The fugacity f and the fugacity coefficient
φ are calculated for water using the
Peng–Robinson equation of state (EOS). Select “fugacity”
and change pressure and volume with sliders; the corresponding state is
indicated by the black dot on the log pressure versus log volume diagram.
The fugacity coefficient indicates how much the fluid deviates from
ideal-gas behavior (φ = 1
for an ideal gas). Select “isotherms” to display isotherms on the
log P– log V
diagram and change temperature with a slider; the horizontal blue line
represents vapor-liquid equilibrium. The yellow areas between the isotherm
and the horizontal blue line are equal when viewed on a linear scale.
The Peng–Robinson EOS is used to calculate pressure:
P=R TV−b−aV2+ 2b V−b2,
where P is pressure (MPa),
R is the ideal gas constant
([cm3 MPa] / [mol K]),
T is temperature (K),
V is volume (cm3) and
a and b are constants:
a=0.457(1 +κ(1 −√T / Tc))2R2 Tc2Pc,
b=0.0778R TcPc,
κ=0.375+1.542ω−0.270ω2.
Here κ is a constant associated with the
acentric factor ω = 0.344,
Tc is the critical temperature (K) and
Pc is the critical pressure (MPa).
The following equation is solved in order to obtain
the compressibility factor Z:
Z3+a2Z2+a1Z+a0= 0 ,
where a2,
a1, a0,
A and B are all constants:
a2=B− 1 ,
a1=A− 3B2− 2B,
a0=−A B+B2+B3,
A=aPR2 T2,
B=bPR T.
The fugacity f and activity
coefficient φ are calculated by:
When the EOS has three roots, the correct solution is
the one that has the lowest fugacity.
This simulation was created in the
Department of Chemical and Biological Engineering
at University of Colorado Boulder for
LearnChemE.com
by John L. Falconer using Claude AI. It is a JavaScript/HTML5 implementation of a
Mathematica simulation
by Rachael L. Baumann, John L. Falconer, and Nick Bongiardina. It was prepared with
financial support from the National Science Foundation (DUE 2336987 and 2336988). Address any questions or comments to
LearnChemE@gmail.com.