Analysis of Large-Scale Averaged Models for Two-Phase Flow in Fractured Reservoirs

Journal of Mathematical Analysis and Applications

Volumn 223, Issue 1, 1998, Pages 158-181

  Chen, Zhangxin ^a  

^a SOUTHERN METHODIST UNIVERSITY   (United States)

Author keywords

Fractured reservoir; degenerate elliptic parabolic system; existence; uniqueness; volume averaging theorem

Indexed keywords

EID: 0000831819     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.1998.5966     Document Type: Article

References (27)

1. Adams R. A. Sobolev Spaces. 1975;Academic Press, New York.
2. Alt H. W., di Benedetto E. Nonsteady flow of water and oil through inhomogeneous porous media. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 12:1985;335-392.
3. Alt H. W., Luckhaus S. Quasilinear elliptic-parabolic differential equations. Math. Z. 183:1983;311-341.
4. Anderson T. B., Jackson R. A fluid mechanical description of fluidized beds. Ind. Engng. Chem. Fundam. 6:1967;527-538.
5. Antontsev S. N. On the solvability of boundary value problems for degenerate two-phase porous flow equations. Dinamika Sploshn. Sredy Vyp. 10:1972;28-53.
6. Antontsev S. N., Kazhikhov A. V., Monakhov V. N. Boundary-Value Problems in the Mechanics of Nonuniform Fluids. Studies in Mathematics and Its Applications. 1990;North-Holland, Amsterdam.
7. Arbogast T. J. The existence of weak solutions to single porosity and simple dual-porosity models of two-phase incompressible flow. Nonlinear Anal. 19:1992;1009-1031.
8. Barenblatt G. I., Zheltov I. P., Kochina I. N. Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks [strata]. Prikl. Mat. Mekh. 24:1960;852-864.
9. Bear J. Dynamics of Fluids in Porous Media. 1972;Dover, New York.
10. Carbonell R., Whitaker S. Heat and mass transport in porous media. Bear J., Corapcioglu M. Fundamentals of Transport Phenomena in Porous Media. 1984;121-198 Nijhoff, Dordrecht.
11. Chavent G., Jaffré J. Mathematical Models and Finite Elements for Reservoir Simulation. 1978;North-Holland, Amsterdam.
12. Chen Z. Large-scale averaging analysis of single phase flow in fractured reservoirs. SIAM J. Appl. Math. 54:1994;641-659.
13. Chen Z. Large-scale averaging analysis of multiphase flow in fractured reservoirs. Transport in Porous Media. 21:1995;269-295.
14. Z. Chen, On the Existence, Uniqueness and Regularity of a Weak Solution to Two Phase Incompressible Flow in Porous Media, 97-10, Southern Methodist University, Dallas, Texas, 1997.
15. Chen Z., Ewing R. Fully-discrete finite element analysis of multiphase flow in groundwater hydrology. SIAM J. Numer. Anal. 34:1997;2228-2253.
16. Douglas J. Jr., Arbogast T. J. Dual-porosity models for foow in naturally fractured reservoirs. Cushman J. H. Dynamics of Fluids in Hierarchical Porous Media. 1990;177-221 Academic Press, London.
17. Douglas J. Jr., Paes Leme P. J., Hensley J. L. A limit form of the equations for immiscible displacement in a fractured reservoir. Transport in Porous Media. 6:1991;549-565.
18. Friedman A. Variational Principles and Free-Boundary Problems. 1982;Wiley.
19. Hornung U. Homogenization and Porous Media. 1997;Springer-Verlag, New York.
20. Kroener D., Luckhaus S. Flow of oil and water in a porous medium. J. Differential Equations. 55:1984;276-288.
21. Kružkov S. N., Sukorjanski i S. M. Boundary problems for systems of equations of two-phase porous flow type; statement of the problems, questions of solvability, justification of approximate methods. Math. USSR-Sb. 33:1977;62-80.
22. Nozad I., Carbonell R., Whitaker S. Heat conduction in multiphase systems. I. Theory and experiment for two-phase systems. Chem. Engng. Sci. 40:1985;843-855.
23. Peaceman D. W. Fundamentals of Numerical Reservoir Simulation. 1977;Elsevier, New York.
24. Quintard M., Whitaker S. Two-phase flow in heterogeneous porous media: The method of large-scale averaging. Transport in Porous Media. 3:1988;357-413.
25. Sanchez-Palencia E. Non-homogeneous Media and Vibration Theory. Lecture Notes in Physics. 127:1980;Springer-Verlag, Berlin/New York.
26. Slattery J. C. Flow of viscoelastic fluids through porous media. AIChE. J. 13:1967;1066-1071.
27. Whitaker S. Diffusion and dispersion in porous media. AIChE. J. 13:1967;420-427.