Page 434 - Air and Gas Drilling Manual

9-38 Air and Gas Drilling Manual
Equation 6-74 for the first increment in the annulus can be solved for the
pressure at bottom of the increment, P a1. 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 that satisfies Equation 6-74 for this annulus section is
,
p a1 1 865 5 psia
.
P a1 p a1 144
2
,
P 268 632 lb/ft abs
a1
Substituting the values of ˙ w , Q g, Q m, P g, P Tee, P a1, T g, T av1, D 1, D 2, f a1, and g
t
into the left side of Equation 6-74 gives
,
! 268 623
#
# dP
,
# 2 6 650
# 36 795 1 .
,
.
# 34 15 0 017 P 0 426
.
.
∀ 9114 3 . 36 795 1 . 1
,
.
.
0 426 18 87 % 0 668 2 0 375 2 &
.
.
P 4

Substituting the value of H 1 into the right side of Equation 6-74 gives
,
6 650
,
1 dh 6 650
0
As can be seen in the above, the right and left hands sides of Equation 6-74 yield the
same answer. This shows that the upper limit pressure is correct.
The second annulus section increment is denoted by length H 2. The temperature
at the bottom of the length H 2 in the cased annulus section of the borehole (bottom
of the drill pipe tool joints lumped geometry), T 2, is
.
T 2 T r 001 ( H 1 H )
2
.
T 2 T r 0 01 6 650 350)
,
(
T 2 574 41.˚R
The average temperature of this cased annulus section H 2 is