On the impact of using volume as an independent variable for the solution of P-T fluid-phase equilibrium with equations of state

The constant pressure-temperature (P− T ) flash plays an important role in the modelling of fluid-phase behaviour, and its solution is especially challenging for equations of state in which the volume is expressed as an implicit function of the pressure. We explore the relative merits of solving the P− T flash in two ensembles: mole numbers, pressure and temperature, in which each free-energy evaluation requires the use of a numerical solver; and mole numbers, volume and temperature, in which free-energy evaluations are straightforward. We examine the performance of two algorithms, HELD (Helmholtz free energy Lagrangian dual) (Pereira et al., 2012) and GILD (Gibbs free energy Lagrangian dual), introduced here, for the fluidphase equilibria of 8 mixtures comprising up to 10 components, using two equations of state. While the reliability of both algorithms is comparable, the computational cost of HELD is consistently lower; this difference becomes increasingly pronounced as the number of components is increased.