Evaluation of the performance of cubic equations of state in predicting the regularities in dense fluids

Abstract

This paper deals with the evaluation of 10 recent van der Waals type equations of state (EOS) for their ability to predict the three important regularities. The studied regularities included: (i) the linearity of Zeno contour of reduced temperature against reduced density from the Boyle temperature to the triple point, (ii) the common bulk modulus point on the isotherms of the reduced bulk modulus versus reduced density, and (iii) the near linearity of reduced isothermal bulk modulus as a function of reduced pressure (Tait–Murnaghan equation) over the vapor pressure curve to the freezing line. The investigated equations of state are Kubic–Martin (KM), Adachi–Lu–Sugie (ALS), Yu–Lu (YL), Trebble–Bishnoi (TB), Iwai–Margerum–Lu (IML), Twu–Coon–Cunningham (TCC), modified Patel–Teja (MPT), Nasrifar–Moshfeghian (NM), Peng–Robinson (PR) and Soave–Redlich–Kwong. The best overall performance for Zeno contour is obtained based on the SRK, TB, KM and PR EOS, whilst the NM and ALS EOS produce the worst performances. The Zeno line prediction using the SRK, TB, KM and PR EOS approach the experimental reduced Boyle temperature at low-density, confirming their accuracy in supercritical region. The low-density region of the isothermal bulk modulus of CH 4, as a spherical molecule, is well matched by SRK and KM EOS, but is closely matched by TB, IML and NM EOS. In compressed liquid, we observe that the slope and curvature of the calculated bulk modulus of CH 4 obtained by SRK and KM EOS consistently performs better than the other EOS. For C 2H 6, C 3H 8 and n-C 4H 10 the predictive ability of the isothermal bulk modulus obtained from the cubic EOS are usually poor, especially at higher densities. We have also shown that the most accurate prediction of Tait–Murnaghan regularity of CH 4 is KM, SRK, PR and MPT EOS for both subcritical and supercritical fluids in a wide pressure range, while the TB and NM EOS predict the Tait–Murnaghan regularity for supercritical fluids.