Korea Institute of Civil Engineering and Building Technology (KICT, President Park, Sun-Kyu) has developed a new cubic equation of state (EOS) that provides a physical justification for a mathematical structure that the chemical and petroleum industries have relied on for more than half a century without a first-principles explanation.
Equations of state are essential tools for designing distillation columns, refrigeration cycles, natural-gas processing, and countless other operations: as they predict how fluid volume changes with temperature and pressure. Since the 1970s, widely used cubic equations such as Soave–Redlich–Kwong (SRK), Peng–Robinson (PR), and Patel–Teja (PT)—have improved accuracy by adopting a specific quadratic form for the mathematical form for reshaping the attractive-force term. However, this mathematical structure was largely developed through trial and error, and why it works so well has remained an open question.
To address this issue, Dr. Lee, Jai-Yeop of Department of Environmental Research Division, traced the origin of the structure to a little-known 1913 idea proposed by Dutch physicist Hugo Tetrode, who described fluids as collections of vibrating oscillators rather than freely moving particles. By incorporating Tetrode's vibrational correction through a new parameter, d, the study shows that the familiar quadratic structure is not arbitrary. Rather, it is the minimal form that simultaneously satisfies three basic physical and mathematical requirements: correctly reducing to the ideal-gas law at low density, remaining solvable as a cubic equation, and retaining sufficient flexibility to reproduce each substance's critical compressibility.
The equation was validated against high-accuracy reference data (NIST REFPROP) for 76 different fluids, ranging from simple gases such as argon and methane to strongly interacting substances such as water and ammonia. In fully predictive mode, using only each substance's basic critical properties and no adjustable "volume-translation" correction, the new model achieved the lowest average error in saturated-liquid volume at 4.0%, compared with 4.6% for VPT, 5.5% for PT, 7.2% for PR, and 13.7% for SRK (Figure 1).
The new parameter d also demonstrated clear physical significance. Its values showed a strong correlation (R² ≈ 0.93) with an empirical constant used in vapor-pressure equations whose theoretical basis had previously been unclear, while also grouping the 76 fluids into four distinct chemical families. As shown in Figure 2, the magnitude of the new correction term d, scaled by molecular size, rises steadily from weakly interacting argon to strongly hydrogen-bonded water, indicating that the parameter reflects the strength of molecular interactions in each fluid.
"Modern cubic equations of state are extraordinarily useful, but part of their success has rested on empirical mathematical structure rather than physical understanding," said Dr. Lee.
Because the new model predicts both liquid and vapor behavior directly from a substance's critical properties, without the additional empirical corrections required by comparable methods, it provides a more transparent foundation for process and equipment design calculations across the chemical, petroleum, and refrigeration industries. Its validation spans fluids such as hydrogen, carbon dioxide, and ammonia, and also suggests potential applications in chemical-process modeling for the low-carbon era, including hydrogen energy, carbon capture and utilization, and clean-ammonia fuels.
