Page 461 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-65
f
0 017
.
i2
Equation 6-82 for the second increment inside the drill string can be solved for
the pressure at the top of the increment, P i1. This involves selecting this lower limit
by a trial and error procedure. The magnitude of the lower 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 lower
limit pressure is
p i1 2 651 9 psia
.
,
P i1 p 144
i1
2
P i1 381 868 lb/ft abs
,
Substituting the values of ˙ w , ˙ w , Q g, Q m, P g, P i1, P i2, T g, T av2, D 6, f i2, and g
g m
into the left side of Equation 6-82 gives
,
! 405 216
#
# dP
# 2 350
# 39 190 3 . 0 426
,
.
# 33 20 0 017 P
.
.
∀ 381 868 39 190 3 . 1
,
,
.
0 426 18 80 0 292 2
.
.
P 4

Substituting the values of H 1, and H 2 into the right side of Equation 6-82 gives
6 650 350
,
1 dh 350
,
6 650
As can be seen in the above, the right and left hand sides of Equation 6-82 yield the
same answer. This shows that the lower limit pressure is correct.
The first drill string section increment is denoted by the length H 1. The
temperature at the bottom of the drill pipe body lumped geometry in the cased
section is
T 1 570 91.˚R
The average temperature of the drill pipe body lumped geometry along H 1 and, thus,
the temperature of the aerated fluid flow inside the this drill string length is