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Graphical abstract Highlights • MSE model reproduces properties of multicomponent systems containing REE sulfates. • Phase behavior and caloric properties are predicted for REE 2 (SO 4) 3 and Na 2 REE 2 (SO 4) 4. • SLE phase diagrams elucidate the solubility of both stable and metastable phases. • Regularities in solubilities are identified as a function of the REE cation radius. • REE 2 Na 2 (SO 4) 4 show a V-shaped solubility pattern with a local minimum for Pr. Abstract A thermodynamic model has been developed for calculating the phase behavior and caloric properties of rare earth elements in multicomponent sulfate solutions over wide ranges of temperature (up to 300 °C) at concentrations extending to solid–liquid saturation. The model has been constructed using the previously developed Mixed-Solvent Electrolyte (MSE) framework, which combines the standard-state thermochemical properties of aqueous and solid species with an ion-interaction formulation for the excess Gibbs energy. The model accurately reproduces the properties of binary aqueous rare earth sulfate solutions and multicomponent systems that include sulfuric acid and/or sodium sulfate. Solid-liquid phase diagrams have been constructed to elucidate the solubility of both stable and metastable solid phases. Regularities in the solubility behavior have been identified as a function of the cation radius for rare earth sulfates and double sodium-rare earth sulfate salts. The solubility of rare earth sulfates at ambient conditions shows an s-shape pattern with a local maximum at Pr, followed by a plateau between Sm and Tb and then an increase starting from Tb. On the other hand, the double salts REE 2 Na 2 (SO 4) 4 show a solubility minimum at Pr, followed by a strong increase in solubility for heavier rare earths. For the double sulfate salts for which no experimental data are available, solubilities have been estimated using an analysis of trends in thermochemical properties across the lanthanide series. The model is part of a systematic effort to develop a comprehensive treatment of the properties of rare earth salt solutions to facilitate the design and optimization of processes for the recovery of rare earth elements. [ABSTRACT FROM AUTHOR]

We apply the SAFT-VR+DE equation of state to the study of experimental mixed-solvent electrolyte solutions. In the non-primitive model based SAFT-VR+DE approach (Zhao et al., JCP 2007, 126 , 244503) the ions are considered fully dissociated within the solvent that is explicitly treated within the model and the theoretical framework. Typically in the study of electrolyte systems the simpler primitive model is used, which requires knowledge of the experimental dielectric constant. With the non-primitive model the dielectric constant is calculated as part of the theory, which is a particularly attractive feature in the study of mixed-solvent electrolyte systems as data for the experimental dielectric constant of such systems is more scarce. Here for the first time as far as the authors are aware, a non-primitive based equation of state has been used for the study of mixed-solvent electrolytes. The solvents considered (water, methanol and ethanol) are modeled using the SAFT-VR+D approach (Zhao et al., JCP 2007, 127 , 084514; Zhao et al., JCP 2006, 125 , 104504) in which the contribution of the dipole to the thermodynamics and structure of the fluid are explicitly accounted for. The theory is found to accurately predict the vapor-liquid equilibrium, as well as dielectric properties of the salt free alcohol-water mixtures both at room and elevated temperatures. Ternary mixtures of salt/water/alcohol are then studied using the SAFT-VR+DE parameters for the salts determined in earlier work (Das et al., AIChE Journal 2015, 61 , 3053-3072) and a cation-alcohol unlike dispersive energy parameter obtained by fitting to mean ionic activity coefficient data at room temperature and pressure. Thus, with only one adjustable parameter, a predictive SAFT-VR+DE equation to study mixed-solvent electrolyte systems is developed. The SAFT-VR+DE predictions are found to be in good quantitative agreement with mean ionic activity coefficient data for several mixed-solvent electrolyte systems over a wide range of molalities and different solvent ratios. The model is parameterized to allow the molecular level interactions between different cations and the surrounding solvent molecules to be explored. [ABSTRACT FROM AUTHOR]

A model has been developed for calculating thermodynamic properties and phase equilibria in binary and multicomponent aqueous systems containing rare earth element chlorides. Here, the rare earth elements encompass the lanthanides except promethium plus yttrium. The model is based on a comprehensive database of solid-liquid equilibria, osmotic and activity coefficients, enthalpies of dilution and heat capacities of solutions. The computational framework relies on the previously developed Mixed-Solvent Electrolyte (MSE) model. The model accurately reproduces the properties of binary rare earth chloride – water systems and of ternary mixtures that additionally include HCl, NaCl, or CaCl 2 . Solid-liquid phase diagrams have been obtained to provide a convenient summary of the solubility of stable and metastable hydrated solid phases. Analysis of the stability of solid hydrates reveals systematic trends within the rare earth series. At ambient and elevated temperatures, the calculations show an increase in the stability range of rare earth chloride hexahydrates with decreasing cation radius, accompanied by a gradual disappearance of the heptahydrate. At low temperatures, the stable solid phases transition from the decahydrate at higher cation radii to octahydrate in an intermediate range and a combination of pentadeca- and nonahydrates at lower radii. The calculated standard-state enthalpies of formation of the hydrates agree with independently obtained values from calorimetric measurements, thus verifying the internal consistency of the model. [ABSTRACT FROM AUTHOR]

The SAFT-VR+DE approach was developed by combining the statistical associating fluid theory for potentials of variable range (SAFT-VR) with integral equation theory and the generalized mean spherical approximation using a non-primitive model, in order to explicitly describe the solvent in electrolyte solutions. Subsequently, the theory was applied to study nineteen different aqueous electrolyte solutions and a range of thermodynamic properties across different temperatures and salt concentrations were successfully predicted. Here, the theory is applied to study several model mixed dipolar solvent electrolytes in order to validate a simple one-fluid-like approximation that is proposed to describe the interactions between ions and dipolar solvents of arbitrary size and dipole moment. Before application to real fluids the approach is extensively tested through comparison with isothermal-isobaric ensemble (NPT) Monte Carlo simulations for a number of model mixed dipolar solvent electrolyte systems. Simulations have been performed for different ionic concentrations, solvent compositions, cation, anion, and solvent segment diameters, and solvent polarity. The results show that the SAFT-VR+DE equation provides a good description of the PVT behavior of the model mixed solvent electrolyte systems studied, with some over-prediction of the PVT behavior observed only at higher ionic concentrations. Additionally, comparisons are made between predictions from the non-primitive and primitive models for electrolytes and the importance of capturing the effect of ions on the solvent dielectric is demonstrated. [ABSTRACT FROM AUTHOR]

We extend the SAFT-VR+DE equation of state to describe 19 aqueous electrolyte solutions with both a fully dissociated and a partially dissociated model. The approach is found to predict thermodynamic properties such as the osmotic coefficient, water activity coefficient, and solution density, across different salt concentrations at room temperature and pressure in good agreement with experiment using only one or two fitted parameters. At higher temperatures and pressures, without any additional fitting, the theory is found to be in qualitative agreement with experimental mean ionic activities and osmotic coefficients. The behavior of the dielectric constant as a function of salt concentration is also reported for the first time using a statistical associating fluid theory (SAFT)-based equation of state. At high salt concentrations, the stronger electrostatic interactions between the ionic species due to the dielectric decrement, is captured through the inclusion of ion association. © 2015 American Institute of Chemical Engineers AIChE J, 61: 3053-3072, 2015 [ABSTRACT FROM AUTHOR]

Graphical abstract Highlights • Comparison of lixiviants for leaching rare earth elements from synthetic phosphogypsum. • Leaching efficiency: H 2 SO 4 > Biolixiviant > Gluconic Acid > H 3 PO 4 for Ce, Nd, Sm, Eu, and Yb. • Thermodynamic simulations consistent with experimental results. Abstract Leaching of six individual rare earth (yttrium, cerium, neodymium, samarium, europium, and ytterbium) doped synthetic phosphogypsum samples using a suite of lixiviants was conducted. The lixiviants chosen for this study were phosphoric acid, sulfuric acid, gluconic acid, and a "biolixiviant" consisting of spent medium containing organic acids from the growth of the bacterium Gluconobacter oxydans on glucose. The biolixiviant had a pH of 2.1 and the dominant organic acid was determined to be gluconic acid, present at a concentration of 220 mM. The leaching behaviors of the studied lixiviants were compared and rationalized by thermodynamic simulations. The results suggest that at equivalent molar concentrations of 220 mM the biolixiviant was more efficient at rare earth element (REE) extraction than gluconic acid and phosphoric acid but less efficient than sulfuric acid. Unlike the organic acids, at pH 2.1 the mineral acids failed to extract REE, likely due to different complexation and kinetic effects. [ABSTRACT FROM AUTHOR]