Page 447 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-51
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 a5 3 512 9 psia
,
.
P p 144
a5 a5
2
P a5 505 858 lb/ft abs
,
Substituting the values of ˙ w , Q g, Q m, P g, P a4, P a5, T g, T av5, D h, D 4, f a5, and g
t
into the left side of Equation 6-74 gives
,
! 505 858
#
# dP
# 2 500
# 41 192 0 .
,
.
# 34 15 0 088 P 0 426
.
.
∀ 456 707 41 192 0 . 1
,
,
.
.
.
.
0 426 599 % 0 656 2 0 563 2 &
P 4

Substituting the values of H 1, H 2, H 3, H 4, and H 5 into the right side of Equation 6-
74 gives
.
,
6 650 350 2 375 125 500
1 dh 500
6 650 350 2 375 125
,
,
As can be seen in the above, the right and left hand sides of Equation 6-74 yield the
same answer. This shows that the upper limit pressure is correct.
Drill Bit Nozzles
It is assumed that the 7 7/8 inch tri-cone roller cone drill bit is equipped with
three 11/32 inch diameter jet nozzles. Therefore, the inside diameter of each nozzle
D n, is
d n 0 3437 inches
.
d n
D n
12
.
D n 0 02865 ft