A database of dissolution and precipitation rates for clay-rocks minerals

Applied Geochemistry 55 (2015) 108–118

Contents lists available at ScienceDirect

Applied Geochemistry journal homepage: www.elsevier.com/locate/apgeochem

A database of dissolution and precipitation rates for clay-rocks minerals Nicolas C.M. Marty a,⇑, Francis Claret a, Arnault Lassin a, Joachim Tremosa a, Philippe Blanc a, Benoit Madé b, Eric Giffaut b, Benoit Cochepin b, Christophe Tournassat a a b

BRGM, 3 Avenue Claude Guillemin, 45060 Orléans, France ANDRA, 1/7 Rue Jean Monnet, 92298 Châtenay-Malabry, France

a r t i c l e

i n f o

Article history: Available online 20 October 2014

a b s t r a c t Many geoscientific fields use reactive transport codes to set up and interpret experiments as well as to understand natural processes. Reactive transport codes are also useful to give insights in the long term evolution of systems such as radioactive waste repositories or CO2 storage sites, for which experiments cannot reach the targeted time scale nor the dimension of those systems. The consideration of kinetic reaction rates is often required to reproduce correctly the geochemical and transport processes of interest. However, kinetic data are scattered in the literature, making data and selection a tedious task. Kinetic parameters on a single system are also highly variable depending on data choice, interpretation and chosen kinetic modelling approaches, thus making inter-comparison of modelling studies difficult. The present work aims at proposing a compilation of kinetic parameters to overcome part of above cited problems. The proposed selection was done (i) to ensure consistency of data selection criteria and data treatment and (ii) to ease the use of common kinetic parameters that are independent of the chosen geochemical modelling code. For those two reasons, the kinetic formalism of the transition state theory (TST) was chosen. The selection of minerals is currently limited to those present in clay rich rocks and cements, reflecting the effort made at predicting the evolution of radioactive waste underground storage systems. Still, the proposed compilation should also be useful for other applications such as CO2 sequestration. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Over the past fifty years, numerical simulations have increasingly been used in geochemical studies. They are used to set up and interpret experiments, to understand natural processes (e.g. Appelo et al., 1998; Mayer et al., 2002; Soler, 2003; Steefel et al., 2005; Steefel and Lichtner, 1998; Steefel and MacQuarrie, 1996), and to predict the long-term behaviour of systems such as radioactive waste repositories (e.g. De Windt et al., 2008; Gaucher et al., 2004; Kosakowski et al., 2009; Kulik et al., 2013; Lu et al., 2011; Marty et al., 2010; Savage et al., 2002, 2010; Shao et al., 2009) or CO2 storage sites (e.g. Gherardi et al., 2012; Hellevang et al., 2013; Kang et al., 2010; Pruess et al., 2004; Trémosa et al., 2014). Reactive transport codes enable us to predict the geochemical behaviour over time scales that cannot be experimentally reproduced and/or for spatial dimensions that cannot be instrumented. Reactive transport models often need to consider reaction rates in order to represent out-of-equilibrium geochemical processes that ⇑ Corresponding author at: BRGM, D3E/SVP, 3 Avenue Claude Guillemin, F-45060 Orléans, Cedex 2, France. Tel.: +33 2 38 64 33 43; fax: +33 2 38 64 30 62. E-mail address: [email protected] (N.C.M. Marty). http://dx.doi.org/10.1016/j.apgeochem.2014.10.012 0883-2927/Ó 2014 Elsevier Ltd. All rights reserved.

occur in laboratory or natural environments (e.g. Appelo et al., 1998; Hellevang et al., 2013; Marty et al., 2010; Trémosa et al., 2014). Amongst existing models, the most popular must be the kinetic model based on the transition state theory (TST model) as described by Lasaga (1981). Other mechanistic models exist, such as ones based on activated surface complexes (Oelkers, 2001), the stepwave model (Lasaga and Luttge, 2001), and the nucleation theory (Dove et al., 2005). However, these formalisms which should be considered for their implementation in geochemical codes are complex and are often applicable to only the simplest cases (e.g. a single mineral phase) due their high computation cost. The use of kinetics in numerical models is facing several challenges. One of the difficulties comes from the representation of incongruent dissolution processes that have been reported for some minerals (Bickmore et al., 2001; Golubev et al., 2006; Kaviratna and Pinnavaia, 1994; Marty et al., 2011). In addition, the numerical representation of the evolution of surface roughness and area during the reaction is very uncertain. Several models calculate the evolution of the reactive surface area as a function of changes in the mineral reaction progress (Cochepin et al., 2008; Emmanuel and Berkowitz, 2005; Lichtner et al., 1996; Noiriel et al., 2009). Moreover, laboratory experimental rates and those

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

measured in situ vary by up to several orders of magnitudes (Lüttge et al., 2013; Marty et al., 2009; Velbel, 1990; White and Brantley, 2003; Zhu, 2005). Significant differences are also observed in similar experiments dealing with the same material. For Lüttge et al. (2013), these discrepancies cannot be attributed to experimental artifacts (analytical uncertainties, data acquisition methods, etc.). Authors identify extrinsic and intrinsic sources of rate variations (depending on the observation scale). Extrinsic sources come from heterogeneities (porosity, mineralogical and chemical compositions, etc.) inside the media that should be represented. From this point of view, their consideration is the responsibility of the modeler. Intrinsic sources of rate variations are also attributed to heterogeneities at the crystal scale (crystal-defect distributions, impurities, etc.). Only kinetic Monte-Carlo models are able to show a large variation in total rate over time (Lüttge et al., 2013). However, this method is limited at the crystal scale. Therefore, the use of TST kinetic models appears to be currently unavoidable for large-scale simulation, even if the use of a mean or rate-limiting value describing the reaction rate appears to be questionable. The purpose of this work is not to provide a realistic description of mechanisms involved in dissolution/precipitation processes (i.e. as done by Monte-Carlo models) since it aims a direct application in widely used geochemical codes currently (e.g. PhreeqC3, Parkhurst and Appelo, 2013; CrunchFlow, Steefel, 2009 and; Steefel et al., in press; ToughReact, Xu et al., 2006 and; Xu et al., 2011). Kinetic parameters are compiled in accordance with the TST formalism. We review below the general principles of reaction kinetics, especially the formalism used in many codes and we also refer to the criteria used to select the reaction rates (experimental data) to extract kinetic parameters. Compilations of kinetic parameters have already been proposed by Marini (2006) and Palandri and Kharaka (2004). The biggest compilation sums up rate parameters for over 70 minerals (i.e. Palandri and Kharaka, 2004). The data selection proposed here, was initially built to model the long-term evolution of clay-rocks (e.g. Callovian-Oxfordian argillites), clayey engineered barrier systems (EBS), and concrete materials. It contains a limited number of mineral phases (15) as compared to the database from Palandri and Kharaka (2004). However, the proposed compilation provides additional kinetic parameters such as those needed to describe the deviation of the kinetic rates as a function of the mineral deviation from equilibrium (DGr). In addition, the selection includes more recent literature data. The proposed database is freely available on http://www.thermochimie-tdb.com and will be updated when new data will be available. All selected experimental data points corresponding selected law can be viewed on a same graph, which enables the database user to criticise the choices made if necessary. Moreover, the database is available in different formats (PhreeqC, CrunchFlow, ToughReact, see electronic supplementary data or the website). 2. Theory and formalism of kinetic laws (TST) 2.1. General expression of the reaction rate The reaction rates taken into consideration by most codes come from the transition state theory (TST). Numerous geochemical codes use the general equation given by Lasaga (1998):

 g r n ¼ kn Sn 1  Xhn 

ð1Þ

where the positive values of rn (mol s1 kg w1) denote dissolution reactions and negative values denote precipitation of the mineral n, kn is the kinetic dissolution or precipitation rate constant (mol m2 s1), Sn is the reactive surface area (m2 kg w1), and Xn

109

is the saturation ratio. The two parameters h and g empirically describe the dependence of the reaction rate on the saturation ratio. Eq. (1) clearly shows that the reaction rate (r) depends on the saturation of the solution (X) and on the reactive surface area (S) for the mineral under consideration. However, the kinetic parameters (k and probably h and g) can vary with the environment in which the reaction takes place depending on the physical and chemical conditions such as pH, temperature or the concentration in a given species as describe hereafter (i.e. catalytic or inhibitory effect). 2.2. Dependence on saturation state The two parameters h and g in Eq. (1) convey the dependence of the dissolution or precipitation rate on the saturation ratio. These two parameters are empirical. They are determined by minimising the variance between the kinetic model and the experimental data taken from the literature. The saturation ratio is expressed by the equation:

X¼

IAP K

ð2Þ

where IAP is the ion activity product calculated from the activities of the dissolved mineral constituents under consideration and K is the solubility product. The free enthalpy of reaction (DGr in J mol1) is linked to the saturation ratio by the following relationship:

DGr ¼ RT ln

  IAP K

ð3Þ

With regard to Eq. (1), the precipitation rate increases with the saturation ratio of the mineral. In contrast, the dissolution rate is independent of the free enthalpy of reaction when placed far from equilibrium, but diminishes close to equilibrium. At thermodynamic equilibrium, DGr is equal to 0 and the reaction rate can be considered to be zero. The two parameters h and g (Eq. (1)) are equal to 1 for ‘‘simple’’ minerals such as quartz or anorthite (Schott and Oelkers, 1995). However, these parameters must be adjusted if we wish to reproduce dissolution rates for more ‘‘complex’’ minerals such as phyllosilicates (e.g. Cama et al., 2000). 2.3. Dependence on temperature The temperature dependence of the dissolution or precipitation rate of a mineral can be described by an Arrhenius-type law:

kT ¼ A exp

  Ea RT

ð4Þ

where Ea is the reaction activation energy (J) and A is the frequency factor (m2 s1). R is the ideal gas constant (8.314 J mol1 K1) and T is the reaction temperature (K). By measuring the reaction rate at different temperatures, we can verify that the logarithm of the rate constant is a linear function of 1/T. The activation energy is generally calculated from rates obtained far from thermodynamic equilibrium. Estimation of the activation energy does not, therefore, depend on the thermodynamic database used. 2.4. pH effect on reaction rate Most geochemical codes use two types of kinetic models to account for variations in dissolution rates according to pH. In the first type of model (the simplest of the two), the dissolution rate constant (k in Eq. (1)) is estimated by linear regression over distinct pH ranges (Fig. 1), while the second model uses a regression curve valid over the entire pH range:

110

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

-5

log (reaction rate)

-6 -7 -8

Input rate = 10-9

slope1 = 1.0

-9

slope2 = 0.5

-10

pH1 = 4

pH2 = 8

-11 0

2

4

6

8

10

12

pH Fig. 1. Linear regression model after Xu et al. (2004).

  X Enu 1 1 i a þ  k25 T 298:15 R i "  #Y Eia 1 1 n  exp  aijij R T 298:15 j nu

k ¼ k25 exp



ð5Þ

where k25 is the intrinsic kinetic constant at 298.15 K (25 °C), nu refers to a neutral environment, i refers to additional mechanisms (e.g. silica inhibition), and j to the species involved in the mechanism i. The term a is the activity of the species j to the power of n. By excluding additional mechanisms, the pH dependence can be expressed by:

"    # Enu 1 1 EHa 1 1 H a þ k25 exp anHH k¼ exp   T 298:15 T 298:15 R R "  # EOH 1 1 OH a OH anOH þ k25 exp  ð6Þ T 298:15 R nu k25



As imposed in ToughReact (Xu et al., 2006, 2011) the first model considers one activation energy (Ea) only over the whole range of pH. In contrast the regression curve can consider one activation energy per mechanism (acid, neutral and basic). The effect of pH on the mineral dissolution rate is well documented in the literature. The process can be easily studied far from thermodynamic equilibrium. Under these conditions, the saturation ratio tends towards 0 (the free enthalpy of reaction tends towards 1) and the dissolution kinetics no longer depends on the saturation ratio. Eq. (1) can then be simplified to:

r n ¼ k n Sn

ð7Þ

Far from thermodynamic equilibrium, the dissolution rate constant is equal to the dissolution rate in relation with the surface area, kn = rn/Sn (in mol m2 s1). It is worth noting that mechanisms involving the influence of species other than H+ and OH can also be added to the dissolution rate constant (Eq. (5)) for specific minerals. For example, a depen dence on CO 3 and HCO3 species is often observed for carbonate minerals. 3. Reactive surface area 3.1. Primary phases The observations of grain dissolution clearly indicate that the dissolution process occurs in a heterogeneous manner at the surface of a mineral (Berner and Schott, 1982; Grandstaff, 1978; Lüttge et al., 2013). Different parts of the surface of the mineral are dissolved at different rates. Only one portion of the mineral

surface can be dissolved, the other being considered to be inert. The mineral surface directly involved in the dissolution/precipitation mechanism is called the reactive surface area (Hochella and Banfield, 1995) or effective surface area (Helgeson et al., 1984). It is significantly less than the total surface of the mineral under consideration. However, the notion is subject to debate (depending on the family of the mineral). Some authors consider that this is the area occupied by high-energy sites, such as defects or dislocations. To test this possibility, studies have linked changes in dissolution rates with dislocation densities, i.e. Casey et al. (1988a) for rutile and Schott et al. (1989) for calcite. None of these studies have shown an increase in dissolution rates beyond a factor of two while the dislocation densities vary by up to five orders of magnitude. Atomic force microscopy (AFM) makes possible the study of the surfaces involved in the precipitation or dissolution mechanisms for scales varying from the nanometre to the micrometre. It has been shown that montmorillonite dissolves mainly from its edge surface areas under basic conditions (Bickmore et al., 2001; Bosbach et al., 2000; Metz et al., 2005b; Murakami et al., 2003; Oelkers, 2001; Tournassat et al., 2003; Yokoyama et al., 2005). This shows how difficult it is to take into consideration mineral surface areas in order to normalise the dissolution or precipitation rates. In most cases, the direct measurement of the surface using nitrogen or krypton with the BET method (Brunauer–Emmett–Teller) is assumed to provide the reactive surface area (Oelkers and Schott, 1995; Oelkers et al., 1994). However, in some cases (e.g. clays), BET normalised rates are inappropriate. One of the main reasons is that the BET measurement is done with dried samples in which clay layers have collapsed to form aggregates of approximately 10– 30 T-O-T layers. In contrast, experimental smectite dissolution occurs in aqueous suspensions where the montmorillonite T-O-T layers are expected to expand and exhibit particles of only one to two T-O-T layers (Schramm and Kwak, 1982a, 1982b; Sposito, 1992). Therefore, in the particular case of clays, rates were normalised to the mass in order to facilitate the comparison of data originating from various sources. The dissolution rates of smectites, illites, chlorites and micas normalised to mass are very similar (Rozalén et al., 2008), whereas rates converted to per-unit area (mol m2 s1) are very different. The parameters from this compilation are then re-normalised with surface area supposed as reactive so that they can be used in most codes (e.g. code constraint in ToughReact). In addition to these difficulties to identify the reactive surface area at the surface of a mineral, it is worth noting that the surface exhibited to the solution in a porous media is different from the surface exhibited by crushed samples at the laboratory or by individual minerals. Moreover, the formation of coatings, surface passivation or the desaturation of the rock can lead to big differences in reactive surface areas in the field and in the laboratory (e.g. Cubillas et al., 2005; Ganor et al., 2005; Helgeson et al., 1984). However this problem is specific to each studied system and it must be treated when defining geochemical/reactive transport model. This is not relevant for a generic database.

3.2. Secondary phases By definition, secondary phases are initially absent from the considered system. Theoretically, those minerals do not have a reactive surface until they have nucleated, which obviously makes it impossible for the precipitation process to begin according to Eq. (1) (if S = 0 then r = 0). Very few codes are able to handle the numerical formalism for nucleation and growth of minerals (e.g. Fritz et al., 2009) and those calculations have usually a high computation cost. A pragmatic approach was chosen that can be handled by most of reactive transport codes: oversaturation must be

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

greater than the critical oversaturation threshold and an existing surface area is assumed to initiate the precipitation of minerals: – either by setting the radius of the spheres while varying the number of nuclei; – or by assuming a fixed number of spheres while varying its radius. It may also be possible to consider a minimum volume fraction (set by the user) or fix an initial precipitation rate (mol s1) to initiate the precipitation process. In the first case, the user must provide a reactive surface (usually m2 g1) to calculate the total surface area reacting with the interstitial fluid of the porous medium (m2 m3 of medium or m2 kg w1).

4. Kinetic data selection The selected data comply as well as possible with the pressure and temperature ranges considered for the storage of radioactive waste (i.e. T < 100 °C and P < 100 bars). The selection depends directly on the parameters to be estimated (i.e. kinetic dissolution, precipitation rate constant, activation energy, etc.). Three types of selection are considered, depending on the process to be modelled: – dependence on pH, with the selected data covering a pH range as large as possible; – dependence on temperature, preferentially selecting data in temperatures that incorporate the effect of pH; – dependence on the saturation ratio. The selection was done according to the acquisition method, the stoichiometry of the reaction, and the dispersion of data that can be extracted from the literature. 4.1. Acquisition methods Stirred flow-through reactor experiments allow a good control of reaction thermo-chemical conditions (e.g. using an input buffered solution). Rates resulting from this kind of experiment were then preferentially selected. The experimental setup makes it possible to estimate reaction rates when steady state is reached. In the case of a congruent reaction (stoichiometric), the following equation is verified (Lasaga, 1998):

dNi ¼ 0 ¼ v ðC out  C in Þ þ ei Sn kn dt

ð8Þ

where Ni is the amount of the specie i (mol), t is the time (s), v is the flow rate (L s1), Cout  Cin is the difference between the inlet and outlet concentrations (mol L1), e is the stœchiometry of the specie i inside the mineral n, S is the reactive surface of the mineral (m2 L1) and k is the kinetic constant (mol m2 s1). Therefore:

kn ¼

v ðC out  C in Þ ei Sn

ð9Þ

In the case of experiments performed with batch reactors, the reaction rate varies with time until thermodynamic equilibrium or steady state is reached. The reaction rate is determined from the tangent to the curve of evolution of the concentration versus time. The slope of the tangent decreases with the reaction time and the reaction rate is equal to 0 at thermodynamic equilibrium (Eq. (1)). The calculation method is sensitive to measurement uncertainty and analysis frequency.

111

4.2. Stoichiometry of the reaction In the cases of incongruent dissolution or incongruent precipitation, kn in Eq. (8) must be replaced by ki, which is the reaction rate of the species (Lasaga, 1998). Mechanisms involved and responsible for these reactions must be clearly identified, e.g. cation–proton exchanges inside octahedral-layer structures in the case of feldspars (Casey et al., 1988b) or smectites (Golubev et al., 2006) alterations. However, any quantification of kinetic rates under such conditions is risky. 4.3. Dispersion of experimental data Strong scattering of kinetic data can be observed even with experimental rates measured under similar conditions. However, this variability seems to decrease with increasing temperature. This is possibly due to a decrease in the analytical errors (because the measured concentration values are higher) as well as an improvement in the congruency of the reactions (e.g. Marty et al., 2011). A simple arithmetic average was used when there was a lack of sorting criteria (like the experimental design). Fitted models and experimental rates were systematically compared (http://www.thermochimie-tdb.com). 4.4. Consistency of the kinetic compilation with the thermochimie database Reaction rates are defined with respect to given reactions and since the equilibrium constant term is involved in the equation of the rate, the thermodynamic data used for the calculation will impact the constant that is obtained from experimental results. The rate law constants are consistent with the thermodynamic database (TDB) under consideration, THERMOCHIMIE (Giffaut et al., in press), within the previously defined pressure and temperature ranges. Values also depend on the structural formula considered, which must be the same in both the database and the reaction under consideration. For example structural formulas have to display the same number of oxygen atoms (for instance smectite or illite clay minerals display, 12 oxygen atoms for – O10(OH)2 based formula or 24 oxygen atoms for –O20(OH)4 based formula as a function of database). 5. Data treatment example: montmorillonite dissolution rates The case of montmorillonite is chosen to illustrate the work done for kinetic rate law selection because of its particular relevancy (e.g. Marty et al., 2010, 2009). 5.1. Reactive surface area Several authors have shown that di-octahedral smectites in a basic environment dissolve for the most part at their lateral surfaces (e.g. Yokoyama et al., 2005). Accordingly, the lateral surface (ESA) represents the reactive surface area better than that measured by BET, most of which would not play any direct role in the dissolution mechanism (Tournassat et al., 2003). Based on the work of Sayed Hassan et al. (2006), Yokoyama et al. (2005) and Tournassat et al. (2003), a reactive surface area of 8.5 m2 g1 was used to normalise the kinetic constants. Marty et al. (2011) used AFM to measure an ESA of 6.2 m2 g1 for montmorillonite purified from MX80 bentonite. This surface area is about 3–4 times less than that of illite, which can appear in lattice or pseudo-hexagonal form. As the idea of a reactive surface is still subject to debate (particularly for clay minerals), the dissolution rate constants were first estimated from experimental data normalised

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

with respect to the mass. Then, for use in most codes, these constants were re-normalised by the surface area assumed to be reactive (i.e. 8.5 m2 g1). 5.2. Linear-regression model It is difficult to propose a model from values obtained at 25 °C because these are extremely scattered. Golubev et al. (2006) and Marty et al. (2011) reported that the alteration of di-octahedral smectite is not done congruently at 25 °C under close to neutral conditions. There are still uncertainties regarding the dissolution mechanism. However, the congruence of the reaction is respected at 80 °C (Cama et al., 2000). In the case of montmorillonite, data measured at 50 °C were selected in order to establish the pH dependence of the dissolution rate. The linear regression model was normalised with respect to the mass, from Yokoyama et al. (2005), Metz et al. (2005a), Amram and Ganor (2005) and Rozalén et al. (2009). At this temperature, uncertainties decrease. Fitted linear regressions are shown in Fig. 2 for acidic and basic conditions. Only data dealing with montmorillonitic smectites have been selected. The dissolution rate constant in a neutral environment was calculated at 50 °C from the lowest rates measured by Rozalén et al. (2009) and Amram and Ganor (2005). The selected values are given in Table 1. The activation energy used for the linear regression was based on data obtained at 25 and 70 °C by Rozalén et al. (2008) and Rozalén et al. (2009). Fitted rate laws were systematically compared to experimental datasets which are different from those selected for the parameterisation of the rate laws (Fig. 3). Kinetic data shown in Fig. 3 deal mainly with montmorillonitic smectites. However, for a comparison purpose, some experiments performed on other di-octahedral or tri-octahedral smectites have been plotted (e.g. data of Bosbach et al., 2000 for hectorite). In contrast, with the next model (see Section 5.3, regression curve model), only one activation energy is calculated with the least square method over the entire pH range. Estimated kinetic parameters are given in Table 2 (for a ToughReact formalism). The constant k25 is normalised, assuming a reac-

-8.0

Rozalèn et al. (2009) Yokoyama et al. (2005) Metz et al. (2005) Amram & Ganor (2005) Rozalèn et al. (2009) Rozalèn et al. (2009) Amram & Ganor (2005)

log r (mol g -1 s-1)

-9.0

-10.0

Table 1 Parameters selected for calculating the dissolution rate of montmorillonitic smectite in a neutral environment at 50 °C. pH

Log r (mol g1 s1)

Source

6.1 7.2 7.8 5.5 Average

12.0 11.7 11.9 11.8 11.8

Rozalén et al. (2009) Rozalén et al. (2009) Rozalén et al. (2009) Amram and Ganor (2005)

1.0E-06

80°C, Bauer & Berger (1998) 80°C, Nakayama et al (2004) 70°C, Amram & Ganor (2005) 60°C, Huertas et al (2001) 50°C, Yokoyama et al (2005) 50°C, Rozalèn et al. (2009) 35°C, Bauer & Berger (1998) 30°C, Yokoyama et al (2005) 25°C, Rozalén et al (2008) 25°C, Zysset & Schindler (1996) 20°C, Huertas et al (2001)

1.0E-07 1.0E-08

r (mol g-1 s-1)

112

80°C, Cama et al. (2000) 70°C, Yokoyama et al (2005) 70°C, Rozalèn et al. (2009) 50°C, Metz et al (2005) 50°C, Amram & Ganor (2005) 40°C, Huertas et al (2001) 35°C, Nakayama et al (2004) 25°C, Golubev et al (2006) 25°C, Amram & Ganor (2005) 22°C, Bosbach et al (2000)

1.0E-09 70°C

1.0E-10

50°C

1.0E-11 25°C

1.0E-12 1.0E-13 1.0E-14 0

2

4

6

8

10

12

14

pH Fig. 3. Linear regression model for montmorillonite dissolution kinetics. The experimental data for di-octahedral smectites were taken from Bauer and Berger (1998), Nakayama et al. (2004), Cama et al. (2000), Amram and Ganor (2005), Yokoyama et al. (2005), Rozalén et al. (2008, 2009), Huertas et al. (2001), Metz et al. (2005a), Zysset and Schindler (1996), Bosbach et al. (2000) and Golubev et al. (2006).

Table 2 Linear regression model for the montmorillonitic smectite dissolution rate. The kinetic constants were normalised, assuming a reactive surface area of 8.5 m2 g1 (Sayed Hassan et al., 2006; Tournassat et al., 2003; Yokoyama et al., 2005). pH1 pH2 Slope1 Slope2

4.7 7.9 0.69 0.34

k25 (mol m2 s1) Ea (kJ mol1)

2.4  1014 63

tive surface area of 8.5 m2 g1 (Sayed Hassan et al., 2006; Tournassat et al., 2003; Yokoyama et al., 2005).

-11.0 y = 0.34x -14.52 R² = 0.91

y = -0.69x - 8.60 R² = 0.90

-12.0

-13.0

-14.0 0

2

4

6

8

10

12

14

pH Fig. 2. Data selected to calculate the linear-regression model for montmorillonite dissolution kinetics. The experimental values were taken from Yokoyama et al. (2005), Metz et al. (2005a), Amram and Ganor (2005) and Rozalén et al. (2009). Red, grey and blue symbols refer to acidic, neutral and basic conditions, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

5.3. Regression curve model To ensure consistency with the previous model and in order to limit the number of variables, slopes of straight lines obtained in acidic and basic environments were retained (Fig. 2). As with the linear regression model, the regression curve is based on data for 50 °C from Yokoyama et al. (2005), Metz et al. (2005a), Amram and Ganor (2005), and Rozalén et al. (2009). The constants in acidic, neutral and basic environments were calculated using the least squares method in order to minimise differences between the model and the data extracted from the literature (Fig. 4). The activation energies in acidic and basic environments were calculated by minimising the variance between the regression curve and the data for 25 °C and 70 °C from Rozalén et al. (2008) and Rozalén et al. (2009). The activation energy in a neutral envi-

113

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

-8.0

-9.0

log r (mol g-1 s-1)

Table 3 Regression curve model for the montmorillonitic smectite dissolution rate. The kinetic constants were normalised, assuming a reactive surface area of 8.5 m2 g1 (Sayed Hassan et al., 2006; Tournassat et al., 2003; Yokoyama et al., 2005).

Rozalèn et al. (2009) Yokoyama et al. (2005) Metz et al. (2005) Amram & Ganor (2005) Rozalèn et al. (2009)

-10.0

kneutral (mol m2 s1) 25

9.3  1015

Eaneutral (kJ mol1)

63

2 1 s ) kH 25 (mol m

5.3  1011

H

-11.0

-12.0

1

Ea (kJ mol ) nH 2 1 kOH s ) 25 (mol m

54 0.69 2.9  1012

EaOH (kJ mol1)

61

nOH

0.34

-13.0 Table 4 Parameters selected for incorporating montmorillonitic smectite dissolution kinetics: deviation at equilibrium.

-14.0 0

2

4

6

8

10

12

14

pH

Domain of validity

Fig. 4. Regression curves based on experimental data for 50 °C from Yokoyama et al. (2005), Metz et al. (2005a), Amram and Ganor (2005) and Rozalén et al. (2009). The dissolution constants (k in Table 3) were calculated by minimising the differences between the model (curve) and the experimental data. Red and blue symbols refer to acidic and basic conditions, respectively. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

1.0E-06

80°C, Bauer & Berger (1998) 80°C, Nakayama et al (2004) 70°C, Amram & Ganor (2005) 60°C, Huertas et al (2001) 50°C, Yokoyama et al (2005) 50°C, Rozalèn et al. (2009) 35°C, Bauer & Berger (1998) 30°C, Yokoyama et al (2005) 25°C, Rozalén et al (2008) 25°C, Zysset & Schindler (1996) 20°C, Huertas et al (2001)

1.0E-07

r (mol g-1 s-1)

1.0E-08

80°C, Cama et al. (2000) 70°C, Yokoyama et al (2005) 70°C, Rozalèn et al. (2009) 50°C, Metz et al (2005) 50°C, Amram & Ganor (2005) 40°C, Huertas et al (2001) 35°C, Nakayama et al (2004) 25°C, Golubev et al (2006) 25°C, Amram & Ganor (2005) 22°C, Bosbach et al (2000)

80 °C and pH 8.8 25 °C and pH 9.0

0.17 10.34

h

g

Parameters h and g are shown in Table 4 together with their fields of validity. The effect of the saturation ratio (g and h) was calculated to minimise the differences between the model and the experimental data. Knowing the reaction rate (experimental data), the reactive surface area, the free enthalpy of reaction, and having estimated the empirical parameters h and g, it is possible to recalculate the intrinsic kinetic constant (k). By definition, its value must be independent of the saturation ratio of the solution (Fig. 6).

1.0E-09 70°C

1.0E-10

50°C

1.0E-11

6. Kinetic data compilation 6.1. Overview

25°C

1.0E-12 1.0E-13 1.0E-14 0

2

4

6

8

10

12

14

The procedure described in Sections 4 and 5 have been applied to 15 minerals of interest in the context of radioactive waste storage in clay-rocks. The resulting dissolution rate parameters for the linear model are given in Table 5 and those for the regression curve model are given in Table 6. Given the dispersion of experimental

pH 1.E-07

Fig. 5. Regression curve model for smectite dissolution kinetics. The experimental values were taken from Bauer and Berger (1998), Nakayama et al. (2004), Cama et al. (2000), Amram and Ganor (2005), Yokoyama et al. (2005), Rozalén et al. (2008, 2009), Huertas et al. (2001), Metz et al. (2005a), Zysset and Schindler (1996), Bosbach et al. (2000) and Golubev et al. (2006).

5.4. Deviation of the dissolution rate close to the thermodynamic equilibrium The deviation of the di-octahedral smectite dissolution rate at equilibrium was studied by Cama et al. (2000) at 80 °C and pH 8.8. Their data were converted in order to (i) comply with the ToughReact formalism and (ii) be consistent with the THERMOCHIMIE TDB (i.e. IAP have been re-calculated and –O10(OH)2 based formula has been considered). The law taken from Cama et al. (2000) can also be applied at 25 °C and pH 9 (Marty et al., 2011).

1.E-08

k (mol g-1 s-1)

ronment obtained for the previous model was retained. Fig. 5 shows the entire kinetic data set listed under this compilation. The kinetic parameters for the regression curve are summarised in Table 3.

θ = 0.17 η = 10.34

1.E-09

1.E-10

1.E-11 -100

-80

-60

-40

-20

0

ΔGr (kJ mol-1) Fig. 6. Intrinsic kinetic constant (k) at 80 °C calculated vs. the Gibbs free energy (DGr) of the dissolution reaction of smectite. The data were mass normalised. Experimental values come from Cama et al. (2000).

114

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

Table 5 Selected parameters for the dissolution rate model: linear regression model. Kinetic constants (k) are expressed in mol m2 s1 and the activation energy (Ea) in kJ mol1. Mineral

Type of surface normalisation

Albite Biotite Celestine Chlorite Cristobalite C–S–H Dolomite Illite Kaolinite Microcline Portlandite Quartz Siderite Montmorillonite a

k25 12

BET BET BET 0.2% BETa BET BET BET ESA BET BET BET BET BET ESA

1.3  10 1.9  1012 8.2  1008 1.0  1010 1.0  1013 8.3  1012 1.1  1008 5.1  1015 2.2  1014 6.9  1013 2.5  1008 1.0  1013 2.5  1009 2.4  1014

pH1

Slope1

pH2

Slope2

Ea

5.6 4.8 12.6 6.9 0.0 14.0 7.4 6.2 5.3 5.3 8.8 0.0 5.7 4.7

0.34 0.67 0.10 0.28 0.00 0.28 0.61 0.52 0.51 0.27 0.60 0.00 0.60 0.69

7.5 7.9 14.0 8.2 4.0 14.0 14.0 7.0 8.4 7.4 14.0 4.0 14.0 7.9

0.32 0.79 0.00 0.32 0.34 0.00 0.00 0.38 0.58 0.35 0.00 0.34 0.00 0.34

57 49 34 16 69 23 31 35 38 31 75 77 56 63

Brandt et al. (2003) used AFM to identify the reactive surface area of chlorite. It corresponds to 0.2% of the measured BET surface.

Table 6 Selected parameters for the dissolution rate model: regression curve model. Kinetic constants (k) are expressed in mol m2 s1 and the activation energy (Ea) in kJ mol1. Mineral Albite Biotite Celestite Chlorite C–S–H Cristobalite Dolomite Gibbsite Illite Kaolinite Microcline Portlandite Quartz Siderite Montmorillonite a

Type of surface normalisation

k25nu

Enu a 20

BET BET BET 0.2% BETa BET BET BET BET ESA BET BET BET BET BET ESA

5.1  10 2.3  1012 2.2  1008 6.4  1017 1.6  1018 6.4  1014 1.1  1008 3.3  1017 1.1  1014 1.0  1014 2.2  1008 6.4  1014 2.1  1009 9.3  1015

57 49 34 16 23 69 31 35 38 31 75 77 56 63

kH+ 25

EaH+ 11

8.5  10 1.1  1009 1.4  1006 8.2  1009 5.9  1008

58 49 33 17 23

nH+ 0.34 0.67 0.10 0.28 0.28

EaOH

nOH

10

1.4  10 9.1  1008

56 49

0.32 0.79

6.9  1009

16

0.34

10

69

0.34

06

3.1  10 3.1  1012 2.5  1011 1.4  1010

48 48 46 31

1.0 0.38 0.58 0.35

1.9  1010

80

0.34

12

61

0.34

kOH 25

1.9  10 2.8  1004

46

0.61

9.8  1012 7.5  1012 1.7  1011 8.0  1004

36 43 31 75

0.52 0.51 0.27 0.60

5.9  1006 5.3  1011

56 54

0.60 0.69

2.9  10

Brandt et al. (2003) used AFM to identify the reactive surface area of chlorite. It corresponds to 0.2% of the measured BET surface.

data, it is not possible to recommend one model rather than another. Both models use the same deviations close to equilibrium for the dissolution processes. Values of h and g parameters associated with their domains of validity are given in Table 7. The parameters for the precipitation kinetics are given in Table 8. Kinetic data selection furnishes information only for some

Table 7 h and g parameters associated with their domains of validity. Mineral

h

g

Remarks

Albite

0.48 0.18 0.76 1 0.49 1 1 1 0.16 1 1 1 0.09 1 1 1 0.17

100 5 96 1 2.06 1 1 1 2.10 1 1 1 2.35 1 1 1 10.34

80 °C and pH  9 150 °C and pH  9 300 °C and pH  9 Default 25 °C and pH  5 Default Default 0 < T < 300 °C and 0 < pH < 14 80 °C and pH  7 50 °C and pH  9 Default Default 150 °C and pH  9 Default 0 < T < 300 °C and 0 < pH < 14 Default 25 < T < 80 °C and pH  9

Biotite Celestite Chlorite C–S–H Cristobalite Dolomite Gibbsite Illite Kaolinite Microcline Portlandite Quartz Siderite Montmorillonite

precipitation processes. Indeed, difficulties in the measurement of precipitation rates increase with the number of elements included in the structural formula of the studied mineral. In this case, the formation of several minerals may occur at the same time, which makes the estimation of reactions rates uncertain. Therefore, the few studies of precipitation rates are limited to ‘‘simple’’ minerals (e.g. quartz, calcite, gibbsite). Moreover, an amorphous form of the studied mineral may precipitate, distorting the estimation of the free enthalpy of reaction, and then the estimation of the reaction rate. 6.2. Particular case: pyrite dissolution The pyrite contained in the Callovian-Oxfordian argillites, under investigation as a potential host rock for a radioactive waste repository, is expected to react under oxidised conditions following the construction and ventilation of tunnels and galleries (Belcourt, 2009). The reaction of pyrite dissolution appears to be an electrochemical process (Cabral and Ignatiadis, 2001; Holmes and Crundwell, 2000; McKibben and Barnes, 1986; Williamson and Rimstidt, 1994). Therefore, the overall reaction is written in terms of half reactions. Holmes and Crundwell (2000) have considered the pyrite oxidation by ferric ions and oxygen to be: þ FeS2 þ 8H2 O þ 14Feþþþ ! 15Feþþ þ 2SO 4 þ 16H

ð10Þ

þ 2FeS2 þ 2H2 O þ 7O2 ! 2Feþþ þ 4SO 4 þ 4H

ð11Þ

115

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118 Table 8 Selected parameters for the precipitation rate model. Kinetic constants (k) are expressed in mol m2 s1 and the activation energy (Ea) in kJ mol1. Mineral

k25pre

Type of surface normalisation

Calcite Celestite C–S–H Cristobalite Dolomite Gibbsite Kaolinite Quartz Siderite

Epre a 07

BET BET BET BET BET BET BET BET BET

1.8  10 5.1  1008 1020 3.2  1012 9.5  1015

66 34 23 53 103

5.5  1013 3.2  1012 1.6  1011

66 50 108

The ferrous ions thus produced are oxidised by oxygen according to:

4Feþþ þ O2 þ 4Hþ ! 4Feþþþ þ 2H2 O

ð12Þ

From electrochemical measurements and theory, the overall reaction kinetics given by Holmes and Crundwell (2000) is written as:

r FeS2 ¼ k½Hþ 

kFeþþþ ½Feþþþ  þ kO2 ½O2 ½Hþ 

1=2

kFeS2 ½Hþ 

1=2

0:14

!1=2

0

1=4

½Feþþþ 

1=2

ð14Þ

with:

kFeþþþ k kFeS2

0

kFeþþþ ¼

2

!1=2 ð15Þ

The rate Eq. (14) for the dissolution of pyrite in solutions containing dissolved ferric iron is similar to the one proposed by McKibben and Barnes (1986). In the absence of iron, the rate equation is (Holmes and Crundwell, 2000): 0

r FeS2 ¼ kO2þþþ ½Hþ 

0:18

½O2 1=2

ð16Þ

with: 2

0 kO2

¼

kO2 k kFeS2

!1=2 ð17Þ

Table 9 Selected parameters for the rate equation derived from Holmes and Crundwell (2000). Kinetic constants (k) are expressed in mol m2 s1 and the activation energy (Ea) in kJ mol1. Kinetic constant (mol m2 s1) k kFeS2 kO2 kFeþþþ kFeþþ

08

1.7  10 2.3  1002 1.1  1003 4.7  1001 1.2  1003

0.5 0.5 8.89 4.58 1 1 0.06 4.58 1

g

Add. mechanism

2 2 0.05 0.54 1 1 1.68 0.54 1

HCO 3

k25add

Eadd a

nadd

03

67

1.63

44

23

5.06

0

1.00

1.9  10

+

H

4.1  10

OH

3.1  1006

Finally, the overall reaction rate is expressed as:

 1=4 þþþ 1=2 0:18 0 0  rFeS2 ¼ kFeþþþ Hþ ½Fe  þ kO2 Hþ ½O2 1=2

ð18Þ

Using parameters of Table 9 as well as Eqs. (15) and (17), calcu0 0 lated values of kO2 and kFeþþþ parameters are given in Table 10. Note that kinetic expressions (13) and (18) have been compared and resulting dissolution rates are almost identical.

ð13Þ

þ kFeþþ ½Feþþ 

The kinetic constants given in Table 9 were determined by fitting data compiled by Williamson and Rimstidt (1994). Reported values as well as several authors (e.g. Cabral and Ignatiadis, 2001; Williamson and Rimstidt, 1994) indicate that the electrochemical behaviour of pyrite is strongly impacted by the presence of ferric ions. Unfortunately, the rate Eq. (13) cannot be directly used in several codes (i.e. when kinetic formalism is imposed). Considering that the effects of ferrous iron (Fe++) and dissolved oxygen can be neglected with regard to the effects of pH and ferric iron (Fe+++),  1  0:14 > respectively (i.e. kFeS2 Hþ 2 > kFeþþ ½Feþþ  and kO2 ½O2  Hþ kFeþþ ½Feþþ ), the rate equation becomes:

r FeS2 ¼ kFeþþþ ½Hþ 

h

Ea (kJ mol1) 80 80 34a 45 45

a Data calculated from activation energies given by Holmes and Crundwell (2000) and one given by McKibben and Barnes (1986) for the overall reaction (13).

7. Example of application In order to validate the kinetic data compilation, it appears interesting to use the selected rate parameters for simulating independent experiments. Suzuki-Muresan et al. (2011), carried out batch experiments on Callovian-Oxfordian argillites at 25, 50 and 90 °C. They followed up the evolving Si-concentration for 281 days. Their data has been used to validate the kinetic data compilation since the material studied is a complex mineralogical assemblage (di-octahedral smectite, calcite, celestite, chlorite, dolomite, illite, quartz, siderite and pyrite) and different temperatures were considered. These experiments were simulated using PhreeqC3 and the THERMOCHIMIE TDB. The detailed mineralogy of the Callovian-Oxfordian clay-rock was described in Claret et al. (2004) and Gaucher et al. (2009). All primary phases were considered to be kinetically controlled. Gibbsite (kinetic control) and goethite (at local equilibrium) were considered to be secondary phases. Reactive surface areas were estimated from average BET and ESA measurements found in the literature (detailed references are given on the THERMOCHIMIE website, http://www.thermochimie-tdb.com). The mineralogical assemblage under consideration is given in Table 11. Exchange models developed by Tournassat et al. (2009) were also introduced in the calculations with the selectivity coefficients following the Gaines and Thomas convention (Gaines and Thomas, 1953; Sposito, 1981). A cation-exchange capacity (CEC) of 17.4 meq/100 g was considered (Gaucher et al., 2009). Measured and calculated Si-concentrations are plotted in Fig. 7. The Si variation with time at the three different temperatures are in good agreement with respect to experimental data, including the initial rapid release of Si during the first weeks of the experiments and the following slower evolution, even including the decrease in Si concentration at 50 °C after 20 days. In addition, Suzuki-Muresan et al. (2011) recorded a pH of 8.3 at the end of

Table 10 Selected parameters for the empirical rate equation proposed for pyrite dissolution kinetics. Kinetic constants (k) are expressed in mol m2 s1 and the activation energy (Ea) in kJ mol1. Kinetic constant (mol m2 s1) 0 kO2 0 kFeþþþ

Ea (kJ mol1)

09

57

7.7  1007

62

3.7  10

116

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

Table 11 Mineralogical assemblage considered for the modelling of batch experiments using Callovian-Oxfodian argillites (solid/solution ratio of 10 g/L). Structural formula

mol L1 of solution

Processing

Reactive surface area (m2 g1)

Primary minerals Calcite Celestite Ripidolite_Cca-2 Dolomite Illite_IMt-2 Montmo-Mg_Ca0.3 Pyrite Quartz Siderite

CaCO3 SrSO4 (Mg2.964Fe1.927Al1.116Ca0.011)(Si2.633Al1.367)O10(OH)8 CaMg(CO3)2 (Na0.044K0.762)(Si3.387Al0.613)(Al1.427Fe0.376Mg0.241)O10(OH)2 Ca0.3Mg0.6Al1.4Si4O10(OH)2 FeS2 SiO2 FeCO3

2.20  1002 5.44  1004 3.24  1004 2.17  1003 8.46  1003 2.16  1003 8.33  1004 3.99  1002 8.63  1004

Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic Kinetic

0.7 40 0.0027 0.09 30 8.5 0.05 0.03 2.7

Secondary minerals Goethite

FeOOH

0

–

Gibbsite

Al(OH)3

0

Local equilibrium Kinetics

Minerals name in THERMOCHIMIE

20

Remarks

Dissolution only

Initial nucleation rate of 1010 mol s1

temperature and time. However the compilation is mostly focused on minerals contained in clay-rocks and will be extended to other minerals and conditions in order to be applied to other objectives (e.g. CO2 storage, Trémosa et al., 2014). Moreover, several simulations point out the lack of kinetic data and parameters for cement phases (e.g. Marty et al., 2009), a gap that must be filled in the future. Kinetic data collection is an on-going process that must be periodically updated as a function of the needs of modelers and depends on omitted/missing or newly provided data. The proposed parameters were systematically compared to all available (to our knowledge) literature data, including data that have not been selected for the calibration of kinetic parameters. This enabled us to identify the uncertainties related to the proposed reaction kinetic parameters values. Fig. 7. Evolution of the Si-concentration in solution versus time for a batch experiment using Callovian-Oxfordian argilites performed at different temperatures. Symbols refer to experimental data from Suzuki-Muresan et al. (2011). Squares, diamonds and triangles were modelled using the proposed kinetic data compilation.

the batch experiment at 25 °C, which was also obtained at the end of the simulation at 25 °C, i.e. pH of 8.5. Note that our calculations assumed an outgassing of the solution during the preparation of the experiments in a glove box, which would have affected the carbonate system. Indeed, the initial increase in Si concentration can only be explained by a disruption of the pH due to this outgassing. Modelling was done without chlorite precipitation. The formation of this phase can be disregarded for short time scales (i.e. t < 1 year). However, extrapolation to long-term evolution is more uncertain (Marty et al., 2010). Moreover, BET and ESA surface areas appear to be well-suited to modelling this type of batch experiments, even though considering them in compacted porous media is subject to debate (Cubillas et al., 2005; Ganor et al., 2005; Helgeson et al., 1984; Lüttge et al., 2013; Marty et al., 2009; Velbel, 1990; White and Brantley, 2003; Zhu, 2005). 8. Conclusion The proposed kinetic data compilation gives (i) a first approximation of reaction rates and (ii) an idea of the amount of literature data that deals with the minerals of interest under consideration. Kinetic parameters derived from selected data compilation seem to be able to precisely reproduce the composition of a solution in contact with a Callovian-Oxfordian sample as a function of

Acknowledgments This research is a part of a project supported by the French National Radioactive Waste Management Agency (Andra) and the French Geological Survey (BRGM). We are grateful to Michael Kersten and Wolfgang Hummel for handling the review process. This manuscript benefited from comments and suggestions of two anonymous reviewers. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.apgeochem.2014. 10.012. References Amram, K., Ganor, J., 2005. The combined effect of pH and temperature on smectite dissolution rate under acidic conditions. Geochim. Cosmochim. Acta 69, 2535– 2546. Appelo, C.A.J., Verweij, E., Schäfer, H., 1998. A hydrogeochemical transport model for an oxidation experiment with pyrite/calcite/exchangers/organic matter containing sand. Appl. Geochem. 13, 257–268. Bauer, A., Berger, G., 1998. Kaolinite and smectite dissolution rate in high molar KOH solutions at 35° and 80 °C. Appl. Geochem. 13, 905–916. Belcourt, O., 2009. La perturbation chimico-minéralogique (Hydratation, état d’oxydation, eau interstitielle) de la zone perturbée excavée et ses relations avec la perturbation texturale et mécanique: application aux argilites des galeries de Bure. Berner, R.A., Schott, J., 1982. Mechanism of pyroxene and amphibole weathering; II, Observations of soil grains. Am. J. Sci. 282, 1214–1231. Bickmore, B.R., Bosbach, D., Hochella, M.F., Charlet, L., Rufe, E., 2001. In situ atomic force microscopy study of hectorite and nontronite dissolution: implications for

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118 phyllosilicate edge surface structures and dissolution mechanisms. Am. Mineral. 86, 411–423. Bosbach, D., Charlet, L., Bickmore, B., Hochella, M.F., 2000. The dissolution of hectorite: in-situ, real-time observations using atomic force microscopy. Am. Mineral. 85, 1209–1216. Brandt, F., Bosbach, D., Krawczyk-Bärsch, E., Arnold, T., Bernhard, G., 2003. Chlorite dissolution in the acid pH-range: a combined microscopic and macroscopic approach. Geochim. Cosmochim. Acta 67, 1451–1461. Cabral, T., Ignatiadis, I., 2001. Mechanistic study of the pyrite–solution interface during the oxidative bacterial dissolution of pyrite (FeS2) by using electrochemical techniques. Int. J. Miner. Process. 62, 41–64. Cama, J., Ganor, J., Ayora, C., Lasaga, C.A., 2000. Smectite dissolution kinetics at 80 °C and pH 8.8. Geochim. Cosmochim. Acta 64, 2701–2717. Casey, W.H., Carr, M.J., Graham, R.A., 1988a. Crystal defects and the dissolution kinetics of rutile. Geochim. Cosmochim. Acta 52, 1545–1556. Casey, W.H., Westrich, H.R., Arnold, G.W., 1988b. Surface chemistry of labradorite feldspar reacted with aqueous solutions at pH = 2, 3, and 12. Geochim. Cosmochim. Acta 52, 2795–2807. Claret, F., Sakharov, B.A., Drits, V.A., Velde, B., Meunier, A., Griffault, L., Lanson, B., 2004. Clay minerals in the Meuse-Haute Marne underground laboratory (France): possible influence of organic matter on clay mineral evolution? Clays Clay Miner. 52, 515–532. Cochepin, B., Trotignon, L., Bildstein, O., Steefel, C.I., Lagneau, V., Van der lee, J., 2008. Approaches to modelling coupled flow and reaction in a 2D cementation experiment. Adv. Water Resour. 31, 1540–1551. Cubillas, P., Köhler, S., Prieto, M., Chaïrat, C., Oelkers, E.H., 2005. Experimental determination of the dissolution rates of calcite, aragonite, and bivalves. Chem. Geol. 216, 59–77. De Windt, L., Marsal, F., Tinseau, E., Pellegrini, D., 2008. Reactive transport modeling of geochemical interactions at a concrete/argillite interface, Tournemire site (France). Phys. Chem. Earth, Parts A/B/C 33 (Suppl. 1), S295–S305. Dove, P.M., Han, N., De Yoreo, J.J., 2005. Mechanisms of classical crystal growth theory explain quartz and silicate dissolution behavior. Proc. Natl. Acad. Sci. USA 102, 15357–15362. Emmanuel, S., Berkowitz, B., 2005. Mixing-induced precipitation and porosity evolution in porous media. Adv. Water Resour. 28, 337–344. Fritz, B., Clément, A., Amal, Y., Noguera, C., 2009. Simulation of the nucleation and growth of simple clay minerals in weathering processes: the NANOKIN code. Geochim. Cosmochim. Acta 73, 1340–1358. Gaines, G.L., Thomas, H.C., 1953. Adsorption studies on clay minerals. II. A formulation of the thermodynamics of exchange adsorption. J. Chem. Phys. 21, 714–718. Ganor, J., Roueff, E., Erel, Y., Blum, J.D., 2005. The dissolution kinetics of a granite and its minerals—implications for comparison between laboratory and field dissolution rates. Geochim. Cosmochim. Acta 69, 607–621. Gaucher, E.C., Blanc, P., Matray, J.-M., Michau, N., 2004. Modeling diffusion of an alkaline plume in a clay barrier. Appl. Geochem. 19, 1505–1515. Gaucher, E.C., Tournassat, C., Pearson, F.J., Blanc, P., Crouzet, C., Lerouge, C., Altmann, S., 2009. A robust model for pore-water chemistry of clayrock. Geochim. Cosmochim. Acta 73, 6470–6487. Gherardi, F., Audigane, P., Gaucher, E.C., 2012. Predicting long-term geochemical alteration of wellbore cement in a generic geological CO2 confinement site: tackling a difficult reactive transport modeling challenge. J. Hydrol. 420–421, 340–359. Giffaut, E., Grivé, M., Blanc, P., Vieillard, P., Colàs, E., Gailhanou, H., Gaboreau, S., Marty, N., Madé, B., Duro, L., in press. Andra thermodynamic database for performance assessment: ThermoChimie. Appl. Geochem. http://dx.doi.org/ 10.1016/j.apgeochem.2014.05.007. Golubev, S.V., Bauer, A., Pokrovsky, O.S., 2006. Effect of pH and organic ligands on the kinetics of smectite dissolution at 25 °C. Geochim. Cosmochim. Acta 70, 4436–4451. Grandstaff, D.E., 1978. Changes in surface area and morphology and the mechanism of forsterite dissolution. Geochim. Cosmochim. Acta 42, 1899–1901. Helgeson, H.C., Murphy, W.M., Aagaard, P., 1984. Thermodynamic and kinetic constraints on reaction rates among minerals and aqueous solutions. II. Rate constants, effective surface area, and the hydrolysis of feldspar. Geochim. Cosmochim. Acta 48, 2405–2432. Hellevang, H., Pham, V.T.H., Aagaard, P., 2013. Kinetic modelling of CO2–water–rock interactions. Int. J. Greenhouse Gas Control 15, 3–15. Hochella, M.F., Banfield, J.F., 1995. Chemical weathering of silicates in nature; a microscopic perspective with theoretical considerations. Rev. Mineral. Geochem. 31, 353–406. Holmes, P.R., Crundwell, F.K., 2000. The kinetics of the oxidation of pyrite by ferric ions and dissolved oxygen: an electrochemical study. Geochim. Cosmochim. Acta 64, 263–274. Huertas, F.J., Caballero, E., Jiménez de Cisneros, C., Huertas, F., Linares, J., 2001. Kinetics of montmorillonite dissolution in granitic solutions. Appl. Geochem. 16, 397–407. Kang, Q., Lichtner, P., Viswanathan, H., Abdel-Fattah, A., 2010. Pore scale modeling of reactive transport involved in geologic CO2 sequestration. Transp. Porous Media 82, 197–213. Kaviratna, H., Pinnavaia, T.J., 1994. Acid hydrolysis of octahedral Mg2+ sites in 2:1 layered silicates; an assessment of edge attack and gallery access mechanisms. Clays Clay Miner. 42, 717–723. Kosakowski, G., Blum, P., Kulik, D., Pfingsten, W., Shao, H., Singh, A., 2009. Evolution of a generic clay/cement interface: first reactive transport calculations utilizing

117

a Gibbs energy minimization based approach for geochemical calculations. J. Environ. Sci. Sust. Soc. 3, 41–49. Kulik, D., Wagner, T., Dmytrieva, S., Kosakowski, G., Hingerl, F., Chudnenko, K., Berner, U., 2013. GEM-Selektor geochemical modeling package: revised algorithm and GEMS3K numerical kernel for coupled simulation codes. Comput. Geosci. 17, 1–24. Lasaga, A.C., 1981. Transition state theory. Rev. Mineral. Geochem. 8, 135–168. Lasaga, A.C., 1998. Kinetic Theory in the Earth Sciences. Princeton University Press, Princeton, NJ. Lasaga, A.C., Luttge, A., 2001. Variation of crystal dissolution rate based on a dissolution stepwave model. Science 291, 2400–2404. Lichtner, P.C., Steefel, C.I., Oelkers, E.H., 1996. Reactive Transport in Porous Media. Mineralogical Society of America. Lu, C., Samper, J., Fritz, B., Clement, A., Montenegro, L., 2011. Interactions of corrosion products and bentonite: an extended multicomponent reactive transport model. Phys. Chem. Earth, Parts A/B/C 36, 1661–1668. Lüttge, A., Arvidson, R.S., Fischer, C., 2013. A stochastic treatment of crystal dissolution kinetics. Elements 9, 183–188. Marini, L., 2006. The Kinetics of Mineral Carbonation, Developments in Geochemistry. Elsevier, pp. 169–317 (Chapter 6). Marty, N.C.M., Tournassat, C., Burnol, A., Giffaut, E., Gaucher, E.C., 2009. Influence of reaction kinetics and mesh refinement on the numerical modelling of concrete/ clay interactions. J. Hydrol. 364, 58–72. Marty, N.C.M., Fritz, B., Clément, A., Michau, N., 2010. Modelling the long term alteration of the engineered bentonite barrier in an underground radioactive waste repository. Appl. Clay Sci. 47, 82–90. Marty, N.C.M., Cama, J., Sato, T., Chino, D., Villiéras, F., Razafitianamaharavo, A., Brendlé, J., Giffaut, E., Soler, J.M., Gaucher, E.C., Tournassat, C., 2011. Dissolution kinetics of synthetic Na-smectite. An integrated experimental approach. Geochim. Cosmochim. Acta 75, 5849–5864. Mayer, K.U., Frind, E.O., Blowes, D.W., 2002. Multicomponent reactive transport modeling in variably saturated porous media using a generalized formulation for kinetically controlled reactions. Water Resour. Res. 38, 1174. McKibben, M.A., Barnes, H.L., 1986. Oxidation of pyrite in low temperature acidic solutions: rate laws and surface textures. Geochim. Cosmochim. Acta 50, 1509– 1520. Metz, V., Amram, K., Ganor, J., 2005a. Stoichiometry of smectite dissolution reaction. Geochim. Cosmochim. Acta 69, 1755–1772. Metz, V., Raanan, H., Pieper, H., Bosbach, D., Ganor, J., 2005b. Towards the establishment of a reliable proxy for the reactive surface area of smectite. Geochim. Cosmochim. Acta 69, 2581–2591. Murakami, T., Utsunomiya, S., Yokoyama, T., Kasama, T., 2003. Biotite dissolution processes and mechanisms in the laboratory and in nature: early stage weathering environment and vermiculitization. Am. Mineral. 88, 377–386. 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. Appl. Clay Sci. 27, 53–65. Noiriel, C., Luquot, L., Madé, B., Raimbault, L., Gouze, P., van der Lee, J., 2009. Changes in reactive surface area during limestone dissolution: an experimental and modelling study. Chem. Geol. 265, 160–170. Oelkers, E.H., 2001. General kinetic description of multioxide silicate mineral and glass dissolution. Geochim. Cosmochim. Acta 65, 3703–3719. Oelkers, E.H., Schott, J., 1995. Experimental study of anorthite dissolution and the relative mechanism of feldspar hydrolysis. Geochim. Cosmochim. Acta 59, 5039–5053. Oelkers, E.H., Schott, J., Devidal, J.-L., 1994. The effect of aluminum, pH, and chemical affinity on the rates of aluminosilicate dissolution reactions. Geochim. Cosmochim. Acta 58, 2011–2024. Palandri, J.L., Kharaka, Y.K., 2004. A Compilation of Rate Parameters of Water– Mineral Interaction Kinetics for Application to Geochemical Modeling. U.S. Dept. of the Interior, U.S. Geological Survey, Menlo Park, Calif. Parkhurst, D.L., Appelo, C.A.J., 2013. Description of Input and Examples for PHREEQC Version 3 – A Computer Program for Speciation, Batch-reaction, Onedimensional Transport, and Inverse Geochemical Calculations. U.S. Geological Survey Techniques and Methods, Book 6, 497p (Chapter A43). . Pruess, K., García, J., Kovscek, T., Oldenburg, C., Rutqvist, J., Steefel, C., Xu, T., 2004. Code intercomparison builds confidence in numerical simulation models for geologic disposal of CO2. Energy 29, 1431–1444. Rozalén, M.L., Huertas, F.J., Brady, P.V., Cama, J., García-Palma, S., Linares, J., 2008. Experimental study of the effect of pH on the kinetics of montmorillonite dissolution at 25 °C. Geochim. Cosmochim. Acta 72, 4224–4253. Rozalén, M., Brady, P.V., Huertas, F.J., 2009. Surface chemistry of K-montmorillonite: ionic strength, temperature dependence and dissolution kinetics. J. Colloid Interface Sci. 333, 474–484. Savage, D., Noy, D., Mihara, M., 2002. Modelling the interaction of bentonite with hyperalkaline fluids. Appl. Geochem. 17, 207–223. Savage, D., Watson, C., Benbow, S., Wilson, J., 2010. Modelling iron–bentonite interactions. Appl. Clay Sci. 47, 91–98. Sayed Hassan, M., Villieras, F., Gaboriaud, F., Razafitianamaharavo, A., 2006. AFM and low-pressure argon adsorption analysis of geometrical properties of phyllosilicates. J. Colloid Interface Sci. 296, 614–623. Schott, J., Oelkers, E.H., 1995. Dissolution and crystallization rates of silicate minerals as a function of chemical affinity. Pure Appl. Chem. 67, 903–910. Schott, J., Brantley, S., Crerar, D., Guy, C., Borcsik, M., Willaime, C., 1989. Dissolution kinetics of strained calcite. Geochim. Cosmochim. Acta 53, 373–382.

118

N.C.M. Marty et al. / Applied Geochemistry 55 (2015) 108–118

Schramm, L.L., Kwak, J.C., 1982a. Influence of exchangeable cation composition on the size and shape of montmorillonite particles in dilute suspension. Clays Clay Miner. 30, 40. Schramm, L.L., Kwak, J.C.T., 1982b. Interactions in clay suspensions: the distribution of ions in suspension and the influence of tactoid formation. Colloids Surf. 4, 43–60. Shao, H., Dmytrieva, S.V., Kolditz, O., Kulik, D.A., Pfingsten, W., Kosakowski, G., 2009. Modeling reactive transport in non-ideal aqueous–solid solution system. Appl. Geochem. 24, 1287–1300. Soler, J.M., 2003. Reactive transport modeling of the interaction between a high-pH plume and a fractured marl: the case of Wellenberg. Appl. Geochem. 18, 1555– 1571. Sposito, G., 1981. The Thermodynamics of Soil Solutions. Oxford University Press. Sposito, G., 1992. The diffuse-ion swarm near smectite particles suspended in 1:1 electrolyte solutions: modified Gouy–Chapman theory and quasicrystal formation. In: N.G.a.R.M.P. (Ed.), Clay–Water Interface and its Rheological Implications. The Clay Minerals Society, Boulder, CO, pp. 128–155. Steefel, C.I., 2009. CrunchFlow. Software for Modeling Multicomponent Reactive Flow and Transport. USER’S MANUAL. Lawrence Berkeley National Laboratory. . Steefel, C.I., Lichtner, P.C., 1998. Multicomponent reactive transport in discrete fractures: I. Controls on reaction front geometry. J. Hydrol. 209, 186–199. Steefel, C.I., MacQuarrie, K.T.B., 1996. Approaches to modeling of reactive transport in porous media. Rev. Mineral. Geochem. 34, 85–129. Steefel, C.I., DePaolo, D.J., Lichtner, P.C., 2005. Reactive transport modeling: an essential tool and a new research approach for the earth sciences. Earth Planet. Sci. Lett. 240, 539–558. Steefel, C.I., Appelo, C.A.J., Arora, B., Jacques, D., Kalbacher, T., Kolditz, O., Lagneau, V., Lichtner, P.C., Mayer, K.U., Meeussen, J.C.L., Molins, S., Moulton, D., Shao, H., Šimu˚nek, J., Spycher, N., Yabusaki, S.B., Yeh, G.T., in press. Reactive transport codes for subsurface environmental simulation. Comput. Geosci. http:// dx.doi.org/10.1007/s10596-10014-19443-x. Suzuki-Muresan, T., Vandenborre, J., Abdelouas, A., Grambow, B., 2011. Solution controls for dissolved silica at 25, 50 and 90 °C for quartz, Callovo-Oxfordian claystone, illite and MX80 bentonite. Phys. Chem. Earth, Parts A/B/C 36, 1648– 1660. Tournassat, C., Neaman, A., Villieras, F., Bosbach, D., Charlet, L., 2003. Nanomorphology of montmorillonite particles: estimation of the clay edge

sorption site density by low-pressure gas adsorption and AFM observations. Am. Mineral. 18 (11–12 Part 2), 1989–1995. Tournassat, C., Gailhanou, H., Crouzet, C., Braibant, G., Gautier, A., Gaucher, E.C., 2009. Cation exchange selectivity coefficient values on smectite and mixedlayer illite/smectite minerals. Soil Sci. Soc. Am. J. 73, 928–942. Trémosa, J., Castillo, C., Vong, C.Q., Kervévan, C., Lassin, A., Audigane, P., 2014. Longterm assessment of geochemical reactivity of CO2 storage in highly saline aquifers: application to Ketzin, In Salah and Snøhvit storage sites. Int. J. Greenhouse Gas Control 20, 2–26. Velbel, M.A., 1990. Influence of temperature and mineral surface characteristics on feldspar weathering rates in natural and artificial systems: a first approximation. Water Resour. Res. 26, 3049–3053. 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? Chem. Geol. 202, 479–506. Williamson, M.A., Rimstidt, J.D., 1994. The kinetics and electrochemical ratedetermining step of aqueous pyrite oxidation. Geochim. Cosmochim. Acta 58, 5443–5454. Xu, T., Sonnenthal, E., Spycher, N., Pruess, K., 2004. TOUGHREACT User’s Guide: A Simulation Program for Non-isothermal Multiphase Reactive Geochemical Transport in Variable Saturated Geologic Media. Lawrence Berkeley National Laboratory. . Xu, T., Sonnenthal, E., Spycher, N., Pruess, K., 2006. TOUGHREACT—a simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media: applications to geothermal injectivity and CO2 geological sequestration. Comput. Geosci. 32, 145–165. Xu, T., Spycher, N., Sonnenthal, E., Zhang, G., Zheng, L., Pruess, K., 2011. TOUGHREACT Version 2.0: a simulator for subsurface reactive transport under non-isothermal multiphase flow conditions. Comput. Geosci. 37, 763– 774. Yokoyama, S., Kuroda, M., Sato, T., 2005. Atomic force microscopy study of montmorillonite dissolution under highly alkaline conditions. Clays Clay Miner. 53, 147–154. Zhu, C., 2005. In situ feldspar dissolution rates in an aquifer. Geochim. Cosmochim. Acta 69, 1435–1453. Zysset, M., Schindler, P.W., 1996. The proton promoted dissolution kinetics of Kmontmorillonite. Geochim. Cosmochim. Acta 60, 921–931.