Page 443 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-47
2 108
N
,
Ra4
The Reynolds number calculation above is greater than 2,000 and less than 4,000.
This indicates that the flow condition is transitional. Therefore, the empirical
Colebrook equation (i.e., Equation 6-77) is used to determine the approximate
Fanning friction factor in this annulus section.
Using Equation 8-2, the average absolute surface roughness of this annulus
section, e av4, is
0 656)
(. (. 2 (. (. 2
0 00015)
001)
0 552)
4 4
e av4
0 656)
0 552)
(. 2 (. 2
4 4
e av4 0 0059 ft
.
Equation 6-77 must be solved by trial and error. A value for f a4 must be selected
that will satisfy the Colebrook equation. This value is
f a4 0 085
.
The Colebrook equation is
.
0 0059
.
.
.
1 0 656 0 552 251
2 log
0 085 37 2 108 0 085
.
,
.
.
The right and left sides of the above yield
.
342 342
.
Equation 6-74 for the fourth increment in the annulus can be solved for the
pressure at the bottom of the increment, P a4. 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 is
,
.
p a4 3 171 6 psia