Environ. Sci. Technol. 2010, 44, 3698–3704
New Experimental Approach for Studying Diffusion through an Intact and Unsaturated Medium: A Case Study with Callovo-Oxfordian Argillite ´ B A S T I E N S A V O Y E , * ,† J A C Q U E S P A G E , † SE ´ LINE PUENTE,† CE CHRISTOPHE IMBERT,§ AND DANIEL COELHO‡ CEA, DEN, Laboratory of Radionuclides Migration Measurements and Modeling, F-91191 Gif-sur-Yvette, France, CEA, DEN, Laboratory of Concrete and Clay Behavior Studies, F-91191 Gif-sur-Yvette, France, and Andra, 1 rue Jean Monnet, F-92298 Chaˆtenay-Malabry, France
Received December 11, 2009. Revised manuscript received March 26, 2010. Accepted April 6, 2010.
The diffusion of tritiated water and anionic species was studied in an unsaturated core of Callovo-Oxfordian claystone, which is a potential host-rock for disposal of high-level radioactive wastes. The diffusion parameters in such conditions were determined using modified through-diffusion cells in which the suction is generated by the osmosis process. This specific device leads to values of saturation degree ranging from 81% to 100%. The results show that the diffusion through unsaturated samples is clearly slower than that in fully saturated samples, with steady-state fluxes decreasing by a factor up to 7 for tritium and up to 50 for anionic species. While tritium porosity values follow volumetric water contents (from 21 to 16%), the porosity accessible to anionic species significantly decreases (from 7.5 to 0.7%). Such diffusive behaviors have been modeled by means of a modified Archie’s law, taking into account a critical water saturation below which no tracer can percolate. These results indicate that the largest pores, which are initially affected by dehydration, would play an important role on the connectivity of the porous medium. This would especially affect anionic species diffusion behavior because they are constrained to diffuse into the largest pores first.
Introduction Most waste disposal facilities are designed so that the transport of contaminants is as slow as possible, with a dominant diffusive component with respect to the advective one (1). For instance, engineered landfill liners are usually constructed using compacted clay with a saturated hydraulic conductivity (Ks) less than 1 × 10-9 m · s-1 (per U.S regulations) to achieve such a transport condition (2, 3). Geological disposal of high-level radioactive waste relies on the very impervious properties of the engineered and natural barriers. * Corresponding author phone: +33 1 69 08 77 51; fax: +33 1 69 08 32 42; e-mail:
[email protected]. † CEA, DEN, Laboratory of Radionuclides Migration Measurements and Modeling. § CEA, DEN, Laboratory of Concrete and Clay Behavior Studies. ‡ Andra. 3698
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In Switzerland and France, such facilities could be hosted in deep argillaceous formations where Ks values are less than 1 × 10-12 m · s-1 (4-6). Moreover, considerable effort has been devoted to estimate diffusion coefficients for solutes transported through all these types of natural materials (7-12). However, there are many situations where the soils or the rocks surrounding such waste disposal facilities can be unsaturated, leading to a change of the diffusive contaminant transport. For example, many landfills are constructed in arid or semiarid environments, where the soil can be unsaturated at great depths (13, 14). For example, the potential repository site for high level nuclear waste in the United States investigated for more than 20 years by the U.S. Department of Energy is located in an unsaturated area at Yucca Mountain (Nevada) (15). In the case of argillaceous formations, the presence of a radioactive waste repository is known to induce a hydraulic disequilibrium directly in the host-rocks. Initially, ventilation of the underground drifts and shafts during the construction and the operation phase would lead to the partial dehydration of the rock around the drift (16, 17). Then, after a resaturation phase, the corrosion of the canisters would produce hydrogen, capable of dehydrating the claystones again (18). Even though this effect should be limited primarily to the fractures of the Excavation Damaged Zone (see ref 19), unfractured argillites could also be unsaturated. According to ref 19, dehydration process could reach up to 20% of the total water content in CallovoOxfordian argillites. Whereas permeability measurements in unsaturated natural media have been described in the literature (20, 21), only a few studies on the diffusive transport in such conditions are available (7, 22-25). Indeed, as mentioned Shackelford (1) who summarized some of these data obtained on several types of unsaturated soils (silt, sand, silty-clay loam), the diffusion coefficient values for nonreactive and reactive solutes in unsaturated soils can be as much as 10 to 20 times lower than the corresponding values in saturated soils. Therefore, it is highly time-consuming to measure such a diffusion coefficient. The authors are aware that there is no study of diffusion through unsaturated intact argillaceous rocks. In this work, the diffusion of two types of species, i.e., uncharged tritiated water (HTO), and two anions, 36Cl- and 125 I , were studied through unsaturated Callovo-Oxfordian (COx) argillite, a consolidated argillaceous rock. The required degrees of saturation were fixed by means of osmotic suction. Such an approach allows for through-diffusion experiments, based on a steady-state method, to be performed after the achievement of suction equilibrium. The present study aims at (i) presenting this new experimental approach, (ii) demonstrating the effect of dehydration on the diffusion of charged and uncharged species through clayey rock, and (iii) bringing new insights about the connectivity of such media.
Materials and Methods Suction Controlled by Osmosis. Osmosis allows for the control of the water suction in the sample while maintaining contact with a chemical solution. Initially developed by biologists (26), this technique was later adopted by soil scientists (27). This technique is an alternative to the widely used saturated salt solution technique in geotechnical engineering (28-30). The suction is generated by the osmosis process between the pore water (present in the pores of the sample) and a highly concentrated solution with large-sized 10.1021/es903738t
2010 American Chemical Society
Published on Web 04/21/2010
FIGURE 1. Cross-section view of the through-diffusion cell. PTFE means polytetrafluoroethylene and PEEK means polyetheretherketone. molecules of polyethylene glycol (PEG). The clay sample is separated from the PEG-solution by a semipermeable membrane (which is permeable to all except PEG). The exclusion of the PEG from the clay sample results in a chemical-potential imbalance between the water in the clay sample and the water in the reservoir chambers. This osmotic suction has the effect of keeping the clay sample unsaturated. The value of the imposed suction depends on the PEG concentration in solution. Delage et al. (28) reported the evolution of the suction as a function of the PEG concentration. Data were obtained from literature experiments for suction up to 1.5 MPa and from their own experiment for higher suctions. All data under 4 MPa (28, 29) fit the following parabolic relation between the suction (Ψ) expressed in MPa and the concentration (c) of PEG (g of PEG per g of water). ψ ) 11c2
(1)
Above 4 MPa, suction values are lower than those expected from eq 1. Nevertheless, suctions up to about 10 MPa can be reached by using solutions highly concentrated in PEG (more than 1 g PEG per g water) (28, 30). Osmotic Method Equipment. In the present study, classical through-diffusion cells (11, 31) have been adapted in order to apply suctions up to 10 MPa. The choice of the highest suction value is based on previous geomechanical studies involving Callovo-Oxfordian samples showing that degrees of saturation of about 80% would be obtained by applying suctions of about 10 MPa (21, 32). Four series of cells were set up to investigate diffusion through samples unsaturated up to 80%. The different states of saturation were reached with chemical solutions prepared by increasing concentrations of PEG 6000 (0, 0.42, 0.76, and 0.95 g per g of solution). A concentration of 0.42 g of PEG per g of solution is assumed to impose a suction of 1.9 MPa from eq 1. The two highest PEG concentrations were derived from the calibration study carried out by Delage et al. (28) and from which suctions of 6.3 and 9 MPa were measured (see the Supporting Information for more details). According to ref 28, semipermeable membranes with 3500 g · mol-1 molecular weight cutoff (MWCO) were chosen with PEG (6000 g · mol-1 molecular weight). A schematic view of the cell is given in Figure 1. A 36-mm-diameter sample is inserted in the stainless steel holder and is sandwiched between two semipermeable membranes fabricated of cellulose acetate (Spectra-Por 3500 Da, Spectrum laboratories, USA). O-rings prevent the PEG solution from bypassing the membranes. Afterward, two polyetheretherketone (PEEK) grids (Polyetheretherketone - Mesh, Goodfellow, England)
with 60 and 45 meshes are put between the O-rings to limit the dead-volume, and then the two end-pieces are placed in position. For each series, one cell was devoted to through-diffusion experiments with the radiotracers, while the other cell was devoted to the determination of the rock sample degree of saturation. In order to verify the reliability of the osmotic method, five other rock samples had undergone hydric treatments by means of the saturated saline solution method (21, 28, 32). Sample Origin and Sample Preparation. The rock samples used for the measurements were obtained from the Meuse/Haute Marne Underground Laboratory, located in the eastern portion of the Paris basin. The sedimentary host formation (152-160 Ma) is a ∼130-m-thick clay-rich CallovoOxfordian formation and with a burial depth of ∼420-550 m below ground level (bgl). According to Gaucher et al. (33), the level from which the core originates (484.5-484.8 m bgl) corresponds to silty and calcareous argillites, containing 35-65% of clay minerals (with 27-38% of mixed layer Illite/ smectite), 15-28% of carbonates, 21-31% of quartz, and accessory minerals. Thirteen samples were sliced from the EST27337 claystone core using a diamond wire saw (no lubricating fluid was used) into 1-cm-thick pieces and then cut as a disk. All the sliced samples were stored at (30.0 ( 0.2)°C in desiccators containing a NaCl-oversaturated solution, until suction equilibrium; which was achieved after ca. 3 months (indicated by mass stabilization). The imposed suction was estimated at 41 MPa by applying the Kelvin’s law with the relative humidity value given by ref 28 at 30 °C (75%). This initial dehydration of the rock samples at a level lower than those imposed by the osmotic method prevents any shrinkage of samples (only hydration pathway). This assumption was verified by mercury injection porosimetry performed on the most and the least dehydrated samples (see the Supporting Information). Desaturation Procedure. Among these 13 samples, one sample stored in the NaCl desiccator was directly analyzed, and eight were partly resaturated with the osmotic technique and four with oversaturated saline solutions with K2SO4, KH2PO4, KNO3, and BaCl2 at (30 ( 0.2)°C, causing four distinct suctions estimated to 4.3, 7.3, 13.5, and 15.1 MPa, respectively, according to refs 28 and 34. The four rock samples were inserted in 18.75-mm inner-diameter cells made up of polypropylene and then sandwiched between two Peekalloyed-with-Teflon filter plates (PAT Filter, Interchim, France). For osmotic resaturation, in addition to PEG 6000 (Merck, Germany), solutions were prepared with ultrapure deionized water (18.2 MΩ cm-1) and commercial salts (American Chemical Society (ACS) reagent grade or higher quality and purity salts), in order to obtain a chemical composition as close as possible to the pore-water one. The recipe given in Table 1 is based upon the chemical composition estimated from in situ water sampling performed at a level close to the sampling level of this study (-475 m bgl) (35). The experimental setup comprises a diffusion cell, as described above, a 16-channel peristaltic pump (IPS, Ismatec, Idex Corporation, USA), and one 100-cm3 reservoir. During the hydric equilibrium phase, both sides of the samples were in contact with the same synthetic water and PEG solution, using a unique reservoir. This configuration allows the estimation
TABLE 1. Pore Water Composition Used for This Study ionic strength (eq · L-1)
pH
0.101
7.38
Ca2+ (mol · L-1) Mg2+ (mol · L-1) Na+ (mol · L-1) K+ (mol · L-1) ΣCO2 (mol · L-1) Cl- (mol · L-1) SO42- (mol · L-1) 6.44 × 10-3
4.48 × 10-3
51.9 × 10-3
1.04 × 10-3
2.57 × 10-3
41.0 × 10-3
15.6 × 10-3
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of the hydric equilibrium achievement for the rock sample by monitoring the weight loss of the reservoir. For the four PEG concentrations, stabilized values of mass were reached after about 2 weeks. Nevertheless, to ensure the complete hydric equilibrium, 2 further weeks of contact time were added before starting either the dismantling of the cells for performing the petrophysical measurements or the diffusion tests (described below). Petrophysical Measurements. In order to determine the water content and the degree of saturation as a function of imposed suctions, petrophysical measurements have been performed as follows: (i) water contents (w) were measured by weighing before and after oven-heating at 105 °C for 48 h and were described on a mass basis relative to the wet mass; (ii) bulk densities (Fbulk,wet, Fbulk,dry) were determined by measuring the pressure exerted by the sample immersed in kerosene according to Archimedes’ principle (36); and (iii) grain density was determined in a Micrometrics Accupyc 1330 helium pycnometer. The volumetric moisture content, θ, is calculated from the water content by using the following expression (9) θ)
w × Fs (1 - w) × Fw + w × Fs
(2)
where Fw ) the density of the pore water (1 g · cm-3), and Fs ) the measured grain density of the rock ((2.7023 ( 0.0016) g · cm-3). The total porosity is deduced from the following equation (9) φ)1-
Fbulk,dry Fs
9
measured by gamma spectrometry. The activities injected in the upstream reservoir were 20 kBq · g-1, 11 kBq · g-1, and 15 kBq · g-1 for HTO, Cl-36, and I-125, respectively. The diffusion modeling is carried out by planar throughdiffusion. During the diffusion process, no chemical interactions are assumed between the radio-tracers (HTO, Cl-36, and I-125) and the medium, such that the following form of the Fick’s second law is applicable
(3)
Finally, the saturation degree (Sw) corresponds to the ratio of volumetric water content over the total porosity. Diffusion Experiments. After 1 month of saturation treatment, cells devoted to diffusion experiments were connected to two distinct reservoirs. The upstream reservoir was filled with 100 cm3 of a fresh solution labeled with tritiated water (HTO) and a 20-cm3 downstream reservoir filled with a fresh solution without tracer was connected to the cell. During the through-diffusion experiment, the solution in the downstream reservoir was regularly replaced in order to maintain the lowest tracer concentration as reasonably possible, i.e., less than 3% of the one measured in the upstream reservoir. Note that tracers diffuse perpendicularly to the bedding plane. After completion of the HTO through-diffusion experiment, the solutions in both reservoirs were replaced with fresh synthetic water without tracer for starting out-diffusion lasting up to 3 weeks. Through-diffusion with 125I- started as soon as the HTO out-diffusion flux was negligible, i.e. for a residual HTO activity close to the detection limit (0.5 Bq). In addition to the radio-tracer, I-125, stable iodide was added to reach a concentration of 10-3 M in the upstream reservoir to avoid any uptake of iodine, as previously observed by Bazer-Bachi et al. (37) for lower concentrations ( 0 C(x,t) ) 0, x ) L, t > 0 where L is the sample thickness (m). Fully analytical solutions of eq 4 are given by Crank (39) t ) S.L.A0. Adif
[
De.t L
2
-
t θdiff 6
t 2.θdiff
π
2
∞
2
.exp ∑ (-1) n 2
n)1
{
-
De.n2.π2.t t L2.θdiff
}]
(6)
Fi )
[
∞
{
De.A0. De.n2.π2.t 1 + 2. (-1)2.exp - 2 t L L .θdiff n)1
∑
}]
(7)
Equations 6 and 7 give respectively the cumulative activity (Atdiff) and the instantaneous flux of tracer (Fi) in the downstream reservoir. S is the surface of the sample (m2). The analysis of the results was performed by a leastsquares fitting of the model to the results of the incoming instantaneous flux in the downstream reservoir, using eq 6 (11).
Results and Discussion Figure 2 shows the evolution of the saturation degrees as a function of the imposed suction. The osmotic method leads to saturation degree values consistent with those measured on samples having undergone desaturation caused by saline
solutions. A gradual increase of the saturation degree can be observed from the initial state (NaCl-filled desiccators) up to the full-saturation one. Figure 3(A-D) shows the flux and the cumulative activity for the four through-diffusion experiments performed with HTO and I-125 (Sw ) 81, 86, 89, and 100%). The effect of desaturation is to decrease both the instant flux and the cumulative mass relative to the full-saturated sample to the more desaturated sample. For example, flux decreases by factors of approximately 7 and 50 for HTO and I-125, respectively. An overview of the values of estimated diffusive parameters for HTO, 36Cl-, and 125I- is given in Table 2. First, in full-saturated conditions (i.e., without PEG solution), comparison of our results with previous data obtained on rock core originating from a close level (12) shows a good consistency for the three tracers, demonstrating that the
FIGURE 3. Total diffused activity and normalized instantaneous fluxes at different values of degree of saturation for HTO (A, B) and for I-125 (C, D). The solid curves for the fluxes were calculated using the analytical solutions with the parameters specified in Table 2. Normalized flux is the ratio of instantaneous flux in Bq · m-2 · s-1 over the concentration in the upstream reservoir in Bq · m-3. The normalized total diffused tracer amount is the ratio of total diffused tracer activity in Bq over the concentration in upstream reservoir in Bq · m-3 times the volume of the sample in m3. VOL. 44, NO. 10, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 2. Values of Effective Diffusion Coefficient (De) and Porosities (θacc) for the Diffusion of HTO, 36Cl-, and Imposed Suctionsc sample and depth
saturation [%]
EST27337 484.5-484.8 m
100 ( 3
De (HTO) [m2 · s-1] × 1012
porosity (HTO) [%]
De/θacc [m2 · s-1] × 1010
anion tracer
23.0 (17.0-28.5)
21.0 (19.0-22.0)
1.1
Cl-36 I-125a
EST27337 484.5-484.8 EST27337 484.5-484.8 EST27337 484.5-484.8 EST05641b 477.0-477.4 EST05649b 478 m
m m m m
89 ( 3 86 ( 4.5 81 ( 3.5
8.2 (5.3-9.7) 4.9 (3.5-6.2) 3.6 (2.2-4.4)
19.5 (16-20) 17.5 (14.0-19.0) 16.0 (13.0-16.0)
100
22 ( 7
19.1 ( 4.2
100
20
20
a
0.4
I-125
0.3
I-125a
0.2
a
I-125
a
I-125 Cl-36
De [m2 · s-1] × 1012 2.70 (2.00-3.20) 2.00 (1.40-2.80) 0.26 (0.17-0.33) 0.07 (0.04-0.08) 0.04 (0.03-0.05) 1.60 4.60
a In addition to I-125, stable iodide (10-3 M) was added in high-concentration reservoir. core from borehole EST205. c Values between brackets indicate the uncertainty ranges.
FIGURE 4. HTO and I-125 accessible volumetric water content as a function of volumetric water content at the four degrees of saturation (Sw ) 100, 89, 86, and 81%). semipermeable membranes do not significantly slow down tracers with respect to the case of the classical setup without such a membrane. In both studies, the effective diffusion coefficient and the porosity of anions (Cl-36 and I-125) are smaller than for HTO, which can be explained by anion exclusion effects (12). Note that no clear discrepancy can be evidenced between diffusive parameters obtained for Cl-36 and I-125. This confirms that iodide at such high concentration (10-3 M) behaves as a conservative tracer, as previously shown (10, 12, 37). Moreover, the effect of desaturation on diffusive parameters is clearly noticeable both for HTO and I-125: the lower the degree of saturation, the lower both effective diffusion coefficient and volumetric water content accessible to the t HTO ). Values of θdiff show roughly the same decrease tracer (θdiff as those of volumetric water content, θ, confirming the extent of the desaturation obtained from petrophysical measureHTO values are always higher ments (Figure 4). However, the θdiff than those obtained by drying at 105 °C, independent of the applied suction. Such a discrepancy has already been observed in previous studies dealing with the CallovoOxfordian argillite (12). Indeed, the temperature of 105 °C 3702
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b
porosity [%] 7.5 (6.0-8.5) 7.5 (7.0-11.0) 2.0 (1.5-2.0) 0.9 (0.6-1.0) 0.7 (0.5-0.8) 3.3 6.5
125 -
I for Various
De/θacc [m2 · s-1] × 1011 3.2 2.7 1.3 0.8 0.5
Data from ref 12 obtained on
would not be sufficiently high to extract all the types of waters, especially water strongly bounded to the clay surface or lying in the smectite interlayer spaces (40), while the tritiated water can diffuse in all the types of connected porosities. The values I-125 exhibit a more significant decrease with suction than of θdiff θ (Figure 4), suggesting that some pores, into which iodide could normally diffuse in full-saturated conditions, become isolated from the diffusive pathway when dehydrating. Note that such a trend occurs from the lowest unsaturated state (Sw ) 89%). This behavior can be inferred to both (i) the anion exclusion effect that imposes the iodide to diffuse into the largest pores and (ii) the connectivity of the porous medium. Thus, when suction is applied, these biggest pores are the first ones to be emptied (diameter of pores > ∼30 nm from the Jurin-Laplace’s law at 9 MPa), preventing iodide from diffusing into all the remaining saturated porosity, normally accessible to anions. In other words, this means that a percolation threshold is reached for anions when only 19% of pores are emptied. t ratio, i.e, Dp, reported in Table 2 show The De over θdiff a clear variation both for HTO and I-125 as a function of Sw. According to eq 5, this implies that the geometrical structure of the diffusion pathway (i.e., tortuosity and constrictivity) largely also depends upon the saturation. Several authors have developed empirical models to predict the diffusion coefficient from physical characteristics of the geological media. A widely used model presented as the Archie’s second law (41) links the diffusivity ratio (De/D0) to the volumetric water content (θ) and the total porosity (φ). De n m ) Sw φ D0
(8)
CRWMS M&O (42) have reported that when the n and m parameters are fixed to 1.849, this relationship produces an excellent fit to numerous data, comprising whole tuff cores, basalt, mudstone, 86 soils, and gravel samples. However, as shown in Figure 5, the result obtained with eq 8 for n ) m ) 1.849 does not match well our experimental data. In fact, some authors (43-45) expect that there is critical water saturation at which the water phase is no longer connected at the scale of a representative volume in the clay rock. When the water saturation reaches this critical value, the tortuosity goes to infinity and the transport of tracers through the pore water is no longer possible. This phenomenon has been taken into account
Supporting Information Available Estimation of suction and incremental intrusion volume curves obtained from MIP test on full-saturated clay sample and the most unsaturated sample. This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited
FIGURE 5. HTO and I-125 diffusivities (De/D0) as a function of the degree of saturation. by introducing a percolation threshold, Sw_c, in the Archie’s second law, as proposed by Martys (43).
(
De Sw - Sw_c ) Dw 1 - Sw_c
)
m
n m .Sw .φ
(9)
When full-saturation occurs, the eq 9 reduces to the Archie’s first law and when the critical water saturation is reached, the expression becomes null. The saturation index, n, is generally assumed to be 2.0 (41, 45). The parameter m, commonly called the cementation exponent, is determined from the full-saturation case, thus allowing us to estimate the percolation threshold from the evolution of diffusivity with saturation, i.e., assuming that n equals 2. For iodide, the total porosity (φ) is reduced to the porosity accessible to this anion determined at full-saturation, as some authors proceeded when applying the Archie’s first law to diffusivity of tracers in saturated Callovo-Oxfordian claystone samples (12). However, the same values of saturation were used in eq 8 for iodide. The best fits for both tritiated water and I-125 are also reported in Figure 5. First of all, the values of the cementation exponent obtained for the two tracers (m(HTO) ) 2.86 and m(I-125) ) 2.65) are consistent with the range of those determined from several consolidated argillaceous rocks (2 < m < 3), especially from the Callovo-Oxfordian argillite (12, 31). The estimation of two distinct values of critical water saturation for tritium and I-125 sounds consistent with their distinct diffusive behavior, even though their reliability is questionable, since no measurements close to the threshold values are available. Given the apparent anion exclusion effect, the percolation threshold of iodide has to be at higher degrees of saturation compared to tritium. The saturation degree at which percolation threshold is reached (Sw-c ) 0.77) is finally very close to the lowest degree of saturation (Sw ) 0.81), agreeing with the very low value of iodide porosity, almost null (0.7%) obtained at this suction. In contrast, the value determined for tritium (Sw-c ) 0.63) is more surprising because this value would signify that, when HTO θdiff is less than 12%, the water phase would not be continuous through the argillite. In other words, this would mean that the largest pores play a significant role in diffusion, preventing from any diffusion when they are emptied. However, new investigations are necessary, because it is difficult to base a definitive conclusion on such an empirical model, especially with the assumption about the n value.
Acknowledgments This work received financial support from ANDRA and CEA. The authors are grateful to Thibault Martin for the petrophysical measurements.
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