Continuous time random walks for analyzing the transport of a passive tracer in a single fissure

Water Resources Research

Volumn 41, Issue 4, 2005, Pages 1-5

  Jimenez Hornero F J ^a   Giraldez J V ^a,c   Laguna, A ^a   Pachepsky, Y ^b  

^a UNIVERSITY OF CÓRDOBA   (Spain)

^b AGRICULTURAL RESEARCH SERVICE   (United States)

^c INSTITUTO DE AGRICULTURA SOSTENIBLE   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; COMPUTER SIMULATION; IMPURITIES; MATHEMATICAL MODELS; PROBABILITY; RANDOM PROCESSES;

ADVECTION DISPERSION EQUATION (ADE) MODEL; CONTAMINATED TRANSPORT; CONTINOUS TIME RANDOM WALKS (CTRW); FISSURES;

HYDROLOGY;

BREAKTHROUGH CURVE; FRACTURED MEDIUM; GROUNDWATER FLOW; POLLUTANT TRANSPORT; TRACER;

EID: 19044388035     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2004WR003852     Document Type: Article

References (23)

1. Benson, D. A., S. W. Wheatcraft, and M. M. Meerschaert (2000), Application of a fractional advection-dispersion equation, Water Resour. Res., 36, 1403-1412.
2. Berkowitz, B. (2002), Characterizing flow and transport in fractured geological media: A review, Adv. Water Resour., 25, 861-884.
3. Berkowitz, B., and H. Scher (1995), On characterization of anomalous dispersion in porous and fractured media, Water Resour. Res., 31, 1461-1466.
4. Berkowitz, B., and H. Scher (1997), Anomalous transport in random fracture networks, Phys. Rev. Lett., 79, 4031-4038.
5. Berkowitz, B., and H. Scher (1998), Theory of anomalous chemical transport in random fracture networks, Phys. Rev. E., 57, 5858-5869.
6. Berkowitz, B., H. Scher, and S. E. Silliman (2000), Anomalous transport in laboratory scale, heterogeneous porous media, Water Resour. Res., 36, 149-158. (Correction, Water Resour. Res., 36, 1371, 2000).
7. Berkowitz, B., G. Kosakowski, G. Margolin, and H. Scher (2001), Application of continuous time random walk theory to tracer test measurements in fractured and heterogeneous porous media, Ground Water, 39, 593-604.
8. Berkowitz, B., J. Klafter, R. Metzler, and H. Scher (2002), Physical pictures of transport in heterogeneous media: Advection-dispersion, random-walk, and fractional derivative formulations, Water Resour. Res., 38, 1191, doi:10.1029/2001WR001030.
9. Bromly, M., and C. Hinz (2004), Non-Fickian transport in homogeneous unsaturated repacked sand, Water Resour. Res., 40, W07402, doi:10.1029/ 2003WR002579.
10. Cortis, A., and B. Berkowitz (2004), Anomalous transport in "classical" soil and sand columns, Soil Sci. Soc. Am. J., 68, 1539-1548.
11. Cortis, A., and B. Berkowitz (2005), Computing "anomalous" contaminant transport in porous media: The CTRW Matlab toolbox, Ground Water, in press.
12. Cortis, A., C. Gallo, H. Scher, and B. Berkowitz (2004), Numerical simulation of non-Fickian transport in geological formations with multiple-scale heterogeneities, Water Resour. Res., 40, W04209, doi:10.1029/2003WR002750.
13. Dentz, M., A. Cortis, H. Scher, and B. Berkowitz (2004), Time behavior of solute transport in heterogeneous media: Transition from anomalous to normal transport, Adv. Water Resour., 27, 155-173.
14. Gelhar, L., C. Welty, and K. R. Rehfeldt (1992), A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28, 1955-1974.
15. Legates, D. R., and G. J. McCabe (1999), Evaluating the use of "goodness-of-fit" measures in hydrologic and hydroclimatic model validation, Water Resour. Res., 35, 233-241.
16. Levy, M., and B. Berkowitz (2003), Measurement and analysis of non-Fickian dispersion in heterogeneous porous media, J. Contam. Hydrol., 64, 203-226.
17. Margolin, G., and B. Berkowitz (2000), Application of continuous time random walks to transport in porous media, J. Phys. Chem. B, 104, 3942-3947. (Correction, J. Phys. Chem. B, 104, 8762, 2000).
18. Margolin, G., and B. Berkowitz (2004), Continuous time random walks revisited: First passage time and spatial distributions, Physica A, 334, 46-66.
19. Mezltler, R., and J. Klafter (2000), The random walk's guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep., 339, 1-77.
20. Mezltler, R., and J. Klafter (2004), The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A, 37, 161-208.
21. Moreno, L., I. Neretnieks, and T. Eriksen (1985), Analysis of some laboratory tracer runs in natural fissures, Water Resour. Res., 21, 951-958.
22. Neretnieks, I., T. Eriksen, and P. Tähtinen (1982), Tracer movement in a single fissure in granitic rock: Some experimental results and their interpretation, Water Resour. Res., 18, 849-858.
23. Pachepsky, Y., D. A. Benson, and W. Rawls (2000), Simulating scale-dependent solute transport in soils with the fractional advective dispersive equation, Soil Sci. Soc. Am. J., 64, 1234-1243.