Parameterization of molecular-based equations of state

Abstract

Despite significant advances in the development and formulation of molecular-based (MB) equations of state (EOS), their practical use has been limited, at least in part, by unavailability of the fluid-specific constants. In this work, we explore the possibility and consequences of obtaining the MBEOS parameters of a fluid directly from its critical constants Tc, Pc and acentric factor ω, as is done with cubic EOS.Four different models are used as examples: perturbed hard chain theory in original (PHCT) and simplified (SPHCT) forms, Huang–Radosz version of the statistical associating fluid theory (SAFT), and the augmented van der Waals theory as implemented in the Boublík–Alder–Chen–Kreglewski (BACK) EOS. For each model, the scaled critical and saturation properties are computed and approximated by polynomial expansions. Using these, the molecular parameters can be related to the macroscopic properties Tc, Pc and ω. In this way it is not necessary to fit the EOS parameters to extensive experimental data, because the parameters obtained are fully equivalent to those generated from complex minimization techniques. In particular, the BACK EOS, parameterized in terms of Tc, Pc, ω and critical compressibility factor Zc, gives excellent representation of the entire phase envelope. An alternative approach is also suggested where the experimental critical volume Vc and ω are matched, and a simple one-dimensional search is used to minimize the average absolute deviation of saturation pressures.The techniques presented in this work provide a simple way to estimate MBEOS parameters for a wide variety of fluids, and can be readily extended to other MBEOS.