Page 17 - Compression Machinery for Oil and Gas

6 SECTION I Fundamentals of Compression

For real gases (for which k and c p in the above equations become functions
of temperature and pressure), the enthalpy of a gas h(p,T) is calculated in a more
complicated way using equations of state [1]. They represent relationships that
allow the calculation of the enthalpy of gas of known composition, if any two of
its pressure, its temperature, or its entropy are known.
We therefore can calculate the actual head for the compression by
ð
Δh ¼ hp 2 , T 2 Þ hp 1 , T 1 Þ
ð
and the isentropic head by
ð
Δh ¼ hp 2 , s 1 Þ hp 1 , T 1 Þ
ð
ð
s 1 ¼ sp 1 , T 1 Þ
The performance quality of a compressor can be assessed by comparing the
actual head (which directly relates to the amount of power we need to spend for
the compression) with the head that the ideal, isentropic compression would
require. This defines the isentropic efficiency:

Δh s
η ¼
s
Δh
The second law tells us:
dq
Z 2
_ ms 2 s 1 Þ ¼ + S irr
ð
1 T
For adiabatic flows, where no heat q enters or leaves, the change in entropy
simply describes the losses generated in the compression process. These losses
come from the friction of gas with solid surfaces and the mixing of gas of dif-
ferent energy levels. An adiabatic, reversible compression process therefore
does not change the entropy of the system, it is isentropic. Our equation for
the actual head implicitly includes the entropy rise Δs, because
ð
Δh ¼ hp 2 , T 2 Þ hp 1 , T 1 Þ ¼ hp 2 , s 1 + Δsð Þ hp 1 , T 1 Þ
ð
ð
If cooling is applied during the compression process (e.g., with intercoolers
between two compressors in series), then the increase in entropy is smaller than
that for an uncooled process. Therefore, the power requirement will be reduced.
Using the polytropic process [2] for comparison reasons works fundamen-
tally the same way as using the isentropic process for comparison reasons. The
difference lies in the fact that the polytropic process uses the same discharge
temperature as the actual process, while the isentropic process has a different
(lower) discharge temperature than the actual process for the same compression
task. In particular, both the isentropic and the polytropic process are reversible
processes. In order to fully define the isentropic compression process for a given
gas, suction pressure, suction temperature, and discharge pressures have to be
known. To define the polytropic process, in addition either the polytropic
compression efficiency, or the discharge temperature has to be known.