Journal of Engineering Mathematics

, Volume 62, Issue 2, pp 103–131 | Cite as

Kinematic instabilities in two-layer eccentric annular flows, part 1: Newtonian fluids

Article
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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.

Keywords

Hele-Shaw flow Interfacial instability Kinematic instability Multi-layer flow stability Primary cementing 
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Copyright information

© Springer Science + Business Media B.V. 2007

Authors and Affiliations

  1. 1.Département de mathématiques et de statistiqueUniversité de MontréalCentre-Ville MontréalCanada
  2. 2.Department of Mathematics and Mechanical EngineeringUniversity of British ColumbiaVancouverCanada

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