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CHEMICAL ENGINEERINGTRANSACTIONS 
 

VOL. 55, 2016 

A publication of 

 
The Italian Association 

of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors:Tichun Wang, Hongyang Zhang, Lei Tian
Copyright © 2016, AIDIC Servizi S.r.l., 
ISBN978-88-95608-46-4; ISSN 2283-9216 

Numerical Simulation Study on Erosive Wear of ESP 

Yanxin Liua,b*, Runtao Wanga, Mingwei Chaoc, Lijun Zhanga 
a
 College of Mechanical Engineering, China University of Petroleum, Qingdao 266580, P.R. China 

b 
College of Petroleum Engineering, China University of Petroleum, Qingdao 266580, P. R. China 

c 
East China Institute of China Petroleum Engineering and Construction Corp, Qingdao 266071, P. R. China 

liuyanxin1985@163.com 

Wear of electric submersible pump (ESP) in oilfield was caused by high sand content in the high water-cut 
stage. RNG k-ε turbulence model and discrete phase model are deployed for numerical simulation to study the 
effect of conditions and structural parameters on the wear of ESP impellers. It is showed that concave side of 
impeller blades and central area of guide impeller’s inner wall are the most eroded area. Wear rate will 
increase with the rising of sand concentration rate and pump speed. With the rising of particle size, impeller’s 
wear rate will increase first then decrease. The average wear rate of impeller will decrease with the increase 
of inlet angle, while the rise of outlet angle will make it rise and fall. Results of numerical simulation can be 
applied to designs of ESPs. 

1. Introduction 
With the continuity of development, a lot of oilfields in china entered the high water-cut stage. Electric 
submersible pump (ESP) became the major lifting method for increasing and stabilizing oil production in this 
stage, due to its wide range of displacement and lift, larger power, high adaptability, long inspection period, 
convenient in management and remarkable economic benefit. However, in the high water-cut stage, ESP’s 
useful life and economic benefit was reduced by the situation of high water-cut, high sand content, high 
salinity and complication of shaft’s condition. Due to the high sand content, severe erosive wear took place on 
impeller, causing efficiency decrease and affecting the normal operation. In severe cases, perforation took 
place and leads to pump shell rupture or unit falling. In order to take appropriate protective measures, it is 
necessary to analyse the wear on the impeller and study the wear mechanism. 
According to statistics, in 2014, there were 261 times of pump operation, 59 times of cylinder 
perforation(Figure1a) and 2 times of unit falling(Figure1b) in Shengtuo oilfield. Wear usually took place at seal 
ring that connects the outlet of impeller and guide impeller, showing a layered circumferential distribution at 
the inner surface of pump shell, while the perforations start from the inside, holes from outside is smaller than 
inside. Perforations in pump shell are corresponding to the site of guide impeller, perforations start from the 
inside, which means perforation in pump shell is caused by the guide impeller’s perforation. 
 

  
(a) Fracture caused by perforations (b) perforations 

Figure 1: The pump barrel perforation failure caused by perforations 

Electric submersible centrifugal pump is a kind of centrifugal pump, the present study focused on the slurry 
pumps and other centrifugal pumps with large diameter, horizontal type, impeller-spiral inlet, high sand content 
(more than 1%), and large solid particles. Limited research about flow field and erosive wear have been done 
on ESPs with small diameter, low sand content (less than 0.05%), high pump speed and small particle size. 
Erosive wear of centrifugal slurry pumps is primarily governed by the particulate motion and concentration 
(Pagalthivarth iet al, 2007; Pagalthivarthi et al, 2011). Using coating method that head of the impeller was 

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1655022

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Liu Y.X., Wang R.T., Chao M.W., Zhang L.J., 2016, Numerical simulation study on erosive wear of esp, Chemical 
Engineering Transactions, 55, 127-132  DOI:10.3303/CET1655022   

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found to be the most eroded area, and bigger outlet angle will lead to a rise in wear rate. Erosive wear 
affected by particle size and flow rate was studied. Solids content of the working fluid, the regions of high wall 
shear, and particle impingement with the walls were major mechanisms associated with the erosive wear (Lee 
et al, 2002). The failure analysis on the centrifugal slurry pump was performed along with the 
countermeasures (Khalid et al, 2007). Erosive wear of slurry pmups was observed while accurate location of 
maximum wear was predicted through CFD (Roudnev et al, 2009). Numerical calculation and analysis on the 
erosive wear of ESP has been done using discrete phase model (Chen et al, 2015; Wang et al, 2014). They 
found that the impact wear will be more severe with the increasing in sand particle size and impeller speed. 
0.07mm is the critical diameter of the erosion’s intensifying. 

2. Solid and liquid governing equation based on discrete phase model (DPM) 
2.1 Liquid phase flow governing equation 
The type line of impeller and guide impeller blade is curved, as well as the flow line of fluid. Turbulence shows 
anisotropy. Comparing with the standard k-ε turbulence model, RNG k-ε turbulence model is more capable of 
being used due to its modification of turbulence viscidity and consideration on rotation of average flow and 
swirling flows. 

( ) ( )  ∂ ∂ ∂ ∂
  ∂ ∂ ∂ ∂ 

f f i
k e k p f

i j j

ρ k ρ u k k
+ = α μ + G + G - ρ ε

t x x x
  

(1) 

( ) ( ) ( )
 ∂ ∂ ∂ ∂
  ∂ ∂ ∂ ∂ 

f f i *
ε e ε k ε f

i j j

ρ ε ρ u ε ε ε
+ = α μ + C G - C ρ ε

t x x x k
1 2

  

(2)

 

In Eq. (1, 2), ρf is density of fluid, k is turbulent kinetic energy, εis turbulent energy dissipation rate, eμ  is 
effective viscosity coefficient, Gp is the turbulent kinetic energy generated by buoyancy, Gk is the turbulent 
kinetic energy by velocity gradient. ∗ , are the parameters, = =1.39. 
2.2 Discrete phase(sand) governing equation 
In discrete phase model, the trajectory of particles can be obtained by solving differential equation of particle 
force in Lagrange coordinate system. Solid particles are subjected to various kinds of forces, such as gravity, 
all kinds of additional forces, centrifugal force, Coriolis force, Basset force, Magnus force, etc. Governing 
equation is as follows. 

( ) 
 
 6

s fs s s
s D V P S o th e r

s

g ρ - ρd u π d ρ
m = + F + F + F + F + F

d t ρ

3

  

(3) 

In Eq. (3), ρs is density of sand particle, g is gravity, FD is circle resistance of fluid, FV is additional mass force, 
FP is additional force by pressure gradient, Fother is sum of centrifugal force, Coriolis force, Basset force, and 
Magnus Force. 

2.3 Calculation model on wear rate 
Wear rate is defined as the material that worn away by particle force from the surface in unit area. 

( ) ( ) ( )


b V'N
p p

wear
p= f

m C d f α V
R =

A1   
(4) 

In Eq. (4), Rwear is wear rate, kg·m
-2·s-1. is mass flow rate presented by sand particle, C(dp) is function 

related to particle size. α is impact angle between sand particle and wall. f(α) is function related to the impact 
angle. V is impact velocity. b(V) is function related to the impact velocity. Af is the area of calculation unit. N is 
granular number that impacts the unit area Af. 

3. Numerical simulation and analysis on wear of ESP  
3.1 Numerical simulation model on wear of ESP 
ESP model W150 with cylindrical impeller is selected. There are 8 blades in impeller while 12 in guide 
impeller. Single-stage flow channel from impeller inlet to the guide impeller outlet are selected as the 
calculation area of simulation. Fig.2 is 3D flow field model of single stage ESP. 
(1) Model selection and coordinate system setup 
DPM and RNG k-ε in turbulence model are selected. The displacement is 150m3/d, particle diameter is 
0.05mm, sand inlet volume fraction 0.03%, sand density is 2700kg/m3. 

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For flow channel model, part of the impeller’s flow channel is rotating at high speed, while the flow channel 
between guide impeller and impeller is stationary. For movable flow region, multi reference frame model 
(MRF), which transforms unsteady flow to steady flow and calculate only the instantaneous flow field in certain 
impeller position, is selected. The result is in that position only. Set the flow region of impeller in kinetic 
coordinate system, and rotation speed at 2300r/min 
 

     
(a) impeller  (b)guide impeller  (c) whole flow field 

Figure 2: 3D flow field model of single stage ESP 

(2) Boundary conditions of inlet and outlet 
Liquid phase: selecting velocity-inlet at inlet, outflow at outlet.  
Particle phase: escape at outlet 
Solid phase inlet: surface injection, particle size, mass flux rate, inert particle, 2700kg/m3. 
(3) Wall condition 
Liquid phase: no slip. 
Solid phase: reflect wall. 

3.2 Wear analysis of submersible pump based on DPM 
(1) Impeller 
Figure 3 is the wear distribution of the impeller cover plate. It can be seen from Figure 3 that except for the 
severe wear at outlet and inlet, rest of the area share an even distribution of wear from the front side, wear 
rate of places near suction surface is a little bit higher than other places. The front side of back cover suffers 
the most of wear while the back side takes less damage. The average wear rate of front side is 5.98×10-5 
kg·m-2·s-1 while it is 1.11×10-4 kg·m-2·s-1 at front side; obviously the back side takes more damage. 
 

 
(a) Front cover (b) Back cover 

Figure 3: The wear distribution on impeller cover plate 

Figure 4 shows wear distribution of impeller blades. It can be seen from Figure 4 that the suction surface of 
impeller blade suffers a wide range of wear; inlet of the blade is heavily eroded while the wear rate of middle 
part is lower and the outlet is barely intact. Erosive wear is mostly taken place at the bottom and the top in the 
pressure surface; the results are in agreement with Xu H.The suction surface (average wear rate 1.46×10-
4kg·m-2·s-1) takes more damage than the pressure surface (average wear rate 4.36×10-5kg·m-2·s-1), and a 
larger wear area. 
 

                        
(a) Overall distribution             (b) Suction surface          (c) Pressure surface 

Figure 4: Wear distribution of impeller blades 

(2) Guide impeller 

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Figure 5 isthe wear distribution of impeller blades. It can be seen from Figure5 that the area suffers from 
highest wear rate is in the central of inner surface, where the sealing ring placed, showcasing a circumferential 
distribution. Some individual points are particularly serious eroded, becoming the most seriously eroded part 
of the pump (Figure 1a). Calculation results are consistent with the wear patterns. At the outlet of impeller 
blade, sand comes out at a high speed with liquid flow, causing the direct impact on the inner wall of the guide 
impeller where the wear rate is much higher than other places. Concave side erodes more seriously than 
convex side in guide impeller. In the concave side wear always happen at the outlet and inlet, central position 
shares an even distribution of wear, while wear place in convex side is located at the inlet of blade. 
 

 
(a) Inner surface                           (b) blade 

Figure 5: The wear distribution of impeller blades 

4. Effect on wear of ESP impellers by working condition and structural parameters 

4.1 Working condition parameters 
The impeller is an essential component of centrifugal pump, providing energy for lifting the drilling fluid. Thus 
become the most vulnerable part of wear. Wear on the impeller wall will lead to a drop of efficiency by losing 
the original type line and series of consequences by imbalance of rotor. The influence on wear of ESP by 
different factors such as working conditions (sand grain size, sand concentration, pump speed) and impeller 
structural parameters (inlet and outlet angle) is discussed. 
(1) Particle size and concentration rate 
In practical environment, sand rate is required to be no more than 0.05%, however, it would be higher at initial 
stage of production. Therefore the simulation working condition is as follows, rated displacement: 50m3/d, 
solid phase volume fraction of solid phase: 0.03%, 0.05%, 0.1%, particle diameter: 0.03mm, 0.04mm, 
0.05mm, 0.06mm, 0.07mm, 0.08mm. 
At the sand concentration rate of 0.03%, 0.05%, and 0.1%, Change the particle size to calculate the influence 
on erosive wear by sand concentration rate and particle size. 0.03% is selected to analyse the erosive impact 
by particle size. Figure 6 is the wear cloud map at the sand concentration rate of 0.03%. It can be seen from 
Figure6 that with the increase of the particle size, eroded area of impeller blade’s suction surface becomes 
larger, the max wear rate first rise then decline. Pressure surface suffers a severe wear from bottom and top, 
with the increase of particle size, outlet takes more damage. 
 

 

0.03mm                0.04mm        0.05mm        0.06mm       0.07mm         0.08mm 
(a) Suction surface under different particle diameter 

 

0.03mm       0.04mm          0.05mm          0.06mm          0.07mm      0.08mm 
(b) Pressure surface under different particle diameter 

Figure 6: Wear cloud map at concentration rate of 0.03% under different particle sizes 

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Figure 7 shows the wear rate varying with particle size at different sand concentration rate.It can be seen from 
Figure 7 that higher concentration rate means higher wear rate. When concentration rate is set, wear rate will 
go up then go down with the increase of the particle size. Wear rate peaked at different particle size in 
different concentration rate, 0.05mm at 0.03%, 0.06mm at 0.05%, 0.06mm at 0.1%. At certain concentration 
rate, mass of the individual particles will increase with the increase of particle size but the number of particles 
will decrease, thereby reducing the number of collisions with the wall of the impeller, the average wear rate of 
impeller blade will increase at first then go down under the combined influence of the quantity and mass of the 
particles. When particle size is set, wear rate will go up with increase of concentration rate. 
 

    

Figure 7: Average wear rate under different 
particle size and concentration rate 

Figure 8: Average wear rate varies under different 
rotational speed 

(2) Pump speed 
Select pump speed at 2300r/min, 2500r/min, 2700r/min, 2900r/min and 3100r/min, solid phase volume fraction 
at 0.05%, particle diameter in 0.05 mm to analyse the effect by pump speed. Figure 8 is the average wear rate 
of different pump speed. According to Figure 8, higher pump speed causes more wear. If moderately reduce 
the rotor speed in the premise of meeting the basic working requirement, it will reduce the damage of the wear 
to a certain extent. 

4.2 Structural parameters 
(1) Inlet angle 
Select the outlet angle β2 at 22°, β1 at 26°, 30°, 34°, 38°, 42°, solid phase volume fraction at 0.03％, particle 
size in 0.05mm, Figure 9shows the results of average wear rate in different inlet angle. 
It can be seen from Figure 9 that at a certain blade outlet angle (β2=22°), with increase of inlet angle, wear 
rate of front cover faces a continuous downtrend, but decrease rate becomes lower. The wear rate of back 
cover faces a linear decline. Wear rate of front cover is higher than back cover when β1<32°, but after that the 
back cover outnumbered. With the increase of inlet angle, wear rate of suction surface shows a trend of 
fluctuation, peaked at 36° then faced a dramatic decline and reached its minimum value at 42°. Average wear 
rate of pressure surface was on a slight decline and always lower than the suction surface. The overall wear 
rate of impeller decreased with the rising of inlet angle. As a result, when the outlet angle is set (β2=22°), with 
the increase of inlet angle, the average wear rate will decrease in general, thus a bigger inlet angle should be 
selected in design stage. 
 

   

Figure 9: The average wear rate under different 
inlet angle 

Figure 10: The average wear rate under different 
outlet angle

(2) Outlet angle 
Select the inlet angle β1 at 38°, β2 at 18°, 22°, 26°, 30°, 34°, solid phase volume fraction at 0.03%, particle 
size in 0.05mm, Figure 10 shows the results of average wear rate in different outlet angle.It can be seen from 

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Figure 10 that at a certain blade inlet angle(β1=38°), with increase of outlet angle, wear rate of front cover 
decrease first then slightly increase. The wear rate in back cover faces a continuous down trend but always 
higher than the front cover. The average wear rate of suction surface shows a trend of fluctuation (decrease 
first, increase and then decrease again), while the wear rate of pressure surface increase first then decrease, 
both of which reach their bottom at β2=26°. The average wear rate of impeller also reaches the lowest point at 
β2=26°. Therefore outlet angle of impeller should be neither too high nor too low. 

5. Conclusion 
1) Sever erosive wear are located at head and middle part of suction surface, as well as the inlet and outlet of 
pressure surface. Inner wall of guide impeller that corresponding to impeller outlet are the most eroded area. 
Thus protective coating in those areas will help to reduce the erosive wear. 
2) With the increase of sand concentration rate and pump speed, wear rate will rise. When the concentration 
rate is set, wear rate will first go up then go down with the rising of particle size. 
3) The average wear rate will go down with increase of inlet angle, while the increase of outlet angle will make 
it increase and then decrease. Therefore in design stage, it is better to select a higher inlet angle, while the 
outlet angle should be neither too high nor too low. 

Acknowledgment 

This work was financially supported by Natural fund of Shandong Province (Approval No. ZR2015EL012). 

References 

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