메뉴 건너뛰기




Volumn 31, Issue 2, 2008, Pages 251-268

Analytical modeling of one-dimensional diffusion in layered systems with position-dependent diffusion coefficients

Author keywords

Diffusion; Eigenfunction; Eigenvalue; Multi layer porous media; Non homogenous boundary conditions; Orthogonal expansion

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFUSION; EIGENVALUES AND EIGENFUNCTIONS; LINEAR EQUATIONS;

EID: 37049006091     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2007.08.008     Document Type: Article
Times cited : (32)

References (56)
  • 1
    • 0001928115 scopus 로고
    • The electrical resistivity log as an aid in determining some reservoir characteristics
    • Archie G.E. The electrical resistivity log as an aid in determining some reservoir characteristics. Trans AIME 146 (1942) 54-62
    • (1942) Trans AIME , vol.146 , pp. 54-62
    • Archie, G.E.1
  • 3
    • 0000761771 scopus 로고
    • Excluded-volume explanation of Archie's law
    • Balberg J. Excluded-volume explanation of Archie's law. Phys Rev B 33 (1986) 3618-3620
    • (1986) Phys Rev B , vol.33 , pp. 3618-3620
    • Balberg, J.1
  • 4
    • 0023285521 scopus 로고
    • Approximations to solute transport in porous media with flow transverse to layering
    • Barry D.A., and Parker J.C. Approximations to solute transport in porous media with flow transverse to layering. Transport Porous Med 21 (1987) 65-82
    • (1987) Transport Porous Med , vol.21 , pp. 65-82
    • Barry, D.A.1    Parker, J.C.2
  • 5
    • 0343451509 scopus 로고
    • Approximations to solute transport in porous media with flow transverse to layering-appendum
    • Barry D.A., Parlange J.Y., Rand R., and Parker J.C. Approximations to solute transport in porous media with flow transverse to layering-appendum. Transport Porous Med 21 (1987) 421-423
    • (1987) Transport Porous Med , vol.21 , pp. 421-423
    • Barry, D.A.1    Parlange, J.Y.2    Rand, R.3    Parker, J.C.4
  • 6
    • 0043235646 scopus 로고    scopus 로고
    • Influence of the percolation network geometry on electron transport in dye-sensitized titanium dioxide solar cells
    • Benkstein K.D., Kopidakis J., van de Lagemaat J., and Frank A.J. Influence of the percolation network geometry on electron transport in dye-sensitized titanium dioxide solar cells. J Phys Chem B 107 (2003) 7759-7767
    • (2003) J Phys Chem B , vol.107 , pp. 7759-7767
    • Benkstein, K.D.1    Kopidakis, J.2    van de Lagemaat, J.3    Frank, A.J.4
  • 7
    • 34547854203 scopus 로고    scopus 로고
    • Diffusion in multilayer media: transient behavior of the lateral diffusion coefficient
    • Berezhkovskii A.M., and Weiss G.H. Diffusion in multilayer media: transient behavior of the lateral diffusion coefficient. J Chem Phys 124 (2006) 154710-154810
    • (2006) J Chem Phys , vol.124 , pp. 154710-154810
    • Berezhkovskii, A.M.1    Weiss, G.H.2
  • 8
    • 0002457368 scopus 로고
    • The clay-varve based Swedish time scale and its relation to the Late Weichselian radiocarbon chronology
    • The last deglaciation: absolute and radiocarbon chronologies. Bard E., and Broecker W.S. (Eds), Springer-Verlag, Berlin
    • Björck S., Cato I., Brunnberg L., and Strömberg B. The clay-varve based Swedish time scale and its relation to the Late Weichselian radiocarbon chronology. In: Bard E., and Broecker W.S. (Eds). The last deglaciation: absolute and radiocarbon chronologies. NATO ASI series I vol. 2 (1992), Springer-Verlag, Berlin 25-44
    • (1992) NATO ASI series I , vol.2 , pp. 25-44
    • Björck, S.1    Cato, I.2    Brunnberg, L.3    Strömberg, B.4
  • 9
    • 0026892921 scopus 로고
    • Analytical approximations for nonlinear adsorbing solute transport in layered soils
    • Bosma W.J.P., and van der Zee S.E.A.T.M. Analytical approximations for nonlinear adsorbing solute transport in layered soils. J Contam Hydrol 10 (1992) 99-118
    • (1992) J Contam Hydrol , vol.10 , pp. 99-118
    • Bosma, W.J.P.1    van der Zee, S.E.A.T.M.2
  • 10
    • 0035545661 scopus 로고    scopus 로고
    • Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity
    • Boving T.B., and Grathwohl P. Tracer diffusion coefficients in sedimentary rocks: correlation to porosity and hydraulic conductivity. J Contam Hydrol 53 (2001) 85-100
    • (2001) J Contam Hydrol , vol.53 , pp. 85-100
    • Boving, T.B.1    Grathwohl, P.2
  • 12
    • 31444447001 scopus 로고    scopus 로고
    • Plume persistence due to aquitard back diffusion following dense nonaqueous phase liquid source removal or isolation
    • 10.1029/2005WR004224
    • Chapman S.W., and Parker B.L. Plume persistence due to aquitard back diffusion following dense nonaqueous phase liquid source removal or isolation. Water Resour Res 41 (2005) W12411 10.1029/2005WR004224
    • (2005) Water Resour Res , vol.41
    • Chapman, S.W.1    Parker, B.L.2
  • 13
    • 33646533581 scopus 로고    scopus 로고
    • A new equation for shallow groundwater flow over a curved impermeable boundary: numerical solutions and laboratory tests
    • 10.1029/2005WR004437
    • Chapman T.G., and Ong G. A new equation for shallow groundwater flow over a curved impermeable boundary: numerical solutions and laboratory tests. Water Resour Res 42 (2006) W03427 10.1029/2005WR004437
    • (2006) Water Resour Res , vol.42
    • Chapman, T.G.1    Ong, G.2
  • 14
    • 25844437434 scopus 로고    scopus 로고
    • Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods
    • 10.1029/2004WR003821
    • Chau J.F., Or D., and Sukop M.C. Simulation of gaseous diffusion in partially saturated porous media under variable gravity with lattice Boltzmann methods. Water Resour Res 41 (2005) W08410 10.1029/2004WR003821
    • (2005) Water Resour Res , vol.41
    • Chau, J.F.1    Or, D.2    Sukop, M.C.3
  • 15
    • 33646497899 scopus 로고    scopus 로고
    • Effect of historical changes in land use and climate on the water budget of an urbanizing watershed
    • 10.1029/2005WR004131
    • Claessens L., Hopkinson C., Rastetter E., and Vallino J. Effect of historical changes in land use and climate on the water budget of an urbanizing watershed. Water Resour Res 42 (2006) W03426 10.1029/2005WR004131
    • (2006) Water Resour Res , vol.42
    • Claessens, L.1    Hopkinson, C.2    Rastetter, E.3    Vallino, J.4
  • 16
    • 36149070341 scopus 로고
    • Gaseous diffusion in porous media, Part 1 - a non-steady state method
    • Currie J.A. Gaseous diffusion in porous media, Part 1 - a non-steady state method. Br J Appl Phys 11 (1960) 314-318
    • (1960) Br J Appl Phys , vol.11 , pp. 314-318
    • Currie, J.A.1
  • 17
    • 0001108063 scopus 로고
    • Gaseous diffusion in porous media. Part 3 - wet granular materials
    • Currie J.A. Gaseous diffusion in porous media. Part 3 - wet granular materials. Br J Appl Phys 12 (1961) 275-281
    • (1961) Br J Appl Phys , vol.12 , pp. 275-281
    • Currie, J.A.1
  • 18
    • 34547866807 scopus 로고    scopus 로고
    • Measurement and modelling of temporal variations in hydrocarbon vapour behaviour in a layered soil profile
    • Davis G.B., Rayner J.L., Trefry M.G., Fisher S.J., and Patterson B.M. Measurement and modelling of temporal variations in hydrocarbon vapour behaviour in a layered soil profile. Vadose Zone J 4 (2005) 225-239
    • (2005) Vadose Zone J , vol.4 , pp. 225-239
    • Davis, G.B.1    Rayner, J.L.2    Trefry, M.G.3    Fisher, S.J.4    Patterson, B.M.5
  • 20
    • 16244415495 scopus 로고    scopus 로고
    • Sandstone vs. carbonate petroleum reservoirs: a global perspective on porosity-depth and porosity-permeability relationships
    • Ehrenberg S.N., and Nadeau P.H. Sandstone vs. carbonate petroleum reservoirs: a global perspective on porosity-depth and porosity-permeability relationships. AAPG Bull 89 (2005) 435-445
    • (2005) AAPG Bull , vol.89 , pp. 435-445
    • Ehrenberg, S.N.1    Nadeau, P.H.2
  • 21
    • 30744439837 scopus 로고    scopus 로고
    • Porosity-permeability relationships in interlayered limestone-dolostone reservoirs
    • Ehrenberg S.N., Eberli G.P., and Keramati M. Porosity-permeability relationships in interlayered limestone-dolostone reservoirs. AAPG Bull 90 (2006) 91-114
    • (2006) AAPG Bull , vol.90 , pp. 91-114
    • Ehrenberg, S.N.1    Eberli, G.P.2    Keramati, M.3
  • 22
    • 33644807283 scopus 로고    scopus 로고
    • An analytical model for solute transport in unsaturated flow through a single fracture and porous rock matrix
    • 10.1029/2004WR003770
    • Houseworth J.E. An analytical model for solute transport in unsaturated flow through a single fracture and porous rock matrix. Water Resour Res 42 (2006) W01416 10.1029/2004WR003770
    • (2006) Water Resour Res , vol.42
    • Houseworth, J.E.1
  • 23
    • 0242424160 scopus 로고    scopus 로고
    • On the vanishing of solute diffusion in porous media at a threshold moisture content
    • Hunt A.G., and Ewing R.P. On the vanishing of solute diffusion in porous media at a threshold moisture content. Soil Sci Soc Am J 67 (2003) 1701-1702
    • (2003) Soil Sci Soc Am J , vol.67 , pp. 1701-1702
    • Hunt, A.G.1    Ewing, R.P.2
  • 24
    • 11044229288 scopus 로고    scopus 로고
    • Continuum percolation theory and Archie's Law
    • Hunt A.G. Continuum percolation theory and Archie's Law. Geophys Res Lett 31 (2004) L19503
    • (2004) Geophys Res Lett , vol.31
    • Hunt, A.G.1
  • 25
    • 0001776690 scopus 로고    scopus 로고
    • 2 efflux assessed with a calibrated soda lime technique
    • 2 efflux assessed with a calibrated soda lime technique. Ecol Lett 1 (1998) 95-98
    • (1998) Ecol Lett , vol.1 , pp. 95-98
    • Janssens, I.A.1    Ceulemans, R.2
  • 27
    • 0021086820 scopus 로고
    • Behavior assessment model for trace organics in soil, 1, Model description
    • Jury W.A., Spencer W.F., and Farmer W.J. Behavior assessment model for trace organics in soil, 1, Model description. J Environ Qual 12 (1983) 558-564
    • (1983) J Environ Qual , vol.12 , pp. 558-564
    • Jury, W.A.1    Spencer, W.F.2    Farmer, W.J.3
  • 28
    • 33846280368 scopus 로고    scopus 로고
    • Gas transport parameters in the vadose zone: development and tests of power-law models for air permeability
    • Kawamoto K., Moldrup P., Schjønning P., Iversen B.V., Komatsu T., and Rolston D.E. Gas transport parameters in the vadose zone: development and tests of power-law models for air permeability. Vadose Zone J 5 (2006) 1205-1215
    • (2006) Vadose Zone J , vol.5 , pp. 1205-1215
    • Kawamoto, K.1    Moldrup, P.2    Schjønning, P.3    Iversen, B.V.4    Komatsu, T.5    Rolston, D.E.6
  • 29
    • 0026359765 scopus 로고
    • Mathematical analysis of one-dimensional solute transport in a layered soil profile
    • Leij F.J., Dane J.H., and van Genuchten M.T. Mathematical analysis of one-dimensional solute transport in a layered soil profile. Soil Sci Soc Am J 55 (1991) 944-953
    • (1991) Soil Sci Soc Am J , vol.55 , pp. 944-953
    • Leij, F.J.1    Dane, J.H.2    van Genuchten, M.T.3
  • 30
    • 0032054529 scopus 로고    scopus 로고
    • Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium
    • Liu C., and Ball W.P. Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium. Adv Water Resour 24 (1998) 297-313
    • (1998) Adv Water Resour , vol.24 , pp. 297-313
    • Liu, C.1    Ball, W.P.2
  • 31
    • 0031831583 scopus 로고    scopus 로고
    • An analytical solution to the one-dimensional solute advection-dispersion equation in multi-layer porous media
    • Liu C., Ball W.P., and Ellis J.H. An analytical solution to the one-dimensional solute advection-dispersion equation in multi-layer porous media. Transport Porous Med 30 (1998) 25-43
    • (1998) Transport Porous Med , vol.30 , pp. 25-43
    • Liu, C.1    Ball, W.P.2    Ellis, J.H.3
  • 32
    • 0343527340 scopus 로고    scopus 로고
    • Use of the generalized integral transform method for solving equations of solute transport in porous media
    • Liu C., Szecsody J.E., Zachara J.M., and Ball W.P. Use of the generalized integral transform method for solving equations of solute transport in porous media. Adv Water Resour 23 (2000) 483-492
    • (2000) Adv Water Resour , vol.23 , pp. 483-492
    • Liu, C.1    Szecsody, J.E.2    Zachara, J.M.3    Ball, W.P.4
  • 33
    • 33745898247 scopus 로고    scopus 로고
    • Simulating the gas diffusion coefficient in macropore network images: Influence of soil pore morphology
    • Liu G., Li B.G., Hu K.L., and van Genuchten M.T. Simulating the gas diffusion coefficient in macropore network images: Influence of soil pore morphology. Soil Sci. Soc Am J 70 (2006) 1252-1261
    • (2006) Soil Sci. Soc Am J , vol.70 , pp. 1252-1261
    • Liu, G.1    Li, B.G.2    Hu, K.L.3    van Genuchten, M.T.4
  • 34
    • 0034163880 scopus 로고    scopus 로고
    • Temporal changes in small depth-incremental soil bulk density
    • Logsdon S.D., and Cambardella C.A. Temporal changes in small depth-incremental soil bulk density. Soil Sci Soc Am J 64 (2000) 710-714
    • (2000) Soil Sci Soc Am J , vol.64 , pp. 710-714
    • Logsdon, S.D.1    Cambardella, C.A.2
  • 35
    • 31444441648 scopus 로고    scopus 로고
    • An analysis of periodic tracers for subsurface characterization
    • 10.1029/2005WR004190
    • Mahinthakumar G.K., Moline G.R., and Webb O.F. An analysis of periodic tracers for subsurface characterization. Water Resour Res 41 (2005) W12426 10.1029/2005WR004190
    • (2005) Water Resour Res , vol.41
    • Mahinthakumar, G.K.1    Moline, G.R.2    Webb, O.F.3
  • 36
    • 33646372101 scopus 로고    scopus 로고
    • Storage and transit time of chemicals in thick unsaturated zones under rangeland and irrigated cropland, High Plains, United States
    • 10.1029/2005WR004417
    • McMahon P.B., Dennehy K.F., Bruce B.W., Böhlke J.K., Michel R.L., Gurdak J.J., et al. Storage and transit time of chemicals in thick unsaturated zones under rangeland and irrigated cropland, High Plains, United States. Water Resour. Res. 42 (2006) W03413 10.1029/2005WR004417
    • (2006) Water Resour. Res. , vol.42
    • McMahon, P.B.1    Dennehy, K.F.2    Bruce, B.W.3    Böhlke, J.K.4    Michel, R.L.5    Gurdak, J.J.6
  • 37
    • 37049019009 scopus 로고    scopus 로고
    • Mikhailov, MD, Özisik, MN. Unified analysis and solutions of heat and mass diffusion; 1984.
  • 38
    • 0002602488 scopus 로고
    • Gas diffusion in porous media
    • Millington R.J. Gas diffusion in porous media. Science 130 (1959) 100-102
    • (1959) Science , vol.130 , pp. 100-102
    • Millington, R.J.1
  • 40
    • 0031197337 scopus 로고    scopus 로고
    • Three-dimensional random walk simulation of diffusion controlled electrode processes. 2. Arrays of growing hemispheres
    • Nagy G., and Denuault G. Three-dimensional random walk simulation of diffusion controlled electrode processes. 2. Arrays of growing hemispheres. J Electroanal Chem 433 (1997) 175-180
    • (1997) J Electroanal Chem , vol.433 , pp. 175-180
    • Nagy, G.1    Denuault, G.2
  • 41
    • 4444265254 scopus 로고    scopus 로고
    • Three-dimensional diffusion of non-sorbing species in porous sandstone: computer simulation based on X-ray microtomography using synchrotron
    • Nakashima Y., Nakano T., Nakamura K., Uesugi K., Tsuchiyama A., and Ikeda S. Three-dimensional diffusion of non-sorbing species in porous sandstone: computer simulation based on X-ray microtomography using synchrotron. J Contam Hydrol 74 (2004) 253-264
    • (2004) J Contam Hydrol , vol.74 , pp. 253-264
    • Nakashima, Y.1    Nakano, T.2    Nakamura, K.3    Uesugi, K.4    Tsuchiyama, A.5    Ikeda, S.6
  • 43
    • 33646520585 scopus 로고    scopus 로고
    • Identifying sources of a conservative groundwater contaminant using backward probabilities conditioned on measured concentrations
    • 10.1029/2005WR004115
    • Neupauer R.M., and Lin R. Identifying sources of a conservative groundwater contaminant using backward probabilities conditioned on measured concentrations. Water Resour Res 42 (2006) W03424 10.1029/2005WR004115
    • (2006) Water Resour Res , vol.42
    • Neupauer, R.M.1    Lin, R.2
  • 44
    • 33644815604 scopus 로고    scopus 로고
    • Nitrate attenuation in agricultural catchments: shifting balances between transport and reaction
    • 10.1029/2004WR003773
    • Ocampo C.J., Oldham C.E., and Sivapalan M. Nitrate attenuation in agricultural catchments: shifting balances between transport and reaction. Water Resour Res 42 (2006) W01408 10.1029/2004WR003773
    • (2006) Water Resour Res , vol.42
    • Ocampo, C.J.1    Oldham, C.E.2    Sivapalan, M.3
  • 48
    • 0034880872 scopus 로고    scopus 로고
    • Nonequilibrium cadmium leaching in layered sandy soils
    • Seuntjens P., Mallants D., Cornelis C., and Geuzens P. Nonequilibrium cadmium leaching in layered sandy soils. Soil Sci 166 (2001) 507-519
    • (2001) Soil Sci , vol.166 , pp. 507-519
    • Seuntjens, P.1    Mallants, D.2    Cornelis, C.3    Geuzens, P.4
  • 49
    • 0026114698 scopus 로고
    • Laboratory diffusion testing for waste disposal - a review
    • Shackelford C.D. Laboratory diffusion testing for waste disposal - a review. J Contam Hydrol 7 (1991) 177-217
    • (1991) J Contam Hydrol , vol.7 , pp. 177-217
    • Shackelford, C.D.1
  • 51
    • 0020414465 scopus 로고
    • Gaseous diffusion equations for porous materials
    • Troeh F.R., Jabro J.D., and Kirkham D. Gaseous diffusion equations for porous materials. Geoderma 27 (1982) 239-253
    • (1982) Geoderma , vol.27 , pp. 239-253
    • Troeh, F.R.1    Jabro, J.D.2    Kirkham, D.3
  • 53
    • 0030620122 scopus 로고    scopus 로고
    • An analytical model for nonlinear adsorptive transport through layered soils
    • Wu Y.S., Kool J.B., and Huyakorn P.S. An analytical model for nonlinear adsorptive transport through layered soils. Water Resour Res 33 (1997) 21-29
    • (1997) Water Resour Res , vol.33 , pp. 21-29
    • Wu, Y.S.1    Kool, J.B.2    Huyakorn, P.S.3
  • 54
    • 0027040922 scopus 로고
    • An analytical solution for one-dimensional transport in porous media with an exponential dispersion function
    • Yates S.R. An analytical solution for one-dimensional transport in porous media with an exponential dispersion function. Water Resour Res 28 (1992) 2149-2154
    • (1992) Water Resour Res , vol.28 , pp. 2149-2154
    • Yates, S.R.1
  • 55
    • 0033854229 scopus 로고    scopus 로고
    • Analytical solutions for the transport of volatile organic chemicals in unsaturated layered systems
    • Yates S.R., Papiernik S.K., Gao F., and Gan J. Analytical solutions for the transport of volatile organic chemicals in unsaturated layered systems. Water Resour Res 36 (2000) 1993-2000
    • (2000) Water Resour Res , vol.36 , pp. 1993-2000
    • Yates, S.R.1    Papiernik, S.K.2    Gao, F.3    Gan, J.4
  • 56
    • 37049039212 scopus 로고    scopus 로고
    • Solute transport in layered soils: nonlinear and kinetic reactivity
    • Zhou L., and Selim H.M. Solute transport in layered soils: nonlinear and kinetic reactivity. Soil Sci Soc Am J 65 (2001) 1056-1064
    • (2001) Soil Sci Soc Am J , vol.65 , pp. 1056-1064
    • Zhou, L.1    Selim, H.M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.