I would like to know how to interpret the roots of the Peng Robinson equation of state for vapor-liquid-liquid equilibrium.
I know that if two phases are present, the largest root is taken as the compressibility factor of the vapor and the smallest root is taken as the compressibility factor of the liquid.
What does the smallest root represent if two liquid phases are present (in addition to the vapor)? Is it meaningful?
And how can I determine the compressibility or molar volume of each liquid phase?
Ultimately my goal is to be able to calculate the fugacity coefficients for components in the vapor phase, liquid phase 1, and liquid phase 2 in order to calculate the K factors for use in a multicomponent equilibrium algorithm - but I believe that I need the molar volume of all three phases in order to do this.