Effects of water content on reactive transport of 85Sr in Chernobyl sand columns

Journal of Contaminant Hydrology 100 (2008) 47–57

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Journal of Contaminant Hydrology j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / j c o n h yd

Effects of water content on reactive transport of Chernobyl sand columns

85

Sr in

Stéphanie Szenknect a,⁎, Christophe Ardois b, Lionel Dewière b, Jean-Paul Gaudet c,⁎ a b c

Laboratoire des Technologies des Traceurs, CEA/DRT/LITEN, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France Laboratoire d'Etude des Transferts dans les Sols et le sous-sol, IRSN/DEI/SARG, BP n°17, 92262 Fontenay aux Roses Cedex, France Laboratoire d'étude des Transferts en Hydrologie et Environnement, CNRS/INPG/IRD/UJF-UMR 5564, BP n°53, 38041 Grenoble Cedex 9, France

a r t i c l e

i n f o

Article history: Received 20 December 2007 Received in revised form 5 May 2008 Accepted 9 May 2008 Available online 23 May 2008 Keywords: Unsaturated zone Strontium Transport model Sorption Physical non-equilibrium

a b s t r a c t It is known that under unsaturated conditions, the transport of solutes can deviate from ideal advective–dispersive behaviour even for macroscopically homogeneous porous materials. Causes may include physical non-equilibrium, sorption kinetics, non-linear sorption, and the irregular distribution of sorption sites. We have performed laboratory experiments designed to identify the processes responsible for the non-ideality of radioactive Sr transport observed under unsaturated flow conditions in an Aeolian sandy deposit from the Chernobyl exclusion zone. Miscible displacement experiments were carried out at various water contents and corresponding flow rates in a laboratory model system. Results of our experiments have shown that breakthrough curves of a conservative tracer exhibit a higher degree of asymmetry when the water content decreases than at saturated water content and same Darcy velocity. It is possible that velocity variations caused by heterogeneities at the macroscopic scale are responsible for this situation. Another explanation is that molecular diffusion drives the solute mass transfer between mobile and immobile water regions, but the surface of contact between these water regions is small. At very low concentrations, representative of a radioactive Sr contamination of the pore water, sorption and physical disequilibrium dominate the radioactive Sr transport under unsaturated flow conditions. A sorption reaction is described by a cation exchange mechanism calibrated under fully saturated conditions. The sorption capacity, as well as the exchange coefficients are not affected by desaturation. The number of accessible exchange sites was calculated on the basis that the solid remained in contact with water and that the fraction of solid phase in contact with mobile water is numerically equal to the proportion of mobile water to total water content. That means that for this type of sandy soil, the nature of mineral phases is the same in advective and non-advective domains. So sorption reaction parameters can be estimated from more easily conducted saturated experiments, but hydrodynamic behaviour must be characterized by conservative tracer experiments under unsaturated flow conditions. © 2008 Elsevier B.V. All rights reserved.

1. Introduction Under unsaturated flow conditions, migration of conservative species deviates from the classical advective–dispersive transport model even in macroscopically homogeneous porous ⁎ Corresponding authors. Fax: +33 4 38 78 51 34. E-mail addresses: [email protected] (S. Szenknect), [email protected] (J.-P. Gaudet). 0169-7722/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.jconhyd.2008.05.004

media (Haga et al., 1999; Padilla et al., 1999). Under saturated conditions, repacked columns generally do not show scale dependence for dispersivity (Khan and Jury, 1990). However, under unsaturated conditions, the dispersivity of macroscopically homogeneous columns increases with travel distance (Padilla et al., 1999; Bromly and Hinz, 2004). That indicates that the advection–dispersion equation does not provide an appropriate description of conservative solute transport. The main explanation is that the number of flow paths decreases,

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and that transport occurs in isolated channels, so a solute plume must travel a greater distance to attain complete lateral mixing and reach advective–dispersive behaviour. Padilla et al. (1999) propose that unsaturated transport undergoes a transition to advection–dispersion transport with distance. This distance could exceed the scale of typical laboratory experiments, even at low pore water velocities. The conclusion is that solute spreading under unsaturated conditions should be studied at different depths (Bromly and Hinz, 2004). Under unsaturated conditions, the dispersivity is also related to water content (Maraqa et al., 1997; Nützmann et al., 2002). Generally, a decrease in the water content leads to an increase of the dispersivity. The main explanation for this observation is that tortuosity and velocity variations increase, leading to greater dispersivity. Moreover, breakthrough curves (BTCs) measured at the outlet of unsaturated laboratory columns of homogeneous materials, often exhibit “anomalous” asymmetry, i.e. a sharp front and tailing. The advection–dispersion model (ADM) cannot describe such transport as the assumption of complete lateral mixing does not allow for a sharp front and long tailing. The Two-Region non-equilibrium Model (TRM) has been extensively used to describe non-ideal transport of solutes under unsaturated conditions (Coats and Smith, 1964; van Genuchten and Wierenga, 1976; Gaudet et al., 1977). The TRM describes in a simple mathematical form the asymmetry of the BTCs. This model assumes that the porous medium contains a mobile water phase in which advective–dispersive transport of solutes occurs, and an immobile water phase with which solutes can exchange. With its two additional parameters, the TRM often provides a better description of the solute BTC than the ADM. As the TRM is being applied with increasing frequency, the question of interpreting the physical meaning of theses parameters has been addressed (Griffioen et al., 1998; Comegna et al., 2001). Experimental studies of transport of strongly sorbing solutes under unsaturated flow conditions are not so common. Analysis in unsaturated porous media is further complicated by the fact that water content and pore water velocity are not independent variables, and by the existence of additional physical non-equilibrium. Experimental evidence that the retardation factor (or the mean travel distance) and the spreading of a reactive solute plume depend on the water saturation may have many causes (Fesch et al., 1998; Maraqa et al., 1999): physical non-equilibrium, sorption kinetics, non-linear sorption, and the irregular distribution of sorption sites. Identification of the processes responsible for the potential non-ideality of reactive solute transport under unsaturated flow conditions requires: (1) separation of the influence of pore water velocity and degree of water saturation, (2) quantification of the relative effect of physical non-equilibrium and chemical non-equilibrium by using a conservative tracer and a reactive tracer representative of the sorbing solute under the same flow conditions, (3) evaluation of the scale dependence by monitoring the plume at different depths under the same flow conditions. Here we are interested in radioactive strontium migration in the unsaturated zone of the Chernobyl Pilot Site (CPS). CPS is an experimental field facility for in situ confirmation and development of theoretical models for radionuclide migration in soils and aquifers. There are ramifications of the research conducted at the CPS for understanding the environmental

impact of the Chernobyl accident. In addition, these studies are of prime importance from the perspective of practical risk assessment for subsurface waste disposal sites and for remedial analyses. The CPS is a trench which contains contaminated surface soil and wood debris. Since 1987, reactor fuel particles in the trench have been dissolving and releasing 90Sr. For 15 years, strontium has been penetrating the unsaturated zone and the water table. Nowadays, 90Sr activity in the aquifer varies between 10 and 2000 Bq L− 1, and the plume can be seen to spread over a few tens of meters downstream of the trench. Radionuclide mass transfer from the trench through the unsaturated zone to the aquifer is controlled by the fuel particle activity available for dissolution process (Dewiere et al., 2004), fuel dissolution mechanisms (Kashparov et al., 2004), sorption parameters and structure of the surrounding undisturbed unsaturated soil layer and the water inflow rate from the surface. In a previous study (Szenknect et al., 2005), we have identified and quantified the main transport and retention mechanisms of strontium in the Aeolian sandy deposit representative of the CPS subsurface under saturated flow conditions. We have seen that transport of conservative species in macroscopically homogeneous saturated columns is governed by the classical advection–dispersion processes. Strontium sorption reaction is instantaneous, reversible and non-linear when aqueous concentration exceeds 10− 6 mol L− 1. This situation has been observed in the groundwater were stable strontium concentration can reach 3.7 · 10− 5 mol L− 1 explaining the mobility of 90Sr in the aquifer. In the unsaturated zone surrounding the trench, strontium concentrations are lower than 10− 6 mol L− 1, so sorption is instantaneous and linear. Regarding the understanding and modelling of the main transport mechanisms of sorbing solute under unsaturated flow conditions, the main question is: does physical non-equilibrium occur and if it is the case, what is its influence on radioactive strontium transport in the unsaturated zone? 2. Materials and methods 2.1. Synthetic groundwater and solutes All column experiments were conducted using synthetic groundwater, formulated to approximate the composition observed in CPS aquifer samples. The chemical composition (major ions and pH) of synthetic groundwater is presented in Table 1. The concentrations of major cations chosen for synthetic water were in the range of field concentrations except for stable Sr (Szenknect et al., 2005). Synthetic groundwater was prepared by adding cations as sulfate salts to distilled, deionized water, except for K, which was added as chloride, and Ca as carbonate. The pH was adjusted to 6.4 ±0.2 by adding 0.1 N H2SO4. The theoretical concentrations were then verified by chemical analysis with a capillary ion analyzer (Waters). Tritiated water was used as the conservative tracer (Wierenga and van Genuchten, 1989). The initial activity of tritiated water was 74 MBq cm− 3. For radiometric measurements spiked strontium solutions were also prepared using 85 Sr as a radioactive tracer. This isotope was chosen as a tracer instead of 90Sr because its good gamma-emission of 514 keV and short radioactive half-life of 64.85 days lead to very low

S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

49

Table 1 Composition of synthetic groundwater used as feed solution in column experiments Component

Base chemistry

Ca2+ K+ Na+ Mg2+ Sr2+ Cl− SO2− 4 Ionic strength pH

7.7 · 10− 5 ± 1 · 10− 5 4.9 · 10− 5 ± 1 · 10− 5 5.7 · 10− 5 ± 1 · 10− 5 2.1 · 10− 5 ± 0.5 · 10− 5 0 4.0 · 10− 5 ± 1 · 10− 5 1.1 · 10− 4 ± 1 · 10− 5 5.72 · 10− 4 6.4 ± 0.2

mol L− 1

concentrations of 4.5 · 10− 10 to 10− 8 mol L− 1 and allowed to monitor activity profiles along the column. 2.2. Column experiments The soil used was an Aeolian sandy deposit representative of the CPS subsurface (Fig. 1). It was an average sample from the Pripyat Zaton exposure, located 2 km north-east of the CPS. Sand from Pripyat Zaton was not contaminated with 90Sr. The soil sample was dry sieved and the b1 mm fraction used for characterization and laboratory experiments. The N1 mm fraction represented less than 1% of the total sample mass. The soil sample was characterized for organic carbon content by wet combustion technique and for particle size distribution using a laser granulometer (Beckam-Coulter LS230, NF ISO 13320-1). The cation exchange capacity (CEC) of the soil was determined using the sodium acetate saturation method (Metson, 1956). Other characteristics of this soil were reported by Szenknect et al. (2005). For the column experiments, a soil sample was packed homogeneously in Plexiglas columns (5 cm ID) of lengths from 28 to 40 cm with polypropylene end pieces. The sand bed length was measured, the amount of sand weighed, and the geometric porosity calculated, assuming a solid-particle density equal to that of quartz, 2.65 g cm− 3 (Bolz and Tuve, 1976, p 192). Characteristics of the packed soil columns and experimental conditions are presented in Table 2. End pieces were equipped with 0.45 µm pore size hydrofoil Teflon membranes (HVLP, Millipore) that function like a capillary barrier at the outflow end of each column. Pulse-type miscible displacement experiments were conducted under both saturated and unsaturated conditions with the same Darcy velocity. The experimental setup is shown in Fig. 2. All column experiments were conducted at 22 ± 2 °C. The solutions were fed to a dual-piston pump (Pharmacia P-500) at a constant-flow rate. The pump was connected to the top of the column, which was open to the atmosphere for unsaturated experiments, maintaining a uniform and fairly constant infiltration rate over the whole cross-section of the column. A Teflon sample loop (1 cm3, Rheodyne) linked to a 2 × 3-way injection valve was coupled up to allow conservative and reactive tracer pulse injections. The column outlet was connected to a pH flow cell connected to a pH-meter (Amersham Pharmacia Biotech). In addition, a beta-gamma flow scintillation analyzer (Packard 500TR Series) was connected to the column outlet to obtain an on-line measurement

Fig. 1. Scanning electron microscope image of Pripyat Zaton sand particles.

of the beta or gamma activity outflow. Teflon 1/16″ or 1/8″ capillaries were used to connect the elements. To establish steady-state flow conditions with uniform water content, suction was applied to the membrane at the bottom of the column with a second dual-piston pump (Pharmacia P-500). A gamma attenuation system was used to determine the local porosity and the water content of the sand (see İshakoğlu and Baytas, (2002) for a detailed explanation of the method). It consists of a NaI(Tl) scintillation detector encased in a lead collimator and a source box with a closing device containing a 1.67 GBq 241Am (59.54 keV) gamma source (Fig. 2). The detector absorbs a narrow beam of gamma rays after passing through the column. A multichannel analyser was used to count the signal magnitude of the transmitted gamma rays. The signal magnitude is a function of the water content in the column. The radiation source and the detector for gamma attenuation measurements could be translated simultaneously along the column vertical axis. The system was designed to measure water content profiles. The column was packed dry and scanned by gamma attenuation method to determine the porosity profile. All the

Table 2 Characteristics of the soil packed columns and corresponding experimental flow conditions Column Experiment L cm 2 11

14

15

8

ρ

ε

bθN

v = q/bθN

De

g cm− 3

−

−

cm min− 1

cm2 min− 1

0.24 ± 0.02 0.13 ± 0.01

1.0 · 10− 3 9.4 · 10− 4

0.17 ± 0.02

6.7 · 10− 4

0.05 ± 0.01

9.7 · 10− 4

0.09 ± 0.01

5.7 · 10− 4

2 11_1

19.7 1.75 40.0 1.80

11_2

40.0 1.80

14_1

28.1

1.80

14_2

28.1

1.80

15_1

28.0 1.81

15_2

28.0 1.81

8

30.1

1.84

0.34 0.34 0.32 0.30 ± 0.02 0.32 0.23 ± 0.02 0.32 0.31 ± 0.02 0.32 0.19 ± 0.02 0.32 0.29 ± 0.02 0.32 0.20 ± 0.02 0.31 0.16 ± 0.02

0.01 ± 0.004 9.1 · 10− 4 0.02 ± 0.005 6.5 · 10− 4 0.05 ± 0.01

5.0 · 10− 4

Water content profiles were measured with the gamma attenuation device. bθN corresponds to the water content averaged over the entire length of the column. Effective diffusion coefficient of tritiated water was calculated using Eqs. (3) and (4).

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S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

Fig. 2. Experimental setup for miscible displacement experiments under unsaturated flow conditions.

soil columns were slowly saturated (at a flow rate of 5 cm3 h− 1) from bottom to top. Then 2 to 10 L synthetic groundwater passed through the column. The aim of this first stage was to equilibrate the porous medium with the Sr-free solution. The pulse of conservative tracer-spiked solution composed of identical major ions composition was then injected from the top to the bottom of the column by switching the injection valve. The pulse was then displaced by the tracer-free synthetic groundwater. Then, the infiltration flow was stopped and the suction pump connected to the bottom of the column and switched on. When the soil column was as dry as possible (preventing air entry through the membrane), the suction pump was stopped and synthetic groundwater was applied to the top of the column using the precision constant-flow pump. During the infiltration step, water content profiles were recorded. As soon as a uniform water content profile was obtained, the suction pump was switched on, maintaining steady flow conditions (both pumps delivering the same flow rate). Under unsaturated steady-state flow conditions, pore water velocity and water content are not independent variables, but are linked through the Darcy–Buckingham equation: q ¼ −K ðθÞ 

∂H v ¼ ∂z θ

ð1Þ

where q [cm min− 1] is the Darcy's velocity, θ [cm3 cm− 3] is the volumetric water content, K(θ) [cm min− 1] is the hydraulic conductivity of the soil, H [cm] is the hydraulic head and v [cm min− 1] is the pore water velocity.

Inflow and outflow rates were constantly measured gravimetrically with two scales (Mettler Toledo PG-S) connected to a data logger. The rates were compared and small corrections were made during the experiments to insure steady flow conditions in the unsaturated columns. Then the pulse of conservative tracer-spiked solution composed of identical major ions composition was injected at the top of the unsaturated column to obtain the BTC. BTCs were determined for the conservative tracer prior to the strontium experiments. For the reactive tracer experiments, 85Sr was added to the synthetic groundwater to prepare the pulse solution. Then a volume, Vinj [cm3], of reactive tracer-spiked solution was injected in the unsaturated column. The pulse was then displaced by the tracer-free solution and 85Sr activity profiles were monitored along the column with the NaI(Tl) collimated detector. 3. Data analysis and modelling BTCs of the conservative tracer were analyzed with the computer code CXTFIT version 2.1 (Parker and van Genuchten, 1984; Toride et al., 1999). The CXTFIT model assumes uniform velocity along the column. However, for some of our experiments the water content was non-uniform, and the velocity slightly varied along the column. We assumed constant velocity over the length of the column. The pore water velocity fitted with CXTFIT was then compared to the experimental velocity calculated by dividing the flow rate by the cross section of the column and the spatial average water content measured by gamma attenuation (Table 2).

S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

Furthermore, De Smedt and Wierenga (1978); Porro et al. (1993); and Padilla et al. (1999) found that despite nonuniform water content distributions, BTCs of solutes moving through unsaturated porous media under steady water flux conditions can be predicted using an average water content and an average dispersion coefficient. To determine the dispersive behaviour of the porous medium under both saturated and unsaturated conditions, we have used the ADM Eq. (2), and the TRM Eqs. (5) and (6), for onedimensional transport of solutes. The dimensionless equilibrium model for a linear sorption reaction is given as: R

AC 1 A2 C ∂ C ¼ − AT Pe AZ 2 ∂ Z

ð2Þ

where,

ð3Þ

where α [cm] is a characteristic property of the homogeneous porous medium referred as dispersivity. De [cm2 min− 1] is the effective diffusion coefficient through the porous medium, τ [−] is a tortuosity factor and Dmol [cm2 min− 1] is the molecular diffusion coefficient of the solute in free solution (for tritium, Dmol = 1.18 · 10− 3 cm2 min− 1 in water at 20 °C, Mills and Harris, 1976). The tortuosity factor is thought to account for the shape and length of the flow paths and depends on water content but not on velocity (Burdine, 1953; Millington and Quirk, 1961). Padilla et al. (1999) used the following expression to estimate τ for a sandy soil: τ ¼ τs

θ−θr θs −θr

Rβ

ACm 1 A2 Cm ∂ Cm ¼ −ωðCm −Cim Þ − Pem AZ 2 AT ∂Z ACim ¼ ωðCm −Cim Þ AT

ð5Þ

ð6Þ

where,

c [mol cm− 3] is the solute concentration, c0 [mol cm− 3] is the solute concentration in the influent solution, z [cm] is distance, L [cm] is the column length, t [min] is time, T is the number of pore volumes, D [cm 2 min − 1 ] is the hydrodynamic dispersion coefficient, Pe [−] is the Peclet number, ρ [g cm− 3] is the soil bulk density, Kd [cm3 g− 1] is the sorption distribution coefficient and R is the retardation factor. For conservative tracer like tritiated water we assume R = 1. The hydrodynamic dispersion coefficient has commonly been expressed as (Bear, 1969): D ¼ αv þ De with De ¼ τDmol

from solute transport experiments under unsaturated flow conditions (Gaudet et al., 1977; De Smedt et al., 1986; Maraqa et al., 1997; Padilla et al., 1999), or in saturated aggregated porous media (Nkeddi-Kizza et al., 1983; Brusseau, 1994). The TRM, also called mobile–immobile model (MIM), assumes that the porous medium contains a mobile water phase in which advective–dispersive transport of solutes occurs, and an immobile water phase with which solutes can exchange (Coats and Smith, 1964; van Genuchten and Wierenga, 1976; Gaudet et al., 1977). The dimensionless equations of the TRM for a linear sorbing solute are given as:

Rð1−βÞ

c z vt vL ρKd C ¼ ; Z ¼ ; T ¼ ; Pe ¼ ; R ¼ 1 þ c0 L L D θ

51

ð4Þ

where τs [−] is the tortuosity factor of the saturated porous medium, θs [cm3 cm− 3] is the volumetric saturated water content and θr [cm3 cm− 3] is the volumetric residual water content of the porous medium. We chose a value of τs = 0.85 representative for sandy soil (Ma and Selim, 1994). The values of θs = 0.32 and θr = 0.02 were obtained from soil–water retention curve of the Aeolian sand. Under unsaturated conditions, packing heterogeneities at a smaller scale can give rise to non-Darcian flow patterns which are distinguished by “anomalous” asymmetry, i.e. sharp front and tailing, in BTCs. In these cases, the ADM fails to describe the BTCs. The TRM describes in a simple mathematical form the asymmetry observed in effluent BTCs

cm c q vm L θm þ f ρKd ; ; C ¼ im ; vm ¼ ; Pem ¼ ;β¼ θm Dm θ þ ρKd c0 im c0 kM L ω¼ q

Cm ¼

The subscripts m and im indicate the mobile and the immobile region respectively, cm [mol cm− 3] is the solute concentration in the mobile water phase, cim [mol cm− 3] is the solute concentration in the immobile water phase, vm [cm min− 1] is the average pore water velocity in the mobile water phase, kM [min− 1] is the mass transfer parameter between the mobile and immobile region and f [−] is the fraction of adsorption sites in the mobile region. A zero initial solute concentration was assumed over the length of the column. The specific solution of the boundary value problem for an input concentration given by the Dirac delta function was used. The non-linear least-squares inversion method implemented in CXTFIT involves an analytical solution of the ADM or the TRM. Since analytical solutions are not available for the non-linearly sorbing solutes, the 85Sr transport experiments were also analyzed with the computer code PHREEQC (Version 2). A full description of its mathematical background can be found in the program manual (Parkhurst and Appelo, 1999). PHREEQC is able to model a one-dimensional, advection–dispersion transport process with diffusive exchange between mobile and immobile water. This process can be combined with equilibrium and kinetic chemical reactions. Conservation of mass for a transported chemical yields the following advection–reaction–dispersion equation:   ACm ASm 1 A2 Cm ∂ Cm u þ þ ωðCm þ Cim Þ ¼ − Pem AZ 2 AT AT ∂Z

ð1− φÞ

  ACim ASim þ ¼ ωðCm −Cim Þ AT AT

where, Sm ¼

sm s θm ; S ¼ im ; u ¼ c0 im c0 θ

ð7Þ

ð8Þ

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S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

Fig. 3. Comparison of tritiated water BTCs measured at the outlet of each column respectively under saturated (□) and unsaturated (Δ) flow conditions. Fine lines are ADM simulations and thick lines are TRM simulations, the fitted parameters are listed in Table 3.

sm and sim [mol cm− 3] are the concentrations of adsorbed species in the solid phase respectively in contact with the mobile and the immobile water regions (s is expressed in the same units as c in AS PHREEQC). AT is the change in concentration in the solid phase due to reactions. Eqs. (7) and (8) can be reduced to Eqs. 5 and 6 in the case of a linear sorbing solute. In the previous study (Szenknect et al., 2005), we have shown that non-linear sorption and competition with stable Sr were the main processes affecting 85 Sr transport. Concentration of stable Sr in deionized water equilibrated with the sand was 10− 6 mol L− 1, and the average concentration measured in the CPS aquifer was 8.4·10− 6 mol L− 1. Due to this high level of stable Sr in the pore water (above the linearity limit of the isotherm), we needed PHREEQC to simulate the initial spatial distribution of stable Sr sorbed onto the sand resulting from the conditioning stage with Sr-free synthetic groundwater and before radioactive 85Sr injection. The simplified Kd approach (Eqs. 5 and 6) could be used to simulate radioactive Sr transport in the Pripyat sand only if the stable Sr resident concentration was uniform, constant and lower than 10− 6 mol L− 1 along the soil profile, as might be the case on site but not in the column leached with Sr-free synthetic groundwater.

Cation exchange is proposed as the mechanism generally controlling Sr adsorption. It was shown earlier that the main chemical reactions, taken into account for reactive transport of radioactive Sr (mainly present in the form of an uncomplexed Sr2+ ion) in the saturated Aeolian sand, were ion exchange equilibria with major cations in solution and isotopic exchange with stable Sr. For most of the chemical processes taken into account in the calculations, the thermodynamic constants given in the PHREEQC default database were used. The selectivity coefficients with respect to Na+ of the major cations, K+, Mg2+, Ca2+, provided by PHREEQC default database were derived from a compilation made by Bruggenwert and Kamphorst, (1982). The selectivity coefficient of Sr2+ with respect to Na+ and the sorption capacity of the Aeolian sand, X− [mol kg− 1], were determined on the basis of the results we obtained in our previous study. The fitted values of these parameters were: X− = 10− 4 mol kg− 1 and log KSr/Na = 2.6. It was assumed that 85Sr had the same chemical characteristics as stable Sr, meaning that it was involved in the same reactions defined with the same thermodynamic constants as stable Sr. “Competition” between 85Sr2+and Sr2+was K Sr=Sr 85 allowed through: 85 Sr2þ þ Sr−X2 85! Sr−X2 þ Sr 2þ with K85Sr/Sr =1. The same reactions and the same constants were used to describe 85Sr transport under unsaturated flow conditions. The only parameter that could change with water content is the amount of exchange sites that remained accessible for 85Sr2+adsorption. The amount of exchange sites, [X−], is expressed in PHREEQC as a concentration of sites per unit volume of water. We made the assumption that the entire solid remained in contact with water under unsaturated conditions and that the fraction of solid phase in contact with mobile water is numerically equal to φ. The concentration of sites accessible for exchange reactions in the mobile and immobile water regions under those conditions is a function of the water content equal to: ½X −  ¼ 10−4 

ρ θ

ð9Þ

This assumption, based on the nature of the Aeolian sand from the Pripyat Zaton, has already been made (Nkeddi-Kizza et al., 1983; Selim and Ma, 1995). The sand packed in the column is unstructured and disaggregated. In this case there is no reason to suppose that the sorption capacity of the solid phases in the immobile water region is higher than the sorption capacity of the solid phases in the mobile water region. The opposite statement was made by Fesch et al. (1998) for a synthetic porous medium containing reactive micro-aggregates of clay minerals sorbents glued together. The cumulative grain size distribution of the Aeolian sand is monomodal (Szenknect et al., 2005), a scanning electron microscope was used to image sand particles and did not reveal the presence of clay micro-aggregates (Fig. 1). The transport parameters fitted with CXTFIT to the conservative tracer BTCs under unsaturated flow conditions were used in the PHREEQC input file to simulate the transport of 85Sr in the same hydrodynamic conditions. Finally, no parameter was fitted with PHREEQC to simulate the 85Sr resident concentration profiles, selectivity coefficients and exchange capacity were determined under saturated condition. We carried out direct simulations in order to assess our

S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57 Table 3 Parameters (bold characters) of the ADM and TRM optimized with CXTFIT associated with 95% confidence intervals

assumption on the concentration of sites that remained accessible to the exchange reactions as the water content decreased. 4. Results 4.1. Conservative tracer Fig. 3 represents the conservative tracer BTCs obtained under saturated and unsaturated flow conditions. Saturated and unsaturated BTCs were analyzed first using the ADM that assumes that the system is under physical equilibrium. Then the unsaturated BTCs were analyzed using the TRM to determine parameter values for the immobile water fraction and mass transfer coefficient. For a conservative tracer, Kd = 0, so R = 1 in Eqs. (5) and (6) and in this case, β is numerically equal to the fraction of mobile water content to the total water content defined as φ. The obtained transport parameters, which refer to all the experiments, are listed in Table 3

53

together with 95% confidence intervals as well as the coefficient of determination R2 for the regression of observed versus fitted values. Pore water velocities were fitted to give more flexibility in the estimation procedure, but the fitted values of pore water velocity were close to the experimental values listed in Table 2 (within experimental errors in water content measurements and spatial averaging). For saturated experiments, the ADM adequately simulates the BTCs. The BTCs are symmetrical with no noticeable tailing, even at high average pore velocity. As there is no evidence from the shape of the BTCs of physical non-equilibrium under saturated flow conditions, and because model selection should be governed by parameter parsimony, we do not use the TRM to describe the transport mechanism of a conservative species in the saturated Aeolian sand. We first try to fit the ADM parameters on the unsaturated BTCs, because even for asymmetrical BTCs the use of the TRM is not always required (Comegna et al., 2001). The values of D-De obtained using the ADM for the saturated and unsaturated experiments are plotted versus the average pore water velocity, v, in Fig. 4. For any saturation level, the mechanical dispersion at a given pore water velocity is higher than its value under saturated condition. When a linear regression of the form (D-De) = αv (Eq. (3)) is used to fit the data under saturated and unsaturated conditions, we found that the ratio αunsat/αsat ≈ 4. Our results suggest that, for a macroscopically homogeneous porous medium, the dispersivity depends on the water content, but the relation found is soil-specific. Similar results were obtained for sandy soils by De Smedt et al. (1986); Maraqa et al. (1997) or Padilla et al. (1999). The higher mechanical dispersion at a given average water velocity under unsaturated conditions was explained by a wider distribution in the microscopic pore water velocities when the soil is desaturated (Yale and Gardner, 1978; Nützmann et al., 2002). It is shown from Fig. 3, that the asymmetry of the BTCs under unsaturated conditions is better described by the TRM, as also confirmed by the higher R2 obtained. Parameter values for the dispersion coefficient Dm, mobile water fraction φ, and mass transfer coefficient kM, are listed in Table 3. Use of the TRM for the unsaturated experiments shows values of φ that range between 0.77–0.89 for spatial average water content between 0.16 and 0.22. In a very well documented review of data from the literature, Griffioen et al. (1998), have already shown that the mobile water fraction φ, was constant or linearly increasing with θ in partially saturated soils and that values of φ are consistently greater than 0.6 for 0.1 b θ b 0.5. Griffioen et al. (1998) have also shown that for a number of published data, the mass transfer coefficient was proportional to the pore water velocity. So, the mass transfer rate is governed by the mobile phase velocity rather than by molecular diffusion. For partially

Table 4 Comparison of timescales for the non-equilibrium physical processes in the different experiments performed under unsaturated conditions Experiment tM = θim/kM ta = L/vm ta / tM tp = d/vm td = d2/Dmol tl = Dm/v2m

Fig. 4. Values of mechanical dispersion, D-De, obtained using the ADM for the saturated (Δ) and the unsaturated (O) experiments are plotted versus the mean pore water velocity, v. A linear regression of the form (D-De) = αv has been fitted to the data under saturated and unsaturated conditions.

11_2 14_2 15_2 8

min

min

−

min

min

min

11 32 74 13

301 379 1699 1140

27 12 23 88

0.17 0.31 1.40 0.87

0.45 0.45 0.45 0.45

1.6 · 10− 4 6.3 · 10− 1 3.1 1.4 · 10− 4

54

S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

saturated porous media (sand or glass beads), as well as for saturated aggregated soils, advection and velocity variations have a significant effect on the mass transfer. To identify the predominant mechanism in the case of unsaturated Pripyat sand columns, we have calculated the timescales for nonequilibrium physical processes. The macroscopic timescale for advection in the column of length L is: ta ¼ vLm , while at the particle scale the advection timescale is given by: tp ¼ vdm , with d, characteristic particle diameter. The longitudinal interaction timescale is obtained by: tl ¼ Dv2m . The timescale for mass transfer m process controlled by diffusion (film diffusion or intra-particle 2 diffusion) is: td ¼ Ddmol , with d, characteristic length of diffusion path (film thickness or particle/aggregate diameter). Timescales for the different experiments performed under unsaturated conditions are listed in Table 4 and compared with the fitted . As Pripyat sand is unstrucmass transfer timescale: tM ¼ θkim M tured and disaggregated, we have chosen d =d50, and from the granulometric curve, d50 = 230 µm. As the timescales for mechanisms at the microscopic scale are several orders of magnitude shorter than mass transfer timescale, we can consider that they are not responsible for the physical nonequilibrium observed. The predominant process might be mobile velocity variations at macroscopic scale. One explanation could be the slight variations of water content and velocity over the length of the column. Haggerty et al. (2004) found that the mass transfer timescale is better correlated with the residence time of water in the column, i.e. the experimental timescale, than with the velocity. Experiments at larger scale should be performed to conclude for the CPS sand. Another explanation proposed by Gaudet (1978) for the long mass transfer timescales measured in unsaturated silty sand columns (d50 =300 µm) compared to microscopic timescales, is that molecular diffusion drives the solute mass transfer between mobile and immobile water region, but the surface of contact between these water regions is small and the characteristic length of transport by diffusion is several orders of magnitude higher that the mean particle diameter. It might be the characteristic length of “spots” of connected pores full with immobile water isolated from the advective water region by air bubbles, rather than film thickness or micro-aggregates diameter. 4.2. Strontium transport under unsaturated flow conditions Before the pulse injection of 85Sr, the unsaturated columns were washed with the Sr-free synthetic groundwater. The duration of the conditioning step, expressed as the number of pore volumes that have passed through the column, is indicated in Table 5, as well as the characteristics of the 85Sr miscible displacement experiments.

85 Sr activity profiles were monitored along the columns with the NaI(Tl) collimated detector. Fig. 5 represents the evolution as a function of time of the 85Sr profiles in the unsaturated flow experiments. It is seen from Fig. 5 that the shape of the total resident concentration profiles is symmetrical for experiment 11_2 (a), but asymmetrical, for experiment 14_2 (b) and 15_2 (c). It is important to note that the water content profile was slightly non-uniform along the column during experiment 15_2, but the averaged value of θ reached 0.14 in the region explored by the 85Sr plume. By means of the simulations with PHREEQC, we made sure that the sand was in equilibrium with the Sr-free synthetic groundwater in the region explored by the 85Sr plume after the conditioning stage. In the range of 85Sr aqueous concentration the sorption isotherm is linear (Szenknect et al., 2005). In our previous study, we have also shown that the characteristic times of sorption and desorption mechanisms were about a few minutes. So we can neither attribute this phenomenon for non-linear sorption, nor for rate-limited sorption/desorption, but for physical disequilibrium. From the shape of these profiles, we can say that, in our experimental conditions, physical non-equilibrium strongly influences the transport of 85Sr as soon as the water content is lower than 0.22 (experiment 11_2). For a quantitative analysis of the impact of physical disequilibrium on the 85Sr transport, we focused on the spatial first moments of the plume, obtained by integration of the total (sorbed and aqueous) resident concentration profiles; ctot (z; t) [mol cm− 3]. The normalized spatial first moment of the plume, bzN [cm], represents the travel distance from the center of the initial plume. It is defined as:

Φ L ∫ zctot ðz; t Þdz; with M0 M0 0 L ¼ Φ ∫0 ctot ðz; t Þdz and assuming ctot ðz; 0Þ ¼ θc0 δðzÞ

hzi ¼

Where Ф [cm2] is the cross-section area of the column, and M0 [mol] is compared to the amount of strontium injected in the column during each experiment (c0. Vinj) to check the mass balance. To determine bzN, we calculated first the zeroorder spatial moment (M0) and we only selected the acquisition times for which the 85Sr mass balance was complete. The “travel distance ratio” is defined as: Travel distance ratio ¼

hzi v Rt

ð11Þ

The predicted retardation factor, R, of the 85Sr plume, assuming the local equilibrium assumption (LEA) has been

Table 5 Characteristics of the 85Sr miscible displacement experiments: mean water content and mean pore water velocity in the region explored by the duration of the conditioning step before 85Sr injection in number of pore volumes, strontium concentration in the pulse and volume of the pulse Experiment

θ

v = q/θ cm min

2 11_2 14_2 15_2

0.34 0.22 0.19 0.14

0.24 0.18 0.09 0.03

Conditioning stage −1

− 20 57 20 14

ð10Þ

[85Sr]0 −1

mol L

−8

1.4 · 10 4.3 · 10− 9 1.5 · 10− 9 4.5 · 10− 10

Vinj cm 0.5 1 1 1

3

Kd L kg 43 43 43 43

−1

85

Sr plume,

R (LEA)

[X−]

−

mol L− 1

223 353 408 557

5.2 · 10− 4 8.2 · 10− 4 9.5 · 10− 4 1.2 · 10− 3

The predicted retardation factors calculated with Eq. (11) are compared. The concentration of exchange sites has been calculated in each case with Eq. (9).

S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

55

Fig. 5. Evolution as a function of time of the 85Sr plume monitored with the gamma ray collimated detector in the (a) 11_2, (b) 14_2, and (c) 15_2 experiment. For each experiment two profiles (Δ and ■) were simulated with the TRM (thick lines). For experiment 11_2, the two profiles were also simulated with the ADM (dashed lines).

defined in Eq. (2) and the Kd value determined in the saturated column experiment, was 43 L kg− 1 (Szenknect et al., 2005). The travel distance ratio allows comparing the distance travelled by the center of mass of the plume, with the distance travelled by the plume if the LEA was valid. Fig. 6(a) shows the evolution as a function of time of the travel distance ratio for each column experiment. It is seen from Fig. 6(a) that the fully saturated case (experiment 2) for which ADM was valid corresponds to a travel distance ratio equal to 1. For unsaturated experiments 14_2 and 15_2, the travel distance ratio is always larger than 1. This means that the plume is moving faster than predicted by the local

equilibrium assumption. It is obvious from Fig. 6(b) that the travel distance ratio is directly correlated to the water content in the region explored by the plume. So the diffusion step in the non-advective water region drives the transport behaviour of 85Sr under unsaturated conditions. As it has already been shown by numerical simulations (Srivastava and Brusseau, 1996), in the case where transport is constrained by diffusive transfer of solute between advective and nonadvective domains, the displacement of the center of mass of the plume is non-uniform during the early stages of transport. This behaviour results in a temporally variable retardation factor (leading to a temporally variable travel distance ratio),

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S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

Fig. 6. (a) Evolution as a function of time of the travel distance ratio for each column experiment performed under unsaturated flow conditions. (b) Relation between asymptotic travel distance ratio and averaged water content in the region explored by the 85Sr plume (top of the column).

that asymptotically reaches a limit value. This effect has been observed during our experiments under unsaturated flow conditions. The travel distance ratio asymptotically reaches 1 for experiment 11_2 (saturation level N 60%) after 8 days of transport, 1.4 for experiment 14_2 after 14 days and is still decreasing with a value of 2.5 for experiment 15_2 (saturation level ≈ 50%) after 18 days. It means that the local equilibrium assumption under unsaturated flow conditions leads to an underestimation of the distance travelled by the center of mass of the radioactive strontium plume, especially for short term simulations and low water content. This supports also the assumption made by Padilla et al. (1999) that unsaturated transport undergoes a transition to advective–dispersive transport with distance. The transition distance was reached during experiment 11_2 after 8 days of transport, but not during experiment 14_2 and 15_2.

Table 6 Comparison of the two first spatial moments of experimental and simulated profiles from experiments under unsaturated flow conditions Experiment

11_2 Experimental Simulated with PHREEQC Predicted by LEAbzN = vt/R Experimental Simulated with PHREEQC Predicted by LEAbzN = vt/R 14_2 Experimental Simulated with PHREEQC Predicted by LEAbzN = vt/R Experimental Simulated with PHREEQC Predicted by LEAbzN = vt/R 15_2 Experimental Simulated with PHREEQC Predicted by LEA bzN = vt/R Experimental Simulated with PHREEQC Predicted by LEAbzN = vt/R

T

M0

bzN

Days

mol

cm

8.8 8.8

4.1 · 10− 12 4.3 · 10− 12

16.3 16.3

4.1 · 10− 12 4.3 · 10− 12

5.9 5.85 (−0.5%) 6.5 (+18%) 11.6 11.3 (−3%) 12.0 ( + 3%)

7.0 7.0

1.5 · 10− 12 1.5 · 10− 12

16.0 16.0

1.4 · 10− 12 1.5 · 10− 12

13.3 13.3

4.4 · 10− 13 4.5 · 10− 13

16.3 16.3

4.4 · 10− 13 4.5 · 10− 13

3.5 3.2 (−7%) 2.2 (−36%) 7.1 7.9 (+11%) 5.1 (− 28%)

2.9 2.7 (+3%) 1.0 (−65%) 3.3 4.5 (+6%) 1.3 (−60%)

The concentrations of exchange sites used for the simulations are indicated in Table 5, others transport parameters are listed in Table 3 (TRM).

Taking into account physical non-equilibrium under unsaturated conditions should lead to a better prediction of the radioactive Sr transport behaviour. For each unsaturated column experiment after the conditioning stage, two 85Sr resident concentration profiles were also simulated with PHREEQC (n.b. at this step, the use of Eqs. (5) and (6) would be also possible). The corresponding exchange sites concentrations were calculated before the simulations and are indicated in Table 5. Fig. 5 represents two 85 Sr total resident concentration profiles simulated with PHREEQC (thick lines). By comparing the first-order spatial moment of experimental and simulated profiles (Table 6), it is seen that the mean travel distance is much better predicted by the TRM than by the ADM based on the local equilibrium assumption, especially for experiments 14_2 and 15_2. The relative error on the first-order spatial moment is less than 11% for the 6 simulated profiles. With the LEA the relative error on the mean travel distance reached -65% for experiment 15_2. The concentrations of sorption sites calculated before the simulations with Eq. (9) (on the basis that all the solid remains in contact with water and that the fraction of solid phase in contact with mobile water is numerically equal to φ) leads to a good prediction of the normalized first-order spatial moment of the 85 Sr plume whatever the water content. It is obvious from Fig. 5 that for experiment 11_2, the LEA is valid and fits the experimental profiles (dashed lines). We have seen earlier that for this experiment, the saturation level was larger than 60%, and the asymptotic travel distance ratio reached 1. 5. Summary and conclusions Our experiments show that under unsaturated flow conditions and at low concentrations of strontium, representative of a radioactive contamination of the pore water, sorption and physical disequilibrium dominate the 85Sr transport. The center of mass of the 85Sr plume was shown to move faster than predicted by the simple advection–dispersion model with retardation factor corrected for the effect of the water content decrease. A more accurate prediction of the 85Sr plume position has been achieved by taking into account the mass transfer step between advective and non-advective water regions and the exchange reactions between 85Sr2+, stable Sr2+and major cations in the system. The exchange coefficients estimated from experiments conducted under saturated flow conditions were not affected by desaturation. The concentration of sites that remained accessible for exchange reactions was calculated as a

S. Szenknect et al. / Journal of Contaminant Hydrology 100 (2008) 47–57

simple function of the water content and is equal in the mobile and immobile region. That means that for this type of disaggregated and unstructured sandy soil, the nature of the mineral phases is the same in advective and non-advective domains. Sorption reaction parameters can be estimated from more easily conducted saturated experiments. As physical nonequilibrium appeared only under unsaturated flow conditions below 60% of saturation, the transport model could not be calibrated under saturated conditions. From the perspective of practical risk assessment of subsurface waste disposal sites, or the analysis of remedial options for such sites, these results show the need for unsaturated-zone characterization. We have shown that even for a macroscopically homogeneous, disaggregated and unstructured soil like CPS sand and steady flow conditions, physical disequilibrium occurred below 60% of saturation. So the use of an advective–dispersive transport model based on the LEA can lead to underestimation of the mean distance travelled by the reactive solute plume, especially for short term simulations and low water content. Accurate predictive modelling of the behaviour of linearly interactive solutes without rate-limited sorption requires at least experimental investigations of conservative solute transport under unsaturated conditions, and for several travel distances. Acknowledgements We express our great gratitude to N. van Meir, V. Barthes, P. Berne and D. Bugaï for technical support and helpful discussions. Financial support was supplied jointly by Radiation Protection and Nuclear Safety Institute (IRSN-Chernobyl Pilote Site project) and by Electricité de France (EDF-CNPE project). References Bear, J., 1969. Hydrodynamic dispersion. In: DeWiest, R.J.M. (Ed.), Flow Through Porous Media. Academic Press, New York, pp. 109–200. Chap. 4. Bolz, R.E., Tuve, G.L., 1976. CRC Handbook of Tables for Applied Engineering Science, 2nd Edition. CRC Press, Inc., Boca Raton (USA). 1166 pp. Bromly, M., Hinz, C., 2004. Non-Fickian transport in homogeneous unsaturated repacked sand. Water Resour. Res. 40, W07402. doi:10.1029/2003WR002579. Bruggenwert, M.G.M., Kamphorst, A., 1982. Survey of experimental information on cation exchange in soil systems. In: Bolt, G.H. (Ed.), Soil Chemistry, B. Physico-chemical Models. Elsevier, Amsterdam, pp. 141–203. Brusseau, M.L., 1994. Transport of reactive contaminants in heterogeneous porous media. Rev. Geophys. 32, 285–313. Burdine, N.T., 1953. Relative permeability calculations from pore size distribution data. Trans. AIME 198, 71–77. Coats, K.H., Smith, B.D., 1964. Dead-end pore volume and dispersion in porous media. Soc. Pet. Eng. J. 4, 73–84. Comegna, V., Coppola, A., Sommella, A., 2001. Effectiveness of equilibrium and physical non-equilibrium approaches for interpreting solute transport through undisturbed soil columns. J. Contam. Hydrol. 50, 121–138. De Smedt, F., Wierenga, P.J., 1978. Solute transfer through soil with nonuniform water content. Soil Sci. Soc. Am. J. 42, 7–18. De Smedt, F., Wauters, F., Sevilla, J., 1986. Study of tracer movement through unsaturated sand. J. Hydrol. 85, 169–181. Dewiere, L., Bugaï, D., Grenier, C., Kashparov, V., Ahamdach, N., 2004. 90Sr migration to the geo-sphere from a waste burial in the Chernobyl exclusion zone. J. Environ. Radioact. 74, 139–150. Fesch, C., Lehmann, P., Haderlein, S.B., Hinz, C., Schwarzenbach, R.P., Flühler, H., 1998. Effect of water content on solute transport in a porous medium containing reactive micro-aggregates. J. Contam. Hydrol. 33, 211–230.

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