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

Thermodynamic models and, in particular, 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 understand parameter confidence intervals and correlations. We identify conserved quantities contributing to significant 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. When incorporating association through additional parameters, relative uncertainties increase, but correlations slightly decrease. We investigate how uncertainties propagate to derived properties and observe small uncertainties for that data with which the parameters were regressed, especially for saturated-liquid volumes. However, extrapolating to saturated-vapour volumes yields larger uncertainties due to the larger isothermal compressibility. Near the critical point, uncertainties in saturated volumes diverge due to increased sensitivity of the isothermal compressibility to parameter uncertainties. This effect significantly impacts bulk properties, particularly isobaric heat capacity, where uncertainties near the critical point become extremely large, even when these uncertainties are small. We emphasize that even small uncertainties near the critical point lead to divergences in predicted properties.