Page 16 - Compression Machinery for Oil and Gas

Oil and Gas Compressor Basics Chapter 1 5

First Law
For a compressor receiving gas at a certain suction pressure and temperature,
and delivering it at a certain output pressure, the isentropic head represents
the energy input required by a reversible, adiabatic (thus isentropic) compres-
sion. The actual compressor will require a higher amount of energy input than
needed for the ideal (isentropic) compression.
It is important to clarify certain properties at this time, and in particular find
their connection to the first and second law of thermodynamics written for
steady-state fluid flows. The first law (defining the conservation of energy)
becomes:

w 2 w 1
2 2
h 2 + + gz 2 h 1 + + gz 1 ¼ q 12 + W t12
2 2
with q¼0 for adiabatic processes and gz¼0 because changes in elevation are
not significant for gas compressors. We can combine enthalpy and velocity into
a total enthalpy by

w 2
h t ¼ h +
2
where W t12 is the amount of work we have to apply to affect the change in
enthalpy in the gas. The work W t12 is related to the required power, P, by mul-
tiplying it with the mass flow.
P ¼ _ mW t12
Power and enthalpy difference are thus related by
P ¼ _ mh t,2 h t,1 Þ
ð
If we can find a relationship that combines enthalpy with the pressure and
temperature of a gas, we have found the necessary tools to describe the gas com-
pression process. For a perfect gas, with constant heat capacity, the relationship
between enthalpy, pressures, and temperatures is

ð
Δh ¼ c p T 2 T 1 Þ
Because, for an isentropic compression, the discharge temperature is deter-
mined by the pressure ratio (with k¼c p /c v ):

k 1
p 2
T 2 ¼ T 1 k + T 1
p 1
We can, for an isentropic compression of a perfect gas, relate the isentropic
head, temperature, and pressures by

k 1
p 2
Δh s ¼ c p T 1 k 1
p 1