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Analysis of a model for foam improved oil recovery

Published online by Cambridge University Press:  20 June 2014

P. Grassia ,
E. Mas-Hernández ,
N. Shokri ,
S. J. Cox ,
G. Mishuris  and
W. R. Rossen
P. Grassia*
Affiliation:
CEAS, The Mill, University of Manchester, Oxford Road, Manchester M13 9PL, UK
E. Mas-Hernández
Affiliation:
CEAS, The Mill, University of Manchester, Oxford Road, Manchester M13 9PL, UK
N. Shokri
Affiliation:
CEAS, The Mill, University of Manchester, Oxford Road, Manchester M13 9PL, UK
S. J. Cox
Affiliation:
DMaP, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK
G. Mishuris
Affiliation:
DMaP, Aberystwyth University, Aberystwyth, Ceredigion SY23 3BZ, UK
W. R. Rossen
Affiliation:
Department of Geotechnology, Delft University of Technology, Stevinweg 1, 2628 CN Delft, Netherlands
*
†Email address for correspondence: [email protected]
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Abstract

During improved oil recovery (IOR), gas may be introduced into a porous reservoir filled with surfactant solution in order to form foam. A model for the evolution of the resulting foam front known as ‘pressure-driven growth’ is analysed. An asymptotic solution of this model for long times is derived that shows that foam can propagate indefinitely into the reservoir without gravity override. Moreover, ‘pressure-driven growth’ is shown to correspond to a special case of the more general ‘viscous froth’ model. In particular, it is a singular limit of the viscous froth, corresponding to the elimination of a surface tension term, permitting sharp corners and kinks in the predicted shape of the front. Sharp corners tend to develop from concave regions of the front. The principal solution of interest has a convex front, however, so that although this solution itself has no sharp corners (except for some kinks that develop spuriously owing to errors in a numerical scheme), it is found nevertheless to exhibit milder singularities in front curvature, as the long-time asymptotic analytical solution makes clear. Numerical schemes for the evolving front shape which perform robustly (avoiding the development of spurious kinks) are also developed. Generalisations of this solution to geologically heterogeneous reservoirs should exhibit concavities and/or sharp corner singularities as an inherent part of their evolution: propagation of fronts containing such ‘inherent’ singularities can be readily incorporated into these numerical schemes.

JFM classification

Mathematical Foundations: Computational methods Complex Fluids: Foams Low-Reynolds-number flows: Porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 751 , 25 July 2014 , pp. 346 - 405
Copyright
© 2014 Cambridge University Press 

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