The paper presents a novel approach for the solution of the isothermal multiphase flash problem with particular application to systems exhibiting liquid‐liquid‐vapor equilibria. The approach includes a rigorous method for thermodynamic stability analysis as a first step and an efficient phase identification procedure. The stability analysis, exercised only once, uses a modification of the Gibbs tangent plane criterion. The identification procedure implements the results of the stability test in a sequence of liquid‐liquid and liquid‐vapor calculations only till the phase configuration with a minimum Gibbs energy is determined. The efficiency and reliability of the proposed new method is illustrated by solving three typical problems encountered in enhanced oil recovery, natural gas processing and petrochemical industry.

The paper introduces new developments of the original AREA method. A rigorous mathematical proof that the equilibrium points are the only ones which satisfy the maximum AREA criterion in the case of a two-component, two-phase system is given for the first time. A rigorous proof that the maximum AREA criterion is a necessary but not a sufficient condition for equilibrium in the case of an N-component, two-phase system is given also for the first time in the paper. Two test examples which reinforce the validity of the theoretical results obtained are presented and discussed.