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Underbalanced Drilling Operations 225

presented a method for foam stability control by adjusting the GLR and
backpressure. It is summarized following.
Equation (10.3) can be rearranged as

4:07T
GLR
Γ = P (10.4)
4:07T Q fx
GLR + 0:09358 + 0:13369
P Q l

If the backpressure is not applied, at the surface (flow line) condition, the
foam quality reaches its highest value. For the foam quality not to exceed
its maximum allowable value of Γ max , the injection GLR should be
controlled. Setting P and T to the atmospheric pressure and temperature,
respectively, the maximum allowable injection GLR can be solved from
Eq. (10.4) as

GLR max = Γ max 0:09358 Q fx + 0:13369 (10.5)
Q l
ð1 − Γ max Þ
Figure 10.13 presents a chart to determine the GLR max for different
values of Γ max and Q fx /Q l .Ifthis GLR max results in a foam quality less
than the minimum allowable value of foam quality Γ min at the bottom-
hole, a gas–liquid ratio value of higher than the GLR max should be used
to achieve the minimum allowable value of foam quality Γ min at the bot-
tomhole. In this situation, backpressure should be applied to reduce the
foam quality within its maximum allowable value of Γ max at the surface.
The minimum required backpressure can be solved from Eq. (10.4) as

4:07Tð1 − Γ max ÞGLR
P min = (10.6)
Q fx
Γ max 0:09358 + 0:13369
Q l

Assuming T = 520 °Rand Γ max = 0.975, the minimum required back-
pressures are calculated and plotted in Figure 10.14 for different values of
Q fx /Q l .
For a given foam drilling operation, the gas injection rate, and thus
GLR, is limited. With this constraint of GLR, the foam quality at the
bottomhole will decrease to its minimum allowable value of quality Γ min
when the bottomhole pressure increases to a critical value. This critical