Modelling the long term alteration of the engineered bentonite barrier in an underground radioactive waste repository

Applied Clay Science 47 (2010) 82–90

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Applied Clay Science j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / c l a y

Modelling the long term alteration of the engineered bentonite barrier in an underground radioactive waste repository Nicolas C.M. Marty a,b,c,d,⁎, Bertrand Fritz b,c, Alain Clément b,c, Nicolas Michau d a

BRGM, 3 Avenue C. Guillemin, F-45060 Orléans, Cedex 2, France Université Louis Pasteur, Centre de Géochimie de la Surface, UMR 7517 CGS, 1 rue Blessig, F-67084 Strasbourg Cedex, France CNRS/INSU, UMR 7517 CGS, 1 rue Blessig, F-67084 Strasbourg Cedex, France d Andra, 1/7 rue Jean Monnet, F-92298 Châtenay-Malabry Cedex, France b c

a r t i c l e

i n f o

Article history: Accepted 8 October 2008 Available online 17 October 2008 Keywords: KIRMAT Coupled transport reaction modeling MX-80 bentonite Engineered barrier Porosity Diffusion

a b s t r a c t In the French design for a High Level Waste (HLW) repository, compacted bentonite may be the main component for the engineered barrier system (EBS) in the spent fuel disposal cell. In such a barrier, the interactions between groundwater and bentonite, as well as between the corrosion products of steel overpacks and bentonite, may modify the chemical and physical properties of the selected swelling clay buffer. Bentonite material has a very low permeability, and consequently molecular diffusion is the main mechanism of mass transport. This study is focused on the possible feedback effects of geochemical reactions on the transport properties (porosity and diffusion) of a compacted bentonite. After 100,000 years of simulated mass transport-reaction, the model predicts mineralogical modifications of the EBS in contact with the geological interacting fluid, and with Fe2+ ions provided by the corrosion of the steel overpacks. This corresponds to a transformation of the initial montmorillonite by partial illitization, saponification and vermiculitization due to chemical diffusion from geological groundwater through the bentonite barrier. The aqueous corrosion of steel overpacks generates a chemical perturbation inside the EBS (low redox potential and high values of pH) which could possibly create locally a destabilization of the montmorillonite, while part of the released Fe2+ ions is incorporated into precipitated chlorites and saponites. Formations of magnetite, laumontite, greenalite, chabazite, phillipsite, and chrysotile are also identified in the numerical simulations. Despite these modifications, the predicted evolution of porosity display decreasing values and are limited to the outer parts of the EBS. A mass transport law applied to this study predicts a decrease of the molecular diffusion correlated with the porosity clogging. © 2008 Elsevier B.V. All rights reserved.

1. Introduction One of the main research topics of the French agency for radioactive waste management (Andra) is to investigate the feasibility of a deep repository for high-level radioactive waste. A multiple barrier concept separates radioactive waste from the CallovoOxfordian clay host rock (COX) by a bentonite engineered barrier system (EBS) (Andra, 2005a). After closure of the disposal facility, the dry barrier will become saturated with the groundwater. The geological porewater, equilibrated with the COX formation, may modify the chemical and physical characteristics of the selected clay material (MX-80 bentonite). Both influences of temperature elevation and Fe2+ ions, provided by the corrosion process of the steel overpacks of the spent fuel package, may change the initial physical

⁎ Corresponding author. BRGM, 3 Av. C. Guillemin, F-45060 Orléans, Cedex 2, France. Tel.: +33 2 38 64 34 34; fax: +33 2 38 64 30 62. E-mail address: [email protected] (N.C.M. Marty). 0169-1317/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.clay.2008.10.002

and chemical properties of the clay barrier. The alteration of clay minerals in contact with steel was studied in the laboratory by several authors, e.g. Bataillon (1997), Guillaume (2002), Perronnet (2004). Iron/clay interactions were also modelled by Montes-H et al. (2005a,b, c) and Bildstein et al. (2006). In addition to experimental approaches on short term time scales, modelling the long-term transformation is necessary in order to estimate the stability of the confinement capacity of the EBS. The aim of this study is to identify the possible neoformed mineral phases and to investigate the consequences on the evolution of diffusion properties of the buffer barrier. The system is modelled in reducing conditions using the KIRMAT code (KInetic Reactions and MAss Transport). The software has been developed (Gérard et al., 1998) from the single-reaction path model KINDIS (Madé et al., 1994) generated from the purely thermodynamic code DISSOL (Fritz, 1975, 1981). KIRMAT resolves the mass balance equations for transport associated with geochemical reactions. A set of rate constants based on the transition state theory (TST) can be used for the dissolution and precipitation of minerals, but the code also allows the processing at local equilibrium for secondary phases.

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2. Initial conditions

Table 2 Mineralogical composition of MX-80 bentonite.

2.1. Geological porewater The characteristic composition of the geological fluid, which is equilibrated under reducing conditions with the COX argillite from the Bure site, was calculated by Gaucher et al. (2006). The Sr, Na, K, Ca and Mg concentrations of the interstitial fluid depend on ion exchange constants. Other parameters are adjusted for the electroneutrality of the solution and result from the thermodynamic equilibrium between the solution and illite, Ca-montmorillonite, microcline, calcite, dolomite, Fechlorite, quartz, siderite, pyrite, celestite and gypsum. A temperature of 25 °C is considered in the geological environment to define this initial composition. The calculated porewater composition is given in Table 1. 2.2. Corrosion of the steel overpack Following the closure of the repository system, oxygen is supposed to be quickly consumed. Based on this assumption, corrosion of the container takes place in anaerobic conditions: Fe0 fFe2 + + 2e− H2 O + 2e− f2OH− + H2 z Fe0 + 2H2 OfFe2 + + 2OH− + H2 z

83

ð1Þ

These reactions create a perturbation into the clay-solution system (high pH and Fe2+ concentration, low redox, significant hydrogen partial pressure). The corrosion rate of the steel overpack was simulated by a standard kinetic equation for mineral dissolution. As shown by reaction (1), the simulated hydrogen pressure depends on the Fe2+ concentration of the interacting fluid which is controlled by the corrosion products. Magnetite and siderite were identified as the main corrosion products of iron in reducing conditions (Andra, 2005a). 2.3. The engineered barrier system The EBS reference material for this study is the compacted MX-80 bentonite (Table 2). This Wyoming bentonite mainly consists of a low charge montmorillonite with both Na+ and Ca2+ as interlayer cations (Guillaume, 2002): ½ðSi3:98 Al0:02 O10 ÞðOHÞ2 ðAl1:55 Mg0:28 FeII0:08 FeIII 0:09 ÞNa0:18 Ca0:1 The total physical porosity of the clay barrier is estimated at 0.39, associated with an initial dry density of about 1.6 g cm− 3 (Sauzéat et al., 2001). The simulation of the long term evolution of the bentonite takes place under fully hydrated conditions. The application of the model considers an initial saturation of MX-80 bentonite with a Table 1 Chemical composition, pH and Eh of a representative geological fluid from CallovoOxfordian (COX) formation (Gaucher et al., 2006).

Mineral

Volume fraction (Xmin)

Pyrite Biotite Calcite Quartz Microcline Albite Montmorillonite Total

0.0031 0.0278 0.0097 0.0703 0.0107 0.0349 0.8435 1

ICP-MS and other complementary analysis (after data from Sauzéat et al., 2001).

solution that is thermodynamically equilibrated with montmorillonite, pyrite, biotite, calcite, quartz, microcline, and albite at 100 °C (Marty, 2006). The Eh value is selected at equilibrium with the S(-II)/S (VI) system due to the presence of both pyrite and sulphate in solution. These types of calculation at equilibrium allow an estimation of a porewater composition (Bradbury and Baeyens, 1998; Pearson et al., 2003; Gaucher et al., 2006). The fluid composition is shown in Table 3. Due to the very low diffusion coefficient and permeability of the COX formation, it must be considered in the present study as a closed system except for the period where concrete, steel containers and clay buffering barriers will be installed. An atmospheric pCO2 is expected at that time. As a consequence, an atmospheric CO2 partial pressure was initially considered in the MX-80 (Table 3). However, after closure of the disposal facility, the pCO2 (and other solution parameters) will reequilibrate slowly with the COX formation. All the intermediate processes — re-saturation, transient thermal gradient etc — were not considered in the present simulations and only the low pCO2 in the barriers and high pCO2 in the COX as a boundary condition were considered. In addition, the pCO2 value may change under the influence of the mineralogical modification during simulation: the solution is not closed to CO2. The thermodynamic constants used to calculate the composition are presented in the following section. 3. Databases and calculation 3.1. Thermodynamic data Thermodynamic data of hydrated phyllosilicates, in particular clay minerals are not well known. A method to estimate the Gibbs free energies of formation of micas, chlorite and smectite has been developed by Vieillard (2000, 2002). In this approach, the Gibbs free energy of formation is supposed to be proportional to both the number of oxides in the composition, and the electronegativity difference between cations around common oxygen atoms. Based on

Table 3 Composition of the solution equilibrated with MX-80 bentonite at 100 °C.

Chemical composition at. 25 °C Eh (mV) pH fCO2 (atm)

− 176 7.28 3.09 × 10− 3

Concentration

mol kg− 1w

Na K Ca Mg Si Cl S Al Fe Sr Alkalinity (eq kg− 1w)

3.20 × 10− 2 7.07 × 10− 3 1.49 × 10− 2 1.41 × 10− 2 9.43 × 10− 5 3.01 × 10− 2 3.40 × 10− 2 8.62 × 10− 9 9.40 × 10− 5 1.12 × 10− 3 1.29 × 10− 3

Chemical composition at 100 °C Eh (mV) pH fCO2 (atm)

− 434.36 8.04 3.16 × 10− 4

Concentration

mol kg− 1w

Na K Ca Mg Si Cl S Al Fe Alkalinity (eq kg− 1w)

1.77 × 10− 3 1.52 × 10− 5 5.62 × 10− 4 1.01 × 10− 6 9.25 × 10− 4 4.62 × 10− 3 4.47 × 10− 6 1.20 × 10− 4 2.56 × 10− 9 1.70 × 10− 4

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Table 4 Thermodynamic constants (100 °C) of the minerals of MX-80 bentonite and the phases tested in precipitation. Mineral

Structural formula

Phases observed in MX-80 bentonite FeIIS2 Pyrite[1] KMg1.5FeII1.5SiAlO10(OH)2 Biotite[1] CaCO3 Calcite[1] SiO2 Quartz[1] Microcline[1] KAlSi3O8 [1] NaAlSi3O8 Albite [2] [(Si3.98Al0.02O10)(OH)2] Montmorillonite (Al1.55Mg0.28FeII0.08FeIII0.09) Na0.18Ca0.1 Phases tested in precipitation FeIII2FeIIO4 Magnetite[1] Hematite[1] FeIII2O3 NaCl Halite[1] FeIICO3 Siderite[1] CaSO4 Anhydrite[1] Mg(OH)2 Brucite[1] CaSO4.2H2O Gypsum[1] [(Si3.5Al0.5O10)(OH)2] Illite[3] (Al1.8Mg0.25)K0.6 [3] Kaolinite Si2Al2O5(OH)4 SiO2 Amorph. Silica[1] SiO2 Cristobalite[1] SiAl2CaO16H8 Laumontite[3] Na2SO4 Thenardite[1] KFeIII3(SO4)2(OH)6 Jarosite[1] [3] [(Si3.19Al0.81O10)(OH)2] Vermiculite (Al0.08FeIII0.295Mg2.61FeII0.015) Mg0.218 [Si8Al4O24]Na3.5Ca0.2513H2O Na Chabazite[3] [Si10Al6O32]Na5Ca0.512H2O Na Phillipsite[3] Mg3Si2O5(OH)4 Chrysotile[2] FeII2Al2SiO5(OH)4 Chamosite-7A[1] [2] FeII3Si2O5(OH)4 Greenalite FeIII2FeII2Si05(OH)4 Cronstedtite[2] FeAl Chlorite[2] [Si2Al2O10(OH)2](FeIIAl2) (FeII3)(OH)6 MgAl Chlorite[2] [Si2Al2O10(OH)2](MgAl2) (Mg3)(OH)6 Na Smectite[2] [(Si3.96Al0.04O10)(OH)2] (Al1.52FeIII0.18Mg0.27)Na0.4 [2] Ca Smectite [(Si3.96Al0.04O10)(OH)2] (Al1.52FeIII0.18Mg0.27)Ca0.2 MgFeIII Saponite[3] [(Si3.67Al0.33O10)(OH)2] (Al0.47FeIII0.46Mg1.52) Ca0.11Na0.11K0.17 [(Si3.67Al0.33O10)(OH)2] FeII Saponite[2] (FeII3)Na0.33 N_Nontronite-A[2] [(Si3.84Al0.94O10)(OH)2] Fe0.9Mg0.33Ca0.105Na0.05K0.2 MgFeII Saponite[3] [(Si3.67Al0.33O10)(OH)2] (Al0.33FeII1.15Mg1.355)Mg0.165 Saponite 341[3] [(Si3.5Al0.5O10)(OH)2] (Al0.25FeII1.25Mg1.5) Ca0.05Na0.15

Log K 100 °C

Molar volume cm3 mol− 1

− 67.89 − 9.39 − 3.09 − 18.10 − 16.04 5.91 − 25.99

23.94 152.00 36.93 22.69 108.69 100.07 145.00

22.65 20.04 1.56 − 11.95 − 5.36 − 11.61 − 5.01 − 33.95

44.52 30.27 27.02 29.38 45.94 24.64 74.31 150.00

− 30.15 − 2.20 − 2.70 − 23.63 − 0.87 − 15.60 6.61

99.52 29.00 25.74 100.00 53.34 153.90 150.00

− 50.90 − 70.30 24.50 − 11.00 17.43 12.18 − 28.05

248.26 302.37 108.50 106.20 115.00 130.00 208.30

− 11.74

208.30

− 25.21

150.00

− 25.18

150.00

− 4.85

150.00

6.93

181.50

− 19.52

150.00

2.82

190.80

4.10

194.60

also influence the behaviour of the geochemical system. Gaucher and Blanc, (2006) explain that supplying the chemical/transport code with a too short list of minerals can bias model results because it forces the system to converge towards a given mineralogical assemblage without alternative choices. The 37 minerals considered in simulations (Table 4) should not force the reaction pathways. The choice of secondary minerals made in this study for the modelling has been clearly based on what was available in databases in terms of thermodynamics and kinetics. Another option could have been to try to consider minerals from natural systems, so called “natural analogues”, if any were available. That brings about the problem already mentioned above: (i) on the one hand, any clay formula from a natural system may appear as more safe, but it will reflect the specific geological history of the considered system and it is quite impossible to find a natural analogue to a clay barrier having undergone the type of heating expected in a nuclear waste storage: short metric distances, high temperatures and short duration (in terms of geological times); (ii) on the other hand, choosing a specific composition of secondary clay would make it necessary to estimate the thermodynamic and kinetic parameters with the same uncertainties already feared from those selected in the database. We believe that the selected minerals are appropriate for describing the general tendency of evolution of such storage systems and this was the aim of that research. 3.2. Kinetic parameters Classic TST kinetic laws, included in the KIRMAT code, describe the dissolution rates of minerals at different pH values:   Q n rd = kd Seff min aHþ 1− K

ð2Þ

where rd is the dissolution rate of a mineral (mol year− 1 kg− 1w), kd is the dissolution rate constant (mol m− 2 year− 1), Seff min is the reactive surface area of this mineral (m2 kg− 1w), aH+ is the activity of hydrogen ion, n is an experimental power, Q is the ion activity product of the mineral, and K is the equilibrium constant, for the hydrolysis reaction. Following the KIRMAT approach, the pH dependence is considered by using three different linear regressions at different pH ranges for each mineral (acidic, neutral and basic). The dissolution rates allow the prediction of the evolution over time of the EBS which tends to a new thermodynamic equilibrium under the mass transport process.

Table 5 Kinetic constants of dissolution (100 °C) of primary minerals and the steel overpack. Mineral

anH+

Kinetic constants (100 °C) mol m− 2 year− 1

Boundary pH

Acid

Neutral

Basic

Acid Basic

1.88 × 10− 18 2.70 × 106 1.33 × 10− 4 5.31 × 10− 3 1.40 2.82 × 10− 1 1.89 × 10− 3 7.04 × 10− 1

1.88 × 10− 18 1.35 × 102 3.34 × 10− 5 3.35 × 10− 4 7.89 × 10− 3 3.90 × 10− 3 3.43 × 10− 6 7.04 × 10− 1

1.88 × 10− 18 1.35 × 102 8.40 × 10− 8 1.68 × 10− 7 5.97 × 10− 6 7.96 × 10− 6 3.67 × 10− 9 7.04 × 10− 1

0 0.86 0.20 0.25 0.50 0.50 0.34 0

Acid Basic

[2]

Pyrite[4] Calcite[5] Quartz[6] Microcline[7] Albite[8] Biotite[9] Montmorillonite[10] Steel overpack[11]

the hydrolysis reactions of the clay phases and the Gibbs free energy of products and reactants at 25 °C, the thermodynamic equilibrium constants are calculated for that temperature and extrapolated for a temperature of 100 °C by using the theoretical curve of Chermak and Rimstidt (1989, 1990). Other minerals, with well known thermodynamic properties, are referenced in the database of the KIRMAT software (Fritz, 1981). Thermodynamic data used in this modelling are available in Table 4. It is clear that the coherence of a database plays an important role for predictive simulations. However processed minerals in models can

The kinetic constants (100 °C) are determined after data from: [4] Holmes and Crundwell (2000), Williamson and Rimstidt (1994). [5] Busenberg and Plummer (1986), Arvidson et al. (2003), Alkattan et al. (1998). [6] Dove (1994). [7] Knauss and Copenhaver (1995), van Hees et al. (2002), Rafal'Skiy et al. (1990), Shillings et al. (1996). [8] Hellmann (1994), Chou and Wollast (1984, 1985). [9] Malmström and Banwart (1997), Kalinowski and Schweda (1996), Acker and Bricker (1992),White et al. (1999). [10] Huertas et al. (2001), Hayashi and Yamada (1990), Zysset and Schindler (1996), Bauer and Berger (1998). [11] Montes-H et al. (2005a,c).

[1]

KIRMAT database (Fritz, 1981). Method developed by Vieillard (2000, 2002). [3] Corrected to respect the initial thermodynamic equilibrium between the interstitial fluid and the MX-80 bentonite.

−0.18 0 −0.50 −0.42 −0.40 −0.35 −0.34 0

2 4.5 2 5.4 4.5 4 8

5.5 7.8 7.8 7 8.5

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Only the dissolution rates of the primary minerals, contained in MX80 bentonite, and of the steel over-pack are taken into account (Table 5). Few studies describe the effect of deviation from equilibrium on smectite dissolution. These formalisms describe dissolution rates under specific conditions (e.g. 80 °C and pH 8.8 for Cama et al., 2000). The application of these laws at other pH and temperature conditions requires additional experimental data not available at present. As a first approximation, data from Huertas et al. (2001), Hayashi and Yamada (1990), Zysset and Schindler (1996) and Bauer and Berger (1998) are used to describe the montmorillonite dissolution rate in our pH conditions ranging from 6 to 11 at 100 °C. A simple method to obtain a preliminary estimation of the mineral/ water interfacial total surface area was used by referring to geometrical models established according to Sali (2003). The values used for primary phases are given in Table 6. This reactive surface area of the montmorillonite is less than 1 m2 g− 1 of bentonite, which is more than 2 orders of magnitude lower than the surface area usually measured by N2 adsorption isotherms (BET): e.g. Huertas et al. (2001) have determined an average value of 57.0 m2 g− 1 of bentonite. This apparent underestimation of the clay reactive surface area leads to an indirect correction of dissolution rates expected in the geological field. Indeed Velbel (1993) established that inverse models with apportioned watershed effluxes (geochemical mass balance) give weathering rates for individual silicate minerals (e.g. feldspar) 1 to 3 orders of magnitude slower than laboratory rates. Feldspar kinetic data recently compiled by White and Brantley (2003) show experimental rates that are 102 to 105 times faster than natural rates. Zhu (2005) estimates that in situ feldspar dissolution rates are 105 times slower than laboratory experimentderived rates under similar pH and temperature. In fact, estimated dissolution rates decrease in the order powder b block b field (Yokoyama and Banfield, 2002). Dissolution of montmorillonite in compacted sandbentonite mixtures has been studied by Nakayama et al. (2004) who pointed out dissolution rates slower (by 1 order of magnitude) than rates estimated based on batch dissolution experiments obtained far from equilibrium. Differences in mineral surface areas between estimations and/or measurements have been proposed as one of the possible sources of the discrepancy between laboratory and field rates (White and Perterson, 1990). The accessible surface area of minerals in a compacted system should be lower than that of powders usually studied in laboratory. However, differences in the overall rates of reaction measured in laboratory and field settings could also be attributed to a variety of factors as surface area, departure from equilibrium, inhibition or catalysis (Maher et al., 2006). Concerning the corrosion reaction, far from equilibrium, the initial rate is supposed to be as high as 5 µm year− 1. According to Montes-H et al. (2005a,c), the rate constant of iron dissolution (Eq. (1)) was then estimated using the following relation: kdFe =

mcorr ρFe MFe

ð3Þ

with kdFe the kinetic constant of dissolution (mol m− 2 year− 1), νcorr the corrosion linear rate (m year− 1), ρFe the specific (grain) density (g m− 3) and MFe the molar mass of iron (g mol− 1). Table 6 Volume of minerals in contact with solution and reactive surface areas for the phases observed in MX-80 bentonite. Mineral

Vp cm3 kg− 1w

Reactive areas m2 kg− 1w

Pyrite Calcite Quartz Microcline Albite Biotite Montmorillonite Total volume

4.85 15.17 109.96 16.74 54.59 43.48 1319.32 1564.11

1.45 4.55 32.99 5.02 16.38 13.04 395.80

85

Table 7 Kinetic constants of precipitation of primary minerals and two secondary phases (magnetite and siderite) at 100 °C. Mineral

Kinetic constants (100 °C)

[12]

Pyrite Calcite[13] Quartz[14] Microcline[15] Albite[16] Biotite[17] Montmorillonite[18] Magnetite[19] Siderite[20]

mol m− 2 year− 1

P

q

1.88 × 10− 18 3.97 × 102 2.93 × 10− 2 1.67 × 10− 4 1.17 × 10− 2 2.88 × 10− 5 5.34 × 10− 7 1.47 × 10− 4 7.02 × 104

1.00 0.50 1.00 0.40 0.76 1.00 1.00 1.00 1.00

1.00 2.00 1.00 14.00 0.90 1.00 1.00 0.08 1.00

The kinetic constants (100 °C) are determined after data from: Holmes and Crundwell (2000), Williamson and Rimstidt (1994). [13] Zhang and Grattoni (1998). [14] Ganor et al. (2005). [15] Soler and Lasaga (1998). [16] Alekseyev et al. (1997), Jacquot (2000). [17] Soler and Lasaga (1998). [18] Jacquot (2000). [19] Faivre et al. (2004). [20] Lopez and Romanek (2004), Kopp and Humayun (2003). [12]

A plane surface of the steel overpack is assumed to be in contact with the solution. In order to simulate the iron dissolution in reducing condition (Eq. (1)), a porosity factor (ωFe) is considered in the modelling cell of the corrosion process. The total iron surface area is supposed as reactive and is given by: SFe =

S VωFe ρwater

ð4Þ

where SFe refers to the iron surface area (m2 kg− 1w), S is the section of the modelled profile (m2), V is the volume of the modelling cell of the corrosion process (m3), and ρwater is the density of water (kg m− 3). The KIRMAT code can also describes the precipitation rates of minerals. The precipitation law is a function of the saturation state given by the following expression: rp = kp Seff min

 p q Q −1 K

ð5Þ

where rp is the precipitation rate of a given mineral (mol year− 1 kg− 1w), kp is the kinetic constant of precipitation (mol m− 2 year− 1), p and q are experimental values describing the saturation state dependence of the reaction. The kinetic precipitation rates of the primary minerals and of the corrosion products (magnetite and siderite) are calculated in the simulations. The other secondary phases are supposed to be formed at thermodynamic equilibrium with the aqueous solution. Their resulting precipitation rates are controlled by evolution of the activities of aqueous species in porewater provided by the dissolution of the primary phases (kinetically controlled) and mass transport. Therefore secondary minerals are under an indirect kinetic control if the dissolution processes are slower than the precipitation ones. The very long computation times, about 4 weeks of computation for 100,000 years of predictive evolution, make any sensitivity analysis quite impossible to be performed, as was done in Trotignon et al. (2007) for less than 10,000 years of simulated interactions. The set of precipitation rate parameters is given in Table 7. The kinetics of precipitation described by Eq. (5) requires reactive surface areas to simulate the precipitation of corrosion products. However, these secondary phases are initially missing in the EBS. Because KIRMAT does not take the nucleation processes into account, surface areas must be introduced in the system in order to allow the phase to grow. The formation of corrosion products on a metallic surface area in

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contact with water saturated FoCa bentonite in a reduced environment was discussed by Bataillon (1997). The results indicate that siderite and magnetite are identified as corrosion products of the iron plate. The magnetite is directly formed from the surface area of the iron. Therefore the reactive surface area necessary to the precipitation of magnetite is assumed to be equal to the reactive surface of the steel overpack (Eq. (4)). The siderite is directly in contact with the bentonite. Then the reactive surface area is considered to be equal to the reactive surface area of the calcite, a primary mineral (Table 6). This assumption is based on the possible ankerite (or calcite–siderite solid solution) formation in clay–iron systems (Bataillon, 1997).

(2005) determined a value of 5.34 for a Na-montmorillonite after data from Sato et al. (1992), Torikai et al. (1996) and Kozaki et al. (1999). For the COX argillite the author gives a cementation factor of about 2. Considering an initial dry density of 1.6 g cm− 3 for the EBS, the calculated effective diffusion coefficient is about 10− 11 m2 s− 1. This value is consistent with the experimental estimations of the diffusion coefficient in MX-80 bentonite (Lehikoinen et al., 1996). Feedback between transport properties and chemistry can be important and has been considered. The effective diffusion coefficient (Eq. (6)) is calculated as a function of the porosity as well as the cementation factor, and updated during the simulation using Archie's law.

3.3. Mass transport parameters

4. Modelling strategy

As the clayey material used in simulations is compacted (1.6 g cm− 3), molecular diffusion is considered to be the main mechanism of mass transport. A single diffusion coefficient in aqueous phases is used to describe the processes (D0 = 10− 10 m2 s− 1). The effective diffusion coefficient is approximated by Archie's relation:

The confinement barrier is subjected to temperature variations (up to 100 °C) (Andra, 2005b). Due to the disintegration reactions of radioactive waste, a temperature gradient must be a function of time and space. In the KIRMAT code, it is not possible to take into account this gradient, and therefore we made our calculations assuming a constant temperature of 100 °C in order to estimate a maximum thermal effect on the mineralogy of the engineered barrier. Considering the temperature and the long term evolution of the system, the mineralogical transformations have been considered as being more important than the surface and ion exchange reactions. As a consequence, these reactions were neglected here. In order to use the mass transport function of the software, a profile must be described. It is 1 meter long (thickness of the barrier), with a section of 25 cm2, and divided into 20 cells (Fig. 1). In the adopted modelling strategy, the cells which represent the steel overpack and the EBS are introduced as two different entities. This strategy allows distinguishing clearly the corrosion products of the steel and the mineralogical transformation phases of the MX-80 bentonite. In addition, the consideration of feedback effects of mineralogical transformations on the mass transport requires a physical separation between the bentonite barrier and the steel overpack. Indeed the exchanges of matter are instantaneous in a single cell. Molecular diffusion (and/or the convection) is established between two consecutive cells. The COX groundwater speciation given at 25 °C (Gaucher et al., 2006) diffuses into the engineered barrier, and KIRMAT initiates the recalculation of the speciation for a temperature of 100 °C. The simulation of the iron corrosion requires a fluid in contact with the lining of the steel overpack (Eq. ((1)). The volume of the considered fluid is the same as the volume present in a modelled cell of the MX-80 bentonite. Siderite and magnetite precipitations are kinetically processed in the modelling cell of the steel overpack alteration. This cell provides Fe2+ ions and changes the pH and redox conditions which are initially adjusted for the thermodynamic equilibrium with the MX-80 bentonite.

D = D0 ωc−1

ð6Þ

where D is the effective diffusion coefficient in the porous media (m2 s− 1), D0 is the diffusion coefficient in aqueous phases (m2 s− 1), ω is the porosity and c is the cementation factor. A cementation factor is used to estimate the effective diffusion coefficient (Eq. (6)). Its evolution must be taken into account during simulations. Rosanne et al. (2003) determine a diffusive formation factor as a function of the porosity for montmorillonite in NaCl and KI solutes: F = 0:36ω−4:4

ð7Þ

Archie (1942) expresses the formation factor as a function of the porosity and the cementation factor: F=

1 ωc

ð8Þ

Then, by using Eqs.(7) and (8), the cementation factor can be obtained by the following relation:
log 0:36ω−4:4 ð9Þ c=− log ω The initial total porosity equals to 0.39 implies a value of 3.3 for the cementation factor. This estimation is in good agreement with cementation factors used by Gérard (1996) who proposed values ranging between 2.5 and 5.4 for clay phases. More recently Leroy

Fig. 1. Profile of the bentonite engineered barrier system (EBS) modelled with KIRMAT.

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5. Results and discussion 5.1. Modelling of mineralogical modifications of the EBS for radioactive waste confinement The modelling considers a bentonite “rock” as an initially equilibrated system, which is in contact with the geological fluid on one side, while the other side is kept in contact with the steel overpack corroded in reduced environment (Fig. 1). The mineralogical modifications of the MX-80 bentonite until 100,000 years are shown in Fig. 2. According to the degree of smectite transformations, these simulations show three distinct zones: (i) The first zone results from the mass transport of the geological groundwater through MX-80 bentonite. The resulting alteration front corresponds to a strong illitization of the montmorillonite together with precipitations of quartz, saponite and vermiculite (zone “1”). (ii) In the middle of the EBS, the volume of montmorillonite remains quite constant. The saponitization and the illitization processes can be distinguished in lower proportions as minor phase (zone “2”). (iii) The third alteration front is constituted by significant precipitations of FeIIAl chlorite, FeII saponite and magnetite in contact with the steel overpack. The strong precipitation of these phases decreases significantly the porosity of the EBS (zone “3”). The alteration front, corresponding to the area “1” extension, progresses with time. It is characterized by the illitization of the MX80 montmorillonite. The reaction is complemented with released silica incorporated in quartz precipitation at a temperature of 100 °C: 3+

Montmorillonite + 0:73Al + 0:6K + + 1:92H2 O f ð10Þ Illite + 0:18Na + + 0:1Ca2 + + 0:08Fe2 + + 0:09Fe3 + + 0:03Mg2 + + 0:48SiðOHÞ04 + 1:92H +

Several studies (e.g. Huang et al., 1993) show that the availability of potassium strongly controls the montmorillonite transformation. In our system the geological environment provides potassium through mass

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transport and the potassium ion concentration increases in the bentonite barrier. The EBS tries to preserve a low potassium concentration with the help of the montmorillonite illitization process (consumption of potassium). However the potassium concentration could have been overestimated in the groundwater (Marty, 2006; Gaucher et al., 2007). In the second part of the profile (zone “2” in Fig. 2), the potassium provided by dissolution of microcline and biotite allows illite neo-formation. However this potassium availability is limited by the amount of microcline and biotite in the bentonite, and illite can only precipitate in small quantities. Under the influence of magnesium concentration from the COX groundwater, and magnesium provided by the dissolution of the MX-80 montmorillonite, vermiculite can be oversaturated in zone “1”. The vermiculite formation is maintained according to the work of Drits et al. (1997) and Meunier et al. (2000) who suggested the possibility of smectite–illite–vermiculite interstratifications. In the major part of the modelled profile, smectite to saponite conversion appears. The mechanism can be described by the relation: Montmorillonite + 1:24Mg2 + + 1:07Fe2 + + 1:242H2 O f 3+ MgFeII Saponite + 0:18Na + + 0:1Ca2 + + 0:09Fe3 + + 0:91Al 0 + + 0:31SiðOHÞ4 + 1:24H

ð11Þ

The major part of iron and magnesium ions necessary to form MgFeII saponite could be extracted from groundwater diffusion and from biotite dissolution. In regard to Eqs.(10) and (11), the saponitization reaction releases the aluminium ions necessary for the formation of illite. The saponitization of the montmorillonite seems to be an early stage for the illitization process. The metallic corrosion provides iron which is incorporated in ferrous minerals mainly near the cell of the steel overpack corrosion (zone “3” in Fig. 2). A massive formation of smectites as ferrous saponites (FeII saponite) occurs that clogs the porosity. Some saponites including less iron precipitate in fewer proportions (MgFeII saponite). Chlorites (FeIIAl chlorite and MgAl chlorite) are stabilized near the steel over-pack. MgAl chlorite appears in a zone more distant from the canister (after the precipitation zone of FeIIAl chlorite). The neo-formation of a ferrous chlorite at 14 Å does not correspond to recent experiments where 14 Å

Fig. 2. Mineralogical evolution at 100 °C of the MX-80 bentonite (EBS) in contact with the Callovo-Oxfordian formation (COX) and with the modelling cell of the steel overpack corrosion.

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Fig. 3. Eh and pH evolutions in the engineered barrier system (EBS) in contact with the Callovo-Oxfordian formation (COX) with the modelling cell of the steel overpack corrosion.

chlorites are precipitated at temperatures over 100 °C (Guillaume, 2002). However, these experiments were performed during short time scales and the results are consequently difficult to extrapolate to our long term modelling evolution of the EBS. A slight neo-formation of greenalite appears near the metallic lining. This 7 Å mineral formation like laumontite and chrysotile are in good agreement with several experiments, e.g. Perronnet (2004). Na-phillipsite is identified as a transient mineral: the phase is completely dissolved after 20,000 years. The magnetite suggested as the main corrosion product of the iron (Andra, 2005a) is oversaturated in the cell of the MX-80 bentonite and stays directly in contact with the steel overpack. Due to the kinetic control of the growing phase extracted from experiments in homogeneous phase (Faivre et al., 2004) rather than heterogeneous phases, the precipitated volume of magnetite is limited. A strong neo-formation of this phase requires a high supersaturation. Then, the magnetite can massively precipitate only over the surface area of the steel overpack. Ferrous oxides in small layers are shown by Bataillon (1997) over an iron plate. The ferrous-clay precipitations consume aluminium from the interstitial fluid of the EBS. Then, the montmorillonite loses its initial thermodynamic stability and dissolves, providing aqueous aluminium necessary for the formation of FeII saponite and the FeIIAl chlorite. The precipitation of albite is predicted by the software up to 10,000 years. After this modelled period, due to aluminium consumption, the phase is dissolved and the released silica is incorporated in quartz. There are only rare occurrences of natural analogues of iron/clay interactions (Apted, 1992). They are mainly related to the instability of metallic iron under atmospheric conditions or in oxic soils. Some archaeological analogues have been studied (e.g. David, 2001; Neff et al., 2006), however corrosion conditions in these cases are far from those expected in the COX formation with higher temperatures and strongly reductive redox conditions. Recent long-term laboratory experiments will further help to constrain the behaviour of these systems (Ishidera et al., 2007) but the results are not yet completely available. However experimental approaches on short time scales (e.g. Perronnet, 2004) make available reaction pathways and reliable data for modelling the long-term transformation of the MX-80 bentonite.

tends to be imposed to the whole profile. For a given fugacity of oxygen (or hydrogen in reducing conditions), there is a linear negative correlation between pH and redox potential (Eh): Eh decreases with increasing pH. The heating of the COX groundwater (from 25 °C to 100 °C) is complemented by a decrease of the redox potential (from −176 mV to −300 mV). As for pH, the redox potential in the bentonite barrier is significantly influenced by the groundwater diffusion process (Fig. 3). The corrosion process (Eq. (1)) goes together with a release of hydroxide ions. These ions migrate into the bentonite under the influence of the effective diffusion (D), and generate an increase of pH values at the interface between the EBS and the steel overpack. After 10,000 years, the porosity clogging significantly decreases the mass transport by molecular diffusion. Then the migration of hydroxide ions decreases as a function of time, and the COX chemical conditions, at 100 °C, tend to be imposed in the EBS. In the cell which models the steel overpack corrosion, the chemical conditions remain quite unchanged (10.5 b pH b 11.5 and −650 mV b Eh b −700 mV). 5.3. Steel overpack alteration In order to model the EBS alteration in contact with the steel overpack, a cell simulates the iron corrosion. In that cell, only siderite and magnetite formations are kinetically processed. The alteration profile of the steel overpack is shown in Fig. 4. As already highlighted by Andra (2005a), magnetite is the main corrosion product in reducing conditions. Siderite precipitates but the corresponding volumes are low and cannot be distinguished in Fig. 4. The siderite precipitation is limited by the CO2 partial pressure which was not imposed at a given value during modelling. The radioactive waste disposal cell is isolated from the

5.2. Eh and pH evolutions The swelling clay buffer is considered as initially saturated with an equilibrated solution. During modelling, chemical parameters like pH and Eh are significantly modified. The consequences on mineralogy are significant and the EBS loses its initial thermodynamic stability. Eh and pH evolutions in the interacting fluid of the engineered barrier are shown on Fig. 3. The pH of the groundwater is 7.3 at a temperature of 25 °C (Gaucher et al., 2006). If the temperature of this fluid increases to 100 °C, the pH decreases to about 6.2. At the end of the simulation, this pH value

Fig. 4. Corrosion products formed in the modelling cell of the steel overpack alteration in reducing conditions.

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atmosphere and the geochemical system is supposed to exhaust its CO2 reserve. This is particularly true near the iron/clay interface where the porosity and the permeability are decreasing and make any renewal of aqueous CO2 quite impossible: magnetite and siderite are taking more volume in the pore space than the initial massive steel. Fig. 4 shows an increase of the container thickness due to the magnetite precipitation. Between the beginning and the end of the simulation, the corrosion rate decreases from 5 µm year− 1 to 0.2 µm year− 1. This rate evolution corresponds to the range of values estimated by Idemitsu et al. (2002) and Xia et al. (2005) who mention rates up to 20 µm year− 1 and down to 0.1 µm year− 1 depending on their experimental conditions. This simulated decrease of the corrosion rate can be explained by high values of pH (around 11) and iron concentrations, as well as by a weak accumulation of hydrogen in the cell, modelling the steel overpack alteration. The availability of hydroxide and ferrous ions as well as hydrogen is also linked to the porosity clogging at the iron/clay interface. Close to equilibrium, the corrosion rate, which is controlled by TST type kinetic, decreases. 6. Conclusions After 100,000 years of simulated mass transport-reaction, the KIRMAT model predicts mineralogical modifications of the engineered barrier in contact with the geological porewater, and with Fe(II) provided by the corrosion of the steel overpack. However, only outer parts of the simulated profiles are significantly affected. The dissolution of the montmorillonite contained in the MX-80 bentonite is mainly observed in the zone influenced by the groundwater mass transport and partly in a zone adjacent to the container. Despite neo-formations of illite, vermiculite, saponite and magnetite detected in the barrier, the predicted evolution of the porosity is limited overall in the main part of the EBS and the porosity even tends to decrease in the perturbed outer zones. A porosity clogging near the steel overpack significantly decreases the molecular diffusion. As a feedback effect, the influence of the iron corrosion on the EBS mineralogy then decreases as a function of time. Due to the adopted modelling strategy, the corrosion rate is not a constant parameter and decreases progressively from 5 to 0.2 µm year− 1. The confinement capacity of the engineered barrier is due to the high proportion of swelling phases. Following these simulations, under repository conditions for safety assessment of the EBS concept, the long term transformations should have only minor influences on the amount of montmorillonite. In our modelling, more than 60% of the initial montmorillonite is preserved after 100,000 years, and additional swelling minerals like vermiculite and saponites are formed. This transformation rate can also be considered as overestimated due to the fact that we used a fixed maximum temperature of 100 °C throughout the simulated interaction instead of progressively decreasing it. This will be considered in future simulations. Acknowledgments This research is a part of a Ph.D. study (N. Marty) initiated, followed and supported by Andra (Agence nationale pour la gestion des déchets radioactifs), the French national radioactive waste management agency, in the framework of its program on the geochemical behaviour of bentonite engineered barrier. We are grateful to Dr. Jordi Bruno and an anonymous reviewer for their helpful comments. References Acker, J.G., Bricker, O.P., 1992. The influence of pH on biotite dissolution and alteration kinetics at low temperature. Geochimica et Cosmochimica Acta 56, 3073–3092. Alekseyev, V.A., Medvedeva, L.S., Prisyagina, N.I., Meshalkin, S.S., Balabin, A.I., 1997. Change in the dissolution rates of alkali feldspars as a result of secondary mineral precipitation and approach to equilibrium. Geochimica et Cosmochimica Acta 61, 1125–1142.

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Alkattan, M., Oelkers, E.H., Dandurand, J.L., Schott, J., 1998. An experimental study of calcite and limestone dissolution rates as a function of pH from − 1 to 3 and temperature from 25 to 80 °C. Chemical Geology 151, 199–214. Andra, 2005a. Dossier 2005, référentiel des matériaux d'un stockage de déchets à haute activité et à vie longue. Matériaux à base d'argiles gonflantes. ANDRA Report n° CRPASCM040015T1.DOC. Andra, 2005b. Dossier 2005, Phenomenological evolution of a geological repository. ANDRA Report n° CRPADS040025. Apted, M.J., 1992. Natural analogues for predicting the reliability of the engineered barrier system for high-level waste. Journal of Geochemical Exploration 46, 35–62. Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Transactions of AIME 146, 54–61. Arvidson, R.S., Ertan, I.E., Amonette, J.E., Luttge, A., 2003. Variation in calcite dissolution rates: a fundamental problem? Geochimica et Cosmochimica Acta 67, 1623–1634. Bataillon, C., 1997. Etude des couches formées sur un acier XC38 corrodé en milieu argileux. CEA Report n° RT-SCECF 441. Bauer, A., Berger, G., 1998. Kaolinite and smectite dissolution rate in high molar KOH solutions at 35 and 80 °C. Applied Geochemistry 13, 905–916. Bildstein, O., Trotignon, L., Perronnet, M., Jullien, M., 2006. Modelling iron–clay interactions in deep geological disposal conditions. Physics and Chemistry of the Earth 31, 618–625. Bradbury, M.H., Baeyens, B., 1998. A physicochemical characterisation and geochemical modelling approach for determining porewater chemistries in argillaceous rocks. Geochimica et Cosmochimica Acta 62, 783–795. Busenberg, E., Plummer, L.N., 1986. A comparative study of the dissolution and crystal growth kinetics of calcite and aragonite. U.S. Geological Survey Bulletin 1578, 139–168. Cama, J., Ganor, J., Ayora, C., Lasaga, C.A., 2000. Smectite dissolution kinetics at 80 °C and pH 8.8. Geochimica et Cosmochimica Acta 64, 2701–2712. Chermak, J.A., Rimstidt, J.D., 1989. Estimating the thermodynamic properties (Gf and Hf) of silicate minerals at 298 K from the sum of polyhedral contributions. American Mineralogist 74, 1023–1031. Chermak, J.A., Rimstidt, J.D., 1990. Estimating the free energy of formation of silicate minerals at high temperatures from the sum of polyhedral contributions. American Mineralogist 75, 1376–1380. Chou, L., Wollast, R., 1984. Study of the weathering of albite at room temperature and pressure with a fluidized bed reactor. Geochimica et Cosmochimica Acta 48, 2205–2217. Chou, L., Wollast, R., 1985. Steady-state kinetics and dissolution mechanisms of albite. American Journal of Science 285, 963–993. David, D., 2001. Analogues archéologiques et corrosion. In: ANDRA (Ed.), collection Sciences et techniques, p. 80. Dove, P.M., 1994. The dissolution kinetics of quartz in sodium chloride solutions at 25 to 300 °C. American Journal of Science 294, 665–712. Drits, V.A., Lindgreen, H., Sakharov, B.A., Salyn, A.S., 1997. Sequence structure transformation of illite–smectite–vermiculite during diagenesis of Upper Jurassic shales, North Sea. Clay Minerals 33, 351–371. Faivre, D., Agrinier, P., Menguy, N., Zuddas, P., Pachana, K., Gloter, A., Laval, J.Y., Guyot, F., 2004. Mineralogical and isotopic properties of inorganic nanocrystalline magnetites. Geochimica et Cosmochimica Acta 68, 4395–4403. Fritz, B., 1975. Etude thermodynamique et simulation des réactions entre minéraux et solutions. Application à la géochimie des altérations et des eaux continentales. Sciences Géologiques, Mémoires 41, Strasbourg, France. Fritz, B., 1981. Etude thermodynamique et modélisation des réactions hydrothermales et diagénétiques. Sciences Géologiques, Mémoires 65, Strasbourg, France. Ganor, J., Huston, T.J., Walter, L.M., 2005. Quartz precipitation kinetics at 180 °C in NaCl solutions—implications for the usability of the principle of detailed balancing. Geochimica et Cosmochimica Acta 69, 2043–2056. Gaucher, E.C., Blanc, P., 2006. Cement/clay interactions — a review: experiments, natural analogues, and modeling. Waste Management 26, 776–788. Gaucher, E.C., Blanc, P., Bardot, F., Braibant, G., Buschaert, S., Crouzet, C., Gautier, A., Girard, J.P., Jacquot, E., Lassin, A., Negrel, G., Tournassat, C., Vinsot, A., Altmann, S., 2006. Modelling the porewater chemistry of the Callovian–Oxfordian formation at a regional scale. Comptes Rendus Geoscience 338, 917–930. Gaucher, E.C., Tournassat, C., Jacquot, E., Altmann, S., Vinsot, A., 2007. Improvements in the modelling of the porewater chemistry of the Callovian–Oxfordian formation. 3rd International Meeting Andra, Clays in natural & engineered barriers for radioactive waste confinement, Pore-water Chemistry, Lille, France,17–20 Sept. 2007, pp. 73–74. Gérard, F., 1996. Modélisation géochimique thermodynamique et cinétique avec prise en compte des phénomènes de transport de masse en milieu poreux saturés. PhD Thesis, Louis Pasteur University, Strasbourg, France, 250 p. Gérard, F., Clément, A., Fritz, B., 1998. Numerical validation of a Eulerian hydrochemical code using a 1D multisolute mass transport system involving heterogeneous kinetically controlled reactions. Journal of Contaminant Hydrology 30, 201–216. Guillaume, D., 2002. Etude expérimentale du système fer-smectite en présence de solution à 80 °C et 300 °C. PhD Thesis, Henri Poincaré University, Nancy, France, 210 p. Hayashi, H., Yamada, M., 1990. Kinetics of dissolution of noncrystalline oxides and crystalline clay minerals in a basic Tiron solution. Clays and Clay Minerals 38, 308–314. Hellmann, R.,1994. The albite-water system: Part I. The kinetics of dissolution as a function of pH at 100, 200 and 300 °C. Geochimica et Cosmochimica Acta 58, 595–611. Holmes, P.R., Crundwell, F.K., 2000. The kinetics of the oxidation of pyrite by ferric ions and dissolved oxygen: an electrochemical study. Geochimica et Cosmochimica Acta 64, 263–274. Huang, W.L., Longo, J.M., Pevear, D.R., 1993. An experimentally derived kinetic model for smectite-to-illite conversion and its use as a geothermometer. Clays and Clay Minerals 41, 162–177.

90

N.C.M. Marty et al. / Applied Clay Science 47 (2010) 82–90

Huertas, F.J., Caballero, E., Jiménez de Cisneros, C., Huertas, F., Linares, J., 2001. Kinetics of montmorillonite dissolution in granitic solutions. Applied Geochemistry 16, 397–407. Idemitsu, K., Yano, S., Xia, X., Inagaki, Y., Arima, T., Mitsugashira, T., Hara, M., Suzuki, Y., 2002. Diffusion behavior of iron corrosion products in buffer materials. Materials Research Society Symposia, Proceedings 713, 113–120. Ishidera, T., Ueno, K., Kurosawa, S., Suyama, T., 2007. Investigation of smectite alteration and form of iron corrosion products in compacted bentonite being in contact with carbon steel for ten years. 3rd International Meeting Andra, Clays in natural & engineered barriers for radioactive waste confinement, Alteration Processes, Lille, France, 17–20 Sept. 2007, pp. 269–270. Jacquot, E., 2000. Modélisation thermodynamique et cinétique des réactions géochimiques entre fluides de bassin et socle cristallin: application au site expérimental du programme européen de recherche en géothermie profonde (Soultz-sousForêts, Bas-Rhin, France). PhD Thesis, Louis Pasteur University, Strasbourg, France, 202 p. Kalinowski, B.E., Schweda, P., 1996. Kinetics of muscovite, phlogopite, and biotite dissolution and alteration at pH 1–4, room temperature. Geochimica et Cosmochimica Acta 60, 367–385. Knauss, K.G., Copenhaver, S.A., 1995. The effect of malonate on the dissolution kinetics of albite, quartz, and microcline as a function of pH at 70 °C. Applied Geochemistry 10, 17–33. Kopp, R.E., Humayun, M., 2003. Kinetic model of carbonate dissolution in Martian meteorite ALH84001. Geochimica et Cosmochimica Acta 67, 3247–3256. Kozaki, T., Sato, H., Sato, S., Ohashi, H., 1999. Diffusion mechanism of cesium ions in compacted montmorillonite. Engineering Geology 54, 223–230. Lehikoinen, J., Carlsson, J., Muurinen, A., Olin, M., Salonen, P., 1996. Evaluation of factors affecting diffusion in compacted bentonite. Materials Research Society Symposia Proceedings 412, 675–682. Leroy, P., 2005. Transport ionique dans les argiles. Influence de la microstructure et des effets d'interface. Application aux argilites du site de Bure (Meuse/Haute-Marne). PhD Thesis, Paul Cezanne University, Aix-Marseille, France, 222 p. Lopez, J., Romanek, C.S., 2004. Precipitation kinetics and carbon isotope partitioning of inorganic siderite at 25 °C and 1 atm. Geochimica et Cosmochimica Acta 68, 557–571. Madé, B., Clément, A., Fritz, B., 1994. Modeling mineral–solutions interactions: the thermodynamic and kinetic laws. Chemical Geology 84, 1347–1363. Maher, K., Steefel, C.I., DePaolo, D.J., Viani, B.E., 2006. The mineral dissolution rate conundrum: insights from reactive transport modeling of U isotopes and pore fluid chemistry in marine sediments. Geochimica et Cosmochimica Acta 70, 337–363. Malmström, M., Banwart, S., 1997. Biotite dissolution at 25 °C: the pH dependence of dissolution rate and stoichiometry. Geochimica et Cosmochimica Acta 61, 2779–2799. Marty, N., 2006. Modélisation couplée (transport-réaction) des interactions fluidesargiles et de leurs effets en retour sur les propriétés physiques de barrières ouvragées en bentonite. PhD Thesis, Louis Pasteur University, Strasbourg, France, 300 p. Meunier, A., Lanson, B., Beaufort, D., 2000. Vermiculitization of smectite interfaces and illite layer growth as a possible dual model for illite–smectite illitization in diagenetic environments: a synthesis. Clay Minerals 35, 573–586. Montes-H, G., Marty, N., Fritz, B., Clément, A., Michau, N., 2005a. Modelling of long-term diffusion-reaction in a bentonite barrier for radioactive waste confinement. Applied Clay Science 30, 181–198. Montes-H, G., Fritz, B., Clément, A., Michau, N., 2005b. Modeling of transport and reaction in an engineered barrier for radioactive waste confinement. Applied Clay Science 29, 155–171. Montes -H, G., Fritz, B., Clément, A., Michau, N., 2005c. A simplified method to evaluate the swelling capacity evolution of a bentonite barrier related to geochemical transformations. Applied Geochemistry 20, 409–422. Nakayama, S., Sakamoto, Y., Yamaguchi, T., Akai, M., Tanaka, T., Sato, T., Iida, Y., 2004. Dissolution of montmorillonite in compacted bentonite by highly alkaline aqueous solutions and diffusivity of hydroxide ions. Applied Clay Science 27, 53–65. Neff, D., Dillmann, P., Descostes, M., Béranger, G., 2006. Corrosion of iron archaeological artefacts in soil: estimation of the average corrosion rates involving analytical techniques and thermodynamic calculations. Corrosion Science 48, 2947–2970. Pearson, F.J., Arcos, D., Boisson, J.-Y., Fernandez, A.M., Gäbler, H.-E., Gaucher, E., Gautschi, A., Griffault, L., Hernan, P., Waber, H.N., 2003. Mont Terri project — geochemistry of water in the Opalinus clay formation at the Mont Terri Rock Laboratory. In: F.O.W.G. (Ed.), Geology Series, Bern.

Perronnet, M., 2004. Réactivité des matériaux argileux dans un contexte de corrosion métallique, application au stockage des déchets radioactifs en site argileux. PhD Thesis, Institut National Polytechnique de Lorraine, Nancy, France, 283 p. Rafal'Skiy, R.P., Prisyagina, N.I., Kondrushin, I.B., 1990. Reaction of microcline–perthite with aqueous solutions at 150 and 250 °C. Geochemistry International 27, 56–66. Rosanne, M., Mammar, N., Koudina, N., Prunet-Foch, B., Thovert, J.F., Tevissen, E., Adler, P.M., 2003. Transport properties of compact clays: II. Diffusion. Journal of Colloid and Interface Science 260, 195–203. Sali, D., 2003. Modélisation du comportement physico-chimique des argiles de barrières ouvragées au contact de solutions naturelles. PhD Thesis, Louis Pasteur University, Strasbourg, France, 241 p. Sato, H., Ashida, T., Kohara, Y., Yui, M., Sasaki, N., 1992. Effect of dry density on diffusion of some radionuclides in compacted sodium bentonite. Journal of Nuclear Science and Technology 29, 873–882. Sauzéat, E., Guillaume, D., Neaman, A., Dubessy, J., François, M., Pfeiffert, C., Pelletier, M., Ruch, R., Barres, O., Yvon, J., Villéras, F., Cathelinau, M., 2001. Caractérisation minéralogique, cristallochimique et texturale de l'argile MX80. ANDRA Report n° CRP0ENG01-001. Shillings, L.L., Drever, J.I., Brantley, S.L., Sun, Y., Oxburg, R., 1996. Rates of feldspar dissolution at pH 3–7 with 0–8 m M oxalic acid. Chemical Geology 132, 79–89. Soler, J.M., Lasaga, A.C., 1998. An advection–dispersion–reaction model of bauxite formation. Journal of Hydrology 209, 311–330. Torikai, Y., Sato, S., Ohashi, H., 1996. Thermodynamic properties of water in compacted sodium montmorillonite. Nuclear technology 115, 73–80. Trotignon, L., Hairapetian, T., Bildstein, O., Jullien, M., 2007. Evaluation of geochemical scenarios for iron/argillite interactions in a deep waste disposal: a sensitivity study on reaction rates and gas partial pressure. 3rd International Meeting Andra, Clays in natural & engineered barriers for radioactive waste confinement, Alteration Processes, Lille, France, 17–20 Sept. 2007, pp. 261–262. van Hees, P.A.W., Lundström, U.S., Mörth, C.M., 2002. Dissolution of microcline and labradorite in a forest O horizon extract: the effect of naturally occurring organic acids. Chemical Geology 189, 199–211. Velbel, M.A., 1993. Constancy of silicate–mineral weathering-rate ratios between natural and experimental weathering: implications for hydrologic control of differences in absolute rates. Chemical Geology 105, 89–99. Vieillard, Ph., 2000. A new method for the prediction of Gibbs free energies of formation of hydrated clay minerals based on the electronegativity scale. Clays and Clay Minerals 48, 459–473. Vieillard, Ph., 2002. A new method for the prediction of Gibbs free energies of formation of phyllosilicates (10 and 14 ) based on the electronegativity scale. Clays and Clay Minerals 50, 352–363. White, A.F., Perterson, M.L., 1990. Role of Reactive-Surface-Area Characterization in Geochemical Kinetic ModelsChemical Modeling of Aqueous Systems II. American Chemical Society, Washington DC. White, A.F., Brantley, S.L., 2003. The effect of time on the weathering of silicate minerals: why do weathering rates differ in the laboratory and field? Chemical Geology 202, 479–506. White, A.F., Blum, A.E., Bullen, T.D., Vivit, D.V., Schulz, M., Fitzpatrick, J., 1999. The effect of temperature on experimental and natural chemical weathering rates of granitoid rocks. Geochimica et Cosmochimica Acta 63, 3277–3291. Williamson, M.A., Rimstidt, J.D., 1994. The kinetics and electrochemical rate-determining step of aqueous pyrite oxidation. Geochimica et Cosmochimica Acta 58, 5443–5454. Xia, X., Idemitsu, K., Arima, T., Inagaki, Y., Ishidera, T., Kurosawa, S., Iijima, K., Sato, H., 2005. Corrosion of carbon steel in compacted bentonite and its effect on neptunium diffusion under reducing condition. Applied Clay Science 28, 89–100. Yokoyama, T., Banfield, J.F., 2002. Direct determinations of the rates of rhyolite dissolution and clay formation over 52,000 years and comparison with laboratory measurements. Geochimica et Cosmochimica Acta 66, 2665–2681. Zhang, Y., Grattoni, C.A., 1998. Comment on “Precipitation kinetics of calcite in the system CaCO3–H2O–CO2: the conversion to CO2 by the slow process H+ + HCO− 3 → CO2 + H2O as a rate limiting step” by W. Dreybrodt, L. Eisenlohr, B. Madry and S. Ringer. Geochimica et Cosmochimica Acta 62, 3789–3790. Zhu, C., 2005. In situ feldspar dissolution rates in an aquifer. Geochimica et Cosmochimica Acta 69, 1435–1453. Zysset, M., Schindler, P.W., 1996. The proton promoted dissolution kinetics of Kmontmorillonite. Geochimica et Cosmochimica Acta 60, 921–931.