Pitzer equations determining parameters

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). 

In this work the temperature dependencies of Pitzer parameters and equilibrium constants were largely determined from isothermal data sets that were then fit to the following equation ... 

The value of C has to be determined experimentally for a particular system but is typically 0.2-0.3. Pitzer presented equations that give activity coefficients for both binary solutions and mixed electrolytes for 7 up to 6 m, but there are several parameters that must be determined empirically. 

Pitzer s equations and available ion-pair parameters allow calculation of mean-ion activity coefficients Y+ in complex, concentrated electrolyte solutions with an accuracy estimated to be better than + 25% in the range 25° - 55°C. The accuracy of calculated activity coefficients is limited to about the same degree by uncertainties in the estimated parameters and by simplifications introduced in the theory both to reduce the number of parameters to be estimated and to reflect the uncertainties of the estimates. Because activity coefficients are determined to quite an extent by the form of Pitzer s equations and are not extremely sensitive to the exact values of parameters, ion-pair parameters only have to be estimated within a reasonable range. 

The equation of state uses corresponding states theory to determine the attractive and volume parameters of each species. Therefore, the pure component critical temperature, 7, and critical pressure, are required. The EOS uses a third parameter, viz. Pitzer s acentric factor, (O, (9)... 

The first two terms are derived from Debye-Hiickel theory, and the third and fourth terms express short-range interactions (e.g., ion-molecular interactions). A( ) can be calculated as a function of temperature using the polynomial equation given by Clegg et al. (1994), which is based on the study of Archer and Wang (1990). Pitzer and Mayorga (1973) determined three parameters mx)... 

The BWRC equation was first tested on nonpolar gases and their mixtures. It is most commonly used in a generalized form [0.49]. The recommended formulas in Ref. [0.49] for the determination of coefficients of Eq. (0.5) are simple functions of critical parameters and of Pitzer s acentric factor (7, Pcr Pi)- In a more general case, it is imperative also to know, for each pair of mixture components, what is termed the constant of binary interaction K j. 

---