Page 136 - Air and gas Drilling Field Guide 3rd Edition

5.6 Prime Mover Input Power Requirements 127

P o ¼ P i r tf
P o ¼ð81170:0Þð21:414Þ
2
P o ¼ 1738174:4 N=m abs
or
2
P o ¼ 1657004:4 N=m gauge:
The rotary compressor volumetric efficiency e v is
e v ¼ 1:0:
The rated volumetric flow rate into the compressor is 448.3 liters/sec. For
this example, the compressor is located at mean sea level (API Standard condi-
tions), thus
3
Q i ¼ 0:4483m =sec:
With the terms just described, the theoretical shaft horsepower required to
compress the air moving through the machine is given by Equation (5-36a). Thus,
the theoretical shaft horsepower is
2 3
ð0:4Þ

ð2Þð1:4Þ 6 1738174:4 ð2Þð1:4Þ 7
_ W s ¼ ð81170:0Þð0:4483Þ 6 1 7
ð0:4Þ 4 81170:0 5
_ W s ¼ 139937 watts:
The actual shaft power _ W as is actual power needed to compress the air to the
2
fixed design pressure of 165.7 N/cm gauge. Equation (5-39) becomes
139937
_ W as ¼ ¼ 147302 watts:
ð0:95Þð1:0Þ
The above determined 147.3 kW is the actual shaft power needed by the com-
2
pressor to produce the 165.7 N/cm gauge fixed design pressure output (at the
surface location elevation of 1829 m above sea level). At this surface location,
the input power available from the prime mover is a derated value (derated from
the rated 261 kW available at 1800 rpm). In order for the compressor system to
operate at this 1829-m surface location elevation, the derated input power avail-
able must be greater than the actual shaft power needed. Figure 5-15 shows that
for an 1829-m elevation the input power of a turbocharged prime mover must be
derated by 15%. The derated input horsepower available from the prime mover
_ W i is

_ W i ¼ 261ð1 0:15Þ¼ 221:9 kW:
For this example, the prime mover’s derated input power is greater than the
actual shaft horsepower needed, thus the compressor system can be operated
at this 6000-ft surface location elevation.