A. Ziani

MATHEMATICAL ANALYSIS FOR COMPRESSIBLE MISCIBLE DISPLACEMENT MODELS IN POROUS MEDIA

We discuss a three-dimensional displacement model of one miscible compressible fluid by another in a porous medium. The motion is modeled by a nonlinear system of parabolic type coupling the pressure and the concentration. We give an existence result of weak solutions for a model with diffusion and dispersion, using the Schauder fixed point theorem. We also study a model in the absence of diffusion and dispersion. The system becomes of parabolic-hyperbolic type, the existence of global weak solutions is then obtained through a compensated compactness argument.

Homogénéisation d'équations hyperboliques du premier ordre et application aux écoulements miscibles en milieu poreux

Resume On s’interesse a l’homogeneisation de l’equation hyperbolique modele ∂ t u e + a e ( t , y ) ∂ x u e = 0 , t > 0 , x ∈ ℝ , y ∈ Ω ⊂ ℝ N , munie d’une condition initiale (et d’une condition aux limites lorsque x ∈]0, 1[). Pour cela, nous caracterisons la limite L∞(Ω) faible * de fonctions du type φ x e ( λ ) = ( λ − A e ( y ) ) − 1 definies pour , λ ∉ [m, M] et verifiant 0

Homogénéisation d'un modèle d'écoulements miscibles en milieu poreux

We consider a 1-D model for incompressible miscible displacements in porous media without any dispersion term. Existence and uniqueness results for nonsmooth data are proved. We study the homogenization of the model. The limit problem is of the same type. The result is obtained thanks to compactness properties of the corresponding characteristic curves.

Asymptotic Behavior of the Solutions of an Elliptic-Parabolic System Arising in Flow in Porous Media

We study the asymptotic behavior, with respect to high Peclet numbers, of the solutions of the nonlinear elliptic-parabolic system governing the displacement of one incompressible fluid by another, completely miscible with the first, in a porous medium. Using compensated compactness techniques, we obtain the existence of a global weak solution to the nonlinear degenerate elliptic-parabolic system modelling the flow when the molecular diffusion effects are neglected.

Classical solutions of a parabolic-hyperbolic system modeling a three-dimensional compressible miscible flow in porous media

Abstract We consider a nonlinear parabolic-hyperbolic system which is a simplified version of the equations of compressible miscible flow in a three-dimensional porous medium. No assumption about the mobility ratio is involved. Under some regularity assumptions on the data, we prove the local existence and uniqueness of a classical solution.