Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

Abstract

Despite intense efforts, general thermodynamic modelling of aqueous electrolyte solutions still presents a difficult challenge, with no obvious method of choice. Even though the Pitzer equations seemingly provide a well-established theoretical framework applicable to many chemical systems over a wide range of temperatures and pressures, they are not as widely adopted as their early promise might have suggested. This is strikingly illustrated by the simultaneous appearance in the literature of numerous, different (and potentially incompatible) Pitzer models alongside a proliferation of alternative theoretical approaches with inferior capabilities.To better understand this problem, the ability of the Pitzer equations to represent the physicochemical properties of aqueous solutions has been systematically investigated for exemplar electrolyte systems. Pitzer ion-interaction parameters have been calculated for selected systems by least-squares regression analysis of published solution data for activity coefficients, osmotic coefficients, relative enthalpies, heat capacities, volumes and densities to high temperatures and pressures. Although satisfactory fits can be achieved when the ranges of conditions are carefully chosen and when sufficient data are available to constrain the regression, the fits obtained tend otherwise to be unsatisfactory. The Pitzer equations do not cope well with gaps and other deficiencies in the regressed data. Profound difficulties, poorly recognized hitherto, can also arise because of variation in the sensitivity of the Pitzer functions to values for different physicochemical properties when these are combined. Given the dimensionality of numerous related thermodynamic properties, all changing as functions of composition, temperature and pressure, these problems are difficult to detect, let alone address, especially in multicomponent systems. The growing practice of improving fits simply by adding basis functions (thereby increasing the number of adjustable parameters) should be deprecated because it increases the likelihood of error propagation, introduces subjectivity, makes independent verification difficult and has deleterious implications for both automated data processing and for consistency between thermodynamic models.

Comparison of the Pitzer and Hückel Equation Frameworks for Activity Coefficients, Osmotic Coefficients, and Apparent Molar Relative Enthalpies, Heat Capacities, and Volumes of Binary Aqueous Strong Electrolyte Solutions at 25 °C

“…These and other conspicuous failures of the Pitzer equations, 11 usually when the fit is not properly constrained by sufficient numbers of accurate data, infer an unreliability that casts doubt on the notion that the Pitzer equations possess any distinctive fundamental power. The term "semiempirical", which is widely used to describe the Pitzer equations, should perhaps mean more than just the sound foundation of Debye−Huckel theory represented in eq 1.…”

Thermodynamic modeling of aqueous Na + –K + –Cl − –SO 4 2− quaternary system with electrolyte NRTL model

“…[11]. Moreover, the Pitzer model requires use of both binary and ternary interaction parameters and the model offers no hints on temperature dependence of such interaction parameters [12,13]. The extended UNIQUAC model has been used for correlation and prediction of mineral solubility of Na + -K + -Cl À -SO 4 2À -H 2 O system at temperatures from 0 to 100 C [14].…”

The composition of groundwater in Palaeogene and older formations in the Netherlands. A synthesis

“…It does not contain Fe as element, so no calculations can be performed for diagenetic Fe minerals such as siderite (FeCO 3 ), which is an important mineral in reservoirs and aquifers. In addition to its limited extent, the Pitzer database has some intrinsic shortcomings (Appelo, 2015;Rowland et al, 2015). A drawback of the regular database is the incorrect calculation procedure used to correct the concentration to activity for saline water.…”