# Phase Identification Parameter

A thermodynamic procedure developed by Venkatarathnam and Oellrich [1] allows identification of the phase of a fluid by using partial derivatives of pressure with respect to volume and temperature.

It is a common practice of all process simulators to return the phase of a supercritical fluid as either liquid or vapor depending on the procedure adopted, though a supercritical fluid is not a liquid. This is essentially done to indicate the liquid-like or vapor like densities and other transport properties of the fluids such as viscosity and thermal conductivity, which are much different in the liquid and vapor regions.

In DWSIM, this procedure is applied by default for every resulting phase after a successful equilibrium calculation. It works like a second check for the flash algorithm, something like "does this phase really is a liquid or it actually behaves like a vapor?". This additional check can be useful to correctly identify the behavior of a supercritical fluid or narrow liquid-liquid equilibrium regions for CH4/H2S mixtures, for instance.

The phase identification procedure can be enabled/disabled in the Advanced Settings section of the Simulation Configuration Panel. If the phase identification is disabled, the result of the equilibrium calculation is sent directly to the property calculator without any intervention, so the resulting equilibrium phase(s) will depend exclusively on the flash algorithm selected by the user.

## Definition

The Phase Identification Parameter ($\Pi$) is defined as

$\Pi=v\frac{\partial^{2}p/\partial v\partial T}{\left(\partial p/\partial T\right)_{v}}-\frac{\left(\partial^{2}p/\partial v^{2}\right)_{T}}{\left(\partial p/\partial v\right)_{T}}$,

where the partial derivatives are calculated analytically for the Peng-Robinson (PR) and Soave-Redlich-Kwong (SRK) Equations of State. The Peng-Robinson EOS anaytical derivatives are used for all Property Packages except for the Soave-Redlich-Kwong (SRK) Property Package, where the corresponding derivatives are used instead.

## $\Pi$ and fluid behavior

The phase is identified as liquid or liquid-like vapor if $\Pi \gt 1$. If $\Pi \lt = 1$, the phase if identified as vapor.

## Practical Examples

### Methane + Hydrogen Sulfide mixture

The image below depicts the phase envelope for a mixture of 23.91% mol CH4 and 76.09% mol H2S, using the Peng-Robinson EOS. For the supercritical region (above 350 K / 12 MPa), the phase identification parameter boundary defines the region where the vapor behaves as a liquid (upper region) and as a vapor (lower region). This mixture doesn't exhibit a liquid-only behavior - that's why the bubble point line calculation fails after a few points. That region actually exhibits a liquid-like-liquid-like equilibrium behavior, as shown by the phase identification parameter value.

With the $\Pi$ calculation disabled, DWSIM calculates VLE at 170 K and 12 MPa, but you can tell from the vapor phase compressibility factor that it looks more like a liquid than like a vapor:

After enabling the phase identification procedure, both phases are correctly identified as being liquids, and DWSIM assigns the equilibrium result to the first two liquid phases. The first phase has a $\Pi$ value of 6.79 and the second phase shows a $\Pi$ value of 12.42, so both phases are identified as liquid, with one being a 'liquid-like' vapor and the other being a 'true' liquid. DWSIM makes no distinction between the two different "liquids", so they are simply treated as two liquid phases with different compositions.

### Supercritical Air

The image below shows the phase diagram for Air. The Phase Identification Parameter boundary delimits the region of vapor (lower part) and liquid-like vapor (upper part) behavior of the supercritical fluid.

With the $\Pi$ calculation disabled, DWSIM calculates a vapor-only phase at 140 K and 10 MPa.

With the $\Pi$ calculation enabled, DWSIM calculates a liquid-like vapor phase at 140 K and 10 MPa, with a $\Pi$ parameter value of 4.466.

## References

1. G. Venkatarathnam, L.R. Oellrich, Identification of the phase of a fluid using partial derivatives of pressure, volume, and temperature without reference to saturation properties: Applications in phase equilibria calculations, Fluid Phase Equilibria, Volume 301, Issue 2, 25 February 2011, Pages 225-233, ISSN 0378-3812, http://dx.doi.org/10.1016/j.fluid.2010.12.001.