Abstract
Porous media such as fractured rock and aggregated soils consist of two pore domains with distinct transport properties. A numerical code was developed to simulate solute concentrations in the two domains using a partitioned solution procedure to efficiently model transport in dual-permeability media. Furthermore, an approximate analytical solution was obtained that allows for different advective and dispersive terms in both flow domains, for a first-type or a third-type inlet condition. Solutions were obtained for local concentrations in both domains as well as effluent concentration and the concentration per medium volume. The problem was solved by decoupling the transport equations using diagonalization. This involves an error for the dispersivity matrix that is related to the difference in dispersivity of both domains. The correctness of the solution was assessed by comparison with numerical results. For low Damköhler numbers the solution was accurate even for a dispersivity ratio of 10. The need for a dual-dispersivity instead of a single-dispersivity model was illustrated with sample breakthrough curves and the solution was applied to optimize experimental breakthrough curves for an Andisol with a distinct intraaggregate and interaggregate porosity.
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Acknowledgments
The authors would like to thank the three anonymous reviewers for their valuable comments on this paper.
References
Baratelli, F., Giudici, M., and Vassena, C. (2011). “Single and dual-domain models to evaluate the effects of preferential flow paths in alluvial sediments.” Transp. Porous Med., 87(2), 465–484.
Bedrikovetskii, P. G. (1992). “Horizontal displacement of miscible fluids from fractured porous media.” Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, 3, 87–95.
Bedrikovetskii, P. G., Istomin, G. D., and Knyazeva, M. B. (1989). “Miscible displacement from fractured porous media.” Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, 6, 100–110.
Bolster, D., Valdés-Parada, F. J., LeBorgne, T., Dentz, M., and Carrera, J. (2011). “Mixing in confined stratified aquifers.” J. Contam. Hydrol., 120–121, 198–212.
Carrera, J., Sánchez-Vila, X., Benet, I., Medina, A., Galarza, G., and Guimerà, J. (1998). “On matrix diffusion: Formulations, solution methods and qualitative effects.” Hydrogeol. J., 6(1), 178–190.
Coats, K. H., and Smith, B. D. (1964). “Dead-end pore volume and dispersion in porous media.” Soc. Pet. Eng. J., 4(1), 73–84.
de Anna, P., Le Borgne, T., Dentz, M., Tartakovsky, A. M., Bolster, D., and Davy, P. (2013). “Flow intermittency, dispersion, and correlated continuous time random walks in porous media.” Phys. Rev. Lett., 110(18), 184502.
Dentz, M., and Bolster, D. (2010). “Distribution- versus correlation-induced anomalous transport in quenched random velocity fields.” Phys. Rev. Lett., 105(24), 244301.
Esfandiari, R. S. (2008). Applied mathematics for engineers, Atlantis, Los Angeles.
Fernàndez-Garcia, D., Sánchez-Vila, X., and Guadagnini, A. (2008). “Reaction rates and effective parameters in stratified aquifers.” Adv. Water Resour., 31(10), 1364–1376.
Haggerty, R., and Gorelick, S. M. (1995). “Multiple-rate mass transfer for modeling diffusion and surface reactions in media with pore-scale heterogeneity.” Water Resour. Res., 31(10), 2383–2400.
Javandel, I., Doughty, Ch., and Tsang, C.-F. (1984). “Groundwater transport: Handbook of mathematical models.”, American Geophysical Union, Washington, DC.
Lapidus, L., and Amundson, N. R. (1952). “Mathematics of adsorption in beds. VI. The effects of longitudinal diffusion in ion exchange and chromatographic columns.” J. Phys. Chem., 56(8), 984–988.
Leij, F. J., and Sciortino, A. (2012). “Solute transport.” Handbook of soil science, P. H. Huang, Y. Li, and M. E. Sumner, eds., 2nd Ed., CRC, Boca Raton, FL.
Leij, F. J., Skaggs, T. H., and van Genuchten, M. Th. (1991). “Analytical solutions for solute transport in three-dimensional semi-infinite porous media.” Water Resour. Res., 27(10), 2719–2733.
Leij, F. J., Toride, N., Field, M., and Sciortino, A. (2012). “Solute transport in dual-permeability porous media.” Water Resour. Res., 48(4), W04523.
Maloszewski, P., and Zuber, A. (1993). “Tracer experiments in fractured rocks: Matrix diffusion and the validity of models.” Water Resour. Res., 29(8), 2723–2735.
Novakowski, K. S., and Lapcevic, P. A. (1994). “Field measurements of radial solute transport in fractured rock.” Water Resour. Res., 30(1), 37–44.
Rasmussen, A., and Neretnieks, I. (1986). “Radionuclide transport in fast channels in crystalline rock.” Water Resour. Res., 22(8), 1247–1256.
Roberts, P. V., Goltz, M. N., Summers, R. S., Crittenden, J. C., and Nkedi-Kizza, P. (1987). “The influence of mass transfer on solute transport in column experiments with an aggregated soil.” J. Contam. Hydrol., 1(4), 375–393.
Ronayne, M. J., Gorelick, S. M., and Zheng, C. (2010). “Geological modeling of submeter scale heterogeneity and its influence on tracer transport in a fluvial aquifer.” Water Resour. Res., 46(10), W10519.
Selim, H. M., and Ma, L. (1998). Physical nonequilibrium in soils: Modeling and applications, Chelsea, Ann Arbor, MI.
Selim, H. M., Schulin, R., and Fluhler, H. (1987). “Transport and ion exchange of calcium and magnesium in an aggregated soil.” Soil Sci. Soc. Am. J., 53(4), 996–1004.
Sun, N-Z. (1996). Mathematical modeling of groundwater pollution, Springer, New York.
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(7), 2167–2182.
Toride, N., Leij, F. J., and van Genuchten, M. Th. (1995). “The CXTFIT code for estimating transport parameters from laboratory or field tracer experiments.”, Riverside, CA.
Tseng, P.-H., Sciortino, A., and van Genuchten, M. Th. (1995). “A partitioned solution procedure for simulating water flow in a variably saturated dual-porosity medium.” Adv. Water Resour., 18(6), 335–343.
Vanderborght, J., et al. (2005). “A set of analytical benchmarks to test numerical models of flow and transport in soils.” Vadose Zone J., 4(1), 206–221.
van Duijn, C. J., and van der Zee, S. E. A. T. M. (1986). “Solute transport parallel to an interface separating two different porous media.” Water Resour. Res., 22(13), 1779–1789.
van Genuchten, M. Th., and Dalton, F. (1986). “Models for simulating salt movement in aggregated field soils.” Geoderma, 38(1–4), 165–183.
van Genuchten, M. Th., and Parker, J. C. (1984). “Boundary conditions for displacement experiments through short laboratory columns.” Soil Sci. Soc. Am. J., 48(4), 703–708.
van Genuchten, M. Th., Šimůnek, J., Leij, F. J., Toride, N., and Šejna, M. (2012). “STANMOD: Model use. Calibration and validation.” Trans. ASABE, 55(4), 1355–1368.
van Genuchten, M. Th., and Wierenga, P. J. (1976). “Mass transfer studies in sorbing porous media: I. Analytical solutions.” Soil Sci. Soc. Am. J., 40(4), 473–480.
Veling, E. J. M. (1989). “Comment on ‘Dispersion in stratified porous media: Analytical solutions’ by A. N. S. A1-Niami and K. R. Rushton.” Water Resour. Res., 25(9), 2081–2082.
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Published In
Journal of Hydrologic Engineering
Volume 20 • Issue 7 • July 2015
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Jun 26, 2013
Accepted: Jul 22, 2014
Published online: Oct 6, 2014
Discussion open until: Mar 6, 2015
Published in print: Jul 1, 2015
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