Thermal diffusion, or Soret effect, in porous media is mathematically modeled with the Firoozabadi model based on non-equilibrium thermodynamics. The Soret effect in a binary mixture is investigated in a vertical cavity with heterogeneous permeability, where natural convection can occur. The thermo solutal convection with heterogeneous permeability was studied in terms of flow pattern, concentration distribution, component separation ratio, and Soret coefficient distribution. A consistent analysis was conducted and it is concluded that the Soret coefficient of thermal diffusion in porous media strongly depends on the heterogeneity of permeability.

1.
Soret
,
C.
, 1880, “
Influence de la Temperature sur la Distribution des Sels dans Leurs Solutions
,”
Acad. Sci., Paris, C. R.
0001-4036,
91
, pp.
289
291
.
2.
Shukla
,
K.
, and
Firoozabadi
,
A.
, 1998, “
A New Model of Thermal Diffusion Coefficients in Binary Hydrocarbon Mixtures
,”
Ind. Eng. Chem. Res.
0888-5885,
37
, pp.
3331
3342
.
3.
Bird
,
R. B.
, and
Stewart
,
W. E.
, 2002,
Transport Phenomena
,
Wiley
, New York.
4.
Dougherty
,
E. L.
, and
Drickamer
,
H. G.
, 1955, “
Thermal Diffusion and Molecular Motion in Liquids
,”
J. Phys. Chem.
0022-3654,
59
, pp.
443
449
.
5.
Riley
,
M. F.
, and
Firoozabadi
,
A.
, 1998, “
Compositional Variation in Hydrocarbon Reservoirs With Natural Convection and Diffusion
,”
AIChE J.
0001-1541,
44
, pp.
452
464
.
6.
Firoozabadi
,
A.
,
Ghorayeb
,
K.
, and
Shukla
,
K.
, 2000, “
Theoretical Model of Thermal Diffusion Factors in Multicomponent Mixtures
,”
AIChE J.
0001-1541,
46
, pp.
892
900
.
7.
Ghorayeb
,
K.
, and
Firoozabadi
,
A.
, 2001, “
Features of Convection and Diffusion in Porous Media for Binary Systems
,”
J. Can. Pet. Technol.
0021-9487,
40
, pp.
21
28
.
8.
Ghorayeb
,
K.
, and
Firoozabadi
,
A.
, 2000, “
Molecular, Pressure and Thermal Diffusion in Nonideal Multicomponent Mixtures
,”
AIChE J.
0001-1541,
46
, pp.
883
891
.
9.
De Groot
,
S. R.
, 1984,
Non-Equilibrium Thermodynamics
,
North-Holland
, Amsterdam.
10.
Rutherford
,
W. M.
, and
Roof
,
J. G.
, 1959, “
Thermal Diffusion in Methane n-Butane Mixture in the Critical Region
,”
J. Phys. Chem.
0022-3654,
63
, pp.
1506
1511
.
11.
Faruque
,
D.
,
Chacha
,
M.
,
Saghir
,
M. Z.
, and
Ghorayeb
,
K.
, 2002, “
Compositional Variation Considering Diffusion and Convection for Binary Mixture in Porous Media
,”
J. Porous Media
1091-028X,
7
(
2
), pp.
1
17.
.
12.
Ingham
,
D. B.
, 2003, “
Basic Equations for Laminar Flows through Porous Media, Current Issues on Heat and Mass Transfer in Porous Media
,”
Proc. of the NATO Advanced Study Institute on Porous Media
, Neptun-Olimp, Black Sea, Romania, pp.
1
10
.
13.
Storesletten
,
L.
, 2003, “
Anisotropy Effects on Convective Flow in Porous Media: Part I and Part II, Current Issues on Heat and Mass Transfer in Porous Media
,”
Proc. of the NATO Advanced Study Institute on Porous Media
, Neptun-Olimp, Black Sea, Romania, pp.
529
546
.
14.
Saghir
,
M. Z.
, and
Islam
,
M. R.
, 1999, “
Double Diffusive Convection in Dual-Permeability, Dual-Porosity Porous Media
,”
Int. J. Heat Mass Transfer
0017-9310,
42
, pp.
437
454
.
15.
Jacqmin
,
D. J.
, 1990, “
Interaction of Natural Convection and Gravity Segregation in Oil∕Gas Reservoirs
,”
SPE Reservoir Eval. Eng.
1094-6470,
289
, pp.
233
238
.
16.
Benano-Melly
,
L. B.
,
Caltagirone
,
J. P.
,
Faissat
,
B.
,
Montel
,
F.
, and
Costeseque
,
P.
, 2001, “
Modelling Soret Coefficient Measurement Experiments in Porous Media Considering Thermal and Solutal Convection
,”
Int. J. Heat Mass Transfer
0017-9310,
44
, pp.
1285
1297
.
17.
Jiang
,
C. G.
,
Saghir
,
M. Z.
,
Kawaji
,
M.
, and
Ghorayeb
,
K.
, 2003, “
Permeability Effects a Vertical Porous Cavity With Soret Contribution, Current Issues on Heat and Mass Transfer in Porous Media
,” in
Proc. of the NATO Advanced Study Institute on Porous Media
, Neptun-Olimp, Black Sea, Romania, pp.
187
197
.
18.
Ingham
,
D. B.
, and
Pop
,
I.
, (eds.), 2002,
Transport Phenomena in Porous Media
,
Pergamon
, Oxford, Vol.
II
.
19.
Pop
,
I.
, and
Ingham
,
D. B.
, 2001,
Convective Heat Transfer: Mathematical and Computational Modeling of Viscous fluids and Porous Media
,
Pergamon
, Oxford.
20.
Nield
,
D. A.
, and
Bejan
,
A.
, 1999,
Convection in Porous Media
, 2nd ed.,
Springer
, New York.
21.
Vafai
,
K.
, (ed.), 2000,
Handbook of Porous Media
,
Marce Dekker
, New York.
22.
Chacha
,
M.
,
Faruque
,
D.
,
Saghir
,
M. Z.
, and
Legros
,
J. C.
, 2002, “
Thermodiffusion in Binary Mixture in the Presence of g-jitter
,”
Int. J. Therm. Sci.
1290-0729,
41
, pp.
899
911
.
23.
Jiang
,
C. G.
,
Saghir
,
M. Z.
,
Kawaji
,
M.
, and
Ghorayeb
,
K.
, 2004, “
Contribution of the Thermal and Molecular Diffusion to Convection in a Vertical Porous Cavity
,”
NATO ASI Series
,
Kluwer
, Dordrecht, Vol.
ASI978745
, pp.
1
13
.
24.
Peng
,
D. Y.
, and
Robinson
,
D. B.
, 1976, “
A New Two-Constant Equation of State
,”
Ind. Eng. Chem. Fundam.
0196-4313,
15
, pp.
59
64
.
25.
Herning
,
F.
, and
Zipperer
,
L.
, 1936, “
Calculation of the Viscosity of Technical Gas Mixtures From the Viscosity of Individual Gases
,”
Gas u. Wasserfach
,
79
,
69
.
26.
Taylor
,
R.
, and
Krishna
,
R.
, 1993,
Multicomponent Mass Transfer
,
Wiley
, New York.
27.
Jiang
,
C. G.
,
Saghir
,
M. Z.
,
Kawaji
,
M.
, and
Ghorayeb
,
K.
, 2004, “
Two-Dimensional Numerical Simulation of Thermo-Gravitational Convection in a Vertical Porous Column Filled With a Binary Fluid Mixture
,”
Int. J. Therm. Sci.
1290-0729,
43
, pp.
1057
1065
.
You do not currently have access to this content.