Page 134 - Air and Gas Drilling Manual

4-20 Air and Gas Drilling Manual
The above expression is valid for a single stage compressor and for any set of
consistent units. With Equation 4-29, the shaft power to compress a continuous
flow rate of gas can be determined knowing properties of the gas (specifically k), the
initial pressure and volumetric flow rate of the gas entering the compressor (state 1),
and the exit pressure of gas exiting the compressor (state 2).
4.5.2 Multistage Shaft Power Requirements
Using the basic expression given in Equation 4-24 (without the kinetic energy
terms), the minimum shaft power required for a multistage compressor can be
derived [10]. Equation 4-24 can be used for each stage of a multistage compressor
and added together for the total shaft work required by the compressor. Such an
expression can be minimized to obtain the conditions for minimum shaft work for a
multistage compressor. Minimum shaft work is attained when a multistage
compressor is designed with equal compression ratios for each stage and with
intercoolers that cool the gas entering each stage to a temperature that is nearly the
same as the temperature entering the first stage of the compressor [10]. Once these
conditions are obtained for the multistage compressor, the expression for the shaft
power can be obtained in the same manner as given in Equations 4-25 to 4-29.
Figure 4-14 shows an example schematic of a two stage compressor with an
intercooler between the compression stages. The temperature exiting stage 1 (at
position 2) will be governed by Equation 4-19. The intercooler cools the gas
between positions 2 and 3 under constant volume conditions. Thus, the temperature
of the gas entering stage 2 (at position 3) is the same as the temperature entering
stage 1 (i.e., position 1). Using these conditions for the minimum shaft power, an
expression for the shaft power of a multistage compressor can be derived. This
expression is

 k−1 
nk   P  nk 
˙
W = s PQ i   o  s −1  (4-30)
s
k −1 i  P 
 i 
 
where n s is the number of compression stages in the multistage compressor,
2
P i is the pressure entering the first stage of the compressor (lb/ft , abs),
2
P o is the pressure exiting the last stage of the compressor (lb/ft , abs),
3
Q i is the volumetric flow rate entering the first stage of the compressor (ft /sec).
The compression ratio for each stage, r s , is given by
1
 P 
r = o n s (4-31)
s  
 P 
i
Again, Equations 4-30 and 4-31 are valid for any set of consistent units.
In what follows, two sets for field equations are derived for determining the
theoretical power to compress the gas passing through the compressor. One set is