Page 444 - Air and Gas Drilling Manual

9-48 Air and Gas Drilling Manual
144
p
P
a4
a4
2
,
P
a4 456 707 lb/ft abs
Substituting the values of ˙ w , Q g, Q m, P g, P a3, P a4, T g, T av4, D h, D 3, f a4, and g
t
into the left side of Equation 6-74 gives
,
! 456 707
#
# dP
# 2 125
# 40 978 2 .
,
.
# 34 15 0 085 P 0 426
.
.
∀ 445 579 40 978 2 . 1
,
,
.
0 426 670 % 0 656 2 0 552 2 &
.
.
.
P 4

Substituting the values of H 1, H 2, H 3, and H 4 into the right side of Equation 6-74
gives
,
.
6 650 350 2 375 125
1 dh 125
,
6 650 350 2 375
,
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.
The fifth annulus section increment is denoted by the length H 5. The
temperature at the bottom of the length H 4 in the openhole annulus section of the
borehole ( bottom of the drill collars lumped geometry), T 5, is
T 5 T r 001 ( H 1 H 2 H 3 H 4 H )
.
5
,
,
.
T 5 T r 0 01 6 650 350 2 375 125 350)
(
T 5 604 41.˚R
The average temperature of this openhole annulus section H 5 is
T 4 T 5
T av5
2
T 601 91.˚R
av5
In order to obtain the approximate value of the Fanning friction factor for
Equation 6-74, it is necessary to estimate the Reynolds number and, thus, the flow
conditions in the openhole annulus section along H 5. This is accomplished by