# Erosion Failure of Horizontal Pipe Reducing Wall in Power-Law Fluid Containing Particles via CFD–DEM Coupling Method

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### Abstract

A CFD–DEM-based two-phase flow model and a test-based erosion model are used to obtain the specific erosion on the reducing wall of sudden contraction section. The dimensionless filtered governing equations are adopted for incompressible power-law fluid flow, and the Hertz–Mindlin (no-slip) model for particle–particle and particle–wall contact. The annular reducing wall is divided into two erosion areas in radial direction based on erosion form and divided into four parts in the circumferential direction. The calculated result is verified with a full-scale experiment, and it shows a good agreement. The calculated results show that the erosion rate of the reducing wall is mainly determined by the flow velocity, and the erosion area is affected by liquid viscosity. The serious erosion region is located in the inner edge of the sample lower part, and this region expends to the outer circumference with the increasing flow velocity and the reducing liquid viscosity. The increase in flow velocity expands the flow region where the particle can impact the wall and thus increases the particle impact numbers.

### Graphical Abstract

## Keywords

Erosion analysis Sudden contraction section Power-law fluid flow CFD–DEM coupling approach## List of symbols

*A*_{p}Particle cross-sectional area (m

^{2})*C*_{d}Drag coefficient (–)

*D*Inside diameter of circular pipe (m)

*d*_{p}Diameter of particle (m)

*E*_{e}The measured erosion rate (mm/h)

*E*_{p}The calculated erosion rate (mm/h)

*F*_{i,n}Normal force of particle (N)

*F*_{t}Total force of particle (N)

*Fd*Fluid–particle drag force (N)

*F*_{d}Inter-particle contact force in tangential direction (N)

*F*_{n,ij}Inter-particle contact force in normal direction, N

*F*_{s}Particle shape coefficient (dimensionless)

*I*_{i}Moment of inertia of particle

*i*(N m)*K*Flow consistency coefficient (Pa s

^{n})*k*_{n}Normal spring stiffness (N/mm)

*L*Distance from the inner edge of the sample (m)

*m*_{p}Single particle mass (kg)

*nij*Normal unit vector (–)

*N*Number of particles in contact (–)

*r*_{p}Radius of particle (m)

*r*_{i}Radius of particle

*i*(m)*r*_{j}Radius of particle

*j*(m)*R*Relative error (%)

*R*_{l}Inside radius of circular pipe (m)

*R*_{p}Particle Reynolds number (–)

*Re*Reynolds number of fluid flow (–)

*T*_{t,i}Torque generated by tangential forces (N m)

*T*_{r,ij}Rolling friction torque (N m)

*u*_{x}Axial velocity of fluid (m/s)

*u*Fluid velocity (m/s)

*V*_{p}Particle volume (m

^{3})*v*Particle velocity (m/s)

- \( a,b,w,x,y,z \)
Empirical constants in angle functions (–)

## Greek symbols

*γ*Shear rate (s

^{−1})*τ*Shear stress (Pa)

*η*Apparent viscosity (mPa s)

*η*_{n}Normal damping coefficient (N/s/m)

*γ*_{d}Dimensionless shear rate (–)

*ρ*_{l}Liquid density (kg m

^{3})*φ*Scaling coefficient (–)

*α*Particle impact angle (°)

*θ*Critical angle of particle impact (°)

## Superscripts

*n*Flow behavior index

*m*Impact velocity power-law coefficient

## Subscripts

*i*First particle

*j*Second particle

*p*Particle

*l*Liquid

## Notes

### Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 51404198), and it was also performed by the group of profession and innovation for well testing integrity and safety of Xi’an Shiyou University.

## References

- 1.C. Rivard, D. Lavoie, R. Lefebvre et al., An overview of Canadian shale gas production and environmental concerns. Int. J. Coal Geol.
**126**(5), 64–76 (2013)Google Scholar - 2.A.K. Mahmood, A.A. Khadom, Erosion–corrosion of low-carbon steel in the absence and presence of slurry in saline water: kinetic and mathematical views. J. Fail. Anal. Prev.
**16**, 1071–1081 (2016)CrossRefGoogle Scholar - 3.R. Malka, S. Nešić, D.A. Gulino, Erosion–corrosion and synergistic effects in disturbed liquid-particle flow. Wear
**262**(7–8), 791–799 (2007)CrossRefGoogle Scholar - 4.C.Y. Wong, C. Solnordal, A. Swallow et al., Experimental and computational modelling of solid particle erosion in a pipe annular cavity. Wear
**303**(1–2), 109–129 (2013)CrossRefGoogle Scholar - 5.Z. Lin, H. Xu, Y. Wang et al., Experimental study of particle erosion in a cavity with a height difference between its walls. Powder Technol.
**286**, 378–384 (2015)CrossRefGoogle Scholar - 6.M.A. Habib, H.M. Badr, R.B. Mansour et al., Erosion rate correlations of a pipe protruded in an abrupt pipe contraction. Int. J. Impact Eng.
**34**(8), 1350–1369 (2007)CrossRefGoogle Scholar - 7.H.M. Badr, M.A. Habib, R.B. Mansour et al., Numerical investigation of erosion threshold velocity in a pipe with sudden contraction. Comput. Fluids
**34**(6), 721–742 (2005)CrossRefGoogle Scholar - 8.S. Dhinakaran, M.S.N. Oliveira, F.T. Pinho et al., Steady flow of power-law fluids in a 1:3 planar sudden expansion. J. Non Newton. Fluid
**198**(8), 48–58 (2013)CrossRefGoogle Scholar - 9.P.S. Gnambode, P. Orlandi, M. Ould-Rouiss et al., Large-Eddy simulation of turbulent pipe flow of power-law fluids. Int. J. Heat Fluid Flow
**54**, 196–210 (2015)CrossRefGoogle Scholar - 10.N. Iqbal, C. Rauh, Coupling of discrete element model (DEM) with computational fluid mechanics (CFD): a validation study. Appl. Math. Comput.
**277**, 154–163 (2016)Google Scholar - 11.P. Gupta, J. Sun, Y.J. Ooi, CFD-DEM simulation of a dense fluidized bed: wall boundary and particle size effects. Powder Technol.
**293**, 37–47 (2016)CrossRefGoogle Scholar - 12.P.A. Cundall, O.D.L. Strack, A discrete numerical model for granular assemblies. Géotechnique
**29**(18), 47–65 (1979)CrossRefGoogle Scholar - 13.X. Chen, B.S. McLaury, S.A. Shirazi, Application and experimental validation of a computational fluid dynamics (CFD)-based erosion prediction model in elbows and plugged tees. Comput. Fluids
**33**(10), 1251–1272 (2004)CrossRefGoogle Scholar - 14.H.C. Meng, K.C. Ludema, Wear models and predictive equations: their form and content. Wear
**181**(95), 181–183 (1995)Google Scholar - 15.B. McLaury, Predicting solid particle erosion resulting from turbulent fluctuations in oilfield geometries, Master’s Thesis, The University of Tulsa, 1996Google Scholar
- 16.K. Ahlert, Effects of particle impingement angle and surface wetting on solid particle erosion of AISI 1018 steel, Master’s Thesis, The University of Tulsa, 1994Google Scholar
- 17.I. Finnie, An experimental study of erosion. Wear
**3**(2), 76 (1960)CrossRefGoogle Scholar - 18.Y.A. Zhao, W.B. Cai, L. Cui, et al, Erosion of premium connection cross-over joint in solid-liquid flow, in
*Proceedings of the International Conference on Engineering Technology and Application*, May 29–30, Xia Men, China, EDP Sciences, 2015Google Scholar - 19.C. Huang, S. Chiovelli, P. Minev et al., A comprehensive phenomenological model for erosion of materials in jet flow. Powder Technol.
**187**(3), 237–279 (2008)CrossRefGoogle Scholar