Testing the ability of various equations of state to reproduce high-pressure isotherm crossings in the (α, P) plane

This paper focuses on a singularity exhibited by most dense fluids in the (α, P) plane (where α denotes the isobaric expansivity and P, the pressure): for a given fluid, nearly all isothermal curves share a common intersection point. In this paper, we test the capacity of a series of equations of state to model this little-known phenomenon. Equations of state that can be written as the sum of an attractive and a repulsive term are first considered. As a result, equations of state involving a Carnahan–Starling repulsive term always predict the aforementioned crossing point contrary to equations of state involving a classical Van der Waals repulsive term. Quantitatively, the Carnahan–Starling–Van der Waals (CS–VdW) equation of state and the Carnahan–Starling–Soave–Redlich–Kwong (CS–SRK) equation of state both lead to satisfactory results. In addition, some pitfalls of the Carnahan–Starling–Peng–Robinson (CS–PR) equation of state are identified which justifies that this model cannot represent dense-fluid behaviors. The Perturbed-Chain Statistical Associating Fluid Theory (PC-SAFT) equation of state is then tested. The obtained results are more extremely satisfactory when compared to the CS–vdW equation of state. Finally, a general criterion that must be verified by equations of state in order to predict isotherm crossings is proposed and illustrated.