  The free energy model can extend the Lattice Boltzmann method to multiphase
systems. However, there is a lack of models capable of simulating
multicomponent multiphase fluids with partial miscibility. In addition,
existing models cannot be generalized to honor thermodynamic information
provided by any multicomponent equation of state of choice. In this paper, we
introduce a free energy Lattice Boltzmann model where the forcing term is
determined by the fugacity of the species, the thermodynamic property that
connects species partial pressure to chemical potential calculations. By doing
so, we are able to carry out multicomponent multiphase simulations of partially
miscible fluids and generalize the methodology for use with any multicomponent
equation of state of interest. We test this fugacity-based Lattice Boltzmann
method for the cases of vapor-liquid equilibrium for two and three-component
mixtures in various temperature and pressure conditions. We demonstrate that
the model is able to reliably reproduce phase densities and compositions as
predicted by multicomponent thermodynamics and can reproduce different
characteristic pressure-composition and temperature-composition envelopes with
a high degree of accuracy. We also demonstrate that the model can offer
accurate predictions under dynamic conditions.
