Homogenization of a three-phase flow model in porous media

References

• Allaire , G . 1992 . Homogenization and two-scale convergence . SIAM J. Math. Anal. , 23 : 1482 – 1518 .
   Web of Science ®Google Scholar
• Alt , HW and Luckhaus , S . 1983 . Quasilinear elliptic-parabolic differential equation . Math. Z. , 183 : 311 – 341 .
   Web of Science ®Google Scholar
• Amaziane , B . 1993 . Global behavior of compressible three-phase flow in heterogeneous porous media . Transport in Porous Media , 10 : 43 – 56 .
   Google Scholar
• Amaziane B Batchi M 1996 Effective relative permeabilities and capillary pressure of a three-phase flow model in heterogeneous porous media In: Y. Abousleiman et al. (Eds.) Computer Methods and Water Resources III pp. 303–314 Computational Mechanics Publications Southampton Boston
   Google Scholar
• Amaziane , B , Hontans , T and Koebbe , J . 2001 . Equivalent permeability and simulation of two-phase flow in heterogeneous porous media . Comput. Geosci. , 5 : 279 – 300 .
   Google Scholar
• Arbogast T 2000 Numerical subgrid upscaling of two-phase flow in porous media In: Z. Chen et al. (Eds.) Numerical Treatment of Multiphase Flows in Porous Media Lect. Notes Phys. 552, pp. 35–49 Springer
   Google Scholar
• Badea A Bourgeat A 1995 Homogenization of two phase flow through randomly heterogeneous porous media In: A. Bourgeat et al. (Eds.) Mathematical Modelling of Flow Through Porous Media pp. 44–58 World Scientific London
   Google Scholar
• Badea A Bourgeat A 1997 Numerical simulations by homogenization of two-phase flow through randomly heterogeneous porous media In: R. Helmig et al. (Eds.) Notes on Numerical Fluid Mechanics, Modeling and Computation in Environmental Sciences 59 pp. 13–24
   Google Scholar
• Bear J Bachmat Y 1991 Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Academic Publishers London
   Google Scholar
• Bourgeat , A and Hidani , A . 1995 . Effective model of two-phase flow in a porous media made of different rock types . Appl. Anal. , 58 : 1 – 29 .
   Google Scholar
• Bourgeat , A , Kozlov , SM and Mikelic , A . 1995 . Effective equations of two-phase flow in random media . Calc. Var. , 3 : 385 – 406 .
   Google Scholar
• Bourgeat , A , Luckhaus , S and Mikelic , A . 1996 . Convergence of the homogenization process for a double-porosity model of immiscible two-phase flow . SIAM J. Math. Anal. , 27 : 1520 – 1543 .
   Web of Science ®Google Scholar
• Bourgeat , A and Panfilov , M . 1998 . Effective two-phase flow through highly heterogeneous porous media: capillary nonequilibrium effects . Comput. Geosci. , 2 : 191 – 215 .
   Web of Science ®Google Scholar
• Chavent G Jaffré J 1986 Mathematical Models and Finite Elements for Reservoir Simulation, North-Holland Amsterdam
   Google Scholar
• Chen , Z and Ewing , RE . 1997 . Comparison of various formulations of three-phase flow in porous media . J. Comput. Phys. , 132 : 362 – 373 .
   Google Scholar
• van Duijn , CJ , Mikelic , A and Pop , IS . 2002 . Effective equations for two-phase flow with trapping on the micro scale . SIAM J. Appl. Math. , 62 : 1531 – 1568 .
   Google Scholar
• Gagneux G Madaune-Tort M 1996 Analyse Mathématique de Modèles non Linéaires de l'Ingénierie Pétrolière, Springer Berlin
   Google Scholar
• Fabrie , P and Saad , M . 1993 . Existence de solutions faibles pour un modèle d'écoulement triphasique en milieu poreux . Ann. Fac. Toulouse , 2 : 337 – 373 .
   Google Scholar
• Hornung U 1997 Homogenization and porous media Interdisciplinary Applied Mathematics, Springer New York
   Google Scholar
• Ondami B 2001 Sur quelques problèmes d'homogénéisation des écoulements en milieux poreux Thèse de Doctorat, Université de Pau
   Google Scholar
• Simon , J . 1979 . Régularité de la composée de deux fonctions et applications . Bolletino U.M.I , 16-B : 501 – 522 .
   Google Scholar
• Zijl , W and Trykozko , A . 2002 . Numerical homogenization of two-phase flow in porous media . Comput. Geosci. , 6 : 49 – 71 .
   Google Scholar