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Asymptotic model of the mobile interface between two liquids in a thin porous stratum

Published online by Cambridge University Press:  13 December 2002

M. PANFILOV  and
M. BUÈS
M. PANFILOV
Affiliation:
Laboratoire Environnement, Géomécanique et Ouvrages – LAEGO – ENSG – INPL, Rue du Doyen Marcel Roubault, BP 40, 54501 Vandoeuvre-lès-Nancy, [email protected]; [email protected] Moscow Lomonosov University, Mechanics/Mathematics Faculty, Leninskiye Gory, 119899 Moscow, Russia
M. BUÈS
Affiliation:
Laboratoire Environnement, Géomécanique et Ouvrages – LAEGO – ENSG – INPL, Rue du Doyen Marcel Roubault, BP 40, 54501 Vandoeuvre-lès-Nancy, [email protected]; [email protected]
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Abstract

We propose a new generalized model to describe deformations of the mobile interface separating two immiscible liquids in a porous medium. The densities and the viscosities of the fluids can have any value. The horizontal size of the interface is much greater than the vertical size of the domain. Unlike the classical theory, the new model describes gravitational non-equilibrium processes, including the Rayleigh–Taylor instability which appears in the form of a negative apparent diffusion parameter. Several flow regimes are established depending on the ratio between gravity and the elastic fluid/medium forces, and between the vertical and horizontal flow rates. The model is used to analyse the evolution of the interface during the free spreading of one liquid over another. This is characterized by the presence of interface degeneration points. The explicit solution to the problem of oil and water flow towards a well is presented as an application to oil reservoirs.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 473 , 10 December 2002 , pp. 59 - 81
Copyright
© 2002 Cambridge University Press

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