Page 440 - Air and Gas Drilling Manual

9-44 Air and Gas Drilling Manual
(.
001)
(.
0 375)
0 00015)
0 656)
4
e
av3
0 375)
0 656)
(. 2 2 (. (. 4 2 (. 2
4 4
.
e av3 0 0076 ft
Equation 6-77 must be solved by trial and error. A value for f a3 must be selected
that will satisfy the Colebrook equation. This value is
f a3 0 065
.
The Colebrook equation is
0 0076
.
.
.
.
1 0 656 0 375 251
2 log
0 065 37 2 688 0 065
,
.
.
.
The right and left sides of the above yield
392 392
.
.
Equation 6-74 for the third increment in the annulus can be solved for the
pressure at the bottom of the increment, P a3. 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 a3 3 094 3 psia
,
.
P a3 p a3 144
2
P a3 445 579 lb/ft abs
,
Substituting the values of ˙ w , Q g, Q m, P g, P a2, P a3, T g, T av3, D h, D 1, f a3, and g
t
into the left side of Equation 6-74 gives