Mixed Solvent Electrolyte Systems Research Articles

Mixed Solvent Electrolyte Solutions: A Review and Calculations with the eSAFT-VR Mie Equation of State.

In this work, mixed-solvent mean ionic activity coefficients (MIAC), vapor-liquid equilibrium (VLE), and liquid-liquid equilibrium (LLE) of electrolyte solutions have been addressed. An extended literature review of existing electrolyte activity coefficient models (eGE) and electrolyte equations of state (eEoS) for modeling mixed solvent electrolyte systems is first presented, focusing on the details of the models in terms of physical and electrolyte terms, relative static permittivity, and parameterization. The analysis of this literature reveals that the property predictions can be ranked, from the easiest to the most difficult, in the following order: VLE, MIAC, and LLE. We have then used our previously developed eSAFT-VR Mie model to predict MIAC, VLE, and LLE in mixed solvents without fitting any new adjustable parameters. The model was parameterized on MIAC of aqueous electrolyte solutions and successfully extended to nonaqueous, single solvent electrolyte solutions without any new adjustable parameters by using a salt-dependent expression for the relative static permittivity. Our approach yields excellent results for MIAC and VLE of mixed solvent electrolyte solutions, while being fully predictive. LLE is significantly more challenging, and an accurate model for the salt-free solution is crucial for accurate calculations. When the compositions of the two phases in the binary salt-free system are accurately captured, then the electrolyte extension of our model shows a lot of potential and is currently among the best eEoS for LLE prediction in the literature.

Modeling vapour-liquid phase equilibrium for the aqueous solutions of formaldehyde and electrolyte

Modeling of vapor-liquid equilibrium for the aqueous solutions of formaldehyde and electrolyte is required for the extractive distillation of formaldehyde-containing multicomponent mixtures using salt as entrainers. Here a revised physicochemical model, which integrates the advantages of the physicochemical model for the vapor-liquid and the chemical equilibria in aqueous formaldehyde solution and the LIFAC model for the phase behavior in mixed-solvent electrolyte systems, has been proposed. The new vapor-liquid equilibrium data in (HCHO–H2O–salt) were systematically measured and utilized to determine newly-introduced model parameters. Comparisons of model calculated and experimental measured values proved that the model presented here provides a reliable method for correlating the vapor-liquid equilibria data in (HCHO–H2O–salt) system. Furthermore, the model established in this work was used to study salts effect on vapor-liquid equilibria. Both the model calculations and the VLE experiments uncover that Zn(NO3)2 is the most promising among all of the entrainers investigated.

Thermodynamic modeling of the water – Nitric acid – Rare earth nitrate systems

An excess Gibbs energy model describing the properties of aqueous electrolyte solutions, mixed solvent electrolyte systems and nonelectrolyte systems, has been developed. The suggested electrolyte version of the Generalized Local Composition Model (eGLCM) contains three contributions to the excess Gibbs energy: a long–range electrostatic interaction term represented by the modified Pitzer-Debye-Hückel equation, which takes into account concentration dependence of the solution dielectric permittivity, the contribution of the short–range interaction between all the species, represented by the GLCM model, and the middle–range interaction term responsible for interactions involving charged species that are not explained by the long–range term. The developed model is applicable over a whole concentration range, from pure water to saturation and fused salts. The water – nitric acid system, 15 water – rare earth element nitrate systems (Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb and Lu) and eight water – nitric acid – REE nitrate systems (Y, La, Ce, Pr, Nd, Sm, Eu and Gd) have been modeled with the proposed electrolyte version of the Generalized Local Composition Model at 25 °C, using experimental data on both the vapor – liquid (VLE) and solid – liquid (SLE) equilibria, in a concentration range from dilute solutions to saturation. SLE data in the ternary systems were critically reviewed and correlated with the thermodynamic properties of the solutions.

Experiment and modeling of vapor–liquid equilibria for H2O+CH3OH+KCl and H2O+CH3OH+NaBr systems

In this work, vapor–liquid equilibrium (VLE) data were reported on mixed solvent electrolyte systems containing H2O+CH3OH+KCl and H2O+CH3OH+NaBr. The measurements were carried out in a computer-controlled glass apparatus. A new model based on UNIQUAC equation was proposed for the correlation of vapor–liquid equilibria in mixed solvent electrolyte systems. The model for the excess Gibbs energy was modified from the UNIQUAC equation, and the activity coefficients were calculated by UNIQUAC terms and solvent-solution effect terms. In addition, an assumption for the solution effect was introduced into this model. Experiment and literature data for mixed solvent electrolyte systems were successfully correlated using the proposed model.

Predicting the thermodynamic properties of experimental mixed-solvent electrolyte systems using the SAFT-VR+DE equation of state

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.

Modeling of mixed-solvent electrolyte systems

Models for mixed-solvent strong electrolytes, using an equation of state (EoS) are reviewed in this work. Through the example of ePPC-SAFT (that includes a Born term and ionic association), the meaning and the effect of each contribution to the solvation energy and the mean ionic activity coefficient are investigated. The importance of the dielectric constant is critically reviewed, with a focus on the use of a salt-concentration dependent function. The parameterization is performed using two adjustable parameters for each ion: a minimum approach distance (σMSA) and an association energy (εAB). These two parameters are optimized by fitting experimental activity coefficient and liquid density data, for all alkali halide salts simultaneously, in the range 298 K–423 K. The model is subsequently tested on a large number of available experimental data, including salting out of Methane/Ethane/CO2/H2S. In all cases the deviations in bubble pressures were below 20% AADP. Predictions of vapor-liquid equilibrium of mixed solvent electrolyte systems containing methanol, ethanol are also made where deviations in bubble pressures were found to be below 10% (AADP).

Simulation Study of Sludge Precipitation in Spent Fuel Reprocessing

A simulation technology with electrolyte thermodynamic model has been developed to evaluate the precipitation behavior in reprocessing solution. In this study, we have chosen the model of OLI system Inc. which combines an excess Gibbs energy model for mixed-solvent electrolyte systems with a comprehensive treatment of chemical equilibrium. The simulation results of precipitation were compared with the experiment data from non-radioactive simulated HLLW and Pu-Zr-Mo solution, and they showed good agreement each other. Most of the precipitation species was zirconium molybdate hydrate (ZMH) from the both data. This study has shown the thermodynamic simulation model is one of the useful tools to estimate the behavior of precipitation species from the reprocessing solution.

A SAFT-VR+DE equation of state based approach for the study of mixed dipolar solvent electrolytes

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.

Liquid–Liquid Equilibria of Some Aliphatic Alcohols + Disodium Hydrogen Citrate + Water Ternary Systems at 298.15 K

In this paper, the liquid–liquid equilibria for 1-propanol, 2-propanol or 2-methyl-2-propanol + disodium hydrogen citrate aqueous two-phase systems at 298.15 K were studied. The experimental binodal curves at 298.15 K are reported, and the parameters of the Merchuk equation, modified as a nonlinear function of mixed solvent properties and used for the simultaneous correlation of the experimental binodal data. Moreover, the salting-out ability of different salts and different alcohols with different anions is discussed. Additionally, experimental tie-line data are reported at 298.15 K. The generalized electrolyte-NRTL model of the mixed solvent electrolyte systems (e-NRTL) satisfactorily used for the correlation of the tie-line compositions; restricted binary interaction parameters were also obtained.

Thermodynamic investigation of the ATPSs composed of some (aliphatic alcohol + sodium carbonate + water) ternary systems

In this work, the (liquid+liquid) equilibrium of 1-propanol, 2-propanol, 2-methyl-2-propanol, 2-butanol, or (ethanol+sodium carbonate+water) ternary systems was studied. Binodal curves and tie-line data at T=298.15K were reported. The effect of temperature was studied using the obtained cloud-point data as a function of alcohol mole fraction at temperature range T=(293.15 to 328.15)K with 5K intervals. The free energy, enthalpy, and entropy of clouding point (CP) estimated using a simple method, and the driving force of the two-phase formation process was discussed on the base of the estimated free energy values. Salting-out effect was discussed using the values of parameters of one parameter effective excluded volume (EEV) model. The effect of different alcohols on the phase-separation ability of the studied systems was discussed on the base of the intermolecular interactions. Also, a new three parameter nonlinear equation developed and successfully used for the correlation of the binodal curves, and the correlation coefficients were also reported. Moreover, the generalized electrolyte-NRTL model to the mixed solvent electrolyte systems (e-NRTL) was satisfactorily used for the correlation of the tie-line compositions, and the binary interaction parameters were also reported.

Liquid–Liquid Equilibrium of Some Aliphatic Alcohols + Disodium Tartrate + Water Aqueous Two-Phase Systems at 298.15 K

In the present work, the liquid–liquid equilibrium of 1-propanol, 2-propanol, 2-methyl-2-propanol, or 2-butanol + disodium tartrate + water aqueous two-phase systems was studied. The experimental binodal curves and tie-line compositions at 298.15 were reported, and the effect of temperature on the phase separation ability of these systems was studied using cloud-point data as a function of alcohol mole fractions at the (293.15 to 323.15) K temperature range with 5 K successive intervals. The effective excluded volume (EEV) model was also was used to describe the salting-out ability in the studied systems. A simple three-parameter empirical equation was successfully used for the correlation of the binodal data, and the modified electrolyte Wilson model for mixed solvent electrolyte systems was used for the correlation of the tie-line compositions. The restricted binary interaction parameters were also reported. Good agreement between the experimental and the calculated tie-line compositions was observed.

Experimental and theoretical study on liquid–liquid equilibrium of 1-butanol + water + NH4Cl at 298.15, 308.15 and 318.15 K

In this work, the phase behavior of mixed solvent electrolyte systems containing 1-butanol+water+ammonium chloride at temperatures of 298.15, 308.15 and 318.15K and at atmospheric pressure have been studied experimentally and theoretically. For the studied systems, liquid–liquid equilibrium has been observed throughout the studied temperature range. Ammonium chloride shows a salting out effect in the two phase region, while temperature has a minor effect on the liquid–liquid equilibria in the studied temperature range. The measured experimental data have been modeled using a modified version of the extended UNIQUAC model. The model has been found to give a satisfactory description of LLE data obtained in this work, with an average absolute deviation of less than 1.5% in calculated mass fractions compared to experimental data.

Modeling Thermal Conductivity of Electrolyte Mixtures in Wide Temperature and Pressure Ranges: Seawater and Its Main Components

A model has been established for calculating the thermal conductivity of aqueous electrolyte solutions containing the Na+, K+, Mg2+, Ca2+, Cl−, SO42−, CO32−, HCO3−, and Br− ions. The model is based on a previously developed computational framework for the thermal conductivity of mixed-solvent electrolyte systems, which has been expanded by explicitly accounting for pressure effects in addition to temperature and electrolyte composition effects. The model consists of a contribution of the solvent, a contribution of individual species expressed using modified Riedel coefficients, and an ionic strength-dependent term that is due to interactions between species. The model accurately represents the thermal conductivity of solutions containing single and multiple salts at temperatures ranging from 273 K to 573 K, pressures up to at least 1400 bar, and concentrations up to the limit of solid saturation. Further, the model has been applied to seawater and used to elucidate the discrepancies between the experimental data for seawater and those for Na–K–Mg–Ca–Cl–SO4 salt solutions. With parameters evaluated on the basis of data for binary and multicomponent salt solutions, the model provides reliable predictions of the thermal conductivity of seawater.

Modeling Surface Tension of Concentrated and Mixed-Solvent Electrolyte Systems

A comprehensive model has been developed for calculating the surface tension of aqueous, nonaqueous, and mixed-solvent electrolyte systems ranging from dilute solutions to fused salts. The model consists of a correlation for computing the surface tension of solvent mixtures and an expression for the effect of electrolyte concentration. The dependence of surface tension on electrolyte concentration has been derived from the Gibbs equation combined with a modified Langmuir adsorption isotherm for modeling the surface excess of species. The model extends the Langmuir adsorption formalism by introducing the effects of binary interactions between solute species (ions or molecules) on the surface. This extension is especially important for high electrolyte concentrations and in strongly speciated systems. The surface tension of mixed solvents is calculated by utilizing the surface tensions of the constituent pure components together with an effective surface concentration, which is defined for each component and takes into account interactions between solvent molecules. This procedure has been shown to reproduce experimental data for a variety of mixtures. In particular, it accurately predicts the surface tension of ternary solvent mixtures using parameters determined from only binary data. The surface tension model has been coupled with a previously developed thermodynamic equilibrium model to provide speciation and activity coefficients, which are necessary for electrolyte systems. This makes it possible to reproduce the effects of complexation or other reactions in solution. In all cases for which experimental data are available and have been tested, the new model has been shown to be accurate in reproducing surface tension over wide ranges of temperature and concentration. The average deviations between the calculated results and experimental data are 0.68% for binary solvent mixtures, 1.89% for ternary solvent mixtures, and 0.71% for salt solutions up to the solid saturation or pure solute limit.

Thermodynamic modeling and experimental measurement of calcium sulfate in complex aqueous solutions

A newly developed database for the Mixed Solvent Electrolyte (MSE) model of the OLI Systems software was employed to model the solid and aqueous phase equilibria of calcium sulfate hydrates in electrolyte solutions containing NiSO 4, H 2SO 4, MgSO 4, Fe 2(SO 4) 3, LiCl and HCl from 25 to 90 °C. The MSE model is a variant of an excess Gibbs free energy model for Mixed Solvent Electrolyte systems which takes into account long-range electrostatic interactions from a Pitzer–Debye–Hückel equation, middle-range interactions from a second virial coefficient-type equation and short-range interactions from the UNIQUAC model. The effect of cations with similar anions on the solubility was investigated and it was found that the solubility depends mainly on the anion type while the cation has a minor effect. The effect of acid addition and the acid type was also studied. The addition of both HCl and H 2SO 4 increases the solubility; however H 2SO 4 has a less pronounced effect due to the common ion effect. Furthermore, the effect of phase transitions between different calcium sulfate hydrates was studied. The transformation of CaSO 4 dihydrate to anhydrite results in a significant decrease in the solubility, which complicates the chemistry of the system. Since it is not practical to measure solubility data under all conditions of interest, the model developed and the experimental results obtained serves the purpose of assessing the calcium sulfate scaling potential for a wide variety of complex aqueous industrial streams.

Symmetric Electrolyte Nonrandom Two-Liquid Activity Coefficient Model

The electrolyte nonrandom two-liquid (eNRTL) model is reformulated as a symmetric activity coefficient model with the reference states chosen to be pure liquids for solvents and pure fused salts for electrolytes. These reference states are consistently used in the local interaction term, represented by a reformulated NRTL expression, and the long-range interaction term, represented by an extended symmetric Pitzer−Debye−Huckel expression. Retaining the local electroneutrality and like-ion repulsion hypotheses, the new symmetric electrolyte NRTL model yields simpler activity coefficient expressions for both molecular and ionic species. The utility of the model is demonstrated with vapor−liquid equilibrium, liquid−liquid equilibrium, and solid−liquid equilibria of several mixed solvent electrolyte systems.

Prediction of solubilities of salts, osmotic coefficients and vapor–liquid equilibria for single and mixed solvent electrolyte systems using the LIQUAC model

The electrolyte model LIQUAC has been used up till now to predict osmotic coefficients, mean ion activity coefficients, the vapor–liquid equilibrium (VLE) behavior, the solubility of gases in single and mixed solvent electrolyte systems, and solubilities of salts in aqueous solutions. In this paper, the required expressions for the calculation of salt solubilities not only in aqueous systems, but also in organic solvents and water–solvent electrolyte systems were deduced in detail based on the LIQUAC model with a fixed reference state and thermodynamic relations. Four salts (NaCl, KCl, NH 4Cl and NaF) and two solvent (water and methanol) were selected to test the derived expressions. The results show that the LIQUAC model with a fixed reference state can be used to predict osmotic coefficients, solubilities of salts in aqueous solutions, vapor–liquid equilibria, and the solubilities of salts in water–organic solvent systems with strong electrolytes.

Modeling Thermal Conductivity of Concentrated and Mixed-Solvent Electrolyte Systems

A comprehensive model has been developed for calculating the thermal conductivity of aqueous, nonaqueous, and mixed-solvent electrolyte systems ranging from dilute solutions to fused salts or pure solutes. The model consists of a correlation for calculating the thermal conductivity of solvent mixtures and a method for predicting the effect of electrolyte components. The thermal conductivity of multicomponent solvent mixtures can be represented using surface area parameters and thermal conductivities of pure solvents in conjunction with a single binary parameter per solvent pair. The effect of electrolytes is modeled by accounting for a contribution of individual ions, which is quantified by the Riedel coefficients, and a contribution of specific interactions between ions or neutral species. Formulations have been developed for the contributions of individual ions and species−species interactions to represent the effect of multiple solvents. In addition to solvent composition, the species−species interacti...

Correlation and Prediction of Thermodynamic Properties of Nonaqueous Electrolytes by the Modified TCPC Model

In this work, the modified three-characteristic-parameter correlation model was introduced to correlate and predict the thermodynamic properties, such as the mean activity coefficient, the osmotic coefficient, and the solvent activity, of different kinds of nonaqueous electrolyte solutions. Two sets of parameters, (b, S) and (b, S, n), for 46 single salts in methanol, ethanol, and 2-propanol, etc., were regressed from literature data at 298.15 K. Results of standard deviations showed the good applicability of our model. The calculated results of the mean activity coefficient by our model and the Pitzer model have been compared with each other with good agreement. Smoothed experimental data of osmotic coefficients and solvent activities were calculated with the present model with three or two parameters, and the one with three parameters showed a better performance. We also extended this model for some nonaqueous systems at elevated temperatures, and we also found good consistency between the results calculated from our model and experimental data. Moreover, we further developed this model for calculating those in the mixed-solvent electrolyte systems. The results showed our modified model could adequately describe these complicated electrolyte solutions.

Modeling acid–base equilibria and phase behavior in mixed-solvent electrolyte systems

A comprehensive thermodynamic framework for mixed-solvent electrolyte systems has been applied to the simultaneous computation of phase behavior and acid–base equilibria. The computational approach combines an excess Gibbs energy model with a formulation for standard-state properties of individual species and an algorithm for speciation calculations. Using this framework, a consistent methodology has been established to calculate the pH of mixed-solvent solutions using a single, aqueous reference state. It has been shown that solid solubilities, vapor–liquid equilibria, solution pH and other properties can be reproduced for mixed solvents ranging from pure water to pure non-aqueous components and for solutes ranging from infinite dilution to the fused salt limit. In particular, the model has been shown to be accurate for mixtures containing hydrogen peroxide and ethylene glycol as solvents and various salts, acids and bases as solutes.