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120 Part II Gas Drilling Systems

(drill cuttings) is called pneumatics. The principle of pneumatics is
governed by the first law of thermodynamics (conservation of energy),
which is stated as
2
ΔP = P 1 −P 2 = g ρΔz + ρ Δu + f ρv L (6.1)
2
g c 2g c 2g c D H
where
2
ΔP = pressure drop, lbf/ft or N/m 2
2 2
P 1 = pressure at point 1, lbf/ft or N/m
2
P 2 = pressure at point 2, lbf/ft or N/m 2
2 2
g = gravitational acceleration, 32.17 ft/s or 9.81m/s
2
g c = unit conversion factor, 32.17 lbm-ft/lbf-s or 1 kg-m/N-s 2
3
ρ = fluid density, lbm/ft or kg/m 3
ΔZ = elevation increase, ft or m
v = gas velocity, ft/s or m/s
f = friction factor
L = length, ft or m
D H = hydraulic diameter, ft or m
The first, second, and third terms on the right side of Eq. (6.1) represent
pressure drops due to changes in elevation, kinetic energy, and friction,
respectively. The second term is usually negligible for gas flow in the pipe
but is very significant for gas flow through the bit and choke.
Equation (6.1) is applicable to any flow configurations, including
downward, upward, horizontal, and deviated flows. In the following sec-
tions, conventional circulation is discussed, where gas flows downward
inside the drill string and upward in the annulus.

6.2.1 Gas Flow in Vertical Holes
Most wells drilled with gas in the oil and gas industry are vertical wells.
The percentage of deviated and horizontal wells has been increasing
rapidly since the 1980s. However, because of the limitations of direc-
tional drilling tools such as measurement while drilling (MWD) in com-
pressible fluid drilling, gas drilling technologies are mostly used for
vertical wells in the petroleum industry.
Consider an infinitesimal element of a conduit at depth H, neglecting
the kinetic energy term. Eq. (6.1) gives
2
fv
dP = γ 1± dH (6.2)
m
2g c D H