Co-precipitation of radium in high ionic strength systems: 2. Kinetic and ionic strength effects

Available online at www.sciencedirect.com

Geochimica et Cosmochimica Acta 75 (2011) 5403–5422 www.elsevier.com/locate/gca

Co-precipitation of radium in high ionic strength systems: 2. Kinetic and ionic strength effects Y.O. Rosenberg a,⇑, V. Metz b, Y. Oren c, Y. Volkman c, J. Ganor a a

Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel b Institute for Nuclear Waste Disposal (INE), Karlsruhe Institute of Technology, P.O. Box 3640, 76021 Karlsruhe, Germany c Department of Desalination and Water Treatment, Zuckerberg Institute for Water Research, Ben-Gurion University of the Negev, Sede Boqer 84190, Israel Available online 19 July 2011

Abstract High concentrations of naturally occurring radium pose environmental and health concerns in natural and industrial systems. The adsorption of Ra2+ in saline water is limited compared to its adsorption in fresh water, but the process of co-precipitation may be effective in decreasing its concentration. However, despite its importance, Ra co-precipitation has rarely been studied in high ionic strength environments such as those in evaporitic systems. The fate of Ra in the reject brine of a desalination plant was studied via evaporation batch experiments at ionic strengths (I) ranging from 0.7 to 7.0 mol kg1. Precipitation sequences revealed that Ra co-precipitated with barite, even though the latter was a trace mineral compared to the precipitated gypsum. The concentration-based effective partition coefficient, K 0D;barite , for the co-precipitation reaction was 1.04 ± 0.01. This value of K 0D is significantly lower than the value for relatively diluted solutions (1.8 ± 0.1). This low value of K 0D;barite is mainly the result of a kinetic effect but is also slightly affected by the ionic strength. Both effects are quantitatively examined in the present paper. It is suggested that a kinetic effect influences the nucleation of (Ra,Ba)SO4, reducing the value of the partition coefficient. This kinetic effect is caused by the favorable nucleation of a more soluble phase (i.e., a phase with a higher BaSO4 fraction). An additional decrease in the partition coefficient results from the ionic strength effect. Considering the activity of Ra2+ and Ba2+ in the solution (rather than their concentration) makes it possible to determine the activity-based partition coefficient (K 00D;barite ), which accounts for the ionic strength effect. K 0D;barite was calculated empirically from the experiments and theoretically via a kinetic model. The two derived values are consistent with one another and indicate the combined effect of ionic strength and precipitation kinetics. Finally, the common assumption that cRa2þ =cBa2þ ¼ 1 was re-examined using a numerical model to predict the experimental results. As the ionic strength increases, this assumption becomes less appropriate for predicting the change in K 0D;barite as calculated in the experiments. Understanding the co-precipitation of Ra in such systems is crucial for risk assessments in which both Ra concentration and ionic strength are relatively high. Ó 2011 Elsevier Ltd. All rights reserved.

1. INTRODUCTION Radium is an abundant naturally occurring radioactive element (NORM) in many aquifers around the world (Minster ⇑ Corresponding author. Tel.: +972 8 6477517; fax: +972 8 6477655. E-mail address: [email protected] (Y.O. Rosenberg).

0016-7037/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.gca.2011.07.013

et al., 2004; Grundl and Cape, 2006; Peri, 2006). There are four naturally occurring radium (Ra) isotopes: 226Ra (half life 1599 years), 228Ra (5.6 years), 224Ra (3.6 days), and 223Ra (11.4 days). In some water resources, the Ra radioactivity concentration exceeds the acceptable threshold levels stipulated by international drinking water standards. Although Ra removal is technologically feasible (e.g., via ion exchange or reverse osmosis desalination), it yields byproducts that require suit-

5404

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

Nomenclature Symbol meaning (Cr,Tr)a solid solution between Cr and Tr where a denotes a counter ion of the solid compound (e.g., (Ba,Ra)SO4) Tr trace element of the solid solution (i.e., Ra2+) Cr carrier element of the solid solution [i] total solution concentration of element i mim+ molality of species i aim+ solution activity of species i cim+ activity coefficient of species I in the solution Xka mole fraction of component k in the solid solution phase k = Cr or Tr). cka rational activity coefficient of component k in the solid solution phase K°sp,ka solubility product of the pure phase end-member ka 0 KD concentration-based effective partition coefficient K00D activity-based effective partition coefficient KD,(I) equilibrium partition coefficient, ionic-strengthdependent KD equilibrium partition coefficient, ionic-strengthindependent Keq equilibrium constant of the solid solution reaction

able disposal. These byproducts are referred to as technologically enhanced NORMs (TENORMs) (EPA, 2008). The radioactivity concentration of Ra isotopes is governed by processes such as decay and new generation from parent isotopes, a-recoil, adsorption and desorption, mineral dissolution and precipitation (Porcelli and Swarzenski, 2003). The rates at which these processes occur depend on the chemistry of the water and the surrounding matrix as well as on the decay constant of the specific Ra isotope. Adsorption is an important sink for Ra in fresh and brackish water. In highly saline water and brines, the competition between Ra2+ and other ions decreases the adsorption of the former, and less Ra can be removed using this mechanism (Hanor, 2007). However, brines can be oversaturated with respect to evaporitic minerals, and Ra may be removed via co-precipitation. Pure Ra phases (e.g., RaSO4) tend not to precipitate because Ra2+ concentrations are too low to reach satu ration (K sp;RaSO4 ¼ 10:26; Langmuir and Riese, 1985). Instead, Ra2+ co-precipitates with a phase that can reach saturation (henceforth referred to as the host mineral phase). Minerals considered to be appropriate hosts for Ra or that have been found to contain Ra include rock-forming minerals such as gypsum (CaSO42H2O), anhydrite (CaSO4), calcite (CaCO3) and aragonite (CaCO3) (Langmuir and Riese, 1985; Chan and Chung, 1987; Gnanapragasam and Lewis, 1995; Yoshida et al., 2009) and minor and trace minerals such as barite (BaSO4) (e.g., Doerner and Hoskins, 1925; Gordon,

Rateka

precipitation rate of component k in the solid solution phase

Symbols used in the kinetic model for solid solution nucleation x ¼ X RaSO4 solid phase composition J(x) nucleation rate of a solid solution of composition x C(x) pre-exponential factor in the classical nucleation theory B a shape factor in the classical nucleation theory (32 for a cubic nucleus) n a correction factor in the classical nucleation theory for heterogeneous nucleation r(x) interfacial tension of a solid solution of composition x (J m2) Vm(x) molecular volume of a solid solution of composition x, expressed as the volume of 1 mol of solid (m3) X(x) degree of supersaturation of a solid solution of composition x D mean diffusion coefficient for ions in water (109 m2 s1)

1955; Gordon and Rowley, 1957), celestine (SrSO4) (Langmuir and Melchior, 1985), Mn and Fe hydrous oxides (Kronfeld et al., 1991), alunite (KAl3(SO4)2(OH)6) and jarosite (KFe(III)3(OH)6(SO4)2) (Dickson and Herczeg, 1992a). The processes governing the fate of Ra2+ in environments with low ionic strength are relatively well characterized (Porcelli and Swarzenski, 2003) and modeled (Agu¨ero, 2005), whereas the question of Ra2+ in high ionic strength environments is generally not discussed in the literature (Langmuir and Melchior, 1985; Paige et al., 1998; Kudryavskii and Rakhimova, 2007). Although highly saline water is not drinkable, a risk assessment of Ra levels is required in natural saline environments such as saline lakes (Chan and Chung, 1987; Dickson and Herczeg, 1992b) and lagoons (El-Reefy et al., 2006) because Ra levels have a direct impact on its bioaccumulation in such systems. Moreover, Ra is the direct parent of radon, a hazardous radioactive noble gas. Therefore, predicting Ra behavior directly influences the ability to assess radon levels and risk. Concerns regarding the fate of Ra TENORMs in high ionic strength environments in general and evaporitic systems in particular have been expressed in two recent technical IAEA (2003) and EPA (2008) reports. Evaporation ponds used to manage residue solutions can contain high levels of Ra, as is the case in geothermal energy production, oil and gas production, and coal mining (in settling ponds), at brackish water treatment plants, in uranium and other mining (typically when the in situ leaching technique is used) and Niobium industries (again, in settling ponds).

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

The possibility of leakage is a concern with any pond, as is the possibility of it causing groundwater contamination. The precipitation of salts in these ponds may pose potential radiological health concerns. For example, the radioactivity concentration of 226Ra precipitated in ponds of the oil and gas industry has been reported at 10–40 Bq g1 (IAEA, 2003), and liquid waste from the uranium mine industry can have a background level of up to 111 Bq L1 (EPA, 2008). In some of these industries, Ra is co-precipitated with barite by adding BaCl2 solutions. In both contexts, the thermodynamics and kinetics of this reaction have practical economical implications because they determine the volume and radioactivity concentration of these salts as well as the residual radioactivity concentration of the solution. The purpose of this study was to elucidate the fate of Ra in evaporitic systems under high ionic strength conditions. For this purpose, evaporation experiments were performed with Ra containing brine effluents from a desalination plant that treats deep well brackish water via reverse osmosis. Due to the high ionic strength of the brine, its complex composition and its oversaturation, a comprehensive description of the system should include the three following elements: (1) the change in the chemical potential of dissolved Ra2+ with changes in ionic strength (i.e., the Ra2+ activity coefficient); (2) sink(s) of Ra2+ under the simultaneous precipitation of more than one phase; and (3) the possible kinetic effects on co-precipitation. 1.1. Thermodynamic properties of Ra2+ in NaCl brine The Pitzer formalism is regarded as the most accurate approach to describe activity coefficients of aquatic species in solutions with high ionic strength. (Harvie et al., 1984; Simon and Michael, 1991). This semi-empirical formalism uses a set of parameters that are usually derived experimentally and that account for the interactions between each cation–anion pair (b(0), b(1), b(2) and C/), each set of cation– cation or anion–anion pairs (h, and each set of cation– cation–anion or anion–anion–cation triplets (w). These parameters are used to calculate the osmotic coefficient of the solution and the activity coefficients for any individual ion. Additional parameters are introduced when interactions with neutral aqueous species become substantial. By its nature, the most significant limitation to the wider application of this semi-empirical model is the lack of experimental data used to derive these parameters (Weare, 1987). In the case of Ra, the only parameters based on experimental data are those governing the interactions in the RaSO4–H2SO4 system (Paige et al., 1998). In many natural and anthropogenic environments, NaCl is the main electrolyte, and the most significant interaction is with Cl. Rosenberg et al. (2011) have discussed the difficulties that radioactive safety issues pose for the experiments required to evaluate the RaCl2 parameters. It is common to assume that the Pitzer parameters of similar ions, in this case those of Ra2+ and Ba2+, are identical. This assumption will yield equal activity coefficients for both ions in any given solution (i.e., cRa2þ =cBa2þ ¼ 1). One alternative to this procedure has been presented by Rosenberg et al. (2011), who extrapolated the RaCl2 parameters (b(0)Ra–Cl, b(1)Ra–Cl

5405

and C/Ra–Cl by linear regression of other MCl2 binary parameters to their respective 8-fold and 12-fold hydrated ionic radii (M2+ = Mg2+, Ca2+, Sr2+ and Ba2+). Their extrapolated parameters for Ra2+–Cl interaction, together with Paige et al.’s (1998) parameters for Ra2þ –SO2 and 4 Ra2þ –HSO 4 interactions, have been used in the thermodynamic calculations made in the present study. As shown by Rosenberg et al. (2011), as NaCl concentration increases, the cRa2þ =cBa2þ ratio decreases, but the decrease is not substantial. Close to halite saturation, its value is 0.75. As will be discussed below, the experimental results cannot be fully supported if the Pitzer parameters of Ra2+ are set equal to those of Ba2+.

1.2. Distribution model of co-precipitation Co-precipitation reactions are commonly described using a distribution model based on an empirical partition coefficient. In the following discussion, a distinction is made between concentration-based effective partition coefficients (designated K 0D ) and activity-based effective partition coefficients (designated K 00D ). The term ‘effective’ indicates that the value of the partition coefficient is determined empirically. Two possible formulations for the equilibrium partition coefficient, which have a thermodynamic basis, are also discussed below and designated KD,(I) and KD. A complete list of the symbols used in the present study is presented in Nomenclature. Traditionally, the basic form of the distribution model is derived using the concentration-based effective partition coefficient (Doerner and Hoskins, 1925): ðTr=CrÞsurface ¼ K 0D  ð½Tr=½CrÞsolution ;

ð1Þ

where Cr and Tr are the concentrations of carrier and trace elements in the host mineral phase respectively (e.g., the concentrations of Ba and Ra in barite), and [Cr] and [Tr] are their total concentration in solution. The subscript ‘surfac’ refers to the molar fraction of each ion in the outermost layer of the mineral and implies that the reaction occurs between the solution and the host mineral surface rather than the bulk solid (Curti, 1999). Although the effective partition coefficient can be expressed on a weight fraction basis (Beattie et al., 1993), all aqueous and solid Tr/Cr ratios in the present paper are calculated according to molal and molar based ratios respectively. In open systems, if steady state can be assumed (i.e., if ([Tr]/[Cr])solution is constant with time), then a homogenous bulk solid is formed. In closed systems, when the ([Tr]/[Cr])solution ratio changes with time, the composition of each incremental newly formed ‘layer’ depends on the solution [Tr]/[Cr] ratio at that time. For the latter case, Doerner and Hoskins (1925) derived an analytical solution to calculate the partition coefficient using solution quantities alone: K 0D ¼

ln ðTrt =Tr0 Þsolution ; ln ðCrt =Cr0 Þsolution

ð2Þ

where Tri and Cri are the quantities (mol) of the tracer and carriers ions in the solution respectively, and the subscripts t and 0 refer to time = t and initial time respectively.

5406

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

When the total concentrations are significantly different from the activities, then it is advisable to replace Eq. (1) by (Langmuir and Riese, 1985): ðTr=CrÞsurface ¼ K 00D  ðaTrmþ =aCrmþ Þsolution ;

ð3Þ

where K 00D is the activity-based effective partition coefficient, and aCrm+ and aTrm+ are the activities of the carrier and trace elements in solution. Because ion pairs and activity coefficients depend on the composition of the entire solution, an analytical solution, such as that derived using Eq. (2), cannot be used to calculate K 00D . From a thermodynamic perspective, the co-precipitation of a solid phase, (Cr,Tr)a, can also be described as a solid solution reaction (Zhu, 2004a): mþ CraðsolidÞ þ Trmþ ðsolutionÞ $ TraðsolidÞ þ CrðsolutionÞ ;

ð4Þ

where a denotes a counter ion of the solid compound (e.g. SO2 4 in (Ba,Ra)SO4). The equilibrium constant, Keq, for the reaction in Eq. (4) can be calculated from any of the terms in the following equation (Mcintire, 1963; Langmuir and Riese, 1985; Zhu, 2004a): 





K eq ¼ expðDGR =RT Þ ¼

K sp;Cra 

K sp;Tra

¼

X Tra cTra X Cra cCra

,

 mTrmþ cTrmþ  ; mCrmþ cCrmþ ð5Þ

°

where K sp,ka is the solubility product constant of the pure phase end-member ka k = Cr or Tr); DGR is the standard state Gibbs free energy for the solid solution reaction (Eq. (4)); R is the gas constant; T is the temperature in Kelvin; mi, ci and m are the molality, activity coefficient and the charge of the aqueous ions i respectively; and Xka and cka are the mole fraction and rational activity coefficient of component k in the solid solution respectively. Also, the ratio XTra/XCra is identical to the ratio (Tr/Cr)solid. Traditionally, the equilibrium value of the partition coefficient was defined using concentration ratios. This partition coefficient (KD,(I)) is related to the solubility products of the end-members as follows (Mcintire, 1963): !    K sp;Cra c mþ  Cr  cCra =cTra K D;ðIÞ ¼  ;Tra cTrmþ K sp   ðTr=CrÞsurface ¼ ; ð6Þ ðmTrmþ =mCrmþ Þsolution eq where the subscript eq denotes the equilibrium. For a specific host mineral, KD,(I) does not depend on the solid Cr and Tr mole fractions if Raoul’s law (cCra  1) and Henry’s law (cTra is constant) apply. As Ra is typically present in trace amounts (on a mole basis), its partition between the aqueous and solid phases can be regarded as a dilute solid solution for which Raoul’s and Henry’s laws apply. The right term in Eq. (6) implies that if the co-precipitation reaction approaches equilibrium, then KD,(I) can be derived empirically. The establishment of equilibrium in a solid solution reaction is not as easily defined as with pure phases because it depends on the chemical potential of the substituting components in the solution and the solid and on the kinetics of the reaction. Inevitably, Eq. (6) refers

to two types of equilibrium: (1) true equilibrium, which is a bulk thermodynamic condition determined by the middle term in Eq. (6) and (2) partial equilibrium, which is determined by the left term in Eq. (6) and implies an equilibrium between the solution and the incremental growth layer. Equality between these two terms can be achieved if each incremental growth layer is given sufficient time to reach equilibrium with the solution through the growth process. Different experimental techniques have been developed in order to overcome these difficulties (Doerner and Hoskins, 1925; Gordon, 1955; Rimstidt et al., 1998; Curti et al., 2010). Practically, if it can be argued that equilibrium is established and if the solubility products of the end-members are well established, then the rational activity coefficient of the solid (cTra) can be calculated using the derived partition coefficient (Zhu, 2004a; Curti et al., 2010). Eqs. (5) and (6) imply that the distribution of the solutes depends on the activity of their free ions in solution (i.e., aTrm+ and aCrm+) and not on their total concentration. This difference accounts for two important processes: (1) the complexation of ion pairs (e.g., CaSO4,(aq)), and (2) changes in the chemical potential of the free ions relative to that of a dilute solution (i.e., cTrm+ – 1). Notably, the Pitzer approach to calculating activity coefficients usually assumes that the solution is completely dissociated (i.e., no ion pair speciation is determined to account for the interactions between ions) unless a specific ion pair is introduced into the calculations. Practically, it may be argued that ion pairs do form in the solution, but from a thermodynamic point of view, both ion pairs and activity coefficients are accounted for by ion interactions (i.e., ci includes the effect of both processes). Equality between K 0D and KD(I) (i.e., Eqs. (1) and (6)) may be interpreted as indicating that the reaction occurs near equilibrium and that the effects of ionic strength on the carrier and the trace element are insignificant or cancel each other out (i.e., cTrm+/cCrm+  1). Although the traditional formulation of the equilibrium partition coefficient (KD,(I) in Eq. (6)) is thermodynamically valid, its value is not constant and is a function of ionic strength (i.e., it is a conditional partition coefficient dependent on the solid and solution composition). Alternatively, the equilibrium partition coefficient can be expressed in terms of solute activity rather than solute concentration yielding a partition coefficient independent of ionic strength (Curti, 1999): !    K sp;Cra ðTr=CrÞsurface KD ¼  cCra =cTra ¼ : ð7Þ  ;Tra ðaTrmþ =aCrmþ Þsolution eq K sp mþ As long as cmþ Tr =cCr  1 the value of KD,(I) is equal to that of KD and the value of K 0D is equal to that of K 00D . In the present study, we will determine both the concentrationbased and activity-based effective partition coefficients and explore the differences between them. It is important to note that the concentration-based effective partition coefficient (K 0D ) is still important as it indicates the ‘tendency’ of the tracer to precipitate into the host mineral phase (i.e., when K 0D < 1, the tracer is enriched in the solution with respect to the carrier component and vice versa). In many studies, neither ion pairs nor activity coefficients are considered. For example, many reported parti-

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

tion coefficients for radionuclides in calcite conform to Doerner and Hoskins’ (1925) definition (Eq. (1)) and therefore use the total ion concentration, although the ion pairs and activity coefficients cannot be neglected (Curti, 1999 and references therein). As a result, the values of these effective partition coefficients diverge from their equilibrium values (also termed phenomenological and thermodynamic partition coefficients, respectively, by Curti (1999)). In other studies, the effect of the ion pairs was considered, but it was assumed that the ratio between the activity coefficients of divalent cations cTr2+/cCr2+)solution ffi 1 (Mcintire, 1963; Tesoriero and Pankow, 1996; Rimstidt et al., 1998), and therefore, this ratio could be neglected in Eqs. (5), (6), and (3). While this approximation may be valid for relatively dilute solutions, it may not be the case for high ionic strength solutions (Langmuir and Riese, 1985; Rosenberg et al., 2011). Although the activity-based effective partition coefficient (K 00D , Eq. (3)) is thermodynamically more rigorous than the concentration-based effective partition coefficient (K 0D , Eqs. (1) and (2)), K 00D is not necessarily equal to the equilibrium partition coefficient (KD, Eq. (7)) because kinetics may affect the value of K 00D . When the distribution of a trace element between phases is not at equilibrium (i.e., when kinetic effects are a factor), K 0D and K 00D diverge from KD,(I) and KD (Mcintire, 1963; Kushnir, 1980; Tesoriero and Pankow, 1996; Rimstidt et al., 1998; Wang and Xu, 2001; Pina and Putnis, 2002; Prieto, 2009). Different models and explanations for kinetic effects have been suggested in the literature. In crystal growth, the boundary layer effect accounts for differences between the concentration of the bulk solution and that of the solution adjacent to the crystal surface, and K 0D is related

5407

to KD,(I) via the degree of saturation (Mcintire, 1963) or the precipitation rate (Wang and Xu, 2001) of the host mineral phase. Both models predict that K 0D will approach unity when the reaction is far from equilibrium. However, Wang and Xu (2001, and references therein) and Kushnir (1980) have reported different results, indicating that K 0D approaches values other than 1 for different tracers in calcite and gypsum. These results have been explained by kinetics factors other than the boundary layer effect. Pina and Putnis (2002) and Pina et al. (2000) introduced a model describing the kinetic effect on the nucleation of solid solutions from aqueous solutions and used that model to explain experimental results for the (Ba,Sr)SO4, (Ba,Sr)CO3, Ba(SO4,CrO4) and (Cd,Ca)CO3 solid solutions. Pina and Putnis (2002) showed that the composition of the solid solution, for which a maximum nucleation rate can be calculated, does not necessarily coincide with that of the thermodynamically most stable solid solution. The less soluble solid composition will tend to have higher nucleation rates, which will in turn lower the effective partition coefficient. This effect will be stronger when the difference between the end-members’ solubility products is higher. The model developed by Pina and Putnis (2002) is further discussed below, and it has been used in this study to examine kinetic effects. 1.3. Simultaneous co-precipitation with more than one phase Barite is a common host mineral for Ra in brines (Langmuir and Melchior, 1985) and fresh water (Grundl and Cape, 2006). The similar ionic radii of Ra2+ and Ba2+, their electronegativities and electronic configuration and the identical crystallographic structure of pure RaSO4 and

Table 1 Concentration-based effective partition coefficient of Ra with different host minerals reported in the literature. Host mineral

T (°C)

Barite

Barite

Barite Barite Gypsum Gypsum Gypsum Gypsum Celestite Calcite Calcite Calcite Calcite Aragonite Anhydrite

50 70 90 25 20 22 ± 3

25 25 25 25

25 25 25

K 0D range

Comments

Source

1.1 ± 0.1 1.6 ± 0.1 1.8 ± 0.1a 1.43 ± 0.07 1.32 ± 0.01 1.21 1.65b 1.84–2.01 0.12–0.61 0.02 0.01–0.03 0.02–0.36 0.32 ± 0.15 280 0.013 1 0.003–0.053 0.82 0.96 800

Experiments conducted without regard to temperature

1 1 1 2 2 2 2 3 10 4 5 6 7 8 6 4 9 8 8 8

Re-crystallization experiments

K 0D depends on [Ra]/[Ca]solution K 0D depends on [Ra]/[Ca]solution Estimated Estimated Estimated Estimated

based on the partition of Ba in calcite via Gibbs free energy regression via Gibbs free energy regression via Gibbs free energy regression

Sources: (1) Doerner and Hoskins (1925); (2) Gordon and Rowley (1957); (3) Marques (1934); (4) Goldschmidt (1940) in Gnanapragasam and Lewis, 1995); (5) Data from Hahn (1926), calculated by Gnanapragasam and Lewis (1995); (6) Gnanapragasam and Lewis (1995); (7) Yoshida et al. (2009); (8) Langmuir and Riese (1985); (9) Curti (1999); (10) Curti et al. (2010). a Considered by Doerner and Hoskins (1925) as representing the thermodynamic value. b Extrapolated in this study based on the temperature dependence expression for K 0D presented by Gordon and Rowley (1957).

5408

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

barite (Curti, 1999; Zhu, 2004a) make barite an ideal host mineral for Ra. However, as discussed above, other minerals had been suggested as host minerals for Ra co-precipitation. Table 1 summarizes values for the effective partition coefficients reported in different studies of Ra co-precipitation, all of which refer to trace amounts of Ra (i.e., dilute solid solutions). The K 0D values that are reported for barite are usually between 1.1 and 2.0 (Table 1). Doerner and Hoskins (1925) have suggested 1.8 as the thermodynamic value since it was evaluated from very slow precipitation experiments. Marques (1934) has evaluated a similar values (1.84–2.01) for K 0D;barite at 20 °C. A similar value (1.65) at 25 C was also extrapolated in the present study using the temperature dependence expression for K 0D;barite proposed by Gordon and Rowley (1957). The range for K 0D;barite reported recently by Curti et al. (2010) is significantly lower (0.12–0.61) and implies a relative enrichment of Ra2+ in the liquid phase and not in the solid phase. However, this lower range was derived via re-crystallization experiments rather than co-precipitation experiments using supersaturated solutions as in other studies and the present study. Therefore, in this paper, K 0D;barite ¼ 1:8 is considered to be the thermodynamic value for a dilute solid solution of Ra in barite. In natural systems the removal of a tracer may occur via several host minerals simultaneously. In such a case, the differential amount of Tr removed by m host minerals will be equal to: dTrsolid ¼ ½Trtþ  

m X 1

K 0D;j 

dCrj;solid ; ½Crj 

ð8Þ

where (K 0D;j is the concentration-based effective partition coefficient of host mineral j. Eq. (8) demonstrates that the amount of Tr that will be removed by each phase will depend on the partition coefficient and the relative amount of that phase (dCrj,solid/[Cr,j]). If the relative amounts of the major and minor phases that precipitate are approximately the same, then the amount of Tr removed will depend solely on the partition coefficients of these two phases. As discussed below, gypsum is the major phase that was precipitated in this study. When the partition coefficient for Ra in barite reported by Curti et al. (2010) (0.12–0.61, Table 1) is excluded, the partition coefficient for Ra in barite is approximately 4–5 times higher than the maximum value reported for the partition coefficient in gypsum. Nevertheless, because kinetic effects may minimize these differences, the potential for significant removal of Ra with gypsum should not be rejected a priori. 2. METHODS 2.1. Solution Fresh concentrate (i.e., reject brine) samples were collected from the desalination plant at the outlet of the membrane modules. Several samples were diluted immediately after collection and used to estimate whether significant Ra precipitation had taken place during transportation

from the field to the lab. These samples showed that the precipitation of all salts including Ra was insignificant during the first two weeks after the collection of the concentrate. 2.2. Experimental setup Ra2+ co-precipitation was determined under different levels of ionic strength by evaporating the fresh concentrate in batch-type experiments. To have enough fluid and solid for the Ra analyses, we used “single-point batch experiments” (i.e., each batch experiment was used to determine one data point). In each experiment, a weighted amount of concentrate (1 kg) was evaporated in an open beaker immersed in a thermostatic water bath. In total 13 experiments were conducted, each being brought to a different degree of evaporation (DE). Small fans were installed 5 cm above 11 of the beakers to enhance the evaporation, whereas evaporation was not enhanced in the remaining two experiments. Because of the evaporation process, the temperature within the beakers was lower than the temperature of the bath (24.4 ± 0.3 °C as compared to 26 °C). The experiments varied in duration, lasting from 2 to 6 days. At the end of each experiment, the degree of evaporation in each of the beakers was measured using the percent of weight loss and the solution was then immediately filtered through a 0.45 lm membrane. Both the precipitated salts and the residual solution were analyzed for their Ra content and chemical composition as described below. 2.3. Salt samples The salt precipitated in each experiment was initially dried for 24 h (60 °C) and then hand-ground with an agate pestle and mortar to homogenize each of the samples and increase their surface area for the purpose of dissolution and physical examinations. Scanning Electron Microscopy and Energy Dispersive Spectrometry (SEM–EDS) studies were carried out using a CamScan FE44 SEM (Obducat CamScan Ltd., Waterbeach-Cambridge, United Kingdom) equipped with a Noran Pioneer SiLi EDX detector. The SEM–EDS measurements were made at an accelerating voltage of 20 kV and a current of 1 nA. The evaluation was performed using Noran Vantage software for the CamScan FE44 instrument. X-ray Diffraction (XRD) measurements were also performed on selected samples. The powder samples were measured using a Bruker D8 Advance diffractometer equipped with a Cu Ka radiation tube and Ni filters working at a current of 25 mA and a voltage of 40 kV. Diffractograms were recorded from 2° to 100° 2H with steps of 0.01° 2H, 8 s of counting time and variable slit widths. The Raman spectra of exemplary powder samples were measured with a BRUKER Senterra Raman microscope using a depolarized 10 mW laser beam at 532 and 785 nm excitation wavelengths. A portion of the salt from each sample was dissolved in double deionized water (DDW) in volumetric bottles at a ratio of approximately 1 g salt per 1 L of DDW. In experiments in which less than 1 g of salt was precipitated, all of the salt was dissolved in 0.5 L of DDW. To ensure complete

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

dissolution, the samples were stirred with a magnetic stirrer for at least a week. Duplicates of the dissolved salts were taken to estimate the degree of error influencing the dissolution procedure (standard deviation); these figures were less than 3% for Ca, Sr and SO4, and less than 15% for Ba and 226Ra. Chemical and Ra analyses were conducted as described below. It is expected that some secondary salts would be precipitated during the drying of the original sample, which contained some solution. This factor was accounted for via an analysis of the conservative ion concentrations within the brine (e.g., Mg, see Electronic Annex, Ea-1).

5409

prevent adsorption to the vial walls. Extensive dilution (<0.1% TDS) was necessary for the ICP-MS measurements, and blanks were prepared to estimate the quantification limits, which were approximately 0.3 and 0.25 ppb for Sr2+ and Ba2+, respectively. 2.6. Thermodynamic calculations Ion activities and the degrees of saturation were calculated using the geochemical speciation code Phreeqc 2.15 (Parkhurst and Appelo, 1999) and the Pitzer formalism. 3. RESULTS

2.4. Radium analysis The samples used for the 226Ra analysis (both from the solution and from the re-dissolved salt samples) were preconcentrated on 10 g of MnOx acrylic fibers (Scientific Computer Instruments; e.g., Moore, 2008). 226Ra measurements were made using a Radon in-Air Monitor (RAD7, Durrige Company). The MnOx fibers were sealed and incubated for over three weeks and then measured using the alpha counter (RAD7) assuming secular equilibrium between radon progeny (214Po), (218Po), radon (222Rn), and 226Ra (Kim et al., 2001). The radon monitor RAD7 is based on an electrically biased solid state detector for alpha spectrometry for the 222Rn daughters 218Po (6 MeV) and 214 Po (7.7 MeV). Any interference by 212Bi (6.08 MeV, 232 Th chain) with 218Po can be corrected by counting 212 Po (8.78 MeV), the direct daughter of 212Bi. The efficiency of the instrument (7%) was calibrated according to external standards based on known 226Ra radioactivity. The analytical uncertainty (standard deviation) for radioactivity between 12 and 0.06 Bq (1.45 1012– 15 7.25 10 mol) is between 5% and 80%, respectively. 2.5. Chemical analysis The concentration of Ca, Na, K and Mg (both in solution and in re-dissolved salt samples) was measured using Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES) with uncertainty better than ±5% (95% confidence limit), whereas that of HCO 3 was measured using titration (±7%); Cl and Br (±12%) and that of SO2 4 (±6%) using ion chromatography; that of Sr and Ba was determined using ICP-MS (±10%). For the tracer analysis (i.e., for the analysis of Sr and Ba), the samples were acidified with 1% trace select nitric acid (70%, Fluka) to

The molal concentration of 226Ra in the feed water of the desalination plant is much higher than that of the other Ra isotopes, i.e., [226Ra]/[Ratotal] = 99.96% (Peri, 2006). Because the half-life of 226Ra (1600 years) is orders of magnitude longer than that of the other Ra isotopes (<6 years) and because isotopic fractionation is insignificant during desalination, evaporation and co-precipitation, the molal concentration of 226Ra can be regarded as representing the total Ra concentration. Also, because the radioactivity of 220Rn was below the detection limit in the RAD7 for all samples, no corrections were made to account for the interference of 212Bi with 218Po. Table 2 presents the chemical composition of the fresh concentrate and the degree of saturation for the sulfate minerals. Because an antiscalant (PermaTreat – PC-191) was used during the desalination to prevent scaling within the reverse osmosis treatment lines, it is reasonable to assume that the remaining concentrate also contained this trace agent which does not pass through reverse osmosis membranes. The maximum concentration of the antiscalant in the concentrate is 45 ppm, as estimated using the original dosage injected during the desalination process. The experimental data and chemical composition of 226 Ra and Ba in the solution and the solid are given in Table 3. The full chemical composition of the remaining ions in the solution and solid salts for all experiments is presented in Table 4. Three series of evaporation experiments with different evaporation rates were conducted. The experiments in series N (n = 9) and F (n = 2) were wind enhanced, whereas the evaporation in the experiments in series S (n = 2) was not enhanced. Fig. 1 presents the change in the degree of evaporation over time for the three series. The evaporation rate for the S series was the slowest, whereas that of the F series was slightly faster than that of the N series.

Table 2 Chemical composition* and degrees of saturation (X) of fresh concentrate from the desalination plant. Na+ mmol/kg

K+ mmol/kg

Mg2+ mmol/kg

Ca2+ mmol/kg

Sr2+ lmol/kg

Ba2+ lmol/kg

Cl mmol/kg

SO2 mmol=kg 4

375

7.6

39

51

911

2.4

449

58

Br mmol/kg

HCO 3 mmol=kg

226

TDS mg/kg

I (m)

Gypsum X

Celestine X

Barite X

0.31

0.87

1.4E12

33,800

0.71

2.1

4.2

18

*

Ra2+ mol/kg

Concentration figures are per kg of H2O.

5410

Table 3 Experimental data, solution and solid composition of Ra2+ and Ba2+. DE

Elapsed time (h)

I (m)

[Ra] solution (m)

Ra2+solid (mol) re-dissolved salts

Ra2+solid (mol) solution mass balance

[Ba] solution (m)

Ba2+solid (mol)

Ra/Ba solution

Ra2+/Ba2+ solida

Barite X

K 0D;barite (Eq. (2))a

cRa2+/cBa2+ solution

N N N N N N N N N F F S S

50 53 54 60 66 69 70 83 84 76 91 79 81

69 90 95 114 115 142 139 144 146 115 135 263 261

1.51 1.52 1.73 1.78 2.24 2.18 2.19 3.89 4.22 2.72 7.04 3.03 3.44

3.0E12 2.9E12 3.1E12 3.3E12 4.3E12 4.5E12 5.1E12 5.1E12 2.5E12 6.2E12 1.4E13 5.1E12 1.3E12

2.2E-15 1.2E-14 2.6E-15 8.3E-15 1.8E-14 2.6E-14 2.5E-14 4.7E-13 1.0E-12 1.9E-13 1.3E-12 4.9E-13 1.2E-12

-2.5E-14 9.0E-14 5.1E-14 1.4E-13 3.5E-14 9.8E-14 -4.3E-14 6.4E-13 1.0E-12 4.0E-14 1.4E-12 4.5E-13 1.2E-12

5.3E-06 5.6E-06 5.8E-06 6.3E-06 6.9E-06 7.3E-06 8.2E-06 9.5E-06 4.7E-06 8.3E-06 BQLb 8.8E-06 2.3E-06

1.9E-09 7.9E-09 9.0E-09 1.6E-08 1.8E-08 9.1E-08 7.9E-08 9.6E-07 1.7E-06 3.6E-07 2.4E-06 6.9E-07 2.3E-06

5.6E-07 5.1E-07 5.4E-07 5.2E-07 6.2E-07 6.2E-07 6.3E-07 5.3E-07 5.2E-07 7.4E-07 4E-07c 5.8E-07 5.6E-07

1.1E-06 1.6E-06 2.9E-07 5.3E-07 1.0E-06 2.9E-07 3.2E-07 6.7E-07 6.3E-07 5.2E-07 5.6E-07 6.4E-07 5.2E-07

40 42 44 50 55 47 52 46 22 42 1–4c 41 11

2 ± 470 3 ± 160 0.5 ± 37 1 ± 31 2 ± 46 0.5 ± 4 0.6 ± 5 1.2 ± 0.5 1.1 ± 0.2 0.9 ± 1.4 1.0 ± 0.1c 1.0 ± 0.6 1.0 ± 0.1

0.97 0.96 0.96 0.96 0.95 0.94 0.94 0.88 0.87 0.92 0.77 0.91 0.89

Concentration figures are in mol (kg H2O)1. a Calculated using the solution mass balance of Ra2+ above 76% DE, as explained in the text. b BQL: below quantification limit. c Calculated by assuming that [Ba] is close to saturation with respect to barite (i.e., that Xbarite is between 1 and 4).

Table 4 Solution and solid composition of major ions and Sr. Concentration in solution

Amount in the solid

series

DE

Na (m)

K (m)

Mg (m)

Ca (m)

Cl (m)

SO4 (m)

Sr (m)

Gypsum X

Total solids (g)

Ca2+solid (mol)

SO2 4

N N N N N N N F N N F S S

50 53 54 60 66 69 70 76 83 84 91 79 81

7.84E-01 7.93E01 8.59E01 9.55E01 1.23E+00 1.31E+00 1.32E+00 1.82E+00 2.80E+00 3.16E+00 4.86E+00 2.18E+00 2.41E+00

1.50E-02 1.60E02 1.79E02 2.16E02 2.62E02 2.28E02 2.73E02 3.25E02 4.88E02 5.35E02 1.14E01 4.19E02 4.12E02

8.51E-02 8.06E02 9.92E02 9.18E02 1.02E01 1.36E01 1.33E01 1.86E01 2.83E01 3.04E01 6.10E01 2.07E01 2.45E01

1.07E-01 1.06E01 1.27E01 1.27E01 1.47E01 9.64E02 1.06E01 6.22E02 3.52E02 2.95E02 9.02E03 4.28E02 3.17E02

0.95 1.01 1.12 1.09 1.49 1.54 1.53 2.10 3.05 3.27 5.62 2.34 2.77

1.24E-01 1.18E01 1.38E01 1.53E01 1.84E01 1.37E01 1.38E01 1.22E01 1.47E01 1.54E01 2.49E01 1.25E01 1.35E01

2.0E-03 2.1E03 2.2E03 2.4E03 2.7E03 2.3E03 2.4E03 1.9E03 2.3E03 2.1E03 7.6E04 2.1E03 2.1E03

4.4 4.3 5.3 5.6 6.9 3.6 3.9 2.0 1.3 1.1 0.8 1.3 1.1

0.05 0.05 0.04 0.07 0.08 3.1 3.3 6.4 7.3 7.3 12.9 7.0 7.4

6.45E05 5.32E05 4.69E05 9.37E05 9.40E05 1.56E02 1.38E02 3.31E02 3.70E02 3.72E02 4.27E02 4.17E02 3.84E02

6.67E05 4.94E05 3.75E05 5.18E05 7.90E05 1.54E02 1.31E02 3.27E02 3.67E02 3.69E02 4.21E02 3.56E02 3.82E02

Concentrations figures are in mol (kg H2O)1.

solid

(mol)

Sr2+solid (mol) 1.03E06 8.59E07 8.93E07 1.32E06 1.82E06 2.09E04 1.67E04 4.61E04 5.13E04 5.34E04 7.95E04 4.64E04 5.10E04

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

Series

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

5411

-6

Ba solution mass balance (mol)

90

80

70

60

-6

y=x

2 10

2

R =0.97 -6

1.5 10

-6

1 10

-7

5 10

a -7

5 10

The degree of ionic strength increased from 0.7 to 1.5 mol kg1 in the first experiment (50% DE) and continued to increase until it reached a level of 7 mol kg1 in the experiment with the highest DE (91% DE, Table 3). The aqueous concentrations of Mg, K and Br increased conservatively. The concentrations of Na and Cl were also conservative except in the case of the experiment with the highest DE (91% DE). A chemical analysis of the re-dissolved salt from the experiment with the highest DE revealed the Na/Cl mol ratio to be 1, indicating that some halite had precipitated (0.08 mol). Although the fresh concentrate was initially oversaturated with respect to gypsum, celestine and barite, the concentrations of Ca, SO4, Sr, Ba and 226Ra initially increased conservatively. Only above 50% DE did significant precipitation commence. This occurrence is probably due to the presence of the antiscalant in the concentrate. 2+ 2+ The amounts of Ca2+, SO2 and 226Ra2+ 4 , Sr , Ba precipitated during each experiment were measured directly using the re-dissolved solids and calculated based on the mass balance using the measured solution concentrations. Fig. 2a and b presents these two values for Ba2+ and 226 Ra2+, whereas in Electronic Annex Ea-2, the corresponding values for Ca2+, SO2 and Sr2+ are presented. 4 For all ions, the two quantities are highly consistent. Uncertainty, presented as one standard deviation, was calculated using error propagation (i.e., the square root of the sum of the square of the standard errors). Because barite is a sparingly soluble salt, it is possible that it did not completely re-dissolve. The significance of such a scenario for the calculations made in this study is discussed below. For all precipitated ions except 226Ra2+, the degree of error associated with the solution mass balance was greater than that associated with the re-dissolved salts (see the error bars in Fig. 2 and Ea-2). Thus, the latter have been used in the present study. Due to the low radioactivity of the re-dissolved salts, the error associated with 226Ra2+ is relatively

-2 10

-7

-6

4 10

-6

-8

8 10

-6

-8

-6

-6

1 10 1.5 10 2 10 2.5 10 3 10 2+ Ba re-dissolved salts (mol)

-12

1.3 10

y=x -12

2

1 10

R =0.97

-13

6.7 10

-13

-13

1.7 10 -13 1.3 10 -14 8.3 10 -14 4.2 10 0 -14 -4.2 10 0

3.3 10

0

2+

Fig. 1. The change in the degree of evaporation (the percentage of weight loss) over time during the evaporation experiments. The evaporation process in experiments in series N and F was enhanced using small fans, whereas this was not the case for series S.

-7

0

-5 10

300 Ra solution mass balance (mol)

250

226

100 150 200 elapsed time (h)

2 10

-7

0

50

-7

0

50 0

4 10

0

2+

degree of evaporation

2.5 10

N F S

-13

-3.3 10

b 0

-13

4 10 226

Ra

2+

-14

1 10 -13

8 10

-14

2 10

-14

3 10 -12

1.2 10

re-dissolved salts (mol)

Fig. 2. Comparisons between precipitated ions calculated by means of solution mass balance and the measurements of redissolved salts for (a) Ba2+ and (b) 226Ra2+. Since the two values are consistent, the amount of Ra2+ calculated using the mass balance of the solution was considered when the degree of error was smaller than the uncertainty of the re-dissolved salt measurements.

large. When it is larger than the error associated with the solution mass balance, the latter value is used. 2+ 2+ 2+ Changes in the amounts of SO2þ and 4 , Ca , Sr , Ba 226 Ra precipitation as a function of evaporation are shown in Fig. 3. Generally, the pattern of increase in Ca2+ and Sr2+ precipitation is very similar to that of SO2þ 4 and differs from those of Ba2+ and 226Ra. The average Ca2+/SO2 4 mol ratio for all salt samples is 1.1 ± 0.2 (one standard deviation), which strongly suggests that the main sulfate phase precipitated was the CaSO4-type solid. The precipitation of 226Ra2+ occurred concurrent with the precipitation of Ba2+ (Fig. 4a), suggesting that Ba2+ is the main carrier ion with which Ra2+ co-precipitates. Regardless of differences in the evaporation rate, the data from all experiment series fit well with a linear regression that crosses the origin between Ra2+ and Ba2+. The precipitation of Ra2+ (and Ba2+) begins only when half of the initial amounts of Ca2+ and Sr2+ have been precipitated (Fig. 4b and c, respectively). Similarly, significant precipitation of both Ba2+ and Ra2+ commenced when 90% of the Ca2+

5412

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

50

55

60

65

DE 70 75

80

85

90

50

55

60

DE 70 75

65

80

85

90

0.05 N F S

0.04

0.04

Ca (mol)

0.03

2+

2-

(mol)

0.03

4

SO

N F S

0.02

0.02

0.01

0.01

a

b

0

0 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 remaining water (kg)

-4

5 10

-4

3 10

-4

1 10

55

60

65

DE 70 75

80

85

90

50

N F S

2+

7 10

50

Ba (mol)

2+

Sr (mol)

9 10

-4

0 .4 5 0 .4 0.35 0.3 0.25 0.2 0.15 0 .1 0 .0 5 remaining water (kg)

-4

2.55 10

-6

2.05 10

-6

1.55 10

-6

1.05 10

-6

5.5 10

-7

5 10

-8

DE 70 75

80

85

90

N F S

65

DE 70 75

80

85

90

N F S

8 10-13

226

Ra

2+

(mol)

1.2 10-12

60

65

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 remaining water (kg)

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 remaining water (kg)

55

60

d

c

50

55

4 10-13

e -15

1 10

0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 remaining water (kg) 2+ 2+ 2+ 226 Fig. 3. Precipitation vs. remaining water mass (and DE) of (a) SO2þ Ra2+. The solid lines in a, b and d 4 , (b) Ca , (c) Sr , (d) Ba , and (e) are best fit regressions used in the model (Section 4.5) to predict gypsum and barite precipitation (Eqs. (17) and (18), respectively).

had precipitated and the solution was close to saturation with respect to gypsum (see X of gypsum Table 4). The (Ra2+/

Ba2+)solid mole ratio is almost constant, with an average (±one standard deviation) of 7 107 ± 4 107 (Table 3).

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

40

of 226Ra2+ at DE 6 70% (30–80% error, inset in Fig. 4a). If these regions are excluded, the (Ra2+/Ba2+)solid ratio is 5.9 107 ± 0.7 107. The solution ratio, [Ra]/ [Ba]solution, is also constant (5.8 107 ± 0.6 107). The value of Ba for the solution from the experiment with the highest DE (91% DE) is below the quantification limit and is therefore excluded from these calculations. Based on the quantification limit for Ba, its highest concentration occurs at this limit (i.e., 0.25 ppb in the diluted sample for measurement). The lowest Ba concentration occurs in a solution which is at saturation with respect to barite. These calculations yield values for [Ba] in the range of 1.2 107– 4.8 107 mol kg1 and values for Xbarite in the range of 1–4, respectively. Taking these considerations into account, the solution ratio, [Ra]/[Ba]solution, for the experiment with the highest DE is 5 107 ± 3 107, which is consistent with the general trend. The XRD examination of the salt samples from the two experiments with the highest DE (DE of 84% and 91%) mainly indicated the presence of gypsum and halite. Weak reflexes of barite were also present (with 2H values of 28.59°, 29.755° and 68.861°). However, only gypsum and halite crystals were observed in the SEM–EDS studies. The XRD reflexes and Raman spectra of the main mineral are consistent with those of pure gypsum and did not show significant shifts to the patterns for (Ca,Sr)SO4 or other CaSO4-dominated solid solutions.

20

4. DISCUSSION

100 2

R = 0.99

precipitated

226

2+

Ra (%)

y = 0.96x

N F S

80

60 3 2.5

40

2 1.5 1

20

0.5

a

0 0 0.5 1 1.5 2 2.5 3 3.5 4

0 0

20

40 60 80 2+ precipitated Ba (%)

100

120

100 N F S

2+

Ra (%)

80

60

226

precipitated

5413

b

4.1. Possible sinks for Ra

0 0

20

40 60 2+ precipitated Ca (%)

80

100

100 N F S

2+

Ra (%)

80

precipitated

226

60

40

20

C 0 0

20

40 60 2+ precipitated Sr (%)

80

100

Fig. 4. Relative precipitation of 226Ra2+ vs. that of (a) Ba2+; (b) Ca2+ and (c) Sr2+ in the evaporation experiment. Percentages are relative to the initial amount present in the solution. Notice that the concurrent precipitation of Ra2+ with Ba2+ is not a function of the evaporation rate (i.e., the different series).

This relatively large standard deviation is associated with the large degree of error associated with the low radioactivity

The XRD, SEM–EDS, Raman spectroscopy analyses (the CaO/SO3 molar ratio measurements) and the (Ca2+/ SO2 4 solid ratios of the re-dissolved solids (1.1 ± 0.2) demonstrate that the dominant Ca2+ phase is gypsum. The similar trend in the precipitation of Ca2+, Sr2+ and SO2 4 may indicate the existence of a (Ca,Sr)SO4 solid solution, but the Sr content (i.e., (Sr2+/Ca2+)solid  1 102) was too small to be detected with XRD, SEM–EDS or Raman spectroscopy. No evidence of calcite or celestite was found using the XRD or SEM–EDS analyses. The feed water to the desalination plant was acidified to remove bi-carbonate prior to the desalination process. This procedure is reflected in the low alkalinity of the fresh concentrate (Table 1), which prevents significant precipitation of calcite. Even though barite is a trace mineral in this system (with initial Ca/Ba and Sr/Ba ratios of 2 104 and 4 102 in the solution, respectively), weak reflexes of barite were identified in the solids from the two experiments with the highest DE (DE of 84% and 91%). Based on the XRD measurements and the non-concurrent precipitation of Ba2+ with Ca2+ (and Sr2+) during the experiments, we conclude that most (if not all) of the Ba2+ precipitated as a separate barite phase. The relationship between the precipitated 226Ra2+ and Ba2+ (Fig. 4a) is linear, with the line crossing the origin, whereas the precipitation of 226Ra2+ with both Ca2+ and Sr2+ was non-concurrent (Fig. 4 b and c). These trends indicate that barite is the main host mineral phase for Ra2+, whereas the co-precipitation of Ra2+ with Ca2+ in gypsum

5414

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

or Sr2+ was insignificant in this study. Notably, the concurrent precipitation of Ra2+ and Ba2+ occurred even though gypsum precipitation preceded barite precipitation and that relative to Ba2+ 102 more Sr2+ and 104 more gypsum were precipitated by the end of the experiments. The fact that Ra2+ co-precipitation with gypsum is insignificant indicates that the partition coefficient of Ra2+ in gypsum is very low (i.e., lower than 0.1) and probably does not reach the highest reported value of 0.3 (Table 1). 4.2. Evaluation of the concentration-based effective partition coefficient of Ra2+ in barite The concentration-based effective partition coefficient, 0 , was calculated separately for every experiment KD,barite (Table 3) using Eq. (2). When both Ra and Ba precipitation was very low (i.e., when DE 6 70%; see the inset in Fig. 4a), the solute quantities (Eq. (2)) were calculated using the mass balance between the fresh concentrate and the precipitated solids in these stages. This was necessary because the uncertainty associated with the solution concentration was bigger than the amount of either Ra or Ba that precipitated. It should be noted that the calculations for K 0D;barite should not have been significantly affected, even if not all of the barite solids re-dissolved, because these calculations employ the (Ra/Ba)solid ratio and not absolute amounts. The degree of uncertainty regarding K 0D;barite was estimated by calculating K 0D;barite using the maximum and minimum (Rat/Ra0) and (Bat/Ba0) ratios, which were in turn determined using the uncertainty of those quantities. The large degree of uncertainty associated with relatively low DE is a result of the large uncertainty associated with the solute quantities. The data from all of the experiments, except the experiment with the highest DE, were plotted on a Ln–Ln plot according to Eq. (2). The best plot fit yielded K 0D;barite ¼ 1:04 0:01 (Fig. 5). The inset in Fig. 5 includes

-2

0

Ln (Ra /Ra )

-1.5

N F S

y = (1.04 ± 0.01)x 2

t

R =0.99 -1

-5

y = (1.00 ± 0.01)x -4 R2=0.99 -3

-0.5

-2 -1 0

0 0

-0.5

0

-1

-1 Ln (Ba /Ba ) t

-2

-3

-1.5

-4

-5

-6

-2

0

Fig. 5. Ln–Ln plot for the evaluation of the concentration-based effective partition coefficient (Eq. (2)); the slope represents K 0D;barite . The inset includes the experiment with the highest DE, for which [Ba] was assumed to be near equilibrium with respect to barite.

the data for the experiment with the highest DE, assuming that the solution is near equilibrium with respect to barite (1 < Xbarite < 4) as estimated above for the [Ba] concentration in this experiment. Under this assumption, the concentration-based partition coefficient for the experiment with the highest DE falls on the same trend as the remaining experiments. Although Eq. (2) corrects for the changing concentrations in the solution, it does not take into account the decreasing (cRa2þ =cBa2þ solution as a consequence of ionic strength increase due to evaporation (I > 4 m, Table 3). The above effective partition coefficient values are much smaller than the value of 1.8 ± 0.1 derived by Doerner and Hoskins (1925) for relatively dilute Ba2+–Ra2+ chloride solutions. Doerner and Hoskins (1925) conducted three series of co-precipitation experiments that differed in their experimental procedure and yielded different precipitation rates for barite: (1) rapid precipitation, (2) slow precipitation, and (3) very slow precipitation via slow evaporation in which 75% of volume was lost. All experiments were performed in hydrochloric acid ranging from 0.04 to 1.1 N; some of the experiments were conducted in solution at elevated temperatures without a control. The average values of K 0D;barite that Doerner and Hoskins (1925) derived from the three series are 1.1 ± 0.1, 1.6 ± 0.1 and 1.8 ± 0.1, respectively. Doerner and Hoskins (1925) have argued that the last series represents the ‘true’ value of KD,barite because the process used made it possible to almost reach equilibrium (i.e., the kinetic effects are insignificant). Zhu (2004b) has noted that the partition coefficients in some of Doerner and Hoskins (1925) experiments were influenced by aqueous complexation (Fig. 1e in Zhu, 2004b). We have calculated the initial ionic strength range for the three series to be 0.15–0.42 mol kg1, 0.42– 1.17 mol kg1 and 0.69–0.83 mol kg1, respectively. These ranges do not take into account the diluted sulfuric acid that Doerner and Hoskins (1925) added to their experiments as seen from the omission of sulfate concentration in the original publication. Furthermore, we have estimated the ionic strength at the end of the evaporation process in the third series to be between 3 and 3.6 mol kg1. We calculated the ðcRa2þ =cBa2þ Þsolution for Doerner and Hoskins’ experiments using the RaCl2 Pitzer parameters reported by Rosenberg et al. (2011). Despite the relatively high ionic strength (dominated by Cl and H+) found for some of the experiments, the ðcRa2þ =cBa2þ Þsolution is 1 in these experiments. It appears that the partition coefficient was not significantly affected by ionic strength in Doerner and Hoskins’ work (1925). The significant difference between the value of K 0D;barite observed in the present study and the presumably thermodynamic partition coefficient obtained by Doerner and Hoskins (1925) may result from kinetic effects and/or to a lesser extent from the effect of salinity. To evaluate the effect of salinity on the co-precipitation and on the value of K 0D;barite , the activity coefficients of Ra2+ and Ba2+ in the solution are considered below. As indicated by Prieto (2009), kinetic effects on a solid solution precipitating from a supersaturated aqueous solution should also be expected. The possible kinetic effect on the nucleation of (Ra,Ba)SO4 is also evaluated in the discussion below.

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

RateTra ¼ RateCra K 00D  ðaTrtþ =aCrtþ Þsolution :

ð10Þ

The changes in 226Ra2+ and Ba2+ precipitated (mol) over time for series N are given in Fig. 6. The precipitation rates for both cations were calculated as the slope of the corresponding amounts in the solid (mol) vs. time for each 2 consecutive experiments. Barite precipitation commenced far from equilibrium and reached a maximum rate of 4.4 107 (mol h1 kginitial1). The precipitation rates for both 226Ra2+ and Ba2+ (barite) abruptly increased by 2– 3 orders of magnitude above 70% DE (Table 5); because the initial mass of the solution was 1 kg in all experiments, the rates were normalized per kg of initial solution.

-12

-6

2 10 3 10

-14

2 10

-14

1 10

-14

-12

1 10

8 10

-8

-6

1.5 10

-13

-6

6 10

-13

4 10

1 10 0 60

0 100

140

(mol)

2+

-8

2+

Ra (mol)

4 10

-13

Ba

8 10

-7

5 10 -13

2 10

0 60

2+

Ra 2+ Ba

80

Fig. 6. The change in time for series N.

100 120 time (h) 226

140

RateRa Elapsed Ratebarite time (h) (mol h1 kginitial1)a (mol h1 kginitial1)a

N N N N N N N N N

50 53 54 60 66 69 70 83 84

69 90 95 114 115 142 139 144 146

a

0 160

Ra2+ and Ba2+ precipitated (mol) over

2.70E10 2.10E10 3.40E10 1.50E09 2.50E09 5.00E09 3.90E07 4.40E07

4.70E16 2.00E15 3.10E16 6.40E15 3.00E16 3.80E16 2.70E13 2.50E13

Rates are per initial kg of solution.

3 10-13

Rate

ð9Þ

and the co-precipitation rate for Tr depends on the precipitation rate of the host mineral:

1.2 10

DE

Ra

ðTr=CrÞsurface ¼ ðdðTrÞ=dtÞsolid =ðdðCrÞ=dtÞsolid   mþ ¼ K 00D  amþ Tr =aCr solution ;

Series

y=(1.3±0.02)x

2.5 10-13 2 10-13

-1

To calculate the concentration-based effective partition coefficient, Eq. (2) was used to take into account the changing (Ra/Ba)surface of each new crystal ‘layer’ due to changes in the concentrations of the carrier and the trace element as the reaction progressed. To calculate the activity-based effective partition coefficient, changes in the concentrations of the major elements (due to evaporation and crystal growth) must be accounted for because these changes affect the activity coefficients. Because the analytical relationship presented in Eq. (2) is not appropriate for use with activity, it is necessary to model co-precipitation using small steps. Such a model will be presented below. First, however, a crude estimation of the partition coefficient will be made under the assumption that the ratio between the activity coefficients of each two consecutive experiments is constant. The Tr/Cr ratio on the surface of the solid can be calculated using the ratio between the respective precipitation rates, RateTra = d(Tr)/dt and RateCra = d(Cr)/dt. Rewriting Eq. (3) in terms of these rates yields:

Table 5 Precipitation rates for barite and Ra2+ in series N.

(mol h kginitial-1)

4.3. Initial approximation of activity-based effective partition coefficient of Ra2+ in Barite

5415

1.5 10-13

8 10-15

1 10-13

4 10-15 0

5 10-14

-4 10-15 1 10-15

0

0 0

Rate

-14

5 10

*(a

barite

1 10

/a

Ra+2

-13

-13

1.5 10

2 10-15

2 10 -1

-13

) (mol h kg

Ba+2

3 10-15

2.5 10-13 -1

initial

)

Fig. 7. 226Ra2+ precipitation rate vs. the product of Ba2+ precipitation rate and the activity ratio in the evaporation experiments (N series). Precipitation rates were calculated as the slope of moles precipitated over time for each 2 consecutive experiments; the rates are normalized per kg of initial solution (1 kg). The slope of the regression is equal to K 00D;barite according to Eq. (10).

In Fig. 7 the 226Ra2+ precipitation rate is plotted against the product of Ba2+ precipitation rate and the average activity ratio, ðaRa2þ =aBa2þ Þsolution . Error bars were calculated using the uncertainty associated with the precipitation amount (i.e., the error bars in Fig. 6); the x axis error bars also include the uncertainty associated with the activity ratio taken as the standard deviation of this ratio for each 2 consecutive points. Because the Ba2+ precipitation rate increased by a few order of magnitudes, K 00D is not expected to remain constant due to kinetic effects. However, to generate a crude estimation, the data were fitted using a linear regression with a slope of 1.3 ± 0.02. Assuming Ra2+–Ba2+ co-precipitation as the main process responsible for Ra removal, this slope represents the average value of K 00D;barite (Eq. (10)) during the evaporation process. Although the data points in Fig. 7 are not well distributed along the linear regression (i.e., the regression is poor and not statistically significant), the calculated average K 00D;barite value will be confirmed in the discussion that follows. The difference between the average value of K 00D;barite (1.3 ± 0.02, Fig 7) and that of K 0D;barite (1.04 ± 0.01, Fig 5) is attributed to the ionic strength effect.

5416

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

4.4. Kinetic effect on (Ra,Ba)SO4 nucleation To demonstrate a possible kinetic effect on the co-precipitation reaction, it is useful to plot the experimental results on a Roozeboom diagram (see for example Prieto, 2009). In this diagram, the solid mole fraction, X RaSO4 , is plotted against the solution activity fraction X ðRa;aqÞ ¼ aRa2þ =ðaRa2þ þ aBa2þ Þ (Fig. 8). In equilibrium, X RaSO4 can be derived according to (Prieto, 2009): 

X RaSO4 ;eq ¼

K sp;BaSO4 cBaSO4 X Ra;aq 





ðK sp;BaSO4 cBaSO4  K sp;RaSO4 cBaSO4 ÞX Ra;aq þ K sp;RaSO4 cRaSO4

:

ð11Þ

1 10

-6

8 10

-7

6 10

-7

4 10

-7

2 10

-7

4 3

5

4

X(RaSO ,solid)

In a non-ideal solid solution, the solid activity coefficients, cRaSO4 and cBaSO4 , are themselves a function of the composition of the solid phase, and Eq. (11) cannot be resolved. In the case of (Ra,Ba)SO4, the solid solution is considered non-ideal for which the solid activity coefficients can be described as a function of the solid composition using a regular model (Curti et al., 2010; Zhu, 2004a). In a regular model, lnðcBaSO4 Þ ¼ a0 ðX RaSO4 Þ2 and lnðcRaSO4 Þ ¼ a0 ðX BaSO4 Þ2 where a0 is a Redlich–Kistler dimensionless interaction parameter (see for example Curti et al. (2010)). Because (Ra,Ba)SO4 represents a very diluted solid solution, it follows that cBaSO4  1 and cRaSO4  constant (i.e., Raoul’s and Henry’s laws apply). Therefore, cBaSO4 was taken as unity, and cRaSO4 was taken as constant. Using  log K sp;RaSO4 ¼ 10:26 (Langmuir and Riese, 1985; Paige et al., 1998) and log K sp;BaSO4 ¼ 9:98 (Blount, 1977), cRaSO4 was determined to be 1.1 according to Eq. (7) assuming KD,barite = 1.8 (Doerner and Hoskins, 1925). Note that

6, Ω=4

6, Ω=1

2 1

0 0

2 10

-7

-7

4 10 6 10 X(Ra,aq)

-7

8 10

-7

1 10

-6

Fig. 8. Roozeboom diagram for a diluted (Ra,Ba)SO4 solid solution. The solid line corresponds with the equilibrium values of X RaSO4 calculated using Eq. (11). The dashed line corresponds to the case in which KD,barite = 1. Circles represent experimental data. Numbers represent the reaction path which indicates a movement toward equilibrium with respect to the (Ra,Ba)SO4 solid solution reaction. The rectangle represents uncertainties in [Ba] concentration for the experiment with the highest DE, as discussed in the result section. The error bar for point #1 is not plotted because it is larger than the axis length.

Zhu (2004a) used Eq. (7) to calculate the value  cRaSO4 ¼ 1:5, however using log K sp;RaSO4 of 10.38 (see Eq. (17) and Table 1 in Zhu (2004a)) and not 10.26. In their re-crystallization experiments, Curti et al. (2010) derived a higher value of approximately 4.5 for cRaSO4 (corresponding to a Redlich–Kistler parameter of approximately 1.5). However, such a large value of cRaSO4 implies that Ra2+ would not be relatively enriched in the solid phase (i.e., K 0D < 1). All other studies of (Ra,Ba)SO4 co-precipitation (see Table 1), including the present study, suggest that this is not the case. Fig. 8 shows the Roozeboom diagram for the dilute (Ra,Ba)SO4 solid solution ðX RaSO4 < 106 Þ. The solid line represents the equilibrium values of X RaSO4 calculated by Eq. (11). The dashed line corresponds to the case in which K 00D;barite ¼ 1, which is often regarded as a limiting case for a kinetic effect because it represents a solid solution with the same stoichiometric proportions as in the aqueous phase. The numbered circles are the experimental data, and the numbers increase with the reaction path. To derive the experimental data, ðX RaSO4 Þsolid (precipitated from the solution with the composition X(Ra,aq) at data point ‘n’) was approximated by: X RaSO4 ;n ¼

ðRasolid;n  Rasolid;n1 Þ : ðRasolid;n  Rasolid;n1 Þ þ ðBasolid;n  Basolid;n1 Þ ð12Þ

Only experiments in which a significant amount of Ra2+ (and Ba2+) was precipitated were plotted (i.e., those in which DE P 70%). The general trend (as indicated by the dotted arrows) suggests that the reaction begins far from equilibrium and moves towards equilibrium as it progresses. Because of the uncertainty regarding [Ba] in the experiment with the highest DE, the last X(Ra,aq) (point 6) can be plotted anywhere along the x axis, and the reaction path is not clear, as is shown by the open rectangle. The data also suggest that at the beginning of the reaction, the preferential distribution of Ra2+ is not limited to K 00D;barite ¼ 1 (i.e., points 1 and 2 plot below the dashed line). Because Ra2+ was present in the solution in trace amounts, it may be assumed that at the time of nucleation, the frequency of arrival of Ra2+ ions at the surface of barite nuclei are the kinetic controlling parameter. To quantitatively account for the kinetic effect, the model introduced by Pina et al. (2000) and Pina and Putnis (2002) is utilized below. This model accounts for the influence of a kinetic effect on the nucleation of a solid solution from an aqueous solution based on classical nucleation theory (see for example Sohnel, 1982; He et al., 1995). The model has been used in this study to examine the nucleation of (Ra,Ba)SO4, which we assumed to be the rate determining precipitation mechanism in the experiments. Regardless, one cannot rule out the possibility that crystal growth of (Ra,Ba)SO4 is also significant. However, the high supersaturation of the solution with respect to barite, the lack of barite surface area, and the abundant amount of gypsum surface area during Ba2+ (and Ra2+) precipitation suggests that (Ra,Ba)SO4 nucleation (homogeneous or heterogeneous on gypsum surface) is the dominant precipitation mechanism. Moreover, as noted above, barite

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

The pre-exponential factor, C(x), depends on the molecular volume (Pina et al., 2000):

nucleation was noticeable in the experiments with a DE greater than 50%, approximately 70 h after the experiments began, when Xbarite > 40 and I > 1.5 m (Table 3). He et al. (1995) studied the homogeneous nucleation kinetics of barite and showed that in 1 mol kgH2O1 of NaCl and Xbarite of 25 and 56, the induction times were 0.6 and 0.09 h, respectively; additionally, the nucleation kinetics increased with NaCl concentration. In the presence of 10 ppm of a phosphonate inhibitor, He et al. (1994) showed that the induction time for homogeneous barite nucleation increased by 3 orders of magnitude at 25°C. Based on these findings, from a kinetic point of view it would seem that the nucleation of a sparingly soluble mineral, such as barite, is possible in the present study. According to classical nucleation theory, the nucleation rate of a pure solid phase depends on solid interfacial tension, molecular volume and on the degree of aqueous saturation. For solid solutions, all of these parameters are a function of solid phase composition. The nucleation rate is thus also a function of solid phase composition as expressed by (Pina and Putnis, 2002): " # Bnr3 ðxÞV 2m ðxÞ J ðxÞ ¼ CðxÞ exp ; ð13Þ ðkT Þ3 ðln XðxÞÞ2

CðxÞ ¼

  ðmRa2þ  cRa2þ Þx  ðmBa2þ  cBa2þ Þð1xÞ mSO2  cSO2 4

D V 5=3 m;ðxÞ

ð15Þ

;

where D  109 m2 s1 is the mean diffusion coefficient for the ions in water. The interfacial tension of the endmembers was calculated according to the approximation by Sohnel (1982): ri = 34.8–17.8 log C0,i where C0,i is the solubility of each end-member (C0,i = K°sp,i1/2). Because this approximation is based on B = 32 (Sohnel, 1982), the same cubic shape factor is considered in the present study. The values of the molecular volume, Vm(x), and interfacial tension, r(x), were approximated to vary linearly with the composition of the solid solution between the end-member values. That is, ZðxÞ ¼ Z RaSO4  x þ Z BaSO4  ð1  xÞ, where Z(x) is either Vm(x) or r(x). Table 6 summarizes all the parameters used to calculate X(x) and J(x). The functions X(x) and J(x) were calculated for each of the experiments. For the experiment with the highest DE (DE = 91%) the functions were calculated twice: for Xbarite values of 4 and slightly above 1. These functions were not calculated for the whole solid composition range for each experiment. Because the study of (Ra,Ba)SO4 deals with a dilute solid solution, X RaSO4 was varied between 5108 and 1.4106 to match the range for K 00D of 0.1 to 2.4. This range for K 00D is consistent with the reported partition coefficient for the (Ra,Ba)SO4 solid solution (see Table 1). A close inspection of Eqs. (13) and (14) reveals that in the above range for X RaSO4 neither X(x) nor J(x) should change much. Additionally, their values should be similar to the values of the pure barite end-member. Fig. 9 demonstrates the calculations for one representative experiment (DE = 66%); the relative value of both functions is presented. Indeed, the variation in X RaSO4 leads to very small changes in X(x) and J(x). However, the maximum supersaturation value, X(x)max, corresponds to a solid solution composition xmax, which is in thermodynamic equilibrium with respect to a saturated aqueous solution with the same aqueous activity composition as the current supersaturated solution (Prieto, 2009). Essentially, if a solid solution with composition xmax is crystallized from the supersaturated solution, the activity-based effective partition coefficient will equal the thermodynamic partition coefficient (i.e., K00D = KD as in Eq. (7)). On the other hand, the maximum nucleation rate, J(x)max, corresponds to the solid solution composition that is most likely to precipitate from a kinetic point of view. Despite the small variations in X(x) and J(x), their maximum values correspond to different solid solution

where x ¼ X RaSO4 represents the solid phase composition, C(x) is a pre-exponential factor, B is a shape factor with a value of 32 for a cubic nucleus (see below), n is a correction factor for heterogeneous nucleation (0 < n < 1, for barite n = 0.12, (He et al., 1995)), r(x) is the interfacial tension of the solid solution (J m2), Vm(x) is the molecular volume expressed as the volume of 1 mol of solid (m3) and X(x) is the degree of supersaturation of the solid. In the case of (Rax,Ba(1x))SO4, the supersaturation function X(x) is as follows (Prieto et al., 1993): XðxÞ ¼

5417

4

ðK sp;RaSO4  cRaSO4  X RaSO4 Þx  ðK sp;barite  cBaSO4  X BaSO4 Þð1xÞ ð14Þ

It should be noted that this supersaturation function does not represent a strict thermodynamic supersaturation of a given aqueous solution to all solid solution compositions; rather, it represents “stoichiometric” supersaturation, in which the solid solution behaves like a pure solid that dissolves or grows congruently (see Prieto, 2009). Despite this limitation, X(x) has been demonstrated to have practical applications and to be particularly useful in nucleation experiments (e.g., Pina et al., 2000; Pina and Putnis, 2002). Table 6 Parameters used to calculate the functions X(x), C(x) and J(x). End-member BaSO4 (barite) RaSO4



log K sp a

9.98 10.26b

r (J m2)

Vm (m3) c

8.60E29 9.28E29d

e

0.124 0.126e

c solid f

1 1.1g

n 0.12

h

B

D (m2 s1)

16p/3

1.00E09i

The solubility constants are derived from the following sources: (a) Blount (1977) and (b) Langmuir and Riese (1985); molecular volume taken from: (c) Pina and Putnis (2002) and (d) Curti et al. (2010); (e) interfacial tension estimated for both end-members according to Sohnel (1982); activity coefficients assigned as: (f) 1 for BaSO4, assuming Raoul’s law and (g) according to Eq. (7) for RaSO4 and assuming that KD = 1.8 (Doerner and Hoskins, 1925); (h) the correction factor for heterogeneous nucleation according to He et al. (1995); and (i) mean diffusion coefficient for ions in water according to Pina and Putnis (2002).

5418

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

compositions, which are reflected in significantly different partition coefficients (vertical dotted lines, Fig. 9). The difference between K 00D as predicted by X(x)max and J(x)max represents a kinetic effect provoked by the higher nucleation rate associated with the more soluble solid solution composition (i.e., the one with less RaSO4) (Pina and Putnis, 2002). This difference is presented for all experiments in Fig. 10. Ω(x) J(x)

Relative value of Ω(x) and J(x)

1 0.9999998 0.9999996 0.9999994 0.9999992 0.999999 0.1

0.5

0.9

1.3 1.7 K''D,barite

2.1

2.5

Fig. 9. Relative values of the degree of supersaturation, X(x), and nucleation rate, J(x), of the (RaxBa(1x))SO4 solid solution as a function of the partition coefficient which represents the solid solution composition, X RaSO4 . Results are for one representative experiment (DE = 66%). The maximum supersaturation value, X(x)max, represents a solid solution composition which is in thermodynamic equilibrium with respect to the aqueous solution composition. The maximum nucleation rate, J(x)max, represents a solid solution that is kinetically likely to precipitate. The difference between the partition coefficients of the two maxima corresponds to the kinetic effect on the co-precipitation reaction.

Fig. 10 shows how the difference between K 00D as predicted by X(x)max and J(x)max changes with increases in X(x)max (i.e., with increases in barite supersaturation). The closed symbols represent theoretical calculations with solutions within the range of the experimental supersaturation data, whereas the open symbols represent the calculation of theoretical solutions beyond the experimental data but with similar solution-activity fractions (X(Ra,aq)). The model predicts that the kinetic effect will diminish as the saturation state approaches 1 (i.e., as the reaction approaches equilibrium, as shown in Fig. 8). Moreover, according to this model, the kinetic partition coefficient is not limited to 1, although within the range of the experimental data, the predicted K 00D value is >1. Fig. 10 presents how the activity-based partition coefficient changes through the reaction. Most of the Ra2+ (85%) was precipitated in the range 1:15 < K 00D;barite < 1:33, as illustrated in Fig. 11. This range was calculated based on theoretical considerations and demonstrates the gradual kinetic effect of solid solution nucleation on the partition coefficient. Nevertheless, this gradual effect is reasonably consistent with the activity-based partition coefficient K 00D;barite ¼ 1:3 0:02, which was calculated using Eq. (10), based on the experimental data, and indicates the average kinetic effect. Because the nucleation rate is mainly determined based on the degree of supersaturation, it is now possible to quantitatively describe the change in K 00D as a function of the degree of supersaturation in the evaporation experiments (as indicated by the dashed line in Fig. 10): K 00D ¼ 1:71  0:346  logðXðxÞmax Þ  1:71  0:346  logðXbarite Þ

ð16Þ

100 1.8

Ω

=

2

(%)

=

2+

barite

1.02

Ω

1.2

barite

precipitated Ra

K''D,barite

barite

1.02

y = 1.71 - 0.346log(x) R = 0.99 Ω

1.4

Ω

=

4

80 1.6

barite

=4

60

40

1 20

K'' of Ω(x)

0.8

D

max

K'' of J(x) D

0 1.1

max

0.6 1

10

Ω(x)

100

1000

max

K 00D

Fig. 10. Difference between as predicted by X(x)max and J(x)max as a function of X(x)max. The closed symbols were calculated from experimental data, whereas the open symbols represent calculations of theoretical solutions with a solution-activity fraction, X(Ra,aq), similar to the experiments. Note that according to this model, the kinetic K 00D is not limited to 1.

1.2

1.3

1.4 K''

D,barite

1.5

1.6

1.7

1.8

of J(x)

max

Fig. 11. The relative amounts of precipitated Ra2+ vs. K 00D;barite as predicted by the kinetic effect for (Ra,Ba)SO4 nucleation. Most of the Ra2+ precipitated when the activity-based partition coefficient was in the range 1:15 < K 00D;barite < 1:33. This range is consistent with K 00D;barite , which was calculated in Fig. 7 for the same amount of precipitated Ra2+. The Xbarite of the two last points indicates the uncertainty regarding [Ba] for the experiment with the highest DE.

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

The simplification on the right hand side of Eq. (16) is an appropriate approximation for the case of a very dilute solid solution. The evaporation rates exhibited in the experiments were not examined systematically. However, it can be assumed that an increase in the evaporation rate will lead to an increase in Xbarite as nucleation commences. Therefore, as suggested by the empirical Eq. (16), the kinetic effect on the co-precipitation of Ra will increase (i.e., a further decrease in K 00D will occur). It is important to note that the outcome of Eq. (16) will barely change if J(x)max is calculated under the assumption that cRa2þ ¼ cBa2þ . This is because the solid solution is very dilute and because the value of J(x)max in each experiment is mainly determined according to the concentration of Ba2+. Therefore, the same kinetic effect can be used to examine the assumption cRa2þ ¼ cBa2þ in a numerical model, as discussed below. 4.5. Forward model of Ra–Ba co-precipitation To numerically model the co-precipitation of Ra2+ in the experiment, it was necessary to follow the precipitation of all solutes. Gypsum and barite precipitation were not greatly affected by differences in the evaporation rates for the N and F series. That is, the changes in amounts of (1) Ca2+ and SO2 4 and (2) Ba2+ precipitated with DE in the two series follow the same trend, as indicated in Fig. 3a, b and d. Therefore, the 2+ model was based on the changes in Ca2+, SO2 in 4 and Ba both series N and F. Based on the observed changes in the 2+ amounts of SO2 and Ba2+ in the solid with evapora4 , Ca tion, the following empirical equations were derived: Y gypsum ¼ 4915  ðmwater Þ3 þ 1951  ðmwater Þ2  305  ðmwater Þ þ 54; 2

R2 ¼ 0:9875

Y barite ¼ 34  ðmwater Þ  22  ðmwater Þ þ 3:7;

ð17Þ 2

R ¼ 0:944

ð18Þ where Ygypsum and Ybarite are the amount precipitated (mol) and mwater is the remaining amount of water (kg). The solid lines in Fig. 3a, b and d correspond to Eqs. (17) and (18), respectively, once the precipitation of each of these minerals initiated. Since the mass balance between the solid and the solution is good (Fig. 2a), Eq. (18) will not change even if some of the barite from the solid samples was not re-dissolved due to its slow kinetics. A forward model representing the co-precipitation of Ra2+ and Ba2+ in the evaporation experiment was simulated using the Phreeqc computer program. The model follows the changes in the concentration of the dissolved ions with evaporation and precipitation. The concentrations of Mg2+ and K+ increased conservatively in the model as water was evaporated, and Na+ and Cl increased conservatively as long as the solution remained undersaturated with respect to halite. Thereafter, halite was kept at saturation. For Ca2+, SO2 4 and Ba2+, the model followed the precipitation of gypsum and barite as represented by Eqs. (17) and (18) and the increases in their concentration due to evaporation. In the model, an initial solution is evaporated in small increments (i.e., dmwater). The size of the increments was lowered until model results converged to ±0.02% of each other and Ra2+ precipitation was predicted using the distri-

5419

bution model. The initial solution represents a concentrate that was already 54% evaporated, but it is still a conservative solution (i.e., no significant amounts of either Ca2+, 2+ Ba2+, SO2 have been precipitated). 4 or Ra The differential amount of Ra2+ precipitated in the model was calculated according to Eq. (3): dRasolid ¼ K 00D;barite  dBasolid  ðaRa2þ =aBa2þ Þsolution

ð19Þ

with K 00D;barite calculated according to Eq. (16). The only assumption regarding Ra2+–Ba2+ co-precipitation that was made was that full equilibrium distribution among the entire solid phase is a slow process that does not affect the equilibrium between the surface of the solid and the solution. 4.6. Model results and discussion Because forward models are affected by analytical uncertainty associated with initial conditions, the initial concentration of all solutes was based on the average fresh concentrate and the figures for the 3 first experiments (i.e., the experiments for which the solute figures were relatively conservative). Table 7 presents these averages calculated along with their relative standard deviations. The model script was initially examined to predict the change in the concentration of the conservative ions (Mg2+) and Cl (Fig. 12); the two dashed lines form the uncertainty envelope representing 5% error with regard to the initial concentration input. The correct modeling of the major ions is crucial because the model is also intended for use in examining the assumption that cRa2þ =cBa2þ versus the Pitzer parameters for RaCl2 proposed by Rosenberg et al. (2011). The calculated values for cRa2þ were mainly determined by the concentrations of the major components (i.e., Cl and SO2 4 ). Fig. 13 shows the model results for the amount of Ra2+ precipitated against the amount of barite precipitated, which represents the progress of the co-precipitation reaction. The dashed lines represent an uncertainty envelope of 8% (two standard deviations) for the initial Ra2+ concentration, and the model is very consistent with the experimental results. The Ra2+ activity coefficient, cRa2þ , was calculated in the model according to the Pitzer parameters for RaCl2 proposed by Rosenberg et al. (2011). Most of the Ra2+ (>75%) was precipitated when the ratio cRa2þ =cBa2þ was not very different from 1 (cRa2þ =cBa2þ > 0:87, see Table 3). Therefore, a forward model under the assumption that cRa2þ =cBa2þ ¼ 1 will yield results within the uncertainty envelope in Fig. 13; i.e., the numerical model will not be significantly different. However, even small differences in the amount of precipitated Ra2+ (due to differences in cRa2þ ) may result in significantly different values of K 0D;barite . To illustrate this, Fig. 14 presents the model results on a Ln–Ln plot. The model was run with (a) the assumption that cRa2þ =cBa2þ ¼ 1 (dashed line) and (b) with the Pitzer parameters for RaCl2 proposed by Rosenberg et al. (2011) (solid line). The difference between these model runs is attributed solely to the calculations of cRa2þ (i.e., the effect of ionic strength, which is not

5420

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

Table 7 Chemical composition (mol kg1H2O) of the initial solution in the forward model. Averagea Std. dev. (%) a

Na+

K+

Mg2+

Ca2+

Cl

SO2 4

Ba2+

Ra2+

0.85 2

0.017 4

0.092 7

0.118 6

1.061 4

0.133 5

5.76E6 2

3.15E12 4

Average of fresh concentrate figures and 3 first experiments, for which the solute figures are conservative.

55

60

65

70

DE 75

-12

80

85

Ra (mol)

0.7

precipitated

0.5 0.4

2+

(m)

-12

1 10

226

2+

0.6

Mg

1.5 10

90

0.3

-14

4 10

-13

5 10

2 10-14

0.2

0

0.1 0 0.4

55

0.35

60

0.3 0.25 0 .2 0 .1 5 water remaining (kg)

65

70

DE 75

80

0.1

85

0.05

90

7

-6

8 10-8

-6

1 10 1.5 10 2 10 2+ precipitated Ba (mol)

1.2 10-7

-6

2.5 10

-2.5

5 -

5 10

-6

Fig. 13. The amount of Ra2+ precipitated as a function of the reaction progress (i.e., the amount of precipitated Ba2+). Closed circles represent the experimental results, and lines represent the model results. Dashed lines delineate the uncertainty envelopes representing ±8% error (2 standard deviations) for the initial concentration of Ra2+.

6

Cl (m)

-7

0

a

4 10-8

0

0

4

-2

0

Ln (Ra /Ra )

Ra2+

γ

Ra2+

/γ

<1

/γ

=1

Ba2+

Ba2+

Reaction progress, Ionic strength increase.

3

-1.5

t

2

γ

1

b

-8

-1

-6

0 0.4

0.35

0.3 0.25 0.2 0.15 remaining water (kg)

0.1

0.05

Fig. 12. Experimental observations (symbols, series N and F) and model results (solid lines) for (a) Mg2+ and (b) Cl as a function of remaining water and DE. Dashed lines designate uncertainty envelopes representing ±5% error in the initial concentrations.

-4

-0.5 -2 0

0 0

-0.5

t

considered when assuming cRa2þ =cBa2þ ¼ 1). This difference increases as the reaction progresses: the level of ionic strength increases due to the evaporation, and consequently, the cRa2þ =cBa2þ ratio decreases. Although the kinetic effect decreases as the reaction progresses (i.e., K 00D;barite increases; see Fig. 10), the ionic strength effect increases, and therefore, K 0D;barite increases very little. Although the precipitation of Ra in this particular case study can be described quantitatively fairly well using the

0

-2

-1 -1.5 Ln (Ba /Ba )

-4

-2

-6

-2.5

0

Fig. 14. Ln–Ln plot showing the results of a numerical model (lines) and experimental results (closed circles). The model was run with the assumption that cRa2þ =cBa2þ ¼ 1 (dashed line) and using the Pitzer parameters of RaCl2 proposed by Rosenberg et al. (2011) (solid line). The increasing difference between the models is attributed to the increase in ionic strength due to evaporation, which lowers the ratio cRa2þ =cBa2þ . The inset includes the experiment with the highest DE, for which [Ba] concentration was below the quantification limit and was therefore estimated.

Radium co-precipitation in high ionic strength systems: 2. Kinetic and ionic strength effects

assumption cRa2þ =cBa2þ ¼ 1, the differences in the two model calculations for K 0D;barite presented in Fig. 14 may become significant in other scenarios that involve very high ionic strength. 5. SUMMARY The present study has addressed co-precipitation of Ra2+ in a multiple-component, high ionic strength and supersaturated system with respect to gypsum, celestine and barite. The main findings of this study are as follows: (1) Although barite precipitation is quantitatively minor compared to that of gypsum (barite/gypsum  104), its role in determining the removal of Ra2+ is immensely significant. These findings are supported by the high partition coefficient of Ra2+ in barite relative to that in gypsum, as shown by the majority of previous studies (see Table 1). (2) The concentration-based partition coefficient in this study is K 0D;barite ¼ 1:04 0:01. This relatively low value of K 0D;barite is mainly a function of the kinetic effect but is influenced to some degree by a minor ionic strength effect. (3) The ionic strength effect was initially estimated by calculating the activity-based partition coefficient according to RateRa ¼ RateBa K 00D;barite  ðaRa2þ =aBa2þ Þsolution . This estimation yielded K 00D;barite ¼ 1:3 0:02. The difference between K 00D;barite and K 0D;barite can be attributed to the ionic strength effect. (4) The kinetic effect on the nucleation of (Ra,Ba)SO4 was quantitatively studied according to the model proposed by Pina and Putnis (2002). In this case, the kinetic effect was caused by the favorable nucleation of a more soluble phase (i.e., more BaSO4), which lowered the value of the thermodynamic partition coefficient KD,barite. The values of K 00D;barite determined theoretically using the kinetic model and empirically via experiments are consistent with each other. To the best of our knowledge, this is the first study that has quantified the kinetic effect on Ra2+ co-precipitation in barite. (5) Finally, the assumption that cRa2þ =cBa2þ ¼ 1 was reexamined using a numerical model. It emerged that the co-precipitation of Ra2+ in the present experiments could be reasonably modeled based on this assumption. However, as the level of ionic strength increases, it becomes impossible to use this assumption to accurately predict the change in K 0D;barite as evidenced by the experiments. Depending on the scenario and the conditions under which Ra2+ is co-precipitated, this difference may yield significantly different estimations of the amount of Ra2+ removed by co-precipitation with barite. ACKNOWLEDGEMENTS We greatly appreciate the assistance of Carlos M. Pina. We would also like to thank Dieter Schild for carrying out the Raman

5421

spectroscopy measurements and Eva Soballa for technical assistance during the SEM-EDS analyses. We gratefully acknowledge Robert H. Byrne for serving as associate editor. The discussions and thorough review of Manuel Prieto as well as the reviews of additional two anonymous reviewers are deeply appreciated. The English editing for this manuscript by the American Journal Experts is greatly appreciated. This study was supported by The Israel Science Foundation (Grant #511/09) and by the US Agency for International Development, the Bureau for Global Programs, Field Support and Research, and the Center for Economic Growth and Agriculture Development’s Middle East Regional Cooperation program (MERC Project M25-060). Y.O. Rosenberg is supported by the Adams Fellowship Program of the Israel Academy of Sciences and Humanities and is also grateful to the Rieger Foundation’s JNF Program for Environmental Studies and the Water Authority of Israel for their generous support.

APPENDIX A. SUPPLEMENTARY DATA Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.gca.2011. 07.013. REFERENCES Agu¨ero A. (2005) Performance assessment model development and parameter acquisition for analysis of the transport of natural radionuclides in a Mediterranean watershed. Science of the Total Environment 348, 32–50. Beattie P., Drake M., Jones J., Leeman W., Longhi J., McKay G., Nielsen R., Palme H., Shaw D., Takahashi E. and Watson B. (1993) Terminology for trace-element partitioning. Geochimica et Cosmochimica Acta 57, 1605–1606. Blount C. W. (1977) Barite solubilities and thermodynamic quantities up to 300 °C and 1400 bars. American Mineralogist 62, 942–957. Chan L. H. and Chung Y. (1987) Barium and radium in the Dead Sea. Earth and Planetary Science Letters 85, 41–53. Curti E. (1999) Coprecipitation of radionuclides with calcite: estimation of partition coefficients based on a review of laboratory investigations and geochemical data. Applied Geochemistry 14, 433–445. Curti E., Fujiwara K., Iijima K., Tits J., Cuesta C., Kitamura A., Glaus M. A. and Mu¨ller W. (2010) Radium uptake during barite recrystallization at 23 ± 2 °C as a function of solution composition: An experimental 133Ba and 226Ra tracer study. Geochimica et Cosmochimica Acta 74, 3553–3570. Dickson B. L. and Herczeg A. L. (1992a) Deposition of trace elements and radionuclides in the spring zone, Lake Tyrrell, Victoria, Australia. Chemical Geology 96, 151–166. Dickson B. L. and Herczeg A. L. (1992b) Naturally-occurring radionuclides in acid – Saline groundwaters around Lake Tyrrell, Victoria, Australia. Chemical Geology 96, 95–114. Doerner H. A. and Hoskins W. M. (1925) Co-precipitation of radium and barium sulfates. Journal of American Chemical Society 47, 662–675. El-Reefy H. I., Sharshar T., Zaghloul R. and Badran H. M. (2006) Distribution of gamma-ray emitting radionuclides in the environment of Burullus Lake: I. Soils and vegetations. Journal of Environmental Radioactivity 87, 148–169. EPA (2008) Technologically Enhanced Naturally Occurring Radioactive Materials from Uranium Mining, Technical Report 402R-08-005.

5422

Y.O. Rosenberg et al. / Geochimica et Cosmochimica Acta 75 (2011) 5403–5422

Gnanapragasam E. K. and Lewis B.-A. G. (1995) Elastic strain energy and the distribution coefficient of radium in solid solutions with calcium salts. Geochimica et Cosmochimica Acta 59, 5103–5111. Goldschmidt B. (1940) Etude du fractionnement par cristallisation mixte a l’aide des radioelements. Annali di Chimica 13, 88–173. Gordon L. (1955) Slow precipitation processes – application of precipitation from homogeneous solution to liquid–solid distribution studies. Analytical Chemistry 27, 1704–1707. Gordon L. and Rowley K. (1957) Coprecipitation of radium with barium sulfate. Analytical Chemistry 29, 34–37. Grundl T. and Cape M. (2006) Geochemical factors controlling radium activity in a sandstone aquifer. Ground Water 44, 518– 527. Hahn O. (1926) Uber die neuen Fuellungs- und Adsorptionssitze und einige ihrer Ergebnisse. Naturwissenschaften 14, 1196–1199. Hanor J. S. (2007) Variation in the composition and partitioning of adsorbed cations at a brine-contaminated crude oil production facility in southeastern Louisiana, USA. Applied Geochemistry 22, 2115–2124. Harvie C. E., Moller N. and Weare J. H. (1984) The prediction of mineral solubilities in natural waters: The Na-K-Mg-Ca-H-ClSO4-OH-HCO3–CO3–CO2–H2O system to high ionic strengths at 25 °C. Geochimica et Cosmochimica Acta 48, 723–751. He S., Oddo J. E. and Tomson M. B. (1994) The inhibition of gypsum and barite nucleation in NaCl brines at temperatures from 25 to 90 °C. Applied Geochemistry 9, 561–567. He S., Oddo J. E. and Tomson M. B. (1995) The nucleation kinetics of barium sulfate in NaCl solutions up to 6 m and 90 °C. Journal of Colloid and Interface Science 174, 319–326. IAEA (2003) Extent of Environmental Contamination by Naturally Occuring Radioactive Material (NORM) and Technological Options for Mitigation, Technical Reports Series No. 419. Kim G., Burnett W. C., Dulaiova H., Swarzenski P. W. and Moore W. S. (2001) Measurement of 224Ra and 226Ra activities in natural waters using a radon-in-air monitor. Environmental Science and Technology 35, 4680–4683. Kronfeld J., Ilani S. and Strull A. (1991) Radium precipitation and extreme 238U-series disequilibrium along the Dead Sea coast, Israel. Applied Geochemistry 6, 355–361. Kudryavskii Y. and Rakhimova O. (2007) Coprecipitation of radium with barium sulfate from salt solutions. Radiochemistry 49, 541–544. Kushnir J. (1980) The coprecipitation of strontium, magnesium, sodium, potassium and chloride ions with gypsum. An experimental study. Geochimica et Cosmochimica Acta 44, 1471– 1482. Langmuir D. and Melchior D. (1985) The geochemistry of Ca, Sr, Ba and Ra sulfates in some deep brines from the Palo Duro Basin, Texas. Geochimica et Cosmochimica Acta 49, 2423–2432. Langmuir D. and Riese A. C. (1985) Thermodynamic Properties of Radium. Geochimica et Cosmochimica Acta 49, 1593–1601. Marques B. E. (1934) La Pre´cipitation Fractionne´e du Sulfate de Baryum Radife`re. Comptes Rendus Hebdomadaires des Se´ances de l’Acade´mie des Sciences 198, 1765–1767. McIntire W. L. (1963) Trace element partition coefficients – a review of theory and applications to geology. Geochimica et Cosmochimica Acta 27, 1209–1264. Minster T., Ilani S., Kronfeld J., Even O. and Godfrey-Smith D. I. (2004) Radium contamination in the Nizzana-1 water well, Negev Desert, Israel. Journal of Environmental Radioactivity 71, 261–273. Moore W. S. (2008) Fifteen years experience in measuring 224Ra and 223Ra by delayed-coincidence counting. Marine Chemistry 109, 188–197.

Paige C. R., Kornicker W. A., Hileman O. E. and Snodgrass W. J. (1998) Solution equilibria for uranium ore processing: The BaSO4–H2SO4–H2O system and the RaSO4–H2SO4–H2O system. Geochimica et Cosmochimica Acta 62, 15–23. Parkhurst D. L. and Appelo C. A. J. (1999) PHREEQC 2.15 a computer program for speciation, batch-reaction, one-dimentional transport and inverse geochemical calculation. Water-Resources Investigation Report 99–4259. Geological Survey, USA. Peri N. (2006) Radium isotopes enrichment in groundwater in the Negev and Arava Valley. M.Sc. Thesis, Ben-Gurion University of the Negev. Pina C. M., Enders M. and Putnis A. (2000) The composition of solid solutions crystallising from aqueous solutions: the influence of supersaturation and growth mechanisms. Chemical Geology 168, 195–210. Pina C. M. and Putnis A. (2002) The kinetics of nucleation of solid solutions from aqueous solutions: a new model for calculating non-equilibrium distribution coefficients. Geochimica et Cosmochimica Acta 66, 185–192. Porcelli D. and Swarzenski P. W. (2003) The behavior of U- and Th-series nuclides in groundwater. In Uranium Series Geochemistry (eds. J. J. Rosso and H. P. Ribbe), pp. 317–361. Prieto M. (2009) Thermodynamics of solid solution-aqueous solution systems. In: Thermodynamics and Kinetics of WaterRock Interaction (eds. E. H. Oelkers and J. Schott). Reviews in Mineralogy and Geochemistry, pp. 47–85. Prieto M., Putnis A. and Fernandez-Diaz L. (1993) Crystallization of solid solutions from aqueous solutions in a porous medium: zoning in (Ba, Sr)SO4. Geological Magazine 130, 289–299. Rimstidt J. D., Balog A. and Webb J. (1998) Distribution of trace elements between carbonate minerals and aqueous solutions. Geochimica et Cosmochimica Acta 62, 1851–1863. Rosenberg Y. O., Metz V. and Ganor J. (2011) Co-precipitation of radium in high ionic strength systems: 1. Thermodynamic Properties of the Na–Ra–Cl–SO4–H2O System–Estimating Pitzer Parameters for RaCl2. Geochimica et Cosmochimica Acta, doi:10.1016/j.gca.2011.06.042 Simon L. C. and Michael W. (1991) Activity coefficients in natural waters. In Activity Coefficients in Electrolyte Solution (eds. Pitzer and S. Kenneth), second ed. CRC Press, Boca Raton, FL. Sohnel O. (1982) Electrolyte crystal-aqueous solution interfacial tensions from crystallization data. Journal of Crystal Growth 57, 101–108. Tesoriero A. J. and Pankow J. F. (1996) Solid solution partitioning of Sr2+, Ba2+, and Cd2+ to calcite. Geochimica et Cosmochimica Acta 60, 1053–1063. Wang Y. and Xu H. (2001) Prediction of trace metal partitioning between minerals and aqueous solutions: a linear free energy correlation approach. Geochimica et Cosmochimica Acta 65, 1529–1543. Weare J. H. (1987) Models of mineral solubility in concentrated brines with applications to field observations. In Review in Mineralogy. Thermodynamic Modeling of Geological Materials: Minerals, Fluids and Melts (eds. I. S. E. Carmichael and H. P. Eugster), vol. 17, pp. 143–176. Yoshida Y., Nakazawa T., Yoshikawa H. and Nakanishi T. (2009) Partition coefficient of Ra in gypsum. Journal of Radioanalytical and Nuclear Chemistry 280, 541–545. Zhu C. (2004a) Coprecipitation in the Barite isostructural family: 1. Binary mixing properties. Geochimica et Cosmochimica Acta 68, 3327–3337. Zhu C. (2004b) Coprecipitation in the barite isostructural family: 2. Numerical simulations of reactions and mass transport. Geochimica et Cosmochimica Acta 68, 3339–3349. Associate editor: Robert H. Byrne