Evaluation of thermodynamic models for the prediction of derivative properties for non-polar compounds

Thermodynamic models have been developed for many decades, while a persistent challenge remains in identifying the most effective model for specific systems. In this study, a wide range of thermodynamic models, including SRK, PR, CPA, CK-SAFT, PC-SAFT, SAFT-VR Mie, SAFT-γ Mie, and GERG-2008, have been analyzed to evaluate their performance in predicting the first- and second-order derivative properties of compounds such as alkanes, N₂, and CO₂. Properties such as saturation pressure, liquid density, isobaric and isochoric heat capacities including their residual terms, speed of sound, and Joule-Thomson coefficient have been examined. While GERG-2008, as a multiparameter equation of state consistently outperforms other models across most properties, among general thermodynamic models, SAFT-VR Mie and SAFT-γ Mie have demonstrated superior performance over conventional cubic models, particularly in predicting second-order derivative properties, and PC-SAFT has shown superior results for isobaric heat capacity and Joule-Thomson coefficient. To gain deeper insights into the results, further examination of the model's performance in predicting selected second-order derivative properties (dP/dT, dP/dV, ${\left({\partial }^2{A}^{\text{res}}/\partial V^2\right)}_{T,n}$, ${\left({\partial }^2{A}^{\text{res}}/\partial T\partial V\right)}_n$, and ${\left({\partial }^2{A}^{\text{res}}/\partial T^2\right)}_{V,n}$) has been conducted. Additionally, the contributions of hard-sphere, chain, and dispersion terms to the second-order derivatives of Helmholtz energy have been analyzed, highlighting the significant impact of these terms on volume and temperature derivatives. This manuscript also discusses possible challenges and potential improvements in these models' predictive capabilities.