Use of the generalized integral transform method for solving equations of solute transport in porous media

Advances in Water Resources

Volumn 23, Issue 5, 2000, Pages 483-492

  Liu, Chongxuan ^a   Szecsody, Jim E ^a   Zachara, John M ^a   Ball, William P ^b  

^a PACIFIC NORTHWEST NATIONAL LABORATORY   (United States)

^b The Johns Hopkins University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTIC METHOD; FLOW KINETICS; POROUS MEDIUM; SOLUTE TRANSPORT; SORPTION;

BOUNDARY CONDITIONS; DECOMPOSITION; DISPERSIONS; FLOW OF WATER; IRON OXIDES; MATHEMATICAL TRANSFORMATIONS; POROUS MATERIALS; REACTION KINETICS; REDUCTION; SOLUTIONS; SORPTION; TRANSPORT PROPERTIES;

BIOREDUCTION; GENERALIZED INTEGRAL TRANSFORM TECHNIQUE; ONE DIMENSIONAL ADVECTION DISPERSION EQUATION; SOLUTE;

HYDROLOGY;

ADVECTION; DISPERSION; POROUS MEDIUM; SOLUTE TRANSPORT;

EID: 0343527340     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0309-1708(99)00048-2     Document Type: Article

References (26)

1. Almeida A.R., Cotta R.M. Integral transform methodology for convection-diffusion problems in petroleum reservoir engineering. Int J Heat Mass Transfer. 38(18):1995;3359-3367.
2. Bear J. Dynamics of fluids in porous media. 1972;Elsevier, New York.
3. Brenner H. The diffusion model of longitudinal mixing in beds of finite length, numerical values. Chem Eng Sci. 17:1962;229-243.
4. Cotta R.M. Hybrid numerical analytical approach to nonlinear diffusion problems. Numer Heat Transfer, Part-B-Fundamental. 17:1990;217-226.
5. Cotta R.M. Integral transforms in computational heat and fluid flow. 1993;CRC Press, Boca Raton.
6. Dagan G. Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifer. Water Resour Res. 24(9):1988;1491-1500.
7. Dankwerts P.V. Continuous flow systems. Chem Eng Sci. 2:1953;1-13.
8. Fredrickson J.K., Zachara J.M., Kennedy D.V., Dong H., Onstott T.C., Hinman N.W., Li S.M. Biogenic iron mineralization accompanying the dissimilatory reduction of hydrous ferric oxide by a groundwater bacterium. Geochimica et Cosmochimica Acta. 62:1998;3239-3257.
9. Freeze R.A., Cherry J.A. Groundwater. 1979;Prentice-Hall, Englewood Cliffs, NJ.
10. Gelhar LW. Stochastic subsurface hydrology. Englewood Cliffs, NJ: Prentice-Hall, 1993.
11. Goode DJ, Konikow LF. Modification of a method-of-characteristics solute-transport model to incorporate decay and equilibrium-controlled sorption or ion exchange. Water-Resources Investigation Report 89-4030, US Geological Survey, Reston, Virginia, 1989.
12. Huang K., Mohanty P.B., Leij F.J., van Genuchten M.T. Solution of the nonlinear transport equation using modified Picard iteration. Adv Water Resour. 21:1998;237-249.
13. IMSL, IMSL Library, Math/Library, Houston, Texas, 1991.
14. Liu C., Ball W.P., Ellis J.H. An analytical solution to one-dimensional solute advection-dispersion equation in multi-layer porous media. Transp Porous Media. 30:1998;25-43.
15. Lovley D.R. Dissimilatory metal reduction. Ann Rev Microbiol. 47:1993;263-290.
16. Mikhailov M.D., Ozisik M.N. Unified analysis and solution of heat and mass diffusion. 1984;Wiley, New York.
17. Moler C., van Loan C. Nineteen dubious ways to compute the exponential of a matrix. SIAM Review. 20(4):1978;801-837.
18. Monod J. The growth of bacterial cultures. Ann Rev Microbiol. 3:1949;371-393.
19. Ozisik MN. Heat Conduction. New York: Wiley, 1993.
20. Parker J.C., van Genuchten M.T. Flux-averaged and volume-averaged concentrations in continuum approaches to solute transport. Water Resour Res. 20:1984;866-872.
21. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. Numerical recipes. 1992;Cambridge University Press, Cambridge, MA.
22. Rugh WJ. Linear system theory. Englewood Cliffs, NJ: Prentice-Hall; Simon & Schuster/A Viacom Company, 1996.
23. Urrutia M.N., Roden E.E., Fredrickson J.K., Zachara J.M. Microbial and surface chemistry controls on reduction of synthetic Fe (III) oxide minerals by the dissimilatory iron-reducing bacterium. Geomicrobiology. 15:1998;269-291.
24. van Genuchten MT, Alves WJ. Analytical solutions of the one-dimensional convective-dispersive solute transport equation. USDA Tech Bull 1982;1661.
25. van Genuchten M.T., Parker J.C. Boundary conditions for displacement experiments through short laboratory soil. Soil Sci Soc Am J. 48:1984;703-708.
26. Zachara JM, Fredrickson JK, Li, S-M., Kennedy DW, Smith SC. Bacterial reduction of crystalline Fe(III) oxides in single phase suspensions and subsurface materials. Am Mineralog 1998;83:1426-43.