Page 547 - Air and Gas Drilling Manual

10-72 Air and Gas Drilling Manual
Using Equation 6-103, the Reynolds number of the aerated drilling fluid as it
enters this drill string section, N Ri2, is
6
(. ) ( .319 )
0
58
N Ri1
. 0 00000973
N 215 692
,
Ri1
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 tool joints is commercial steel with the
surface roughness
e 0 00015 ft
.
p
With the above, Equation 6-106 becomes
2
1
f i1 0 319
.
2 log 114
.
.
0 00015
.
f i1 0 016
Equation 6-102 for the first increment inside the drill string can be solved for
the pressure at the top of the increment, P in. 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
commercial analytic software programs. The trial and error magnitude of the lower
limit pressure is

p 229 3 psia
.
in
P in p 144
in
2
P 33 022 lb/ft abs
,
in
Substituting the values of ˙ w , ˙ w , Q g, Q w, P g, P in, P i1, T g, T av1, D 7, f i1, and g
w
g
into the left side of Equation 6-102 gives