Page 133 - Air and Gas Drilling Manual

It is more useful to have Equation 4-24 written in terms of pressure instead of
temperature. This can be accomplished by substituting Equations 4-17 and 4-19
into Equation 4-24. This gives
 k−1  2 − Chapter 4: Compressors 4-19
2
2
W = k Pv     P   k −1   + V 2 V 1 (4-25)
s
k −1 1 1  P  2 g
 1 
 
The last term (the kinetic energy) in Equation 4-25 can be shown in practical
applications to be quite small relative to the first term. Thus, this later term is
usually neglected. Therefore, the shaft work for compression of gas in a compressor
is reduced to
 k−1 
2
W = k Pv     P   k −1   (4-26)
s
k −1 1 1  P 
  1  
Compressors can actually be considered steady state flow mechanical devices
(even intermittent flow machines). If the weight rate of flow through the compressor
«
is, « w (lb/sec), then the time rate of shaft work done, W (ft-lb/sec), to compress gas

s
in a compressor can be obtained by multiplying Equation 4-26 by « w . This gives
 k−1 
k   P  k 
2
˙
W = Pw ˙ v −1 (4-27)
s 1 1    
k −1  P 
 1 
 
«
The term, W (ft-lb/sec), is the theoretical power required by the compressor to
s
compress the gas. Using the general relationship between specific volume and
specific weight given in Equation 4-15, the volumetric flow rate at state 1 conditions
(entering the compressor), Q 1 , is
w «
Q = = « (4-28)
wv
1
γ 1 1
Therefore, Equation 4-27 can be rewritten as
 k−1 
k   P  k 
2
˙
W = PQ    −1  (4-29)
s
k −1 1 1  P 
  1  