Solute convection in porous media at high Rayleigh-Darcy numbers has important fundamental features and may also bear implications for geological CO2 sequestration processes. With the aid of direct numerical simulations, we examine the role of anisotropic permeability on the distribution of solutal concentration in fluid saturated porous medium. Our computational analyses span over few decades of Rayleigh-Darcy number and confirm the linear scaling of Nusselt number that was previously found in the literature. In addition, we find that anisotropic permeability γ < 1, i.e., with vertical permeability smaller than horizontal permeability, effectively increases the Nusselt number compared with isotropic conditions. We link this seemingly counterintuitive effect with the occurring modifications to the flow topology in the anisotropic conditions. Finally, we use our data computed for the two-sided configuration (i.e., Dirichlet conditions on upper and lower boundaries) to examine the time evolution of solutal dynamics in the one-sided configuration, and we demonstrate that the finite-time (short-term) amount of CO2 that can be dissolved in anisotropic sedimentary rocks is much larger than in isotropic rocks.

1.
C. W.
Horton
and
F. T.
Rogers
, Jr.
, “
Convection currents in a porous medium
,”
J. Appl. Phys.
16
(
6
),
367
370
(
1945
).
2.
E. R.
Lapwood
, “
Convection of a fluid in a porous medium
,”
Proc. Cambridge
44
,
508
521
(
1948
).
3.
D. R.
Hewitt
,
J. A.
Neufeld
, and
J. R.
Lister
, “
Ultimate regime of high Rayleigh number convection in a porous medium
,”
Phys. Rev. Lett.
108
(
22
),
224503
(
2012
).
4.
J.
Otero
,
L. A.
Dontcheva
,
H.
Johnston
,
R. A.
Worthing
,
A.
Kurganov
,
G.
Petrova
, and
C. R.
Doering
, “
High-Rayleigh number convection in a fluid-saturated porous layer
,”
J. Fluid Mech.
500
,
263
281
(
2004
).
5.
S.
Backhaus
,
K.
Turitsyn
, and
R. E.
Ecke
, “
Convective instability and mass transport of diffusion layers in a Hele-Shaw geometry
,”
Phys. Rev. Lett.
106
(
10
),
104501
(
2011
).
6.
G. J.
Weir
,
S. P.
White
, and
W. M.
Kissling
, “
Reservoir storage and containment of greenhouse gases
,”
Transp. Porous Media
23
(
1
),
37
60
(
1996
).
7.
H. E.
Huppert
and
J. A.
Neufeld
, “
The fluid mechanics of carbon dioxide sequestration
,”
Annu. Rev. Fluid Mech.
46
,
255
272
(
2014
).
8.
B.
Metz
,
O.
Davidson
,
H.
de Coninck
,
M.
Loos
,
L.
Meyer
 et al, Carbon dioxide capture and storage: Special report of the IPCC, 2005.
9.
D. P.
Schrag
, “
Preparing to capture carbon
,”
Science
315
(
5813
),
812
813
(
2007
).
10.
S.
Julio Friedmann
, “
Geological carbon dioxide sequestration
,”
Elements
3
(
3
),
179
184
(
2007
).
11.
X.
Xu
,
S.
Chen
, and
D.
Zhang
, “
Convective stability analysis of the long-term storage of carbon dioxide in deep saline aquifers
,”
Adv. Water Res.
29
(
3
),
397
407
(
2006
).
12.
D. R.
Hewitt
,
J. A.
Neufeld
, and
J. R.
Lister
, “
Convective shutdown in a porous medium at high Rayleigh number
,”
J. Fluid Mech.
719
,
551
586
(
2013
).
13.
A. C.
Slim
, “
Solutal-convection regimes in a two-dimensional porous medium
,”
J. Fluid Mech.
741
,
461
491
(
2014
).
14.
A.
Riaz
,
M.
Hesse
,
H. A.
Tchelepi
, and
F. M.
Orr
, “
Onset of convection in a gravitationally unstable diffusive boundary layer in porous media
,”
J. Fluid Mech.
548
,
87
111
(
2006
).
15.
P.
Cheng
,
M.
Bestehorn
, and
A.
Firoozabadi
, “
Effect of permeability anisotropy on buoyancy-driven flow for CO2 sequestration in saline aquifers
,”
Water Resour. Res.
48
(
9
),
1
16
, doi:10.1029/2012WR011939 (
2012
).
16.
J.
Ennis-King
,
I.
Preston
, and
L.
Paterson
, “
Onset of convection in anisotropic porous media subject to a rapid change in boundary conditions
,”
Phys. Fluids (1994-present)
17
(
8
),
084107
(
2005
).
17.
A. J.
Landman
and
R. J.
Schotting
, “
Heat and brine transport in porous media: The Oberbeck-Boussinesq approximation revisited
,”
Transp. Porous Media
70
(
3
),
355
373
(
2007
).
18.
D. R.
Hewitt
,
J. A.
Neufeld
, and
J. R.
Lister
, “
Stability of columnar convection in a porous medium
,”
J. Fluid Mech.
737
,
205
231
(
2013
).
19.
F.
Zonta
and
A.
Soldati
, “
Effect of temperature dependent fluid properties on heat transfer in turbulent mixed convection
,”
J. Heat Transfer
136
(
2
),
022501
(
2014
).
20.
M. D.
Graham
and
P. H.
Steen
, “
Plume formation and resonant bifurcations in porous-media convection
,”
J. Fluid Mech.
272
,
67
90
(
1994
).
21.
J.
Schumacher
, “
Lagrangian studies in convective turbulence
,”
Phys. Rev. E
79
(
5
),
056301
(
2009
).
22.
C. P.
Green
and
J.
Ennis-King
, “
Steady dissolution rate due to convective mixing in anisotropic porous media
,”
Adv. Water Resour.
73
,
65
73
(
2014
).
23.
J. A.
Neufeld
,
M. A.
Hesse
,
A.
Riaz
,
M. A.
Hallworth
,
H. A.
Tchelepi
, and
H. E.
Huppert
, “
Convective dissolution of carbon dioxide in saline aquifers
,”
Geophys. Res. Lett.
37
(
22
),
1
5
, doi:10.1029/2010GL044728 (
2010
).
24.
F.
Paparella
and
J.
von Hardenberg
, “
Clustering of salt fingers in double-diffusive convection leads to staircaselike stratification
,”
Phys. Rev. Lett.
109
(
1
),
014502
(
2012
).
25.
E. S. C.
Ching
,
H.
Guo
,
X.-D.
Shang
,
P.
Tong
, and
K.-Q.
Xia
, “
Extraction of plumes in turbulent thermal convection
,”
Phys. Rev. Lett.
93
(
12
),
124501
(
2004
).
26.
E. P.
van der Poel
,
R.
Verzicco
,
S.
Grossmann
, and
D.
Lohse
, “
Plume emission statistics in turbulent Rayleigh–Bénard convection
,”
J. Fluid Mech.
772
,
5
15
(
2015
).
27.
A. C.
Slim
,
M. M.
Bandi
,
J. C.
Miller
, and
L.
Mahadevan
, “
Dissolution-driven convection in a Hele–Shaw cell
,”
Phys. Fluids (1994-present)
25
(
2
),
024101
(
2013
).
28.
J. J.
Hidalgo
,
J.
Fe
,
L.
Cueto-Felgueroso
, and
R.
Juanes
, “
Scaling of convective mixing in porous media
,”
Phys. Rev. Lett.
109
(
26
),
264503
(
2012
).
29.
M.
Bickle
,
A.
Chadwick
,
H. E.
Huppert
,
M.
Hallworth
, and
S.
Lyle
, “
Modelling carbon dioxide accumulation at Sleipner: Implications for underground carbon storage
,”
Earth Planet. Sci. Lett.
255
(
1
),
164
176
(
2007
).
30.
G. S. H.
Pau
,
J. B.
Bell
,
K.
Pruess
,
A. S.
Almgren
,
M. J.
Lijewski
, and
K.
Zhang
, “
High-resolution simulation and characterization of density-driven flow in CO2 storage in saline aquifers
,”
Adv. Water Resour.
33
(
4
),
443
455
(
2010
).
31.
F.
Zonta
,
C.
Marchioli
, and
A.
Soldati
, “
Modulation of turbulence in forced convection by temperature-dependent viscosity
,”
J. Fluid Mech.
697
,
150
174
(
2012
).
32.
B.
Wen
,
G. P.
Chini
,
N.
Dianati
, and
C. R.
Doering
, “
Computational approaches to aspect-ratio-dependent upper bounds and heat flux in porous medium convection
,”
Phys. Lett. A
377
(
41
),
2931
2938
(
2013
).
You do not currently have access to this content.