Page 460 - Standard Handbook Petroleum Natural Gas Engineering VOLUME2

418 Production

What does "fi" mean?
The equilibrium constants, or K values, are defined as the ratio of vapor and
liquid compositions:

(6-36)

The Gibbs free energy is a property of particular importance because it can
be related to the equilibrium state and at the same time can be expressed as a
function of T and P:
dGi = -SdT + VdP (6-37)
If Equation 6-37 is applied to an ideal gas it becomes

dGi = RT d(ln P) (638)

If we now define a property such that Equation 6-38 will apply for all gases
under all conditions of temperature and pressure
dGi = RT d(ln fi) (6-39)

fi is called the fugacity of component "i" and has a units of pressure. If Equation
639 is integrated for an ideal gas:

f, = CP (640)
'c" is constant and for an ideal gas is equal to 1.0. For real gases the only
condition under which the gas will behave ideally is at zero pressure. This can
be expressed as

amf. = 1.0
P+O p
The fugacity of a single component in a mixture is defined in a manner
similar to Equation 6-36:

dG = RTd(1n fi) (6-42)

and by analogy to Equation 6-39

The fugacity is sometimes referred to as a corrected pressure. A more valuable
parameter for use in correlative procedures would be a variable with char-
acteristics similar to fugacity, but which ranged over a much smaller range of
numbers. It is the fugacity coefficient $,.
For a pure component

qi =- (644)
fi
P