Stability analysis of two-phase buoyancy-driven flow in the presence of a capillary transition zone

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

Volumn 87, Issue 3, 2013, Pages

  Emami Meybodi, Hamid ^a   Hassanzadeh, Hassan ^a  

^a UNIVERSITY OF CALGARY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BUOYANCY DRIVEN FLOWS; DIFFUSIVE BOUNDARY LAYERS; FLUID-SATURATED POROUS LAYERS; MULTIPHASE FLOW IN POROUS MEDIAS; NONLINEAR SIMULATIONS; QUANTITATIVE DESCRIPTION; QUASI STEADY STATE APPROXIMATION; SATURATED POROUS MEDIUM;

BOUNDARY LAYERS; MULTIPHASE FLOW; NATURAL CONVECTION; POROUS MATERIALS; SYSTEM STABILITY;

BUOYANCY;

EID: 84875485636     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.87.033009     Document Type: Article

References (53)

1. D. A. Nield and A. Bejan, Convection in Porous Media (Springer Verlag, Berlin, 2006).
2. V. Frette, J. Feder, T. Jøssang, and P. Meakin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.68.3164 68, 3164 (1992).
3. R. L. Van Dam, C. T. Simmons, D. W. Hyndman, and W. W. Wood, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2008GL036906 36, L11403 (2009).
4. J. J. Hidalgo, J. Fe, L. Cueto-Felgueroso, and R. Juanes, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.109.264503 109, 264503 (2012).
5. J. T. H. Andres and S. S. S. Cardoso, Chaos CHAOEH 1054-1500 10.1063/1.4748866 22, 037113 (2012).
6. C. Horton and F. Rogers, J. Appl. Phys. JAPIAU 0021-8979 10.1063/1.1707601 16, 367 (1945).
7. E. R. Lapwood, Math. Proc. Cambridge Philos. Soc. 0305-0041 10.1017/S030500410002452X 44, 508 (1948).
8. H. J. G. Diersch and O. Kolditz, Adv. Water Res. 0309-1708 10.1016/S0309-1708(02)00063-5 25, 899 (2002). (Pubitemid 36000077)
9. P. Vadasz, Emerging Topics in Heat and Mass Transfer in Porous Media (Springer, Dordrecht, Netherlands, 2008), Vol. 22, p. 85.
10. P. Cheng, Advances in Heat Transfer 0065-2717 10.1016/S0065-2717(08) 70085-6 14, 1 (1978).
11. M. Kaviany, Principles of Convective Heat Transfer (Springer Verlag, Berlin, 2001).
12. A. J. Smith, Water Resour. Res. WRERAQ 0043-1397 10.1029/2003WR002977 40, W08309 (2004). (Pubitemid 39247127)
13. J. A. Neufeld, M. A. Hesse, A. Riaz, M. A. Hallworth, H. A. Tchelepi, and H. E. Huppert, Geophys. Res. Lett. GPRLAJ 0094-8276 10.1029/2010GL044728 37, L22404 (2010).
14. J. T. H. Andres and S. S. S. Cardoso, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.046312 83, 046312 (2011).
15. P. A. Tsai, K. Riesing, and H. A. Stone, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.87.011003 87, 011003 (2013).
16. H. Emami Meybodi and H. Hassanzadeh, Water Resour. Res. WRERAQ 0043-1397 10.1029/2011WR010949 47, W12504 (2011).
17. H. Emami Meybodi and H. Hassanzadeh, AlChE J., doi: 10.1002/aic.13891 (2012).
18. M. T. Elenius, J. M. Nordbotten, and H. Kalisch, IMA J. Appl. Math. 0272-4960 10.1093/imamat/hxs054 77, 771 (2012).
19. B. Morton, Q. J. Mech. Appl. Math. QJMMAV 0033-5614 10.1093/qjmam/10.4. 433 10, 433 (1957).
20. M. Kaviany, Int. J. Heat Mass Transf. IJHMAK 0017-9310 10.1016/0017-9310(84)90197-2 27, 2101 (1984).
21. M. C. Kim and S. Kim, Int. Commun. Heat Mass Transfer 0735-1933 10.1016/j.icheatmasstransfer.2004.06.002 32, 416 (2005). (Pubitemid 40426542)
22. W. Lick, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112065000332 21, 565 (1965).
23. T. D. Foster, Phys. Fluids PFLDAS 1070-6631 10.1063/1.1761393 8, 1249 (1965).
24. T. D. Foster, Phys. Fluids PFLDAS 1070-6631 10.1063/1.1692095 11, 1257 (1968).
25. J. Ennis-King, I. Preston, and L. Paterson, Phys. Fluids PFLDAS 1070-6631 10.1063/1.2033911 17, 084107 (2005). (Pubitemid 41226576)
26. L. Cueto-Felgueroso and R. Juanes, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.79.036301 79, 036301 (2009).
27. S. Backhaus, K. Turitsyn, and R. E. Ecke, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.106.104501 106, 104501 (2011).
28. M. C. Kim and C. K. Choi, Phys. Fluids PFLDAS 1070-6631 10.1063/1.3703330 24, 044102 (2012).
29. A. C. Slim and T. Ramakrishnan, Phys. Fluids PFLDAS 1070-6631 10.1063/1.3528009 22, 124103 (2010).
30. A. Riaz, M. Hesse, H. Tchelepi, and F. Orr, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112005007494 548, 87 (2006). (Pubitemid 43193132)
31. A. Selim and D. A. S. Rees, J. Porous Media 1091-028X 10.1615/JPorMedia.v10.i1.10 10, 1 (2007). (Pubitemid 46512187)
32. J. P. Caltagirone, Q. J. Mech. Appl. Math. QJMMAV 0033-5614 10.1093/qjmam/33.1.47 33, 47 (1980).
33. X. Xu, S. Chen, and D. Zhang, Adv. Water Res. 0309-1708 10.1016/j.advwatres.2005.05.008 29, 397 (2006).
34. H. Hassanzadeh, M. Pooladi-Darvish, and D. W. Keith, Transp. Porous Media TPMEEI 0169-3913 10.1007/s11242-005-6088-1 65, 193 (2006). (Pubitemid 44756409)
35. K. K. Tan, T. Sam, and H. Jamaludin, Int. J. Heat Mass Transf. IJHMAK 0017-9310 10.1016/S0017-9310(03)00045-0 46, 2857 (2003). (Pubitemid 36658975)
36. G. Homsy, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S002211207300008X 60, 129 (1973).
37. D. Y. Yoon and C. K. Choi, Korean J. Chem. Eng. 0256-1115 10.1007/BF02697493 6, 144 (1989).
38. K. Ghesmat, H. Hassanzadeh, and J. Abedi, J. Fluid Mech. JFLSA7 0022-1120 10.1017/S0022112010006282 673, 480 (2011).
39. J. Robinson, Phys. Fluids PFLDAS 1070-6631 10.1063/1.861570 19, 778 (1976).
40. K. Aziz and A. Settari, Petroleum Reservoir Simulation (Applied Science Publishers London, 1979).
41. J. Bear, Dynamics of Fluids in Porous Media (Dover, London, 1988).
42. M. C. Leverett, Trans. Am. Inst. Min., Metall. Pet. Eng. 142, 152 (1941).
43. P. G. De Gennes, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.57. 827 57, 827 (1985).
44. M. T. Van Genuchten, Soil Sci. Soc. Am. J. 0361-5995 10.2136/sssaj1980. 03615995004400050002x 44, 892 (1980).
45. Y. Mualem, Water Resour. Res. WRERAQ 0043-1397 10.1029/WR012i006p01248 12, 1248 (1976).
46. A. T. Corey, Mechanics of Immiscible Fluids in Porous Media (Water Resources Publication, Colorado, 1994).
47. M. N. Ozisik, Heat Conduction (John Wiley & Sons, New York, 1993).
48. C. Tan and G. Homsy, Phys. Fluids PFLDAS 1070-6631 10.1063/1.865832 29, 3549 (1986).
49. J. D. Hoffman, Numerical Methods for Engineers and Scientists (CRC Press, New York, 2001).
50. A. K. Singh and B. Bhadauria, Int. J. Math. Anal. 3, 815 (2009).
51. A. Riaz and H. A. Tchelepi, Phys. Fluids PFLDAS 1070-6631 10.1063/1.1812511 16, 4727 (2004). (Pubitemid 41015851)
52. C. Marle, Multiphase Flow in Porous Media (Éditions technip, Paris, 1981).
53. H. Hassanzadeh, M. Pooladi-Darvish, A. M. Elsharkawy, D. W. Keith, and Y. Leonenko, Int. J. Greenhouse Gas Control 1750-5836 10.1016/S1750-5836(07)00010- 2 2, 65 (2008).