Page 433 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-37
0 0000238)
.
(
1 282)(
.
31 92)(
.
.
ava1
.
.
2 1 282 ( 31 92 0 0002691)
0 000260 ft /sec
.
ava1
The approximate average velocity of the aerated drilling fluid as it exits this
annulus section, V a1, is
.
1 826 6 537 66
,
.
(. 0 426
19 47)
.
9 114 3 519 67
.
.
,
V
a1 % 2 2 &
.
.
4 0 668 0 375
V 18 59 ft/sec
.
a1
Using Equation 6-75, the Reynolds number of the aerated drilling fluid as it
exits this annulus section, N Ra1, is
(.59 ) ( .668 . 0 375 )
18
0
N Ra1
. 0 000260
,
N Ra1 20 980
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 a1 0 668 0 375
.
.
2 log 114
.
0 00015
.
.
f a1 0 017