In this study, we use an analytical approach and the interpolation-supplemented lattice Boltzmann method (ISLBM) to quantify convective and diffusive transport during CO2 dissolution. In the first step, we use a turbulence analogy and the ISLBM to determine the relationship between the Rayleigh number (Ra) and the ratio of the pseudo-diffusion coefficient to the molecular diffusion coefficient (D*D). We then use experimental data from two oil samples, condensate and crude oils, to validate the obtained relationship between D*D and Ra. We also use the Sherwood number (Sh) and total mixing and diffusive transport curves to analyze different periods during CO2 dissolution for condensate and crude oils. We focus, in particular, on how Ra affects the characteristics of density-driven fingers and the convection field. Our results show that there is a logarithmic trend between D*D and Ra. Analysis of the total mixing and diffusive curves indicates that the CO2 dissolution process can be divided into three distinct periods, namely, diffusive transport, early convection, and late convection. We find that more than 50% of the ultimate CO2 dissolution occurs in the early convection period. We also show that the analytical results obtained for the critical time and critical depth at the onset of convection is in good agreement with those of the ISLBM. After the onset of convection, the formation of initial fingers leads to enhanced convective transport, with marked implications for the concentration variance and mixing rate.

1.
C.
Song
and
D.
Yang
, “
Experimental and numerical evaluation of CO2 huff-n-puff processes in Bakken formation
,”
Fuel
190
,
145
162
(
2017
).
2.
K.
Damen
,
A.
Faaij
,
F.
van Bergen
,
J.
Gale
, and
E.
Lysen
, “
Identification of early opportunities for CO2 sequestration—Worldwide screening for CO2-EOR and CO2-ECBM projects
,”
Energy
30
,
1931
1952
(
2005
).
3.
V.
Vilarrasa
,
D.
Bolster
,
S.
Olivella
, and
J.
Carrera
, “
Coupled hydromechanical modeling of CO2 sequestration in deep saline aquifers
,”
Int. J. Greenhouse Gas Control
4
,
910
919
(
2010
).
4.
E.
Mohagheghian
,
H.
Hassanzadeh
, and
Z.
Chen
, “
CO2 sequestration coupled with enhanced gas recovery in shale gas reservoirs
,”
J. CO2 Util.
34
,
646
655
(
2019
).
5.
S.
Li
,
C.
Qiao
,
C.
Zhang
, and
Z.
Li
, “
Determination of diffusion coefficients of supercritical CO2 under tight oil reservoir conditions with pressure-decay method
,”
J. CO2 Util.
24
,
430
443
(
2018
).
6.
A.
Haas
,
L.
Gmelin
,
R. J.
Meyer
,
E.
Pietsch
, and
E.
Fluck
,
Gmelins Handbuch der Anorganischen Chemie, 8th aufl. Ergänzungswerk
, Bd. 9: Perfluorhalogenorgano-Verbindungen der Hauptgruppenelemente, Tl. 1: Verbindungen von Schwefel: Perfluorhalogenorgano-Verbindungen der Hauptgruppenelemente Vol. 1 (
Verlag Chemie
,
1973
).
7.
S. J.
Ashcroft
and
M. B.
Isa
, “
Effect of dissolved gases on the densities of hydrocarbons
,”
J. Chem. Eng. Data
42
,
1244
1248
(
1997
).
8.
E.
Lindeberg
and
D.
Wessel-Berg
, “
Vertical convection in an aquifer column under a gas cap of CO2
,”
Energy Convers. Manage.
38
,
S229
S234
(
1997
).
9.
C.
Yang
and
Y.
Gu
, “
Accelerated mass transfer of CO2 in reservoir brine due to density-driven natural convection at high pressures and elevated temperatures
,”
Ind. Eng. Chem. Res.
45
,
2430
2436
(
2006
).
10.
R.
Farajzadeh
,
A.
Barati
,
H. A.
Delil
,
J.
Bruining
, and
P. L.
Zitha
, “
Mass transfer of CO2 into water and surfactant solutions
,”
Pet. Sci. Technol.
25
,
1493
1511
(
2007
).
11.
E.
Lindeberg
and
P.
Bergmo
, “
The long-term fate of CO2 injected into an aquifer
,”
Greenhouse Gas Control Technol.
1
,
489
494
(
2003
).
12.
H.
Hassanzadeh
,
M.
Pooladi-Darvish
, and
D.
Keith
, “
Modelling of convective mixing in CO2 storage
,”
J. Can. Pet. Technol.
44
,
43
51
(
2005
).
13.
H.
Hassanzadeh
, “
Mathematical modeling of convective mixing in porous media for geological CO2 storage
,” Ph.D. thesis (
University of Calgary
,
Canada
,
2006
).
14.
S.
Rapaka
,
S.
Chen
,
R. J.
Pawar
,
P. H.
Stauffer
, and
D.
Zhang
, “
Non-modal growth of perturbations in density-driven convection in porous media
,”
J. Fluid Mech.
609
,
285
303
(
2008
).
15.
K.
Zhang
,
C.
Doughty
,
Y.-S.
Wu
, and
K.
Pruess
, “
Efficient parallel simulation of CO2 geologic sequestration insaline aquifers
,” in
SPE Reservoir Simulation
(
Ernest Orlando Lawrence Berkeley National Laboratory
,
Berkeley, CA, USA
,
2007
).
16.
C.
Lu
and
P. C.
Lichtner
, “
High resolution numerical investigation on the effect of convective instability on long term CO2 storage in saline aquifers
,”
J. Phys.: Conf. Ser.
78
,
012042
(
2007
).
17.
R. N.
Moghaddam
,
B.
Rostami
,
P.
Pourafshary
, and
Y.
Fallahzadeh
, “
Quantification of density-driven natural convection for dissolution mechanism in CO2 sequestration
,”
Transp. Porous Media
92
,
439
456
(
2012
).
18.
N.
Karimi
,
S.
McGrath
,
P.
Brown
,
J.
Weinkauff
, and
A.
Dreizler
, “
Generation of adverse pressure gradient in the circumferential flashback of a premixed flame
,”
Flow, Turbul. Combust.
97
,
663
687
(
2016
).
19.
Q.
Xiong
,
I.
Tlili
,
R. N.
Dara
,
A.
Shafee
,
T.
Nguyen-Thoi
,
A.
Rebey
,
R.-u.
Haq
, and
Z.
Li
, “
Energy storage simulation involving NEPCM solidification in appearance of fins
,”
Physica A
544
,
123566
(
2020
).
20.
Z.
Guo
and
C.
Shu
,
Lattice Boltzmann Method and Its Applications in Engineering
(
World Scientific
,
2013
).
21.
N.
Chen
,
Z.
Jin
,
Y.
Liu
,
P.
Wang
, and
X.
Chen
, “
Lattice Boltzmann simulations of droplet dynamics in two-phase separation with temperature field
,”
Phys. Fluids
32
,
073312
(
2020
).
22.
E. K.
Ahangar
,
S.
Fallah-Kharmiani
,
S. D.
Khakhian
, and
L.-P.
Wang
, “
A lattice Boltzmann study of rarefied gaseous flow with convective heat transfer in backward facing micro-step
,”
Phys. Fluids
32
,
062005
(
2020
).
23.
G.
Kefayati
, “
An immersed boundary-lattice Boltzmann method for thermal and thermo-solutal problems of Newtonian and non-Newtonian fluids
,”
Phys. Fluids
32
,
073103
(
2020
).
24.
M.
Kalteh
and
H.
Hasani
, “
Lattice Boltzmann simulation of nanofluid free convection heat transfer in an L-shaped enclosure
,”
Superlattices Microstruct.
66
,
112
128
(
2014
).
25.
K.
Ghasemi
and
M.
Siavashi
, “
Lattice Boltzmann numerical simulation and entropy generation analysis of natural convection of nanofluid in a porous cavity with different linear temperature distributions on side walls
,”
J. Mol. Liq.
233
,
415
430
(
2017
).
26.
M.
Jami
,
F.
Moufekkir
,
A.
Mezrhab
,
J. P.
Fontaine
, and
M.
Bouzidi
, “
New thermal MRT lattice Boltzmann method for simulations of convective flows
,”
Int. J. Therm. Sci.
100
,
98
107
(
2016
).
27.
F.
Kuznik
,
J.
Vareilles
,
G.
Rusaouen
, and
G.
Krauss
, “
A double-population lattice Boltzmann method with non-uniform mesh for the simulation of natural convection in a square cavity
,”
Int. J. Heat Fluid Flow
28
,
862
870
(
2007
).
28.
R.
Vishnampet
,
A.
Narasimhan
, and
V.
Babu
, “
High Rayleigh number natural convection inside 2D porous enclosures using the lattice Boltzmann method
,”
J. Heat Transfer
133
,
062501
(
2011
).
29.
H. N.
Dixit
and
V.
Babu
, “
Simulation of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method
,”
Int. J. Heat Mass Transfer
49
,
727
739
(
2006
).
30.
M. R.
Yassin
,
A.
Habibi
,
A.
Zolfaghari
,
S.
Eghbali
, and
H.
Dehghanpour
, “
An experimental study of nonequilibrium carbon dioxide/oil interactions
,” SPE-187093-PA,
2018
, Vol. 23, pp.
1768
1783
.
31.
T. V.
Santos
,
M. F.
Pereira
,
H. M.
Avelino
,
F. J.
Caetano
, and
J. M.
Fareleira
, “
Viscosity and density measurements on liquid n-tetradecane at moderately high pressures
,”
Fluid Phase Equilib.
453
,
46
57
(
2017
).
32.
Y.
Zhang
,
C.
Hyndman
, and
B.
Maini
, “
Measurement of gas diffusivity in heavy oils
,”
J. Pet. Sci. Eng.
25
,
37
47
(
2000
).
33.
P.
Berkhin
, “
A survey of clustering data mining techniques
,” in
Grouping Multidimensional Data
(
Springer
,
2006
), pp.
25
71
.
34.
M.
Siavashi
,
H. R.
Talesh Bahrami
, and
H.
Saffari
, “
Numerical investigation of flow characteristics, heat transfer and entropy generation of nanofluid flow inside an annular pipe partially or completely filled with porous media using two-phase mixture model
,”
Energy
93
,
2451
2466
(
2015
).
35.
R.
Yaghoubi Emami
,
M.
Siavashi
, and
G.
Shahriari Moghaddam
, “
The effect of inclination angle and hot wall configuration on Cu-water nanofluid natural convection inside a porous square cavity
,”
Adv. Powder Technol.
29
,
519
536
(
2018
).
36.
R.
Khosrokhavar
,
Mechanisms for CO2 Sequestration in Geological Formations and Enhanced Gas Recovery
(
Springer
,
2015
).
37.
A.
Izadi
,
M.
Siavashi
,
H.
Rasam
, and
Q.
Xiong
, “
MHD enhanced nanofluid mediated heat transfer in porous metal for CPU cooling
,”
Appl. Therm. Eng.
168
,
114843
(
2020
).
38.
O.
Satbhai
and
S.
Roy
, “
Criteria for the onset of convection in the phase-change Rayleigh-Bénard system with moving melting-boundary
,”
Phys. Fluids
32
,
064107
(
2020
).
39.
F. J.
Guerrero-Martínez
,
P. L.
Younger
,
N.
Karimi
, and
S.
Kyriakis
, “
Three-dimensional numerical simulations of free convection in a layered porous enclosure
,”
Int. J. Heat Mass Transfer
106
,
1005
1013
(
2017
).
40.
B.
Jha
,
L.
Cueto-Felgueroso
, and
R.
Juanes
, “
Fluid mixing from viscous fingering
,”
Phys. Rev. Lett.
106
,
194502
(
2011
).
41.
A.
Fattahi
,
S. M.
Hosseinalipour
, and
N.
Karimi
, “
On the dissipation and dispersion of entropy waves in heat transferring channel flows
,”
Phys. Fluids
29
,
087104
(
2017
).
42.
Z.
Ghorbani
,
A.
Riaz
, and
D.
Daniel
, “
Convective mixing in vertically-layered porous media: The linear regime and the onset of convection
,”
Phys. Fluids
29
,
084101
(
2017
).
43.
G. T.
Csanady
,
Turbulent Diffusion in the Environment
(
Springer Science & Business Media
,
2012
).
44.
Q.
Xiong
,
M.
Ayani
,
A. A.
Barzinjy
,
R. N.
Dara
,
A.
Shafee
, and
T.
Nguyen-Thoi
, “
Modeling of heat transfer augmentation due to complex-shaped turbulator using nanofluid
,”
Physica A
540
,
122465
(
2020
).
45.
H.
Hassanzadeh
,
M.
Pooladi-Darvish
, and
D. W.
Keith
, “
Scaling behavior of convective mixing, with application to geological storage of CO2
,”
AIChE J.
53
,
1121
1131
(
2007
).
46.
A.
Einstein
, “
Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen
,”
Ann. Phys.
322
,
549
560
(
1905
).
47.
K.-K.
Tan
,
T.
Sam
, and
H.
Jamaludin
, “
The onset of transient convection in bottom heated porous media
,”
Int. J. Heat Mass Transfer
46
,
2857
2873
(
2003
).
48.
P. G.
Drazin
,
Introduction to Hydrodynamic Stability
(
Cambridge University Press
,
2002
).
49.
V.
Costa
, “
A time scale-based analysis of the laminar convective phenomena
,”
Int. J. Therm. Sci.
41
,
1131
1140
(
2002
).
50.
A.
Bejan
,
Advanced Engineering Thermodynamics
(
John Wiley & Sons
,
2016
).
51.
T. M.
Squires
and
S. R.
Quake
, “
Microfluidics: Fluid physics at the nanoliter scale
,”
Rev. Mod. Phys.
77
,
977
1026
(
2005
).
52.
P.
Le Quéré
, “
Accurate solutions to the square thermally driven cavity at high Rayleigh number
,”
Comput. Fluids
20
,
29
41
(
1991
).
53.
N. C.
Markatos
and
K.
Pericleous
, “
Laminar and turbulent natural convection in an enclosed cavity
,”
Int. J. Heat Mass Transfer
27
,
755
772
(
1984
).
54.
Y.
Song
,
M.
Hao
,
Y.
Liu
,
Y.
Zhao
,
B.
Su
, and
L.
Jiang
, “
CO2 diffusion in n-hexadecane investigated using magnetic resonance imaging and pressure decay measurements
,”
RSC Adv.
4
(
91
),
50180
50187
(
2014
).
You do not currently have access to this content.