Page 425 - Air and Gas Drilling Manual

19
(.47
V
2
. 0 469
4
V sr 115 3 ft/sec . 0 4256 ) Chapter 9: Aerated Fluid Drilling 9-29
.
sr
Equation 6-74 can be altered to allow its application to the horizontal flow in
the surface flow line. Thus, the Reynolds number of the aerated drilling fluid as it
exits the surface return flow line, N Rsr, is
VD sr
sr
N
Rsr
sr
3
0
(115 . ) ( .469 )
N Rsr
. 0 000263
N Rsr 205 100
,
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 6-48) must be used to determine the Fanning friction factor for the aerated
fluid flow inside the return flow line. Equation 6-48 can be modified for application
to the surface return flow line situation.
The surface roughness of the inside of the steel surface return flow line is the
absolute surface roughness of commercial steel pipe, e . This is
p
e 0 00015 ft
.
p
The Fanning friction factor, f , for flow inside the return flow line is
sr
2
1
f sr
.
.
2 log 0 469 114
.
0 00015
f 0 015
.
sr
Equation 9-11 for the surface return flow line increment can be solved for the
pressure at the entrance end of the line, P . This involves selecting this upper limit
sr
of the left side intergal 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