Experimental and computational advances on the impact of non-

Newtonian rheologies in centrifugal pumps performances: An

umbrella review

Presented by Diego Roncancio

Advisors: Juan Pablo Valdés, Nicolas Ratkovich, University of Los Andes

Abstract: Centrifugal pumps nowadays form part of a large number of industrial processes and day-

to-day tasks. Therefore, this equipment is operated with a broad range of fluids that can have

significant deviations from Newtonian rheology. Thus, an extensive literature review on the advances

in experimental and computational estimations on the impact of non-Newtonian fluids is carried out

in this article. It was observed a general degradation of pump performances with an increase in

effective viscosity. Moreover, viscosity modeling was found lacking for non-Newtonian fluids when

changes in rheology were significant. Furthermore, possible lines of investigation were determined.

Computational approaches showed RANS models' preference to simulate the operation of the

centrifugal pump with either Newtonian or non-Newtonian flows. Finally, essential parameters for

the performance of the pumps operating with liquid-liquid or solid-liquid flows were determined to

be particle properties and tracking (either droplets or solids), and the dispersed volume fractions.

Keywords: Centrifugal pumps, non-Newtonian, rheology, performance.

Nomenclature Subscripts

𝑎, 𝑏 Ofuchi’s coefficients [-] 𝑑𝑒𝑠 Design

𝑥, 𝑦 Gülich’s coefficients [-] 𝑜𝑝 Operating point over the baseline curve

provided in the datasheet

𝐶𝑄 Flow rate correction factor [-] 𝑣 Operating with a viscous fluid

𝐶𝐻 Head correction factor [-] 𝑤 Value for water

𝐶𝜂 Efficiency correction factor [-] 𝑜𝑝𝑡 Operating at best efficiency (BEP)

𝑅𝑒𝑂𝑓𝑢𝑐ℎ𝑖 Ofuchi’s proposed Reynolds

number [-]

𝑅𝑒𝐺ü𝑙𝑖𝑐ℎ Gülich’s proposed Reynolds

number [-]

𝑅𝑒𝜔 Rotational Reynolds number

[-]

𝐻 Head [m]

𝑄 Volumetric flow rate [m3/s]

𝜂 Overall pump efficiency [-]

g Gavitational acceleration

[m/s2]

fq Coefficient of the number of

entries for the pump [-]

𝐷2 Impeller vanes outlet diameter

[m]

𝐷1 Impeller inlet outer diameter

[m]

𝛽2 Impeller vanes outlet angle

[rad]

𝛺 Impeller angular speed [rad/s]

𝜔𝑠 Universal specific speed [-]

𝑛𝑞 Specific speed standard

definition in Europe [-]

𝑁𝑠 Specific speed defined with

customary US units [-]

𝜈 Kinematic viscosity [m2/s]

1. Introduction

A turbomachine is a device that exchanges energy between the continuous flow of a fluid and a

rotating blade system, said energy exchange might occur from the flow to the rotating machine

components or vice versa. In the first case, the machine is referred to as power delivery or turbines. In

the latter case, when energy is supplied to the fluid, the machine is referred to as power receiving, for

example, pumps, compressors, and fans. Furthermore, the mechanical energy provided in these

machines can only take two forms: velocity-associated energy (kinetic energy) and pressure-

associated energy (pressure potential energy in case of a constants density fluid) (Dick,

2015). Pumps are turbomachines whose function is to displace a fluid by imprinting pressure through

mechanical energy and plays an essential role in several industry

sectors' processes. This equipment can be divided into two major categories: i) dynamic, in which

energy is continuously added, and ii) displacement, in which energy is periodically added by

application of force to one or more movable boundaries (Karassik et al., 2001; Nesbitt,

2006). Precisely, a type of pumps known as centrifugal pumps consists of an axial intake to radial

discharge impellers, resulting in a radial discharge through a diffuser. These machines are particularly

noteworthy due to its extensive implementation. For example, in the food-processing, cosmetic,

pharmaceutical, and water treatment industries, centrifugal pumps are often used to transport fluids

such as diary, emulsions, dosage forms, and sewage, respectively.

Nowadays, the importance of motor-driven pumps in the industry can be seen in its energy

consumption, which accounted for 43% to 46% of the global electricity consumption (Stoffel,

2015). Specifically, 22% of the motor electricity consumption in the European industry is caused by

pumping systems, and 43% of the industrial electricity consumption in the EU corresponds to the

total share of the pump, fan, and compressor systems (Ahonen et al., 2012). For example, in a

multiple-effect distillation (MED), pumping power ranges from 0.7 to 1.2 kWh/ton, and in multi-

stage flash (MSF) ranges from 5 to 6 kWh/ton of distilled water (Šavar et al., 2009). In

the O&G industry, a type of centrifugal pump known as the electrical submersible pump (ESP) is

used as an artificial lift method in over 100.000 wells across the globe. Therefore, it is of great interest

to reduce this consumption by increasing the pump's efficiency, and one of the factors which

have a more significant impact on performance is the liquid's properties (Nesbitt, 2006).

Taking into account the liquid's properties, it is known that highly viscous and multiphase flow (solid-

liquid, gas-liquid, liquid-liquid, etc.) bring complications in the operation of this equipment, such as

sudden pressure drops that can lead to cavitation and an increase in the energy required to

pump (Karassik et al., 2001; Nesbitt, 2006). Notably, effective viscosity can significantly impact a

pump's functioning. Depending on the rheological behavior of a fluid, it can be divided into two

categories: Newtonian and non-Newtonian. The former is defined as those in which the effective

viscosity is not affected by variations on the shear rate or stress, contrary to non-Newtonian fluids,

which presents an effective variable viscosity as a function of either the shear rate or stress (Chhabra,

2010). Furthermore, the variation in the fluid's viscosity due to the shear rate establishes multiple

categories, depending on the tendencies developed due to said relationship. Figure 1 shows the most

common non-Newtonian fluids and highlights shear-thinning behavior since it is one of the most

frequent rheological behaviors observed in either unconventional reservoirs in the O&G (Kaminsky,

1998; Rønningsen, 2012) or multiphase pharmaceutical dosage forms (J Mastropietro, 2013).

Figure 1. Qualitative general rheogram for Newtonian and non-Newtonian fluids. Taken and adapted from (Chhabra,

2010).

Regarding multiphase flows, the most straightforward type is two-phase flows, which include liquid-

liquid, solid-liquid, and gas-liquid, and they are mostly present in both natural and industrial processes

(Yeoh & Tu, 2019). These complex flows are characterized by the existence of interfaces between

the phases and discontinuities of associated properties (Liao & Lucas, 2009). Furthermore, multiphase

flows tend to present a non-Newtonian behavior due to interaction between phases, which may be

altered by the shear rates experienced within the impellers (Yeoh & Tu, 2019). Liquid-liquid flows

are a common occurrence in the O&G (oil-water), chemical (paints), pharmaceutical (essential oils-

water), and cosmetic (emulsions) industries. There are five dominant flow patterns: disperse, mixed,

stratified, intermittent, and annular flows (Kolev, 2012). Solid-liquid flows patterns are mainly

classified as homogeneous, heterogeneous, heterogeneous, and sliding, and saltation, and stationary

bed flow (Doron & Barnea, 1996). This type of multiphase flow is often present in the O&G (sand/oil)

and water treatment (sewage) industries as slurries. The development of these particular flow patterns

depends on the flow parameters of both phases, the relative magnitudes of these flow patterns, the

fluid properties, and the pipe size or orientation (Liao & Lucas, 2009). Finally, the influence of the

viscosity does not play a significant role in the phenomena observed in pumps when handling gas-

liquid two-phase flows. Instead, gas locking and cavitation phenomena are investigated mainly due

to the discontinuities brought by a large bubble size (Nädler & Mewes, 1995). Therefore, this type of

multiphase flow will not be covered in this review.

The objective of this umbrella review is to reflect the current status of experimental and computational

advances on the impact of non-Newtonian rheologies in centrifugal pumps, critically examine the

growth in this field, provide current limitations, and from there identify directions for future

research. An understanding of this phenomenon can be implemented to reduce and optimize energy

usage by centrifugal pumps in the industry. Furthermore, the design and implementation of these

pumps can be improved with the clarification of these interactions. Therefore, this review will inquire

briefly on the impact of Newtonian rheologies in pumps as a base and starting point of this area, and

from there, review current approaches of single-phase, solid-liquid, and liquid-liquid non-Newtonian

approaches. Mainly, experimental processes, results, and achievements are summarized for each

paper considered.

2. Newtonian studies

This section can be summarized in Figure 2 in which the determining focuses of the experimental and

computational approaches can be observed. Further analysis is performed for this focus, including

contributions to the field and lacking areas.

Figure 2. Newtonian experimental and computational focuses.

2.1. Experimental

One of the first realizations with the implementation of pumps in the industry was: pumping highly

viscous Newtonian fluids with centrifugal pumps has been regarded as a complication in the operation

of these machines. Ippen (1946) conducted one of the first studies of the effect of said viscosity in the

performance of the pump under controlled laboratory conditions. In this study, over 220 tests with

varying viscosities (up to 2200 cP) on four variants of centrifugal pumps with no special cooling or

heating equipment. The investigation focused on the influence of varying Reynolds numbers, which

were defined in terms of the rotational speed and kinematic viscosity, over performance parameters

(efficiency loss, head ratio, and input power ratio). The results depicted three different performance

regions (𝑅𝑒 < 104, 104 < 𝑅𝑒 < 106, and 𝑅𝑒 > 106) and were associated with their

respective significant losses. The fluid's viscosity impact became significant in the third region (𝑅𝑒 <104), presenting a downward trend in the head rise and capacity.

Following closely, the Hydraulic Institute (HI) (1948) proposed the implementation of empirical

viscosity correction factors, as can be seen in Error! Reference source not found., to predict the

performance of centrifugal pumps based on its operation with water. This method predicted a

decrease in the head delivered and the flow handled for highly viscous fluids, considering a range of

viscosities up to 3000 cP. Nonetheless, this study only estimates four operational flowrates from

the Best Efficiency Point (BEP) (60%, 80%, 100%, and 120%), and thus the remaining

flowrates must be extrapolated.

In the same line as Ippen, Stepanoff (1948) proposed corrections using specific definitions of

Reynolds numbers. In this investigation, the experiments were conducted on an ESP with viscous

fluids up to 2020 cSt. The results of the study reported significant head degradation because of an

increase in viscosity. However, it was noted that the specific speed at the BEP remains constant,

regardless of the fluid's viscosity. Therefore, only one correction factor, either head or capacity, was

proposed based on the calculation of the Reynolds number and the specific speed when operating

with water at the BEP. As these were the first investigations in this field, it is noted that all of the

research focused on statistical analyses and purely experimental methods to explore the behavior of

the centrifugal pumps with particular success in the prediction of their performance. Nonetheless,

these estimations present significant constraints in the operation range of the pump to be accurate.

With the improvement in pumping technology and varying operational conditions, the HI

approach presented significant discrepancies between the predicted and measured values resulting

in Gülich (1999a) questioning the accuracy of this method and researching its limits. The

investigation revealed that the HI procedure was well fitted for a narrow range of specific speeds.

After that, Gülich (1999b) proposed a new procedure for highly viscous fluids based on the

assumption of dominating disk friction losses and friction losses in the hydraulic passages of the

pump. The relevant equations of this model are depicted in Error! Reference source not found.,

where the modified Reynolds is calculated based on the rotating Reynolds, universal specific speed,

and impeller eyes per impeller. The advantage of this method, as pointed out by the author, is that it

can be applied to any pump and consider its features.

Given the rapid development of technology, new devices capable of thorough measurements

contributed to deepening the research capabilities. For example, by employing laser Doppler

velocimetry (LDV) techniques, Li (2000) focused on the effect of viscosity on the pump performance

and flow patterns at the impeller. It was noted that the flow patterns near the inlet section (blade

suction side) at the BEP vary significantly for different viscosities. The oil's relative velocities were

lower in comparison to those of water, implying a higher energy transfer to the oil by the impeller at

the same work conditions. Additionally, this work agreed with Gulich (1999b) on the dominance of

frictional losses over the performance degradation noted when handling viscous fluids. In further

research, Li et al. (2002) criticized the HI approach stating the lacking applicability of this method

given the advances in the currently used oil pumps. Moreover, it was noticed that head correction

factors were independent of the operational condition for oil viscosities under 100 cSt but heavily

depended on these conditions for larger viscosities.

Contrary to Gülich and Li, Turzo and Takacs (2000) proposed a computational procedure, based on

the HI method and experimental databases, to calculate head and efficiency derating factors for a

given operational condition. This procedure consists of a set of equations used for computer

programming instead of the traditional HI charts. This model was developed to be valid for the

relative capacity range from 20 to 120%, and the results show that errors in pumping head calculations

were less than 2.5% for pumping capacity less than 100%. Above 100% pumping capacity, the error

increases but is still less than 4%—this procedure allowed for a faster estimation of the performance

of the pump. However, since the equations were obtained from the regression of digitalized HI charts,

this procedure is also restricted by the operation range of the pumps considered in the charts.

Furthering the procedure proposed by Gülich, Amaral (2009) studied as well the impact of viscosity

on pump performance but concentrated on the energy-transfer processes taking place inside the

pump's internal components. His work showed experimentally that the HI correlations were unable

to predict the head rise correctly for a three-stage ESP handling viscous Newtonian flow up to 1020

cP. This was attributed to the lack of representation of the flow interactions present in the impellers

and diffusers in the available pump models. The author concluded that any generalizing approach

dealing with the influence of viscosity on the pump performance must consider physical dimensions,

operational conditions, fluid properties, and these interactions, in order to give a proper measure of

the derating factors over an extended range of operating conditions.

Simultaneously, Solano (2009) developed a dimensionless analysis based on the conservation

equations as a method for calculating ESP viscous performance. These research tests were

conducted from 3600 to 2400 rpm using water and mineral oil. The results of the validation of the

affinity laws showed an average error of 3% and 10% for the total pump head and single-

stage head, respectively. Thus, concluding that the use of dimensionless analysis is a proper

procedure to determine the performance of the pump when handling viscous fluids.

Fleischfresser et al. (2015) validated, with experimental data, a simple single-phase approach that

predicts the pump's hydraulic performance based on a few accessible hydraulic dimensions. This

validation comprised 80 tests with different pumps covering a wide range of specific speeds. An

empirical expression based on geometrical parameters (impeller diameter, outlet flow angle) and the

specific speed at the BEP was proposed and is shown in Error! Reference source not found.. Each

coefficient was correlated and adjusted based on the experimental data gathered.

On the other hand, a new model to predict the head degradation when handling viscous fluids was

proposed by Ofuchi et al. (2020), and it depends only on the water baseline curve and ordinary design

quantities that are usually available in pump datasheets. To examine the head degradation of

centrifugal pumps due to viscosity, Buckingham’s Pi method was used considering the head

degradation coefficient, the flow coefficient, the rotational Reynolds number, and the specific speed

as relevant. Furthermore, this model was constructed considering a broad range of Reynolds numbers,

which includes high liquid viscosities and low rotating speeds. The correction factors used for the

model calculations are summarized in Error! Reference source not found., and it can be seen the

advantage in the use of few and easily obtained parameters for the calculations. The predictions

obtained with this model and others found in the literature (HI and KSB methods) are compared to

the data used. The significant advantage of this model is that it does not depend on any geometric

parameters of the pumps, which are often difficult to obtain. At the same time, this can also represent

a weakness since accuracy is affected, as can be seen in the maximum deviations reported in the

study: 53.3% (Ofuchi), 176.5% (HI), and 136.2% (KSB).

Table 1. Correction factors.

Reference Correction

Factor Expression Observations

Hydraulic Institute,

1948

Head 𝐶𝐻 =𝐻𝑣𝑖𝑠

𝐻𝑊

A similar approach by

(KSB, 2005) but with

expanded operational range

(6.5< 𝑛𝑞 < 45 𝑎𝑛𝑑 𝑣 <

4000 𝑐𝑆𝑡)

Flow 𝐶𝑄 =𝑄𝑣𝑖𝑠

𝑄𝑊

Efficiency 𝐶𝜂 =𝜂𝑣𝑖𝑠

𝜂𝑊

Gülich, 1999b Head

𝐶𝐻 = 𝑅𝑒𝐺ü𝑙𝑖𝑐ℎ

−6.7𝑅𝑒𝐺ü𝑙𝑖𝑐ℎ

𝑥

𝑅𝑒𝐺ü𝑙𝑖𝑐ℎ = 𝑅𝑒𝜔𝜔𝑠

1.5fq0.75

0.68 ≤ 𝑥 ≤ 0.81

0.65 ≤ 𝑦 ≤ 0.77 Flow 𝐶𝑄 = 𝐶𝐻,𝑜𝑝𝑡

Efficiency 𝐶𝜂 = 𝑅𝑒

𝐺ü𝑙𝑖𝑐ℎ

−19

𝑅𝑒𝐺ü𝑙𝑖𝑐ℎ𝑦

(Fleischfresser et

al., 2015) Head

𝐶𝐻 =1

4− 𝑘4 + (−𝑘1

+ 2𝑘4𝑘5)𝐶𝑄

+ (−𝑘4𝑘52

− 𝑘6)𝐶𝑄2

𝑘1 = 𝑓(𝐷2, 𝛽2) 𝑘4 = 𝑓(𝑁𝑠, 𝐷1, 𝐷2)

𝑘5 = 𝑓(𝑁𝑠)

𝑘6 = 𝑓(𝑁𝑠)

(Ofuchi et al.,

2020)

Head 𝐶𝐻 = 𝑅𝑒

𝑂𝑓𝑢𝑐ℎ𝑖

−𝑎

𝑅𝑒𝑂𝑓𝑢𝑐ℎ𝑖𝑏

𝑅𝑒𝑂𝑓𝑢𝑐ℎ𝑖 =𝛺𝑣𝑄𝑑𝑒𝑠

𝑣√𝑔𝐻𝑑𝑒𝑠

1

𝜔𝑠,𝑜𝑝

Flow 𝐶𝑄 = 𝐶𝐻1.5

*𝑁𝑠 = 51.6𝑛𝑞 ∗∗ 𝜔𝑠 =𝑛𝑞

52.9

Finally, along this section, two major distinct approaches were used in these studies: i) pump

performance and internal flow analysis, and ii) correction factors and dimensional analyses. The

explorative work approach allowing to develop an initial analysis of the losses occurring inflows

through the pump and started the construction of an expansive database, as can be seen in Table 2.

The table summarizes the usual operational ranges for centrifugal pumps: in the earlier references a

focus on the viscosity can be seen and defines the range limits researched (1 to 4042.36 cSt); with

time a more pronounced emphasis on the characteristics of the pumps can be seen in the expansive

ranges of specific speeds and Reynolds studies, reaching the limits of the ranges observed (9 to 91,

and 1296 to 38644103 respectively). These ranges served as a foundation for correction factors, which

provide fast estimations for the degradation of a centrifugal pump’s performance: some correction

factors take into account the geometry of the pump (Gülich), which sometimes cannot be obtained,

and often results in a better estimation for a broader selection of operating conditions; others are based

solely on charts obtained for a range of operating conditions (HI and KSB), and thus are inaccurate

outside of said range; and lastly, others simplify the input data to easily obtainable parameters which

give a balance of the other cases. For the empirical models, the experimental data used constricts the

validity of the model to said conditions. Lastly, affinity laws for pumping viscous fluids obtained by

dimensional analyses proved to work until a specific value of viscosity, after which the pump curves

do not follow a single curve.

Table 2. Summary of the operating conditions ranges tested at the BEP in multiple studies.

Reference 𝝂 [cSt] 𝒏𝒒 Re min Re max

Mawson, 1927 1 - 104.05 14 - 37 17891 4654176

Tetlow, 1943 1 - 4042.36 26 - 32 5373 21721168

Ippen, 1946 1 - 436.52 19 - 52 23389 10209628

W. G. Li, 2000 1 - 48 19 - 21 104968 5038486

Asuaje, 2003 1 29 - 48 24403492 25675412

Shojaee Fard et al., 2005 62 29 - 106979

Amaral et al., 2009 1 - 809.52 12 - 35 2613 5635598

Barrios & Prado, 2011 1 - 3231.40 45 - 63 3628 11721901

Monte Verde, 2011 1 26 - 995382

Shojaeefard et al., 2012 1 - 43.00 24 - 27 154248 6632682

Poursharifi et al., 2012 1 - 70.62 28 - 29 55048 3887197

Varon, 2013 1 - 197.50 33 - 53 14843 4275079

Barriatto, 2014 1 21 - 25 3811539 6352564

Biazussi, 2014 1 24 - 62 - 4275079

W. G. Li, 2014 1 - 60.7 20 81050 4919734

Stel et al., 2014 1 - 833.33 28 - 55 1844 2903198

Adhav et al., 2015 1 32 - 3437267

Le Fur et al., 2015 1 - 1751.07 25 - 29 17725 37140665

Monte Verde, 2016 1 - 853.93 17 - 34 1296 3190509

Siddique et al., 2016 44.44 - 149.05 33 - 35 23062 77356

Babayigit et al., 2017 1 15 - 13092522

Bai et al., 2018 1 18 - 22 19322051 38644103

N. A. Bulgarelli, 2018 60 - 346 54 - 91 2826 48595

Valdés et al., 2019 1 - 74.94 9 - 10 29939 2240520

Global 1 - 4042.36 9 - 91 1296 38644103

2.2. Computational

CFD is a tool that has been in constant development throughout the years, from the earliest

developments (around 1950-1960) consisting in approximations of compressible inviscid flows to the

current era of automating runs of thousands of simulations to find optimal results for a specific process

with realistic physics. It has become a powerful tool to understand in further detail the operation of

pumping systems, among others.

Taking a computational approach to the system studied by Amaral (2009), Sirino et al. (2013) and

Stel et al. (2014) considered fluids of different viscosities for the three-stage pump. Both studies

varied the rotational speed at which the ESP operated to ascertain the internal flow at design and off-

design flowrates. Good agreement was attained against the experimental data by considering a U-

RANS 𝑘 − 𝜔 SST modeling for all conditions considered. The results showed that fluids with higher

viscosities than water will not always attain a blade-oriented flow at the BEP. Large separation zones

were noticed at the impellers and diffusers for part-load conditions. The general effect on performance

degradation due to viscosity and rotational speed was explored as well, and highly viscous fluids

presented the best agreement with the experimental data.

Shortly after, Stel et al. (2015) expanded the previous study with the application of the finite method

for the numerical solution of the internal flow of the pump. This study obtained a detailed CFD

analysis on the flow field patterns at the impellers of each stage at different flowrates and

upstream/downstream flow at the diffusers. From these profiles, it was observed that the flow

behavior is significantly different for each stage, including high flow rates. In conclusion, the internal

flow features inside a multi-stage ESP are inherently unstable and non-periodic.

Some studies compared the estimations obtained with the application of different CFD models. For

example, De Maitelli et al. (2015) simulated in ANSYS CFX an ESP stage for two oils and water,

comparing two RANS turbulence models and various mesh configurations. The study found that the

𝑘 − 𝜖 model provided a very good estimation at high flow rates, while the SST model gave more

accurate calculations at low flowrates. Multiple recirculation zones and pockets of low pressure were

identified from the CFD contours and flow fields computed.

Zhu et al. (2016) studied as well the effect of Newtonian viscosity in a multi-stage ESP employing

commercial CFD code ANSYS CFX and validated with experimental data. The computational model

considered a steady RANS Shear Stress Transport turbulence modeling. Nevertheless, various RANS

two-equation models were tested, and very similar results between all cases were observed for the

ESP general performance. As with previous studies, flow structures within the impellers and diffusers

were examined. The result of this examination showed that recirculation flows at the impeller blade

becomes prominent at lower flowrates. Moreover, both experimental and CFD results showed that

ESP pressure rise decreased for increasing oil viscosity, and a more linear H-Q performance curve

was observed, which indicates flow regime transition from turbulent flow to laminar flow resulting

in the equipment becoming ineffective for viscosities over 200 cP.

Ofuchi et al. (2017a; 2017b) evaluated two multi-stage mixed-flow ESPs operating with several

viscosities and rotational speeds, and with the numerical head curves, obtained a dimensionless

analysis was carried out resulting in the proposal of a general method to estimate performance

degradation of the pumps. For the numerical simulation, a U-RANS 𝑘 – ω SST turbulence modeling

was implemented in both works. The results of the simulations showed that the ESP’s head curve

suffers a degradation for higher viscosities as expected, especially along curves of constant

normalized specific speeds, regardless of the pump’s geometry. Furthermore, a change of behavior

in the pressure head curves due to viscosity increase, a saddle-type of behavior was presented by

water and gradually smoothed with the increase in viscosity. These behaviors can be attributed to the

dominance of frictional losses when high viscosities are present, resulting in the geometry and

features of the pump to become less impactful for these fluids. Nevertheless, data from different

pumps cannot be directly correlated based on dimensionless parameters such as the rotational

Reynolds number as it discards several variations between both ESPs. Finally, the flow pattern fields

obtained through CFD depicted significant variations for different rotational Reynolds numbers.

Mainly, separation zones arose at low Reynolds numbers, and recirculation at the diffusers was seen

to influence the performance by altering the turbulence profiles at each of the stages.

Implementing a similar dimensional analysis to Ofuchi et al. (2017b), Morrison et al. (2017) studied

a single-stage ESP. The numerical model was defined through CFD code ANSYS Fluent using a

standard 𝑘 − 𝜖 turbulence model. The results of this dimensional analysis showed that pump

performance is more sensitive to the rise of viscosity at higher flowrates. Moreover, the CFD-based

analysis revealed that high flowrates at the diffuser could cause pressure losses rather than positive

hydraulic head for viscous fluids. On further study, Morrison et al. (2018) developed modified affinity

laws for viscous fluids to predict the head and efficiency of the pump. It was possible to obtain a

single characteristic curve for all operating conditions of a specific pump. Nonetheless, it is suggested

that further research is still necessary to develop a relationship between design parameters, which will

enable this prediction for any pump.

In conclusion, the computational approach in Newtonian fluids can accurately predict the

performance of a centrifugal pump for an ample range of operational conditions. Furthermore, the

advantage of this approach is the ability to change the viscosity and other fluid properties while

maintaining constant the rest of the conditions. It was noted that this approach has three primary

focuses: i) pump performance and internal flow analysis, ii) dimensional analyses, and iii)

computational modeling. Studying pump performance and internal flow with CFD modeling has

notably improved the comprehension of flow in the pump since it allowing to completely visualize

flow patterns in the machine in a way that results in challenging to replicate in experimental setups.

Moreover, the turbulence models (i.e., 𝑘 – ω SST or 𝑘 – 𝜖) used for these simulations do not

significantly differ in the results, often a 12% difference as reported by De Maitelli et al. (2015), since

the models are sufficiently robust at present to handle an ample range of operating conditions

retaining considerable accuracy.

Nonetheless, as stated by Zhu et al. (2016), while no prominent variance is presented among different

turbulence model predictions, certain models may display advantages in capturing specific behaviors

occurring in the pump. It was observed that most studies used RANS based models. Therefore, it is

crucial to justify the reasons for such a focused RANS approach in modeling, since other

computational modeling approaches (i.e., Reynolds Stress Transport) may display better results in

capturing the behavior of fluids in the pump. For example, Gerolymos and Vallet (2002) developed

and validated a near-wall wall-normal-free Reynolds stress model for transonic three-dimensional

flows in turbomachinery that resulted in a substantial improvement of the agreement compared with

a 𝑘 – 𝜖 model. Furthermore, this can result vital in the design of this equipment by accurately

estimating turbulence, recirculation, dead zones, etc. Finally, one of the significant disadvantages of

computational approaches is that it does require precise knowledge of the pump’s geometry that is

often not available for commercial reasons.

3. Non-Newtonian studies

3.1. Experimental

This section can be summarized in Figure 3 in which the determining focuses of the experimental

approach can be observed. Further analysis is performed for this focus, including contributions to the

field and lacking areas.

Figure 3. The non-Newtonian experimental approach focuses.

3.1.1. Slurries

Four explorative studies (Bonnington, 1957; Fairbank, 1942; Govier & Charles, 1961; Gregory,

1927), mentioned by Walker and Goulas (1984), showed the deterioration of the performance for

single-stage pumps when handling non-Newtonian slurries; and most of these studies attributed the

change in performance to changes in the mixture’s apparent viscosity. Nonetheless, said studies did

not present complete rheological data of the pumped fluids, and thus the changes in performance are

hard to correlate. Therefore, Walker and Goulas (1984) studied the operation of these pumps when

handling homogenous slurries, and complete rheological characterization of the slurries was reported.

The results showed a reduction in both the pump's head and efficiency, creating an unstable curve of

operation and decreasing flowrates near the BEP. As one of the firsts complete exploratory works on

pump performance with slurries, these studies gave no significant into internal flow features or local

variables due to their focus on global performance parameters. Furthermore, the authors suggested

extending the Hydraulic Institute Chart to non-Newtonian slurries.

Following Walker and Goulas suggestion, several studies (C. Buratto et al., 2017; Graham et al.,

2009; Kabamba, 2006; Kalombo et al., 2014; Pullum et al., 2007; Sery et al., 2006, 2002) proposed

and evaluated Hydraulic Institute Chart based methods for the prediction on the performance of

centrifugal pumps operating with non-Newtonian slurries. Overall, the effective viscosity employed

and calculated for these methods showed significant differences in the predictions obtained. The study

performed by Kalombo et al. showed the two majors approach, one uses the Bingham plastic

viscosity, and the other one uses the apparent viscosity. The results of the two approaches were not

found in the agreement. Furthermore, the apparent viscosity approach gave better head prediction,

and the Bingham plastic viscosity approach resulted in a better efficiency prediction. This comes to

show that further research must be carried out for the models of viscosity employed as stated by

Buratto et al. these viscosities do not consider numerous variables that influence the rheological

behavior of these slurries.

Other experimental model approaches were tried for predicting the performance of centrifugal pumps

with slurries. For example, a polynomial regression model was proposed by Mrinal et al. (2018) based

on the experimental data measured for mixtures prepared with bentonite powder, water, and Na2CO3.

This model for head and efficiency is a function of discharge, slurry viscosity, and rotational speed.

The model results showed acceptable agreement with experimental results, the relative errors for head

and efficiency being around 3%, and 5%, respectively. Nonetheless, the model does not consider the

characteristics of the pump, for which further validation must be carried out to observe the

performance with other geometries.

In conclusion, the articles considered in this section showed a considerable focus on the adaptation

of the previous prediction method from the HI charts for non-Newtonian estimations. As previously

stated, these efforts consisted of the modification of the HI method by considering different viscosities

that could capture the non-Newtonian rheology. This kind of method retains the advantages of fast

and straightforward estimations based on a few parameters on the fluid and can achieve an acceptable

agreement with experimental results (around 5% error). Nonetheless, the disadvantage when

operating outside of the considered operating conditions remains and can be worse due to the

changing viscosity or further losses resulted from the interaction and collision of the solid particles.

Furthermore, a lack of studies of the phenomenological on the changes of viscosity caused by the

pump was observed, and pragmatical approached for performance predictions were preferred.

3.1.2. Liquid-Liquid

Ibrahim and Maloka (2006) performed the first experimental study for secondary oil/water

dispersions occurring in the operation of centrifugal pumps. The focus of this work was the

characterization, through novel laser analytical techniques, of the droplet size distribution at the inlet

of the pump. Subsequently, new theoretical mean drop diameter equations were developed and

compared to the experimental data. These equations showed a maximum error of 16% against the

correlated data.

Khalil et al. (2008) study was one of the firsts to determine experimentally the performance of

centrifugal pumps operating underflow of stable and unstable oil-water emulsions. The impact of

temperature and holdup were also studied in the operation of the pump. Overall, the results showed a

decrease in the performance of the pump when handling emulsion systems in comparison to water.

Furthermore, the unstable emulsions were reported to show a slighter decrease in the head-flow rate

than the stable emulsions. It was also observed that the surfactant type affected the head-flow-rate.

Moreover, higher holdups and lower temperatures resulted in a higher reduction in the pump’s

performance. Therefore, this behavior was attributed to the changes in the rheology of the emulsions

when subjected to different holdups and temperatures.

As it is known, the droplets formed in oil/water flow are an essential factor in the perceived viscosity

of the mixture. Therefore, Morales et al. (2012) analyzed experimentally and theoretically, the

formation of droplets in oil/water flow through centrifugal pumps. Droplet-size distribution was

measured at the outlet of the pump as a function of pump speed, mixture flow rate, and water cut. The

results showed a strong dependence of the distribution size on the pump speed and rather weak

influence on the flow rate and water cut. This dependence showed that the mean droplet size

decreased at higher rotational speed, resulting in narrower distributions. Therefore, the turbulent

breakup was identified as the primary mechanism of droplet formation. Furthermore, the most likely

size distribution for oil/water flow systems in the studied pump was determined to be the Rosin-

Tammler distribution, according to the four goodness-of-fit criteria applied by the authors. Previous

physical derivations corroborated the conclusion of the Rosin-Tammler distribution to be appropriate

for breakup-dominating mechanisms. Nonetheless, further studies for the high-viscosity-oil

continuous phase were suggested to be required as a different breakup mechanism may occur in the

pump.

Further experimental research into the behavior of both oil (Perissinotto, Verde, et al., 2019, 2019)

and water (Perissinotto et al., 2020) droplets in dispersed oil-water two-phase flow within a

centrifugal pump impeller was carried out in order to study its influence in the pump’s performance.

The motion of these droplets was captured up to 2000 frames per second with a 1500x1500 resolution

using a high-speed camera with lighting set in an ESP prototype with a transparent shell. Regarding

oil drops, the images captured and processed revealed that the drops were generally spherical or

elliptical, and only a few broke up in the impeller. Furthermore, the studies contrasted with Morales

et al., stating that while the characteristic size of the drops does depend on the rotational speed, it was

mainly dependent on the water flow rate. In addition, the interaction with water caused the drops to

rotate, deform, and deviate, thus moving in random paths. Nonetheless, a unique flow pattern within

the impeller was observed for the conditions tested, and a detailed analysis of the kinematics and

trajectories of the oil drops was given related to their position in the impeller (suction/pressure blade

or central channel). Coalescence was not observed for the low oil fractions tested, though collisions

were observed it appeared that the attractive forces were not enough to result in aggregation. Contrary

to oil droplets, the water drops showed significant break up along their paths in the channels. This

break up was attributed to the low viscosity ratio and low interfacial tension, thus elongating and

easily deforming. In consequence, water drops showed a decrease in size as the impeller rotation

speeds, and oil flow rates increased. Finally, the water droplets showed no significant impact on the

performance of the pump, but this was a result of the low water cuts achieved (around 1%).

A possible phenomenon that occurs in the operation of a centrifugal pump under oil-water flows is

phase inversion. Bulgarelli et al. (2017a; 2017b) analyzed the influence of viscosity on phase

inversion phenomena in an 8-stage electrical submersible pump handling oil-water flow

experimentally and investigated the chord length distribution at different water cuts. Three different

rotational speeds were considered for both studies. The chord length distribution analysis at the outlet

was performed with a focused beam reflectance measurement technique (FBRM). This analysis

revealed an increase in droplet chord length as the water cut increased up to the phase inversion point,

regardless of the pump’s speed. After the inversion point, the droplet chord length dropped as the

water cut kept increasing. As expected, results showed that emulsions further deteriorated the lifting

capacity of the ESP with higher effective viscosities. Furthermore, performance significantly

improved after the inversion point, where the continuous phase-shifted to water. Therefore, the

continuous phase of the emulsion system directly determined the effective viscosity attained. This

can constitute an essential fact for the estimation of a pump’s performance when operating with

emulsion systems.

Later on, Bulgarelli (2018) compiled both studies previously discussed and incorporated an empirical

predictive model of the lift coefficient of the ESP tested when operating with emulsion systems. This

empirical model was based on previous viscous single-phase models, and viscous monophasic

performance curves experimentally obtained. The model was also used to indirectly determine the

effective viscosity on the ESP by fitting the geometric parameters with single-phase (oil and water)

data and then inverting the model with the emulsion experimental data. In addition, different behavior

of the effective viscosity between the pipeline flow and within the ESP was observed for the water-

in-oil emulsion and was attributed to the high centrifugal field in the ESP. Finally, to analyze the

phase inversion in more realistic conditions, three-phase tests were carried out, and by including the

presence of gas, the phase inversion event was detected at lower water cuts and high rotational speeds.

Zhu et al. (2019) proposed a new model for predicting oil-water emulsion rheology and its impact on

the boosting pressure in ESPs. The mechanistic model is based on Euler’s equations for centrifugal

pumps and introduces a conceptual best-match flowrate term, relating the outlet flow direction of the

impeller with the designed flow direction. Thus, this term is used to derive recirculation losses at the

impellers, and further losses due to direction change, friction, and leakage flow are incorporated by

other means. The rheology model based on previous studies accounts for rotational speed, stage

number, interfacial properties, and other parameters. Therefore, by complementing the mechanistic

model with the rheology prediction, a consolidated effort that correlates the emulsion’s properties

with the ESP’s predicted performance is achieved. The results of the model were found comparable

with experimental data, with an average error of 10% and a maximum error of 50% and -15%.

Further research conducted by Valdés et al. (Valdés et al., 2020) analyzed the performance of a four-

stage ESP operating with the oil-water flow, mainly focus on the characterization of the two-phase

flow/emulsions and their influence on the ESP’s global performance was observed. Three main

phases regimes were identified when changing the water cut of the two-phase flow i) a diluted pseudo-

stable W/O emulsions at high oil fractions (>80% oil), ii) at 70% oil fraction the phase inversion

occurred and resulted in a concentrated O/W emulsions and iii) beyond that point, the microscopic

emulsion was lost resulting in a multiple regime system. Considering that the emulsions were not

prepared using surfactants, the author attributed the pseudo-stabilization achieved to the shear rate

performed by the pump and the presence of amphiphilic molecules in the oil acting as surfactants. As

for the pump performance, a general gradual deterioration was observed as the oil fraction increased

from 1 to 2% on average between adjacent compositions. Moreover, mixtures with water or oil

fractions superior to 80% showed no significant variation when compared to their respective single-

phase tests. Nonetheless, severe performance degradation (average head reduction of 6 to 7%) was

perceived with the increase of oil fractions through the inversion point.

Interest by the industry sector on the research of this kind of multiphase flow can be seen in this

section, given that all the references, found and reviewed, treated with an oil-water two-phase flow.

Nonetheless, three primary focuses were observed for this kind of flow: i) droplets behavior, ii)

water/oil fractions impact, and iii) mechanistic models. The phenomenological investigation on the

behavior of the droplets for these kinds of fluids can give significant insight into the dynamics and

mechanisms occurring to the flow inside the pump. For example, significant differences in the

behavior of water and oil droplets were found, resulting in a variable impact on the performance of

the centrifugal pumps, and this could further present variations by introducing stabilizing agents for

the emulsions. Thus, establishing the influencing factors in the behavior of the droplets for an accurate

representation could significantly increase the agreement of theoretical and experimental models in

both viscosity and pump performance predictions. As for the impact of water/oil fractions, it was

noted that generally, the viscosity perceived by the pump was that of the continuous phase.

Nonetheless, variations with the increase/decrease of these fractions are still present and result most

significant when the inversion point is reached. Finally, mechanistic models for pump performance

prediction and effective viscosity calculations were proposed. The agreement achieved by this model

still showed a need for further research and refinement, since errors up to 50% are still present. Thus,

using the findings of the two previous focuses, a more robust model may be developed. It was noted

that the impact on the type of oil on these mixtures was not widely investigated and can result in a

vital variable for the stabilization of the emulsions, as was observed in the study by Váldes et al.

(2020).

3.2. Computational

This section can be summarized in Figure 4, in which the determining focuses of the computational

approach can be observed. Further analysis is performed for this focus, including contributions to the

field and lacking areas.

Figure 4. The non-Newtonian computational approach focuses

3.2.1. Single-phase

A review by Shah et al. (2013) collected two previous woks related to single-stage centrifugal pumps

with non-Newtonian fluids. The first study conducted by Yu et al. (2000) investigated the effects of

impeller geometry on the performance of a centrifugal blood pump. Four impellers' designs were

modeled and tested in ANSYS Fluent. Some simplifications of the model were made to decrease

computational requirements by considering the axial velocity component negligible compared to the

radial and angular components and, therefore, approximating the passage flow as a two-dimensional

problem. It was found that although the flow patterns inside the impeller passages appeared to be

three-dimensional, the two-dimensional numerical approach shows good qualitative agreements with

flow visualization results. Regarding the differences between the performance of the impellers

designs, none were found significantly different and the results indicated that stress levels were

generally below the threshold for extensive erythrocyte damage to occur. The second study by

Pagalthivarthi (2011) simulated a dense slurry flow through the pump’s casing, further details of these

research are displayed in section 3.2.2

The food industry presents several cases of centrifugal pumps handling non-Newtonian fluids,

Buratto et al. (2015) studied a food-processing pump handling non-Newtonian tomato paste with CFD

with the commercial code ANSYS CFX. Sensitivity analyses on the flow regime modeling were

performed by using laminar and turbulent RANS models (both 𝑘 − 𝜖 and 𝑘 – 𝜔). The non-Newtonian rheological behavior was defined with the Power-Law model. It was found that the pump curves and 3D flow structures obtained with non-Newtonian fluid are like those obtained with the high viscosity Newtonian fluid with a dynamic viscosity value of 1 Pa.s. However, substantial differences were observed in the volute losses for both fluids, having an impact on global pump performances.

Shortly after, another study considered tomato paste as one of the operating fluids for a pump. Aldi

et al. (2016) performed a comparative analysis for a single-stage centrifugal pump with a semi-open

impeller operating with both Newtonian and non-Newtonian fluids using three different CFD

software: OpenFOAM, PumpLinx, and ANSYS CFX. The non-Newtonian fluid studied is shear-

thinning, and it was modeled following the Power-Law approach. Of the three CFD software

considered, OpenFOAM with a first-order upwind scheme resulted in the most accurate

approximation against experimental data. The results showed that, for the non-Newtonian fluid, the

pump’s head was a third of the one obtained when using water. It was also observed that the efficiency

of the pump dropped significantly when handling these fluids.

Following this study, Aldi et al. (2017) expanded on previous work by investigating through CFD the

operation of a semi-open impeller centrifugal pump handling three non-Newtonian fluids. The non-

Newtonian fluids were obtained by mixing kaolin powder with water in different weight fractions

(30%, 35%, and 40%). The CFD software used was the commercial code ANSYS CFX, in which a

𝑘 − 𝜔 turbulence model was implemented. The rheological characterization of each fluid tested was

reported and accounted for in the numerical model by the Power-Law approach, and the performance

of the pump was presented along the flow field. The results indicated that non-Newtonian fluids with

low apparent viscosities performed similarly to water. However, fluids with higher apparent

viscosities showed a high derating of pump performance compared to water, especially at higher

flowrates. Furthermore, the numerical results presented a high agreement with experimental data for

water, kaolin 30%, and 35% with a maximum error of 6%. Nonetheless, high deviations were found

between the numerical estimations and the experimental data with a maximum error of 33%. These

deviations were considered acceptable given the complexities of the non-Newtonian behavior and the

particular conditions of the experimental tests, besides the rheological characterization showed a

considerable jump in viscosity for kaolin 40%, which can be a result of additional interactions not

fully accounted for with the Power-Law.

Several studies researching Carboxymethyl Cellulose (CMC) in pumps have been carried out.

Nguyen and Lai (2017) simulated the flow characteristics of a centrifugal pump impeller operating

with an aqueous solution of CMC at 7.5% weight concentration. The implementation of a Power-

Law-non-Newtonian model described the rheological behavior of the CMC solution. Furthermore, a

standard 𝑘 – 𝜖 turbulence model was used to capture the flow within the pump. Major differences

between the impeller’s operation with water and with the non-Newtonian fluid were found and

highlighted. Later, Dönmez and Yemenici (2019) numerically studied a single-stage centrifugal pump

operating with three different concentrations of CMC at two rotational speeds. The simulations were

carried out in FLUENT and, as the previous study, considered as well a 𝑘 − 𝜖 turbulence model and

a Power-Law viscosity model. In terms of performance, the study concluded that an improvement

occurred for the non-Newtonian fluids at high rotational speeds (3300 rpm) in comparison to water.

However, water presented better performance at lower speeds (1400 rpm) than the CMC solutions.

Furthermore, the best performing fluid, at design parameters, was the least concentrated CMC

solution. These results show that some non-Newtonian rheological behavior can result beneficial for

certain operational ranges for pumps and further research of these operating conditions can lead to

reduced energy consumption, and stress for the centrifugal pumps.

Finally, for the study of single-phase non-Newtonian flows, there were: i) pump performance and

internal flow analysis, and ii) computational modeling. The study of the pump performance and

internal flow analysis performed was found comparable with experimental results when the non-

Newtonian behavior was mild. This can be the result of a pragmatical approach in the effective

viscosity modeling, as it was noted that almost all the references reviewed used the Power-Law to

account for the rheological behavior. Regarding the computational modeling, a similar RANS

depending approached to the one presented in Newtonian fluid computational approaches were

observed. Moreover, turbulence modeling was reduced to consideration regarding standard 𝑘 – 𝜖 or 𝑘 – ω due to, as stated by Buratto et al. (2015), proven reliability in applications where high

viscosity or non-Newtonian fluids are present for the former, and a demonstrated reliability with low

Reynolds number flows and non-Newtonian turbulent flow for the latter. As already discussed in

section 2.2, evaluating non-RANS approaches may prove beneficial for the accuracy of the

simulations. Nonetheless, if such approaches are evaluated, a cost/benefit analysis of computational

time and resources versus accuracy to estimate the value of said alternatives is necessary.

3.2.2. Slurries

Continuing with the other non-Newtonian study collected by Shah et al. (2013), Pagalthivarthi et al.

(2011) simulated a dense slurry through centrifugal pump casing using an Eulerian multiphase

approach and a mixture 𝑘 − 𝜖 turbulence model. The results were validated and presented an

acceptable accuracy within 12% for the estimations. Subsequently, several geometrical parameters of

the casing were studied together with the flowrate and the inlet concentration of particles to observe

their effect on wall stress distribution along the casing.

Recently, Buratto et al. (2017) reviewed previous analytical methods for predicting the performance

of single-stage pumps operating with non-Newtonian fluids. They performed CFD simulations

focusing on the apparent viscosity correction involved in the performance of two open-impeller

centrifugal pumps of different typology and compared the results with the methods reviewed. The

methods considered were the Walker and Goulas method (1984), and the Pullum et al. method (2007).

The comparison showed the differences presented by the CFD estimation with the methods. These

differences were attributed, in full description, to a lack of consideration of how pump geometry, flow

rate, rotational velocity, and fluids characteristics can impact the shear rate presented in the pump,

among other considerations. It was observed that the pump’s efficiency and head decreased while the

shaft power increased. This was linked to changes in effective viscosity due to varying shear rates.

Moreover, it was noticed that pumps with higher specific speeds were less sensitive to the fluid’s

viscosity.

Huang et al. (2015) stated that solid-liquid flow simulations in the CFD method are generally analyzed

by treating the solid particles as a quasi-fluid element. Thus, it does not consider the effects of the

physical features of the solid particles and collisions among them. Therefore, the authors coupled the

discrete element method (DEM) with the CFD method to analyze the transient two-phase solid-liquid

flow in a single-stage centrifugal pump considering the particle-particle and particle-structure

interactions. The numerical simulation was carried out using EDEM and FLUENT software by using

the Euler-Lagrange method. The setup employs DEM for simulating the solid particle dynamics in

conjunction with the transient fluid flow solution given by CFD. The turbulence model considered

was the standard 𝑘 – 𝜖. As expected, the DEM-CFD coupling process resulted in a significant increase

in the computational time due to the DEM iterations being performed in an independent integration

time step following the convergence corresponding to each CFD time step solution. The results for

the densely distributed solid-liquid flow showed a substantial degradation of the pump head compared

to the liquid-only flow. Furthermore, an increase in the total volume of the particles inside the pump

during the start-up period was observed. Finally, a comparison between the pseudo-fluid multiphase

approach and the developed coupling was not carried out.

A study conducted a numerical investigation to optimize a centrifugal slurry pump using CFD (Cellek

& Engin, 2016). This optimization was focused on the impeller characteristics, particularly

considering the blade discharge angle, addition splitter blades, and modified blade type. The tongue

region of the pump was also re-design. The numerical simulation considered a standard 𝑘 – 𝜖

turbulence model. The numerical results showed an improvement in the hydraulic efficiency of the

pump. Furthermore, the effect of the blade angle proved to be crucial for the impeller performance,

given that it caused a 10.6% increase of the hydraulic efficiency at the nominal flow rate with a

variation of 20°. Moreover, blade height and leading angle also showed to be essential parameters for

the design of the impeller. This study displays the role CFD methods can perform in the design and

optimization of centrifugal pumps considering specific fluids.

The computational approaches observed had two focuses: i) internal flow analysis, pump performance

and design optimization, and ii) particle properties and tracking. The internal flow analysis is a

particularly important focus when handling solid-liquid flow to estimate the wear and stress at which

the pump will be subjected while performing on the field. Furthermore, due to the presence of a solid

phase evaluating design changes to the pump through simulations can prove to be a powerful tool in

improving pump performance. Nonetheless, experimental results are still needed to validate the

simulations more so considering that effective viscosity models cannot yet fully predict the

rheological behavior. For this, tracking the solid particles and accounting for its properties leads to

useful insight in the losses caused by collisions (either particle-particle or particle-structure). An

exciting alternative for considering these properties was proposed by DEM-CFD coupling.

Regardless, it has yet to be evaluated if the predictions obtained are worthwhile the computational

time required for these simulations compared with the CFD only approach. Regarding turbulence

models, the overall use of the 𝑘 – 𝜖 turbulence model was observed.

3.2.3. Liquid-Liquid

Croce (2014) and Croce et al. (2019) studied oil/water flow, particularly unstable emulsion formations

and phase inversion during the operation of multi-stage ESPs, through experimental and

computational approaches. The focus in both studies was to evaluate the influence of changes in water

volume fractions in the performance of the ESP and the impact of said fractions in the rheological

behavior perceived. Though the study considered a multi-stage centrifugal pump, only the third stage

of the ESP presented a detailed analysis. Considering that the emulsions were unstable, the inversion

point was reported in the range of 35% to 40% water fraction. The experimental results showed a

significant increase in the emulsion's effective viscosity at higher water fractions before the inversion

point was reached (W/O topology). After the inversion point was reached (O/W topology), the

opposite behavior was observed. Thus, the impact of the emulsion’s effective viscosity on the head

delivered by the pump was inversely proportional. For the CFD simulations, a mechanistic model

was implemented using the experimental data of the effective viscosity of the emulsion to calculate

the maximum stable droplet size. Furthermore, the model permitted to change the droplet diameter

for each water fraction according to the energy dissipation caused by the energy input of the ESP to

the emulsion. As for the turbulence model, BSL was implemented due to presenting a combination

of the 𝑘 – 𝜖 and 𝑘 – ω models where the first one was used for the outer region and the second one

for the area near the wall. The results of the CFD simulations replicated the ESP’s experimental

performance for the dispersed fractions tightly up to 20%.

Banjar (2018) and Banjar et al. (2019) studied the effects of oil and emulsion viscosity in the

performance of a seven stage ESP. Similar to Croce, the performance of the third stage of the ESP

was emphasized by measuring at different oil/water fractions, rotational speeds, and temperatures. In

addition, a mechanistic model based on Euler’s centrifugal pump equations, including all possible

losses, was proposed. The results obtained for this model showed an accurate prediction with

experimental data at high rotation speeds, but the estimation at lower speeds needs further

improvement. Furthermore, an emulsion rheology model was developed through a dimensional

analysis resulting in a relation between several dimensionless numbers (𝑊𝑒, 𝑅𝑒 𝑎𝑛𝑑 𝑆𝑡) in a similar

fashion to Zhu et al. (2019). This model provided good agreement, with an average of 5% error,

against medium oil viscosities but showed more significant discrepancies at low effective viscosities.

The inversion points found for all uncontaminated emulsions tested ranged between 20% and 30%

water fraction. Moreover, rheological stability was determined to be lost after the emulsion becomes

water continuous. Non-Newtonian behavior was reported to be not significant in the test performed.

The results obtained with CFD showed a considerable deviation against experimental results, up to

40%; this was attributed to pump wear and possible neglect of leakage losses. Additionally, the CFD

model employed a two-phase Eulerian approach, for which the real emulsion rheological behavior

was not reflected, thus possible resulting in the discrepancies presented.

Continuing with their previous experimental work, Perissinotto et al. studied numerically (2019) the

motion of oil drops in an ESP impeller handling oil-water flow at different operational conditions.

The numerical model utilized the realizable 𝑘 − 𝜖 turbulence model with a scalable wall function to

determine the turbulent kinetic energy and its dissipation and, thus, be able to calculate the effective

viscosity. For the droplets, a Lagrangian particle tracking was implemented in the fixed velocity field

to study the dominant forces on the particles. The results showed that of the three-body forces

considered, between virtual mass, pressure gradient, and drag, the dominant force involved in the oil

drop motion was determined to be the pressure gradient. Furthermore, when comparing the qualitative

paths followed by the droplets, as well as the magnitudes of the velocity and acceleration components

along with the radial position with the experimental results, an acceptable agreement was met.

Similar to the experimental approach, the primary focus observed were: i) droplets behavior, ii)

water/oil fractions impact, and iii) mechanistic models; the behavior of the droplets was tracked in

some studies by the use of Eulerian or Lagrangian approaches. Thus, an analysis of the dominant

forces on the droplets can be more easily accounted for with computational approaches than

experimental wise. Another approach for accounting for droplets was proposed by applying a

mechanistic model that to calculate the maximum droplet size, attaining a close replication of the

experimental results for low dispersed fractions. Turbulence modeling showed no significant

variations with the other non-Newtonian fluids computational approaches, a combination of the 𝑘 –

𝜖 and 𝑘 – ω models (BSL) were used with acceptable results.

4. Conclusions and prospects

In this umbrella review, several Newtonian and non-Newtonian studies approach, for both

computational and experimental, were explored. Furthermore, methodology and results were briefly

summarized, and some lacking areas of research were identified. The following conclusions were

drawn:

• As expected, due to the relative novelty of studying non-Newtonian behavior, the recent

literature is still lacking in comparison with the former, especially in the experimental side.

Furthermore, the nature of the rheological behavior for non-Newtonian fluids proves a

difficult challenge to unify viscosity models, given the considerable amount of variations

presented in said behavior. Therefore, a more pragmatic approach to the viscosity modeling

was observed by developing experimental coefficients used for models such as the Power-

Law.

• Pump performance was primarily affected by the viscosity perceived, regardless of

Newtonian or non-Newtonian behavior, as it continued to derate with higher effective

viscosities.

• Experimental approaches for Newtonian fluids firstly consisted of purely explorative works

that permitted to expand the experimental database for a considerable range of viscosities.

Based on these results, then the impact of characteristics of the pump on the performance was

analyzed. They were resulting in more robust predicting methods developed by various

means.

• Computational approaches for Newtonian fluids closely predicted the deration of the pump

observed in experimental data. Furthermore, thorough internal flow analysis was made more

accessible and provided with useful insight into the dynamics of design changes of the pump.

Nonetheless, most computational approaches were based on RANS methods. Evaluation of

non-RANS methods is recommended to determine if further improvement is required and

possible.

• Experimental approaches for non-Newtonian fluids attempted to modify Newtonian

prediction methods, especially for centrifugal pump performance with the slurry flow. The

results were acceptable for low concentration of solid particles, but quickly diverged from

estimations for higher solid particle concentrations were the rheology presented significant

changes. This approach can prove to be viable if, as stated previously, a more

phenomenological understanding of the effective viscosity is achieved. Therefore, the

influence of water cuts and particle behavior were studied for both slurry and liquid-liquid

flows.

• Computational approaches for non-Newtonian fluids followed the experimental data for low

concentrations of the dispersed phase closely. Thus, the analysis of phase inversion with CFD

approaches for liquid-liquid flow has still not been achieved. Nonetheless, an essential

development for particle tracking was observed with the implementation of Eulerian,

Lagrangian, among other methods. A comparison of the former approach has not been carried

out and could provide useful insight into the advantages and disadvantages over each other.

Once again, a heavy RANS approach was observed for the simulation as convergence and

computational time may prove significant derisive factors in the implementation of other

approaches.

References

Adhav, R., Samad, A., & Kenyery, F. (2015). Design optimization of electric centrifugal pump by

multiple surrogate models. SPE Middle East Oil and Gas Show and Conference, MEOS,

Proceedings, 2015-Janua(1979), 199–211. https://doi.org/10.2118/172536-ms

Ahonen, T., Kortelainen, J. T., Tamminen, J. K., & Ahola, J. (2012). Centrifugal pump operation

monitoring with motor phase current measurement. International Journal of Electrical Power

and Energy Systems, 42(1), 188–195. https://doi.org/10.1016/j.ijepes.2012.04.013

Aldi, N., Buratto, C., Casari, N., Dainese, D., Mazzanti, V., Mollica, F., Munari, E., Occari, M.,

Pinelli, M., Randi, S., Spina, P. R., & Suman, A. (2017). Experimental and Numerical

Analysis of a Non-Newtonian Fluids Processing Pump. Energy Procedia, 126, 762–769.

https://doi.org/10.1016/j.egypro.2017.08.247

Aldi, N., Buratto, C., Pinelli, M., Spina, P. R., Suman, A., & Casari, N. (2016). CFD Analysis of a

Non-Newtonian Fluids Processing Pump. Energy Procedia, 101, 742–749.

https://doi.org/10.1016/j.egypro.2016.11.094

Amaral, G., Estevam, V., & Franca, F. (2009). On the Influence of Viscosity on ESP Performance.

Society of Petroleum Engineers, 24(2), 303–310. https://doi.org/10.2118/110661-PA

Asuaje, M. (2003). Méthodologie et optimisation dans la conception et l’analyse des performances

des turbomachines à fluide incompressible. Arts et M_etiers Paris- Tech.

Babayigit, O., Ozgoren, M., Aksoy, M. H., & Kocaaslan, O. (2017). Experimental and CFD

investigation of a multi-stage centrifugal pump including leakages and balance holes.

DESALINATION AND WATER TREATMENT, 67, 28–40.

https://doi.org/10.5004/dwt.2017.20153

Bai, Y., Kong, F., Zhao, F., Wang, J., Xia, B., & Hu, Q. (2018). Experiments and Numerical

Simulation of Performances and Internal Flow for High-Speed Rescue Pump with Variable

Speeds. Mathematical Problems in Engineering, 2018. https://doi.org/10.1155/2018/9168694

Banjar, H. (2018). Experiments, CFD Simulation and Modeling of Oil Viscosity and Emulsion

Effects on ESP Performance.

Banjar, H., & Zhang, H. Q. (2019). Experiments and emulsion rheology modeling in an electric

submersible pump. International Petroleum Technology Conference 2019, IPTC 2019.

https://doi.org/10.2523/iptc-19463-ms

Barriatto, L. C. (2014). Desempenho de Bombas Centrífugas Submersíveis em Escoamento Bifásico

Gás-Líquido. Universidade Estadual de Campinas.

Barrios, L., & Prado, M. G. (2011). Experimental visualization of two-phase flow inside an

electrical submersible pump stage. Journal of Energy Resources Technology, 133(4).

Biazussi, J. L. (2014). Modelo de deslizamento para escoamento gás-líquido em bomba centrífuga

submersa operando com líquido de baixa viscosidade.

Bonnington, S. T. (1957). The effects of included solids on the characteristics of centrifugal pumps.

BHRA.

Bulgarelli, N. A. (2018). Experimental Study of Electrical Submersible Pump (ESP) Operating with

Water/Oil Emulsion. Universidade Estadual de Campinas.

Bulgarelli, N. A. V., Biazussi, J. L., de Castro, M. S., Verde, W. M., & Bannwart, A. C. (2017).

Experimental Study of Phase Inversion Phenomena in Electrical Submersible Pumps Under

Oil Water Flow. ASME 2017 36th International Conference on Ocean, Offshore and Arctic

Engineering, V008T11A043-V008T11A043. https://doi.org/10.1115/OMAE2017-61865

Bulgarelli, N. A. V., Biazussi, J. L., Perles, C. E., Verde, W. M., de Castro, M. S., & Bannwart, A.

C. (2017). ANALYSIS OF CHORD LENGTH DISTRIBUTION IN PHASE INVERSION OF

WATER-OIL EMULSIONS AT ELECTRICAL SUBMERSIBLE PUMP OUTLET. 9th

World Conference on Experimental Heat Transfer, Fluid Mechanics and Thermodynamics.

Buratto, C., Occari, M., Aldi, N., Casari, N., Pinelli, M., Spina, P. R., & Suman, A. (2017).

Centrifugal pumps performance estimation with non-Newtonian fluids: Review and critical

analysis. 12th European Conference on Turbomachinery Fluid Dynamics and

Thermodynamics, ETC 2017, April 2018. https://doi.org/10.29008/etc2017-248

Buratto, C, Pinelli, M., Spina, P. R., Vaccari, A., & Verga, C. (2015). CFD study on special duty

centrifugal pumps operating with viscous and non-Newtonian fluids. 11th European

Conference on Turbomachinery Fluid Dynamics and Thermodynamics, ETC 2015.

Buratto, Carlo, Occari, M., Aldi, N., Casari, N., Pinelli, M., Spina, P. R., & Suman, A. (2017).

Centrifugal pumps performance estimation with non-Newtonian fluids: review and critical

analysis. 12 Th European Conference on Turbomachinery Fluid Dynamics &

Thermodynamics.

Cellek, M. S., & Engin, T. (2016). 3-D Numerical investigation and optimization of centrifugal

slurry pump using Computational Fluid Dynamics. Of Thermal Science and Technology,

36(1), 69–83.

Chhabra, R. P. (2010). Non-Newtonian Fluids: An Introduction. In Rheology of Complex Fluids

(pp. 3–34). Springer New York. https://doi.org/10.1007/978-1-4419-6494-6_1

Croce Mundo, D. D. (2014). Study of Water/Oil Flow and Emulsion Formation in Electrical

Submersible Pumps. The University of Tulsa.

Croce Mundo, D. D., & Pereyra, E. (2019). Study of Oil/Water Flow and Emulsion Formation in

Electrical Submersible Pumps. SPE Production & Operation.

De Maitelli, C. W. S. P., & De Bezerra, V. M. F. (2015). Numerical simulations of 3D single-phase

flow in a stage of a centrifugal pump of ESP systems. 2015 SPE Artificial Lift Conference -

Latin America and Caribbean, 130–148. https://doi.org/10.2118/173934-ms

Dick, E. (2015). Fundamentals of Turbomachines. In Fluid Mechanics and Its Applications.

Springer Netherlands. https://doi.org/10.1007/978-94-017-9627-9

Donmez, M., & Yemenici, O. (2019). A Numerical Study on Centrifugal Pump Performance with

the Influence of Non-Newtonian Fluids. International Journal of Sciences, 8(04), 39–45.

https://doi.org/10.18483/ijSci.2010

Doron, P., & Barnea, D. (1996). Flow pattern maps for solid-liquid flow in pipes. International

Journal of Multiphase Flow, 22(2), 273–283.

Fairbank, L. A. (1942). Solids in suspension; effects on the characteristics of centrifugal pumps.

Trans. ASCE, 68, 1563–1572.

Fleischfresser, N. A. L. P., Biazussi, J. L., & Bannwart, A. C. (2015). Correlations for the prediction

of the head curve of centrifugal pumps based on experimental data. Proceedings of the 23rd

ABCM International Congress of Mechanical Engineering. https://doi.org/10.20906/cps/cob-

2015-0496

Gerolymos, G. A., & Vallet, I. (2002). Wall-normal-free Reynolds-stress model for rotating flows

applied to turbomachinery. AIAA Journal, 40(2), 199–208.

Govier, G. W., & Charles, M. E. (1961). The hydraulics of the pipeline flow of solid-liquid

mixtures. 75th EIC Annual General Meeting.

Graham, L. J. W., Pullum, L., Slatter, P., Sery, G., & Rudman, M. (2009). Centrifugal pump

performance calculation for homogeneous suspensions. Canadian Journal of Chemical

Engineering, 87(4), 526–533. https://doi.org/10.1002/cjce.20192

Gregory, W. B. (1927). Pumping clay slurry through a four-inch pipe. Mech. Eng, 49(6), 609.

Gülich, J. F. (1999a). Pumping highly viscous fluids with centrifugal pumps - Part 1. World Pumps,

1999(395), 30–34. https://doi.org/10.1016/S0262-1762(00)87528-8

Gülich, J. F. (1999b). Pumping highly viscous fluids with centrifugal pumps - Part 2. World Pumps,

1999(396), 39–42. https://doi.org/10.1016/S0262-1762(00)87492-1

Huang, S., Su, X., & Qiu, G. (2015). Transient numerical simulation for solid-liquid flow in a

centrifugal pump by DEM-CFD coupling. Engineering Applications of Computational Fluid

Mechanics, 9(1), 411–418.

Hydraulic Institute. (1948). Tentative Standards of Hydraulic Institute : Charts for the

Determination of Pump Performance When Handling Viscous Liquids. The Institute.

Ibrahim, S. Y., & Maloka, I. E. (2006). Emulsification of secondary oil/water dispersions using a

centrifugal pump. In Petroleum Science and Technology (Vol. 24, Issue 5, pp. 513–522).

https://doi.org/10.1081/LFT-200041121

Ippen, A. T. (1946). The Influence of Viscosity on Centrifugal Pump Performance. Trans. ASME,

68, 823–848.

J Mastropietro, D. (2013). Rheology in Pharmaceutical Formulations-A Perspective. Journal of

Developing Drugs, 02(02). https://doi.org/10.4172/2329-6631.1000108

Kabamba, B. M. (2006). Evaluation of centrifugal pump performance derating procedures for non-

Newtonian slurries. Cape Peninsula University of Technology.

Kalombo, J. J. N., Haldenwang, R., Chhabra, R. P., & Fester, V. G. (2014). Centrifugal pump

derating for non-Newtonian slurries. Journal of Fluids Engineering, 136(3).

Kaminsky, R. D. (1998). Predicting Single-Phase and Two-Phase Non-Newtonian Flow Behavior in

Pipes. Journal of Energy Resources Technology, 120(1), 2–7.

https://doi.org/10.1115/1.2795006

Karassik, I. J., Messina, J. P., Cooper, P., & Heald, C. C. (2001). Pump handbook (Vol. 3).

McGraw-Hill New York.

Khalil, M., Kassab, S., Ismail, A., & Elazab, I. (2008). CENTRIFUGAL PUMP PERFORMANCE

UNDER STABLE AND UNSTABLE OIL-WATER EMULSIONS FLOW. Twelfth

International Water Technology Conference IWTC12.

Kolev, N. I. (2012). Multiphase flow dynamics 1: Fundamentals. In Multiphase Flow Dynamics 1:

Fundamentals (Vol. 9783642206). https://doi.org/10.1007/978-3-642-20605-4

KSB. (2005). Selecting Centrifugal Pumps. http://www.ksb.com/linkableblob/ksb-en/1549040-

408445/data/Selecting-Centrifugal-Pumps-data.pdf

Le Fur, B., Moe, C. K., & Cerru, F. (2015). High Viscosity Test of a Crude Oil Pump. 44th

turbomachinery and 31st Pump Symposium, Houston, TX, Sept, 14–17.

Li, W.-G. (2014). Mechanism for onset of sudden-rising head effect in centrifugal pump when

handling viscous oils. Journal of Fluids Engineering, 136(7).

Li, W. G. (2000). Effects of viscosity of fluids on centrifugal pump performance and flow pattern in

the impeller. International Journal of Heat and Fluid Flow, 21(2), 207–212.

https://doi.org/10.1016/S0142-727X(99)00078-8

Li, W. G., Su, F. Z., Xue, J. X., & Xiao, C. (2002). Experimental investigations into the

performance of a commercial centrifugal oil pump. World Pumps, 425, 26–28.

https://doi.org/10.1115/1.1458581

Liao, Y., & Lucas, D. (2009). A literature review of theoretical models for drop and bubble breakup

in turbulent dispersions. Chemical Engineering Science, 64(15), 3389–3406.

https://doi.org/10.1016/j.ces.2009.04.026

Mawson, H. (1927). Characteristic Laws for a Centrifugal Pump with Fluids other than Water.

Proceedings of the Institution of Mechanical Engineers, 113(1), 1037–1045.

Monte Verde, W. (2011). Estudo experimental de bombas de BCS operando com escoamento

bifásico gás-líquido. [sn].

Monte Verde, W. (2016). Modelagem do desempenho de bombas de BCS operando com misturas

gás-óleo viscoso.

Morales, R., Pereyra, E., Wang, S., & Shoham, O. (2012). Droplet formation through centrifugal

pumps for oil-in-water dispersions. SPE Journal, 18(1), 172–178.

https://doi.org/10.2118/163055-PA

Morrison, G., Yin, W., Agarwal, R., & Patil, A. (2017). Evaluation of Effect of Viscosity on an

Electrical Submersible Pump. https://doi.org/10.1115/FEDSM2017-69157

Morrison, G., Yin, W., Agarwal, R., & Patil, A. (2018). Development of Modified Affinity Law for

Centrifugal Pump to Predict the Effect of Viscosity. Journal of Solar Energy Engineering,

Transactions of the ASME, 140(9), 1–9. https://doi.org/10.1115/1.4039874

Mrinal, K. R., Siddique, M. H., & Samad, A. (2018). Performance prediction of a centrifugal pump

delivering non-Newtonian slurry. Particulate Science and Technology, 36(1), 38–45.

https://doi.org/10.1080/02726351.2016.1205690

Nädler, M., & Mewes, D. (1995). Effects of the liquid viscosity on the phase distributions in

horizontal gas-liquid slug flow. International Journal of Multiphase Flow, 21(2), 253–266.

Nesbitt, B. (2006). Handbook of Pumps and Pumping. Handbook of Pumps and Pumping.

https://doi.org/10.1016/B978-1-85617-476-3.X5000-8

Nguyen, X. L., & Lai, H. (2017). The Simulation of non-Newtonian Power-law Fluid Flow in a

Centrifugal Pump Impeller. Journal of the Chinese Society of Mechanical Engineers,

Transactions of the Chinese Institute of Engineers, Series C/Chung-Kuo Chi Hsueh Kung

Ch’eng Hsuebo Pao, 38(4), 381–390. https://doi.org/10.4172/2168-9873.1000230

Ofuchi, E. M., Cubas, J. M. C., Stel, H., Dunaiski, R., Vieira, T. S., & Morales, R. E. M. (2020). A

new model to predict the head degradation of centrifugal pumps handling highly viscous

flows. Journal of Petroleum Science and Engineering, 187(November 2019), 106737.

https://doi.org/10.1016/j.petrol.2019.106737

Ofuchi, E. M., Stel, H., Sirino, T., Vieira, T. S., Ponce, F. J., Chiva, S., & Morales, R. E. M. (2017).

Numerical investigation of the effect of viscosity in a multi-stage electric submersible pump.

Engineering Applications of Computational Fluid Mechanics, 11(1).

https://doi.org/10.1080/19942060.2017.1279079

Ofuchi, E. M., Stel, H., Vieira, T. S., Ponce, F. J., Chiva, S., & Morales, R. E. M. (2017). Study of

the effect of viscosity on the head and flow rate degradation in different multi-stage electric

submersible pumps using dimensional analysis. Journal of Petroleum Science and

Engineering, 156, 442–450. https://doi.org/10.1016/j.petrol.2017.06.024

Pagalthivarthi, K. V, Gupta, P. K., Tyagi, V., & Ravi, M. R. (2011). CFD Predictions of Dense

Slurry Flow in Centrifugal Pump Casings. International Journal of Mechanical and

Mechatronics Engineering, 5(3), 538–550.

Perissinotto, R. M., Monte Verde, W., Gallassi, M., Gonçalves, G. F. N., Castro, M. S. de, Carneiro,

J., Biazussi, J. L., & Bannwart, A. C. (2019). Experimental and numerical study of oil drop

motion within an ESP impeller. Journal of Petroleum Science and Engineering, 881–895.

https://doi.org/10.1016/j.petrol.2019.01.025

Perissinotto, R. M., Verde, W. M., Biazussi, J. L., de Castro, M. S., & Bannwart, A. C. (2019).

Experimental analysis on the velocity of oil drops in oil-water two-phase flows in electrical

submersible pump impellers. Journal of Offshore Mechanics and Arctic Engineering, 141(4).

https://doi.org/10.1115/1.4042000

Perissinotto, R. M., Verde, W. M., Perles, C. E., Biazussi, J. L., de Castro, M. S., & Bannwart, A.

C. (2020). Experimental analysis on the behavior of water drops dispersed in oil within a

centrifugal pump impeller. Experimental Thermal and Fluid Science, 112, 109969.

Poursharifi, Z., Bonab, M. B. E., & Majidi, S. H. (2012). Experimental study of loss coefficients of

hydraulic parameters for a centrifugal pump when pumping viscous liquids. International

Journal of Fluid Mechanics Research, 39(1), 75–84.

https://doi.org/10.1615/InterJFluidMechRes.v39.i1.50

Pullum, L., Graham, L. J. W., & Rudman, M. (2007). Centrifugal pump performance calculation for

homogeneous and complex heterogeneous suspensions. Journal of the Southern African

Institute of Mining and Metallurgy, 107(6), 373–379.

Rønningsen, H. P. (2012). Rheology of Petroleum Fluids. Annual Transactions of The Nordic

Rheology Society, 20, 11–18.

Šavar, M., Kozmar, H., & Sutlović, I. (2009). Improving centrifugal pump efficiency by impeller

trimming. Desalination TA - TT -, 249(2), 654–659.

https://doi.org/10.1016/j.desal.2008.11.018 LK -

https://univdelosandes.on.worldcat.org/oclc/5900148777

Sery, G., Kabamba, B., & Slatter, P. (2006). Paste Pumping with Centrifugal Pumps: Evaluation of

the Hydraulic Institute Chart De-Rating Procedures. Proceedings of the Ninth International

Seminar on Paste and Thickened Tailings, 403–412.

https://doi.org/10.36487/acg_repo/663_35

Sery, G., Slatter, P. T., & Heywood, N. (2002). Centrifugal pump derating for non-Newtonian

slurries. Proc. Hydrotransport, 15, 679–692.

Shah, S. R., Jain, S. V, Patel, R. N., & Lakhera, V. J. (2013). CFD for centrifugal pumps: A review

of the state-of-the-art. Procedia Engineering, 51, 715–720.

https://doi.org/10.1016/j.proeng.2013.01.102

Shojaee Fard, M. H., Ehghaghi, M. B., & Boyaghchi, F. A. (2005). Experimental and numerical

investigation of centrifugal pump performance when handling viscous fluids. American

Society of Mechanical Engineers, The Fluid Power and Systems Technology Division, FPST,

12 FPST(1996), 139–146. https://doi.org/10.1115/IMECE2005-79154

Shojaeefard, M. H., Tahani, M., Ehghaghi, M. B., Fallahian, M. A., & Beglari, M. (2012).

Numerical study of the effects of some geometric characteristics of a centrifugal pump

impeller that pumps a viscous fluid. Computers and Fluids, 60, 61–70.

https://doi.org/10.1016/j.compfluid.2012.02.028

Siddique, M. H., Manayilthodiyil, S., Husain, A., Samad, A., & Kenyery, F. (2016). Numerical

Analysis of Fluid Flow Through an Electrical Submersible Pump for Handling Viscous

Liquid. Fluids Engineering Division Summer Meeting, 50282, V01AT02A004.

Sirino, T., Stel, H., & Morales, R. E. M. (2013). Numerical Study of the Effect of Viscosity on an

Electrical Submersible Pump. 22nd Internation Congress of Mechanical Engineering, 9164–

9175.

Solano, E. (2009). VISCOUS EFFECTS ON THE PERFORMANCE OF ELECTRO SUBMERSIBLE

PUMPS (ESP’s).

Stel, H., Sirino, T., Ponce, F. J., Chiva, S., & Morales, R. E. M. (2015). Numerical investigation of

the flow in a multi-stage electric submersible pump. Journal of Petroleum Science and

Engineering, 136, 41–54. https://doi.org/10.1016/j.petrol.2015.10.038

Stel, H., Sirino, T., Prohmann, P. R., Ponce, F., Chiva, S., & Morales, R. E. M. (2014). CFD

investigation of the effect of viscosity on a three-stage electric submersible pump. American

Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM, 1B.

https://doi.org/10.1115/FEDSM2014-21538

Stepanoff, A. J. (1948). Centrifugal and Axial Flow Pumps: Theory, Design and Application. John

Wiley and Sons.

Stoffel, B. (2015). Physical and Technical Background of the Electrical Power Input of Pump Units.

In Assessing the Energy Efficiency of Pumps and Pump Units (pp. 63–75). Elsevier.

https://doi.org/10.1016/b978-0-08-100597-2.00005-7

Tetlow, N. (1943). A survey of modern centrifugal pump practice for oilfield and oil refinery

services. Proceedings of the Institution of Mechanical Engineers, 150(1), 121–134.

Turzo, Z., Takacs, G., & Zsuga, J. (2000). Equations correct centrifugal pump curves for viscosity.

Oil and Gas Journal, 98(22), 57–67.

Valdés, J. P., Asuaje, M., & Ratkovich, N. (2020). Study of an ESP’s performance handling liquid-

liquid flow and unstable O-W emulsions Part I: Experimental. Chemical Engineering Science,

223, 115726. https://doi.org/10.1016/j.ces.2020.115726

Valdés, J. P., Becerra, D., Rozo, D., Cediel, A., Torres, F., Asuaje, M., & Ratkovich, N. (2019).

Comparative analysis of an electrical submersible pump’s performance handling viscous

Newtonian and non-Newtonian fluids through experimental and CFD approaches. Journal of

Petroleum Science and Engineering, 187. https://doi.org/10.1016/j.petrol.2019.106749

Varon, M. P. (2013). Estudo de uma bomba centrífuga submersa (BCS) como medidor de vazão.

Walker, C. I., & Goulas, A. (1984). Performance characteristics of centrifugal pumps when

handling non‐Newtonian homogeneous slurries. ARCHIVE: Proceedings of the Institution of

Mechanical Engineers, Part A: Power and Process Engineering 1983-1988 (Vols 197-202),

198(1), 41–49. https://doi.org/10.1243/PIME_PROC_1984_198_006_02

Yeoh, G. H., & Tu, J. (2019). Computational techniques for multiphase flows. Butterworth-

Heinemann.

Yu, S. C. M., Ng, B. T. H., Chan, W. K., & Chua, L. P. (2000). The flow patterns within the

impeller passages of a centrifugal blood pump model. Medical Engineering and Physics,

22(6), 381–393. https://doi.org/10.1016/S1350-4533(00)00045-X

Zhu, J., Banjar, H., Xia, Z., & Zhang, H. Q. (2016). CFD simulation and experimental study of oil

viscosity effect on multi-stage electrical submersible pump (ESP) performance. Journal of

Petroleum Science and Engineering, 146, 735–745.

https://doi.org/10.1016/j.petrol.2016.07.033

Zhu, J., Zhu, H., Cao, G., Banjar, H., Peng, J., Zhao, Q., & Zhang, H.-Q. (2019). A New

Mechanistic Model for Oil-Water Emulsion Rheology and Boosting Pressure Prediction in

Electrical Submersible Pumps ESP. https://doi.org/10.2118/196155-ms