An accurate direct technique for parametrizing cubic equations of state: Part III. Application of a crossover treatment

This work presents an extension of a generalized van der Waals-type equation of state by including a crossover treatment to consider the fluctuations in the critical region. The original cubic equation depends on simple parameters of pure fluids, and it is able to reproduce vapor pressures and densities over a wide range of conditions, once the appropriate parametrization techniques are used. The equation is forced to reproduce the critical point by explicitly including this point into the fitting procedure. However, as all mean field theories, the equation does not take into account the fluctuations appearing as the critical region is approached. Hence, the non-analytical asymptotic behavior in the vicinity of the critical point is not well reproduced, leading to some inaccuracies in liquid and/or gas phase equilibria density calculations. To overcome this limitation we have applied a specific crossover treatment, based on White's work [J. White, Fluid Phase Equilib. 75 (1992) 53–64; L.W. Salvino, J.A. White, J. Chem. Phys. 96 (1992) 4559–4568] from the renormalization group (RG) theory [K. Wilson, Phys. Rev. B4 (1971) 3174–3205]. This treatment is done by incorporating the scaling laws valid asymptotically close to the critical point. In addition to accurate density estimations far from and close to the critical point, the extended equation is also able to reproduce the universal critical exponents describing the approach to the critical point. The extended equation has been applied to two chemical families: the n-alkanes and 1-alkanols, as well as to other compounds of industrial interest, including carbon dioxide, ethylene, toluene, xenon and water, providing excellent agreement with experimental data.