About the Relation between the Empirical and the Theoretically Based Parts of van der Waals-like Equations of State

Abstract

It is demonstrated that empirical temperature functionalities for the cohesive parameter in van der Waals-like equations can be responsible for prediction of nonphysical results such as fictitious critical points of pure compounds, that can result in prediction of unrealistic phase behavior in the entire thermodynamic phase space. Simple numerical tests for detecting this pitfall are proposed, and the roles played by the empirical and the theoretically based parts in semiempirical engineering equations are investigated. In particular, it is demonstrated that improvement of the accuracy with which equations of state approximate the hard sphere virial coefficients makes the theoretical part more self-sufficient for an accurate description of data. This significantly reduces the contribution of the corresponding empirical part and has a positive effect on the overall robustness and reliability of the model. In addition, an improved theoretical base contributes to the ability of the model so simultaneously and accurately predict both liquid and vapor densities.

Estimation of Liquid−Liquid−Vapor Equilibria in Binary Mixtures of n-Alkanes

“…These pitfalls may lead to prediction of nonphysical phase diagrams, as described previously. [25][26][27][28] PSRK implements eq 19 for b and the modified Huron-Vidal mixing rule 29 for a as follows:…”

“…where Equation 25 suffers from the same numerical pitfalls as eq 21. [25][26][27][28] LCVM implements the classical van der Waals mixing rule for b and the following mixing rule for a:…”

“…This behavior resembles the closed loops of LLE (type VI), which may be occasionally reproduced by semiempirical equations because of numerical pitfalls. 25,26 In particular, the high-pressure critical lines that create the closed loops of LLE predicted by G Ebased models originate at the fictitious high-temperature pure compound critical points. Although these points are located outside the physically meaningful temperature range (above 1000 K), they seriously affect the predicted phase diagrams at ordinary temperatures.…”

“…This nonphysical LLE shape leads PSRK and LCVM to the prediction of the erroneous global phase behavior shown in Figure 2. Such results can originate from the numerical pitfalls generated either by the empirical temperature functionalities (incorporated by Soave's temperature functionality [25][26][27][28] ) or by the G E mixing rules. To detect the part of the model responsible for the prediction of nonphysical results, we have replaced the original Soave temperature functionality of PSRK and LCVM by the temperature functionality given by eq 1, which does not generate numerical pitfalls.…”

Estimation of Liquid−Liquid−Vapor Equilibria Using Predictive EOS Models. 1. Carbon Dioxide−n-Alkanes

“…Moreover, it has been shown that RKS 6,16 and PR 8,26 may generate undesirable numerical pitfalls, which are responsible for predicting nonphysical phase behavior in mixtures. [29][30] Thus, appreciation of the fact that all parts of the thermodynamic phase space are closely interrelated encourages the development of an equation of state, which would be simultaneously accurate for the largest number of properties and be free of numerical pitfalls. Recently, we have proposed the following EOS that meets these requirements in a satisfactory manner: 22 where m 1 and m 2 are adjustable parameters for the appropriate presentation of the vapor pressure curve.…”