Page 265 - Air and gas Drilling Field Guide 3rd Edition

256 CHAPTER 10 Stable Foam Drilling

10.5.1 Nonfriction Approximation
The simple nonfriction methodology allows straightforward deterministic approx-
imate solutions of stable foam drilling problems. However, the practical applica-
bility of these nonfriction solutions is limited to simple geometric borehole
profiles.
The simple nonfriction solution is obtained from Equation (10-8) by letting
f ! 0. The nonfriction approximation is

P bh

T av Q g Q f
H
¼j h j : (10-11)
P g ln P þ P 0
T g _ w t _ w t

P s
The aforementioned equation can be integrated into the following equation:

T av P bh
Q g ln þ Q f ðP bh P s Þ¼ _ w t H: (10-12)
P g
Tg P s
Illustrative Example 10.1 The borehole used in this illustrative example is
7
the basic example used in Chapters 8 and 9. The 7 8 = -in (200 mm)-diameter
5
borehole is drilled out of the bottom of API 8 8 = -in (219 mm)-diameter 32.00-
lb/ft (14.00 kg/m) nominal casing set to 7000 ft (2134 m) (see Figure 10-2 for well
casing and open hole geometric configuration). This is special clearance casing fabri-
7
cated by Lonestar Steel that has a drift diameter that will pass a 7 8 = -in (200 mm)-
7
diameter drill bit. The drill bit used to drill the interval is a 7 8 = -in (200 mm)-diameter
12
tricone roller cutter insert type with three = -in (9.5 mm) nozzles. The anticipated
32
drilling rate in a sandstone and limestone sequence (sedimentary rock) is approxi-
mately 60 ft/hr (18.3 m/hr). The open hole interval below the casing shoe to be
drilled is from 7000 ft (2134 m)to 10,000 ft(3047 m). A back pressure of 80 psig
2
(55.2 N/cm gauge) is applied to the end of the return line to control the foam quality
at the top of the annulus. This back pressure is selected so that the foam quality just
upstream from the back pressure valve will be approximately 0.98.
The drill string for this illustrative example is made up of 500 ft (152.4 m)of
13
1
6 4 = -in (158.8 mm)by 2 = -in (71.4mm) drill collars above the drill bit and
16
1
API 4 2 = -in (114 mm), 16.60-lb/ft (7.52 kg/m) nominal, IEU-S135, NC46 to the
1
surface. The tool joints of this drill pipe have an outside diameter of 6 4 = in
3
(154.8 mm) and an inner diameter of 2 4 = in (69.9 mm). The drilling is carried
out at a surface location of 4000 ft (2129 m) above sea level (see Table 5-1 and
Appendix B). The regional geothermal gradient is approximately 0.01 F/ft

(0.018 C/m). The borehole is drilled with a stable foam drilling fluid composed
of fresh water (with a surfactant) and compressed air.
Appendix E gives the Mathcad detailed solution of Illustrative Example 10.1.
The nonfriction solution is sometimes used to obtain the lower boundary of the
bottom hole pressure. This value is useful for the efficient initiation of the friction
solution. In this nonfriction solution, the return line and the small geometric