L10 Real Gases
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Transcript of L10 Real Gases
PETE 310
Lecture # 10
Real Gases
1RT
PVideal
M
ZRT
PVreal
M
Equations of State for Gases
Ideal gas
Real gas
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.
Material properties are usually expressed in terms of reduced parameters such as:
Reduced Temperature:
Typical Reduced Parameters
cr TTT /
Reduced Pressure:
Reduced Molar Volume:
cr PPP /
cMMrVVV /
Typical Reduced Parameters
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)
This third parameter is called the acentric factor.
It takes into account the non-spherical nature of molecules
Peng Robinson and the Soave Redlich Kwongequations of state (EOS) are examples of three parameter corresponding states models.
Generalized Corresponding States Three-Parameter
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 “pseudo-reduced 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
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
211
2
2 5 22 3 4 5 7 8 7 81 6 9 10 113 4 5 2 2 3
1 1 prApr
pr pr pr pr
pr pr pr pr pr pr pr pr pr
A A A A A A A Az A A A A A e
T T T T T T T T T
pcpr
pcpr
p/pp
T/TT
0.27pr
pr
pr
p
zT
Pseudocritical Properties of Natural Gases
Pseudoreduced Pressure
Pseudoreduced Temperature
pc
prP
PP
pc
prT
TT
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…
cii
N
i
pc PyPc
1
cii
N
i
pc TyTc
1
Pseudo reduced Temperature
Pseudo reduced Pressure
Evaluate Z
Once Pseudocriticals are Found…
pcpr TTT /
pcpr PPP /
Pseudocritical Properties of Natural Gases
Once Z is evaluated you can find the gas density as
3/ ftlbm
V
Mg
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