The HELD algorithm for multicomponent, multiphase equilibrium calculations with generic equations of state

The HELD (Helmholtz free Energy Lagrangian Dual) algorithm is proposed to solve the isothermal, isobaric phase equilibrium problem (P,T flash). The flash is posed as a minimisation of the Helmholtz free energy in the volume–composition space, reformulated through duality theory. The proposed solution strategy consists of: an initialisation stage, containing a stability test; a phase identification stage, in which linear and nonconvex optimisation problems are solved alternatively; and an acceleration and convergence stage. The stability test is solved with a tunneling algorithm and the nonconvex part of the second stage with a multistart approach. Examples are presented for three equations of state, SRK, SAFT-HS and SAFT-VR. Non-ideal mixtures of up to fifteen components are examined; they exhibit features such as azeotropy, liquid–liquid, and liquid–liquid–liquid equilibria. The HELD algorithm is found to be reliable over a variety of challenging phase behaviour, converging to the best known solution in all of the calculations undertaken.

► The HELD algorithm is presented to solve isothermal–isobaric phase equilibrium.
► Formulated as a dual problem in Helmholtz free energy/volume/composition.
► Random multi-start used for nonconvex inner problems.
► Applicable to any equation of state, type of mixture and fluid-phase behaviour.
► Reliable for highly non-ideal mixtures modelled with SRK and SAFT equations.