Summary
Drift-flux models represent multiphase flow in wellbores or pipes in terms
of a number of empirically determined parameters. Because of the lack of data
for two- and three-phase flow in large-diameter inclined pipes, existing
parameters are commonly based on small-diameter pipe experiments, which can
lead to significant errors when the models are applied to wellbore flows. In
this work, we use recent large-diameter experimental data for the determination
of drift-flux parameters for oil/water/gas flow. The parameters are computed
through application of an optimization procedure. It is shown that in-situ gas
volume fraction in three-phase systems can be estimated using a two-phase flow
model by viewing the system as an effective gas/liquid system, with oil and
water constituting the “liquid” phase. This approach is, however, generally
inaccurate for the determination of oil and water holdups, in which case the
effect of gas must be taken into account. Specifically, for pipe inclinations
away from horizontal, even small amounts of gas can act to eliminate the slip
between oil and water. As the pipe deviation approaches horizontal, however,
oil/water slip persists, even in the presence of gas. We develop and apply a
unified two- and three-phase flow model to capture this gas effect. The
new model is shown to provide much more accurate predictions for oil and water
holdups in three-phase systems than were achievable with previous models.
Introduction
Drift-flux modeling techniques are commonly used to represent two- and
three-phase flow in pipes and wellbores. These models are well-suited for use
in reservoir simulators because they are relatively simple, continuous, and
differentiable. 1,2 Drift-flux models require a number of empirical parameters.
Most of the parameters used in current simulators were determined from
experiments in small-diameter (5 cm or less) pipes and may therefore not be
appropriate for large-diameter wellbores. 3,4
In recent work, 5 we described a new research program, which includes
experimental and modeling components, aimed at the determination of drift-flux
parameters for large-diameter deviated wells. The experimental work entailed
water/gas, oil/water, and oil/water/gas flows in a 15-cm-diameter, 11-m-long
pipe at eight deviations ranging from vertical to 2 DEGREE downward. Unique
steady-state holdup data were measured using several different experimental
techniques. 6 Our previous work provided optimized drift-flux parameters for
two-phase water/gas and oil/water flows. Here, we extend the analysis to
three-phase flows.
Even though the simultaneous flow of oil, water, and gas is very common in
wellbores and pipelines, systems of this type are not fully understood. Most of
the studies to date have focused on horizontal or near-horizontal flows. 7--12
Acikgoz et al. 7 classified the observed 10 flow patterns in a horizontal
1.9-cm pipe into two categories: oil-based and water-based flows, depending on
which phase is dominant in the liquid. No three-layer stratified flows were
observed in their experiments. Following the work of Acikgoz et al. , Lahey et
al. 8 used the same experimental facility to collect three-phase holdup data.
These data were then used to determine the drift-flux parameters C 0 and V .for
each of the 10 flow patterns. They found that the values of C 0 and V .could be
significantly different from one flow pattern to another and, as expected, the
drift velocities were quite small compared with those in vertical flows. It is,
however, clear that general simulation models are still lacking for three-phase
stratified flows. 13 The state of three-phase flow modeling is even less
developed for deviated pipes and wells.
Because comprehensive three-phase flow models are lacking, one treatment for
three-phase flow is to combine oil and water into a single "liquid"
phase and to then model the system as a two-phase liquid/gas flow. In this
treatment, the slip between oil and water is ignored, and a homogeneous mixture
is assumed for the liquid phase. Some studies indicate that this simple
treatment can lead to significant errors in phase holdup predictions, 10,14
while other observations suggest that this approach is valid. 15,16 In this
work, we will use our experimental data and model to clearly quantify the range
of validity of this approach.
An alternate two-stage technique was proposed to model three-phase flow in
wellbores. 1,2 This approach uses two-phase liquid/gas and oil/water flow
models. In the first stage, oil/water/gas flow is treated as a liquid/gas flow
with flow-weighted average properties for the liquid phase. The liquid/gas
drift-flux model is applied to determine the gas volume fraction and liquid
holdup. In the second stage, the oil/water drift-flux model is applied to
compute the oil and water holdups within the liquid phase. This idealized
approach ignores the effect of the third phase on the two-phase flow models.
Nevertheless, it does produce the expected qualitative behavior in some cases.
For example, it enables a stagnant three-phase mixture to separate into gas,
oil, and water zones through countercurrent flow.
In this work, we first evaluate the use of our optimized two-phase
drift-flux parameters for the modeling of the 15-cm-diameter oil/water/gas
volume fraction data collected by Oddi.et al. 6 We show that the two-phase
water/gas drift-flux parameters can be used directly to provide gas volume
fraction in three-phase systems. However, direct application of the two-phase
oil/water parameters leads to considerable error in the predicted oil and water
holdups. This error is shown to be caused by the effect of even small amounts
of gas on the slip between the oil and water phases. We demonstrate that, for
gas-volume fractions greater than a certain critical value, the slip between
the water and oil phases vanishes (except at inclinations very near horizontal,
in which the gas is separated from the oil/water mixture). We determine this
critical gas volume fraction as a function of inclination angle from the
experimental measurements and introduce an additional parameter into the
drift-flux model to capture this effect. The resulting three-phase drift-flux
model provides predictions in close agreement with the experimental data over
the entire range of inclinations and additionally reduces to our previous
two-phase model if one of the phases is not present.
© 2005. Society of Petroleum Engineers
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History
- Original manuscript received:
2 June 2004
- Revised manuscript received:
9 March 2005
- Manuscript approved:
20 March 2005
- Version of record:
15 June 2005
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