Comparisons of Property Formulations

Regardless of whether the property formulation for a particular fluid is explicit in pressure, Helmholtz energy, Gibbs energy, or another property, the user must be given an assessment of the uncertainty of the predicted properties so that the equation can be considered practical. The quality of a thermodynamic property formulation is best determined by its ability to model the physical behaviour to represent the measured properties of the fluid. Statistics and deviation plots are used to show how thermodynamic properties calculated from equations of state compare to experimental data. 

Group statistics typically used are based on the per cent deviation of a particular property X given by  

Another quantitative measure of the ability of an equation of state to represent experimental data for a thermodynamic property is obtained from the average absolute relative deviation (AARD) that is given by  

2 Fractional deviations Aw = w(expt) wtcalc) of the measured Uquid phase speed of sound w(expt) for propane from values estimated with the equation of state of Lemmon et al  

The extrapolation behaviour of empirical multi-parameter equations of state has been summarized by Span and Wagner. Aside from the representation of shock tube data for the Hugoniot curve at very high temperatures and pressures, an assessment of the extrapolation behaviour of an equation of state can also be based on the so called ideal curves that were first discussed by Brown. While reference equations of state generally result in reasonable estimates for the Boyle, ideal, and Joule-Thomson inversion curves, the prediction of reasonable Joule inversion curves is still a challenge. Equations may result in unreasonable estimates of Boyle, ideal and Joule-Thomson plots especially when the equations are based on limited experimental data. 

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