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.