Summary
Probabilistic/mechanistic modeling was carried out to develop a predictive
model for initiated slug-length distribution at the lower elbow of a
hilly-terrain pipeline. Statistical analysis suggested the appropriateness of a
Log-Normal model over an Inverse Gaussian model. The Log-Normal model is
correlated by two empirical relationships developed for mean slug length and
slug-length standard deviation. Based on experimental observations, the
approach of critical liquid level (instead of critical liquid volume) was
adopted as the slug initiation criterion at the lower elbow. Consequently, the
critical liquid level was mechanistically modeled and empirically correlated to
the initiated mean slug length and standard deviation. A model validation study
demonstrated the capability of the probabilistic/mechanistic models to
reproduce experimental data with a satisfactory match. The match is improved
when the developed correlations were tuned using the statistical confidence
intervals of their coefficients.
Introduction
Several slug formation models have been developed, mostly for horizontal
co-current flow. These models are based on the stability of the liquid film and
predicting the onset of slugging. The Kordyban and Ranov (1970) horizontal
co-current slug formation model is based on Kelvin-Helmholtz (K-H) instability
and finite-amplitude wave analysis, as the second-order and first-order terms
in the Laplace formulation of 2D potential flow, respectively. The Wallis and
Dobson (1973) model considers slug formation as a result of the instability of
small sinusoidal waves at the interface. 2D velocity potentials in a moving
coordinate system were derived and solved for the critical slug formation gas
velocity. The Taitel and Dukler (1976) slug formation model is based on a
simple force balance between gravity and Bernoulli forces on a finite-amplitude
wave, assuming the motion of the wave can be neglected. Gardner (1979) claimed
that the onset of slug formation is a result of energy transfer from the gas
phase to the liquid phase. As the energy transfer reaches its maximum level,
slug formation takes place, assuming a lossless wave system exists on the
interface. Mishima and Ishii (1980) modified the Kordyban and Ranov slug
formation model by introducing the most dangerous wave. This modification
indicates that slug formation is governed by the largest linear growth rate of
a finite-amplitude wave.
Flooding is a different phenomenon of slug formation and is characterized by
countercurrent flow. Although several flooding models have been developed for
annular flow in vertical pipes (Wallis 1961; Hewitt 1977; Shearer and Davidson
1965; Imur et al. 1977), few models exist for slightly inclined upward
stratified flow. Lee and Bankoff (1983) investigated the flooding phenomenon in
slightly and moderately upward inclined (symbol = 2.9°, 4.5, and 33.5°) ducts
using steam and saturated water and developed an envelope theory for the onset
of slugging based on the momentum balance equation. When compared with
experimental data, a satisfactory agreement was found. They also compared the
slug formation models of Kordyban and Ranov, Wallis and Dobson, Taitel and
Dukler, Gardner, and Mishima and Ishii with the same experimental data. The
results show reasonable agreement for some of the models. They concluded that
although the co-current slug formation models were developed under different
assumptions, they could be applied for countercurrent flow (flooding) with
minor modifications. A recent experimental study by Choi and No (1995) on
flooding in stratified flow in slightly upward inclined pipes
(0°<symbol<1°) showed two slug-formation mechanisms, namely entrance
and inner mechanisms. The entrance mechanism is similar to the wave-growth
mechanism observed at the entrance of the uphill section of the hilly-terrain
pipeline in our experiments. The inner mechanism is characterized by wave
growth at a location further downstream from the entrance, which is also
similar to our observation of the wave coalescence mechanism as the waves
coalesce and form a pseudoslug further downstream of the elbow.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
14 June 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
24 March 2007
- Manuscript approved:
25 April 2007
- Version of record:
20 February 2008
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