Macroscopic equations of motion for two-phase flow in porous media

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 58, Issue 2, 1998, Pages 2090-2096

  Hilfer, R ^a,b  

^a UNIVERSITY OF STUTTGART   (Germany)

^b JOHANNES GUTENBERG UNIVERSITY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000299374     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.58.2090     Document Type: Article

References (47)

1. F. Dullien, Porous Media—Fluid Transport and Pore Structure (Academic, San Diego, 1992).
2. P. Adler, Porous Media (Butterworth-Heinemann, Boston, 1992).
3. M. Sahimi, Rev. Mod. Phys. 65, 1393 (1993).RMPHAT
4. M. Sahimi, Flow and Transport in Porous Media and Fractured Rock (VCH Verlagsgesellschaft mbH, Weinheim, 1995).
5. R. Hilfer, Adv. Chem. Phys. 92, 299 (1996).ADCPAA
6. M. Blunt and P. King, Phys. Rev. A 42, 4780 (1990).PLRAAN
7. N. Martys, M. Cieplak, and M. Robbins, Phys. Rev. Lett. 66, 1058 (1991).PRLTAO
8. R. Hilfer, Phys. Rev. B 44, 60 (1991).PRBMDO
9. U. Oxaal, Phys. Rev. A 44, 5038 (1991).PLRAAN
10. U. Oxaal, F. Boger, J. Feder, T. Jøssang, P. Meakin, and A. Aharony, Phys. Rev. A 44, 6564 (1991).PLRAAN
11. R. Hilfer, Phys. Rev. B 45, 7115 (1992).PRBMDO
12. P. Meakin, J. Feder, V. Frette, and T. Jøssang, Phys. Rev. A 46, 3357 (1992).PLRAAN
13. V. Frette, J. Feder, T. Jøssang, and P. Meakin, Phys. Rev. Lett. 68, 3164 (1992).PRLTAO
14. M. Blunt and H. Scher, Phys. Rev. E 52, 6387 (1995).PLEEE8
15. M. Blunt, M. King, and H. Scher, Phys. Rev. A 46, 7680 (1992).PLRAAN
16. M. Kataja, K. Hiltunen, and J. Timonen, J. Phys. D 25, 1053 (1992).JPAPBE
17. M. Kataja, A. Rybin, and J. Timonen, J. Appl. Phys. 72, 1271 (1992).JAPIAU
18. R. Hilfer and P. Øren, Transp. Porous Media 22, 53 (1996).TPMEEI
19. S. Schwarzer, Phys. Rev. E 52, 6461 (1995).PLEEE8
20. V. Horvat and H. Stanley, Phys. Rev. E 52, 5166 (1995).PLEEE8
21. L. Furuberg, K. Maloy, and J. Feder, Phys. Rev. E 53, 966 (1996).PLEEE8
22. J. Andrade, M. Almeida, J. M. Filho, S. Havlin, B. Suki, and H. Stanley, Phys. Rev. Lett. 79, 3901 (1997).PRLTAO
23. C. Marle, Multiphase Flow in Porous Media (Institut Francais du Petrole, Paris, 1981).
24. Interfacial Phenomena in Petroleum Recovery, edited by N. Morrow (Dekker, New York, 1991), Vol. 36.
25. A. Scheidegger, The Physics of Flow Through Porous Media (University of Toronto Press, Toronto, 1974).
26. J. Bear, Dynamics of Fluids in Porous Media (Elsevier, New York, 1972).
27. J. Trangenstein, in Multiphase Flow in Porous Media, edited by M. Allen, G. Behie, and J. Trangenstein (Springer-Verlag, Berlin, 1988), p. 87.
28. R. Helmig, Multiphase Flow and Transport Processes in the Subsurface (Springer, Berlin, 1997).
29. H. Dombrowski and L. Brownell, Ind. Eng. Chem. 46, 1207 (1954).IECHAD
30. J. Taber, Soc. Petr. Eng. J. 9, 3 (1969).SPTJAJ
31. J. Taber, J. Kirby, and F. Schroeder, AIChE Symp. Ser.69, 53 (1973).ACSSCQ
32. A. Abrams, Soc. Petr. Eng. J. 15, 437 (1975).SPTJAJ
33. I. Chatzis, M. Kuntamukkula, and N. Morrow, SPE Reservoir Eng., August 1988, p. 902.
34. N. Wardlaw and M. McKellar, Can. J. Chem. Eng. 63, 525 (1985).CJCEA7
35. R. Larson, H. Davis, and L. Scriven, Chem. Eng. Sci. 36, 75 (1981).CESCAC
36. N. Morrow, I. Chatzis, and J. Taber, in Proceedings of the 60th Society of Petroleum Engineers Conference, Las Vegas, 1985, Number 14423 (unpublished).
37. P. Øren, J. Billiotte, and W. Pinczewski, SPE Formation Evaluation, March 1992, p. 70.
38. P. de Gennes, Europhys. Lett. 5, 689 (1988).EULEEJ
39. F. Kalaydijan, in Proceedings of the 67th Society of Petroleum Engineers Conference, Washington, DC, 1992, Number 24813 (unpublished).
40. C. Marle, Int. J. Eng. Sci. 20, 643 (1982).IJESAN
41. S. Whitaker, Transp. Porous Media 1, 105 (1986).TPMEEI
42. D. Pavone, Rev. Inst. Francais Petrole 44, 29 (1989).RFPTBH
43. M. Allen, in Multiphase Flow in Porous Media, edited by M. Allen, G. Behie, and J. Trangenstein (Springer-Verlag, Berlin, 1988), p. 1.
44. Rational Thermodynamics, edited by C. Truesdell (Springer, Berlin, 1984).
45. H. Besserer and R. Hilfer (unpublished).
46. Because the rock matrix is assumed to be rigid and impermeable one has RR1=RR2=RR3=RR4=∞, which implies dissipation. Because of this and Eq. (25) the balance laws for the matrix phase would either be trivial or ill defined.
47. Balance equations for the rock matrix do not arise (see Ref. 46).