Page 436 - Air and Gas Drilling Manual

9-40 Air and Gas Drilling Manual
The approximate average velocity of the aerated drilling fluid as it exits this
annulus section, V a2, is
.
.
1 826 6 572 66
,
19 47)
.
(. 0 426
.
268 632 519 67
,
V a2 % 2 2 &
.
.
4 0 668 0 552
V a2 514 ft/sec
.
Using Equation 6-75, the Reynolds number of the aerated drilling fluid as it
exits this annulus section, N Ra2, is
5
0
(.14 ) ( .668 . 0 552 )
N Ra2
. 0 000259
,
N Ra2 8 333
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 6-78) is used to determine the approximate Fanning friction factor for the
aerated flow in this annulus section.
Both annulus section surfaces are commercial steel with the surface roughness
e p 0 00015 ft
.
Therefore, Equation 6-78 becomes
2
1
f a2
.
.
0 668 0 552
.
2 log 114
.
0 00015
f 0 021
.
a2
Equation 6-74 for the second increment in the annulus can be solved for the
pressure at the bottom of the increment, P a2. This involves selecting this upper
limit 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 6-74 for this annulus section is