crude oil-water flow in horizontal...
TRANSCRIPT
Crude oil-water flow in horizontal pipes
Robbert Kroes, Lene Amundsen and Rainer Hoffmann
August 27, 2013
Abstract
Flow experiments are presented for three different crude oil - water systems in horizontal pipes. An X-
ray tomograph is used to determine the concentration distribution of water over the cross section of the pipe.
The three crude oil - water systems showed different behavior than model oil - water systems in previously
published studies, both in terms of the concentration distribution and the pressure gradient. An oil-water flow
model has been developed by Amundsen et al. (2009). This model of the oil-water flow is tested against the
experimental data. The model is able to replicate both the pressure gradient and the concentration distribution
of crude oil - water flow for almost all operating conditions. The model does not apply in the region of
transition from stratified to fully dispersed flow.
1 Introduction
The complicated rheological behavior of oil-water mixtures makes transportation of these fluids complex. Much
research has been performed on oil-water flows, but a complete understanding has not yet been obtained.
The distance of pipeline transport of the well fluids has increased due to intensifying of offshore oil and gas
exploration. Optimizations of pipeline operations for simultaneous transport of oil and water requires knowl-
edge of the behavior of the flow of oil - water mixtures.
Transportation of oil and water can result in different characteristic distributions of oil and water. The
different distributions are often called flow regimes or flow patterns. Reliable estimation of the flow regimes
in oil-water pipe flows are required for many processes in the petroleum industry. The pressure gradient of
horizontal pipe flows can be very much dependent on the flow regimes that occur. Better prediction of flow the
pattern will yield a better design of multiphase pipeline systems in the petrochemical industry.
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Dense packed water droplets Dense packed oil droplets
Inhomogeneous water in oil Inhomogeneous oil in water
Homogeneous water in oil Homogeneous oil in water
(a) Dispersed flows
Smooth interface, full seperation Wavy with partly dispersed layers
Wavy with fully dispersed layers
(b) Stratified flows
Figure 1: Flow regimes (Elseth (2001); Amundsen (2011))
1.1 Oil-water flow regimes
Since the 1950’s a large number of researchers has studied the flow regimes occurring in oil-water flows. Dif-
ferent researchers have used different classifications of the flow patterns. In the present study, two main flow
regimes are discussed: Stratified flow and dispersed flow. Both flow regimes can be divided into sub regimes
with a more detailed description of the flow structures.
Dispersed flows have only one continuous phase. The other phase is dispersed in the continuous phase in
the form of droplets. The droplets can be dispersed over the whole pipe cross-section, but they can also form a
densely packed layer. Furthermore, the dispersion over the whole pipe cross-section can be either homogeneous
or inhomogeneous. Figure 1a shows examples of different flows that are classified as dispersed flows.
Stratified flows have two separate layers, each with a different continuous phase. Each layer can be partly
or fully dispersed (Soleimani, 1999). According to Elseth (2001), the interface between the two continuous
layers can be either smooth or wavy. A schematic representation of stratified flow regimes is shown in figure
1b.
Studies of the flow regimes of real crude oil and water flows at real life conditions are very scarce. Valle
and Utvik (1997) published one of the first studies on crude oil-water systems. They observed that the mixture
velocity has a minor influence on the water cut at which the transition takes place from dispersed flow to
stratified flow. When the mixture velocity is above the critical velocity for which dispersed flow appears, then
a dispersed flow appears for water cuts below 45% and stratified flows appear for water cuts above 45%. Valle
(2000), who has used both model oils and crude oil, observed that in most cases the mixture velocity does
influence the transition from dispersed flow to stratified flow.
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1.2 Pressure gradient
Different studies show that the flow regime affects the pressure gradient of multiphase pipe flow. Trallero
(1995) observed a small decrease in the pressure gradient when the flow transits from stratified to dispersed. A
decrease of the pressure gradient was also observed in the transition from stratified with a smooth interface to
stratified with a wavy interface by Valle and Kvandal (1995). Valle (2000) measured similar pressure gradients
for stratified flows and single-phase flows, while Lovick and Angeli (2004) measured a lower pressure gradient
in two-phase flow than in single-phase oil flow. In crude oil experiments, Valle (2000), Valle and Utvik (1997)
and Utvik et al. (2001) observed a peak in the pressure gradient during the transition from oil continuous flow
to stratified flow. Wahumpurage et al. (2008) and Elseth (2001) found a peak in the pressure drop at high water
cuts in model oil systems.
Valle (2000), Solbakken and Schüller (2001) and Utvik et al. (2001) showed the differences between flows
of a recombined hydrocarbon-water system and a system with a model fluid. The differences are significant
in terms of flow regimes and pressure drops. Although the physical properties of the fluids were similar, they
found that the relative pressure drop of real crude oil flows can be up to 50% lower than that of the systems with
the model fluid.
1.3 Concentration distribution experiments
Experiments in which the concentration distributions have been measured are quite rare, especially for crude
oil flows. Both Elseth (2001) and Amundsen (2011) measured the concentration distribution of a of a mixture
of Exxsol and water using a traversing gamma densitometer. Amundsen (2011) states that crude oil - water
systems are expected to behave differently from Exxsol - water systems. Fairuzov et al. (2000) measured the
concentration distribution in experiments with crude oil and water, employing a multi-point sampling probe. He
found that in stratified oil-water flow, complete separation does not occur. According to Fairuzov et al. (2000),
there is always a small amount of water dispersed in the oil layer (> 1.5%) .
1.4 Modeling oil-water flows
A model that can successfully predict the behavior of simultaneous flow of oil and water is of great value in
the petroleum industry. Accurate models for the prediction of the concentration profiles are not yet available in
commercial software. Models for fully dispersed flows were outlined by Mols and Oliemans (1998) and Valle
(2000). Amundsen et al. (2009) presented a model to simulate both fully dispersed flow and stratified flow.
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1.5 Objectives
Many experimental work has been performed on flows of model oil and water. However, more detailed ex-
periments for real life conditions are necessary to develop and validate simulation models and to improve our
understanding of the behavior of oil-water flows.
In this study, we present results of experiments on two-phase flow regimes for three different crude oil-
water systems in horizontal steel pipes. An X-ray tomograph enables us to obtain the concentration distribution
of the phases in the oil-water flow. This information is used to investigate the behavior of oil-water flows at
different flow conditions. Experiments have been performed for different inlet water cuts and mixture velocities.
The experimental data is used to find the effects of water-cut and mixture velocity on the flow behavior, as
recommended by Amundsen (2011). Different water salinities have been used in the experiments to study
the influence of the water salinity on the concentration profiles. A comparison between the concentration
distributions measured in the present crude oil experiments and the concentration distributions measured in
model oil experiments performed by Elseth (2001) gives more insight in the differences between the behavior
of model oil and that of crude oil.
The results from the present experiments are used to test the performance of a model that is able to predict
the concentration distribution and pressure gradient of oil-water pipe flows. An investigation of the differences
between the predictions of the oil-water flow model and the experimental data from four different experimental
campaigns highlights the future work that is needed in the modeling of oil-water flows.
2 Experimental facilities
The experiments have been performed in the test rig that is located in the Multiphase Flow Laboratory at
Statoil’s Research Centre Porsgrunn, Norway. A schematic layout of the test rig is shown in figure 2. This test
facility has been used for flow regime studies (Hoffmann et al. (2012b)), as well as for wax deposition studies,
as described by Hoffmann et al. (2012a). The test section consists of a two-inch pipe of stainless steel. The
latter is important for simulating flow at field conditions, see Angeli and Hewitt (2000).
Before the experiments start, both phases are preheated in a heat exchanger. During the experiments, water
and oil are pumped separately from the separation tank. The oil and water streams are led into an Y-shaped
mixing device, which initializes a stratified flow at the inlet of the pipe. The Y-shaped mixing device has an
internal separating blade inside, which prevents excessive mixing of the two phases (figure 3). Oil and water
then flow through a 17 m long pipe section in which the flow develops.
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Oil heatexchanger
Water pump
Water heatexchanger
Mixingdevice
Test section withwater annulus
X-raytomograph
Window
Inflow
straighteningsection
Oil pump
Water heatexchanger
Viscometer &Pre-separator
Tank/separatorwithphaseindicator
Oil
Water
Emulsionzone
Figure 2: Schematic overview of the test rig
After the inflow section, the flow enters a window section for visual observation of the flow structure.
Downstream of the window section the concentration distribution is measured by an X-ray tomograph (see
section 2.3). Subsequently, the fluids enter the test section, which can be cooled by a water annulus. The
cooling enables to to simulate subsea conditions and creates the possibility to trigger wax deposition. For the
experiments in this study, the water temperature of the cooling water was set equal to the temperature of the
oil-water flow.
separatingblade
oil
water
Figure 3: Mixing device
Downstream of the test section, the flow is pre-separated and finally the oil and water enter the main sepa-
rator. This large separation vessel with a maximum volume of 4200 liters has been designed to provide a long
retention time and to prevent wax depletion of the circulating oil. In the vessel oil and water are separated by
gravity so that separate mono-phases can be pumped again into the test section. Density measurements in front
of each pump monitor the separation quality for the oil and for the water phase.
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During an experiment, all standard parameters are logged continuously: Temperature, flow rates, density
and pressure drops over two parts of the inflow section and over the whole test section.
2.1 Flow development section
The mixing device introduces oil into the upper half of the joint pipe and water into the lower half. Downstream
of the mixing device it is important to have a flow development section before the actual test section in order
to achieve a fully developed flow. According to Grassi et al. (2008), the literature does not provide the length
after which liquid-liquid flows are fully developed. In his literature study, Grassi pointed out that many authors
use data from their facilities for the validation of fully-developed flow models, though being aware of a possible
mismatch. The flow development lengths considered in the study of Grassi vary between 80 and 275 times the
pipe diameter. In addition there is one straightening section of 480 times the pipe diameter. In the present set-up,
the entry length is well above the average used length: it is more than 300 times the pipe diameter. However,
the flow development section is curved, which can have an adverse effect on the flow development.
2.2 Separation
Inspection of the density of both phases before they re-enter the mixing device, enables to check whether or
not the phases have been separated sufficiently in the settling tank. Analysis of the constantly logged density of
both phases indicate that the separator is able to separate the oil and water completely in almost all cases. There
were only two experiments in which the phases were not completely separated before re-entering the mixing
device. In the experiments with oil A (see section 3), up to 8% water was still dispersed in oil in the experiment
for the case of an inlet water cut of 40% and a total flow rate of 15m3/h. Up to 5% oil was still dispersed in
water, in the experiments with oil B and high salinity water for the case of an inlet water cut of 50% and a total
flow rate of 20m3/h.
Analysis of the constantly logged pressure gradient showed that the influence of these small amounts of
dispersions had no effect on the pressure drop. A constant pressure gradient was measured over the complete
duration of these experiments.
2.3 X-ray tomography
An X-ray tomograph was used to measure the concentration distribution over the cross section of the pipe before
the flow enters the test section. The tomograph was built by Innospexion AS. It consists of two pairs of X-ray
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sources and detectors, so that the concentration distribution can be measured along a horizontal and a vertical
transverse.
The water concentration is calculated from X-ray measurements, averaged over 30 seconds. The water
concentration for a two-phase flow as a function of the vertical position y (figure 4) is calculated by comparing
the measured X-ray intensities for the oil-water flow with the intensity for single-phase oil flow and the one for
single-phase water flow (see Hoffmann and Johnson (2011)).
source1
Test section
source2
cam2
cam1
oil
water
x-raydetectors
Po
sitio
n (
y)
Position (x)
Figure 4: Layout x-ray measurement in the present study
3 Fluid properties
Three measurement campaigns have been performed for three different combinations of oil and water. Two
different types of North Sea gas condensates were used, and three different water compositions. In the experi-
ments, the density is measured online using a Coriolis flow meter (Correolus Promass 63F), the viscosities are
measured using a rheometer (Physica MCR 301) and the interfacial surface tension is measured using a pendant
drop method (Teclis equipment).
In addition to the experiments with crude oil, data of an experimental campaign with Exxsol D60 (model
oil) and water are used for comparison. The experiments with Exxsol D60 and water were presented by Elseth
(2001). That experimental campaign was also performed in a two inch steel pipe test section and the oil and
water flows were mixed by a Y-shaped mixing device, similar to the one described in section 2. The physical
fluid parameters of Exxsol D60 are listed in table 2.
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3.1 Oil A and water
The first experimental campaign has been conducted using a North Sea gas condensate and formation water
(see table 1). The physical fluid properties are listed in table 2. These properties are shown for the operating
conditions: p = 1 bar and T = 25◦C (wax appearance temperature (WAT ) = 30◦C)
In order to enhance fast separation, an emulsion breaker was added to the oil. A concentration of 100 ppm of
the emulsion breaker Tretolite DMO 86538 of Baker Petrolite was present in the oil A during the experiments.
All measurements of the physical properties were performed after the addition of the emulsion breaker.
Salt Concentration [mg/l]Na2SO4 49
NaCl 361KCl 389
CaCl2 44
Table 1: Salt concentration in the formation water in experiments with oil A
3.2 Oil B and water
Two experimental campaigns have been performed using another North Sea gas condensate. Both campaigns
have been performed with water with different salt contents, one series with a low salinity (LS) water and one
series with a high salinity (HS) water. The physical fluid properties for the fluids in these experiments are
included in table 2. Again, these properties are shown for the operating conditions, which are: p = 1 bar and
T = 40◦C (WAT = 30◦C) for the experiments with the different water salinities.
In a previously conducted wax deposition campaign, a wax inhibitor had been added to the oil phase. The
used wax inhibitor is FX2886 from Nalco with a concentration of 500 ppm. All physical property measurements
were performed after the addition of this wax inhibitor.
The low salinity water has a concentration of 3g/l NaCl, the high salinity water has a concentration of
300g/l NaCl.
Physical property Oil A -water
Oil B -LS-water
Oil B -HS-water
Exxsol D60 -water
Oil density(kg/m3
)8.5 ·102 8.1 ·102 8.1 ·102 7.90 ·102
Water density(kg/m3
)1.00 ·103 1.00 ·103 1.15 ·103 1.00 ·103
Oil viscosity (Pa s) 6.2 ·10−3 3.2 ·10−3 3.2 ·10−3 1.64 ·10−3
Water viscosity (Pa s) 8.9 ·10−4 1.0 ·10−3 1.4 ·10−3 1.02 ·10−3
Interfacial tension (N/m) 1.6 ·10−2 1.6 ·10−2 1.6 ·10−2 4.3 ·10−2
Table 2: Physical properties of the fluids used
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4 Experimental results
4.1 Experimental matrix
Experiments have been performed for different flow rates and input water cuts. The experiments with oil A
have been performed at total flow rates of 5 m3
h (0.64m/s), 10 m3
h (1.28m/s) and 15 m3
h (1.92m/s) and water cuts
varing from 10% to 90%, in steps of 10%. The experiments with oil B have been performed at total flow rates
of 5 m3
h (0.64m/s), 10 m3
h (1.28m/s), 15 m3
h (1.92m/s), 20 m3
h (2.57m/s) and 25 m3
h (3.21m/s) and water cuts
again varing from 10% to 90%, in steps of 10%.
4.2 Visual observations
Camera pictures of the flow regimes of all crude oil experiments are shown in figure 5. The stratified flow
regimes that occur in the experiments at low flow rates are clearly visible. As the total flow rate increases,
the flow becomes more and more dispersed and the mixtures appear dark. At the low velocity experiments, the
observed layer if clear water at the bottom of the pipe corresponds with the results from the X-ray measurements
(see section 4.3). Simultaneously, in the high velocity experiments, the dark mixture that is observed visually
corresponds to the high amounts of dispersions measured by the X-ray thomograph.(see section 4.3)
4.3 Concentration distributions
4.3.1 Comparison between experimental results for oil A-water and oil B - LS-water
X-ray tomography is used to determine the concentration distribution along a vertical line in the cross section
of the pipe. Figure 6 shows the water concentrations, determined from the X-ray tomography, as function of
height in the pipe for the experiments with oil A and water, compared with the results of the experiments with
oil B and low salinity water.
For the lowest mixture velocity, the flow is stratified with almost no dispersion in both layers for both
oil-water systems. Only for an inlet water cut of 20%, the water layer contains some dispersed oil.
In the experiments with a total flow rate of 10m3/h (1.28 m/s), the flow is mostly in the dispersed flow
regime. The stratified flow regimes that do occur for this flow rate have more dispersion in both layers. However,
complete separation still occurs for an inlet water cut between 50% and 60%. At this flow rate, the flow with oil
B and low salinity water shows more separation than the flow with oil A and water.
The effect, that the flow is mostly in the dispersed flow regime becomes even more clear for a total flow rate
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0.64 m/s
20% 30% 40% 50% 60% 70% 80%
1.28 m/s
1.92 m/s
(a) Oil A - water
(b) Oil B - LS water
(c) Oil B - HS water
Figure 5: Visual observations for various combinations of flow rate (m/s) and water cut(%)
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of 15m3/h (1.92 m/s). Stratified flow regimes still appear for water cuts around 50%, but complete separation
is not observed anymore. At this flow rate, the flow with oil A and water is an almost homogeneous dispersion,
especially for high and low water cuts. For oil B and low salinity water the flow is less homogeneous, especially
for water cuts around 50%.
An explanation for the differences between the behavior of the two mixtures is the difference in the fluid
properties. The viscosity of oil A (µ=6.2 cP) is larger than the viscosity of oil B (µ=3.2 cP). Due to this higher
viscosity, turbulent dispersive forces are more prominent and therefore less separation occurs. This corresponds
with the observations: the differences are most significant in the high velocity experiments, for which the
dispersive forces are most prominent.
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/s
Figure 6: Comparison between the concentration distributions of oil A - water and oil B - LS-water along avertical transverse through the pipe
4.3.2 Comparison between experimental results for oil B - LS-water and oil B - HS-water
The concentration distributions obtained for oil B - high salinity water and for oil B - low salinity water are
compared in figure 7. Again, the flow patterns for the lowest total flow rate are all stratified. The results for the
flow with low and high salinity water hardly differ for the lowest flow rate, because the phases are in both cases
completely separated. A small difference between the high and low salinity results is observed for inlet water
cuts of 20%. The water layer of the flow with low salinity water has slightly more dispersion than the water
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layer of the flow with high salinity water.
For the total flow rates of 10m3/h (1.28 m/s), 15m3/h (1.92 m/s) and 20m3/h (2.57 m/s) the flows are
stratified for water cuts around 50% and dispersed for other values of the water cut. The flow is more dispersed
for the higher total flow rates. Also increasingly more homogeneous dispersions are observed for increasing
flow rates. The differences between the results of the experiments with high salinity water and the ones with
low salinity water are more significant at these flow rates for water cuts around 50%.
The results for the highest flow rate show almost only dispersed flow. Just as for the lowest total flow rate,
the difference between the flows with high salinity water and those of the low salinity water is very small.
The main difference between the flows with high and low salinity water is the density ratio (B-LS: ρwρo
= 1.23,
B-HS: ρwρo
= 1.42). The higher density ratio in the flows with high salinity water will cause stronger buoyancy
forces. At the lowest velocity, the flow is almost fully separated and therefore differences in the buoyancy forces
have only a small effect on the concentration profiles. The differences are clearly visible in the flow regime for
which the flow is not fully separated, but also not homogenous dispersed. The stronger buoyancy forces cause
more separation in the case of flow with high salinity water. For the higher velocities, the turbulent forces are
dominant and the difference in buoyancy forces has negligible effect.
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7 m
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2 m
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/s0.6
4 m
/s
Figure 7: Concentration distributions for flows of oil B - LS-water and for oil B - HS-water along the verticaltransverse through the pipe
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4.3.3 Comparisons with Exxsol D60
Figure 8 shows the concentration profiles for comparable mixture velocities obtained for Exxsol D60 - water,
oil A - water and oil B - low salinity water. The measured concentration profiles for the model oil systems differ
significantly from the ones for the crude oils, especially at the high mixture velocities. The results for Exxsol
D60 and water show stratified flow for a larger range of velocities than seen for the crude oil - water systems.
For the crude oil, dispersed flows appears over a large range of conditions, while the model oil shows stratified
flow for almost all water cuts.
Due to the higher interfacial tension between the model oil and water (σ = 4.3 ·10−2 N/m), than between
crude oil and water(σ = 1.6 · 10−2 N/m), the drop size in both layers increases. This, together with a larger
density ratio for Exxsol - water ( ρwρo
= 1.27) compared to crude oil - water (B-LS: ρwρo
= 1.23, A: ρwρo
= 1.18),
causes stronger separation effects driven by gravity. Furthermore, due to the lower viscosity of Exxsol D60
compared to that of crude oil, the wall shear stress becomes smaller, leading to smaller effects due to turbulent
dispersion.
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Exxsol D60 - water
Figure 8: Concentration distributions for oil A - water, oil B - LS-water and Exxsol D60 - water, along a verticaltransverse through the pipe
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4.4 Standard deviations of the measured water concentration
The X-ray measurements have been performed over a period of 30 seconds with a sample frequency of 40 Hz.
By analyzing the time variation of the measured water concentration, interfacial characteristics can be detected.
Figure 9 shows the standard deviation of the water concentration for the measurement results for the three crude
oil systems.
In Figure 9, a clear distinction is visible between the standard deviations of the measurements of the water
concentration in stratified flow compared to that in dispersed flows. The peaks in the distribution of the standard
deviation indicate the position of the interface between the oil and water continuous phases. The position of
the interfaces hardly differs in the stratified flow regimes in all the three oil-water systems, which results in the
clear peak in the standard deviations, especially for the lowest flow rates.
For higher flow rates and water cuts around 50%, the flow is still stratified. For these measurements, the
standard deviation is therefor still higher than for the dispersed flow regime, but the peak broadens. The wavi-
ness of the interface spreads over a larger area, but the variation over time decreases. This is because there is no
sharp interface anymore between the two continuous phases, because the dispersion is relatively dense close to
the interface.
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/s2
.57
m/s
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/s1
.28
m/s
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4 m
/s
Figure 9: Standard deviations of measurements of the water concentration in flows of oil A - water, oil B-LS-water and oil B - HS-water, along a vertical transverse through the pipe.
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4.5 Pressure Gradient
The measured pressure gradient is shown as a function of the water cut in figure 10. For oil A - water flow, the
dispersions with an oil continuous phase result in a higher pressure gradient than the dispersions with a water
continuous phase. This is as expected since the viscosity of oil A is higher than that of water.
For oil B - water, a peak in the pressure gradient is observed at higher velocities and water cuts around 50%.
At this flow conditions, the flow is dispersed with oil as the continuous phase with high amounts of dispersed
water. After transition to water as the continuous phase and oil as the dispersed phase, the pressure gradient
drops to approximately the pressure gradient of single-phase water flow. According to crude oil experiments by
Valle (2000), an oil continuous layer becomes more viscous when the amount of dispersed water increases. A
higher fluid viscosity will result in a higher pressure gradient.
The pressure gradient as a function of the water cut for the model oil shows a different behavior than that for
the crude oils. A decrease in the pressure drop is observed for low values of the water cut for mixture velocities
of 2m/s and 2.5m/s. According to Soleimani (1999), the presence of the water drops can suppress turbulence,
which will cause a reduction of the drag and therefor a decrease in the required pressure gradient.
The differences between the pressure gradient required for the crude oil - water systems and the ones for
model oil - water system can be caused by the different surface-active chemicals that are present in the crude
oils. Also the added wax inhibitor and emulsion breakers can affect the apparent viscosity of the emulsion and
therefor the required pressure gradient.
0 20 40 60 80 1000
200
400
600
800
1000
1200
water cut [%]
Pre
ssu
re g
rad
ien
t [P
a/m
]
Oil A - water
0.64m/s
1.28m/s
1.92m/s
(a) Oil A - water
0 20 40 60 80 1000
500
1000
1500
2000
2500
3000
water cut [%]
Pre
ssu
re g
rad
ien
t [P
a/m
]
Oil B − LS water
Oil B − HS water
0.64m/s
1.28m/s
1.92m/s
2.57m/s
3.21m/s
(b) Oil B - HS-water and oil B - LS-water
0 20 40 60 80 1000
100
200
300
400
500
600
700
800
900
1000
water cut [%]
Pre
ssu
re g
rad
ien
t [P
a/m
]
Exxsol D60 − water
0.67m/s
1.34m/s
2.00m/s
2.50m/s
(c) Exxsol D60 - water
Figure 10: Pressure gradient required for the flow of oil - water systems as function of the water cut. Differentvalues of the mixture velocity.
15
4.6 Flow regimes
4.6.1 Phase inversion
In order to set up the flow regime map, the water cut must be known for which the flow changes from oil
continuous to water continuous. The pressure gradient as function of the water cut (see section 4.5) reveals at
which inlet water cut the flow switches from oil continuous to water continuous.
For the flow with oil A at a mixture velocity of 1.92m/s, the first water continuous dispersion appears at an
inlet water cut of 60%. From figure 6 it can then be seen that the water cut at which phase inversion occurs is
about 50%, which is just below the minimum local water concentration at these conditions.
A similar approach is used to determine the water cut at which phase inversion occurs for the flows with oil
B - low salinity water and oil B - high salinity water. In both systems, for a mixture velocity of 3.21m/s, the first
water continuous dispersion with appears at an inlet water cut of 60%. From figure 7 it can now be seen that
also for these flows, the inversion water cut is around 50%, just below the minimum local water concentration
at these conditions.
The value of the water cut for phase inversion for Exxsol is assumed to be 50%, which is the same value as
used by Amundsen (2011).
4.6.2 Flow regime maps
The flow regimes observed for the four different oil-water systems, based on a inversion water cut of 50%, are
shown in figure 11. In these flow regime maps, the orange color indicates the region of operating conditions
in which oil continuous dispersed flows occur (x), the green color indicates the region in which stratified flows
occur (o) and the blue color indicates the region in which the flow is water continuous (+). Within the regime
with stratified flow and the regime with dispersed flow, the flows can be subdivided into different types. In this
study we only focus on the transition between dispersed flow and stratified flow, in which the dispersed flow has
only one continuous phase and the stratified flow has two layers with different continuous phases. Three effects
are observed:
First, from a comparison between figures 11c and 11d it becomes clear that the water salinity has influence
on the flow regime that will appear. Since the density difference is larger in the case of high salinity water, the
region with stratified flow is somewhat larger.
Secondly, the region with stratified flow for the oil A - water system is smaller than that for the oil B - low
salinity water system. This can be explained by the viscosity of oil A being almost twice as high as the viscosity
of oil B. A higher viscosity will cause more turbulent dispersion, and therefore phase separation takes place at
16
higher water cuts. In addition, the density ratio of oil A - water ( ρwρo
= 1.18) is slightly larger than the density
ratio of oil B and low salinity water( ρwρo
= 1.23). This will cause more phase separation in the oil B-LS water
system.
Finally, large differences are observed between the flow regime map of the Exxsol D60 - water system and
that of the crude oil - water systems. The lower oil viscosity of Exxsol D60 compared to that of the crude oils,
yields less turbulent dispersion. Besides that, the interfacial surface tension of Exxsol D60 and water is much
higher than that of the crude oil - water systems (Exxsol D60: σ = 43 mN/m, crude oils: σ = 16 mN/m). The
drop sizes will be larger in the Exxsol - water systems due to the higher interfacial surface tension. Gravitational
forces have more effect on larger droplets and therefore separation will be more important for the Exxsol - water
systems.
0
0.5
1
1.5
2
2.5
3
3.5
0% 20% 40% 60% 80% 100%
Mix
ture
ve
loci
ty [
m/s
]
Water cut [-]
Oil continuousdispersions
Water continuousdispersions
Stratified flows
(a) Oil A - water
0
0.5
1
1.5
2
2.5
3
3.5
0% 20% 40% 60% 80% 100%
Mix
ture
ve
loci
ty[m
/s]
Water cut [-]
Oil continuousdispersions
Stratified flows
Water continuousdispersions
(b) Exxsol D60 - water
0
0.5
1
1.5
2
2.5
3
3.5
0% 20% 40% 60% 80% 100%
Mix
ture
ve
loci
ty [
m/s
]
Water cut [-]
Oil continuousdispersions
Water continuousdispersions
Stratified flows
(c) Oil B - LS-water
0
0.5
1
1.5
2
2.5
3
3.5
0% 20% 40% 60% 80% 100%
Mix
ture
ve
loci
ty [
m/s
]
Water cut [-]
Oil continuousdispersions
Water continuousdispersions
Stratified flows
(d) Oil B - HS-water
Figure 11: Flow regime maps for the four oil-water systems considered, determined from the results of X-raytomography
17
5 Model
The experimental data are compared with results of a model that is able to predict the concentration of the
dispersed phase in each liquid layer. This model, in which a two-fluid model is combined with a dispersion
model, has been presented by Amundsen et al. (2009) and Amundsen (2011). In the numerical simulations
of this study, which are based on this model, all parameters are computed in the same way as described by
Amundsen (2011), unless stated otherwise.
5.1 Dispersion model
The essential building blocks of the dispersion model are the computation of the turbulent forces and the buoy-
ancy forces acting on droplets in a dispersed flow. The concentration profile of the dispersed phase is modeled as
a balance between these forces. The concentration profile in the dispersed layer of a fully developed steady-state
flow is described by:
Vtφ +Γdφ
dz= 0 (1)
In this equation, Vt is the terminal velocity, Γ is the turbulent diffusion coefficient and φ(z) is the local con-
centration of the dispersed phase at a distance z from the interface. The first term in equation 1 represents the
buoyancy effects acting on the particles (droplets) and the second term represents the dispersion effects acting
on the particles (droplets) .
In order to solve equation 1, expressions for the terminal velocity Vt and the turbulent diffusion coefficient
Γ are required, as well as one closure relation from mass conservation.
5.1.1 Terminal velocity
In order to determine the terminal velocity, an approximation for the size of the droplets of the dispersed phase
is needed. In the present simulations, the drop size model as proposed by Brauner (2001) is used, which predicts
the maximum drop size. For the computation of the maximum drop size in dense dispersions, in which local
coalescence is prominent, the Brauner model uses the well-known Hinze model (Hinze, 1955) combined with a
model based on the local energy balance The expression for the maximum drop size according to Hinze (1955)
is given as:
(dmax)0 = 0.725(
σ
ρc
)0.6( D2 f u3
ρc (1−φ)
ρm
)0.4
(2)
18
Where σ is the interfacial tension, ρc the density of the continuous phase, ρm the mixture density, u the mixture
velocity, f the Darcy friction factor, φ the local concentration of the dispersed phase and D the hydraulic
diameter. The expression for the maximum drop size as a result of energy conservation follows from:
(dmax)ε = 3.06(dmax)0 CH
(φ
1−φ
)0.6
(3)
CH is a constant which needs to be specified by the user. In the numerical simulation, the maximum drop size
is assumed to be the maximum of both values:
dmax = (dmax)0Max
[1, 3.06CH
(φ
1−φ
)0.6]
(4)
An advantage of the model by Brauner (2001) compared to the Hinze model used by Amundsen (2011) is that
the Brauner model is able to predict the maximum drop size in both dilute and non-dilute systems, while the
Hinze model needs to be corrected in case of non-dilute systems.
As expressed by Amundsen (2011), the well-known terminal velocity V∞ in an infinite homogeneous medium
is determined based on the assumptions that the drop size distribution is given by a Rosin-Rambler distribution
(dmean = 0.557dmax) and the drag coefficient is given by the relation of Jayanti and Hewitt (1991) (CD = 18.5Re0.6p
).
V∞ =−sign(∆ρ)
√4dmean|∆ρ|g
3ρ fCD(5)
With ∆ρ = ρp − ρ f , g the gravitational acceleration and ρp and ρ f denoting the particle and fluid density
respectively. The modified terminal velocity Vt in a dispersed medium is subsequently determined:
Vt =V∞(1−φ)n (6)
V∞is the terminal velocity of a single particle falling in a stagnant liquid. In equation 6, the exponent n needs to
be specified by the user within the range of 2.39 - 4.65, see Richardson and Zaki (1954), under the assumption
that the droplet diameter is small compared to the pipe diameter.
5.1.2 Turbulent diffusion coefficient
As in the model of Amundsen (2011), the turbulent diffusion coefficient Γ is expressed according to Mols
and Oliemans (1998). With the assumption that particle inertia and crossing trajectories do not influence the
19
turbulent diffusion, the turbulent diffusion coefficient can be expressed as a function of the hydraulic diameter
D and the friction velocity u∗.
Γ = 0.049u∗D (7)
With the friction velocity following from τw and ρm denoting the wall shear stress and the mixture velocity
respectively:
u∗ =√
τw/ρm (8)
5.1.3 Closure relations
In case of fully dispersed flow, with only one continuous phase and assuming no slip between the droplets and
the continuous phase, the closure relation is given by the area averaged volume fraction of the dispersed phase
being equal to the input volume fraction.
In case of stratified flow, it is assumed that the concentration of the dispersed phase at the interface is known.
The concentration at the interface has to be specified by the user. Given that the concentration at the height of
the interface is known, the holdup profiles in the water layer (0 < z < h) and the oil layer (h < z < D) can be
determined from the closure relation that the concentration at z = h equals the inversion concentration.
5.2 Two fluid model
In the two layers, the concentration profiles of the dispersed phase can be computed when the height of the
interface is known. This height is computed in an iterative procedure of the two fluid model. This procedure is
similar to that described by Amundsen (2011).
When an interface height is assumed, the concentration of the dispersed phase can be computed and the
mixture properties can be determined. Once the mixture properties are known in the two layers, the expression
for conservation of momentum can be expressed as a function of the interface height hi:
F(hi) =−τoc(hi)Soc(hi)
Aoc(hi)+
τwc(hi)Swc(hi)
Awc(hi)+ τi(hi)Si(hi)
(1
Awc(hi)+
1Aoc(hi)
)(9)
In equation 9, A denotes the cross-sectional area of the flow, S the perimeter and τ the shear stress. Momentum
is conserved when F(hi) = 0. When the interface height is found to be at a position for which the thickness
of one of the layers is smaller than three times the drop size, the flow is assumed to be fully dispersed and the
concentration profile can then be calculated from the dispersion model.
In order to be able to calculate the shear stresses, the mixture viscosity must be known. In the model, the
20
mixture viscosity is determined as proposed by Pal and Rhodes (1989), who described the mixture viscosity as
a function of the viscosity of the continuous phase and the dispersed phase concentration.
µm = µc
1+φ
φ0
µ0.40
µ0.40 −1
− φ
φ0
2.5
(10)
in which µc denotes the viscosity of the continuous phase, µ0 is a dimensionless reference viscosity and φ0 =
φµ=µ0 . We use µ0 = 100 and φ0 = 0.765 for an oil continuous flow and µ0 = 10 and φ0 = 0.642 for a water
continuous flow.
6 Results numerical simulations
For the numerical simulations, the fluid properties are set to have the values as shown in table 2 and the inversion
water cut is set to be 50% (see section 4.6.1). Two simulation parameters have to be chosen. For the hindered
settling factor n (eq. 6) a value of 3.0 is used in the simulations and the constant CH (eq. 3) is set to be 1.
6.1 Concentration distributions
In figures 12, 13, 14 and 15, the results from the numerical simulations are compared with the experimental data
presented earlier in section 4. The present method is seen able to predict the concentration distribution with a
reasonable accuracy in most cases.
The differences between the predicted results and the measured results are very small at the lowest mixture
velocities, for which the phases are completely separated. The method is also successful in predicting the
concentration profile for the high velocities at which the flows are fully dispersed, but the method predicts
slightly more separation in this case.
The largest differences occur in the profiles that are marked with a gray background. These are all in the
transition region from stratified to fully dispersed flows. At these conditions, neither the separation forces, nor
the dispersive forces are dominant, but the concentration distribution is a result of a sensitive equilibrium be-
tween those two forces. The method is probably too general to compute the correct drop sizes for all conditions.
21
1.9
2 m
/s
Oil A - water
Simulation
1.2
8 m
/s0.6
4 m
/s
Top Bot0
1W
ate
r fr
actio
n
Water cut 20%
Top Bot0
1Water cut 30%
Top Bot0
1Water cut 40%
Top Bot0
1Water cut 50%
Top Bot0
1Water cut 60%
Top Bot0
1Water cut 70%
Top Bot0
1Water cut 80%
Top Bot0
1
Wa
ter
fra
ctio
n
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Wa
ter
fra
ctio
n
Height Top Bot0
1
Height Top Bot0
1
Height Top Bot0
1
Height Top Bot0
1
Height Top Bot0
1
Height Top Bot0
1
Height
Figure 12: Comparison between predicted and measured concentration distributions: oil A - water
Simulation
Oil B -LS-Water
wa
ter
fra
ctio
n
3.2
1 m
/s
Water cut 10%
Top Bot0
1Water cut 20%
Top Bot0
1Water cut 30%
Top Bot0
1Water cut 40%
Top Bot0
1Water cut 50%
Top Bot0
1Water cut 60%
Top Bot0
1Water cut 70%
Top Bot0
1Water cut 80% Water cut 90%
Top Bot0
1
wa
ter
fra
ctio
n
2.5
7 m
/s
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
wa
ter
fra
ctio
n
1.9
2 m
/s
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
wa
ter
fra
ctio
n
1.2
8 m
/s
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Height
wa
ter
fra
ctio
n
0.6
4 m
/s
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Figure 13: Comparison between predicted and measured concentration distributions: oil B - LS-water
22
Simulation
Oil B -HS-Water
Top
wate
r fr
action
Water cut 10%
Top Bot0
1Water cut 20%
Top Bot0
1Water cut 30%
Top Bot0
1Water cut 40%
Top Bot0
1Water cut 50%
Top Bot0
1Water cut 60%
Top Bot0
1Water cut 70%
Top Bot0
1Water cut 80% Water cut 90%
Top Bot0
1
wate
r fr
action
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
wate
r fr
action
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
wate
r fr
action
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Height
wate
r fr
action
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
Top Bot0
1
Height
3.2
1 m
/s2.5
7 m
/s1.9
2 m
/s1.2
8 m
/s0.6
4 m
/s
Figure 14: Comparison between predicted and measured concentration distributions: oil B - HS-water
Wa
ter
fra
ctio
n
2.5
0 m
/s
Wa
ter
fra
ctio
n
2.0
0 m
/s
1.3
4 m
/s0.6
7 m
/s
Wa
ter
fra
ctio
nW
ate
r fr
actio
n
Exxsol D60 - water
Simulation
Top Bot0
1Water cut 20%
Top Bot0
1Water cut 30%
Top Bot0
1Water cut 40%
Top Bot0
1Water cut 50%
Top Bot0
1Water cut 60%
Top Bot0
1Water cut 70%
Top Bot0
1Water cut 80%
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
Top Bot0
1
HeightTop Bot0
1
HeightTop Bot0
1
Height
Figure 15: Comparison between predicted and measured concentration distributions: Exxsol D60 - water
6.2 Pressure gradients
The pressure gradients that have been measured during the experiments are shown together with the predictions
in figure 16. The red lines show the predictions of the simulation method. Discontinuities are seen at the
transitions between fully dispersed flows and stratified flows. Different models and closure relations used for
23
fully dispersed flows and stratified flows lead to the observed discontinuities.
The simulation method is successful in predicting the pressure gradients of the crude oil experiments, but
the pressure drop is slightly over-predicted. The method predicts a stronger increase in the pressure drop for an
increasing concentration of water in the oil continuous flows than is observed in the experiments. The viscosity
model over-predicts the apparent viscosity, resulting in this over-prediction of the pressure drop.
In figure 16a, the prediction of the pressure gradient in the stratified region for the highest mixture velocity
shows some unexpected behavior. This can be a result of closure relations in the dispersion model which are
too general to produce good predictions in all cases.
Large differences are observed between the prediction of pressure gradient and the experimental data for
the case of Exxsol D60 - water flows, as can be seen in figure 16b. The present method does not capture the
drag reduction effects that are discussed in section 4.5. Furthermore, the method does not predict a peak in the
pressure gradient for high water cuts and low mixture velocities.
Simulation program:
Oil A − water: 0.64m/s 1.28m/s 1.92m/s
0 20 40 60 80 1000
500
1000
1500
water cut [%]
Pre
ssure
gra
die
nt [P
a/m
]
(a) Oil A
Simulation program:
Exxsol D60 - water: 0.67m/s 1.34m/s 2.00m/s 2.50m/s
0 20 40 60 80 1000
200
400
600
800
1000
1200
water cut [%]
Pre
ssure
gra
die
nt [P
a/m
]
(b) Exxsol D60
Simulation program:
Oil B − LS water: 0.64m/s 1.28m/s 1.92m/s 2.57m/s 3.21m/s
0 20 40 60 80 1000
500
1000
1500
2000
2500
3000
water cut [%]
Pre
ssure
gra
die
nt [P
a/m
]
(c) Oil B-LS
Simulation program:
Oil B − HS water: 0.64m/s 1.28m/s 1.92m/s 2.57m/s 3.21m/s
0 20 40 60 80 1000
500
1000
1500
2000
2500
3000
water cut [%]
Pre
ssure
gra
die
nt [P
a/m
]
(d) Oil B-HS
Figure 16: Comparison of predicted and measured pressure gradients
24
7 Conclusions
Results of crude oil-water flow experiments have been presented in which the concentration distribution was
captured by an X-ray tomograph. The X-ray tomograph has proved to be a valuable tool in analyzing the details
of oil-water flows. The information from these detailed measurements has been used to validate the oil-water
model from earlier publications. In addition, data from these crude oil - water experiments have been compared
with data from model oil - water experiments. The crude oil - water flows were found to show a behavior
different from that of the model oil-water flows. This suggests that when the behavior of crude oils is to be
investigated, real crude oils should be used.
As expected, a higher density ratio in the oil - high salinity water system, compared to that of the oil - low
salinity water systems, affects the flow behavior. The concentration distributions of the oil - high salinity water
system showed more separation than that of the oil - low salinity water systems . Although the different density
ratio resulted in different concentration distributions, only small differences were observed in the flow regimes
that occurred. A different oil viscosity has larger effects on the flow regime map. A higher oil viscosity causes
more turbulent dispersion and therefore less stratification and more dispersed flows.
A comparison between results of a two-fluid dispersion model and the experimental data showed that the
model is able to predict both the concentration distribution and the pressure gradient of crude oil-water flows.
The largest uncertainties in the prediction of the concentration distributions were found in the transition region
between stratified flow and fully dispersed flow. Further work should be focused on computation of the size of
the drops in this part of the flow regime map.
In general, the used prediction method is able to predict the pressure drop of crude oil - water systems,
but again more work is needed to improve the performance in the transition region between fully dispersed and
stratified flows. The method however failed to predict the pressure drop of model oil-water flow. Drag reduction
effects that were presumably present in the model oil-water flows were not captured by this method.
Acknowledgments
The authors would like to thank Dr. Hu of Institute for Energy Technology Norway, Prof. Dr. Ir. H.W.M.
Hoeijmakers of the University of Twente, The Netherlands, and Dr. Valle and Dr. Yang of Statoil ASA, Norway,
for sharing their knowledge and their valuable suggestions and discussions.
25
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