# Cubic Equation of State for the Compressibility Factor

Cubic Equation of State for the Compressibility Factor

In the Soave–Redlich–Kwong (SRK) equation of state (EOS), the compressibility factor occurs as a solution of the following cubic equation:

f(Z)=-+(A-B-)Z-AB=0

3

Z

2

Z

2

B

where and with , , , and . Here is the acentric factor, and are the critical temperature and pressure, and = is the reduced pressure.

A=

aP

2

(RT)

B=

bP

RT

a=0.42748α

2

(R)

T

c

P

c

b=0.08664R/

T

c

P

c

α=

2

1+m1-

T

re

m=0.480+1.574ω-0.176

2

ω

ω

T

c

P

c

T

re

T

T

c

When and = are greater than one, the supercritical behavior is observed with varying continuously between low (close to zero, liquid-like behavior) and high values (near one, vapor-like behavior).

T

r

P

r

P

P

c

Z

For specific values of and (when , the saturation pressure, and ), one gets three roots with the smallest and largest corresponding to the liquid and vapor phases. The intermediate value of has no physical significance.

T

r

P

r

P=

sat

P

T<

T

c

Z

The Demonstration plots for ethane (=305.43K, =48.84bar, and ) and displays the location and values of its real roots.

f(Z)

T

c

P

c

ω=0.09860