Skip to main content
Top

2015 | OriginalPaper | Chapter

6. Random Walk Particle Tracking

Authors : Yuanyuan Sun, Chan-Hee Park, Geraldine Pichot, Joshua Taron

Published in: Thermo-Hydro-Mechanical-Chemical Processes in Fractured Porous Media: Modelling and Benchmarking

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The classical advection-dispersion equation of a conservative solute in porous media can be written as [1]

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference J. Bear. Hydraulics of groundwater. McGraw-Hill, New York, 1979. J. Bear. Hydraulics of groundwater. McGraw-Hill, New York, 1979.
2.
go back to reference K. Ito. On stochastical differential equations. American Mathematical Society, 4:289–302, 1951. K. Ito. On stochastical differential equations. American Mathematical Society, 4:289–302, 1951.
3.
go back to reference W. Kinzelbach. Groundwater Modelling. Elsevier, Amsterdam, 1986. W. Kinzelbach. Groundwater Modelling. Elsevier, Amsterdam, 1986.
4.
go back to reference A.F.B. Tompson and L.W. Gelhar. Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media. Water Resour. Res., 26(10):2541–2562, 1990. A.F.B. Tompson and L.W. Gelhar. Numerical simulation of solute transport in three-dimensional, randomly heterogeneous porous media. Water Resour. Res., 26(10):2541–2562, 1990.
5.
go back to reference E.M. LaBolle, G.E. Fogg, and A.F.B. Tompson. Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods. Water Resour. Res., 32(3):583–593, 1996. E.M. LaBolle, G.E. Fogg, and A.F.B. Tompson. Random-walk simulation of transport in heterogeneous porous media: Local mass-conservation problem and implementation methods. Water Resour. Res., 32(3):583–593, 1996.
6.
go back to reference W. Kinzelbach. The random-walk method in pollutant transport simulation. NATO ASI Ser, Ser. (C224):227–246, 1988. W. Kinzelbach. The random-walk method in pollutant transport simulation. NATO ASI Ser, Ser. (C224):227–246, 1988.
7.
go back to reference H. Hoteit, R. Mose, A. Younes, F. Lehmann, and Ph. Ackerer. Three-dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random-walk methods. Mathe. Geology, 34(4):435–456, 2002. H. Hoteit, R. Mose, A. Younes, F. Lehmann, and Ph. Ackerer. Three-dimensional modeling of mass transfer in porous media using the mixed hybrid finite elements and the random-walk methods. Mathe. Geology, 34(4):435–456, 2002.
8.
go back to reference T. Harter and S. Wagner. Colloid transport and filtration of Cryptosporidium parvum in sandy soils and aquifer sediments. Environ. Sci. Technol., 34:62–70, 2000. T. Harter and S. Wagner. Colloid transport and filtration of Cryptosporidium parvum in sandy soils and aquifer sediments. Environ. Sci. Technol., 34:62–70, 2000.
9.
go back to reference M. van Genuchten. Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first order decay. Jour. of Hydrol., 49:213–233, 1981. M. van Genuchten. Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first order decay. Jour. of Hydrol., 49:213–233, 1981.
10.
go back to reference W.P. Johnson, K.A. Blue, and B.E. Logan. Modeling bacterial detachment during transport through porous media as a residence-time-dependent process. Water Resour. Res., 31:2649–2658, 1995. W.P. Johnson, K.A. Blue, and B.E. Logan. Modeling bacterial detachment during transport through porous media as a residence-time-dependent process. Water Resour. Res., 31:2649–2658, 1995.
11.
go back to reference A. Ogata and R.B. Banks. A solution of the differential equation of longitudinal dispersion in porous media. Technical report, USGS, Washington, D.C., 1961. A. Ogata and R.B. Banks. A solution of the differential equation of longitudinal dispersion in porous media. Technical report, USGS, Washington, D.C., 1961.
12.
go back to reference A.E. Hassan and M.M. Mohamed. On using particle tracking methods to simulate transport in single-continuum and dual continua porous media. Jour. of Hydrol., 275:242–260, 2003. A.E. Hassan and M.M. Mohamed. On using particle tracking methods to simulate transport in single-continuum and dual continua porous media. Jour. of Hydrol., 275:242–260, 2003.
13.
go back to reference S. Whitaker. Advances in theory of fluid motion in porous media. Ind. Eng. Chem., 61(12):14–28, 1969. S. Whitaker. Advances in theory of fluid motion in porous media. Ind. Eng. Chem., 61(12):14–28, 1969.
14.
go back to reference F.A.L. Dullien and M.I.S. Azzam. Flow rate - pressure gradient measurements in periodically nonuniform capillary tubes. A. I. Ch. E. J., 19:222–229, 1973. F.A.L. Dullien and M.I.S. Azzam. Flow rate - pressure gradient measurements in periodically nonuniform capillary tubes. A. I. Ch. E. J., 19:222–229, 1973.
15.
go back to reference P. Forchheimer. Wasserbewegung durch Boden. Zeitschrift des Vereines Deutscher Ingenieur, 1901. P. Forchheimer. Wasserbewegung durch Boden. Zeitschrift des Vereines Deutscher Ingenieur, 1901.
16.
go back to reference S. Ergun and A. A. Orning. Fluid flow through randomly packed columns and fluidized beds. Ind. & Engng. Chem., 41(6):1179–1184, 1949. S. Ergun and A. A. Orning. Fluid flow through randomly packed columns and fluidized beds. Ind. & Engng. Chem., 41(6):1179–1184, 1949.
17.
go back to reference T.H. Chilton and A.P. Colburn. Pressure drop in packed tubes. Ind. & Engng. Chem., 23(8):913–919, 1931. T.H. Chilton and A.P. Colburn. Pressure drop in packed tubes. Ind. & Engng. Chem., 23(8):913–919, 1931.
18.
go back to reference M. Balhoff, A. Mikelic, and M. Wheeler. Polynomial filtration laws for low reynolds number flows through porous media. Transport in Porous Media, 81:35–60, 2010. M. Balhoff, A. Mikelic, and M. Wheeler. Polynomial filtration laws for low reynolds number flows through porous media. Transport in Porous Media, 81:35–60, 2010.
19.
go back to reference D.W. Ruth and H. Ma. On the derivation of the forchheimer equation by means of the averaging theorem. Transport in Porous Media, 7:255–264, 1992. D.W. Ruth and H. Ma. On the derivation of the forchheimer equation by means of the averaging theorem. Transport in Porous Media, 7:255–264, 1992.
20.
go back to reference G.H. Fancher and J.A. Lewis. Flow of simple fluids through porous materials. Ind. & Engng. Chem., 25(10):1139–1147, 1933. G.H. Fancher and J.A. Lewis. Flow of simple fluids through porous materials. Ind. & Engng. Chem., 25(10):1139–1147, 1933.
21.
go back to reference L. Jr. Green and P. Duwez. Fluid flow through porous metals. J. Appl. Mech., pages 39–45, 1951. L. Jr. Green and P. Duwez. Fluid flow through porous metals. J. Appl. Mech., pages 39–45, 1951.
22.
go back to reference S. Ergun. Fluid flow through packed columns. Chem. Engng. Prog., 48(2):89–94, 1952. S. Ergun. Fluid flow through packed columns. Chem. Engng. Prog., 48(2):89–94, 1952.
23.
go back to reference S.M. Hassanizadeh and W.G. Gray. High velocity flow in porous media. Transport Porous Media, 2:521–531, 1987. S.M. Hassanizadeh and W.G. Gray. High velocity flow in porous media. Transport Porous Media, 2:521–531, 1987.
24.
go back to reference A.R. Piggott and D. Elsworth. Laboratory assessment of the equivalent apertures of a rock fracture. Geophysical Research Letters, 20(13):1387–1390, 1993. A.R. Piggott and D. Elsworth. Laboratory assessment of the equivalent apertures of a rock fracture. Geophysical Research Letters, 20(13):1387–1390, 1993.
Metadata
Title
Random Walk Particle Tracking
Authors
Yuanyuan Sun
Chan-Hee Park
Geraldine Pichot
Joshua Taron
Copyright Year
2015
DOI
https://doi.org/10.1007/978-3-319-11894-9_6