Accurate prediction of physical properties such as liquid density, vapor pressure, and freezing point is crucial for the safe and efficient design of cryogenic systems, particularly in the liquefied natural gas (LNG) industry. A robust equation of state (EOS) plays a vital role in ensuring reliable property estimations. However, unmodified EOS models often exhibit significant errors when predicting liquid density under cryogenic conditions. In this study, the parameters of three widely used cubic EOS—Peng-Robinson (PR), Soave-Redlich-Kwong (SRK), and Nasrifar-Bolland (NB)—were modified to improve the accuracy of liquid density prediction for LNG at cryogenic temperatures. A generalized reduced gradient (GRG) nonlinear regression algorithm was applied using MATLAB to optimize five key EOS parameters, including alpha (α), beta (β), and three parameters related to the acentric factor (m₀, m₁, m₂). Over 100 real data points, including nitrogen-rich and ethane-rich data, were used to enhance the reliability and accuracy of the modified models. The optimized models significantly improved the prediction accuracy, reducing the average absolute deviation (AAD%) to 0.07%, 0.11%, and 0.09% for PR, SRK, and NB, respectively. These results demonstrate that modifying the EOS parameters using GRG regression can substantially enhance the predictive accuracy of LNG density at low temperatures, providing valuable insights for the design and operation of cryogenic systems.
