Abstract
We consider a simplified model for two-phase flows in one-dimensional heterogeneous porous media made of two different rocks.We focus on the effects induced by the discontinuity of thecapillarity field at interface. We first consider a model withcapillarity forces within the rocks, stating an existence/uniquenessresult. Then we look for the asymptotic problem for vanishingcapillarity within the rocks, remaining only on the interface. Weshow that either the solution to the asymptotic problem is theoptimal entropy solution to a scalar conservation law withdiscontinuous flux, or it admits a non-classical shock at theinterface modeling oil-trapping.
Highlights
We are interested in a simplified model of incompressible immiscible two-phase flows within heterogeneous porous media made of several rock types
The equation 1 turns to a first order scalar conservation law with a discontinuous flux function
It will be shown that, under technical assumptions, if both phases move in the same direction or if the capillary forces at the interface and the buoyancy work in the same sense, the saturation profile is the unique optimal entropy solution
Summary
On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types. Networks and Heterogeneous Media, AIMS-American Institute of Mathematical Sciences, 2010. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés
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