Page 19 - Compression Machinery for Oil and Gas

8 SECTION I Fundamentals of Compression

Equations of State
Understanding gas compression requires an understanding of the relationship
between pressure, temperature, and density of a gas. An ideal gas exhibits
the following behavior:
P
¼ RT
ρ
where R is the gas constant, and as such is constant as long as the gas compo-
sition is not changed. Any gas at very low pressures can be described by this
equation.
For the elevated pressures we see in natural gas compression, this equation
becomes inaccurate, and an additional variable, the compressibility factor Z, has
to be added:
P
¼ ZRT
ρ
Unfortunately, the compressibility factor itself is a function of pressure,
temperature, and gas composition.
A similar situation arises when the enthalpy has to be calculated: For an
ideal gas, we find

T 2
Z
Δh ¼ C p ΔT ¼ C p dT
T 1
where C p is only a function of temperature.
In a real gas, we get additional terms for the deviation between real gas
behavior and ideal gas behavior (Poling et al., 2001):
T 2
Z

0 0
ðÞ
ðÞ
Δh ¼ h hp 1 + C p dT h hp 2
T 1 T 2
T 1
0 0
are called departure functions,
The terms (h h(p 1 )) T 1 and (h h(p 2 )) T 2
because they describe the deviation of the real gas behavior from the ideal
gas behavior. They relate the enthalpy at some pressures and temperatures to
a reference state at low pressure, but at the same temperature. The departure
functions can be calculated solely from an equation of state, while the term
R
T 2
C p dT is evaluated in the ideal gas state. Fig. 1.2 shows the path of a calcu-
T 1
lation using an equation of state.
Equations of state are semiempirical relationships that allow to calculate the
compressibility factor, as well as, the departure functions. For gas compression
applications, the most frequently used equations of state are Redlich-Kwong,
Soave-Redlich-Kwong, Benedict-Webb-Rubin, Benedict-Webb-Rubin-
Starling, and Lee-Kessler-Ploecker (Poling et al., 2001).
In general, all of these equations provide accurate results for typical appli-
cations in pipelines, that is, for gases with a high methane content, and at