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Covariance-based uncertainty analysis of reference equations of state



Howard Cheung, Jerome Frutiger, Ian Bell, Jens Abildskov, Gurkan Sin, Shengwei Wang


This work presents a detailed methodology for uncertainty analysis applied to a reference equation of state (EOS) 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, literature relating to EOS either does not report uncertainties or report underestimated values. This work addresses the issue by introducing a methodology of uncertainty analysis based on 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. A comparison of the uncertainties by different methods reveals that the proposed method estimates larger and more reasonable uncertainties than ones in previous studies. The uncertainty methodology is general and is applicable to any novel or existing EOS because it does not re-train the EOS. The study demonstrates the insights a thorough uncertainty analysis can give for EOS users and developers. For example, high and low property uncertainties occur in different temperature and pressure ranges, uncertainties of saturation properties are highly subjected to Maxwell criteria, etc.
Journal of Chemical and Engineering Data


uncertainty, equation of state, thermodynamics


Cheung, H. , Frutiger, J. , Bell, I. , Abildskov, J. , Sin, G. and Wang, S. (2020), Covariance-based uncertainty analysis of reference equations of state, Journal of Chemical and Engineering Data, [online],, (Accessed April 15, 2024)
Created January 5, 2020, Updated October 12, 2021