Related Experiment Video
Updated: Aug 7, 2026
10:22
Split Point Analysis and Uncertainty Quantification of Thermal-Optical Organic/Elemental Carbon Measurements
Published on: September 7, 2019
Covariance-based uncertainty analysis of reference equations of state
Howard Cheung1, Jérôme Frutiger2, Ian H Bell3
1Carbon Exchange (Hong Kong) Ltd., Shatin, Hong Kong.
Journal of Chemical and Engineering Data
|August 6, 2026
Summary
This study introduces a new method for uncertainty analysis in equations of state (EOS). It quantifies property uncertainties, crucial for thermal process models, by analyzing parameter covariance for accurate confidence intervals.
Area of Science:
- Thermodynamics
- Chemical Engineering
- Physical Chemistry
Background:
- Accurate quantification of uncertainties in thermal process models is increasingly important.
- Existing equations of state (EOS) often lack reliable uncertainty reporting or underestimate them.
- Reliable uncertainty data is essential for robust process design and safety.
Purpose of the Study:
- To develop and present a robust methodology for uncertainty analysis of equations of state (EOS).
- To address the gap in literature regarding accurate uncertainty quantification for EOS properties.
- To provide insights into the impact of state points and phase behavior on property uncertainties.
Main Methods:
- A covariance-based methodology for uncertainty analysis using linear approximation.
- Calculation of 95% confidence intervals for EOS properties via parameter covariance matrix and linear error propagation.
- Application and validation of the methodology to a Helmholtz energy-based EOS for propane.
Main Results:
- Demonstrated a generalizable methodology applicable to any EOS without retraining.
- Showcased significant variations in uncertainties based on the state point.
- Identified substantially larger uncertainties for saturation properties compared to vapor properties due to Maxwell criteria.
Conclusions:
- The developed uncertainty analysis methodology provides valuable insights for EOS users and developers.
- Accurate uncertainty quantification is critical for reliable thermal process modeling.
- The methodology highlights the importance of considering state-dependent uncertainties and phase behavior in EOS applications.
Related Concept Videos
01:27Variables and Equations of State
The physical state of a pure substance can be defined by certain state variables such as volume (V), pressure (p), temperature (T), and amount of substance (n). When two gases are separated by a movable wall, the gas with the higher pressure naturally compresses the gas with the lower pressure. This causes the high-pressure gas to expand and the low-pressure gas to compress until both gases achieve mechanical equilibrium. At this point, their pressures equalize, and the movement of the wall...
01:07Equation of State
The equation of state is an equation that relates physical quantities, such as pressure, volume, temperature, and the number of moles, of a thermodynamics system with each other. The equation relating physical quantities with each other can be a simple mathematical expression or too complicated to express in mathematical form. In either case, a relationship between physical quantities exists. If the equation of state cannot be expressed in a mathematical form, then experimental data and...
00:59Uncertainty: Overview
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate errors. Despite the cares we take, the presence of random errors means that repeated measurements almost never have exactly the same magnitude. The collective difference between these measurements - observed values - and the estimated or expected value is called uncertainty. Uncertainty is conventionally written after the estimated or expected value.
01:10Propagation of Uncertainty from Systematic Error
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its average atomic mass. For instance, if we were to measure the atomic mass of oxygen from a sample, the mass would be a weighted average of the isotopic masses of oxygen in that sample. Since a single sample is not likely to perfectly reflect the true atomic mass of oxygen for all the molecules of oxygen on Earth, the mass we obtain from this particular...
01:26The Van der Waals Equation
The ideal gas law is based on two simplifying assumptions: first, that there are no intermolecular attractions between gas molecules, and second, that the volume occupied by the molecules themselves is negligible compared with the volume of the container. However, these assumptions don't hold up under all conditions - specifically, at high pressures and low temperatures, as gas tends to deviate from ideal gas behavior.The van der Waals equation is an enhanced version of the ideal gas law,...
01:23Correlation of Experimental Data
Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...
For example, a spherical particle moving through a viscous fluid experiences drag. Dimensional analysis shows that the drag force depends on the particle's diameter, velocity, and...