(382q) The Role of Mathematical Artifacts in Deteriorating the Physical Behavior in SAFT Theories

In recent years, statistical mechanical theories have widely been used in developing equations of state. To overcome the mathematical difficulties associated with these theories, various empirical approximations have been used to produce analytical expressions. In this work, we propose a new method to critically evaluate the impact of such empirical approximations in deteriorating the physical behavior of equations of state of pure fluids. The proposed method utilizes bifurcation analysis to discover unphysical behavior in any equation of state. The bifurcation analysis studies how molar volume bifurcates as temperature varies at constant pressure. The new method efficiently discovers spurious two-phase separation regions, shows unphysical branches, determines multiplicities in volume roots and demonstrates how unphysical branches deteriorate the physical behavior. The bifurcation analysis is applied to study several versions of statistical association fluid theories including SAFT-VR Mie, soft-SAFT, PC-SAFT and CKSAFT.