  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.
