Abstract
Primary-cementing displacement flows occur in long narrow eccentric annuli during the construction of oil and gas wells. A common problem is that the displacing fluid fingers up the upper wide side of the annulus, leaving behind a “mud channel” of displaced fluid on the lower narrow side of the annulus. Tehrani et al. report that the interface between displacing fluid and mud channel can in certain circumstances become unstable, and a similar phenomenon has been observed in our ongoing experiments. Here an explanation for these instabilities is provided via analysis of the stability of two-layer eccentric annular Hele-Shaw flows, using a transient version of the usual Hele-Shaw approach, in which fluid acceleration terms are retained. Two Newtonian fluids are considered, as a simplification of the general case in which the fluids are shear-thinning yield-stress fluids. It is shown that negative azimuthal buoyancy gradients are in general stabilizing in inclined wells, but that buoyancy may also have a destabilizing effect via axial buoyancy forces that influence the base-flow interfacial velocity. In a variety of special cases where buoyancy is not dominant, it is found that instability is suppressed by a positive product of interfacial velocity difference and reduced Reynolds-number difference between fluids. Even a small positive azimuthal buoyancy gradient, (heavy fluid over light fluid), can be stabilized in this way. Eccentricity of the annulus seems to amplify the effect of buoyancy on stability or instability, e.g. stably stratified fluid layers become more stable as the eccentricity is increased.
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References
Economides MJ (1990) Implications of cementing on well performance. In: Nelson EB (ed) Well cementing. Schlumberger Educational Services
Primary and Remedial Cementing Guidelines. Drilling and Completions Committee, Alberta, April 1995. Distributed by the Petroleum Industry Training Service
Nelson EB (ed) (2001) Well cementing. Schlumberger Educational Services
Bittleston SH, Ferguson J and Frigaard IA (2002). Mud removal and cement placement during primary cementing of an oil well; laminar non-Newtonian displacements in an eccentric annular Hele-Shaw cell. J Engng Math 43: 229–253
Pelipenko S and Frigaard IA (2004). On steady state displacements in primary cementing of an oil well. J Engng Math 46(1): 1–26
Pelipenko S and Frigaard IA (2004). Two-dimensional computational simulation of eccentric annular cementing displacements. IMA J Appl Math 64(6): 557–583
Pelipenko S and Frigaard IA (2004). Visco-plastic fluid displacements in near-vertical narrow eccentric annuli: prediction of travelling wave solutions and interfacial instability. J Fluid Mech 520: 343–377
Guillot D, Hendriks H, Callet F, Vidick B (1990) Mud Removal. In: Nelson EB (ed) Well cementing. Schlumberger Educational Services
Lockyear CF, Ryan DF, Gunningham MM (1989) Cement channelling: how to predict and prevent. Society of Petroleum Engineers paper number SPE 19865
McLean RH, Manry CW, Whitaker WW (1966) Displacement mechanics in primary cementing. Society of Petroleum Engineers paper number SPE 1488
Moyers-González MA (2006) Transient effects in oilfield cementing flows. Dissertation, University of British Columbia
Moyers-González MA, Frigaard IA, Scherzer O and Tsai T-P (2007). Transient effects in oilfield cementing flows: Qualitative behaviour. Euro J Appl Math 18: 477–512
Tehrani A, Ferguson J, Bittleston SH (1992) Laminar displacement in annuli: a combined experimental and theoretical Study. Society of Petroleum Engineers paper number SPE 24569
Tehrani A, Bittleston SH and Long PJG (1993). Flow instabilities during annular displacement of one non-Newtonian fluid by another. Exp Fluids 14: 246–256
Homsy GM (1987). Viscous fingering in porous media. Annu Rev Fluid Mech 19: 271–311
Raghavan R and Marsden SS (1973). A theoretical study of the instability in the parallel flow of immiscible liquids in a porous medium. Quart J Mech Appl Math 26: 205–216
Zeybek M and Yortsos YC (1991). Long waves in parallel flow in Hele-Shaw cells. Phys Rev Lett 67: 1430–1433
Zeybek M and Yortsos YC (1992). Parallel flow in Hele-Shaw cells. J Fluid Mech 244: 421–442
Miranda JO and Widom M (2000). Parallel flow in Hele-Shaw cells with ferrofluids. Phys Rev E 61: 2114–2117
Gondret P, Rakotomalala N, Rabaud M, Salin D and Watzky P (1997). Viscous parallel flows in finite aspect ratio Hele-Shaw cell: Analytical and numerical results. Phys Fluids 9(6): 1841–1843
Gondret P and Rabaud M (1997). Shear instabillity of two-fluid parallel flow in a Helle-Shaw cell. Phys Fluids 9(11): 3267–3274
Gondret P, Ern P, Meignin L and Rabaud M (1999). Experimental evidence of a nonlinear transition from convective to absolute Instability. Phys Rev Lett 82(7): 1442–1447
Hinch EJ and Plouraboué F (2005). Kelvin-Helmholtz instability in a Hele-Shaw cell: Large effect from the small region near the meniscus. Phys Fluids 17: 052107 (13 pages)
Meignin L, Ern P, Gondret P and Rabaud M (2001). Gap size effects for the Kelvin-Helmholtz instability in a Hele-Shaw cell. Phys Rev E 64: 026308
Meignin L, Gondret P, Ruyer-Quil C and Rabaud M (2003). Subcritical Kelvin-Helmholtz Instability in a Hele-Shaw Cell. Phys Rev Lett 90: 234502
Plouraboué F and Hinch EJ (2002). Kelvin-Helmholtz instability in a Hele-Shaw cell. Phys Fluids 14(3): 922–929
Joseph DD, Renardy YY (1993) Fundamentals of two-fluid dynamics. Interdisciplinary Applied Mathematics, Springer
Schmid PJ and Henningson DS (2001). Stability and transition in shear flows. Springer-Verlag, New York, Inc
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Moyers-Gonzalez, M.A., Frigaard, I.A. Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids. J Eng Math 62, 103–131 (2008). https://doi.org/10.1007/s10665-007-9178-y
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DOI: https://doi.org/10.1007/s10665-007-9178-y