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Gas Compressors 125

The average roughness of an annulus can be estimated using the
following formula:

e p d i + e h d b
ðH−H c Þ + e p H c
e = d i + d b (6.20)
H

where
d i = ID of annulus (OD of drill pipe), in or m
e p = roughness of commercial steel drill pipe and casing, in or m
(a minimum value of 0.0018 in should be used if the tool joints
of the drill pipe are not considered)
e h = roughness of borehole, in or m
H c = depth of casing shoe, ft or m

6.2.2 Gas Flow in Deviated Holes
Deviated holes represent hole sections below the kickoff points (KOPs)
of directional or horizontal wells. The angle-building and angle-dropping
sections can be divided into a series of slant hole segments with different
inclination angles. For a small length of hole, Eq. (6.1) degenerates to

dP = γ dH ± γ fv 2 dS (6.21)
m
m
2gD H
where
S = segment length, ft or m
The depth and length incrementals are related through the inclination
angle by

dH = cos ðI s ÞdS (6.22)

where
I s = inclination angle of slant hole section, radians

Substituting Eq. (6.22) into Eq. (6.21) gives

fv 2
dP = γ m cos ðIÞ ± dS (6.23)
2gD H