Page 519 - Air and Gas Drilling Manual

10-44 Air and Gas Drilling Manual
144
P
p
a3
a3
2
,
P
a3 132 346 lb/ft abs
Substituting the values of ˙ w , Q g, Q w, P g, P a2, P a3, T g, T av3, D h, D 2, f a3, and g
t
into the left side of Equation 6-88 gives
,
∃ 132 346
&
& dP
& 2 2 375
,
,
& 56 959 5 . !
.
& 17 37 0 055 P 0 234
.
.
% 78 039 56 959 5 . 1 ∀
,
,
.
.
.
0 234 18 10 0 656 2 0 375 2
.
P 4
#
Substituting the value of H 1, H 2 and H 3 into the right side of Equation 6-88 gives
,
6 650 350 2 375
,
,
1 dh 2 375
6 650 350
,
As can be seen in the above, the right and left hand sides of Equation 6-88 yield the
same answer. This shows that the upper limit pressure is correct.
The fourth annulus section increment is denoted by the length H 4. The
temperature at the bottom of the length H 4 in the openhole annulus section (bottom
of the drill pipe tool joints lumped geometry), T 4, is
T 4 T r 001 ( H 1 H 2 H 3 H )
.
4
(
,
,
T 4 T r 0 01 6 650 350 2 375 125)
.
.
T 4 599 41˚R
The average temperature of this openhole annulus section H 4 is
T 3 T 4
T av4
2
T 598 79˚R
.
av4
In order to obtain the approximate value of the Fanning friction factor for
Equation 6-88, it is necessary to estimate the Reynolds number and, thus, the flow
conditions in the openhole annulus section along H 4. This is accomplished by
determining the Reynolds number at the exit end of this annulus section and