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Analytical Modeling of Nonaqueous Phase Liquid Dissolution with Green's Functions

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Abstract

Equilibrium and bicontinuum nonequilibrium formulations of the advection–dispersion equation (ADE) have been widely used to describe subsurface solute transport. The Green's Function Method (GFM) is particularly attractive to solve the ADE because of its flexibility to deal with arbitrary initial and boundary conditions, and its relative simplicity to formulate solutions for multi‐dimensional problems. The Green's functions that are presented can be used for a wide range of problems involving equilibrium and nonequilibrium transport in semi‐infinite and infinite media. The GFM is applied to analytically model multi‐dimensional transport from persistent solute sources typical of nonaqueous phase liquids (NAPLs). Specific solutions are derived for transport from a rectangular source (parallel to the flow direction) of persistent contamination using first‐, second‐, or third‐type boundary or source input conditions. Away from the source, the first‐ and third‐type condition cannot be expected to represent the exact surface condition. The second‐type condition has the disadvantage that the diffusive flux from the source needs to be specified a priori. Near the source, the third‐type condition appears most suitable to model NAPL dissolution into the medium. The solute flux from the pool, and hence the concentration in the medium, depends strongly on the mass transfer coefficient. For all conditions, the concentration profiles indicate that nonequilibrium conditions tend to reduce the maximum solute concentration and the total amount of solute that enters the porous medium from the source. On the other hand, during nonequilibrium transport the solute may spread over a larger area of the medium compared to equilibrium transport.

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References

  • Beck, J. V., Cole, K. D., Haji-Sheikh, A. and Litkouhi, B.: 1992, Heat Conduction Using Green's Functions, Hemisphere Publ., Washington, DC.

    Google Scholar 

  • Boucher, D. F. and Alves, G. E.: 1959, Dimensionless numbers, Chem. Engng Progr. 55, 55–64.

    Google Scholar 

  • Bradford, S. A., Abriola, L. M. and Rathfelder, K.: 1998, Flow and entrapment of dense nonaqueous phase liquids in physically and chemically heterogeneous aquifer formations, Adv. Water. Resour. 22, 117–132.

    Google Scholar 

  • Carslaw, H. S., Jaeger, J. C.: 1959, Conduction of Heat in Solids, Clarendon Press, Oxford.

    Google Scholar 

  • Carnahan, B., Luther, H. A. and Wilkes, J. O.: 1969, Applied Numerical Models, Wiley, New York.

    Google Scholar 

  • Chrysikopoulos, C. V.: 1995, Three-dimensional analytical models of contaminant transport from nonaqueous phase liquid pool dissolution in saturated subsurface formations, Water Resour. Res. 31, 1137–1145.

    Google Scholar 

  • Chrysikopoulos, C. V., Voudrias, E. A. and Fyrillas, M. M.: 1994, Modeling of contaminant transport from dissolution of nonaqueous phase liquid pools in saturated porous media, Transport in Porous Media 16, 125–145.

    Google Scholar 

  • Cleary, R.W. and Adrian, D. D.: 1973, Analytical solution of the convective-dispersive equation for cation transport in soils, Soil Sci. Soc. Am. Proc. 37, 197–199.

    Google Scholar 

  • Coats, K. H. and Smith, B. D.: 1964, Dead-end pore volume and dispersion in porous media, Soc. Petrol. Engng J. 4, 73–84.

    Google Scholar 

  • De Smedt, F. and Wierenga, P. J.: 1979, A generalized solution for solute flow in soils with mobile and immobile water, Water Resour. Res. 15, 1137–1141.

    Google Scholar 

  • Ellsworth, T. R. and Butters, G. L.: 1993, Three-dimensional analytical solutions to the advection- dispersion equation in arbitrary Cartesian coordinates, Water Resour. Res. 29, 3215–3225.

    Google Scholar 

  • Galya, D. P.: 1987, A horizontal plane source model for ground-water transport, Ground Water 25, 733–739.

    Google Scholar 

  • Van Genuchten, M. Th. and Alves, W. J.: 1982, Analytical solutions of the one-dimensional convective-dispersive solute transport equation, Tech. Bull., U.S. Dep. Agric., 1661.

  • Van Genuchten, M. Th. and Wierenga, P. J.: 1976, Mass transfer studies in sorbing porous media. I. Analytical solutions, Soil Sci. Soc. Am. J. 53, 1303–1310.

    Google Scholar 

  • Greenberg, M. D.: 1971, Application of Green's Functions in Science and Engineering, Prentice Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Güven, O., Molz, F. J. and Melville, J. G.: 1984, An analysis of dispersion in a stratified aquifer, Water Resour. Res. 20, 1337–1354.

    Google Scholar 

  • Holman, H.-Y. N. and Javandel, I.: 1996, Evaluation of transient dissolution of slightly water-soluble compounds from a light nonaqueous phase liquid pool, Water Resour. Res. 32, 915–923.

    Google Scholar 

  • Leij, F. J., Toride, N. and van Genuchten, M. Th.: 1993, Analytical solutions for nonequilibrium solute transport in three-dimensional porous media, J. Hydrol. 151, 193–228.

    Google Scholar 

  • Leij, F. J., Priesack, E. and Schaap, M. G.: 1999, Transport from persistent solute sources modeled with Green's functions, J. Contam. Hydrol. (in press).

  • Prakash, A.: 1984, Ground-water contamination due to transient sources of pollution, J. Hydraul. Engng 110, 1642–1658.

    Google Scholar 

  • Renardy, M. and Rogers, R. C.: 1993. An Introduction to Partial Differential Equations, Springer-Verlag, New York.

    Google Scholar 

  • Roach, G. F.: 1982, Green's Functions, Cambridge Univ. Press.

  • Shan, C. and Javandel, I.: 1997, Analytical solutions for solute transport in a vertical aquifer section, J. Contam. Hydrol. 27, 63–82.

    Google Scholar 

  • Sneddon, I. H.: 1995, Fourier Transforms, Dover, New York.

    Google Scholar 

  • Spiegel, M. R.: 1965, Theory and Problems of Laplace Transforms, Schaum's Outline Ser., McGraw-Hill, New York.

    Google Scholar 

  • Stakgold, I.: 1979, Green's Functions and Boundary Value Problems, Wiley, New York.

    Google Scholar 

  • Toride, N., Leij, F. J. and Van Genuchten, M. Th.: 1993, A comprehensive set of analytical solutions for nonequilibrium solute transport with first-order decay and zero-order production, Water Resour. Res. 29, 2167–2182.

    Google Scholar 

  • Walker, G. R.: 1987, Solution to a class of coupled linear partial differential equations, IMA J. Appl. Math. 38, 35–48.

    Google Scholar 

  • Yeh, G. T.: 1981, AT123D: Analytical transient one-, two-, and three-dimensional simulation of waste transport in an aquifer system, Rep. ORNL-5602. Oak Ridge National Laboratory, Oak Ridge, TN.

    Google Scholar 

  • Yeh, G. T. and Tsai, Y.-J.: 1976, Analytical three-dimensional transient modeling of effluent discharges, Water Resour. Res. 12, 533–540.

    Google Scholar 

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Leij, F.J., van Genuchten, M.T. Analytical Modeling of Nonaqueous Phase Liquid Dissolution with Green's Functions. Transport in Porous Media 38, 141–166 (2000). https://doi.org/10.1023/A:1006611200487

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