Transport in Porous Media

, Volume 83, Issue 1, pp 29–53 | Cite as

Slumping Flows in Narrow Eccentric Annuli: Design of Chemical Packers and Cementing of Subsurface Gas Pipelines

Article

Abstract

In well construction, there are an increasing number of scenarios in which plugs are being set in annular geometries, whether as cement plugs or simply in the form of chemical packers. The generic reason for setting of such plugs is to hydraulically isolate different regions of a wellbore (or hole). An interesting practical problem in such situations is to predict the rheological properties that are necessary to prevent the annular plug fluid from flowing under the action of buoyancy, or indeed to predict how far the plug material may flow for given rheological properties. The answers to these questions provide valuable information for operational design. Mathematically, these flows are modeled using a Hele-Shaw style approximation of the narrow annulus. Since fluids used in the wellbore are non-Newtonian, typically shear-thinning and with a yield stress, the relationship between the local modified pressure gradient and the gap-averaged velocity field is nonlinear. If the yield stress of the fluids is sufficiently large, relative to the applied pressure over the gap, there is no flow. In the porous media context, there is direct analogy with problems of nonlinear seepage and in particular with non-Darcy flows with limiting pressure gradient. The study of such flows was both pioneered and developed by V.M. Entov, to whose memory this paper is dedicated.

Keywords

Visco-plastic fluid Nonlinear seepage Cementing Yield stress Variational method 

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References

  1. Alexandrou A.N., Entov V.: On the steady-state advancement of fingers and bubbles in a HelebShaw cell filled by a non-Newtonian fluid. Eur. J. Appl. Math. 8, 73–87 (2000)Google Scholar
  2. Barenblatt, G.I., Entov, V.M., Ryzhik, V.M.: Theory of Fluid Flows through Natural Rocks. Theory and Applications of Transport in Porous Media, vol. 3. Kluwer, Dodrecht (1990)Google Scholar
  3. Bittleston S.H., Ferguson J., Frigaard I.A.: Mud removal and cement placement during primary cementing of an oil well; laminar non-Newtonian displacements in an eccentric annular Hele-Shaw cell. J. Eng. Math. 43, 229–253 (2002)CrossRefGoogle Scholar
  4. Carrasco-Teja M., Frigaard I.A., Seymour B., Storey S.: Viscoplastic fluid displacements in horizontal narrow eccentric annuli: stratification and travelling waves solutions. J. Fluid Mech. 605, 293–327 (2008)CrossRefGoogle Scholar
  5. Carrasco-Teja M., Frigaard I.A.: Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder. Phys. Fluids 21, 073102 (2009) doi:10.1063/1.3193712 CrossRefGoogle Scholar
  6. Coussot P.: Saffman-Taylor instability in yield-stress fluids. J. Fluid Mech. 380, 363–376 (1999)CrossRefGoogle Scholar
  7. Fortin M., Glowinski R.: Augmented Lagrangian Methods. North-Holland, Amsterdam (1983)Google Scholar
  8. Frigaard I.A.: Stratified exchange flows of two Bingham fluids in an inclined slot. J. Non-Newton. Fluid Mech. 78, 61–87 (1998)CrossRefGoogle Scholar
  9. Frigaard I.A., Crawshaw J.: Preventing buoyancy-driven flows of two Bingham fluids ina closed pipe - Fluid rheology design for oilfield plug cementing. J. Eng. Math. 36, 327–348 (1999)CrossRefGoogle Scholar
  10. Frigaard I.A., Scherzer O.: The effects of yield stress variation on uniaxial exchange flows of two Bingham fluids in a pipe. SIAM J. Appl. Math. 60(6), 1950–1976 (2000)CrossRefGoogle Scholar
  11. Frigaard I.A., Ngwa G.A.: Upper bounds on the slump length in plug cementing of near-horizontal wells. J. Non-Newton. Fluid Mech. 117(2-3), 147–162 (2004)CrossRefGoogle Scholar
  12. Glowinski R.: Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York (1983)Google Scholar
  13. Goldstein R.V., Entov V.M.: Qualitative Methods in Continuum Mechanics. Longman Scientific & Technical, Harlow, UK (1994)Google Scholar
  14. Lindner, A.: L’instabilité de Saffman-Taylor dans les fluides complexes: relation entre les propriétéshéologiques et la formations de motifs. These de l’Universite Paris VI (PhD thesis), Paris, France, (2000)Google Scholar
  15. Lindner A., Coussot P., Bonn D.: Viscous fingering in a yield stress fluid. Phys. Rev. Lett. 85, 314–317 (2000)CrossRefGoogle Scholar
  16. Lindner A., Bonn D., Poire E.C., Ben-Amar M., Meunier J.: Viscous fingering in non-Newtonian fluids. J. Fluid Mech. 469, 237–256 (2002)CrossRefGoogle Scholar
  17. Maleki-Jirsaraei N., Lindner A., Rouhan S., Bonn D.: Saffman-Taylor instability in yield stress fluids. J. Phys. Condens. Mater. 17, 1209–1218 (2005)CrossRefGoogle Scholar
  18. Martin, M., Latil, M., Vetter, P.: Mud displacement by slurry during primary cementing jobs—predicting optimum conditions. Society of Petroleum Engineers paper number SPE 7590 (1978)Google Scholar
  19. Moyers-González M.A., Frigaard I.A., Scherzer O., Tsai T.-P.: Transient effects in oilfield cementing flows: qualitative behaviour. Euro. J. Appl. Math. 18, 477–512 (2007)CrossRefGoogle Scholar
  20. Moyers-González M.A., Frigaard I.A.: Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids. J. Eng. Math. 62, 103–131 (2008a)CrossRefGoogle Scholar
  21. Moyers-González, M.A., Frigaard, I.A.: Kinematic instabilities in two-layer eccentric annular flows, part 2: shear thinning and yield stress effects. J. Eng. Math. (2008b). doi:10.1007/s10665-008-9260-0
  22. Nelson, E.B.: Well Cementing, Schlumberger Educational Services, Houston (1990)Google Scholar
  23. Pascal H.: Rheological behaviour effect of non-Newtonian fluids on dynamic of moving interface in porous media. Int. J. Eng. Sci. 22(3), 227–241 (1984a)CrossRefGoogle Scholar
  24. Pascal H.: Dynamics of moving interface in porous media for power law fluids with a yield stress. Int. J. Eng. Sci. 22(5), 577–590 (1984b)CrossRefGoogle Scholar
  25. Pascal H.: A theoretical analysis of stability of a moving interface in a porous medium for Bingham displacing fluids and its application in oil displacement mechanism. Can. J. Chem. Eng. 64, 375–379 (1986)CrossRefGoogle Scholar
  26. Pelipenko S., Frigaard I.A.: On steady state displacements in primary cementing of an oil well. J. Eng. Math. 46, 1–26 (2004a)CrossRefGoogle Scholar
  27. Pelipenko S., Frigaard I.A.: Two-dimensional computational simulation of eccentric annular cementing displacements. IMA J. Appl. Math. 64(6), 557–583 (2004b)CrossRefGoogle Scholar
  28. Pelipenko S., Frigaard I.A.: Visco-plastic fluid displacements in near-vertical narrow eccentric annuli: prediction of travelling wave solutions and interfacial instability. J. Fluid Mech. 520, 343–377 (2004c)CrossRefGoogle Scholar
  29. Tehrani, A., Ferguson, J., Bittleston, S.H.: Laminar displacement in annuli: a combined experimental and theoretical study. Society of Petroleum Engineers paper number SPE 24569 (1992)Google Scholar
  30. Tehrani A., Bittleston S.H., Long P.J.G.: Flow instabilities during annular displacement of one non- Newtonian fluid by another. Expend. Fluids 14, 246–256 (1993)Google Scholar
  31. Zalesak S.T.: Fully multi-dimensional flux-corrected transport. J. Comp. Phys. 31, 355–362 (1979)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of British ColumbiaVancouverCanada
  2. 2.Department of Mechanical EngineeringThe University of British ColumbiaVancouverCanada
  3. 3.Department of MathematicsUniversity of BueaBueaCameroon

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