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Equations of State

The document discusses several equations of state used to model the thermodynamic behavior of gases and liquids including the ideal gas law, van der Waals, Redlich-Kwong, Peng-Robinson, and Benedict-Webb-Rubbin equations. The equations relate pressure, volume, temperature, and compressibility factor and include constants that are empirically determined for different substances. The equations can be used to calculate properties like compressibility factor and density and are important tools for modeling real gas behavior and phase equilibria calculations in the oil and gas industry.

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366 views11 pages

Equations of State

The document discusses several equations of state used to model the thermodynamic behavior of gases and liquids including the ideal gas law, van der Waals, Redlich-Kwong, Peng-Robinson, and Benedict-Webb-Rubbin equations. The equations relate pressure, volume, temperature, and compressibility factor and include constants that are empirically determined for different substances. The equations can be used to calculate properties like compressibility factor and density and are important tools for modeling real gas behavior and phase equilibria calculations in the oil and gas industry.

Uploaded by

aguswiadi
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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EQUATIONS OF STATE

Ideal Gas
(Only valid for gas at low pressure conditions)

Pv RT
Van der Waals

RT
a
2
v b v

or P 2 v b RT
v

Relation with Z = compressibility factor:

Pv
b
a
Z
1

RT
v b RTv
27 R 2Tc2
a
64 Pc

and

RTc
8Pc

For mixtures:

a xi ai

and

b xibi

Van der Waals EOS, in term of Z:

Z 3 B 1Z 2 AZ AB 0

with

bP
RT

and

aP
RT 2

Redlich-Kwong

RT
a
0.5
v b T vv b

Relation with Z = compressibility factor:

a / R 2T 2.5 b / v
Pv
1


RT 1 b / v b / RT 1 b / v
0.4278R 2Tc2.5
a
Pc

and

0.0867 RTc
Pc

For mixtures:

a xi ai

and

b xibi

Redlich-Kwong EOS, in term of Z:

Z 3 Z 2 A B 2 B Z AB 0

with

bP
RT

and

aP
RT 2

Peng-Robinson

RT
aT
P

v b vv b bv b
Relation with Z = compressibility factor:

Pv
1
aT

RT 1 b / v v b b1 b / v RT

0.45724 R 2Tc2
aT
T
Pc

and

0.0778RTc
Pc

T 1 / 2 1 0.37464 1.54226 0.26992 2 1

T
Tc

For mixtures:

a xi ai

b xibi

and

Peng-Robinson EOS, in term of Z:

Z 3 B 1Z 2 A 3B2 2B Z B2 B3 AB 0

with

bP
RT

and

aP
RT 2

Benedict-Webb-Rubbin (BWR)
2
Co 2

3
6
3 1 d
P RTd Bo RT Ao 2 d bRT a d ad cd
exp d 2
2
T
T

Relation with Z = compressibility factor:


A
C
Pv
a
Z
Bo o o 2 d b
RT
RT RT
RT

where

2
2 a 5
2 1 d
d cd
exp d 2
d
3
RT
RT

1
;
v

Bo, Ao, Co, b, a, c, , are emphirical constants

for each substances.


For mixtures, use appropriate mixing rules such as:

Bo xi Boi

x b

1/ 3 3

1/ 3 3

Calculations of other properties from EOS

Assignment
1)Use NIST software to calculate Z for Natural Gas as examples conditions
(pseudocritical method). Compare with these two methods and PR-EOS
method.
2)Use NIST software, and PR-EOS method to calculate density of LNG as
an example above. Discuss the results !

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