Page 123 - Air and gas Drilling Field Guide 3rd Edition

114 CHAPTER 5 Compressors and Nitrogen Generators

where n s is the number of compression stages in the multistage compressor, P i is the
2
2
pressure entering the first stage of the compressor (lb/ft abs, N/m abs), P o is the
2
2
pressure exiting the last stage of the compressor (lb/ft abs, N/m abs), and Q i is
3
3
the volumetric flow rate entering the first stage of the compressor (ft /sec, m /sec).
The compression ratio for each stage r s is given by
1

P o n s
r s ¼ : (5-31)
P i
Again, Equations (5-30) and (5-31) 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 derived for use with the USCS unit and the other set for use with the
SI unit.
Equation (5-30) is obtained in USCS units by substituting the following for P i ,
P o , and Q i (and dividing by 550 ft-lb/hp):
P i ¼ p i 144 (5-32)
P o ¼ p o 144 (5-33)
q i
Q i ¼ ; (5-34)
60
where p i is input pressure (psia), p o is output pressure (psia), and q i is the input
3
volumetric flow rate (ft /min).
The expression for theoretical shaft power _ W s in USCS units (horsepower) is
k 1
2 3

n s k p o n s k
7
_ W s ¼ p i q i 6 15: (5-35a)
k 1 229:17 p i
4
Using Equation (5-13), an alternate expression of Equation (5-35a) can be
obtained. Equation (5-35b) is convenient for booster compressor calculations
k 1
2 3

n s k _ w g p o n s k
7
_ W s ¼ R e T i 6 15; (5-35b)
4
k 1 550 S g p i
where T i is the input gas temperature ( R) and _ w g is the weight of flow of gas

through the compressor (lb/sec).
The expression for theoretical shaft power _ W s in SI units (watts) is
k 1
2 3

n s k P o n s k
6 7
_ W s ¼ P i Q i4 15; (5-36a)
k 1 P i
3
where Q i is the input volumetric flow rate (m /sec), P i is the input pressure
2
2
(N/m abs), and P o is the output pressure (N/m abs).