Multiphysics and multiscale methods for modeling fluid flow through naturally fractured carbonate karst reservoirs

SPE Reservoir Evaluation and Engineering

Volumn 12, Issue 2, 2009, Pages 218-231

  Popov, P ^a   Qin, G ^b   Bi, L ^a   Efendiev, Y ^a   Kang, Z ^c   Li, J ^c  

^a TEXAS A AND M UNIVERSITY   (United States)

^b UNIVERSITY OF WYOMING   (United States)

^c SINOPEC   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CAVES; FRACTURE; POROUS MATERIALS;

BRINKMAN EQUATION; FRACTURE NETWORK; FRACTURED CARBONATES; KARST RESERVOIRS; MULTIPHYSICS PHENOMENA; MULTISCALE METHOD; NUMERICAL RESULTS; SYSTEM OF EQUATIONS;

FLOW OF FLUIDS;

CARBONATE; CAVE; DARCY LAW; EQUATION; FLOW MODELING; FLUID FLOW; KARST; OIL FIELD; PERMEABILITY; PHYSICS; POROUS MEDIUM; RESERVOIR; STOKES FORMULA;

ASIA; CHINA; EURASIA; FAR EAST;

EID: 67649549928     PISSN: 10946470     EISSN: None     Source Type: Journal    
DOI: 10.2118/105378-PA     Document Type: Conference Paper

References (27)

1. Allaire, G. 1991. Homogenization of the Navier-Stokes equations and derivation of Brinkman's law. Mathématiques appliquées aux sciences de l'ingénieur (Santiago, 1989), 7-20, Cépaduès, Toulouse.
2. Arbogast, T. and Lehr, H.L. 2006. Homogenization of a Darcy-Stokes system modeling vuggy porous media. Computational Geosciences 10 (3): 291-302. DOI:10.1007/s10596-006-9024-8.
3. Bear, J. 1972. Dynamics of Fluids in Porous Media. Oxford, UK: Environmental Science Series, Elsevier.
4. Beavers, G.S. and Joseph, D.D. 1967. Boundary conditions at a naturally permeable wall. Journal of Fluid Mechanics 30 (1): 197-207. DOI:10.1017/S0022112067001375.
5. Brinkman, H.C. 1947. A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1 (1): 27-34. DOI:10.1007/BF02120313.
6. Burman, E. and Hansbo, P. 2007. A unified stabilized method for Stokes' and Darcy's equations. Journal of Computational and Applied Mathematics 198 (1): 35-51. DOI:10.1016/j.cam.2005.11.022.
7. Ciarlet, P.G. 2002. The Finite Element Method for Elliptic Problems, second edition, No. 40. Philadelphia, Pennsylvania: Classics in Applied Mathematics, SIAM.
8. Darcy, H. 1856. Les Fontaines Publiques de la Ville de Dijon. Paris: Victor Dalmont.
9. Ene, H. 1990. Application of the homogenization method to transport in porous media. In Dynamics of Fluids in Hierarchical Porous Media, ed. J. Cushman, 223-241. London: Academic Press.
10. Hornung, U. 1997. Homogenization and Porous Media, Vol. 6. New York: Interdisciplinary Applied Mathematics, Springer-Verlag.
11. Jäger, W. and Mikelić, A. 1996. On the boundary conditions at the contact interface between a porous medium and a free fluid. Ann. Sc. Norm. Super. Pisa, Cl. Sci. 23 (4): 403-465.
12. Jäger, W. and Mikelić, A. 2000. On the interface boundary condition of Beavers, Joseph, and Saffman. SIAM J. Appl. Math. 60 (4): 1111-1127. DOI:10.1137/S003613999833678X.
13. Jäger, W., Mikelić, A., and Neuss, N. 2001. Asymptotic analysis of the laminar viscous flow over a porous bed. SIAM J. Sci. Comput. 22 (6): 2006-2028. DOI:10.1137/S1064827599360339.
14. Kaviany, M. 1999. Principles of Heat Transfer in Porous Media, second edition. New York: Mechanical Engineering Series, Springer.
15. Koplik, J., Levine, H., and Zee, A. 1983. Viscosity renormalization in the Brinkman equation. Physics of Fluids 26 (10): 2864-2870. DOI: 10.1063/1.864050.
16. Laptev, V. 2003. Numerical solution of coupled flow in plain and porous media. PhD dissertation, Universität Kaiserslautern, Germany.
17. Levy, T. and Sanchez-Palencia, E. 1975. On boundary conditions for fluid flow in porous media. Internat. J. Engineering Sci. 13: 923.
18. Lundgren, T.S. 1972. Slow flow through stationary random beds and suspensions of spheres. Journal of Fluid Mechanics 51 (2): 273-299. DOI: 10.1017/S002211207200120X.
19. Martys, N., Bentz, D.P., and Garboczi, EJ. 1994. Computer simulation study of the effective viscosity in Brinkman's equation. Physics of Fluids 6 (4): 1434-1439. DOI:10.1063/1.868258.
20. Neale, G. and Nader, W. 1974. Practical significance of Brinkmans extension of Darcys law: Coupled parallel flows within a channel and a bounding porous-medium. Canadian Journal of Chemical Engineering 52: 475-478.
21. Philip, Z.G., Jennings, J.W. Jr., Olson, J.E., Laubach, S.E., and Holder, J. 2005. Modeling Coupled Fracture-Matrix Fluid Flow in Geomechani-cally Simulated Fracture Networks. SPEREE 8 (4): 300-309. SPE-77340-PA. DOI: 10.2118/77340-PA.
22. Saffman, P.G. 1971. On the boundary condition at the surface of a porous medium. Stud. Appl. Math. 50: 93.
23. Sahraoui, M. and Kaviany, M. 1992. Slip and no-slip velocity boundary conditions at interface of porous, plain media. International Journal of Heat and Mass Transfer 35 (4): 927-943. DOI: 10.1016/0017-9310(92) 90258-T.
24. Sanchez-Palencia, E. 1980. Non-Homogeneous Media and Vibration Theory, Vol. 127. Berlin: Lecture Notes in Physics, Springer-Verlag.
25. Sanchez-Palencia, E. and Ene, H. 1975. Equations et phenomenes de surface pour l'-ecoulement dans un modele de milieu poreux," Journal de Mecanique (1975) 14, 73.
26. Turek, S. 1999. Efficient Solvers for Incompressible Flow Problems: An Algorithmic and Computational Approach, Vol. 6. New York: Lecture Notes in Computational Science and Engineering, Springer-Verlag.
27. Zhikov, V., Kozlov, S., and Oleinik, O. 1994. Homogenization of Differential Operators and Integral Functionals. Berlin: Springer-Verlag.