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Gas Compressors 129

particles, Gray (1958) presents the following equation to determine term-
inal settling velocity:
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ψ
s
v sl = (6.31)
g
4gD s ðρ −ρ Þ
3ρ C D 1 + D s /D H
g
where
v sl = terminal settling velocity, ft/s or m/s
D s = equivalent solid particle diameter, ft or m
3
ρ s = density of solid particle, lbm/ft or kg/m 3
3 3
ρ g = density of gas, lbm/ft or kg/m
C D = drag coefficient accounting for the effect of particle shape: 1.40
for flat particles (shale and limestone) and 0.85 for angular to
subrounded particles (sandstone)
ψ = particle sphericity factor, dimensionless
D H = hydraulic diameter of flow path, ft or m
If no other data are available, the maximum particle size can be esti-
mated based on the maximum penetration depth per bit revolution:

D s ≈ R p (6.32)
60N
where
R p = rate of penetration, ft/hr or m/hr
N = rotary speed of bit, rpm

The minimum required gas velocity to transport the solid particles
upward can be formulated as follows:
(6.33)
v g = v sl + v tr
where
v g = gas velocity, ft/s or m/s
v tr = required particle transport velocity, ft/s or m/s
The required particle transport velocity depends on how fast the parti-
cles are generated by the drill bit and the amount of moving particles
allowed in the borehole during drilling. The volumetric solid flow rate at
which the particles are generated by the bit is expressed as

2 R p
Q s = π d b = 1:52 × 10 d R p (6.34)
−6 2
4 12 3,600 b