(382f) A Cubic Equation of State for Compounds with No Critical State

One key aspect of all cubic EOS modeling is that they rely heavily on the use of critical properties [i.e., critical temperature and pressure] to compute the molecular co-volume, b , and the energy (or attraction) parameter, a. However, there are many compounds (e.g., polymers, asphaltenes, biological molecules, ionic liquids, metallic glasses, etc.) that do not have critical properties because they decompose before reaching a critical state. Instead they often exhibit a glass transition region. What happens then? Two general approaches are commonly used. That is, either (1) fictitious critical properties estimated by either group contribution methods or correlations or (2) a more complex equation are used. For example, asphaltenes are typically fractions of heavy oils and bitumen and their critical properties are often estimated for phase equilibrium modeling using correlations despite the fact that they generally decompose around 300 - 350 C.

In this work, the Gibbs-Helmholtz Constrained (GHC) equation of state framework is extended to compounds without critical properties. In particular, a numerical methodology is developed for determining the boundary condition for the energy parameter, which is then used in the GHC equation to predict thermo-mechanical and physical properties as well as phase equilibrium involving glassy materials. Several examples are used to illustrate the key features and efficacy of the proposed approach, including a model asphaltene fluid proposed by Mullins (2010). Computational results clearly show that the GHC equation can accurately and reliably predict mass and molar densities, molar volumes, isothermal compressibility, coefficients of thermal expansion, and phase behavior of glassy materials over wide ranges of temperature and pressure and that GHC-predicted properties and phase equilibrium agree favorably with available values reported in the open literature.