Quasi-Newton single-phase stability testing without explicit Hessian calculation

A robust solver for testing the single-phase stability of a multi-component fluid under isochoric-isobaric conditions is developed. The approach is based on quasi-Newton minimization of Helmholtz free energy. The solver does not need explicit Hessian calculation when used with properly scaled variables. The solver is not tied to a specific equation of state and is applicable when the derivatives are calculated using automatic differentiation. The generation of initial estimates only needs an auxiliary cubic equation of state. We analyze robustness and performance of the solver and present calculations of phase boundary for a number of mixtures using a cubic and a SAFT-type equations of state.