58788 - Supercritical Pseudo Boiling in Cubic Equations of State 

Increasing the operating pressure is a proven way to increase the efficency of heat engines. In propulsion and energy this has led to pressures that exceed the thermodynamic critical pressures of working fluids and fuels. Supercritical fluids have unique properties that are different from low-pressure liquids and gases, but also suprising similarities. E.g., a liquid-gas phase equilibrium no longer exists beyond the critical point, a supercritical coexistence line does not exist. Pseudo boiling is the state transition between supercritical liquid states and supercritical gaseous states, associated with peaks in heat capacity and thermal expansion. Like subcritical boiling, pseudo boiling is characterized by an expansion of the fluid upon adding a latent heat. This transition occurs across a finite temperature interval around the Widom line, a continuation of the subcritical coexistence line. An accurate representation of the pseudo boiling process, its start and end temperature, as well as the predicted latent heat are thus important parameters to assess an EOS. So far, the relation between the Widom line and pseudo boiling of tabulated hi-fi p-v-T data, the behavior of cubic equations of state (EOS), and an analytical representation of the coexistence line at near-critical conditions is unclear. In the present paper, we calculate the slope of the Widom line analytically from cubic equations of state. The Redlich-Kwong EOS leads to a constant value for all species, Peng-Robinson and Soave-Redlich-Kwong EOS yield a cubic de-pendency of the slope on the acentric factor. For more than twenty compounds with acentric factors ranging from −0.38 to 0.57, calculated slopes are compared with NIST data and vapor pressure correlations. Particularly the Peng-Robinson EOS matches reference data very well. Classical empirical values of Guggenheim or Plank & Riedel are obtained analytically. Then, pseudo boiling predictions of the Peng Robinson EOS are compared to NIST data. Deviations in Widom line, transition temperature interval, and nondimensional parameters of the distributed latent heat are compared. Particularly the different caloric behavior of tabulated fluid data for H2, N2, CO2, and H2O cannot be reproduced by the Peng Robinson EOS. These results may open the way towards new EOS with specific emphasis on Widom line and supercritical transition behavior.