Stability of two-phase vertical flow in homogeneous porous media

Physics of Fluids

Volumn 19, Issue 7, 2007, Pages

  Riaz, Amir ^a   Tchelepi, Hamdi ^a  

^a STANFORD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHARACTERIZATION; EIGENVALUES AND EIGENFUNCTIONS; LINEAR STABILITY ANALYSIS; VORTICITY;

ASYMPTOTIC EXPANSION ANALYSIS; FLOW STABILITY; FRACTIONAL FLOW; GRAVITY NUMBER; RAREFACTION WAVE;

TWO PHASE FLOW;

CHARACTERIZATION; EIGENVALUES AND EIGENFUNCTIONS; LINEAR STABILITY ANALYSIS; TWO PHASE FLOW; VORTICITY;

EID: 34547819663     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2742975     Document Type: Article

References (24)

1. M. Sahimi, "Flow phenomena in rocks: From continuum models to fractals, percolation, cellular automate, and simulated annealing," Rev. Mod. Phys.RMPHAT0034-686110.1103/RevModPhys.65.1393 65, 1393 (1993).
2. P. G. Saffman and G. I. Taylor, "The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid," Proc. R. Soc. London, Ser. APRLAAZ1364-5021 245, 312 (1958).
3. R. A. Wooding, "Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell," J. Fluid Mech.JFLSA70022-112010.1017/S002211206900228X 39, 477 (1969).
4. L. Zhan and Y. C. Yortsos, "The shape of a gravity finger in a rectangular channel in homogeneous porous media," Transp. Porous MediaTPMEEI0169-391310.1023/A:1016042630712 49, 77 (2002).
5. J. Bear, Dynamics of Fluids in Porous Media (Wiley, New York, 1972).
6. P. M. Adler and H. Brenner, "Multiphase flow in porous media," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/annurev.fluid.20.1.35 20, 35 (1988).
7. S. Whitaker, "Flow in porous media: II. The governing equations for immiscible, two-phase flow," Transp. Porous MediaTPMEEI0169-391310.1007/BF00714688 1, 105 (1986).
8. W. Proskurowski, "A note on solving the Buckley-Leverett equation in the presence of gravity," J. Comput. Phys.JCTPAH0021-999110.1016/ 0021-9991(81)90083-8 41, 136 (1981).
9. M. Wangen, "Vertical migration of hydrocarbons modeled with fractional flow theory," Geophys. J. Int.GJINEA0956-540X10.1111/ j.1365-246X.1993.tb05592.x 115, 109 (1993).
10. Y. C. Yortsos and A. S. Fokas, "An analytical solution for linear waterflood including the effects of capillary pressure," SPEJSSPJDN0197-7520 23, 115 (1983).
11. Y. C. Yortsos, "Stability of certain class of miscible displacement processes in porous media," IMA J. Appl. Math.IJAMDM0272-496010.1093/imamat/38.3.167 38, 167 (1987).
12. A. Riaz and H. A. Tchelepi, "Linear stability analysis of immiscible two-phase flow in porous media with capillary dispersion and density variation," Phys. FluidsPHFLE61070-663110.1063/1.1812511 16, 4727 (2004).
13. S. C. Chen and K. Vafai, "Non-Darcian surface tension effects on free surface transport in porous media," Numer. Heat Transfer, Part ANHAAES1040-7782 31, 235 (1997).
14. B. Alazmi and K. Vafai, "Analysis of variable porosity, thermal dispersion, and local thermal nonequilibrium on free surface flows through porous media," ASME J. Heat TransferJHTRAO0022-148110.1115/ 1.1723470 126, 389 (2004).
15. J. W. Sheldon, B. Zondek, and W. T. Cardwell, "One-dimensional, incompressible, noncapillary, two-phase fluid flow in a porous medium," Petrol. Trans. AIME 216, 290 (1959).
16. G. I. Barenblatt, V. M. Entov, and V. M. Ryzhik, Theory of Fluid Flows Through Natural Rocks (Kluwer Academic, Boston, 1990).
17. M. Honarpour, L. Koederitz, and A. H. Harvey, Relative Permeability of Petroleum Reservoirs (CRC, Boca Raton, FL, 1986).
18. A. Riaz and H. A. Tchelepi, "Influence of relative permeability on the stability characteristics of immiscible flow in porous media," Transp. Porous MediaTPMEEI0169-391310.1007/s11242-005-4312-7 64, 315 (2006).
19. A. Riaz and H. A. Tchelepi, "Numerical simulation of immiscible two-phase flow in porous media," Phys. FluidsPHFLE61070-663110.1063/ 1.2166388 18, 014104 (2006).
20. Y. C. Yortsos and A. B. Huang, "Linear stability analysis of immiscible displacement: Part 1-Simple basic flow profiles," SPE Reservoir Eng.SREEEF0885-9248 1, 378 (1986).
21. Y. C. Yortsos and F. J. Hickernell, "Linear stability of immiscible displacement in porous media," SIAM J. Appl. Math.SMJMAP0036-139910.1137/0149043 49, 730 (1989).
22. O. Manickam and G. M. Homsy, "Stability of miscible displacements in porous media with nonmonotonic viscosity profiles," Phys. Fluids APFADEB0899-821310.1063/1.858571 5, 1356 (1993).
23. C. Pankiewitz and E. Meiburg, "Miscible porous media displacements in the quarter five-spot configuration. Part 3. Non-monotonic viscosity profiles," J. Fluid Mech.JFLSA70022-112010.1017/S0022112099004735 388, 171 (1999).
24. A. Riaz, H. Hesse, H. A. Tchelepi, and F. M. Orr, Jr., "Onset of convection in a gravitationally unstable diffusive boundary layer in porous media," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112005007494 548, 87 (2006).