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228 Part III Underbalanced Drilling Systems

This critical depth is called the maximum depth for stable foam drilling,
and it can be solved from Eq. (9.3) as

L max = 1
2
að1 + d eÞ
8 9

2
bðP max −P s−min Þ +
> 1 − 2bm >
> ðP max + mÞ + n >
> >
2 ðP s−min + mÞ + n
> ln 2 >
< =
2
> >
−
> m + bn/c − bm −1 P max + m −1 P s−min + m >
> >
> tan − tan >
: p ffiffiffi p ffiffiffi p ffiffiffi ;
n n n
(10.8)
o
Assuming T =520 R, Γ min = 0.55, and a 12.25-in × 6.325-in annulus,
the maximum depths and corresponding equivalent circulating densities
(ECDs) are calculated and plotted in Figure 10.16 for Q fx = 0. The figure
indicates that the maximum depth is less than 5,000 ft even with a GLR
value of 20 scfm/gpm. Again, this does not mean that wells cannot be
drilled with foams at depths greater than 5,000 ft. In fact, many wells have
been drilled with foams at depths deeper than 5,000 ft. The explanation is
8.00
Maximum depth
5000
ECD at maximum depth
7.00
4000 6.00
Maximum Depth (ft) 3000 5.00 (ppg) ECD

2000

1000 4.00
3.00

0 2.00
0 2 4 6 8 10 12 14 16 18 20
GLR (scfm/gpm)
Figure 10.16 Effect of injection GLR on the maximum depth and ECD.