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

+…

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 …

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


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 /


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

L10 Real Gases

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