[en] Diffusion is an important transport process in low permeability media, which play an important role in contamination and remediation of natural environments. The calculation of equivalent diffusion parameters has however not been extensively explored. In this paper, expressions of the equivalent diffusion coefficient and the equivalent diffusion accessible porosity normal to the layering in a layered porous medium are derived based on analytical solutions of the diffusion equation. The expressions show that the equivalent diffusion coefficient changes with time. It is equal to the power average with p = -0.5 for small times and converges to the harmonic average for large times. The equivalent diffusion accessible porosity is the harmonic average of the porosities of the individual layers for all times. The expressions are verified numerically for several test cases.
Research Center/Unit :
Aquapôle - ULiège
Disciplines :
Geological, petroleum & mining engineering
Author, co-author :
Huysmans, Marijke; KULeuven > Department of Earth and Environmental Sciences > Applied geology and mineralogy
Dassargues, Alain ; Université de Liège - ULiège > Département Argenco : Secteur GEO3 > Hydrogéologie & Géologie de l'environnement
Language :
English
Title :
Equivalent diffusion coefficient and equivalent diffusion accessible porosity of a stratified porous medium
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Bibliography
M. Aertsens I. Wemaere L. Wouters 2004 Spatial variability of transport parameters in the Boom Clay Appl. Clay Sci. 26 37-45 10.1016/ j.clay.2003.09.015
R. Ash R.M. Barrer J.H. Petropoulos 1963 Diffusion in heterogeneous media: Properties of a laminated slab Br. J. Appl. Phys. 14 854-862 10.1088/0508-3443/14/12/307
J.A. Barker R. Herbert 1982 Pumping tests in patchy aquifers Ground Water 20 130-155
Barrer, R.M.: Diffusion and permeation in heterogeneous media (Chapter 6), in Crank, J., Park, G.S. (eds.) Diffusion in Polymers, pp. 165-215. Academic Press, New York (1968)
J.A. Barrie J.D. Levind A.S. Michaels P. Wong 1963 Diffusion and solution of gases in composite rubber membranes Trans. Faraday Soc. 59 854-862 10.1039/tf9635900869
J.J. Butler Jr. 1988 Pumping tests in nonuniform aquifers: The radially symmetric case J. Hydrol. 101 15-30 10.1016/0022-1694(88)90025-X
J.J. Butler Jr. C.D. McElwee 1990 Variable rate pumping tests for radially symmetric nonuniform aquifers Water Resour. Res. 26 291-306 10.1029/89WR01580
M.H. Chambers D.S.L. Lawrence B.W. Sellwood A. Parker 2000 Annual layering in the Upper Jurassic Kimmeridge clay formation, UK, quantified using an ultra-high resolution SEM-EDX investigation Sediment Geol 137 9-23 10.1016/S0037-0738(00)00092-0
C.V. Chrysikopoulos P.K. Kitanidis P.V. Roberts 1992 Macrodispersion of sorbing solutes in heterogeneous porous formations with spatially periodic retardation factor and velocity field Water Resour. Res. 28 1517-1529 10.1029/92WR00010
V. Cvetkovic A. Shapiro 1990 Mass arrival of sorptive solute in heterogeneous porous media Water Resour. Res. 26 2057-2067 10.1029/ 90WR00603
G. Dagan 1982 Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2, The solute transport Water Resour. Res. 18 835-848
G. Dagan 1984 Solute transport in heterogeneous porous formations J. Fluid Mech. 145 151-177 10.1017/S0022112084002858
G. Dagan 1987 Theory of solute transport by groundwater Annu. Rev. Fluid Mech. 19 183-215 10.1146/annurev.fl.19.010187.001151
G. Dagan 1988 Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers Water Resour. Res. 24 1491-1500
D.E. Desaulniers J.A. Cherry P. Fritz 1981 Origin, age and movement of pore water in argillaceous quaternary deposits at four sites in southwestern Ontario J. Hydrol. 50 231-257 10.1016/0022-1694(81)90072-X
M. Descostes V. Blin B. Grenut P. Meier I. Pointeau E. Tevissen 2004 I-125(-) and Cl-36(-) diffusion in Oxfordian limestones and Callovo-Oxfordian argillites formations Geochim Cosmochim Acta 68 11 A507-A507
S. Didierjean D. Maillet C. Moyne 2004 Analytical solutions of one-dimensional macrodispersion in stratified porous media by the quadrupole method: Convergence to an equivalent homogeneous porous medium Adv. Water Res. 27 657-667 10.1016/j.advwatres.2004.02.022
L.W. Gelhar C.L. Axness 1983 Three-dimensional stochastic analysis of macrodispersion in aquifers Water Resour. Res. 19 161-180
R.W. Gillham M.J.L. Robin D.J. Dytynyshyn H.M. Johnston 1984 Diffusion of nonreactive and reactive solutes through fine-grained barrier materials Can. Geotech. J. 21 3 541-550
B.X. Hu F.W. Deng J.H. Cushman 1995 Nonlocal reactive transport with physical and chemical heterogeneity-linear nonequilibrium sorption with random Kd Water Resour. Res. 31 2239-2252 10.1029/95WR01395
Indelman, P.: Transient well-type flows in heterogeneous formations. Water Resour. Res. 39(3), 1064, doi:10.1029/2002WR001407 (2003)
Y.-S. Jang Y.-I. Kim 2003 Behavior of a municipal landfill from field measurement data during a waste-disposal period Env. Geol. 44 592-598 10.1007/s00254-003-0796-z
J.L. Jensen 1998 Some statistical properties of power averages for lognormal samples Water Resour. Res. 34 2415-2418 10.1029/98WR01557
R.L. Johnson J.A. Cherry J.F. Pankow 1989 Diffusive contaminant transport in natural clay: A field example and implications for clay-lined waste disposal sites Environ. Sci. Technol. 23 340-349 10.1021/es00180a012
Z.J. Kabala G. Sposito 1991 A stochastic model of reactive solute transport with time-varying velocity in a heterogeneous aquifer Water Resour. Res. 27 341-350 10.1029/90WR01906
P. Landais 2004 Clays in natural and engineered barriers for radioactive waste confinement Appl. Clay Sci. 26 1-4 110.1016/j.clay.2003.12.006
C. Liu W.P. Ball 1998 Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium Adv. Water Resour. 21 297-313 10.1016/S0309-1708(97)00013-4
A.V. Luikov 1968 Analytical Heat Diffusion Theory 2 Academics Press New York
D. Mallants J. Marivoet X. Sillen 2001 Performance assessment of the disposal of vitrified high-level waste in a clay layer J. Nucl. Mat. 298 125-135 10.1016/S0022-3115(01)00577-3
D. Metzger H. Kinzelbach W. Kinzelbach 1996 Effective dispersion of a solute cloud in a chemically heterogeneous porous medium: Comparison of two ensemble-averaging procedures Water Resour. Res. 32 3311-3319 10.1029/96WR01777
J.A.S. Navarro C. Lopez A.P. Garcia 2000 Characterization of groundwater flow in the Bailin hazardous waste-disposal site (Huesca, Spain) Env. Geol. 40 1-2 216-222 10.1007/s002540000154
S.P. Neuman C.L. Winter C.M. Newman 1987 Stochastic theory of field-scale Fickian dispersion in anisotropic porous media Water Resour. Res. 23 453-466
D.S. Oliver 1990 The average process in permeability estimation from well-test data SPE Form. Eval. 5 319-324
M.N. Özisik 1993 Heat Conduction 2 Wiley New York
Patriarche, D., Michelet, J.-L., Ledoux, E., Savoye, S.: Diffusion as the main process for mass transport in very low water content argillites: 1. Chloride as a natural tracer for mass transport-Diffusion coefficient and concentration measurements in interstitial water. Water Resour. Res. 40(1), W01517, doi:10.1029/2003WR002700 (2004)
T. Ptak G. Schmid 1996 Dual-tracer transport experiments in a physically and chemically heterogeneous porous aquifer: Effective transport parameters and spatial variability J. Hydrol. 183 117-138 10.1016/ S0022-1694(96)80037-0
R. Reichle W. Kinzelbach H. Kinzelbach 1998 Effective parameters in heterogeneous and homogeneous transport models with kinetic sorption Water Resour. Res. 34 583-594 10.1029/97WR03518
P. Renard G. Marsily de 1997 Calculating equivalent permeability: A review Adv. Water Resour. 20 253-278 10.1016/S0309-1708(96)00050-4
P.V. Roberts M.N. Goltz D.M. Mackay 1986 A natural gradient experiment on solute transport in a sand aquifer, 3, Retardation estimates and mass balances for organic solutes Water Resour. Res. 22 2047-2058
C.D. Shackelford D.E. Daniel 1991 Diffusion in saturated soil, I, Background J. Geotech. Eng. 117 467-484
R. Therrien E.A. Sudicky 1996 Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media J. Cont. Hydrol. 23 1-2 1-44 10.1016/0169-7722(95)00088-7
Therrien, R., Sudicky, E.A., McLaren, R.G.: FRAC3DVS: An Efficient Simulator for Three-dimensional, Saturated-Unsaturated Groundwater Flow and Density dependent, Chain-decay Solute Transport in Porous, Discretely-Fractured Porous or Dual-Porosity Formations. User's guide (2003)
L.R. Loon Van J.M Soler A. Jakob M.H. Bradbury 2003 Effect of confining pressure on the diffusion of HTO, 36Cl- and 125I- in a layered argillaceous rock(Opalinus Clay): Diffsion perpendicular to the fabric Appl. Geochem 18 1653-1662 10.1016/S0883-2927(03)00047-7
Van Marcke, Ph., Laenen, B.: The Ypresian Clays as Possible Host Rock for Radioactive Waste Disposal: An Evaluation, ONDRAF/NIRAS, Brussel (2005)
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