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Eubank and Hall have shown recently that the tangent-line criterion reduces to an equal area construction for the derivative of the total Gibbs energy plotted against composition. This paper presents another criterion along with a thermodynamic proof, the maximum partial area rule (MPAR), which establishes an area on the plot of the derivative of the Gibbs energy with respect to composition which is always a maximum at equilibrium. The method based upon this criterion is especially powerful for complex phase equilibria involving multiple components and phases.

Cubic equations of state (EOS) cannot provide accurate multithermophysical properties over wide ranges of temperature and pressure for pure components in the fluid state. More complex, noncubic EOS are required, but only recently has their use been made feasible by advances in computing. These equations often produce isotherms on a pressure-specific volume (P−V) plot with more than one van der Waals loop. This produces multiple solutions to the Maxwell Equal Area Rule (MEAR) criterion for determining the saturated vapor pressure, P^σ, at a fixed temperature. A mechanical stability test is used to determine which one of these solutions gives stable vapor and liquid phases at equilibrium. We have developed a new corollary of MEAR, called the Maximum Positive Area (MPA) criterion, for determining the correct P^σ of pure components regardless of the complexity of the EOS used. In the MPA criterion, the correct P^σ occurs when the positive area, determined in the MEAR criterion, is maximized.