Helgeson-Kirkham-Flowers equation

The solubilities of gibbsite, boehmite and diaspore in alkaline solutions between 20 and 350°C are evaluated and their thermodynamic properties reconciled. The thermodynamic properties of the aluminate ion, Al(OH)4, are derived over the same temperature range and compared with predictions based on the revised Helgeson-Kirkham-Flowers equation of state. Preliminary thermodynamic properties of bayerite and AGf°298 for nordstrandite are also derived from solubility data in alkaline solutions. Log Kg4 values for gibbsite, bayerite, boehmite and diaspore between 0 and 350°C, and thermodynamic data for A1(0H)4 or AIO2, re tabulated for use in distribution-of-species computer codes. 

More recently, Brossia et al. [35] introduced an approach based on new correlations for activity coefficients in concentrated solutions. This proach [101] is based on the Helgeson-Kirkham-Flowers equation for standard-state properties with a nonideal solution model based on the activity coefficient expression developed by Bromley and Pitzer. Using specific software, Brossia et al. were able to predict the dominant ionic species and the salt precipitation in Ni, Fe, Cr, and 308 stainless steels crevice solutions. Fair agreement was observed with the in situ analyses of these crevice solutions by Raman spectroscopy. 

The next better approximation is to allow the linear coefficient to be a function of the ionic strength (Pitzer and Brewer, 1961) and was utilized by Helgeson and Kirkham (1974a,b, 1976), Helgeson et al. (1981), and Tanger and Helgeson (1988) in the development of the Helgeson-Kirkham-Flowers (HKF) equations, which include consideration of the Born function and ion hydration. 

C. An electrolyte model is therefore needed to extrapolate another 50°C. The recently revised version of the Helgeson, Kirkham, Flowers (H.K.F.) equation of state by Tanger and Helgeson (70) was used to perform this extrapolation. 

Three other options are presently being studied, with an eye on including them in the forthcoming 3270 version. One of these is the equations of Helgeson, Kirkham, and Flowers (41). for which further model development is required. The second (42) is based on the hydration theory concept of Stokes and Robinson (43). This also requires further model development. The third set is a model (44) recommended by the European Nuclear Energy Agency for obtaining equilibrium constants for the formation of aqueous complexes of interest in nuclear waste disposal, such as of uranium and plutonium. 

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