A practical method for the calculation of liquid–liquid equilibria in multicomponent organic–water–electrolyte systems using physicochemical constraints

Liquid mixtures containing a variety of organic compounds, water, and dissolved electrolytes are prone to liquid–liquid phase separation, owing to non-ideal interactions between water, ions, and organic compounds. Such systems are of practical importance in the design of chemical separation processes as well as the partitioning of semivolatile species in atmospheric aerosols. In this study, a practical phase separation calculation method based on a system of nonlinear equations is presented, applicable to multicomponent systems containing inorganic ions. Expressions are derived that allow consistent use of activity coefficients defined on molality basis for ionic species in combination with mole fraction-based activity coefficients for nonelectrolyte components. Physicochemical considerations are applied together with preliminary evaluation of generated trial compositions to automatically obtain a set of feasible initial guesses. A successive substitution procedure with component-specific step length damping is then employed, followed by a rapid convergence part using a globally convergent solver for systems of nonlinear equations. We discuss several examples that demonstrate the method's remarkable level of reliability even in the case of systems showing highly non-ideal mixing behavior, and we highlight the importance of providing a good initial guess.