Journal of Contaminant Hydrology 160 (2014) 30–41

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Transport of selenium oxyanions through TiO2porous media: Column experiments and multi-scale modeling K. Nsir a,b, L. Svecova c, M. Sardin a,b,⁎, M.O. Simonnot a,b a

CNRS, Laboratoire Réactions et Génie de Procédés, UMR 7274, 1 rue Grandville, BP 20451, 54001 Nancy, France Université de Lorraine, Laboratoire Réactions et Génie de Procédés, UMR 7274, 1 rue Grandville, BP 20451, 54001 Nancy, France Laboratoire d'Electrochimie et de Physicochimie des Matériaux et des Interfaces, UMR 5279, CNRS/Grenoble-INP/Université de Savoie/Université Joseph Fourrier, 1130 rue de la Piscine, 38402 Saint-Martin d'Hères, France b c

a r t i c l e

i n f o

Article history: Received 26 October 2013 Received in revised form 10 February 2014 Accepted 17 February 2014 Available online 22 February 2014 Keywords: Selenium TiO2 Batch sorption Isotherm Reactive transport modeling

a b s t r a c t The present work deals with the modeling of selenium oxyanion (selenite/selenate) retention in TiO2 rutile porous media. A set of chemical interactions was elaborated from spectroscopic measurements and adsorption experiments in batch and column reactors, and a model of transient transport of the selenium species through laboratory column was developed. The adsorption model considered that both forms of selenium (Se) compete for the same sorption sites, hydroxyl groups, allowing taking into account a competitive adsorption. Stoichiometry and equilibrium constants of adsorption reactions were determined on the basis of spectrometric measurement and adsorption isotherm curve fitting. This approach led to a model of Sips type isotherm including a pH-dependence. It offers an excellent fitting compared to the classical Langmuir equation and provides a unique set of parameters for both oxyanions. IMPACT code and associated modeling method were then used to couple transport and chemical reactions. The obtained numerical results showed a reasonable prediction of the shape and the time location of selenium oxyanions and pH breakthrough curves. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Selenium (Se) pollution of the environment comes mainly from combustion of fossil fuels and its widespread use in agriculture, electronics and glass industry (Lemly, 2004). Furthermore, radioactive isotopes of selenium especially Se-79 are long half-life fission products of uranium ranging from 105 to 11 × 105 years (Bienvenu et al., 2007). Their fate and behavior in the environment are important issues in nuclear waste management (Aguerre and Frechou, 2006). Attention is particularly given to its transport properties through porous media (Beauwens et al., 2005). This behavior strongly depends on speciation. In a geochemical context, selenium can exist as soluble selenium oxyanions, selenate, ⁎ Corresponding author at: CNRS, Laboratoire Réactions et Génie de Procédés, UMR7274, 1 rue Grandville, BP 20451, 54001 Nancy, France. E-mail address: [email protected] (M. Sardin).

http://dx.doi.org/10.1016/j.jconhyd.2014.02.004 0169-7722/© 2014 Elsevier B.V. All rights reserved.

Se(VI), and selenite, Se(IV), as sparingly soluble Se(0), as selenides Se(-II) or Se(-I) that commonly form highly insoluble compounds such as FeSe. Under reducing conditions, selenium main aqueous species is Se(-II) whereas Se(IV) is the dominant aqueous species under mildly reducing conditions and presents as its protonated form HSeO− 3 at acidic to neutral pH, or as at alkaline pH. Under oxidizing condiselenite anion SeO2− 3 tions, Se(VI) is the main species, either as selenate anion 2− HSeO− 4 or SeO4 , depending on pH conditions (Beauwens et al., 2005). The sorption of selenium oxyanions onto different types of minerals has been investigated to explain the mobility of selenium species in the environment. For instance, adsorbing materials such as iron oxides and hydroxides (Catalano et al., 2006; Duc et al., 2003; Peak et al., 2006; Rovira et al., 2008; Wijnja and Schulthess, 2000), manganese oxides (Foster et al., 2004), titanium dioxide (Svecova et al., 2011), cements and clays (Charlet et al., 2007), biomass filters (Alvarado-Rodriguez

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

et al., 2013) or soils (Collins et al., 2006; Nakamaru et al., 2005) have been considered in the literature. In most cases, Se(IV) appeared to be more retained by solid surfaces than Se(VI). Sorption onto either oxide or hydroxide minerals was found to be pH dependent, which suggested a surface complexation mechanism. Most of these works showed that the optimum adsorption pH was generally met in the acidic area. Due to its low solubility and its value of the point of zero charge near to the neutrality, TiO2 has been regarded as a model mineral in sorption studies. In a previous investigation, Svecova et al. (2011) reported a detailed experimental study on the sorption of selenite and selenate anions onto TiO2 rutile surface at acidic pH. A combined approach was chosen and the crystallographic properties were linked to the sorption behavior in batch reactor and through TiO2 porous media in column experiment. EXAFS spectra confirmed that for selenite anions, an inner-sphere mechanism was the most probable process observed. Dynamic sorption experiments using a column filled with rutile powder not only substantiated that a part of the surface complexes follows the inner-sphere mechanism, but also evidenced that an outer-sphere mechanism cannot be excluded, especially for selenate anions. This finding represent very useful information to predict the Se susceptible to migrate under specific conditions, but a satisfactory modeling and mathematical parameterization of obtained experimental data is still necessary for applications in the field of contaminant migration. The adsorption process of many inorganic oxyanions onto mineral surfaces has been commonly described by chemical Surface Complexation Models (SCMs) (Gunneriusson et al., 1994; Lackovic et al., 2004; Hizal and Apak, 2006). Unlike empirical models (e.g. Langmuir and Freundlich models), chemical models (SCM) have the advantage to explicitly define surface species, chemical reactions and equilibrium constant expressions. The SCM approach can also be readily incorporated within solute transport models (Kent et al., 2000; Kohler et al., 1996). Despite the numerous contributions, to our knowledge, there is no consistent modeling approach able to link TiO2 mineral surface properties to a same set of experiments performed in batch or column. Thus, there is a real need to develop modeling approaches including transport mechanisms to predict quantitatively the reactions occurring at the solid surface and the fate of contaminant in contact with these surfaces that can have practical environment implications. The present study is essentially methodological and carried out with the aim to develop a model able to describe the interactions of selenium oxyanions with TiO2 rutile that accounted for competitive adsorption, and that can be applicable in various experimental conditions around pH 3. A step-by-step modeling process from the spectroscopic determination of interactions to the transient transport of Se-oxyanions in a laboratory column was developed. A set of adsorption reactions, so-called “phenomenological mechanism”, was built to describe batch and column sorption experiments of selenite and selenate. Transport simulations were then performed with the IMPACT code (Baranger et al., 2002; Jauzein et al., 1989; Lefèvre et al., 1993; Scholtus et al., 2009; Simonnot and Ouvrard, 2005) and the calculated and experimental breakthrough curves of selenium oxyanions and pH behavior were compared.

31

2. Materials and methods 2.1. Adsorbent The adsorbent used in laboratory experiments was a very fine powder of titanium dioxide in rutile allotropic form (CERAC Inc., Milwaukee, USA). Pre-treatment and physicochemical parameters of this rutile powder have been reported in detail (Svecova et al., 2008, 2011). The particle size was between 200 nm and 1 μm, the specific surface area was 5 m2 g−1 and the point of zero charge was around 4.5 to 5.0. For column experiments, the powder was compacted under the effect of a certain compaction pressure of 20, 30, and 40 kN using an instron 5569 traction machine. The size of the formed aggregates varied from 112 to 200 μm. The physico-chemical parameters of the aggregates were close to those of the initial powder (Svecova et al., 2008) except the BET surface area that reached 7 m2 g−1. This increase was assigned to surface activation by compacting and grinding. 2.2. Batch sorption experiments Adsorption isotherms of Se(IV) and Se(VI) onto rutile powder were previously determined by batch reactor experiments at constant temperature, ionic strength and pH. In the first step, the rutile powder (0.2 g) was contacted with 10 mL of sodium perchlorate solution at the selected ionic strength for 12 h at 22 °C; pH was adjusted to 3 by addition of 1 mol L−1 HClO4 stock solution (Svecova et al., 2011). Then, a given volume of a stock solution of selenium oxyanions was added to the suspensions in order to obtain concentrations ranging from 5 × 10−5 to 5 × 10−3 mol L−1 at pH 3 and sorption time was set at 100 h (Svecova et al., 2011). The supernatant was further filtered at 0.22 μm before being analyzed by ion chromatography. Empirical fittings of experimental points by Langmuir or Freundlich isotherms were available in annexes jointed to a previous paper (Svecova et al., 2011). 2.3. Column experiments Column experiments were performed at 22 °C in a set-up composed of: two reservoirs of solutions degassed by nitrogen bubbling, a pump feeding the packed column at constant flow rate in the up-flow direction, two continuous detectors (pH and conductivity) and a fraction collector (Svecova et al., 2011). The collected samples were analyzed by ion chromatography (ICS 3000 by Dionex, Sunnyvale, USA). The transient measurements of pH during column experiments were considered as qualitative. In a typical experiment, the column was filled with 7.88 g TiO2 aggregates corresponding to a total volume of 5.5 mL (length, 7.0 cm; diameter: 1.0 cm). The flow rate was 0.2 mL min−1, which corresponded to a mean residence time of 17.5 min. The accessible pore volume was determined by residence time distribution measurements performed with NaClO4 solutions: its value was 3.47 mL. Total accessible porosity of column bed was 63.5% including external (about 0.4) porosity of packing and internal (about 0.39) porosity of agglomerated grains. Pressure drop was negligible.

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The Péclet number at the aggregate scale, Pem was calculated: Pem ¼

u dp ¼ 10 Dm

ð1Þ

where u (m s−1) is the velocity in the external pore volume (0.64 × 10−3 m s−1), dp (m) is the mean aggregate diameter (156 μm, arithmetic mean value) and Dm (m2s−1) is the molecular diffusivity of the tracer (Dm,NaClO4 = 1.56 × 10− 9 m2 s− 1 from Cussler (1989)). The Péclet number being largely higher than one, axial dispersion was mainly governed by the statistical dispersion (Saffman, 1959). The theoretical axial dispersion coefficient DA (van Deemter et al., 1956) is given by: −8

DA ¼ 2dp u ≅ 3:3 10

2

−1

m s

:

ð2Þ

Consequently, the Péclet number of the column was theoretically deduced as follows: Pe ¼

uL L ¼ ¼ 224: DA 2dp

ð3Þ

model include local equilibrium, steady flow, and constant temperature, pressure and pore geometry. Hydrodynamics is modeled by the mixing cells in series model (MC) (Sardin et al., 1991), alternative at the column scale to the classical continuous approach for modeling one-dimensional convective–dispersive flow. The MC model involves two parameters: the volume of porous medium, Vp, and the number J of cells in series. The parameter J is related to the axial dispersion coefficient DA, (Eq. (2)) and Pe (Eq. (3)) by the relationship (Sardin et al., 1991): Pe ¼

uL ¼ 2 ð J−1Þ DA

ð4Þ

where L is the column length (m). The integration of the differential system coupled to a nonlinear algebraic system is performed with the help of a predictor–corrector method with variable integration steps using the equilibrium constraints, whereas the local equilibrium is calculated at each step by a modified Newton– Raphson algorithm. 3.2. Adsorption model

3. Theory

According to crystallographic measurements, the site capacity was 6.2 TiOH sites nm−2 (Vandenborre, 2005). Combined with the BET surface areas of 5–7 m2 g−1, the maximum capacity ranged between 5.15 × 10−5 and 7.21 × 10−5 mol site g−1. In the chosen pH range around 3, the concentration of sites in the form of TiOH+ 2 can be considered constant and close to the maximum capacity. Nevertheless, pH variation must be taken into account by introducing surface ionization into the phenomenological model because during transient transport in column a large range of pH can be explored because of H+ consumption during adsorption process. To reduce the complexity in solution, the species that were 2− for taken into account were HSeO− 3 for selenite and SeO4 selenate, since previous speciation calculations had shown that they were predominant in this pH range (Svecova et al., 2011). In the liquid phase only water dissociation (reaction R1) was taken into account in the proposed model:

3.1. Modeling principles

H2 O ¼ H þ OH ;

A set of relevant chemical reactions at equilibrium was elaborated to describe the physico-chemical interaction system. It was composed of both reactions in the liquid phase and adsorption reactions. Adsorption constants of oxyanions and adsorption capacity of TiO2 were deduced from the isotherms resulting from the batch experiments at constant pH. Then, thanks to the theory of non-linear chromatography, the concentration of adsorption sites in the column was fitted from the mean position of the breakthrough curve measured in mono-component experiments. IMPACT code, devoted to the simulation of multi-component transport, was then used to calculate the breakthrough curves (Jauzein et al., 1989). The simulator combines an advective–dispersive flow model with a set of homogeneous and heterogeneous chemical reactions describing the physico-chemical system. The basic assumptions of this

with the equilibrium constant:

The measurement of axial dispersion from tracer test has given Pe = 40. It means that dispersion was not only due to statistical dispersion but also due to the existence of a velocity profile in a cross-section. We will see the importance of this remark on the interpretation of further numerical simulations (Subsection 6.1). Then, the packing was conditioned at pH = 3 with HCl acid solution (for suspensions in sodium chloride) or HClO4 (for suspensions in sodium perchlorate) in a 0.05 or 0.1 mol L−1 NaClO4 solution. The solution was pumped into the column until the effluent pH was stable and equal to the inlet value. Selenium inlet concentration was then set at the constant concentration C0 chosen in the range 0.0005 mol L−1 to 0.002 mol L−1 while maintaining the background ion concentration at 0.05 or 0.1 mol L−1 NaClO4. The effluent pH and conductivity were monitored online and the effluent samples were collected and analyzed by ion chromatography.

þ

−

h i þ − −14 2 −2 K1 ¼ H ½OH  ¼ 10 mol L :

ð5Þ

ð6Þ

In order to model the ionization of TiO2 surface in acidic medium, it was considered that each hydroxyl group offered one positive sorption site noted as X1+, due to the association with one proton according to the equilibrium relationship noted (R2): þ

þ

TiOH þ H ¼ X1 ;

ð7Þ

with an equilibrium constant defined as: K2 ¼

 þ X1 : ½TiOH½Hþ 

ð8Þ

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

The point of zero charge for TiO2 is in the range of pH 5–6 (Janssen and Stein, 1985). Thus, K2 was fixed at 106 indicating a low variation of [X1+] in the range of pH 2–4. Se-oxyanions are adsorbed as bidentate inner-sphere surface complexes formed with terminal hydroxyl groups involving H+ proton consumption (Svecova et al., 2011). Following these assumptions, surface interactions for each oxyanion can be described by the following reactions: Reaction (R3) for selenite: −

þ

þ

0:5HSeO3 þ 0:5H þ X1 ¼ X1ðSeO3 Þ0:5 :

ð9Þ

−−

þ

þ

þ H þ X1 ¼ X1ðSeO4 Þ0:5 :

ð10Þ

The corresponding equilibrium constants are defined as: K3 ¼ K4 ¼

h

  X1ðSeO3 Þ0:5 ½X1þ ½Hþ 0:5 ½HSeO3 0:5   X1ðSeO4 Þ0:5 ½X1þ ½Hþ ½SeO4 0:5

with: i     þ X1 þ X1ðSeO3 Þ0:5 þ X1ðSeO4 Þ0:5 ¼ 2qmax

3.3. Adsorption isotherm equations Reactions (R3) and (R4) enable us to deduce the function linking the concentration of adsorbed oxyanions, q, to the oxyanion concentration in solution, C, at equilibrium. The parameters q and C can be defined as follows:     ð16Þ q ¼ 2 X1ðSeO3 Þ0:5 þ 2 X1ðSeO4 Þ0:5

C ¼ ½HSeO3  þ ½SeO4 :

q ¼ qmax ð12Þ

ð13Þ

where the 8 columns represent (from left to right) the mobile − species: H+, OH−, HSeO− 3 , and SeO4 , and the stationary species (linked to the surface): TiOH, X1+, X1(HSeO3)0.5, and X1(SeO4)0.5. The 4 rows correspond to the 4 reactions (R1) to (R4). The rank of the matrix R is 4, equal to the number of reactions, indicating that the system is composed of independent reactions (Schweich et al., 1993). This matrix is composed of two parts with suffixes m and s referring to mobile and stationary species, respectively. The matrix [ν] is thus written:

ð17Þ

The equation of selenite adsorption isotherm deduced from reaction (R3) yields:  0:5 0:5 K3 Hþ C

ð11Þ

where qmax (mol g−1) is the maximum amount of adsorbed oxyanions at a given pH. The proportionality coefficient 2 in Eq. (13) is due to the formation of a bidentate complex. The values of the stoichiometric coefficients of H+ were deduced from the transient behavior observed in the column, showing adsorption a strong consumption of H+ during the SeO2− 4 process (Fig. 5) and a weak one with HSeO− 3 (Fig. 6). K3 and K4 were determined on the basis of least squares fitting on adsorption experimental points at constant pH. Finally, four main stoichiometric relationships govern the distribution of species between the solutions and the surface. The resulting stoichiometric matrix of the so built phenomenological mechanism yields: 1 0 1 1 0 0 0 0 0 0 B −1 0 0 0 −1 1 0 0 C C ð14Þ ½v4;8 ¼ B @ −0:5 0 −0:5 0 0 −1 1 1 A −0:5 0 0 −0:5 0 −1 1 1

½ν4;8 ¼ ½νm 4;4 ½νs 4;4 :

composition waves in the analysis of multicomponent column experiments (Subsection 5.2).

and

Reaction (R4) for selenate: 0:5SeO4

33

1 þ K3 ½Hþ 0:5 C0:5

ð18Þ

and the equation of selenate adsorption isotherm deduced from reaction (R4) yields: q ¼ qmax

 þ  0:5 K4 H C 1 þ K4 ½Hþ C0:5

:

ð19Þ

As pH being constant, a pseudo equilibrium constant Ki′ (i = 3,4) was introduced and calculated from the following relationships: h i0:5 h i ′ þ ′ þ K3 ¼ K3 H and K4 ¼ K4 H :

ð20Þ

Eqs. (18) and (19), deduced from the stoichiometry of adsorption reactions (11) and (12), offered a consistent interpretation of measured isotherms. These equations were recently proposed by Jeppu and Clement (2012) to simulate pH-dependent adsorption effects. Then, the adsorption of selenite and selenate at constant pH is viewed as a process involving the same sites (same capacity, qmax, assumed to be constant in the considered range of pH), and is modeled for each oxyanion by the following equation type: q K′C0;5 ¼ : qmax 1 þ K′C0;5

ð21Þ

This form of equation has been initially proposed by Sips (1948) empirically, and further derived from stoichiometric relationship at equilibrium by Hammes (2000) and Liu and Liu (2008). This relationship was compared with the classical Langmuir and Freundlich equations, respectively (Table 1): q KL C ¼ qmax 1 þ KL C

ð22aÞ

ð15Þ and

The ranks of the two submatrices are Rm = 4 and Rs = 3. These results will be used to calculate the number of

n

q ¼ K FC :

ð22bÞ

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K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

Table 1 Results of isotherm experimental point fittings by Langmuir, Freundlich and Sips models. Sips model

Selenite Selenate a

Langmuir model 2

Freundlich model 2

qmax

K′

R

qmax

KL

R

KF

n

R2

1.5 × 10−5a 1.5 × 10−5a

210 4.7

0.981a 0.981a

1.4 × 10−5 4.4 × 10−6

35 1.0

0.929 0.859

2.85 × 10−5 3.4 × 10−5

0.1172 0.414

0.917 0.968

Same value for selenite and selenate, the fit was performed on the two curves simultaneously.

4. Batch experiment results and determination of adsorption parameters 4.1. Experimental observations The adsorption isotherms of selenium oxyanions (Figs. 1 and 2) revealed that, at the same contact time and pH, selenite adsorption was stronger than selenate adsorption as previously described in the chosen pH range (Svecova et al., 2011). At the highest initial concentration in solution (5.0 × 10−3 mol L−1), the adsorption capacities reached 13 μmol g−1 for selenite against only 4 μmol g−1 for selenate. This difference is the consequence of the binding strength and the adsorption reaction stoichiometry, particularly the role of protons in the adsorption mechanism. In the conventional classification, selenite isotherm is an H form one whereas selenite isotherm is an L form one (Giles et al., 1974; Limousin et al., 2007). In the studied case, this apparent difference of behavior covers the same type of adsorption process (surface complexation) with different interaction strengths. 4.2. Adsorption parameters of the Sips model and comparison with Langmuir and Freundlich models Model parameters were determined by least square fitting. For the Langmuir and Freundlich models, fitting has been performed curve by curve. For the Sips model the parametric optimization has been performed on the set of experimental points. The obtained results are given in Table 1. Results showed that the Langmuir model is adapted in the case of selenite and Freundlich model fits better the

experimental points of selenate, while a good fit of the Sips model (Figs. 1 and 2) was obtained on both experimental curves with a unique set of parameters. Consequently, from a global perspective, the Sips model appears to be a good approach to represent the experimental points. The value qmax = 1.5 × 10−5 mol g−1, unique in the Sips model (maximum capacity of adsorbed oxyanion at pH 3), can be used to calculate the maximum concentration of site knowing that one molecule of oxyanion whatever its speciation in solution interacts with two sites X1+. The maximum concentration of occupied sites [X1+]max is 3.0 × 10−5 mol g−1 at pH 3. This value is lower than the one obtained by crystallographic measurements, 5.15 × 10−5 mol g−1 (Subsection 3.2) but in the same order of magnitude. This result is satisfactory, keeping in mind that the total theoretical number of sites deduced from crystallographic measurements is experimentally very difficult to reach. 5. Interpretation of column results by the theory of nonlinear chromatography 5.1. Analysis of mono-constituent breakthrough curves from adsorption isotherm The breakthrough curves of 7 column experiments (Runs 1–7) performed with mono-constituent injection of selenate at different concentrations (from 0.0005 to 0.002 mol L−1) and selenite at 0.001 mol L−1 for two ionic strengths (0.05 and 0.1 mol L−1) and at pH around 3 are presented in Fig. 3. As observed in batch reactor experiments (Subsection 4.1), a significant difference of capacity factor between selenite and selenate sorption is clearly displayed. For instance, the reduced

Uptake amount, q (mol g-1)

2.0E-06

1.5E-06

1.0E-06 Experimental points

SIPS Model

0.5E-06

LANGMUIR Model FREUNDLICH Model

0.0E+00 1.0E-06

0.1E-04

1.0E-04

Concentration, C (mol L-1) Fig. 1. Adsorption isotherm of selenite onto TiO2 powder measured in batch at pH 3 and [NaClO4] = 10−2 mol L−1. Semi-log plot. Fit on the experimental points: Langmuir, Freundlich and Sips model comparison.

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

35

Uptake amount, q (mol g-1)

0.5E-06 0.4E-06

Experimental points SIPS Model LANGMUIR Model

0.3E-06

FREUNDLICH Model

0.2E-06 0.1E-06 0.0E+00 1.0E-06

0.1E-04

1.0E-04

Concentration, C (mol L-1) Fig. 2. Adsorption isotherm of selenate on TiO2 powder measured in batch at pH 3 a [NaClO4] = 10−2 mol L−1. Semi-log plot. Fit on the experimental points: Langmuir, Freundlich and Sips model comparison.

breakthrough curves for the selenite and selenate at a same injected solution concentration of about 1.0 × 10−3 mol L−1 and same ionic strength, occurred at 37.7 V/Vp (Run 7 Table 2) and 8.82 V/Vp (Run 4 Table 2), respectively. The mean breakthrough positions were very sensitive to the injection concentration because of adsorption non-linearity. As shown in Table 2, the influence of ionic strength was of second order on the oxyanion retention, which confirms the theoretical approach in terms of surface complexation. The theory of non-linear chromatography was used to deduce the mean position of breakthrough fronts from isotherms shown in Figs. 1 and 2. In the case of a concave isotherm and a step injection at concentration C0, the reduced breakthrough volume VVΔp is calculated using the following relationship (Schweich et al., 1993; Simonnot et al., 1995): VΔ m Δq ¼1þ Vp Vp Δc

ð23Þ

where Δc is the difference between the injection concentration and the initial concentration. Here, Δc was considered equal to C0, concentration of the step injection, and Δq corresponded to the difference between the amount fixed at

injection concentration C0 at equilibrium and at the initial concentration. Considering that the initial concentration is zero and using Eq. (21) it becomes: Δq ¼ q ðC0 Þ−0 ¼

qmax K′i C0:5 0 1 þ K′i C0:5 0

ð24Þ

with K′i = K′3 or K′4. Combining with Eq. (23) leads to: 0

VΔ m Ki C0 0:5 ¼1þ qmax 0 Vp Vp 1 þ Ki C0:5 0

ð25Þ

The calculated values of the theoretical breakthrough volume are function of C0 only. For both oxyanions, they have been compared to the mean values of the breakthrough volumes of experimental fronts. That was obtained by integration of the breakthrough curves on reduced eluted volume V/Vp by the relationship: VΔ 1 ¼ Vp Vp

Z∞  1− 0

 C dV: C0

ð26Þ

Fig. 3. Comparison of experimental breakthrough curves for both selenium oxyanions to the deduced ones from the theory of non-linear chromatography. The front positions were calculated with qmax = 1.94 mol g−1.

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K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

Table 2 Comparison of experimental column data and reduced breakthrough volumes obtained by Eq. (26) and those deduced from the theory of non-linear chromatography (Eq. (25)) with m = 7.88 g, Vp = 3.5 × 10−3 mL, and qmax = 1.94 × 10−5 mol (of oxyanions) g−1. Run SeO− 4

HSeO− 3

1 2 3 4 5 6 7

Initial concentration, C0 (M) 4.5 6.5 9.87 1.01 2.05 1.01 9.53

× × × × × × ×

−4

10 10−4 10−4 10−3 10−3 10−3 10−4

Ionic strength (NaClO4)

Final pH measured

vΔ vP

vΔ vP

0.1 0.1 0.05 0.1 0.1 0.05 0.1

2.85 2.7 2.9 3.0 3.05 3.15 2.9

9.8 8.2 6.7 6.7 4.8 38.9 40.4

9.23 9.7 7.02 8.82 4.2 44.4 37.7

The maximum adsorption capacity of the packing, qmax in Eq. (25), can be directly deduced from the value calculated in batch system (e.g., 5 × 10−5 mol g−1). As the TiO2 used in the column experiments is in aggregate form and not in the powder form as in batch experiments, the BET surface area of aggregates is higher than the one of powder (7 against 5 m2 g−1, see Subsection 2.1). Thus, to determine the optimal value of qmax, a fit on all breakthrough curves has been performed which has given a value of qmax equal to 1.94 × 10−5 mol g−1, corresponding to a surface area of 6.5 m2 g−1. The final adjustment results are summarized in Table 2 where the experimental and calculated reduced breakthrough volumes were compared. Fig. 3 shows the experimental breakthrough curves compared to the predicted front positions for both the selenite and the selenate. Obviously, neither axial dispersion (due to hydrodynamics or mass transfer kinetics) nor multicomponent effects were taken in account in this prediction. Numerical simulations described later in Section 6 focus on these points. 5.2. Analysis of multicomponent breakthrough curves The previous analysis ignored changes in H+ concentration during the transient transport before the equilibrium steady state and gave only the mean position of the wave front at a given concentration and pH. Breakthrough curves, consequence of a multicomponent system, are more complex and follow some simple rules defined by Schweich et al. (1993). Breakthrough curves for any species are composed of successive waves separated by equilibrium plateau zones and the number of retarded waves, F, is directly given from the analysis of the stoichiometric matrix by the following relationship: F ¼ Rm þ Rs −R

ð27Þ

where Rm, Rs and R are respectively the ranks of matrices of mobile species, and stationary species and the rank of the stoichiometric matrix. From the matrix (Eq. (15)) and the relationship (Eq. (16)), we deduced Rm = 4, Rs = 3 and R = 4, hence F = 3. We had to observe at most 3 composition waves, as a function of the range of pH and the number of species and reactions involved actually in the system. In the case when only one oxyanion species is injected (selenite or selenite), the previous rule (Eq. (27)) predicts the existence of two retarded composition waves (3 adsorbed species, 3 reactions).

6. Numerical simulations of multicomponent transport The IMPACT code (Jauzein et al., 1989) was applied to simulate the multicomponent behaviors of experimental results. The specified phenomenological mechanism combining the defined reactions and the measured hydrodynamic parameters was incorporated in the code to simulate the transport process of selenium oxyanions on TiO2 rutile. Numerical simulations included experiments where only selenate or selenite was injected in the column as well as an experiment conducted with simultaneous injection of selenate and selenite in order to study competition effects. The number of ideal mixing cells in numerical experiments was fixed to J = 20. This value has been deduced from the column Péclet number measured on NaClO4 breakthrough curves, following the relationship given by Eq. (4).

6.1. Response to a mono-component step injection (selenite or selenate) The physico-chemical system combined reactions R1, R2 and R3 into one phenomenological mechanism for selenite and the reactions R1, R2 and R4 for selenate. The set of simulation parameters is summarized in Table 3. Two examples of comparison between the computed breakthrough curves of pH and selenium oxyanions compared to the measured ones are shown in Figs. 4 and 5 for the selenate and selenite, respectively. For selenate (Fig. 4), the position and shape of the breakthrough curves were consistent with the multicomponent chromatography theory, which validated the simulation results. We observe two fronts. The shoulder initially present on the breakthrough curves is equally present in the simulation, representing an equilibrium plateau between the two fronts. The position of the fronts is alike the experimental observation with a gap of approximately 1 porous volume for that no consistent explanation has been found yet. In the case of selenite breakthrough simulation (Fig. 5), the mean position and shape of the breakthrough curve were also consistent with the theory of multicomponent chromatography. On the experimental selenite breakthrough curves Table 3 Parameters of numerical simulations. Vp

m

J

Capacity of sorption sites

K1

K2

K3

K4

3.47 cm3

7.88 g

20

0.088 mol L−1

10−14

107.56

103.82

103.67

37

1.2E-03

5.0

1.0E-03

4.5 4.0

8.0E-04 Measured [SeO4 --] Simulated [SeO4--] Measured pH Simulated pH

6.0E-04

3.5

4.0E-04

3.0

2.0E-04

2.5

0.0E+00 0

5

10

15

20

25

30

35

40

45

pH

Concentration (Mol L-1)

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

2.0 50

V/Vp Fig. 4. Comparison of computed selenate and pH breakthrough curves to the measured ones (Run 4, C0 = 0.987 × 10−3 mol L−1, pH 3). Case of mono-component sorption.

two retarded fronts were highlighted, as predicted by theory. Whereas simulation just exhibited one steep front. The parametric study in Subsection 6.3 showed a very high sensitivity on the existence of one or two fronts. The comparison of numerical simulations to experimental results showed a large difference in the steepness of the selenite front. A priori, the H-form adsorption isotherm with a steep initial slope (Fig. 2) must theoretically cause a strong compression effect which plays against the dispersion. A shock effect of the front was effectively observed on the simulation. The simulated breakthrough of pH front appeared after one Vp whereas it was observed after injection of 3 Vp in the experiment. In the chosen mechanism, this front is not a retarded front, but just the consequence of a change in normality (step injection of selenite). More, the experimental excursion of pH is not as high as simulated, but in terms of consumption of H+ the difference is not much important (pH is a nonlinear representation), indicating that the stoichiometry chosen for the adsorption reaction R4 is close to the experimental behavior. One can note that the choice of only one species for selenite is restrictive and the existence of the species H2SeO3 in the range of considered pH can largely decrease the H+ consumption.

The discrepancies observed between the experimental shape of the front and the calculated ones can be explained either by a kinetic limitation to mass transfer or a slow chemical kinetics of selenite sorption. The kinetic measurement in a batch reactor on the powder published by Svecova et al. (2011) showed a large gap between the characteristic adsorption times for selenate (b 3 min) and for selenite (about 1 h). However, experiments performed at different flow rates have not presented significant difference on the hydrodynamic dispersion. Additionally, H+ consumption may directly influenced the electronic configuration of the selenite oxyanion leading to a local change of bonding environment not precisely accounted for in the model. There may also be some steric hindrance of other selenite absorption sites caused by a transition from outer to inner sphere complex particularly in aggregate pores that are not also considered in the proposed model. Another consistent explanation can be found in the interpretation of dispersion process. Indeed, the theoretical value of the Péclet number at the column scale (Eq. (4)) is largely higher than the one deduced from tracer dispersion measurement (224 against40). Moreover, the dispersion of the breakthrough curves of selenite (Fig. 5) led to a Péclet number of 38, which

3.8 3.6

1.0E-03

3.4 3.2

8.0E-04

3.0

6.0E-04

2.8

4.0E-04

2.6

Simulated [HSeO3-] Measured [HSeO3 -]

2.4

Simulated pH

2.0E-04

2.2

Measured pH

0.0E+00 0

pH

Concentration (Mol L-1)

1.2E-03

2.0 10

20

30

40

50

60

70

80

V/Vp Fig. 5. Comparison of computed selenite and pH breakthrough curves to the measured ones (Run 7, C0 = 1 × 10−3 mol L−1, pH 2.9). Case of mono-component sorption.

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

Concentration (Mol L-1)

1.4E-03

Simulated [SeO4--] Measured [SeO4--] Simulated pH

1.2E-03

5

Simulated [HSeO3-] Measured [HSeO3-] Measured pH

4.5

1.0E-03

4

8.0E-04 3.5 6.0E-04

pH

38

3

4.0E-04

2.5

2.0E-04 0.0E+00 0

10

20

30

40

50

60

70

80

90

2 100

V/Vp Fig. 6. Comparison of computed selenate, selenite and pH breakthrough curves to the measured ones (Se(IV) = 0.8 × 10−3 mol L−1, Se(VI) ≈ 0.98 × 10−3 mol L−1, IS = 0.05 mol L−1, pH ≈ 2.8). Case of multi-component sorption.

was very close to the dispersion of the tracer, as if the chromatographic process was linear. This behavior is found when a velocity profile is superimposed to the statistical dispersion and is dominant. In this case of a short column, the

radial dispersion is not sufficient to ensure the radial mixing in a cross-section and does not influence the selenate breakthrough because of its weak non-linear effect in the range of investigated concentrations.

Fig. 7. a. Sensitivity of simulated breakthrough curve shapes and positions to initial concentration of selenite at constant pH (pH = 3). b. Sensitivity of simulated breakthrough curve shapes to initial concentration C0 for selenate at constant pH (pH = 3). The experimental curve obtained at C0 = 10−3 mol L−1.

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

6.2. Response to a multi-component injection Fig. 6 compared the experimental and computed breakthrough curves obtained when selenite and selenate oxyanions were injected simultaneously at a concentration around 10−3 mol L−1 (IS = 0.05 M, pH = 3). Globally, the simulations reasonably predicted the observed behaviors. At first, both anionic forms were retained in the medium involving a pH wave that appeared at 1 Vp. This behavior was essentially due to the consumption of H+ by the oxyanion adsorption reactions (R3) and (R4). Then early selenate breakthrough was due to its lower affinity to surface sites. Its concentration rapidly exceeded the inlet concentration and reached a plateau. This phenomenon commonly called “overshoot” was observed in the case of multi-component sorption and showed explicitly that the two species compete on the same sites. The selenite oxyanions of higher affinity displaced the selenate oxyanions whose concentration increased in the solution. When the selenite oxyanions broke through, the concentrations of all species reached the inlet values in the final equilibrium plateau. 6.3. Parametric study: influence of initial concentration and pH Two operating parameters might be determinant in the positioning of breakthrough curves: the initial concentration C0 and the pH. The influence of initial concentration was theoretically illustrated for the case of selenate, in the range of concentration going from 5 to 20 × 10−4 mol L−1 (see Fig. 3). A complementary illustration is given in Fig. 7a and b for both selenite and selenate, respectively, according to numerical simulations with IMPACT code at pH 3 and a range of concentration between 5 and 15 × 10−4 M. The behavior of two oxyanions is nonlinear and very sensitive to the transient evolution of pH along the column. Numerical simulations shown in Fig. 7a illustrated the change in the breakthrough curve shape and position as a function of selenite concentration. The higher the injection concentration, the higher the H+ consumption. Consequently, the pH increases and the number of sites X1+ decreases because of the equilibrium shifting of reaction R2 that

39

induces the formation of two composition waves. Indeed, in this case, the reaction (R2) was involved and two composition transitions appeared in accordance with the rule described in Subsection 5.2. The first one was due to selenite adsorption at higher pH. The second one was the consequence of the stabilization of pH at 3. When the initial concentration was lower, the quantity of adsorbed H+ within the selenite sorption was lower too and the increase in pH is not sufficiently high to modify the active site concentration [X1+]. Fig. 7b exhibits the behavior of selenite. One or two fronts are present and reflect the consumption steps of H+ during the adsorption. A high pH wave propagates in front of the adsorption front of selenate inducing a first front of selenate. The second front is due to the final equilibrium at pH 3. The theory of multicomponent chromatography let us calculate the position of these fronts as shown by Simonnot et al. (1995). Fig. 8 displays the influence of pH on the position and the shape of the breakthrough curves for selenite and selenate. The simulations had been performed at C0 = 1.0 × 10−3 mol L−1 for selenate and 0.8 × 10−3 mol L−1 for selenite. Selenate adsorption was very sensitive to pH, because the association with the surface sites consumed twice more H+ than in the case of selenite reaction. Moreover, if the increase in pH for selenite was lower than for selenate, the displaced amount of H+ was higher than by selenate, the amount of fixed selenite being higher. The combination of a large consumption by selenite and a high sensitivity to pH of the selenate interaction had for consequence the behavior observed. Finally, a fitting could be performed to find the better set of thermodynamic constants. However, this strongly non-linear system required many numerical simulations. No algorithm was available to lead to a unique and optimal solution. 7. Conclusion The numerical results clearly confirmed that the proposed model is an effective approach for describing the sorption isotherms and to simulate the complex breakthrough curves of selenium oxyanions on a TiO2 rutile surface. A set of surface complexation reactions were generated to describe

Concentration (Mol L-1)

1.4E-03 1.2E-03 1.0E-03 8.0E-04 6.0E-04

[SeO4--]_pH2.53 [SeO4--]_pH2.63 [SeO4--]_pH2.73 [SeO4--]_pH_real [SeO4--]_pH2.93 [SeO4--]_pH3 [SeO4--]_measured

4.0E-04 2.0E-04 0.0E+00

0

10

20

30

40

50

60

[HeSO3-]_pH2.53 [HeSO3-]_pH2.63 [HSeO3-]_pH2.73 [HSe03 -]_pH_real [HSeO3-]_pH2.93 [HSeO3-]_pH3 [HSeO3-]_measured

70

80

V/Vp Fig. 8. Sensitivity of breakthrough curve shapes and positions for selenite and selenite as a function of pH in the range 2.53–3, around pH real value of 2.83.

40

K. Nsir et al. / Journal of Contaminant Hydrology 160 (2014) 30–41

their adsorption and retention properties. One of the main features of the physico-chemical model is that it offers a good fitting on experimental isotherm points and a unique set of parameters for the two-oxyanion species. Coupled with transport equation through the IMPACT code, the model predicts the form and the position of breakthrough fronts, in good agreement with the experimental measurements and in coherence with the batch experiment results. The computed pH jumps are consistent with the experiments, indicating that the stoichiometries chosen for the adsorption reactions are consistent. The so-built transport model reasonably reproduces global behavior of competition effect selenite/ selenate, especially the observed overshoot phenomenon. However, the effect of shock noted on the computed breakthrough selenite curves and not observed in experiments shows that the hydrodynamic model has to be better interpreted. As explanation, both kinetic limitation to mass transfer, slow chemical kinetics of the sorption or existence of a velocity profile in a cross-section superimposed to the statistical dispersion can be invoked. The latter seems to be the most consistent among the three. One of the challenges to improve and extend this modeling approach is to establish a better characterization of the dispersion parameter in the model. In addition, the relatively simple model so elaborated can be improved by introducing a more complex description of speciation in solution, particularly to have better representation of pH jumps in selenite transport simulation. Complementary experiments, not presented here, have shown that the model can be generalized to other competitive oxyanions as sulfate and phosphate. Acknowledgments The financial support for this research work was received from the Carnot Institute for Energy and Environment in Lorraine (ICEEL) in the frame of the CARNOT program, supported by the French Research Agency (ANR). It is gratefully acknowledged. The experimental results have been performed in the frame of ANR-Midis project. Thanks to Dr. Manuel Dossot (Laboratory of Microbiology and Physical-Chemistry for the Environment, CNRS — Lorraine University), for the fruitful discussions. The authors would also like to thank anonymous reviewers for their valuable comments and suggestions, which helped to improve the article. References Aguerre, S., Frechou, C., 2006. Development of a radiochemical separation for selenium with the aim of measuring its isotope 79 in low and intermediate nuclear wastes by ICP-MS. Talanta 69, 565–571. Alvarado-Rodriguez, C.E., Rodriguez-Martinez, E., Klapp-Escribano, J., Duarte-Pérez, R., Teresa-Olguin, M., Alguilera-Alvarado, A.F., CanoAlguilera, I., Gonzales-Acevedo, Z., 2013. Simulation of breakthrough curves of selenium absorbed in two biomass filters using a dispersion and sorption model. Use for a hypothetical case. Rev. Mex. Fis. 59, 258–265. Baranger, Ph., Azaroual, M., Freyssinet, Ph., Lanini, S., Piantone, P., 2002. Weathering of a MSW bottom ash heap: a modelling approach. Waste Manag. 22, 173–179. Beauwens, T., De Cannière, P., Moors, H., Wang, L., Maes, N., 2005. Studying the migration behaviour of selenate in Boom Clay by electromigration. Eng. Geol. 77, 285–293. Bienvenu, F., Cassette, F., Andreoletti, G., Be, M.M., Comte, J., Lépy, M.C., 2007. A new determination of 79Se half-life. Appl. Radiat. Isot. 65, 355–364.

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