Page 270 - Compression Machinery for Oil and Gas

Screw Compressors Chapter 6 255

The built-in volume ratio v i is an important value for the design of screw
compressors and is determined by the shape and size of the discharge opening.
In oil-free screw compressors, the v i is a fixed value. In oil-flooded screw com-
pressors, some models are available with an adjustable v i slide that is indepen-
dent of the capacity slide valve; however, even for those without this adjustable
v i feature, the v i is only truly realized when the capacity slide valve is in the
maximum capacity position. When the slide valve moves toward the minimum
capacity position, the effective v i is reduced due to the shorter effective rotor
length.
Due to the size reduction of the working chamber, the gas is compressed as it
is moved by the screws, and the gas pressure and temperature increase. At the
end of the compression phase the internal pressure p 2i is reached. As described
in the following equation, p 2i is a function of p 1 , v i , and k.
k
p 2i ¼ p 1 v i (6.2)
with k being the isentropic exponent of the gas.
For ideal gases:
(6.3)
k ¼ c p =c v
k
The ratio p 2i /p 1 , also expressed as v i , is often called the “compression ratio.”
It should be noted that the “built-in volume ratio” is a design property of a cer-
tain screw compressor, the “compression ratio” depends on the volume ratio and
the kappa value of the gas, and the “pressure ratio” (p 2 /p 1 ) also depends on the
discharge line pressure. Therefore, when discussing the pressure ratio for screw
compressors, it is important to distinguish whether the discussion is about the
“pressure ratio” or the “compression ratio.”
Discharge phase: When the compression chamber has reduced its size to the
volume V 2 , the rotor lobes pass the outlet port in the casing and the chamber is
connected to the discharge line. This is the beginning of the discharge phase. By
further rotation of the rotors the working chamber reduces its size to zero and
the gas is ejected into the discharge line at the discharge pressure p 2 . The screw
compressor has no dead volume like a reciprocating compressor therefore no
reexpansion of trapped gas happens.
During all phases, a small amount of gas leaks across the rotor clearances
from the discharge line into the compression chamber. Another leakage flow
occurs during compression from the closed compression chamber to the trailing
chambers with lower pressure and to the suction line. The leakage to the suction
line acts like an internal bypass and reduces the inlet volume flow. This is
known as slippage, which also has thermal effects on the compressor: the
gas that “slips” backwards from higher pressure to lower pressure has already
been heated by the compression process. As it is recompressed, the heat
increases further. Thus, higher slippage leads to higher discharge temperature.
Slippage increases as internal clearances increase, as pressure ratio increases,