Summary
A mechanistic two-fluid model with new closure relationships is proposed to
predict liquid holdup and pressure gradient of stratified flow. The
proposed closure relationships include correlations of wetted-wall fraction
factor, liquid-wall friction factor, and interfacial-friction factor. An
iterative calculation procedure is implemented to solve for liquid holdup and
pressure gradient for a given set of operating conditions, pipe geometry, and
fluid properties.
Two sets of facilities, a small-scale facility with 51-mm internal diameter
(ID) and a large-scale facility with 150-mm-ID test sections, were used to tune
the model. Superficial gas and liquid velocities were varied from 5 to 25
m/s and 0.00025 to 0.03 m/s, respectively, in the small-scale facility while
they were varied from 7.5 to 21 m/s and 0.005 to 0.05 m/s, respectively, in the
large-scale facility. The pipe inclination angle varied from −2 to
2°. The liquid holdup was ranged between 0.003 and 0.12, emphasizing the
low-liquid-loading two-phase flow.
The tuned model performance was then benchmarked against the high-pressure
(up to 90 bar) SINTEF-stratified flow data. The model predictions agreed well
with measured values of liquid holdup and pressure gradient. The comparison
between the present model and OLGA® (a commercial transient multiphase-flow
simulator by Scandpower Petroleum used widely in the petroleum industry)
performance was also presented.
Literature Review
Stratified flow with a low-liquid loading (< 1100
sm3/MMsm3) is a dominant-flow pattern in wet-gas
pipelines. A good prediction of liquid holdup and pressure gradient is
critical to pipeline size selection and the design of downstream facilities
(e.g., slug catcher). Model underestimation of pressure gradient will give a
smaller pipe size than required, and the transportation capacity will be
restricted; model overestimation of pressure gradient will result in an
oversized pipeline, worse sweeping characteristics, and possible solids dropout
and corrosion issues. In this section, some of the previous work on stratified
flow were reviewed.
Taitel and Dukler (1976) proposed a 1D two-fluid model that assumed a flat
gas/liquid interface. A Blasius-type equation was used to calculate gas-wall
and liquid-wall friction factors. The effect of interfacial shear stress was
taken into account. It was assumed that the interfacial friction factor was
equal to the gas-wall friction factor for stratified-smooth flow, and 0.014 for
stratified-wavy flow. Cheremisinoff and Davis(1979) collected experimental data
of air/water flow in a 63.5-mm-ID horizontal-flow loop. The liquid-phase flow
was modeled using an eddy-viscosity expression developed for single-phase flow.
To simplify the problem, the authors assumed that the shear stress was constant
in the liquid region, and liquid velocity was dependent only on radial distance
from the pipe wall. Akai et al.(1981) solved the momentum equations for both
phases. The turbulence effect was considered by using a modified model, which
is applicable to low-Reynolds-number cases. Shoham and Taitel(1984) numerically
solved the liquid-phase momentum equation, considering the gas phase as a bulk
flow. The eddy-viscosity model was applied to simulate the turbulence
effect in the liquid phase. Issa(1988) solved the momentum equations for both
gas and liquid phases to calculate pressure gradient and liquid holdup. The
author used the two-equation model to simulate the turbulence effect in both
phases.
© 2007. Society of Petroleum Engineers
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History
- Original manuscript received:
28 October 2005
- Meeting paper published:
9 October 2005
- Revised manuscript received:
12 September 2006
- Manuscript approved:
28 February 2007
- Version of record:
20 June 2007
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