PETE 310

PETE 310
Lecture # 10
Real Gases
Equations of State for Gases
Ideal gas
PV
ideal
M
RT
Real gas
PV
RT
1
real
M
Z
Experimental Observation…
The Principle of Corresponding
States
“All fluids when compared at
the same reduced temperature
and reduced pressure, have
approximately the same
compressibility factor, and all
deviate from ideal gas behavior
to about the same degree”
The Principle of Corresponding states (POC)
originated with single component fluids.
Typical Reduced Parameters
Material properties are usually expressed
in terms of reduced parameters such as:
Reduced Temperature:
Tr
T / Tc
Typical Reduced Parameters
Reduced Pressure:
Pr
P / Pc
Reduced Molar Volume:
Vr
V M / VM c
Reduced Parameters
Usually Tr and Pr  Vr obtained as a
function of Tr and Pr
These are called two-parameter
Corresponding States models
Three-parameter corresponding states
models improve predictions but third
parameter is not Vr (not independent
variable)
Generalized Corresponding States
Three-Parameter
This third parameter is called the acentric factor.
It takes into account the non-spherical nature of
molecules
Peng Robinson and the Soave Redlich Kwong
equations of state (EOS) are examples of three
parameter corresponding states models.
Compressibility Factor Charts
Following the POC only one
compressibility factor chart can be used to
determine volumetric properties of any
pure fluid by using its reduced properties.
The shape of this chart is in general.
Corresponding States Correlations
& Models
The objective is then to find a model (models) to
predict the Z factor.
Ideal gas behavior is described from the ideal gas
Equation of State (EOS) with a compressibility
factor of 1.
Extension of Corresponding States
to Mixtures
Z factor charts (all built from EOS) are also
used for multicomponent systems in this
case the coordinates used are “pseudoreduced properties”
For a mixture you can use the same charts
as for a pure component.
Compressibility
factor Z as a
function or
pseudoreduced
pressure
Z-Factor Equation
Equation used
z 1
A1
A2
Tpr
A3
Tpr3
A4
Tpr4
A5
Tpr5
pr
A6
A7
Tpr
A8
Tpr2
2
pr
A
A9 7
Tpr
A8
Tpr2
Tpr
T / Tpc
ppr
p / ppc
5
pr
A10
T
2
pr
3
pr
1 A11
Coefficients
A1
0.3265
A2
-1.07
A3
-0.5339
A4
0.01569
A5
-0.05165
A6
0.5475
A7
-0.7361
A8
0.1844
A9
0.1056
A10
0.6134
A11
0.721
pr
0.27
p pr
zT pr
2
pr
e
A11
2
pr
Pseudocritical Properties of Natural
Gases
Pseudoreduced Pressure
Ppr
P
Ppc
Pseudoreduced Temperature
T pr
T
T pc
Defining Pseudocritical Properties
Would require knowing Pc and Tc for each
component in the mixture…
Define some sort of mixing rule
What about Pc and Tc for C7+ …?
Given Specific Gravity and
Molecular Weight for C7+…
Given Specific Gravity and
Molecular Weight for C7+…
A Note on Specific Gravity
SG of a natural gas and SG of C7+ which is a
component of the natural gas ARE NOT
THE SAME
A Note on Specific Gravity
Do NOT Confuse C7+ with this …
Do NOT Confuse C7+ with this …
Defining Pseudocritical Properties
Several methods available (book & SPE
paper  will use later) when…
Given all mixture compositions
Correction schemes for ‘impurities’
When just gas gravity is known
Pseudocritical Properties of Natural
Gases
The simplest mixing rule to define
pseudocritical properties when
composition is known is…
Nc
Ppc
yi Pci
i 1
Nc
T pc
yiTci
i 1
Once Pseudocriticals are Found…
Pseudo reduced Temperature
Tpr
T / Tpc
Pseudo reduced Pressure
Ppr
P / Ppc
Evaluate Z
Pseudocritical Properties of Natural
Gases
Once Z is evaluated you can find the gas
density as
g
M
3
lbm / ft
V
Z-factor chart
for low
reduced
pressures
A Practical Application
Find amount of
natural gas that
can be stored at a
given P and T in a
salt cavern of a
given volume