Compare the phi-phi and gamma-phi approaches for VLE calculations. When would you use each?

The phi-phi approach uses equations of state for both phases: y_i*phi_V*P = x_i*phi_L*P, where fugacity coefficients are calculated from EOS for vapor and liquid. Best for: high pressure systems, near-critical conditions, light hydrocarbons, and systems where both phases are well-described by the EOS. The gamma-phi approach uses activity coefficient for liquid and EOS for vapor: y_i*phi_V*P = x_i*gamma_i*P_sat*phi_sat. Best for: low to moderate pressure, polar/non-ideal liquids, and when reliable activity coefficient model parameters exist. Phi-phi is thermodynamically consistent at all conditions but requires good EOS parameters; gamma-phi handles liquid non-ideality better but fails near critical points.