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Gas Compressors 131
where
Q go = volumetric flow rate of gas in the standard condition, scf/min
or scm/min
Since this equation still involves in situ pressure P, it has to be combined
with Eq. (6.18) to solve the minimum required gas flow rate Q go .
Illustrative Example 6.1
5
A well is cased from the surface to 7,000 ft with API 8 / 8 -in-diameter, 28-lb/ft
7
nominal casing. It is to be drilled ahead to 10,000 ft with a 7 / 8 -in-diameter
rotary drill bit, using air as a circulating fluid at an ROP of 60 ft/hr and a
3
rotary speed of 50 rpm. The drill string is made up of 500 ft of 6 / 4 -in OD by
1
13
2 / 16 -in ID drill collars and 9,500 ft of API 4 / 2 -in-diameter, 16.60-lb/ft nominal
EU-S135, NC 50 drill pipe. The bottomhole temperature is expected to be
o
160 F. We assume in this example that the annular pressure at the collar
shoulder is 85 psia. Calculate the minimum required gas injection rate when
the bit reaches the total depth (TD), using the minimum velocity criterion.
Solution
The maximum particle size can be estimated based on the maximum penetra-
tion depth per bit revolution:
D s ≈ ð60Þ = 0:02 ft ½0:006 m
ð60Þð50Þ
Assuming a spherical sandstone particle has a specific gravity of 2.6, the term-
inal settling velocity can be estimated as
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
v sl = ð4Þð32:2Þð0:02Þ½ð62:4Þð2:6Þ − 0:37 1:0
1 +
ð3Þð0:37Þð0:85Þ ð0:02Þð12Þ
ð7:875 − 4:5Þ
= 20:96 ft/s½6:39 m/s
The required cuttings transport velocity can be estimated as
2
v tr = πð7:875Þ 60
π 2 2 i 3,600
h
4ð0:04Þ ð7:875 − 4:5 Þ
4
= 0:62 ft/s½0:19 m/s
The gas velocity required to transport the solid particles can be calculated as
v g = 20:96 + 0:62 = 21:58 ft/s ½6:58 m/s
(Continued )
