NACE 11005

 
 
 
 
 
 
 
Evaluation of Different Modelling Methods Used 
for Erosion Prediction 
 
Mysara Eissa Mohyaldinn 1
, Noaman Elkhatib 1
, Mokhtar Che Ismail
2
, Razali Hamzah2
1
Geoscience and Petroleum Engineering Department, University Teknologi PETRONAS, Malaysia
31750 Bandar Seri Iskandar, Tronoh, Perak, Malaysia
E-mail: mysara12002@yahoo.com
2
Mechanical Engineering Department,Universiti Teknologi PETRONAS, Malaysia
31750 Bandar Seri Iskandar, Tronoh, Perak, Malaysia
 
ABSTRACT
In this paper, the three methods of modeling erosion in pipe components due to sand production with oil and gas
are investigated by the mean of comparison of results obtained from Salama model, DIM model, and DPM model,
the three models selected to represent empirical, semi-empirical, and CFD methods, respectively.  The DPM
model was assumed as a benchmark based on which Salama model and DIM model were investigated. The results
obtained from the DIM model agree fairly with those obtained from the DPM model whereas Salama model
highly overestimates the DPM model. Based on the comparison, Salama model was modified to increase its
accuracy, from one hand, and to extend it to application to oil, from the other hand.
 
Keywords: erosion, Salama, direct impingement, discrete phase, model
 
 
INTRODUCTION
 
The entrainment of sand particles in fluids flowing through horizontal or vertical pipes is frequently encountered
during oil and gas production and transportation. In conventional oil production, sand is produced with oil and gas
from a sandstone reservoir under certain conditions, such as are unconsolidated formation, water breakthrough,
Paper No. 
11005
 reservoir pressure depletion, and high lateral tectonics  (Carlson  et al. October 1992). In unconventional oil or
crude bitumen, which is a mixture of sand, bitumen, and water  (Tian 2007); sand is produced with very high
volume fraction. 
The entrainment of sand in fluids causes wear of pipes and fittings through which it flows due to the impingement
of sand particles on internal surface of the pipes and fittings. The erosion may take place in different subsurface
and surface components such as in sand control screen  (Colwart et al. 2007), choke  (Haugen et al. 1995), valve
(Mazur et al. 2004), plugged tee, and elbow (Chen et al. 2006) 
The severity of the wear depends on many factors related to the  fluid, sand particles, and target material  (Finnie
1972)  (Deng et al. 2005),  (Barton 2003)  (Ahlert 1995),  (Karelin 2002). N A Barton  (Barton 2003) has arranged
the components, where the erosion takes place according to erosion vulnerability, in eight ranks ranging from
chokes as the most vulnerable component to straight pipes as the least vulnerable component.  
The wear (erosion) rate for a material used in any flow process can be determined either by field or laboratory
tests under simulated conditions or by calculating it using a selected mathematical or computational model,
providing that all the flow parameters are included in the model. Although field and laboratory tests guarantee
more accurate results than modeling, but the later eliminates some disadvantages of the former such as:
1.   The cost required to set up the experimental rig.
2.   The difficulties of controlling the process parameters during the test.
3.   Longer time required for a test run
4.   In the case of some field tests, the interruption of the process and destruction of the material. 
Modeling erosion requires proper selection of the model that suitable to the specified process, from one hand,
and provides accepted accuracy, from the other hand.
The models in open literature used for prediction of erosion due to sand flow with oil or gas can be grouped
into three categories as shown in Table 1. 
 
 
 
Table 1: Methods of erosion modeling  
Category   Advantages  Disadvantages  Examples 
CFD models  The most accurate, provides erosion rate
distribution, solve for the primary (fluid)
and secondary (sand particles) phases
Costly (Mostly commercial
software), time consuming,
high difficulties
Fluent, Ansys
Semi-
empirical
models
Accuracy to be examined, solve for the
secondary (sand particles) phase
Moderate difficulty  Direct
impingement
model
Empirical
models
Accuracy to be examined, very easy  No particles solution  API model,
Salama model
 
One model has been selected from the empirical method and another one from the semi-empirical method. The
two models have been employed to develop a computational code for erosion rate prediction. The results obtained
from the code were compared to those obtained  from the CFD model to evaluate their accuracy, considering the
CFD model as a benchmark.
 
1.1 Empirical method
In this method, erosion is predicted for a component (most probably elbow or tee) by using the fluid velocity (no
particles or bubbles tracking). This method is commonly based on simple empirical correlations that predict
erosional velocity (the velocity above which erosion occurs) and erosion rate, and it is more applicable to gas flow
where the dispersed phase (particles or bubbles) is almost flowing  at the fluid mean velocity. The erosional
velocity,
e V
is widely predicted using the American Petroleum Institute Recommended Practice equation (API RP
14 E) (Institiute 1991). 
f
e
c
V


 
(1) Where C is constant, its value as proposed by API RP 14 E is 100 for continuous service and 125 for intermittent
service, and
f

 is density of the fluid. 
Many researchers and investigators have questioned the accuracy of equation (1) on the ground of neglecting of
other important factors such as particles size and shapes, component geometries and fluid density. Therefore
many attempts have been made to enhance the accuracy, and to extend the applicability of RP 14 E equation.
Salama and Venkatesh proposed a model for prediction of penetration rate  in elbows and tees  (Salama and
Venkatesh 1983). Their model in SI units, assuming a sand density of 2650 kg/m3
, can be written as follows:
2
2
585 . 37
PD
WV
ER 
 
(2)
Where ER is the erosion rate (mm/year), W is sand production rate (Kg/s), V is the fluid flow velocity (m/s), P is
the hardness parameter (Bar), and D is the pipe diameter (m). Salama and Venkatesh used equation (2) to
calculate the erosional velocity for steel pipes using a P value of 1.05X104
 Bar for allowable erosion rate of 0.254
mm/year. This resulted in the following equation for erosional velocity. 
W
D Ve
0152 . 0

 
(3)
The shortcomings of Salama and Venkatesh model (equation  (3)) are its neglect of sand particle size and shape,
and its inapplicability to two-phase (liquid-gas) flow. Their model  also neglects   sand hardness, but since the
model only deals with sand particulates where their hardness varies slightly, so we believe that neglecting the
hardness is logical. The material hardness is also not considered due to the fact that the model only deals with
carbon steel materials. Salama  (Salama, 2000)  incorporated the effect of two-phase mixture density and particle
size into equation 2-15 and proposed the following equation. 
m
m
m D
d WV
S
ER
 2
2
574 . 11

 
(4)
Where ER is the erosion rate (mm/year), W  is the sand production rate kg/s, d is particle diameter (micron), D is
the pipe internal diameter (m), and   and   are mixture velocity (m/s) and density (kg/m3), respectively. In
equation 2-17, Sm  is a geometry-dependant constant as given in Table 1. 
Equation (4) was developed through numerous tests that were carried out using water and nitrogen gas. Since
water and gas viscosities are almost constant, therefore  the viscosity parameter  has not been included in the
equation. Salama, however, expected that higher viscosity will result in reduction of erosion rate (Salama, 2000).
Table 1: The geometry-dependent constant in Salama equation (Salama, 2000)
Geometry   Elbow (1.5 and
5D
Seamless and
cast elbows (1.5
to 3.25 D)
Plugged tee
(gas-liquid)
Plugged tee (gas
flow)
m S
  5.5  33  68  1379
 
In this work, Salama model has been selected as an example of empirical method for sand erosion prediction.
A predictive tool has been developed by employing Salama model to Visual Basic programming. In the predictive
tool, from the input data form of Salama model shown in Figure 1, the user can select the geometry and input
fluid and sand properties, which include flow velocity, sand production rate, sand size, pipe diameter, and fluid
density. To examine the results of Salama model, the data shown in Figure 1 for velocity, sand production rate,
sand size, and pipe diameter was used. Three values of density were used to predict erosion rate in gas (with
density of 1.2015 kg/m3), water (with density of 1000 kg/m3), and oil (with density of 850 kg/m3). The variation
of erosion rate with velocity for the three fluids is shown in Table 2.   
Figure 1: Input data form of Salama model
 
 
Table 2: Variation of erosion rate with velocity for gas, water, and oil (Salama model)
Velocity m/s
Erosion rate mm/year
gas  water  oil
0  0  0  0
0.8  0.81551  0.00098  0.00115
1.6  3.26206  0.00392  0.00461
2.4  7.33963  0.00882  0.01037
3.2  13.0482  0.01568  0.01844
4  20.3879  0.0245  0.02882
4.8  29.3585  0.03527  0.0415
5.6  39.9602  0.04801  0.05648
6.4  52.1929  0.06271  0.07378
7.2  66.0566  0.07937  0.09337
8  81.5514  0.09798  0.11528
8.8  98.6772  0.11856  0.13948
9.6  117.434  0.1411  0.166
10.4  137.822  0.16559  0.19482
11.2  159.841  0.19205  0.22594
12  183.491  0.22046  0.25937
12.8  208.772  0.25084  0.2951
13.6  235.684  0.28317  0.33315 14.4  264.227  0.31747  0.37349
15.2  294.401  0.35372  0.41614
16  326.206  0.39194  0.4611
16.8  359.642  0.43211  0.50836
By comparing column 3 and column 4 in Table 2, we can notice that the erosion rate for oil is greater than
that of water, which is enological result. This error is due to the fact that no account is taken for viscosity in the
Salama model and erosion rate changes inversely with fluid density. This result is shown graphically in Figure 2.
 
 
 
Figure 2: Variation of erosion rate with velocity for water and oil (Salama model)
 
1.2 Semi-empirical method
Direct impingement model (DIM) was selected as an example for this method. In the DIM method, erosion is
predicted by using simplified particles trajectory equations (the direct impingement model). This is a mechanistic
model developed by Erosion/Corrosion research center (E/CRC) at University of Tulsa to predict the penetration
rate of direct impingement of elbows and tees. The direct impingement model can predict the penetration rate
after determining the direct impact velocity. The data required for the direct impingement model are those relating
to the component (geometry and size), flow (velocity, density and viscosity), and particle (density, size, and
shape). To account for the particle trajectory along the flow stream, the concept of equivalent stagnation length
has been introduced. The concept of equivalent stagnation length can be explained by the same way as  the
equivalent  length used to predict local pressure loss in fittings, in  which, different component geometries have
different equivalent stagnation lengths (McLaury 1996) . 
The DIM model has been employed to develop a predictive tool for easy and quick prediction of erosion rate. The
tool development involves a numerical solution to the simplified equation of particle motion proposed by E/CRC
(Equation 5). Our numerical solution algorithm is shown in Figure 3 with

 and
Re
are the dimensionless
particle mass ratio and particle Reynolds number defined previously by E/CRC (McLaury 1996).
 
 
(5)
The solution of the above equation enables tracking sand particles to calculate their velocity within the stagnation
zone and their impingement velocity. The impingement velocity is then introduced to a sand  erosion prediction
formula to predict sand erosion rate.







 

 

















p f p
p f f
p
p f p f
p
f
p
p
d V
V V
V
V V V V
d dx
dV



 ) ( 24 ) ( 5 . 0 1
75 . 0 
 
��𝑅�
� = � + 1
��� = 1, 𝑇� = 1, � = (� − 0.5)��,�� = �0,�� = �0
��� > �𝑆 & 
𝑇� < 100
�0 = 1 ,��  =  0.01, �𝑆  =  0.00001, � = 1
 
� < 100
 
�� = 0.5(�� + �0)
  �� = 0.75   1 – X – VA 
 VA
(0.5 1  −  X  −  VA  + 
24
��
 )∅ × ��
 
�� = �0  +  ��, ��  =   �� − �� 
��  = ��, 𝑇�  =  𝑇�  +  1
 
�𝐷
�0 = ��
Yes
Yes
No
No
 
 
Figure 3: The numerical solution of the equation of particles motion.
 
The DIM model input data form is shown in Figure 4. The user can input data related to the fluid, sand, and
target material to this form; and select the geometry. 
Figure 4: Input data form of the DIM model
 
The change of the particle’s velocity depends on many factors that are related to the carrier fluid, geometry of the
target material and the properties of the dispersed particles.
Three fluids have been considered to analyze the effect of fluid properties on particle’s velocity in elbow. These
fluids are air, water, and crude oil with properties shown in Table 3. Similar properties and geometry of sand are
assumed for all fluids.
Table 3: Input data for erosion simulation
Property  Unit  Gas  Water  Oil
Density  Kg/m3
1.2015  1000  900
Viscosity  Pa.s  0.0000182  0.00018  0.009
Velocity  m/s  20
Sand size  Micron  300
Sand density  Kg/m3
2650
Elbow ID  m  0.05
 
The results of sand trajectories for the three fluids are shown in Figure 5. The impingement velocities are 19.77
for air, 1.28 for water, and 0.39 for oil. In air, sand velocity changes very slightly to the extent that the
impingement velocity can be assumed as equal to the air velocity. For liquids, sand decelerates rapidly to hit the
target wall with very low velocity.   
 
Figure 5: Sand trajectory along the stagnation zone for air, water, and oil
 
The rapid deceleration of liquids is mainly due to effect of viscosity, which is expressed mathematically by
rewriting of the equation of particle motion (Equation 5) in the following form:
p
p b
a
dx
dV
Re
 
 
(6)
With







  









p
p f p f
p p
f
V
V V V V
d
a
) ( 375 . 0


 
f
p p
f
V
d
b










 16
 
) ( Re p f
f
p f
p V V
d
 


 
It means that,
dx
dVp
 for liquids with high viscosity (i.e. low Reynolds number) are high, in contrast to gases.
For more investigation of the effect of viscosity and density on erosion rate, the variation of erosion rate with flow
velocity for oil with density of 850 kg/m3
 at different viscosity is shown in Figure 6 and the variation of erosion
rate with flow velocity for oil with viscosity of 0.009 Pa.s at different density is shown in Figure 7 (other
parameters are same to those used in Table 3). It is clear that erosion rate decreases with increase of both density
and viscosity. The effect of viscosity, however, is more significant.  
 
Figure 6: Variation of erosion rate with flow velocity for oil with different viscosity
 
 
 
Figure 7: Variation of erosion rate with flow velocity for oil with different viscosity
 
1.3 Computational Fluid Dynamics (CFD) method
The CFD is the simulation of fluids in dynamic (motion) state using numerical methods. The solution is attained
using many models and techniques that suit several applications. CFD simulation of sand erosion is generally
performed in four steps. In the first step, the model is built and divided into sub domains using a grid generation
technique. In the second step, the fluid velocity values are predicted along the flow direction by solving a flow
model and a turbulence model. In the third step, sand particles velocity and angle of impingement are predicted
using a particle equation of motion (Eulerian or Lagrangian). And finally, the data of particle velocity  and angle
of impingement are introduced to a selected erosion prediction model to predict the erosion rate. Figure 8 shows
the simulation procedure using the CFD Fluent software.
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 8: Sand Erosion Simulation Using Fluent Software
 
In this paper, discrete phase model (DPM) model the CFD Fluent software was selected as an example of the CFD
method to predict sand erosion in an elbow. The result of the CFD simulation was considered as a benchmark for
investigation of the other two methods to determine the accuracy of each for application in gas, oil, and water
flow. 
 
1.3.1 Model creation and grid generation
A 2-D geometry has been created and meshed in Gambit and then transferred to Fluent software for CFD solution.
The geometry is 50 mm (2 in) internal diameter elbow ended with two straight pipes 100 mm each and the elbow
outer wall curvature length is 157 mm.  Quadratic mesh type with size 1 mm has been selected to obtain a total of
17850 cells. Four boundaries have been selected as shown in Figure 9. The INLET VELOCITY boundary is the
boundary from where flow is solved and particles are tracked along the stream until the outflow boundary. The
erosion is then simulated in one of the two “wall” boundaries.  
 
Grid Generation
Flow Solution
(Navier-Stokes equation and turbulence model) 
Sand Trajectory 
Sand Erosion Calculation 
 
Figure 9: The model generation and meshing
 
1.3.2 Solution of fluid and particles trajectory
Sand erosion has been simulated using the computational fluid dynamics (CFD) Fluent V6.2.16 commercial
software. Sand flow rate of 0.000886 kg/s was  injected from the INLET VELOCITY boundary shown  in the
geometry. The sand erosion simulation has been performed following the flow solution and particle trajectory
steps. In the flow solution, the
  k
 model was selected for turbulence solution. The fluid velocity at the inlet
was set  to 20 m/s. The solution was initialized, requesting 170 iterations; the solution converged after 157
iterations.
The flow is assumed to be two phases (air+ sand) dilute slurry flow. The main parameters of the primary and
dispersed phases are as shown in Table 4.
Table 4: The main parameters of the phases
Parameter  Unit  Value 
Air (continuous phase)
Density  Kg/m3
  1.2015
Viscosity  Pa.s  0.0000182
Sand (dispersed phase)
Density  Kg/m3
2650
Size  m  0.0003
Mass flow rate  Kg/s  0.000886
 
Figure 10 shows the velocity contours of the primary phase in the elbow.  The maximum fluid velocity is
26.7 m/s in the vicinity of curvature of the inner wall. 
 
Figure 10: Velocity contours of the primary phase
 
After the solution of the primary phase, sand has been tracked along the axial position. The particle trajectory
allowed acquiring of particles velocity (Figure 11 and Figure 12) and particles angles of impingement (Figure 13).
The particles angle of impingement as shown in Figure 13) keeps constant at zero in the horizontal pipe until the
start point of the elbow curvature, where it starts to increase to reach 90o at the end point of the elbow curvature
and the start point of the vertical pipe to remain constant until the end of the vertical pipe.  
Figure 12 shows that no particles impinge the inner wall at this condition, and the impingement velocities at the
outer wall are in the range from 16.34 to 20.14 m/s. The variation of the velocity of a single particle along the
path length is shown in Figure 14.
 
 
Figure 11: Particle velocity tracking
 
 
Figure 12: Particle velocity along the flow path
 
Figure 13: Particle velocity angles
 
1.3.3 Erosion rate calculations
The calculated particle velocities and angles of impingement are  substituted into the following equation to
calculate the erosion rate at every node in the assigned wall.
 

N
p face
v b
p p
A
v f d C m
ER
1
) (
) ( ) ( 
 
(7)
Where 
p m
 and
p d
 are particle mass flow rate and size, respectively,  

 is the angle of impingement,  
v
 is the
particle velocity, and
face A
 is the area of target subject to erosion
 
. C, f, and b are functions of particle size, angle
of impingement, and velocity, respectively. 
In this work, the impact angle function has been defined to Fluent using a piece-linear profile with values shown
in Table 5; and the diameter function and velocity exponent function were set to values of 1.8e-09 and 2.6,
respectively. 
 
 
Table 5: Values of angle function defined to the model
 (degrees)
 
0  0
20  0.8
30  1
45  0.5
90  0.8
 
It is assumed that particle’s velocity changes after hitting a solid wall. The particle velocity  
2 p u
 after the
impingement is related to that before the impingement
1 p u
 as follows:
11 2 p p eu u 
 
(8)
Where
e
 =the coefficient of restitution, the value of which depends on many factors such as the coefficient of
kinetic friction, particle velocity, angle of impingement and the materials of particles and substrates   (Sommerfeld 1992)  . Grant and Tapakof proposed two relationships between the coefficient of restitution in parallel and
perpendicular directions, and angle of impingement. The relationships are expressed as follows  (Chen et al. 2006): 
3 2
67 . 0 11 . 2 66 . 1 998 . 0        parallel
e
 
(9)
3 2
49 . 0 56 . 1 76 . 1 993 . 0        perp e
 
(10)
Comparing Table 5 with Figure 13, we can conclude that the maximum angle of impingement function is,
approximately, at the position 150 mm of the path which is emphasized by the maximum erosion rate in Figure 14.
The maximum erosion rate is 7.56E-7 kg/m2.s.
Erosion rate unit in Fluent is kg/m2
.s. The maximum erosion rate for the outer wall can be obtained in mm/year as
follows:
 
 
The total erosion rate is 5.512E-05 kg/m2.s which is equivalent to 255.7 mm/year.
 
 
 
Figure 14: Erosion rate variation along the path (outer wall)
To analyze the effect of velocity on the maximum erosion rate and total erosion rate, different values of inlet
velocity were entered. The variation of maximum erosion rate with velocity is shown in Table 6 and Figure 15;
and the variation of total erosion rate with velocity is shown in Table 7. 
 Table 6: Variation of maximum erosion rate with velocity
Velocity m/s  Max Erosion rate
Kg/m2
.s  mm/year
5  4.102377e-9  0.0166
10  1.053087e-7  0.426
15  3.29e-7  1.33
20  6.66027e-7  2.693
25  1.212146e-6  4.9
30  1.97e-6  7.97
 
Table 7: Variation of total erosion rate with velocity
Velocity m/s  Total Erosion rate 
Kg/m2
.s  mm/year
5  6.529167e-07  2.64
10  6.395296e-06  26
15  2.58961e-05  105
20  5.5120436e-05  222.4
25      9.6189249e-05  389
30  0.000156  631
 
 
 
Figure 15: Variation of erosion rate with air velocity
 
1.4 Comparison between the three methods
The Salama and DIM models have been compared with the CFD results using the same parameters of the CFD
simulation as input data to the code. Figure 16 shows fair agreement between DIM and CFD models, whereas the
Salama model predicts much higher erosion rate as compared to the other two models. 
 
 
Figure 16: Comparison of results of Salama, DIM, and CFD models
 
The CFD model can be considered as a benchmark for evaluating the Salama and DIM models as it employs
more sophisticated solutions for the primary and secondary phases before predicting erosion rate. As the DIM
model agreed fairly with the CFD  results, the Salama model can then be improved further by comparing it with
the DIM model.
Comparing the salama model with DIM model resulted in unexpected outcome. It was attained that the
erosion rates from Salama model are higher than those from the DIM model for gas flow, whereas they are lower
than the DIM model for liquids (water and oil); and the underestimation is more in water than it is in oil. Figures
17-19 show comparison between Salama model and DIM model for gas, water, and oil flow, respectively.
 
Figure 17: Comparison between Salama model and DIM model (gas)
 
Figure 18: Comparison between Salama model and DIM model (water)
 
Figure 19: Comparison between Salama model and DIM model (oil)
 
From Figure 17 to Figure 19, Salama model can be improved based on the comparison with the DIM model.
Three models are proposed for erosion prediction of gas, water, and oil as follows:
 







Oil
Water
Gas
ER ER
ER
ER
ER
s s
s
s
m
268 . 0 428 . 0
492 . 3
474 . 0
2
 
(11)
Where
s
ER
is the erosion rate calculated by Salama model and
m ER
 is the modified erosion rate.
 
 
 Conclusion
Salama model and DIM model have been employed to develop a computational code for prediction of particles
(sand) erosion in pipes components. The two models have been investigated against results obtained from the
CFD Fluent commercial software. The investigation results in fair agreement of the DIM model with the CFD,
whereas Salama model highly overestimates the CFD. Based on comparison of Salama model with DIM model,
an improvement to Salama model  has been proposed to account for viscosity which is not considered in the
original model. This improvement increases its accuracy and extends the model applicability to oil flow. The
developed code allows prediction of erosion rate with the same accuracy of CFD while eliminating its limitations
of high cost, difficulty, and time-consuming. 
 
 
References
[1] Ahlert, K. (1995). The effects of particle impingement angle and surface wetting on solid particle erosion on
AISI 1018 steel, U of Tulsa. M Sc.
[2] Barton, N. A. (2003). Erosion in Elbows in hydrocarbon production systems: Review document. 
[3] Carlson, J., Curley, D., King, G., Price-Smith, C. and Waters, F. (October 1992). Sand control: why and how?
[4] Chen, X., Mclaury, B. S. and Shirazi, S. A. (2006). "Numerical and experimental investigation of the relative
erosion severity between plugged tees and elbows in dilute gas/solid two-phase flow." Wear  261: 715–
729. 
[5] Colwart, G., Burton, R. C., Eaton, L. F. and Hodge, R. M. (2007). Lessons Learned on Sand-Control Failure
and Subsequent Workover at Magnolia Deepwater Development. SPE/IADC Drilling Conference,
Amsterdam.
[6] Deng, T., Chaudhry, A. R., Patel, M., Hutchings, I. and Bradley, M. S. A. (2005). "Effect of particle
concentration on erosion rate of mild steel bends in a pneumatic conveyor." Wear 258: 480-487. 
[7] Finnie, I. (1972). "Some observations on the erosion of ductile materials." Wear 19.
[8] Haugen, K., Kvernvold, O., Ronold, A. and Sandberg, R. (1995). "Sand erosion of wear-resistant meterials:
erosion in choke valves." Wear Cambridge, UK: 186-187.
[9] Institiute, A. P. (1991). API RP 14 E Recommended Practice for Design and Installation of Offshore
Production Platform Piping Systems. Washington DC, American Petroleum Institiute: p. 22.
[10] Karelin, C. G. D. A. V. Y. (2002). Abrasive erosion and corrosion for hydraulic machinary Vol 2, Imprial
college press.
[11] Mazur, Z., Campos-Amezcua, R. and G. Urquiza-Beltr
an, A. G.-G. (2004). "Numerical 3D simulation of
the erosion due to solid particle impact in the main stop valve of a steam turbine."  Applied Thermal
Engineering  24: 1877–1891.
[12] Mclaury, B. S. (1996). Predicting Solid Particle Erosion Resulting from Turbulent Fluctuations in Oilfield
Geometries, University of Tulsa. PhD Thesis.
[13] Salama, M. M. and Venkatesh, E. S. (1983). Evaluation of Erosional Velocity Limitations in Offshore Gas
Wells OTC 15th Annual OTC. Houston, Texas.
[14] Sommerfeld, M. (1992). " Modelling of particle-wall collisions in confined gas-particle flows "  Int. J.
Multiphase Flow 18, 6: 905-926.
[15] Tian, B. (2007). mechanistic understanding and effective prevention of erosion-corrosion of hydrotransport
pipes in oil sand slurries, U of Calgary. M Sc. .
 
 
 2722