Page 18 - Compression Machinery for Oil and Gas

Oil and Gas Compressor Basics Chapter 1 7

The polytropic efficiency η p is defined such that it is constant for any infinites-
imally small compression step, which then allows to write

1 Z p 2 Δh p
Δh ¼ vdp ¼
η p p 1 η p
and
p 2
Z
Δh p ¼ vdp
p 1
or, to define the polytropic efficiency:

Δh p
η ¼
p
Δh
For designers of compressors, the polytropic efficiency has an important
advantage: If a compressor has five stages, and each stage has the same isentropic
efficiency η s , then the overall compressor efficiency will be lower than η s .If, for
the same example, we assume that each stage has the same polytropic efficiency
η p , then the polytropic efficency of the entire machine is also η p .
Because the enthalpy definition above is on a per mass flow basis, the
absorbed gas power P g (i.e., the power that the compressor transferred into
the gas) can be calculated as

P g ¼ _ mΔh
The mechanical power P necessary to drive the compressor is the gas
absorbed power increased by all mechanical losses (friction in the seals and
bearings), expressed by a mechanical efficiency η m (typically in the order of
1% or 2% of the total absorbed power):
1 _ mΔh s
P ¼ _ mΔh ¼
η m η η
m s
We also encounter energy conservation on a different level in turboma-
chines: The aerodynamic function of a turbomachine relies on the capability
to trade two forms of energy—kinetic energy (velocity energy) and potential
energy (pressure energy). This will be discussed in a subsequent section.

Intercooling

A compression process where the gas is cooled as part of the compression is no
longer adiabatic. It is thus not appropriate to state isentropic or polytropic pro-
cesses for comparison. In some instances, an isothermal efficiency might be
suitable to compare different configurations. Since the cooling process moves
entropy from the compressed gas to the environment, the overall compression
will consume less power than the same process without intercooling.