Model evaluation of geochemically induced swelling ...

Applied Clay Science 97–98 (2014) 24–32

Contents lists available at ScienceDirect

Applied Clay Science journal homepage: www.elsevier.com/locate/clay

Research paper

Model evaluation of geochemically induced swelling/shrinkage in argillaceous formations for nuclear waste disposal Liange Zheng ⁎, Jonny Rutqvist, Hui-Hai Liu, Jens T. Birkholzer, Eric Sonnenthal Berkeley National Laboratory (LBNL), Berkeley, CA 94720, USA

a r t i c l e

i n f o

Article history: Received 4 October 2013 Received in revised form 7 May 2014 Accepted 16 May 2014 Available online xxxx Keywords: Argillaceous Swelling Diffuse double layer Geochemistry Nuclear waste disposal

a b s t r a c t Argillaceous formations are being considered as host rocks for geologic disposal of nuclear waste in a number of countries. One advantage of emplacing nuclear waste in such formations is the potential self-sealing capability of clay due to swelling, which is of particular importance for the sealing and healing of disturbed rock zones (DRZ). It is therefore necessary to understand and be able to predict the changes in swelling properties within clay rock near the waste-emplacement tunnel. In this paper, considering that the clay rock formation is mostly under saturated conditions and the swelling property changes are mostly due to geochemical changes, we propose a modeling method that links a THC simulator with a swelling module that is based on diffuse double layer theory. Simulations were conducted to evaluate the geochemically induced changes in the swelling properties of the clay rock. Our findings are as follows: (1) geochemically induced swelling/shrinkage occurs exclusively in the EBS– clay formation interface, within a few meters from the waste-emplacement tunnels; (2) swelling/shrinkageinduced porosity changes are generally much smaller than those caused by mineral precipitation/dissolution processes; (3) geochemically induced swelling/shrinkage of the host clay rock is affected by variations in the pore water chemistry, exchangeable cations, and smectite abundance. Neglecting any of these three factors might lead to a miscalculation of the geochemically induced swelling pressure. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Argillaceous formations are primary host-rock candidates for nuclear waste disposal, and have therefore been studied extensively, especially in Europe. Extensive studies on the behavior of clays have been conducted in Underground Research Laboratories (URLs), such as in Opalinus Clay at Mont Terri, Switzerland (Bossart and Thury, 2008; Pearson et al., 2003; Thury, 2002), and in Callovo-Oxfordian Clay at Bure, France (Andra, 2005; Jougnot et al., 2010; Samper et al., 2008). Research and development efforts for shale repository investigations were also undertaken in the U.S. from the 1970s until the mid-1980s (Gonzales and Johnson, 1984; Hansen et al., 2010), before the U.S. nuclear waste program was directed to exclusively characterize the volcanic tuffs at Yucca Mountain in Nevada. In fact, the U.S. has many clay/ shale/argillite basins with positive attributes for permanent disposal of nuclear waste. Recently, Hansen et al. (2010) presented a feasibility study, indicating that shale formations provide a technically advanced, scientifically sound disposal option for the U.S. One advantage of emplacing nuclear waste in clay formations is the potential self-sealing capability of clay due to swelling. The self-sealing capability might have particular importance for disturbed rock zones (DRZ). These are zones that form near emplacement tunnels as a result ⁎ Corresponding author. E-mail address: [email protected] (L. Zheng).

http://dx.doi.org/10.1016/j.clay.2014.05.019 0169-1317/© 2014 Elsevier B.V. All rights reserved.

of excavation and tunnel disturbance. It is, therefore, necessary to evaluate and be able to predict the changes in swelling properties within clay rock, especially in the near-field area. In the long run, the clay rock in the near field area stays in a saturated condition although it undergoes desaturation in the short term, the swelling-property changes in a clay rock are therefore mostly due to the geochemical changes, including (1) changes in ion concentration of the pore water, (2) cation exchange changes in the composition of the water in the interlayer space, and (3) changes in the abundance of swelling minerals such as smectite. Geochemically induced changes in the swelling properties of clay rock have been reported in both short-term and small-scale laboratory tests (Thury, 2002; Wakim et al., 2009). Thury (2002) reported that decompressed Opalinus Clay swells in contact with water and that the magnitude of swelling varied with the water chemistry (deionized water, low mineralized water, synthetic pore water, and KCl solution). Wakim et al. (2009) experimentally evaluated the effect of aqueous solution chemistry on the swelling and shrinkage of shales under saturated conditions, and reported that more concentrated solution led to less swelling. Kamei et al. (2005) and Cuadros (2006) indicated that illitization, i.e., the transformation from smectite to illite, changes the swelling properties of the clay. Although whether illitization would occur in a nuclear waste disposal site and to what degree it happens is still an issue that requires more studies, the changes in the swelling properties of clay rock demonstrated in these studies point out the need to evaluate geochemically induced swelling/shrinkage within the

L. Zheng et al. / Applied Clay Science 97–98 (2014) 24–32

25

TOUGHREACT is a numerical simulator for chemically reactive nonisothermal flows of multiphase fluids in porous and fractured media (Sonnenthal et al., 2005; Spycher et al., 2003; Xu and Pruess, 2001; Xu et al., 2006, 2011; Zhang et al., 2008; Zheng et al., 2009). The code was developed by introducing reactive chemistry into the multiphase fluid and heat flow simulator TOUGH2 (Pruess, 2004). The code accommodates any number of chemical species present in liquid, gas, and solid phases and considers a variety of subsurface thermal, physical, chemical, and biological processes, under a wide range of pressure, temperature, water saturation, ionic strength, pH and Eh conditions. The major chemical reactions that can be considered in TOUGHREACT include aqueous complexation, acid–base, redox, gas dissolution/exsolution, cation exchange, mineral dissolution/precipitation, and surface complexation.

relation, such as incorporation of the concentration of exchangeable cations (Guimarães et al., 2007) and consideration of the aqueous concentration via chemical potential (Ghassemi and Diek, 2003). Another approach involves a constitutive equation to relate the deformation of compacted bentonite to the distance between two montmorillonite layers based on the DDL theory (e.g., Komine and Ogata, 1996; 2003; Schanz and Tripathy, 2009). Based on the fact that: (1) the host argillaceous formations stay fully saturated despite a short desaturation period in the near field and, (2) the driving force is mostly the geochemical changes, the clay rocks will undergo osmotic swelling when in contact with the engineered barrier system (EBS). Typically, the argillaceous host rock has a pore water ion concentration higher than the bentonite in the EBS, which implies that near the interface, ions will diffuse between the host rock and the EBS bentonite, which will induce a disequilibrium of chemical potential and therefore osmotic swelling. This will occur depending on the degree of compaction of the bentonite and if changes in dry densities are allowed. During the osmotic swelling process, the swelling pressure is the difference between the osmotic pressure in the central plane between two clay plates and the osmotic pressure in the equilibrium solution according to the DDL theory (Bolt, 1956). In other words, the swelling pressure is the pressure required to keep the clay–water system at the required void ratio when it is allowed to adsorb water or electrolytes (Tripathy et al., 2004). Bolt (1956) and van Olphen (1977) presented a method for calculating the swelling pressure in a clay–water electrolyte system. Sridharan and Jayadeva (1982) improved that method and presented the diffuse double layer theory in a lucid form that could be readily used for understanding the engineering behavior of clays. According to Sridharan and Jayadeva (1982), swelling pressure is determined through a combination of Eqs. (1) to (5) as follows:

3. Application of DDL theory to calculate swelling pressure

e ¼ Gγ w Sd

In expansive clay–water–ion systems, there are basically two types of swelling processes: crystalline and osmotic. Crystalline swelling refers to swelling that occurs at relatively low water content and is primarily a consequence of the hydration of interlayer exchangeable cations. Swelling occurs as water enters the mineral interlayer as a sequence of successive molecular layers, which results in a step-wise separation of the interlayer for up to three or four layers of water. Osmotic swelling occurs at higher water contents and is associated with continuing interlayer separation that develops from movement of water into the interlayer due to the difference in ion concentration within the interlayer and within the bulk pore water. Osmotic water adsorption results from concentration differences among dissolved ions between the interlayer pore water (overlapping double layers) and the free (bulk) water. It is a long-range interaction, which mostly depends on ionic strength or ion concentration, the type of exchangeable ion (e.g., Ca vs. Na), pH of the pore water, and clay mineralogy (van Olphen, 1977). Corresponding osmotic swelling results from the balance of attractive and repulsive forces that develop between overlapping electrical double layers. Crystalline swelling, which occurs mainly in the initial hydration, will be transformed to osmotic swelling when the clay approaches full saturation. Wayllace (2008) reported that such a transformation will occur when the relative humidity (RH) is around 97%, and Onikata et al. (1999) indicated, from a microscopic point of view, that the d(001)-value of 20 to 40 Å is probably a critical value, where the electrostatic attractive force between the 2:1 layers by way of the cations is so weak that the crystalline swelling is transformed into osmotic swelling. The swelling of clays can be modeled in several ways. Elastoplastic models (Gens and Alonso, 1992; Thomas and He, 1998), such as the Barcelona Basic Model (BBM) (Alonso et al., 1990) and the Barcelona Expansive Model (BExM) (Alonso et al., 1999) are widely used. Recently, chemical components are also incorporated into the stress–strain

where, e is the void ratio, G is the specific gravity of soil solids, γw is the unit weight of water, S is the specific surface area of soil (m2/g swelling clay), and d is half the distance between parallel clay platelets.

clay rock hosting a nuclear waste repository, and to the best of our knowledge, no such evaluation has been reported in the literature. It has been recognized that the self-sealing of DRZ fractures could lower the risk brought by the DRZ (Tsang et al., 2010) and it is largely determined by the swelling of the clay minerals (Rothfuchs et al., 2007). Although attention has been paid to self-sealing due to hydraulic effect (Zhang, 2011), the effect of geochemical changes on the swelling and the subsequent self-healing of clayey rock has not been evaluated. In this paper, after linking the thermal, hydrological and chemical (THC) simulator TOUGHREACT (Xu et al., 2011) with a swelling model based on the Gouy–Chapman diffuse double layer (DDL) theory, generic simulations were conducted to evaluate the geochemically induced changes in the swelling properties of clayey host rock in the near field of a nuclear waste repository. 2. The simulator—TOUGHREACT

Z

u z

ð1Þ

1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidy ¼ ð2 cosh y−2 cosh uÞ

Z

d 0

dξ ¼ −Kd

ð2Þ

where, u is the nondimensional midplane potential, z is the nondimensional potential at the clay surface, y is the nondimensional potential at distance x from the clay surface, and ξ is the distance function (=Kx). K (1/m) is the double layer parameter: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2n e0 2 v2 K¼ εkT

ð3Þ

where, e′ is the elementary electric charge (1.6 · 10−19 C), k is Boltzmann's constant (1.3806 · 10−23 J/K), n is the molar concentration of ions in pore fluid (molal), v is the valence of the interlayer cation, T is the absolute temperature (K), ε is the dielectric constant of the pore fluid and given by ε = ε0D in which ε0 is the permittivity of the vacuum (8.8542 · 10−12 C2 J−1 m−1), and D is the ratio of the electrostatic capacity of condenser plates separated by the given material to that of the same condenser with vacuum between the plates (Mitchell and Soga, 2005). qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dy ¼ ð2 cosh z−2 cosh uÞ − dξ x¼0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s 1 ¼Γ at x ¼ 0; y ¼ z 2εnkT ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi s B 1 ¼ S 2εnkT

ð4Þ

26


where, Γ is the surface charge density (base exchange capacity per specific surface), and B is the base exchange capacity of the clayey material (meq/100 g solid). p ¼ 2nkT ð coshu−1Þ

ð5Þ

where, p is the osmotic pressure or swelling pressure (Pa). For any given pore fluid medium, determination of the swelling pressure using Langmuir's equation (i.e., Eq. (5)) requires the nondimensional midplane potential function, u. Determination of u is an indirect and elaborate process. A relationship between u and the non-dimensional distance function, Kd, must be established to determine u for any given value of Kd and vice versa. Eqs. (1) to (5) are used for this purpose. Details of the procedure of obtaining the u–Kd relation are given by Tripathy et al. (2004). For any given pressure, u can be found from Eq. (5). If B, S, n, and u values are known, (dy/dξ)x = 0, then z can be calculated from Eq. (4). From Eq. (2), for known u and z values, Kd can be found. After determining u and Kd values for a series of pressures, a u–Kd relation can be established for one particular group of B, S, and n. For any void ratio, e, knowing K from Eq. (3) and d from Eq. (1), Kd can be found. Then the u value for the corresponding Kd value can be determined from the established u–Kd relationship. Therefore, the swelling pressure can be calculated from Eq. (5). Eq. (1) implies that the solid phase is only composed of clay platelets that can swell and therefore the use of DDL theory to calculate the swelling pressure ideally should be limited to pure swelling clay minerals, i.e. smectite. Natural argillaceous formations, however, are composed of mixtures of smectite and other non-swelling minerals. For example, the Opalinus Clay, a candidate host-rock formation for nuclear waste disposal in Europe (Bossart and Thury, 2008), contains only about 10% of the mixed-layer illite–smectite with about half being smectite. For clay formations that have a mixture of swelling and non-swelling minerals, Eq. (1) is obviously questionable, because the pore space includes not only the interlayer space where the swelling occurs, but also the pore spaces that are surrounded by non-swelling minerals. The derivation of Eq. (1) is based on the assumption that the clay platelets are parallel, as shown in Fig. 1(a). To extend the idealized structure of pure swelling clay (Fig. 1(a)) to a mixture of swelling clay and nonswelling minerals (Fig. 1(b)), Eq. (1) will be modified correspondingly. Assuming that the platelet (both swelling and non-swelling minerals) has a plan area of A, the volume of the void is V v ¼ 2Aðd þ DÞ:

ð6Þ

The volume of the solids is: V s ¼ 2Aðt þ T Þ

ð7Þ

and the void ratio is: e¼

Vv d þ D ¼ : Vs tþT

ð8Þ

Neglecting the contribution due to the edges, the specific area (surface area per unit mass) of the swelling clay is given by: S¼

2A Mt f s

ð9Þ

where, Mt is the total mass of the solid and f s is the mass fraction of the swelling clay in the mixture. The specific gravity of the solid is given by: G¼

Mt : V s γw

ð10Þ

The mass of the solid is: Mt ¼ GV s γw ¼

Gγw 2Aðd þ DÞ : e

ð11Þ

Substituting Mt in Eq. (11) back into Eq. (9), we have: s

e ¼ Gγ w S f ðd þ DÞ:

ð12Þ

Letting fd = D/d, Eq. (12) can be rewritten as: s d e ¼ Gγ w S f d 1 þ f :

ð13Þ

Typically a non-swelling clay mineral, such as kaolinite or illite, has a d(001) basal spacing of ~10 Å, whereas a swelling clay (smectite) that suffers osmotic swelling may have a d(001) value from 20 to 40 Å (Onikata et al., 1999). Therefore, the value for fd ranges from 0.25 to 0.5. Note that in a broader sense, fd represents the ratio of pore space associated with non-swelling minerals to that associated with swelling minerals. 4. Model setup Equations in Section 3 have been programmed in a subroutine that performs DDL-based swelling pressure calculation. After being verified and validated against swelling pressure data from the FEBEX bentonite (ENRESA, 2000) and the Lower Dogger Opalinus Clay from Mont Terri at Switzerland (Sridharan and Jayadeva, 1982), the subroutine was linked with TOUGHREACT such that TOUGHREACT feeds relevant chemical properties into the subroutine, which subsequently calculates the swelling pressure. In this paper, a 1-D THC model with radial symmetric mesh is developed to evaluate the geochemically induced swelling-pressure change in an argillaceous formation hosting a nuclear waste emplacement tunnel. The model is composed of a heat source, a bentonite EBS and a host T

2D

2d

t

a

b

Fig. 1. (a) A representative unit layer separation for parallel clay platelets (Schanz and Tripathy, 2009), where t is the thickness of the swelling clay platelets. (b) A representative unit layer structure for parallel swelling clay and non-swelling mineral platelets, where D is the half width between two non-swelling mineral platelets and T is the thickness one non-swelling mineral platelet.


Heat source

0.45

1.14

27

17.5m

1.64

Bentonite

DRZ

Clay formation

Fig. 2. Schematic representation of the 1-D THC model.

clay formation with 0.5 m thick DRZ to represent the natural system (NS) (Fig. 2). First, the change in geochemical parameters (i.e., the concentration of the bulk pore water solution, the exchangeable cations, and the volume fraction of swelling clay minerals) in the host clay rock is calculated with the THC model using TOUGHREACT, and then the swelling pressure is calculated based on the input from the THC model. Eventually, the changes in hydraulic properties are computed and fed back to the THC model as needed. The change of pore volume as a result of swelling is not considered in the THC model, as such effect can only be taken into accounted by a fully coupled THMC code. The mineralogical composition of the bentonite (Table 1) is taken from the Kunigel-V1 bentonite (Ochs et al., 2004). The argillaceous formation is assumed to be Opalinus Clay, investigated in the Mont Terri Underground Rock Laboratory in Switzerland (Thury, 2002), and the mineral composition is also given in Table 1. Mineral dissolution/ precipitation is kinetically controlled, except for calcite, which is assumed to be in equilibrium. The kinetic law for mineral dissolution/ precipitation is given in Xu et al. (2006). The pore water composition of the bentonite (Sonnenthal, 2008) and the Opalinus Clay formation (Fernández et al., 2007) are shown in Table 2. In the current model, it is assumed that smectite is the only swelling mineral that has a specific surface area of 800 m2/g (Sridharan and Jayadeva, 1982). The cation exchange capacity for the argillaceous formation is taken from Thury (2002) which is 11.68 meq/100 g solid. The mass fraction of smectite f s is assumed to be equal to its volume fraction, which is shown in Table 1. Table 3 lists the thermal and hydrodynamic parameters used in the model. Those for the bentonite are taken from Sonnenthal (2008), while those for the clayey formation mostly are taken from Thury (2002) except for permeability. Soler (2001) reported that the Opalinus Clay has permeability ranging from 10−21 to 10−19 m2, with lower values of 10−21 to 8 · 10−21 m2 (De Windt and Palut, 1999; Harrington and Horseman, 1999) as evaluated from laboratory measurements, whereas higher value of 10−18 has been estimated from field tests (Nagra, 1989). Permeability of 10−19 m2 is used in the base case and a sensitivity run with permeability of 10−20 is reported as well. The DRZ is 0.5 m thick with a permeability of 10−17 m2 which is two orders of magnitude higher than the undisturbed argillaceous formation (Thury, 2002). Initially the EBS bentonite has a saturation degree of 65% and the clay formation is fully saturated. The initial temperature is 25 °C. A thermal decay function is applied to the heat source. The shape of the

Table 1 The abundance (volume fraction, dimensionless) of minerals in bentonite (Ochs et al., 2004) and Opalinus Clay Formation (Thury, 2002).

function is similar to that used in Rutqvist et al. (2011) for a 2D model, but the magnitude is scaled down so that the temperature in the EBS close to the heat source is slightly lower than 100 °C as shown in the temperature profile (Fig. 3(a)). The EBS bentonite is gradually hydrated and becomes fully saturated in about 10 years (Fig. 3(b)). 5. Model results for the base case Although the current simulation domain includes both the EBS (bentonite) and the natural system (NS: clayey rock + DRZ), we present only the chemical changes and subsequent swelling pressure change for clay rock, as this study is focused on the swelling pressure changes in the argillaceous formation. During the period of EBS hydration, chemical species are transported from the clayey rock to EBS by advection and diffusion. Fig. 4(a) shows the spatial distribution of ionic strength at different times. Ionic strength represents the total ion concentration, and its evolution is largely determined by the evolution of chloride and sodium which experience mainly advection and diffusion, and changes of calcium (Fig. 4(b)) which is mainly controlled by the dissolution of calcite. As illustrated in Fig. 4(a), for species that are less affected by chemical reactions a sharp decrease occurs at the very beginning in the area close to the EBS–NS interface when water is sucked into the initially dry bentonite buffer. Such a decrease propagates further away from the EBS–NS interface as time increases, although after longer time (e.g. 100 years), the concentrations rebound because of the inflow of water from the surrounding far-field area. Calcium concentration

Table 2 Pore water composition of the Kunigel bentonite (Sonnenthal, 2008) and the argillaceous host rock (Fernández et al., 2007).

pH Eh Cl SO−2 4 HCO− 3 +2 Ca Mg+2 Na+ K+ Fe+2 SiO2(aq) AlO− 2

Kunigel bentonite

Opalinus Clay Formation

8.40 −0.23 1.50 1.10 3.50 1.10 5.50 3.60 6.20 1.00 3.40 3.54

7.60 −0.27 3.32 1.86 5.20 2.26 2.09 2.76 2.16 2.96 1.16 3.89

· · · · · · · · · ·

10−5 10−4 10−3 10−4 10−5 10−3 10−5 10−10 10−4 10−8

· · · · · · · · · ·

10−1 10−2 10−3 10−2 10−2 10−1 10−3 10−7 10−4 10−6

Table 3 Thermal and hydrodynamic parameters (Sonnenthal, 2008; Thury, 2002).

Mineral

Opalinus Clay Formation

Kunigel bentonite

Parameter

Opalinus Clay

Kunigel bentonite

Calcite Dolomite Illite Kaolinite Smectite-Na Chlorite Quartz K-feldspar Siderite Ankerite Pyrite

0.1 0 0.223 0.174 0.1426 0.1445 0.1845 0.0 0.01256 0.00798 0.01

0.0235 0.029 0 0 0.475 0 0.335 0.041 0.0 0.0 0.006

Grain density [kg/m3] Porosity ϕ Saturated permeability [m2] Relative permeability, krl Van Genuchten α [1/Pa] Van Genuchten m Compressibility, β [1/Pa] Thermal expansion coeff., [1/°C] Dry specific heat, [J/kg °C] Thermal conductivity [W/m °C] Tortuosity for vapor phase

2700 0.15 1.0 · 10−19 m = 0.6, Srl = 0.01 6.8 · 10−7 0.6 3.2 · 10−9 0.0 800 2.2 (dry) / 2.2 (wet) ϕ1=3 Sg 10=3

2700 0.41 2.0 · 10−21 Krl = S3 3.3 · 10−8 0.3 5.0 · 10−8 1.0 · 10−4 1247 0.5/1.3 ϕ1=3 Sg 10=3

28


1.05

100 0 yr 0.1 yr 1 yr 10 yr 100 yr

Temperature oC

80 70 60

1

Water saturation

90

50 40 30 20

0.95 0.9

0 yr 0.1 yr 1 yr 10 yr 100 yr

0.85 0.8 0.75 0.7 0.65

10

0.6

0 0.4

1.4

2.4

3.4

0.4

4.4

Radial distance (m)

1.4

2.4

3.4

4.4

Radial distance (m)

a

b

Fig. 3. Spatial distribution of temperature (a) and water saturation (b) at different times.

the sediments, and the availability of potassium (Honty et al., 2004; Pusch and Madsen, 1995; Pusch et al., 2010), illitization which is usually part of the diagenesis process of a clay formation (Cuadros, 2006; Kamei et al., 2005) is widely observed in geological systems (Wersin et al., 2007). While details of the reactions are still of debate, two mechanisms seem to be generally agreed: (1) solid state transformation by substitution of intercrystal cations (e.g., Cuadros and Linares, 1996) and (2) a dissolution–precipitation process, i.e. the dissolution of smectite and the neo-formation of a separate illite phase (e.g. Pusch and Madsen, 1995), and either of them could occur depending the physico-

0.41

0.08

0.39

0.07

0.37

0.06

Ca (molal)

Ionic strengh (Molal)

keeps increasing due to the dissolution of calcite over time and spatially the profile shows higher concentration near the EBS–NS interface where calcite dissolution is more significant (Fig. 4(b)). Note that we use ionic strength to represent the ion concentration n (e.g., Eq. (3)) in the swelling model. The swelling capability of clay formation is largely determined by the smectite content. Illitization, the transformation from smectite to illite (a non-swelling clay mineral), results in a loss of swelling capability. Although the occurrence of illitization depends on many factors such as hydrothermal conditions, aqueous and mineralogical composition of

0.35

0 yr

0.33

0.1 yr

0.31

1 yr

0 yr 0.1 yr 1 yr 10 yr 100 yr

0.05 0.04 0.03

0.29

10 yr

0.02

0.27

100 yr

0.01 0

0.25

1

2

3

4

1

5

2

Radial distance (m)

3

5

4

5

b

a 0 -0.001

Illite volume fraction change

Smectite volume fraction change

4

Radial distance (m)

-0.002 -0.003

0 yr 0.1 yr 1 yr 10 yr 100 yr

-0.004

-0.005 -0.006 -0.007 -0.008 -0.009 -0.01 1

2

3

Radial distance (m)

c

4

5

0.007 0.006

0 yr 0.1 yr 1 yr 10 yr 100 yr

0.005 0.004 0.003 0.002 0.001 0 1

2

3

Radial distance (m)

d

Fig. 4. Spatial distribution of ionic strength (a), calcium (b), the smectite volume fraction change (dimensionless) (c) and illite volume fraction change (dimensionless) (d) at different times.


29

Weighted average Valence

Exhangeable Na mol/Kg solid)

1.55

1.E-01 1.E-02 1.E-03 1.E-04 1.E-05

X-Na 0 yr X_K 100 yr X_Mg 0 yr

X_Na 100 yr X_Ca 0 yr X_Mg 100 yr

X_K 0 yr X_Ca 100 yr

2

3

0 yr 0.1 yr 1 yr 10 yr 100 yr

1.45 1.4 1.35 1.3 1.25

1.E-06 1

1.5

4

5

1

2

Radial distance (m)

3

4

5

Radial distance (m)

a

b

Fig. 5. The concentration of exchangeable cations (a) and weighted average valence of exchangeable cations (b) at the 0 and 100 year.

þ

Smectite þ 0:52H þ 0:63AlO2

−

þ2

þ 0:6K ¼ illite þ 0:26H2 O þ 0:08Mg

Model results confirm a small dissolution of smectite, especially at the DRZ (Fig. 4(c)), and the precipitation of illite (Fig. 4(d)). Mineral dissolution/precipitation affects the concentration of aqueous cations, which subsequently induces changes in the composition of exchangeable cations. The concentration of calcium increases because of the dissolution of calcite, the concentration of potassium and magnesium decreases because of the precipitation of illite and chlorite, respectively. Fig. 5(a) shows the concentration of exchangeable cations at the beginning and at 100 years. The increase in aqueous calcium drives the exchangeable calcium to an elevated level, whereas the decrease in aqueous potassium and magnesium leads to a significant drop in exchangeable potassium and magnesium. Exchangeable sodium decreases due to the exchange with aqueous calcium. In the formulations using DDL to calculate the swelling pressure, the composition of the exchangeable cations is not specifically included. Instead, the weight average of the valence of exchangeable cations (Tripathy et al., 2004) is used to account for how the changes in exchangeable cations affect the swelling pressure. Weight averages for the valence of exchangeable cations at different times are therefore plotted (see Fig. 5(b)), which exhibits a significant increase especially near the EBS–NS interface and it is the consequence of the increase in exchangeable calcium and the decrease of exchangeable sodium (see Fig. 5(a)). The geochemical evolution in the host clay rock, including the decrease in the ionic strength of the pore water, loss of the smectite due to illitization, and changes in exchangeable cations, could lead to changes in the swelling pressure. Fig. 6 shows the calculated swelling pressure at different times. The initial swelling pressure is~14 bars, which is similar to the measured swelling pressure (ranging from 5 to 25 bars) of the Opalinus Clay (Madsen and Muller-vonmoss, 1985). The temporal and spatial change in swelling pressure, as shown in Fig. 6, is the result of the interplay of three geochemical driving forces: the ionic strength of the bulk solution, the abundance of smectite and the weight average of the valence of exchangeable cations. At early times, e.g. 0.1 year and 1 year, the decrease of ionic strength (see Fig. 4(a)) plays the major role so that swelling pressure increases. Later on, as the dissolution of smectite (Fig. 4(c)) and increase of weighted average of valence of exchange cations take over, swelling pressure starts decreasing, and after 100 years, in the area close to the EBS–NS interface, the swelling pressure could decrease to 8.5 bars. Note that the area that undergoes

significant swelling pressure changes only extends about 1.5 to 2 m into the clay rock. If the relative change in swelling pressure is defined as: t 0 0 P s −P s =P s 100

ð14Þ

þ

þ 0:33Na þ 0:5SiO2 ðaqÞ:

where, P0s and Pts are swelling pressure initially and at a given time, respectively, then after 100 years, the swelling pressure decreases by about 35%. The DRZ is one of the important concerns in the performance assessment of nuclear waste repositories in an argillaceous formation (Tsang et al., 2010), but the self-sealing of DRZ fractures could lower the risk brought by the DRZ. Self-sealing of clayey formations has been observed in laboratory tests (Van Geet et al., 2008; Zhang, 2011). The self-sealing (and self-healing) potential is largely determined by the swelling of the clay minerals (Rothfuchs et al., 2007). While great attention has been paid to the swelling caused by moisture change (e.g. Alonso et al., 1999) and self-sealing due to hydraulic effect (Zhang, 2011), our model results indicate that geochemical changes could modify the swelling capability in the clayey formation and potentially lower or enhance the self-sealing potential. Specifically it has been shown that an increase of exchangeable calcium due to the dissolution of calcite has an adverse effect on the swelling capability of the Opalinus Clay. The change in swelling pressure induces a change in porosity. Liu et al. (2011) proposed the following porosity–stress relation: σ ϕ ¼ ϕe ð1−C e σ Þ þ γ t exp Kt

ð15Þ

19

Swelling pressure (bar)

chemical conditions. The current model takes into account the second mechanism, i.e. the dissolution of smectite and precipitation of illite with the following reaction:

17 15 13

0 yr 0.1 yr 1 yr 10 yr 100 yr

11 9 7 1

2

3

4

Radial distance (m) Fig. 6. Spatial distribution of swelling pressure at different times.

5

30


γt ¼

16

ð16Þ

V 0;t V0

Swelling pressure (Bar)

ϕe ¼ ϕ0 −γ t

ð17Þ

where, Ce is the compressibility for the hard fraction of pore volume, ϕ0 is the porosity under the unstressed state, V0 is the total volume under the unstressed state, V0,t is the volume of soft fraction, Kt is the bulk modulus for the soft parts, and σ is the stress. Neglecting the soft part Eq. (4) can be simplified as:

14 12 10 8 6 4

base model

2

sensitivity run

0

ϕ ¼ ϕ0 ð1−C e σ Þ:

ð18Þ

1

If assuming a mechanically confined system, the change in swelling pressure causes an equal change in stress. Eq. (19) is therefore can be written in term of swelling pressure as:

Ce is not widely reported but ϕ0Ce can be approximated by the reciprocal of Young's modulus. Opalinus Clay has a Young's modulus of 2000–5000 MPa. With a porosity of 0.15, Ce is 2 · 10−9 Pa−1. The calculated porosity changes due to swelling are shown in Fig. 7(a). After 100 years, the porosity decreases insignificantly due to swelling, only about 0.1%. On the other hand, porosity is also changed by mineral dissolution/precipitation: porosity increases about 1.4%, resulting from geochemical effects that overshadow the porosity change due to swelling (Fig. 7(b)).

Porosity chagne by mineral dis/pre (%)

5.1.1. Sensitivity analysis Three types of geochemical changes may affect the swelling pressure of clay rock: ionic strength (the ion concentration of pore water), abundance of the smectite, and exchangeable cations. Exchangeable cations affect the swelling pressure by changing the weighted average valence of interlayer cations. The increase in weighted average valence tends to decrease the swelling pressure; the decrease in ionic strength tends to increase the swelling pressure; the decrease in the volume fraction of smectite tends to lower the swelling pressure, and the overall effect shown in the base case (Fig. 6) is that the swelling pressure increases at early time but eventually decrease after 100 years. In comparison with previous applications of DDL theory to calculate swelling pressure (e.g. Schanz and Tripathy, 2009; Tripathy et al., 2004), one major improvement introduced in this paper is to account for the changes of abundance of swelling clay through the parameter f s in Eq. (13).

Porosity change by swelling (%)

5

In order to evaluate how much the decrease in the volume fraction of smectite contributes to the final swelling-pressure change, we conducted a sensitivity run in which the effect of the decrease in the volume fraction of smectite is not considered. As expected, the sensitivity run does not result in as much decrease in swelling pressure as the basecase model does (Fig. 8). Although the difference could be as high as 10% at the EBS–NS interface, in most part it is only about 2–3%, indicating that moderate overestimation of swelling pressure could happen if the loss of smectite due to illitization was not considered. Because the interaction of the EBS with the host clay rock triggers the geochemical changes, the hydration rate of the bentonite is expected to play a significant role in the near-field geochemical evolution and subsequently in the changes in swelling properties. One of the key parameters that determine the hydration rate is the permeability of host clay formation. In a sensitivity run, the permeability is 10−20 m2 for undisturbed clay formation and 10−18 m2 for DRZ, both are one order of magnitude lower than that in base case. A decrease in permeability leads to a slower hydration of the bentonite and therefore slower transport of ions from the clay host rock to the bentonite. As shown in Fig. 9(a), at 1 year, ionic strength drops slightly in the sensitivity run, and after 100 years, the ionic strength is very similar to the initial values. As a result of the slow hydration of the bentonite, mineral dissolution/precipitation and the subsequent cation exchange are greatly inhibited. In contrast to the increase of exchange calcium and decrease of exchangeable sodium in the base case, exchangeable calcium and sodium after 100 years remain very similar to initial values in the sensitivity run and subsequently the weighted average of valence of exchangeable cations does not change significantly in the sensitivity run (Fig. 9(b)). Therefore, in the sensitivity run, swelling pressure only undergoes slight changes as shown in Fig. 10.

ð20Þ

0.14 0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08

4

Fig. 8. Comparison of swelling pressure at 100 years computed in the base model and a sensitivity run that does not consider the effect of the decrease of the volume fraction of smectite.

ð19Þ

Δϕ ¼ −ϕ0 C e ΔP s :

3

Radial distance (m)

Writing Eq. (18) in incremental form, we have: Δϕ ¼ −ϕ0 C e Δσ :

2

0 yr 0.1 yr 1 yr 10 yr

1.4 1.2 1

0 yr 0.1 yr 1 yr 10 yr 100 yr

0.8 0.6 0.4 0.2 0

1

2

3

4

Radial distance (m)

a

5

1

2

3

4

Radial distance (m)

b

Fig. 7. The change of porosity due to swelling pressure changes (a) and mineral precipitation/dissolution (b) at different times.

5


1.55

Weighted average Valence

0.45 0.4

Ionic strengh (Molal)

31

0.35 0.3 1 yr sensitivity run 100 yr sensitivity run 1 yr base run 100 yr base run

0.25 0.2 0.15

1 yr sensitivity run 100 yr sensitivity run 1 yr base run 100 yr base run

1.5 1.45 1.4 1.35 1.3 1.25

1

2

3

4

5

1

2

Radial distance (m)

3

4

5

Radial distance (m)

a

b

Swelling pressure chagne (%)

Fig. 9. Computed ionic strength (a) and weighted average valence (b) at 1 and 100 year in base and sensitivity run which has lower permeability for Opalinus Clay.

30 1 yr sensitivity run 100 yr sensitivity run 1 yr base run 100 yr base run

20 10 0 -10 -20 -30 -40 1

2

3

4

5

Radial distance (m) Fig. 10. Computed swelling pressure at 1 and 100 year in the base and sensitivity run which has more rapid hydration of the bentonite in the EBS.

6. Conclusions The swelling properties of argillaceous rocks close to the interface of engineered barrier system and host rock around an emplacement tunnel of a nuclear waste repository might change as a result of geochemical changes such us changes in ion concentration, exchangeable cations or the amount of swelling clay minerals. Host clayey rocks, especially in the near-field area, undergoes geochemical changes due to their interaction with the EBS components, as demonstrated by THC models for EBS and host rock (Sonnenthal, 2008). Therefore, it is necessary to evaluate the geochemically induced changes in swelling properties in the near-field of an argillaceous host rock. In this paper, coupled THC models are linked with a swelling model based on DDL theory, and these models are used to evaluate swelling pressure changes in the near field of a waste emplacement tunnel in clayey formation. A swelling model based on DDL theory allows the consideration of how the pore water ion concentration, the presence of exchangeable cations, and the abundance of swelling minerals affect the swelling properties of clay minerals in an argillaceous formation. However, it also has some limitations. First, the U–Kd relation derived from the DDL theory does not always lead to satisfactory prediction of swelling pressure. In fact, as noted in Schanz and Tripathy (2009), we must back-calculate the U–Kd relation based on experimental data in order to fit the measured data for compacted bentonite. Second, the effect of exchangeable cations is incorporated as the weighted average valence of exchangeable cations, which reflects only partially the impact of exchangeable cations on the overall swelling-property changes in the clay. For example, when sodium exchanges with potassium, the swelling properties could change significantly, but such phenomenon is not

captured by the swelling model based on DDL theory, as the weighted average valence of exchangeable cations remains the same. Third, such model can only be used at a fully saturated or close to fully saturated conditions and it only accounts for the swelling caused by geochemical changes. As a result, it cannot be used to calculate the swelling in the EBS bentonite that is induced by both moisture and geochemical changes. In the future the implementation of a combination of Barcelona Expansive Model (BExM) (Alonso et al., 1999) and DDL theory into TOUGHREACT-FLAC3D (Rutqvist et al., 2013), a simulator for modeling coupled thermal, hydrological, mechanical and chemical processes, will provide us the capability of calculating the swelling of EBS bentonite as a result of both moisture and geochemical changes. We developed a generic 1-D model that involves a heat source, a bentonite EBS, and an argillaceous host formation with a DRZ representing the natural system to evaluate the geochemically induced swelling-pressure change in the near field. Major findings based on this modeling work include: 1. Moderate changes in swelling pressure can be expected, but the extent of change depends on many hydrogeological and geochemical parameters. The change in EBS hydration rate could have a significant effect on the swelling pressure. 2. Geochemically induced swelling/shrinkage occurs exclusively in the near field, approximately a couple of meters away from the EBS–NS interface. 3. The swelling/shrinkage induced porosity change is generally much smaller than that caused by mineral precipitation/dissolution. 4. The geochemical induced swelling/shrinkage of host clay rock involves the combined effect of variation in pore water ion concentration, exchangeable cations, and amount of smectite. Neglecting any of these three factors might lead to miscalculation of the geochemically induced swelling pressure. Acknowledgments Funding for this work was provided by the Used Fuel Disposition Campaign, Office of Nuclear Energy, of the U.S. Department of Energy under Contract Number DE-AC02-05CH11231 with Berkeley Lab. References Alonso, E.E., Gens, A., Josa, A., 1990. A constitutive model for partially saturated soils. Geotechnique 40 (3), 405–430. Alonso, E.E., Vaunat, J., Gens, A., 1999. Modeling the mechanical behaviour of expansive clays. Eng. Geol. 54, 173–183. Andra, 2005. Dossier 2005 Argille. Synthesis. Evaluation of the feasibility of a geological repository in an argillaceous formation. ANDRA Report Series. Meuse/Haute-Marne site. Bolt, G.H., 1956. Physico-chemical analysis of the compressibility of pure clays. Geotechnique 6 (2), 86–93.

32


Bossart, P., Thury, M., 2008. Mont Terri Rock Laboratory — project, programme 1996 to 2007 and results. Reports of the Swiss Geological Survey No. 3. Swiss Geological Survey, Wabern (193 pp.). Cuadros, J., 2006. Modeling of smectite illitization in burial diagenesis environments. Geochim. Cosmochim. Acta 70 (16), 4181–4195. Cuadros, J., Linares, J., 1996. Experimental kinetic study of the smectite-to-illite transformation. Geochim. Cosmochim. Acta 60 (3), 439–453. De Windt, L., Palut, J.M., 1999. Tracer feasibility experiment FM-C, DI. In: Thury, M., Bossart, P. (Eds.), Geol. Ber., vol. 23. Swiss National Hydrological and Geological Survey, Bern. ENRESA, 2000. Full-scale engineered barriers experiment for a deep geological repository in crystalline host rock FEBEX Project, European Commission, (EUR 19147 EN). Fernández, A.M., Turrero, M.J., Sánchez, D.M., Yllera, A., Melón, A.M., Sánchez, M., Peña, J., Garralón, A., Rivas, P., Bossart, P., Hernán, P., 2007. On site measurements of the redox and carbonate system parameters in the low-permeability Opalinus Clay formation at the Mont Terri Rock Laboratory. Phys. Chem. Earth A/B/C 32 (1–7), 181–195. Gens, A., Alonso, E.E., 1992. A framework for the behaviour of unsaturated expansive clays. Can. Geotech. J. 29, 1013–1032. Ghassemi, A., Diek, A., 2003. Linear chemo-poroelasticity for swelling shales: theory and application. J. Pet. Sci. Eng. 38 (3–4), 199–212. Gonzales, S., Johnson, K.S., 1984. Shale and other argillaceous strata in the United States. ORNL/Sub/84-64794/1 Oak Ridge National Laboratory, Oak Ridge, TN. Guimarães, L.D., Gens, A., Olivella, S., 2007. Coupled thermo-hydro-mechanical and chemical analysis of expansive clay subjected to heating and hydration. Transp. Porous Media 66 (3), 341–372. Hansen, F.D., Hardin, E.L., Robert, L., Rechard, P., Freeze, G.A., Sassani, D.C., Brady, P.V., Stone, C.M., Martinez, M.J., Holland, J.F., Dewers, T., Gaither, K.N., Sobolik, S.R., Cygan, R.T., 2010. Shale Disposal of U.S. High-Level Radioactive Waste, SAND20102843. Sandia National Laboratories, Albuquerque, New Mexico. Harrington, J.F., Horseman, S.T., 1999. Laboratory experiments on hydraulic and osmotic flow. In: Thury, M.Ž., Bossart, P. (Eds.), Mont Terri Rock Laboratory: Results of the Hydrogeological, Geochemical and Geotechnical Experiments Performed in 1996 and 1997. Geol. Ber., vol. 23. Swiss National Hydrological and Geological Survey, Bern. Honty, M., Uhlik, P., Sucha, V., Caplovicova, M., Francu, J., Clauer, N., Biron, A., 2004. Smectite-to-illite alteration in salt-bearing bentonites (the East Slovak Basin). Clay Clay Miner. 52 (5), 533–551. Jougnot, D., Revil, A., Lu, N., Wayllace, A., 2010. Transport properties of the CallovoOxfordian clay rock under partially saturated conditions. Water Resour. Res. 46, W08514. Kamei, G., Mitsui, M.S., Futakuchi, K., Hashimoto, S., Sakuramoto, Y., 2005. Kinetics of long-term illitization of montmorillonite — a natural analogue of thermal alteration of bentonite in the radioactive waste disposal system. J. Phys. Chem. Solids 66 (2–4), 612–614. Komine, H., Ogata, N., 1996. Prediction for swelling characteristics of compacted bentonite. Can. Geotech. J. 33, 11–22. Komine, H., Ogata, N., 2003. New equations for swelling characteristics of bentonite-based buffer materials. Can. Geotech. J. 40, 460–475. Liu, H.H., Rutqvist, J., Birkholzer, J.T., 2011. Constitutive relationships for elastic deformation of clay rock: data analysis. Rock Mech. Rock. Eng. 44, 463–468. Madsen, F.T., Muller-vonmoss, M., 1985. Swelling pressure calculated from mineralogical properties of a Jurassic opalinum shale, Switzerland. Clay Clay Miner. 33 (6), 501–509. Mitchell, J.K., Soga, K., 2005. Fundamentals of Soil Behavior, Third edition. John Wiley & Sons, INC., p. 577. Sedimentstudie-Zwischenbericht, 1988Nagra, 1989. Moglichkeiten zur Endlagerung Langlebiger Radioaktiver Abfalle in den Sedimenten der Schweiz. Also executive summary in English, Nagra Technical Report 88-25E. Nagra Technischer Bericht 88-25, Nagra, Baden, Switzerland. Ochs, M., Lothenbach, B., Shibata, M., Yui, M., 2004. Thermodynamic modeling and sensitivity analysis of porewater chemistry in compacted bentonite. Phys. Chem. Earth A/B/C 29 (1), 129–136. Onikata, M., Kondo, M., Hayashi, N., Yamanaka, S., 1999. Complex formation of cationexchanged montmorillonites with propylene carbonate; osmotic swelling in aqueous electrolyte solutions. Clay Clay Miner. 47 (5), 672–677. Pearson, F.J., Arcos, D., Bath, A., Boisson, J.Y., Fernández, A.Mª., Gäbler, H.-E., Gaucher, E., Gautschi, A., Griffault, L., Hernán, P., Waber, H.N., 2003. Geochemistry of water in the Opalinus Clay Formation at the Mont Terri Rock Laboratory. Swiss Federal Office for Water and Geology Series, No. 5, (319 pp.). Pruess, K., 2004. The TOUGH codes: a family of simulation tools for multiphase flow and transport processes in permeable media. Vadose Zone J. 3, 738–746. Pusch, R., Madsen, F.T., 1995. Aspects on the illitization of the kinnekulle bentonites. Clay Clay Miner. 43 (3), 261–270.

Pusch, R., Kasbohm, J., Thao, H.T.M., 2010. Chemical stability of montmorillonite buffer clay under repository-like conditions—a synthesis of relevant experimental data. Appl. Clay Sci. 47 (1–2), 113–119. Rothfuchs, T., Jockwer, N., Zhang, C.L., 2007. Self-sealing barriers of clay/mineral mixtures — the SB project at the Mont Terri Rock Laboratory. Phys. Chem. Earth A/B/C 32 (1–7), 108–115. Rutqvist, J., Ijiri, Y., Yamamoto, H., 2011. Implementation of the Barcelona Basic Model into TOUGH-FLAC for simulations of the geomechanical behavior of unsaturated soils. Comput. Geosci. 37, 751–762. Rutqvist, J., Zheng, L., Chen, F., Liu, H.H., Birkholzer, J., 2013. Modeling of coupled thermohydro-mechanical processes with links to geochemistry associated with bentonitebackfilled repository tunnels in clay formations. Rock Mech. Rock. Eng. 1–20. Samper, J., Yang, Q., Yi, S., Garcia-Gutierrez, M., Missana, T., Mingarro, M., Alonso, U., Cormenzana, J.L., 2008. Numerical modeling of large-scale solid-source diffusion experiments in Callovo-Oxfordian clay. Phys. Chem. Earth 33, S208–S215. Schanz, T., Tripathy, S., 2009. Swelling pressure of a divalent-rich bentonite: diffuse double-layer theory revisited. Water Resour. Res. 45, W00C12. Soler, J.M., 2001. The effect of coupled transport phenomena in the Opalinus Clay and implications for radionuclide transport. J. Contam. Hydrol. 53 (1–2), 63–84. Sonnenthal, E., 2008. $132#Chapter 5. Long-term permeability/porosity changes in the EDZ and near field due to THM and THC processes in volcanic and crystalline–bentonite systems. In: Birkholzer, J. Rutqvist, Sonnenthal, E., Barr, D. (Eds.), DECOVALEX-THMC Project Task D Final Report. Sonnenthal, E., Ito, A., Spycher, N., Yui, M., Apps, J., Sugita, Y., Conrad, M., Kawakami, S., 2005. Approaches to modeling coupled thermal, hydrological, and chemical processes in the Drift Scale Heater Test at Yucca Mountain. Int. J. Rock Mech. Min. Sci. 42, 698–719. Spycher, N.F., Sonnenthal, E.L., Apps, J.A., 2003. Fluid flow and reactive transport around potential nuclear waste emplacement tunnels at Yucca Mountain, Nevada. J. Contam. Hydrol. 62–63, 653–673. Sridharan, A., Jayadeva, M.S., 1982. Double layer theory and compressibility of clays. Geotechnique 32 (2), 133–144. Thomas, H.R., He, Y., 1998. Modelling the behaviour of unsaturated soil using an elastoplastic constitutive model. Geotechnique 48 (5), 589–603. Thury, M., 2002. The characteristics of the Opalinus Clay investigated in the Mont Terri underground rock laboratory in Switzerland. C. R. Phys. 3 (7–8), 923–933. Tripathy, S., Sridharan, A., Schanz, T., 2004. Swelling pressures of compacted bentonites from diffuse double layer theory. Can. Geotech. J. 41, 437–450. Tsang, C.F., Birkholzer, J., Liu, H.H., 2010. A review of key processes and outstanding issues related to radioactive waste repositories in clay formations. DOE Used Fuel Disposition CampaignLawrence Berkeley National Laboratory. Van Geet, M., Bastiaens, W., Ortiz, L., 2008. Self-sealing capacity of argillaceous rocks: review of laboratory results obtained from the SELFRAC project. Phys. Chem. Earth A/B/C 33 (Supplement 1(0)), S396–S406. van Olphen, H., 1977. An Introduction to Clay Colloid Chemistry: For Clay Technologists, Geologists and Soil Scientists. Wiley-Interscience, New York. Wakim, J., Hassen, F., DeWindt, L., 2009. Effect of aqueous solution chemistry on the swelling and shrinkage of the Tournemire shale. Int. J. Rock Mech. Min. Sci. 46, 1378–1382. Wayllace, A., 2008. Volume change and swelling pressure of expansive clay in the crystalline swelling regime. University of Missouri, (Ph.D.). Wersin, P., Johnson, L.H., McKinley, I.G., 2007. Performance of the bentonite barrier at temperatures beyond 100 °C: a critical review. Phys. Chem. Earth A/B/C 32 (8–14), 780–788. Xu, T., Pruess, K., 2001. Modeling multiphase non-isothermal fluid flow and reactive geochemical transport in variably saturated fractured rocks: 1. Methodology. Am. J. Sci. 301, 16–33. 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. 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 (6), 763–774. Zhang, C.-L., 2011. Experimental evidence for self-sealing of fractures in claystone. Phys. Chem. Earth A/B/C 36 (17–18), 1972–1980. Zhang, G., Spycher, N., Sonnenthal, E., Steefel, C., Xu, T., 2008. Modeling reactive multiphase flow and transport of concentrated aqueous solutions. Nucl. Technol. 164, 180–195. Zheng, L., Apps, J.A., Zhang, Y., Xu, T., Birkholzer, J., 2009. On mobilization of lead and arsenic in groundwater in response to CO2 leakage from deep geological storage. Chem. Geol. 268, 281–297.