Pitzer ion-interaction model

Because of the high ionic strength of the brines, the calculations were carried out using a Pitzer ion interaction model (US DOE, 1996) for the activity coefficients of the aqueous species (Pitzer, 1987, 2000). Pitzer parameters for the dominant non-radioactive species present in WIPP brines are summarized in Harvie and Weare (1980), Harvie et al. (1984), Felmy and Weare (1986), and Pitzer (1987, 2000). For the actinide species, the Pitzer parameters that were used are summarized in the WIPP Compliance Certification Application (CCA) (US DOE, 1996). Actinide interactions with the inorganic ions H, Na, K, Mg, CU, and HCO /COa were considered. 

Christov calculated the parameters in the Pitzer ion interaction model from isopiestie measurements at 298.15 K by Ojkova and Staneva [890JK/STA]. This reference contains (interpolated) osmotic coefficients of zinc, magnesium, cobalt, and nickel selenate solutions from 0.1 mol-kg to saturated solution. Sodium chloride standards were used and the agreement between duplicate determinations was 0.2% or better. 

The osmotic coefficients were used to find the parameters in the Pitzer ion interaction model. These parameters (see Table A-121) were then employed to find the activity coefficients in saturated solution. 

Because in the west of China some salt lake brines contain abundant boron and lithium, in which solute-solvent and solute-solute interactions are complex, studies on the ihermochemical properties for the systems related with the brines are essential to understand the effects of temperature on excess free energies and solubility, and to build a thermodynamic model that can be applied for prediction of the properties. Yin et al. [43] measured the enthalpies of dilution for aqueous Li2B407 solutions from 0.0212 to 2.1530 mol/kg at 298.15 K. The relative apparent molar enthalpies and relative partial molar enthalpies of the solvent and solute were also calculated, and the thermodynamic properties of the complex aqueous solutions were represented by a modified Pitzer ion-interaction model. 

Felmy et al, (18) investigated foe solubility of Pu(OH)3 under reducing conditions in deioni water and brine solution. They deriv a much lower solubility product (log K = -26.2) (see Table I) than foe value (log K = -19.6) reported in foe literature (iP). However, foe solubility in brines [I 6 2Uid I - 10] was found to be larger than foat in deionized (I = 0) waters. The solubility of Pu(OH)3 in brines was accurately predicted with foe Pitzer ion-interaction model using only foe parameters for binary interactions between Pu and Cl". 

As to any electrolyte, its thermodynamic prosperity varied from weak solution to high concentration could be calculated through 3 or 4 Pitzer parameters. Pitzer ion-interaction model and its extended HW model of aqueous electrolyte solution can be briefly introduced in the following (Pitzer, 1975, 1977, 2000 Harvie Wear, 1980 Harvie et al, 1984 Kim Frederich, 1988a-b). 

On Pitzer ion-interaction model and its extended HW model, a numbers of papers were successfully utilized to predict the solubility behaviors of natural water systems, salt-water... 

The dissociation degree, a, is obtained fi om Equation (2.24) assuming that the activity coefficient of the ion pair to be equal to unity and resorting to an extended DHLL equation for the activity coefficient for the free ions, as the expression given by the Pitzer ion interaction model (Pitzer, 1995). The calculation of y is iterative because the activity coefficient of the electrolyte depends on the degree of dissociation. 

In actual experiments, as indicated above, ionization quotients Q are usually measured in a solution at finite ionic strength made up by the addition of supporting electrolytes such as NaCl, KCl, or NaCFsSOs. Therefore, activity coefficient models are needed to extrapolate the Q values to infinite dilution for such equilibria. All of these models are based on some version of the Debye-Hiickel equation, which determines the initial slope the logio0 versus ionic strength dependence, with additional empirical ionic strength terms which are typically derived from those used in the Pitzer ion interaction model (Pitzer, 1991). An example of this empirical approach is given in Equation (3.29). 

An important series of papers by Professor Pitzer and colleagues (26, 27, 28, 29), beginning in 1912, has laid the ground work for what appears to be the "most comprehensive and theoretically founded treatment to date. This treatment is based on the ion interaction model using the Debye-Huckel ion distribution and establishes the concept that the effect of short range forces, that is the second virial coefficient, should also depend on the ionic strength. Interaction parameters for a large number of electrolytes have been determined. 

One method takes into account the individual characteristics of the ionic media by using a medium-dependent expression for the activity coefficients of the species involved in the equilibrium reactions. The medium dependence is described by virial or ion interaction coefficients as used in the Pitzer equations and in the specific ion interaction model. 

Pitzer (1973) re-examined the statistical mechanics of aqueous electrolytes in water and derived a different but semi-empirical method for activity coefficients, commonly termed the Pitzer specific-ion-interaction model. He fitted a slightly different function for behavior at low concentrations and used a virial coefficient formulation for high concentrations. The results have proved extremely fruitful for modeling activity coefficients over a very large range of molality. The general equation is... 

The purpose of this paper is to review two thermodynamic models for calculating aqueous electrolyte properties and give examples of parameter evaluations to high temperatures and pressures as well as applications to solubility calculations. The first model [the ion-interaction model of Pitzer (1) and coworkers] has been discussed extensively elsewhere (1-4) and will be reviewed only briefly here, while more detail will be given for an alternate model using a Margules expansion as proposed by Pitzer and Simonson (5). 

The principal interests in this study are osmotic and activity coefficients of NaCl(ac ) and KCl(aq) solutions at temperatures to 350°C and up to saturation concentration. In the range 25-300 C and at 1 bar or saturation pressure, NaCl(aq) osmotic coefficients up to 4 m were taken from a comprehensive thermodynamic treatment of Pitzer et al. (9). Above 4 m, the values were taken from Liu and Lindsay (39). At temperatures above 300°C, osmotic coefficients were calculated from vapor pressure data of Wood et al. (4. Additional vapor pressure data are given in Refs. 41-47, but a critical evaluation of these data indicated that these are less precise measurements and were therefore given smaller weights in the regression. For KCl(aq), osmotic coefficients to 6 m at temperatures from 25-325 C at 1 bar or saturation pressure were taken from the ion interaction model of Pabalan and Pitzer (9). Additional values up to 350 C and saturation concentration were derived from Refs. 40,41, and 48. 

To calculate the partial pressures of volatile electrolytes above solutions of known composition, values of the activity coefficients of the dissolved components are needed in addition to the appropriate Henry s law constants. In this work activity coefficients are calculated using the ion-interaction model of Pitzer (4). While originally formulated to describe the behavior of strong electrolytes, it is readily combined with explicit recognition of association equilibria (1,1), and may be extended to include neutral solutes (4, . The model has previously been used to describe vapor-liquid equilibria in systems of chiefly industrial interest (2). 

Alternatively, water activities can be taken from Table B-1. These have been calculated for the most common ionic media at various concentrations applying Pitzer s ion interaction model and the interaction parameters given in [91PIT]. Data in italics have been calculated for concentrations beyond the validity of the parameter set applied. These data are therefore extrapolations and should be used with care. 

Figure 1. Experimental and calculated solubiliti ofSr(OH) 8H20 in NaOK Patterned line represents calculations with Sr OH interactions described solely with the use ofPitzer s form of the extended Debye-HOckel equation. Solid line represents the calculations of our final thermodynamic model, which includes values for the Pitzer ion interaction parameters. Total concentrations in units of molarity. From (3).

Pitzer and co-workers have developed an ion interaction model and published a series of papers (Pitzer, 1973a-b, 1974a-b, 1975, 1977, 1995, 2000 Pabalan Pitzer, 1987) which gave a set of expressions for osmotic coefficients of the solution and mean activity coefficient of electrolytes in the solution. Expressions of the chemical equilibrium model for conventional single ion activity coefficients derived are more convenient to use in solubility calculations (Harvie Weare, 1980 Harvie et al.l984 Felmy Weare, 1986 Donad Kean, 1985). 

As to the ion-interaction model, it is a semiempirical statistical thermodynamics model. In this model, the Pitzer approach begins with a virial expansion of the excess free energy of the form to consider the three kinds of existed potential energies on the ion-interaction potential energy in solution. 

Pitzer (1973) developed a semi-empirical equation (ion-interaction model) to reproduce accurately the volumetric properties of aqueous electrolyte solutions. This model has been used to calculate accurately other thermodynamic properties such as expansivity, compressibility, free energy, enthalpy, and heat capacity. The ion-interaction model... 

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