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Gas Compressors 127

presented the following solution to gas pressure at the bottom of an arc
section below the KOP:

s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

P = P K + 2abRT av I exp 2aR sinðIÞ (6.29)
2
T av
where
2
P K = pressure at the KOP, lbf/ft or N/m 2
T av = average temperature in the arc section, R° or K°
I = inclination angle at the bottom of the arc section, radians

6.2.3 Gas Flow through the Bit
Nozzles are normally not installed on drill bits in gas drilling. Part of the
reason is to reduce the problems of hole washout and “frozen” bits (see
Chapter 7). Still, a significant amount of pressure drop can occur at the
bit. It is preferable to have a subsonic flow of gas through the drill bits
for pressure communication between the annular space and the standpipe
so the pressure changes due to solid accumulation in the annulus can be
identified by reading the standpipe pressure gauge (see Chapter 7).
Assuming an isentropic process, based on the second term on the right
side of Eq. (6.1), the gas flow through the bit orifice obeys the following
relation under subsonic flow conditions:

v ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2 3
k+1
u
2
u k k
k
u P dn − P dn
Q g = 6:02CA o P up t 4 5 (6.30)
ðk −1ÞS g T up P up P up
where
C = flow coefficient, approximately 0.6 for bit orifices
2
A o = total bit orifice area, in or m 2
2 2
P up = upstream pressure, lb/ft or N/m
2
P dn = downstream pressure, lb/ft or N/m 2
T up = upstream temperature, R or K
k = specific heat ratio of gas, 1.4 for air and 1.28 for natural gas
Because the gas specific heat ratio is not an integer, a numerical method
must be used to solve Eq. (6.30) for upstream or downstream pressures.