Phenomenological High-Pressure Equation of State for Nitrogen, Methane, Methanol, Carbon Dioxide, and Helium

The vapor-liquid phase equilibria, saturation curves and pressure isotherms of nitrogen, methane, methanol, carbon dioxide and helium are modeled with a closed-form non-cubic equation of state (EoS), developed to describe high-pressure and high-density properties of fluids. The EoS is analytic and applicable to pure compounds as well as mixtures in the full temperature range above the melting point (or lambda point in the case of normal fluid helium) and up to the limit density where the pressure singularity occurs. The temperature evolution of the EoS is determined by four temperature-dependent scale factors on which the EoS linearly depends. Above the critical temperature, these scale factors can be regressed from empirical supercritical isotherms. Based on the proposed EoS, the Helmholtz and Gibbs free energies of the mentioned fluids are calculated, also in closed form. In the subcritical regime, a convex Helmholtz free energy is obtained by way of the common tangent construction. The subcritical scale factors of the EoS are inferred from the empirical liquid and vapor saturation densities, so that the EoS is consistent with the common tangent construction and the measured coexistence curve.