# Numerical Simulation of Pulsed Gravel Packing Completion in Horizontal Wells

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^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Pulsed Gravel Packing Numerical Model

#### 2.1. Solid-Liquid Two-Phase Flow Governing Equation

_{l}, ε

_{s}represent the concentration of the liquid phase and solid phase, dimensionless; ρ

_{l}, ρ

_{s}represent the density of liquid phase and solid phase, kg/m

^{3}; and ${\overrightarrow{v}}_{\mathrm{l}}$, ${\overrightarrow{v}}_{\mathrm{s}}$ represent the velocity of the liquid phase and solid phase, m/s.

^{2}; p

_{l}is the liquid phase pressure, MPa; p

_{s}is the solid phase pressure, MPa; β is the drag force coefficient between liquid phase and solid phase, dimensionless; μ

_{l}is the shear viscosity of liquid phase, Pa·s; μ

_{s}is the shear viscosity of solid phase, Pa·s; ξ

_{s}is the dynamic viscosity of solid phase, Pa·s; and $\overrightarrow{I}$ is the unit vector.

^{2}/s

^{2}; ε is the dissipation rate of turbulent kinetic energy, m

^{2}/s

^{2}; ρ

_{m}is the mixed density of two phases, kg/m

^{3}; ρ

_{i}is the density of phase i, kg/m

^{3}; ν

_{m}is the mixed velocity of two phases, m/s; ν

_{i}is the velocity of phase i, m/s; α

_{i}is the volume fraction of phase i, dimensionless; μ

_{m}is the mixed dynamic viscosity of two phases, Pa·s; μ

_{t,m}is the mixed turbulent viscosity of two phases, Pa·s; G

_{k,m}is the increment of turbulent kinetic energy caused by the average velocity gradient; C

_{1εRNG}is the turbulent kinetic energy coefficient, dimensionless; and the constants in the equation as follows: C

_{μRNG}= 0.085, C

_{2εRNG}= 1.68, σ

_{kRNG}= 0.7179, σ

_{εRNG}= 0.7179, β

_{RNG}= 0.012.

#### 2.2. Physical Models and Boundary Conditions

## 3. Parameter Analysis of Pulsed Gravel Packing

#### 3.1. Optimization of Pulsed Gravel Packing Parameters

#### 3.2. Optimal Analysis of Pulsed Gravel Packing Waveform in Horizontal Wells

#### 3.3. Comparative Analysis of Pulsed Gravel Packing and Conventional Gravel Packing in Horizontal Wells

## 4. Analysis of Influencing Factors for the Pulsed Gravel Packing

#### 4.1. Impact of Displacement on Pulsed Gravel Packing in Horizontal Wells

^{3}/h to 70 m

^{3}/h on gravel migration and volume fraction was studied. At 30 s, the volume fraction and velocity of the section at a distance of 10 m from the inlet was extracted, and the results are shown in Figure 10 and Figure 11. It can be seen from Figure 10 that, with the increase of displacement, the volume fraction of fixed bed decreased from 6.38% to 1.83%, when the displacement reached 50 m

^{3}/h, the reduction trend of fixed bed volume fraction tended to be flat. The volume fraction of the mobile bed also decreased gradually with the increase of displacement, and when the displacement reached 60 m

^{3}/h, the reduction trend of the volume fraction of the mobile bed increased. The volume fraction of the floating bed increased rapidly with the increase of displacement. The results indicate that with the increase of displacement, the gravel migration ability increased, and after the displacement reached a certain critical value, the gravel migration ability increased slowly.

#### 4.2. Impact of the Viscosity of the Carrying Fluid on Pulsed Gravel Packing in Horizontal Wells

#### 4.3. Impact of Particle Size on Pulsed Gravel Packing in Horizontal Wells

#### 4.4. Impact of Sand Carrying Ratio on Pulsed Gravel Packing in Horizontal Wells

#### 4.5. Impact of String Eccentricity on Pulsed Gravel Packing in Horizontal Wells

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Joshi, S.D. Cost/Benefits of Horizontal Wells. In Proceedings of the SPE Western Regional/AAPG Pacific Section Joint Meeting, Long Beach, CA, USA, 19–24 May 2003; p. 9. [Google Scholar]
- Alekperov, V.Y.; Lyashko, N.N.; Gavura, A.V.; Fedotov, I.B.; Kibalenko, I.A. Application of horizontal wells to accelerate commissioning of wells and to increase development efficiency of offshore oil and gas fields in the Northern Caspian (Russian). Oil Ind. J.
**2018**, 2018, 72–76. [Google Scholar] [CrossRef] - Ali, S.A.; Grigsby, T.F.; Vitthal, S. Advances in Horizontal Openhole Gravel Packing. SPE Drill. Complet.
**2006**, 21, 23–31. [Google Scholar] [CrossRef] - Parlar, M.; Albino, E.H. Challenges, Accomplishments, and Recent Developments in Gravel Packing. J. Pet. Technol.
**2000**, 52, 50–58. [Google Scholar] [CrossRef] - Forrest, J.K. Horizontal Gravel Packing Studies in a Full-Scale Model Wellbore. In Proceedings of the SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, 23–26 September 1990; p. 9. [Google Scholar]
- Maly, G.P.; Robinson, J.P.; Laurie, A.M. New Gravel Pack Tool for Improving Pack Placement. J. Pet. Technol.
**1974**, 26, 19–24. [Google Scholar] [CrossRef] - Doron, P.; Granica, D.; Barnea, D. Slurry flow in horizontal pipes—experimental and modeling. Int. J. Multiph. Flow
**1987**, 13, 535–547. [Google Scholar] [CrossRef] - Doron, P.; Barnea, D. Effect of the no-slip assumption on the prediction of solid-liquid flow characteristics. Int. J. Multiph. Flow
**1992**, 18, 617–622. [Google Scholar] [CrossRef] - Doron, P.; Barnea, D. A three-layer model for solid-liquid flow in horizontal pipes. Int. J. Multiph. Flow
**1993**, 19, 1029–1043. [Google Scholar] [CrossRef] - Gruesbeck, C.; Salathiel, W.M.; Echols, E.E. Design of Gravel Packs in Deviated Wellbores. J. Pet. Technol.
**1979**, 31, 109–115. [Google Scholar] [CrossRef] - Peden, J.M.; Russell, J.; Oyeneyin, M.B. The Design and Optimisation of Gravel Packing Operations in Deviated Wells. In Proceedings of the European Petroleum Conference, London, UK, 22–25 October 1984; p. 22. [Google Scholar]
- Peden, J.M.; Russell, J.; Oyeneyin, M.B. A Numerical Approach to the Design of a Gravel Pack for Effective Sand Control in Deviated Wells. In Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, TX, USA, 16–19 September 1984; p. 15. [Google Scholar]
- Peden, J.M.; Russell, J.; Oyeneyin, M.B. Design of an Effective Gravel Pack for Sand Control: A Numerical Approach. In Proceedings of the SPE California Regional Meeting, Bakersfield, CA, USA, 27–29 March 1985; p. 14. [Google Scholar]
- Wahlmeier, M.A.; Andrews, P.W. Mechanics of Gravel Placement and Packing: A Design and Evaluation Approach. SPE Prod. Eng.
**1988**, 3, 69–82. [Google Scholar] [CrossRef] - Chen, Z. Horizontal Well Gravel Packing: Dynamic Alpha Wave Dune Height Calculation and Its Impact on Gravel Placement Job Execution. In Proceedings of the SPE Annual Technical Conference and Exhibition, Anaheim, CA, USA, 11–14 November 2007; p. 10. [Google Scholar]
- Penberthy, W.L., Jr.; Bickham, K.L.; Nguyen, H.T.; Paulley, T.A. Gravel Placement in Horizontal Wells. SPE Drill. Complet.
**1997**, 12, 85–92. [Google Scholar] [CrossRef] - Penberthy, W.L., Jr. Gravel Placement Through Perforations and Perforation Cleaning for Gravel Packing. J. Pet. Technol.
**1988**, 40, 229–236. [Google Scholar] [CrossRef] - Osisanya, S.O.; Ayeni, K.B.; Osisanya, K.P. Factors Affecting Horizontal Well Gravel-Pack Efficiency. In Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 24–27 September 2006; p. 7. [Google Scholar]
- Nguyen, P.D.; Fitzpatrick, H.J.; Woodbridge, G.A.; Reidenbach, V.G. Analysis of Gravel Packing Using 3-D Numerical Simulation. In Proceedings of the SPE Formation Damage Control Symposium, Lafayette, LA, USA, 26–27 February 1992; p. 12. [Google Scholar]
- Martins, A.L.; Magalhaes, J.V.M.; Calderon, A.; Chagas, C.M. A Mechanistic Model for Horizontal Gravel Pack Displacement. SPE J.
**2005**, 10, 229–237. [Google Scholar] [CrossRef] - Pu, C.S. A New Intelligent Computer System for Horizontal Wells Gravel-Packing. In Proceedings of the International Conference on Horizontal Well Technology, Calgary, AB, Canada, 18–20 November 1996; p. 8. [Google Scholar]
- Ojo, K.P.; Osisanya, S.O.; Ayeni, K.B. Development of a 3D Numerical Simulator of Horizontal Well Gravel Pack. In Proceedings of the Canadian International Petroleum Conference, Calgary, AB, Canada, 13–15 June 2006; p. 14. [Google Scholar]
- Ojo, K.P.; Osisanya, S.O.; Ayeni, K. Factors Affecting Horizontal Well Gravel Pack Efficiency. J. Can. Pet. Technol.
**2008**, 47, 50–54. [Google Scholar] [CrossRef] - Changyin, D.; Jiajia, L.; Yanlong, L.; Huaiwen, L.; Lifei, S. Experimental and Visual Simulation of Gravel Packing in Horizontal and Highly Deviated Wells. In Proceedings of the SPE Latin America and Caribbean Petroleum Engineering Conference, Maracaibo, Venezuela, 21–23 May 2014; p. 13. [Google Scholar]
- Dong, C.Y.; Gao, K.G.; Dong, S.X.; Shang, X.S.; Wu, Y.X.; Zhong, Y.X. A new integrated method for comprehensive performance of mechanical sand control screens testing and evaluation. J. Pet. Sci. Eng.
**2017**, 158, 775–783. [Google Scholar] [CrossRef] - Dong, C.Y.; Zhou, Y.G.; Chen, Q.; Zhu, C.M.; Li, Y.L.; Li, X.B.; Liu, Y.B. Effects of fluid flow rate and viscosity on gravel-pack plugging and the optimization of sand-control wells production. Pet. Explor. Dev.
**2019**, 46, 1251–1259. [Google Scholar] [CrossRef] - Adamczyk, W.P.; Klimanek, A.; Białecki, R.A.; Węcel, G.; Kozołub, P.; Czakiert, T. Comparison of the standard Euler–Euler and hybrid Euler–Lagrange approaches for modeling particle transport in a pilot-scale circulating fluidized bed. Particuology
**2014**, 15, 129–137. [Google Scholar] [CrossRef] - Pang, B.X.; Wang, S.Y.; Liu, G.D.; Jiang, X.X.; Lu, H.L.; Li, Z.J. Numerical prediction of flow behavior of cuttings carried by Herschel-Bulkley fluids in horizontal well using kinetic theory of granular flow. Powder Technol.
**2018**, 329, 386–398. [Google Scholar] [CrossRef] - Ravnik, J.; Škerget, L.; Hriberšek, M. The wavelet transform for BEM computational fluid dynamics. Eng. Anal. Bound. Elem.
**2004**, 28, 1303–1314. [Google Scholar] [CrossRef] - Wodołażski, A.; Skiba, J.; Zarębska, K.; Polański, J.; Smolinski, A. CFD Modeling of the Catalyst Oil Slurry Hydrodynamics in a High Pressure and Temperature as Potential for Biomass Liquefaction. Energies
**2020**, 13, 5694. [Google Scholar] [CrossRef] - Ofei, T.; Irawan, S.; Pao, W. CFD Method for Predicting Annular Pressure Losses and Cuttings Concentration in Eccentric Horizontal Wells. J. Pet. Eng.
**2014**, 2014, 1–16. [Google Scholar] [CrossRef][Green Version] - Argyropoulos, C.D.; Markatos, N.C. Recent advances on the numerical modelling of turbulent flows. Appl. Math. Model.
**2015**, 39, 693–732. [Google Scholar] [CrossRef] - Costamte, Y.R.; Trondsen, A.; Bergkvam, R.M.; Hodne, H.; Saasen, A. Horizontal Openhole Gravel Packing in Wells With Long Blank Pipe and Screen Sections. In Proceedings of the SPE Deepwater Drilling and Completions Conference, Galveston, TX, USA, 20–21 June 2010; p. 21. [Google Scholar]
- Vaziri, E.; Simjoo, M.; Chahardowli, M. Application of foam as drilling fluid for cuttings transport in horizontal and inclined wells: A numerical study using computational fluid dynamics. J. Pet. Sci. Eng.
**2020**, 194, 107325. [Google Scholar] [CrossRef] - Vincent, S.; Caltagirone, J.; Lubin, P.; Randrianarivelo, N. Local Mesh Refinement and Penalty Methods Dedicated to the Direct Numerical Simulation of Incompressible Multiphase Flows. In Proceedings of the ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference, Honolulu, HI, USA, 6–10 July 2003. [Google Scholar]
- Patankar, S.V.; Spalding, D.B. A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Int. J. Heat Mass Transf.
**1972**, 15, 1787–1806. [Google Scholar] [CrossRef]

**Figure 5.**Schematic diagram of the three-layer hydraulic flow pattern during gravel migration process.

**Figure 7.**Graph of volume fraction and migration velocity for pulsed gravel packs and convention’s in horizontal wells.

**Figure 12.**Graph of the effect of carrying-fluid viscosity on the volume fraction and transport velocity.

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**MDPI and ACS Style**

Zhang, Z.; Yang, J.; Chen, S.; Ou, Q.; Zhang, Y.; Qu, X.; Guo, Y. Numerical Simulation of Pulsed Gravel Packing Completion in Horizontal Wells. *Energies* **2021**, *14*, 292.
https://doi.org/10.3390/en14020292

**AMA Style**

Zhang Z, Yang J, Chen S, Ou Q, Zhang Y, Qu X, Guo Y. Numerical Simulation of Pulsed Gravel Packing Completion in Horizontal Wells. *Energies*. 2021; 14(2):292.
https://doi.org/10.3390/en14020292

**Chicago/Turabian Style**

Zhang, Zhenxiang, Jin Yang, Shengnan Chen, Qibin Ou, Yichi Zhang, Ximo Qu, and Yafei Guo. 2021. "Numerical Simulation of Pulsed Gravel Packing Completion in Horizontal Wells" *Energies* 14, no. 2: 292.
https://doi.org/10.3390/en14020292