Non-modal growth of perturbations in density-driven convection in porous media

Journal of Fluid Mechanics

Volumn 609, Issue , 2008, Pages 285-303

  Rapaka, Saikiran ^a   Chen, Shiyi ^a,b   Pawar, Rajesh J ^c   Stauffer, Philip H ^c   Zhang, Dongxiao ^d  

^a Johns Hopkins University   (United States)

^b PEKING UNIVERSITY   (China)

^c LOS ALAMOS NATIONAL LABORATORY   (United States)

^d University of Southern California ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AQUIFERS; CARBON DIOXIDE; HYDROGEOLOGY; INITIAL VALUE PROBLEMS; POROUS MATERIALS;

CONVECTION IN POROUS MEDIAS; GEOLOGIC SEQUESTRATIONS; GOVERNING EQUATIONS; INITIAL PERTURBATION; LINEAR STABILITY THEORY; NORMAL MODE ANALYSIS; ONSET OF CONVECTION; QUASISTATIC APPROXIMATIONS;

MODAL ANALYSIS;

BRINE; CARBON DIOXIDE; CONVECTION; DISSOLUTION; PERTURBATION; POROUS MEDIUM;

EID: 48949086862     PISSN: 00221120     EISSN: 14697645     Source Type: Journal    
DOI: 10.1017/S0022112008002607     Document Type: Article

References (37)

1. BAUER, F. & NOHEL, J. A. 1969 The Qualitative Theory of Ordinary Differential Equations: An Introduction. Dover.
2. BEN, Y., DEMEKHIN, E. A. & CHANG, H.-C. 2002 A spectral theory for small-amplitude miscible fingering. Phys. Fluids 14 (3 , 999-1010.
3. CALTAGIRONE, J.-P. 1980 Stability of a saturated porous layer subject to a sudden rise in surface temperature: Comparison between the linear and energy methods. Q. J. Mech. Appl. Maths 3, 47-58.
4. CANUTO, C., HUSSAINI, M. Y., QUARTERONI, A. & ZANG, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.
5. CASTINELL, G. & COMBARNOUS, M. 1977 Natural convection in an anisotropic porous medium. Intl Chem. Engng 17, 605-613.
6. CHANDRASEKHAR, S. 1961 Hydrodynamic and Hydromagnetic Stability Clarendon.
7. 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, 349-356.
8. ENNIS-KING, J., PRESTON, I. & PATERSON, L. 2005 Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions. Phys. Fluids 17 (8), 084107.
9. EPHERRE, J. F. 1977 Criterion for the appearance of natural convection in an anisotropic porous layer. Intl Chem. Engng 17 615-616.
10. FARRELL, B. F. & IOANNOU, P. J. 1996a Generalized stability theory. part i: Autonomous operators. J. Atmos. Sci. 53 (14), 2025-2040.
11. FARRELL, B. F. & IOANNOU, P. J. 1996b Generalized stability theory. part ii: Nonautonomous operators. J. Atmos. Sci. 53 (14), 2041-2053.
12. FOSTER, T. D. 1965 Stability of a homogeneous fluid cooled uniformly from above. Phys. Fluids 8 (7), 1249-1257.
13. 2. Tech. Rep. LBNL-49023. Lawrence Berkeley National Laboratory.
14. GARCIA, J. E. 2003 Fluid dynamics of carbon dioxide disposal into saline aquifers. PhD thesis, University of California, Berkeley.
15. GOLUB, G. H. & VAN LOAN, C. F. 1996 Matrix Computations. The Johns Hopkins University Press.
16. HASSANZADEH, H., POOLADI-DARVISIE M. & KEITH, D. W. 2006 Stability of a fluid in a horizontal saturated porous layer: Effect of non-linear concentration profile, initial, and boundary conditions. Transport in Porous Media 65 (2), 193-211.
17. HOMSY, G. M. 1973 Global stability of time-dependent flows: impulsively heated or cooled fluid layers. J. Fluid Mech. 60 (1), 129-139.
18. HORTON, C. W. & ROGERS JR, F. T. 1945 Convection currents in a porous media. J. Appl. Phys. 16, 367-370.
19. IPCC 2005 IPCC Special Report on Carbon Dioxide Capture and Storage. Prepared by Working Group III of the Intergovernmental Panel on Climate Change (B. Metz, O. Davidson, H. C. de Coninck, M. Loos and L. A. Meyer). Cambridge University Press.
20. KIM, M. C., KIM, K. Y. & KIM, S. 2004 The onset of transient convection in fluid-saturated porous layer heated uniformly from below. Int. Comm. Heat Mass Transfer 31 (1), 53-62.
21. LAPWOOD, E. R. 1948 Convection of a fluid in a porous medium. Proc. Camb. Phil. Soc. 44, 508-521.
22. 2 injected into an aquifer. In Greenhouse Gas Control Technologies (ed. J. Gale & Y. Kaya), vol. 1, pp. 489-495. Elsevier.
23. 2 sequestration in geologic media. Fourth Annual Conference on Carbon Capture and Sequestration.
24. NIELD, D. & BEJAN, A. 1999 Convection in Porous Media. Springer.
25. PARK, J. H., CHUNG, T. J., CHOI, C. K. & KIM, M. C. 2006 The onset of mixed convection in a porous layer heated with constant heat flux. AIChE J. 52 (8), 2677-2683.
26. PEYRET, R. 2002 Spectral Methods for Incompressible Viscous Flow. Springer.
27. PRASAD, A. & SIMMONS, C. T. 2003 Unstable density-driven flow in heterogeneous porous media: A stochastic study of the Elder(1967b) "short heater" problem. Water Resour. Res. 39 (1), 1007.
28. PRUESS, K. 1991 TOUGH2, a general-purpose numerical simulator for multiphase fluid and heat flow. Report LBL-29400, Lawrence Berkeley Laboratory.
29. RIAZ, A., HESSE, M., TCHELEPI, H. A. & ORR JR, F. M. 2006 Onset of convection in a gravitationally unstable diffusive boundary layer in porous media. J. Fluid Mech. 548, 87-111.
30. ROGERS, F. T. & MORRISON, H. L. 1950 Convection currents in porous media. III: Extended theory of the critical gradient. J. Appl. Phys. 21, 1177.
31. SCHMID, P. J. 2007 Non-modal stability theory. Annu. Rev. Fluid Mech. 39, 129-162.
32. SCHMID, P. J. & HENNINGSON, D. S. 2001 Stability and Transition in Shear Flow. Springer.
33. STRAUGHAN, B. 2004 The Energy Method, Stability and Nonlinear Convection. Springer.
34. TAN, C. T. & HOMSY, G. M. 1986 Stability of miscible discplacements in porous media: Rectilinear flow. Phys. Fluids 29 (11), 3549.
35. TREFETHEN, L. N. & EMBREE, M. 2005 Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators. Princeton University Press.
36. XU, X., CHEN, S. & ZHANG, D. 2006 Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers. Adv. Water Resour 29, 397-407.
37. ZYVOLOSKI, G. A., ROBINSON, B. A., WOLFSBERG, A. V., PAWAR, R. J., VISWANATHAN, H., KELKAR, S. & DASH, Z. V. http://fehm.lanl.gov/ Finite element heat and mass transfer code (FEHM). http://fehm.lanl.gov/.