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Homogenization of two-phase flows in porous media with hysteresis in the capillary relation

Published online by Cambridge University Press:  17 March 2003

A. BELIAEV
A. BELIAEV
Affiliation:
Water Problem Institute, 3 Gubkina Str., GSP-1, 117735 Moscow, Russia Current address: Divisie Wiskunde en Informatica, Vrije Universiteit Amsterdam, De Boeleln 1081a, 1081 HV Amsterdam, The Netherlands. Email: beliaev@cs.vu.nl.
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Abstract

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The homogenization problem is considered for the equations of two-phase flow in porous media with a periodic or random small-scale structure of inhomogeneities. The capillary relation between saturation and the drop in pressures at microscales accounts for hysteresis and dynamic memory effects. Homogenized equations are derived, and convergence of solutions to the solution of the homogenized problem is proved. Properties of averaged capillary relation are described in the particular case of a two-component porous medium.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 14 , Issue 1 , February 2003 , pp. 61 - 84
Copyright
2003 Cambridge University Press