Evaluation of primary data

6.2.1 Thermal conductivity determinations

Laboratory measurements of the thermal conductivity and thermal diffusivity of water saturated rock samples have been performed using the TPS (Transient Plane Source) method (see description in /Sundberg 2003a/). The measurements are made on small rock volumes (approximately 10 cm³).

Summary statistics of thermal conductivity for each rock type are presented in Table 6-1. The results of all thermal conductivity measurements are visualised in Figure 6-1. The dominant granitoid rocks in domains RFM029 and RFM045 have high thermal conductivity, whereas granite, granodiorite and tonalite (101051) and amphibolite (102017) have intermediate or low thermal conductivity.

A comparison of data from different boreholes and different depths (Figure 6-1) indicates limited large-scale spatial variation in thermal conductivity for the dominant granite (101057) (for sample locations, see Table 3-2 in /Back et al. 2007/).

The difference in thermal conductivity between fresh and altered (albitized) samples of aplitic metagranite (101058) based on TPS measurements is statistically insignificant.

Thermal conductivities have also been determined with the SCA-method /Back et al. 2007/, based on mineral compositions (from modal analysis) and thermal conductivities of different minerals.

Investigations of fresh and oxidised samples of granite to granodiorite (101057)- and granite, granodiorite and tonalite (101051) show that, for a given quartz content, the calculated thermal conductivity for oxidised samples is consistently higher than that for unaltered samples.

6.2.2 Relationship between thermal conductivity and density

A relationship between density and measured (TPS) thermal conductivity for Ävrö granite in Laxemar/Simpevarp is well established /Sundberg et al. 2005b, Wrafter et al. 2006, Sundberg et al.

2008b/, and when applied to borehole density logging data, has been used for modelling of thermal conductivity along continuous sections of boreholes.

Establishing relationships between density and thermal conductivity is important since it provides support for the use of borehole density data for analysing the spatial correlation structure of thermal properties as described in section 6.4.5. The relationship between density and thermal conductivity for all investigated rock types is illustrated in Figure 6-2. For rock types other than fine- to medium-grained granite, granodiorite and tonalite (101051) and amphibolite (102017), no obvious relation-ships are apparent within individual rock types. However, the observed relationship between density and thermal conductivity for all rock types together is a function of the mineral constituents and is consistent with the results of theoretical calculations of density and thermal conductivity based on the mineralogy of different rock types presented in /Sundberg et al. 2008b/. It provides support for the modelling assumption that the spatial correlation structure of density and thermal conductivity are similar within different rock types.

Table 6‑1. Measured thermal conductivity (W/(m·K)) at room temperature (20–25°C) of different rock types using the TPS method.

Rock code Rock name Mean St. dev. Max Min Number

of samples 101057 Granite to granodiorite, metamorphic, medium-grained 3.68 0.17 4.01 3.25 74¹

101056 Granodiorite, metamorphic 3.04 0.09 3.20 2.98 5

101054 Tonalite to granodiorite, metamorphic 2.73 0.19 2.94 2.45 5 101051 Granite, granodiorite and tonalite, metamorphic, fine- to

medium-grained 2.85 0.26 3.39 2.46 12

101058 Granite, metamorphic, aplitic 3.85 0.13 4.06 3.68 12²

101061 Pegmatite, pegmatitic granite 3.33 0.20 3.50 3.07 4

Figure 6‑1. Thermal conductivity versus elevation for different rock types. Samples measured using the TPS method.

Figure 6‑2. Relationships between density and thermal conductivity for all rock types (left) and for granite, granodiorite and tonalite (101051) and amphibolite (102017) (right). Model refers to granite, granodiorite and tonalite (101051).

-900 -800 -700 -600 -500 -400 -300 -200 -100 0

2.0 2.4 2.8 3.2 3.6 4.0

Thermal conductivity, W/(m·K) (TPS measurements)

Elevation (m)

Diorite, quartz diorite, gabbro -101033

Granodiorite to tonalite -101051

Tonalite to granodiorite -101054

Granodiorite - 101056 Granite to granodiorite -101057

Amphibolite - 102017 Granite - 101058 Pegmatite, pegmatitic granite - 101061

Granite - 111058 Felsic-intermediate volcanic rock - 103076

2.0 2.4 2.8 3.2 3.6 4.0

2550 2650 2750 2850 2950 3050

Density, kg/m³

Thermal conductivity, W/(m*K)

Granite to granodiorite (101057) Granite, granodiorite and tonalite (101051)

Granite (101058) Amphibolite (102017)

Fine grained granite (111058) Felsic to mafic volcanic rock (103076)

Pegmatite (101061) Granodiorite (101056)

Tonalite to granodiorite (101054) Diorite, quartz diorite and gabbro (101033) Model for 101051

2.0 2.4 2.8 3.2 3.6 4.0

2650 2700 2750 2800 2850 2900 2950 3000 3050

Density, kg/m³

Thermal conductivity, W/(m*K)

Granite, granodiorite and tonalite (101051) Amphibolite (102017)

Model 101051

Based on the relationship between density and thermal conductivity, thermal conductivity has been calculated for granite, granodiorite and tonalite (101051) from the density logging of boreholes. The results of these calculations are further described in section 3.4.3 in

/Back et al. 2007/.

6.2.3 Measurement of anisotropy of thermal conductivity associated with foliation

All rock types in rock domains RFM029 and RFM045 have been subjected to some degree of ductile deformation, which has produced both a lineation and a foliation. The preferred alignment of mineral grains produced by this deformation may produce anisotropy in thermal transport properties.

A higher thermal conductivity can be assumed parallel to the alignment of minerals compared to the perpendicular direction, in analogy with parallel and serial connection of resistors. Anisotropy of thermal properties in the rock mass may impact on the design of a deep repository. For this reason, the directional dependence of thermal properties caused by foliation within deformed granite at the Forsmark site has been investigated in a large-scale field experiment, combined with laboratory and field testing at a smaller scale /Sundberg et al. 2007/.

The investigations were carried out in the vicinity of drill site 7, situated in the north-western, marginal part of the Forsmark tectonic lens (see sections 5.2.1 and 5.2.4). The rock at this site is characterised by a relatively strong tectonic foliation that strikes NNW and dips steeply. Laboratory measurements at the centimetre scale, using a modified TPS method, indicate that thermal conductivity parallel with the foliation is, on average, a factor of 1.4 times greater than conductivity perpendicular to the foliation. Field measurements, including a large-scale experiment that measured larger volumes of rock, have yielded anisotropy factors of approximately 1.15, considerably lower than for the laboratory measurements. A distinct scale dependence on the anisotropy factor is indicated. The results of this investigation are summarised in Table 6-2 with regard to the scale dependence of anisotropy of thermal conductivity.

Given that most of the rock mass displays less intense deformation than that shown by the rock close to drill site 7, lower anisotropy factors would be expected for the greater part of the target volume.

However, the anisotropy cannot be neglected.

6.2.4 Heat capacity

Heat capacity has been determined indirectly from thermal conductivity and diffusivity measurements using the TPS method, and directly using the calorimetric method. Results, for samples for which both direct and indirect methods have been used are shown in Table 6-3 and Figure 6-3.

Since the calorimetric measurements are considered to be more reliable, Figure 6-3 indicates that there probably is a bias in the heat capacity determined by the TPS method. The bias is probably caused by the anisotropy in the samples in combination with how thermal conductivity and diffusivity are measured by the TPS method. This is further discussed in section 6.6.1. Calorimetric measure-ments have been used in the modelling when available.

Table 6‑2. Results of investigation of scale dependence on anisotropy of thermal conductivity in the dominant granite. Factor of anisotropy and the effective thermal conductivity (geometric mean of the two principal directions).

Scale Thermal conductivity

Mean factor of anisotropy λpa/λpe Geometric mean W/(m·K)

Centimetre scale 1.40 3.45

Table 6‑3. Heat capacity, determined at room temperature by TPS and the calorimetric method (direct measurement) (MJ/m³·K) on the same samples.

Rock type TPS Calorimetric Number of samples

Mean Std dev. Mean Std dev.

Granite to granodiorite, 101057 2.09 0.17 2.06 0.06 14*

Granite, granodiorite and tonalite, 101051 2.23 0.13 2.15 0.05 8 Granite, metamorphic, aplitic, 101058 2.05 0.05 2.01 0.02 3

Amphibolite, 102017 2.43 0.05 2.41 0.11 8

Felsic to intermediate volcanic rock, 103076 2.33 – 2.42 – 1 Granite, fine- to medium-grained, 111058 2.14 0.10 2.06 0.05 5

* Includes three altered samples, see /Back et al. 2007/.

Figure 6‑3. Comparison between heat capacity determined by two different methods, TPS and direct measurement (calorimetric method). Correlation coefficient = 0.709.

1.75 2.00 2.25 2.50 2.75

1.75 2.00 2.25 2.50 2.75

Heat capacity, direct measurement (MJ/m³·K)

Heat capacity, TPS (MJ/m³·K)

x=y

6.2.5 Thermal conductivity vs heat capacity

The relationship between thermal conductivity and density is discussed in section 6.2.2. It is reasonable to assume a corresponding relationship between density and heat capacity. Such a relationship has been found previously /Sundberg 2003b/, although weaker than that for thermal conductivity versus density. In Figure 6-4, heat capacity determined by both the TPS and the calorimetric methods are plotted against thermal conductivity. For the investigated rock types, the relationship between the more reliable heat capacity values from calorimetric measurements and the thermal conductivity measurements is described by a second-order regression equation. The relationship is described in Figure 3-11 in /Back et al. 2007/ and further developed in /Sundberg et al. 2008a/.

6.2.6 Temperature dependence of thermal properties

The temperature dependence of the thermal properties has been investigated by TPS measurements on 18 samples of the dominant rock type, granite to granodiorite (101057), at three different temper-atures (20, 50 and 80°C); see section 4.3.3 in /Sundberg et al. 2005a/. With increasing temperature, the mean value of the thermal conductivity decreases by 9.8%/100°C temperature increase. The decrease in thermal conductivity varies from 6.6% to 11.7% for the individual samples. With increasing temperature, the heat capacity increases by 28.9%/100°C temperature increase. The increase varies from 16.4% to 63.1% for the individual samples.

For rock types with a lower quartz content than granite to granodiorite (101057), the temperature dependence in thermal conductivity is expected to be less pronounced /Sundberg et al. 2008a/.

6.2.7 Pressure dependence in thermal conductivity

The thermal conductivity is lower in stress-released samples compared with determinations at higher pressure (larger depths). The reason is assumed to be the closing of micro cracks at higher pressure.

However, the pressure influence is low if the samples are water saturated /Walsh and Decker 1966/.

All determinations of thermal conductivity in the site investigation programme have been made on water-saturated samples. The pressure dependence has therefore been neglected in the evaluation.

6.2.8 Coefficient of thermal expansion

The coefficient of thermal expansion has been measured on samples from five different rock types, see Table 6-4. The mean values of measured thermal expansion for the different rock types are rather similar. Samples of amphibolite (102017) have not been investigated.

Table 6‑4. Measured thermal expansion (m/(m·K)) on samples with different rock types (interval of temperature: 20–80°C).

Rock code Rock name Arithmetric mean St. dev. Min Max No. of samples

Thermal conductivity vs. heat capacity 101057, 101051, 101058, 102017, 103076 and 111058

y = 0.1311x² - 1.0368x + 4.0812 R² = 0.8154

1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7

2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0

Thermal conductivity, W/(m·K)

Heat capacity, MJ/(m³·K)

TPS

Direct measurements Poly. (Direct measurements)

Figure 6‑4. Heat capacity vs. thermal conductivity (room temperature). The heat capacity is calculated from TPS determinations and from calorimetric (direct) measurements. The second-order relationship is based on calorimetric measurements only.

6.2.9 In situ temperature

Fluid temperature has been measured in most cored boreholes at Forsmark. Large differences in logged temperature for the same depth in different boreholes were noted in earlier model stages.

Uncertainties associated with the data were judged to be high. For this reason, the fluid temperature loggings for each borehole have been re-evaluated with the objective of assessing their reliability.

The criteria considered were 1) errors associated with the logging probe, and 2) time between drilling and logging. The evaluation of temperature data on the basis of these criteria has resulted in a number of “approved” boreholes (see /Sundberg et al. 2008a/).

The results from the temperature loggings, and the calculated gradients, for the “approved” boreholes are shown in Figure 6-5. In Table 6-5, the fluid temperature at depths 400 m, 500 m and 600 m in the boreholes are presented. The measured temperatures at 500 m depth fall within the interval 11.2–12.0°C for the boreholes KFM01A, KFM02A, KFM03A, KFM04A, KFM06C and KFM08C (see Figure 6-5). A trend of increasing gradient with depth can be observed, from about 10°C/km at 300 m to about 13°C/km at 700 m depth (see also /Sundberg et al. 2008a/).

Mean annual air temperatures recorded at meteorological stations close to the Forsmark area are between 5°C and 5.5°C /Johansson et al. 2005/.

Figure 6‑5. Summary of fluid temperature (a) and vertical temperature gradient calculated for nine metres intervals (b) for eight boreholes at Forsmark. The results are from fluid temperature loggings.

4 8 12 16 20

Temperature (°C)

-1000 -800 -600 -400 -200 0

Elevation (metres)

KFM01A KFM02A KFM03A KFM04A KFM06C KFM07C KFM08C KFM09B

-20 0 20 40

Gradient (°C/km)

-1000 -800 -600 -400 -200 0

Elevation (metres)

KFM01A KFM02A KFM03A KFM04A KFM06C KFM07C KFM08C KFM09B

a) b)

In document Site description of Forsmark at completion of the site (Page 175-182)