Experimental analysis on the behavior of water drops dispersed in oil within a centrifugal pump impeller

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Experimental Thermal and Fluid Science 112 (2020) 109969

Contents lists available at ScienceDirect

Experimental Thermal and Fluid Science journal homepage: www.elsevier.com/locate/etfs

Experimental analysis on the behavior of water drops dispersed in oil within a centrifugal pump impeller

T

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Rodolfo Marcilli Perissinottoa, , William Monte Verdeb, Carlos Eduardo Perlesb, Jorge Luiz Biazussib, Marcelo Souza de Castroa, Antonio Carlos Bannwarta a b

School of Mechanical Engineering, University of Campinas, Mendeleyev Street, 200, Campinas, São Paulo, Brazil Center for Petroleum Studies, University of Campinas, Cora Coralina Street, 350, Campinas, São Paulo, Brazil

A R T I C LE I N FO

A B S T R A C T

Keywords: Centrifugal pump Two-phase liquid-liquid ﬂow Water-in-oil dispersion Flow visualization Water drops

This paper aims to investigate the behavior of water drops in a continuous oil medium inside a centrifugal pump impeller working at eight operational conditions (up to 1200 rpm and 2.8 m3/h) with two-phase liquid-liquid ﬂows. Water-in-oil dispersions were produced with low water cuts of about 1% in volume, thus the dispersed phase became arranged as water drops. Experiments for pump performance and ﬂow visualization were conducted using a high-speed camera and a pump prototype with a transparent shell. Flow images revealed that the large water drops usually deform, elongate, and break up into smaller ones, especially at high pump rotations and oil ﬂow rates, while small water drops tend to keep their spherical geometry without deformations and fragmentations. A sample of drops were tracked and their equivalent diameters, residence times, and velocities were calculated. The tracking indicated that the water drops travel random trajectories in the channels, generally undergoing a deceleration along their pathway. Furthermore, the residence times and the average velocities of water drops strongly depend on the ﬂow conditions. For the conditions tested, the water drops presented equivalent diameters between 0.1 and 5.0 mm, average velocities from 0.4 to 1.7 m/s, and residence times between 30 and 152 ms. For a more complete analysis, the results achieved in this study are constantly compared with results available in literature regarding oil drops in oil-in-water dispersions.

1. Introduction Two-phase liquid-liquid ﬂows are present in the daily life of human beings, from simple activities to complex industrial processes. In a wide range of industries, in food, chemical, and pharmaceutical processes, the liquid-liquid dispersions are usually a desirable product. However, in some situations, their presence may be harmful to the whole process. The last case is the situation frequently found in the petroleum production systems. In the petroleum industry, centrifugal pumps are widely employed to lift ﬂuids from wells to topside facilities, for example. Nowadays, it is estimated that approximately 10% of the oil supply in the world is produced with centrifugal pumping installations [1], which are used as an artiﬁcial lift method named electrical submersible pumping (ESP). This important technique can be applied in onshore and oﬀshore wells, being able to handle high volumes of ﬂuid with high temperatures in abrasive environments [2]. When water is present inside the petroleum reservoir, the high shear

and turbulence inside the ESP system can promote the breakup of the phases into small drops, producing dispersions and emulsions, which can be oil-in-water (O/W) or water-in-oil (W/O) types. As an important characteristic of W/O mixtures, it can be highlighted that their apparent viscosity may be higher than the viscosity of the separated liquids [3–5]. Therefore, W/O dispersions can represent top issues related to ﬂow assurance in oil production because their high eﬀective viscosity can aﬀect the pump performance and, consequently, can cause a substantial increase in the operational costs. Improving the physical understanding on multiphase ﬂows in centrifugal pumps is fundamental to the advancement of technologies that can lead to more eﬃcient ESP designs. The ﬁrst studies on multiphase ﬂows inside rotating machinery had their focus on two-phase gas-liquid ﬂows. These initial investigations were motivated by the nuclear industry, where centrifugal pumps were used in reactor cooling systems. In the petroleum industry, Estevam [6] was the ﬁrst researcher to develop a pump prototype for visualization of gas-liquid ﬂows. The author observed two patterns: dispersed bubbles

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Corresponding author. E-mail addresses: [email protected] (R.M. Perissinotto), [email protected] (W. Monte Verde), [email protected] (C.E. Perles), [email protected] (J.L. Biazussi), [email protected] (M.S. de Castro), [email protected] (A.C. Bannwart). https://doi.org/10.1016/j.expthermﬂusci.2019.109969 Received 3 July 2019; Received in revised form 26 August 2019; Accepted 26 October 2019 Available online 06 November 2019 0894-1777/ © 2019 Elsevier Inc. All rights reserved.

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Nomenclature

mo Qo Qw ϕ T1 T2 N ω ωs P1 P2 ΔP g ρw ρo μw μo σo / w Fi Δpi τd τσ τμ ε R D A d d32 d 95 n ReS ReG ReMV

Reω H Hw, BEP Q w, BEP CH , BEP CQ, BEP t Δt tres x, y x ̇, y ̇ V V Vavg f (t ) f ̇ (t ) Ca

oil mass ﬂow rate [kg/s] oil volume ﬂow rate [m3/s] water volume ﬂow rate [m3/s] water cut [v/v%] temperature in the prototype [°C] temperature in the separator [°C] impeller rotational speed [Hz] impeller angular speed [rad/s] pump speciﬁc speed [–] pressure in prototype inlet [Pa] pressure in prototype outlet [Pa] pressure increment [Pa] gravity [m/s2] water density [kg/m3] oil density [kg/m3] water viscosity [Pa s] oil viscosity [Pa s] interfacial tension [N/m] interfacial force [N] pressure jump across interface [Pa] disruptive stress [Pa] interfacial stress [Pa] viscosity stress [Pa] turbulent energy dissipation [m2/s3] impeller outer radius [m] impeller diameter [m] surface area of a drop [m2] equivalent diameter of a drop [m] Sauter mean diameter [m] 95% maximum diameter [m] number of drops [#] Reynolds number – Stepanoﬀ [–] Reynolds number – Gülich [–] Reynolds number – Monte Verde [–]

rotational Reynolds number [–] pump head [m] water pump head at BEP [m] water ﬂow rate at BEP [m3/s] correction factor for pump head [–] correction factor for ﬂow rate [–] instant of time [s] time interval [s] residence time of a drop [s] position of a drop [m] time derivatives of position [m/s] relative velocity vector [m/s] velocity magnitude of a drop [m/s] average velocity of a drop [m/s] generic function of time [–] derivative of generic function [–] capillary number [–]

Subscripts

i w o

i-th value of a discrete parameter water oil

Abbreviations ESP BEP HSC FC O/W W/O VSD LED PIV CFD

and segregated ﬂow. Zhu and Zhang [7] wrote a recent review of studies focused on twophase gas-liquid ﬂows in electrical submersible pumps. Using highspeed cameras, such authors as Barrios and Prado [8], Trevisan and Prado [9], Zhang et al. [10], Monte Verde et al. [11], and Cubas Cubas [12] identiﬁed ﬂow patterns within impellers and analyzed the behavior of bubbles at diﬀerent ﬂow conditions. Other authors as Murakami and Minemura [13], Minemura and Murakami [14], Sabino [15], and Ofuchi et al. [16] investigated the forces that govern the dynamics of individual gas bubbles in rotating equipment. The comparison between bubbles and drops, however, is not appropriate, as liquid-liquid interactions may be quite diﬀerent from liquid-gas interactions, which are mainly dominated by gas compressibility, turbulence, and drag imposed by the liquid motion. On the other hand, forces acting on liquid drops are often attributed to properties such as viscosities and interfacial tensions. A quantitative relationship between interfacial and viscous forces is frequently obtained by calculating non-dimensional numbers, such as the capillary [17] and Ohnesorge [18] numbers. The shape of a single drop, for example, can be predicted by the Bond, Morton, and droplet Reynolds numbers [19]. However, all these numbers have been developed for pipe ﬂows, so they are not suitable for dispersed drops in impellers. Further studies with focus on liquid-liquid interactions would be appreciated as they could include important factors, such as centrifugal eﬀects, in the analysis of drops in pumping devices. Nevertheless, there are few studies on two-phase liquid-liquid ﬂows in pump impellers available in the literature and they rarely focus on

electrical submersible pumping best eﬃciency point high-speed camera ﬂow condition oil-in-water water-in-oil variable speed drive light-emitting diode particle image velocimetry computational ﬂuid dynamics

drop dynamics. Khalil et al. [20], Morales et al. [21], Bulgarelli et al. [22,23], and Perissinotto et al. [24,25] are examples of authors who experimentally investigated dispersions within centrifugal pumps. Khalil et al. [20] investigated centrifugal pumps working with stable and unstable O/W emulsions. The authors observed that the presence of emulsions reduced the head and the ﬂow rate in the pump. Morales et al. [21] studied the formation of O/W dispersions inside a centrifugal pump where the turbulent breakup was identiﬁed as the main mechanism of drop formation. The authors noticed a clear dependence between the pump rotation speed and the oil drop characteristic size: as the rotation increased the oil drops became smaller. Bulgarelli et al. [22,23] investigated the phase inversion phenomena and the drop size distribution in an eight-stage pump working with O/W and W/O dispersions. The authors concluded the phase inversion occurred at water cuts from 10% to 30%, for water and oil as working ﬂuids, and the drop size raised up to the phase inversion point, falling after it. Using a high-speed camera, Perissinotto et al. [24] studied the behavior of oil drops in O/W dispersions in a centrifugal pump impeller. The researchers qualitatively investigated the ﬂow pattern and geometric shape of oil drops with a viscosity of 0.220 Pa s (220 cP). Characteristic sizes were analyzed with histograms for equivalent diameter distributions. The researchers also studied the kinematics and dynamics of a sample of oil drops, with an evaluation of the forces that govern their motion. The experimental analyses conducted by the authors were numerically investigated by Perissinotto et al. [25] using computational ﬂuid dynamics (CFD) simulations and it was observed a satisfactory agreement between both studies. 2

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The studies on multiphase ﬂows within impellers, such as the ones reported above, are generally performed at operational conditions corresponding to the best eﬃciency point (BEP) of the pumps at each rotational speed. The BEP is usually obtained from an analysis of the pump performance when this equipment is working with single-phase water ﬂow. However, if the pump operates with viscous ﬂuids, the BEP must be corrected, in order to consider the harmful eﬀect of the viscosity on its performance. In this sense, some authors such as Stepanoﬀ [26], Gülich [27], and Monte Verde [28] developed methods that correct the BEP for viscous liquids using performance data from water ﬂows and also modiﬁed Reynolds numbers. Stepanoﬀ [26] carried out an important experimental study to verify the inﬂuence of eleven types of oil with diﬀerent viscosities on the performance of centrifugal pumps. The author proposed correction coeﬃcients for pressure increment, ﬂow rate, and eﬃciency of centrifugal pumps operating with viscous ﬂuids. The procedure performed by the author was restructured decades later, as reported by Solano [29], by the artiﬁcial lift research group of The University of Tulsa (TUALP) in the United States. Gülich [27] proposed an empirical procedure for performance correction based on tests and on a model developed years before [30,31], which considers the friction in the impeller channels as the main cause of energy dissipation in the centrifugal pump. The researcher created correction factors for viscous ﬂuids using the operation with water as a reference. Monte Verde [28] conducted tests with a three-stage ESP working at two rotations with glycerin at ten viscosities. Then, the author proposed a new model with correlations and compared the experimental results with data corrected using the methods of Stepanoﬀ [26] and Gülich [27]. This comparison indicated signiﬁcant deviations of up to 152% between the methods. Therefore, as can be seen, many authors explored gas-liquid ﬂows inside pumps [6–16], while a few analyzed O/W dispersions and individual oil drops [20–25]. Some authors also studied the inﬂuence of viscous liquids on the performance of centrifugal pumps [26–31]. W/O dispersions and water drops within impellers, however, have not been studied yet, as there are no works available in the literature on this subject. Therefore, this current paper was written to serve as a contribution for the investigation of W/O dispersions in centrifugal pumps and electrical submersible pumps. High-speed imaging is an interesting technique that provides ﬂow images with high spatial and temporal resolutions [32]. In this context, ﬂow visualization with a high-speed camera (HSC) was adopted in this study to allow the analysis of water drops behavior in a pump impeller at diﬀerent operational conditions. Characteristics of the water drops such as shape, size, and trajectory were qualitatively investigated, while other parameters such as equivalent diameter, residence time, and velocity were calculated. The performance of the centrifugal pump working with the W/O dispersion was evaluated as well. The objective of this study is to improve the phenomenological comprehension on two-phase liquid-liquid ﬂows in rotating machinery, in which the mixture may be subjected to shear stresses, turbulent phenomena, and intense forces. This paper provides a basis for further studies. The results can be used to support new numerical simulations, as the experiments generate relevant information to make computer simulations closer to the real case. In a long-term application focused on the petroleum industry, the results may be useful to propose simple models that represent the performance and eﬃciency of various centrifugal pumps, in order to predict the best type of pump for each desired application.

production, i.e., an ESP model P23, series Centrilift 538, manufactured by GE Baker-Hughes. It was designed and built by Monte Verde et al. [11], who reports in detail its geometric characteristics. Essentially, the prototype has an impeller with a transparent top shroud made of acrylic glass, which allows ﬂow visualization in all the impeller channels simultaneously. The setup used in this study is an updated version of the one used by Perissinotto et al. [24], in which modiﬁcations were made to allow the investigation of W/O dispersions. The new facility is illustrated by the scheme in Fig. 2. The oil circuit is composed of a 500-liter tank, a booster pump, a mass ﬂow meter, a thermal control system, and pipes with two inches in diameter. The water injection system is composed of a 10-liter tank, a peristaltic pump, and thin capillary tubes made of stainless steel. When both liquids enter the prototype, the water becomes dispersed in the oil phase. An HSC then captures images of the ﬂow inside all the impeller channels. The mixture ﬁnally ﬂows out of the prototype and goes into a heated tank for phase separation. After reaching the complete separation, both water and oil return to their respective reservoirs. The phase separation system is the main diﬀerence between this updated facility and the previous one used by Perissinotto et al. [24]. The device consists of a 100-liter reservoir with three electrical heaters (380 V; 1450 W each) and an electronic controller. In the tests conducted in this study, the undesirable formation of emulsions (Section 4.2) was the major motivation for the construction of this separator. For an eﬃcient operation, when the device is completely ﬁlled with W/O mixture, the experiments must be interrupted and the mixture must be heated to 80 °C. Then, this temperature must be maintained for approximately six hours, the time necessary for a complete separation. The device can be turned oﬀ and, when the liquids cool to 25 °C, they can be ﬁnally removed from the separator and ﬂow to their respective tanks. New experiments can be performed and the whole procedure repeated. Five measuring instruments collect information during the experiments. The oil ﬂow rate (Qo ) is calculated from the data measured by a Coriolis mass ﬂow meter, series F200, manufactured by Emerson Micro Motion. The mixture temperatures are measured in the pump prototype (T1) and in the separation device (T2 ) by PT100 sensors manufactured by Encil. The impeller rotation speed (N ) is measured by a tachometer, model MDT-2238A, manufactured by Minipa. The pressures in the prototype inlet (P1) and outlet (P2 ) are measured by capacitive transducers, series 2051, manufactured by Emerson Rosemount. A National Instruments acquisition system, with module NI 9203 and chassis NI cDAQ 9178, obtains analog signals from the measuring instruments, while a LabView code monitors, processes, and stores the data. All the instruments have a satisfactory accuracy since their uncertainties are

2. Experimental facility Single and two-phase ﬂow experiments were performed using the facility displayed in Fig. 1. The experimental setup consists of an oil circuit, a water injection system, and a pump prototype for ﬂow visualization. The prototype is based on a real centrifugal pump used for oil ﬁeld

Fig. 1. Experimental setup with transparent top shroud for ﬂow visualization. 3

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Fig. 2. Schematic diagram of the experimental setup with a new separation device.

prototype working with a single-phase water ﬂow. A procedure based on Stepanoﬀ [26], Gülich [27], and Monte Verde [28] was adopted to indirectly determine the best eﬃciency point (BEP) related to the operation with mineral oil, a viscous liquid. Results are available in Sections 3.1 and 3.2. They are used as a reference for the visualization experiments that will be discussed in Section 4.1.

less than 0.2% of the measurement. The water ﬂow rate, however, cannot be measured directly by instruments. In fact, the water injection rate is constant at 0.0072 m3/h (or 2 ml/s), the maximum ﬂow rate of the peristaltic pump model Dura 10, manufactured by Verderﬂex. Since this peristaltic pump is a positive displacement type, the water injection rate is quantiﬁed indirectly by using the pump rotational speed, controlled via a variable speed drive (VSD). As the water injection rate is limited by the peristaltic pump, the oil is the predominant ﬂuid composing the continuous medium in the twophase ﬂow experiments. Indeed, the oil fractions represent more than 98% of the water-in-oil dispersions (Section 4.1). Therefore, a thermal control system is required to regulate the oil temperature and, consequently, its viscosity. As presented in Fig. 2, this system is composed of a thermo-chiller and shell-and-tube heat exchanger. The thermal equipment was conﬁgured to keep the oil at 25 °C during the tests. The maintenance of the oil temperature is crucial to minimize variations in the oil properties, ensuring reliable experimental results. The water-in-oil dispersion is a mixture of tap water and a mineral oil, both originally transparent. In the visualization experiments, the water was dyed with methylene blue to enhance the contrast between the liquids. The dye does not aﬀect the oil color nor the water properties, such as density (ρw ) of 998 kg/m3 and viscosity ( μ w ) of 0.00090 Pa s (0.90 cP) at 25 °C. The mineral oil was also characterized at 25 °C and the tests yielded the following mean data: density ( ρo ) of 838 kg/m3, viscosity ( μo ) of 0.018 Pa s (18 cP), and oil/water interfacial tension (σo / w ) of 24 mN/m. An HSC model VEO 640, fabricated by Phantom, was used for ﬂow visualization. This monochrome high-speed camera is capable of capturing images at 1400 frames per second with a maximum resolution of 2560 × 1600 pixels. A lens manufactured by Canon with a focal length of 50 mm was used together with the camera and light-emitting diode (LED) reﬂectors were also used as light sources.

3.1. Performance curves The procedure adopted for single-phase ﬂow tests is consistent with the recommended practice API 11S2 [33], but discretized in more points. The prototype is initially conﬁgured to rotate at a constant speed. The oil ﬂow rate is then adjusted to a maximum value related to a zero pressure increment in the pump. The experimental data is acquired and the average values of Qo , P1, and P2 are stored in the computer. Then, the oil ﬂow rate is gradually reduced by closing the valves and operating the VSD and the data is collected again. This procedure is repeated until the last operational condition is achieved, which occurs when the oil ﬂow rate reaches zero, i.e., a minimum value associated with a maximum pressure increment. The whole procedure is ﬁnally repeated for a diﬀerent impeller rotational speed. The performance curves for single-phase ﬂow are exhibited in Fig. 3. As can be seen, four rotation speeds were investigated, from 300 rpm to 1200 rpm. In the graph, the curves experimentally obtained with oil can be compared to the results achieved by Monte Verde et al. [11] with water. The x-axis contains the volumetric ﬂow rate while the y-axis represents the pump head, H . In the oil tests, neglecting variations in gravitational and kinetic terms, this parameter is obtained from the pressure increment, ΔP , oil density, ρo , and gravity, g , as follows.

H=

ΔP P − P1 = 2 ρo g ρo g

(1)

The curves shown in Fig. 3 indicate that the oil viscosity (18 cP) impairs the pump performance. At a constant ﬂow rate, the oil is responsible for a lower head in comparison with water. Similarly, for a constant head, the oil leads the pump to operate at a lower ﬂow rate when compared with water. The performance decrease is explained by the increase in the viscous dissipation within the pump. These results agree with studies available in the literature that investigated the performance of

3. Pump performance Experiments for pump performance were carried out with the prototype operating with single-phase oil ﬂow and then with two-phase water-in-oil ﬂow. The performance curves were compared with the results presented by Monte Verde et al. [11], who investigated the 4

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viscosity ( μo ) of the continuous oil phase, and on the outer radius (R ) and angular speed (ω ) of the pump impeller. The prototype used in this paper has an impeller with R = 55 mm and its angular speed (ω ) is calculated directly from the rotational speed (N ).

Reω =

pumps working with viscous liquids [26–28]. Regarding the two-phase ﬂow experiments, the procedure adopted is very similar to that used for the single-phase oil ﬂow. The only difference is the injection of water at a constant ﬂow rate. In this case, as the oil ﬂow rate decreases during the test, the water cut increases. Nevertheless, as reported in Section 2, the water injection rate is limited by the peristaltic pump and, as a consequence, the water cuts are always low. For the performance tests executed in this section, the selected water ﬂow rate was only 0.0072 m3/h (2 ml/s). At such low value, the head curves of the two-phase water-in-oil ﬂow presented values quite similar to the data displayed in Fig. 3 for the single-phase oil ﬂow. Eventual diﬀerences can be neglected since they are lower than 2%, a deviation smaller than the total experimental uncertainty. Therefore, it can be assumed that the presence of water dispersed in the oil medium does not inﬂuence the pump performance. In this case, the water phase behavior can be totally investigated without signiﬁcant eﬀects to the pump performance and vice-versa, an approach that will be accomplished in Sections 4 and 5.

4. Flow visualization Using the results obtained in Section 3.2, a test matrix with eight ﬂow conditions (FC) was deﬁned for the visualization experiments, in which thousands of images were captured. These tests were carried out with the prototype operating with two-phase water-in-oil ﬂow. The test matrix is described in Section 4.1, while ﬂow images are presented in Section 4.2 along with interesting qualitative observations on the behavior of water drops. The images are useful for the calculation of quantitative parameters as the ones that will be discussed in Section 5.

3.2. Best eﬃciency points The best eﬃciency points of the prototype operating with water were used by Monte Verde et al. [11] and Perissinotto et al. [24] as reference conditions for the two-phase ﬂow experiments in which water was the continuous phase. In this current work, however, oil is the continuous phase, so the BEP must be redeﬁned to be compatible with a viscous ﬂuid. As reported in Section 1, there are some studies in the literature [26–28] that provide interesting methods to correct the BEP of centrifugal pumps working with viscous liquids. The main equations used in these methods are described in Table 1. The procedure consists in calculating correction factors CQ, BEP and CH , BEP , which are then multiplied by the water ﬂow rate and pump head at the BEP, resulting in new corrected BEP for the viscous liquid. In Eqs. (4), (6), and (9), the parameters ReS , ReG , ReMV are the Reynolds numbers adopted by each author [26–28]. ReG and ReMV are functions of Reω and ωs , which represent the rotational Reynolds number and the non-dimensional speciﬁc speed, respectively. The non-dimensional speciﬁc speed (ωs ) is a function of the impeller angular speed (ω ), water ﬂow rate at BEP (Q w, BEP ), water pump head at BEP (Hw, BEP ), and gravity ( g ).

Table 1 Correlations to determine the BEP for viscous liquids.

(g Hw, BEP

Author

Procedures and equations

Stepanoﬀ [26]

1. Calculate ReS (use FPS units) 2. Verify plotted curves in diagram 3. CalculateCQ, BEP

1.5 CQ, BEP = CH , BEP

(5)

1. Calculate ReG (use MKS units)

ReG = Reω ωs1.5 f 0.75 where f = 1 for simple-entry pump

(6)

Gülich [27]

ReS =

ρo Qo N μo (Hw, BEP )0.5

Monte Verde [28]

3. CalculateCQ, BEP 1. Calculate ReMV (use MKS units) 2. CalculateCH , BEP

⎛ − 6.7 ⎞ ⎜ Re 0.735 ⎟ ReG⎝ G ⎠

CH , BEP = CQ, BEP = CH , BEP

ReMV = Reω ωs1.5

CH , BEP =

⎛ − 145.965 ⎞ ⎜ Re1.139 ⎟ MV ⎠ ⎝ ReMV

CQ, BEP =

⎛ − 9.257 ⎞ ⎜ Re 0.610 ⎟ ⎝ MV ⎠ ReMV

3. CalculateCQ, BEP

(2)

In addition, for W/O dispersions, Reω depends on the density (ρo ) and 5

(4)

Find CH , BEP in diagram

2. CalculateCH , BEP

ω Qw0.5, BEP )0.75

(3)

In this sense, the correlations of Stepanoﬀ [26], Gülich [27], and Monte Verde [28] were employed in this paper and yielded the results presented in Fig. 4. As can be observed, none of the calculated BEP coincided with the experimental curves, since the methods of Stepanoﬀ [26] and Monte Verde [28] resulted in overestimated values, while the correlation of Gülich [27] produced underestimated values. Although no correction factor can calculate a BEP with values that match the curves in Fig. 4, it is possible to note that the correlation of Monte Verde [28] is able to provide the best prediction with the lowest deviation from the experimental data. Therefore, in this study, the corrected oil ﬂow rates obtained via Monte Verde [28] will be considered as the ones that correspond to the BEP. For these ﬂow rates (xaxis), the corrected pump heads (y-axis) will be extracted from the performance data acquired in the experiments (curves). As a result, a matrix for the two-phase ﬂow tests will be deﬁned in Section 4.1. The reason for the method of Monte Verde [28] to provide the best results is related to the type of pump studied by each author. While Stepanoﬀ [26] and Gülich [27] investigated common centrifugal pumps, usually with large impellers and volutes, Monte Verde [28] conducted tests with an actual ESP employed in the petroleum industry, a mixed ﬂow pump with small impellers. Therefore, the method of Monte Verde [28] is the most suitable for this paper, in which an ESP prototype is used instead of a standard centrifugal pump.

Fig. 3. Performance curves of the prototype working with water and oil. The water curves were extracted from Monte Verde et al. [11].

ωs =

ρo ω R2 μo

(7)

(8) (9) (10)

(11)

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water drops appear in dark color because of the dye added to enhance the contrast between the phases. A single water drop can present several geometries along its path through the impeller. As shown in Fig. 8, a water drop enters the channel with a spread shape and undergoes deformation due to the interaction with the continuous oil phase. This circumstance causes the water drop to acquire an elongated shape in the middle of the channel. The elongated drop has a nucleus and a tail (a). As this water drop moves, its tail becomes thinner and longer, and new nuclei are formed (b). The water drop ﬁnally breaks up into many smaller, elliptical drops (c), which remain elliptical until the end of their trajectories. Perissinotto et al. [24], working with oil drops in a water continuous medium, did not observe such dependence between size and shape. In their case, breakage events were not detected inside the impeller, and only spherical and elliptical oil drops geometries were identiﬁed. These divergences are possibly explained by diﬀerences in liquids properties. Perissinotto et al. [24] investigated oil drops with a viscosity of 0.220 Pa s (220 cP) and an interfacial tension of 34 mN/m, in O/W dispersions with a viscosity ratio ( μo / μ w ) of about 240. On the other hand, in this current study, the water drops have a considerably lower viscosity of 0.00090 Pa s (0.90 cP) and an interfacial tension with a 30% lower value of 24 mN/m, in W/O dispersions with a viscosity ratio ( μ w / μo ) of about 0.05. Still regarding the morphology of water drops, the ﬂow images suggest a considerable variation in the geometric shapes and characteristic sizes as a function of the operational conditions. As the impeller rotation and the oil ﬂow rate increase, the water drops become gradually smaller, as can be seen in Fig. 9. High rotations and ﬂow rates lead to larger centrifugal forces and oil velocities, which intensify the shear stresses in the oil medium and increase the energy available for water drop deformation with consequent breakup. More detailed results are available in Video 1, which contains ﬂow images of the four conditions shown in Fig. 9 (FC-1, FC-2, FC-3, FC-4). The reproduction rates vary from 10 fps to 15 fps, meaning that the images are 100–166 times slower than the real impeller. As can be noted in the video, the occurrence of deformation and breakage events depends on the ﬂow conditions. The characteristic size of the water drops is inversely proportional to the impeller rotational speed and the oil ﬂow rate. The isolated inﬂuence of the oil ﬂow rate is illustrated in Figs. 10 and 11, for constant rotational speeds of 600 rpm and 900 rpm, respectively. As the ﬂow rate increases, the water drops become smaller, showing a clear eﬀect on the breakage events that occur within the impeller. This connection between water drop size and pump operational condition agrees with the results achieved by Perissinotto et al. [24]. Despite the diﬀerences in ﬂuids properties reported above, both oil and water drops have similar qualitative behaviors regarding the dependence of the characteristic sizes on the ﬂow conditions. This result is consistent, as the rotations (300 rpm to 1200 rpm) and ﬂow rates

Fig. 4. Best eﬃciency points calculated via correlations and compared to experimental curves.

4.1. Test matrix The visualization tests were conducted at eight ﬂow conditions presented in Table 2. Four rotational speeds (N ) were chosen for the prototype and the oil ﬂow rates (Qo ) were selected according to the BEP at each rotation. These points were previously deﬁned, in Section 3.2, from the analysis of single-phase performance curves. As stated in Section 3.1, water was injected into the prototype at 0.0072 m3/h (2 ml/s), a value that corresponds to a constant timeaveraged ﬂow rate, because the peristaltic pump works in pulses of approximately three seconds. This time-averaged injection rate is very low in comparison with the oil ﬂow rates, resulting in a mixture with quite low water cuts (ϕ ) between 0.26% and 1.33%, as can be seen in Table 2. It is important to explain that the water cut (ϕ ) is not controlled during the experiments, as the water injection rate cannot be modiﬁed. Thus, the diﬀerent water cuts introduced in the test matrix are just the mathematical result of a constant water injection rate divided by the sum of a variable oil ﬂow rate and the constant water injection rate. The ﬂow conditions FC-1 to FC-8 are highlighted in Fig. 5. The red points FC-1 to FC-4 represent the operational conditions at the BEP, while the blue points FC-5 to FC-8 correspond to 80% and 120% of BEP. As can be observed, the rotations (300; 600; 900; and 1200 rpm) and ﬂow rates (80; 100; and 120% of BEP) analyzed in this current paper are the same conditions deﬁned by Perissinotto et al. [24] to investigate oil drops in O/W dispersions. 4.2. Qualitative analysis The two-phase water-in-oil ﬂow within the impeller was visualized with an HSC. This equipment was conﬁgured to capture ﬂow images with a size of 1500 × 1500 pixels, at acquisition rates from 1000 to 2000 fps, and an exposure time of 12 µs. The ﬂow visualization allows a qualitative analysis on the topological arrangement of the phases. In this context, the captured images reveal that, in all the operational conditions FC-1 to FC-8 (Table 2), the same ﬂow pattern is observed within the pump impeller, with the presence of water drops dispersed in a continuous oil ﬂow, as shown in Fig. 6. The ﬂow images also facilitate the investigation on the morphological attributes of the dispersed phase, making possible to observe that the geometric shape of the water drops is strongly aﬀected by their size. The smaller drops always have a spherical or elliptical shape, while the larger drops usually have irregular geometries. As Fig. 7 displays, it is common to identify drops with an elongated (a) or a spread shape (b). The oil phase is transparent in the image, the impeller is white, and the

Table 2 Test matrix with eight operational conditions. Flow condition

80% BEP

100% BEP

120% BEP

N = 300 rpm

–

–

N = 600 rpm

Qo = 0.97 m3/h ϕ = 0.74 v/v% (FC-5) Qo = 1.57 m3/h ϕ = 0.46 v/v% (FC-7) –

Qo = 0.54 m3/h ϕ = 1.33 v/v% (FC-1) Qo = 1.21 m3/h ϕ = 0.60 v/v% (FC-2) Qo = 1.96 m3/h ϕ = 0.37 v/v% (FC-3) Qo = 2.76 m3/h ϕ = 0.26 v/v% (FC-4)

N = 900 rpm

N = 1200 rpm

6

Qo = 1.45 m3/h ϕ = 0.50 v/v% (FC-6) Qo = 2.35 m3/h ϕ = 0.31 v/v% (FC-8) –

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phase probably has a lower intensity, as the oil is a much more viscous liquid ( μo = 18 cP ) than water. For the same reason, however, it is expected that the oil is exposed to more intense forces due to higher shear stresses inside the impeller channels, considering a simple analysis on viscous terms in the Navier-Stokes equation for Newtonian ﬂuids. These shear stresses combined with the liquids properties reported above, i.e., a low viscosity ratio ( μ w / μo = 0.05) and a relatively low interfacial tension (σo / w = 24 mN/m ), possibly explain the frequent occurrence of breaking processes detected in the ﬂow images for the W/O system. (Other important mechanisms for water drop breakup will be discussed in Section 6). Therefore, when the required energy is available, the water drops seem to break up very easily. This fact became quite evident during preliminary experiments, in which emulsion formation was observed in the test facility, probably produced outside the impeller, in the pipes and accessories (elbows, tees, valves) or within the booster pump. The identiﬁcation was possible by a simple visual inspection, since the mixture acquired a turbid appearance with a light blue color due to the dye added into the water phase. An emulsion sample was extracted from the test setup and observed through an optical microscope Leica DM 2700, resulting in the image displayed in Fig. 12. As can be seen, the water drops identiﬁed in the emulsion have spherical shapes with maximum equivalent diameters of 50 µm, approximately. In order to avoid the undesirable formation of emulsions, a separator was designed to heat the mixture, installed in downstream of the prototype, and used during the visualization tests. Details about this separation device and its operational procedure are available in Section 2.

Fig. 5. Operational conditions FC-1 to FC-8 (colored points) plotted on the performance curves.

5. Quantitative results Fig. 6. Water drops dispersed in continuous oil ﬂow at ﬂow condition FC-2.

The ﬂow images introduced in Section 4.2 were processed with computational codes. These routines are used in Section 5.1 to evaluate equivalent diameters and in Section 5.2 to investigate the motion and paths of water drops within the channels. The kinematics of a sample of water drops is then analyzed in Section 5.3 with the calculation of quantitative parameters such as velocities and residence times.

(80–120% of BEP) investigated by Perissinotto et al. [24] on O/W dispersions are identical to the conditions analyzed in this paper on W/ O dispersions. However, a relevant diﬀerence can be noticed with regard to the region of the impeller where the breakage events occur. While, in this study, it was noted that many water drops break up within the impeller channels, Perissinotto et al. [24] observed that most oil drops did not break up inside the impeller, but just before entering it, in a region where the HSC could not capture images. In this prototype region, the ﬂow undergoes a sudden change of momentum due to the presence of a curve and a contraction. For O/W dispersions, these pump geometric characteristics were numerically investigated by Perissinotto et al. [25], who identiﬁed high turbulent energy dissipation rates in the continuous water ﬂow phase, a condition believed to be the main cause of the oil drop breakup in the impeller entrance zone. Nevertheless, in the case of the W/O dispersions studied in this paper, it is possible to predict that the turbulence in the continuous oil

5.1. Equivalent diameter and size distribution A MATLAB routine was developed to quantify the characteristic size of water drops. The code opens an image, converts it into a new binary image, selects a single channel as the region of interest, and analyzes it to detect diﬀerences between the black and the white pixels. Each element larger than one pixel, or 0.10 mm approximately, is considered as a water drop, whose area is quantiﬁed by counting the pixels that compose it. The resultant value is converted into an equivalent diameter, deﬁned as the diameter of a circle with the same area of the selected water drop. It is important to highlight that, as the ﬂow images are captured

Fig. 7. Water drops at FC-2 with irregular geometries: (a) elongated shape; (b) spread shape. 7

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Fig. 8. Water drop breaking into new drops at FC-2: (a) original drop with elongated shape; (b) long and thin tail with nuclei indicated by arrows; (c) new small drops indicated by numbers.

between 0.10 and 5.0 mm, where the majority of them (nearly 25%) was found between 0.75 and 1.00 mm. The results are all displayed in Fig. 13, which contains histograms of size distribution in terms of number of water drops, as well as adjustments of log-normal distribution for comparison. The y-axis represents the frequency by number, which is the number of drops with a given diameter divided by the total number of drops. The impeller rotations and oil ﬂow rates clearly modify the drop sizes. For instance, at FC-1, 62% of the water drops are smaller than 1 mm and 10% are bigger than 3 mm while, at FC-4, 82% of them are smaller than 1 mm and only 0.2% are bigger than 3 mm. This dependence between ﬂow condition and drop diameter is also

from the front plane of the impeller, the code detects only the front area of the water drops instead of their volume. The third dimension, therefore, is not considered in the estimation of equivalent diameters. However, although volumes are not detected by the MATLAB code, they can be calculated posteriorly from the equivalent diameters, supposing the water drops are perfect spheres. Using this routine, almost 5000 water drops were analyzed from 40 ﬂow images at the conditions FC-1, FC-2, FC-3, and FC-4. The selected images were evenly distributed in the total set of captured images. Hence, these images were completely independent from each other and, as a result, each drop was detected only once by the computer code. The investigated water drops presented equivalent diameters

(a)

(b)

(c)

(d)

Fig. 9. Water drops in the impeller at (a) FC-1; (b) FC-2; (c) FC-3; and (d) FC-4. 8

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Fig. 10. Water drops in the impeller at 600 rpm: (a) FC-5 and (b) FC-6.

observed in the log-normal distributions: as the rotational speeds and oil ﬂow rates increase, the peak frequency gradually rises and shifts to left, while the standard deviation decreases. According to Crow and Shimizu [34], the log-normal distribution is suitable to describe drop sizes in systems where drop breakup is dominant. Other distributions are also relevant for this purpose, such as the Rosin-Rammler or Weibull one. Many experimental studies use these distributions to describe drop sizes, e.g. Morales et al. [21] for centrifugal pumps. Therefore, the quantitative results displayed in Fig. 13 are totally congruent with the qualitative observations made in Fig. 9. As discussed in Section 4.2, high pump rotations and ﬂow rates are associated with more intense shear stresses in the continuous phase ﬂow, creating a quite favorable condition for water drop breakup, which leads to a consequent reduction in the equivalent diameters. Some authors, such as Galassi et al. [35], prefer to present size distributions in terms of volumes. In centrifugal pumps, the volume distribution is particularly useful to identify the presence of large drops and the volume they occupy in the impeller channels. For spherical drops, e.g., volume is a function of the diameter to the third power, therefore a 3 mm drop occupies a volume 27 times larger than a 1 mm drop. In this sense, the same 5000 water drops analyzed by the MATLAB routine had their volumes calculated from their equivalent diameters. The results are displayed in Fig. 14, with histograms of size distribution and log-normal adjustments for a comparison. The y-axis represents the

Fig. 12. Water-in-oil emulsion observed with an optical microscope.

frequency by volume, deﬁned as the volume occupied by a sample of drops with a given diameter divided by the total volume of the entire population. As can be noticed in Fig. 14, the distribution by volume emphasizes the dependence between drop size and ﬂow condition. The histogram bars are concentrated on the right at FC-01 and gradually move to the

Fig. 11. Water drops in the impeller at 900 rpm: (a) FC-7 and (b) FC-8. 9

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Fig. 13. Size distributions by number of drops at: (a) FC-1, (b) FC-2, (c) FC-3, (d) FC-4.

left, up to FC-4, as rotation and ﬂow rate increase. Signiﬁcant diﬀerences can be observed between Figs. 13 and 14, especially for FC-1 and FC-2. For instance, at FC-1, only 10% of the water drops are bigger than 3 mm (Fig. 13), but they are responsible for 58% of the volume occupied by the population (Fig. 14). Similarly, at FC-4, 82% of the drops are smaller than 1 mm, but they represent only 26% of the total volume. Diﬀerences in drop diameters at each ﬂow condition become more evident with the cumulative distributions displayed in Fig. 15. The Sauter diameter (d32 ) is a very useful parameter to evaluate the mean diameter of dispersed liquid drops [36]. It depends on the measured diameter of each drop (d) in the analyzed population (n ), as Eq. (12) shows. Besides the Sauter diameter d32 , another interesting parameter is d 95 , which represents a measure of the maximum diameter. Essentially, d 95 is the diameter below which 95% of the population is contained, i.e., 95% of the population have diameters smaller than d 95 .

and maximum diameters are often observed in size distributions. For example, Morales et al. [21] found d32 = 0.495 d 95 for O/W dispersions within a centrifugal pump, while in this current paper d32 = 0.835 d 95 is valid for W/O dispersions. The results achieved in this section on W/O dispersions agree with the results obtained by Perissinotto et al. [24] on the characteristic size of oil drops in O/W ﬂows. Estimating and controlling the size of ﬂuid particles is crucial to many engineering processes in food, cosmetic, pharmaceutical, and other industries. 5.2. Motion and trajectory Another MATLAB routine was developed, this time to remove the rotation from the impeller in the ﬂow images. As the impeller moves clockwise, the routine should move each image counterclockwise at the same rotation speed. As a result, it is produced a static impeller in the processed images, something equivalent to performing tests with an HSC that rotates integrally with the pump shaft. The rotation removal enables an analysis on the trajectories of water drops inside each channel. Without the MATLAB routine, the drop trajectory would have a spiral shape crossing all the channels, therefore the analysis would be much more diﬃcult. Using a sample of processed images, thirty water drops were tracked at the condition FC-3. As can be seen in Fig. 17, these drops execute random paths within the channels. Some perform central trajectories while others remain close to a blade. Many water drops are deviated along their path, possibly as a consequence of particle-wall, particleparticle, and particle-ﬂuid interactions, with presence of pressure, drag, and lift forces, virtual mass, and other eﬀects frequently reported in the literature [37,38]. Ten other drops were tracked in a single channel at condition FC-2.

n

d32 =

∑i = 1 di3 n ∑i = 1

di2

(12)

The same 5000 water drops had their d32 and d 95 diameters calculated and the results are available in Table 3. The diameters conﬁrm that higher rotational speeds and oil ﬂow rates cause the characteristic sizes to decrease: d32 and d 95 undergo 56% of reduction as the ﬂow conditions change from FC-1 to FC-4. Table 3 also contains the rotational Reynolds number (Reω ) estimated for W/O ﬂows. Reω is calculated according to Eq. (3). There is no consensus on the critical Reynolds number that establishes the transition from laminar to turbulent regime inside rotating machines. As can be seen in Fig. 16, there is an almost linear relation between d32 and d 95 for the analyzed data. In fact, linear relations between mean 10

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Fig. 14. Size distributions by volume of drops at: (a) FC-1, (b) FC-2, (c) FC-3, (d) FC-4.

Fig. 15. Cumulative size distributions by volume of water drops. Table 3 Mean and maximum diameters of a sample of water drops in diﬀerent ﬂow conditions. Flow condition

Rotational Reynolds, Reω

Number of drops, n

Sauter mean diameter, d32

95% maximum diameter, d95

FC-1 FC-2 FC-3 FC-4

4516 9032 13,548 18,064

524 1140 1482 1496

2.76 mm 2.18 mm 1.48 mm 1.20 mm

3.26 mm 2.24 mm 1.62 mm 1.42 mm

Fig. 16. Mathematical relation between maximum diameter d 95 and mean diameter d32 .

Their trajectories are shown in Fig. 18, composed of eight ﬂow images, each one captured at a diﬀerent time instant (t ) displayed on the top right corner. As can be observed, the water drops take less than 0.1 s to cross the channel in trajectories parallel to the pressure blade. Fig. 18 also suggests that most water drops are grouped on the left side of the channel, i.e., they move closer to the pressure blade than to the suction blade. These two blades are named with the abbreviations PB and SB, respectively, in the ﬁrst image that composes Fig. 18. 11

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V=

dy dx îx + îy = x ̇ îx + y ̇ îy dt dt

(13)

In this case, the magnitude V of the velocity vector V is obtained as follows. 1/2

dy 2 dx 2 V = ⎡⎛ ⎞ + ⎛ ⎞ ⎤ ⎢ ⎝ dt ⎠ ⎝ dt ⎠ ⎥ ⎣ ⎦

= [(x ̇)2 + (y )̇ 2]1/2

(14)

As a consequence of the MATLAB code used for rotation removal in Section 5.2, the coordinate system employed to deﬁne the water drop position is considered a non-inertial frame of reference that rotates integrally with the impeller. Thus, the velocity vector (V) calculated in Eq. (13) does not include the tangential component due to the impeller rotation, proportional to the angular speed (ω ) and outer radius (R ). Using the velocity diagram of elementary turbomachinery theory [40] as a reference, V is equivalent to a relative velocity vector that, in an idealized condition, would have a direction parallel to the impeller blades. Since the positions are available as discrete values in a table, the velocities must be determined via numerical derivations. In this paper, a central ﬁnite-diﬀerence method is employed with a step in the order of Δt , the time interval between two consecutive images captured by the camera during the experiments, i.e., a number around 0.001 s. The derivatives are calculated as follows, where f (t ) represents x and y and f ̇ (t ) symbolizes dx / dt or dy / dt [41]. As can be observed, in this ﬁnitediﬀerence method, the i-th value of f ̇ (ti ) depends on the adjacent values of f (ti ) in the table, i.e., f (ti + 1) and f (ti − 1) in the instants ti + Δt and ti − Δt . The results are ﬁnally corrected with the moving average, an important statistical method used to smooth out the short-term ﬂuctuations and highlight the long-term trends.

Fig. 17. Trajectories of 30 water drops at condition FC-3.

This preferential trajectory of water drops, next to pressure blades, was not identiﬁed by Perissinotto et al. [24] in the case of O/W dispersions. The authors actually noticed that the oil drops initiated their movement near the suction blade and gradually deviated toward the pressure blade. A deeper analysis is needed, in a future study, to investigate the causes of such diﬀerences between the trajectories of drops dispersed in W/O and O/W ﬂows. Lateral deviations in rotative environments may be generated by the Coriolis eﬀect, as a result of geometry and angular rotation. In addition, numerical simulations conducted by Perissinotto et al. [25] on O/W dispersions revealed the existence of velocity and pressure gradients in the channels, which were likely to be the cause of oil drops laterally deviating from suction to pressure blades. These results, however, are not necessarily valid for W/O dispersions, for which a further analysis is required and suggested as a future study. In multiphase ﬂows, small ﬂuid particles may work as tracers that indicate the possible path lines of the continuous phase [39]. In this context, the results achieved on water drops in this section possibly reveal the main characteristics of the oil phase. A suggestion for a future study on W/O mixtures is to further research the behavior of the continuous oil ﬂow around the dispersed water drops using experimental methods such as the Particle Image Velocimetry (PIV) or even CFD numerical simulations.

f ̇ (t ) =

f (t + Δt ) − f (t − Δt ) 2 Δt

(15)

Four water drops were tracked in the conditions FC-1 to FC-4 and had their velocities calculated, as presented in Fig. 19. In each graph, the positions x (t ) and y (t ) deﬁne the trajectory displayed in blue color on the xy plane, where the channel blades are also drawn. The impeller center corresponds to the position x , y = 0, 0 . In the vertical axis, the red curve represents the intensity, V , of the relative velocity vector, V, whose direction is always tangent to the drop trajectory. The graphs also contain information regarding the equivalent diameter (d ), the residence time (tres ), and the average velocity (Vavg ) of the water drops. The residence time is a measure of how much time the drop spends inside the channel, from the impeller entrance to its exit, while the average velocity is the ratio between the distance traveled by the drop and the time elapsed during its path in the impeller. As can be seen in Fig. 19, the velocity curves suggest that the water drops undergo a deceleration from the impeller inlet to the outlet. This reduction in relative velocity V is coherent because the channel behaves like a nozzle: its cross-sectional area increases with the impeller radius [40] leading the ﬂow velocity to decrease. This result is accordant with the one achieved by Perissinotto et al. [24] for oil drops tracked in a non-inertial frame of reference. Still, it is important to remember that V does not take into account the tangential velocity due to the impeller rotation, which always increases along with the radius. Furthermore, Fig. 19 indicates that the water drops undergo an intense acceleration near the impeller outlet. In this exit region, the liquids move from a rotating zone (impeller) to an adjacent stationary zone (diﬀuser). Signiﬁcant diﬀerences between rotational speeds, in the moving impeller and motionless diﬀuser, aﬀect the acceleration of the water drops. This result is completely consistent with the one obtained by Perissinotto et al. [24] with regard to their oil drops. The water drop velocity depends on the ﬂow condition as well. As the impeller rotation increases from 300 to 1200 rpm and the oil ﬂow rate increases from 0.54 to 2.76 m3/h, the average velocity (Vavg ) rises proportionally from 0.36 to 1.66 m/s. In the W/O dispersion, the water

5.3. Water drop kinematics The activity of tracking water drops, presented in Section 5.2, resulted in a table with the position of each drop as a function of time. This data was processed for an analysis of the water drop kinematics. The procedure and the results are described in this section. The drop position, in pixels, is ﬁrstly obtained in a Cartesian coordinate system with its origin in the upper left corner of the images. The origin is translated to the impeller center while the pixels are easily converted to millimeters. As a result, the position values can be used to calculate the velocity in a Lagrangian approach, considering the water drop as a rigid particle of negligible size. The velocity vector (V) is then determined from the ﬁrst derivatives in time (t ) of the position vectors, which have magnitudes x and y in the directions îx and îy respectively, as follows [40].

12

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Fig. 18. Trajectories of 10 water drops at condition FC-2.

impeller rotation and oil ﬂow rate, decreasing from 152 ms at FC-1 to 30 ms at FC-4. The residence time is a relevant parameter to understand the dynamics of the water drop motion, because it reﬂects the time that the dispersed drops are exposed to forces, shear rates, and other phenomena that may induce the occurrence of breakage events, as

drops are transported by the continuous oil, so higher oil ﬂow rates imply larger water drop velocities. This dependence between water drop velocity and pump operational condition also agrees with the results reached by Perissinotto et al. [24] on O/W mixtures. Otherwise, the residence time (tres ) is inversely proportional to the 13

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Fig. 19. Velocity of individual water drops at (a) FC-1; (b) FC-2; (c) FC-3; and (d) FC-4.

order of 1 m/s, while, using the data from Perissinotto et al. [24], Ca is estimated to be around 0.03 for an O/W ﬂow. Therefore, as can be noticed, O/W dispersions have lower capillary numbers, a fact that suggests that the cohesion forces of the dispersed phase are suﬃciently strong for the oil drops not being deformed by the drag forces imposed by the continuous water medium. The opposite interpretation is valid for the higher capillary numbers found in the W/O dispersions. The capillary numbers calculated for the W/O and O/W mixtures corroborate with the qualitative observation of ﬂow images in this paper and in other studies in the literature, such as Bazhlekov et al. [44]. While oil drops have lower Ca related to a spherical shape without deformations [24], the water drops present higher Ca associated with irregular morphology with occurrence of elongations and fragmentations, as reported in Section 4.2. Considering the ratio between the viscosities of continuous and dispersed phases, these observations are all consistent with the results achieved by Bazhlekov et al. [44], a study partially based on the Grace curve [45], a diagram often used in literature to deﬁne critical capillary numbers in ﬂows subjected to shear stresses. Other non-dimensional numbers may be interesting to explain the phenomena observed in this paper. The Ohnesorge number [18] also relates viscous forces to surface forces and the Bond and Morton numbers are used together for the prediction of bubbles and drops

discussed in Section 4. Although the four water drops are a quite small sample, the velocity results are already consistent with other studies described in Section 1, such as Perissinotto et al. [24]. In fact, tracking water drops is a diﬃcult task, because many of them deform and break up in the channels, giving rise to new water drops along the trajectory, as reported in Section 4. The calculation of velocities allows the estimation of interesting parameters such as drag force and virtual mass eﬀect [42], as well as non-dimensional numbers such as the Weber number and the capillary number (Ca ). This number, the ratio of viscous forces to surface forces, depends on the velocity of the continuous phase [17]. For W/O dispersions in pump impellers, however, it can be assumed that the velocity of the water drops is similar to the velocity of the continuous oil phase, so that Ca may be written as a function of the water drop velocity (V ), as well as of oil viscosity ( μo ) and oil/water interfacial tension (σo / w ).

Ca =

μo V σo / w

(16)

Inside the porous environment of petroleum reservoirs, Ca can reach 10-8, indicating a relevant presence of capillary forces [43]. In this study, Ca is about 0.8 for a W/O system with a water velocity (V ) in the 14

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shapes in unhindered gravitational motions of continuous ﬂuids [19]. However, as reported in Section 1, these numbers do not consider the rotating environment of the impeller, where important eﬀects arise, such as the centrifugal and Coriolis forces. These forces, in addition to drag forces, pressure gradients, and oil velocity proﬁles would be necessary for a deeper understanding on the dynamics of W/O dispersions, a subject that is beyond the scope of this paper and, therefore, will be suggested as a future study.

water drop to break up.

Fi = (πd 2) ⎛ ⎝

According to Carneiro et al. [46], existing drops in a continuous phase may break up because of interactions with local velocity or strain gradients in the ﬂow. Another relevant condition for fragmentation may be related to interfacial waves generated by shear ﬂows such as in the case of liquid jets, in processes named capillary breakup and atomization. Furthermore, interfacial instabilities may create new dispersed drops in a condition called entrainment. Such processes for drop breakup are usually dependent on the ﬂow ﬁeld, the ﬂuids compositions, the phases concentrations, among other variables. As discussed in the last sections, turbulence may also play an important role on drop breakup, especially for pumps operating with twophase ﬂows in which the continuous phase has a low viscosity in comparison to the dispersed phase [24,25]. In this context, Morales et al. [21] studied O/W dispersions in centrifugal pumps and then developed an expression for the turbulent energy dissipation rate (ε ), which was considered proportional to the hydraulic energy provided by the device. Turbulent ﬂows are composed of turbulent eddies of diﬀerent sizes, where the largest ones contain most part of the kinetic energy in the spectrum. This energy is supplied at the large scales, transferred successively to the smaller scales, and ﬁnally dissipated into heat by the ﬂuid viscosity. Mechanisms for turbulent drop breakup have been investigated for many decades since the initial studies by Kolmogorov [47,48]. According to Hinze [49], when a drop size is smaller than the largest eddies and larger than the smallest eddies, the inertial forces produced by turbulent velocity ﬂuctuations are assumed to be responsible for drop breakup. However, cohesive stresses due to interfacial tension and internal viscous stresses inside the drop act against the drop deformation. The breakage events are thus the result of a balance between disruptive and cohesive stresses. For a spherical water drop dispersed in an oil ﬂow, the disruptive (τd ) and the cohesive stresses induced by interfacial tension (τσ ) and viscosity (τμ ) are functions of the turbulent energy dissipation rate (ε ), the water drop diameter (d ), the oil ( ρo ) and water densities ( ρw ), the interfacial tension (σo / w ), and the water viscosity ( μ w ), as follows [46]. (17)

σo / w τσ ∝ d

(18) 1/2

τμ ∝

μ w ⎛ τd ⎞ ⎜ ⎟ d ⎝ ρw ⎠

(20)

Hence, according to Eq. (20), for a constant interfacial tension, the larger water drops are more susceptible to rupture than the smaller ones. This mechanism for drop breakup based on interfacial forces is quite frequent in pumps, valves, and chokes used in the petroleum industry, where high shear stresses develop. The impeller blades of electrical submersible pumps, for example, are a propitious region for breakage events caused by intense shear rates, which generate very stable W/O dispersions and emulsions undesirable for the oil production [46]. Using the concepts discussed above, some authors estimated the maximum stable drop diameter, which was found to be a function of liquids properties and velocity ﬂuctuations. For agitated systems, such as stirred tanks, the studies by Chen and Middleman [52], Brown and Pitt [53], Nienow [54], and Boxall et al. [55] suggested the maximum drop diameter is inversely proportional to the impeller diameter and rotational speed. In the case of pumps, Wichterle [56] proposed a model to estimate the drop breakup caused by shear stresses in impeller blades, and Lutz et al. [57] used an electrodiﬀusional technique to investigate the inﬂuence of the operational conditions on the shear stresses. To summarize, the equations presented in this section may explain mathematically the observations performed in the last sections. Large water drops easily deform, elongate, and break up due to a high d that increases τd and reduces τσ , τμ , and the required Δpi . The opposite is analogously true for small drops. In addition, the liquids properties also facilitate the breakage events, since the low μ w and σo / w cause a reduction in τσ , τμ , and in the required Δpi . Moreover, when the pump works at high rotation speeds and ﬂow rates, the dispersion experiences high shear stresses which easily exceed the required Δpi , leading to water drop breakup within the channels. If the water drops were replaced by the oil drops studied by Perissinotto et al. [24], the equations would reveal an increment in τσ , τμ , and in the required Δpi , by action of the higher viscosity and interfacial tension of the dispersed oil phase. These parameters may express why the water drop breaking (W/O dispersion) is more frequent than the oil drop breaking (O/W dispersion). Unfortunately, it is diﬃcult to quantitatively estimate τd and τμ , as they depend on the turbulent energy dissipation rate (ε ), a variable that was not investigated in this paper. Morales et al. [21] proposed an expression that relates ε with d and concluded that only 0.19% of the hydraulic energy input is responsible for drop breakage in centrifugal pumps. Despite these relevant results, the authors studied O/W dispersions, while this current paper focuses on W/O mixtures. Therefore, the results achieved by Morales et al. [21] are not necessarily true for the water drops investigated in this paper. A future study based on the methodology of Morales et al. [21] would be appreciated to allow a further development of drop size models in pump impellers working with W/O dispersions as well.

6. Physical interpretation

τd ∝ ρo d 2/3ε 2/3

4 σo / w ⎞ = (A)(Δpi ) d ⎠

(19)

7. Conclusions

Besides the turbulence, another important mechanism for drop breakup is related to the interfacial energy. Tabor [50] and Adamson and Gast [51] explain that a clean liquid-liquid interface can be deﬁned as a membrane which tries to minimize the interfacial energy. The mathematical diﬀerentiation of this energy produces an interfacial force perpendicular to the interface. For a spherical water drop dispersed in an oil ﬂow, this force (Fi ) is proportional to the water drop diameter (d ) and the interfacial tension (σo / w ). It can be arranged as a function of the interfacial area ( A ) and the pressure jump across the interface (Δpi ). When the ﬂuid stresses exceed Δpi , it is expected the interface to be destabilized, leading the

In this study, experiments with single-phase oil ﬂow and two-phase W/O dispersions were performed using a pump prototype with a transparent shroud for ﬂow visualization. Eight operational conditions were investigated, in which the pump rotation varied from 300 to 1200 rpm. The oil ﬂow rates were selected according to the BEP at each rotational speed, calculated with correction factors available in the literature. In the water-in-oil experiments, a constant water ﬂow rate produced mixtures with low water cuts of about 1%. Pump performance was evaluated for operation with single-phase oil ﬂow. Compared to water, the results revealed an appreciable 15

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R.M. Perissinotto, et al.

between 30 and 152 ms, are both very dependent on the pump operational conditions. The results revealed that the relative velocity vector is also a function of the drop position, as the water drops tend to decelerate during their motion from the impeller inlet to the outlet. Near this exit zone, however, the water drops are dragged from the impeller to the diﬀuser, so they accelerate due to the diﬀerence between angular velocities in both regions. This study intends to contribute for an improved physical understanding on two-phase liquid-liquid ﬂows in centrifugal pumps, with focus on water drops and W/O dispersions. This paper can be used to support numerical simulations and to promote the proposition of simpliﬁed models with applications in the engineering industry. For a complete analysis, all the results achieved in this paper were compared with results by Perissinotto et al. [24], who investigated oil drops and O/W dispersions using the same pump prototype.

performance degradation caused by the higher oil viscosity. In the case of two-phase W/O ﬂows, the performance curves were very similar to those for single-phase oil ﬂow, as a result of very low water cuts around 1%. Thus, for the conditions investigated in this study, the presence of water dispersed in the oil medium did not inﬂuence the pump performance considerably. Flow images were captured with a high-speed camera and processed with computational routines for qualitative and quantitative analyses. For all ﬂow conditions tested, the mixture was arranged to as water drops, with equivalent diameters from 0.10 to 5.00 mm, dispersed in a continuous oil medium. Breakage events were frequently observed in the ﬂow images, indicating that the drops tend to break up along their paths in the channels, since they easily deform and elongate due to properties as a low viscosity ratio and a low interfacial tension, both related to low cohesive stresses. A strong dependence between water drop morphology and pump operational condition was also identiﬁed in the images, revealing that the drops become smaller as the impeller rotation speeds and oil ﬂow rates increase, a fact associated with larger centrifugal forces and oil velocities, which intensify the disruptive stresses and interfacial forces. Histograms with drop size distributions were determined with a computational code and compared to log-normal distributions. The diagrams conﬁrmed a dependence between ﬂow condition and drop diameter. Volume distributions highlighted the presence of large drops at low rotational speeds while cumulative distributions accentuated the diﬀerences between drop diameters in the analyzed ﬂow conditions. Drops were also tracked in ﬂow images processed with another computational code. The results suggested that many of them undergo deviations along their trajectories, as a consequence of interactions with the oil, solid walls, and other water drops. The average velocities, with values from 0.36 to 1.66 m/s, and residence times, with numbers

Declaration of Competing Interest None. 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 study. The authors also thank Artiﬁcial Lift & Flow Assurance Research Group (ALFA), Center for Petroleum Studies (CEPETRO), and School of Mechanical Engineering (FEM), all part of the University of Campinas (UNICAMP). The acknowledgements are extended to FAPESP – Process 2017/15736-3 and CAPES – Finance Code 001.

Appendix A. Velocity uncertainty Experimental measurements do not always have a complete accuracy. The reliability of a measurement depends on its maximum deviation around the best predicted value of the parameter. Moﬀat [58] oﬀers an interesting methodology to estimate uncertainties based on statistics and error propagation. This methodology can be applied to the velocity of water drops, which are calculated from the tracking procedure (Section 5.2) followed by the numerical diﬀerentiation of the position in time (Section 5.3). For the position x , for example, Eq. (15) can be rewritten as follows, where ẋi is a function of the adjacent discrete values x i − 1 and x i + 1 in the instants ti − Δt and ti + Δt respectively.

x i̇ =

xi+1 − xi−1 2 Δt

(21)

A similar idea is valid for the position y and its time derivative ẏi , as follows.

yi̇ =

yi + 1 − yi − 1 (22)

2 Δt

Using the Eqs. (21) and (22), the magnitude V of the velocity vector, previously deﬁned in Eq. (14), can be also rewritten for the instant t , as follows.

y − yi − 1 2⎤1/2 x − xi−1 2 ⎞ + ⎛ i+1 ⎞ Vi = ⎡ ⎛ i + 1 ⎢ ⎝ 2Δ t ⎠ ⎥ ⎣⎝ 2 Δ t ⎠ ⎦

(23)

As can be noted, ẋi and ẏi represent the components, in the instant t , of the velocity vector V in directions îx and îy . They depend on the variables Δt , x i − 1, x i + 1, yi − 1, and yi + 1, which have uncertainties associated with the image acquisition and tracking process. Therefore, the total uncertainty of ẋi , represented by δẋi , can be estimated as follows. 2

1/2

2

2 ⎛ ∂x i̇ ⎞ ⎞ ⎛ ∂x i̇ ⎛ ∂x i̇ ⎞⎤ δx i̇ = ⎡ ⎢ ∂x i + 1 δx i + 1 + ∂x i − 1 δx i − 1 + ⎝ ∂ Δt δ Δt ⎠ ⎥ ⎠ ⎝ ⎠ ⎦ ⎣⎝ ⎜

⎟

⎜

⎟

(24)

2 1/2

2 2 δx δx x − xi−1 δx i̇ = ⎧ ⎛ i + 1 ⎞ + ⎛ i − 1 ⎞ + ⎡ i + 1 δ Δt⎤ ⎫ 2 ⎢ ⎥ ⎨ ⎝ 2 Δt ⎠ 2 Δ t ⎝ ⎠ ⎣ 2 (Δt ) ⎦⎬ ⎩ ⎭

(25)

A similar analysis is valid for ẏi , for which it is expected an uncertainty δẏi in the same order of magnitude of δẋi . The drop tracking consists of determining the position x and y with uncertainties δx and δy , both related to errors in the selection of the exact point that corresponds to the center of the water drop in each image. These errors exist due to the computational method and also due to the user who is operating the software to track the drop. It can be deﬁned that δx and δy have values in the order of one pixel, which represents a tenth of a millimeter, or 0.10 mm. This number is constant during the tracking process, hence the uncertainties δx i + 1 and δx i − 1 in Eq. (25) have approximately a 16

Experimental Thermal and Fluid Science 112 (2020) 109969

R.M. Perissinotto, et al.

same magnitude δx ~ 10−4 m . This number is also valid for the analogous case of δyi + 1 and δyi − 1, for which δy ~ 10−4 m as well. The velocity calculation is a function of the time interval Δt between two consecutive images acquired by the HSC. This equipment, with very high temporal resolution and small uncertainty, was used in the experiments at a minimum acquisition rate of 1000 fps, which corresponds to Δt = 10−3 s . In this situation, the maximum uncertainty in the camera system can be estimated as δ Δt ~10−6 s , according to information from the manufacturer. As can be observed, δ Δt diﬀers from δx and δy by two orders of magnitude, thus the uncertainty related to the time interval is completely negligible in comparison to the uncertainty related to the water drop position. With the considerations made in the last paragraphs, Eq. (25) can be arranged as follows. With δx = 10−4 m and Δt = 10−3 s , the estimated δẋi would be 0.071 m/s. For a hypothetical water drop with a velocity ẋi in îx of approximately 1 m/s, the relative uncertainty would be about 7%. Similar values are also expected for δẏi .

δx i̇ =

2 δx 2 Δt

(26)

The same water drop, with velocities x i̇ = yi̇ = 1 m/s in the directions îx and îy , would have a resultant velocity with a magnitude of Vi = 1.41 m/s . Considering the uncertainties δx i̇ = δyi̇ = 0.071 m/s as determined above, the uncertainty δVi of the resultant velocity would present a value of about δVi = 0.071 m/s as well, estimated as follows. 2

2

2

1/2

2

2 ∂Vi ∂Vi ∂Vi ∂V ⎤ ⎡ ∂Vi δVi = ⎢ ⎛ δx i + 1 ⎞ + ⎛ δx i − 1 ⎞ + ⎜⎛ δyi + 1 ⎟⎞ + ⎜⎛ δyi − 1 ⎟⎞ + ⎛ i δ Δt ⎞ ⎥ ∂x i − 1 ∂yi + 1 ∂yi − 1 ∂x i + 1 ∂ Δt ⎝ ⎠ ⎠ ⎝ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎦ ⎣ ⎜

δVi =

⎟

⎜

⎟

2 δx 2 Δt

(27) (28)

The ﬁnal Eq. (28) was obtained with all the hypotheses discussed in the last paragraphs: Δt = 10−3 s ; δ Δt = 0 ; and δx i + 1 = δx i − 1 = δx = δyi + 1 = δyi − 1 = δy = 10−4 m . Therefore, using this example as a reference, the relative uncertainty associated with the water drop velocity would be approximately 5%. This uncertainty, however, can be reduced by statistical methods such as the cumulative moving average, which was used in this paper with sequences of three values. In this case, it is possible to estimate that the average velocities obtained from the curves of Fig. 19 have uncertainties between 2.5% (FC-4) and 11.4% (FC-1). Appendix B. Supplementary material Supplementary data to this article can be found online at https://doi.org/10.1016/j.expthermﬂusci.2019.109969.

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Experimental analysis on the behavior of water drops dispersed in oil within a centrifugal pump impeller

Experimental analysis on the behavior of water drops dispersed in oil within a centrifugal pump impeller

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