Title: Reactive transport modeling of concrete-clay interaction during 15 years at the Tournemire Underground Rock Laboratory Running title: Reactive transport modeling of concrete-clay interaction Plan: Abstract 1. Introduction 2. Description of the reactive transport code 3. Model setup 3.1. Dimensions 3.2. Composition of rock and concrete 3.3. Solution composition 3.4. Thermodynamic data 3.5. Reaction rates 3.6. Cation exchange 3.7. Transport parameters 4. Results 4.1. Concrete – bulk rock 4.2. Concrete – fracture in rock 5. Summary and conclusions Acknowledgements References Mailing address: Josep M. Soler, Institute of Environmental Assessment and Water Research (IDAEA-CSIC), Jordi Girona 18-26, 08034 Barcelona, Catalonia, Spain E-Mail:
[email protected] Phone: +34 934006100 Fax: +34 932045904 Computer: PC Operating System: Windows XP Word processor: Microsoft Office Word 2003 Number of characters (not including this page): 50148, including spaces
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Reactive transport modeling of concrete-clay interaction during 15 years at the
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Tournemire Underground Rock Laboratory
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Josep M. Soler
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Institute of Environmental Assessment and Water Research (IDAEA-CSIC)
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Jordi Girona 18-26, 08034 Barcelona, Catalonia, Spain
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[email protected]
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1
Soler
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Abstract
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Hydrated cement and concrete are major components of the engineered barrier system
11
in proposed underground repositories for radioactive waste. Concrete was in contact
12
with a clay-rich rock during 15 years in a borehole at the Tournemire Underground
13
Rock Laboratory in France. Overcoring of the borehole and mineralogical analyses have
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shown a reduction of porosity at the interface due to the precipitation of ettringite, C-S-
15
H/C-A-S-H and calcium carbonate, together with dissolution of portlandite in the
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cement.
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In the framework of the GTS-LCS project (JAEA, Japan; NAGRA, Switzerland;
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NDA, UK; POSIVA, Finland; SKB, Sweden), new reactive transport modeling (solute
19
diffusion + mineral reaction) has been performed, including a sensitivity analysis with
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respect to several compositional and kinetic parameters. Results using the CrunchFlow
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code show sealing of porosity at the rock side of the interface (mm scale) due to the
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precipitation of C-A-S-H (calcium aluminum silicate hydrate), calcite and ettringite,
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together with some clay dissolution. The location of sealing is influenced by cation
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exchange. Inclusion of cation exchange results in sealing at the rock side of the interface.
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Without cation exchange, sealing is at the concrete side of the interface.
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Calculated alteration profiles along cm-scale fractures show increased alteration
27
distances. Sealing of porosity is at the concrete side of the interface, due to the smaller
28
effect of cation exchange.
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Keywords
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Cement, concrete, clay, diffusion, porosity, modeling, C-S-H, C-A-S-H, cation
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exchange
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1. Introduction
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Hydrated cement and concrete are major components of the engineered barrier system
37
in proposed underground repositories for radioactive waste. The interaction between
38
groundwater and cement causes the generation of hyperalkaline solutions (pH 12.5 –
39
13.5), which may react with the rocks hosting the repositories and change their physical
40
and chemical properties. Experimental and modeling studies of such interactions have
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been common in the last years (e.g. Adler, 2001; Read et al., 2001; Savage et al., 2002,
42
2011; Soler, 2003; Gaucher et al., 2004; Hoch et al., 2004; Mäder et al., 2005; Soler &
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Mäder, 2005, 2007, 2010; Sánchez et al., 2006; Marty et al., 2009; Honty et al., 2010;
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Soler et al., 2011; Kosakowski & Berner, 2013). A common finding of these studies has
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been a reduction of porosity near the cement-rock interface due to the precipitation of
46
secondary phases. This decrease in porosity would be beneficial for the performance of
47
a repository (decrease in flow and transport properties). However, these studies are
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mainly based on laboratory experiments or are only modeling studies of larger systems
49
without the corresponding experimental data.
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Low-permeability clay-rich formations are being considered internationally as host
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rocks for radioactive water disposal. IRSN (French Institute of Radioprotection and
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Nuclear Safety) has performed an in-situ test at the Tournemire Undergound Rock
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Laboratory (SE France). A deep borehole (DM borehole; depth > 100 m) drilled normal
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to the bedding through the Toarcian argillite was filled with cement paste in the deeper
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parts and cement paste and concrete in the upper 2 m (Techer et al., 2012). After 15
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years, the upper part of this borehole was overcored and detailed mineralogical and
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porosity analyses of rock and cement/concrete were performed (Tinseau et al., 2006; De
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Windt et al., 2008; Gaboreau et al., 2011; Techer et al., 2012). Initially it had been
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considered that the samples were outside the Excavation Disturbed Zone (EDZ) induced
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by the construction of the tunnel, but it seems that they may still be within this EDZ
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(Techer et al., 2012; Bartier et al., 2013). However, the samples do not appear to have
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been affected by unsaturated conditions (De Windt et al., 2008). The concrete-rock
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system was initially modeled by De Windt et al. (2008). The observed features
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included: (1) Formation of a millimetric zone at the concrete-rock interface containing
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crusty Ca-carbonates (aragonite, calcite, vaterite), C-S-H (calcium silicate hydrate),
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gypsum and ettringite, with a concurrent decrease in clay and quartz contents. Gaboreau
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et al. (2011) and Bartier et al. (2013) studied a very similar experiment, where cement
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paste (the same paste used in the concrete) was in contact with the same rock. They 3
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noted that at least part of this C-S-H can be classified as C-A-S-H (calcium aluminum
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silicate hydrate). (2) The first zone was followed by a centimeter-scale zone with
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precipitation of calcite and clays. (3) A third centimeter-scale zone included calcite
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precipitation and possible K-feldspar overgrowth. Some Na-zeolite was also reported in
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a first characterization study (Tinseau et al., 2006), but its presence could not be
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confirmed in later studies.
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De Windt et al. (2008) concluded that a kinetic description of mineral dissolution and
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precipitation in the model was needed for a better reproduction of the observed
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mineralogical alterations in both bulk rock and along small cm-scale fractures normal to
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the concrete-rock interface.
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Within the GTS-LCS project (Grimsel Test Site - Long-Term Cement Studies, funded
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by JAEA-Japan, NAGRA-Switzerland, NDA-UK, POSIVA-Finland and SKB-Sweden),
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it was decided to update this modeling study (De Windt et al., 2008), including more
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recent thermodynamic data regarding cement phases (e.g. calcium silicate hydrates,
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monocarboaluminate). Cation exchange in the rock has also now been included. The
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interest in this system resides in that it is an analogue of cement-clay interaction in an
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underground repository for radioactive waste and it covers a time (15 a) longer than
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typical laboratory experiments. Modeling studies of this type of systems are still scarce.
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Three parallel modeling exercises have been running simultaneously within the project,
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led by Quintessa/SavageEarth (see e.g. Watson et al., 2012), JAEA and IDAEA-CSIC.
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This paper reports on the modeling study performed at IDAEA-CSIC with the
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CrunchFlow reactive transport code (Steefel, 2009). A detailed comparison of the three
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studies will be published in the future, once all the exercises and their comparison are
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completed.
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2. Description of the reactive transport code
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Reactive transport modeling was performed using CrunchFlow (Steefel, 2009). Details
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of the code can be found in the user’s manual (downloadable from www.csteefel.com).
97
Only an outline will be given here.
98 99
Crunchflow solves numerically the advection-dispersion-reaction equations
( (C mob j
C immob )) j t
D C mob j
qC mob j
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Rj
(j=1,2,…,Ntot)
(1)
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is porosity, C mob is the total concentration of mobile component or primary j
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where
101
species j in solution, C immob is the total concentration of immobile component j per j
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volume of solution (sorbed by surface complexation or ion exchange), D is the
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combined dispersion-diffusion coefficient, q is Darcy velocity, Rj is the total reaction
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rate affecting component j, t is time and Ntot is the total number of independent aqueous
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chemical components (primary species).
106
The combined dispersion-diffusion coefficient D is defined as the sum of the
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mechanical or kinematic dispersion D* and the effective diffusion coefficient De
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D = D* + De
109
(2)
The kinematic dispersion coefficient is written as qi q j
110
Dij*
111
where
112
is the magnitude of the Darcy velocity. The model assumes that the principal direction
113
of flow is aligned with the grid, i.e., Dij* is a diagonal matrix.
114 115
q
T
L
L
and
T
T
q
(3)
are the longitudinal and transverse dispersivities, respectively, and q
The total reaction rate for component j, Rj, is given by Rj
jm
Rm
(4)
m
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where Rm is the rate of precipitation ( Rm > 0) or dissolution ( Rm < 0) of mineral m per
117
unit volume of rock, and
118
mineral reactions are described using kinetic rate laws, initial mineral surface areas and
119
several reaction rate parameters have to be supplied by the user as input. In this set of
120
simulations, the reaction rate laws that have been used are of the form
121
Rm
Am
k 25 exp terms
jm
Ea 1 R T25
is the number of moles of j per mole of mineral m. Since
1 T
aini f m ( G)
(5)
i
122
where R m is the reaction rate for a given mineral in units of mol/m3rock/s, Am is the
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mineral surface area (m2/m3rock), k 25 is the reaction rate constant (mol/m2/s) at 25oC, R
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is the gas constant (8.3144 J/mol/k), Ea is the activation energy (J/mol), T is temperature
125
(K), a ini is the term describing the effect of species i on the rate (e.g. effect of H+), and
126
f m ( G) is the function describing the dependence of the rate on solution saturation
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state. The summation term indicates that several parallel rate laws may be used to
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describe the dependence of the rate on pH or on other species.
129 130
The f m ( G) function has the form 1 exp m2 g m3
f m ( G)
m1
(6)
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where
132
g
133
and G is the Gibbs energy of the reaction (J/mol), IAP is the ionic activity product of
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the solution with respect to the mineral and Keq is the equilibrium constant for that
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mineral reaction (ionic activity product at equilibrium). m1, m2 and m3 are parameters
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defining the shape of the fm( G) function. They are empirically determined through
137
experiments. Otherwise, they are assumed to be equal to 1 (single elementary reaction
138
controlling the reaction mechanism; Lasaga, 1998).
139 140
G RT
ln
IAP K eq
(7)
Changes in mineral surface area A (m2/m3bulk) due to reaction are calculated according to 2
141
A
A
initial
A
initial
m
initial m
2
3 initial
2
3
(dissolution)
(8)
3
142
A
143
where
144
terms including mineral volume fractions corresponds to the proportionality between
145
mineral areas (ideally proportional to grain size squared) and mineral volumes
146
(proportional to grain size cubed). The inclusion of a 2/3 dependence also on porosity is
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chiefly to ensure that as the porosity goes to 0, so too does the mineral surface area
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available for reaction (no reaction if there is no porosity). This formulation is used for
149
primary minerals (that is, minerals with positive initial volume fractions and surface
150
areas). For secondary minerals which precipitate, the value of the initial bulk surface
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area specified in the input files is used as long as precipitation occurs—if this phase
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later dissolves, an arbitrary “initial volume fraction” of 0.01 is assumed.
initial
(precipitation)
refers to porosity and
m
(9)
to mineral volume fraction. The 2/3 exponent in the
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Regarding the treatment of solid solutions, a kinetic approach similar to the one
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proposed by Carey & Lichtner (2006, 2007) and Lichtner & Carey (2006) has been
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used. Given a binary solid solution with compositional end-members AC and BC,
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solids with discrete compositions such as BC, A0.1B0.9C, A0.2B0.8C, …, AC are defined.
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The dissolution reaction for each of these solids can be written as
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AxB1-xC
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xA + (1-x) B + C
(10)
The equilibrium constant for this reaction will be defined as xss
1 xss
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K ss ( xss )
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where K1 and K2 are the equilibrium constants for the dissolution reactions of end-
162
members AC and BC, respectively, xss is the mol fraction of AC and
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activity coefficients of end-members AC and BC in the solid solution, respectively.
164
Once defined in this manner, the reaction of each discrete solid composition in a solid
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solution is treated just as any other phase (Eq. 5), and there is no need to implement 2
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different and simultaneous equilibrium requirements for each composition. For the sake
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of simplicity, only a few intermediate terms in the solid solution series have been taken
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into account.
K1 1 xss
K2
2
(1 xss )
(11)
1
and
2
are the
169 170
3. Model setup
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Several cases were taken into account in the calculations:
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Case 1 is a reference case, based mainly on the previous calculations by De
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Windt et al. (2008) and including also cation exchange in the rock (Beaucaire et
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al., 2008). Variant cases with larger (×100) and smaller (/100) surface areas for
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primary minerals in the rock, and with larger (×100) surface areas for primary
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phases in the cement, have also been considered.
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Case 2 is equivalent to case 1, but taking explicit account of the detailed
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structure of the borehole section, which includes an inner plastic tubing, a first
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annular section filled with cement paste and an outer annular section filled with
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concrete.
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Case 3 is equivalent to case 1 but including also zeolites as potential secondary
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phases in the rock.
183
Case 4 corresponds to the reference case 1, but without cation exchange in the
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rock.
185
Case 5 corresponds to the reference case 1, but without cation exchange and
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without prehnite (here an analogue for C-A-S-H) as a potential secondary phase.
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Case 6 corresponds to the reference case 1, but using an initial rock porewater
188
composition and rock cation exchange model from Tremosa et al. (2012).
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Case 7 corresponds to case 6, but without cation exchange.
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Case 8 is a simplification of the reference case 1. Montmorillonite, which did
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not show any significant reaction in case 1, was not included as a primary
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mineral. The missing volume fraction and surface area of montmorillonite were
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assigned to illite. Also, no saponites were included as potential secondary
194
phases. This case was used in the 2D calculation, which included a fracture in
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the rock.
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3.1. Dimensions
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Two types of simulations were performed: (1) 1D with symmetry around borehole axis,
199
simulating concrete – bulk rock interaction (Fig. 1a), and (2) 2D with symmetry around
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borehole axis, simulating concrete – fractured rock interaction (Fig. 1b). In case 2, the
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borehole is further subdivided into an inner inert zone (diameter 2.8 cm), corresponding
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to the tubing, a first annular zone (outer diameter 8.4 cm) filled with cement paste, and
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an outer annular zone filled with concrete (outer diameter 11 cm).
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The length of the numerical domain in the 1D simulations was 1.155 m. Grid spacing
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was 0.5 mm within 1 cm of the concrete-rock interface and it increased up to 1 mm in
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the concrete and 2 cm in the rock. In the 2D simulations, the size of the domain was
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1.155 m x 0.1 m. Grid spacing in the direction of the fracture was the same as in the 1D
208
simulations. Normal to the fracture, spacing increased from 0.2 mm in the fracture up to
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1 cm in the rock.
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3.2. Composition of rock and concrete
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Tables 1 and 2 show the initial composition of rock and concrete in the calculations.
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Both compositions, including surface areas (calculated from specific surface areas and
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mineral contents), are based on those reported by De Windt et al. (2008). In the
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concrete, monocarboaluminate was used instead of the monosulfoaluminate reported by
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De Windt et al. (2008). Monocarboaluminate is the stable phase when calcite is present
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(Lothenbach & Winnefeld, 2006). Actually, calculations were also performed using
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monosulfoaluminate in the initial composition (not shown here). The result was the
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quick transformation into monocarboaluminate. 8
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Table 3 shows the composition of the cement paste (CEM II) used in the calculations
221
for case 2. The composition is the same as in the concrete but without the calcite
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aggregate and with a porosity of 0.4 (Gaboreau et al., 2011).
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The potential secondary phases taken into account were C-S-H solid solution (Ca/Si =
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1.67, 1,4, 1.2, 1.0, 0.8, 0.6, 0.4, 0.2, 0.0), several crystalline C-S-H phases (foshagite,
225
gyrolite, hillebrandite, okenite, tobermorite-14A), prehnite (here as an analogue for C-
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A-S-H), gypsum, monosulfoaluminate and saponites. Inclusion of crystalline C-S-H
227
(tobermorite) allowed a better fit of solution chemistry in the study by Soler & Mäder
228
(2010). Prehnite is a mineral that forms under low-grade metamorphic conditions (e.g.
229
prehnite-pumpellyite facies) and is therefore not expected to precipitate as such in low-
230
T conditions. However, it has been shown in modeling studies (Soler & Mäder 2007,
231
2010) that it precipitates in the simulations when C-A-S-H phases are expected, roughly
232
between zones containing secondary C-S-H and zeolites (see e.g. Savage, 2013).
233
Therefore, prehnite is considered here as a suitable analogue of C-A-S-H phases, given
234
the lack of more appropriate thermodynamic data.
235
Additionally, zeolites (analcime, laumontite, natrolite, scolecite, gismondine,
236
mordenite, wairakite) were included in case 3. Mesolite and stilbite (included in the
237
thermodynamic database) were not considered in the calculations because the rock
238
porewater was already supersaturated with respect to those phases (they would
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precipitate in the model regardless of the influence from concrete).
240
Aragonite and vaterite have not been considered as potential secondary calcium
241
carbonates; only calcite has been taken into account. The issue of precipitation of
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metastable precursors has not been addressed here. Small amounts of barite were also
243
reported by De Windt et al. (2008), although celestite was identified instead by Techer
244
et al. (2012). For the sake of simplicity, Ba, barite and celestite have not been included
245
in the calculations.
246
The 2D calculations were only based on the simplified case 8. Primary mineral
247
contents and surface areas in the fracture were scaled (× 0.552) so the resulting porosity
248
was 0.5.
249 250
3.3. Solution composition
251
Initial solution compositions in the concrete and rock domains are shown in Table 4.
252
Initial concrete porewater has been modeled assuming an initial pH equal to 13.4 (De
253
Windt et al., 2008). Initial rock porewater in cases 1 to 5 and case 8 corresponds to the 9
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254
first sampling of borehole M2 (Beaucaire et al., 2008; Savoye, pers. comm.). The
255
original porewater composition has been forced to be in equilibrium with respect to
256
calcite, illite and kaolinite, resulting in small changes in pH and in K+, Cl- and Al3+ total
257
concentrations. In cases 6 and 7, the initial rock porewater composition is from Tremosa
258
et al. (2012; borehole M2) and equilibrated with calcite and illite.
259
The main difference between the 2 different rock porewaters is in total K+
260
concentration, with a smaller value in cases 5 and 6. That water composition also leads
261
to slight supersaturation with respect to kaolinite (log IAP/Keq = 0.24).
262 263
Sr2+ was only included in cases 5-6, in order to use the same cation exchange models as in Tremosa et al. (2012).
264 265
3.4. Thermodynamic data
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44 species in solution (49 when Sr was also taken into account) and a total of 45 solid
267
phases were considered in the simulations. All the equilibrium constants at 15oC (Tables
268
5 and 6) were taken from the database included in CrunchFlow, which is based on the
269
EQ3/6 database (Wolery et al., 1990), except for the C-S-H solid solution phases
270
(calculated from the data in Kulik & Kersten, 2001), hydrotalcite (value at 25oC from
271
Lothenbach & Winnefeld, 2006) ettringite, monosulfoaluminate and
272
monosulfocarbonate (Matschei et al., 2007). Molar volumes for gismondine (315.15
273
cm3/mol), illite (139.60 cm3/mol), tobermorite-14A (321.73 cm3/mol) and
274
montmorillonites (M-Ca 155.76 cm3/mol, M-K 158.44 cm3/mol, M-Mg 154.66
275
cm3/mol, M-Na 156.18 cm3/mol) were not provided in the database and had to be
276
added. They were calculated from reported densities. Activity coefficients are calculated
277
using the extended Debye-Hückel formulation (b-dot model). The activity of water is
278
taken to be unity.
279 280
3.5. Reaction rates
281
Table 7 shows the rate parameters used for the primary minerals in the rock. Regarding
282
the secondary minerals (except saponites and non-Ca montmorillonites), fast kinetics
283
have been assumed (Am = 1e5 m2/m3, km = 1e-9 mol/m2/s), simulating local equilibrium.
284
For all montmorillonites and saponites the rate laws shown in Table 7 have been used.
285
Initial surface areas for secondary montmorillonites and saponites were 1e5 m2/m3.
286
Fast kinetics (km = 1e-9 mol/m2/s) have also been assumed for the primary phases in the
287
concrete (transport control by slow diffusion results also in local equilibrium). 10
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288 289
3.6. Cation exchange
290
3.6.1. Cases 1-3, 8
291
Cation exchange capacity (81 meq/kg_solid) and selectivity coefficients (Table 8) for
292
the clay rock have been taken from Beaucaire et al. (2008). In this model, capacities are
293
defined on the bulk solid and not on individual minerals. Initial cation occupancies (Ca:
294
37eq%; Mg: 20eq%; Na: 19eq%; K: 24eq%) are at equilibrium with solution
295
composition.
296
In the 2D calculations, exchange capacity in the fracture was scaled to the same extent
297
as mineral contents (× 0.552).
298
3.6.2. Case 6
299
The cation exchange model used by Tremosa et al. (2012) has been applied in this case
300
(Table 9). This model is based on data from Bradbury & Baeyens (2000), Baeyens &
301
Bradbury (2004), Missana et al. (2008) and Tournassat et al. (2009). It includes 3 sites
302
on illite (planar, type-II and frayed edge sites) and 1 site on the primary Ca-
303
montmorillonite. Initial cation occupancies are at equilibrium with solution
304
composition.
305 306
3.7. Transport parameters
307
Diffusion is the only transport mechanism in the simulations. The effective diffusion
308
coefficient for all the species in the grout is calculated using the expression
309
De
310
with D0 equal to 1e-9 m2/s. Initial diffusion coefficients are given in Table 10. Diffusion
311
was anisotropic in the 2D calculations, with De normal to bedding smaller than parallel
312
to bedding (De,y = 0.33 De,x; Motellier et al., 2007). In case 2, the value for cement
313
paste was calculated from the value for concrete by assuming that there was no
314
diffusion through the aggregate. De of the concrete was divided by 1 minus the volume
315
fraction of calcite in the concrete (De,paste = De,concrete/(1-vol.fr.calcite)).
D0
(12)
316 317
4. Results
318
4.1. Concrete – bulk rock
319
Figure 2 shows mineral content in the domain near the concrete-rock interface after 15
320
years for case 1, together with a summary plot of observed secondary phases after De
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321
Windt et al., 2008 (see also Fig. 1 in Watson et al., 2012). Figure 3 shows mineral
322
contents for cases 2 to 5.
323 324
4.1.1. Case 1 (reference case)
325
The results show:
326
(1) Concrete:
327
Dissolution of portlandite within 3 mm from the interface
328
Minor decalcification of C-S-H (dissolution of C-S-H 1.67 and precipitation of
329
tobermorite).
330
(2) Interface:
331
Precipitation of ettringite across the interface (about 2 mm thick).
332
Precipitation of monocarboaluminate on both sides (only in 1 node on each
333
side).
334
Minor precipitation of tobermorite (1 node on each side).
335
(3) Rock. First 4 mm’s:
336
Precipitation of calcite near the interface (crust).
337
Dissolution of calcite between 2 and 4 mm.
338
Precipitation of prehnite (C-A-S-H), linked to the dissolution of clay (mainly
339
illite; source of Al3+).
340
Net dissolution of illite, kaolinite.
341
Dissolution of dolomite and precipitation of hydrotalcite (up to about 1 cm).
342
(4) Rock. From 4 mm up to ca. 1 cm:
343
Minor precipitation of illite and calcite.
344
Dissolution of kaolinite.
345
The dissolution of portlandite and increase in porosity in the cement was also
346
observed by Gaboreau et al. (2011) in their study of the interaction between cement
347
paste and argillite at Tournemire. Bartier et al. (2012) also reported decalcification of
348
the C-S-H. It has to be noted that, in the model, this decalcification is more intense in
349
early stages, and it reverses once porosity at the interface is sealed. Therefore, the
350
absolute degree of decalcification in the final resutls will be sensitive to the details in
351
the timing of the process.
352 353
Gaboreau et al. (2011) also observed that the decrease in porosity happened on the rock side of the interface. Again, this is not exactly the same case as the concrete – rock
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354
interaction studied here. The cement paste has a higher porosity (0.4) and lacks the
355
calcite aggregate (sand and gravel) added to make the concrete.
356
Bartier et al. (2013) have observed the neoformation of illite on mixed-layer
357
illite/smectite in distal parts of the alteration halo in the case of cement paste – rock
358
interaction. This newly formed illite was interpreted as the result of the illitization of
359
montmorillonite, although the dissolution of montmorillonite is not directly evident
360
from the observations. The results from this modeling study show precipitation of illite
361
in distal parts of the alteration halo, but no dissolution of montmorillonite. The issue of
362
illitization of smectite is still open. Besides the reactivity of the clays, differences
363
between cement and concrete (larger alkali inventories in the cement case) could also
364
play a role in this process.
365
No feldspar overgrowth in the rock is indicated by the results. However, the initial
366
rock porewater was supersaturated with respect to microcline (log IAP/Keq = 0.84).
367
Precipitation did not occur because the f( G) function used (see Table 7) was
368
formulated to avoid precipitation without a further perturbation from concrete.
369
However, it is possible that this initial supersaturation would lead, with time, to some
370
precipitation.
371
Additional simulations with higher initial surface areas for secondary
372
montmorillonites and saponites were also performed (not shown here). A surface area
373
value equal to 5e6 m2/m3 (equal to that of Ca-montmorillonite) was used. No significant
374
differences were observed (still negligible montmorillonite dissolution and saponite
375
precipitation).
376 377
4.1.2. Case 2
378
Case 2 takes explicit account of the detailed structure of the borehole section, which
379
includes an inner plastic tubing (inert in the simulations), a first annular section filled
380
with cement paste and an outer annular section filled with concrete. The result is that the
381
total pore volume and inventory of alkalies in the borehole (cement paste + concrete) is
382
twice as much as in the reference case (only concrete). However, the effect is small and
383
results (Fig. 3) are very similar to those of the reference case (Fig. 2).
384 385
4.1.3. Case 3
386
Case 3 includes zeolites as potential secondary minerals. Gismondine (a Ca zeolite)
387
does indeed appear as a secondary mineral. Results show a narrower zone of prehnite 13
Soler
388
precipitation, followed by a zone of about 1.5 cm where gismondine has precipitated.
389
However, the presence of zeolites in the rock has not been confirmed. It is therefore
390
concluded that the inclusion of zeolites leads to a poorer match of the observations at
391
Tournemire.
392 393
4.1.4. Case 4
394
Case 4 corresponds to the reference case 1 but without including cation exchange in the
395
rock. The following differences can be observed when cation exchange is not included:
396
Calcite precipitates on the concrete side of the interface.
397
Ettringite precipitates only on the concrete side of the interface.
398
Tobermorite replaces C-S-H 1.67 on the concrete side of the interface.
399
There is no calcite precipitation (crust) on the rock side of the interface.
400
Porosity sealing is on the concrete side of the interface (see below).
401 402
4.1.5. Case 5
403
Case 5 tested a case without cation exchange and without precipitation of prehnite as a
404
potential secondary phase. The results show only minor precipitation of C-S-H
405
(tobermorite) and calcite on the rock side of the interface. Another consequence of the
406
lack of a C-A-S-H phase is that illite does not dissolve (only minor dissolution of
407
kaolinite). Also, the precipitation of calcite further into the rock is negligible (less than
408
0.5 vol%). Clearly, the inclusion of C-A-S-H in the calculations improves the results.
409 410
4.1.6. Case 1 with different surface areas of primary minerals
411
The values of the primary mineral surface areas in the rock, taken from De Windt et al.
412
(2008), were based on specific surface areas (clays) and geometric surface areas (non-
413
clay primary minerals). Additional calculations were also performed with the reference
414
case 1, but (1) reducing the surface areas of primary minerals in the rock by a factor of
415
100, and (2) increasing the surface areas of primary minerals in the rock by a factor of
416
100. Results for the case with small surface areas (Fig. 4a) show only minor alteration
417
in the rock, not matching the observed alteration at Tournemire. Besides, the minor
418
precipitation of secondary phases (prehnite, ettringite, tobermorite, hydrotalcite) extends
419
up to about 5.5 cm into the rock, which is much further into the rock than reported (De
420
Windt et al., 2008).
14
Soler
421
Results for the case with larger surface areas (Fig. 4b) show calcite precipitation on
422
the concrete side of the interface and C-A-S-H (prehnite) precipitation on the rock side
423
of the interface. Prehnite precipitation is more concentrated in a narrow band (1.5 mm
424
thick), coupled to the complete dissolution of illite. Ettringite precipitates only on the
425
concrete side of the interface, while there is minor hydrotalcite precipitation across the
426
interface. Calcite precipitation in the rock is almost negligible (precipitation ≤ 1 vol%).
427
The results from a calculation using increased surface areas (×100) of the primary
428
phases in the concrete are basically identical to those of the reference case, which is
429
consistent with the large reaction rate constants and small diffusion coefficients in the
430
concrete (transport control of the reactions).
431 432
4.1.7. Cases 6 and 7
433
Recently, Tremosa et al. (2012) have formulated a model for the geochemistry of the
434
Tournemire porewater. Case 6 corresponds to calculations using a porewater
435
composition and cation exchange model from their model. Case 7 does not include
436
cation exchange. The results from these 2 cases are shown in Fig. 5. Results are fairly
437
similar to those from cases 1 and 4. However, the amounts of mineral dissolution and
438
precipitation in case 6 are somewhat smaller than in case 1, although with the same
439
phases and zonations. Again, not including cation exchange leads to sealing of porosity
440
on the concrete side of the interface.
441 442
4.1.8. Comparison of the different cases (porosities)
443
Figure 6 shows porosity distributions at different times for case 1. Figure 7 shows
444
porosity distributions for cases 2 to 5. The results from case 1 show the sealing of
445
porosity on the rock side of the interface and an increase in porosity on the concrete side
446
due to portlandite dissolution. Porosities tend to become stable once sealing prevents
447
solute exchange by diffusion between the two domains. Case 2 is similar to case 1, but
448
with a narrower (×0.5) zone of porosity sealing. Porosity distributions from case 3 are
449
also similar to those from case 1, but without the zone of porosity increase in the rock at
450
about 3.5 cm from the interface. In case 4 (no cation exchange), porosity clogs on the
451
concrete side of the interface. And in case 5, (no cation exchange and no prehnite),
452
porosity clogs across the interface (one node on each side).
453 454
Gaboreau et al. (2011) measured porosities across the contact between cement paste and rock from the DM borehole at Tournemire. The studied samples come from the 15
Soler
455
same borehole studied by De Windt et al (2008) and modeled again in this study, but
456
they are from a deeper level (3 m instead of 1.55 m; Techer et al., 2012), where cement
457
paste was used instead of concrete to fill the borehole. Porosities were measured by
458
water content determination (drying at 150oC during 48 hours) and also by
459
autoradiography (MMA resin impregnated with 3H and 14C). Comparison of the
460
modeling results with the case of cement paste – rock interaction studied by Gaboreau et
461
al. (2011) shows that for cement paste – rock interaction, (i) no thin (1 mm) crust at the
462
interface is formed and (ii) the altered zone in the clay rock is thicker. The thickness of
463
the zone with reduced porosity is of the order of 1 cm, compared to 1 mm for the
464
concrete – rock case. This may related to the fact that porosity in the cement paste
465
(40%) is larger than in the concrete (13%), which will result in larger De values and
466
alkali inventories (basically a larger amount of K+), allowing increased alteration in the
467
rock. Additionally, the zone of porosity sealing is not right at the concrete – rock
468
interface, but a few mm into the rock.
469
Figure 8 shows porosity distributions for the modified case 1 with (1) smaller (/100)
470
and (2) larger surface areas (×100) for primary mineral. Notice the sealing of porosity
471
right at the interface for the case with larger surface areas. No sealing is calculated for
472
the case with smaller areas.
473
Figure 9 shows porosity distributions for cases 6 and 7 (porewater composition and
474
cation exchange from Tremosa et al., 2012). Again, the results are fairly similar to those
475
from cases 1 and 4. Not including cation exchange leads to sealing of porosity on the
476
concrete side of the interface.
477 478
4.1.9. Exchange complex and solution composition
479
Further details regarding solution composition and evolution of the exchange complex
480
are referred to the reference case 1. Figure 10 shows pH near the interface at different
481
times. Notice the initial decrease of pH in the concrete from 13.4 to 12.8 due to the
482
diffusion of alkalies (mostly K+) from concrete into the rock. Concrete porewater is
483
always at equilibrium with respect to portlandite. The sharp pH gradient at the interface
484
at late times is caused by the sealing of porosity.
485
Figure 11 shows solute concentrations along the domain at different times. Notice the
486
initial fast decrease in K+ concentration in the concrete due to diffusion into the rock. At
487
later times, the sharp gradients across the concrete-rock interface are caused by sealing
488
of porosity at the interface. Solute profiles in the concrete become flat due to the lack of 16
Soler
489
transport caused by the sealing of porosity at the interface. Profiles of the major
490
components (Na+, SO42-) in the rock also become flatter due to the lack of significant
491
mineral reaction. However, the components in smaller concentrations still show
492
gradients. Reactions still happen at very slow rates (calcite precipitation, C-S-H/C-A-S-
493
H and aluminosilicate conversions) and are sufficient to maintain the small gradients
494
(balance between reaction and slow diffusive solute transport).
495
Figure 12 shows cation occupancies on the exchange complex at different times
496
(reference case 1). Initially, K+ diffusing from the concrete porewater displaces Ca2+
497
and Mg2+ from the exchange complex. Na+, also diffusing from the concrete, displays
498
weaker sorption. K+ and Na+ in the concrete are limited by their initial concentrations in
499
the porewater and are not supplied by any mineral. The consequence is that K+ and Na+
500
peaks in the exchange complex propagate away from the interface as a single pulse,
501
allowing the partial recovery of the initial Ca2+ occupancies due to diffusion from the
502
rock.
503 504
4.2. Concrete – fracture in rock
505
The calculations for this two-dimensional case were based on the simplified model (case
506
8). Model setup is shown in Fig. 1b. Figures 13 and 14 show mineral contents in the
507
domain near the concrete-rock interface for 1D (only bulk rock) and 2D calculations
508
(1D profile along fracture), respectively. Figure 14 (2D calculation) corresponds to t = 5
509
a (interface already sealed). The following observations can be made:
510
Results are similar to the concrete – bulk rock case, but the zone of mineral alteration
511
along the fracture is longer by a factor close to 2, which is consistent with observations.
512
Mineralogy is similar to the concrete – bulk rock case without cation exchange (e.g.
513
calcite precipitation and porosity sealing on the concrete side of the interface; see Fig.
514
3c), due to the smaller cation exchange capacity in the fracture (× 0.552).
515 516
5. Summary and conclusions
517
The interaction between concrete and clay rock at Tournemire has been modeled using
518
the CrunchFlow code, and the results have been compared with field observations.
519
Results are consistent with diffusion-controlled solute transport between concrete and
520
rock. No apparent effect of advective water flow has been observed. A limited sensitiviy
521
analysis has evaluated the effects of including the detailed experimental setup in the
522
borehole (inner tubing, first annular section filled with cement paste, outer annular 17
Soler
523
section filled with concrete), inclusion or not of zeolites as potential secondary
524
minerals, inclusion or not of cation exchange in the rock and inclusion or not of prehnite
525
as an analogue for C-A-S-H phases. The effect of changing the surface areas of primary
526
minerals in the rock has also been studied. Additionally, a rock porewater composition
527
and cation exchange model from the recent study by Tremosa et al. (2012) have also
528
been evaluated. Finally, a single 2D calculation has addressed the case of a small
529
fracture in the rock.
530
The calculation including the detailed experimental setup in the borehole shows very
531
similar results compared to those of the reference case, with a somewhat narrower zone
532
of porosity sealing in the rock next to the concrete-rock interface.
533
The interaction between concrete and clay rock leads to the sealing of porosity at or
534
very close to the interface (despite dissolution of clay) and an increase in porosity on the
535
cement side of the interface (portlandite dissolution). The sealing of porosity is due to
536
the precipitation of C-A-S-H, calcite and ettringite. The most reactive clays in the
537
calculations are illite and kaolinite. Montmorillonite shows no significant reaction.
538
Calculation results have also shown that the inclusion or not of saponites as potential
539
secondary minerals has no great effect.
540
When including cation exchange, the initial supply of Ca2+ by cation exchange
541
(displaced by K+ and Na+) determines that calcite precipitation and porosity sealing
542
occur on the rock side of the interface. This effect is shown when using either the cation
543
exchange model by Beaucaire et al. (2008) or the model from Tremosa et al. (2012).
544
The inclusion of cation exchange determines the detailed position of the zone of
545
porosity sealing, but since sealing does happen regardless of the inclusion of this
546
process, it is probable that it does not have a large effect over the the long time scales
547
relevant for waste disposal (thousands of years).
548
The values of the primary mineral surface areas in the rock, taken from De Windt et
549
al. (2008), were based on specific surface areas (clays) and geometric surface areas
550
(non-clay primary minerals). Smaller surface areas (/100) led to little mineral alteration,
551
not consistent with observations, and no porosity sealing. Larger surface areas (×100)
552
led to a narrower band of prehnite precipitation and complete dissolution of illite.
553
Calcite precipitation (and also ettringite) was mainly on the concrete side of the
554
interface, with minor precipitation in the rock. The results with the large surface areas
555
cannot be said to be incompatible with observations at Tournemire.
18
Soler
556
The inclusion of zeolites as potential secondary minerals in the calculations, under a
557
local equilibrium approach, does have an important effect. Gismondine (a Ca zeolite)
558
does precipitate in the calculations. It has to be noted that the precipitation of zeolites, at
559
least under significant quantities, has not been confirmed. The outcome is that inclusion
560
of zeolites, at least under a local equilibrium approach (fast kinetics), does not improve
561
the results of the modeling. Actually, results without zeolites are a better approximation
562
of the observed alteration at Tournemire.
563
Not including prehnite as an analogue of a C-A-S-H phase leads to a worse
564
approximation of the observed mineralogical alteration (smaller precipitation of C-S-H
565
and calcite; smaller dissolution of clay), besides the obvious lack of a C-A-S-H phase.
566
The final conclusion is that an overall fit of the observations can be effectively
567
achieved by modeling (mainly reference case 1: portlandite dissolution in the concrete,
568
sealing of porosity at the interface, C-A-S-H – carbonate – ettringite crust, minor clay
569
and carbonate precipitation further into the rock, spatial extent of alteration). Besides a
570
decrease in clay content at the concrete-rock interface, De Windt el al. (2008) also
571
reported a decrease in quartz content at the interface. Model results do not show any
572
significant dissolution of quartz. However, the reported decrease in quartz content could
573
be due to the precipitation of other phases, which leads to the sealing of porosity and
574
results in a smaller mass percentage of quartz. It should also be noted that Bartier et al.
575
(2013) did not confirm the dissolution of quartz in their study of cement paste – rock
576
interaction in another borehole at the same site.
577
Gypsum does not precipitate as a secondary phase in any of the simulations. De Windt
578
et al. (2008) argued that this gypsum may possibly be the result of the oxidation of the
579
small amounts of pyrite in the rock (less than 1 wt%) after drilling the borehole.
580
Calculated alteration profiles along cm-scale fractures show increased alteration
581
distances. Sealing of porosity is at the concrete side of the interface, due to the smaller
582
effect of cation exchange.
583
Finally, the observed sealing of porosity near the concrete/cement – rock interface,
584
despite the dissolution of clays in the rock, would be beneficial for the performance of
585
a repository (reduced transport properties). However, some issues clearly deserve
586
further attention, including the detailed characterization of C-S-H phases (composition
587
and crystallinity), the development of thermodynamic models for C-A-S-H phases, or
588
the study of the factors controlling zeolite precipitation in these systems.
589 19
Soler
590 591 592 593
Acknowledgements
594
The financial support from Posiva Oy, the discussions with the LCS team under the lead
595
of Jörg Rüedi, ant the detailed comments from two anonymous reviewers and from the
596
editor, Prof. Manuel Prieto, are gratefully acknowledged.
597 598
References
599
Adler, M. (2001): Interaction of claystone and hyperalkaline solutions at 30°C: A
600
combined experimental and modeling Study. PhD Dissertation, Univ. Bern.
601
Baeyens, B. & Bradbury, M.H. (2004): Cation exchange capacity measurements on
602
illite using the sodium and cesium isotope dilution technique: effects of the index
603
cation, electrolyte concentration and competition: modelling. Clays Clay Miner., 52,
604
421–431.
605
Bandstra, J.Z., Buss, H.L., Campen, R.K., Liermann, L.J., Moore, J., Hausrath, E.M.,
606
Navarre-Sitchler, A.K., Jang, J.-H., Brantley, S.L. (2008): Appendix: Compilation
607
of mineral dissolution rates. in “Kinetics of Water-Rock Interaction”, S.L. Brantley,
608
J.D. Kubicki, A.F. White, eds., Springer, New York, 737-823.
609
Bartier, D., Techer, I., Dauzères, A., Boulvais, P., Blanc Valleron, M.-M., Cabrera, J.
610
(2013): In situ investigations and reactive transport modelling of cement
611
paste/argillite interactions in a saturated context and outside an excavated disturbed
612
zone. Appl. Geochem., 31, 94-108.
613
Beaucaire, C., Michelot, J.-L., Savoye, S., Cabrera, J. (2008): Groundwater
614
characterisation and modelling of water-rock interaction in an argillaceous
615
formation (Tournemire, France). Appl. Geochem., 23, 2182-2197.
616
Bradbury, M.H. & Baeyens, B. (2000): A generalised sorption model for the
617
concentration dependent uptake of caesium by argillaceous rocks. J. Cont. Hydrol.,
618
42, 141–163.
619 620 621 622
Burch, T.E., Nagy, K.L., Lasaga, A.C. (1993): Free energy dependence of albite dissolution kinetics at 80oC and pH 8.8. Chem. Geol., 105, 137-162. Cama, J., Ganor, J., Ayora, C., Lasaga, A.C. (2000): Smectite dissolution kinetics at 80 C and pH 8.8. Geochim. Cosmochim. Acta, 64, 2701-2717.
20
Soler
623
Carey, J.W. & Lichtner, P.C. (2006): Calcium silicate hydrate solid solution model
624
applied to cement degradation using the continuum reactive transport model
625
FLOTRAN. Report LA-UR-06-0636, Los Alamos National Laboratory, Los
626
Alamos.
627
Carey, J.W. & Lichtner, P.C. (2007): Calcium silicate hydrate (C-S-H) solid solution
628
model applied to cement degradation using the continuum reactive transport model
629
FLOTRAN. in “Transport Properties and Concrete Quality: Materials Science of
630
Concrete”, Mobasher, B., Skalny, J., eds., American Ceramic Society, Special
631
Volume, 73-106.
632
De Windt, L., Marsal, F., Tinseau, E., Pellegrini, D. (2008): Reactive transport
633
modeling of geochemical interactions at a concrete/argillite interface, Tournemire
634
site (France). Phys. Chem. Earth, 33, S295-S305.
635
Gaboreau, S., Prêt, D., Tinseau, E., Claret, F., Pellegrini, D., Stammose, D. (2011): 15
636
years of in situ cement-argillite interaction from Tournemire URL: Characterisation
637
of the multi-scale spatial heterogeneities of pore space evaluation. Appl. Geochem.,
638
26, 2159-2171.
639 640 641
Gaucher, E.C., Blanc, Ph., Matray, J.-M., Michau, N. (2004): Modeling diffusion of an alkaline plume in a clay barrier. Appl. Geochem., 19, 1505–1515. Hoch, A.R., Linklater, C.M., Noy, D.J., Rodwell, W.R. (2004): Modelling the
642
interaction of hyperalkaline fluids with simplified rock mineral assemblages. Appl.
643
Geochem., 19, 1431-1451.
644
Honty, M., De Craen, M., Wang, L., Madejová, J., Pentrák, M., Strícek, I., Van Geet, M.
645
(2010): The effect of high pH alkaline solutions on the mineral stability of the
646
Boom Clay - Batch experiments at 60 oC. Appl. Geochem., 25, 825-840.
647
Kosakowski, G. & Berner, U. (2013): The evolution of clay rock/cement interfaces in a
648
cementitious repository for low- and intermediate level radioactive waste. Phys.
649
Chem. Earth, in press.
650
Kulik, D.A. & Kersten, M. (2001): Aqueous solubility diagrams for cementitious waste
651
stabilization systems: II, end-member stoichiometries of ideal calcium silicate
652
hydrate solid solutions. J. Am. Ceram. Soc., 84, 3017-3026.
653 654
Lasaga, A.C. (1998): Kinetic theory in the earth sciences. Princeton Univ. Press, Princeton, NJ, 811 p.
21
Soler
655
Lichtner, P.C. & Carey, J.W. (2006): Incorporating solid solutions in reactive transport
656
equations using a kinetic discrete-composition approach. Geochim. Cosmochim.
657
Acta, 70, 1356-1378.
658 659 660
Lothenbach, B., Winnefeld, F. (2006): Thermodynamic modelling of the hydration of Portland cement. Cem. Concr. Res., 36, 209-226. Mäder, U.K., Fierz, Th., Frieg, B., Eikenberg, J., Rüthi, M., Albinsson, Y., Möri, A.,
661
Ekberg, S. (2005): Interaction of hyperalkaline fluid with fractured rock: field and
662
laboratory experiments of the HPF project (Grimsel Test Site, Switzerland). J.
663
Geochem. Explor., 90, 68–94.
664
Marty, N.C.M., Tournassat, C., Burnol, A., Giffaut, E., Gaucher, E.C. (2009): Influence
665
of reaction kinetics and mesh refinement on the numerical modelling of
666
concrete/clay interactions. J. Hydrol., 364, 58-72.
667
Matschei, T., Lothenbach, B., Glasser, F.P. (2007): Thermodynamic properties of
668
Portland cement hydrates in the system CaO-Al2O3-SiO2-CaSO4-CaCO3-H2O.
669
Cem. Concr. Res., 37, 1379-1410.
670 671 672 673
Missana, T., García-Gutiérrez, M., Alonso, U. (2008): Sorption of strontium onto illite/smectite mixed clays. Phys. Chem. Earth, 33, S156–S162. Morse, J.W. & Arvidson, R.S. (2002): The dissolution kinetics of major sedimentary carbonate minerals. Earth-Sci. Rev., 58, 51-84.
674
Motellier, S., Devol-Brown, I., Savoye, S., Thoby, D., Alberto, J.-C. (2007): Evaluation
675
of tritiated water diffusion through the Toarcian clayey formation of the Tournemire
676
experimental site (France). J. Cont. Hydrol., 94, 99-108.
677
Palandri, J.L. & Kharaka, Y.K. (2004): A compilation of rate parameters of water-
678
mineral interaction kinetics for application to geochemical modeling. Open File
679
Report 2004-1068, U.S. Geological Survey, Menlo Park.
680
Read, D., Glasser, F.P., Ayora, C., Guardiola, M.T., Sneyers, A. (2001): Mineralogical
681
and microstructural changes accompanying the interaction of Boom Clay with
682
ordinary Portland cement. Adv. Cem. Res., 13, 175-183.
683
Sánchez, L., Cuevas, J., Ramírez, S., Riuiz De León, D., Fernández, R., Vigil Dela Villa,
684
R., Leguey, S. (2006): Reaction kinetics of FEBEX bentonite in hyperalkaline
685
conditions resembling the cement-bentonite interface. Appl. Clay Sci., 33, 125-141.
686
Savage, D. (2013): Constraints on cement-clay interaction. Procedia Earth Planet. Sci.,
687
7, 770-773.
22
Soler
688 689 690
Savage, D., Noy, D., Mihara, M. (2002): Modelling the interaction of bentonite with hyperalkaline fluids. Appl. Geochem., 17, 207–223. Savage, D., Soler, J.M., Yamaguchi, K., Walker, C., Honda, A., Inagaki, M., Watson,
691
C., Wilson, J., Benbow, S., Gaus, I., Rueedi, J. (2011): A comparative study of the
692
modelling of cement hydration and cement-rock laboratory experiments. Appl.
693
Geochem., 26, 1138-1152.
694
Soler, J.M. (2003): Reactive transport modeling of the interaction between a high-pH
695
plume and a fractured marl: the case of Wellenberg. Appl. Geochem., 18, 1555–
696
1571.
697 698 699
Soler, J.M. & Lasaga, A.C. (1996): A mass transfer model of bauxite formation. Geochim. Cosmochim. Acta, 24, 4913-4931. Soler, J.M. & Mäder, U.K. (2005): Interaction between hyperalkaline fluids and rocks
700
hosting repositories for radioactive waste: reactive transport simulations. Nucl. Sci.
701
Eng., 151, 128–133.
702
Soler, J.M. & Mäder, U.K. (2007): Mineralogical alteration and associated permeability
703
changes induced by a high-pH plume: Modeling of a granite core infiltration
704
experiment. Appl. Geochem., 22, 17-29.
705 706 707
Soler, J.M. & Mäder, U.K. (2010): Cement-rock interaction: Infiltration of a high-pH solution into a fractured granite core. Geol. Acta, 8, 221-233. Soler, J.M., Vuorio M., Hautojärvi, A. (2011): Reactive transport modeling of the
708
interaction between water and a cementitious grout in a fractured rock. Application
709
to ONKALO (Finland). Appl. Geochem., 26, 1115-1129.
710 711
Steefel, C.I. (2009): CrunchFlow. Software for modeling multicomponent reactive flow and transport. User’s manual. Lawrence Berkeley National Laboratory, Berkeley.
712
Techer, I., Bartier, D., Boulvais, Ph., Tinseau, E., Suchorski ,K., Cabrera, J., Dauzères,
713
A. (2012): Tracing interactions between natural argillites and hyper-alkaline fluids
714
from engineered cement paste and concrete: Chemical and isotopic monitoring of a
715
15-years old deep-disposal analogue. Appl. Geochem., 27, 1384-1402.
716
Tinseau, E., Bartier, D., Hassouta, L., Devol-Brown, I., Stammose, D. (2006):
717
Mineralogical characterization of the Tournemire argillite after in situ interaction
718
with concretes. Waste Manage., 26, 789–800.
719
Tournassat, C., Gailhanou, H., Crouzet, C., Braibant, G., Gautier, A., Gaucher, E.C.
720
(2009): Cation exchange selectivity coefficient values on smectite and mixedlayer
721
illite/smectite minerals. Soil Sci. Soc. Am. J., 73, 928–942. 23
Soler
722
Tremosa, J., Arcos, D., Matray, J.M., Bensenouci, F., Gaucher, E.C., Tournassat, C.,
723
Hadi, J. (2012): Geochemical characterization and modelling of the
724
Toarcian/Domerian porewater at the Tournemire underground research laboratory.
725
Appl. Geochem., 27, 1417-1431.
726
Watson, C.E., Savage, D., Wilson, J., Walker, C., Benbow, S.J. (2012): The long-term
727
cement studies project: the UK contribution to model development and testing.
728
Mineral. Mag., 76, 3445-3455.
729
Wolery, T. J., Jackson, K.J., Bourcier, W.L., Bruton, C.J., Viani, B.E., Knauss, K.G.,
730
Delany, J.M. (1990): Current status of the EQ3/6 software package for geochemical
731
modeling. in “Chemical Modeling of Aqueous Systems II”, G. Melchior & R.L.
732
Bassett, eds., ACS Symposium Series No 416, 104-116.
24
Soler
Concrete
Symmetry around borehole axis
Rock
1D domain
(a)
11 cm
Concrete
Symmetry around borehole axis
Rock = 0.095
2D domain
(b)
Fracture: 3 cm long 1.2 mm wide Porosity = 0.5 10 cm
11 cm
Fig. 1. Schematic representation of the numerical domains and dimensions. (a) Concrete – bulk rock; (b) concrete – fractured rock.
Case 1, t = 15 a 60 Calcite
Prehnite (C-A-S-H)
50
Montmor.-Ca
Vol%
40
Calcite
30
Illite Quartz
20
C-S-H 1.67
10 Portl.
Calcite Microcline
Ettringite
Kaolinite
Monocarb.
0 0.050
Toberm.
0.055
Hydrotalcite
0.060
Dolomite
0.065
x (m)
aragonite/calcite/vaterite C-S-H ettringite barite, clayey phases calcite calcite
Fig. 2. Calculated mineral volume fractions vs. distance from center of borehole at t = 15 a for case 1 (reference case). Concrete – rock interface is at x = 0.055 m. At the bottom there is a summary plot of observed secondary phases, after De Windt et al. (2008).
(a) Case 2, t = 15 a
(c) Case 4, t = 15 a
60
100
Prehnite (C-A-S-H)
Vol%
Montmor-Ca
Calcite
40
Illite
30 20
C-S-H 1.67
60
20
Microcline
Monocarb.
Kaolinite Dolomite
0.055
0.060 x (m)
(d) Case 5, t = 15 a
Calcite
50
Prehnite (C-A-S-H)
Illite
30
C-S-H 1.67 Portl.
0 0.050
Calcite Montmor-Ca
40
Vol%
Vol%
0.065
Kaolinite
60
40
10
Microcline
0.060
Hydrotalcite x (m)
(b) Case 3, t = 15 a
20
Calcite
0.055
Hydrotalcite
60 50
Illite
C-S-H 1.67 Portl. Ettr.
0 0.050
0.065
Quartz
Toberm.
40
Calcite
Portl.
0 0.050
Prehnite (C-A-S-H)
Quartz
Ettringite 10
Calcite 80
Vol%
Calcite
50
Quartz Gismondine Calcite
Monocarb. 30 20
Quartz
C-S-H 1.67 Ettringite
Microcline
10 Portl.
Ettr. 0.055Toberm. x (m)
0.060
Dolomite
0.065
0 0.050
Illite
0.055
Kaolinite Toberm. 0.060
0.065
x (m)
Fig. 3. Calculated mineral volume fractions vs. distance from center of borehole at t = 15 a for cases 2 to 5. Concrete – rock interface is at x = 0.055 m. (a) Case 2: Including tubing, cement paste and concrete in the borehole. (b) Case 3: Including zeolites. (c) Case 4: No cation exchange. (d) Case 5: No cation exchange and no prehnite.
(a) Case 1, small A’s, t = 15 a
(b) Case 1, large A’s, t = 15 a
10
80
4
60
Kaolinite
Vol%
Vol%
6
Prehnite (C-A-S-H) Ettringite
Hydrotalcite Dolomite
0.06
0.07
Toberm.
0.08 x (m)
0.09
0.10
Calcite
Microcline Toberm.
40
20
2 0 0.05
Prehnite (C-A-S-H)
Montmorillonite-Ca
8
Illite Quartz
C-S-H 1.67 Portl.
0 0.050
Kaolinite Mont.-Ca0.060 0.065 Ettringite Hydrotalc. Dolomite x (m) 0.055
Fig. 4. Calculated mineral volume fractions vs. distance from center of borehole at t = 15 a for case 1 with (a) reduced (/100) and (b) increased (×100) surface areas for primary minerals. (a) only shows a detail of the precipitated secondary phases. Concrete – rock interface is at x = 0.055 m.
(a) Case 6, t = 15 a
(b) Case 7, t = 15 a
60 50
100
Calcite
Prehnite (C-A-S-H)
Montmor-Ca
80
Illite Quartz
30 20
C-S-H 1.67 Ettringite
10
Calcite
Portl.
0 0.050
Vol%
Vol%
40
Microcline Dolomite 0.060 Kaolinite
0.055 x (m)
0.065
60
Calcite
40
Ettringite
20
C-S-H 1.67 Portl.
0 0.050
Prehnite (C-A-S-H)
Illite Quartz Calcite
0.055 Toberm.
0.060
0.065
x (m)
Fig. 5. Calculated mineral volume fractions vs. distance from center of borehole at t = 15 a for cases 6 and 7 (based on Tremosa et al., 2012). Concrete – rock interface is at x = 0.055 m.
Case 1 30
Porosity (%)
25 20
t=1 a t=5 a
15
t=10 a t=15 a
10 5 0 0.049
0.052
0.055
0.058
0.061
x (m)
Fig. 6. Porosity vs. distance from center of borehole at different times for case 1 (reference case). Concrete – rock interface is at x = 0.055 m.
(a) Case 2
(c) Case 4
35
25 20
25 t=1 a t=5 a
20
t=10 a
15
t=15 a
10
Porosity (%)
Porosity (%)
30
t=10 a
10
t=15 a
5
5 0 0.049
t=1 a t=5 a
15
0.052
0.055
0.058
0 0.049
0.061
0.052
x (m)
(b) Case 3
0.061
(d) Case 5 25
25
20
20
t=1 a t=5 a
15
t=10 a t=15 a
10
Porosity (%)
Porosity (%)
0.058
x (m)
30
t=1 a t=5 a
15
t=10 a
10
t=15 a
5
5 0 0.049
0.055
0.052
0.055 x (m)
0.058
0.061
0 0.049
0.052
0.055
0.058
0.061
x (m)
Fig. 7. Porosity vs. distance from center of borehole at different times for cases 2 to 5. Concrete – rock interface is at x = 0.055 m. (a) Case 2: Including tubing, cement paste and concrete in the borehole. (b) Case 3: Including zeolites. (c) Case 4: No cation exchange. (d) Case 5: No cation exchange and no prehnite.
(a) Case 1, small A’s
(b) Case 1, large A’s
30
25 20
20
t=1 a t=5 a
15
t=10 a t=15 a
10
t=1 a t=5 a
15
t=10 a
10
t=15 a
5
5 0 0.049
Porosity (%)
Porosity (%)
25
0.052
0.055 x (m)
0.058
0.061
0 0.049
0.052
0.055
0.058
0.061
x (m)
Fig. 8. Porosity vs. distance from center of borehole at different times for case 1 with (a) reduced (/100) and (b) increased (×100) surface areas for primary minerals. Concrete – rock interface is at x = 0.055 m.
(b) Case 7 25
20
20 t=1 a t=5 a
15
t=10 a
10
t=15 a
5 0 0.049
Porosity (%)
Porosity (%)
(a) Case 6 25
t=1 a t=5 a
15
t=10 a
10
t=15 a
5
0.052
0.055 x (m)
0.058
0.061
0 0.049
0.052
0.055
0.058
0.061
x (m)
Fig. 9. Porosity vs. distance from center of borehole at different times for cases 6 and 7 (based on Tremosa et al., 2012). Concrete – rock interface is at x = 0.055 m.
Case 1 14 13
pH
12 t=1 a
11
t=5 a t=10 a
10
t=15 a
9 8 7 0.00
0.02
0.04
0.06
0.08
0.10
x (m)
Fig. 10. pH vs. distance from center of borehole at different times for case 1 (reference case). Concrete – rock interface is at x = 0.055 m.
(a) Case 1, t = 1 a
(c) Case 1, t = 10 a 1.0E-01
K+
Na+
C (mol/kg_H2O)
Ca++ Mg++ Na+
1.0E-03
K+
1.0E-04
Na+
Ca++ SiO2(aq)
1.0E-02
ClSO4--
SiO2(aq)
HCO3-
1.0E-05
SiO2(aq)
1.0E-02 C (mol/kg_H2O)
1.0E-01
Ca++
K+
HCO3-
Mg++ Na+
1.0E-03
K+
1.0E-04
HCO3-
1.0E-05
Al+++
1.0E-06
Al+++
1.0E-06 0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.0
0.1
0.2
x (m)
0.4
0.5
0.6
(d) Case 1, t = 15 a
1.0E-01
1.0E-01
Ca++
Na+ Mg++ Na+
K+
K+ ClSO4--
SiO2(aq)
HCO3-
1.0E-05
Al+++
1.0E-06
SiO2(aq)
1.0E-02 C (mol/kg_H2O)
Ca++
1.0E-04
Na+
Ca++ SiO2(aq)
1.0E-02 C (mol/kg_H2O)
0.3 x (m)
(b) Case 1, t = 5 a
1.0E-03
ClSO4--
SiO2(aq)
K+
Ca++
HCO3-
Mg++ Na+
1.0E-03
K+
1.0E-04
ClSO4--
SiO2(aq)
HCO3-
1.0E-05
Al+++
1.0E-06 0.0
0.1
0.2
0.3 x (m)
0.4
0.5
0.6
0.0
0.1
0.2
0.3
0.4
0.5
0.6
x (m)
Fig. 11. Total solute concentration (mol/kg_H2O) vs. distance from center of borehole at different times for the reference case 1. Concrete – rock interface is at x = 0.055 m.
(a) Case 1, t = 1 a
(c) Case 1, t = 10 a
180
180
K 150
120
TOUR-Na TOUR-K
Na
90
TOUR2-Ca TOUR2-Mg
60
C (mol/m3)
C (mol/m3)
150
Ca
30
K
120
TOUR-Na TOUR-K
90 60
TOUR2-Ca TOUR2-Mg
Na
30
Ca
Mg 0 0.05
0.10
0.15
Mg
0 0.05
0.20
0.10
x (m)
0.20
x (m)
(b) Case 1, t = 5 a
(d) Case 1, t = 15 a
180
180
K
150
120
TOUR-Na TOUR-K
90
TOUR2-Ca
Na
TOUR2-Mg
60 30 0 0.05
Ca Mg 0.10
0.15 x (m)
0.20
C (mol/m3)
150
C (mol/m3)
0.15
120
K
TOUR-Na TOUR-K
90
TOUR2-Ca
60
Na
30
Ca
0 0.05
TOUR2-Mg
Mg 0.10
0.15
0.20
x (m)
Fig. 12. Cation occupancies on the exchange complex (in mol/m3rock) vs. distance from center of borehole at different times for the reference case 1. Concrete – rock interface is at x = 0.055 m.
Case 8, t = 15 a (1D) 60
Calcite
50
Illite
30 20
Hydrotalcite
Calcite
40 Vol%
Prehnite (C-A-S-H)
Quartz C-S-H 1.67 Calcite Microcline Kaolinite Dolomite
Ettringite 10 Portl. 0 0.050
Monocarb.0.055
0.060
0.065
x (m)
Fig. 13. Calculated mineral volume fractions vs. distance from center of borehole at t = 15 a for the simplified case 8 (no montmorillonite). Concrete – rock interface is at x = 0.055 m. To check the validity of the simplified case, compare with case 1 (Fig. 2).
Case 8 (2D including fracture) 100
Vol%
80
(a) Calcite
60 40
C-S-H 1.67 20 0 0.050
Illite
0.055
0.060
0.065
0.070
0.075
x (m)
25
(b)
Hydrotalc. 20
Toberm. Vol%
Illite
C-S-H 1.67
Prehnite (C-A-S-H) Quartz
15
Ettring. 10
Calcite Microcline Kaolinite
Portl.
5
Dolom. 0 0.045
0.050
0.055
0.060
0.065
0.070
0.075
x (m)
Fig. 14. Calculated mineral volume fractions vs. distance from center of borehole at t = 5 a (porosity at interface already sealed) for the simplified case 8 (2D calculation including fracture; plot is a 1D profile along the fracture). Concrete – rock interface is at x = 0.055 m. Fracture length is 3 cm. The lower plot (b) shows a detail of the secondary phases in the rock.
Table 1. Initial composition of the rock. Adapted from De Windt et al. (2008).
Vol. A frac. (m2/m3) Cases 1-7
Vol. frac.
Calcite
0.142
1.0e4
0.142
1.0e4
Dolomite
0.008
5.0e2
0.008
5.0e2
Illite
0.279
1.0e7
0.356
1.5e7
Montmor-Ca
0.077
5.0e6
------
------
Kaolinite
0.060
5.0e6
0.060
5.0e6
Microcline
0.103
2.5e3
0.103
2.5e3
Quartz
0.236
1.0e4
0.236
1.0e4
Porosity
0.095
-------
0.095
-------
MINERAL
A (m2/m3) Case 8
Table 2. Initial composition of the concrete. Calcite corresponds to the aggregate. Adapted from De Windt et al. (2008).
MINERAL
Vol. frac.
A (m2/m3)
Calcite
0.564
2.5e4
C-S-H Ca/Si=1.67
0.192
1.0e7
Ettringite
0.019
2.5e5
Hydrotalcite-OH
0.006
5.0e4
Monocarboalum.
0.017
2.5e5
Portlandite
0.072
1.0e6
Porosity
0.130
-------
Table 3. Initial composition of the cement paste (used only in case 2). Calcite is reported here as a potential secondary phase.
MINERAL
Vol. frac.
A (m2/m3)
Calcite
0.0
2.5e4
C-S-H Ca/Si=1.67
0.376
1.0e7
Ettringite
0.038
2.5e5
Hydrotalcite-OH
0.011
5.0e4
Monocarboalum.
0.034
2.5e5
Portlandite
0.141
1.0e6
Porosity
0.400
-------
Table 4. Initial solution compositions (total molalities, pH and T). Imposed constraints (equilibrium with solids or charge balance) are also indicated.
T (oC)
CONCRETE CEMENT PASTE 15
ROCK Cases 1 – 5, 8 15
ROCK Cases 6 – 7 15
pH
13.4
7.86 Calcite
7.89
SiO2
4.54e-5 C-S-H 1.67
1.20e-4
1.20e-4
2.61e-3 Portl.
1.11e-3
1.11e-3
1.27e-10 Hydrotalc.
9.00e-4
9.00e-4
5.00e-2
1.86e-2
1.86e-2
1.10e-1 charge bal.
7.44e-4 Illite
2.20e-4
1.00e-6
6.37e-3 charge bal.
6.17e-3 charge bal.
3.68e-4 Ettringite
6.76e-3
6.76e-3
4.32e-5 Calcite
3.55e-3
3.26e-3 Calcite
Al3+
3.18e-5 Monocarb.
5.46e-9 Kaolinite
7.78e-9 Illite
2+
1.00e-9 (cases 6-7)
---------
2.5e-5
Ca
2+ 2+
Mg Na
+
K+ -
Cl
SO42HCO3 Sr
-
Table 5. Equilibrium constants (log Keq) at 15oC for equilibria in solution. Reactions are written as the destruction of 1 mole of the species and using the primary species SiO2(aq), Ca2+, Mg2+, Na+, K+, Cl-, SO42-, HCO3-, H+, Al3+, Sr2+ and H2O.
Species Al(OH)2+ Al(SO4)2AlO2AlOH2+ AlSO4+ CO2(aq) CO32CaCO3(aq) CaCl+ CaCl2(aq) CaHCO3+ CaOH+ CaSO4(aq) H2SiO42HAlO2(aq) HSO4HSiO3KCl(aq) KHSO4(aq)
log Keq 1.1187E+01 -4.9000E+00 2.3980E+01 5.2549E+00 -3.0100E+00 -6.4124E+00 1.0423E+01 7.1962E+00 7.0439E-01 6.0320E-01 -1.0448E+00 1.2850E+01 -2.0746E+00 2.2960E+01 1.7305E+01 -1.8612E+00 1.0093E+01 1.5848E+00 -6.3955E-01
Species KOH(aq) KSO4Mg4(OH)44+ MgCO3(aq) MgCl+ MgHCO3+ MgSO4(aq) NaAlO2(aq) NaCO3NaCl(aq) NaHCO3(aq) NaHSiO3(aq) NaOH(aq) NaSO4OHSrCO3(aq) SrCl+ SrOH+ SrSO4(aq)
log Keq 1.4460E+01 -8.6532E-01 3.9750E+01 7.5022E+00 1.2368E-01 -1.0317E+00 -2.2981E+00 2.4779E+01 9.7931E+00 8.0833E-01 -2.3870E-01 8.3570E+00 1.5123E+01 -8.2000E-01 1.4338E+01 7.6737E+00 2.9184E-01 1.3290E+01 -2.3000E+00
Table 6. Equilibrium constants (log Keq) at 15oC for mineral reactions, written as the destruction of 1 mole of the mineral and using the primary species SiO2(aq), Ca2+, Mg2+, Na+, K+, Cl-, SO42-, HCO3-, H+, Al3+, Sr2+ and H2O.
Mineral Calcite Dolomite Quartz Microcline Illite Kaolinite Gypsum Portlandite CSH-1667 CSH-14 CSH-12 CSH-10 CSH-08 CSH-06 CSH-04 CSH-02 CSH-00 Prehnite Foshagite Gyrolite Hillebrandite Okenite Tobermorite
Formula
log Keq
CaCO3
2.0050E+00
CaMg(CO3)2
2.8779E+00
SiO2
-4.2222E+00
KAlSi3O8
-2.0041E-01
K.6Mg.25Al2.3Si3.5O10(OH)2
9.9867E+00
Al2Si2O5(OH)4
7.6850E+00
CaSO4·2H2O
-4.4740E+00
Ca(OH)2
2.3340E+01
SiO2·1.67Ca(OH)2·1H2O
3.0164E+01
SiO2·1.4Ca(OH)2·0.95H2O
2.3942E+01
SiO2·1.2Ca(OH)2·0.91H2O
1.9458E+01
SiO2·Ca(OH)2·0.86H2O
1.5080E+01
2.27SiO2·1.82Ca(OH)2·1.82H2O
2.5433E+01
1.72SiO2·1.03Ca(OH)2·1.03H2O
1.3710E+01
1.39SiO2·0.56Ca(OH)2·0.56H2O
6.6928E+00
1.16SiO2·0.23Ca(OH)2·0.23H2O
2.0311E+00
SiO2
-1.2416E+00
Ca2Al2Si3O10(OH)2
3.4756E+01
Ca4Si3O9(OH)2·0.5H2O
6.8048E+01
Ca2Si3O7(OH)2·1.5H2O
2.3353E+01
Ca2SiO3(OH)2·0.17H2O
3.8035E+01
CaSi2O4(OH)2·H2O
1.0464E+01
Ca5Si6H21O27.5
6.5137E+01
Mineral Hydrotalcite Ettringite Monosulfate Monocarb. Mont-Ca Mont-K Mont-Mg Mont-Na Saponite-Ca Saponite-H Saponite-K Saponite-Mg Saponite-Na Analcime Laumontite Mesolite Natrolite Scolecite Stilbite Gismondine Mordenite Wairakite
Formula
log Keq
Mg4Al2(OH)14·3H2O
7.7969E+01
Ca6Al2(SO4)3(OH)12·26H2O
5.9313E+01
Ca4Al2(SO4)(OH)12·6H2O
7.5813E+01
Ca4Al2(CO3)(OH)12·5H2O
8.3936E+01
Ca.165Mg.33Al1.67Si4O10(OH)2
3.0111E+00
K.33Mg.33Al1.67Si4O10(OH)2
2.5849E+00
Mg.495Al1.67Si4O10(OH)2
2.9186E+00
Na.33Mg.33Al1.67Si4O10(OH)2
2.9583E+00
Ca.165Mg3Al.33Si3.67O10(OH)2
2.7474E+01
H.33Mg3Al.33Si3.67O10(OH)2
2.6469E+01
K.33Mg3Al.33Si3.67O10(OH)2
2.7121E+01
Mg3.165Al.33Si3.67O10(OH)2
2.7453E+01
Na.33Mg3Al.33Si3.67O10(OH)2
2.7490E+01
Na.96Al.96Si2.04O6·H2O
6.5548E+00
CaAl2Si4O12·4H2O
1.4698E+01
Na.676Ca.657Al1.99Si3.01O10·2.647H2O
1.4645E+01
Na2Al2Si3O10·2H2O
1.9590E+01
CaAl2Si3O10·3H2O
1.7055E+01
Ca1.019Na.136K.006Al2.18Si6.82O18·7.33H2O
1.4087E+00
Ca2Al4Si4O16·9H2O
4.1717E+01
Ca.2895Na.361Al.94Si5.06O12·3.468H2O
-5.4107E+00
CaAl2Si4O10(OH)4
1.9428E+01
Table 7. Rate parameters for the primary minerals in the rock. The different parallel rate laws for a given mineral are used simultaneously (summation terms in Eq. 5) and describe the dependence of the rates on pH.
MINERAL Calcite Calcite Dolomite (diss) Dolomite (diss) Dolomite (prec) Dolomite (prec) Quartz (diss) Quartz (diss) Quartz (prec) Quartz (prec)
log k25 (mol/m2/s) -6.0 -2.0 -7.7 -3.1 -7.7 -3.1 -11.4 -14.9 -11.4 -14.9
Ea (kcal/mol) 8 8 11 11 11 11 18 18 18 18
n (aH+)n 0 0.66 0 0.63 0 0.63 0.3 -0.4 0.3 -0.4
m1 1 1 1 1 1 1 1 1 1 1
m2 1 1 1 1 4e-5 4e-5 1 1 1e-3 1e-3
m3 1 1 1 1 6 6 1 1 6 6
REFS.
Morse & Arvidson, 2002 Same as above Same as above Morse & Arvidson, 2002 Same as above Same as above Bandstra et al., 2008 Same as above Bandstra et al., 2008 Same as above Palandri & Kharaka, Microcline (diss) -10.06 12.4 0.5 14 0.4 1 2004; Burch et al., 1993; Soler & Lasaga, 1996 Microcline (diss) -12.41 9.08 0 14 0.4 1 Same as above Microcline (diss) -9.68 22.5 (aOH-)0.823 14 0.4 1 Same as above Palandri & Kharaka, Microcline (prec) -10.06 12.4 0.5 1 4e-5 6 2004; Burch et al., 1993; Soler & Lasaga, 1996 Microcline (prec) -12.41 9.08 0 1 4e-5 6 Same as above Microcline (prec) -9.68 22.5 (aOH-)0.823 1 4e-5 6 Same as above Palandri & Kharaka, Illite -11.85 13 0.37 1 1 1 2004 (muscovite) Illite -13.55 13 0 1 1 1 Same as above Illite -14.55 13 -0.22 1 1 1 Same as above Kaolinite -11.31 16 0.777 1 1 1 Palandri & Kharaka,2004 Kaolinite -13.18 16 0 1 1 1 Same as above Kaolinite -17.05 16 -0.472 1 1 1 Same as above Palandri & Kharaka, Montmor. (diss) -12.71 11.47 0.22 12 0.09 1 2004; Cama et al. (2000) Montmor. (diss) -14.41 11.47 0 12 0.09 1 Same as above Montmor. (diss) -14.41 11.47 -0.13 12 0.09 1 Same as above Palandri & Kharaka, Montmor. (prec) -12.71 11.47 0.22 1 1e-3 6 2004 Montmor. (prec) -14.41 11.47 0 1 1e-3 6 Same as above Montmor. (prec) -14.41 11.47 -0.13 1 1e-3 6 Same as above m2 and m3 values for the precipitation of dolomite, quartz, microcline and montmorillonite are only a means to avoid initial precipitation from the rock porewater, which is supersaturated with respect to these minerals. With this formulation, supersaturation in the rock has to increase to induce precipitation. m1, m2 and m3 values for the dissolution of microcline and montmorillonite provide the reported dependencies of dissolution rate on solution saturation state. The results for albite (Burch et al., 1993, as applied by Soler & Lasaga, 1996) are applied here to microcline. Montmorillonite rate laws are also applied to saponites.
Table 8. Cation exchange model for the rock (Gaines-Thomas convention). Cases 1-3, 8. Site capacity (cation exchange capacity) is also shown.
REACTION
log K
Site capacity (meq/kg_solid)
Site-K + Na+ = Site-Na + K+
-1.5
81.0
Site2-Ca + 2 Na+ = 2 Site-Na + Ca2+
-0.69
Site2-Mg + 2 Na+ = 2 Site-Na + Mg2+
-0.55
Table 9. Cation exchange model for the rock (Gaines-Thomas convention). Case 6. Site capacities for each type of site are also given.
REACTION
log K
Site cap. (meq/kg)
Ill-PS-K + Na+ = Ill-PS-Na + K+
-1.10
16.0
Ill-PS2-Ca + 2 Na+ = 2 Ill-PS-Na + Ca2+
-1.04
Ill-PS2-Mg + 2 Na+ = 2 Ill-PS-Na + Mg2+
-1.04
Ill-PS2-Sr + 2 Na+ = 2 Ill-PS-Na + Sr2+
-1.44
Ill-II-K + Na+ = Illite-II-Na + K+
-2.10
4.0
Ill-FES-K + Na+ = Ill-FES-Na + K+
-2.40
0.005
Mont-S-K + Na+ = Mont-S-Na + K+
-0.850
75.0
Mont-S2-Ca + 2 Na+ = 2 Mont-S-Na + Ca2+
-0.615
Mont-S2-Mg + 2 Na+ = 2 Mont-S-Na + Mg2+
-0.545
Mont-S2-Sr + 2 Na+ = 2 Mont-S-Na + Sr2+
-0.165
Table 10. Initial effective diffusion coefficients and constant tortuosity factors. Cement paste is only included in case 2.
DOMAIN
De (m2/s), initial
Cement paste
6.9e-12
0.01725
Calculated from concrete
Concrete
3.0e-12
0.0231
De Windt et al., 2008
Rock
2.7e-11
0.284
Motellier et al., 2007
Fracture
2.5e-10
0.5
De Windt et al., 2008
, constant
Reference
