Diffusion of Water through the Dual-Porosity Swelling Clay Mineral

Subscriber access provided by READING UNIV

Article

Diffusion of water through the dual porosity swelling clay mineral vermiculite Emmanuel Tertre, Sébastien SAVOYE, Fabien Hubert, Dimitri Prêt, Thomas Dabat, and Eric Ferrage Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b05343 • Publication Date (Web): 23 Jan 2018 Downloaded from http://pubs.acs.org on January 23, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Environmental Science & Technology is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 29

Environmental Science & Technology

1

Diffusion of water through the dual porosity swelling clay mineral vermiculite

2 3

Emmanuel Tertre*,a, Sebastien Savoyeb, Fabien Huberta, Dimitri Prêta, Thomas Dabata and

4

Eric Ferragea.

5 6

a

7

Bât. B8, TSA - 51106, 86073 Poitiers cedex 9, France.

8

b

9

Radionucléides, F-91191 Gif-sur-Yvette, France.

Université de Poitiers/CNRS, UMR 7285 IC2MP, Equipe HydrASA, 5 rue Albert Turpain,

CEA, DEN/DANS/DPC/SECR/Laboratoire de Mesures et Modélisation de la Migration des

10 11

*Email of the corresponding author:

12

Emmanuel Tertre ([email protected])

13 14 15 16 17 18 19 20 21 22 23 24 25 1 ACS Paragon Plus Environment


Page 2 of 29

26

Abstract

27

Prediction of water and solute migration in natural clay-based materials requires a detailed

28

understanding of the roles played by different porosity types (around or inside clay particles)

29

on the overall transfer process. For smectite, a reference material for the design of migration

30

models, this discrimination is complex due to osmotic swelling of the structure in water-

31

saturated conditions. Diffusion experiments with water tracer (HDO) were conducted on 0.1-

32

0.2, 1-2 and 10-20 µm size fractions of Na-vermiculite, a swelling clay mineral with no

33

osmotic swelling. Results obtained for the two finest fractions suggest that osmotic swelling

34

and associated impact in pore structure is responsible of the low De values reported in

35

literature for smectite compared to vermiculite. When considering only interparticle porosity,

36

De values for vermiculite are similar to those reported for non-porous grains (Na-kaolinite,

37

Na-illite). This indicates that interparticle porosity has a primary effect on the overall water

38

diffusion process, whereas interlayer porosity is shown to imply a small proportion of HDO

39

adsorption. This study provides evidence that vermiculite is a promising reference mineral for

40

the understanding of the roles played by pore structure and mineral-water interaction on

41

transport properties of water in claystones and for associated refinement of dual-porosity

42

diffusion models.

43 44 45 46 47 48 49 50 51 52 2 ACS Paragon Plus Environment

Page 3 of 29


53 54

Introduction

55 56

Chemical and transport properties of natural clayey rocks, such as argillites (i.e., claystones),

57

have been widely studied in the context of the disposal of waste materials and sequestration of

58

energy resources. These media are known to have high confinement properties with respect to

59

water and solutes due to their low hydraulic conductivity1, making diffusion the main

60

transport process occurring in these systems.2,3

61

disposal, many studies have focused on obtaining macroscopic diffusion data (i.e., the

62

effective diffusion coefficient) from diffusion experiments (e.g., through-diffusion

63

experiments) performed on compacted clayey systems made either of pure minerals

64

(kaolinite, illite, montmorillonite) or complex natural clayey rocks (bentonite, argillite).

65

Swelling clay-based materials, such as argillite, characterized by the presence of smectite

66

minerals feature two types of porosity. The first type of porosity results from the crystal

67

structure of smectite particles, which are composed of stacks of solid layers separated by an

68

interlayer space. This interlayer porosity is filled with water molecules exposed to 2-

69

dimensional confinement and cations compensating the negative layer charge. The second

70

type of porosity results from the mutual arrangement of smectite particles in the porous

71

media, leading to the development of an interparticle pore network, which most often includes

72

the external diffuse double layer of particles.4 Due to the small size of clay particles, both

73

interlayer and interparticle porosities are subject to water and cationic diffusion, and in some

74

cases the interlayer porosity can be the dominant pathway at low porosity values in very dense

75

media composed of smectite particles.5 Diffusion experiment data obtained from smectite-

76

based materials have been widely used in the literature to constrain transport models based on

77

these two types of porosity (e.g., interparticle and interlayer).6-8

among others

In the context of nuclear waste

3 ACS Paragon Plus Environment


Page 4 of 29

78

In addition to well-known crystal swelling due to hydration of interlayer cation9,

79

smectite minerals exhibit interlayer and interparticle osmotic swelling under water-saturated

80

conditions.10-15 The extent of swelling depends on the characteristics of the clay particles

81

(particle size and nature of the cation compensating the layer charge) and pore water

82

chemistry (especially ionic strength).16

83

exfoliation of individual layers from smectite particles, which in turn leads to an ill-defined

84

interlayer volume, and a reorganization of the medium. The presence of osmotic swelling in

85

compacted swelling clay-based materials then hampers the discrimination between interlayer

86

and interparticle porosities in the sample although diffusivities of water and solutes are

87

extremely contrasted in both types of porosity. As an illustration, several authors17,18

88

demonstrated that the mobility of water molecules in the interlayer space of smectite could be

89

at least 3 times lower than the mobility in interparticle porosity. Moreover, some authors19

90

observed a significant variation in water diffusion in smectite when varying the nature of the

91

cation compensating the layer charge and concluded that this phenomenon was related to the

92

development of a colloidal gel phase for some specific compensating cations.

and references therein

Osmotic swelling provokes the

93

In this study, diffusion experiments were carried out with vermiculite, a swelling clay

94

mineral having a structure similar to smectite, but having a higher layer charge allowing to

95

prevent osmotic swelling under water-saturated conditions.20 This lack of swelling implies

96

that the size and shape of the particles are preserved once in suspension, resulting in a well-

97

constrained interlayer porosity. In addition, this mineral forms centimeter-sized monocrystals,

98

from which different particle size fractions can be obtained.21-25 Water (HDO) diffusion

99

experiments were performed on three size fractions of vermiculite particles using a through-

100

diffusion set-up adapted from previous studies.26,27 The through-diffusion experiments were

101

performed at different degrees of compaction (i.e., porosity) in order to vary the proportion of

102

interparticle porosity to total porosity (interlayer + interparticle). The obtained experimental


Page 5 of 29


103

data allow a direct evaluation of the influence of particle size on the effective diffusion

104

coefficient of water, and a comparison with values found in the literature for water diffusion

105

in smectite-rich samples is used to determine the effects of the modification of pore structure

106

by osmotic swelling. Finally, the implications of the results obtained in this study are

107

discussed in terms of predicting the diffusion of water in polymineral and natural clayey

108

samples.

109 110

Materials and methods

111 112

Sample preparation and characterization. Compacted vermiculite samples were prepared

113

from three different size fractions of particles, i.e., 0.1-0.2, 1-2 and 10-20 µm. These particles

114

were obtained using a previously established protocol based on the sonication of vermiculite

115

macro crystals (1-4 mm) immersed in water.21 The crystal chemistry and morphology of each

116

size fraction were obtained previously.21 The crystal chemistry and aspect ratio (i.e., particle

117

thickness over equivalent disk diameter) were identical for the three size fractions, while

118

specific surface areas of the external surfaces vary from ~1 m2·g-1 for the 10-20 µm size

119

fraction to ~100 m2·g-1 for the 0.1-0.2 µm size fraction.

120

Prior to the HDO diffusion experiments, the size fractions were Na-saturated using

121

five saturation cycles in a 1 mol·L-1 NaCl solution. A dialysis procedure was used to remove

122

chloride from the samples until the silver nitrate test for Cl- was negative. Then, each size

123

fraction was air-dried, sieved through a 150 µm mesh to avoid coarse aggregates and stored at

124

25°C. Drying at a higher temperature was not performed to avoid collapse of the vermiculite

125

interlayers. In its Na+-saturated form, vermiculite features interlayers displaying a bihydrated

126

(2W) state, i.e., two water layers with a layer-to-layer distance (d001) of 15 Å, at both high

127

relative humidity (>70%) and water-saturated conditions.28,29



Page 6 of 29

128 129

Through-diffusion experiments. Diffusion of the water tracer (HDO) through the

130

vermiculite samples was studied using the through-diffusion technique intensively used in the

131

literature30,31 and

132

clayey samples. The set-up used in this study was adapted from the one proposed by Van

133

Loon et al.27 and is described below. According to this set-up, diffusion was studied

134

perpendicularly to the compaction plane of the particles.

references therein

to study the diffusion of water and solutes through compacted

135 136

Experimental set-up. The set-up consisted of a PEEK diffusion cell characterized by an

137

inner diameter of 9.49 mm and two aqueous reservoirs (i.e., an upstream reservoir and a

138

downstream reservoir) containing 50 mL of a 10-2 M NaCl solution. The sample was directly

139

compacted in the diffusion cell at a given bulk dry density (i.e., porosity) based on the dry

140

mass of the solid put in the cell and the volume of the cell. The typical thickness (L) used in

141

this study for the compacted samples varied from 3.4 to 8.4 mm (Table 1). The compacted

142

sample was mechanically maintained in the cell by the following components on each side of

143

the sample, listed in order from the sample to the exterior: (i) a VCWP cellulose membrane

144

with a pore size of 0

Equation 5

214

where Co is the HDO concentration in the upstream reservoir (mol·m-3) corrected from the

215

natural concentration of HDO present in ultra-pure water (see details in the Aqueous analysis

216

section) and L is the thickness of the sample. By considering these conditions, Equation 2 was

217

solved by using Equation 6, which describes the diffusive flux (i.e., J(x=L,t) in mol·s-1) in the

218

downstream reservoir, as reported by Crank35:

219

= , ) =

220

where S is the cross-sectional area perpendicular to the diffusive direction (m2). All other

221

parameters have been defined for Equations 2, 4 and 5.

222

The corresponding total amount of cumulative tracer in the downstream reservoir (i.e., n(x=L,

223

t) in mol) is as follows:

224

0 = , ) = 123 4 − − ∑&./ 5 ,

& 1 + 2 ∑&./−1) exp

6

+ & ,

+/)7 &

))

exp −

Equation 6

& ,

8

Equation 7



Page 10 of 29

225

Characteristic diffusion parameters (i.e., De and α) were obtained by least-square

226

fitting of the experimental results for diffusive flux incoming in the downstream reservoir.

227

Fully analytical solutions were obtained in Laplace space and were then subsequently

228

numerically inverted to provide the solution in time, as performed by Savoye et al.36 based on

229

a previous method.37 Several authors demonstrated that the effective diffusion coefficients of

230

clayey porous media can be underestimated if diffusion through the stainless-steel filter is not

231

taken into account in the modelling procedure.38 For this reason, interpretation of the

232

experimental data obtained in this present study was performed by considering this effect.

233

Consequently, a porosity equal to 0.28 and a De of HDO equal to 2.3×10-10 m2·s-1 were used

234

for the stainless-steel filters, as proposed by several authors38,39 for these materials.

235

The uncertainties in both De and α were calculated by taking into account uncertainties

236

in the measured tracer fluxes (corresponding to the uncertainty in the concentration

237

measurements) and the thickness of the sample (an error of 0.1 mm). Finally, the uncertainty

238

in the total porosity of the samples was assessed to be ± 0.025 and was assumed to be mainly

239

due to the uncertainty associated with the sample volume (see Table 1).

240 241

Validation of the through-diffusion set-up. Although the experimental through-diffusion

242

set-up used in the present study is based on the one developed by Van Loon et al.27, it differs

243

from the latter in terms of sample size and volumes of the reservoirs. A preliminary

244

experiment was performed to validate the set-up used through the comparison of the water

245

diffusion parameters (i.e., De and α) with literature data obtained with a reference material.

246

For that purpose, the same experiment as that proposed by some authors39 using a porous

247

medium made of Na-saturated kaolinite particles (KGa-2) and compacted to a total porosity

248

(ε) of 0.26 (i.e., a dry bulk density of 1.9 g.cm-3) was performed (Table 1). Experimental data

249

(flux and cumulative amount) measured for this experiment are reported in Figure S1. 10 ACS Paragon Plus Environment

Page 11 of 29


250

Obtained De and α values used to reproduce experimental data with Equation 2 were found to

251

be 1.8±0.5×10-10 m2·s-1 and 0.25±0.025, respectively (Table 1). Given the associated

252

uncertainties, the diffusion parameters obtained in the present study for a porous medium

253

composed of Na-kaolinite particles were in good agreement with those reported by Gonzalez

254

Sanchez et al.39 (De=1.34±0.15×10-10 m2·s-1 and α=0.28±0.16) and Faurel29 (De=1.4×10-10

255

m2·s-1 and α=0.25) for the same medium. Therefore, these results validate the approach used

256

in this study to acquire the diffusion parameters of vermiculite samples. Finally, the α value

257

calculated from the data is equal to the total porosity of the sample, confirming well that HDO

258

can be considered as an inert tracer (i.e., =0) for diffusion in kaolinite compacted samples.

259 260

Results and discussion

261

Figures 1A, 1B and 1C show experimental data (i.e., instantaneous fluxes and cumulative

262

amount of diffused HDO) obtained for the 0.1-0.2, 1-2 and 10-20 size fractions of Na-

263

vermiculite, respectively. The respective De and α values interpreting these data are reported

264

in Table 1.

265 266

Effect of particle size and porosity on the rock capacity factor (α α). By analyzing the α

267

values interpreting the data (Table 1), the sole experiment for which HDO can be considered

268

as a conservative tracer (inert tracer) is the one performed with the sample composed of the

269

0.1-0.2 size fraction compacted to a total porosity ε of 0.5. Indeed, this is the sole case for

270

which the data yield a α value equal to ε, indicating the absence of HDO adsorption in the

271

sample. In all other cases, the α values interpreting data are systematically higher than the

272

total porosity of the samples, indicating that HDO is adsorbed in the samples. The distribution

273

ratios () corresponding to these α values are reported in Table 1 and are between 0.1 and

274

0.5 mL·g-1. Note that uncertainties on calculated values also plead for potential HDO 11 ACS Paragon Plus Environment


Page 12 of 29

275

adsorption for sample with 0.1-0.2 size fraction compacted at ε=0.5 (Table 1). All attempts to

276

derive HDO adsorption from batch experiments proved unsuccessful owing to (i) the lower

277

solid/solution ratio in batch experiments (typically 10 g·L-1) than in diffusion experiments

278

(typically 1000 g·L-1) and (ii) the high associated uncertainties in the HDO aqueous

279

concentrations measured before and after adsorption (data not shown). Although significant,

280

the overall proportion of adsorbed HDO does not exceed 0.3-2% of the total amount of

281

interlayer water molecules in the vermiculite interlayers, indicating an extremely limited

282

adsorption effect for all size fractions and ε values tested. Interestingly, although most

283

experimental studies devoted to diffusion of water tracers (mainly HTO) in compacted

284

swelling clay minerals showed that water tracers can be considered inert, a few studies have

285

previously reported a slight adsorption of HDO or HTO during diffusion. For example, some

286

authors40 reported a non-zero distribution ratio for HTO in argillite samples ( equal to 0.01

287

mL·g-1).

288

In the case of diffusion in vermiculite-based materials, the adsorption effect can be

289

tentatively assigned to the high layer charge in this swelling clay mineral and associated

290

enhancement of water confinement compared to low-charge montmorillonite. Indeed,

291

different studies using molecular simulations have evidenced the coexistence of different

292

populations of water molecules in high-charge swelling clay interlayers with contrasting

293

structural and dynamical properties.17,25,41 Note that the range of (HDO) parameters (i.e.,

294

0.1-0.5 mL/g, Table 1) used to interpret our experimental data is in agreement with the

295

(HDO) value of 0.11 mL/g which can be calculated according to HDO/H2O fractionations

296

between bulk water and water confined in mesoporous silica deduced from experimental data

297

reported in literature.42,43

298

materials made of high charge swelling clays, and likely linked to the nature of the

Such retardation of HDO (≠0) during diffusion in clayey


Page 13 of 29


299

confinement, should thus be considering when interpreting mineral-water interactions on the

300

basis of isotopic analyses.

301 302

Effect of particle size and porosity on effective water diffusion coefficients (De). For the

303

two finest size fractions (i.e., 0.1-0.2 and 1-2 µm), De values are reduced when decreasing the

304

total porosity of the samples (Table 1, Figure 2A). The same correlation is also observed by

305

plotting pore diffusion coefficient values (Dp; see data analysis section for definition) as a

306

function of the total porosity (not shown). Such behavior is in agreement with literature data44

307

and references therein

308

interpreted by an increase in the tortuosity of the pathways (i.e., change of pore structure)

309

with decreasing sample porosity. This behavior can be also attributed to an increase in the

310

relative proportion of interlayer porosity when total porosity ε decreases as previously

311

mentioned for cations.5 Indeed, diffusion in the interlayers of the swelling clays is reduced

312

compared to diffusion in the interparticle porosity. Furthermore, for the same ε value between

313

~0.3 and ~0.5, the De values obtained for the size fractions 0.1-0.2 µm and 1-2 µm follow

314

similar trends. For this range of particle sizes, this behavior indicates that there is no effect of

315

the particle size on the diffusion of the water tracer in compacted swelling clays.

on diffusion in bentonites or other related montmorillonite-rich media and is

316

The De value obtained for the 10-20 µm size fraction at ε ≈ 0.35 is approximately two

317

times lower than those obtained for the finest size fractions at the same total porosity. Note

318

that a replication of the experiment led to similar value whereas the high permeability for this

319

size fraction did not allow exploring porosity value higher than 0.35 without significant

320

contribution from advective flow (results not shown). A broader distribution in particle size

321

for the 10-20 µm fraction compared to finer ones could be responsible of the observed lower

322

De values. According to a previous study23, the morphological analysis revealed a narrower

323

distribution for the 10-20 µm fraction compared to finer fractions, thus discarding a potential 13 ACS Paragon Plus Environment


Page 14 of 29

324

effect from geometrical properties of particles to explain contrasted De values between the

325

different samples for a given porosity. The contrasted behavior for this sample made with the

326

coarsest size fraction could possibly be explained by variation in the particle organization.

327

Indeed, the organization of porous media composed of clayey particles can be highly

328

contrasted (ranging from isotropic to anisotropic22,23,45) due to the low aspect ratios of the

329

particles (0.1 for vermiculite particles used in this study).21 In addition, as discussed in the

330

case of the 10-20 µm size fraction used in the present study22,23, the preparation of the sample

331

can also lead to the segregation of domains with contrasting degrees of particle orientation

332

anisotropy. This anisotropic characteristic in particle orientation is known to influence the De

333

value obtained from a given sample.46-48 For instance, in clay-rich samples, previous authors47

334

have reported De values for water molecules that are from 3 to 6 times lower in the direction

335

perpendicular to the sedimentation plane than in the parallel direction. This effect is

336

interpreted by a higher tortuosity of the diffusion pathways in the direction perpendicular to

337

the sedimentation plane than in the parallel direction. However, to the best of our knowledge,

338

no experimental data has been published regarding the degree of anisotropy in clayey media

339

compacted to the same total porosity but made with different particle sizes. Van Loon et al.47

340

mentioned that the degree of anisotropy of a porous clayey media is directly related to the

341

aspect ratio of the particles and that the length of the particle governs the ability to form a

342

perfectly layered media. Although the samples of the different size fractions were prepared

343

differently in the present study and in the work of Hubert et al.22, the 10-20 µm fraction was

344

the sole sample exhibiting the coexistence of domains with isotropic and highly anisotropic

345

particle orientations.22,23 Hence, the possible contribution of a fraction of very oriented

346

particles in this sample could in turn explain the low De values. This interpretation clearly

347

highlights the need for in situ organization measurements of particle orientations as well as

348

for more in-depth theoretical analysis of the roles played by particle orientation anisotropy


Page 15 of 29


349

and heterogeneity in the distribution of anisotropy within samples on the diffusional

350

properties of water.

351 352

Effect of osmotic swelling on water diffusion. For the same ε value, experimental De values

353

for water tracers reported in literature for smectitic porous media19,49,50 are systematically

354

lower than values reported for media composed of non-porous clayey particles, such as Na-

355

saturated kaolinite and illite.39, 50, this study Several of these data are reported as a function of ε

356

value in Figure 2A. This behavior is commonly attributed to the lower mobility of water

357

molecules in the vicinity of charged particle surfaces, including interlayer surfaces (which are

358

accessible to diffusion), than in the interparticle porosity.19,44,51-54

359

Comparison of the experimental data obtained from the two finest vermiculite size

360

fractions (i.e., 0.1-0.2 and 1-2 µm) and the data reported for montmorillonite with similar

361

particle sizes reveals that the De values are systematically higher in vermiculite-rich samples

362

than in smectite-rich samples for a given value of ε. This difference highlights the singular

363

behavior of vermiculite compared to smectite and likely also the role played by osmotic

364

swelling in smectitic porous media on the overall water diffusion. Indeed, the higher layer

365

charge of vermiculite should in principle slow down diffusion of water molecules in the

366

interlayer space, in agreement with molecular simulations17. For instance, several authors17,41

367

showed that the self-diffusion coefficient of water molecules in bihydrated Na+-saturated

368

smectite decreases with tetrahedral layer charge (from ~7×10-10 for a layer charge of

369

0.8/O20(OH)4 (approximately the layer charge of montmorillonite55) to ~3×10-10 m2·s-1 for a

370

layer charge of 1.8/O20(OH)4 (approximately the layer charge of vermiculite25)). Accordingly,

371

a lower water mobility in macroscopic diffusion experiments should be expected for

372

vermiculite samples compared to smectite samples (Figure 2A). Observation of the inverse

373

case likely pleads for an influence of osmotic swelling on water diffusion in smectite-based 15 ACS Paragon Plus Environment


Page 16 of 29

374

materials. On the basis of HTO diffusion experiments in smectite saturated with different

375

cations, Melkior et al.19 indeed noted that the presence of colloidal gels in Na- and Ca-

376

smectite was likely responsible for the decrease in the obtained HTO diffusion coefficients

377

compared to Cs-smectite for which large aggregates of layers were observed. Such variation

378

in the same smectite sample is thus related to layer aggregation, which depends on the nature

379

of the interlayer cation and induces a change in the relative proportion of interlayer and

380

interparticle porosity. Beneficiating for the stable 2W hydrate of vermiculite once immersed

381

in water, experimental data obtained in the present study can be used to obtain additional

382

insights into the role played by different types of porosity (interlayer and interparticle) on the

383

overall water diffusion process. In Figure 2B, the obtained De values for the two finest size

384

fractions of vermiculite (i.e., 0.1-0.2 and 1-2 µm) are plotted as a function on the interparticle

385

porosity. For a given total porosity ε, the interparticle porosity εinterp. can be obtained with the

386

following equation:

387

9:&;.??

Equation 8

>.5@

390

Interestingly, the higher porosity vermiculite data points in Figure 2B are close to the

391

values reported in the literature for media composed of Na-saturated kaolinite and illite

392

particles, which are non-porous grains that exhibit only interparticle porosity. This can be

393

seen as a reminiscence of the findings obtained from numerical random-walk simulations by

394

Churakov and Gimmi.56 These authors indeed showed a limited influence of the change in the

395

amount of interlayers for a given interparticle porosity value on the overall diffusion

396

coefficient of water in very compacted clay media. In the same fashion, the results obtained in

397

the present study for vermiculite in less dense porous media thus represent experimental

398

evidence indicating that interparticle porosity is a first order parameter in the overall water 16 ACS Paragon Plus Environment

Page 17 of 29


399

diffusion process compared to interlayer diffusion. Note that this situation would differ in the

400

case of cation or anion diffusion due to the contribution of the diffuse double layer at particle

401

surface that would significantly modify the dynamics depending on the charge of the clay

402

material.8,57

403 404

Implications for water and solute diffusion in natural and complex clayey environments.

405

Clayey rocks, such as argillites58, considered for the storage of nuclear waste are composed of

406

complex mineralogical assemblages. The clay mineralogy of these rocks is indeed composed

407

of non-porous grains, such as kaolinite or illite, and partially porous grains, mainly smectite or

408

illite-smectite mixed-layered minerals.59,60 Understanding the roles played by the different

409

type of minerals and porosities is thus crucial for predicting the long-term behavior of water

410

and solutes in these geological media.4,58,61 and references therein In that regard, the results obtained

411

in this study allow deriving two major conclusions.

412

First, the vermiculite used here exhibits a clear dual-porosity behavior and represents a

413

promising reference swelling clay mineral for the refinement of migration models in the

414

context of nuclear waste storage in argillite rocks including diffusive and/or advective

415

processes.62 Indeed, the smectite in these rocks is largely present as smectitic layers in illite-

416

smectite mixed-layer minerals.59,60 In water-saturated conditions, these minerals most often

417

preserve the particle morphology due to little or no layer exfoliation due to osmotic swelling.

418

Accordingly, the results obtained for vermiculite can likely be considered representative of

419

water diffusing through the smectite layers in illite-smectite minerals in argillites and could

420

help in the development of dual-porosity models for the interpretation of diffusion

421

experiments. Owing to this well-constrained porosity distribution, the diffusion data reported

422

here also represent an experimental dataset for designing simulations based on Brownian

423

dynamics or random walk displacements45,56,61,63-64 and for considering the dual-porosity



Page 18 of 29

424

nature of swelling clay-based materials. Once constrained by experimental data, these

425

simulations could help to decipher the role played by different parameters (e.g., mineralogy,

426

particle size, anisotropy and porosity distribution) on the overall diffusional process of water

427

and solutes (cations and anions) occurring in compacted swelling clays.

428

Second, the small adsorption of HDO evidenced in the transient state for most of the

429

samples is probably due to the high structural layer charge of vermiculite and differs from the

430

general assumption that HDO is an inert water tracer in swelling clay minerals. Further

431

investigation regarding on the role played by layer charge and confinement on the adsorption

432

of the HDO tracer is needed in order to assess the potential implications of this adsorption on

433

the interpretation of experimental diffusion in natural clay-rich media. Indeed, clay minerals

434

in natural polyphasic rocks such as argillites commonly display noticeable chemical

435

heterogeneity, leading to a wide range of layer charges. Additional studies regarding HDO

436

adsorption in high-charge clay mineral as vermiculite could thus highlight potential mineral-

437

water interaction effects on the isotopic measurements commonly used to investigate water

438

transport in clayey matrices.

439 440

Acknowledgements

441

The French national program EC2CO “Biohefect” (Project DIFFMATARG) and the CNRS

442

interdisciplinary “défi Needs” through its “MiPor” program (Project TRANSREAC) are

443

acknowledged for providing financial support for this study. The authors would like to thank

444

Alfred Delville (ICMN, Orléans) for discussion of the dynamics of water in clayey materials

445

and Fabien Baron and Céline Boissard (IC2MP, Poitiers) for sampling assistance during the

446

diffusion experiments. The manuscript was much improved by the constructive comments of

447

four anonymous reviewers and by the associate editor Daniel Giammar.

448


Page 19 of 29


449

Supporting Information

450

Data (Figure S1) obtained for kaolinite (validation of the through-diffusion set-up).

451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508

References: (1) Pusch, R. Highly compacted sodium bentonite for isolating rock-deposited radioactive-waste products. Nuclear Technology 1979, 45, 153-157. (2) Bourg, I.A.; Bourg, A.C.M.; Sposito, G. Modeling diffusion and adsorption in compacted bentonite: a critical review. J. Contam. Hydrol. 2003, 61, 293-302. (3) Charlet, L; Alt-Epping, P.; Wersin, P.; Gilbert., B. Diffusion transport and reaction in clay rocks : a storage (nuclear waste, CO2, H2), energy (shale gas) and water quality issue. Advances Water Research 2017, 106, 39-59. (4) Tournassat, C; Appelo, C.A.J. Modeling approaches for anion-exclusion in compacted Na-bentonite. Geochim. Cosmochim. Acta 2011, 75, 3698-3710. (5) Glaus, M. A.; Baeyens, B.; Bradbury, B.; Jakob, A.; Van Loon, L.R.; Yaroshchuk, A. Diffusion of 22Na and 85Sr in montmorillonite: Evidence of interlayer diffusion being the dominant pathway at high compaction. Environ. Sci. Technol. 2007, 41, 478–485. (6) Appelo, C. A. J.; Wersin, P. Multicomponent diffusion modeling in clay systems with application to the diffusion of tritium, iodide, and sodium in Opalinus clay. Environ. Sci. Technol. 2007, 41, 5002–5007. (7) Bourg, I. C.; Sposito, G.; Bourg, A. C. M. Modeling cation diffusion in compacted water-saturated sodium bentonite at low ionic strength. Environ. Sci. Technol. 2007, 41, 8118–8122. (8) Tinnacher, R.M.; Holmboe, M.; Tournassat, C.; Bourg, I.A.; Davis, J.A. Ion adsorption and diffusion in smectite: molecular, pore and continuum scale views. Geochim. Cosmochim. Acta 2016, 177, 130-149. (9) Ferrage, E. Investigation of the interlayer organization of water and ions in smectite from the combined use of diffraction experiments and molecular simulations. A review of methodology, applications, and perspectives. Clays Clay Miner. 2016, 64, 348-373. (10) Norrish, K. The swelling of montmorillonite. Discuss. Faraday Soc. 1954, 18 (0), 120–134. (11) Madsen, F.T., Müller-Vonmoos, M. The swelling behaviour of clays. Appl. Clay Sci. 1989, 4, 143–156. (12) Morvan, M.; Espinat, D.; Lambard, J.; Zemb, T. Ultrasmall-and small-angle X-ray scattering of smectite clay suspensions. Colloids Surf. A 1994, 82, 193-203. (13) Segad, M., Jonsson, B., Åkesson, T., Cabane, B. Ca/Na montmorillonite: structure, forces and swelling properties. Langmuir 2010, 26, 5782–5790. (14) Abend, S.; Lagaly, G. Sol-gel transitions of sodium montmorillonite dispersions. Appl. Clay Sci. 2000, 16, 201-227. (15) Liu, L. Prediction of swelling pressures of different types of bentonite in dilute solutions. Colloids Surf. A Physicochem. Eng. Asp. 2013, 434, 303–318. (16) Michot, L.J.; Bihannic, I.; Porsch, K.; Maddi, S.; Baravian, C.; Mougel, J.; Levitz, P. Phase diagrams of Wyoming Namontmorillonite clay. Influence of particle anisotropy. Langmuir 2004, 20, 10829-37. (17) Michot, L.J.; Ferrage, E.; Jimenez-Ruiz, M.; Boehm, M.; Delville, A. Anisotropic features of water and ion dynamics in synthetic Na- and Ca-smectites with tetrahedral layer charge. A combined quasi-elastic neutron-scattering and molecular dynamics simulations study. J. Phys. Chem. C 2012, 116, 16619-16633. (18) Porion, P.; Faugère, A.M.; Delville, A. Structural and dynamical properties of water molecules confined within clay sediments probed by deuterium NMR spectroscopy, multiquanta relaxometry and two-time stimulated echo attenuation. J. Phys. Chem. C 2014, 118, 20429-20444.



509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572

Page 20 of 29

(19) Melkior, T.; Gaucher, E. C.; Brouard, C.; Yahiaoui, S.; Thoby, D.; Clinard, Ch.; Ferrage, E.; Guyonnet, D.; Tournassat, C.; Coelho, D. Na+ and HTO diffusion in compacted bentonite: Effect of surface chemistry and related texture. J. Hydrol. 2009, 370, 9-20. (20) Lagaly, G.; Dékány, I. Chapter 8 – Colloid Clay Science. In Handbook of Clay Science; Bergaya, F., Lagaly, G. Eds; Elsevier: Amsterdam 2013, pp 102. (21) Reinholdt, M.X.; Hubert, F.; Faurel, M.; Tertre, E.; Razafitianamaharavo, A.; Francius, G.; Prêt, D.; Petit, S.; Béré, E.; Pelletier, M.; Ferrage, E. Morphological properties of vermiculite particles in size-selected fractions obtained by sonication. Appl. Clay Sci. 2013, 77-78, 18-32. (22) Hubert, F.; Bihannic, I.; Prêt, D.; Tertre, E.; Nauleau, B.; Pelletier, M.; Demé, B.; Ferrage, E. Investigating the anisotropic features of particle orientation in synthetic swelling clay porous media. Clays Clay Miner. 2013, 61, 397-415. (23) Ferrage, E.; Hubert, F.; Tertre, E.; Delville, A.; Michot, L.J.; Levitz, P. Modeling the mesoscopic arrangement of particles in natural clay porous media using 3D packing of elliptic disks. Phys. Rev. E. 2015, 91, 062210-1 062210-18. (24) Dzene, L.; Tertre, E.; Hubert, F.; Ferrage, E. Nature of the sites involved in the process of cesium desorption from vermiculite. J. Colloid Interf. Sci. 2015, 455, 254–260. (25) Dzene, L.; Ferrage, E.; Hubert, F.; Delville, A.; Tertre, E. Experimental evidence of the contrasting reactivity of external vs. interlayer adsorption sites on swelling clay minerals: the Case of Sr2+-for-Ca2+ exchange in vermiculite. Appl. Clay Sci. 2016, 132-133, 205-215. (26) Oscarson, D.W. Surface diffusion: is it an important transport mechanism in compacted clays? Clays Clay Min. 1994, 42 (5), 534-543. (27) Van Loon, L.R.; Glaus, M.A.; Müller, W. Effect of confining pressure on the diffusion of HTO, 36Cl- and layered argillaceous rock (Opalinus Clay): diffusion perpendicular to the fabric. Appl. Geochem. 2003, 18, 1653.

125 -

I in a

(28) de la Calle, C. ; Suquet, H. ; Dubernat, J. ; Pezerat, H. Mode d’Empilement des feuillets dans les vermiculites hydratées à « deux couches ». Clay Min. 1978, 13, 275-297. (29) Faurel, M. Conception et mise en place d’expériences de diffusion de l’eau et de solutés dans des milieux poreux modèles d’argiles gonflantes. Ph. D. Dissertation, Poitiers, France, 2012. (30) Benning, J.L.; Barnes, D.L. Comparison of modeling methods for the determination of effective porosities and diffusion coefficients in through-diffusion tests. Water Resour. Res. 2009, 45, W09419, doi:10.1029/2008WR007236. (31) Savoye, S.; Frasca, B.; Grenut, B.; Fayette, A. How mobile is iodide in the Callovo-Oxfordian claystones under experimental conditions close to the in situ ones? J. Contam. Hydrol. 2012, 142-143, 82-92. (32) Melkior, T. Etude méthodologique de la diffusion de cations interagissants dans les argiles. Application ; mise en œuvre expérimentale et modélisation du couplage chimie-diffusion d'alcalins dans une bentonite synthétique. Ph. D. Dissertation, Ecole Centrale Paris, France, 2000. (33) Kakiuchi, M. Distribution of isotopic water molecules, H2O, HDO, and D2O, in vapor and liquid phases in pure water and aqueous solution systems. Geochim. Cosmochim. Acta 2000, 64, 1485-1492. (34) Sturm, P.; Knohl, A. Water vapor δ2H and δ18O measurements using off-axis integrated cavity output spectroscopy. Atmosph. Measurem. Tech. 2010, 3, 67-77. (35) Crank, J. The Mathematics of Diffusion, 2nd, ed.; Oxford University Press: London, 1975. (36) Savoye, S.; Beaucaire, C.; Grenut, B.; Fayette, A. Impact of the solution ionic strength on strontium diffusion through the Callovo-Oxfordian clayrocks: an experimental and modelling study. Appl. Geochim. 2015, 61, 41-52. (37) Moridis, G.J. A set of semi-analytical solution for parameter estimation in diffusion cell experiments. Report LBNL41857. Lawrence Berkeley National Laboratory, Berkeley, California, 1998. (38) Glaus, M.A.; Rossé, R.; Van Loon, L.R.; Yaroshchuk, A.E. Tracer diffusion in sintered stainless steel filters: measurement of effective diffusion coefficients and implications for diffusion studies with compacted clays. Clays Clay Min. 2008, 56, 677-685.


Page 21 of 29

573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639


(39) González Sánchez, F.; Van Loon, L. R.; Gimmi, T.; Jakob, A.; Glaus, M. A.; Diamond, L. W. Self-diffusion of water and its dependence on temperature and ionic strength in highly compacted montmorillonite, illite and kaolinite. Appl. Geochem. 2008, 23, 3840-3851. (40) Van Loon, L.R.; Jakob, A. Evidence for a second transport porosity for the diffusion of tritiated water (HTO) in a sedimentary rock (Opalinus clay – OPA): application of through- and out-diffusion techniques. Transport Porous Media 2005, 61, 193-214. (41) Tertre, E.; Delville, A.; Prêt, D.; Hubert, F.; Ferrage, E. Cation diffusion in the interlayer space of swelling clay minerals - a combined macroscopic and microscopic study. Geochim. Cosmochim. Acta 2015, 149, 251–267. http://dx.doi.org/10.1016/j.gca.2014.10.011. (42) Richard, T.; Mercury, L.; Massault, M., Michelot, J.L. Experimental study of D/H isotopic fractionation factor of water adsorbed on porous silica tubes. Geochim. Cosmochim. Acta 2007, 71, 1159-1169. (43) Lin, Y; Horita, J. An experimental study on isotope fractionation in a mesoporous silica-water system with implications for vadose-zone hydrology. Geochim. Cosmochim. Acta 2016, 184, 257-271. (44) Bourg, I.C.; Tournassat, T. Self-Diffusion of water and ions in clay barriers. In Natural and Engineered Clay Barriers; Tournassat, C., Steefel, C.I., Bourg, I.C., Bergaya, F., Eds.; Elsevier: Amsterdam 2015; pp 432. (45) Tyagi, M; Gimmi, T., Churakov, S.V. Multi-scale micro-structure generation strategy for up-scaling transport in clays. Advances Water Resources 2013, 59, 181-195. (46) Sato, H.; Suzuki, S. Fundamental study on the effect of an orientation of clay particles on diffusion pathway in compacted bentonite. Applied Clay Science Clay Microstructure. Proceedings of a Workshop held in Lund 2003, Sweden, 15-17 October 2002, 23, 51-60. (47) Van Loon, L.R.; Soler, J.M., Müller, W.; Bradbury, M.H. Anisotropic diffusion in layered argillaceous rocks: a case study with Opalinus clay. Environ. Sci. Technol. 2004, 38, 5721-5728. (48) Sato, H. Effects of the orientation of smectite particles and ionic strength on diffusion and activation enthalpies of I- and Cs+ ions in compacted smectite. Appl. Clay Sci. 2005, 29, 267-281. (49) García-Gutiérrez, M.; Cormenzana, J. L.; Missana, T.; Mingarro, M. Diffusion coefficient and accessible porosity for HTO and 36Cl, compacted FEBEX bentonite. Appl. Clay Sci. 2004, 26, 65-73. (50) Glaus M. A.; Frick, S.; Rossé, R.; Van Loon, L. R. Comparative study of tracer diffusion of HTO, compacted kaolinite, illite and montmorillonite. Geochim. Cosmochim. Acta 2010, 74, 1999-2010.

22

Na+ and

36

Cl− in

(51) Kemper, W.D.; Maasland, D.E.L.; Porter, L.K. Mobility of water adjacent to mineral surfaces. Soil Sci. Society America Proceedings 1964, 28, 164-167. (52) Duval, F.P., Porion, P.; Van Damme, H. Microscale and macroscale diffusion of water in colloidal gels. A pulsed field gradient and NMR imaging investigation. J. Phys. Chem. B 1999, 103, 5730-5735. (53) Nakashima, Y.; Mitsumori, F. H2O self-diffusion restricted by clay platelets with immobilized bound H2O layers: PGSE NMR study of water-rich saponite gels. Appl. Clay Sci. 2005, 28, 209-221. (54) Tournassat, C.; Steefel, C.I. Ionic transport in nano-porous clays with consideration of electrostatics effects. Rev. Mineral. Geochem. 2015, 80, 287-329. (55) Mermut, A.R.; Lagaly, G. Baseline Studies of the Clay Minerals Society Source Clays: Layer-Charge Determination and Characteristics of those Minerals Containing 2:1 Layers. Clays Clay Min. 2001, 49, 393-397. (56) Churakov, S. V.; Gimmi, T. Up-scaling of molecular diffusion coefficients in clays: A two-step approach. J. Phys. Chem. C 2011, 115, 6703–6714. (57) Bourg, I.C; Sposito, G. Molecular dynamic simulations of the electrical double layer on smectite surfaces contacting concentrated mixed electrolyte (NaCl-CaCl2) solutions. J. Colloid Interf. Sci. 2011, 360, 701-715. (58) Altmann, S.; Tournassat, C.; Goutelard, F.; Parneix, J.C.; Gimmi, T.; Maes, N. Diffusion-driven transport in clayrock formations. Appl. Geochem. 2012, 27, 463-478. (59) Claret, F.; Sakharov, B.A.; Drits, V.A.; Velde, B.; Meunier, A.; Griffault, L.; Lanson, B. Clay minerals in the MeuseHaute Marne underground laboratory (France): possible influence of organic matter on clay mineral evolution. Clays Clay Min. 2004, 52 (5), 515-532.



640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660

Page 22 of 29

(60) Beaucaire, C.; Tertre, E.; Ferrage, E.; Grenut, B.; Pronier, S.; Madé, B. A thermodynamic model for the prediction of pore water composition of clayey rock at 25 and 80°C – Comparison with results from hydrothermal alteration experiments. Chem. Geol. 2012, 334, 62-76. (61) Robinet, J.-C.; Sardini, P.; Coelho, D.; Parneix, J.-C.; Prêt, D.; Sammartino, S.; Boller, E.; Altmann, S. Effects of mineral distribution at mesoscopic scale on solute diffusion in a clay-rich rock: Example of the Callovo-Oxfordian mudstone (Bure, France). Water Resour. Res. 2012, 48, 5554-5571. (62) Bourg, I.C.; Ajo-Franklin, J.B. Clay, water and salt: controls on the permeability of fine-grained sedimentary rocks. Accounts Chem. Res. 2017, 50, 2067-2074. (63) Churakov, S. V.; Gimmi, T.; Unruh, T.; Van Loon, L. R.; Juranyi, F. Resolving diffusion in clay minerals at different timescales: Combination of experimental and modeling approaches. Appl. Clay Sci. 2014, 96, 36–44. (64) Bacle, P.; Dufrêche, J.F.; Rotenberg, B.; Bourg, I.C.; Marry, V. Modeling the transport of water and ionic tracers in a micrometric clay sample. Appl. Clay Sci. 2016, 123, 18-28. (65) Hassan, M.S.; Villieras, F.; Gaboriaud, F.; Razafitianamaharavo, A. AFM and low-pressure argon adsorption analysis of geometrical properties of phyllosilicates. J. Colloid Interf. Sci. 2006, 296, 614-623.


Page 23 of 29


Figure captions:

Figure 1: Instantaneous flux and cumulative total amount of HDO diffusing through porous media composed of the (A) 0.1-0.2 µm, (B) 1-2 µm, and (C) 10-20 µm size fractions of Navermiculite. Data are plotted as a function of time and for different total porosities of the media. Symbols represent experimental data, while full lines correspond to the fit of the experimental flux. Dotted lines are simulated flux curves calculated by considering the error range of diffusion parameters (see Table 1). Simulated cumulative curves calculated by considering the diffusion parameters interpreting average experimental flux are reported in dashed lines.

Figure 2: Comparison between effective diffusion coefficients (De) reported in the literature and those obtained in this present study for clayey porous media composed of porous (i.e., Na-montmorillonite, Na-smectite-rich materials and Na-vermiculite) and non-porous grains (i.e., Na-kaolinite and Na-illite). (A) As a function of the total porosity ε. (B) As a function of the interparticle porosity εinterp. only (see Table 1 for details).

Table caption:

Table 1: Summary of the diffusion experiments, including characteristics of the compacted sample and diffusion parameters (effective diffusion coefficient and rock capacity factor) interpreting experimental data. The uncertainty ranges for the diffusion parameters are written in brackets (see text for details). 23 ACS Paragon Plus Environment


Page 24 of 29


Page 25 of 29


Table 1 De -11 (10 m2.s-1)d

d

Rdd (mL.g-1)

amount of adsorbed HDO -5 (10 mol.g-1)

18 (14-24) 26 (19-42)

0.25 (0.2-0.3) 0.5 (0.5-0.8)

0 (0-0.08) 0 (0-0.22)

0 (0-2.1) 0 (0-6.0)

0.557

15.2 (10.5-19)

0.89 (0.6-0.9)

0.30 (0.12-0.31)

8.1 (3.2-8.3)

0

0.487

9.7 (7-14.5)

0.25 (0.13-0.32)

5.8 (3.0-7.4)

0.50

0.25

0.539

38.5 (25-55)

0.77 (0.550.9) 1.1 (1.0-1.2)

0.44 (0.37-0.52)

11.6 (9.7-13.5)

5.1

0.31

0

0.472

10.2 (6-17)

0.75 (0.5-0.9)

0.24 (0.10-0.32)

5.4 (2.3-7.2)

6.8

0.35

0.03

0.555

3.58 (2.5-4.5)

0.86 (0.60.86)

0.29 (0.14-0.29)

7.8 (3.8-7.8)

Nature of the clay

size fraction (µm)

thickness of compacted sample L (mm) ± 0.1

total porosity a ± 0.025

Nakaolinite

≈ 0.1-1e

6.0

0.26

0.26

0.555

0.1-0.2

8.4

0.50

0.25

0.547

0.1-0.2

7.0

0.41

0.12

0.1-0.2

3.4

0.31

1-2

6.1

1-2 10-20

Navermiculite

interparticle [HDO] porosity concentration in the upinterp.b stream ± 0.025 reservoir (M)c



a

calculated as 𝜀 = 1 −

𝜌𝑎𝑝𝑝. 𝜌𝑠

Page 26 of 29

where s is the real grain density (2.6 for kaolinite according to Hassan et al.65 and 2.7 g.cm-3 for vermiculite as calculated by Reinholdt et al.21 on

the basis of the structural formula). app. is the bulk dry density calculated considering the volume of diffusion cell and the mass of samples measured at 25°C and corrected from mass of interlayer water of Na-vermiculite at room humidity (approximatively 10%) as performed in literature.24 b calculated by considering Equation 8 (see text). c note that the maximum decrease of the HDO concentration in the upstream reservoir due to diffusion is around 3% all along an experiment allowing to assume a constant gradient between two aqueous reservoirs for modelling. d see equation 2 in the text. e from 65


Page 27 of 29 Figure 1


A. 0.1-0.2µm size fraction

6.E-05

6.E-04

4.E-05

4.E-04

flux cumulative amount

2.E-04

0.E+00 4

6

8

6.E-04 4.E-05 4.E-04

2.E-05


2

4

porosity e = 0.50

12

2.0E-04


0.0E+00

0.0E+00

4

6

instantaneous flux (mol/day)

5.0E-05

4.0E-05 4.0E-04


2.0E-04

0.0E+00

0.0E+00 8

12

ACS Paragon Environment timePlus (days)

4.E-04

2.0E-05

flux

2.E-04

cumulative amount

0.E+00 0

2

4

6

8

10

12

16

20

porosity e = 0.35

2.0E-05

1.0E-03

6.0E-04

4

4.0E-05

C. 10-20µm size fraction 8.0E-04

0

6.E-04

time (days)

6.0E-05

2.0E-05

6.0E-05

1.6E-04

1.5E-05

1.2E-04

1.0E-05

8.0E-05

5.0E-06

4.0E-05

flux

cumulative amount

0.0E+00

0.0E+00 0

2

4

6

time (days)

8

10

cumulative total amount (mol)

4.0E-04

8.E-04

14


1.0E-04

time (days)

10

porosity e = 0.31

8.0E-05



8.0E-04

6.0E-04

2

8

time (days)

B. 1-2µm size fraction

0

6

8.0E-05

0.0E+00

0.E+00

0

10

time (days)

1.5E-04

2.E-04


2

8.E-04 6.E-05

0.E+00

0.E+00 0

1.E-03


8.E-04


8.E-05

8.E-05


1.E-03


1.E-04

2.E-05

porosity e = 0.31

porosity e = 0.41 cumulative total amount (mol)


porosity e = 0.50


Page 28 of 29

Figure 2 A

B Na-kaolinite – Na-illite – 0.1/0.2 and 1/2 size fractions of Na-vermiculite

0.1/0.2 and 1/2 size fractions of Na-vermiculite 1.0E-09

1.0E-09

Na-montmorillonite ; Glaus et al., 2010 (50)

Na-kaolinite; Gonzalez Sanchez et al., 2008 (39)

Na-kaolinite – Na-illite

Febex bentonite; Garcia Gutirerez et al., 2004 (49) Na-bentonite ; Melkior et al., 2009 (19)

Na-kaolinite; this study

Na-illite ; Glaus et al., 2010 (50)

Na-kaolinite; this study

De (m²/s)

De (m²/s)

Na-kaolinite; Gonzalez Sanchez et al., 2008 (39)

1.0E-10 Na-illite ; Glaus et al., 2010 (50)

1.0E-10 Na-illite ; Gonsalez Sanchez et al., 2008 (39)

Na-illite ; Gonsalez Sanchez et al., 2008 (39)

Na-smectite 10/20 size fraction of Na-vermiculite

0.1 0.2 Na-vermiculite

0.1 0.2 Na-vermiculite

1 2 Na-vermiculite 1 2 Na-vermiculite

10 20 Na-vermiculite

1.0E-11

1.0E-11 0

0.2

0.4 0.6 total porosity (e)

0.8

0

ACS Paragon Plus Environment

0.05

0.1

0.15 0.2 0.25 0.3 interparticle porosity (einterp.)

0.35

Page 29 of 29


TOC

1.0E-09

high charge swelling clays (vermiculite)

=

De (m²/s)

non-swelling clays (kaolinite - illite)

Na-vermiculite 1-2 µm Na-vermiculite 0.1-0.2 µm

1.0E-10

low charge swelling clays (Na-smectite)

1.0E-11 0.1

0.2

0.3

0.4 0.5 total porosity

0.6

0.7

0.8

ACS Paragon Plus Environment

Diffusion of Water through the Dual-Porosity Swelling Clay Mineral

Recommend Documents