Page 453 - Air and Gas Drilling Manual

Chapter 9: Aerated Fluid Drilling 9-57
g
m
into the left side of Equation 6-82 gives
,
612 640
! Substituting the values of ˙ w , ˙ w , Q g, Q m, P g, P i4, P i5, T g, T av5, D 5, f i5, and g
#
# dP
# 2 500
,
# 41 192 0 .
.
# 33 20 0 018 P 0 426
.
.
∀ 573 888 41 192 0 . 1
,
,
.
0 426 15 07 0 234 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-
82 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 6-82 yield the
same answer. This shows that the lower limit pressure is correct.
The fourth drill string section increment is denoted by the length H 4. The
temperature at the bottom of the drill pipe tool joints lumped geometry in the
openhole section is
T 4 599 41.˚R
The average temperature of the drill pipe tool joints lumped geometry along H 4 and,
thus, the temperature of the aerated fluid flow inside the this drill string length is
T av4 598 79.˚R
In order to obtain the approximate value of the Fanning friction factor for
Equation 6-82, it is necessary to estimate the Reynolds number and, thus, the flow
conditions inside the drill pipe tool joints lumped geometry along H 4. This is
accomplished by determining the Reynolds number at the entrance end of the inside
of this drill string section and assuming this Reynolds number approximates the
flow conditions throughout the inside this drill string section.
Using Equation 4-11, the approximate specific weight of the gas as it enters this
drill string section is determined from P i4. This is
,
( 573 888) ( 1 0)
.
gi4
( 53 36) ( 598 79)
.
.
17 96 lb/ft 3
.
gi4