Page 518 - Air and Gas Drilling Manual

absolute surface roughness values with those of known engineering pressure
conduits. From this table the absolute surface roughness for the inside wall of a
borehole in the example sandstone and limestone sequence, e oh, is
e oh 001 ft Chapter 10: Stable Foam drilling 10-43
.
The inner surface of this annulus section is the outer surface of the drill pipe body
lumped geometry has the absolute surface roughness of commercial steel pipe, e p.
The surface roughness of commercial steel pipe is
e p 0 00015 ft
.
Thus, using Equation 8-2, the average absolute surface roughness of this annulus
section, e av3, is

001)
0 656)
0 00015)
(. (. 2 (. (. 2
0 375)
4 4
e av3
(. 2 (. 2
0 656)
0 375)
4 4
.
e 0 0076 ft
av3
Therefore, Equation 6-92 becomes
2
1
f a3
.
0 656 0 375
.
2 log 114
.
0 0076
.
.
f a3 0 055
Equation 6-88 for the third increment in the annulus can be solved for the
pressure at bottom of the increment, P a3. This involves selecting this upper limit of
the intergral by a trial and error procedure. The magnitude of the upper limit
pressure on the left side of the equation is selected to allow the left side integral to
equal the right side integral. The integration can be carried out on the computer
using one of the commercial analytic software programs. The trial and error
magnitude of the upper limit pressure that satisfies Equation 6-88 for this annulus
section is
p a3 919 1 psia
.