Impact of permeable conduits on solute transport in aquitards: Mathematical models and their application

Water Resources Research

Volumn 43, Issue 5, 2007, Pages

  Harrington, Glenn A ^a,b   Hendry, M Jim ^b   Robinson, Neville I ^c  

^a Department of Water Land and Biodiversity Conservation ^*  (Australia)

^b UNIVERSITY OF SASKATCHEWAN   (Canada)

^c FLINDERS UNIVERSITY   (Australia)

Author keywords

[No Author keywords available]

Indexed keywords

AQUIFERS; COMPUTER SIMULATION; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; SORPTION;

PARALLEL-PLATE MODEL; POROUS CONDUITS; ROCK AQUIFERS;

SOLUTE TRANSPORT;

AQUIFERS; COMPUTER SIMULATION; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; SOLUTE TRANSPORT; SORPTION;

AQUIFER; AQUITARD; CHLORIDE; DIFFUSION; FLOW MODELING; GROUNDWATER FLOW; NUMERICAL MODEL; PERMEABILITY; POLLUTANT TRANSPORT; POREWATER; POROUS MEDIUM; SOLUTE TRANSPORT;

CANADA; NORTH AMERICA; SASKATCHEWAN;

EID: 34347245963     PISSN: 00431397     EISSN: None     Source Type: Journal    
DOI: 10.1029/2005WR004144     Document Type: Article

References (53)

1. Abramowitz, M., and I. A. Stegun (1965), Handbook of Mathematical Functions, pp. 1046, Dover, Mineola, N. Y.
2. Blanch, G., and D. S. Clemm (1969), The double points of Mathieu's differential equation, Math. Comput., 23, 97-108.
3. Boldt-Leppin, B. E. J., and M. J. Hendry (2003), Application of harmonic analysis of water levels to determine vertical hydraulic conductivities in clay-rich aquitards, Ground Water, 41(4), 514-522.
4. Carslaw, H. S., and J. C. Jaeger (1959), Conduction of Heat in Solids, pp. 510, Oxford Univ. Press, New York.
5. Chaos-Caldor, L., and E. Ley-Koo (2002), Matrix evaluation revisited: Matrix evaluation and generating functions, Rev. Mex. Fis., 48(1), 67-75.
6. Christiansen, E. A. (1971), Tills in southern Saskatchewan, Canada, in Till: A symposium, edited by R. P. Goldthwait, pp. 402, Ohio State Univ. Press, Columbus.
7. Christiansen, E. A. (1986), Geology of Luck Lake irrigation project, Rep. 0114-002, Sask. Water Corp., Moose Jaw, Saskachewan, Can.
8. deHoog, F. R., J. M. Knight, and A. N. Stokes (1982), An improved method for the Laplace inversion problem, SLAM J. Stat. Comput, 3, 357-366.
9. Fetter, C. W. (1999), Contaminant Hydrogeology, 500 pp., Prentice-Hall, Upper Saddle River, N. J.
10. Gelhar, L. W., C. Welty, and K. R. Rehfeldt (1992), A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28(7), 1955-1974.
11. Gerber, R. E., J. I. Boyce, and K. W. F. Howard (2001), Evaluation of heterogeneity and field-scale groundwater flow regime in a leaky till aquitard, Hydrogeol. J., 9, 60-78.
12. Grisak, G. E., and J. F. Pickens (1980), Solute transport through fractured media. 1: The effect of matrix diffusion, Water Resour. Res., 16(4), 719-730.
13. Harrington, G. A., and M. J. Hendry (2005), Chemical heterogeneity in diffusion-dominated aquitards, Water Resour. Res., 41(12), W12432, doi:10.1029/2004WR003928.
14. Harrington, G. A., and M. J. Hendry (2006), Using direct-push EC logging to delineate heterogeneity in a clay-rich aquitard, Ground Water Monit. Rem., 26(1), 92-100.
15. Harrison, B., E. A. Sudicky, and J. A. Cherry (1992), Numerical-analysis of solute migration through fractured clayey deposits into underlying aquifers, Water Resour. Res., 28(2), 515-526.
16. Hazen, A. (1892), Some Physical Properties of Sand and Gravels, pp. 539-556, Mass. State Board of Health, Ann. Rep.
17. Hendry, M. J. (1982), Hydraulic conductivity of a glacial till in Alberta, Ground Water, 20(2), 162-169.
18. Hendry, M. J., and L. I. Wassenaar (1999), Implications of the distribution of δD in pore waters for groundwater flow and the timing of geologic events in a thick aquitard system, Water Resour. Res., 35(6), 1751-1760.
19. Hendry, M. J., and L. I. Wassenaar (2000), Controls on the distribution of major ions in pore waters of a thick surficial aquitard, Water Resour. Res., 36(2), 503-513.
20. Hendry, M. J., and L. I. Wassenaar (2005), Origin and migration of dissolved organic carbon fractions in a clay-rich aquitard: 14C and δ13C evidence, Water Resour., 41.
21. Hendry, M. J., L. I. Wassenaar, and T. Kotzer (2000), Chloride and chlorine isotopes (36Cl and δ37Cl) as tracers of solute migration in a thick, clay-rich aquitard system, Water Resour. Res., 36(1), 285-296.
22. Hendry, M. J., C. J. Kelln, L. I. Wassenaar, and J. Shaw (2004), Characterizing the hydrogeology of a complex clay-rich aquitard system using detailed vertical profiles of the stable isotopes of water, J. Hydrol., 293, 47-56.
23. Hvorslev, M. J. (1951), Time lag and soil permeability in ground-water observations, Bull. No. 36, pp. 1-50, U.S. Army Corps, Vicksburg, Mississippi.
24. Jørgensen, P. R., L. D. McKay, and J. P Kistrup (2004), Aquifer vulnerability to pesticide migration through till aquitards, Ground Water, 42(6), 841-855.
25. Kucuk, F., and W. E. Brigham (1979), Transient flow in elliptical systems, SPE J., 401-410.
26. Lever, D. A., and M. H. Bradbury (1985), Rock-matrix diffusion and its implications for radionuclide migration, Mineral. Mag., 49, 245-254.
27. Maloszewski, P., and A. Zuber (1985), On the theory of tracer experiments in fissured rocks with a porous matrix, J. Hydrol., 79(3-4), 333-358.
28. Maloszewski, P., and A. Zuber (1990), Mathematical modeling of tracer behavior in short-term experiments in fissured rocks, Water Resour. Res., 26(7), 1517-1528.
29. Maloszewski, P., and A. Zuber (1991), Influence of matrix diffusion and exchange reactions on radiocarbon ages in fissured carbonate aquifers, Water Resour. Res., 27(8), 1937-1945.
30. McKay, L. D., R. W. Gillham, and J. A. Cherry (1993), Field experiments in a fractured clay till. 2: Solute and colloid transport, Water Resour. Res., 29(12), 3879-3890.
31. McLachlan, N. W. (1947), Theory and Application of Mathieu Functions, 401 pp., Clarendon, Oxford, U.K.
32. Neretnieks, I. (1980), Diffusion in the rock matrix: An important factor in radionuclide retardation?, J. Geophys. Res., 85(B8), 4379-4397.
33. Neretnieks, I. (1981), Age dating of groundwater in fissured rock: influence of water volume in micropores, Water Resour. Res., 17(2), 421-422.
34. Obut, S. T., and T. Ertigen (1987), A composite system solution in elliptic flow geometry, SPE Form. Eval., 227-236, Sept.
35. Piessens, R., and R. Huysmans (1984), Algorithm 619: Automatic numerical inversion of the Laplace transform, Trans. Math. Software, 10, 348-353.
36. Robinson, P. C., and P. R. Maul (1991), Some experience with the numerical inversion of Laplace transforms, Math. Eng. Ind., 3, 111-131.
37. Robinson, N. I., and J. M. Sharp Jr. (1997), Analytical solution for contaminant transport in a finite set of parallel fractures with matrix diffusion, CSIRO Mathematical and Information Sciences Report CMIS-C23, Commonwealth Scientific and Industrial Research Organisation, Adelaide.
38. Robinson, N. I., J. M. Sharp Jr., and I. Kriesel (1998), Contaminant transport in sets of parallel fractures with fracture skins, J. Contam. Hydrol., 31, 83-109.
39. Shaw, J. (1997), Hydrogeology of a thick clay-rich till and Cretaceous bed-rock clay sequence in Saskatchewan, Canada, M. Sc. thesis, University of Saskatchewan.
40. Shaw, R. J., and M. J. Hendry (1998), Hydrogeology of a thick clay till and Cretaceous clay sequence. Saskatoon, Saskatchewan, Canada, Can. Geotech. J., 35, 1041-1052.
41. Smith, B. T., J. M. Boyle, J. J. Dongarra, B. S. Garbow, Y. Ikebe, V. C. Klema, and C. B. Moler (1976), Matrix eigensystem routines-EISPACK guide, Lecture Notes in Computer Science, vol. 6, Springer, New York.
42. Spath, J. B., and R. K. M. Thambynayagam (1997), Well test solutions for vertically fractured injection wells, Transp. Porous Media, 29, 27-45.
43. Stammes, J. J., and B. Spjelkavik (1995), New method for computing eigenfunctions (Mathieu functions) for scattering by elliptic cylinders, Pure Appl. Opt., 4, 251-262.
44. Stanislav, J. F., C. V. Easwaran, and S. L. Kokal (1987), Analytical solutions for vertical fractures in a composite system, J. Can. Petrol. Technol., 26(5), 51-56.
45. Stanislav, J. F., C. V. Easwaran, and S. L. Kokal (1992), Elliptical flow in composite reservoirs, J. Can. Petrol. Technol., 31(10), 47-50.
46. Sudicky, E. A., and E. O. Frind (1981), Carbon 14 dating of groundwater in confined aquifers: Implications of aquitard diffusion, Water Resour. Res., 17(4), 1060-1064.
47. Sudicky, E. A., and E. O. Frind (1982), Contaminant transport in fractured porous media: analytical solutions for a system of parallel factures, Water Resour. Res., 18(6), 1634-1642.
48. Talbot, A. (1979), The accurate numerical inversion of Laplace transforms, J. Inst. Math. Appl., 23, 97-120.
49. Tang, D. H., E. O. Frind, and E. A. Sudicky (1981), Contaminant transport in fractured porous media: Analytical solution for a single fracture, Water Resour. Res., 17(3), 555-564, Errata: Davis, G. B. and C. D. Johnston (1984), Water Resour. Res., 20, 1321-1322.
50. Vega, J. C. G. (2003), Theory and Numerical Analysis of the Mathieu Functions, http://homepages.mty.itesm.mx/jgutierr (accessed August 25, 2006).
51. 11B systematics of a thick clay-rich aquitard system, Water Resour. Res., 37(5), 1437-1444.
52. Wassenaar, L. I., and M. J. Hendry (2000), Mechanisms controlling the distribution and transport of 14C in a clay-rich till aquitard, Ground Water, 38(3), 343-349.
53. Yan, X.-P., R. Kerrich, and M. J. Hendry (2001), Distribution of the rare earth elements in porewaters from a clay-rich aquitard sequence. Saskatchewan, Canada, Chem. Geol., 176, 151-172.