Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium

Advances in Water Resources

Volumn 21, Issue 4, 1998, Pages 297-313

  Liu, Chongxuan ^a   Ball, William P ^a  

^a Johns Hopkins University   (United States)

Author keywords

Analytical solutions; Aquitards; Clay; Contamination; Diffusion; Groundwater; Modeling; Porous media; Sediments; Sorption

Indexed keywords

BINOMIAL THEOREM; CRANK NICOLSON FINITE DIFFERENCE METHOD;

BOUNDARY CONDITIONS; CLAY; COMPUTATIONAL METHODS; CONTAMINATION; DECONTAMINATION; GREEN'S FUNCTION; GROUNDWATER POLLUTION; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; POROUS MATERIALS; SEDIMENTS; SORPTION;

DIFFUSION IN SOLIDS;

DIFFUSION; POLLUTION; POROUS MEDIUM; SOLUTE TRANSPORT;

AQUITARD; CONTAMINANT TRANSPORT; DIFFUSION; GROUNDWATER POLLUTION; POROUS MEDIUM;

EID: 0032054529     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(96)00062-0     Document Type: Article

References (40)

1. Ball, W. P. & Roberts, P. V., Diffusive rate limitations in the sorption of organic chemicals, In Organic Substances and Sediments in Water: Processes and Analytical, ed. R. A. Baker, Lewis Publishers: Chelsea, MI, 1991, Vol. 2, pp. 273-310.
2. Ball, W. P. & Roberts, P. V., Long-term sorption of halogenated organic chemicals - part 2. Intraparticle diffusion. Environmental Science and Technology, 25 (1991) 1237-1249.
3. Ball, W. P., Xia, G., Durfee, D. P., Wilson, R., Brown, M., & Mackay, D. M., Hot-methanol extraction for the analysis of volatile organic chemicals in subsurface samples from Dover AFB, DE. Submitted for publication in Groundwater Monitoring and Remediation, Winter (1997) 104-121.
4. Ball, W. P., Xia, G., Liu, C., Brown, M., & Mackay, D., Aquitard contamination from a groundwater plume - in situ concentrations as evidence of vertical diffusion. 1995 Spring Meeting, American Geophysical Union, Baltimore, MD, (1995), S135.
5. Barone, F. W., Rowe, R. K., & Quigley, R. M., A laboratory estimation of diffusion and adsorption coefficients for several volatile organics in a natural clayey soil. J. Contaminant Hydrology, 10 (1992) 225-250.
6. Bellman, R., Marshak, R. E., & Wing, G. M., Laplace transform solution of two-medium neutron aging problem. Philosophical Mag., 40 (1949) 297-308.
7. Burgener, M. L. & Reedy, R. E., Temperature distributions produced in a two-layer structure by a scanning CW laser or electron beam. J. Appl. Phys., 53 (1982) 4357-4363.
8. Carslaw, H. S. & Jaeger, J. C., Conduction of Heat in Solids. Clarendon Press (1959).
9. Chen, C.-S., Analytical and approximate solution to radial dispersion from an injection well to a geological unit with simultaneous diffusion into adjacent strata. Water Resour. Res., 21 (1985) 1069-1076.
10. Coats, K. H. & Smith, B. D., Dead-end pore volume and dispersion in porous media. Soc. Petroleum Engs J. 4(1) (1964) 73-84.
11. Cotta, R. M., Integral Transforms in Computational Heat and Fluid Flow. CRC Press, Inc, Florida (1993).
12. Crank, J., The Mathematics of Diffusion, 2nd Edition. Oxford University Press, Oxford (1975).
13. Dagan, G., Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifer. Water Resour. Res. 24 (1988) 1491-1500.
14. Dettman, J. H., Mathematical Methods in Physics and Engineering. McGraw-Hill Book Company, Inc (1962).
15. Fetter, C. W., Contaminant Hydrogeology. Macmillan Publishing Co., New York (1992).
16. Freeze, R. A. & Cherry, J. A., Groundwater. Prentice-Hall, Inc, Englewood Cliffs (1979).
17. Gelhar, L. W., Stochastic subsurface hydrology - from theory to applications. Water Resour. Res., 22 (1986) 135S-145S.
18. Goltz, M. N. & Roberts, P. V., Three-dimensional solutions for solute transport in an infinite medium with mobile and immobile zones. Water Resour. Res. 22 (1986) 1139-1148.
19. Goltz, M. N. & Roberts, P. V., Simulations of physical solute transport models: application to a large-scale field experiment. J. Contaminant Hydrology, 3 (1988) 37-63.
20. Horgan, C. O., Lower bounds for eigenvalues of Sturm-Liouville problems with discontinuous coefficients: integral equation methods. Quantitative Appl. Math. 39 (1982) 455-465.
21. Johnson, R. L., Cherry, J. A., & Pankow, J. F., Diffusive contaminant transport in natural clay: a field example and implications for clay-lined waste disposal sites. Environmental Science and Technol. 23 (1989) 340-349.
22. Johnston, P. R., Diffusion in composite media: solution with simple eigenvalues and eigenfunctions. Mathematical and Computer Modeling, 15(10) (1991) 115-123.
23. Lee, R. G. & Weber, T. W., Isothermal adsorption in fixed beds. Canadian J. Chem. Eng. 47(1) (1969) 54-59.
24. Lockwood, J. D. & Mulholland, G. P., Diffusion through laminated composite cylinders subjected to a circumferentially varying external heat flux. Heat Transfer, 95 (1973) 487-491.
25. Luikov, A. V., Analytical Heat Diffusion Theory, 2nd edn, Academics Press, New York, London (1968).
26. Madison, M. R. & McDaniel, T. W., Temperature distribution produced in an N-layer film structure by scanning laser or electron beam with application to magneto-optical media. J. Appl. Phys. 66 (1989) 5738-5748.
27. Masamune, S. & Smith, J. M., Adsorption rate studies -interaction of diffusion and surface processes. AICHE J. 11 (1965) 34-40.
28. McGahan, W. A. & Cole, C. D., Solution of heat conduction equation in multilayers for photothermal deflection experiments. J. Appl. Phys. 72 (1992) 1362-1373.
29. Mikhailov, M. D., Ozisik, M. N., & Vulchanov, N. L., Diffusion in composite layers with automatic solution of the eigenvalue problem. Int. J. Heat and Mass Transfer, 26(8) (1983) 1131-1141.
30. Mulholland, G. P. & Cobble, M. H., Diffusion through composite media. Int. J. Heat and Mass Transfer, 15(1) (1972) 147-160.
31. Ozisik, M. N., Heat Conduction, 2nd edn, John Wiley & Son, Inc (1993).
32. Rasmuson, A. & Neretnieks, I., Exact solution of a model for diffusion in particles and longitudinal dispersion in packed beds. AICHE J. 26 (1980) 686-690.
33. Sauty, J. P., An analysis of hydrodispersive transfer in aquifers. Water Resour. Res. 75 (1980) 4382-4395.
34. Shih, O. W., A multilayer heat conduction solution for magneto-optical disk recording. J. Appl. Phys. 75 (1994) 4382-4395.
35. Sudicky, E. A. & Frind, E. O., Contaminant transport in fractured porous media: analytical solution for a system of parallel fractures. Water Resour. Res. 18 (1982) 1634-1642.
36. Thoma, G. J., Reible, D. D., Valsaraj, K. T., & Thibodeaux, L. J., Efficiency of capping contaminated sediments in situ. 2. Mathematics of diffusion-adsorption in the capping layer. Environmental Science and Technol. 27 (1993) 2412-2419.
37. Valocchi, A. J., Effect of radial flow on deviation from local equilibrium during sorbing solute transport through homogeneous soils. Water Resour. Res. 22 (1986) 1693-1701.
38. van Genuchten, M. T., A general approach for modeling solute transport in structured soils. Proceedings of the 17th Congress, Int. Assoc. of Hydrogeologists: Hydrogeology of Rocks of Low Permeability, IAH Press, Tucson, AZ (1985).
39. van Genuchten, M. T. & Wierenga, P. J., Mass transfer studies in sorbing porous media: I. Analytical solutions. Soil Science Society of America J. 40(4) (1976) 473-480.
40. Wang, X. Q., Thibodeaux, L. J., Valsaraj, K. T., & Reible, D. D., The efficiency of capping contaminated sediments in situ. I. Adsorption/desorption in the capping layers. Environmental Science and Technol. 25 (1991) 1578-1584.