Abstract
We analysed the asymptotic behaviour of breakthrough curves (BTCs) obtained after a single pulse injection in a 1D flow domain. Five different types of solute transport with nonequilibrium sorption were considered. The properties of the porous medium were assumed to be spatially constant. For long times, the concentration at a fixed position in time was found to decay like exp(−βt) where β depends on both the transport parameters and the parameters describing the nonequilibrium process. The results from the asymptotic analysis were compared with 1D numerical transport calculations. For all cases examined a good agreement between numerical calculations and the asymptotic analysis was found. The results from the asymptotic analysis provide an alternative way to determine transport and sorption related parameters from BTCs. The derived relationships between β and the model parameters are however only valid for large times. This requires that the very low concentrations need to be measured and not only the bulk mass, too. By either increasing or decreasing the velocity during BTC experiments additional asymptotic equations are obtained which can be used to determine the value of the model parameters. The results from the asymptotic analysis can also be used in standard inverse modelling techniques to either obtain good initial guesses or to reduce the parameter space. The fact that linear nonequilibrium processes decay like exp(−βt) can be used to qualitatively evaluate observed BTCs. The asymptotic analysis can also be easily extended to a larger class of transport problems (e.g. transport of solutes with microbial decay) provided that the overall transport problem remains linear in the concentration.
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Brusseau, M. L. and Rao, P. S. C.: 1992, Modeling solute transport influenced by multiprocess nonequilibrium and transformation reactions, Water Resour. Res. 28(1), 175–182.
Brusseau, M. L. and Rao, P. S. C.: 1989, Sorption nonideality during organic contaminant transport in porous media, Crit. Rev. Environ. Control 19, 33–99.
Braun, A.: 1996, Modellierung von reaktivem Stofftransport in einem heterogenen Grundwasserleiter auf der Grundlage eines Tracertestes. Institut f¨ur Geographie und Geo¨okologie der Technischen Universit¨at Braunschweig, p. 134.
Cameron, D. R. and Klute, A.: 1977, Convective-dispersive solute transport with a combined equilibrium and kinetic adsorption model, Water Resour. Res. 13, 183–188.
Coats, K. H. and Smith, B. D.: 1964, Dead-end pore volume and dispersion in porous media, Soc. Pet. Engng. J. 4, 73–84.
Georgescu, A.: 1995, Asymptotic Treatment of Differential Equations, Chapman and Hall, London, p. 268.
Hoffman, D. L. and Rolston, D. E.: 1980, Transport of organic phosphate in soil as affected by soil type, Soil Sci. Soc. Am. J. 44, 46–52.
Jaekel, U., Georgescu, A. and Vereecken, H.: 1996, Asymptotic analysis of nonlinear equilibrium solute transport in porous media, Water Resour. Res. 32(10), 3093–3908.
Lindstrom, F. T. and Boersma, L.: 1976, A theory on the mass transport of previously distributed chemicals in a water-saturated sorbing porous media: III. Exact solution for first-order kinetic sorption, Soil Sci. 115, 5–10.
Nkedi-Kizza, P., Rao, P. S. C Jessup, R. E. and Davidson, J. M.: 1982, Ion exchange and diffusive mass transfer during miscible displacement through an aggregated oxisol, Soil Sci. Soc. Am. J. 46, 471–476.
Parker, J. C. and van Genuchten, M. Th.: 1984, Determining transport parameters from laboratory and field tracer experiments, Virginia Agricultural Experiment Station, Virginia Polytechnic Institute and State University, Bulletin 84-3, p. 97.
Quinodoz, H. A. M. and Vallochi, A. J.: 1993, Stochastic analysis of the transport of kinetically sorbing solutes in aquifers with randomly heterogeneous hydraulic properties, Water Resour. Res. 29(9), 3227–3240.
Rao, P. S. C., Davidson, J. M., Jessup, R. E. and Selim, H. M.: 1979, Evaluation of conceptual models for describing non-equilibirum adsorption-desorption of pesticides during steady-state flow in soils, Soil Sci. Soc. Am. J. 43, 22–28.
Sardin, M., Schweich, D., Leij, F. J. and van Genuchten, M. Th.: 1991, Modeling the nonequilibrium transport of linearly interacting solutes in porous media: a review, Water Resour. Res. 27(9), 2287–2307.
Selim, H. M., Davidson, J. M. and Mansell, R. S.: 1976, Evaluation of a two-site adsorptiondesorption model for describing solute transport in soils, Paper presented at Summer Computer Simulation Conference, Am. Inst. of Chem. Engng., Washington DC.
Sugita, F. and Gillham, R.W.: 1995, Pore scale variation in retardation factor as a cause of nonideal reactive breakthrough curves. 1. Conceptual model and its evaluation,Water Resour. Res. 31(1), 103–112.
Thorbjarnarson, K. W. and Mac Kay, D.: 1994, A forced-gradient experiment on solute transport in the Borden aquifer. 3. Nonequilibrium transport of the sorbing organic compounds, Water Resour. Res. 30(2), 41–419.
Toride, N., Leij, F. 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(7), 2167–2182.
Vanclooster, M., Vereecken, H., Diels, J., Huysmans, F., Verstraete, W. and Feyen, J.: 1992, Effect of mobile and immobile water in predicting nitrogen leaching from cropped soils, Modelling Geo-Biosphere Processes, Vol. I, pp. 23–40.
Van Genuchten, M. T.: 1981, Non-equilibrium transport parameters from miscible displacement experiments, Research Report No.119, United States Department of Agriculture, USSL, Riverside, California.
Van Genuchten, M. T. and Wierenga, P. J.: 1976, Mass transfer studies in sorbing porous media: I. Analytical solutions, Soil Sci. Soc. Am. J. 40, 473–479.
Van Genuchten, M. T. and Wierenga, P. J.: 1977, Mass transfer studies in sorbing porous media: II. Experimental evaluation with tritium 3H2O, Soil Sci. Soc. Am. J. 41, 272–278.
Van Genuchten, M. T., Wierenga, P. J. and O'Connor, G. A.: 1977, Mass transfer studies in sorbing porous media: experimental evaluation with 2,4,5-T, Soil Sci. Soc. Am. J. 41, 272–278.
Van Genuchten, M. T. and Alves, W. J.: 1982, Analytical solutions of the one-dimensional convective-dispersion solute transport equations, U. S. Dept. of Agriculture, Techn. Bull. No. 1661, p. 151.
Villermaux, J.: 1987, Chemical engineering approach to dynamic modeling of linear chromatography, a flexible method for representing complex phenomena from simple concepts, J. Chromatography, 406, 11–26.
Walker, A., Cox, L. and Edwards, J. A.: 1996, Changes in adsorption of isoproturon with residence time in soil, Proc. COST 66 Workshop, Stratford-upon-Avon, pp. 87–88.
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Vereecken, H., Jaekel, U. & Georgescu, A. Asymptotic Analysis of Solute Transport with Linear Nonequilibrium Sorption in Porous Media. Transport in Porous Media 36, 189–210 (1999). https://doi.org/10.1023/A:1006553713516
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DOI: https://doi.org/10.1023/A:1006553713516