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174 Part III Underbalanced Drilling Systems

models frequently conflict because of assumptions made in the mathema-
tical formulas (Nakagawa, 1999). Steady-state flow models are widely
used for designing multiphase flow hydraulics programs, while transient
flow models are often employed for extreme case studies.

9.2.1 Flow Regimes
Multiphase flow is much more complicated than single-phase flow due to
the variation of flow regimes (or flow patterns). Fluid distribution changes
greatly in different flow regimes, which significantly affects pressure gradi-
ents inside and outside the drill string. As shown in Figure 9.1 (Govier
and Aziz, 1977), at least five flow regimes have been identified for gas-
liquid two-phase flow in vertical conduits: bubble, slug, churn, annular,
and mist flow. These flow regimes occur as a progression with an increas-
ing gas flow rate for a given liquid flow rate. The former three flow
regimes are often observed in UBD operations, while the latter two are
most often encountered in gas drilling operations.
In a bubble flow, the gas phase is dispersed in the form of small bub-
bles in a continuous liquid phase. In a slug flow, gas bubbles coalesce
into larger bubbles that eventually fill the entire pipe cross-section.
Between the large bubbles are slugs of liquid that contain smaller bubbles
of entrained gas. In a churn flow, the larger gas bubbles become unstable
and collapse, resulting in a highly turbulent flow pattern with both phases
dispersed. In an annular flow, gas becomes the continuous phase, with
liquid flowing in an annulus coating the surface of the pipe and with
droplets entrained in the gas phase. In a mist flow, liquid is entrained in
the continuous gas phase in the form of mist.

9.2.2 Liquid Holdups
The liquid phase always flows slower than the gas phase in upward flow
streams and faster in downward flow streams. The differences in phase
velocities cause the in situ volume fractions of fluids to be different from
the volume fractions at the injection point (surface). To be more specific,
the amount of pipe occupied by a phase is often different from its pro-
portion of the total volumetric flow rate. This is due to the differences in
density between the phases. Gravity causes the dense phase to slip down
in an upward flow—that is, the lighter phase moves upward faster than
the denser phase.