Skip to main content
Erschienen in: Geotechnical and Geological Engineering 6/2015

28.08.2015 | Original paper

Modeling Bromide Transport in Undisturbed Soil Columns with the Continuous Time Random Walk

verfasst von: Shahram Shahmohammadi-Kalalagh, Hossein Beyrami

Erschienen in: Geotechnical and Geological Engineering | Ausgabe 6/2015

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Nowadays, mathematical models are commonly used as efficient tools in solute transport studies and management in porous media. In this paper, we evaluated the continuous time random walk (CTRW) theory for its capability to characterize bromide transport in one-dimensional saturated undisturbed clay loam and sandy loam soil columns (10 cm in diameter and 40 cm long). The transport process was also simulated by using the advection–dispersion equation (ADE) for comparison. The values of CTRW parameter, β, for clay loam and sandy loam soil columns were derived at 1.71 and 1.73, respectively. This indicated that the bromide transport behavior within the clay loam and sandy loam soil columns was anomalous transport or non-Fickian transport and CTRW model was more suitable for simulation of bromide transport through undisturbed clay loam and sandy soil columns compared to ADE model with Fickian diffusion law basis. The graphical and statistical analysis confirmed the efficiency of CTRW model for simulation of bromide transport.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
Zurück zum Zitat Benson DA (1998) The fractional advection–dispersion equation: development and application. Dissertation, University of Nevada Reno Benson DA (1998) The fractional advection–dispersion equation: development and application. Dissertation, University of Nevada Reno
Zurück zum Zitat Benson DA, Wheatcraft SW, Meerschaert MM (2000) Application of a fractional advection–dispersion equation. Water Resour Res 36(6):1403–1412CrossRef Benson DA, Wheatcraft SW, Meerschaert MM (2000) Application of a fractional advection–dispersion equation. Water Resour Res 36(6):1403–1412CrossRef
Zurück zum Zitat Berkowitz B, Scher H (1995) On characterization of anomalous dispersion in porous and fractured media. Water Resour Res 31(6):1461–1466CrossRef Berkowitz B, Scher H (1995) On characterization of anomalous dispersion in porous and fractured media. Water Resour Res 31(6):1461–1466CrossRef
Zurück zum Zitat Berkowitz B, Scher H (1997) Anomalous transport in random fracture networks. Phys Rev Let 79(20):4038–4041CrossRef Berkowitz B, Scher H (1997) Anomalous transport in random fracture networks. Phys Rev Let 79(20):4038–4041CrossRef
Zurück zum Zitat Berkowitz B, Scher H (1998) Theory of anomalous chemical transport in fracture networks. Phys Rev E 57(5):5858–5869CrossRef Berkowitz B, Scher H (1998) Theory of anomalous chemical transport in fracture networks. Phys Rev E 57(5):5858–5869CrossRef
Zurück zum Zitat Berkowitz B, Scher H (2001) The role of probabilistic approaches to transport theory in heterogeneous media. Trans Porous Media 42:241–263CrossRef Berkowitz B, Scher H (2001) The role of probabilistic approaches to transport theory in heterogeneous media. Trans Porous Media 42:241–263CrossRef
Zurück zum Zitat Berkowitz B, Scher H (2008) Exploring the nature of non-Fickian transport in laboratory experiments. Adv Water Resour 32(5):750–755CrossRef Berkowitz B, Scher H (2008) Exploring the nature of non-Fickian transport in laboratory experiments. Adv Water Resour 32(5):750–755CrossRef
Zurück zum Zitat Berkowitz B, Scher H, Silliman SE (2000) Anomalous transport in laboratoryscale, heterogeneous porous media. Water Resour Res 36(1):149–158CrossRef Berkowitz B, Scher H, Silliman SE (2000) Anomalous transport in laboratoryscale, heterogeneous porous media. Water Resour Res 36(1):149–158CrossRef
Zurück zum Zitat Berkowitz B, Kosakowski G, Margolin G, Scher H (2001) Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media. Ground Water 39(4):593–604CrossRef Berkowitz B, Kosakowski G, Margolin G, Scher H (2001) Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media. Ground Water 39(4):593–604CrossRef
Zurück zum Zitat Berkowitz B, Klafter J, Metzler R, Scher H (2002) Physical pictures of transport in heterogeneous media: advection–dispersion, random-walk, and fractional derivative formulations. Water Resour Res 38:1191. doi:10.1029/R001030 CrossRef Berkowitz B, Klafter J, Metzler R, Scher H (2002) Physical pictures of transport in heterogeneous media: advection–dispersion, random-walk, and fractional derivative formulations. Water Resour Res 38:1191. doi:10.​1029/​R001030 CrossRef
Zurück zum Zitat Cherubini C (2008) A modeling approach for the study of contamination in a fractured aquifer. Geotech Geol Eng 26(5):519–533CrossRef Cherubini C (2008) A modeling approach for the study of contamination in a fractured aquifer. Geotech Geol Eng 26(5):519–533CrossRef
Zurück zum Zitat Cortis A, Berkowitz B (2004) Anomalous transport in ‘‘classical” soil and sand columns. Soil Sci Soc Am J 68:1539–1548CrossRef Cortis A, Berkowitz B (2004) Anomalous transport in ‘‘classical” soil and sand columns. Soil Sci Soc Am J 68:1539–1548CrossRef
Zurück zum Zitat Cortis A, Berkowitz B (2005) Computing “anomalous” contaminant transport in porous media: the CTRW MATLAB toolbox. Ground Water 43(6):947–950CrossRef Cortis A, Berkowitz B (2005) Computing “anomalous” contaminant transport in porous media: the CTRW MATLAB toolbox. Ground Water 43(6):947–950CrossRef
Zurück zum Zitat Cortis A, Harter T, Hou L, Atwill ER, Packman AI, Green PG (2006) Transport of Cryptosporidium parvum in porous media: long-term elution experiments and continuous time random walk filtration modeling. Water Resour Res 42:W12S13. doi:10.1029/2006WR004897 Cortis A, Harter T, Hou L, Atwill ER, Packman AI, Green PG (2006) Transport of Cryptosporidium parvum in porous media: long-term elution experiments and continuous time random walk filtration modeling. Water Resour Res 42:W12S13. doi:10.​1029/​2006WR004897
Zurück zum Zitat Dagan G (1988) Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water Resour Res 24(9):1491–1500CrossRef Dagan G (1988) Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers. Water Resour Res 24(9):1491–1500CrossRef
Zurück zum Zitat Dagan G (1989) Flow and Transport in Porous Formations. Springer, Berlin. ISBN 978-3-540-51098-7CrossRef Dagan G (1989) Flow and Transport in Porous Formations. Springer, Berlin. ISBN 978-3-540-51098-7CrossRef
Zurück zum Zitat Dai Z, Wolfsberg A, Lu Z, Ritzi R (2007) Representing aquifer architecture in macrodispersivity models with an analytical solution of the transition probability matrix. Geophys Res Lett 34:L20406. doi:10.1029/2007GL031608 CrossRef Dai Z, Wolfsberg A, Lu Z, Ritzi R (2007) Representing aquifer architecture in macrodispersivity models with an analytical solution of the transition probability matrix. Geophys Res Lett 34:L20406. doi:10.​1029/​2007GL031608 CrossRef
Zurück zum Zitat Dentz M, Cortis A, Scher H, Berkowitz B (2004) Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport. Adv Water Resour 27(2):155–173CrossRef Dentz M, Cortis A, Scher H, Berkowitz B (2004) Time behavior of solute transport in heterogeneous media: transition from anomalous to normal transport. Adv Water Resour 27(2):155–173CrossRef
Zurück zum Zitat Ersahin S, Papendick RI, Smith JL, Keller CK, Manoranjan VS (2002) Macropore transport of bromide as influenced by soil structure differences. Geoderma 108:207–223CrossRef Ersahin S, Papendick RI, Smith JL, Keller CK, Manoranjan VS (2002) Macropore transport of bromide as influenced by soil structure differences. Geoderma 108:207–223CrossRef
Zurück zum Zitat Estabragh AR, Pereshkafti MRS, Javadi AA (2013) Comparison between analytical and numerical methods in evaluating the pollution transport in porous media. Geotech Geol Eng 31(1):93–101CrossRef Estabragh AR, Pereshkafti MRS, Javadi AA (2013) Comparison between analytical and numerical methods in evaluating the pollution transport in porous media. Geotech Geol Eng 31(1):93–101CrossRef
Zurück zum Zitat Estabragh AR, Pereshkafti MRS, Javadi AA (2014) Numerical analysis of advection-dominated contaminant transport in saturated porous media. Eur J Environ Civ En 18(5):536–549CrossRef Estabragh AR, Pereshkafti MRS, Javadi AA (2014) Numerical analysis of advection-dominated contaminant transport in saturated porous media. Eur J Environ Civ En 18(5):536–549CrossRef
Zurück zum Zitat Gao G, Zhan H, Feng S, Huang G, Mao X (2009) Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column. J Contam Hydrol 377:391–404CrossRef Gao G, Zhan H, Feng S, Huang G, Mao X (2009) Comparison of alternative models for simulating anomalous solute transport in a large heterogeneous soil column. J Contam Hydrol 377:391–404CrossRef
Zurück zum Zitat Gelhar LW (1993) Stochastic Subsurface Hydrology. Prentice-Hall, Englewood Cliffs Gelhar LW (1993) Stochastic Subsurface Hydrology. Prentice-Hall, Englewood Cliffs
Zurück zum Zitat Gelhar LW, Welty C, Rehfeldt KR (1992) A critical review of data on field scale disppersion in aquifers. Water Resour Res 28(7):1955–1974CrossRef Gelhar LW, Welty C, Rehfeldt KR (1992) A critical review of data on field scale disppersion in aquifers. Water Resour Res 28(7):1955–1974CrossRef
Zurück zum Zitat Khan AUH, Jury WA (1990) Alaboratory test of the dispersion scale effect. J Contam Hydrol 5:119–132CrossRef Khan AUH, Jury WA (1990) Alaboratory test of the dispersion scale effect. J Contam Hydrol 5:119–132CrossRef
Zurück zum Zitat Lee J, Horton R, Noborio K, Jaynes DB (2001) Characterization of preferential flow in undisturbed structured soil columns using a vertical TDR probe. J Contam Hydrol 51:131–144CrossRef Lee J, Horton R, Noborio K, Jaynes DB (2001) Characterization of preferential flow in undisturbed structured soil columns using a vertical TDR probe. J Contam Hydrol 51:131–144CrossRef
Zurück zum Zitat Levy M, Berkowitz B (2003) Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 64:203–226CrossRef Levy M, Berkowitz B (2003) Measurement and analysis of non-Fickian dispersion in heterogeneous porous media. J Contam Hydrol 64:203–226CrossRef
Zurück zum Zitat Li N, Ren L (2009) Application of continuous time random walk theory to non-equilibrium transport in soil. J Contam Hydrol 108(3):134–151CrossRef Li N, Ren L (2009) Application of continuous time random walk theory to non-equilibrium transport in soil. J Contam Hydrol 108(3):134–151CrossRef
Zurück zum Zitat Montroll EW, Scher H (1973) Randomwalks on lattices, IV, Continuous-time walks and influence of adsorbing boundaries. J Stat Phys 9:101–135CrossRef Montroll EW, Scher H (1973) Randomwalks on lattices, IV, Continuous-time walks and influence of adsorbing boundaries. J Stat Phys 9:101–135CrossRef
Zurück zum Zitat Montroll EW, Weiss GH (1965) Random walks on lattices. II. J Math Phys 6:167–183CrossRef Montroll EW, Weiss GH (1965) Random walks on lattices. II. J Math Phys 6:167–183CrossRef
Zurück zum Zitat Mörters P, Peres Y (2010) Brownian motion, vol 30. Cambridge University Press, Cambridge, p 357CrossRef Mörters P, Peres Y (2010) Brownian motion, vol 30. Cambridge University Press, Cambridge, p 357CrossRef
Zurück zum Zitat Pachepsky Y, Benon D, Rawls W (2000) Simulating scale-dependent solute transport in soils with the fractional advective–dispersive equation. Soil Sci Soc Am J 64(3):1234–1243CrossRef Pachepsky Y, Benon D, Rawls W (2000) Simulating scale-dependent solute transport in soils with the fractional advective–dispersive equation. Soil Sci Soc Am J 64(3):1234–1243CrossRef
Zurück zum Zitat Pickens JF, Grisak GE (1981a) Scale-dependent dispersion in a stratified granular aquifer. Water Resour Res 17(4):1191–1211CrossRef Pickens JF, Grisak GE (1981a) Scale-dependent dispersion in a stratified granular aquifer. Water Resour Res 17(4):1191–1211CrossRef
Zurück zum Zitat Pickens JF, Grisak GE (1981b) Modeling of scale-dependent dispersion in hydrogeologic systems. Water Resour Res 17(6):1701–1711CrossRef Pickens JF, Grisak GE (1981b) Modeling of scale-dependent dispersion in hydrogeologic systems. Water Resour Res 17(6):1701–1711CrossRef
Zurück zum Zitat Scher H, Lax M (1973) Stochastic transport in a disordered solid: I. Theory. Phys Rev B 7(10):4491–4502CrossRef Scher H, Lax M (1973) Stochastic transport in a disordered solid: I. Theory. Phys Rev B 7(10):4491–4502CrossRef
Zurück zum Zitat Scher H, Montroll EW (1975) Anomalous transit-time dispersion in amorphous solids. Phys Rev B 12(6):2455–2477CrossRef Scher H, Montroll EW (1975) Anomalous transit-time dispersion in amorphous solids. Phys Rev B 12(6):2455–2477CrossRef
Zurück zum Zitat Soltanian MR, Ritzi RW, Dai Z, Huang CC, Dominic D (2014) Transport of kinetically sorbing solutes in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales. Stochastic Environ Res Risk Asses. 29(3):709–726CrossRef Soltanian MR, Ritzi RW, Dai Z, Huang CC, Dominic D (2014) Transport of kinetically sorbing solutes in heterogeneous sediments with multimodal conductivity and hierarchical organization across scales. Stochastic Environ Res Risk Asses. 29(3):709–726CrossRef
Zurück zum Zitat Soltanian MR, Ritzi RW, Dai Z, Huang CC (2015a) Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: the Lagrangian approach. Chemosphere 122:235–244CrossRef Soltanian MR, Ritzi RW, Dai Z, Huang CC (2015a) Reactive solute transport in physically and chemically heterogeneous porous media with multimodal reactive mineral facies: the Lagrangian approach. Chemosphere 122:235–244CrossRef
Zurück zum Zitat Soltanian MR, Ritzi RW, Huang CC, Dai Z (2015b) Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 2. Particle displacement variance. Water Resources Research 51(3):1601–1618CrossRef Soltanian MR, Ritzi RW, Huang CC, Dai Z (2015b) Relating reactive solute transport to hierarchical and multiscale sedimentary architecture in a Lagrangian-based transport model: 2. Particle displacement variance. Water Resources Research 51(3):1601–1618CrossRef
Zurück zum Zitat Sudicky EA, Cherry JA (1979) Field observations of tracer dispersion under natural flow conditions in an unconfined sandy aquifer. Water Pollut Res Can 14:1–17 Sudicky EA, Cherry JA (1979) Field observations of tracer dispersion under natural flow conditions in an unconfined sandy aquifer. Water Pollut Res Can 14:1–17
Zurück zum Zitat Toride N, Leij F, van Genuchten MTh (1999) The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. Version 2.1, Research Rep. 137. US Salinity Lab, Riverside, CA, USA Toride N, Leij F, van Genuchten MTh (1999) The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments. Version 2.1, Research Rep. 137. US Salinity Lab, Riverside, CA, USA
Zurück zum Zitat Xiong Y, Huang G, Huang Q (2006) Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk. J Contam Hydrol 86:163–175CrossRef Xiong Y, Huang G, Huang Q (2006) Modeling solute transport in one-dimensional homogeneous and heterogeneous soil columns with continuous time random walk. J Contam Hydrol 86:163–175CrossRef
Metadaten
Titel
Modeling Bromide Transport in Undisturbed Soil Columns with the Continuous Time Random Walk
verfasst von
Shahram Shahmohammadi-Kalalagh
Hossein Beyrami
Publikationsdatum
28.08.2015
Verlag
Springer International Publishing
Erschienen in
Geotechnical and Geological Engineering / Ausgabe 6/2015
Print ISSN: 0960-3182
Elektronische ISSN: 1573-1529
DOI
https://doi.org/10.1007/s10706-015-9917-1

Weitere Artikel der Ausgabe 6/2015

Geotechnical and Geological Engineering 6/2015 Zur Ausgabe