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Non-Newtonian fluid displacements in horizontal narrow eccentric annuli: effects of slow motion of the inner cylinder

Published online by Cambridge University Press:  02 June 2010

M. CARRASCO-TEJA  and
I. A. FRIGAARD
M. CARRASCO-TEJA
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, CanadaV6T 1Z2
I. A. FRIGAARD*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, CanadaV6T 1Z2 Department of Mechanical Engineering, University of British Columbia, 2054-6250 Applied Science Lane, BC, CanadaV6T 1Z4
*
†Email address for correspondence: [email protected]
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Abstract

We study non-Newtonian fluid displacements in horizontal narrow eccentric annuli in the situation where the inner cylinder is moving. This represents a practically important extension of the model analysed by Carrasco-Teja et al. (J. Fluid Mech., vol. 605, 2008, pp. 293–327). When motion of the inner cylinder is included, the Hele-Shaw model closure becomes significantly more complex and extremely costly to compute, except for Newtonian fluids. In the first part of the paper we address the model derivation and closure relations. The second part of the paper considers the limit of large buoyancy number, in which the interface elongates along the annulus. We derive a lubrication-style model for this situation, showing that the leading-order interface is symmetric. Rotation of the inner cylinder only affects the length of the leading-order interface, and this occurs only for non-Newtonian fluids via shear-thinning effects. At first order, casing rotation manifests in an asymmetrical ‘shift’ of the interface in the direction of the rotation. We also derive conditions on the eccentricity, fluid rheology and inner cylinder velocity, under which we are able to find steady travelling wave displacement solutions.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 653 , 25 June 2010 , pp. 137 - 173
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Barenblatt, G. I., Entov, V. M. & Ryzhik, V. M. 1990 Theory of Fluid Flows Through Natural Rocks. Theory and Applications of Transport in Porous Media, vol. 3. Kluwer.CrossRefGoogle Scholar
Bittleston, S. H., Ferguson, J. & Frigaard, I. A. 2002 Mud removal and cement placement during primary cementing of an oil well; laminar non-Newtonian displacements in an eccentric Hele-Shaw cell. J. Engng Maths 43, 229–253.CrossRefGoogle Scholar
Carrasco-Teja, M. & Frigaard, I. A. 2009 Displacement flows in horizontal, narrow, eccentric annuli with a moving inner cylinder. Phys. Fluids 21, 073102.CrossRefGoogle Scholar
Carrasco-Teja, M., Frigaard, I. A., Seymour, B. R. & Storey, S. 2008 Viscoplastic fluid displacements in horizontal narrow eccentric annuli: stratification and travelling waves solutions. J. Fluid Mech. 605, 293–327.CrossRefGoogle Scholar
Dutra, E., Naccache, M., Souza-Mendes, P., Souto, C., Martins, A. & de Miranda, C. 2004 Analysis of interface between Newtonian and non-Newtonian fluids inside annular eccentric tubes. In Proceedings of ASME-IMECE, Anaheim, CA. Paper number 59335.Google Scholar
Ekeland, I. & Témam, R. 1976 Convex Analysis and Variational Problems. North-Holland.Google Scholar
Fitt, A. D. & Please, C. P. 2001 Asymptotic analysis of the flow of shear-thinning foodstuffs in annular scraped heat exchangers J. Engng Maths 39, 345–366.CrossRefGoogle Scholar
Goldstein, R. V. & Entov, V. M. 1989 Qualitative Methods in Continuum Mechanics. Academic Press.Google Scholar
Glowinski, R. 1983 Numerical Methods for Nonlinear Variational Problems. Springer.Google Scholar
Jakobsen, J., Sterri, N., Saasen, A., Aas, B., Kjosnes, I. & Vigen, A. 1991 Displacements in eccentric annuli during primary cementing in deviated wells. Soc. Petrol. Engrs. Paper number SPE 21686.CrossRefGoogle Scholar
Martin, M., Latil, M. & Vetter, P. 1978 Mud displacement by slurry during primary cementing jobs – predicting optimum conditions. Soc. Petrol. Engrs. Paper number SPE 7590.CrossRefGoogle Scholar
McLean, R. H., Manry, C. W. & Whitaker, W. W. 1966 Displacement mechanics in primary cementing. Soc. Petrol. Engrs. Paper number SPE 1488.Google Scholar
Moyers-González, M. A. & Frigaard, I. A. 2008 Kinematic instabilities in two-layer eccentric annular flows. Part 1. Newtonian fluids. J. Engng Maths 62, 103–131.Google Scholar
Moyers-González, M. A. & Frigaard, I. A. 2009 Kinematic instabilities in two-layer eccentric annular flows. Part 2. Shear thinning and yield stress effects J. Engng Maths 65, 25–52.CrossRefGoogle Scholar
Moyers-González, M. A., Frigaard, I. A., Scherzer, O. & Tsai, T.-P. 2007 Transient effects in oilfield cementing flows: qualitative behaviour Eur. J. Appl. Maths 18, 477–512.CrossRefGoogle Scholar
Nelson, E. B. & Guillot, D. 2006 Well Cementing, 2nd edn. Schlumberger Educational Services.Google Scholar
Nguyen, Q. D., Deawwanich, T., Tonmukayakul, N., Savery, M. R. & Chin, W. 2008 Flow visualization and numerical simulation of viscoplastic fluid displacements in eccentric annuli. In AIP Conference Proceedings: XVth International Congress on Rheology: The Society of Rheology 80th Annual Meeting, Monterey, CA, July 7, 2008, vol. 1027, pp. 279–281, doi:10.1063/1.2964662.CrossRefGoogle Scholar
Payne, M. L., Wilton, B. S. & Ramos, G. G. 1995 Recent advances and emerging technologies for extended reach drilling. Soc. Petrol. Engrs. Paper number SPE 29920.CrossRefGoogle Scholar
Pelipenko, S. & Frigaard, I. A. 2004 a On steady state displacements in primary cementing of an oil well. J. Engng Maths 48 (1), 1–26.CrossRefGoogle Scholar
Pelipenko, S. & Frigaard, I. A. 2004 b Two-dimensional computational simulation of eccentric annular cementing displacements. IMA J. Appl. Maths 64 (6), 557–583.Google Scholar
Pelipenko, S. & Frigaard, I. A. 2004 c Visco-plastic fluid displacements in near-vertical narrow eccentric annuli: prediction of travelling wave solutions and interfacial instability. J. Fluid Mech. 520, 343–377.CrossRefGoogle Scholar
Sabins, F. L. 1990 Problems in cementing horizontal wells. J. Pet. Technol. 42 (4), 398–400.CrossRefGoogle Scholar
Savery, M., Darbe, R. & Chin, W. 2007 Modeling fluid interfaces during cementing using a 3D mud displacement simulator. Offshore Tech. Conf. Paper number 18513. Curran Associates, Inc., ISBN 9781604231465.Google Scholar
Szabo, P. & Hassager, O. 1995 Simulation of free surfaces in 3-D with the arbitrary Lagrange–Euler method. Intl J. Numer. Methods Engng 38, 717–734.CrossRefGoogle Scholar
Szabo, P. & Hassager, O. 1997 Displacement of one Newtonian fluid by another: density effects in axial annular flow. Intl J. Multiphase Flow 23, 113–129.CrossRefGoogle Scholar
Tehrani, A., Ferguson, J. & Bittleston, S. H. 1992 Laminar displacement in annuli: a combined theoretical and experimental study. Soc. Petrol. Engrs. Paper number SPE 24569.CrossRefGoogle Scholar
Vefring, E. H., Bjorkevoll, K. S., Hansen, S. A., Sterri, N., Saevareid, O., Aas, B. & Merlo, A. 1997 Optimization of displacement efficiency during primary cementing. Soc. Petrol. Engrs. Paper number SPE 39009.CrossRefGoogle Scholar