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124 Part II Gas Drilling Systems

did not use the friction factor provided by either source. It is well known
today that Moody’s friction factor chart should be used whenever possible.
However, it is difficult to use the chart directly when a large amount of
computation is involved.
In this situation, a correlation is more convenient to use than the
chart because it is easy to program in a computer. It is generally believed
that in gas drilling the fluid flow in the annulus falls into the complete
turbulent flow regime. In this flow regime, the friction factor is a strong
function of the relative roughness and a weak function of the Reynolds
number. Nikuradse’s friction factor correlation is still the best available
for fully developed turbulent flow in rough pipe:
2 3 2
f = 6 1 7 (6.19)
6
7
2e
4 5
1:74 − 2 log
d H
where
e = the absolute wall roughness in in or m
Equation (6.19) is valid for large values of the Reynolds number
where the effect of relative roughness is dominant, which is consistent
with Moody’s chart. The major difficulty in determining the friction fac-
tor in gas drilling is estimating the absolute roughness of the wall of open
holes. Although examining formation core samples indicates that for most
formation rocks the absolute roughness of the drilled rock surface looks
similar to that of a coarse concrete road, which has an absolute roughness
of 0.06 to 0.12 in, the absolute roughness of the open holes does not
necessarily fall into this range. Examining the cuttings should help locate
the absolute roughness of the drilled hole.
Mason and Woolley (1981) reported that cuttings recovered at the sur-
face are generally fine- or dust-sized particles. But there is a possibility that
big cuttings that are not removed from the vicinity of the bit by the circulat-
ing air are reground by the action of the bit teeth. Large chips usually are
recovered while drilling shallow holes, in deeper holes when misting and
foaming, and from uphole cavings. Caliper logs indicate that wellbores nor-
mally are enlarged 0 to 15% due to fluid washout. Washout is even more
notable in air drilling. Assuming a 7.5% wellbore enlargement, a 7⅞-in drill
bit should generate a borehole with a wall roughness of about 0.3 in.