Initialization of phase fractions in Rachford–Rice equations for robust and efficient three-phase split calculation

A key element of efficient and robust three-phase split calculation is the initialization of phase mole fractions. While the initial guess of equilibrium ratios is made from two-phase split calculation and two-phase stability testing, initializing phase fractions through solving three-phase Rachford–Rice equations can be a challenge especially close to the bicritical points and phase boundaries. In this research, we examine three different methods: the improved two-dimensional bisection method, the minimization method, and the direct Newton method. We present a large number of three-phase examples of various degrees of complexity to demonstrate both robustness and efficiency of all these methods. The direct Newton method combined with the starting guess of phase fractions from two-phase split calculation and two-phase stability testing is the most efficient approach.