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130 Part II Gas Drilling Systems

where
3
3
Q s = volumetric flow rate of solid particles, ft /sec or m /s
d b = bit diameter, in or m
The unit conversion factor 12 becomes 1 in SI units. The volumetric
flow rate at which the solid particles are transported in the flow path is
expressed as
A

Q tr = v tr C p (6.35)
144
where
2
A = cross-sectional area of annular space, in or m 2
3 3
Q tr = volumetric flow rate of transported particles, ft /sec or m /sec
C p = particle concentration in the flow path, volume fraction

Based on the material balance for solid particles, the volumetric flow
rate of particle transport must be equal to the volumetric flow rate of
particles generated by the drill bit:
(6.36)
Q tr = Q s
Substituting Eqs. (6.34) and (6.35) into Eq. (6.36) gives

2
v tr = πd b R p (6.37)
4C p A 3,600

Bradshaw (1964) concludes that at solid concentrations in excess of
volume fraction 0.04, the tendency for solids in air to slug and interfere
materially with each other becomes critical. This indicates that the critical
particle concentration may be assumed to be C p = 0.04.
Once the minimum required gas velocity is determined from Eq.
(6.33), the required minimum in situ air flow rate at the collar shoulder
can be estimated by
A

Q g = 60 v g (6.38)
144
The required minimum in situ air flow rate is converted to the gas flow
rate at the standard condition (14.7 psia, 60F) using the ideal gas law:

Q go = T o P Q g (6.39)
P o T