Development of Volume Translation Models for PC-SAFT Equation of State
Creators: Shi, Jialin
Publisher: name: University of Alberta Library
Year: 2024

<p>Statistical associating fluid theory (SAFT)-type equations of states (EOSs) are commonly utilized in the chemical and petroleum industry to model the phase behavior of both pure and complex fluids because of its solid theoretical framework based on a perturbation theory. For the most SAFT-type EOSs (such as the perturbed-chain SAFT EOS (PC-SAFT EOS) proposed by Gross and Sadowski (2001)), one main drawback is that they fail to accurately describe the phase behavior of pure fluids near the critical region. They fail to reproduce the critical temperature and critical pressure of pure fluids, resulting in imprecise predictions of thermophysical properties (such as liquid density) in the vicinity of the critical point. This study aims to explore the development of more accurate volume translation models for PC-SAFT EOS that could work well at both near-critical and far-critical conditions.<br>
Inspired by the re-parametrization method with the exact representation of critical temperature and critical pressure (Anoune et al., 2021), we first develop a nonlinear temperature-dependent volume translation model in the PC-SAFT EOS for more accurate density predictions for CO2 over a wide range of temperatures and pressures. The developed nonlinear temperature-dependent volume translation model can capture the general trend of the practically needed volume residuals for CO2 (i.e., the molar volume calculated by the critical-point rescaled PC-SAFT EOS (CPPC-SAFT EOS) (Anoune et al., 2021) minus the experimental one). Using the proposed volume translated PC-SAFT EOS, critical temperature and critical pressure of CO2 can be exactly reproduced. In addition, more accurate predictions of liquid density and vapor pressure of CO2 can be achieved with the proposed volume translated PC-SAFT EOS.<br>
Although the above proposed nonlinear temperature-dependent volume translation model can partially remedy the prediction accuracy of critical properties, the accuracy of liquid density prediction is still compromised in the vicinity of the critical region. Thus, to further improve the prediction accuracy of thermodynamic properties near the critical region, we integrate a distance-function-based volume translation model into the CPPC-SAFT EOS, generating a volume-translated rescaled PC-SAFT EOS (VTR-PC-SAFT EOS). It is found that the proposed distance-function-based volume translation model can well capture the practically needed volume residuals. The proposed VTR-PC-SAFT EOS can exactly reproduce the critical temperature, critical pressure, and critical molar volume of a pure compound. Compared to the state-of-the-art PC-SAFT models in the literature (i.e., PC-SAFT EOS (Gross and Sadowski, 2001), I-PC-SAFT EOS (Moine et al., 2019), and CPPC-SAFT EOS (Anoune et al., 2021)), the VTR-PC-SAFT EOS yields more accurate predictions of several important thermodynamic properties (including saturated liquid density, liquid density, and vapor pressure) of 39 pure compounds at both critical and non-critical regions. In addition, we propose a generalized version of the VTR-PC-SAFT EOS model for n-alkanes (except CH4). Furthermore, we explore if the proposed VTR-PC-SAFT EOS can also work well for more compounds that are not examined in the initial stage of the study. In the follow-up study, we examine the performance of the VTR-PC-SAFT EOS in correlating the vapor pressure, liquid density, vapor density, supercritical density, saturated-liquid density, and saturated-vapor density of 251 compounds from 20 chemical families. The testing results show that VTR-PC-SAFT EOS can yield a better performance in predicting both critical and non-critical properties in comparison to the other PC-SAFT-type EOSs.<br>
Finally, we assess the performance of different PC-SAFT-type EOSs in reproducing various thermodynamic derivative properties of pure compounds, including thermal expansion coefficient, isothermal compressibility coefficient, heat capacities, Joule-Thomson coefficient, and speed of sound. The comparative analysis shows that the proposed VTR-PC-SAFT EOS outperforms the other models (PC-SAFT EOS, CPPC-SAFT EOS, and I-PC-SAFT EOS) in predicting most of the derivative properties. Specifically, it yields the smallest %AADs in reproducing thermal expansion coefficient, isothermal compressibility coefficient, Joule-Thomson coefficient, and speed of sound. However, the accuracy of VTR-PC-SAFT in reproducing the isobaric heat capacity is slightly lower than that of the original PC-SAFT EOS.</p>