The HKF Model for Aqueous Electrolytes

The other major contribution to the systematization of our knowledge of aqueous electrolyte solutions at elevated temperatures and pressures takes a completely different approach. This was presented in a series of four papers by H.C. Helgeson and co-workers between 1974 and 1981, with fairly extensive modifications added by Tanger and Helgeson (1988). We present here an outline of this model, with some explanation and comparison with the Pitzer model. We refer to it as the HKF or revised 

HKF model, after the three authors of Part IV of the series of papers just mentioned, Helgeson, Kirkham, and Howers. 

The HKF model is semiempirical, in the sense that it uses a number of empirical parameters within a framework suggested by fundamental physics and thermodynamics. The variation of the Gibbs energy of individual ions with T, P, and composition can be represented by writing the total differential of the (partial molar) Gibbs energy of the jth ion, giving 

The Bom function was introduced in 6.2.4. It is qualitatively accurate but quantitatively inaccurate. However the fact that it succeeds as well as it does suggests that it contains a large part of the tmth, and might serve as the basis of a more satisfactory model. In fact it serves as the basis of the HKF model, which uses the Bom function to provide the Gibbs energy of solvation (or hydration in 

Representation of the integration of dGj from reference conditions to conditions of interest, where j is an ion in an aqueous solution of any composition. The path from 7, Pf, no to T, P, n is represented by Equation (15.45). 

A number of theoretical difficulties in equating the Born function with this process are believed to be accommodated in the j parameter, which in the Bom model is the ion radius, but in the HKF model is an adjustable parameter called the effective ionic radius. The r j parameters were originally related to crystallographic ionic radii (r ) and ionic charge Zj in a simple linear fashion in the HKF model, and were independent of T and P 

---

Helgeson and co-workers (Helgeson and Kirkham, 1974, 1976 Helgeson et al, 1981) developed an equation of state for aqueous electrolytes based on this continuum model. The model, known as HKF, has two contributions to the standard partial volume an electrostatic part given by Equation (2.78) and the nonelectrostatic part having an intrinsic term, temperature and pressure independent, and a short-range term related to the electrostriction of water around the ion, equivalent to a change of density and dielectric constant of the continuum near the ion. This last contribution was considered to be dependent on temperature and pressure. 

For most electrolyte solutions at or near room temperature, there have been two main approaches, exemplified by the Pitzer and HKF models to be described below. (These two approaches were also mentioned on page 304.) In one, referred to as ion-interaction theory and embodied in the Pitzer equations, no attempt is made (except if there are very strong complexes present) to identify species. Components are treated stoichiometrically, and all ion interactions are accounted for in the form of fit coefficients in some form of equation. Advocates of this approach point to the rather uncertain nature of our knowledge of aqueous species. Molecular dynamics simulations of these solutions... 

---