About the relation between the empirical and the theoretically based parts of van der Waals-like equations of state

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.