Three-phase compressible flow in porous media: Total Differential Compatible interpolation of relative permeabilities

Journal of Computational Physics

Volumn 229, Issue 12, 2010, Pages 4762-4780

  di Chiara Roupert, R ^a   Chavent, G ^b,c   Schafer G ^a  

^a UNIVERSITÉ DE STRASBOURG EOST   (France)

^b INRIA ROCQUENCOURT   (France)

^c UNIVERSITÉ PARIS DAUPHINE   (France)

Author keywords

Biharmonic equation; Compressible flow; Global pressure; Mathematical modeling; Multiphase flow; Porous media

Indexed keywords

CAPILLARY TUBES; COMPRESSIBLE FLOW; COMPUTATIONAL EFFICIENCY; INCOMPRESSIBLE FLOW; INTERPOLATION; LAPLACE TRANSFORMS; POROUS MATERIALS;

BIHARMONIC EQUATIONS; FLOWS IN POROUS MEDIA; GLOBAL MOBILITY; GLOBAL PRESSURE; MATHEMATICAL MODELING; PHASE DATA; POROUS MEDIUM; THREE PHASE; THREE PHASIS; TOTAL DIFFERENTIAL;

CAPILLARITY;

EID: 77951622386     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2010.03.013     Document Type: Article

References (21)

1. Amaziane B., Jurak M. A new formulation of immiscible compressible two-phase flow in porous media. C.R. Mécanique 2008, 336:600-605.
2. Antoncev S.N., Monahov V.N. Three-dimensional problems of time-dependent two-phase filtration in non-homogeneous anisotropic porous media. Soviet Math. Dokl. 1978, 19:1354-1358.
3. Argyris J., Fried I., Scharpf D. The tuba family of plate elements for the matrix displacement method. J. Roy. Aeronaut. Soc. 1968, 72:701-709.
4. Bear J. Dynamics of Fluids in Porous Media 1972, Elsevier, New York.
5. Bell K. A refined triangular plate bending finite element. Int. J. Numer. Methods Eng. 1969, 1:101-122.
6. M. Bernadou, J.M. Boisserie, K. Hassan, Sur l'implémentation des éléments finis de Hsieh-Clough-Tocher complet et réduit, Inria Research Report RR-4, 1980.
7. M. Bernadou, K. Hassan, Basis functions for general Hsieh-Clough-Tocher triangles complete or reduced, Inria Research Report RR-5, 1980.
8. Chavent G. A new formulation of diphasic incompressible flows in porous media. Lecture Notes in Mathematics 1976, vol. 503. Springer, Berlin. A. Dold, B. Eckman (Eds.).
9. G. Chavent, G. Salzano, Un algorithme pour la détermination de perméabilités relatives triphasiques satisfaisant une condition de différentielle totale, Inria Research Report RR-0355, 1985.
10. Chavent G., Jaffré J. Mathematicals Models and Finite Elements of Reservoir Simulation 1986, North-Holland, Amsterdam.
11. G. Chavent, R. di Chiara Roupert, G. Schäfer, A fully equivalent global pressure formulation for three-phase compressible flows, in: Conference Scaling'Up 08, Dubrovnik, October 13-16, 2008.
12. Chavent G. A fully equivalent global pressure formulation for three-phase compressible flow. Appl. Anal. 2009, 88:1527-1541.
13. Chen Z., Ewing R. Comparison of various formulations of three-phase flows in porous media. J. Comput. Phys. 1997, 132:362-373.
14. Chen Z. Finite Element Methods and Their Applications. Scientific Computation 2005, Springer, Berlin.
15. Ciarlet P. The finite element method for elliptic problems, society for industrial and applied mathematics. J. Comput. Phys. 1978, 132:362-373.
16. R.W. Clough, J.L. Tocher, Finite element stiffness matrices for analysis of plate bending, in: Proceedings of the Conference on Matrix Methods in Structural Mechanics, Wright Patterson A.F.B., OH, 1965.
17. T.A. Davis, I.S. Duff, A combined unifrontal/multifrontal method for unsymmetric sparse matrices, Technical Report TR-97-016, Computer and Information Science and Engineering Department, University of Florida, 1997.
18. Eisenstat S.C. Efficient implementation of a class of preconditioned conjugate gradient methods. SIAM J. Sci. Statist. Comput. 1981, 2:1-4.
19. S. Jégou, Estimation des perméabilités relatives dans des expériences de déplacements triphasiques en milieu poreux, Thése, Université Paris IX Dauphine, 1997.
20. Quarteroni A., Sacco R., Saleri F. Méthodes Numériques - Algorithme, analyse et applications 2007, Springer, Italia.
21. Stone H.M. Probability model for estimating three-phase relative permeabilitiy. J. Petrol. Technol. 1970, 22:214-218.