On the effects of discontinuous capillarities for immiscible two-phase flows in
      porous media made of several rock-types

Clément Cancès; Clément Cancès

doi:10.3934/nhm.2010.5.635

Networks and Heterogeneous Media

2010, Volume 5, Issue 3: 635-647. doi: 10.3934/nhm.2010.5.635

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On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types

Clément Cancès ^{1
,}

1.
Laboratoire JLL, Université Pierre et Marie Curie, Boîte courrier 187, 4 place Jussieu, 75952 PARIS Cedex 05

Received: 01 January 2010 Revised: 01 April 2010
Primary: 35L60, 35L67; Secondary: 76S05, 76T99.

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 the capillarity field at interface. We first consider a model with capillarity forces within the rocks, stating an existence/uniqueness result. Then we look for the asymptotic problem for vanishing capillarity within the rocks, remaining only on the interface. We show that either the solution to the asymptotic problem is the optimal entropy solution to a scalar conservation law with discontinuous flux, or it admits a non-classical shock at the interface modeling oil-trapping.
- scalar conservation laws,
- discontinuous flux,
- non-classical shock,
- oil-trapping
Citation: Clément Cancès. On the effects of discontinuous capillarities for immiscible two-phase flows in porous media made of several rock-types[J]. Networks and Heterogeneous Media, 2010, 5(3): 635-647. doi: 10.3934/nhm.2010.5.635

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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 the capillarity field at interface. We first consider a model with capillarity forces within the rocks, stating an existence/uniqueness result. Then we look for the asymptotic problem for vanishing capillarity within the rocks, remaining only on the interface. We show that either the solution to the asymptotic problem is the optimal entropy solution to a scalar conservation law with discontinuous flux, or it admits a non-classical shock at the interface modeling oil-trapping.
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