Experiments on air-water two phase flow in inclined pipes have been made, with emphasis on the roll wave regime. The motivation for the work is the improving of 1D flow models for multiphase pipeline transport of oil and gas mixtures. Pressure and liquid fractions are recorded in time, together with video recordings. The results show that large amplitude roll waves have associated pressure jumps across the fronts. Some implications for the flow modelling are discussed

De Leebeeck, A.

Hoel Gaarder, A.

Jørgen Nydal, O.

University of Queensland eSpace

16th Australasian Fluid Mechanics Conference 
Crown Plaza, Gold Coast, Australia 
2-7 December 2007 
 
Experiments on Roll Waves in Air-Water Pipe Flow 
 
Angela De Leebeeck, Andreas Hoel Gaarder, Ole Jørgen Nydal1) 
Department of Energy and Process Technology 
Norwegian University of Science and Technology, Trondheim, Norway. 
1 Visiting the Department of Mechanical Engineering 
University of Western Australia 
 
 
             
Abstract 
Experiments on air-water two phase flow in inclined pipes have 
been made, with emphasis on the roll wave regime. The 
motivation for the work is the improving of 1D flow models for 
multiphase pipeline transport of oil and gas mixtures. Pressure 
and liquid fractions are recorded in time, together with video 
recordings. The results show that large amplitude roll waves have 
associated pressure jumps across the fronts. Some implications 
for the flow modelling are discussed.  
 
Introduction  
Multiphase flow simulators are very important tools for the 
design and operation of sub-sea pipelines carrying mixtures of oil 
and gas from wells to a processing facility on a floater, or 
onshore. Design considerations include both steady operation 
(pressure drop, liquid content, temperatures) and dynamic flow 
conditions (operational transients, unstable flows). The basic 
flow models in these simulators are one dimensional, and as the 
closure relations cover averaged physical phenomena (averaged 
wall friction, interface drag, cross sectional phase distribution 
etc.) they are normally empirically determined. Experimental 
data at realistic flow conditions then become an important basis 
for the modelling work. 
 
Flow with large amplitude roll waves is a regime which occurs in 
gas condensate pipelines, in particular for high pressure systems 
(high gas densities). Although this regime has some similarities 
with slug flow, it is often treated as averaged stratified flow in 
the flow models.  
 
In slug flow, liquid slugs block the pipe cross section and the 
slug lengths normally exceed 10 number of diameters. The slugs 
carry the major part of the liquid transport and they propagate 
faster than the total mixture velocity. The slug fronts propagate 
over a liquid layer, which is absorbed and accelerated to the 
liquid velocity in the slug front. Liquid is then shed at the tail of 
the slugs (which has the form of a bubble nose), and decelerated 
as the trailing bubble propagates over it.  
 
Some similarities can be noted for flows with large amplitude roll 
waves. The waves have sharp propagating fronts overrunning a 
liquid layer. The liquid layer behind a wave can decelerate from a 
larger velocity in the wave, see Figure 1 for schematic drawings. 
 
 
Figure 1. Sketch of a slug (top) and large amplitude waves (bottom) 
 
Typical differences between the two flow regimes are the length 
scales (waves are in the order of a few diameters long) and the 
front velocities (waves propagate much slower than slugs). The 
wave regime is also more irregular, with larger spread in 
velocities and amplitudes. Waves can be seen to collapse and to 
merge with other waves, and the roll wave regime can indeed be 
speculated to be a transitional regime towards slug flow.
 
 
Figure 2. Location of liquid fraction probes, pressure sensor video and camera
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Objectives 
The objective of the work is to measure some characteristics of 
roll waves: pressures, amplitudes and propagation velocities. 
Some experimental studies have been made on roll waves before 
(10 cm internal diameter (I.D.) high gas densities, [1]). The 
added value of the present experiments will be the pressure 
response of individual waves, which is information lacking in 
most other previous experimental studies [1, 2, 3, 4, 5, 6]. An 
atmospheric flow loop with air and water is available for the 
experiments. 
 
Experiments 
Flow loop and instrumentation 
The flow laboratory is located at the Norwegian University of 
Science and Technology. The experiments were made in a 16 m 
long acrylic pipe of 6 cm I.D. Pipe inclinations varied in the 
range of -1 to 3 degrees with the horizontal. The loop pressure 
was atmospheric.  
The single phase flow rates are measured with electromagnetic 
meters (water) and vortex meters (air). The liquid fraction is 
recorded in time with impedance ring probes at 4 locations along 
the pipe, see Figure 2 and 3. Pressure is recorded with an 
absolute sensor located close to the last liquid fraction probe.  
A video camera was used to monitor the flow at the position of 
the pressure sensor. The video has a time stamp, making it 
possible to identify the video picture of a wave with the time 
recordings of pressure and liquid fraction.  
 
Figure 3. Image of internal flush mounted conductance ring probes for 
liquid fraction measurement. 6 cm I.D. 
 
Experimental Procedure and Data Analysis 
Qualitative observations were first made over quite a large range 
of air and water flow rates and pipe inclinations in search of the 
occurrence of roll waves at low frequencies. When several waves 
or slugs are present at the same time in the pipe, it becomes 
difficult to interpret the dynamics of the pressure recordings.  
After the initial screening, measurements and video recordings 
were made at selected flow conditions. 
 
The time trace analysis should provide velocities and amplitudes 
of liquid fractions and pressures variations relative to each wave 
phenomenon. Automatic data analysis for this purpose turned out 
to be difficult, because waves could decay or emerge in between 
the liquid fraction sensors, making the time traces non-coherent 
between the probes. 
 
A simple first analysis was made by obtaining an averaged wave 
velocity from cross correlating the liquid fraction time traces 
from the four probes, giving three velocity measurements. The 
averaged amplitudes were taken as the 95% percentile value in 
the statistical distributions of all pressure and liquid fraction 
samples in a time series.  
 
Results 
The typical differences between a case with slug flow and a case 
with wavy flow are shown in Figures 4-6. The time traces have 
been shifted in time according to the cross correlation time, so 
that the waves should appear at the same location in the time 
plots.  Usg and Usl are the superficial velocities of gas and liquid 
(volumetric flow rate pr. pipe area). 
 
Overlapped liquid fraction time traces and the pressure time trace 
are matched to the corresponding video snapshot for an 
individual wave in Figure 6. The experiment has a cross 
correlated wave velocity of 1.86 m/s, a 95% percentile pressure 
value of 0.014 bar, and a 95% percentile liquid fraction of 0.28 
from liquid fraction time trace 4. The individual wave moves 
with a velocity of 1.67 m/s, it has a peak pressure of 0.027 bar, 
and a peak liquid fraction of 0.32 in time trace 4. 
 
The slug and the wave time traces have similarities with sharp 
fronts and a decaying tail. It can be difficult from liquid fraction 
time traces alone to discriminate between liquid waves and 
aerated slugs, so the synchronised video pictures were useful in 
the identification of the type of the phenomena which was 
recorded. The time traces in Figure 4 and 5 are predominantly 
waves and slugs. Other flow conditions could show a mixture of 
waves and slugs, making the averaged time trace analysis more 
uncertain.  
 
Slugs travel faster than waves. Figure 7 shows the velocities from 
the cross correlations as function of total volumetric flow rates. 
Slug velocities increase with the flow rates, whereas the trends 
for the wave velocities are less clear.  
 
Slugs exhibit a strong pressure jump across the liquid-gas front. 
The interesting results here is that waves also can show a 
pressure jump, although of a smaller magnitude than for slugs, 
Figure 8.  
 
 
 
 
 
 
 
 
 
Figure 4. Time traces of liquid fraction probes (no. 1 at the top) and of 
pressure in bar (at the bottom). 1 degree upwards pipe inclination, Usg = 
4.34 m/s and Usl = 0.13 m/s. The video snap shot is for the wave 
enclosed in the first rectangle (green). 
 
 
292
 
 
 
 
 
 
 
 
 
 
 
Figure 5. Time traces of liquid fraction probes (no. 1 at the top) and of 
pressure in bar (at the bottom). 0 degrees pipe inclination, Usg = 1.53 m/s 
and Usl = 0.34 m/s.  The video snap shot is for the wave enclosed in the 
first rectangle (green). 
 
 
 
 
 
 
 
 
 
Figure 6: Overlapped signals for liquid fraction time trace 3 and 4 and the 
pressure time trace and the matching video snapshot for the 0 degrees, 
Usg = 5.89 m/s and Usl = 0.17 m/s. The pressure signal is multiplied by a 
factor of 10 so that it can be seen on the same plot as the liquid fraction. 
 
 
 
 
 
Slugs 
Waves
Figure 7: Velocities from cross correlation of time traces no. 3 and 4.  
 
 
Figure 8: 95% percentile pressure in bar vs. the cross correlated 
disturbance velocity between liquid fraction time trace 3 and 4 in m/s for 
all experiments. Experiments with both waves and slugs are included in 
the plot. 
 
 
Flow Models
On the length scale of a pipe diameter, slug flow and wavy flow 
appears as dynamic flows, with time fluctuations in the flow 
parameters. General 1D models can be solved numerically on a 
small grid, in order to capture the dynamics of individual slugs. 
This has been demonstrated using a two fluid model, with a set of 
conservation equations for both phases [7,8]. Such models are, 
however, very sensitive to the numerical scheme, and the 
computational times are prohibitive for simulation of long two 
phase flow pipelines.  
 
Alternative schemes bases on slug tracking instead of capturing 
have been tested [9]. These schemes employ a grid moving with 
the fronts, allowing for computations with orders of magnitudes 
less grid points than with an Eulerian front capturing scheme. 
The grid velocities in such tracking schemes are the characteristic 
bubble propagation velocity in slug flow and the front velocities, 
as derived from mass balances across the fronts.   
 
For simulation of long pipelines with lengths in the order of 10 or 
100 kilometers, the small scale dynamics of slug flow is often of 
less importance, and slug flow is then treated as a quasi 
stationary flow, with averaged pressure drop and liquid fraction 
over several slug-bubble units. The numerical grid in such 
simulations would typically be much larger than slug-bubble 
293
units, and the dynamics of such simulations would typically be 
on pipeline scales (transport times and riser lengths) and not on 
diameter scales. Quasi steady state slug flow models “unit cell 
models” can be formulated as a combination of models for 
bubbly flow in the slug region and separated flow in the bubble 
region, with the two regions coupled with mass balances for gas 
and liquid [10]. Such “unit cell models” can be solved as a point 
model, and integrated into dynamic simulators for resolving the 
large scale dynamics.  
 
Wavy flows
Wavy flow is often modelled as averaged separated flow, 
assuming flat interface geometry, and with empirically tuned 
wall and interface friction relations. This is probably a reasonable 
approach when the waves are small. For the roll wave regime, 
with breaking waves and significant liquid transport in the waves, 
the question is whether improvements can be made along the 
modelling lines similar as for slug flow.  
 
As for slug flow, it has been demonstrated that numerical 
schemes can be designed to capture formation and propagation 
[8] of large amplitude waves. Point models have also been 
derived for the roll wave regime, based on the combination of 
discontinuous numerical solutions of the set of momentum and 
mass conservation equations for gas and liquid [1].   
 
The present experiments have shown that a pressure jump over 
the waves constitutes a large part of the pressure drop in large 
amplitude wavy flows. This could suggest a modelling approach 
along similar lines as for slug flow, including both “unit cell” 
point models as well as dynamic tracking models. An integral 
wave model is then needed, providing in particular relations for 
the wave velocity, wave amplitude and pressure drop across the 
wave. The present experimental data needs further analysis to 
extract single wave data as a basis for the further modelling 
considerations.   
 
 
Conclusions 
Experiments have been made with air-water, near horizontal pipe 
flows in order to measure details in the pressure response related 
to large amplitude waves.  
 
Time trace recordings of four liquid fraction probes and one 
pressure sensor, together with synchronised video recordings, 
show that large amplitude roll waves are associated with a 
pressure jump.  
 
This suggests that further modelling efforts of roll waves could 
be made along similar lines as for slug flow, both regarding 
steady state and dynamic models. 
 
 
Acknowledgments 
The work has been sponsored by Total EP Stavanger, Norway. 
The work is part of a joint PhD program with industry on 
“Multiphase Transport” at the Norwegian University of Science 
and Technology, Trondheim, Norway.  
O.J. Nydal acknowledges the support of the University of 
Western Australia for hosting him as a visitor.  
 
 
References 
[1] Johnson, G. W.,  A Study of Stratified Gas-Liquid Pipe 
Flow, PhD thesis, University of Oslo, 2005. 
[2] Lin & Hanratty, Detection of slug flow from pressure
 Measurements, Int. J. of Multiphase Flow, 13, 1987, 13-21.
 
[3] Miya et al. A model for roll waves in gas-liquid flow, 
Chemical Engineering Science, 26, 1971, 1915-1931. 
[4] Soleimani & Hanratty, Critical liquid flows for the transition 
from the pseudo-slug and stratified patterns to slug flow, Int. 
J. Multiphase Flow, 29, 2003, 51-67. 
[5] Woods et al., Mechanism of slug formation in downwardly 
inclined pipes, Int. J. of Multiphase Flow, 26, 2000, 977-
998. 
[6] Woods et al., Frequency and development of slugs in a 
horizontal pipe at large liquid flows, Int. J. of Multiphase 
Flow, 32, 2006, 902-925. 
[7] Issa, R & Kempf, M.H.W. Simulation of slug flow in 
horizontal and nearly horizontal pipes with the two fluid 
model.  Int. J. of Multiphase Flow, 29, 2003, 69-95. 
[8] Fabien, R. A Lagrangian slug capturing scheme for gas-
liquid flows in pipes PhD thesis, Norwegian University of 
Science and Technology, 2007.  
[9] Nydal, O.J., Audibert M., Johansen, M. Experiments and 
modelingof gas-liquid flow in an S-shaped riser. 10th Int. 
Conference on Multiphase Technology, BHRG Cannes  2001  
[10] Bendiksen, K., Malnes, D. Nydal, O.J. On the modeling of 
slug flow.  Chem. Eng. Com. 1414,  1996,  71-102. 
 
 
 
 
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Experiments on Roll Waves in Air-Water Pipe Flow

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Experiments on Roll Waves in Air-Water Pipe Flow

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