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Perturbation theory for a displacement front passing discontinuities in capillary pressure and permeability in a porous medium

Part of: Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  26 February 2010

D. C. Shaw  and
R. A. Dawe
D. C. Shaw
Affiliation:
School of Mathematics, University of Bath, Bath. BA2 7AY
R. A. Dawe
Affiliation:
Department of Mineral Resources Engineering, Imperial College, London. SW7 2BP
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Abstract

When a displacement front meets a heterogeneity in a porous medium, its shape will be altered. The amount of distortion depends on the size and shape of the heterogeneity, the amount of variation of the heterogeneous properties, and the mobility ratio between the displaced and displacing fluids. The solution for a circular permeability discontinuity is known when the capillary pressure is uniform and the mobility ratio M is unity [4]. Here, we extend the theory to the case where there is a small change ε in capillary pressure as well as a nearly unit mobility ratio M = 1 + εγ. Corrections can then be found, in closed form, to first order in ε, to the shape of the front and the pressure field. Computations using these expressions are simpler than the full free-boundary problem, and some analytical estimates are possible in further limits. Finally, the theory is extended to the case of a front passing a number of such heterogeneous patches which are widely spaced.

MSC classification

Secondary: 76S05: Flows in porous media; filtration; seepage
Type
Research Article
Information
Mathematika , Volume 32 , Issue 1 , June 1985 , pp. 75 - 89
Copyright
Copyright © University College London 1985

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References

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