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A new equation of state derived by the statistical mechanical perturbation theory

Shokouhi, M ; Sharif University of Technology | 2008

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  1. Type of Document: Article
  2. DOI: 10.1016/j.fluid.2007.10.002
  3. Publisher: Elsevier , 2008
  4. Abstract:
  5. We have derived an analytical equation of state (EOS) based on the soft-core statistical mechanical perturbation theory for fluids, using the Weeks-Chandler-Andersen (WCA) theory recently developed by Ben-Amotz-Stell (BAS) for the choice of the hard-sphere diameter, but with a new algorithm for calculation of the pair and many-body interactions. We have used Carnahan-Starling expression with the Boltzmann factor criterion (BFC) as an effective hard-sphere diameter for the reference system, and also decomposed the perturbed pair potential to symmetric and asymmetric terms. The former term is due to the many-body interactions at high densities as was used in the linear isotherm regularity known as LIR EOS, and the latter term supports the interaction of two isolated particles that is dominating at low densities. The resulting EOS is obtained as Z = Zcs + αρ + Aρ3 + Bρ5, in which Zcs is the Carnahan-Starling expression for the compressibility factor of the reference system which contains the effective van der Waals co-volume, and α is due to the asymmetric interaction term, or the attraction contribution of the second virial coefficient. The A and B parameters are the attractive and repulsive contributions of symmetric term, respectively. The temperature-dependencies of all parameters of the EOS are obtained. We select some different fluids, namely Ar, N2, CH4, Ne, CO2, C2H6, C3H8, NH3 and H2O which are spherical, roughly spherical, non-spherical, polar and associated fluids, due to their abundance of P-V-T experimental data. We have found that, except for the critical region, 0.8 < ρr ≤ 1.5, 1 ≤ Tr ≤ 1.5, the new EOS is accurate for all temperatures and densities available in the literatures, in such a way that the average percent deviation of density for Ar, Ne, N2, CH4, CO2, C2H6, C3H8, and NH3 is less than 2.81%. Then some thermodynamic properties including vapor-pressure curve, Joule-Thomson inversion curve, P-T isochors curves, and the second virial coefficient have been applied to check the accuracy of the new EOS. Results for some isochors of argon show that the new EOS gives a small negative curvature for all isochors. The new EOS prediction of the inversion Joule-Thomson curve is reasonable, and its prediction of Clausius-Clapeyron diagram for neon and argon is very accurate, but small deviation for methane and nitrogen can be seen. © 2007 Elsevier B.V. All rights reserved
  6. Keywords:
  7. Statistical methods ; Asymmetric interactions ; Effective hard-sphere diameter ; First-order perturbation theory ; Computational fluid dynamics ; Algorithms ; Boltzmann equation ; Computation theory ; Methane ; Nitrogen ; Perturbation techniques
  8. Source: Fluid Phase Equilibria ; Volume 264, Issue 1-2 , 2008 , Pages 1-11 ; 03783812 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S037838120700636X