Multiparameter crossover equation of state: Generalized algorithm and application to carbon dioxide

In this work, we propose a new optimization algorithm for the development of multiparameter crossover equations of state (MC EOS), which incorporates the asymptotic scaling laws near the critical point. This algorithm is based on stepwise regression, which reduces the intercorrelations among the functional terms in the equation and enables the incorporation of the universal crossover formulation into the development of equations of state. The EOS developed is optimized in structure and gives correct prediction of caloric properties in the immediate vicinity of the critical point. For the determination of the linear, analytical coefficients and the non-linear crossover parameters in the crossover EOS for a given fluid, both linear and non-linear optimization procedures are used. By applying this algorithm we have developed a wide-range crossover equation of state (EOS) for carbon dioxide in the form of dimensionless Helmholtz energy. The derived MC EOS contains only 26 functional terms, and gives excellent descriptions of experimental data over a wide-range of states. Compared to the extremely accurate standard reference equation of state of Span and Wagner (SW EOS), the MC EOS yields a very good description of thermodynamic surfaces away from the critical point. In one-phase region, the MC EOS represents the experimental values of density with an average absolute deviation (AAD) of about 0.1%, and pressure with an AAD of about 0.3%. However, unlike the SW EOS, the MC EOS reproduces the well-established scaling laws behavior in the asymptotic critical region as T → Tc.