Page 130 - Air and Gas Drilling Manual

4-16 Air and Gas Drilling Manual
compression, and delivery of the gas under conditions which are assumed to be ideal
(absence of fluid or mechanical friction, and mechanically reversible).

Figure 4-13: Basic pressure-volume diagram.

The total shaft work, W s (ft-lb/lb), required for compression can be written as
V 2 2 V 1 2  2 
W = − Pv − ∫ P dv − P v  (4-6)

s +  2 2 1 1 
2 g 2 g 1
or

V 2 V 2  1 
W = 2 − 1 +  2 + ∫ P dv − P v  (4-7)
Pv
s
2 g 2 g  2 2 1 1 
where W s is the total shaft work (ft-lb/lb),
V 1 is the velocity of the gas entering the compressor (ft/sec),
V 2 is the velocity of the gas exiting the compressor (ft/sec),
2
g is the acceleration of gravity (32.2 ft/sec ).
Equation 4-6 can be rewritten as
V 1 2 V 2 2 2
W + − + Pv − P v = − ∫ P dv (4-8)
s
2 g 2 g 1 1 2 2 1
n
n
n
Assuming a polytropic process, where Pν = P ν = Pν = constant, and the
11 22
simplest polytropic process where the exponent term n ≈ k, where k is the ratio of
specific heats for the gas involved in the process (e.g., for air, k = 1.4), Equation 4-8
can be written as