Covariance-Based Uncertainty Analysis of Reference Equations of State

Cheung, Howard; Frutiger, Jérôme; Bell, Ian H.; Abildskov, Jens; Sin, Gürkan; Wang, Shengwei

doi:10.1021/acs.jced.9b00689

Cited by 5 publications

(6 citation statements)

References 39 publications

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“…Another interesting behavior to note is that, in all cases, as we approach the critical temperature, the uncertainties in the saturated volumes begin to diverge, becoming exceptionally large. This behavior has also been observed in multiparameter equations of state as well . This divergence arises from the fact that, as we approach the critical temperature, fluctuations become extremely large, with the isothermal compressibility diverging to infinity.…”

Section: Resultssupporting

confidence: 69%

“…As such, an alternative strategy is required to determine the confidence intervals of our parameters. In a similar fashion to prior works, ,, we leverage Monte Carlo Markov-Chain (MCMC) simulations to sample the distribution p ( θ | x , y ).…”

Section: Methodsmentioning

confidence: 99%

“…However, to our knowledge, no one has devised a rigorous strategy to evaluate the confidence intervals of the SAFT parameters, and even more, no one has examined how the uncertainties in the parameters might then impact the predictions made using the models. This is more commonly done in simpler empirical equations − and high-accuracy, multiparameter equations of state. − The closest study was that by Frutiger et al where they performed confidence-interval and uncertainty-propagation analysis with the PC-SAFT equation with only a single, nonassociating species. It is the objective of this work to perform such analysis not only for multiple species but for multiple SAFT equations of state as well.…”

Section: Introductionmentioning

confidence: 99%

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Confidence-Interval and Uncertainty-Propagation Analysis of SAFT-type Equations of State

Walker,

Mueller,

Smirnova

2023

J. Chem. Eng. Data

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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.

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Section: Resultssupporting

confidence: 69%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Confidence-Interval and Uncertainty-Propagation Analysis of SAFT-type Equations of State

Walker,

Mueller,

Smirnova

2023

J. Chem. Eng. Data

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“…Furthermore, novel analysis techniques need to be developed to better ascertain the uncertainty in residual properties in general because they are not measurable quantities. Some progress has been made in this direction from the quantification of equation of state statistical uncertainty. , …”

Section: Discussionmentioning

confidence: 99%

“…100,101 ■ ASSOCIATED CONTENT * sı Supporting InformationThe Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jced.0c00209.Python modules thermo and implementation as text files (ZIP) Complete set of experimental data considered from the original publications and the unit conversion script (ZIP) Additional analysis and figures not suitable for inclusion in the main manuscript (PDF)…”

mentioning

confidence: 99%

Entropy Scaling of Viscosity—I: A Case Study of Propane

Bell

2020

J. Chem. Eng. Data

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In this work, a broadly applicable and simple approach for building high accuracy viscosity correlations is demonstrated for propane. The approach is based on the combination of a number of recent insights related to the use of residual entropy scaling, especially a new way of scaling the viscosity for consistency with the dilute-gas limit. With three adjustable parameters in the dense phase, the primary viscosity data for propane are predicted with a mean absolute relative deviation of 1.38%, and 95% of the primary data are predicted within a relative error band of less than 5%. The dimensionality of the dense-phase contribution is reduced from the conventional two-dimensional approach (temperature and density) to a one-dimensional correlation with residual entropy as the independent variable. The simplicity of the model formulation ensures smooth extrapolation behavior (barring errors in the equation of state itself). The approach proposed here should be applicable to a wide range of chemical species. The Supporting Information includes the relevant data in tabular form and a Python implementation of the model.

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