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An implicit unsteady hydraulic solver for suspended cuttings transport in managed pressure wells


We present a simulation tool for transient events in complex hydraulic networks. The code includes modelling of the transport of suspended cuttings in near-vertical wells. An unstructured finite volume formulation with implicit time integration has been chosen. The unconditional stability of the integrator makes the method suitable for the simulation of transient events over a wide range of characteristic timescales. It handles both very fast transients (e.g. fluid hammer events) and the long-term evolution of the well (e.g. hole cleaning operations). The software has been developed to address the need of the oil industry for a robust and efficient predictive tool allowing effective well control in managed pressure drilling operations. The physical modelling follows the standard practices accepted by the industry (e.g. mud rheology computations). The mathematical foundation of the algorithm is described followed by validation cases that illustrate its capabilities and accuracy. Finally, a practical industrial application example is provided to demonstrate the real-world performance of the software.

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  1. 1.

    Malloy KP et al. (2009) Managed-pressure drilling: what it is and what it is not. In: IADC/SPE Managed pressure drilling and underbalanced operations conference and exhibition, San Antonio TX

  2. 2.

    Elliot D et al (2011) Managed pressure drilling erases the lines. Schlumberger Oilfield Rev 23(1):14–23

    Google Scholar 

  3. 3.

    van Riet EJ, Reitsma D (2003) Development and testing of a fully automated system to accurately control downhole pressure during drilling operations. In: SPE/IADC Middle East drilling technology conference and exhibition, Abu Dhabi

  4. 4.

    Guo C et al (2010) Managed pressure drilling micro flux technology allows safer drilling in highly sour reservoirs. In: International oil and gas conference and exhibition in China, Beijing

  5. 5.

    Streeter VL, Wylie EB (1998) Fluid mechanics, international 9th revised edn. McGraw-Hill Higher Education, New York

  6. 6.

    Lohrasbi AR, Attarnejad R (2008) Water hammer analysis by characteristic method. Am J Eng Appl Sci 1(4):287–294

    Article  Google Scholar 

  7. 7.

    Amein M, Chu HL (1975) Implicit numerical modeling of unsteady flows. J Hydraul Div ASCE 101(6):717–731

    Google Scholar 

  8. 8.

    Wylie EB, Streeter VL (1970) Network system transient calculations by implicit method. In: 45th Annual meeting of the society of petroleum engineers of AIME, Houston TX

  9. 9.

    Ghidaoui M et al (2005) A review of water hammer theory and practice. Appl Mech Rev ASME 58:49–76

    Article  Google Scholar 

  10. 10.

    Greyvenstein GP (2002) An implicit method for the analysis of transient flows in pipe networks. Int J Numer Methods Eng 53:1127–1143

    Article  Google Scholar 

  11. 11.

    Anderson JD (1995) Computational fluid dynamics: the basics with applications. McGraw-Hill, New York

    Google Scholar 

  12. 12.

    (2010) Rheology and hydraulics of oil-well fluids—API recommended practice 13D, 6th edn. American Petroleum Institute, Washington DC

  13. 13.

    Herschel WH, Bulkley R (1926) Konsistenzmessungen von Gummi-Benzollösungen. Kolloid Zeitschrift 39:291–300

    Article  Google Scholar 

  14. 14.

    Celigueta MA et al (2016) A FEM-DEM technique for studying the motion of particles in non-Newtonian fluids. Application to the transport of drill cuttings in wellbores. Comput Part Mech 3(2):263–276

    Article  Google Scholar 

  15. 15.

    Walker RE, Mayes TM (1975) Design of muds for carrying capacity. J Pet Technol 259:893–900

    Article  Google Scholar 

  16. 16.

    Bourgoyne AT, Millheim KK, Chenevert ME, Young FS (1986) applied drilling engineering. SPE Textbook Series, Richardson, pp 173–183

    Google Scholar 

  17. 17.

    Lomax H, Pulliam TH, Zingg DW (2003) Fundamentals of computational fluid dynamics. Springer, Berlin

    MATH  Google Scholar 

  18. 18.

    Godunov SK (1954) Different methods for shock waves. Ph.D. thesis, Moscow State University

  19. 19.

    Stein E, de Borst R, Hughes TJR (eds) (2004) Encyclopedia of computational mechanics, vol 1, Chapter 14, Wiley, Hoboken

  20. 20.

    Sifferman TR, Mayers GM, Haden EL, Wahl HA (1974) Drill-cutting transport in full-scale vertical annuli. J Pet Technol 26(11):1295–1302

    Article  Google Scholar 

  21. 21.

    Araya W, Chaudhry M (2001) Unsteady friction in rough pipes. J Hydraul Eng 127(7):607–618

    Article  Google Scholar 

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This research was partially funded by Weatherford International.

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Correspondence to R. Flores.

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Flores, R., Ortega, E., Ilin, A. et al. An implicit unsteady hydraulic solver for suspended cuttings transport in managed pressure wells. Comp. Part. Mech. 6, 163–175 (2019).

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  • Unsteady
  • Hydraulics
  • Oil well
  • Cuttings transport