The evolution of miscible gravity currents in horizontal porous layers

Journal of Fluid Mechanics

Volumn 719, Issue , 2013, Pages 82-96

  Szulczewski, M L ^a   Juanes, R ^a  

^a Massachusetts Institute of Technology Cambridge   (United States)

Author keywords

gravity currents; mixing and dispersion; porous media

Indexed keywords

AQUIFERS; DISPERSIONS; ENHANCED RECOVERY; FLUIDITY; GRAVITATION; GRAVITY WAVES; MIXING; POROUS MATERIALS;

ENGINEERING PROJECT; ENHANCED OIL RECOVERY; FLUID FLUID INTERFACES; GRAVITY CURRENTS; HORIZONTAL POROUS LAYERS; HORIZONTAL VELOCITY; MIXING AND DISPERSIONS; SIMPLIFYING ASSUMPTIONS;

DIFFUSION IN LIQUIDS;

ADVECTION; AQUIFER; DIFFUSION; GRAVITY FLOW; MASS TRANSFER; MIXING; POROUS MEDIUM;

EID: 84874268554     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/jfm.2012.631     Document Type: Article

References (31)

1. ASCHER, U. M., RUUTH, S. J. & SPITERI, R. J. 1997 Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations. Appl. Numer. Maths 25, 151-167
2. BARENBLATT, G. I. 1952 On some unsteady motions of fluids and gases in a porous medium. Prikl Mat. Mekh. 16, 67-78, English translation in Appl. Math. Mech
3. BARENBLATT, G. I. 1996 Scaling, Self-Similarity, and Intermediate Asymptotics. Cambridge University Press
4. BEAR, J. 1972 Dynamics of Fluids in Porous Media. Elsevier, reprinted with corrections, Dover
5. CRANK, J. 1980 The Mathematics of Diffusion. Oxford University Press
6. DE JOSSELIN DE JONG, G. 1981 The simultaneous flow of fresh and salt water in aquifers of large horizontal extension determined by shear flow and vortex theory. Proc. Euromech. 143 75-82
7. DENTZ, M., TARTAKOVSKY, D. M., ABARCA, E., GUADAGNINI, A., SANCHEZ-VILA, X. & CARRERA, J. 2006 Variable-density flow in porous media. J. Fluid Mech. 561, 209-235
8. DUSSAN, V. & AUZERAIS, E. B. 1993 Buoyancy-induced flow in porous media generated near a drilled oil well. Part 1. The accumulation of filtrate at a horizontal impermeable boundary J. Fluid Mech. 254, 283-311
9. ENNIS-KING, J. & PATERSON, L. 2005 Role of convective mixing in the long-term storage of carbon dioxide in deep saline formations. SPE J. 10 (3), 349-356
10. ERDOGAN, M. E. & CHATWIN, P. C. 1967 The effects of curvature and buoyancy on the laminar dispersion of solute in a horizontal tube. J. Fluid Mech. 29 (3), 465-484
11. HENRY, H. R. 1964 Effects of dispersion on salt encroachment in coastal aquifers. Tech. Rep -C. USGS
12. HESSE, M. A., TCHELEPI, H. A., CANTWELL, B. J. & ORR, F. M. 2007 Gravity currents in horizontal porous layers: Transition from early to late self-similarity. J. Fluid Mech. 577 363-383
13. HUPPERT, H. E. & WOODS, A. W. 1995 Gravity-driven flows in porous layers. J. Fluid Mech. 292 55-69
14. LAKE, L. 1989 Enhanced Oil Recovery. Prentice Hall
15. LAMBERT, J. D. 1991 Numerical Methods for Ordinary Differential Systems: The Initial Value Problem. Wiley
16. LANDMAN, A. J. & SCHOTTING, R. J. 2007 Heat and brine transport in porous media: The Oberbeck-Boussinesq approximation revisited. Transp. Porous Med. 70, 355-373
17. LEVEQUE, R. J. 2002 Finite Volume Methods for Hyperbolic Problems. Cambridge University Press
18. DE LOUBENS, R. & RAMAKRISHNAN, T. S. 2011 Analysis and computation of gravity-induced migration in porous media. J. Fluid Mech. 675, 60-86
19. LYLE, S., HUPPERT, H. E., HALLWORTH, M., BICKLE, M. & CHADWICK, A. 2005 Axisymmetric gravity currents in a porous medium. J. Fluid Mech. 543, 293-302
20. MACMINN, C. W., SZULCZEWSKI, M. L. & JUANES, R. 2011 CO2 migration in saline aquifers Part 2. Capillary and solubility trapping. J. Fluid. Mech. 688, 321-351
21. NGUYEN, N. 2011 Micromixers: Fundamentals, Design and Fabrication. Elsevier
22. NORDBOTTEN, J. M. & CELIA, M. A. 2006 Similarity solutions for fluid injection into confined aquifers. J. Fluid Mech. 561, 307-327
23. PASTER, A. & DAGAN, G. 2007 Mixing at the interface between two fluids in porous media: A boundary-layer solution. J. Fluid Mech. 584, 455-472
24. RIAZ, A., HESSE, M., TCHELEPI, H. A. & ORR, F. M. Jr. 2006 Onset of convection in a gravitationally unstable, diffusive boundary layer in porous media. J. Fluid Mech. 548 87-111
25. SMITH, R. 1976 Longitudinal dispersion of a buoyant contaminant in a shallow channel. J. Fluid Mech. 78 (4), 677-688
26. SZULCZEWSKI, M. L., MACMINN, C. W., HERZOG, H. J. & JUANES, R. 2012 Lifetime of carbon capture and storage as a climate-change mitigation technology. Proc. Natl Acad. Sci. USA 109 5185-5189), 5185-5189
27. TARTAKOVSKY, D. M., GUADAGNINI, A., SANCHEZ-VILA, X., DENTZ, M. & CARRERA, J.
28. A perturbation solution to the transient Henry problem for sea water intrusion. In Developments in Water Science, vol. 55, pp. 1573-1581. Elsevier
29. TAYLOR, G. I. 1953 Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219 (1137), 186-203
30. VELLA, D. & HUPPERT, H. E. 2006 Gravity currents in a porous medium at an inclined plane J. Fluid Mech. 555, 353-362
31. YORTSOS, Y. C. 1995 A theoretical analysis of vertical flow equilibrium. Transp. Porous Med. 18 (2), 107-129