Combined tracer through-diffusion of HTO and 22Na through Na-montmorillonite with different bulk dry densities

Accepted Manuscript Combined tracer through-diffusion of HTO and different bulk dry densities

22

Na through Na-montmorillonite with

Martina Bestel, Martin A. Glaus, Sabrina Frick, Thomas Gimmi, Fanni Juranyi, Luc R. Van Loon, Larryn W. Diamond PII:

S0883-2927(18)30092-1

DOI:

10.1016/j.apgeochem.2018.04.008

Reference:

AG 4071

To appear in:

Applied Geochemistry

Received Date: 22 November 2017 Revised Date:

20 April 2018

Accepted Date: 21 April 2018

Please cite this article as: Bestel, M., Glaus, M.A., Frick, S., Gimmi, T., Juranyi, F., Van Loon, L.R., 22 Diamond, L.W., Combined tracer through-diffusion of HTO and Na through Na-montmorillonite with different bulk dry densities, Applied Geochemistry (2018), doi: 10.1016/j.apgeochem.2018.04.008. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Combined tracer through-diffusion of HTO and 22Na through Na-

RI PT

montmorillonite with different bulk dry densities

M AN U

SC

Martina BESTEL1,3, Martin A. GLAUS*2, Sabrina FRICK2, Thomas GIMMI2,3, Fanni JURANYI1, Luc R. VAN LOON2 and Larryn W. DIAMOND3

1

*

AC C

EP

TE D

Laboratory for Neutron Scattering, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 2 Laboratory for Waste Management, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland 3 Institute of Geological Sciences, University of Bern, 3012 Bern, Switzerland

Corresponding author: Martin Glaus Paul Scherrer Institut OHLD/002 CH-5232 Villigen PSI Switzerland [email protected]

1

ACCEPTED MANUSCRIPT

Abstract - The suitability of swelling clays as a barrier to isolate nuclear waste in deep

RI PT

geological disposal is based on their microstructure, characterized by pore sizes down to the nanometre scale, and by their physico-chemical properties such as an excellent

SC

retention capacity for many radionuclides. A process-based understanding of the key features of radionuclide migration in such environments is required to demonstrate a

M AN U

valuable performance under all feasible conditions. In this study, the diffusion of tritiated water (HTO) and 22Na through Na-montmorillonite was studied as a function of the bulk dry density, the concentration of the background electrolyte (0.1, 1 and 5 M

TE D

NaClO4) and the temperature (between 0 and 80 °C). We observed that the diffusion of neutral species, such as water, depended on temperature and the bulk dry density only,

EP

while the diffusive fluxes of 22Na+ were additionally influenced by the concentration of

AC C

the background electrolyte. The experimental data were in agreement with both a single porosity and a parallel flux model demonstrating the validity of both approaches for rather low bulk dry densities and high concentrations of the background electrolyte. Some discrepancies between the model predictions and the experimental data were, however, noted. Assuming a reduced molecular mobility in the clay phase strongly reduced those discrepancies. Activation energies measured on samples with high bulk

2

ACCEPTED MANUSCRIPT

dry density were slightly higher than values measured for bulk water (17 kJ mol-1),

RI PT

those on low bulk dry density samples rather smaller. The activation energies of 22Na+ and HTO were similar indicating possibly a dynamical coupling of the diffusion of

SC

water and cations.

AC C

EP

TE D

M AN U

Key words – Smectites, tracer diffusion, activation energy, surface diffusion

3

ACCEPTED MANUSCRIPT 1.

Introduction

Due to the low hydraulic conductivity and the excellent uptake properties for radionuclides, compacted clay minerals or clay rocks are considered in many countries as a sealing or host rock material to isolate nuclear waste repositories from

RI PT

the environment (ANDRA, 2005; Nagra, 2002; ONDRAF/NIRAS, 2013). In

particular, bentonite is mainly foreseen as a backfill and/or buffer material for the

waste packages (Nagra, 2002; SKB, 2013; Wersin et al., 2014). The main component

SC

of bentonite is montmorillonite, a phyllosilicate mineral which consists of a central

M AN U

octahedral (O) alumina sheet sandwiched between two tetrahedral (T) silica sheets forming a so-called TOT layer. The layers are negatively charged because of isomorphic substitutions mainly located in the octahedral sheet for cations with lower valence. Electroneutrality is maintained by the presence of charge-compensating cations near those surfaces. In the hydrated state, the space between individual TOT

TE D

layers – frequently denoted to as the interlayer space – is filled with water molecules and the charge-compensating cations, such as Na+. Depending on the composition of the aqueous phase, varying numbers of individual TOT layers aggregate in stacks to

EP

form clay particles, varying in sizes (Brigatti et al., 2006). The particles are assembled

AC C

in a so-called house of cards structure. Depending on the bulk dry density and the particle structure, interparticle pores exhibiting larger dimensions than interlayer pores, may be located between these aggregates. Water is thus present in different pore environments. Controversial views exist in the literature of how to treat these different pore compartments in the modelling of mass transport (Birgersson and Karnland, 2009; Bourg et al., 2007; Tournassat and Appelo, 2011). Bestel et al. (2018) demonstrated the existence of two different types of water in compacted hydrated montmorillonite using neutron backscattering spectroscopy. They denoted these types

4

ACCEPTED MANUSCRIPT as ‘bound pore water’ located most likely in the interlayer pores and near the external clay particle surfaces, and ‘(quasi-) free pore water’ presumably present in the larger (interparticle) pores. The subsequent use of these terms in the present work is therefore referring to the definition by Bestel et al. (2018). Water contents from

RI PT

geometrical calculations based on neutron diffraction and surface area measurements were in good agreement with those derived from the neutron backscattering

spectroscopy for low total water contents (high bulk dry densities). This is in

SC

agreement with the finding of Pusch (2001) that most water molecules are located in the interlayers at low water contents. With decreasing clay density, a fraction of

monotonically (Bestel et al., 2018).

M AN U

(quasi-) free pore water in Na-montmorillonite started to appear and then increased

Diffusion is the main transport process through bentonites compacted to high bulk dry densities or in natural claystones and clay minerals (Altmann et al., 2012; Miller and

TE D

Wang, 2012; Shackelford, 2014). To predict the diffusive mass transport of neutral species in compacted swelling clay minerals, the influence of pore geometry has to be taken into account. This is typically done by introducing empirical factors such as

EP

geometrical tortuosity and constrictivity (van Brakel and Heertjes, 1974) or a lumped

AC C

geometrical factor G(–) (e.g. Bourg et al. (2006); González Sánchez et al. (2009)) in the definition of the effective diffusion coefficient (De, m2 s-1): De = D0 ε G

(1)

D0 (m2 s-1) is the self-diffusion coefficient in bulk water and ε (-) the diffusionaccessible porosity. Effective diffusion coefficients for tritiated and deuterated synthetic pore water were experimentally obtained and decrease with increasing compaction (González Sánchez et al., 2008; Nakazawa et al., 1999; Sato and Suzuki,

5

ACCEPTED MANUSCRIPT 2003; Suzuki et al., 2004). The diffusive behaviour of charged species, however, is not only influenced by geometric properties of the clay (cf. eq. (1)), but additionally by electrostatic and/or chemical interaction between the charged surfaces and the charged solutes. Extensive

RI PT

research has been carried out to characterize the semi-permeable membrane properties of a bentonite liner in terms of solute diffusion (see Shackelford and Moore (2013)

and references cited therein). Different concepts exist for the implementation of such

SC

charge effects, which basically all lead to an extension of eq. (1). The concepts can be

M AN U

divided into two groups. In the single porosity concept, a homogeneous pore space made up of water exhibiting interlayer water properties only is considered (Birgersson and Karnland, 2009). Cation and anion concentrations within this clay pore space are enriched and depleted, respectively, compared to the external solution according to cation exchange and Donnan equilibrium. In order to explain the observed diffusive

TE D

cation fluxes, all cations present in the clay phase are viewed as mobile. Birgersson and Karnland (2009) were able to approximately model literature data for 22Na+ (Glaus et al., 2007) and 36Cl– (Van Loon et al., 2007) in a consistent manner using the

EP

calculated tracer concentrations in the montmorillonite pore space as the driving force

AC C

for Fickian diffusion. Other approaches use a so-called electrical constrictivity to describe the enrichment or the depletion of the pore space from charged species (Ochs et al., 2001; Tachi et al., 2014). Different pore spaces are considered in the case of multi-porosity models (Bourg et al., 2006; Bradbury and Baeyens, 2003). The (i) distribution of pore water between different pore compartments (Bourg et al., 2006), (ii) the different transport-accessible porosities for ions compared to neutral species, and (iii) the specific interactions of ions with the charged surfaces (e.g. sorption) are taken into account in those models.

6

ACCEPTED MANUSCRIPT For a simple apportionment of the pore space into interlayer and interparticle porosity, a dual-flux diffusion model according to Fick's first law can be formulated at a microscopic scale as (cf. e.g. van Schaik et al. (1966))

(2)

RI PT

J tot = J IL + J IP = De , IL ⋅ ∇ C IL + D e , IP ⋅ ∇ C IP

where J is the diffusive flux (mol m-2 s-1), ∇C the local concentrations gradients (mol m-4) with the subscripts tot referring to total, IL to interlayer and IP to

SC

interparticle porosity. Note that water near the charged external clay particles may also be allocated to interlayer water for example, because it has similar physico-

M AN U

chemical properties as the latter (Bestel et al., 2018). No unambiguous assignment to geometric entities is implied by the subdivision of the pore space in eq. (2). The use of this equation in combination with eq. (1) has largely operational character for a macroscopic description and does not imply physically parallel diffusion paths at the

TE D

scale of a cm-sized sample. The model expressed by eq. (2) can also be based on pore diffusion coefficients (Dp, m2 s-1) using the relations De,IL= εIL Dp,IL and De,IP=

εIP Dp,IP. The two flux contributions are coupled through the respective

EP

concentrations. Depending on the species under consideration CIL is directly related to

AC C

CIP by a thermodynamic equilibrium condition (such as cation exchange or a Donnan equilibrium). CIP is mostly assumed to equal the concentration of the diffusing species in the external bulk solution. If the interlayer cations are considered as mobile, eq. (2) equals a surface diffusion model for parallel transport of sorbed cations on the surfaces and cations in solution (Gimmi and Kosakowski, 2011; Molera and Eriksen, 2002). Such models suffer from the dilemma of an unambiguous assignment of species to the solid and the liquid phase. While cations in the interlayer are assigned to the solid phase from the view of cation distribution equilibria between the clay and

7

ACCEPTED MANUSCRIPT the water phase (viz. sorption), they are rather viewed as part of the liquid phase from the point of view of diffusion. The term 'sorbed cations' used here is thus equivalent to cations present in the interlayers and/or near the external particle surfaces. Gimmi and Kosakowski (2011) proposed a scaling procedure in which the effective

RI PT

diffusion coefficient of a cationic species is normalized by its bulk water diffusion coefficient and the respective diffusion coefficients of a neutral water tracer (indicated by the superscript w). The relative contribution from the sorbed cations to diffusive

SC

transport is expressed by a relative surface mobility (µs, –) and the capacity ratio (κ, – ). The resulting normalized relative effective diffusion coefficient (Derw, –) is related

M AN U

to these quantities in the following manner:

Derw =

De D0w ≈ 1 + κµs D0 Dew

(3)

TE D

The capacity ratio is defined as the amount of sorbed cations per amount of cations in the liquid phase (assumed to be given by the external concentrations). Accordingly, it

EP

can be related to the sorption distribution coefficient (Rd, m3 Mg-1) by:

κ=

ρ bd Rd ε

(4)

AC C

where ρbd (Mg m-3) is the bulk dry density, which is defined as dry mass of clay per total volume of clay (including porosity). Owing to the lack of the exact knowledge of porosity distribution in their data compilation, Gimmi and Kosakowski (2011) chose to relate their normalisation scheme to the total porosity. From the dependence of κ on the salinity of the background electrolyte solution, the diffusion of 22Na is expected to be related inversely with the concentration of the background electrolyte. Indeed, the diffusive flux of 22Na increases with decreasing

8

ACCEPTED MANUSCRIPT concentration of the background electrolyte (Glaus et al., 2007; Glaus et al., 2013; Glaus et al., 2010; Melkior et al., 2009). At high sorption capacities, i.e., low salinities, the slope in a double logarithmic representation of effective diffusion coefficients measured as a function of the concentration of the background electrolyte

RI PT

solution allows for conclusions to be drawn regarding the individual contribution of

different pathways to the overall flux. From the observation of integer values of -1 for Na+ and -2 for Sr2+, respectively, for the slopes in such a representation, Glaus et al.

SC

(2007) concluded that the transport in the interlayers dominated the overall flux Jtot of these species with JIP (eq. (2)) being negligible. The authors ended with a single

M AN U

diffusion coefficient valid for diffusion in the interlayer pores for all conditions after correcting for the dependency of the gradients for salinity effects. Norrish (1954) and Amorim et al. (2007) studied the swelling of montmorillonite in contact with different electrolyte solutions using X-ray diffraction. They interpreted

TE D

the measured d value between 20 to 40 Å as the formation of electrical double layers with thicknesses depending on the background electrolyte solution. The variation of the concentration of the background electrolyte may thus not only influence the

EP

distribution of cationic species between the clay and the aqueous phase, it may also

AC C

affect the volume of the respective transport-accessible porosity. It can be expected that at sufficiently low degrees of compaction or at large external salinities the contribution from the interparticle pore space has an increasing importance and that the simple relationships used by (Glaus et al., 2007) may be no longer valid. However, no systematic data measured under such conditions are available from the literature. The activation energy (Ea, kJ mol-1) for diffusion is the minimum amount of energy for molecules to undergo diffusive transport. It is seen as an indicator for the state of

9

ACCEPTED MANUSCRIPT confined water in compacted clay systems (Kozaki et al., 1998a; Kozaki et al., 1998b; Kozaki et al., 1996; Liu et al., 2003; Suzuki et al., 2004; Van Loon et al., 2005). The activation energy for the diffusion of water and Na+ through less compacted bentonite is lower compared to that of bulk water (17 ± 1 kJ mol-1; Low (1962)). In the case of

RI PT

highly compacted Na-montmorillonite the activation energy increases with increasing bulk dry density to a value higher than that for bulk water (Kozaki et al., 1996). The diffusion of the ionic radionuclides is additionally influenced by sorption processes.

SC

Thus, the activation energy for diffusion of sorbed cations might differ from that of water. Except for Cs which has predominantly larger Ea values at high degree of

M AN U

compaction, most cations and anions have a similar activation energy (Kozaki et al., 1998b).

The aim of this work was to investigate the diffusive transport of HTO and 22Na+ as a function of the bulk dry density of the clay samples, the concentration of the

TE D

background electrolyte solution and temperature. The former two variations shall give information on an appropriate description of the diffusive transport of these species. For this purpose, the conditions were chosen such as to cover ranges in which

EP

significant fractions of (quasi-) free pore water are expected to be present.

AC C

Simultaneous diffusion measurements were applied for HTO and 22Na+ in order to obtain results with a maximum of internal consistency. The temperature was varied in the experiments in order to observe effects of the bulk dry density on the activation energy deduced.

2.

Material and Methods

2.1

Clay preparation

A homoionic Na-montmorillonite (Milos, Greece) with identical chemical 10

ACCEPTED MANUSCRIPT composition as used in Bestel et al. (2018) was investigated. Because slightly humid samples were easier to compact, the powder was partially hydrated from the vapour phase in a first step to a gravimetric water content of ~0.1 g g-1. After compaction of the wetted clay, the samples were placed between porous filters and subsequently

RI PT

saturated under constant volume conditions using NaClO4 solutions of various

concentrations (0.1, 1 and 5 M). The diameter and the thickness of the cylindrical clay pellets was 10 mm. The thickness of the confining filters was 1.65 mm. Diffusion

SC

cells with an appropriate sealing system enabling a continuous flow of the contacting solutions through the confining filters were used to minimize concentration gradients

M AN U

in the filters (Glaus et al., 2015b). The background electrolyte solution circulated through the confining filters at a flow rate of 0.1 cm3 min-1 maintaining an almost homogeneous concentration in the filters. Low (0.80, 1.07), intermediate (1.32, 1.33, 1.35) and high (1.56, 1.63, 1.68, 1.70) bulk dry densities were used (cf. Table 1). The

TE D

exact dry weights of the clay samples were determined from water loss at 110 °C in a separate representative aliquot of wetted clay. Bulk dry densities were derived from the dry weight of the clay samples and the cavity volume of the diffusion cell

EP

involving an overall relative uncertainty of 1% for the bulk dry density. Total porosity

AC C

was calculated from bulk dry density using the relationship

ε =1−

ρbd ρs

(5)

where ε is the porosity (–) and ρs (Mg m-3) the solid density of the clay mineral.

2.2

Through-diffusion experiments

We applied the continuous method of temperature variation (Van Loon et al., 2005) in

11

ACCEPTED MANUSCRIPT which the temperature is changed as soon as an adequately long steady-state phase has been observed for a given temperature. Temperatures between 0 and 80 °C were applied by keeping the diffusion cells in a thermostat laboratory incubator (Friocell 111, IG Instrumentengesellschaft, Zürich, Switzerland). Two different flux phases

RI PT

built up: (i) a short transient state for the initial temperature only and (ii) quasi steadystate phases during which the flux remained almost constant, viz. decreasing only as the result of a decrease in concentration in the source reservoir. Data at 25 ºC were

SC

measured at the beginning and at the end of the temperature cycle in order to verify

that the properties for diffusion such as the clay structure remained unchanged during

M AN U

the entire experiment.

Owing to the long duration of the experiment (~250 d) involving several temperature steps, the tracer reservoir volumes were chosen relatively large (2 L) in order to avoid drastic changes in the tracer concentration. For HTO, the reservoir concentration

22

TE D

remained virtually unchanged, while a measurable decrease could be noticed for Na+. No true steady-state flux could therefore be observed for the latter tracer. The

solution at the downstream side (0.05 L) was changed three times a week against

EP

tracer free solutions to keep the tracer concentrations as low as reasonably possible.

AC C

No measures were taken to control pH in the solutions contacting the clay sample. Measured pH values in such solutions were of the order of 7.5. The tracer fluxes at the ∆ti downstream filter boundary were calculated from the activities Adif (Bq) accumulated

during each time interval ∆ti (s) in the downstream reservoir, the cross-section area S (m2) of the clay plug and the specific activity of the tracer Asp (Bq mol-1):

J tot =

∆ti Adif

S∆ti Asp

12

(6)

ACCEPTED MANUSCRIPT The activities of HTO and 22Na (half-lives of 12.3 and 2.6 years, respectively) were measured by liquid scintillation counting. β–β discrimination using two energy windows was used to determine the activities of HTO and 22Na+ separately. The two windows were 0 to 20 keV for the combined contribution of HTO and 22Na+ and 20 to

RI PT

∆t i 600 keV for the contribution of 22Na+ only. All values for Adif were corrected for

2.3

SC

radioactive decay using a unique reference date for all samples.

Evaluation of diffusion data

M AN U

De values were calculated from Fick’s first law for each set of the measured flux data.

Despite the advective flushing of the filters, some heterogeneities in solution concentrations are to be expected due to an inhomogeneous flow in the filters. For simplicity, these inhomogeneities are treated as a diffusive resistance of an isotropic

TE D

medium in the flushed filters. A formal effective diffusion coefficient for the filter Df (m2 s-1) was estimated to be 1.50×10-9 m2 s-1 at 25 ºC. The respective values for other temperatures were derived using the Arrhenius relation assuming an activation

EP

energy, Ea (kJ mol-1), of 17 kJ mol-1 (Low, 1962). According to the serial arrangement of filter-clay-filter, De was calculated from the one-dimensional steady state flux (Jtot)

AC C

at time t, the respective tracer concentration in the upstream reservoir Ctusb (Glaus et al., 2008) and the thickness of the clay (dc) and of the filters (df), assuming negligible concentrations in the downstream reservoir:

De =

J tot d c D f Ctusb D f − 2 J tot d f

(7)

Average values (denoted to by the bar signs) for a given temperature were calculated from bunched data with near-constant flux values. Such conditions justified the data 13

ACCEPTED MANUSCRIPT bunching as outlined in Yaroshchuk et al. (2008). Rock capacity factors (α) were calculated by the relationship (Glaus et al., 2008) 6 J tot t bt C tusb (D f )

2

d c (Ctusb ) 2 ( D f ) 2 + 2d f d c Ctusb D f J tot − 2d c ( d f ) 2 ( J tot ) 2

(8)

RI PT

α=

using break-through times, tbt (s), determined from the intersection of the abscissa with the extension of the linear part of the plot of

∆t i dif

versus time in the dataset

SC

measured at 25 °C.

∑A

M AN U

Rd values were derived from α according to the following relationship valid for linear

sorption conditions

Rd =

α −ε ρbd

(9)

eq. (9) leading to

TE D

Similarly, the capacity ratio κ was calculated from a combination of eq. (4) and

EP

κ=

α −1 ε

(10)

AC C

Alternatively, κ may be calculated from the cation exchange capacity CEC (mmol g-1) for a homo-ionic clay according to:

κ=

CEC ρ bd ε [ A]

(11)

where [A] is the molar concentration of the background electrolyte in the contacting solution.

14

ACCEPTED MANUSCRIPT 2.4

Activation energy

The dependence of the effective diffusion coefficient on temperature T (K) was

De = A exp

− Ea RT

RI PT

evaluated from the Arrhenius equation (González Sánchez et al., 2008):

(12)

where A is the pre-exponential factor and R = 8.314 J K-1 mol-1 is the molar gas

SC

constant. The activation energy was estimated from the linear regression of the plotted

3.

Results and Discussion

M AN U

logarithmic effective diffusion coefficients versus reciprocal temperature.

For the purpose of comparing De values from different experiments, it is essential that the clay samples are fully saturated. Unsaturated clay samples may exhibit lower De

TE D

values than fully saturated samples (Savoye et al., 2010), which may thus introduce additional unwanted parameter dependencies. In agreement with previous findings in our laboratory (Van Loon et al., 2007), we

EP

presume that the re-saturation time was sufficient to produce fully saturated clay plugs. It is therefore reasonable to assume that the obtained diffusion coefficients

AC C

measured under the different experimental conditions are directly comparable. It is further equivalent to express the degree of clay compaction as the water-to-clay ratio or as the bulk dry density. For the present purpose, we prefer the latter option. Representative experimental raw data are shown in Fig. 1 for HTO and Fig. 2 for 22

Na+. The complete set of experimental raw data can be found in an Appendix as

Supplementary Material. Also shown in these Figures is the evolution of the tracer concentration in the upstream reservoir which acts as a concentration boundary

15

ACCEPTED MANUSCRIPT condition for diffusion. As expected Jtot increases with increasing temperature. For HTO, the quasi-steady-state flux and the diffusion coefficients at 25 ºC are equal within the error bars at the beginning and at the end of the experiment indicating that no major structural changes occurred over the entire duration of the temperature

RI PT

cycle. The respective values for 22Na are however significantly higher at the

beginning than at the end of the experiment. This is explained by the decrease of C tusb during the temperature cycle; the diffusion coefficients remained equal within the

SC

error bars (with a single exception). The 22Na+ fluxes show somewhat larger scatter

than the HTO data. This can be explained by stronger oscillations of the local tracer

M AN U

concentration gradients near the downstream clay boundary resulting from the sample exchange regime (Glaus et al., 2015b).

Average values for the tracer concentrations in the upstream reservoir and the tracer fluxes at the downstream boundary of all experiments carried out at 25 °C are given in

TE D

Tables 2 and 3. An overview of the derived De, α, Rd, κ and Ea values is shown in Table 4 for HTO and Table 5 for 22Na+, respectively. Large uncertainties are

EP

inherently associated with the α values for HTO because of the very short breakthrough times. The values are similar to ε which can be expected for a non-sorbing

AC C

diffusing species. For 22Na, α is higher than ε for all samples except of the sample saturated with 5 M NaClO4, for which α is similar to ε. Note the good consistency between κ values calculated from α and values calculated from CEC (Table 5).

3.1

Dependence of De on the background electrolyte concentration and bulk dry

density

The dependency of logDe values for HTO at 25 ºC on the concentration of the

16

ACCEPTED MANUSCRIPT background electrolyte [A] is illustrated in Fig. 3. The measured De for HTO showed no significant dependence on [A]. As evidenced by the equality of α and ε, the entire porosity is accessible for HTO, diffusing through the interlayer and interparticle porosity. As indicated by neutron spectroscopy (Bestel et al., 2018; González Sánchez

RI PT

et al., 2008) the molecular movement of a water molecule in the bound pore water is

lower than in bulk water by a factor of 2–3. Consequently, a certain dependence of De values would be expected for different ratios of bound pore water to (quasi-) free pore

SC

water. If this ratio varied with the ionic strength, this should also lead to a certain

dependence of De values on the solution ionic strength. The present observation of De

M AN U

values independent of the concentration of the background electrolyte at a given bulk dry density, is thus in agreement with the findings of Bestel et al. (2018), who hypothesized that this ratio is largely determined by the bulk dry density only. In order to relate De values measured at different bulk dry densities, empirical

TE D

relationships such as Archie’s law (Archie, 1942) are useful (Van Loon et al., 2007): log De = log D0' + m log ε

(13)

EP

with D'0 (m2 s-1) the diffusion coefficient extrapolated to a limiting porosity of ε = 1,

AC C

m (-) an empirical exponent often denoted as the cementation factor. m is influenced

by the type and degree of consolidation (Archie, 1942), pore geometry (Thompson et al., 1987), rock texture and particle geometry like preferred orientation (Sen, 1984). Fig. 4 shows the results obtained for HTO in a representation according to eq. (13). In agreement with a broad variety of literature data from Glaus et al. (2010); González Sánchez et al. (2008); Nakazawa et al. (1999); Sato and Suzuki (2003); Suzuki et al. (2004), the De values for HTO increased monotonously with increasing porosity. A completely different situation was observed for the diffusion of the 22Na tracer, for

17

ACCEPTED MANUSCRIPT which the De values were mostly larger than those of HTO. Only for the experiment carried out using 5 M NaClO4 an inverse ratio was measured. The dependence of De values on the concentration of the background electrolyte is shown in Fig. 5a in a double-logarithmic representation. Because these data were measured at very different

RI PT

bulk dry densities, the dependence of the respective De values on the background

electrolyte concentration cannot be compared directly. For such purposes, the data were bunched into different groups of rather similar bulk dry densities. They were

SC

further normalized within those groups according to the Archie's relationship shown

in eq. (13) using the parameters obtained for HTO diffusion, resulting in normalized

M AN U

effective diffusion coefficients for 22Na+ (De,n):

De ,n

ε  = De,i  n   εi 

m

(14)

TE D

where the subscript n denotes the target values and the subscript i the values at the conditions of the measurements. The target bulk dry densities chosen for normalisation were 1.3, 1.6 and 1.9 Mg m-3. The respective porosities were calculated

EP

using eq. (5) with ρs = 2.8 Mg m-3. Slopes of -0.52 and -0.76 were obtained for the present data at the target bulk dry densities of 1.3 Mg m-3 and 1.6 Mg m-3,

AC C

respectively (Fig. 5). This is significantly larger than the slopes of approximately -1.0 obtained by Glaus et al. (2007) for a bulk dry density of 1.9 Mg m-3 and by Glaus et al. (2013) for bulk dry densities of 1.3 and 1.6 Mg m-3, also shown in Fig. 5a. The reason for the discrepancy with the latter data is not clear. It is a general experience that the parameter uncertainties derived for a single diffusion experiments may strongly underestimate the true uncertainties involved. In view of the rather few data available, a bias of regression introduced by a single data point cannot be excluded.

18

ACCEPTED MANUSCRIPT Despite these inherent uncertainties, it is interesting to compare the overall picture of experimental 22Na+ data with modelling predictions involving different conceptual approaches. The single porosity diffusion model proposed by Birgersson and Karnland (2009) was chosen as a first case. The concentration gradients of 22Na+ in

RI PT

the clay phase are derived in that model from the amounts of 22Na+ required to

neutralize the negatively charged planar cation exchange sites and the amounts of

bulk electrolyte anions present in the clay phase according to Donnan equilibrium. De

SC

values were calculated using the following relationship, in which the activity

(Birgersson and Karnland, 2009)

M AN U

coefficients in the clay volume and the external solution are assumed to be equal

2 κ  κ   De = Dpε  +   + 12  2  2  

(15)

TE D

Dp is defined here as a virtual pore diffusion coefficient for 22Na+ excluding all

influences from charged surfaces and κ is calculated from the CEC using eq. (11). Note that the latter relationship is only valid for the use of homo-ionic clays. Dp is

EP

equivalent to Dc used by Birgersson and Karnland (2009) and was calculated for the

AC C

present purpose from Archie’s relationship for HTO in analogy to eq. (13)

Dp = D

' 0,HTO

ε

( m −1)

D0Na D0HTO

(16)

The Archie's parameter values were D'0,HTO = 9.8×10-10 m2 s-1 and m = 3.6 according to our own data (Fig. 4), while the bulk diffusion coefficients (D0) for Na+ (1.3×10-9 m2 s-1) and HTO (2.3×10-9 m2 s-1) were taken from Li and Gregory (1974). Note that the value calculated for Dp for a bulk dry density of 1.9 Mg m-3 (2.9×10-11 m2 s-1) is exactly coincident with the value used by Birgersson and Karnland (2009). The CEC

19

ACCEPTED MANUSCRIPT of the Milos montmorillonite was 0.82 mol kg-1. The model calculations obtained from the single porosity model for different bulk dry densities are shown in Fig. 5b as solid lines. A comparison with the experimental data in Fig. 5a shows that the model generally overpredicts the experimental data by

RI PT

factors mostly near ~2. Further the model predicts approximate slopes of -1 for all

target bulk dry densities for background electrolyte concentrations < 1 M. The model is thus in some disagreement with the present experimental data for 22Na+ in both

SC

qualitative and quantitative respect. It is, however, only in quantitative disagreement with our former data (Glaus et al., 2007; Glaus et al., 2013). Fig. 5b also shows the

M AN U

model predictions for a bulk dry density of 1.0 Mg m-3. The reason is the bunching of experimental data comprising bulk dry densities between 0.8 and 1.3 Mg m-3 to a target bulk dry density of 1.3 Mg m-3. As indicated by the vertical shift of the model curves, the bias introduced by bunching such large ranges is generally of the order of

TE D

~0.1 log units for the relevant range of background electrolyte concentrations. It can therefore be concluded that the uncertainty of the respective regression curve is not

EP

severely affected by this extended range of data bunching. As a second case, an electrical double layer model for illite (Glaus et al., 2015a),

AC C

representing a parallel flux type model, was adopted for the present case of montmorillonite in a simplified manner. Cations are assumed to diffuse in a pore water fraction (ffree) exhibiting bulk properties and in the so-called diffuse layer fraction, in which they are enriched with respect to the bulk water fraction according to Donnan equilibrium. Speciation in the two phases was calculated using the geochemical speciation and transport code Phreeqc (Parkhurst and Appelo, 2013) assuming the presence of negatively charged surface sites according to the CEC and setting the equilibrium constant for the formation of surface complexes ("Stern layer")

20

ACCEPTED MANUSCRIPT to very low values. This results in the entire amount of Na+ cations in the clay phase being present as diffuse layer species (Gimmi and Alt-Epping, 2018). A planar pore geometry with pore thicknesses between 2.0 nm and 0.5 nm (in agreement with a specific internal surface area of 650 m2 g-1) was assumed for the pertinent range of

RI PT

bulk dry densities between 1.9 Mg m-3 and 1.0 Mg m-3. The G factors (eq. (1)) used for the calculation of De values were again based on the Archie's parameter values

evaluated for the HTO diffusion data (Fig. 4). The model simplification regards the

SC

assumptions of porosity distribution. A constant value for ffree of 0.5 was assumed for all bulk dry densities and all concentrations of the background electrolyte. In view of

M AN U

the findings with regard to the potential presence of quasi-free pore water in montmorillonite (Bestel et al., 2018), this assumption can be regarded rather as an upper limiting case. Further it does not take into account the dependence of the extension of the Donnan volume on the ionic strength in the external water phase.

TE D

However, a respective refinement of the model curves does not lead to a qualitatively different picture. De values were calculated using eq. (8) given in Glaus et al. (2015a) assuming a viscosity ratio between the Donnan and the bulk aqueous phase of 1. The

EP

model results are shown in Fig. 5b as dotted lines. For verification purposes, parallel

AC C

flux model calculations were also performed for very low ffree values of 0.01. This resulted in identical predictions as the single porosity model, demonstrating the formal equivalence between the two calculations. As shown by Fig. 5b, the differences between the two modelling approaches are of marginal nature within the parameter ranges of interest. In view of this wide similarity, the previous conclusions regarding the consistency between the experimental data and the model predictions can therefore also be drawn for the parallel flux model.

21

ACCEPTED MANUSCRIPT For the purpose of addressing the effects of reduced molecular mobility in the clay phase and in the sense of a best-fit parameter value evaluation, we further applied the scaling procedure proposed by Gimmi and Kosakowski (2011). This approach is also based on a formal parallel flux concept comprising a surface and pore diffusion

RI PT

component (cf. eq. (3)). The resulting picture is given in Fig. 6 on a double-

logarithmic scale. This representation is used for a better visibility of all data points. It has, however, the drawback that the simple mathematical structure of eq. (3) is less

SC

obvious. If (i) κµs << 1, Derw approaches the limiting value of 1, while for κµs >> 1, a linear dependence of Derw on κ becomes evident. We therefore distinguish between

M AN U

groups of data in the "constant-Derw" range referring to the former case and "linearDerw" range for the latter case. The latter range is also identical with conditions, under

which surface diffusion is the dominant transport process. Most of the data in the compilation of Gimmi and Kosakowski (2011) belong rather to the linear data range.

TE D

Owing to the broad variety of different materials used for that data compilation and the resulting scatter in the data, a transition between the two ranges cannot unambiguously be verified. This is now clearly possible for the data shown in Fig. 6,

EP

which can best be described as the transition between the two ranges. The best-fit

AC C

parameter value for the surface mobility obtained from weighted linear regression of the present data (µ s=0.36±0.05) is similar to the median value (µ s = 0.45) from Gimmi and Kosakowski (2011). Despite the existing discrepancies between the present diffusion data for 22Na+ and our former literature data (Glaus et al., 2007; Glaus et al., 2013), the overall picture shown in Fig. 6 with the experimental data demonstrates that this model approach can be successfully applied to describe experimental data in parameter ranges characterized by rather low bulk dry densities and high concentrations of the

22

ACCEPTED MANUSCRIPT background electrolyte. The best-fit parameter value for µ s being < 1 shows that the molecular mobility of 22Na+ cations sorbed in the clay phase is less than in bulk water. For the experiment in which the background electrolyte concentration was 5 M, De for Na+ was found to be significantly smaller than for HTO. Neutron diffraction

RI PT

measurements of the average basal spacing (d value) of two samples with a similar bulk dry density saturated with 5 M and pure water, respectively, revealed rather

similar d values. The derived fractions of bound pore water per total water were thus

SC

also rather similar (Bestel et al., 2018). This observation together with the

M AN U

homogeneity of the diffusion data shown in Fig. 6 are a clear indication that the cation distribution between a sorbed phase (with a non-zero, but reduced mobility) and an aqueous phase is the dominant factor determining the overall diffusion rate of cations. The sorbed cations are probably mostly associated with bound pore water, the

3.2

TE D

aqueous cations with (quasi-)free pore water.

Activation energy versus bulk dry density

EP

The dependence of Ea on ρbd for HTO and 22Na is shown in Fig. 7. The Ea values derived for both tracers are similar to literature values (González Sánchez et al., 2008;

AC C

Kozaki et al., 1998a; Suzuki et al., 2004). Further they are similar for both tracers under all experimental conditions. This indicates possibly the presence of a dynamic coupling between HTO and 22Na meaning that both species move together, e.g. HTO in hydration shells around Na+ provided that the residence time of water in the hydration shell is exceeding the time scale of diffusion at the molecular scale. The activation energy slightly increases with increasing bulk dry density. For low consolidation, the activation energy is slightly lower than for bulk water. For intermediate consolidation Ea is higher than for bulk water. The predominantly larger 23

ACCEPTED MANUSCRIPT Ea for 134Cs (Kozaki et al., 1996) compared to HTO indicates a non-coupled diffusive

transport.

4.

Conclusions

RI PT

The results obtained in the present work for a broad variety of bulk dry densities of Na-montmorillonite and concentrations of the background electrolyte, give clear

evidence that the equilibrium distribution of cations between the clay phase and the

SC

external aqueous phase is the main parameter influencing the observed overall

M AN U

diffusive fluxes of cations. Whether the observed overall diffusive fluxes are described by a physical subdivision of the pore space into domains containing different species (e.g. the model proposed in Appelo and Wersin (2007) or Bourg et al. (2007)), or whether they are the result of the concentration gradients of such species in a single type of pore (e.g. the model proposed by Birgersson and Karnland (2009)),

TE D

cannot be decided unambiguously from the available data – notably because of the wide similarity of the model predictions and because of some internal inconsistencies in the experimental data. Both types of models would require some adjustments in

EP

order to fully match the data. The diffusion data of 22Na+ can equally be described by

AC C

a surface diffusion model with a reduced, but non-zero mobility of sorbed cations, similar to the median value determined in Gimmi and Kosakowski (2011). The activation energies of 22Na and HTO are similar for all samples, which possibly indicates a dynamic coupling between the diffusion of water and cations.

Acknowledgments

24

ACCEPTED MANUSCRIPT We gratefully acknowledge the financial support of the Swiss National Foundation (SNF). This work is partly based on experiments performed at the Swiss spallation

Appendix A

AC C

EP

TE D

M AN U

SC

Supplementary material can be found at …

RI PT

neutron source (SINQ) at the Paul Scherrer Institut, Switzerland.

25

ACCEPTED MANUSCRIPT Table 1. Sample properties of the compacted Na-montmorillonite plugs. Sample 1 2 3 4 5 6 7 8 9 [NaClO4] (M) 0.1 0.1 0.1 0.1 0.1 0.1 1 1 1

10 1

11 5

0.79

1.02 1.09 1.34 1.62 1.64 1.32 1.33

1.68

1.70

1.30

ε (-)

0.72

0.64 0.61 0.52 0.42 0.42 0.53 0.53

0.40

0.39

0.54

RI PT

ρbd (Mg m-3)

Table 2. Average HTO concentrations in the upstream reservoir and average fluxes at the downstream boundary in the experiments carried out at 25ºC. The bunching of data for average formation is shown in Fig. 1. Sample 1 2 3 4 5 6 7 8 9 10 11 9.64

9.79

9.83

1.16

0.69

0.38

0.35

5.18 5.13 5.24 5.28 3.86

SC

4.05

0.44 0.47 0.19 0.17 0.45

M AN U

Ctusb ·107 4.03 4.09 (mol m-3) J tot · 1014 1.12 0.73 (mol m-2 s-1)

TE D

Table 3. Average 22Na concentrations in the upstream reservoir and average fluxes at the downstream boundary in the experiments carried out at 25ºC. The bunching of data for average formation is shown in Fig. 2. Sample 1 2 3 4 5 6 7 8 9 10 11 0.21 0.056 0.12

0.12

0.51

0.81

0.51

0.52

0.20

0.15 0.025 0.038 0.040 0.061 0.084 0.027 0.026 0.012

AC C

EP

Ctusb ·107 0.21 0.22 -3 (mol m ) J tot · 1014 0.15 0.14 (mol m-2 s-1)

26

ACCEPTED MANUSCRIPT

Table 4: Best-fit parameter and derived values from the diffusion experiments with HTO.

1

2

3

4

5

6

7

8

9

10

11

T (°C)

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

25

28 ± 4.35

18 ± 3.0

29 ± 4.5

7.2 ± 1.1

3.9 ± 0.6

3.6 ± 0.6

8.5 ± 1.4

9.1 ± 1.4

3.5 ± 0.6

3.3 ± 0.5

12 ± 1.8

16 ± 1.4

8.9 ± 1.4

8.3 ± 1.9

19 ± 3.1

19 ± 3.0

8.7 ± 1.2

7.7 ± 1.8

22 ± 1.9

12 ± 1.9

12 ± 1.8

26 ± 4.2

11 ± 1.7

11 ± 1.7

SC

60

RI PT

Sample

69 ± 12

47 ± 7.5

70 ± 12

60

54 ± 9.0

35 ± 5.7

54 ± 9.0

40

38 ± 6.3

25 ± 4.0

39 ± 6.5

11 ± 0.9

5.8 ± 0.9

5.4 ± 0.8

13 ± 2.1

13 ± 2.0

5.3 ± 0.8

5.3 ± 0.8

17 ± 2.9

0

14 ± 2.3

8.7 ± 1.4

14 ± 2.3

3.2 ± 0.2

1.5 ± 0.2

1.5 ± 0.2

4.0 ± 0.6

3.9 ± 0.6

1.5 ± 0.2

1.4 ± 0.2

5.3 ± 2.0

25

28 ± 4.6

18 ± 2.9

28 ± 4.6

7.3 ± 0.6

3.7 ± 0.6

3.6 ± 0.6

8.5 ± 1.4

8.4 ± 1.3

3.4 ± 0.5

3.2 ± 0.5

12 ± 1.9

α (25°C) a

0.90 ± 0.6

0.75 ± 0.5

0.70 ± 0.4

0.90 ± 0.2

0.58 ± 0.1

0.58 ± 0.1

0.56 ± 0.2

0.90 ± 0.4

0.56 ± 0.1

0.47 ± 0.1

0.58 ± 0.2

Ea (kJ mol-1)

15.9 ± 0.9

16.6 ± 0.7

16.6 ± 0.7

19.1 ± 0.8

21.3 ± 1.2

20.2 ± 0.8

19.0 ± 0.8

19.0 ± 0.8

21.5 ± 1.1

20.4 ± 0.7

18.0 ± 1.0

TE D

EP

Calculated from the tracer breakthrough according to eq. (8).

AC C

a

27 ± 4.4

M AN U

80

27

34 ± 5.4 22 ± 9.8

ACCEPTED MANUSCRIPT

Table 5: Best-fit parameter and derived values from the diffusion experiments with 22Na.

1

2

3

4

5

6

7

8

9

10

11

T (°C)

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

De×1011

25

71 ± 13

62 ± 11

71 ± 13

45 ± 4.4

34 ± 6.2

35 ± 6.5

12 ± 0.8

10 ± 0.7

5.3 ± 0.3

5.0 ± 0.3

5.8 ± 0.6

111 ± 14

88 ± 7.3

87 ± 6.5

23 ± 1.5

23 ± 1.6

14 ± 3.1

13 ± 0.8

148 ± 14

109 ± 41

115 ± 14

33 ± 2.1

19 ± 1.2

18 ± 1.1

149 ± 27

60

132 ± 24

115 ± 20.7 134 ± 24

40

96 ± 17

82 ± 15

99 ± 18

78.7 ± 8.9

46 ± 7.0

53.4 ± 6.2

15 ± 1

15.1 ± 1

8.6 ± 0.5

8 ± 0.5

8.4 ± 0.7

0

38.4 ± 7

30.5 ± 5.6

37 ± 6.7

23.6 ± 2.2

12 ± 1.3

17 ± 1.7

4.2 ± 0.3

4.2 ± 0.3

2.1 ± 0.1

2.1 ± 0.2

2.1 ± 1.4

25

74 ± 13

59 ± 11

70 ± 13

53.7 ± 4.9

23 ± 2.7

33 ± 3.3

10 ± 0.9

10 ± 1

5.6 ± 0.5

5.4 ± 0.4

4.9 ± 0.6

α (25°C) a

10 ± 6

8.9 ± 2.7

11 ± 4.2

18 ± 1.5

17 ± 1.3

20 ± 1.6

1.6 ± 0.4

2.0 ± 0.6

1.9 ± 0.3

2.0 ± 0.3

0.7 ± 0.3

Rd (m3 Mg-1)b

12 ± 7

8.1 ± 2.5

9.7 ± 3.6

13 ± 1.1

10 ± 0.8

12 ± 1

0.8 ± 0.2

1.1 ± 0.3

0.9 ± 0.1

0.9 ± 0.1

0.1 ± 0.1

κexp (–) c

13 ± 8

13 ± 4

17 ± 6.5

34 ± 2.8

40 ± 3

46 ± 3.8

2.0 ± 0.5

2.8 ± 0.8

3.8 ± 0.6

4.1 ± 0.6

0.3 ± 0.1

κcalc (–) d

11 ± 1.1

13 ± 1.3

15 ± 1.5

21 ± 2.1

32 ± 3.2

32 ± 3.2

2.1 ± 0.2

2.1 ± 0.2

3.4 ± 0.3

3.5 ± 0.4

0.4 ± 0

Ea (kJ mol-1)

14.8 ± 0.8

15.8 ± 0.7

15.1 ± 0.8

22.8 ± 2

19.9 ± 0.8

20.2 ± 1.4

20.3 ± 0.9

22.1 ± 1.2

21.5 ± 0.9

20.6 ± 1.5

b c d

EP

AC C

a

164 ± 30

SC

171 ± 31

18.7 ± 1.2

34 ± 2.2

M AN U

80

TE D

60

RI PT

Sample

Calculated from the tracer breakthrough according to eq. (8). Calculated from the tracer breakthrough according to eq’s. (8) and (9). Calculated from the tracer breakthrough according to eq’s. (8) and (10). Calculated from eq. (11) using a CEC of 0.82 mmol g-1.

28

18 ± 1.4 11 ± 4.8

ACCEPTED MANUSCRIPT

1.2 10

-7

-7

8.0 10 1.2 10 -14 1.0 10

-14

8.0 10

-15

6.0 10

-15

Average flux

T = 80 °C

T = 60 °C

T = 40 °C T = 25 °C

4.0 10 -15

RI PT

9.3 10

SC

C tot

J (t) (mol m-2 s-1)

-6

1.1 10 -6

usb

-3

(t) (mol m )

Figures

T = 25 °C

2.0 10 -15 0.0 0

50

M AN U

T = 0 °C

100

150

200

250

Time (d)

Fig. 1: Temperature variation in the diffusion of HTO through compacted Na-montmorillonite (1.64 Mg m-3, sample 6) at 0.1 M NaClO4. The upper plot shows the concentration in the upstream solution reservoir and the lower plot the flux measured at the downstream boundary.

AC C

EP

TE D

The bars indicate the data bunching used for deriving the effective diffusion coefficients.

29

1.4 10

-8

1.2 10 -8 1.0 10

-8

-15

Average flux

tot

J (t) (mol m-2 s-1)

1.2 10 -15

T = 80 °C

1.0 10 -15 T = 60 °C

8.0 10 -16 6.0 10 -16 4.0 10

-16

2.0 10

-16

T = 25 °C T = 40 °C

RI PT

1.4 10

SC

C

usb

-3

(t) (mol m )

ACCEPTED MANUSCRIPT

T = 25 °C

T = 0 °C

0

50

M AN U

0.0 100

150

200

250

Time (d)

Fig. 2: Temperature variation in the diffusion of 22Na through compacted Na-montmorillonite (1.64 Mg m-3, sample 6) at 0.1 M NaClO4. The upper plot shows the concentration in the upstream solution reservoir and the lower plot the flux measured at the downstream boundary.

AC C

EP

TE D

The bars indicate the data bunching used for deriving the effective diffusion coefficients.

30

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 3: Dependence of the effective diffusion coefficients (De) for HTO on the concentration

AC C

EP

TE D

of the background electrolyte at 25 ºC for different bulk dry densities.

31

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 4:. Dependence of De for HTO on the porosity at a temperature of 25 ºC for different concentrations of the background electrolyte. The solid line is the fit with Archie’s law (eq. (12)) to data measured in the present work and data from González Sánchez et al. (2008); Glaus et al. (2013); Glaus et al. (2010). Other literature data are from Kozaki et al. (1999);

TE D

Miyahara et al. (1991); Nakashima (2000); Nakazawa et al. (1999); Phillips and Brown

AC C

EP

(1968); Sachs et al. (2007); Sato et al. (1992); Tanaka et al. (2008).

32

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 5: Dependence of De for 22Na+ on the concentration of the background electrolyte [A] at 25 ºC for different bulk dry densities. The left-hand plot shows normalized experimental data and their behaviour in linear regression. Normalisation was performed by recalculating the measured De values from the prevailing bulk dry density to the target bulk dry density given in the legend. The right-hand plot shows model prediction by the single porosity model of

TE D

Birgersson and Karnland (2009) as solid lines, while the dotted lines represent a simplified

AC C

EP

electrical double layer parallel flux model adopted from Glaus et al. (2015a).

33

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 6: Scaled diffusion coefficients (Derw) for 22Na as a function of the capacity ratio for sorption. The dashed line represents the surface diffusion model from Gimmi and Kosakowski (2011) fitted to the data measured in the present work. Literature data from Glaus

AC C

EP

NaClO4.

TE D

et al. (2007) are for samples compacted to 1.95 Mg m-3 and saturated with 0.1 and 1.0 M

34

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

Fig. 7: Activation energies for the diffusion of 22Na and HTO as a function of bulk dry

TE D

density. The dashed area represents the activation energy for bulk water of 17±1 kJmol-1 Low (1962). The values of González Sánchez et al. (2008) and (Suzuki et al., 2004) are derived from effective diffusion coefficients and of Kozaki et al. (1998a); Kozaki et al. (1996) from

AC C

EP

apparent diffusion coefficient of water saturated samples.

35

ACCEPTED MANUSCRIPT References Altmann, S., Tournassat, C., Goutelard, F., Parneix, J.-C., Gimmi, T., Maes, N., 2012. Diffusion-driven transport in clayrock formations. Appl. Geochem. 27, 463-

RI PT

478.Altmann, S., Tournassat, C., Goutelard, F., Parneix, J.-C., Gimmi, T., Maes, N., 2012. Diffusion-driven transport in clayrock formations. Appl. Geochem. 27, 463-478.

Amorim, C.L.G., Lopes, R.T., Barroso, R.C., Queiroz, J.C., Alves, D.B., Perez, C.A., Schelin,

SC

H.R., 2007. Effect of clay-water interactions on clay swelling by X-ray diffraction. Nuclear Instruments & Methods in Physics Research Section a-Accelerators

M AN U

Spectrometers Detectors and Associated Equipment 580, 768-770.

ANDRA, 2005. Dossier 2005 argile – Tome – Evolution phénoménologique du stockage géologique. Rapport Andra no. C.RP.ADS.04.0025, France,

http://www.andra.fr/download/site-principal/document/editions/182.pdf.

TE D

Appelo, C.A.J., Wersin, P., 2007. Multicomponent diffusion modeling in clay systems with application to the diffusion of tritium, iodide, and sodium in Opalinus Clay. Environ. Sci. Technol. 41, 5002–5007.

EP

Archie, G.E., 1942. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans. AIME 146, 54–62.

AC C

Bestel, M., Gimmi, T., Glaus, M.A., Van Loon, L.R., Zamponi, M., Diamond, L.W., Jurányi, F., 2018. Quantification of water distribution in Na- and Cs-montmorillonite based on water mobility. Clays Clay Miner. submitted, review comments received October 26, 2017.

Birgersson, M., Karnland, O., 2009. Ion equilibrium between montmorillonite interlayer space and an external solution – consequences for diffusional transport. Geochim. Cosmochim. Acta 73, 1908–1923.

36

ACCEPTED MANUSCRIPT Bourg, I.C., Sposito, G., Bourg, A.C.M., 2006. Tracer diffusion in compacted, water-saturated bentonite. Clays Clay Miner. 54, 363–374. Bourg, I.C., Sposito, G., Bourg, A.C.M., 2007. Modeling cation diffusion in compacted watersaturated sodium bentonite at low ionic strength. Environ. Sci. Technol. 41, 8118–8122.

bentonite. J. Contam. Hydrol. 61, 329-338.

RI PT

Bradbury, M.H., Baeyens, B., 2003. Porewater chemistry in compacted re-saturated MX-80

Brigatti, M.F., Galan, E., Theng, B.K.G., 2006. Structures and mineralogy of clay minerals,

SC

in: Bergaya, F., Theng, B.K.G., Lagaly, G. (Eds.), Handbook of clay science. Elsevier,

M AN U

Oxford OX5 1GB, UK.

Gimmi, T., Kosakowski, G., 2011. How mobile are sorbed cations in clays and clay rocks? Environ. Sci. Technol. 45, 1443–1449.

Gimmi, T., Alt-Epping, P., 2018. Simulating Donnan equilibria based on the Nernst-Planck equation. Geochim. Cosmochim. Acta In press, accepted manuscript,

TE D

https://doi.org/10.1016/j.gca.2018.04.003.

Glaus, M.A., Baeyens, B., Bradbury, M.H., Jakob, A., Van Loon, L.R., Yaroshchuk, A., 2007. Diffusion of 22Na and 85Sr in montmorillonite: Evidence of interlayer diffusion being the

EP

dominant pathway at high compaction. Environ. Sci. Technol. 41, 478–485.

AC C

Glaus, M.A., Rossé, R., Van Loon, L.R., Yaroshchuk, A.E., 2008. Tracer diffusion in sintered stainless steel filters: Measurement of effective diffusion coefficients and implications for diffusion studies with compacted clays. Clays Clay Miner. 56, 677–685.

Glaus, M.A., Frick, S., Rossé, R., Van Loon, L.R., 2010. Comparative study of tracer diffusion of HTO, 22Na+ and 36Cl– in compacted kaolinite, illite and montmorillonite. Geochim. Cosmochim. Acta 74, 1999–2010.

37

ACCEPTED MANUSCRIPT Glaus, M.A., Birgersson, M., Karnland, O., Van Loon, L.R., 2013. Seeming Steady-State Uphill Diffusion of 22Na+ in Compacted Montmorillonite. Environmental Science & Technology 47, 11522-11527. Glaus, M.A., Aertsens, M., Appelo, C.A.J., Kupcik, T., Maes, N., Van Laer, L., Van Loon,

RI PT

L.R., 2015a. Cation diffusion in the electrical double layer enhances the mass transfer rates for Sr2+, Co2+ and Zn2+ in compacted illite Geochim. Cosmochim. Acta 165, 376– 388.

SC

Glaus, M.A., Aertsens, M., Maes, N., Van Laer, L., Van Loon, L.R., 2015b. Treatment of

boundary conditions in through-diffusion: A case study of 85Sr2+ diffusion in compacted

M AN U

illite. J. Contam. Hydrol. 177-178, 239-248.

González Sánchez, F., Van Loon, L.R., Gimmi, T., Jakob, A., Glaus, M.A., Diamond, L.W., 2008. Self-diffusion of water and its dependence on temperature and ionic strength in highly compacted montmorillonite, illite and kaolinite. Appl. Geochem. 23, 3840–3851.

TE D

González Sánchez, F., Gimmi, T., Jurányi, F., Van Loon, L.R., Diamond, L.W., 2009. Linking the diffusion of water in compacted clays at two different time scales: Tracer throughdiffusion and quasielastic neutron scattering. Environ. Sci. Technol. 43, 3487–3493.

EP

Kozaki, T., Sato, H., Fujishima, A., Sato, S., Ohashi, H., 1996. Activation energy for diffusion

AC C

of cesium in compacted sodium montmorillonite. J. Nucl. Sci. Technol. 33, 522–524. Kozaki, T., Fujishima, A., Sato, S., Ohashi, H., 1998a. Self-diffusion of sodium ions in compacted sodium montmorillonite. Nucl. Technol. 121, 63–69.

Kozaki, T., Saito, N., Fujishima, A., Sato, S., Ohashi, H., 1998b. Activation energy for diffusion of chloride ions in compacted sodium montmorillonite. J. Contam. Hydrol. 35, 65–75.

38

ACCEPTED MANUSCRIPT Kozaki, T., Sato, Y., Nakajima, M., Kato, H., Sato, S., Ohashi, H., 1999. Effect of particle size on the diffusion behavior of some radionuclides in compacted bentonite. J. Nucl. Mat. 270, 265–272. Li, Y.H., Gregory, S., 1974. Diffusion of ions in sea water and in deep-sea sediments.

RI PT

Geochim. Cosmochim. Acta 38, 703–714. Liu, J.H., Yamada, H., Kozaki, T., Sato, S., Ohashi, H., 2003. Effect of silica sand on

activation energy for diffusion of sodium ions in montmorillonite and silica sand

SC

mixture. J. Contam. Hydrol. 61, 85-93.

Low, P.F., 1962. Influence of adsorbed water on exchangeable ion movement. Clays Clay

M AN U

Miner. 9, 219–228.

Melkior, T., Gaucher, E.C., Brouard, C., Yahiaoui, S., Thoby, D., Clinard, C., Ferrage, E., Guyonnet, D., Tournassat, C., Coelho, D., 2009. Na+ and HTO diffusion in compacted bentonite: Effect of surface chemistry and related texture. J. Hydrol. 370, 9–20.

TE D

Miller, A.W., Wang, Y., 2012. Radionuclide Interaction with Clays in Dilute and Heavily Compacted Systems: A Critical Review. Environmental Science & Technology 46, 19811994.

EP

Miyahara, K., Ashida, T., Kohara, Y., Yusa, Y., Sasaki, N., 1991. Effect of bulk density on

AC C

diffusion for cesium in compacted sodium bentonite. Radiochim. Acta 52/53, 293–297. Molera, M., Eriksen, T., 2002. Diffusion of 22Na+, 85Sr2+, 134Cs+ and 57Co2+ in bentonite clay compacted to different densities: experiments and modeling. Radiochim. Acta 90, 753– 760.

Nagra, 2002. Project Opalinus Clay – Safety report, demonstration of disposal feasibility for spent fuel, vitrified high-level waste and long-lived intermediate-level waste ("Entsorgungsnachweis"). Nagra Technical Report NTB 02-05, Nagra, Wettingen, Switzerland.

39

ACCEPTED MANUSCRIPT Nakashima, Y., 2000. Pulsed field gradient proton NMR study of the self-diffusion of H2O in montmorillonite gel: Effects of temperature and water fraction. Am. Mineralogist 85, 132–138. Nakazawa, T., Takano, M., Nobuhara, A., Torikai, Y., Sato, S., Ohashi, H., 1999. Activation

RI PT

energies of diffusion of tritium and electrical conduction in water-saturated compacted sodium montmorillonite. Radioactive Waste Management and Environmental Remediation ASME, 5p.

SC

Norrish, K., 1954. The swelling of montmorillonite. Discuss. Faraday Soc. 18, 120–134. Ochs, M., Lothenbach, B., Wanner, H., Sato, H., Yui, M., 2001. An integrated sorption–

M AN U

diffusion model for the calculation of consistent distribution and diffusion coefficients in compacted bentonite. J. Contam. Hydrol. 47, 283–296.

ONDRAF/NIRAS, 2013. Research, development and demonstration (RD&D) plan for the geological disposal of high-level and/or long-lived radioactive waste including irradiated

TE D

fuel if considered as waste. State-of-the-art report as of December 2012. ONDRAF/NIRAS, report NIROND-TR 2013-12 E. Parkhurst, D.L., Appelo, C.A.J., 2013. Description of input and examples for PHREEQC

EP

version 3 - A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations. U.S. Geological Survey Techniques and

AC C

Methods, book 6, chap. A43, 497 p.

Phillips, R.E., Brown, D.A., 1968. Self-diffusion of tritiated water in montmorillonite and kaolinite clay. Soil Sci. Soc. Am. Proc. 32, 302–306.

Pusch, R., 2001. The buffer and backfill handbook. Part 2: Materials and techniques. SKB Technical Report TR-02-12, SKB, Stockholm, Sweden. Sachs, S., Krepelova, A., Schmeide, K., Koban, A., Günther, A., Mibus, J., Brendler, V., Geipel, G., Bernhard, G., 2007. Joint project: Migration of actinides in the system clay,

40

ACCEPTED MANUSCRIPT humic substance, aquifer – Migration behavior of actinides (uranium, neptunium) in clays: Characterization and quantification of the influencce of humic substance. Wissenschaftlich-Technischer Bericht FZD-460, Forschungszentrum Dresden, Rossendorf, Germany.

RI PT

Sato, H., Ashida, T., Kohara, Y., Yui, M., Sasaki, N., 1992. Effect of dry density on diffusion of some radionuclides in compacted sodium bentonite. J. Nucl. Sci. Technol. 29, 873– 882.

SC

Sato, H., Suzuki, S., 2003. Fundamental study on the effect of an orientation of clay particles on diffusion pathway in compacted bentonite. Appl. Clay Sci. 23, 51–60.

M AN U

Savoye, S., Page, J., Puente, C., Imbert, C., Coelho, D., 2010. New experimental approach for studying diffusion through an intact and unsaturated medium: A case study with CallovoOxfordian argillite. Environ. Sci. Technol. 44, 3698–3704.

Sen, P.N., 1984. Grain shape effects on dielectric and electrical-properties of rocks.

TE D

Geophysics 49, 586-587.

Shackelford, C.D., Moore, S.M., 2013. Fickian diffusion of radionuclides for engineered containment barriers: Diffusion coefficients, porosities, and complicating issues.

EP

Engineering Geology 152, 133-147.

AC C

Shackelford, C.D., 2014. The ISSMGE Kerry Rowe Lecture: The role of diffusion in environmental geotechnics. Canadian Geotechnical Journal 51, 1219-1242.

SKB, 2013. RD&D programme 2013, programme for research, development and demonstration of methods for the management and disposal of nuclear waste. SKB Technical Report TR-13-18, Stockholm, Sweden. Suzuki, S., Sato, H., Ishidera, T., Fujii, N., 2004. Study on anisotropy of effective diffusion coefficient and activation energy for deuterated water in compacted sodium bentonite. J. Contam. Hydrol. 68, 23–37.

41

ACCEPTED MANUSCRIPT Tachi, Y., Yotsuji, K., Suyama, T., Ochs, M., 2014. Integrated sorption and diffusion model for bentonite. Part 2: porewater chemistry, sorption and diffusion modeling in compacted systems. J. Nucl. Sci. Technol. 51, 1191-1204. Tanaka, S., Noda, N., Higashihara, T., Sato, S., Kozaki, T., Sato, H., Hatanaka, K., 2008.

RI PT

Kinetic behavior of water as migration media in compacted montmorillonite using H218O and applying electric potential gradient. Phys. Chem. Earth 33, S163–S168.

Thompson, A.H., Katz, A.J., Krohn, C.E., 1987. The microgeometry and transport-properties

SC

of sedimentary-rock. Advances in Physics 36, 625-694.

Tournassat, C., Appelo, C.A.J., 2011. Modelling approaches for anion-exclusion in compacted

M AN U

Na-bentonite. Geochim. Cosmochim. Acta 75, 3698–3710.

van Brakel, J., Heertjes, P.M., 1974. Analysis of diffusion in macroporous media in terms of a porosity, a tortuosity and a constrictivity factor. Int. J. Heat Mass Transfer 17, 1093-1103. Van Loon, L.R., Müller, W., Iijima, K., 2005. Activation energies of the self-diffusion of

TE D

HTO, 22Na+ and 36Cl– in a highly compacted argillaceous rock (Opalinus Clay). Appl. Geochem. 20, 961–972.

Van Loon, L.R., Glaus, M.A., Müller, W., 2007. Anion exclusion effects in compacted

EP

bentonites: Towards a better understanding of anion diffusion. Appl. Geochem. 22,

AC C

2536–2552.

van Schaik, J.C., Kemper, W.D., Olsen, S.R., 1966. Contribution of adsorbed cations to diffusion in clay-water systems. Soil Sci. Soc. Am. Proc. 30, 17–22.

Wersin, P., Kiczka, M., Rosch, D., 2014. Safety case for the disposal of spent nuclear fuel at Olkiluoto, radionuclide solubility limits and migration parameters for the canister and the buffer. Posiva Report 2012-39. Posiva Oy, Eurajoki, Finland. Yaroshchuk, A.E., Glaus, M.A., Van Loon, L.R., 2008. Diffusion through confined media at variable concentrations in reservoirs. J. Membr. Sci. 319, 133–140.

42

AC C

EP

TE D

M AN U

SC

RI PT

ACCEPTED MANUSCRIPT

43

ACCEPTED MANUSCRIPT

•

Effective diffusion coefficient of tritiated water is independent of ionic strength Effective diffusion coefficients of sodium tracer depend on ionic strength

•

Temperature has a similar impact on diffusion of tritiated water and sodium

RI PT

•

tracer

No preference for single porosity or parallel flux modelling noted

AC C

EP

TE D

M AN U

SC

•