Abstract
The development of a plume of pollutant in a two-dimensional heterogeneous medium with anisotropy in the correlation structure of the transmissivity (T) field is studied. In particular, we analyze the dispersion of the plume when the mean flow is tilted with respect to the principal directions of anisotropy. Of special interest is the angle between the main axes of the developed plume compared to the direction of the mean flow. T is considered locally isotropic, but the anisotropy in the correlation structure leads to anisotropic effective transmissivity. Dispersion is analyzed using a particle tracking scheme in a Monte Carlo framework.
When flow is tilted with respect to the directions of anisotropy, stochastic theories based upon ergodicity conclude that the plume gets oriented in the mean flow direction. In our non-ergodic simulations, for each single realization the plume gets oriented in an angle that is offset from the mean flow direction. The mean of the offset angles from the different realizations is again offset towards the direction of maximum anisotropy, as ergodicity is not achieved in our simulated domain.
Comparing the plume evolution for each realization, a wide range of plume configurations is found both in terms of displacement of the center of mass and in dispersion around these centers (plume sizes). A statistical analysis of the ensemble average of the plumes for the 500 realizations is also carried out. The plume obtained from ensemble averaging is oriented closer to the mean flow direction than the average offset angle for the different plumes considered separately. This work poses some important questions regarding the different types of plume averaging within a stochastic framework.
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References
Cordes, C. and W. Kinzelbach, Continuous groundwater velocity fields and path lines in linear, bilinear and trilinear finite elements, Water Resources Research, 28(11), 2903–2911, 1992.
Cushman, J.H. and T.G. Ginn, Non-local dispersion in porous media with continuously evolving scales of heterogeneity, Transport in Porous Media, 13(1), 123–138, 1993.
Dagan, G., Solute transport in heterogeneous porous formations, Journal of Fluid Mechanics, 14, 151–177, 1984.
Dagan, G., Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers, Water Resources Research, 24, 1491–1500, 1988.
Dagan, G., Flow and Transport in Porous Formations, Springer-Verlag, New York, 465 pp., 1989.
Dagan, G., Transport in heterogeneous porous formations: spatial moments, ergodicity, and effective dispersion, Water Resources Research, 26(6), 1281–1290, 1990.
Gelhar, L. W. and C. L. Axness, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resources Research, 19(1), 161–180, 1983.
Gómez-Hernández, J. J. and A. G. Journel, Joint sequential simulation of multiGaussian fields, in A. Soares (Ed.), Geostatistics Troia’92, Kluwer, Dordrecht, v. 1, 85–94, 1993.
Indelman, P. and B. Abramovich, A higher-order approximation to effective conductivity in media of anisotropic random structure, Water Resources Research, 30(6), 1875–1864, 1994.
Kapoor, V. and L. W. Gelhar, Transport in three-dimensionally heterogeneous aquifers, 1, Dynamics of concentration fluctuations, Water Resources Research, 30(6), 1775–1788, 1994.
Kitanidis, P. K., Prediction by the method of moments of transport in a heterogeneous formation, Journal of Hydrology, 102, 453–473, 1988.
Koch, D. L. and J. F. Brady, A nonlocal description of advection diffusion with application to dispersion in porous media, Chem. Eng. Sci., 42, 1377–1392, 1987.
Sánchez-Vila, X., I. Colominas, and J. Carrera, FAITH: User’s Guide, ETSE Camins, UPC, Barcelona, 1993.
Wen, X-H. and C-S. Kung, A Q-BASIC program for modeling advective mass transport with retardation and radioactive decay by particle tracking, Computers & Geosciences, 21(4), 463–480, 1995.
Zhang, D., Impacts of local dispersion and first-order decay on solute transport in randomly heterogeneous porous media, Transport in Porous Media, 21, 123–144, 1995.
Zhang, Y.K. and S.P. Neuman, A quasi-linear theory of non-Fickian and Fickian subsurface dispersion, 2. Application to anisotropic media and the Borden site, Water Resources Research, 26(5), 903–913, 1990.
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Sánchez-Vila, X., Wipfler, E.L., Carrera, J., Solís-Delfín, J. (1999). Simulation of Non-Ergodic Transport in 2-D Heterogeneous Anisotropic Media. In: Gómez-Hernández, J., Soares, A., Froidevaux, R. (eds) geoENV II — Geostatistics for Environmental Applications. Quantitative Geology and Geostatistics, vol 10. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9297-0_28
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DOI: https://doi.org/10.1007/978-94-015-9297-0_28
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