2017.03 ex hft-2017_perissinotto_et_al_final_paper_02

9th World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics
12-15 June, 2017, Iguazu Falls, Brazil
OIL DROPLETS WITHIN AN ESP IMPELLER:
EXPERIMENTAL ANALYSIS OF VELOCITIES AND ACCELERATIONS
Rodolfo M. Perissinotto*,1
, William Monte Verde**,1
, Jorge L. Biazussi2
, Marcelo S. Castro1
, Antônio C. Bannwart1
1
School of Mechanical Engineering - University of Campinas, UNICAMP, Campinas, 13083-860, Brazil
2
Center for Petroleum Studies - University of Campinas, UNICAMP, Campinas, 13083-970, Brazil
*rodolfoperissinotto@gmail.com
**williammonteverde@gmail.com
Abstract. This research aims to investigate the motion of oil drops within an Electrical Submersible Pump (ESP) impeller
working with an oil-water flow. The main objective is to evaluate velocity and acceleration of individual drops subjected
to different ESP rotational speeds. An experimental study was conducted using an ESP prototype designed to allow flow
visualization within the impeller through a transparent shell. A high-speed camera captured images of the oil droplets at
a rate of 1000 fps. The set of data was performed at five rotational speeds for water flow rates at the best efficiency point
(BEP). The images reveal that the oil drops become smaller when the rotational speed increases. The droplets have random
trajectories, but some patterns were identified and explored in this paper. Results reveal that the average velocity depends
on the drop trajectory and the ESP rotational speed. The drop velocity varies between 0.3 m/s and 3.0 m/s, approximately.
The acceleration fluctuates between positive and negative values. The average acceleration assumes high values in the
order of dozens of meters per second squared. The resultant force acting on oil droplets is proportional to the acceleration
and assumes small values around thousandths of Newton.
Keywords: Electrical Submersible Pump, Flow Visualization, Two-Phase Flow, Oil Droplets, Droplet Trajectory
1. INTRODUCTION
The Electrical Submersible Pump (ESP) is the second most popular artificial lift method used in oil production,
especially for offshore operations. Nowadays, it is estimated that more than 100,000 wells use ESPs to produce oil. The
ESP is essentially a multistage centrifugal pump that provides energy to the fluids present in the reservoir, lifting them
through the well to the production facilities. The ESP usually works with multiphase flows, with oil, water and gas. The
operation with presence of gas or high viscosity fluids affects the pump behavior and may cause significant performance
losses. An example of high viscosity fluid is the formation of emulsions in applications with oil and high water fractions.
The visualization of flows inside ESPs is an interesting way of studying the interaction between the mixing phases present
in an emulsion.
In this work, an experimental study is conducted focusing on flow visualization to investigate the motion of oil drops
in a water flow within an ESP impeller. Some parameters as size, velocity and acceleration are evaluated as functions of
the ESP rotational speed. The determination of velocities and accelerations can improve the understanding of the forces
acting on the oil droplets, responsible for their movement in the impeller channels. Also, as the water velocity is known,
the slip between the liquid phases can be estimated, considering the drift-flux model. The industrial application of this
work is to find a one-dimensional model that represents efficiency and performance of ESPs for use in the petroleum
industry, for example, to predict the best type of pump for each application.
This paper contains eight sections. Initially, previous works are discussed in a literature review. Next, the experimental
apparatus and the test procedure are presented. Finally, results are discussed and conclusions are proposed. Nomenclature,
acknowledgements and references are at the end.
2. LITERATURE REVIEW
There are many studies on gas-liquid flow in the literature. In the last years, some authors investigated the performance
of ESPs working with two-phase flows, such as Lea and Bearden (1982) and Biazussi (2014), while other authors studied
the flow patterns that occur inside ESPs, as Gamboa and Prado (2010) and Monte Verde (2016). A few authors also
analyzed the motion of air bubbles and the forces that govern their behavior within ESP impellers, as described in the
next paragraphs, which present a succinct review of works that focus on individual air bubble dynamics.
Minemura and Murakami (1980) investigated the motion of small air bubbles in a rotating impeller. According to
them, five forces govern the motion of air bubbles in an impeller: the drag force due to motion of the bubble relative to
the water; the force due to the pressure gradient in the water surrounding the bubble; the body force due to the difference
in densities between water and air; the force needed to accelerate the water displaced by bubble motion; and the force due
to a history term showing the effect of previous acceleration, called Basset’s term.

Estevam (2002) developed the first visualization prototype for the petroleum industry. The author designed and built
a scaled pump with a transparent shell to investigate the movement of bubbles within an impeller. He observed the
formation of stationary bubbles depending on the amount of air injected.
Barrios (2007) studied flow patterns and bubble behavior inside an ESP impeller. Images captured with a high-speed
camera revealed trajectories of air bubbles in water flow. According to the author, the most important forces acting on a
bubble consist on the drag force and the pressure force, acting on opposite directions.
Sabino (2015) visualized the movement of bubbles in a water flow inside a pump impeller. The author identified three
typical trajectories: bubbles next to the suction blade, bubbles that enter the channel near the suction blade but deviate to
the center and bubbles that enter the channel near the suction blade but deviate to the pressure blade. The author calculated
the velocity of bubbles as a function of their position inside the channel, for different rotational speeds. The velocities
exhibited a random behavior. Even so, a dependence between velocity and rotational speed was noticed. Higher rotational
speeds resulted in faster bubbles. The type of trajectory also influenced the bubble velocity. Bubbles next to the suction
blade moved faster than bubbles far from it.
Zhang et al. (2016) investigated flow patterns and individual bubbles inside a three-stage pump. The authors studied
parameters as size, trajectory and motion of air bubbles. According to them, the main forces on an isolated bubble within
the impeller channel are the drag force, the centrifugal force and the force due to the pressure gradient.
In short, it seems consensual to consider the drag force and the pressure force as the most significant forces acting on
air bubbles. The forces influence the bubble acceleration, which changes the instantaneous velocity and defines the bubble
trajectory inside the impeller channel. The bubble velocity seems proportional to the ESP rotational speed and dependent
on the distance between the bubble and the channel blades.
According to Mohammadi and Sharp (2013), the flow visualization using a high-speed photography technique enables
the observation of fast transient phenomena with high spatial and temporal resolutions. The use of high-speed cameras
offers the possibility to identify flow patterns, track particles immersed in the fluids and evaluate variables like bubble
size and velocity.
High-speed imaging seems to be a powerful tool for analyzing oil drops as well. Although there are many works on
gas-liquid flows, there are few studies in the literature on liquid-liquid flows, such as Hosogai and Tanaka (1992), Boxall
et al. (2011) and Maaß and Kraume (2012). This paper contributes to the area, with an analysis of the oil-water flow.
3. EXPERIMENTAL DESCRIPTION
This section describes the experimental device, the measuring instruments and the camera used for visualization of
oil droplets. The procedure adopted to perform the experiments is discussed as well.
3.1. Experimental Apparatus
The experimental facility uses an ESP prototype designed to allow flow visualization within the impeller through a
transparent shell, as can be seen in Fig. 1. It was developed and built by Monte Verde et al. (2017) and adapted to perform
tests with two-phase liquid-liquid mixtures. To achieve this, an oil injection system was designed and built.
Figure 1. Experimental facility with a focus on the transparent shell (bottom right corner)

The experimental loop consists of a water flow line with a tank, a booster pump and a water flow meter. The oil inject
system is composed of peristaltic pump, oil reservoir and stainless steel capillary tubes. A schematic illustration is shown
in Fig. 2. The oil line is the main difference between the new and the original facility built by Monte Verde et al. (2017).
Figure 2. Layout of the experimental apparatus
The flow visualization is performed using a camera IDT MotionProX® with a resolution of 1024 x 1024 pixels at
1000 frames per second and a lens Nikon Micro-Nikkor® f/2.8 with a focal length of 60mm. Five measuring instruments
collect information during the experiments: a flow meter, a thermocouple, a tachometer and two pressure transducers. At
the inlet, the pressure transducer is installed in the water suction tube. At the outlet, the pressure is measured in the diffuser
by a ring that connects different points radially. The technical features of the equipment are described in Table 1.
Table 1. Features of the measuring instruments
Instrument Measurement Brand/Model Range Uncertainty
Flow meter Water mass flow rate (mL) Metroval RHM12 120 - 6000 kg/h ± 0.2%
Thermocouple Water temperature (T) PT 100 RTD 0 - 100 ºC ± 0.5%
Pressure transducers Pressures at ESP
inlet and outlet (P1, P2) Rosemount 2088 0 - 2000 kPa ± 0.075%
Tachometer ESP rotational speed (N) Minipa MDT 2238A 2.4 - 99999 rpm -
3.2. Experimental Procedure
Tests are conducted using an oil with density of 880 kg/m³ and viscosity of 220 cP at 25 °C. The oil is darkened with
a black dye to facilitate its observation. The dye does not affect the oil properties, as viscosity and surface tension. The
colored oil is injected near the impeller inlet at a constant flow rate of 2 ml/s. This flow rate was measured previously and
agrees with the peristaltic pump manufacturer's data.
Images were captured at five rotational speeds – 300 rpm, 600 rpm, 900 rpm, 1200 rpm and 1500 rpm – for water
flow rates at the best efficiency point – 1.06 m³/h, 2.13 m³/h, 3.20 m³/h, 4.26 m³/h and 5.33 m³/h. The experiments were
conducted at University of Campinas, in Brazil. The ESP rotational speed is measured using a tachometer. The water flow
rate depends on the rotational speed of the booster pump, which is set through a frequency inverter. A flow control valve
installed in the ESP prototype defines the intake pressure, kept constant at 50 kPa.
The rotational speeds normally used in typical ESP applications are quite larger than the rotational speeds investigated
in this study. The selection of lower rotations was required due to limitations in the visualization equipment. At higher
rotational speeds, the oil droplets become so small and fast that the high-speed camera resolution is insufficient to obtain
satisfactory images. Thus, the analysis of drops becomes impracticable.
To carry out the experiments, the following procedure was adopted:
1. Turn on camera and lights. Connect the camera to the computer. Adjust the position of the reflector luminaires.
2. Turn on the measuring instruments. Connect them to the computer. Check if they are working properly.
3. Turn on the pumps. Set the desired rotational speed and water flow rate.
4. Acquire pressure, temperature and flow rate data using a software designed in LabVIEW® platform.
5. Capture images of oil drops at a rate of 1000 fps. Save the images in the computer.

4. RESULTS AND DISCUSSION
This section presents the results. Firstly, some flow images characterize sizes and trajectories of oil droplets. Then,
the tracking of oil droplets gives an analysis of their velocities and accelerations inside the impeller channels, in different
experimental conditions.
4.1. Size and Trajectory
The images reveal a population of oil droplets within the impeller channels. The oil drops become smaller when the
rotational speed increases, as shown in Fig. 3. A higher rotational speed implies higher velocities, more turbulence and
intense forces, conditions that facilitate the breaking up of oil droplets. Apparently, most drops break up before entering
the impeller. Probably this phenomenon is due to the geometry of the impeller inlet, where the fluids change suddenly
their direction. Only a few droplets break up inside the channels.
Figure 3. Images of oil droplets within the impeller at different rotational speeds
Examples of trajectories can be seen in Fig. 4. The majority of oil droplets present random trajectories (Fig. 4a), but
several droplets have identifiable patterns. Some drops move near the suction blade or near the pressure blade of a channel
(Fig. 4b). A few droplets move parallel to the blades, but far from them. Other drops start the movement next to a pressure
blade, deviate to center and return to the pressure blade (Fig. 4c). However, the most frequent pattern occurred to central
droplets that start the movement near a suction blade and end the trajectory near a pressure blade (Fig. 4d).
The droplet path depends on the water velocity profile inside the impeller channels. The droplets are subject to water
flow phenomena, such as vortices, jets and recirculation, typical to turbulent flows within rotating impellers.
Figure 4. Examples of oil droplet paths: identifiable patterns and random trajectories
Generally, the droplets have spherical and elliptical shapes, as presented in Fig. 5. Their sizes can be easily determined.
The drop diameter can be estimated by counting pixels in the images.
Figure 5. Oil droplets with spherical and elliptical shapes at 300 rpm
a b c d

4.2. Velocity and Acceleration
The images were processed to calculate the velocity and the acceleration of 41 oil droplets with different trajectories,
at various rotational speeds, using a lagrangian approach. A LabVIEW® routine was developed to remove rotation from
impeller. The rotation removal allows the analysis of only the relative terms of droplet velocity and acceleration, without
components due to rotation. The idea of removing the impeller rotation is equivalent to using a non-inertial coordinate
system that rotates integrally with the impeller.
The software IDT Motion Studio® was used to determine the position of droplets by identifying differences between
consecutive images. The position of the droplets as a function of time, t, was firstly determined in a Cartesian coordinate
system with origin at the center of the impeller. Then the position x and y of each drop was converted to a new position r
and θ, in a polar coordinate system. The values of r and θ were used to calculate the radial velocity, Vr, and the transverse
velocity, Vθ, as a function of the impeller radius, r, which varies between 25 mm (channel input) and 56 mm (output).
The resultant velocity, V, was finally calculated. The procedure was repeated to determine the accelerations Ar, Aθ, A.
The relationship between Cartesian and polar coordinate systems is given by Eq. (1).
𝑟 = √𝑥2 + 𝑦2 ; 𝜃 = 𝑡𝑎𝑛−1
(𝑦/𝑥) (1)
Velocities are found using Eqs. (2), (3), (4) and accelerations are determined with Eqs. (5), (6), (7). The accelerations
are defined from the velocities, using time derivatives and the chain rule. A finite-difference method is used to calculate
the derivatives numerically.
𝑉
𝑟 =
𝑑𝑟
𝑑𝑡
(2)
𝑉𝜃 = 𝑟
𝑑𝜃
𝑑𝑡
(3)
𝑉 = √𝑉
𝑟
2 + 𝑉𝜃
2
(4)
𝐴𝑟 =
𝑑2𝑟
𝑑𝑡2 − 𝑟 (
𝑑𝜃
𝑑𝑡
)
2
(5)
𝐴𝜃 = 𝑟
𝑑2𝜃
𝑑𝑡2 + 2
𝑑𝑟
𝑑𝑡
𝑑𝜃
𝑑𝑡
(6)
𝐴 = √𝐴𝑟
2 + 𝐴𝜃
2
(7)
For the analysis, droplets were chosen with two types of trajectory: drops that remain close to one of the blades and
central drops that move from the suction blade to the pressure blade. These trajectories guarantee positive values of Vr
and Vθ, since the droplets always go from channel inlet to channel outlet, in the positive direction of r, and from right to
left, in the positive direction of θ.
4.2.1. Random Single Droplet
A random drop in the rotational speed of 900 rpm was tracked. The results are shown in Fig. 6, which presents curves
of velocities and accelerations versus time. The droplet takes 0.050 seconds to pass through the impeller channel. For the
analyzed drop, velocities are positive about units of meters per second, while the accelerations oscillate between positive
and negative values in the order of dozens of meters per second squared.
Figure 6. Velocities and accelerations of a random single oil droplet at 900 rpm
Velocities and accelerations are calculated every millisecond, through the comparison between the droplet position in
two consecutive images. Thus, a minimal change in velocity causes a high acceleration, since the time interval is very
small. This fact may explain the fluctuations that occur to the instant acceleration curves. Therefore, the analysis of an
average acceleration seems more appropriate to study the oil droplet behavior.

4.2.2. Influence of Droplet Trajectory
Still at 900 rpm, other twelve drops were tracked. The selected drops have trajectories close to the blades and diameters
between 1.11 and 2.56 mm. The results are presented in Figs. 7 and 8.
(a) (b)
(c) (d)
Figure 7. Velocities at 900 rpm: (a) radial velocity of drops near a suction blade; (b) radial velocity of drops near a pressure
blade; (c) transverse velocity of drops near a suction blade; (d) transverse velocity of drops near a pressure blade
(a) (b)
(c) (d)
Figure 8. Accelerations at 900 rpm: (a) radial acceleration of drops near a suction blade; (b) radial acceleration of drops near a
pressure blade; (c) transverse acceleration of drops near suction blade; (d) transverse acceleration of drops near pressure blade

The figures compare velocities and accelerations of droplets next to the suction blade with velocities and accelerations
of droplets next to the pressure blade.
In Fig. 7, the colored curves denote the individual droplet velocities. The black curve is the average velocity, presented
with a polynomial. The graphs show significant differences. The velocities of the drops close to the suction blade suffer
a reduction with the radius, while the velocities of the drops close to the pressure blade suffer an abrupt reduction followed
by a large increase. In addition, the drops on the suction blade have higher velocities than the drops on the pressure blade,
in practically the entire trajectory.
Similarly, in Fig. 8 the colored curves are individual drop accelerations. The black curve is the average acceleration,
shown with a polynomial. In general, the average acceleration is consistent with the average velocity, for all cases. In
other words, when the average velocity increases, the average acceleration is positive, and when the average velocity
decreases, the average acceleration is negative. The polynomials show positive or negative values depending on the drop
position in the channel. It indicates that the resulting force acting on each drop changes its direction as the drop moves.
Accelerations and decelerations are consequences of the balance between drag and pressure forces, as explained in
the literature review. The drag force carries the drops out of the impeller, while the pressure force acts contrarily to their
movement. When the acceleration is positive, drag force governs the droplet motion. When the acceleration is negative,
pressure force rules the drop behavior.
4.2.3. Influence of Rotational Speed
Fourteen droplets were studied in the 600-rpm case, with an average diameter of 2.02 mm. They take 0.061 to 0.082
second to enter and exit the channel. Fourteen drops were also analyzed in the 1200-rpm case, with an average diameter
of 1.64 mm. Their movement take between 0.031 and 0.037 second. Velocities and accelerations are shown in Fig. 9,
where the colorful curves represent the drops. Polynomials are presented in black curves. They were adjusted considering
the average values of velocities and accelerations as functions of the radius.
(a) (b)
(c) (d)
Figure 9. Velocities and accelerations of central oil droplets: (a) resultant velocity at 600 rpm; (b) resultant
acceleration at 600 rpm; (c) resultant velocity at 1200 rpm; (d) resultant acceleration at 1200 rpm

It is observed that the resultant velocity undergoes a pronounced reduction as the droplet moves through the channel,
followed by an increase near the channel outlet. The polynomial reveals that the average velocity varies between 0.7 m/s
and 1.4 m/s for 600 rpm, approximately, and between 1.4 m/s and 3.0 m/s, for 1200 rpm. The acceleration presents a
similar behavior. The intensity of the average acceleration varies from 40 m/s² to 90 m/s² for 600 rpm, approximately,
and from 100 m/s² to 340 m/s² for 1200 rpm. Therefore, the results indicate that the oil drop velocity and acceleration are
proportional to the ESP rotational speed.
4.3. Evaluation of Forces
The drag and the pressure forces mainly govern the movement of oil droplets. The drag force occurs due to the slip
between the phases. The pressure force occurs due to the pressure gradient in the channel. Therefore, accelerations and
decelerations are the result of the balance between both forces.
Considering spherical droplets, the drag force Fd, given by Eq. (8), is a function of the water density ρw, the drop
diameter d, the drag coefficient Cd, the drop velocity V and the water velocity W. The pressure force Fp, defined in Eq.
(9), depends on the pressure gradient ∇p along a streamline. The velocity V was studied in the last sections.
𝐹𝑑 = (
1
2
𝜌𝑤) (
𝜋𝑑2
4
) 𝐶𝑑(𝑉 − 𝑊)|𝑉 − 𝑊| (8)
𝐹𝑝 = − (
𝜋𝑑3
6
) 𝛻𝑝 (9)
According to Newton’s second law, presented in Eq. (10), the resultant force FR is a function of the oil density ρo and
causes an absolute acceleration Aabs. The absolute acceleration Aabs measured in a fixed coordinate system includes the
relative acceleration A measured by an observer attached to the ESP impeller, the angular acceleration effect caused by
rotation, ω × (ω × r), and the combined effect of translation and rotation, 2ω × V, as given by Eq. (11), where ω is the
angular velocity, r is the impeller radius and V is the drop velocity. The acceleration A was studied in the last sections.
𝐹𝑅 = 𝜌𝑜 (
𝜋𝑑3
6
) 𝐴𝑎𝑏𝑠 (10)
𝐴𝑎𝑏𝑠 = 𝐴 + 𝜔 × (𝜔 × 𝑟) + 2𝜔 × 𝑉 (11)
This simple analysis helps to evaluate the magnitude of forces acting on oil droplets. For example, a drop with density
of 880 kg/m³, diameter of 1.5 mm and absolute acceleration of 50 m/s² is subject to a force around 0.000078 N. At first
glance, the force seems small, but it must be remembered that it is sufficient to cause a great acceleration to the oil drop.
The maximum resultant force occurs to the largest droplet subject to the highest absolute acceleration, which depends
on the relative acceleration, the ESP rotation speed, the droplet position inside the channel and the drop relative velocity.
For example, considering a droplet with a diameter of 3 mm in a region of the channel with an absolute acceleration of
300 m/s², the force has an intensity of 0.0037 N. Thus, even a higher value of acceleration leads to a small force, with
intensity in the order of thousandths of Newton.
The evaluation of drag and pressure forces is more complicated because they depend on unknown parameters such as
water velocity profile and pressure gradient in the channel.
4.4. Number of Droplets
In total, 41 drops were analyzed in this paper. This is a small sample compared to the huge population observed in the
impeller images. High-speed photography reveals hundreds of droplets for each second of flow. At higher rotation speeds,
the number is estimated to be in the thousands.
The large amount of drops impairs the detailed study of an individual droplet. When the channel is full of drops, it is
difficult to follow a single droplet alone. The neighboring drops influence the tracking and make the observation confusing
and uncertain. Among the droplets that are actually analyzed, most present a random trajectory. The search for patterns
in droplet behavior leads to discarding the massive majority of observed droplets. Only a few options remain.
Tracking a drop to determine parameters such as velocity and acceleration is a task that requires some time and effort.
Because of the problems discussed in the last paragraphs, only a few dozens of droplets were studied. Nevertheless, the
amount of analyzed drops was sufficient to reveal interesting results about the drop behavior within ESP impellers.
5. CONCLUSIONS
The images of the ESP impeller revealed that the oil droplets become smaller when the ESP rotational speed increases.
Higher rotation speeds increase the turbulence, intensify the forces and facilitate the drop breakage. Most oil droplets
have random trajectories, but some patterns were identified. The analysis of a random single droplet revealed positive
velocities around units of meters per second and accelerations that oscillate between positive and negative values in the

order of dozens of meters per second squared. Velocities and accelerations are calculated every millisecond. A minimal
change in velocity causes a high acceleration, since the time interval is very small. This fact may explain the oscillations
that occur to the instant acceleration.
Twelve droplets were tracked at 900 rpm to investigate the effect of trajectory on velocities and accelerations. Results
showed that drops on the suction blade have higher velocities than drops on the pressure blade. Velocities vary between
0.3 and 1.5 m/s. Accelerations fluctuate, but the average acceleration takes values from -150 m/s² to 150 m/s².
Twenty-eight droplets were analyzed at 600 rpm and 1200 rpm to study the effect of the ESP rotational speed. In this
case, central oil droplets that move from suction blade to pressure blade were selected. Results indicate that the velocity
decreases as the drop moves through the channel, from the inlet to a radius of 50 mm. From the radius of 50 mm to the
outlet, the droplet velocity increases and recovers part of the previous reduction. Furthermore, the average velocity varies
between 0.7 m/s and 1.4 m/s for 600 rpm and between 1.4 m/s and 3.0 m/s for 1200 rpm, while the intensity of the average
acceleration varies from 40 m/s² to 90 m/s² for 600 rpm, approximately, and from 100 m/s² to 340 m/s² for 1200 rpm.
In short, results suggest that velocity and acceleration depend on the droplet trajectory and the ESP rotational speed.
The balance of forces acting on the droplets causes the accelerations and decelerations. When the pressure force prevails,
the drops decelerate. When the drag force is predominant, the drops accelerate. The resultant force assumes small values
around thousandths of Newton. As a future task, a further analysis can be done to evaluate each force and improve the
understanding about the droplet dynamics within ESP impellers.
6. NOMENCLATURE
N - rotational speed [rpm]
Q - volumetric water flow rate [m³/h]
mL - mass water flow rate [kg/h]
T - water temperature [ºC]
P1, P2 - pressures at ESP inlet and outlet [N/m²]
d - diameter of oil droplet [m]
x, y - position of oil droplet in a Cartesian system [m]
r, θ - position of oil droplet in a polar system [m]
r - impeller radius [m]
t - time [s]
Vr, Vθ, V - radial, transverse and resultant velocity of oil droplet [m/s]
Ar, Aθ, A - radial, transverse and resultant acceleration of oil droplet [m/s²]
Aabs - absolute acceleration of oil drop in a fixed coordinate system [m/s²]
Fd, Fp, FR - drag force, pressure force and resultant force [N]
ρw, ρo - water density and oil density [kg/m³]
Cd - drag coefficient
W - velocity of water [m/s]
p - absolute static pressure [N/m²]
7. ACKNOWLEDGEMENTS
Authors would like to thank Statoil Brazil, ANP ("Compromisso de Investimentos com Pesquisa e Desenvolvimento"),
and PRH/ANP for providing financial support for this work. Acknowledgments are extended to CEPETRO/UNICAMP
and ALFA – Artificial Lift & Flow Assurance Research Group.
8. REFERENCES
Barrios, L.J., 2007. “Visualization and modeling of multiphase performance inside an electrical submersible pump”. PhD
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Biazussi, J.L., 2014. “Modelo de deslizamento para escoamento gás-líquido em bombas centrífugas submersas operando
com fluido de baixa viscosidade”. PhD Thesis. Universidade Estadual de Campinas.
Boxall, J.A., Koh, C.A., Sloan, E.D., Sum, A.K., Wu, D.T., 2011. “Droplet size scaling of water-in-oil emulsions under
turbulent flow”. Langmuir, Vol. 28, pp. 104-110.
Estevam, V., 2002. “Uma análise fenomenológica da operação de bomba centrífuga com escoamento bifásico”. PhD
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Gamboa, J., Prado, M.G., 2010. “Visualization study of performance breakdown in two-phase performance of an electrical
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Hosogai, K., Tanaka, M., 1992. “Effect of impeller diameter on mean droplet diameter in circular loop reactor”. The
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Lea, J.F., Bearden, J.L., 1982. “Effect of gaseous fluids on submersible pump performance”. Journal of Petroleum
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Minemura, K., Murakami, M., 1980. “A theoretical study on air bubble motion in a centrifugal pump impeller”. ASME
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Mohammadi, M., Sharp, K.V., 2013. “Experimental techniques for bubble dynamics analysis in microchannels: a
review”. Journal of Fluids Engineering, 135/021202-1.
Monte Verde, W., 2016. “Bombas centrífugas submersas: visualização do escoamento bifásico gás-líquido, operação com
fluido viscoso e modelagem de desempenho”. PhD thesis. Universidade Estadual de Campinas.
Monte Verde, W., Biazussi, J.L., Sassim, N.A., Bannwart, A.C., 2017. “Experimental study of gas-liquid two-phase flow
patterns within centrifugal pumps impellers”. Experimental Thermal and Fluid Science, Vol. 85, pp. 37-51.
Sabino, R.H.G., 2015. “Análise da dinâmica de uma bolha de gás em uma bomba centrífuga”. Master’s thesis.
Universidade Tecnológica Federal do Paraná.
Zhang, J., Cai, S., Li, Y., Zhu, H., Zhang, Y., 2016. “Visualization study of gas-liquid two-phase flow patterns inside a
three-stage rotodynamic multiphase pump”. Experimental Thermal and Fluid Science, Vol. 70, pp. 125-138.

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