In the transportation process of oil and gas, solid particle erosion in pipelines is an inevitable problem. The erosion usually occurs in fittings with changing flow directions, such as elbows. A theoretical model based on mechanism analyses is developed for predicting the solid particle erosion on the symmetry plane of elbows for annular flow. This model is a sort of generalized erosion prediction procedure, which resolves the erosion process into the description of the flow field velocity profile, particle motion rules, and penetration calculation. The 1/7th power law is adopted to represent the velocity profile of gas core, and a linear velocity profile is assigned to the liquid film. The trajectories of particles in the gas core and the liquid film are discretized, and a mathematical model is developed by analyzing external forces acting on particles. The impact speeds and angles of particles can be obtained from the mathematical model, and the penetration ratios are then estimated by incorporating the impingement information of particles into the erosion formulas. By contrast with experimental data, the mechanistic model is validated and indicates advantages in both accuracy and efficiency. Furthermore, the effects of different parameters on penetration ratios are discussed in detail, including the superficial gas velocity, superficial liquid velocity, pipe diameter, particle diameter, curvature radius, and liquid viscosity.

References

References
1.
Salama
,
M.
, and
Venkatesh
,
E.
,
1983
, “
Evaluation of API RP 14E Erosional Velocity Limitations for Offshore Gas Wells
,”
Fifth Annular Offshore Technology Conference
, Houston, TX, May 2–5, OTC Paper No.
4485
.
2.
Salama
,
M. M.
,
2000
, “
An Alternative to API 14E Erosional Velocity Limits for Sand-Laden Fluids
,”
ASME J. Energy Resour. Technol.
,
122
(
2
), pp.
71
77
.
3.
Bourgoyne
,
A. T.
, Jr.
,
1989
, “
Experimental Study of Erosion in Diverter Systems Due to Sand Production
,”
SPE/IADC Drilling Conference
, New Orleans, LA, March 28, SPE Paper No.
SPE-18716-MS
.
4.
Mazumder
,
Q. H.
,
Shirazi
,
S. A.
, and
McLaury
,
B. S.
,
2008
, “
Prediction of Solid Particle Erosive Wear of Elbows in Multiphase Annular Flow-Model Development and Experimental Validations
,”
ASME J. Energy Resour. Technol.
,
130
(
2
), p.
023001
.
5.
McLaury
,
B. S.
, and
Shirazi
,
S. A.
,
2000
, “
An Alternate Method to API RP 14E for Predicting Solids Erosion in Multiphase Flow
,”
ASME J. Energy Resour. Technol.
,
122
(
3
), pp.
115
122
.
6.
Det Norske Veritas
,
2011
, “
Recommended Practice RP O501 Erosive Wear in Piping Systems
,” DNV Recommended Practice, Oslo, Norway.
7.
McLaury
,
B. S.
,
1996
, “
Predicting Solid Particle Erosion Resulting From Turbulent Fluctuations in Oilfield Geometries
,” Ph.D. thesis, University of Tulsa, Tulsa, OK.
8.
Edwards
,
J. K.
,
2000
, “
Development, Validation, and Application of a Three-Dimensional, CFD-Based Erosion Prediction Procedure
,” Ph.D. thesis, University of Tulsa, Tulsa, OK.
9.
Chen
,
X. H.
,
McLaury
,
B. S.
, and
Shirazi
,
S. A.
,
2006
, “
A Comprehensive Procedure to Estimate Erosion in Elbows for Gas/Liquid/Sand Multiphase Flow
,”
ASME J. Energy Resour. Technol.
,
128
(
1
), pp.
70
78
.
10.
Zhang
,
Y.
,
McLaury
,
B. S.
,
Shirazi
,
S. A.
, and
Rybicki
,
E. F.
,
2010
, “
A Two-Dimensional Mechanistic Model for Sand Erosion Prediction Including Particle Impact Characteristics
,”
NACE International Corrosion 2010 Conference and Exhibition
, San Antonio, TX, Mar. 14–18, NACE Paper No.
10378
https://www.onepetro.org/conference-paper/NACE-10378.
11.
Zhang
,
R.
,
Liu
,
H. X.
, and
Zhao
,
C. T.
,
2013
, “
A Probability Model for Solid Particle Erosion in a Straight Pipe
,”
Wear
,
308
(
1–2
), pp.
1
9
.
12.
Liu
,
M. Y.
, and
Liu
,
H. X.
,
2015
, “
A Numerical Procedure to Estimate Sand Erosion in Elbows for Annular-Mist Flow Based on Film Thickness and Droplet Diameter Prediction
,”
25th International Ocean and Polar Engineering Conference
, Kona, HI, June 21–26, ISOPE Paper No.
0525
.https://www.onepetro.org/conference-paper/ISOPE-I-15-299
13.
Liu
,
M. Y.
,
Liu
,
H. X.
, and
Zhang
,
R.
,
2015
, “
Numerical Analyses of the Solid Particle Erosion in Elbows for Annular Flow
,”
Ocean Eng.
,
105
, pp.
186
195
.
14.
Liu
,
H. X.
,
Zhou
,
Z. W.
, and
Liu
,
M. Y.
,
2015
, “
A Probability Model of Predicting the Sand Erosion Profile in Elbows for Gas Flow
,”
Wear
,
342
, pp.
377
390
.
15.
Zahedi
,
P.
,
Vieira
,
R. E.
,
Shirazi
,
S. A.
, and
McLaury
,
B. S.
,
2016
, “
Liquid Film Thickness and Erosion of Elbows in Gas-Liquid Annular Flow
,”
NACE International Conference
, Vancouver, BC, Canada, Mar. 6–10, NACE Paper No.
7711
.https://www.onepetro.org/conference-paper/NACE-2016-7711
16.
Zahedi
,
P.
,
Zhang
,
J.
,
Arabnejad
,
H.
,
McLaury
,
B. S.
, and
Shirazi
,
S. A.
,
2017
, “
CFD Simulation of Multiphase Flows and Erosion Predictions Under Annular Flow and Low Liquid Loading Conditions
,”
Wear
,
376
, pp.
1260
1270
.
17.
Zhang
,
Y.
,
Lian
,
Z. H.
,
Abdelal
,
G. F.
, and
Lin
,
T. J.
,
2018
, “
Numerical and Experimental Investigation on Flow Capacity and Erosion Wear of Blooey Line in Gas Drilling
,”
ASME J. Energy Resour. Technol.
,
140
(
5
), p.
054501
.
18.
Cheng
,
X.
, and
Amano
,
R. S.
,
2018
, “
Effects of Asymmetric Radial Clearance on Performance of a Centrifugal Compressor
,”
ASME J. Energy Resour. Technol.
,
140
(
5
), p.
052003
.
19.
McLaury
,
B. S.
,
Shirazi
,
S. A.
,
Viswanathan
,
V.
,
Mazumder
,
Q. H.
, and
Santos
,
G.
,
2011
, “
Distribution of Sand Particles in Horizontal and Vertical Annular Multiphase Flow in Pipes and the Effects on Sand Erosion
,”
ASME J. Energy Resour. Technol.
,
133
(
2
), p.
023001
.
20.
Vieira
,
R. E.
,
Parsi
,
M.
,
Zahedi
,
P.
,
McLaury
,
B. S.
, and
Shirazi
,
S. A.
,
2017
, “
Ultrasonic Measurements of Sand Particle Erosion Under Upward Multiphase Annular Flow Conditions in a Vertical-Horizontal Bend
,”
Int. J. Multiphase Flow
,
93
, pp.
48
62
.
21.
Oka
,
Y. I.
,
Okamura
,
K.
, and
Yoshida
,
T.
,
2005
, “
Practical Estimation of Erosion Damage Caused by Solid Particle Impact—Part 1: Effects of Impact Parameters on a Predictive Equation
,”
Wear
,
259
(
1–6
), pp.
95
101
.
22.
Oka
,
Y. I.
, and
Yoshida
,
T.
,
2005
, “
Practical Estimation of Erosion Damage Caused by Solid Particle Impact—Part 2: Mechanical Properties of Materials Directly Associated With Erosion Damage
,”
Wear
,
259
(
1–6
), pp.
102
109
.
23.
Gill
,
L. E.
, and
Hewitt
,
G. F.
,
1964
, “
Sampling Probe Studies of the Gas Core in Annular Two-Phase Flow—II: Studies of the Effect of Phase Flow Rates on Phase and Velocity Distribution
,”
Chem. Eng. Sci.
,
19
(
9
), pp.
665
682
.
24.
Turner
,
J. M.
,
1966
, “
Annular Two-Phase Flow
,” Ph.D. thesis, Dartmouth College, Hanover, NH.
25.
Zhang
,
H. Q.
,
Wang
,
C.
,
Sarica
,
C.
, and
Brill
,
J. P.
,
2003
, “
Unified Model for Gas-Liquid Pipe Flow Via Slug Dynamics—Part 1: Model Development
,”
ASME J. Energy Resour. Technol.
,
125
(
4
), pp.
266
273
.
26.
Kaji
,
R.
, and
Azzopardi
,
B. J.
,
2010
, “
The Effect of Pipe Diameter on the Structure of Gas/Liquid Flow in Vertical Pipes
,”
Int. J. Multiphase Flow
,
36
(
4
), pp.
303
313
.
27.
Ambrosini
,
W.
,
Andreussi
,
P.
, and
Azzopardi
,
B.
,
1991
, “
A Physically Based Correlation for Drop Size in Annular Flow
,”
Int. J. Multiphase Flow
,
17
(
4
), pp.
497
507
.
28.
Holt
,
A.
,
Azzopardi
,
B.
, and
Biddulph
,
M.
,
1999
, “
Calculation of Two-Phase Pressure Drop for Vertical Upflow in Narrow Passages by Means of a Flow Pattern Specific Model
,”
Chem. Eng. Res. Des.
,
77
(
1
), pp.
7
15
.
29.
Clift
,
R.
,
Grace
,
J. R.
, and
Weber
,
M. E.
,
1978
,
Bubbles, Drops, and Particles
, Academic Press,
New York
.
30.
Ishii
,
M.
, and
Zuber
,
N.
,
1979
, “
Drag Coefficient and Relative Velocity in Bubbly, Droplet or Particulate Flows
,”
AIChE J.
,
25
(
5
), pp.
843
855
.
31.
Belt
,
R.
,
Van't Westende
,
J.
, and
Portela
,
L.
,
2009
, “
Prediction of the Interfacial Shear-Stress in Vertical Annular Flow
,”
Int. J. Multiphase Flow
,
35
(
7
), pp.
689
697
.
32.
Magrini
,
K. L.
,
2009
, “
Liquid Entrainment in Annular Gas/Liquid Flow in Inclined Pipes
,” M.S. thesis, University of Tulsa, Tulsa, OK.
33.
Schubring
,
D.
,
Ashwood
,
A.
,
Shedd
,
T.
, and
Hurlburt
,
E.
,
2010
, “
Planar Laser-Induced Fluorescence (PLIF) Measurements of Liquid Film Thickness in Annular Flow—Part I: Methods and Data
,”
Int. J. Multiphase Flow
,
36
(
10
), pp.
815
824
.
34.
Alamu
,
M.
, and
Azzopardi
,
B.
,
2011
, “
Simultaneous Investigation of Entrained Liquid Fraction, Liquid Film Thickness and Pressure Drop in Vertical Annular Flow
,”
ASME J. Energy Resour. Technol.
,
133
(
2
), p.
023103
.
35.
Kvernvold
,
O.
, and
Sandberg
,
R.
,
1993
, “
Production Rate Limits in Two-Phase Flow Systems: Erosion in Piping Systems for Production of Oil and Gas
,” Det Norske Veritas (DNV), Oslo, Norway, Report No. 93-3252.
36.
Birchenough
,
P. M.
,
Dawson
,
S. G. B.
,
Lockett
,
T. J.
, and
McCarthy
,
P.
,
1995
, “
Critical Flow Rates Working Party
,” AEA Technology, Harwell, UK, Report No. AEA-TSD-0348.
37.
Mazumder
,
Q. H.
,
2004
, “
Development and Validation of a Mechanistic Model to Predict Erosion in Single-Phase and Multiphase Flow
,” Ph.D. thesis, University of Tulsa, Tulsa, OK.
38.
Vieira
,
R. E.
,
Parsi
,
M.
,
Zahedi
,
P.
,
McLaury
,
B. S.
, and
Shirazi
,
S. A.
,
2017
, “
Electrical Resistance Probe Measurements of Solid Particle Erosion in Multiphase Annular Flow
,”
Wear
,
382
, pp.
15
28
.
39.
Hewitt
,
G. F.
, and
Roberts
,
D.
,
1969
, “
Studies of Two-Phase Flow Patterns by Simultaneous X-Ray and Flash Photography
,” Atomic Energy Research Establishment, Harwell, UK.
40.
Parsi
,
M.
,
Al-Sarkhi
,
A.
,
Kara
,
M.
,
Sharma
,
P.
,
McLaury
,
B. S.
, and
Shirazi
,
S. A.
,
2017
, “
A New Dimensionless Number for Solid Particle Erosion in Natural Gas Elbows
,”
Wear
,
390
, pp.
80
83
.
41.
Parsi
,
M.
,
Arabnejad
,
H.
,
Al-Sarkhi
,
A.
,
Zahedi
,
P.
,
Vieira
,
R. E.
,
Sharma
,
P.
, and
McLaury
,
B. S.
,
2018
, “
A New Correlation for Predicting Solid Particle Erosion Caused by Gas-Sand Flow in Elbows
,”
Offshore Technology Conference
, Houston TX, Apr. 30–May 3, OTC Paper No.
28995
.
42.
Liu
,
H. X.
,
Yang
,
W. X.
, and
Kang
,
R.
,
2018
, “
A Correlation for Sand Erosion Prediction in Annular Flow Considering the Effect of Liquid Dynamic Viscosity
,”
Wear
,
404
, pp.
1
11
.
You do not currently have access to this content.