Calculation of Multiphase Equilibria Containing Mixed Solvents and Mixed Electrolytes: General Formulation and Case Studies

Aqueous and non-aqueous electrolyte solutions are ubiquitous in chemical and biochemical applications, especially in innovative processes, and they play a major role in geochemistry, environmental science, and numerous other scientific fields. Despite the obvious importance of electrolyte systems, research success on electrolyte thermodynamics is still behind all of the advances on non-electrolyte thermodynamics. After decades of research, several issues of thermodynamic models for electrolytes remain the object of discussion in the thermodynamic community. Still today, only a few simulation packages offer a general approach to calculate phase equilibria of electrolyte systems in a broad application range regarding the kind of salts and solvent, the number of phases, and the number of non-ionic or ionic species involved. In this work, the general background and the assumptions behind the equilibrium conditions of multiphase electrolyte systems with distributed ions are reviewed. A general methodology is proposed, which can be used to determine the number of liquid phases and their composition at equilibrium of any electrolyte system independent of the number of components. The algorithm was implemented in a FORTRAN routine using the equation of state "ePC-SAFT advanced" (Bulow, M.; Ascani, M.; Held, C. ePC-SAFT advanced-Part I: Physical meaning of including a concentration-dependent dielectric constant in the born term and in the Debye-Huckel theory. Fluid Phase Equilib. 2021, 535, 112967) to estimate the fugacity of each species. The algorithm was successfully tested against experimental data using case studies including three-phase liquid-liquid-liquid equilibria with two ionic species and two-phase liquid-liquid equilibria with three ionic species.