Simultaneous Description of Activity Coefficients and Solubility with eCPA

Abstract

In the many developments of electrolyte equations of state presented over the past decades several different properties have been in focus. A property that has not been widely used as a fitting property is salt solubility. This work presents a new parameterization of the eCPA equation of State with salt specific parameters. The focus is on accurate description of the salt solubility, and low deviation correlations are obtained for all salts investigated. The inclusion of the solubility data in the parameterization has, compared to parameters only parameterized to osmotic coefficients and activity coefficients, not significantly affected the deviations of the osmotic coefficients and activity coefficients. The average deviations of the activity coefficient does increase slightly and it was found that the increase in deviations was almost entirely due to reduced accuracy at high temperature and high molality. The model is, furthermore, compared to the activity coefficient model, Extended UNIQUAC. It is shown that the eCPA provides more accurate solubility description at higher temperatures than Extended UNIQUAC, but also that Extended UNIQUAC is slightly better at describing the activity coefficients. Overall the two models perform similarly.

The Debye-Hückel theory and its importance in modeling electrolyte solutions

“…As Schlaikjer et al 2017 50,52 have noticed satisfactory correlation of both activity coefficients and salt solubilities required that both data are included in a simultaneous parameter estimation of the model parameters (e-CPA in that case). We suspect that a similar approach may be needed for most models and thus models (e-EoS) with parameters estimated by ignoring salt solubilities may not perform satisfactory for SLE.…”

“…It is interesting that, despite its "apparent" importance, the Born term had been ignored in most electrolyte EoS for many years, possibly because the static permittivity was considered to be independent of concentration. In the recent years, the use of Born term in e-EoS has become quite popular and several approaches within the primitive framework (e-PR by Myers et al 32 , e-CPA by Maribo-Mogensen et al 46 and Schlaikjer et al 50 , e-SAFT VR-Mie by Jackson, Galindo and coworkers 42,43 , PC-SAFT by de Hemptinne and co-workers 33,35 , and by Shahriari and Dehghani 44 ) as well as the non-primitive approaches by Das et al 22 and Herzog et al 23 are using it. In some of these studies, hydration enthalpies and Gibbs free energy of solvation calculations are presented for several salts which are found to be in reasonably good agreement with experimental data.…”

Modeling of mixed-solvent electrolyte systems

“…However, most of them rely on fitting salt specific binary parameters which compromises with the predictive capability of the model [69]. [75] CPA DH Born T, V, i -Mogensen et al [54] CPA DH Born T, V, i -Courtial et al [61] CPA nRP-MSA Born T, V, i e-BH Harvey et al [18] BH nRP-MSA Born T, V e-PT (salt specific) Zuo/Guo [76] PT DH -T -SAFT based models e-SAFT (ion specific)…”

eCPA: An ion-specific approach to parametrization

“…Here a i is the component activity and K s is the equilibrium constant calculated based on the standard state properties: standard state Gibbs energy of formation, standard state enthalpy of formation and standard state heat capacity. In the work of Schlaikjer et al [17] a thorough description and investigation of eCPA applied to solid-liquid equilibrium is presented using salt-specific parameters. The standard state properties are, for some salts, available from Wagman et al [36], however, for most hydrated salts these standard state properties are not available.…”

“…This could be a cubic EoS, as the extension to Peng-Robinson by Wu and Prausnitz [9], but also in many cases Statistical Associating Fluid Theory (SAFT) based EoSs [10,11,12], which are derived from statistical thermodynamics and also account for association. The Cubic Plus Association (CPA) EoS, which uses the attraction and repulsion interactions of the cubic EoS, Soave-Redlich-Kwong (SRK), but also accounts for association in a similar way to SAFT, has also been extended to electrolytes [13,14,15,16,17]. Most of these extensions rely on one of two models for the long range interaction between charged species; the Mean Spherical Approximation (MSA) [18] or the Debye-Hückel [19].…”