Page 452 - Air and Gas Drilling Manual

9-56 Air and Gas Drilling Manual
.
V
11 42 ft/sec
i5
Using Equation 6-83, the Reynolds number of the aerated drilling fluid as it
enters this drill collar section, N Ri5, is
(.42 ) ( .234 )
11
0
N Ri5
. 0 000259
N Ri5 10 350
,
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 drill collars.
The inside surface of the drill collars is commercial steel with the surface
roughness
.
e p 0 00015 ft
With the above, Equation 6-86 becomes
2
1
f i5 0 234
.
2 log 114
.
0 00015
.
f i5 0 018
.
Equation 6-82 for the fifth increment inside the drill string can be solved for the
pressure at the top of the increment, P i4. 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 i4 3 985 5 psia
,
.
P i4 p 144
i4
2
P i4 573 888 lb/ft abs
,