7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Pattern transition and holdup behaviors of horizontal oilwater pipe flow
M. Xu R.H. Xiong', Y.F. Li1, J.M. Yang', X. Luo1, Y.B. Yu2, T.Z. Zhao2
1Dept. of Modem Mechanics, University of Science and Technology of China, Hefei, 230026
2Logging and Testing Service Company, Daqing Oilfield Company Ltd., Daqing, China, 163412
Keywords: Oilwater flow; Flow pattern; Holdup; horizontal pipe flow
Abstract An experimental investigation was carried out on the Pattern transition and holdup
behaviors of horizontal oilwater pipe flow. The experiments were conducted in a 7 m long, 20
mm diameter, acrylic resin pipe using diesel oil and tap water. The characterization of flow
patterns and identification of their boundaries was achieved via observation of the recorded high
speed movies combined with the help of conductance probe, and steadystate data of the flow
patterns and holdup were obtained. The new experimental data, shown as a function of the
superficial velocities, were compared with some existing prediction models, which use the area
averaged steadystate twofluid model for stratified flow and the homogeneous model for
dispersed flow, and fairly good agreement was found.
1. Introduction
Oil/water twophase flows or threephase oil/water/gas flows, although quite complex, are
very common phenomena in modern petroleum exploitation and transportation. The near
horizontal multiphase flows occur quite often in transportation and nearhorizontal well which is
more effective than vertical well in oil exploitation. It will be helpful to predict phase holdup and
pressure loss from oil, gas and water flow rates in the transportation case, although it is inverse
problem in the production logging analysis. The twophase flows are much simpler than the
threephase flows in the nearhorizontal conditions, because the fluids can adopt different and
complex spatial configurations known as flow patterns. And, in the twophase flows, it has been
shown (Rodriguez et al., 2004) that it is possible to derive oil and water superficial velocities
from holdup and pressure gradient measurements via an inverse mode prediction technique.
However, there are only very few number of publications that address horizontal flow in liquid
liquid systems, especially for small diameter cases (Brauner and Maron, 1992a, b, 1999;
Trallero, 1995; Trallero et al., 1997; Brauner, 2001; Rodriguez and Bannwart, 2004).
In present work, a study was focused on pattern transition and holdup characteristics of
horizontal oilwater pipe flows for various of mixture flow rate and input water fractions, with
main interests in small diameter case.
2. Experimental setup
The oilwater twophase flow experiments were conducted in a 7 m long, 20 mm diameter
acrylic resin pipe using diesel oil (density of 830 kg/m3 and viscosity of 3.0 mPa s) and tap water
(density of 980 kg/m3 and viscosity of 1.0 mPa s). The input water fraction (water cut), as well as
the oil fraction were obtained with high accuracy flow meters installed ahead of the inlet,
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
respectively, and the superficial velocities of oil and water tested in the experiments were from
0.1 to 0.8m/s and 0.1 to 1.8m/s, respectively, which covers most of the flow patterns of our
interests. At the test section, a rectangle transparent container full with water was fixed around
the pipe to correct the optical distortion caused by the cylindrical acrylic resin tube. The
characterization of flow patterns and identification of their boundaries were achieved based on
the observation of high speed camera (SUPERMICRO Company, 1000 fps in 1280x512 pixels).
Furthermore, an annular conductance sensor, and a pair of fast action (quick closing) valves were
equipped to measure the absolute in situ volumetric fraction (holdup) of water phase.
3. Experimental results and model comparisons
3.1. Flow patterns
Typical photographs obtained in the experiments are shown in Fig. 1, which were taken in
the case of horizontal flow and represent most of the flow patterns in the present discussion.
When the flow velocities of both oil and water are slow enough, the behaviors of the mixture is
very stable, or the flow configuration can be easily characterized as so called Stratified smooth
(ST) pattern, in which the oil and water move forward at upper and downside separately with a
clear interface (as shown in Fig. la). But the interface becomes unstable as the flow speed
increases, and the wavy interface will breakup eventually and the flow configuration behaves
differently, which is called ST&MI (Stratified flow with mixing at the interface) pattern as
shown in Fig. lb.
More severe interaction between the two phases can be observed for higher velocities of the
mixture, and the semistratified flow patterns o/w&w (Dispersion of oil in water and water, see
Fig. Ic) and o/w (Oil in water homogeneous dispersion, see Fig. Id) still can be recognized with
high speed photograph thanks to the transparency of the water, when the oil fraction is less
enough. But it was difficult to distinguish between the w/o (waterinoil homogeneous dispersion)
and a possible w/o&o/w (Dispersions of water in oil and oil in water) flow pattern in the oil
dominated region through the visualization results, because the diesel oil is not well transparent
(see Fig. le and Fig. If, respectively). In present work the response of conductance probe was
analyzed to figure out the above two flow patterns. The conductance probe attached to the inner
wall of the tube has two detective annular electrodes, so we can measure the conductance of the
mixture between the two electrodes. The conductance in w/o dispersion flow is nearly equal to
the pure oil which can be measured first; while the conductance in w/o&o/w flow pattern
behaves a litter higher than the pure oil due to the conductivity of continuous water.
It should be noted that the slug flow and annular flow patterns have not been found in the
present experiments.
a Stratified smooth ( ST ) b. Stratified flow with mixing at the
interface (ST&MI)
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
c. Dispersion of oil in water and water (o/w&w) d. Dispersion of oil in water (o/w)
e. Dispersion of oil in water and water in oil (o/w&w/o) f. Dispersion of water in oil (w/o)
Fig. 1. Typical photographs obtained in the experiments representing various flow patterns
3.2. Flow patterns transition
Fig.2 shows the collection of the experimental flow pattern map distribution as a function of
the water oil superficial velocity (Usw and Uso). One of our key interests is to make a
comparison of the present data with some existing pattern transition models.
SW&OIW
18 OW
ST
.s v ST&MI
S. W/O
1.4 < WIO&OW
12
0.6 *
t _, .
04
0.0 0.1 0.2 0.3 04 0.5 06 07 0.8 0.9
Uso nml
Fig.2. pattern map and transition model comparison.
One candidate model applied for the transition between ST and ST&MI is linear stability
analysis to the areaaveraged steadysate onedimensional twofluid model for stratified flow,
which can be found in Trallero (1995). For clarity, a shortened description is given in the
following part. In the twofluid model, it is supposed that the flow is onedimensional and the
pressure drop of water and oil is equal. Thus, eliminating the pressure drop from the momentum
equation of two phases, the final form equation is obtained,
"S+ roo ,S,( + ) (p po)gsin()= 0. (1)
A A0 Aw A
Here r stands for the shear stress, Sx the wetted perimeter, Ax the cross sectional area, px the
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
density and 0 the inclination angle from the horizontal. The upper sign of the interfacialstress
term corresponds to the upper phase (oil) flowing faster than the bottom phase (water). Since all
the geometrical variables (Ao, Aw, So, Sw and Si) are function of holdup and they can be found
in Trallero (1995), and shear stresses can be calculated from the known variables (Usw, Uso) and
holdup. So, the equation can be solved for the water holdup or the liquid level (Hw) using a
standard numerical method. The water holdup prediction result will be discussed in section 3.3.
Then the pattern transition criterion derives form the stability analysis of interfacial wave
(change of Hw in one dimension) from equation (1), namely
P2 PA p  ) p c A 2
(C, C,, + (U, U)2 w g cos(O) k2<0. (2)
pAwAo P P A'
In Equation (2), Cv is the wave velocity at the onset of instability, C,, is the critical velocity,
P is the density of whole pipe, Uw and Uo are the real velocity, is the tension coefficient, k is
A' dA / dh
the wave number, and w is expressed as wA dh
For the transition from ST&MI to o/w&w and o/w&w to o/w, the two models from Clarlos
(2006) have been chosen, based on which the first step is to find the maximum droplet diameter
of the experimental condition. For dilute flow, a dimensionless maximum droplet diameter can
be obtained, namely,
d dmax 0.549
dmax 
d weO"fm ; (3)
For dense flow, the maximum droplet diameter can be written as
ddmax a 2.221
dm ( = )
d 1, weo, (4)
Where the Weber number is defined as
we = U2dpm (5)
a
Here the fm is friction factor of mixture, ad is the rate of dispersion phase, Um is the mixture
velocity, and d is the pipe's internal diameter.
As presented in Clarlos (2006), it is proposed that the transition to o/w&w takes place when
the continuous phase turbulence is sufficiently large to prevent coalescence of droplets, which
remain stable spherical droplets. This criterion can be represented as
1.265 dcd
1.26= dcd < dmax. (6)
[cos(O)Eo]05 d
Where the Eo number is defined as
Eo = Pc P gd2
U (7)
The subscript c stands for continuous phase, d stands for dispersion phase, and g stands for
acceleration of gravity.
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Also, Clarlos (2006) proposed that the transition to fullydispersion flow pattern occurs when
the continuousphase turbulence energy is large enough to prevent the migration of the droplets
toward the pipe wall due to buoyancy forces, namely,
3 Pc dcb
f, PFr = dcb < dmax. (8)
8 pc Pd cos(O) d
Where he f/ is friction factor of continuous phase, and the Fr number is defined as
U2
Fr =( ). (9)
dg
Finally, the results calculated based on the above prediction models are given in Fig. 2 as
solid lines. It can be found from Fig. 2 that the transition border between each neighbor flow
patterns observed from our experiment matches quite well with the above predictions, which
implies that candidate prediction models work well at least for the present small diameter pipe
flow cases.
3.3. Holdup
The comparison of water holdup data between the experiments and the predictions (based on
equation (1)) was also made in present study and special attentions were paid to low speed flow
cases because: 1) the velocity difference between oil and water phases is more obvious when the
flow is slow; 2) quick closing valve works better and can get more accurate holdup data for
lower speed case and 3) the prediction model (equation (1)) fits stratified flow pattern, which
also limits the flow speed.
Uso rirs 0m 1
0.2
1.06 A 0.3
1.w04 0V 4
1.03 Uso 0.2ris
1.02 
1.99 Us" 0.2Urod0.4
0.9 
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Fig.. Cw/Ew as a function of the water superficial velocity
Fig.3. Cw/Ew as a function of the water superficial velocity
7th International Conference on Multiphase Flow,
ICMF 2010, Tampa, FL, May 30 June 4, 2010
Both experimental data (symbols) and the predictions results (solid line) are shown in Fig. 3.
in which the ratio between the water cut and holdup (Cw/Ew) is shown to demonstrate the
difference of water holdup and input water fraction. It can be found from the figure that the water
cut/holdup ratio, for which Cw/Ew>l represents the water real velocity faster than oil, reaches a
peak and becomes more obvious especially for low mixture flow rate and low oil fraction, and
then tends to be close to the homogenous line (Cw/Ew=l) after Usw is higher than about 0.4 m/s.
The prediction results (solid lines), which is based on the twofluid model, reasonably represent
the trend of the experimental points, although the lines do not match the experimental data points
very well. This might be due to the calculate method of shear stresses in the twofluid model is
not sufficiently accurate and further improvements are needed in the future.
4. Concluding remarks
Steadystate data on oil water flow patterns and holdup of 20 mm inner diameter acrylic pipe
were obtained. And the two fluid model for stratified flow and the homogeneous model for
dispersed flow were used to predict the flow patterns transition and water holdup. It showed that
the model works well for pattern transition prediction at least for the present small diameter pipe
flow cases, and reasonably well represent the trend of the water holdup change, although more
accurate calculate method of shear stresses need to developed.
References
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horizontal tubes. Int. J. Multiphase Flow 18, 123140.
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