Evaluation of volume translation models in PC-SAFT EoS for carbon dioxide

Accurate ${\mathrm{CO}}_2$ properties are crucial for the development of carbon capture, utilization, and storage (CCUS) technologies. This work assesses the performance of two volume translation models for ${\mathrm{CO}}_2$, integrated into the I-PC-SAFT equation of state (EoS) to refine the original volume translation constant ($c$). The models introduce a temperature-dependent volume translation function and a distance function-based volume translation function, with the latter explored in two forms: ${\left(\frac{\partial P}{\partial V}\right)}_T$ and ${\left(\frac{\partial T}{\partial V}\right)}_P$. The outcomes reveal that the I-PC-SAFT models, incorporating either the temperature-dependent function or the distance functions ${\left(\frac{\partial P}{\partial V}\right)}_T$ and ${\left(\frac{\partial T}{\partial V}\right)}_P$, enhance the prediction accuracy of ${\mathrm{CO}}_2$ saturated densities over the baseline I-PC-SAFT and PC-SAFT models. Specifically, when estimating liquid ${\mathrm{CO}}_2$ densities at fixed pressures ranging from 0.5$P_c$ to 10.0$P_c$, the I-PC-SAFT model with the temperature-dependent volume translation function exhibits reduced predictive deviation at lower pressures. At elevated pressures, however, the deviation is more pronounced. In contrast, the I-PC-SAFT model utilizing the distance function based on ${\left(\frac{\partial T}{\partial V}\right)}_P$ achieves the lowest percentage average deviation ($\text{\%}AAD$) of 0.63%.