Page 455 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-59
The Reynolds number calculation above is greater than 4,000. This indicates that
the flow condition is turbulent. Therefore, the empirical von Karman equation (i.e.,
Equation 6-86) is used to determine the approximate Fanning friction factor for the
aerated fluid flow inside this drill string section.
The inside surface of the drill pipe tool joints is commercial steel with the
surface roughness
.
e p 0 00015 ft
With the above, Equation 6-86 becomes
2
1
f
i4 0 292
.
2 log 114
.
0 00015
.
.
f i4 0 017
Equation 6-82 for the fourth increment inside the drill string can be solved for
the pressure at the top of the increment, P i3. This involves selecting this lower limit
by a trial and error procedure. The magnitude of the lower 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 lower
limit pressure is
.
,
p i3 3 924 7 psia
P i3 p 144
i3
2
,
P 565 157 lb/ft abs
i3
Substituting the values of ˙ w , ˙ w , Q g, Q m, P g, P i3, P i4, T g, T av4, D 6, f i4, and g
g
m
into the left side of Equation 6-82 gives
,
! 573 888
#
# dP
# 2 125
# 40 978 5 .
,
.
# 33 20 0 017 P 0 426
.
.
∀ 565 157 40 978 5 . 1
,
,
.
.
0 426 18 80 0 292 2
.
P 4