On Molecular-Based Equations of State: Perturbation Theories, Simple Models, and SAFT Modeling

Abstract

With the exception of purely empirical equations of state, the remaining equations can bear the tag “molecular based.” Depending on their derivation, their molecular basis varies from those having only some traits of ideas/results of molecular considerations to equations obtained truly by application of statistical mechanics. Starting from formulations of statistical mechanics of liquids, a general scheme for derivation of truly perturbed equations is formulated. Two approaches, Bottom-Up and Top-Down, are identified, and the individual steps are discussed in detail along with several rules that reflect the essentials of the physics of fluids, which should be observed. Approximations and simplifications used in the implementation of the scheme are then analyzed in light of these rules, and a classification of equations of state is introduced. To exemplify these approaches in detail, theoretical and SAFT routes toward an equation of state are considered for water along with a potential way of merging these two approaches to obtain a reliable equation with a potential to predict the behavior of real fluids and not only to correlate them.