Page 94 - Handbook of Natural Gas Transmission and Processing Principles and Practices

In the middle of the 20th century, Redlich and Kwong (1949) published a new model derived
from Van der Waals' equation, in which the attractive term was modified to obtain better fluid
phase behavior at low and high densities:

(2.27)

Similarly, to Clausius' equation, a temperature dependency is introduced in the attractive term.
The “a” parameter is expressed as the product of the constant coefficient and (named
alpha function), which is unity at the critical point. Note that only the two pure-component critical
parameters T and P are required to evaluate a and b. The modifications of the attractive term
c
c
proposed by Redlich and Kwong, although not based on strong theoretical background, showed the
way to many contributors on how to improve Van der Waals' equation. For a long time, this model
remained one of the most popular cubic equations, performing relatively well for simple fluids with
acentric factors close to zero (such as Ar, Kr, or Xe) but representing with much less accuracy
complex fluids with nonzero acentric factors. Let us recall that the acentric factor ω , defined by
i
Pitzer et al. (1955), as

(2.28)

where refers to the vaporization pressure of pure component, i is a measure of the acentricity
(i.e., the noncentral nature of the intermolecular forces) of molecule i. The success of the Redlich–
Kwong equation has been the impetus for many further empirical improvements. In 1972 the Italian
engineer Soave suggested to replace in Eq. (2.27) the function by a more general temperature-
dependent term. Considering the variation in behavior of different fluids at the same reduced
pressure ( ) and temperature ( ), he proposed to turn from a two-parameter EoS (the two
parameters are T and P ) to a three-parameter EoS by introducing the acentric factor as a third
c
c
parameter in the definition of . The acentric factor is used to take into account molecular size
and shape effects because it varies with the chain length and the spatial arrangement of the
molecules (small globular molecules have a nearly zero acentric factor). The resulting model was
named the Soave–Redlich–Kwong (SRK) equation (Soave, 1972) and writes as

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