Investigation of mixture stability at given volume, temperature, and number of moles

General algorithm for multiphase equilibria calculation at given volume, temperature, and moles

“…In the previous work [22,23,9], we dealt with the single-phase stability analysis and the two-phase split calculation, both at constant volume, temperature, and moles. Now, we extend these results and present a general strategy for -phase equilibrium computation at constant volume, temperature, and moles in a multicomponent mixture, where ∈ N is the number of phases which is now not known a priori.…”

“…It can be proven that testing the stability of an -phase equilibrium state is thermodynamically equivalent to the single-phase stability testing of any of the equilibrium phases [11,6]. The constant-volume single-phase stability test from [23] decides whether the single phase is stable or not at given volume, temperature, and moles. The stability investigation is based on testing trial phases of different compositions in order to find out if there is a composition for which transfer of a small amount of the trial phase from the initial phase causes a decrease in the Helmholtz energy.…”

“…The stability investigation is based on testing trial phases of different compositions in order to find out if there is a composition for which transfer of a small amount of the trial phase from the initial phase causes a decrease in the Helmholtz energy. The criterion of stability at constant volume, temperature, and moles is formulated using the so-called tangent plane distance D function (see [23] for details). The single phase is stable if …”

“…If a trial phase composition is found such that the D function is negative, the mixture is unstable and splits into two phases. In the two-phase case, concentrations of the trial phase, for which the value of D is negative, can be found using the algorithm from [23] and used in the construction of an initial guess for the phase-split calculation.…”

“…Furthermore, as the method guarantees decrease of the total Helmholtz energy of the system in every iteration, it always converges to a state corresponding to at least a local minimum of the energy. To initialize the algorithm, the results of the constant-volume stability algorithm, which has been developed in [23], are used. In this work, we extend the method and propose a general strategy forphase equilibrium computation at constant volume, temperature, and moles, where ∈ N is the number of phases.…”