Covariance-Based Uncertainty Analysis of Reference Equations of State

This work presents
a detailed methodology for uncertainty analysis applied to a reference equation
of states (EOSs) based on Helmholtz energy. With increasing interest
in uncertainties of thermal process models, it is important to quantify
the property uncertainties from the EOS. However, the literature relating
to EOS development and parameter estimation either does not report
uncertainties or report underestimated values. This work addresses
the issue by introducing a covariance-based methodology of uncertainty
analysis based on a linear approximation. The uncertainty ranges of
the EOS properties (95% confidence intervals) are calculated from
the experimental values and the EOS model structure through the parameter
covariance matrix and subsequent linear error propagation. In this
case study, the Helmholtz-based EOS of propane is analyzed. The uncertainty
methodology is general, and it is applicable to any novel or existing
EOS because it does not retrain the EOS. The study demonstrates the
insights a thorough uncertainty analysis can give for EOS users and
developers. Uncertainties vary strongly as a function of the state
point, and uncertainties of saturation properties are much larger
than the uncertainties of the vapor region due to the use of Maxwell
criteria to calculate the saturation properties.