Confidence-Interval and Uncertainty-Propagation Analysis of SAFT-type Equations of State

Thermodynamic models and, in particular, Statistical Associating Fluid Theory (SAFT)-type equations, are vital in characterizing complex systems. This paper presents a framework for sampling parameter distributions in PC-SAFT and SAFT-VR Mie equations of state to examine parameter confidence intervals and correlations. Comparing the equations of state, we find that additional parameters introduced in the SAFT-VR Mie equation increase relative uncertainties (1%-2% to 3%-4%) and introduce more correlations. These correlations can be attributed to conserved quantities such as particle volume and interaction energy. When incorporating association through additional parameters, relative uncertainties increase further while slightly reducing correlations between parameters. We also investigate how uncertainties in parameters propagate to the predicted properties from these equations of state. While the uncertainties for the regressed properties remain small, when extrapolating to new properties, uncertainties can become significant. This is particularly true near the critical point where we observe that properties dependent on the isothermal compressibility observe massive divergences in the uncertainty. We find that these divergences are intrinsic to these equations of state and, as a result, will always be present regardless of how small the parameter uncertainties are.