Asymptotic behavior of two-phase flows in heterogeneous porous media for capillarity depending only on space. II. Non-classical shocks to model oil-trapping

Clément Cancès (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We consider a one-dimensional problem modeling two-phase flow in heterogeneous porous media made of two homogeneous subdomains, with discontinuous capillarity at the interface between them. We suppose that the capillary forces vanish inside the domains, but not on the interface. Under the assumption that the gravity forces and the capillary forces are oriented in opposite directions, we show that the limit, for vanishing diffusion, is not the entropy solution of the hyperbolic scalar conservation law. A non-classical shock occurs on the interface, modeling oil-trapping.

Mots clés: scalar conservation laws with discontinuous flux; non-classical shock; two-phase flow; porous media; discontinuous capillarity

Domaines: Equations aux dérivées partielles [math.AP]

Clément Cancès. Asymptotic behavior of two-phase flows in heterogeneous porous media for capillarity depending only on space. II. Non-classical shocks to model oil-trapping. 2009. ⟨hal-00360295v6⟩