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.
Similar content being viewed by others
References
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)
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)
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)
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)
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
Coussot P.: Saffman-Taylor instability in yield-stress fluids. J. Fluid Mech. 380, 363–376 (1999)
Fortin M., Glowinski R.: Augmented Lagrangian Methods. North-Holland, Amsterdam (1983)
Frigaard I.A.: Stratified exchange flows of two Bingham fluids in an inclined slot. J. Non-Newton. Fluid Mech. 78, 61–87 (1998)
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)
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)
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)
Glowinski R.: Numerical Methods for Nonlinear Variational Problems. Springer-Verlag, New York (1983)
Goldstein R.V., Entov V.M.: Qualitative Methods in Continuum Mechanics. Longman Scientific & Technical, Harlow, UK (1994)
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)
Lindner A., Coussot P., Bonn D.: Viscous fingering in a yield stress fluid. Phys. Rev. Lett. 85, 314–317 (2000)
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)
Maleki-Jirsaraei N., Lindner A., Rouhan S., Bonn D.: Saffman-Taylor instability in yield stress fluids. J. Phys. Condens. Mater. 17, 1209–1218 (2005)
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)
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)
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)
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
Nelson, E.B.: Well Cementing, Schlumberger Educational Services, Houston (1990)
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)
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)
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)
Pelipenko S., Frigaard I.A.: On steady state displacements in primary cementing of an oil well. J. Eng. Math. 46, 1–26 (2004a)
Pelipenko S., Frigaard I.A.: Two-dimensional computational simulation of eccentric annular cementing displacements. IMA J. Appl. Math. 64(6), 557–583 (2004b)
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)
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)
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)
Zalesak S.T.: Fully multi-dimensional flux-corrected transport. J. Comp. Phys. 31, 355–362 (1979)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Frigaard, I.A., Ngwa, G.A. Slumping Flows in Narrow Eccentric Annuli: Design of Chemical Packers and Cementing of Subsurface Gas Pipelines. Transp Porous Med 83, 29–53 (2010). https://doi.org/10.1007/s11242-009-9467-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-009-9467-1