Numerical solutions of a generalized theory for macroscopic capillarity

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 81, Issue 3, 2010, Pages

  Doster, F ^a   Zegeling, P A ^b   Hilfer, R ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

BIPHASIC FLOW; DRAINAGE PROCESS; DRIVEN FLUIDS; FLOW PROCESS; FLUID REGIONS; GENERALIZED THEORY; IMMISCIBLE FLUIDS; LABORATORY EXPERIMENTS; MACROSCOPIC THEORY; NON-PERCOLATING; NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS; NUMERICAL RESULTS; NUMERICAL SOLUTION; ONE DIMENSION; POROUS MEDIUM; PROCESS DEPENDENCE; SATURATION PROFILES; TWO-FLUID;

EXPERIMENTS; FLUIDS; NONLINEAR EQUATIONS; NUMERICAL ANALYSIS; PARTIAL DIFFERENTIAL EQUATIONS; POROUS MATERIALS;

FLOW OF FLUIDS;

EID: 77749334487     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.81.036307     Document Type: Article

References (56)

1. J. Jamin, Acad. Sci., Paris, C. R. 50, 172 (1860).
2. L. A. Richards, Physics 1, 318 (1931). 10.1063/1.1745010
3. P. deGennes, EPL 5, 689 (1988). 10.1209/0295-5075/5/8/004
4. R. Hilfer and P. Øren, Transp. Porous Media 22, 53 (1996). 10.1007/BF00974311
5. L. Anton and R. Hilfer, Phys. Rev. E 59, 6819 (1999). 10.1103/PhysRevE.59.6819
6. M. van Dijke and K. Sorbie, Phys. Rev. E 66, 046302 (2002). 10.1103/PhysRevE.66.046302
7. M. Ferer, G. S. Bromhal, and D. H. Smith, Phys. Rev. E 67, 051601 (2003). 10.1103/PhysRevE.67.051601
8. I. I. Bogdanov, V. V. Mourzenko, J. F. Thovert, and P. M. Adler, Phys. Rev. E 68, 026703 (2003). 10.1103/PhysRevE.68.026703
9. M. Muskat and M. Meres, Physics (N.Y.) 7, 346 (1936). 10.1063/1.1745403
10. R. Wyckoff and H. Botset, Physics (N.Y.) 7, 325 (1936). 10.1063/1.1745402
11. M. Muskat, R. Wyckoff, H. Botset, and M. Meres, Trans. AIME 123, 69 (1937).
12. M. Leverett, Trans. AIME 142, 152 (1941).
13. A. Scheidegger, The Physics of Flow Through Porous Media (University of Toronto Press, Canada, 1957).
14. J. Bear, Dynamics of Fluids in Porous Media (Elsevier, New York, 1972).
15. F. Dullien, Porous Media-Fluid Transport and Pore Structure (Academic, San Diego, CA, 1992).
16. E. Donaldson, R. Thomas, and P. Lorenz, Soc. Pet. Eng. J. 9, 13 (1969). 10.2118/2338-PA
17. W. England, A. Mackenzie, D. Mann, and T. Quigley, J. Geol. Soc. (London) 144, 327 (1987). 10.1144/gsjgs.144.2.0327
18. K. Wu, M. Dijke, G. Couples, Z. Jiang, J. Ma, K. Sorbie, J. Crawford, I. Young, and X. Zhang, Transp. Porous Media 65, 443 (2006). 10.1007/s11242-006- 0006-z
19. Z. Zhang and J. Smith, Transp. Porous Media 48, 41 (2002). 10.1023/A:1015675404195
20. A. Ebigbo, H. Class, and R. Helmig, Comput. Geosci. 11, 103 (2007). 10.1007/s10596-006-9033-7
21. M. Kataja, K. Hiltunen, and J. Timonen, J. Phys. D 25, 1053 (1992). 10.1088/0022-3727/25/7/004
22. U. Pasaogullari and C. Wang, J. Electrochem. Soc. 151, A399 (2004). 10.1149/1.1646148
23. A. Babchin, I. Brailovsky, P. Gordon, and G. Sivashinsky, Phys. Rev. E 77, 026301 (2008). 10.1103/PhysRevE.77.026301
24. M. R. Deinert, A. Dathe, J. Y. Parlange, and K. B. Cady, Phys. Rev. E 77, 021203 (2008). 10.1103/PhysRevE.77.021203
25. P. Lehmann, S. Assouline, and D. Or, Phys. Rev. E 77, 056309 (2008). 10.1103/PhysRevE.77.056309
26. S. Naumov, A. Khokhlov, R. Valiullin, J. Kärger, and P. A. Monson, Phys. Rev. E 78, 060601 (R) (2008). 10.1103/PhysRevE.78.060601
27. L. Cueto-Felgueroso and R. Juanes, Phys. Rev. Lett. 101, 244504 (2008). 10.1103/PhysRevLett.101.244504
28. R. Hilfer, Adv. Chem. Phys. 92, 299 (1996). 10.1002/9780470141519.ch3
29. R. Hilfer, Phys. Rev. E 73, 016307 (2006). 10.1103/PhysRevE.73.016307
30. R. Hilfer, Physica A 371, 209 (2006). 10.1016/j.physa.2006.04.051
31. N. Morrow, in Interfacial Phenomena in Petroleum Recovery, edited by, N. Morrow., Surfactant Science Series Vol. 36 (Dekker, New York, 1991), p. 1.
32. Y. Mualem, Water Resour. Res. 9, 1324 (1973). 10.1029/WR009i005p01324
33. J. Kloubek, J. Adhes. Sci. Technol. 6, 667 (1992). 10.1163/ 156856192X01033
34. A. Abrams, Soc. Pet. Eng. J. 15, 437 (1975). 10.2118/5050-PA
35. P. Sheng and M. Zhou, Phys. Rev. A 45, 5694 (1992). 10.1103/PhysRevA.45. 5694
36. S. Hassanizadeh, M. Celia, and H. Dahle, Vadose Zone J. 1, 38 (2002). 10.2113/1.1.38
37. C. Tsakiroglou, D. Avraam, and A. Payatakes, Adv. Water Resour. 30, 1981 (2007). 10.1016/j.advwatres.2007.04.002
38. C. Marle, Int. J. Eng. Sci. 20, 643 (1982). 10.1016/0020-7225(82)90118-5
39. D. G. Avraam and A. C. Payatakes, Transp. Porous Media 20, 135 (1995). 10.1007/BF00616928
40. R. Hilfer, Physica A 359, 119 (2006). 10.1016/j.physa.2005.05.086
41. R. Hilfer, in CP1091, Modeling and Simulation of Materials, edited by, P. Garrido.., P. Hurtado., and, J. Marro, (AIP, New York, 2009), p. 141.
42. R. Hilfer, Phys. Rev. E 58, 2090 (1998). 10.1103/PhysRevE.58.2090
43. R. Hilfer and H. Besserer, Physica B 279, 125 (2000). 10.1016/S0921-4526(99)00694-8
44. J. Blom and P. Zegeling, ACM Trans. Math. Softw. 20, 194 (1994). 10.1145/178365.178391
45. P. Zegeling, I. Lagzi, and F. Izsak (unpublished).
46. B. Ataie-Ashtiani, S. Hassanizadeh, O. Oung, F. Westrate, and A. Bezuijen, Environ. Modell. Software 18, 231 (2003). 10.1016/S1364-8152(02)00092- 0
47. L. Petzold, Sandia National Laboratories Technical Report No. SAND82-8637, 1982 (unpublished).
48. A. van Dam and P. Zegeling, J. Comput. Phys. 216, 526 (2006). 10.1016/j.jcp.2005.12.014
49. P. Zegeling, J. Comput. Appl. Math. 166, 343 (2004). 10.1016/j.cam.2003. 09.018
50. P. Zegeling, in Adaptive Computations: Theory and Algorithms, edited by, T. Tang, and, J. Xu, (Science, Peking, 2007), p. 251.
51. K. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science, London, 1979).
52. R. Helmig, Multiphase Flow and Transport Processes in the Subsurface (Springer, Berlin, 1997).
53. A. Chorin, J. Comput. Phys. 2, 12 (1967). 10.1016/0021-9991(67)90037-X
54. R. Rannacher, in The Navier-Stokes Equation II-Theory and Numerical Methods, edited by, J. Heywood.., K. Masuda.., R. Rautmann., and, V. Solonnikov, (Springer Verlag, Berlin, 1992), pp. 167-183. 10.1007/BFb0090341
55. J. Shen, in Advances in Computer Methods for Partial Differential Equations, edited by, R. Vichnevestsky.., D. Knight., and, G. Richter, (International Association for Mathematics and Computers in Simulation, New Brunswick, 1992), p. 658.
56. R. Hilfer and F. Doster, Trans. Porous Media (2009), doi: 10.1007/s11242-009-9395-0