 1.46 0.83 486.0 – 487.5 VGN 4.29 2.00 2.62 3.50 1.30 1.76 2.00 491.0 – 492.5 VGN 3.94 1.75 2.99 - 1.49 - - 502.0 – 503.5 VGN 3.88 1.71 2.62 3.47 1.28 1.62 1.52

506.25– 507.75 VGN 4.54 2.02 3.22 3.49 1.59 1.58 1.06 510.65– 512.35 VGN 3.97 1.77 3.25 4.19 1.65 2.17 1.36 526.0 – 527.5 VGN 4.02 1.72 2.44 3.52 1.21 1.76 1.72

λH = thermal conductivity determined in drillhole (W m-1 K-1) numerical result sH = thermal diffusivity determined in drillhole (10-6 m2 s-1) numerical result λa = thermal conductivity along the drillhole axis determined in laboratory from core samples (W m-1 K-1) λp = thermal conductivity perpendicular to drillhole axis determined in laboratory from core samples sa = thermal diffusivity along to drillhole axis determined in laboratory from core samples (10-6 m2 s-1) sp = thermal diffusivity perpendicular to drillhole axis determined in laboratory from core samples (10-6 m2 s-1) F λ = anisotropy factor of thermal conductivity (= sp / sa, where sa is axial diffusivity value)

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5.4.2 Rapid slope method estimates in OL-KR2 Heating element in TERO devices is a foil which is glued on the inner surface of the aluminium tube. The measured resistance of the heater is 97.2 and the length of the foil is 1.5 m. Thus, regarding the foil as a line source, the resistance per unit length of the line source (R) is 64.8 /m. Heater current is not monitored in the tube itself but at the earth surface (TERO56 device). Using measured current values, heating power can be written as

oo TtTRitRitg )(1)()( 22 (5.1)

Fitting results (linear and logarithmic) at depth of 470.00 meters are printed in Figures 31-33 using the infinite line source model (Eq. 3.6) and Blackwell’s hollow tube model (Eq. 3.10). Fitting result or from the slope calculated estimate of conductivity is 4.26 Wm-1K-1 when a late heating period is used (Figure 31). When late times in cooling period are used the corresponding thermal conductivity value is 4.03 Wm-1K-1 (Figure 32). The infinite hollow tube estimate is 4.26 Wm-1K-1 for the late heating period (Figure 33). The rock type at depth of 470.00 m is VGN (Table 2) with heat capacity value of 725 Jkg-1K-1 and density value of 2741 kgm-3 (Table 1). Thus, the theoretical diffusivity is 2.1510-6m2s-1 for the late heating period and 2.0310-6m2s-1 for the late cooling period using the infinite line model. In Blackwell’s hollow tube model the diffusivity is 2.1410-6m2s-1 from the late heating period.

Figure 31. Fitting results in KR2 (470.00 m) from heating period with infinite line source model. Linear and logarithmic curves are printed.

Figure 32. Fitting results in KR2 (470.00 m) from cooling period with infinite line source model. Linear and logarithmic curves are printed.

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Figure 33. Fitting results in KR2 (470.00 m) from heating period with Blackwell’s hollow tube model. Linear and logarithmic curves are printed. Fitting results (linear and logarithmic) at depth of 445.00 meters are presented in Figures 34-36 using the infinite line source model (Eq. 3.6) and Blackwell’s hollow tube model (Eq. 3.10). Fitting result or from the slope calculated estimate of conductivity is 3.96 Wm-1K-1 when late heating period is used (Figure 34). When late times in the cooling period are used the corresponding thermal conductivity value is 3.91 Wm-1K-1 (Figure 35). The infinite hollow tube result is 3.96 Wm-1K-1 for the late heating period (Figure 36). The rock type at depth of 445.00 is PGR (Table 2) with a heat capacity value of 689 Jkg-1K-1 and density value of 2635 kgm-3 (Table 1). Thus, the theoretical thermal diffusivity is 2.1110-6m2s-1 for the late heating period and 2.0910-

6m2s-1 for late cooling period using the infinite line model. In Blackwell’s hollow tube model, the thermal diffusivity estimated from the late heating period is 2.1110-6m2s-1.

Figure 34. Fitting results in KR2 (445.00 m) from heating period with infinite line source model. Linear and logarithmic curves are printed.

Figure 35. Fitting results in KR2 (470.00 m) from cooling period with infinite line source model. Linear and logarithmic curves are printed.

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Figure 36. Fitting results in KR2 (470.00 m) from heating period with Blackwell’s hollow tube model. Linear and logarithmic curves are printed. Summarized results from the rapid slope method are listed in Tables 3-6 using both the heating and cooling periods using infinite line source model. In Blackwell’s hollow tube model the user can use only the late times of the heating periods. Comparing with numerical values (Table 2) the estimated rapid slope conductivity values are lower in depth range between 326 and 350 meters. The reason was the different current values used in calculations generating different heating powers. Current values used are read directly from the original data files. But in deeper parts conductivity values are in very good agreement. Conductivities estimated from the late cooling period differ from the values of the late heating period, as it was expected.

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Table 3. Summary of thermal conductivity and diffusivity estimates of the rapid slope method in drillhole OL-KR2 (thermistor number 1).

Depth (m)

Rock type

λLHeat sLHeat λLCool sLCool λBHeat sBHeat

326.0-327.5 TGG 2.49±0.14 1.28±0.07 2.45±0.18 1.26±0.10 2.49±0.14 1.28±0.07

335.0-336.5 TGG 2.75±0.18 1.38±0.09 2.69±0.20 1.35±0.10 2.72±0.18 1.37±0.09

340.0 – 341.5 VGN 2.55±0.14 1.28±0.07 2.51±0.18 1.26±0.09 2.55±0.14 1.28±0.07

345.5 – 347.0 TGG 2.42±0.13 1.29±0.07 2.38±0.16 1.27±0.09 2.42±0.13 1.29±0.07

350.0 – 351.5 TGG 2.47±0.15 1.32±0.08 2.13±0.16 1.13±0.09 2.47+0.15 1.31±0.08

354.5 – 356.0 TGG 3.51±0.22 1.87±0.11 3.25±0.22 1.73±0.12 3.51±0.22 1.87±0.11

365.0 – 366.5 TGG 3.45±0.20 1.90±0.11 3.32±0.21 1.83±0.11 3.45±0.20 1.90±0.11

379.9 – 381.4 TGG 3.20±0.18 1.71±0.10 3.22±0.19 1.72±0.10 3.20±0.18 1.71±0.10

386.0 – 387.5 TGG 3.28±0.19 1.74±0.10 3.23±0.19 1.72±0.10 3.28±0.19 1.74±0.10

446.5 – 448.0 PGR 3.98±0.28 2.19±0.15 3.91±0.27 2.15±0.15 3.98±0.28 2.19±0.15

467.0 – 468.5 VGN 4.29±0.32 2.36±0.18 4.20±0.21 2.31±0.12 4.28±0.32 2.36±0.18

470.85 – 472.35 VGN 4.29±0.32 2.16±0.16 3.97±0.26 2.00±0.13 4.29±0.32 2.16±0.16

476.0 – 477.5 VGN 4.28±0.32 2.16±0.16 4.64±0.75 2.33±0.38 4.28±0.32 2.16±0.16

481.0 – 482.5 PGR 4.07±0.29 2.24±0.16 3.92±0.39 2.16±0.21 4.07±0.29 2.24±0.16

486.0 – 487.5 VGN 4.20±0.31 2.11±0.16 3.41±0.29 1.71±0.15 4.20±0.31 2.11±0.16

491.0 – 492.5 VGN 4.08±0.29 2.25±0.16 3.87±0.34 2.13±0.19 4.08±0.29 2.25±0.16

502.0 – 503.5 VGN 3.83±0.26 1.93±0.13 3.83±0.34 1.93±0.17 3.83±0.26 1.93±0.13

506.25 – 507.75 VGN 4.45±0.35 2.24±0.18 4.38±0.35 2.20±0.18 4.45±0.35 2.24±0.18

510.65 – 512.35 VGN 4.15±0.31 2.29±0.17 3.55±* 1.95±* 4.15±0.31 2.29±0.17

526.0 – 527.5 VGN 4.96±0.40 2.50±0.20 4.12±0.24 2.08±0.12 4.96±0.40 2.50±0.20

λLH eat = thermal conductivity (W m-1 K-1) and sLHeat= thermal diffusivity (10-6 m2 s-1) , line model (heating) λLCool = thermal conductivity (W m-1 K-1) ansd sLCool= thermal diffusivity (10-6 m2 s-1), line model (cooling) λBHeat = thermal conductivity (W m-1 K-1) and sBHeat = thermal diffusivity (10-6 m2 s-1), tube model (heating) * value couldn't be estimated

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Table 4. Summary of thermal conductivity and diffusivity estimates of the rapid slope method in drillhole OL-KR2 (thermistor number 2). Depth (m)

Rock type


326.0-327.5 TGG 2.48±0.14 1.28±0.07 2.45±0.17 1.26±0.09 2.49±01.4 1.28±0.07

335.0-336.5 TGG 2.73±0.18 1.37±0.09 2.69±0.20 1.35±0.10 2.73±0.18 1.37±0.09

340.0 – 341.5 VGN 2.59±0.15 1.30±0.07 2.50±0.18 1.26±0.09 2.59±0.15 1.30±0.07

345.5 – 347.0 TGG 2.40±0.13 1.28±0.07 2.37±0.16 1.26±0.09 2.40±0.13 1.28±0.07

350.0 – 351.5 TGG 2.46±0.14 1.31±0.08 2.12±0.16 1.13±0.09 2.46+0.14 1.31±0.08

354.5 – 356.0 TGG 3.50±0.21 1.86±0.11 3.25±0.22 1.73±01.2 3.50±0.21 1.86±0.11

365.0 – 366.5 TGG 3.43±0.20 1.89±0.11 3.31±0.21 1.82±0.11 3.43±0.20 1.89±0.11

379.9 – 381.4 TGG 3.19±0.18 1.70±0.10 3.20±0.19 1.71±0.10 3.19±0.18 1.70±0.10

386.0 – 387.5 TGG 3.25±0.19 1.73±0.10 3.22±0.19 1.71±0.10 3.25±0.19 1.73±0.10

446.5 – 448.0 PGR 3.96±0.27 2.18±0.15 3.87±0.26 2.13±0.15 3.96±0.27 2.18±0.15

467.0 – 468.5 VGN 4.27±0.32 2.35±0.18 4.19±0.21 2.31±0.12 4.27±0.32 2.35±0.18

470.85 – 472.35 VGN 4.26±0.32 2.15±0.16 3.97±0.26 2.00±0.13 4.26±0.32 2.14±0.16

476.0 – 477.5 VGN 4.27±0.32 2.15±0.16 4.57±0.74 2.30±0.37 4.27±0.32 2.15±0.16

481.0 – 482.5 PGR 4.05±0.28 2.23±0.16 3.91±0.39 2.15±0.21 4.07±0.28 2.24±0.16

486.0 – 487.5 VGN 4.18±0.31 2.10±0.16 3.38±0.29 1.70±0.15 4.18±0.31 2.10±0.16

491.0 – 492.5 VGN 4.04±0.28 2.22±0.16 3.85±0.34 2.12±0.19 4.03±0.28 2.22±0.16

502.0 – 503.5 VGN 3.82±0.26 1.92±0.13 3.81±0.34 1.92±0.17 3.82±0.26 1.92±0.13

506.25 – 507.75 VGN 4.46±0.35 2.24±0.17 4.36±0.35 2.19±0.17 4.46±0.35 2.24±0.17

510.65 – 512.35 VGN 4.12±0.30 2.27±0.17 3.59±* 1.98±* 4.12±0.30 2.27±0.17

526.0 – 527.5 VGN 5.00±0.41 2.50±0.20 4.02±0.27 2.02±0.14 5.00±0.41 2.52±0.21


38

Table 5. Summary of thermal conductivity and diffusivity estimates of the rapid slope method in drillhole OL-KR2 (thermistor number 3). Depth (m)

Rock type


326.0-327.5 TGG 2.50±0.14 1.29±0.07 2.45±0.18 1.26±0.09 2.50±01.4 1.29±0.07

335.0-336.5 TGG 2.75±0.18 1.39±0.09 2.70±0.20 1.36±0.10 2.75±0.18 1.39±0.07

340.0 – 341.5 VGN 2.59±0.15 1.30±0.07 2.51±0.18 1.26±0.09 2.59±0.15 1.30±0.07

345.5 – 347.0 TGG 2.41±01.3 1.28±0.07 2.37±0.16 1.26±0.09 2.41±0.13 1.28±0.07

350.0 – 351.5 TGG 2.48±0.15 1.32±0.08 2.13±0.16 1.13±0.09 2.48+0.15 1.32±0.08

354.5 – 356.0 TGG 3.51±0.22 1.87±0.11 3.25±0.22 1.73±01.2 3.51±0.22 1.87±0.11

365.0 – 366.5 TGG 3.45±0.20 1.90±0.11 3.32±0.21 1.83±0.11 3.45±0.20 1.90±0.11

379.9 – 381.4 TGG 3.20±0.18 1.70±0.10 3.22±0.19 1.71±0.10 3.20±0.18 1.70±0.10

386.0 – 387.5 TGG 3.26±0.19 1.74±0.10 3.23±0.19 1.72±0.10 3.26±0.19 1.74±0.10

446.5 – 448.0 PGR 3.98±0.28 2.19±0.15 3.89±0.27 2.15±0.15 3.98±0.28 2.19±0.15

467.0 – 468.5 VGN 4.29±0.32 2.37±0.18 4.19±0.21 2.31±0.12 4.29±0.32 2.37±0.18

470.85 – 472.35 VGN 4.27±0.32 2.15±0.16 3.99±0.26 2.01±0.13 4.27±0.32 2.15±0.16

476.0 – 477.5 VGN 4.28±0.32 2.15±0.16 4.62±0.76 2.33±0.38 4.28±0.32 2.15±0.16

481.0 – 482.5 PGR 4.07±0.29 2.24±0.16 3.92±0.39 2.16±0.22 4.07±0.29 2.24±0.16

486.0 – 487.5 VGN 4.19±0.31 2.11±0.16 3.41±0.29 1.71±0.15 4.19±0.31 2.11±0.16

491.0 – 492.5 VGN 4.04±0.28 2.22±0.16 3.87±0.34 2.13±0.19 4.04±0.28 2.22±0.16

502.0 – 503.5 VGN 3.84±0.26 1.93±0.13 3.83±0.34 1.93±0.17 3.84±0.26 1.93±0.13

506.25 – 507.75 VGN 4.45±0.35 2.24±0.17 4.40±0.35 2.21±0.18 4.45±0.35 2.24±0.17

510.65 – 512.35 VGN 4.11±0.29 2.27±0.16 3.59±* 1.98±* 4.11±0.29 2.27±0.16

526.0 – 527.5 VGN 4.99±0.42 2.51±0.21 4.01±0.32 2.02±0.16 4.99±0.42 2.51±0.21


39

Table 6. Summary of thermal conductivity and diffusivity estimates of the rapid slope method in drillhole OL-KR2 (thermistor number 4).

Depth

(m)

Rock

type


326.0-327.5 TGG 2.49±0.14 1.28±0.07 2.44±0.17 1.26±0.10 2.49±0.14 1.28±0.07

335.0-336.5 TGG 2.73±0.18 1.37±0.09 2.69±0.20 1.36±0.10 2.73±0.18 1.37±0.09

340.0 – 341.5 VGN 2.58±0.15 1.30±0.07 2.50±0.18 1.26±0.09 2.58±0.15 1.30±0.07

345.5 – 347.0 TGG 2.41±0.13 1.28±0.07 2.37±0.16 1.26±0.09 2.41±0.13 1.28±0.07

350.0 – 351.5 TGG 2.47±0.15 1.31±0.08 2.12±0.16 1.13±0.09 2.47+0.15 1.31±0.08

354.5 – 356.0 TGG 3.49±0.21 1.86±0.11 3.25±0.22 1.73±01.2 3.49±0.21 1.86±0.11

365.0 – 366.5 TGG 3.44±0.20 1.89±0.11 3.31±0.21 1.82±0.11 3.44±0.20 1.89±0.11

379.9 – 381.4 TGG 3.19±0.18 1.70±0.10 3.21±0.19 1.71±0.10 3.19±0.18 1.70±0.10

386.0 – 387.5 TGG 3.26±0.18 1.74±0.10 3.22±0.19 1.71±0.10 3.26±0.18 1.74±0.10

446.5 – 448.0 PGR 3.97±0.28 2.19±0.15 3.87±0.26 2.13±0.15 3.97±0.28 2.19±0.15

467.0 – 468.5 VGN 4.28±0.32 2.36±0.18 4.18±0.21 2.30±0.12 4.28±0.32 2.36±0.18

470.85 – 472.35 VGN 4.27±0.32 2.15±0.16 3.97±0.26 2.00±0.13 4.27±0.32 2.15±0.16

476.0 – 477.5 VGN 4.26±0.32 2.14±0.16 4.55±0.75 2.29±0.37 4.26±0.32 2.14±0.16

481.0 – 482.5 PGR 4.06±0.29 2.23±0.16 3.91±0.39 2.15±0.21 4.06±0.29 2.23±0.16

486.0 – 487.5 VGN 4.18±0.31 2.10±0.15 3.39±0.29 1.71±0.15 4.18±0.31 2.10±0.15

491.0 – 492.5 VGN 4.03±0.28 2.22±0.16 3.87±0.34 2.12±0.19 4.03±0.28 2.22±0.16

502.0 – 503.5 VGN 3.82±0.26 1.92±0.13 3.85±0.34 1.92±0.17 3.82±0.26 1.92±0.13

506.25 – 507.75 VGN 4.43±0.34 2.23±0.17 4.36±0.35 2.20±0.18 4.43±0.34 2.23±0.17

510.65 – 512.35 VGN 4.09±0.31 2.25±0.17 3.58±* 1.97±* 4.09±0.31 2.25±0.17

526.0 – 527.5 VGN 4.92±0.40 2.48±0.20 3.95±0.34 1.99±0.17 4.92±0.40 2.48±0.20


The heating power is approximated according to Eq. 5.1. The approximation may cause uncertainty but the greatest error in is characterized by the uncertainty in the slope of the straight line fit to the experimental data. Measurement depth 525.0 m contained noisy data in the late heating period which might generate the confusing conductivity value of 4.99 Wm-1K-1 or the accurate determination of the slope was difficult (Figure 37).

40

Figure 37. Fitting result in OL-KR2 (525.00 m) from heating period with infinite line source model. Logarithmic plotting is presented. The accuracies of thermal properties in Tables 3-6 are limited principally by the accuracy with which the temperature changes can be measured. Thermistors can reliably detect temperature changes of about 0.01 K. Thus, calculating the partial derivative of K2 with respect to the temperature change (Eq. 3.6), we can estimate the measurement error by which the temperature changes could be determined in the corresponding time range. Furthermore, taking the partial derivative of the diffusivity (s=K2/c) with respect to K2, we can estimate the measurement error of the diffusivity. 5.4.3 Numerical estimates and laboratory values in OL-KR14 The numerically inverted results are presented in Table 7 (Kukkonen et al. 2007) together with the rapid slope method results from the infinite line model (late heating period). When discussing about numerical inversion results, it should be kept in mind that the fluid flow effects may have produced biasing. The numerically inverted thermal conductivities range from 2.95 to 3.78 Wm-1K-1 and diffusivities from 1.71 to 2.1210-6 m2s-1. The differences between numerical results calculated from the complete heating-cooling cycle and those from the cooling part are small for conductivity (less than 1 %) but higher for diffusivity (up to 13 %). In our earlier study, theoretical considerations with simulated data suggested that inversion results from the cooling part are less affected by various sources of bias, such as hole calliper uncertainties (Kukkonen et al. 2005). The obtained thermal conductivities are in agreement with previous laboratory measurements of rocks in Olkiluoto (Kukkonen & Lindberg 1995, 1998; Kukkonen 2000). The section of OL-KR14 with gneiss at 394.75 m shows schistoseity more or less perpendicular to the drill hole. Thus, it can be expected that the TERO76 results, which are sensitive particularly for conductivity in the radial direction from the drill hole, would show relatively high value of conductivity in the anisotropic gneiss (e.g. Kukkonen & Lindberg 1995, 1998; Kukkonen 2000). This is exactly, what was obtained in the drill hole measurement at laboratory (3.78 Wm-1K-1).

41

Table 7. Results of thermal inversions for drill hole OL-KR14. Both numerical (Kukkonen et al. 2007) and rapid slope method (infinite line source) results are presented.

Depth (m)

Rock Type

H

Wm-1

K-1

c Jm

-3K

-1

sH

10-6

m2

s-1

LH

Wm-1

K-1

sLH

10-6

m2

s-1

394.75 VGN 3.78 1796655 2.11 3.87±0.30 1.95±0.15 400.75 PGR 3.70 1744022 2.12 3.93±0.32 1.98±0.16 415.55 TGG 3.14 1707312 1.84 3.18±0.28 1.69±0.15 438.25 TGG 3.00 1750760 1.71 3.04±0.21 1.62±0.11 439.75 TGG 2.95 1724756 1.71 3.08±0.15 1.64±0.08 439.75 TGG 2.95 1671983 1.76 3.03±0.38 1.61±0.20 463.85 TGG 3.52 1533549 2.08 3.55±0.34 1.79±0.17

VGN is veined gneiss, PGR pegmatitic granite, TGG tonalitic-granodioritic-granitic gneiss λH is thermal conductivity from numerical inversion ρc volumetric heat capacity, and sH thermal diffusivity λLH is thermal conductivity from rapid inversion (infinite line source model) sLH is thermal diffusivity from rapid inversion (infinite line source model) Laboratory measurements on thermal conductivity of tonalite and granite (four samples) in Olkiluoto have yielded values in the range of 2.76–4.68 Wm-1K-1 (Kukkonen & Lindberg, 1995, 1998). Variations in conductivity can be attributed to variations in contents of quartz and biotite. We can conclude that the present TERO76 results are in general agreement with laboratory measurements of conductivity. 5.4.4 Rapid estimates in OL-KR14 Fitted results from the rapid interpretation (linear and logarithmic) at depth of 394.75 meters are printed in Figures 38-40 using the infinite line source model (Eq. 3.6) and Blackwell’s hollow tube model (Eq. 3.10). Fitting result from the slope calculated estimate of thermal conductivity is 3.85 Wm-1K-1 when the late heating period is used (Figure 38). When late times in cooling period are used the corresponding conductivity value is 3.82 Wm-1K-1 (Figure 39). The corresponding infinite hollow tube result is 3.85 Wm-1K-1 for the late heating period (Figure 40). The rock type at depth of 394.75 m is VGN (Table 2) with heat capacity value of 725 Jkg-1K-1 and density value of 2741 kgm-3 (Table 1). Thus, the theoretical thermal diffusivity is 1.9410-6m2s-1 for the late heating period and 1.9210-6m2s-1 for the late cooling period with the infinite line model. Diffusivity from the late heating period for Blackwell’s hollow tube model is 1.9410-6m2s-1.

42

Figure 38. Fitting results in KR14 (394.75 m) from heating period of infinite line source mode approximation. Linear and logarithmic curves are printed.

Figure 39. Fitting results in KR14 (394.75 m) from cooling period of infinite line source mode approximation. Linear and logarithmic curves are printed.

Figure 40. Fitting results in KR14 (394.75 m) from heating period with Blackwell’s hollow tube model approximation. Linear and logarithmic curves are printed. Fitting results (linear and logarithmic) at depth of 415.55 meters are printed in Figures 41-43 using the infinite line source model (Eq. 3.6) and Blackwell’s hollow tube model (Eq. 3.10). Fitting result from the slope calculated estimate of conductivity is 3.16 Wm-1K-1 when the late heating period is used (Figure 41). When late times in cooling period are used the corresponding thermal conductivity value is 3.2 Wm-1K-1 (Figure 42). The corresponding infinite hollow tube thermal conductivity is 3.17 Wm-1K-1 for the late heating period (Figure 43). The rock type at depth of 415.55 m is TGG (Table 2) with a heat capacity value of 696 Jkg-1K-1 and density value of 2700 kgm-3 (Table 1). Thus, the theoretical diffusivity is 1.6810-6m2s-1 for the late heating period and 1.710-

6m2s-1 for the late cooling period with the infinite line model. Diffusivity from the heating period for Blackwell’s hollow tube model is 1.6910-6m2s-1.

43

Figure 41. Fitting results in KR14 (415.55) from heating period of infinite line source model approximation. Linear and logarithmic curves are printed.

Figure 42. Fitting results in KR14 (415.55) from heating period of infinite line source model approximation. Linear and logarithmic curves are printed.

Figure 43. Fitting results in KR14 (415.55) from heating period with Blackwell’s hollow tube model approximation. Linear and logarithmic curves are printed. Summarized results of rapid inversions for all thermistors are gathered in Tables 8-11. Heat capacity values (c) are calculated using known values of the specific heat capacity and density of Olkiluoto rock types in Table 1.

44

Table 8. Rapid slope method results of thermal parameters for drill hole OL-KR14 (thermistor number 1).

Depth (m)

Rock Type

LH

Wm-1

K-1

LC

Wm-1

K-1

BH

Wm-1

K-1

c Jm

-3K

-1 sLH

10-6

m2

s-1

394.75 VGN 3.87±0.30 3.86±0.29 3.87±0.30 724*2742 1.95±0.15

400.75 PGR 3.93±0.32 3.82±0.29 3.93±0.32 724*2742 1.98±0.16

415.55 TGG 3.18±0.28 3.22±0.26 3.18±0.28 696*2700 1.69±0.15

438.25 TGG 3.04±0.21 3.04±0.19 3.04±0.21 696*2700 1.62±0.11

439.75 TGG 3.08±0.38 3.16±0.14 3.08±0.15 696*2700 1.64±0.08

439.75 TGG 3.03±0.38 2.98±0.34 3.03±0.38 696*2700 1.61±0.20

463.85 TGG 3.55±0.34 3.58±0.30 3.55±0.34 724*2742 1.79±0.17 VGN is veined gneiss, PRG pegmatitic granite, TGG tonalitic-granodioritic-granitic gneiss λLH is thermal conductivity for infinite line source model from heating period λLC is thermal conductivity for infinite line source model from cooling period λBH is thermal conductivity for hollow tube source model from heating period sLH is thermal diffusivity for infinite line source model (values of other models deviate only slightly from values infinite line model and are not displayed) ρc volumetric heat capacity (Table 1) Table 9. Rapid slope method results of thermal parameters for drill hole OL-KR14 (thermistor number 2).

Depth

(m)

Rock Type

LH

Wm-1

K-1

LC

Wm-1

K-1

BH

Wm-1

K-1

c Jm

-3K

-1 sLH

10-6

m2

s-1

394.75 VGN 3.85±0.30 3.83±0.29 3.85±0.30 724*2742 1.94±0.15

400.75 PGR 3.91±0.31 3.80±0.29 3.91±0.31 724*2742 1.97±0.16

415.55 TGG 3.16±0.27 3.20±0.26 3.16±0.27 696*2700 1.69±0.15

438.25 TGG 3.03±0.20 3.00±0.19 3.02±0.20 696*2700 1.61±0.11

439.75 TGG 3.07±0.14 3.14±0.14 3.07±0.14 696*2700 1.63±0.08

439.75 TGG 3.03±0.38 3.00±0.34 3.03±0.38 696*2700 1.61±0.20

463.85 TGG 3.53±0.34 3.55±0.30 3.53±0.34 724*2742 1.78±0.17 VGN is veined gneiss, PGR pegmatitic granite, TGG tonalitic-granodioritic-granitic gneiss λLH is thermal conductivity for infinite line source model from heating period λLC is thermal conductivity for infinite line source model from cooling period λBH is thermal conductivity for hollow tube source model from heating period sLH is thermal diffusivity for infinite line source model (values of other models deviate only slightly from values infinite line model and are not displayed) ρc volumetric heat capacity (Table 1)

45

Table 10. Rapid slope method results of thermal parameters for drill hole OL-KR14 (thermistor number 3).

Depth (m)

Rock Type

LH

Wm-1

K-1

LC

Wm-1

K-1

BH

Wm-1

K-1

c Jm

-3K

-1 sLH

10-6

m2

s-1

394.75 VGN 3.83±0.30 * 3.83±0.30 724*2742 1.93±0.15

400.75 PGR 3.92±0.31 3.80±0.18 3.91±0.31 724*2742 1.97±0.16

415.55 TGG 3.17±0.27 3.20±0.19 3.16±0.27 696*2700 1.69±0.15

438.25 TGG 3.03±0.21 3.01±0.19 3.02±0.20 696*2700 1.61±0.11

439.75 TGG 3.07±0.14 3.14±0.14 3.07±0.14 696*2700 1.63±0.08

439.75 TGG 3.03±0.38 2.98±0.34 3.03±0.38 696*2700 1.61±0.20

463.85 TGG 3.53±0.34 3.55±0.30 3.54±0.34 724*2742 1.78±0.17 VGN is veined gneiss, PGR pegmatitic granite, TGG tonalitic-granodioritic-granitic gneiss λLH is thermal conductivity for infinite line source model from heating period λLC is thermal conductivity for infinite line source model from cooling period λBH is thermal conductivity for hollow tube source model from heating period sLH is thermal diffusivity for infinite line source model (values of other models deviate only slightly from values infinite line model and are not displayed) ρc volumetric heat capacity (Table 1) * data strongly corrupted

Table 11. Rapid slope method results of thermal parameters for drillhole OL-KR14 (thermistor number 4).

Depth

(m)

Rock Type

LH

Wm-1

K-1

LC

Wm-1

K-1

BH

Wm-1

K-1

c Jm

-3K

-1 sLH

10-6

m2

s-1

394.75 VGN * * * 724*2742 *

400.75 PGR 3.92±0.31 3.80±0.29 3.91±0.31 724*2742 1.97±0.16

415.55 TGG 3.15±0.27 3.20±0.16 3.16±0.27 696*2700 1.68±0.14

438.25 TGG 3.02±0.20 3.00±0.16 3.02±0.20 696*2700 1.61±0.11

439.75 TGG 3.07±0.14 * 3.07±0.14 696*2700 1.63±0.08

439.75 TGG 3.03±0.38 2.97±0.34 3.03±0.38 696*2700 1.61±0.20

463.85 TGG 3.52±0.34 3.53±0.30 3.53±0.34 724*2742 1.71±0.17 VGN is veined gneiss, GRAN pegmatitic granite, TGG tonalitic-granodioritic-granitic gneiss λLH is thermal conductivity for infinite line source model from heating period λLC is thermal conductivity for infinite line source model from cooling period λBH is thermal conductivity for hollow tube source model from heating period sLH is thermal diffusivity for infinite line source model (values of other models deviate only slightly from values infinite line model and are not displayed) ρc volumetric heat capacity (Table 1) * data strongly corrupted

46

The estimated thermal conductivity values (Tables 7-11) are in very good agreement. Conductivity values estimated from the late cooling period (LC) may differ from values of late heating period as it should, because late times of cooling period describe properties further from the hole. Laboratory values for drill cores were not available in OL-KR14. All theoretical diffusivity values sLH estimated by the rapid slope method are <2.0*10-6m2s-1 unlike the values of veined gneiss (VGN) and granite (PGR) which are >2.0*10-6m2s-1.

47

6 SUMMARY OF RESULTS The original intention of this work was to develop and introduce a rapid interpretation tool of in-situ thermal measurements made by the TERO devices as the thermal conductivities of rocks can be estimated from the late heating periods under certain conditions. Namely, the late times of the heating period can be applied when the temperature increase of the probe has reached the asymptotic constant value as a function of the logarithm of time. Thus, the late temperature rise is dependent on the thermal conductivity of surroundings. The quality of the result is highly dependent on the goodness of the data fitting. The introduced analytical method cannot be used to estimate the thermal diffusivity or the volumetric heat capacity directly from the heating period but diffusivity may be calculated simply using measured laboratory values of specific heat capacity and density of Olkiluoto rock types (Kukkonen et al. 2011). Although the laboratory measurements can be made on core samples, thus offering a high degree of control through the selection of the sample measured, the fact that the sample is not measured in place is a disadvantage. The core sample represents only a small volume of rock, whereas the in-situ measurement integrates a volume about 3 orders of magnitude bigger. The numerical optimization method, allowing to take into account the detailed construction of the device, is time-consuming and a skilled operator is required to handle the interpretation procedure. As a final step of this work, a comparison between laboratory measurements and present study and numerical interpretation (Kukkonen et al. 2005; Kukkonen et al. 2007) was conducted from drillholes OL-KR2 and OL-KR14. The first TERO model was designed and constructed to be used in Ø56 mm drillholes. The laboratory data from OL-KR2 was available for the comparisons. Figures 44-47 present the results from the different interpretation methods, the numerical and rapid slope method. In drillhole OL-KR2, the laboratory results were available but not in drillhole OL-KR14 (Ø76 mm drillhole).

Figure 44. Thermal conductivities in drillhole OL-KR2. The numerical results using the complete heating-cooling period are plotted as red symbols, laboratory measurements and analytical solution (the mean value of four thermistors) using the heating curve are shown as blue and brown symbols, respectively.

48

Figure 45. Thermal diffusivities in drillhole OL-KR2. The numerical results using the complete heating-cooling period are plotted as red symbols, laboratory and analytical solution (a mean value of four thermistors) using the heating curve are shown as blue and brown symbols, respectively. Figures 44-45 present the results from drillhole OL-KR2. The interpreted conductivity values are consistent with the thermal conductivities measured in the laboratory (Figure 44), except for the upper and deepest depth positions. In the upper positions, the conductivity values of different interpretation methods differ significantly due to the used different power values. In the deepest position, the difference was generated by the data fitting problem (Figure 37). As a whole, the correspondence is good, although statistics of data set is quite poor. The above mentioned reasons also generate the largest differences in the diffusivity values in the corresponding data points. In the middle depth positions, the analytical method seems to generate slightly larger diffusivity values using the late heating period than the laboratory values whereas the numerical method gives smaller diffusivity values when the complete heating-cooling periods were used.

Figure 46. Thermal conductivities in drillhole OL-KR14. The numerical results using the complete heating-cooling period are plotted as red symbols and using the cooling period as blue symbols. The analytical solution (a mean value of four thermistors) using the heating curve are shown as brown symbols, respectively.

49

Figure 47. Thermal diffusivities in drillhole OL-KR14. The numerical results using the complete heating-cooling period are plotted as red symbols and using the cooling period as blue symbols. The analytical solution (a mean value of four thermistors) using the heating curve are shown as brown symbols, respectively. Figures 46-47 present the results from drillhole OL-KR14. Laboratory values are not available. The complete heating-cooling or cooling period used in the numerical optimization of thermal conductivity. The correspondence between the conductivity estimates is good, except for the upper depth positions (Figure 46) where the rapid method gives slightly higher conductivities. The numerical conductivity estimates are not dependent on the period that is used in the estimation. The behaviour of diffusivities has the same trends but the numerical estimates based on the complete heating-cooling period are ~10 % larger than the values generated by the rapid slope method. When the cooling period is used, the numerical diffusivity estimates are approaching the rapid method estimates. The rapid interpretation is based on an infinitely long cylindrical heat source model and the numerical model is a finite 2-dimensional cylinder symmetric model, thus the measurement time might have influence on the estimated parameters. There are also many other possible factors, e.g. time-dependent temperature, convection etc., that can generate errors in the numerical estimates. In the rapid method, the thermal conductivity was estimated using the late part of heating period but the numerical solution using the complete heating-cooling period (Kukkonen et al. 2005; Kukkonen et al. 2007 ). Due to the above mentioned error sources and according to Kukkonen et al. (2007), the parameters contribute differently in different periods of the measurement. However, only small differences were generated in numerical conductivity estimates (Figure 46). The thermal diffusivity was estimated simply by using the laboratory results on diffusivity-conductivity relationship (Kukkonen et al. 2011) of different rock types in the rapid slope method (page 9). Thus, diffusivity is calculated from the regression line

153.05754.0 xs . In the numerical solution, the complete heating-cooling period or the cooling period was used. Now, the influence of different periods is emphasized or the numerical diffusivities estimated from the cooling period are ~13 % lower (Figure 47) than from the heating-cooling period. In the previous reports (Kukkonen et. al. 2005; Kukkonen et. al. 2007), it is emphasized that even with this kind of detailed finite model, the more precise estimation of rock's thermal diffusivity is difficult and needs the accurate knowledge of heat capacity of the TERO-device.

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7 DISCUSSION AND CONCLUSIONS A new graphical interface (Rapid Interpretation Tool) has been developed during the TERO76 project to study the behaviour of different heat sources: an infinite long line source and an infinite long hollow cylinder source and to estimate the thermal properties of rocks surrounding the sources. The both models can be solved analytically, thus the implementation is straightforward and is done in Matlab. The numerical models must be taken in use when the 3D behaviour of temperature profiles are needed. The late time times of heating period when the temperature rise has been slowed down to an asymptotic phase can be used to estimate the thermal conductivity. The time interval of heating period is set to an appropriate value but a user may change the interval to discover the effect of different interval selections on the conductivity estimates. Thus, the first results of thermal properties are available already in the field. In the TERO56 device the electric current is monitored during measurements at the earth surface but the voltage in the probe. On the other hand, in the TERO76 device, the both parameters (current and voltage) are monitored in the probe, thus the heating power is accurately determined. The largest error in the thermal conductivity is caused by the uncertainty in the slope of fitted line to the experimental data and by the measurements errors if the model based systematic error sources (e.g. length of the heating period, finite length of the probe, water-layer) are excluded. The recent model studies suggest that the systematic error due to the water-layer can be as low as ~2 %. when the temperature rise has been slowed down to an asymptotic phase. Furthermore, the influence of finite length of the probe would seem to become significant when the heating period is > 6 hours (conductivity > 3.5 Wm-1K-1). The corresponding systematic error is ~3 %. In the range of < 3.5 Wm-1K-1, the heating period up to 6 hours seems to be reasonable. On the contrary, our previous theoretical studies using finite line source models suggest that the axial condition generates a detectable deviation from the infinite source result when the heating time exceeds ~11 hours (Kukkonen & Suppala 1999). Banaszkiewicz et al. (1997) reported the results of their studies which suggest that the error for the thermal conductivity amounts to a few percent but the corresponding error of thermal diffusivity is about 15 %. As a final product of interpretation rock’s thermal conductivity and diffusivity of the rock surrounding the drillhole must be estimated. According to published papers (Batty et al. 1984; Blackwell 1954; Blackford 1985; Buettner 1955; Goodhew et al. 2004; Jager & Charles-Edwards 1968, Vries 1952), the slope method is a rapid and accurate mean to estimate thermal conductivity of rocks using late times of heating periods from the slope of the straight line correlating the temperature rise with logarithm time data. The thermal conductivity of the rock may be determined, since the slope of the straight line is equal to 4/Q ([Q]=W/m). The thermal diffusivity and volumetric heat capacity can't be estimated directly. Consequently, diffusivity must be estimated by using known values of specific heat capacity and density of rock types from laboratory measurements (Kukkonen et al. 2011). The main reason is the close relationship of diffusivity and the contact resistance layers in the cylinder heat source conduction problem. The measurement configuration with the TERO devices is such that both heating and measurements are taken in the same place on the inner side of the aluminium tube and the contact resistance, i.e. water layer between the probe and rock,

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is not accurately known. More sophisticated and numerical methods must be used where the detailed features of the measurement geometry and the device can be taken accurately into account to understand in more detail the measurements over the whole period. Even then it is not guaranteed that diffusivity estimates are acceptable but thermal conductivities can be estimated in practice in the same acceptable accuracy with simple and advanced methods. In this report we gathered and compared the results from the numerical and sophisticated inversion (Kukkonen et al. 2005; Kukkonen et al. 2007), rapid slope method and laboratory measurements (Kukkonen et al. 2011). Field measurements were done in two drillholes OL-KR2(TERO56) and OL-KR14(TERO76) The thermal conductivity values determined are in a good agreement. Numerical values range from 3.31 to 4.54 Wm-1K-1 and from 2.40 to 4.46 Wm-1K-1 with the rapid slope method in OL-KR2. The difference in conductivity values in the depth range between 325 and 350 meters can be attributed to differences input heat powers and means of estimating the power. In OL-KR14 the numerical estimation provided conductivity values of 2.95-3.78 Wm-1K-1 with the corresponding rapid slope method estimates of 3.03-3.92 Wm-1K-1 According to the laboratory results the estimated in-situ conductivities seemed to be at higher level than the laboratory values. One explanation could be anisotropy as the TERO measurements are more sensitive for the thermal conductivity in the radial direction. Numerically estimated diffusivities were in the range between 1.3510-6 and 2.0410-6 m2s-1 in OL-KR2. Rapid slope method estimates were calculated using known values of the specific heat capacity and density resulting in the range between 1.3110-6

and 2.2810-6 m2s-1. In OL-KR14 the corresponding values were in range between 1.7110-6 and 2.1210-6 m2s-1 when numerical approach was used and for the rapid slope method in the range between 1.5410-6 and 1.9510-6 m2s-1. Both methods estimated the diffusivity values at a higher level than laboratory values. This report describes the use of transient thermal measurements to determine the thermal properties of rocks simply and efficiently. The following conclusions have been drawn from the work described. The results of this study have demonstrated the ability of the TERO devices to provide reliable measurements of rock's thermal properties. The interpretation of thermal response data using analytically resolvable models has an advantage of simple programming and use. It offers also speed and reliable results. The analysis based on the simple infinite heat source models generally provides good estimates of the thermal conductivity that coincide with the estimates from the numerical finite 2-dimensional cylinder symmetric model. The estimation of thermal diffusivity is more problematic and much more difficult to estimate with high accuracy due to correlation with thermal contact resistance between the probe and the borehole wall as well as uncertainties in the probe parameters. Thus, further research must be undertaken in order to get more reliable diffusivity estimates.

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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. Batty, S. W., Probert, S. D., Ball, M. & O'Callaghan, P. W. 1984. Use of the thermal-probe technique for the measurement of the apparent thermal conductivity of moist materials. Applied Energy 18/(1984), p. 301-317. Blackford, M. G. & Harries, J. R. 1985. A heat source probe for measuring thermal conductivity in waste rock dumps. Lucas heights research laboratories. Australian atomic energy commission. AAEC/E609. 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. 137-144. Buettner, K. 1955. Evaluation of soil heat conductivity with cylindrical test probes. Transactions American Geophysical Union, volume 36, number 5, p. 831-837. Carslaw, H. S. & Jaeger, J. C. 1959. Conduction of heat in solids. Oxford University Press, Oxford, 510 p. Dennis, J. E. & Schnabel, R. B. 1996. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. (Classics in Applied Mathematics 16) SIAM Society for Industrial & Applied Mathematics, Philadelphia, 378 p. Goodhew, S. & Griffiths, R. 2004. Analysis of thermal-probe measurements using an iterative method to give sample conductivity and diffusivity data. Applied Energy, vol. 77, 2004, p. 205-223. Jager, J. M. de. & Charles-Edwards, J. 1968, Thermal Conductivity Probe for Soil-moisture Determinations. Journal of Experimental Botany, Vol. 20, No. 62, p. 46-51. Kjørholt, H. 1992. Thermal properties of rocks. Teollisuuden Voima Oy, TVO/Site investigations, work report 92-56, 13 p. Kluitenberg, G. J., Ham, J. M. & Bristow, K. I. 1993. Error analysis of the heat pulse method for measuring soil volumetric heat capacity. Soil Sci. Soc. Am. J., 1993, 57, p. 1444-1451. Korpisalo, A. 2005. User’s Guide: TERO Graphical interface in Matlab/Femlab environment. Geological Survey of Finland, Espoo Office, Geophysical Research, Report Q17/2005/1, 88 p.

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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 2011-17, 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 2007-01, 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 2005-09, 96 p. Kukkonen, I. 2000. Thermal properties of the Olkiluoto mica gneiss: Results of laboratory measurements. Posiva Oy, Working Report 2000-40, 28 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 99-1, 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 98-09e, 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 YJT-98-08, 29 p. Madsen, K., Nielsen, H. B. & Tingleff, O. 2004. Methods for Non-Linear Least Squares Problems, IMM, DTU, 2nd Edition, April 2004. Available at http://www.imm.dtu.dk/courses/02611/nllsq.pdf Niinimäki, R. 2001. Core drilling of deep borehole OL-KR14 at Olkiluoto in Eurajoki 2001. Posiva, Working Report 2001-24, 140 p. Pöllänen, J. & Rouhiainen, P. 2002. Difference flow and electric conductivity measurements at the Olkiluoto site in Eurajoki, boreholes KR13 and KR14. Posiva Oy, Working Report 2001-42, 100 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 R-03-18, 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 2004-20, 43 p. (in Finnish) Vries, D. A. de. 1952. A Nonstationary method for determining thermal conductivity of soil in-situ. Soil Science, 73, 1952, no:2, p. 83-89.

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