Peng-Robinson Equation of State for Mixtures

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This Demonstration uses the Peng–Robinson equation of state for mixtures to plot isotherms for -butane(1)/
-octane(2) mixtures on a log pressure versus log volume graph. Select the temperature with a slider. Selecting the mole fraction
of the liquid yields the isotherm for the liquid in blue. The green isotherm is for the vapor phase (mole fraction
) that is in equilibrium with the liquid; the values of
and pressure are determined from Raoult's law and are displayed in the upper-right corner. The dashed black line connects the blue isotherm to the green isotherm at the VLE pressure.
Contributed by: Rachael L. Baumann (February 2016)
Additional contributions by: John L. Falconer
(University of Colorado Boulder, Department of Chemical and Biological Engineering)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The Peng–Robinson equation of state for mixtures is used to plot pressure versus volume
on a log-log graph:
,
where is the gas constant (
),
is temperature (K),
is in MPa and
is in
.
is the attraction parameter and
is the repulsion parameter for the mixture:
,
,
where is the component mole fraction,
is the binary interaction parameter and
and
are the attraction and repulsion parameters for a pure component.
The binary interaction parameter can be calculated [1]:
,
for an alkane/alkane mixture and
.
The attraction and repulsion parameters for a pure component are:
,
,
where is the critical temperature (K) and
is the critical pressure (MPa).
,
where is a simplification term and
is the acentric factor.
Raoult's law is used to calculate the pressure of the mixture at VLE:
,
and is used to determine the vapor mole fraction:
,
where and
are the liquid and vapor mole fractions of hexane, and
is the saturation pressure that is calculated using the Antoine equation:
,
where ,
and
are Antoine constants.
The screencast video at [2] explains how to use this Demonstration.
References
[1] A. O. Elnabawy, S. K. Fateen and M. M. Khalil, "Semi-empirical Correlation for Binary Interaction Parameters of the Peng–Robinson Equation of State with the van der Waals Mixing Rules for the Prediction of High-Pressure Vapor–Liquid Equilibrium," Journal of Advanced Research, 4(2), 2013 pp. 137–145. doi:10.1016/j.jare.2012.03.004.
[2] Peng-Robinson Equation of State for Mixtures [Video]. (Sep 1 2016) www.colorado.edu/learncheme/thermodynamics/PengRobinsonEOSMixtures.html.
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