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Gravity-driven flow in a horizontal annulus

Published online by Cambridge University Press:  02 October 2017

Marcus C. Horsley Open the ORCID record for Marcus C. Horsley [Opens in a new window]  and
Andrew W. Woods Open the ORCID record for Andrew W. Woods [Opens in a new window]
Marcus C. Horsley
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
Andrew W. Woods*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: andy@bpi.cam.ac.uk
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Abstract

A theory for the low-Reynolds-number gravity-driven flow of two Newtonian fluids separated by a density interface in a two-dimensional annular geometry is developed. Solutions for the governing time-dependent equations of motion, in the limit that the radius of the inner and outer boundaries are similar, and in the case that the interface is initially inclined to the horizontal, are analysed numerically. We focus on the case in which the fluid is arranged symmetrically about a vertical line through the centre of the annulus. These solutions are successfully compared with asymptotic solutions in the limits that (i) a thin film of dense fluid drains down the outer boundary of the annulus, and (ii) a thin layer of less dense fluid is squeezed out of the narrow gap between the base of the inner annulus and dense fluid. Application of the results to the problem of mud displacement by cement in a horizontal well is briefly discussed.

JFM classification

Low-Reynolds-number flows: Hele-Shaw flows Low-Reynolds-number flows: Low-Reynolds-number flows Low-Reynolds-number flows: Lubrication theory
Type
Papers
Information
Journal of Fluid Mechanics , Volume 830 , 10 November 2017 , pp. 479 - 493
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Copyright
© 2017 Cambridge University Press 

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References

Acheson, D. J. 1990 Elementary Fluid Dynamics. Oxford University Press.Google Scholar
Ames, W. F. 2014 Numerical Methods for Partial Differential Equations. Academic.Google Scholar
Eduardo, S., Dutra, S. & Monica, F. 2004 Liquid displacement during oil well cementing operations. Annu. Trans. Nordic Rheol. Soc. 1, 93–100.Google Scholar
Gunn, I. & Woods, A. W. 2011 On the flow of buoyant fluid injected into a confined, inclined aquifer. J. Fluid Mech. 672, 109–129.Google Scholar
Huppert, H. E. 1982 The propagation of two-dimensional and axisymmetric viscous gravity currents over a rigid horizontal surface. J. Fluid Mech. 121, 43–58.CrossRefGoogle Scholar
Kudaikulova, G. 2015 Rheology of drilling muds. J. Phys.: Conf. Ser. 602, 012008.Google Scholar
Matson, G. P. & Hogg, A. J. 2012 Viscous exchange flows. Phys. Fluids 24 (2), 023102.Google Scholar
Myers, T. G. 1998 Thin films with high surface tension. SIAM Rev. 40 (3), 441–462.Google Scholar
Sauer, C. W. & Till, M. V. 1987 Mud displacement during cementing: a state of the art. J. Petrol. Technol. 39 (9), 1–91.CrossRefGoogle Scholar
Shahriar, A.2011 Investigation on rheology of oil well cement slurries. PhD thesis, University of Western Ontario.Google Scholar
Siddiqi, Z. A. 2012 Concrete Structures Part-II, vol. 2. Zahid Ahmad Siddiqi.Google Scholar
Takagi, D. & Huppert, H. E. 2007 The effect of confining boundaries on viscous gravity currents. J. Fluid Mech. 577, 495–505.Google Scholar
Zheng, Z., Rongy, L. & Stone, H. A. 2015 Viscous fluid injection into a confined channel. Phys. Fluids 27 (6), 062105.CrossRefGoogle Scholar