Page 214 - Compression Machinery for Oil and Gas

Reciprocating Compressors Chapter 5 203

How valid is the assumption that the compression and expansion events are
adiabatic? For a compressor with a rotating speed of 300rpm (a slow rotating
speed) one P-V cycle takes only 0.2s to complete. Assuming each of the four
events of the P-V cycle take equal time, that is 0.05s (or 50ms) per event. That
is not much time for any significant amount of heat to transfer, therefore lending
credibility totheadiabaticassumption.Yes, the gas doesget hotas it is compressed
but not from heat being transferred to the gas. That heat is the heat of compression.
Inefficiency in the P-V diagram is the pressure drop incurred in moving the
gas from the inlet flange of the cylinder into the compression chamber and in
moving the gas from the compression chamber to the outlet flange. Overcoming
this pressure drop requires energy. This energy is represented by the areas
1-4-4A-1 (suction valve loss power (VLP)) and 2-2A-3-2 (discharge VLP) in
Fig. 5.24. It should be noted that in this initial ideal valve loss discussion,
the assumption is that the gas at the cylinder flange is at a constant pressure,
and that pulsation bottle and orifice plate pressure losses are ignored. These
(very real) additional losses are discussed subsequently.
This VLP represents the majority of the inefficiency in the P-V diagram. Addi-
tional small losses include piston ring and valve leakage, especially on nonlube
machines. Other losses can arise if the gas temperature at the start of compression
(point 1) is warmer than the incoming gas temperature, or if significant heat transfer
between the cylinder walls and the gas occurs. Friction is the remaining inefficiency
and is discussed later. The VLP can be expressed by the following relationship:
3 3
ð
ð
ð MWÞ PðÞ VEÞ R P Þ A BORE Þ S RPMÞ
ð
ð
VLP
2
ð
Z ðÞ TðÞ N A VLVPKT Þ
where:
MW¼gas mole weight
P ¼pressure, suction or discharge
VE¼volumetric efficiency
R P ¼resistance factor
A BORE ¼cross-sectional area of the cylinder bore
S ¼stroke
RPM¼rotating speed, rpm
Z ¼compressibility factor at suction or discharge
T ¼temperature, suction or discharge
N ¼number of suction or discharge valves feeding a head-end or crank-end
compression chamber
A VLV PKT ¼cross-sectional area of the valve bore
S RPM¼piston speed, fpm. As used in this relationship, it is the average
piston speed during the valve open time
This relationship in an even simpler form
ð A BORE Þ S RPMÞ
ð
V
ð N A VLVPKT Þ
is discussed in some detail.