Experimental investigation of oil drops behavior in dispersed oil-water two-phase flow within a centrifugal pump impeller

Accepted Manuscript Experimental investigation of oil drops behavior in dispersed oil-water twophase flow within a centrifugal pump impeller Rodolfo Marcilli Perissinotto, William Monte Verde, Marcelo Souza de Castro, Jorge Luiz Biazussi, Valdir Estevam, Antonio Carlos Bannwart PII: DOI: Reference:

S0894-1777(18)31775-8 https://doi.org/10.1016/j.expthermflusci.2019.03.009 ETF 9763

To appear in:

Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

9 November 2018 25 February 2019 14 March 2019

Please cite this article as: R. Marcilli Perissinotto, W. Monte Verde, M. Souza de Castro, J. Luiz Biazussi, V. Estevam, A. Carlos Bannwart, Experimental investigation of oil drops behavior in dispersed oil-water two-phase flow within a centrifugal pump impeller, Experimental Thermal and Fluid Science (2019), doi: https://doi.org/ 10.1016/j.expthermflusci.2019.03.009

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Experimental investigation of oil drops behavior in dispersed oil-water two-phase flow within a centrifugal pump impeller Rodolfo Marcilli Perissinotto, William Monte Verde, Marcelo Souza de Castro, Jorge Luiz Biazussi, Valdir Estevam, Antonio Carlos Bannwart. School of Mechanical Engineering, University of Campinas, São Paulo, Brazil. ABSTRACT In oil production, one important artificial lift method involves the commonly used centrifugal pump. The use of this pump in the petroleum industry, however, is hindered by some unfavorable operational conditions. Operating centrifugal pumps with gas and viscous fluids, such as dispersions, may lead to a degradation of their performance. The objective of this paper is to analyze oil-water dispersions in a pump impeller, in order to investigate the behavior of oil drops, which may influence the pump working. Thus, experiments were carried out at different pump rotation speeds and water flow rates. Researchers used a facility with a pump prototype that enabled them to visualize the flow in all the impeller channels. Images, captured through a high-speed camera, revealed a unique flow pattern of oil drops dispersed in water. Processed with computer codes, the images indicated that the oil drops were, in general, spherical or elliptical, and only a few broke up in the impeller. The interaction with water caused the oil drops to rotate, deform, and deviate, thus moving in random paths. Size distributions suggested that the drops became smaller as the impeller rotation speed and water flow rate increased. This behavior was due to the turbulence-induced shear stress and kinetic energy. The oil drops’ equivalent diameters ranged from 0.1 to 6.0 mm; velocities took values measurable by units of m/s; accelerations reached hundreds of m/s²; and forces had magnitudes of thousandths of N. Researchers observed a clear dependence between flow conditions and drop dynamics. Carried by the water flow, the oil drops on the suction blade moved faster than those on the pressure blade of a channel. The drop dynamics were significantly influenced by the presence of adverse pressure gradients and water velocity fields. Keywords: centrifugal pump, two-phase liquid-liquid flow, flow visualization, flow pattern, oil drop.

Nomenclature 3

t

time (s)

Qw

water flow rate (m /h)

Δt

time between two consecutive images (s)

T1

inlet temperature (ºC)

tres

residence time (s)

P1

pump pressure at inlet (kPa)

W

water velocity (m/s)

P2

pump pressure at outlet (kPa)

VNI

oil drop velocity in rotating system (m/s)

N

impeller rotational speed (rpm)

VI

oil drop velocity in fixed system (m/s)

ω

impeller angular speed (rad/s)

Vavg

Ri , Ro *

impeller inner and outer radius (mm)

VR , Vθ

oil drop average velocity (m/s) velocity components in îR and îθ (m/s)

R

dimensionless radial position (-)

ANI

oil drop acceleration in rotating system (m/s²)

d32

Sauter mean diameter (mm)

AI

oil drop acceleration in fixed system (m/s²) acceleration components in îR and îθ (m/s²)

dMAX

maximum diameter (mm)

AR , Aθ

d

equivalent diameter (mm)

F

resultant force (N)

n

number of oil drops (-)

FD

drag force (N)

ρo

oil specific mass or density (kg/m³)

CD

drag coefficient (-)

ρw

water specific mass or density (kg/m³)

FP

pressure gradient force (N)

μo

oil viscosity (cP)

μw

water viscosity (cP)

σa/o

oil-air surface tension (mN/m)

σw/o

oil-water interfacial tension (mN/m)

ESP

electrical submersible pump

x,y

oil drop position in cartesian reference (m, rad)

BEP

best efficiency point

R,θ

oil drop position in polar reference (m, rad)

VSD

variable speed driver

R ,θ

first derivatives of drop position (m/s, rad/s)

HSC

high-speed camera

R ,θ

second derivatives of drop position (m/s², rad/s²)

CFD

computational fluid dynamics

∂p/∂s

pressure gradient along the streamline (Pa/m)

Abbreviations

îR , îθ

radial and transverse directions (-)

1. Introduction In the field of oil production, one of the most relevant artificial lift methods, especially for offshore operations, is the Electrical Submersible Pumping (ESP) system. The main component of an ESP system is the multistage centrifugal pump. Today, centrifugal pumps are used in, it is estimated, 150,000 to 200,000 wells [1]. The centrifugal pump provides energy to the fluids present within the reservoir, lifting them through the well to the production facilities. In this case, the device usually works with multiphase flows, which means it operates in the presence of viscous oil, water, and gas. These sorts of conditions affect the pump behavior and may cause significant changes in its operation, such as performance loss and instabilities. Such changes may result in reduction of oil flow, interruptions in production, increase in well workover, and shortening of equipment lifetime. An example of multiphase flow operation is the liquidliquid mixtures of viscous oil and water. Depending on the superficial velocities, the phases can be arranged according to a dispersion flow pattern. The dispersion viscosity may be higher than that of pure oil, and its stability is a function of the fluids properties and the amount of energy dissipated in the flow. Understanding the flow within the pump impeller is crucial to build a set of assumptions regarding the energy dissipation that occurs in dispersions. Therefore, the ESP system designers must have a detailed comprehension of the phases dynamics, since the observed behavior of real flows is completely different from the single-phase flow operation. The flow complexity represents a great challenge due to the necessity of studying the coupled phases dynamics. For this reason, many researchers are adopting numerical simulations with Computational Fluid Dynamics (CFD). Nevertheless, these investigations also require detailed information on the flow for closure models and results validations. The literature contains many studies on liquid-liquid two-phase flows inside tubes [2-12]. However, there is a lack of studies on these types of flows within centrifugal pumps. A few of the exceptions to this include studies by Morales [13], Khalil [14], and Bulgarelli [15]. Morales [13] explored, theoretically and experimentally, the drop formation in a centrifugal pump operating with a mixture of water and mineral oil. The main mechanism of liquid drop formation identified by the researchers was the turbulent breaking. With a particle size analyzer based on ultrasound, the authors measured the drop size distribution at the pump outlet. Results showed that the drop size heavily depended on the pump rotational speed, while the mixture flow rate and water fraction had a small influence on size distribution. As the pump rotation increased, drops became smaller with narrower curves of size distribution.

PIV

particle image velocimetry

Khalil [14] determined experimentally the performance of centrifugal pumps operating with oil-in-water dispersions. The authors observed that the presence of dispersions reduced the head, flow rate, and efficiency of the pumps. As the holdup and the temperature decreased, the dispersion viscosity increased and the pump performance decreased. The researchers investigated the effects of stable dispersions and observed that adding surfactants degraded the pump performance more intensely. Bulgarelli [15] studied the phase inversion phenomena within an 8-stage centrifugal pump operating with oil-water dispersions. The experiments were performed at different rotational speeds, viscosities, and water fractions. For low water fractions, the continuous phase is the oil, the effective viscosity is higher, and the pump performance is severely degraded. For high water fractions, the continuous phase becomes the water, the effective viscosity is lower, and the head and efficiency increase. The authors observed that the phase inversion point occurred at water fractions between 10 and 30% approximately, depending on the oil viscosity and the pump rotational speed. When compared with literature models for phase inversion in tubes, the results presented a satisfactory agreement. In contrast to the dearth of studies on liquid-liquid twophase flows within centrifugal pumps, the literature contains a large number of studies on gas-liquid two-phase flows in pumps. Many researchers identified the flow patterns and analyzed the performance of pumps working with gas. Initial studies were carried out in the nuclear industry, motivated by the application of centrifugal pumps in reactor cooling systems and by the risk of radioactive fluid leakage [16-18]. In the petroleum industry, works were initiated by Estevam [19], who designed the first visualization pump prototype using an ESP, and investigated the bubbles dynamics in the pump impeller. Other oil industry researchers also produced studies concerning the pumps operating with two-phase gas-liquid flows; they include Barrios [20], Trevisan [21], Zhang [22], and Monte Verde [23]. Using high-speed cameras, the authors explored the gas phase behavior in pump impellers. Flow visualization in pumps is a powerful methodology of studying the interaction between the phases present in a two-phase mixture, whether of gas-liquid or liquid-liquid type. According to Mohammadi and Sharp [24], high-speed cameras enable the observation of fast transient phenomena and provide high spatial and temporal resolutions. In fact, this interesting visualization technique offers the possibility of identifying flow patterns, tracking fluid particles, and evaluating variables as size distributions and velocities. In light of this literature review, it can be concluded that researchers are still without a firm grasp on two-phase liquid-liquid flows in centrifugal pumps, despite their very relevant practical applications. The few studies available in literature investigate the overall pump performance with

oil-water dispersions, in which the authors execute pump inlet and outlet measurements only. There are no studies available in literature that investigate the dynamics of dispersions in pump impellers with the use of flow visualization techniques. Therefore, this comes to be the main contribution of this current research, which aims to add new information to the body of knowledge on the field of liquid-liquid flows in rotating environments. Using high-resolution images as well as computer codes, this paper focuses on examining the flow inside the impeller channels of a centrifugal pump prototype, with the main purpose of understanding the behavior of oil drops in a dispersed oil-water flow. To achieve the goal, this pioneer paper investigates the shape, size, path, and dynamics of oil drops as functions of different pump operational conditions. The results achieved in this paper will provide a better phenomenological understanding about pump operation with dispersed liquid-liquid two-phase flow. A future application of this research is to help the development of a model to theoretically represent the dynamics of fluid particles. In future studies, this paper can serve as a basis for the validation of CFD simulations, such as those performed by Perissinotto [25]. From the petroleum industry point of view, the long-term application of this kind of research is the elaboration of one-dimensional models focused on the ESPs performance, such as the model developed by Biazussi [26], which enable the prediction of the type of pump suitable for each particular application.

2. Experimental facility

Experiments were performed using the facility presented in Figure 1. The experimental apparatus is composed of a water circulation line and an oil injection system, in addition to a centrifugal pump prototype based on the ESP model P23, series Centrilift 538, manufactured by Baker-Hughes. The prototype was developed by Monte Verde [23], who presents in detail the pump design and the impeller geometry. This ESP model P23, operating with water at 3500 rpm, provides the best performance at the flow rate of 15.2 m³/h and head of 17 m per stage. The maximum head is 21.6 m while the maximum flow rate is 21.6 m³/h. To enable visual access to the flow within the channels, the top shroud of the original impeller was removed and replaced by another made of transparent plexiglass. Monte Verde [23] used the prototype to study gas-liquid two-phase flows. The experimental setup was then updated for liquidliquid two-phase flow investigations in the impeller. In the experimental facility, a booster pump draws water from the separation tank; the liquid passes through the heat exchanger and the Coriolis flow meter and then reaches the suction of the visualization prototype. At the same time, a peristaltic pump takes oil out of the oil tank and injects it in the prototype, where the oil becomes dispersed in the water flow. The dispersion is then pumped back to the separation tank, where the oil is gravitationally separated, while the water returns to its line, in a closed loop. The separated oil is finally dewatered and flows back to the oil tank. The separation tank is made of polypropylene and has a capacity of 500 liters, while the oil tank, made of aluminum, has a lower volume of 10 liters. The single stage booster pump (water pump), series Meganorm Bloc, manufactured by KSB, has an impeller with a diameter of 238 mm.

Figure 1 - Schematic diagram of the experimental facility. The peristaltic pump (oil), model Dura10, fabricated by Verderflex, can work at a low maximum flow rate of only 0.2 m³/h, which causes a limitation in the oil injection. Thus, due to its reduced value, the oil flow rate is not measured directly. Since the peristaltic pump is a positive displacement pump, the oil flow rate is indirectly quantified by the pump rotation speed. Each pump is driven by a Variable Speed Drive (VSD), which allows the rotation adjustment and, consequently, the flow control. Furthermore, control valves assist in regulating the line pressure and the phases flow rates. As the facility is a closed loop, fluids tend to heat up, and a temperature control system is required to regulate the fluids viscosities. As Figure 1 shows, the facility contains a system composed of a shell-and-tube heat exchanger and a thermo-chiller, both installed in the water circuit. The thermo-chiller, series 30RH, fabricated by Carrier, has a capacity of 62 kW for cooling or heating and can operate in temperatures from 3 to 60 ºC. In the experiments, the thermal equipment was configured to maintain the water at 25ºC. This is the same temperature of the laboratory where the experimental facility is placed. The thermal control system does not modify directly the oil temperature. However, this is not a problem, as the oil fractions represent less than 1% of the mixture volume in the experiments (see Section 3). The oil is carried by the water; it is thus expected the former to have the same temperature as the latter. All these facts conducted the

researchers to the decision of installing the thermal control equipment in the water circulation line instead of in the oil injection system. In the experimental setup, the variables necessary to calculate the prototype performance are all measured. The pump rotational speed (N) is quantified manually using a tachometer, model MDT-2238A, fabricated by Minipa, with an accuracy of 0.05% of the measurement. The water flow rate (Qw) is quantified with a Coriolis meter, series RHM12, manufactured by Metroval. This instrument has a limit range of 6000 kg/h and an accuracy of 0.2% of the measurement. The dispersion temperature (T1) in the prototype inlet is measured with a resistance temperature detector, type PT100, with 1/10 DIN accuracy. The inlet (P1) an outlet (P2) pressures are quantified using two capacitive transducers, manufactured by Emerson Rosemount, series 2051, with an accuracy of 0.05% of the measured value. The analog output signals from the instruments are obtained through a National Instruments acquisition system, and a LabView® code monitors, processes, and stores the data. During the experiments, the liquid-liquid two-phase flow within the impeller was visualized using the HighSpeed Camera (HSC) technique. For this purpose, it was adopted the HSC model VEO 640, manufactured by Phantom. This equipment has a maximum resolution of 2560 x 1600 pixels at 1400 fps acquisition rate. A Canon 50mm f/1.4 lens was used together with the HSC. Three

LED reflectors were used as light sources, each with 84 watts and 7700 lumens. Figure 2 shows a photograph of the experimental facility, highlighting the impeller visualization window. As can be observed, the setup is the same used by Perissinotto [25] to validate some numerical results.

Figure 2 - Experimental facility, highlighting the transparent window for flow visualization. As noted above, the liquid-liquid two-phase flows are composed of tap water and mineral oil. Chemical tests were performed prior to determine the oil properties. The chosen mineral oil has a specific mass (ρo) of 880 kg/m³, dynamic viscosity (μo) of 220 cP, surface tension (σa/o) of 32 mN/m, and interfacial tension (σw/o) of 34 mN/m, at 25 ºC. The transparent oil was darkened with a black dye. This technique enhances the contrast between phases, increasing the sensitivity of the camera and improving image quality. The dye affects neither the water color nor the oil properties.

rotational speed in order to maintain the inlet pressure (P1) above the cavitation limit. For the oil-water two-phase flow, the experimental procedure is similar to the previous one. In addition, though, oil was injected at a constant flow rate throughout the test. Thus, as the water flow rate was reduced, the oil fraction increased. The thermal control system operated during the tests, in order to maintain the fluids at constant temperature. At the flow conditions analyzed in this study, with low oil fractions, the pump performance curves with oil-inwater dispersions indicate that the injection of oil did not change the pump performance significantly. This result agrees with the experimental and numerical data by Perissinotto [25]. The curves for oil-water two-phase flow are quite similar to the water single-phase flow curves, with differences of 2% or less in the pressure increment. This deviation is smaller than the experimental uncertainty. Thus, it can be assumed there is no change in the pump performance, so the oil drop dynamics can be really analyzed. Obviously, however, at larger oil fractions, there would be a performance decrease, besides other phenomena, as continuous phase inversion and instabilities. Figure 3 exhibits the performance of the pump operating with oil dispersed in a continuous water flow, for rotational speeds between 300 and 1200 rpm. Based on performance tests, it is possible to determine the Best Efficiency Point (BEP) and its limits, which are the conditions of interest in this study. The points marked from C1 to C8 refer to the eight experimental conditions adopted to investigate the oil drops behavior within the impeller. The conditions C1, C2, C3, and C4 are related to the water flow rates corresponding to BEP (QBEP) at different pump rotations, while C5, C6, C7, and C8 represent points at 80% of QBEP and 120% of QBEP.

3. Pump performance The performance curves were initially determined for the prototype pump operating with water single-phase flow and then for oil-water two-phase flow. These data were used as reference for the visualization tests. For the single-phase flow performance experiments, the experimental procedure is in accordance with recommended practice API 11S2 [27]. With the prototype pump operating at a constant rotation speed, the water flow rate was adjusted to a value that corresponds to zero differential pressure, a condition called open-flow. Next, data acquisition was carried out with a frequency of 1 kHz during 30 seconds and the measurements average was stored. Then, closing the control valve, the water flow rate was reduced, and data was collected again. This procedure was repeated until the water flow reached zero, a condition called shut-off, when the pressure increment is the highest. When needed, the VSD could control the booster pump

Figure 3 - Performance of pump prototype operating with two-phase oil-water flow. C1 to C8 are flow conditions related to 80%, 100%, and 120% of flow rates at BEP. According to Monte Verde [23], the performance curves for the visualization prototype operating with single-phase

water flow reveal satisfactory agreement with the curves for the original ESP. These results indicate that the changes made in the impeller did not affect the pump characteristics. Therefore, the dynamic similarity is maintained and the flow fields within the pump impeller are representative. Table 1 details the water flow rates corresponding from C1 to C8, conditions selected for the flow visualization tests. As can be observed, this current test matrix is more complete than the conditions investigated by Perissinotto [25], which focused on numerical simulations. Table 1 - Experimental matrix with eight flow conditions. N (rpm)

0.8·QBEP (m³/h)

1.0·QBEP (m³/h)

1.2·QBEP (m³/h)

300

-

1.06 (C1)

-

600

1.70 (C5)

2.13 (C2)

2.56 (C6)

900

2.56 (C7)

3.20 (C3)

3.84 (C8)

1200

-

4.26 (C4)

-

As stated in Section 2, a peristaltic pump injects the oil in the prototype. Thus, the injection rate is not constant, as the peristaltic pump works in pulses. The average oil flow rate, however, was controlled during the experiments. It was kept constant in 2 ml/s, or 0.0072 m³/h, for all the conditions from C1 to C8. Therefore, the time-averaged oil fractions are quite low, i.e., they vary from a minimum of 0.17% (C4) to a maximum of 0.68% (C1). Although larger rotational speeds are commonly adopted in petroleum industrial applications, some

limitations in flow visualization must have been considered when defining the test matrix. At rotational speeds higher than 1200 rpm, the oil drops become too small and fast for the HSC resolution to be able to capture images with a satisfactory quality. Furthermore, high pressures make the transparent top shroud susceptible to damage, and should thus be avoided.

4. Flow visualization The oil-in-water two-phase flow within the impeller was visualized with the HSC for flow conditions C1 through C8. In the experiments, flow images with 1500 x 1500 pixels were captured at 1000, 1500, and 2000 frames per second, and a short exposure time of 12 µs was set. The lens worked with an aperture of f/2.8. The qualitative analyses conducted in this section aim to identify key features on the topological arrangement of the phases. For the matrix tested, an arrangement of dispersed oil drops in continuous water flow was observed for all flow conditions. Qualitatively, the images make it easy to identify the influence of the operational parameters. Figure 4 and Video 1 reveal the effect of rotational speed and water flow rate with images of the impeller at 300, 600, 900, 1200 rpm, at 1.06, 2.13, 3.20, 4.26 m³/h (QBEP), related to the conditions C1, C2, C3, C4, respectively. The characteristic size of the oil drops clearly decreases with the increasing rotation speed and water flow rate. An increment in the impeller rotational speed represents an increment in the flow rate at BEP, which results in higher turbulence, intensifying the drop breakage.

Figure 4 - Oil drops in the impeller at QBEP and 300 rpm (C1), 600 rpm (C2), 900 rpm (C3), 1200 rpm (C4). The effect of water flow rates at constant rotation speeds is exposed in Video 2 at 600 rpm, and in Video 3 at 900 rpm. Video 2 compares the images acquired at conditions C5 and C6, while Video 3 compares C7 and C8. As can be seen, for a constant rotational speed, the increment in water flow rate from 80% to 120% of QBEP clearly reduces the characteristic size of the oil drops. On the other hand, these observations are not valid when the rotation speed changes and the absolute water flow rate is kept constant. In the test matrix, the flow

conditions C6 and C7 correspond to the same water flow rate (2.56 m³/h) at two diverse rotations (600 rpm and 900 rpm). When only the rotation speed increases at a constant water flow, there are, as shown in Figure 5, no distinguishable changes in the shape and size of oil drops.

Figure 5 - Oil drops in the impeller at 2.56 m³/h, for 600 rpm (C6) and 900 rpm (C7). The explanation for these findings is related to the region where most oil drops break up. Some of them really break up in the images; in general, though, the majority do not break up within the channels. This fact suggests that the breakage mainly occurs before the impeller inlet, in a region where the HSC cannot capture flow images. Actually, in the trajectory from the oil injection point to the impeller inlet, the mixture undergoes a sudden change of momentum and direction, due to a contraction followed by an abrupt curve of 90º. Such geometric characteristics were investigated by Perissinotto [25] with CFD simulations, and the authors identified high turbulent energy dissipation rates in the impeller entrance region. As the turbulence intensity is highly affected by the water flow, it is expected that the water flow rate has a greater influence on oil drop breakage than does the impeller rotation speed. As can be noticed, the numerical results achieved by Perissinotto [25] agree with the experimental results of this current paper. The drops do not present coalescence at all. The images reveal a small interaction between drops. When two oil drops move toward each other, the attractive force is insufficient to cause their aggregation. As Kim and Karrila [28] explain, the fluid medium transmits the motion of one drop to the other, disrupting their approximation. Moreover, although some oil drops eventually do collide with one another, the contact is not capable of causing their coalescence.

5. Images processing The flow images obtained with the HSC were processed in order to analyze the size, trajectory, velocity, acceleration, and forces acting on the oil drops. These experimental data are valuable for the validation of numerical simulations and the development of models with application in the industry, as discussed in Section 1.

5.1 Size distribution

A computational routine was developed to evaluate the size distribution of the oil drops. This code opens an image, selects a channel as the region of interest, creates a new black and white binary image, and detects elements larger than one pixel. The image calibration indicates that the pixel length is 0.09 mm. The routine then specifies the center of mass and quantifies the area of each drop by counting the number of pixels. The result is converted to an equivalent diameter, defined as the diameter of a circle that has the same area of the selected drop. Figure 6 illustrates how the code works. A population of 13,000 oil drops was analyzed using 500 images for the operational conditions C1, C2, C3, and C4. Figure 7 shows the histograms of drop size distribution and the adjustment of normal distribution for the flow conditions, which correspond to 300, 600, 900, and 1200 rpm and water flow rates at BEP, i.e., 1.06, 2.13, 3.20, and 4.26 m³/h. The procedure was then repeated for 11,000 oil drops at C5, C6, C7, and C8, operational conditions that correspond to 600 rpm and 900 rpm, at 0.8 QBEP and 1.2 QBEP. Figure 8 shows the histograms and the normal adjustment of the oil drop size distribution.

Figure 6 - Conversion of an irregular oil drop into a circular drop with an equivalent area. Figure 7 reveals that the oil drop size is clearly modified by the prototype rotation speed and the water flow rate. As rotation increases for BEP, the water flow rate also increases, and the drops gradually become smaller. This result agrees with the observations made in Figure 4. At 300 rpm (C1), 60% of oil drops are smaller than 1 mm and 8.5% are larger than 3 mm. At 1200 rpm (C4), on the other hand, almost 80% of oil drops are smaller than 1 mm and only 0.2% are larger than 3 mm. An increment in the water flow rate intensifies the turbulence and the energy dissipation in the flow, as discussed in Section 4. The experimental data can be compared to the adjustment of normal distribution. As can be seen, increasing rotations and flow rates also modify the normal distribution. The peak frequency rises and shifts to the left, suggesting that what prevail in the population are smalldiameter oil drops. In addition, the standard deviation gradually decreases with the increments in rotation speeds and flow rates.

Figure 7 - Drop size distribution at QBEP and 300 rpm (C1), 600 rpm (C2), 900 rpm (C3), 1200 rpm (C4). Figure 8 reveals the isolated influence of water flow rate. The comparison between C5 and C6, and then C7 and C8, indicates that the oil drops become smaller as the water flow increases at a constant impeller rotation. At 600 rpm and 0.8 QBEP (C5), 56% of oil drops are smaller than 1 mm and 5.6% are larger than 3 mm, while at 600 rpm and 1.2 QBEP (C6), these numbers change to 63% and 1.2%, respectively. The same behavior is noticed at 900 rpm: at 0.8 QBEP (C7), 65% are smaller than 1 mm and 1.4% are larger than 3 mm, while at 1.2 QBEP (C8), the numbers become 75% and 0.2%. Figure 8 also exposes the separated influence of impeller rotation speed. The comparison between C6 and C7 reveals that the rotation does not significantly modify the diameters.

The results agree with the observations made in Figure 5. As explained in Section 4, the entrance zone of the impeller has a geometry that implies a change in the momentum and direction of the dispersion. As a consequence, this region is related to intense turbulence dissipation rates, according to Perissinotto [25]. This turbulence is intensified by increases in the water flow rate. Thus, regarding the oil drop breakage, the water flow has a much stronger effect than the impeller rotational speed does. As can be observed in Figure 7 and Figure 8, the majority of oil drops have diameters between 0.75 and 1.0 mm. From 22% to 36% of them, depending on the flow condition, take equivalent diameters in this band.

Figure 8 - Drop size distribution at 600 rpm, 0.8 (C5) and 1.2 QBEP (C6), and 900 rpm, 0.8 (C7) and 1.2 QBEP (C8). According to Tadros [29], Sauter mean (d32) is frequently used to describe the mean diameter of drops in a dispersion. The Sauter mean d32 is defined as the ratio of a volume to a surface area: d32 

 

n i 1 n

di 3

(1)

d2 i 1 i

where d is the drop diameter and n is the number of oil drops considered in the calculation. The determination of the Sauter mean confirms that the average diameters of the oil drops change as a function of the flow conditions. Results are presented in Table 2. Table 2 - Sauter mean and maximum diameters of oil drops samples at conditions C1 to C8. Condition

dMAX (mm)

d32 (mm)

n (-)

C1

6.22

2.58

2,232

C2

5.12

1.98

2,216

C3

3.86

1.40

3,692

C4

3.80

1.24

4,956

C5

5.00

2.28

1,666

C6

3.90

1.65

2,805

C7

4.14

1.72

2,286

C8 3.18 1.20 4,552 Table 2 also contains the maximum diameter (dMAX) of the biggest oil drop detected at each flow condition. As can be seen, among all the 24,000 drops analyzed in this section, the biggest one presented an equivalent diameter of 6.22 mm and occurred at the lowest rotation speed and flow rate. As can be observed, as the pump rotation speed and water flow rate increase, the Sauter mean decreases from 2.58 mm at 300 rpm and 1.06 m³/h (C1) to 1.24 mm at 1200 rpm and 4.26 m³/h (C4). It agrees with Video 1, Figure 4, Figure 7. Similarly, for a constant rotational speed, when the water flow rate raises from 0.8 to 1.2 QBEP, the Sauter mean

reduces from 2.28 mm (C5) to 1.65 mm (C6) at 600 rpm, and from 1.72 mm (C7) to 1.20 mm (C8) at 900 rpm. For a constant water flow rate of 2.56 m³/h, however, an increment in the rotation speed from 600 rpm (C6) to 900 rpm (C7) does not cause significant variations in the Sauter mean diameter. The results agree with Video 2, Video 3, Figure 5, and Figure 8. The values of the Sauter mean diameter for conditions C1 through C8 are finally displayed in Figure 9 as functions of the water flow rate. As can be seen, the reduction in oil drop diameter is not linear with the increasing water flow rate. The Sauter mean diameters actually decrease faster at low values of Qw and slower at high values of Qw. According to Clift [30], the fluid particles (bubbles and drops) dispersed in multiphase flows can break up due to the interaction with velocity gradients and turbulent flow fields. In this sense, the condition for breaking can be related to the total local shear stress or to the turbulent kinetic energy. Higher pump rotations and water flow rates lead to larger centrifugal forces and water velocities, which act directly on turbulence inside the pump. Some drops break up within the channels; however, as explained in Section 4, most of them break up before entering the impeller. The geometry of this entrance region increases the turbulent energy dissipation in the flow, providing the sufficient energy required for drop breakage.

Figure 9 - Sauter mean diameter as a function of water flow rate for flow conditions C1 to C8. Essential to many industrial processes is the capacity to predict and control the characteristic size of fluid particles. In this study, an analysis of equivalent diameters is relevant to understanding and evaluating the forces that govern the drops behavior in the impeller. A more detailed discussion about the dynamics of oil drops can be found in Section 5.3.

phenomena associated with single-phase flows in centrifugal pumps. The oil-in-water dispersion may be subjected to inlet pre-rotation, secondary flows, vortices, jets, and other effects frequently reported in the literature.

5.2 Trajectories A computational routine was developed to remove the rotation from the impeller. This code rotates each image at an angle defined by the impeller rotational speed. Since the impeller rotates clockwise, the code has to move the images counterclockwise. The result is a stationary impeller in the processed images, as if the camera rotated integrally with the impeller during the experiments. The processed images enable the path investigation of the individual oil drops in the channel where they are moving. Without the rotation correction, the oil drop trajectory would have a spiral shape passing through all the channels. Video 4 illustrates the difference between tracking a drop with and without the image processing. As can be seen in the video, in the original images the camera is stationary and the impeller is moving. The oil drop position is thus defined by an inertial fixed coordinate system, and the trajectory has a spiral path crossing the channels. In the processed images, however, the impeller appears to be stationary, as if the camera and the impeller were both moving with the same rotation speed. In this last case, the drop position is defined by a non-inertial rotating system, and the trajectory is inside the single channel only, where the oil drop is moving. Thirty oil drops were tracked in a channel with images captured at the flow condition C3. Trajectories are shown in Figure 10. As can be observed, the drops generally present random paths. Only a few enter the impeller near the blades and remain close to them during the entire trajectory. The smallest path that a drop can make in the channel is around 33 mm. This is the difference between the impeller’s outer radius (Ro = 55 mm) and inner radius (Ri = 22 mm). However, the oil drops tend to follow longer paths, with up to 70 mm in some cases. In their trajectories, the oil drops clearly undergo lateral deviations. This fact may be explained by important flow

Figure 10 - Path of 30 drops at 900 rpm and QBEP (C3). Ten oil drops were tracked using images at operational condition C2. Trajectories are shown in Figure 11. As can be observed, most oil drops start moving parallel to the suction blade (SB), but suffer a deviation to the pressure blade (PB), especially near the impeller outlet. In addition, the drops take about 0.1 second to traverse the channel. This residence time (tres) is a function of the flow condition. In the figure, the top right corners display the instant of time when each image was captured. The reference is the first image (t = 0.00 s). Experimental and numerical studies on single-phase flow [31-33] indicate the occurrence of turbulent phenomena and complex velocity and pressure fields in centrifugal pumps. Velocity profiles, pressure gradients, and Coriolis forces are all present in the impeller channels. In the case of two-phase oil-water flow, they possibly influence the streamlines of the continuous water phase and, consequently, the trajectories of the dispersed oil drops.

Figure 11 - Trajectories as a function of time for 10 oil drops in a channel at 600 rpm and QBEP (C2) (t represents the time, PB indicates the pressure blade, and SB symbolizes the suction blade). At the suction blade, the single-phase water velocity is generally larger than at the pressure blade, especially at flow rates corresponding to BEP. Influenced by the water flow, the oil drops also tend to move faster in the suction blade region than in the pressure blade region. Due to such velocity differences, the oil drops may also be subjected to rotation, deformation, and lateral deviation. Other effects may also explain why most drops carry out their trajectories away from the blades. According to CFD numerical analyses conducted by Perissinotto [25], adverse pressure gradients cause the dispersion to deviate while the fluids are moving through the channels. The

Coriolis force due to the impeller rotation probably acts on the dispersion as well, pushing it laterally. Despite the apparent randomness in trajectories, patterns could be proposed, as displayed in Figure 12. The trajectories were classified into three categories: (a) central region, (b) suction blade, and (c) pressure blade. This categorization is quite important to the analysis, in Section 5.3, of oil drop dynamics. These trajectory patterns coincide with the classification embraced by Perissinotto [25] in computational simulations. However, in that case, the researchers adopted mathematical criteria to distinguish the three types of trajectories.

Figure 12 - Classification of trajectories: (a) central region, (b) suction blade region, (c) pressure blade region (PB refers to the pressure blade and SB refers to the suction blade). The three trajectory categories are easily identified in the channels. An oil drop is classified as belonging to the central pattern if it enters the impeller near the suction side of the blade (SB) and gradually deviates toward the pressure side of the blade (PB), where the path ends and the oil drop leaves the channel. Similarly, an oil drop has a peripheral path if it stays next to the blades, without significant lateral deviations, during its entire motion within the channel. In this case, the drop can move near a suction blade (SB) or near a pressure blade (PB). In this paper, the investigations into the oil drop paths indirectly reveal the water flow characteristics and provide an idea about the forces that act on the mixture. In future studies, experiments with Particle Image Velocimetry (PIV) may be useful for gaining a greater understanding on single-phase flows in the visualization prototype. Such studies may allow a comparison between the motions of continuous and dispersed phases.

5.3 Drop dynamics New oil drops were tracked using processed images at various flow conditions. A total number of 43 oil drops with different trajectories were investigated at conditions C2, C3, C4, which correspond to impeller rotations of 600 rpm, 900 rpm, and 1200 rpm, and water flow rates at QBEP, i.e., 2.13, 3.20, and 4.26 m³/h. The procedure is similar to that used by Perissinotto [25] to track drops from experimental images. The tracking process generates a table with the oil drop position in each image, as well as the corresponding instant of time related to the camera acquisition rate. Primarily, the position has coordinates x and y in a cartesian system with origin in the impeller center. Then, the position is converted to R and θ, in the directions îR and îθ of a polar coordinate system, as Figure 13 exemplifies.

As in the trajectory analysis performed in Section 5.2, a computer code was used to remove rotation from the images. As noted in Section 5.2, the code results in processed images of an apparently static impeller. This is equivalent to using a high-speed camera that rotates integrally with the impeller during the experiments. Thus, the polar coordinates system shown in Figure 13 is a noninertial (NI) frame of reference, which rotates along with the pump impeller. The subscript NI in the next equations refers to the non-inertial frame of reference. This rotation correction technique is indispensable to begin studying the oil drop dynamics. Indeed, the method facilitates the identification of diverse oil drop paths inside the channels and, therefore, enable the analysis of oil drops with similar trajectories. With R and θ values, the drop velocities and accelerations can be determined. The procedure considers each drop as a rigid particle of negligible size, as expounded by Hibbeler [34]. Both the velocity and the acceleration have radial and transverse components, in the directions îR and îθ of the non-inertial rotating frame of reference. They are obtained by the first and second derivatives of position.

V NI  R îR  Rθ îθ

(2)

ANI  ( R  Rθ 2 ) îR  ( Rθ  2Rθ ) îθ

(3)

The calculated velocity and acceleration are converted to new ones related to an inertial (I) fixed frame of reference. The subscript I in the equations that follow refers to inertial coordinates. In this new system, the observer is static and the impeller is moving. Hence, it is equivalent to tracking the oil drops using a set of images without the rotation correction executed by the computer routine. As White [35] explains, the calculation procedure consists of including effects such as tangential velocity, centrifugal acceleration, and Coriolis acceleration, ω  (ω  R) , 2ω  VNI , respectively.

i.e., ω  R ,

V I  R îR  ( Rθ  ωR) îθ

(4)

AI  [ R  (ω  θ )2 R] îR  [ Rθ  2(ω  θ ) R] îθ

(5)

Resuming, VNI and ANI are calculated for oil drops when the impeller and coordinate system are both rotating. In this situation, the images were processed, so the impeller seems stationary to the observer. Then, velocity and Figure 13 - Position of oil drop in a non-inertial (NI) rotating polar coordinate system.

acceleration are mathematically converted to VI and AI . The result is the same as tracking the oil drops once again, without processing the images. In this last situation, the impeller is moving but the coordinate system is stationary. Both conditions NI and I are illustrated in Video 4.

The dots on R and θ represent derivatives in time, that is, dR/dt, dθ/dt, d²R/dt², d²θ/dt². The derivatives are determined via numerical derivation since the drop position is given in the form of a table and thus the analytical derivation is not practicable. In this study, a central finitedifference method was adopted with a step Δt, the time interval between two consecutive flow images. Basically, the finite-difference method indicates that the i-th value of dR/dt or dθ/dt in instant t = ti depends on the adjacent values of R or θ corresponding to ti+1 = (ti + Δt) and ti-1 = (ti – Δt). R  Ri 1 Ri  i 1 2 Δt θi 

θi 1  θi 1 2Δt

are the drag force, FD , and the force due to the pressure gradient, FP . Therefore, the resultant force is a sum of FD

(6)

with FP . The analysis can be extended to oil drops. The drag force is defined by:

(7)

FD 

The same argument is valid for d²R/dt² or d²θ/dt². Their i-th value at t = ti is a function of R or θ at ti+1 = (ti + Δt) and ti-1 = (ti – Δt). Ri 

Ri 1  2 Ri  Ri 1 (Δt )2

(8)

θi 

θi 1  2θi  θi 1 (Δt )2

(9)

Velocity and acceleration can be corrected by a statistical method such as the moving average. This method defines an average behavior and results in smoother curves in graphs and smaller fluctuations in data. Fundamentally, the centered method corrects the i-th value of a variable by the calculation of a simple mean with earlier and later data from the table. Finally, the resultant force is determined from Newton's second law. Considering an oil drop with a spherical shape, the force F is estimated as a function of the oil density, ρo, the drop equivalent diameter, d, and the acceleration, AI .

π d3 (10) AI 6 According to Crowe [36], fluid particles dispersed in a continuous phase are subjected to phenomena classified as particle-fluid, particle-particle and particle-wall interaction. They are all responsible for mass, momentum, and energy transfers that occur in the two-phase flows. These exchanges define the particle behavior and characteristics such as size, shape, trajectory, residence time, velocities, accelerations. The interaction of an oil drop with the surrounding water involves forces such as the drag force due to relative velocity between phases, the force caused by pressure gradients, the force required to accelerate the water around the drop (virtual mass effect), and the force by reason of the development of a boundary layer with relative accelerations (Basset’s term). The oil drop may be also influenced by the channel walls. The drop may collide with the blades, which causes F  ρo

kinetic energy losses due to friction and inelasticity. In this case, the oil drop may deform and change direction as well. The same situation happens if two drops collide with each other. When the concentration of oil drops becomes sufficiently large, the interparticle collisions cannot be neglected. This condition is called dense particle flow and occurs when the interparticle spacing is relatively small. As reported by Minemura and Murakami [37], the most important forces acting on air bubbles within an impeller





1 π d2 ρwCD W  V NI W  V NI 2 4

(11)

where ρw is the water density, CD is the drag coefficient, d is the oil drop diameter, W and VNI are the water and oil local velocities. There are many correlations to describe the drag coefficient in the literature. They depend on the Reynolds number based on the relative speed between the phases. The drag force is a consequence of the slippage between the phases. If the water velocity is larger, FD is directed to the impeller outlet, so the water tends to carry the oil drops. If an oil drop moves faster than water, however, FD is directed to the impeller inlet and acts decelerating the oil drop. The force due to the pressure gradient is defined as:

π d 3 p (12) 6 s where ∂p/∂s is the pressure gradient along a streamline. The pressure gradient is evaluated in the equation of motion for the continuous water. It usually includes the centrifugal and Coriolis effects that act on the moving impeller due to its rotational speed. As can be observed, FP is proportional to ∂p/∂s, but in the opposite direction. The calculation of both forces depends on the evaluation of the water velocity and the pressure gradient. In this study, these two forces were not obtained because W and ∂p/∂s are both experimentally unknown, and the scope is limited to the analysis of oil velocities, accelerations, and resultant forces. Nevertheless, the reader can find interesting results such as velocity fields for water flows, vectors of pressure gradients, and estimation of drag force and pressure force, in the study by Perissinotto [25], all obtained via numerical simulations. FP  

5.3.1 Individual oil drops: preliminary results Three individual oil drops with random trajectories were tracked at operational conditions C2, C3, and C4. The results can be seen in the graphs of Figure 14. In the vertical axis, each graph presents the velocity curve, which,

according to equation 2, reveals the intensity of the velocity vector V NI . Each graph of Figure 14 displays information about the oil drop equivalent diameter, d, residence time, tres, and average velocity, Vavg. The velocity vector has its direction always tangent to the oil drop trajectory, reproduced on the horizontal plane. The oil drop path is defined by its position, x and y, according to the cartesian coordinate system with the origin at the impeller center, in position (0,0). The channel blades are also plotted on the xy horizontal plane.

Results reveal that the velocity behavior depends on the drop position inside the channel. For the three oil drops, the magnitude curves of the vectors VNI have approximately the same shape. As can be seen, each oil drop enters the channel with its greatest velocity, possibly influenced by the impeller inlet region. As explained in the last sections, this entrance zone is composed of a geometry that induces a high kinetic energy in the flow, increasing significantly the drop velocity.

Figure 14 - Velocity curve, trajectory, equivalent diameter, residence time and average velocity of oil drops at C2, C3, C4. Then, in the middle of its trajectory, the drop undergoes an intense deceleration and reaches its smallest velocity. This situation may be explained by the presence of forces acting on the drop, such as FD and FP , given by equations 11 and 12. The forces are a consequence of relative velocities and pressure gradients within the impeller. Turbulent phenomena such as secondary flows, vortices, and jets can influence the oil drop motion as well, causing variations in the velocity. Finally, as the oil drop approaches the impeller outlet, it undergoes a new acceleration. The drop partly recovers its initial velocity before leaving the channel. Again, there are forces governing the oil drop due to complex velocity and pressure fields related to the water flow. However, the drops may also be affected by a boundary condition in the impeller exit, a region characterized by large velocity differences. In this outlet zone, the impeller is rotating at its maximum linear velocity, while the adjacent diffuser is completely stationary. This boundary region possibly drags out the oil drop, making its velocity increase intensely. Besides depending on the drop position, the velocity is also a function of the prototype operational parameters. As can be seen in Figure 14, velocities are directly proportional to the impeller rotation speed and the water flow rate. They range from an average value (Vavg) of 0.98 m/s at condition C2 to 2.16 m/s at C4. Consequently, the time intervals that

each oil drop takes to pass through the impeller (tres) change from 0.050 second at condition C2 to 0.022 second at C4. Although a sample of three oil drops is very small, the analysis already provides a general understanding on the dynamics of the dispersion in the impeller. The following Sections, 5.3.2 and 5.3.3, study the dynamics of the other 40 drops with behaved trajectories, divided into the patterns defined in Figure 12. The analysis aims to evaluate the influence of the flow condition and the oil drop position onto parameters as velocity, acceleration, and resultant force. 5.3.2 Influence of flow conditions and drop diameter on the dynamics of oil drops with a central trajectory In order to further investigate the influence of prototype rotation and water flow rate on drop dynamics, two samples of 14 oil drops were tracked at conditions C2 (600 rpm, 2.13 m³/h) and C4 (1200 rpm, 4.26 m³/h). The chosen drops have diameters between 1 mm and 3 mm, but all of them execute trajectories in the central zone, as shown in Figure 12 (a). As discussed in Section 5.2, central oil drops enter the impeller near the suction blade (SB) and gradually deviate toward the pressure blade (PB). Figure 15 displays a drop in the central region. Only oil drops with a trajectory

rigorously identical to Figure 15 are considered in this section.

Figure 16 - Velocity magnitude of 28 drops at conditions C2 and C4 in the polar rotating frame of reference. Figure

17

displays

the

radial

and

transverse

components, VR and Vθ , of the velocity in the inertial fixed coordinate system, VI , according to equation 4. Again, the oil drop velocity is directly proportional to the impeller rotations with water flow rates at BEP. The radial term is always positive and reaches 2.5 m/s, approximately. The transverse term is negative and ranges from -0.5 to -5.5 m/s. Thus, the inertial velocity has a radial outward direction and a tangential clockwise direction. The transverse velocity, Vθ , is influenced by the rotational

Figure 15 - Oil drop with a central trajectory. The next analysis presents velocities and accelerations as functions of the dimensionless radial position, R*, which depends on the oil drop radial position, R, and the impeller’s internal and external radii, Ri = 22 mm and Ro = 55 mm. R* 

R  Ri Ro  Ri

speed: the term ω  R reaches -7,0 m/s at 1200 rpm, near the impeller outlet.

(13)

The graphs are composed of sets of points. Each point relates a velocity or acceleration to the dimensionless radial position of the oil drop at a given instant of time. The points are plotted for all 28 oil drops without distinction. The objective is to investigate the average behavior of the entire population. The magnitudes of velocities in the non-inertial rotating coordinate system, VNI , are shown in Figure 16. The results confirm the dependence between oil drop velocity, impeller rotation speed and water flow rate. By doubling the rotation speed, the absolute water flow rates at BEP also double, and the average oil drop velocity increases from 0.92 m/s to 1.90 m/s. As can be observed, the sets of points at conditions C2 and C4 have similar shapes. The drops decelerate from R*=0 (channel inlet) to R*=0.7, and then recover part of their velocities from R*=0.7 to R*=1 (outlet). This behavior is analogous to that observed in Section 5.3.1 for the three individual drops.

Figure 17 - Velocity components of 28 drops at conditions C2 and C4 in the fixed frame of reference. Figure 18 and Figure 19 present the magnitudes of radial and transverse components, AR and Aθ , of the acceleration in the inertial fixed polar coordinate system, AI , according to equation 5.

Figure 18 - Radial acceleration components of 28 oil drops at C2 and C4 in the fixed frame of reference.

Figure 19 - Transverse acceleration components of 28 oil drops at C2 and C4 in the fixed frame of reference. As the oil drop acceleration is derived from the velocity, it is also proportional to the rotational speed and water flow rate combined. As can be seen, the acceleration has a high magnitude, in the hundreds of m/s². Both the radial and transverse terms are mostly negative and vary from about zero to -600 m/s². The inertial acceleration is thus directed radially to center and tangentially to clockwise. This result already considers the centrifugal and Coriolis accelerations, as AR and Aθ are influenced by ω  (ω  R) and 2ω  VNI . The centrifugal acceleration, for example, reaches numbers around -870 m/s² at 1200 rpm, near the impeller outlet. Inertial accelerations support the estimation of resultant forces. In this case, the drop diameter has a great influence, as the equation for force calculation predicts. As can be seen in equation 10, the oil drop diameter is raised to the cube to represent the mass, which is then multiplied by the inertial acceleration. The dependence between force and equivalent diameter is illustrated in Figure 20, which exhibits curves of resultant force as a function of radial position for oil drops at C2.

Figure 20 - Resultant force acting on oil drops at C2. As can be observed, the resultant forces are of quite small intensities, on the order of thousandths of Newton. However, such magnitude is sufficient to generate

accelerations around hundreds of meters per second squared. The resultant force F is oriented in the same direction of the acceleration AI in the fixed inertial frame of reference. An oil drop with a diameter of 1 mm has a mass around 0.5 microgram, while another oil drop with 3 mm has about 12 micrograms, a mass 24 times greater. Larger drops are thus governed by larger forces. At condition C2, the smallest drop has a resultant force between 3.10-5 and 8.10-5 N, while the largest drop has a force that reaches 1.10-3 to 3.10-3 N, a difference of two orders of magnitude. The resultant force is also affected by the pump rotation speed and the water flow rate. By the action of acceleration, an oil drop is subjected to larger forces at 1200 rpm, 4.26 m³/h (C4) than at 600 rpm, 2.13 m³/h (C2). The differences are directly proportional to the inertial accelerations shown above in Figure 18 and Figure 19. 5.3.3 Influence of trajectory pattern and drop diameter on the dynamics of oil drops at flow condition C3 Aiming to study the influence of trajectories on the drop dynamics, two samples of six oil drops were tracked in the flow condition C3. The oil drops have diameters between 1.1 mm and 2.6 mm and perform trajectories next to the blades, in the peripheral zones illustrated in Figure 12 (b) and (c). Figure 21 shows two oil drops that move very close to a suction blade (SB) and a pressure blade (PB), almost sliding over the solid walls. This section considers only drops with a trajectory rigorously identical to that displayed in Figure 21. The radial and transverse components of velocities in the non-inertial rotating frame of reference, VNI , can be seen in Figure 22 and Figure 23. The radial term, VR , has an average value of 1.0 m/s for oil drops in the suction blade zone and 0.44 m/s for drops in the pressure blade zone. Similarly, the transverse term, Vθ , assumes an average magnitude of 1.3 m/s for oil drops in the suction blade region and 0.66 m/s for drops in the pressure blade region. These results reveal that the velocity is dependent on the trajectory. Oil drops close to a suction blade move faster than oil drops close to a pressure blade. This observation is in alignment with those of authors who investigated singlephase flows [31-33] and two-phase gas-liquid flows [37-38] within pump impeller channels.

Figure 21 - Trajectory of oil drops next to a suction blade (SB) and a pressure blade (PB) at condition C3.

Figure 22 - Radial velocity terms in rotating system of 12 drops with trajectories on suction and pressure blades.

Figure 23 - Transverse velocity terms in rotating system of 12 drops with trajectories on suction and pressure blades. Pedersen [31], Byskov [32], and Westra [33] performed experiments, as well as numerical simulations, to study the single-phase water flow in impellers. The authors concluded that the liquid moves faster when it is next to a suction blade and slower when it is close to a pressure blade. In this paper, as the oil drops are being carried by the water, they also tend to present higher velocities in the suction region than in the pressure region of the channels. Minemura and Murakami [37] and Sabino [38] studied, theoretically and experimentally, the dynamics of air bubbles in the two-phase air-water flow. Sabino [38] tracked a few bubbles, identified their typical trajectories, and calculated their velocities. The authors concluded that air bubbles next to a suction blade moved faster than bubbles far from it. The air bubble behavior regarding the velocities is similar to that observed for the oil drops analyzed in this paper. As can be noticed, the sets of points in Figure 22 and Figure 23 also present different average behaviors for each trajectory pattern. Oil drops on a suction blade tend to slow

down over the entire trajectory, while oil drops on a pressure blade undergo a sudden deceleration from R*=0 (channel inlet) to R*=0.3 and then recover part of their velocity from R*=0.3 to R*=1 (outlet). Figure 24 displays the radial and transverse components, VR and Vθ , of velocity in the fixed coordinate system, VI . The radial term is positive and reaches approximately 1.5 m/s, while the transverse term is negative and ranges from -1.0 to -4.5 m/s, approximately. Figure 25 and Figure 26 show the accelerations of drops in the inertial fixed frame of reference, AI . The magnitudes and shapes of the average curves vary widely as functions of the path pattern. As accelerations are directly obtained from velocities, this result was totally expected. As can be seen in Figure 25 and Figure 26, both the radial and transverse terms are mostly negative and range from approximately zero to -350 m/s². The inertial acceleration has a radial direction to the pump impeller center and a tangential direction to clockwise.

Figure 24 - Velocity components in polar fixed system of 12 drops with trajectories on suction and pressure blades.

Figure 25 - Average acceleration components of 12 oil drops with trajectories on the suction blade.

Figure 26 - Average acceleration components of 12 oil drops with trajectories on the pressure blade. Finally, Figure 27 reveals the forces for oil drops on the pressure blades. The resultant force has only slight intensity, around thousandths of N, but this magnitude is sufficiently high to induce accelerations on the order of hundreds of m/s². The force F is oriented toward the direction of acceleration AI , displayed in Figure 26.

Figure 27 - Resultant force acting on oil drops in the pressure blade region. To summarize, the results for oil drops with central paths indicate that oil drop velocity is directly dependent on flow conditions. When the pump rotation speed doubles from 600 to 1200 rpm, the water flow rate at BEP doubles, from 2.13 to 4.26 m³/h, and the velocities consequently double as well. Thus, the velocity of the dispersed phase probably describes the velocity field of the continuous phase. The oil drops may serve as tracers that reveal the water velocities along central pathlines. The results for peripheral oil drops reveal a dependence between drop velocity and drop trajectory. The oil drops in the suction blade zone have larger velocities than those in the pressure blade region. This fact is still related to the velocity profiles of the continuous phase in the impeller [31-33].

The accelerations also change as a function of operational condition and drop trajectory. The pump rotation acts on the Coriolis and centrifugal effects, which are proportional to ω and ω2, respectively. Thus, the average accelerations at 1200 rpm can be almost four times greater than those at 600 rpm. What is not so clear is the influence of the equivalent diameters on the velocities and accelerations. The resultant forces depend, otherwise, on the equivalent diameter, as F is proportional to d³. Although the forces have intensities of thousandths of Newton, they are sufficient to generate accelerations around hundreds of m/s². The next step going beyond this study is to investigate the single-phase water flow in the prototype using a PIV technique. With the evaluation of water velocity profiles, the results achieved in this current paper can be used to estimate the slip between phases. We expect that the results regarding water and oil can be combined to help researchers develop new models to be used in the petroleum industry. 6. Conclusions This paper has investigated the behavior of oil drops within a pump impeller. Experiments with a two-phase oilwater flow were conducted at different pump rotation speeds and water flow rates. A facility with a pump prototype was employed for flow visualization. During the tests, a high-speed camera captured images, which were then processed using computer codes for particle tracking. The qualitative observation of flow images revealed that: - For the conditions tested, a unique flow pattern of oil drops dispersed in water was identified within the impeller. - As a result of the oil properties, such as a high viscosity compared with water, most oil drops presented spherical and elliptical geometries. Due to their interactions with water, however, some oil drops occasionally underwent rotations and deformations; this was probably caused by the action of velocity profiles and pressure gradients. In this case, the oil drops became irregular in shape. - The images revealed that only a few oil drops broke up inside the channels. The drop breakage would actually occur before the impeller inlet, where the geometry of the pump caused the drops to undergo a sudden change of direction and momentum to enter the channel. This condition increased the turbulence and caused the oil drops to break up due to high local shear stress and turbulent kinetic energy. - For the low oil fractions tested in this study, coalescence was not observed. Although some oil drops collided with one another, the attractive forces were not capable of causing them to aggregate. The force due to surface tension, in this case, was probably dominant over other external effects.

- The characteristic sizes of oil drops depend on the pump rotational speed and, mainly, on the water flow rate. As they increased in number, the drops clearly became smaller, due to turbulent effects related to the water flow. Results suggest the influence of water flow is stronger than that of impeller rotational speed. The images processing and oil drop tracking generated such quantitative results as size distribution, residence time, trajectories, velocities, accelerations, and forces: - Histograms with size distributions indicated that the oil drops had equivalent diameters of up to 6.0 mm for the flow conditions tested. Most drops presented diameters between 0.75 and 1.0 mm, but the average diameter decreased with increases in pump rotation and, mainly, in water flow rate. - The drops executed random paths inside the channels. Some remained close to the blades, but most performed central trajectories. These central drops started their motion parallel to a suction blade, but underwent a lateral deviation toward a pressure blade. Such a trajectory pattern may have been influenced by complex velocity profiles and pressure gradients, usually observed in one-phase flows inside pumps. - Graphs with velocity values revealed that the oil drops moved in the channels at units of m/s. The accelerations were obtained directly from velocities, with quite small intervals defined by the HSC acquisition rate. Therefore, accelerations reached high values, in the hundreds of m/s². Nevertheless, the forces associated with these accelerations exhibited low intensities, around thousandths of Newton. - A dependence clearly exists between oil drop dynamics and pump operational parameters. Results for central drops revealed that, as both impeller rotation speed and water flow rate increased together, the velocities, accelerations, and forces increased as well. Higher rotations and flow rates implied more turbulence with larger forces that accelerated the dispersion. - The dynamics is also a function of the oil drop position and trajectory. Results for peripheral oil drops indicated that oil drops near a suction blade had larger velocities than those near a pressure blade. This observation may be explained by the interaction between oil drops and the surrounding water. As the continuous phase tended to carry the dispersed phase, the drops probably served as tracers that revealed the water behavior, including its velocities in different positions. - The relation between characteristic size and dynamics is still uncertain. However, results suggest that the resultant force, which governs the motion of the oil drops, strongly depends on their equivalent diameters. The analysis of drop motion seems to be a statistical task, which must account for samples with many fluid particles to correctly represent the entire population. Therefore, this paper has provided a phenomenological understanding about the behavior of two-phase liquid-liquid

dispersions in centrifugal pump impellers and other rotating environments. We hope the results can contribute to other theoretical, numerical, and experimental studies.

Acknowledgements The authors would like to thank Equinor Brazil, ANP (“Compromisso de Investimentos com Pesquisa e Desenvolvimento”) and PRH/ANP for providing financial support for this work. The acknowledgements are also extended to Center for Petroleum Studies (CEPETRO), University of Campinas (UNICAMP) and Artificial Lift & Flow Assurance Research Group (ALFA).

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Graphical abstract

Highlights

-in-water dispersions in a rotating environment were experimentally studied.