The final disposal of spent nuclear fuel in Finland is planned to be carried out in the crystalline bedrock at the Olkiluoto nuclear power plant site in western Finland by Posiva Oy. The heat transfer properties (thermal conductivity and diffusivity) of the bedrock define the necessary extent of the repository footprint, and knowledge of these parameters is thus important. Heat in a material is generated by vibrations and random motions of particles (such as electrons and atoms). Thus, good electrical conductors (e.g. metals such as copper and aluminium having numerous approximately free or loosely bound electrons) are generally also good heat conductors. The thermal conductivity of a material is its ability to conduct heat (in watts per metre-kelvin (Wm-1K-1)), and thermal diffusivity is a measure of the transient response of a material to a change in temperature (in square metres per second (m2s-1)).
However, accurate measurement of these parameters can pose many challenges. Characterization must be strictly based on an understanding of the thermophysical fundamentals. Potential errors that may affect the final results must also be recognized. Heat due to radioactive decay will emanate from the disposal canisters and diffuse into the surrounding rock. Thus, knowledge of the heat transfer behavior in the surrounding rocks and the filling material of the tunnels is extremely important when estimating the shortest safe canister spacing to ensure the most effective usage of the repository. The final disposal of spent nuclear fuel is scheduled to start at the beginning of the 2020s and will probably continue for one hundred years, after which, the entire repository will be sealed by the 2120s.
At the beginning of the 2000s, Posiva Oy and the Geological Survey of Finland (GTK) started co-operation to design and construct “termiset ominaisuudet” (TERO) devices (in English, “thermal properties”), in which an electrically heated cylinder probe was used to determine the thermal properties of crystalline rock in drillholes in the area of the repository of spent nuclear fuel (referred to as ONKALO). The use of such devices to determine the thermal properties of rocks was in no sense novel. However, the TERO devices were specifically designed for the drillhole conditions at Olkiluoto and therefore had to meet specific design prerequisites for that site. Further development of the use of TERO devices for the drillholes in the Olkiluoto area was seen as a practical way to continue the earlier work conducted elsewhere. The first model, TERO56, was planned to be used in Ø56 mm drillholes. The probe itself had a diameter of 50 mm. Later, a newer model (TERO76) was constructed for larger, Ø76 mm drillholes, the diameter of the probe being 70 mm. This co-operation has now continued for almost twenty years, and numerous experiments costing hundreds of thousands euros have successfully been completed during this era. Over twenty deep surface drillholes in the Olkiluoto area and several shallow research drillholes in ONKALO have been measured. Altogether, almost 350 measurements have been conducted in the crystalline rock of Olkiluoto up until the present time, and these measurements have seemingly increased our knowledge of variation in the thermal properties of bedrock at the repository site. The TERO system has also been used to determine thermal properties in situ in Oskarshamn and Forsmark at the Svensk Kärnbränslehantering AB (SKB) study sites in Sweden.
The logging system consists of a modern winch, winch cable, winch control unit and additional electronics, a laptop for the real-time monitoring of measurements and the TERO probe containing a SinglePoint sensor (used in the localization of the probe in the drillhole) and additional weights. The armoured cable (3/16 of an inch in diameter) is 640 m long and has four conductors. The winch is equipped with a separate control panel. The winch system has an option for automated operation, but this is not included in the present system. Posiva Oy is the owner of the TERO system, the main components of which are illustrated in Figure 2.
TERO measurements rely on a thermistor-based method. A thermistor is a temperature- dependent resistor. Negative temperature coefficient thermistors (NTC) are commonly used for thermal property measurements, as their resistance decreases when their temperature is increased. The number of thermistors in the early TERO models was 28 and they were firmly integrated into the heating foil. During the upgrade, the number was decreased and only four thermistors were left in the current model and they are no longer integrated into the heating foil. The heating foil is pressed against the inner surface of the aluminium tube to provide a uniform heat source. The end frames of the drillhole probes are made of a polyacetate plastic (POM, ertalyte) to reduce axial conduction. The plastic parts also serve as housing for the electronics of the probe. The total length of the heating part is 1640 mm, and high length-to-diameter ratios are thus ensured, being approximately 33 with TERO56 and approximately 23 with TERO76. In addition, the power fed to the foil during the heating period can be determined more precisely, resulting in more reliable estimates of thermal conductivity and diffusivity. The precise heat capacity of the probe is unknown, but this knowledge would be of importance in the interpretation of measurements. Thermal heat capacity is the ability of a material to store and release heat energy (in joule per kelvin (JK-1)) (Figure 3).
Before reliable measurements could be conducted, the thermistors were calibrated. The calibration is considered to have a maximum error of approximately 0.03 K. The resolution of the thermistors is 1 mK. The power fed to the heating foil during the heating period must be recorded as accurately as possible, because the input power used is an important variable in the interpretation. The power is linearly related to the measured temperatures, and thus both the heating current and voltage need to be accurately calibrated. It would be particularly important to calibrate the whole probe for different materials to improve accuracy, but this has not been performed.
Water flow through the space between the tube and drillhole wall might interfere with the measurement, and the probes are thus fitted with simple hydraulic packers made of soft silicon rubber to hinder the circulation of water and thereby preserve the measurement conditions as close as possible to pure conductive heat transfer (Figure 3). It is assumed that the packers will prevent water flow as long as the hydraulic pressure difference between inside and outside the packer-isolated area does not exceed the pressure of a water column of a few metres. Heating of the probe is not expected to generate water circulation, because the water space between the tube and rock is restricted to a minimum practical width of approximately 3 mm. In addition, the increase in temperature is moderate and of the order of 2–3 oC in a typical measurement.
Some requirements for the measurement can be mentioned. The probe should not be situated between different rock types. Open and flowing fractures should not be present near the measurement depth and the drillhole should be vertical. The monitoring of temperatures during the stabilization period helps in the decision as to when the next measurement can be started or when the temperature readings of the thermistors have clearly stabilized at constant levels. The depth steps between the sequential measurement points must be long enough to prevent any confounding heat disturbance from the previous measurement, or it must be ensured that thermal disturbance from the previous measurement point is no longer present. The correct utilization of devices such as TERO also requires that certain prerequisites are met. The contact layer (water column) between the probe and drillhole wall must be small enough to keep heat transfer across the contact layer purely conductive as much as possible. The length- to-diameter ratio of the probe must be >20. Thus, an increase in the diameter of the drillhole also increases the overall length of the probe, and movement of the probe in the narrow drillhole becomes more difficult. The heated drillhole section must be sealed to prevent heat loss from both ends of the probe during the heating period.
The measurement principle is thus to heat a cylinder and monitor its temperature behaviour during a heating-cooling period. The thermal properties of the surrounding rock affect the thermal response of the probe. A new drillhole measurement typically starts with a stabilization period of 4–5 hours to minimize and eliminate the possibly temporal drift from the measurement, which might disturb the estimation of the thermal properties. After the temperatures have been allowed to equilibrate, a heating period of 6 hours follows. At the beginning, a rapid increase in temperature is generated, which is followed by a more moderate increase. Nowadays, a short cooling period of approximately 30 minutes completes the measurement, instead of longer cooling periods of approximately 10–12 hours that were used in the early measurements. A cooling period begins with a rapid temperature drop followed by a slower decrease in temperature. Measurements are monitored in real time at the surface, and thus a rapid decision can be made about the continuation of the measurement. After checking the results, the device is moved to the next position. Thus, two measurements can be conducted within 24 hours (Figure 4).
Both numerical and analytical methods are utilized in the interpretation of TERO data. The numerical inversion approach is based on infinite and finite cylinder models. Fitting the measured data to the forward model of conductive heat transfer enables the calculation of numerical estimates of the thermal properties. However, accurate determination of thermal diffusivity is difficult due to the strong coupling of diffusivity and the water layer between the probe and drillhole wall in the solution of the heat conduction equation. Thus, thermal diffusivity is generally estimated by using the conductivity-diffusivity relationship (diffusivity = 0.5754 x conductivity – 0.153), which has been determined from laboratory measurements of Olkiluoto-type rocks.
Analytical interpretation is based on infinite line and hollow cylinder models in which the probe is assumed to be a perfect conductor. A user-friendly interface was designed to estimate the thermal conductivity immediately after a TERO measurement has been completed. The data are fitted to the asymptotic functions of infinite source models and thermal conductivity is calculated from the slope of the fitted line. After the conductivity estimate is calculated, diffusivity is estimated from the conductivity-diffusivity relationship (Figure 5).
Using the analytical interpretation method, the first analytical estimates can be calculated after only 2500 seconds have elapsed from the beginning of the heating period. For instance, disturbances in the temperature response of the device generated by water circulation can be recognized and the measurement can be interrupted at the measurement depth in good time, and the device moved to a new position.
Nine deep drillholes were investigated with the TERO76 device in an experiment conducted during 2014–2015 (Figure 6). The cost of the project was approximately 200 000 euros. The drillholes mostly intersected veined gneiss (VGN), pegmatitic granite (PGR) and diatexitic gneiss (DGN). The measurement points were in the range of 350−640 m (drilling depths), which covered the whole vertical depth range of the repository.
In typical cases, drillholes intersected the foliation planes approximately perpendicularly, and the TERO measurements thus provided higher estimates of the radial conductivity than the corresponding laboratory measurements. The less the foliation plane deviates from the perpendicular, the more the TERO results tend to overestimate conductivity. The possible reasons for this phenomenon include anisotropic conductivity (conductivity has a different value in different directions), geological heterogeneity, the measurement geometry and foliation angle. In the analytical analysis, the later times of the heating period were used to ensure that appropriate conditions for conductivity estimates prevailed (a pseudo-stationary regime). In contrast, in the numerical estimation, data from the longer interval of the heating period were used. Despite these differences, the correspondence between the results from the different methods was good. The numerical method systematically produced approximately 6−8% higher conductivity and diffusivity values on average than the corresponding values obtained using the analytical method. On the other hand, the analytical values were approximately 15−20% higher than the values measured for the core samples at GTK. The same behaviour was also recognized in previous experiments at OIkiluoto. Posiva has repeated the laboratory measurements from the rock samples. After carefully verifying the results from the new measurements, the detailed report will be published during following years.
In drillhole OL-KR47, the main rock type was found to be veined gneiss, but pegmatitic and tonalitic gneiss sections could also be localized. In Figure 7, the analytical and numerical interpretation results of the corresponding data from drillhole OL-KR47 are presented.
All the results from the recent study are gathered in two data diagrams consisting of the rock types in the drillholes and the estimated thermal parameters from both the analytical and numerical interpretation (Figures 8−9).
At Olkiluoto, the migmatitic gneisses are anisotropic and heterogeneous and their effect on the conductivity is evident. The TERO measurements provided radial thermal data in the range of the measurement that depended on the thermal properties and the duration of measurement (resulting in higher conductivity values), whereas the laboratory samples represented conductivity in the direction of the drillhole axis perpendicular to the foliation. It must be noted that the laboratory values may deviate significantly from the in situ drillhole measurements, even when the real conditions in the drillholes are taken into account. This is because the laboratory measurements were conducted on small samples, whereas the in situ measurements represent much larger rock volumes, and small-scale features can therefore be lost. The coring of a sample from deep bedrock and the preparation of the sample result in a vertical rock pillar may also generate irreversible changes in thermal conductivity. The anisotropy and heterogeneity of the Olkiluoto gneissic rocks cannot be separated in the TERO measurements.
We have designed and constructed drillhole devices, collectively referred to as TERO, and have developed interpretation methods for determining the in situ thermal properties of crystalline rock in the area of the final repository for spent nuclear fuel at Olkiluoto. The TERO device acts as a heated cylinder, releasing a heat pulse for 6 hours that slowly diffuses to a distance of approximately 35 cm from the probe into the surrounding rock. The thermal properties of the surrounding medium affect the thermal response of the probe, and its time-dependent volumetric thermal properties can be estimated. A long stabilization period is utilized to minimize transient drift, as any possible drift must be eliminated. The probe itself may be a source of a transient trend due to the heat generation generated by and subsequently emanating from the electronics of the probe. The power fed to the heating foil must be kept constant, and the voltage and current in the drillhole probe are thus precisely monitored during the heating period. Any variation in the power is effectively linked to the uncertainties of the conductivity estimates. The width of the water layer is appropriately restricted to 3 mm to avoid convective heat transfer, which could disturb the conductive heat transfer assumption through the water layer. In addition, leakage of the packers might result in inconsistent conductivity values. An open fracture between the packers would produce heat loss during the heating period and result in high conductivity values.
In order to provide accurate results, temperature readings must be accurately measured and the drillhole caliper must be accurately known when estimating diffusivity. Calibration of the probe in different materials could additionally improve the accuracy of the estimations. The symmetry of the cylinder is the key issue when interpreting the collected TERO data. Analytical solutions consist of infinite line source and hollow cylinder models for determining conductivity. Diffusivity is determined by using the conductivity-diffusivity relationship of the Olkiluoto-type rocks. This approach serves as a stable and pragmatic means for estimating diffusivity. A full numerical solution of the conduction equation based on infinite and finite cylinder models has been developed. Conductivity can normally be estimated much more robustly than diffusivity because inaccuracy of the drillhole caliper may generate errors of several tens of percent. The parameters can either be simultaneously solved or the estimate of conductivity from the heating period can be used to estimate diffusivity and the drillhole caliper, or the conductivity-diffusivity relationship can be directly used. Laboratory measurements of drillhole samples to determine their thermal properties were conducted along the drillhole axis at GTK. It would be vital, however, to also conduct laboratory measurements perpendicular to the axis.
The TERO device is easy to operate, and the analytical results can be calculated immediately after a measurement has been completed. Thus, preliminary analytical results can be provided to the customer when all the measurements points in the drillhole have been conducted. The characteristic behaviour of heat transfer from the probe and the fact that drillholes are usually drilled perpendicularly to the foliation planes ensure that TERO measurements are sensitive to the radial properties of rocks. Such enhanced sensitivity would appear to result in essentially higher conductivities than were obtained from the corresponding laboratory measurements at GTK. Nevertheless, the results from the recent experiment were consistent with those results of previous measurements from the Olkiluoto site, and the measurements produced data that substantially increase our knowledge of the variation in the thermal properties of the bedrock. Such data are of considerable support when dimensioning and designing subsurface repository projects where thermal properties are important.
Korpisalo, A., Suppala, I., Kukkonen, I., and Koskinen, T., 2015. Determination of In Situ Thermal Properties of Rocks in Drillholes OL-KR6, OL-KR14, OL-KR43, OL-KR45, OL-KR47, OL-KR49, OL-KR51, OL-KR54 and OL-KR55 at Olkiluoto 2014–2015. Posiva Oy, Working Report 2015-39, 79 p.
Kukkonen, I., Korpisalo, A., Suppala, I., and Koskinen, T., 2013. In situ determination of thermal properties of rocks in crystalline rock drill holes with TERO56 and TERO76 devices. Posiva Oy, Posiva Report 2013-06, 56 p.
Korpisalo, A., Kukkonen, I., and Suppala, I., 2012. Determination of thermal conductivity and thermal diffusivity of rocks from transient in-situ measurements using rapid slope method. Posiva Oy, Working Report 2012-57, 54 p.
Kukkonen, I., Suppala, I., Korpisalo, A., and Koskinen, T., 2007. Drillhole logging device TERO76 for determination of rock thermal properties. Posiva Oy, Posiva Report 2007-01, 38 p.
Kukkonen, I., Suppala, I., Korpisalo, A., and Koskinen, T., 2005. TERO borehole logging device and test measurements of rock thermal properties in Olkiluoto. Posiva Oy, Posiva Report 2005-09, 96 p.
Text: Arto Korpisalo
Arto Korpisalo received his MSc (1996) in medical physics from Kuopio Korkeakoulu (Finland) and PhD (2016) in physics from Helsinki University. He has worked since 1997 in Geological Survey of Finland (GTK) as a physicist. His research interests include forward and inverse problems in drillhole thermophysics and electromagnetism.