Improved Compartmental Modeling and Application to Three-Phase Contaminant Transport in Unsaturated Porous Media
Publication: Journal of Environmental Engineering
Volume 132, Issue 2
Abstract
The compartmental modeling approach has been widely used for simulating contaminant transport in porous media and surface waters. Yet a commonly used compartmental model that has only first-order accuracy may introduce considerable numerical errors under certain circumstances. Following a review of compartmental systems and compartmental modeling methodologies, performance and limitations of such a compartmental model are discussed. In particular, improvement approaches, including multipoint, high-order, linear, and nonlinear methods, are presented in detail. Finally, a number of testing problems are examined and various compartmental models that describe three-phase (dissolved, adsorbed, and vapor phases) contaminant transport in unsaturated porous media are compared with each other and also with standard numerical and analytical counterparts. The comparisons highlight the accuracy, applicability, and limitations of different compartmental models.
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Acknowledgments
This work was supported by the U.S. Environmental Protection Agency (USEPA) (Grant No. R819658) Center for Ecological Health Research at the University of California, Davis, and the UC Toxic Substances Research and Teaching Program. Although the information in this document has been funded in part by the USEPA, it may not necessarily reflect the views of the agency and no official endorsement should be inferred.
References
Chu, X., and Mariño, M. A. (2004). “Semidiscrete pesticide transport modeling and application.” J. Hydrol., 285(1–4), 19–40.
Crank, J. (1975). The mathematics of diffusion, 2nd Ed., Clarendon, Oxford.
Godfrey, K. (1983). Compartmental models and their application, Academic, London.
Harrington, G. A., Walker, G. R., Love, A. J., and Narayan, K. A. (1999). “A compartmental mixing-cell approach for the quantitative assessment of groundwater dynamics in the Otway Basin, South Australia.” J. Hydrol., 214(1–4), 49–63.
Jacquez, J. A., and Simon, C. P. (1993). “Qualitative theory of compartmental systems.” SIAM Rev., 35(1), 43–79.
Jury, W. A., Gardner, W. R., and Gardner, W. H. (1991). Soil physics, 5th Ed., Wiley, New York.
Laney, C. B. (1998). Computational gasdynamics, Cambridge Univ. Press, Cambridge, U.K.
Leonard, B. P. (1979). “A stable and accurate convective modelling procedure based on quadratic upstream interpolation.” Comput. Methods Appl. Mech. Eng., 19(1), 59–98.
Mazanov, A. (1976). “Stability of multi-pool models with lags.” J. Theor. Biol., 59(2), 429–442.
Moler, C., and Van Loan, C. (1978). “Nineteen dubious ways to compute the exponential of a matrix.” SIAM Rev., 20(4), 801–836.
Ogata, K. (1987). Discrete-time control systems, Prentice-Hall, Englewood Cliffs, N.J.
Pennington, S. V., and Berzins, M. (1994). “New NAG library software for first-order partial differential equations.” ACM Trans. Math. Softw., 20(1), 63–99.
Schnoor, J. L. (1996). Environmental modeling: Fate and transport of pollutants in water, air, and soil, Wiley, New York.
van Eijkeren, J. C. H., de Haan, B. J., Stelling, G. S., and van Stijn, T. L. (1993). “Linear upwind biased methods.” Numerical methods for advection-diffusion problems, C. B. Vreugdenhil, and B. F. Koren, eds., Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig/Wiesbaden, Germany, 55–91.
van Genuchten, M. T., and Alves, W. J. (1982). “Analytical solutions of the one-dimensional convective-dispersive solute transport equation.” Technical Bulletin No. 1661, Agricultural Research Service, U.S. Dept. of Agriculture, Riverside, Calif.
van Leer, B. (1974). “Towards the ultimate conservative difference scheme. II: Monotonicity and conservation combined in a second order scheme.” J. Comput. Phys., 14(4), 361–370.
Wang, G.-T., Li, B. Q., and Chen, S. (1999). “A semianalytical method for solving equations describing the transport of contaminants in two-dimensional homogeneous porous media.” Math. Comput. Modell., 30(9–10), 63–74.
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Information
Published In
Journal of Environmental Engineering
Volume 132 • Issue 2 • February 2006
Pages: 211 - 219
Copyright
© 2006 ASCE.
History
Received: Jul 29, 2004
Accepted: May 23, 2005
Published online: Feb 1, 2006
Published in print: Feb 2006
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