Peng-Robinson Equation of State for Mixtures

temperature (K)

390

n-butane liquid mole fraction

x

1

0.55

This Demonstration uses the Peng–Robinson equation of state for mixtures to plot isotherms for

n

-butane(1)/

n

-octane(2) mixtures on a log pressure versus log volume graph. Select the temperature with a slider. Selecting the mole fraction

x

1

of the liquid yields the isotherm for the liquid in blue. The green isotherm is for the vapor phase (mole fraction

y

1

) that is in equilibrium with the liquid; the values of

y

1

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.

Details

The Peng–Robinson equation of state for mixtures is used to plot pressure

P

versus volume

V

on a log-log graph:

P=

RT

V-

b

m

-

a

m

2

V

+2V

b

m

-

2

b

m

,

where

R

is the gas constant (

[

3

cm

MPa]/[molK]

),

T

is temperature (K),

P

is in MPa and

V

is in

3

cm

/mol

.

a

m

is the attraction parameter and

b

m

is the repulsion parameter for the mixture:

a

m

=

2

∑

i=1

2

∑

j=1

z

i

z

j

1-

k

ij



a

i

a

j

,

b

m

=

2

∑

i=1

z

i

b

i

,

where

z

is the component mole fraction,

k

ij

is the binary interaction parameter and

a

and

b

are the attraction and repulsion parameters for a pure component.

The binary interaction parameter can be calculated[1]:

k

ij

=1=

1

2

b

2

b

1

a

1

a

2

-

1

2

b

1

b

2

a

2

a

1

+

1

2

b

2

RT

a

1

a

2

θ

1

θ

2

T

T

c,1



,

for an alkane/alkane mixture

θ

1

=0.22806

and

θ

2

=0.18772

.

The attraction and repulsion parameters for a pure component are:

a=0.457

2

R

2

T

c

P

c

2

1+κ1-

T/

T

c



,

b=0.0778

R

T

c

P

c

,

where

T

c

is the critical temperature (K) and

P

c

is the critical pressure (MPa).

κ=0.37464+1.54226ω-0.26992

2

ω

,

where

κ

is a simplification term and

ω

is the acentric factor.

Raoult's law is used to calculate the pressure of the mixture at VLE:

P

vle

=

x

1

sat

P

1

+(1-

x

1

)

sat

P

2

,

and

P

vle

is used to determine the vapor mole fraction:

y

1

=

x

1

sat

P

1



P

vle

,

where

x

1

and

y

1

are the liquid and vapor mole fractions of hexane, and

sat

P

i

is the saturation pressure that is calculated using the Antoine equation:

sat

P

i

=10^

A

i

-

B

i

T+

C

i

,

where

A

i

,

B

i

and

C

i

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.

Permanent Citation

Rachael L. Baumann, John L. Falconer

"Peng-Robinson Equation of State for Mixtures"
http://demonstrations.wolfram.com/PengRobinsonEquationOfStateForMixtures/
Wolfram Demonstrations Project
Published: February 17, 2016