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192 Part III Underbalanced Drilling Systems

N vG N 0:38
However, ψ = 1:0 should be used for L ≤ 0:01.
N 2:14
D
Finally, the liquid holdup can be calculated by

y L = ψ y L (9.36)
ψ

The interfacial tension is a function of pressure and temperature. The
following correlation is employed by Lyons and colleagues (2009):

σ = σ 74 − ðσ 74 − σ 280 Þðt − 74Þ (9.37)
206
where the temperature t is in °F, or

σ = σ 74 − ðσ 74 − σ 280 Þð1:8t C − 42Þ (9.38)
206
where temperature t C is in °C, and

σ 74 = 75 − 1:108p 0:349 (9.39)
and

σ 280 = 53 − 0:1048p 0:637 (9.40)

where pressure p is in psi, or
0:349
σ 74 = 75 − 6:323p MPa (9.41)
and
0:637
σ 280 = 53 − 2:517p MPa (9.42)
where pressure p MPa is in MPa.

Illustrative Example 9.3
A well was cased to 5,552 ft with an 8⅝-in, 28-lb/ft (8.017-in ID) casing. Starting
from the kickoff point at 5,575 ft, the hole was drilled with mud using a 7⅞-in
bit to build an inclination angle at a constant build rate of 5°/100 ft until the
maximum inclination angle of 90 degrees was reached at the depth of 7,358 ft.
Then the drilling fluid was shifted from mud to stable foam to drill to the TD of
8,045 ft while the inclination angle was maintained at 90 degrees.