Modeling of dynamic systems with a variable number of phases in liquid-liquid equilibria

Modeling of dynamic systems with a variable number of phases is still a challenge, especially for multiple liquid phases. A common approach from literature derives first-order Karush-Kuhn-Tucker (KKT) conditions of the Gibbs free energy minimization and relaxes these if a phase does not exist. It aims at enabling dynamic simulation in all phase regimes of systems in vapor-liquid equilibrium by following a nonphysical continuous solution. In this work, we demonstrate that this continuous solution is not always possible in liquid-liquid equilibrium problems. The demonstration is done both theoretically and for illustrative examples. To overcome the demonstrated issues, we review the use of negative flash approach that allows negative molar amounts of nonexisting phases and propose a hybrid continuous formulation that explicitly assigns phase variables in the single-phase regime and solves flash equations otherwise. Various dynamic case studies demonstrate the applicability and limitations of all three approaches. (c) 2018 American Institute of Chemical Engineers AIChE J, 65: 571-581, 2019