Symbolic-Regression Aided Development of a New Cubic Equation of State for Improved Liquid Phase Density Calculation at Pressures Up to 100 MPa

For over a century, cubic equations of state (EoS) have been used to calculate density and phase equilibria of pure fluids and mixtures. Despite a century’s development with hundreds of resulting cubic EoS, their accuracy in liquid phase density calculations is still unsatisfactory. In this work, a new cubic EoS was developed to improve the accuracy of liquid phase density calculation while keeping similar accuracy of other properties. The new cubic EoS, named YFR (Yang-Frotscher-Richter) EoS, was developed based on the functional form of the Patel–Teja (PT) EoS [p = RT/(v − b) − a/(v(v + b) + c(v − b)]. In the PT EoS, parameters b and c are linked to an empirical critical compressibility factor ξ_c, and all these three parameters are constants for a pure fluid. By contrast, in the YFR EoS, ξ_c, b, and c are functions of temperature, and the equations describing this dependency were developed with symbolic regression. This is the key to improving liquid phase density calculation, although it leads to thermodynamic inconsistencies at high pressures. The application range of the new cubic EoS is thus limited to pressures up to 100 MPa. The YFR EoS was developed using nearly all pure fluids available in NIST’s REFPROP 10.0 database, with reference values computed with REFPROP. The average of the absolute value of relative deviations (AARD) of liquid phase densities calculated with the YFR EoS from reference values is approximately 2 %, compared to 3 % when using the Patel–Teja–Valderrama (PTV) EoS and 6 % when using the Peng-Robinson (PR) EoS. The YFR EoS has been implemented in our self-developed OilMixProp 1.0 software package.