Pitzer equation applications

Equilibrium constants calculated from the composition of saturated solutions are dependent on the accuracy of the thermodynamic model for the aqueous solution. The thermodynamics of single salt solutions of KC1 or KBr are very well known and have been modeled using the virial approach of Pitzer (13-15). The thermodynamics of aqueous mixtures of KC1 and KBr have also been well studied (16-17) and may be reliably modeled using the Pitzer equations. The Pitzer equations used here to calculate the solid phase equilibrium constants from the compositions of saturated aqueous solutions are given elsewhere (13-15, 18, 19). The Pitzer model parameters applicable to KCl-KBr-l O solutions are summarized in Table II. 

Previous Applications of the Pitzer Equation to Weak Electrolytes... 

Two activity coefficient models have been developed for vapor-liquid equilibrium of electrolyte systems. The first model is an extension of the Pitzer equation and is applicable to aqueous electrolyte systems containing any number of molecular and ionic solutes. The validity of the model has been shown by data correlation studies on three aqueous electrolyte systems of industrial interest. The second model is based on the local composition concept and is designed to be applicable to all kinds of electrolyte systems. Preliminary data correlation results on many binary and ternary electrolyte systems suggest the validity of the local composition model. 

Chen, C., H. I. Britt, J. F. Boston, and L. B. Evans, "Extension and Application of the Pitzer equation for Vapor-Liquid Equilibrium of Aqueous Electrolyte Systems with Molecular Solutes," AIChE J., 1979, 25, 820. 

Numerous studies on the thermodynamics of calcium chloride solutions were published in the 1980s. Many of these were oriented toward verifying and expanding the Pitzer equations for determination of activity coefficients and other parameters in electrolyte solutions of high ionic strength. A review article covering much of this work is available (7). Application of Pitzer equations to the modeling of brine density as a function of composition, temperature, and pressure has been successfully carried out (8). 

When Pitzer developed these equations, the ultimate form for describing the interaction terms was based on both theoretical models and experimental data. On the other hand, the number of terms to include in the equations is left to the user s discretion. For example, are neutral-neutral species interaction terms needed In some applications, yes in other applications, no. See Harvie et al. (1984), He and Morse (1993), and Pitzer (1995) for examples where different terms were selected. In what follows, we will specify the exact form of the Pitzer equations used in the FREZCHEM model. For a discussion of the connection between these equations (2.39 to 2.42) and Eq. 2.38, see Pitzer (1991, 1995). 

This assumption limits application of the latter chemistries to low pressures. Activity coefficients for aqueous-phase gases (CO2, O2, and CH4) are calculated using the Pitzer equation for neutral species (Eq. 2.42). Activity coefficients for aqueous acids are calculated using the Pitzer equations for ions (Eqs. 2.40 and 2.41). For the case of HC1, the Henry s law constant is given by... 

A number of limitations of the FREZCHEM model can be broadly grouped under Pitzer-equation parameterization, modeling (mathematics, convergence, and coding), and applications. The first two limitations are discussed in this chapter. Application limitations are discussed in Chap. 5 after presentation of multiple applications. 

If the ionic strength exceeds 6 mol/L, the PITZER equation is no longer applicable though. 

In 1988, a version of PHREEQE was written including PITZER equations for ionic strengths greater 1 mol/L thus applicable for brines or highly concentrated electrolytic solutions (PHRQPITZ, Plummer et al. 1988). PHREEQM (Appelo Postma 1994) included all options of PHREEQE and additionally a one-... 

Overall, it seems that PHREEQC, except for the problems with high ionic strengths that require the application of PITZER equations, is the optimal program for the solution of both simple and more complex exercises and for onedimensional transport modehng with regard to user-friendliness, numerical stability, compactness and clarity of the data format as well as flexibility. It will be used for the solution of the exercises in chapter 3. The utilization of PHREEQC is presented in detail in chapter 2.2. 

Plummer L. N. and Parkhurst D. L. (1990) Application of the Pitzer equations to the PHREEQE geochemical model. In Chemical Modelling of Aqueous Systems II, Symp. Ser. 416 (eds. D. C. Melchior and R. L. Bassett). American Chemical Society, Washington, DC, pp. 128-137. 

The applicable Pitzer equations for the activity coefficients of cation M and anton X from Miliero... 

The parameters for these equations are tabulated in the appropriate tables in reference (4). Activity coefficients for these charge types may also be calculated from the Pitzer equations for the uni-univalent and uni-bi and bi-univalent salts. In these cases, the Pitzer equations are sometimes applicable to a more limited concentration range. If the concentration being investigated is beyond the range of validity specified by Pitzer, the Hamer-Wu, Lietzke-Stoughton equations are recommended. 

Few parameters for ion-neutral interactions are available as yet G.,5,9). However, we have recently derived parameters for NH3-salt interactions, using partial pressure, liquid phase partitioning and salt solubility data (, which may serve as a model for the treatment of other weak and nonelectrolytes. The results of this work, and the application of the Pitzer equations to the calculation of neutral species solubility, are discussed below. 

This work and others (5, 51) have shown how the Pitzer model, together with appropriate Henry s law constants, can be used to calculate the solubility of volatile strong electrolytes in multicomponent solutions. The treatment of NH3 summarized above shows that Pitzer formalism can also be used to describe the solubility of weak and non-electrolytes. We have noted how, for low concentrations of NH3, the Pitzer equations reduce to a series of binary interaction terms similar in form to those of the well known Setchenow equations. However, the thermodynamically based approach constitutes a significant improvement over the use of purely empirical equations to predict individual thermodynamic properties because it is equally applicable to both electrolytes and uncharged species, and provides a unified description of a number of important solution properties. 

Application of the Pitzer Equations to the PHREEQE Geochemical Model... 

Details of the Pitzer equations and definitions of the notations utilized in this paper and in PHRQPITZ are given in the literature (3-lOL As the focus of this report is on the capabilities and limitations of PHRQPITZ in relation to its application to geochemical problems, only selected aspects of the implementation of the Pitzer equations in PHRQPITZ are presented. 

One of the first applications of the Pitzer equations to highly complex natural systems were made by Weare, Harvie, and their associates on marine evaporites (Harvie and... 

The above procedure has been coded in FORTRAN as the program EQBRM and a copy suitable for personal computers is included in this book as Appendix E, along with an example showing the proper format for input data. For different applications it is necessary to choose among the available methods of estimating activity coefficients. For example, the Debye-Huckel equation can often be used for dilute systems such as rivers and groundwater, but concentrated brines will require the Pitzer equations or measured coefficients if they are available. For this reason, a subroutine should be written to calculate activity coefficients for your application. 

However, determining for multicomponent electrolyte aqueous solutions has proved to be a difficult task. Virtually all applications these days use the formulation of K.S. Pitzer and his colleagues, developed during the 1970s and 1980s, which we discuss in Chapter 15. Equation (10.52) and its derivatives are the essential first step in the development of the Pitzer equations. 

In a binary electrolyte solution such as this one, terms containing A, 0, or tf/ are zero, since these involve interactions with two dissimilar anions or cations. In most such cases, the parameter is unnecessary, because it is invoked to account for exceptionally strong ion-ion interactions. In fact, Pitzer shows that should approach -K/2 in the limit of infinite dilution, where K is the association constant for the ion-pair. The work of Harvie and Weare (1980), Eugster, Harvie and Weare (1980), and Harvie, Eugster and Weare (1982), who modeled solubility equilibria in the multicomponent oceanic salt system is considered a milestone in the application of the Pitzer equations, and the set of parameters in Harvie, Mller and Weare (1984) is considered a sort of standard for modeling of seawater evaporitic systems. 

P2. a. Chen, C-C H.I. Britt, J.F. Boston, L.B. Evans, "Extension and application of the Pitzer equation for vapor-liquid equilibrium of aqueous electrolyte systems with molecular solutes", AIChE J, v25, 5, pp820-831 (1979)... 

Equations for single ion activity coefficients [4], osmotic coefficients [17], and other thermodynamic quantities [28], as well as applications in different cases (e.g., H2SO4 and H3PO4 solutions) have been given by Pitzer and coworkers [4,20]. 

The three appendices in this volume give selected sets of thermodynamic data (Appendix 5), review the statistical calculations covered in Principles and Applications (Appendix 6), and summarize the equations and parameters required to calculate the properties of electrolyte solutions, principally from Pitzer s equations (Appendix 7). 

The expression for the excess Gibbs energy is built up from the usual NRTL equation normalized by infinite dilution activity coefficients, the Pitzer-Debye-Hiickel expression and the Born equation. The first expression is used to represent the local interactions, whereas the second describes the contribution of the long-range ion-ion interactions. The Bom equation accounts for the Gibbs energy of the transfer of ionic species from the infinite dilution state in a mixed-solvent to a similar state in the aqueous phase [38, 39], In order to become applicable to reactive absorption, the Electrolyte NRTL model must be extended to multicomponent systems. The model parameters include pure component dielectric constants of non-aqueous solvents, Born radii of ionic species and NRTL interaction parameters (molecule-molecule, molecule-electrolyte and electrolyte-electrolyte pairs). 

Felmy A. R. and Rai D. (1999) Application of Pitzer s equations for modeling aqueous thermodynamics of actinide species in natural waters a review. J. Solut. Chem. 28(5), 533-553. 

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