Comparative modeling of an in situ diffusion experiment in granite at the Grimsel Test Site

Journal of Contaminant Hydrology 179 (2015) 89–101

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Comparative modeling of an in situ diffusion experiment in granite at the Grimsel Test Site Josep M. Soler a,⁎, Jiri Landa b, Vaclava Havlova b, Yukio Tachi c, Takanori Ebina c, Paul Sardini d, Marja Siitari-Kauppi e, Jost Eikenberg f, Andrew J. Martin g a

IDAEA-CSIC, Jordi Girona 18-26, 08034 Barcelona, Catalonia, Spain UJV-Rez, Rez 130, 250 68, Czech Republic c JAEA, 4-33 Muramatsu, Tokai-mura, Naka-gun, Ibaraki 319-1194, Japan d Université de Poitiers, HYDRASA/IC2MP 4, rue Michel Brunet – TSA 51106, 86073 Poitiers Cedex 9, France e Laboratory of Radiochemistry, Department of Chemistry, A.I.Virtasen Aukio 1, FIN-00014 University of Helsinki, Helsinki, Finland f Paul Scherrer Institut, CH-5232 Villigen PSI, Switzerland g NAGRA, Hardstrasse 73, Postfach 280, CH-5430 Wettingen, Switzerland b

a r t i c l e

i n f o

Article history: Received 25 February 2015 Received in revised form 28 May 2015 Accepted 1 June 2015 Available online 6 June 2015 Keywords: Grimsel Diffusion Granite Modeling

a b s t r a c t An in situ diffusion experiment was performed at the Grimsel Test Site (Switzerland). Several tracers (3H as HTO, 22Na+, 134Cs+, 131I− with stable I− as carrier) were continuously circulated through a packed-off borehole and the decrease in tracer concentrations in the liquid phase was monitored for a period of about 2 years. Subsequently, the borehole section was overcored and the tracer profiles in the rock analyzed (3H, 22Na+, 134Cs+). 3H and 22Na+ showed a similar decrease in activity in the circulation system (slightly larger drop for 3H). The drop in activity for 134 + Cs was much more pronounced. Transport distances in the rock were about 20 cm for 3H, 10 cm for 22Na+, and 1 cm for 134Cs+. The dataset (except for 131I− because of complete decay at the end of the experiment) was analyzed with different diffusion-sorption models by different teams (IDAEA-CSIC, UJV-Rez, JAEA) using different codes, with the goal of obtaining effective diffusion coefficients (De) and porosity (ϕ) or rock capacity (α) values. From the activity measurements in the rock, it was observed that it was not possible to recover the full tracer activity in the rock (no activity balance when adding the activities in the rock and in the fluid circulation system). A Borehole Disturbed Zone (BDZ) had to be taken into account to fit the experimental observations. The extension of the BDZ (1–2 mm) is about the same magnitude than the mean grain size of the quartz and feldspar grains. IDAEA-CSIC and UJV-Rez tried directly to match the results of the in situ experiment, without forcing any laboratory-based parameter values into the models. JAEA conducted a predictive modeling based on laboratory diffusion data and their scaling to in situ conditions. The results from the different codes have been compared, also with results from small-scale laboratory experiments. Outstanding issues to be resolved are the need for a very large capacity factor in the BDZ for 3H and the difference between apparent diffusion coefficients (Da) from the in situ experiment and out-leaching laboratory tests. © 2015 Elsevier B.V. All rights reserved.

1. Introduction ⁎ Corresponding author. Tel.: +34 934006100. E-mail addresses: [email protected] (J.M. Soler), [email protected] (V. Havlova), [email protected] (Y. Tachi), [email protected] (P. Sardini), marja.siitari-kauppi@helsinki.fi (M. Siitari-Kauppi), [email protected] (J. Eikenberg), [email protected] (A.J. Martin).

http://dx.doi.org/10.1016/j.jconhyd.2015.06.002 0169-7722/© 2015 Elsevier B.V. All rights reserved.

The deep geological disposal of radioactive waste is based on a multi-barrier principle, by which multiple human-made and natural barriers are placed between the waste and the biosphere. Each barrier has its own isolation and retardation

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properties with respect to water flow and radionuclide transport and offers also mechanical protection (Astudillo Pastor, 2001). The main artificial barriers are the chemical form of the waste (slow corrosion and low solubility), the metallic canisters where the waste is emplaced (slow corrosion, mechanical protection, radionuclide sorption), and the bentonite clay backfill of cavities and galleries (low permeability, swelling/sealing capacity, mechanical protection, dissipation of heat, sorption of radionuclides). Beyond the artificial barrier, the host rocks or geosphere offer additional isolation and protection (stable rocks with low permeabilities, favorable sorption properties). In situ matrix diffusion in granite is the main topic of the GTS-LTD project (Grimsel Test Site, Long Term Diffusion), which is financed by the University of Helsinki (Finland), JAEA (Japan), UJV-Rez and SURAO (Czech Republic), and NAGRA (Switzerland). In the framework of the geological disposal of radioactive waste, matrix diffusion is a key process for radionuclide retention in crystalline rocks. It is the mechanism by which solutes, being transported within fractures of a porous medium, are transferred to the stagnant water of the rock matrix adjacent to these fractures (Jakob, 2004). An early study by Foster (1975) looked into the issue of thermonuclear 3H in chalk and its diffusion into the porous rock matrix. Soon, there were studies looking at the importance of this mechanism for the retention of radionuclides (Glueckauf, 1980; Grisak and Pickens, 1980; Neretnieks, 1980), especially for non-sorbing species. The study of matrix diffusion has continued since then (e.g. Bibby, 1981; Carrera et al., 1998; Grisak and Pickens, 1981; Guimerà and Carrera, 2000; Haggerty et al., 2000; Maloszewski and Zuber, 1990; Neretnieks, 2002; Ota et al., 2003; Polak et al., 2003; Shapiro, 2001; Skagius and Neretnieks, 1986; Wood et al., 1990), including also field experiments (Aalto et al., 2009; Birgersson and Neretnieks, 1990; Cramer et al., 1997; Cvetkovic, 2010; Hartikainen et al., 1996; Hodgkinson et al., 2009; Ohlsson et al., 2001; Vilks et al., 2003; Waber et al., 2011; Widestrand et al., 2010; Zhou et al., 2007). Based on the design of in situ diffusion experiments in the Opalinus Clay at Mont Terri (Appelo and Wersin, 2007; Gimmi et al., 2014; Palut et al., 2003; Samper et al., 2006; Soler et al., 2008, 2013a; Tevissen et al., 2004; Van Loon et al., 2004; Wersin et al., 2004, 2008; Yi et al., 2012a,b; Yllera et al., 2004), an in situ diffusion experiment in unfractured granite was performed at the Grimsel Test Site (Switzerland). The aim was to study radionuclide diffusion and retention in the rock matrix. Grimsel groundwater (pH 9.5, ionic strength 10−3; Mäder et al., 2006) containing several tracers (11 MBq/L 3H as HTO, 0.54 MBq/L 22Na+, 0.54 MBq/L 134Cs+, 1.4 MBq/L 131I− with stable I− as carrier) was continuously circulated through a packed-off borehole (single pulse of tracers) and the decrease in tracer concentrations in the liquid phase was monitored for a period of about 26 months (stable iodide was not monitored). Subsequently, the borehole section was overcored (diameter 30 cm) and the tracer profiles in the rock analyzed (3H, 22Na+, 134 + Cs ). The complete dataset (except for 131I− because of complete decay at the end of the experiment) was analyzed with different diffusion-sorption models. Modeling by different teams using different codes, which is common practice in the interpretation of field and laboratory experiments (e.g. Savage et al., 2011; Soler et al., 2006, 2008, 2014; Wersin et al., 2006,

2010), allows the use and comparison of different model concepts and approaches. The derived diffusion and sorption parameters from the different models were compared, also with laboratory results.

2. Overview of the experiment The experimental setup is shown in Fig. 1. The length and radius of the injection interval were 70 cm and 2.8 cm, respectively. The total volume of solution in the circulation system was 8 L. The reference value for porosity in the bulk rock was 0.0065, based on porosity measurements by (i) water gravimetry and (ii) 14C-PMMA resin impregnation in the laboratory at the University of Helsinki (0.0065 ± 0.001). The experimental results included the evolution of tracer concentrations (activities of 3H, 22Na+, 134Cs+) in the circulation system and tracer distribution profiles in the rock around the injection interval. Overcored rock samples corresponding to 2 radial profiles from the central part of the circulation interval were received by UJV-Rez. The gamma nuclides 22Na+ and 134Cs+ in each sample were measured by gamma spectrometry using a HPGe detector (35%, FWHM 1.9 keV for 60Co, 1332 keV) and an Inspektor 2 k analyzer from Canberra. Spectra were analyzed using the commercial program Genie 2000. 3H was analyzed using liquid scintillation counting spectrometry of water after its distillation from the samples. After an ultrasonic bath each sampling vial was attached to the distillation apparatus, which contained a gas receiver cooled by liquid nitrogen. H2O distillation was performed at T -150 °C and pressure less than 90 Pa. Condensed liquid was transferred to the measurement vial and mixed with the scintillation cocktail (LLT, Canberra). The spectra were measured using a WinSpectral 1414-003 (Wallac; PerkinElmer). Spectra were analyzed using the commercial program. The final results from the measurements

Pressure Regulator Tracer supply On-line Detection System

Pressure Monitoring Interval

Injection Interval Fig. 1. Schematic diagram showing the experimental setup.

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101

were radial profiles of 3H, 22Na+, and 134Cs+ across the rock overcore. At the University of Helsinki, activities of 22Na+ and 134Cs+ were measured from a subsample of the rock overcore corresponding to the central part of the circulation interval. A subcore (diameter 5 cm, length 15.7 cm) was drilled perpendicular to the original injection borehole. Slices were cut from this subcore, and activities (Bq/g_rock) were measured using a gamma detector (Jokelainen et al., 2013). The rock slices near the borehole wall were 1.5–2 mm thick. As activities decreased when moving further from the borehole, thicker samples were used further away. After sawing, the slices of rock were weighed and placed into plastic cups for gamma measurements. The gamma measurements were carried out using a Canberra XtRa (Extended Range Coaxial Ge Detector) detector which has a resolution of 2.1 keV. 22Na+ was measured from the 1274.5 keV gamma peak (99% intensity) and 134Cs+ from the 605 keV peak (97.6% intensity). The spectra were analyzed with the Genie 2000 Gamma Acquisition and Analysis software. The effect of the measurement geometry was determined using a multinuclide standard solution obtained from Eckert and Ziegler. The detection limits for 134Cs+ and 22Na+ (0.02 Bq/g and 0.07 Bq/g, respectively) were calculated using the Currie equation. Regarding activities in solution (circulation system), a liquid scintillation spectrometer (LSC) was used for the radio-analysis of pure beta-radiation-emitting 3H. All other radioactive tracers were beta/gamma emitters and could be measured directly from small aliquots in a calibrated geometry by means of highresolution gamma spectrometry using intrinsic Germanium detectors. The samples for LSC were also measured in a calibrated geometry by using scintillation cocktails with a 10:10 vol/vol mixture of aqueous phase and scintillation cocktail (product Ultima Gold LLT). Corrections for quench were performed automatically using chemically corresponding quench curves and the fraction of the beta counts from the other tracers in the low energy region of 3H was performed by determining the fraction of these isotopes in the 3H region and over the full LSC-energy region by single isotope measurements. Since the activities of 3H compared to all other tracers were always orders of magnitude higher, this tailing correction was less than 5%. 3 H and 22Na+ showed a similar decrease in activity in the circulation system (slightly larger drop for 3H). The drop in activity for 134Cs+ was much more pronounced. Transport distances in the rock were about 20 cm for 3H, 10 cm for 22Na+, and 1 cm for 134Cs+. I− diffusion was only evaluated from results of out-leaching tests performed on overcored rock blocks (reported in Soler et al., 2013b).

91

1D

Symmetry around borehole axis Fig. 2. Conceptual layout of the calculation domain in the simulations (1D model with symmetry around borehole axis).

The equation of conservation of mass for a given tracer can be written as ∂ctot ¼ ∇  ðDe ∇cÞ ∂t

ð1Þ

where c is concentration in solution (moles per volume of solution), t is time, De = ϕDp is the effective diffusion coefficient, ϕ is the porosity accessible for the tracer, Dp the pore diffusion coefficient, and ctot is the total concentration of tracer (moles per bulk volume), which is given by ctot ¼ ϕc þ ρd s ¼ ϕc þ ð1−ϕÞρs K d c ¼ ðϕ þ ð1−ϕÞρs K d Þc ¼ αc

ð2Þ

where ρd is the bulk dry density, s is the concentration of sorbed tracer (moles per mass of solid), ρs is the density of solids (2660 kg/m3), Kd is the distribution coefficient and α is the rock capacity factor. Only linear sorption (s = Kdc) has been considered in the calculations. Radioactive decay was taken into account by correcting the measured activities back to the beginning of the experiment. The geometry of the problem is schematically shown in Fig. 2. The initial conditions were Borehole

cðx; t ¼ 0Þ ¼ c0

3. Modeling by NAGRA/IDAEA-CSIC 3.1. Model description Due to the short tracer transport distances (shorter than the length of the injection interval) and the absence of any substantial foliation in the rock, the simulations were performed using a one-dimensional model with symmetry around the borehole axis (Fig. 2). The CrunchFlow numerical reactive transport code (Steefel, 2009; Steefel el al., 2014) was used to solve the diffusion problem.

Rock ctot ðx; t ¼ 0Þ ¼ 0 In all the calculations, the capacity of the borehole per unit volume was increased to take into account the full volume of the injection system (8 L). All the boundaries of the 1D domain are no-flux boundaries. A large value of De equal to 1e-5 m2/s was used in the borehole section of the model to ensure good mixing in the borehole.

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3.2. Results

1.1

Tracer activities in the circulation system and tracer profiles in the rock were simultaneously fitted by means of the diffusion-sorption calculations. A BDZ (Borehole Disturbed Zone) was required to fit model calculations to experimental data. The values of α in the BDZ were given by the magnitude of the initial drop in activity in the circulation system. The slope of that initial drop will be given by the value of De (a larger De will give a steeper slope). In the bulk rock, the apparent diffusion coefficient (Da = De/α) will control transport distances. However, the magnitudes of De and α will largely control the evolution of activities in the circulation system. Larger values will give a steeper slope of the tracer curve in the circulation system. Therefore, combining (i) tracer profiles in the rock and (ii) tracer activities in the circulation system allows the determination of both De and α in the bulk rock. However, and due to large amounts of tracer activity missing from the rock (no activity balance when adding to the activity in the circulation system; Havlová et al., 2011), the measured tracer profiles in the rock were arbitrarily scaled (multiplied by an arbitrary factor) so only the shape and extension of the profiles were maintained. Comparison between calculated and measured profiles in the rock is only qualitative at best. Given the fact that no activity balance was achieved in the measurements (significant activity losses in the solid), it is difficult to give reliable uncertainties to the calculated transport and sorption parameters. Factoring that uncertainty out, i.e. looking only at the tracer activities in the circulation system and based on a limited sensitivity analysis, uncertainties are of the order of a few tens per cent.

1.0

3.2.1. 3H Fig. 3 shows experimental data and model results (best fits) for the cases when no BDZ (Borehole Disturbed Zone) and a BDZ have been assumed. In both cases, and due to the large amount of activity missing from the rock (98% of theoretical activity in the rock lost; no activity balance when adding to the activity in the circulation system; Havlová et al., 2011), the measured tracer profiles in the rock have been arbitrarily scaled (multiplied by an arbitrary factor) so only the shape and extension of the profiles are maintained. Comparison between calculated and measured profiles in the rock is only qualitative at best. Correction of the measured profiles was done as follows. Tracer profile data were given in Bq per mass of saturated rock. First, total concentration (or activity) per mass of saturated rock (ctot′ in Bq/kg) can be expressed as

0

″

ctot ¼ ctot

ϕ ϕρwater þ ð1−ϕÞρs

ð3Þ

3H, A/A0

Data Model-BDZ

Model-NoBDZ

0.9

0.8

0.7 0

″

ctot ¼

α c ϕ

ð4Þ

400

600

800

t (d)

1.0 S-1

S-2

0.8

Model-BDZ

Model-NoBDZ

A/A0

0.6

0.4

0.2

0.0 0

5

10

15

20

d (cm)

Fig. 3. 3H. Experimental data and model results. Top: Relative activities in solution in the circulation system. Bottom: Tracer profiles in the rock (relative activities vs. distance from borehole wall). S-1 and S-2 refer to profiles measured by UJV-Rez, which are further scaled in order to compare with modeled profiles (see text). Model curves correspond to activities in the porewater.

Combining Eqs. (3) and (4) 0

ctot ¼ c

α ϕρwater þ ð1−ϕÞρs

ð5Þ

Then, applying an arbitrary correction to the tracer profile data, relative concentration (or activity) in solution is expressed as c 0 ¼ ctot  number c0

ð6Þ

number is the arbitrary value that has been used to scale the measured profiles. number contains also the scaling factor fc. Therefore number ¼

where c″tot is here total concentration in Bq/m3water (c″tot = ctot/ϕ), and

200

c ϕρwater þ ð1−ϕÞρs fc f ¼ c0 c0tot c c0 α

ð7Þ

and the scaling factor will be given by

fc ¼

number  c0 α ϕρwater þ ð1−ϕÞρs

ð8Þ

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101

Lost activity can be calculated from
 1  100 lost activityð%Þ ¼ 1− fc

ð9Þ

When no BDZ is assumed, the shape and extension of the tracer profiles can be qualitatively fitted but the calculated evolution of tracer concentrations in the circulation system does not adequately match the observed data (Fig. 3; model parameters: De = 6e-12 m2/s, α = 0.4, Kd = 1.49e-4 m3/kg for a porosity ϕ = 0.0065). The data show a fast initial drop (up to about 100 d) and a slower decrease afterwards. This trend can be reproduced when adding a BDZ in the model (Fig. 3; model parameters rock: De = 2e-13 m2/s, α = 0.0065; model parameters BDZ: De = 1e-12 m2/s, α = 10, Kd = 3.8e-3 m3/ kg for a porosity ϕ = 0.0065). The thickness of the BDZ used in the model (1.5 mm) is based on the measured profile data for 22 Na+ and 134Cs+, which only show anomalous large concentrations for distances less than 2 mm from the borehole wall. It was assumed that 3H does not sorb in the bulk rock (α = ϕ), but a large value for α in the BDZ had to be used to reproduce the fast initial drop in activity (up to about 100 d). For this case, the calculated activity loss is zero for profile S1 and 46% for

1.2 Data

Model-BDZ

22Na, A/A0

1.1

1.0

0.9

0.8 0

200

400

600

800

t (d) 1.6 S-1

93

profile S2. These values were calculated from the correction needed to scale the measured data up to the modeled profiles, and they are smaller than the theoretical value (98%; Havlová et al., 2011) due to the larger activity in the BDZ calculated by the model. 3.2.2. 22Na+ Fig. 4 shows experimental data and model results (best fits). A BDZ has been assumed in the model (thickness = 1.5 mm). The value of α in the BDZ will be given by the magnitude of the initial drop in activity in the circulation system. The slope of that initial drop will be given by the value of De (a larger De will give a steeper slope). Like 3H, due to the large amount of activity missing from the rock (87% of theoretical activity in the rock lost; no activity balance when adding to the activity in the circulation system; Havlová et al., 2011), the measured tracer profiles in the rock have been arbitrarily scaled (multiplied by an arbitrary factor), so only the shape and extension of the profiles are maintained. Comparison between calculated and measured profiles in the rock is only qualitative at best. Notice the large measured activities in the rock for distances less than 2 mm from the borehole wall. These large activities are consistent with a larger Kd in the BDZ compared with the bulk rock. 3.2.3. 134Cs+ Fig. 5 shows the evolution of tracer activities in the circulation system. Again, the value of α in the BDZ will be given by the magnitude of the initial drop in activity in the circulation system, while the slope of that initial drop will be given by the value of De. Notice that an overall good match between model and measurements is obtained. However, the calculated drop in activity is still slightly too slow for very early times (less than about 8 d), even with the large value of De in the BDZ. Fig. 6 shows the calculated and measured tracer profiles in the rock. As with 3H and 22Na+, arbitrarily scaled data have been used to compare with model results (Fig. 6, top). However, since the amount of lost activity is not as large (32%

S-2 1.2

H-1 1.0 Data

Model-BDZ

0.8

Model-BDZ

0.8

134Cs, A/A0

A/A0

H-2

0.4

0.0 0

2

4

6

8

10

12

0.6 0.4 0.2

d (cm) Fig. 4. 22Na+. Experimental data and model results. BDZ assumed in the model. Top: Relative activities in solution in the circulation system. Bottom: Tracer profiles in the rock (relative activities vs. distance from borehole wall). S-1 and S-2 refer to profiles measured by UJV-Rez; H-1 and H-2 refer to profiles measured by Univ. of Helsinki. The measured data are further scaled in order to compare with modeled profiles (see text). The model curve corresponds to activities in the porewater. Model parameters – rock: De = 2e-12 m2/s, α = 0.2 (Kd = 7.3e-5 m3/kg for a porosity ϕ = 0.0065). Model parameters – BDZ: thickness = 1.5 mm, De = 3e-12 m2/s, α = 3 (Kd = 1.1e-3 m3/kg for a porosity ϕ = 0.0065).

0.0 0.1

1.0

10.0

100.0

1000.0

t (d) Fig. 5. 134Cs+. Relative tracer activities in the circulation system. Experimental data and model results. BDZ assumed in the model. Logarithmic time scale to see details at early times. Model parameters – rock: De = 3e-12 m2/s, α = 20 (Kd = 7.6e-3 m3/kg for a porosity ϕ = 0.0065). Model parameters – BDZ: thickness = 1.5 mm, De = 6e-11 m2/s, α = 110 (Kd = 4.2e-2 m3/kg for a porosity ϕ = 0.0065).

94

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101 1.2

Inner boundary condition: S-1

1.0

S-2

−λt

cðt; r0Þ ¼ cT ð0Þ  e

H-1

A/A0

0.8

ZrR

H-2



H-3

0.6

Model-BDZ

−

2πl VT

ϕðr Þ  Rðr; KdÞ  cðt; r Þ  r  dr

ð12Þ

r0

0.4

Outer boundary condition: 0.2 0.0 0.0

0.5

1.0

1.5

2.0

8.0 S-1

S-2 A/A0 (mL/g)

H-1 H-2 H-3

4.0

Model-BDZ

2.0

0.0 0.0

0.5

1.0

1.5

ð13Þ

c is concentration in the porewater, Dp is the pore diffusion coefficient, Kd is the distribution coefficient, l is the length of the circulation interval in the borehole, r is radius, R is the retardation factor in rock matrix (R = α/ϕ), r0 is inner radius (borehole wall), rR is outer radius (end of the calculation domain), t is time, VT is the volume of solution in the circulation system, λ is the decay constant, and ϕ is porosity. A finite difference scheme was used to discretize the diffusion-sorption equation in space and time. Regarding the presence of a BDZ, three variant cases were used:

d (cm)

6.0

∂cðt; r R Þ ¼0 ∂r

2.0

d (cm) 134

Fig. 6. Cs+. Tracer profiles in the rock. Top: Arbitrarily scaled data and calculated activity in the porewater. Bottom: Measured data and calculated activity in the rock. S-1 and S-2 refer to profiles measured by UJV-Rez; H-1 to H3 refer to profiles measured by Univ. of Helsinki. Model parameters – rock: De = 3e-12 m2/s, α = 20 (Kd = 7.6e-3 m3/kg for a porosity ϕ = 0.0065). Model parameters – BDZ: thickness = 1.5 mm, De = 6e-11 m2/s, α = 110 (Kd = 4.2e-2 m3/kg for a porosity ϕ = 0.0065).

of theoretical activity in the rock lost; Havlová et al., 2011), the real measured data have also been compared with the calculated activities in the solid (Fig. 6, bottom). As expected, real measured data and model results do not coincide but are at least comparable.

(1) The first case did not consider a BDZ at all (NO BDZ). All granite parameters were constant within the domain. (2) The second case assumed that the BDZ was 3 mm thick (BDZ, 3 zones). This consideration was based on results from Möri (2009). He found that only the first 2–3 mm of the rock around the borehole can be influenced by drilling. In this case, the BDZ was assumed to be heterogeneous. It was represented by 3 zones, differing namely in the porosity value (1: x1 = 0–0.0005 m, ϕ1 = 0.04. 2: x2 = 0.0005–0.0015 m, ϕ2 = 0.03. 3: x3 = 0.0015–0.003 m, ϕ3 = 0.01; 4: undisturbed rock ϕ = 0.0065). For each zone different properties, including De, Kd and α had to be specified for each tracer. (3) The third case considered a homogeneous BDZ with a thickness of 1.5 mm (BDZ, 1 zone). A smaller rock matrix porosity ϕ was considered (0.005), assuming that laboratory and in situ porosity would differ due to lithostatic pressure release.

4. Modeling by UJV-Rez

4.2. Results

4.1. Model description

The data sets consisted of tracer activity evolution with time in the circulation system and tracer activity profiles in the rock. Only tracer profile S-1, measured at UJV-Rez, was taken into account. In some cases (134Cs+), profiles measured at the University of Helsinki were also used for comparison. All data were corrected for decay to the end of the experiment. Due to the rather high loss of tracers 3H and 22Na+ in the rock (98% and 87%, respectively), emphasis was placed on tracer activity evolution in the circulation system. Measured tracer profiles in the rock were corrected in order to compare with model results. Two different types of correction were implemented:

A Fortran77 program was written to solve numerically the diffusion-sorption equations. Calculations considered symmetry around the borehole axis (1D cylindrical coordinates) and explicitly included radioactive decay (Eqs. (10) to (13)). Main equation—1D – cylindrical coordinates: ! ∂cðt; r Þ Dp ∂2 cðt; r Þ 1 ∂cðt; r Þ : þ : ¼ −λ:cðt; rÞ Rðr; KdÞ r ∂t ∂r ∂r 2

ð10Þ

Initial condition: c j ð0; r Þ ¼ 0

ð11Þ

Correction (i) The activity measured in the rock samples (Bq.g−1) was multiplied by a correction factor in order to obtain full activity balance when adding to the activity in the circulation system.

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101 samples BDZ 0

correction i BDZ 3 lin.

correction ii BDZ 1 const.

1.E+04

3H (Bq.g-1)

Background values were omitted (low activity values at the end of the profile for 22Na+ and 134 + Cs ). Correction (ii) All the missing activity was assumed to be lost from the borehole surface. The activity in the first node close to the borehole wall was multiplied by a factor to obtain full activity balance.

95

1.E+02

1.E+00

4.2.1. 3H Figs. 7 and 8 show the evolution of activities in the circulation system and activity profiles in the rock for the cases where NO BDZ (Borehole Disturbed Zone) and BDZ have been assumed. For model parameters see Table 1. The results are presented in relative values (%) for activity decrease in the circulation system and in absolute values (Bq.g−1) for the rock profile. Due to the large amount of activity missing from the rock (loss of 98% of theoretical activity in the rock), the measured values in the rock samples had to be arbitrarily corrected (multiplied by an arbitrary factor towards 100% activity balance). For the case with no BDZ, the shape and extension of the tracer profile in the rock could be qualitatively fitted only after arbitrary correction towards activity balance, assuming that only 2% of the activity was measured in the rock samples. However, concerning tracer activity decrease in the circulation system, the modeled trend could not represent sufficiently well the measured activities. The conclusion was that a BDZ had to be included in the calculation. Including the BDZ with 3 different zones did not achieve a good fit for tracer activity decrease in the circulation system. The very best fit was obtained assuming that most of the missing 3H activity was present in the BDZ zone (α = 11.53). Porosity in the bulk rock was set to 0.005. This value, slightly lower than the measured valued (0.0065), was used assuming that porosity in situ would be lower than measured in laboratory. The best fit is presented in Figs. 7 and 8 by the solid line. All the relevant data are given in Table 1, including the input parameters for the model (ϕ, Kd, Dp). Model results are sensitive only to De (De = ϕ Dp) and α. Surprisingly, sorption had to be included in the BDZ to reach consistency with measured data. Teng et al. (2011) reported a samples

BDZ 0

BDZ 3 lin.

BDZ 1 const.

100 95

A/A0 (%)

90 85 80

75

1.E-02 0

2

4

6

8 10 d (cm)

12

14

16

3

Fig. 8. H. Tracer profiles in the rock. Experimental data and model results. NO BDZ, 1-zone BDZ, and 3-zone BDZ were assumed in the modeling. For model parameters, see Table 1.

small but noticeable sorption of 3H in soils, but their reported Kd value was less than 4.10−4 m3.kg−1, which is smaller than the values in Table 1 (BDZ 1). This issue clearly needs further investigation. 4.2.2. 22Na+ Figs. 9 and 10 show the evolution of activities in the circulation system and activity profiles in the rock. For model parameters see Table 2. Due to the large amount of activity missing from the rock (loss of 87% of theoretical activity in the rock), the measured values in the rock samples had to be arbitrarily corrected (multiplied by an arbitrary factor towards 100% activity balance). The last measured point in the profile (Fig. 10) is assumed to correspond to background activity in the rock. Once again, the best fit was achieved when considering a BDZ only with 1 zone (Fig. 10). The resulting parameters are presented in Table 2. Notice however the large scatter in the initial measured data in the circulation system (Fig. 9). The large increase in 22Na+ activity in the circulation system after 1 month from injection could be explained either by mixing problems in the circulation system (tank, lines, borehole interval) or by sample disturbance prior to analysis. 4.2.3. 134Cs+ Figs. 11 and 12 show the evolution of activities in the circulation system and activity profiles in the rock. For model parameters, see Table 3. A smaller amount of activity was missing from the rock (32%), compared to 3H and 22Na+. Both uncorrected and corrected activities in the rock are shown in Fig. 12. Fig. 12 also includes activity profiles measured at the University of Helsinki. The last measured point in the profile (Fig. 12) is assumed to correspond to background activity in the rock. Again, the best fit was achieved when considering a BDZ only with 1 zone (Fig. 11). 5. Modeling by JAEA

70 0

3

200

400 t (d)

600

800

Fig. 7. H. Relative activities in solution in the circulation system. Experimental data and model results. NO BDZ, 1-zone BDZ, and 3-zone BDZ were assumed in the modeling. For model parameters, see Table 1.

5.1. Codes and setup The modeling approach was different from the other two modeling exercises and focused on blind predictions based on results from laboratory measurements.

96

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101

Table 1 3 BDZ properties (length, mm) and rock migration parameters for H used in the modeling by UJV-Rez. Bold characters correspond to input parameters used for simulation. ρs and ρb correspond to density of solids and bulk dry density, respectively. R is the retardation factor (α = Rϕ). Dp, De, and Da are pore, effective, and apparent diffusion coefficients, respectively. 3

ϕ

H

l

Code

mm

BDZ 0 BDZ 3 lin.

0+ 0 0.5 1.5 3+ 0+ 1.5+

BDZ 1 konst.

0.0065 0.04 0.03 0.01 0.0065 0.04 0.005

ρs

ρb

Kd

kg · m−3

kg · m−3

m3 · kg−1

2660 2660

2643 2554 2580 2633 2643 2554 2647

0.00009 0.003 0.0007 0.00021 0.00007 0.0045 0

2660

The commercial codes GoldSim (ver. 10.1; GoldSim Technology Group, 2010) and COMSOL Multiphysics (ver. 4.2; COMSOL Inc., 2011) were used in the calculations. The GoldSim code simulated simplified one-dimensional (1D) radionuclide transport, while COMSOL simulated three-dimensional (3D) transport in a more realistic geometry of the in situ test. Both codes solved the same diffusion-sorption equation (Eq. (1)), assuming isotropic porous media and reversible instantaneous sorption with a linear isotherm. Radioactive decay was not explicitly included because activities were corrected for decay. The conceptual model for the 1D simulation using GoldSim is equivalent to those used in Sections 2 and 3 (see Fig. 2). 1D transport was assumed in the direction perpendicular to the axis of the borehole, from the borehole wall through the borehole disturbed zone (BDZ) and the surrounding rock matrix. The diffusion-accessible area in the borehole corresponds to inner surface area of the borehole interval with a length of 0.7 m. The reservoir of solution containing the tracer is assumed to have a total tracer volume of 8 L. The conceptual model for 3D simulation using COMSOL is illustrated in Fig. 13. Because of axisymmetric geometry, only one fourth of the geometry of the in situ test was considered. An additional dummy space was included to take into account the full volume of circulation system. The BDZ was arranged along the borehole including test interval and packer zones. An automatically generated triangular-element-grid was optimized by refining grid spacing near the borehole wall and in the BDZ.

α

R

0.24 7.70 1.84 0.56 0.19 11.53 0.005

38 193 61 56 29 288 1

Dp

De

Da

m2 · s−1

m2 · s−1

m2 · s−1

1.2E-09 1.0E-09

7.8E-12 4.0E-11 3.0E-11 1.0E-11 6.5E-12 1.3E-12 1.7E-13

3.2E-11 5.2E-12 1.6E-11 1.8E-11 3.4E-11 1.1E-13 3.3E-11

3.3E-11

This exercise consisted of blind predictions based on model parameter setting from laboratory measurements and in situ porosity (Tachi et al., 2015). Five different cases were set by considering model and parameter variations. The transport and retention parameters (ϕ, De, Kd) were scaled from laboratory to in situ conditions assuming a linear relation with porosity. − Case 1: Homogeneous rock matrix without BDZ; unscaled lab data (ϕmatrix = 0.012) − Case 2: Homogeneous rock matrix without BDZ; scaled parameters from lab data (ϕmatrix = 0.0065) − Case 3: Rock matrix with BDZ (0.5 mm); scaled parameters from lab data (ϕmatrix = 0.0065, ϕBDZ = 0.012) − Case 4: Rock matrix with BDZ (0.5 mm); scaled parameters from lab data including near-surface profile (ϕmatrix = 0.0065, ϕBDZ = 0.012) − Case 5: Rock matrix with BDZ (1 mm); scaled parameters from lab data including near-surface profile (ϕmatrix =0.004, ϕBDZ = 0.008) Effective diffusivities (De) and rock capacity factors (α) of Cs+, 22Na+, 125I− and 3H in rock samples from the in situ test borehole were measured in through-diffusion tests using synthetic groundwater. The derived parameters are summarized in Table 4. The De values were in the order Cs+ N Na+ N 3H N I–, presumably indicating cation excess and anion exclusion effects. The α and Kd values for these tracers showed the same trends as a result of sorption (Cs+, Na+) 137

samples BDZ 0

correction i BDZ 3 lin.

correction ii BDZ 1 const.

1.E+03 samples

BDZ 0

BDZ 3 lin.

BDZ 1 const.

115

1.E+02 22Na (Bq.g-1)

110

A/A0 (%)

105 100 95

90

1.E+01 1.E+00 1.E-01

85

1.E-02

80 0

200

400

600

0

800

t (d) 22

Fig. 9. Na+. Relative activities in solution in the circulation system. Experimental data and model results. NO BDZ, 1-zone BDZ, and 3-zone BDZ were assumed in the model. For model parameters see Table 2.

22

2

4 d (cm)

6

8

Fig. 10. Na+. Tracer profiles in the rock. Experimental data and model results. NO BDZ, 1-zone BDZ, and 3-zone BDZ were assumed in the model. For model parameters see Table 2.

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101

97

Table 2 22 BDZ properties (length, mm) and rock migration parameters for Na+ used in the modeling by UJV-Rez. Bold characters correspond to input parameters used for simulation. ρs and ρb correspond to density of solids and bulk dry density, respectively. R is the retardation factor (α = Rϕ). Dp, De, and Da are pore, effective, and apparent diffusion coefficients, respectively. 22

Na+

ϕ

l

Code

mm

BDZ 0 BDZ 3 lin.

0+ 0 0.5 1.5 3+ 0+ 1.5+

BDZ 1 konst.

0.0065 0.04 0.03 0.01 0.0065 0.04 0.005

ρs

ρb

Kd

kg · m−3

kg · m−3

m3 · kg−1

2660 2660

2643 2554 2580 2633 2643 2554 2647

0.00022 0.00024

2660

5.2. Results 1D (GoldSim) and 3D (COMSOL) simulations were compared. Very similar results were obtained (tracer evolution in the circulation system and tracer profiles in the rock perpendicular to the borehole axis), with only very minor differences in some of the cases. Differences in the profiles close to borehole wall (Fig. 14 bottom; distance less than 1 cm) are due to the coarse numerical mesh used in the 1D calculations (grid size 1 cm). Only results from case 5 were able to approximately reproduce the measured data. Several calculations were conducted by changing the BDZ depth (0.5–1.0 mm), the BDZ porosity (0.8–1.6%), and the matrix porosity (0.4–1.2%). The transport and retention parameters were always set by the scaling approach (linear scaling with porosity, keeping the relation in parameters

BDZ 0

BDZ 3 lin.

0.59 0.65 0.65 0.64 0.64 5.66 0.13

0.0022 0.000048

and anion exclusion (I−). These trends are consistent with those observed for compacted montmorillonites (Tachi and Yotsuji, 2014) and argillaceous rocks (Tachi et al., 2011). Dual depth profiles (equivalent to a BDZ in a borehole) for sorbing Cs+ and Na+ were observed by abrasive profiling of the granite samples after the diffusion tests. Dual profiles have been observed in granitic rocks by many researchers and interpreted by different models (e.g., Byegård et al., 1998; Idemitsu et al., 1992). Using a simple separation between nearsurface (within ca. 1 mm for the surface) and far-from-surface profiles, near-surface profiles could be reasonably well interpreted using higher α and lower De values (Table 5).

samples

α

R

90 16 22 64 99 141 26

Dp

De

Da

m2 · s−1

m2 · s−1

m2 · s−1

3.0E-10 3.2E-10

2.0E-12 1.3E-11 9.6E-12 3.2E-12 2.1E-12 4.8E-12 6.0E-13

3.3E-12 2.0E-11 1.5E-11 5.0E-12 3.2E-12 8.5E-13 4.5E-12

1.2E-10

between tracers). One of these sets of modeling results, which were comparable to the experimental data, was extracted as case 5. Results are shown in Fig. 14. The tracer depletions and depth profiles for both Na+ and Cs+ were reasonably consistent with the predicted curves, with the exception of the systematic disparity in the Cs+ profile. On the other hand, it was impossible to reproduce the 3H results in the parameter space considered here, without changing the relation between tracers. 6. Comparison of results and final conclusions Three different teams (NAGRA/IDAEA-CSIC, UJV-Rez, JAEA) performed modeling of the in situ diffusion experiment based on (i) the measured drop in tracer activities in the circulation system and (ii) measured tracer distribution profiles in the rock. Tables 6 and 7 compile the best-fit parameters for the in situ experiment from NAGRA/IDAEA-CSIC, UJV-Rez, and JAEA. NAGRA/IDAEA-CSIC and UJV-Rez tried directly to fit the results of the in situ experiment, while JAEA conducted a predictive modeling based on laboratory diffusion data and their scaling to in situ conditions. This different modeling approach by JAEA could approximately reproduce the results for 22Na+ and 134 + Cs , but it was not possible to reproduce the 3H results. Overall there is a reasonable agreement between the values from NAGRA/IDAEA-CSIC and UJV-Rez, due clearly to the use of the same modeling concept. The largest differences are for 22 Na+ in the bulk rock (a factor of about 3 for De and about 1.5 for α) and for 134Cs+ in the BDZ (a factor of about 2 for De and

BDZ 1 const.

UJV samples UJV cor. ii BDZ 0

75

Helsinki samples Helsinki cor. i BDZ 3 lin.

UJV cor. i Helsinki cor. ii BDZ 1 const.

1.E+04

65

134Cs (Bq.g-1)

A/A0 (%)

55 45 35

25

1.E+02

1.E+00

15 0

200

400

600

800

1.E-02

t (d)

0

0.5

1

1.5

2

2.5

d (cm) 134

Fig. 11. Cs+. Relative tracer activities (%) in the circulation system. NO BDZ, 1zone BDZ, and 3-zone BDZ were assumed in the model. For parameters, see Table 3.

134

Fig. 12. Cs+. Tracer profiles in the rock. NO BDZ, 1-zone BDZ, and 3-zone BDZ were assumed in the model. For model parameters, see Table 3.

98

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101

Table 3 134 BDZ properties (length, mm) and rock migration parameters for Cs+ used in the modeling by UJV-Rez. Bold characters correspond to input parameters used for simulation. ρs and ρb correspond to density of solids and bulk dry density, respectively. R is the retardation factor (α = Rϕ). Dp, De, and Da are pore, effective, and apparent diffusion coefficients, respectively. 134

Cs+

l

Code

mm

BDZ 0 BDZ 3 lin.

0+ 0 0.5 1.5 3+ 0+ 1.5+

BDZ 1 konst.

ϕ

0.0065 0.04 0.03 0.01 0.0065 0.04 0.005

ρs

ρb

Kd

kg · m−3

kg · m−3

m3 · kg−1

2660 2660

2643 2554 2580 2633 2643 2554 2647

0.02 0.1 0.032 0.02 0.019 0.06 0.0085

2660

about 1.4 for α). α for 22Na+ also shows a difference by a factor of 2 in the BDZ. De values from JAEA for 22Na+ and 134Cs+ in the bulk rock are also in good agreement with the values obtained by NAGRA/IDAEA-CSIC and UJV-Rez. α values are smaller by a factor of 2–4. As mentioned in Section 5.2, it was not possible by JAEA to obtain a good match for 3H data. Concerning the impact of these uncertainties on transport calculations (e.g. in repository performance assessment), it should be noticed that diffusional transport distance scales with the square root of the apparent diffusion coefficient (Da = De/α). Therefore, for a given value of the capacity factor α, a difference by a factor of 4 in De translates to a difference by a factor of 2 in transport distances. Differences by a factor of 4 in both De and α could mean differences up to a factor of 4 in transport distances. De and α values from JAEA for the different tracers in the BDZ are larger than the respective values in the bulk rock. De values are larger by a factor of 2, due to the linear scaling between porosity and De. The best agreement with the values obtained by NAGRA/IDAEA-CSIC and UJV-Rez is shown by 22 Na+. Values for 134Cs+ are also in fair agreement. De is smaller by a factor of 4 to 8 and α is larger by a factor of about 2. The difference in the value for α (134Cs+) seems related to the different extension of the BDZ. The smaller extension of the

Packer, Test interval

BDZ 0.1mm× 10 MESH

Rock matrix 2mm× 10 MESH + 5mm× 40 MESH

Dummy space for 8L reservoir

α

53 255 83 53 50 153 23

8132 6385 2753 5268 7726 3831 4500

Dp

De

Da

m2 · s−1

m2 · s−1

m2 · s−1

1.2E-09 1.2E-09

7.8E-12 4.8E-11 3.6E-11 1.2E-11 7.8E-12 3.2E-11 4.0E-12

1.5E-13 1.9E-13 4.4E-13 2.3E-13 1.6E-13 2.1E-13 1.8E-13

8.0E-10

BDZ assumed by JAEA translates into a BDZ volume smaller by a factor of 2.25 (cylindrical geometry), which would in turn require a value of α larger by the same factor to cause the same effect (the same drop in activity in the circulation system). Out-leaching of overcored rock samples from the in situ experiment was performed at the University of Helsinki (Soler et al., 2013b). 3H and stable iodide were simultaneously leached from two overcored samples using several small boreholes located around the central borehole (circulation interval of the in situ experiment). Two-dimensional modeling of these tests was performed at the University of Poitiers. The modeling of radionuclide diffusion through rock porosity was undertaken using the TDD (time domain diffusion) method (Delay et al., 2002; Robinet et al., 2008, 2012; Sardini et al., 2003, 2007). This is a finite volume approach solved by a Lagrangian method (particle tracking) which works under the time domain. Fixing rock porosity at 0.0065 and without considering any BDZ, results from University of Poitiers gave an apparent diffusion coefficient Da equal to 3e-10 m2/s as consistent with the results from the out-leaching tests for 3H and I− and also from previous tests with 36Cl− (Univ. of Helsinki). This value is not consistent with the results from NAGRA/IDAEA-CSIC and UJV-Rez, which gave Da values (De/ ϕ) for 3H about 3e-11 m2/s in the bulk rock (3H profiles measured by UJV-Rez). Calculation of a mean transport distance b d N after 780 days from Einstein's equation (2D: bd N 2 = 4 Dat) gives 9 cm for Da = 3e-11 m2/s and 28 cm for Da = 3e-10 m2/s. Transport distances from 3H distribution profiles in the rock measured by UJV-Rez are much more consistent with a Da = 3e-11 m2/s. The outcomes from the two sets of data are clearly different. Regarding the values obtained from through-diffusion experiments in the laboratory using synthetic Grimsel groundwater (Table 8), there are some significant differences between the results from UJV-Rez and JAEA (e.g. 2 orders of magnitude for Cs+ De; 1 order of magnitude for 3H De and 22Na+ α), although the trend in sorption is clear, from no or very weak

Table 4 Effective diffusion coefficients and capacity factors from centimeter-scale through-diffusion experiments at JAEA.

3

Fig. 13. Conceptual model for the 3D simulations.

R

H 125 I− 22 Na+ 137 Cs+

De (m2/s)

α

3.3E-12 2.0E-12 8.7E-12 1.2E-11

1.2E-2 7.8E-3 1.9E-1 1.6E+1

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101 Table 5 Effective diffusion coefficients and capacity factors from centimeter-scale through-diffusion experiments after abrasive peeling (JAEA).

22

Na

137

+

Cs

Near Far Near + far Near Far Near + far

+

De (m2/s)

α

Kd (m3/kg)

1.5E-13 9.7E-12 9.2E-12 2.2E-13 1.0E-11 1.3E-11

5.40 0.70 0.26 410 5.1 14

2.0E-3 2.6E-4 9.6E-5 1.5E-1 1.9E-3 5.2E-3

sorption for 3H to stronger sorption for Cs+. A clear reason for the difference in the results for Cs+ is the fact that stable Cs+ (10− 6 mol/L) was added as carrier in the experiments performed by JAEA. No clear reason has been found that can explain the differences for 3H and 22Na+. Comparing laboratory and in situ values (bulk rock), De for 3H is larger in the laboratory, De's for 22Na+ are also larger in the laboratory but comparable to in situ values, and in situ De for Cs+ is intermediate between the laboratory values from UJV-Rez and JAEA. α values are comparable. The largest difference is shown by 22Na+ relative to the laboratory value from UJV-Rez. A possible effect caused by the loss of rock confining pressure after overcoring and sampling could be responsible for the observed discrepancy in De values for 3H and 22Na+, with larger values measured in the laboratory. However, this same effect is not shown by Cs+, probably due at least in part to the large difference between the 2 sets of laboratory

1.2 3H

1.0

22Na

134Cs

A/A0 [-]

0.8

GoldSim 3H

0.6

GoldSim 22Na GoldSim 134Cs

0.4

COMSOL 3H

0.2

COMSOL 22Na

COMSOL 134Cs

0.0 0

200

400 t [d]

600

800

1.E+4

3H (S-1) 22Na (S-1)

Activity [Bq g-1]

1.E+3

22Na (H-1) 22Na (H-2)

1.E+2

134Cs (S-1)

134Cs (H-1)

1.E+1

134Cs (H-2)

99

Table 6 Best-fit parameters from the different modeling exercises: De(m2/s) and α values for bulk rock. TRACER De (IDAEA) 3

H Na+ Cs+

22

134

2E-13 2E-12 3E-12

De (UJV)

De (JAEA)

α (IDAEA)

α (UJV)

α (JAEA)

1.7E-13 6.0E-13 4.0E-12

2.9E-12 3.8E-12

0.0065 0.2 20

0.005 0.13 23

0.062 5.2

values. Disturbed zones in the laboratory samples may also have an effect on the calculated De and α values, as indicated by the dual profiles measured by JAEA in the laboratory (different behavior of sorbing tracers close to the inlet side of the samples). The loss of confining pressure could also be behind the large values for Da obtained in the out-leaching tests (3H, I−). A still open issue is the large value of α for 3H in the BDZ (NAGRA/IDAEA-CSIC, UJV-Rez). This large value was necessary to fit the large initial drop in activity in the circulation system. If this drop in activity were caused by some other process, unknown at this moment, then the value of α would not have any meaning in terms of sorption. It is striking that α for 3H is larger than α for 22Na+. Possible water flow across the borehole (with little change in water volume in the circulation system; no net in- or out-flow was measured), as suggested by calculations for a second in situ experiment (W. Lanyon, pers. comm.) could be a possible cause for the loss of 3H. However, the two 3H rock profiles measured by UJV-Rez were perpendicular to each other and showed no significant asymmetry. Asymmetry would be expected in the case of flow across the borehole. Also, initial results from the second in situ experiment (tracer activities in the circulation system), started in March 2014, do not show any apparent effect from a BDZ (no large initial drop in activities; Soler and Martin, 2015). Another significant observation is that all tracers sorb more strongly in the BDZ than in the bulk rock, with larger differences for the weakest sorbing tracers. This observation would be consistent with more accessible surface area in the BDZ. The large value of De (3–6e-11 m2/s) for 134Cs+ in the BDZ could be related to the large Kd. Gimmi and Kosakowski (2011) have shown that the relationship between large De and Kd values in clays for tracers sorbing by cation exchange (mainly Na+, Sr2+, Cs+, Ca2+ in their analysis) is consistent with a surface diffusion mechanism. 134Cs+ most probably sorbs on the mica surfaces in the granite, which could lead to a similar role of surface diffusion in the granite. The extension of the BDZ deduced from the rock measurements (maximum 2 mm), is about the same magnitude than the mean grain size of the quartz and feldspar grains (grain

134Cs (H-3)

1.E+0

GoldSim 3H GoldSim 22Na

1.E-1

GoldSim 134Cs COMSOL 3H

1.E-2 0.1

1 d [cm]

10

COMSOL 22Na COMSOL 134Cs

Fig. 14. Top: Relative tracer activities in the circulation system. Bottom: Tracer profiles in the rock. Symbols correspond to measured data (S-1 profile measured at UJV-REZ; H-1 to H-3 profiles measured at Univ. of Helsinki) and lines to simulation results.

Table 7 Best-fit parameters from the different modeling exercises: De(m2/s) and α values for the BDZ (NAGRA/IDAEA-CSIC, UJV-Rez:1.5 mm thick; JAEA: 1 mm thick). TRACER De (IDAEA) 3

H Na+ Cs+

22

134

1E-12 3E-12 6E-11

De (UJV)

De (JAEA)

α (IDAEA)

α (UJV)

α (JAEA)

1.3E-12 4.8E-12 3.2E-11

5.8E-12 8.0E-12

10 3 110

11.53 5.66 153

3.6 270

100

J.M. Soler et al. / Journal of Contaminant Hydrology 179 (2015) 89–101

Table 8 Parameters from centimeter-scale through-diffusion experiments: De(m2/s) and α values derived from evolution of tracer concentrations in the inlet and outlet reservoirs. TRACER 3

H 22 Na+ Cs+

De (UJV)

De (JAEA)

α (UJV)

α (JAEA)

1.6–2.9e-11 5.4–7.2e-12 134 1.0e-13 Cs+

3.3e-12 8.7e-12 137 1.2e-11 Cs+

b0.2 1.4 134 42.4 Cs+

0.012 0.19 137 16 Cs+

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