Crossover multiparameter equation of state: General procedure and demonstration with carbon dioxide

Abstract

The multiparameter equation of state represents experimental data in wide ranges of temperature and density with superb accuracy. However, at the critical point, all classical models fail in describing the asymptotic behavior of thermodynamic properties, which is governed by the renormalization group (RG) theory. Using the crossover method, the classical models far from the critical point can be transformed to the RG theory at the critical point. Here we validate the procedure of combining the crossover method with the multiparameter equation of state through comparison with experimental data and the original multiparameter equation of state, and testing against the qualitative criterion of characteristic curves. We select carbon dioxide as a demonstration due to its data availability and qualification as a benchmark fluid for thermodynamic property modeling. We describe in detail the contribution of different types of terms in the crossover method and original multiparameter equation of state to thermodynamic properties. Furthermore, we propose twin Gaussian terms to compensate for the loss of accuracy near the coexistence curve upon removing the non-analytical terms and leave the analytical part of the formulation (terms and coefficients) unaltered. With a slight and acceptable loss of accuracy in the crossover region, the crossover method enforces the asymptotic singular behavior and critical exponents at the critical point. Far from the critical point, the present model transforms to the original model and retains the superb accuracy of the latter.