Rigorous Phase Equilibrium Calculation Methods for Strong Electrolyte Solutions: The Isothermal Flash

Abstract

New algorithms for vapor – liquid (VLE) and liquid - liquid (LLE) equilibrium calculations at constant temperature, pressure and feed phase composition (PT flash), with application to mixtures containing fully dissociating electrolytes are presented. A new approach is proposed and is rigorously derived by treating phase equilibrium as a minimization problem of the Gibbs free energy, while utilizing the electro-neutrality condition as a constraint. In this way, an augmented function (Lagrange function) is formulated which serves as the basis for the equations that govern phase equilibrium. It is shown that the Lagrange multiplier which corresponds to the electro-neutrality constraint has theoretical meaning and direct relation to the electrostatic potential difference between inhomogeneous phases. Based on the new approach, named Electrochemical Ionic Approach (EIA), two new numerical methods are presented; a successive substitution method similar to the classical Rachford-Rice method and a second-order one, which is based on Newton's method. The new algorithms are general and can be readily applied to mixtures of multiple solvents and one or multiple salts without any modifications. Finally, the Mean Ionic Approach (MIA) for mixtures with multiple solvents and only one salt is discussed in detail and a successive substitution and a second-order method are formulated. Moreover, the MIA is formally extended and presented for mixtures of multiple solvents and multiple salts. All the resulting methods are applied to mixtures with multiple solvents and one or multiple strongly dissociating electrolytes. The performance and technical details of each method are discussed and compared. The calculations are performed with the electrolyte Statistical Associating Fluid Theory with the Mie potential of variable range (eSAFT-VR Mie) equation of state but the proposed methods are general and could be used with any other thermodynamic model.