Numerical simulation of two-phase inertial flow in heterogeneous porous media

Azita Ahmadi-Senichault (1, 2) , Ali Akbar Abbasian Arani (1) , Didier Lasseux (2, 2, 1)

1 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux
2 TREFLE - Transferts, écoulements, fluides, énergétique

In this study, non-Darcy inertial two-phase incompressible and non-stationary flow in heterogeneous porous media is analyzed using numerical simulations. For the purpose, a 3D numerical tool was fully developed using a finite volume formulation, although for clarity, results are presented in 1D and 2D configurations only. Since a formalized theoretical model confirmed by experimental data is still lacking, our study is based on the widely used generalized Darcy–Forchheimer model. First, a validation is performed by comparing numerical results of the saturation front kinetics with a semi-analytical solution inspired from the Buckley–Leverett model extended to take into account inertia. Second, we highlight the importance of inertial terms on the evolution of saturation fronts as a function of a suitable Reynolds number. Saturation fields are shown to have a structure markedly different from the classical case without inertia, especially for heterogeneous media, thereby, emphasizing the necessity of a more complete model than the classical generalized Darcy’s one when inertial effects are not negligible.

Mots clés: Inertial two-phase flow; Numerical simulations; Generalized Darcy–Forchheimer model; Heterogeneous porous media

Domaines: Mécanique des fluides [physics.class-ph]

Azita Ahmadi-Senichault, Ali Akbar Abbasian Arani, Didier Lasseux. Numerical simulation of two-phase inertial flow in heterogeneous porous media. Transport in Porous Media, 2010, 84 (1), pp.177-200. ⟨10.1007/s11242-009-9491-1⟩. ⟨hal-01174073⟩