A gravity current model with capillary trapping for oil migration in multilayer geological basins

Clément Cancès (1) , David Maltese (2)

1 RAPSODI - Reliable numerical approximations of dissipative systems
2 LAMA - Laboratoire Analyse et de Mathématiques Appliquées

We propose a reduced model accounting capillary trapping to simulate oil migration in geological basins made of several rock types. Our model is derived from Darcy type models thanks to Dupuit approximation and a vertical integration in each geological layer. We propose a time-implicit finite volume scheme which is shown to be unconditionally stable and to admit discrete solutions. Numerical outcomes are then provided in order to illustrate the behavior of our reduced model.

Mots clés: Large scale basin modeling; Multilayer Dupuit approximation; Capillary trapping; Finite Volumes

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Sciences de la Terre

Clément Cancès, David Maltese. A gravity current model with capillary trapping for oil migration in multilayer geological basins. SIAM Journal on Applied Mathematics, 2021, 81 (2), pp.454-484. ⟨10.1137/19M1284233⟩. ⟨hal-02272965v3⟩