Development of a Generalized Quartic Equation of State for Pure Fluids

A generalized quartic equation of state has been developed for pure simple fluids. It is a four parameter perturbed hard sphere equation of state. The four parameters of the equation of state for any fluid depend only on three properties of the fluid, namely critical temperature, critical volume and the acentric factor. The repulsive contribution to the pressure has been modelled using an mathematical approximation of a hard-sphere equation of state. An empirical equation is used to model the attractive contributions to the pressure. Being a quartic equation of state, it yields four roots when solved. One root of the quartic equation is always less than the close packed volume of the fluid and hence has no physical meaning. The remaining three roots behave like the three roots of a cubic equation of state. Thus, the equation of state has the advantages of the cubic equation of state, namely, simplicity and unequivocal identification of the roots. The quartic equation of state models the attractive and repulsive contributions to the pressure correctly, unlike cubic equations of state.

The constants in the equation of state have been obtained by performing multiproperty regressions using data for 16 pure fluids. These constants have been generalized and are functions of the acentric factor of the fluid. Comparison of the new equation of state with the Peng-Robinson and the Kubic's quartic equation of state has been presented. Density and thermodynamic properties such as the second virial coefficient and residual enthalpy predictions have been compared. The new equation of state is more accurate than the Peng-Robinson and the Kubic equation of state, particularly, in the supercritical region and the compressed liquid region.