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In this paper, theoretical considerations on electrolyte thermodynamic models are discussed for single and mixed solvent solutions. A literature review has revealed that for many fundamental issues there is no consensus amongst researchers in this field. Specific questions have been formulated to enable the clarification of these issues, and then answered. Electrolyte terms are considered to belong to a different framework (McMillan-Mayer) than the physical terms of the thermodynamic models (Lewis-Randall). The electrolyte terms should be converted to the framework of the physical model, prior to the combination of the physical and electrolyte terms. If the RSP of the solution (mixed or single) does not depend on the ion concentration, then the two frameworks are equivalent for equations of state (EoS). For activity coefficient models (GE), a pressure correction term is needed to consistently combine the electrolyte to the physical model. These corrections are more important for higher concentrations. However, many electrolyte models adopt ion-concentration dependent RSP, which violates the aforementioned conversion between the different frameworks; in other words, it breaks the link between electrostatic theories and thermodynamic models. This weakens the physical background of the thermodynamic models but does not make them thermodynamically inconsistent. Last but not least, we confirm the importance of the Born term for LLE calculations. The Born term (or an equivalent term) is required in all models (EoS and GE) to consistently convert the reference state used by the models (ideal gas and ideal solution) to the real system. The functionality of the Born term is highly related to the RSP and the Born term is only consistent when the compositional derivatives of the RSP are used. If either of these conditions are not met, the model will not be able to accurately calculate mixed solvent LLE.

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.

In this work, the eSAFT-VR Mie equation of state (EoS) is extended to low relative permittivity, non-aqueous solutions. The effect of using different relative permittivity relations for the electrolyte solutions is studied, ranging from experimentally measured values to a salt-composition independent relative permittivity. Furthermore, the effect of using different approaches for the characteristic diameters in the Debye-Hückel and Born terms is presented. The eSAFT-VR Mie EoS is reparametrized using aqueous mean ionic activity coefficients, individual ion activity coefficients and densities with different relations for the relative permittivity. Afterwards, the performance of these models on non-aqueous solutions is evaluated based on the Mean Ionic Activity Coefficients of salts in non-aqueous solutions. The conclusion is that a mole fraction based mixing rule for the relative permittivity yields the best extrapolation from aqueous to non-aqueous solutions, and achieves quantitative predictions for the mean ionic activity coefficients of monovalent salts in methanol and ethanol without additional adjustable parameters.

In this work, the eSAFT-VR Mie equation of state (EoS) is applied to water-methane-salt and water-carbon dioxide-salt mixtures. Initially, the EoS parameters for nonelectrolyte systems are fitted, and temperature-dependent water-ion interaction parameters are introduced to improve the behavior of the model at high temperatures. Furthermore, a database of experimental methane and carbon dioxide solubility in single-salt aqueous solutions was compiled. Four different parameterization schemes regarding gas-ion dispersion energy have been pursued in this work, namely, (a) setting the gas-ion dispersion energy parameter to zero, (b) using the SAFT-VR Mie combining rules without any binary interaction parameters, (c) using the predictive Hudson-McCoubrey combining rules, and last but not least (d) fitting to experimental solubility of gases in aqueous solutions of single salts. The fitting approach yields an average deviation from experimental data of about 10%, compared to more than 25% for the other approaches. However, despite the great overall deviations of the predictive methods, there are cases where they yield excellent results, such as methane solubility in aqueous NaCl solutions. The salting-out behavior predicted with the fitted parameters is excellent at room temperature but deviates from experimental data at higher temperatures. Finally, the model is applied to gas solubility in mixed-salt solutions, without further adjustable parameters, and the predictions are in excellent agreement with experiments. Overall, eSAFT-VR Mie shows great potential for gas solubility calculations under salinity.

The study of water-hydrocarbon phase equilibria is very important for both scientific and industrial purposes. This work is a thorough investigation of the predictive capability of SAFT-VR Mie equation of state (EoS) for aqueous hydrocarbon phase equilibria, including n-alkanes, alkenes, cycloalkanes, branched alkanes, and aromatic hydrocarbons. For alkenes and alkyl benzenes, induced association (solvation) with water is considered. The model is able to capture the correct phase equilibrium topology for mixtures of n-alkanes and alkyl-benzenes with water as type III according to Van Konynenburg and Scott, but it is not able to predict the barometric shift for alkanes longer than n-hexacosane due to the overshoot of the critical temperature of water. Quantitative results for the solubility of water in light hydrocarbons such as methane, ethane, and ethylene, as well as the mutual solubility of hydrocarbons and water above the solubility minimum, are possible. The latter is not predicted with SAFT-VR Mie EoS similar to other EoSs in literature. Accurate predictions are also reported for the pressure of the three-phase equilibrium and the critical lines for the binary mixtures. Henry's law constant is often used for the prediction of low-pressure vapor-liquid equilibrium due to the low mutual solubility of hydrocarbons and water. EoS calculations are in reasonable agreement with experimental data for Henry's constant, especially at higher temperatures. Qualitatively, SAFT-VR Mie captures the maximum of Henry's constant with temperature, as well as the shift with the carbon number at temperatures near critical to water. SAFT-VR Mie is shown to be overall capable of straightforward prediction of phase equilibria of aqueous hydrocarbon mixtures.