Multi-parameter equations of state

Because the current estimates of the interaction parameters are used when solving the above equations, convergence problems are often encountered when these estimates are far from their optimal values. It is therefore desirable to have, especially for multi-parameter equations of state, an efficient and robust estimation procedure. Such a procedure is presented next. 

Chapter 12 describes Helmholtz-function based multi-parameter equations of state and provides the mixing and combining rules used to extend the equations for pure fluids to mixtures. In this approach, the Helmholtz function equations of state for the components in a mixture are combined with an excess function to effectively account for the interactions between unlike molecules.Of particular importance to this field is the work of Kunz et that provided... 

Multi-parameter Equations of State for Pure Fluids and Mixtures... 

Although modern empirical equations of state are usually formulated in terms of the reduced Helmholtz energy, the most common form used in the 20 century for multi-parameter equations of state in technical applications was the pressure-explicit form. The discussion that follows highlights several practical forms of multi-parameter pressure-explicit equations of state and indicates applications for each. The virial equation of state is not detailed in this work, but can be found in Chapter 3 of this book. 

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. 

Most reference equations of state provide reasonable estimates when extrapolated out of the range of the experimental data and in some case the extrapolation can extend to the limits of chemical stability of the substance. However, in general, multi-parameter equations of state should not be extrapolated beyond the range of validity cited. When extrapolation of the equation is necessary for the intended application, the reliability of the results might be reported by the authors. 

Table 12.2 lists sources of multi-parameter equations of state for a set of substances that are considered by the authors as providing the most precise representation of the thermodynamic properties that can be used for system design and analysis, as well as in scientific applications. However, the uncertainty of an equation for a substance depends on the available measurements as well as the method used to correlate them and the precision of the equations listed in Table 12.2 could vary significantly. The assessment of the suitability of an equation for an application might be reported by the authors of the particular formulation. 

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