Page 541 - Air and Gas Drilling Manual

10-66 Air and Gas Drilling Manual
Using the inside diameter of the drill pipe tool body, D 7, the approximate
average velocity of the aerated drilling fluid as it enters this drill string section, V i3,
is
.
1 826 6 . 586 29
,
( 27 64) 0 234
.
.
273 856 519 67
,
.
V i3
.
0 319 2
4
V i3 554 ft/sec
.
Using Equation 6-103, the Reynolds number of the aerated drilling fluid as it
enters this drill string section, N Ri3, is
(.54 ) ( .319 )
0
5
N
Ri3
. 0 00000969
,
N Ri3 182 182
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 6-106) 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 body is commercial steel with the surface
roughness
.
e p 0 00015 ft
With the above, Equation 6-106 becomes
2
1
f
i3 0 319
.
2 log 114
.
.
0 00015
f i3 0 016
.
Equation 6-102 for the third increment inside the drill string can be solved for
the pressure at the top of the increment, P i2. 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