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.