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Monte Carlo GRW Simulations of Passive Transport in Groundwater

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Diffusion in Random Fields

Part of the book series: Geosystems Mathematics ((GSMA))

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Abstract

Monte Carlo GRW simulations of passive transport in groundwater are used to investigate ergodic properties, dependence on initial conditions, and the occurrence of anomalous diffusion. It is shown that memory effects produced by dependence on initial conditions are responsible for the lack of ergodicity of the transport, in the sense of approach to the theoretical upscaled process. Evolving scale heterogeneity of groundwater systems, consisting of a superposition of spatial scales, enhances the memory effects and may explain the occurrence of anomalous diffusion behavior.

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References

  1. Bellin, A., Pannone, M., Fiori, A., Rinaldo, A.: On transport in porous formations characterized by heterogeneity of evolving scales. Water Resour. Res. 32, 3485–3496 (1996)

    Article  Google Scholar 

  2. Bouchaud, J.-P., Georges, A.: Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127–293 (1990)

    Article  MathSciNet  Google Scholar 

  3. Cintoli, S., Neuman, S.P., Di Federico, V.: Generating and scaling fractional Brownian motion on finite domains. Geophys. Res. Lett. 32, L08404 (2005)

    Article  Google Scholar 

  4. Dagan, G.: Flow and Transport in Porous Formations. Springer, Berlin (1989)

    Book  Google Scholar 

  5. Dagan, G.: Transport in heterogeneous porous formations: spatial moments, ergodicity, and effective dispersion. Water Resour. Res. 26(6), 1281–1290 (1990)

    Article  Google Scholar 

  6. Dagan, G.: The significance of heterogeneity of evolving scales and of anomalous diffusion to transport in porous formations. Water Resour. Res. 30, 3327–3336 (1994)

    Article  Google Scholar 

  7. Di Federico, V., Neuman, S.P.: Scaling of random fields by means of truncated power variograms and associated spectra. Water Resour. Res. 33, 1075–1085 (1997)

    Article  Google Scholar 

  8. Eberhard, J., Suciu, N., Vamos, C.: On the self-averaging of dispersion for transport in quasi-periodic random media. J. Phys. A: Math. Theor. 40, 597–610 (2007)

    Article  MathSciNet  Google Scholar 

  9. Fiori, A.: On the influence of local dispersion in solute transport through formations with evolving scales of heterogeneity. Water Resour. Res. 37(2), 235–242 (2001)

    Article  Google Scholar 

  10. Gelhar, L.W.: Stochastic subsurface hydrology from theory to applications. Water Resour. Res. 22(9S), 135S–145S (1986)

    Article  Google Scholar 

  11. Gelhar, L.W., Axness, C.: Three-dimensional stochastic analysis of macrodispersion in aquifers. Water Resour. Res. 19(1), 161–180 (1983)

    Article  Google Scholar 

  12. Jeon, J.-H., Metzler, R.: Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries. Phys. Rev. E 81, 021103 (2010)

    Article  MathSciNet  Google Scholar 

  13. Kraichnan, R.H.: Diffusion by a random velocity field. Phys. Fluids 13(1), 22–31 (1970)

    Article  Google Scholar 

  14. Liu, H.H., Molz, F.J.: Block scale dispersivity for heterogeneous porous media characterized by stochastic fractals. Geophys. Res. Lett. 24(17), 2239–2242 (1997)

    Article  Google Scholar 

  15. McLaughlin, D., Ruan, F.: Macrodispersivity and large-scale hydrogeologic variability. Transp. Porous Media 42, 133–154 (2001)

    Article  Google Scholar 

  16. Sposito, G., Jury, W.A., Gupta, V.K.: Fundamental problems in the stochastic convection-dispersion model of solute transport in aquifers and field soils. Water Resour. Res. 22(1), 77–88 (1986)

    Article  Google Scholar 

  17. Suciu, N.: Spatially inhomogeneous transition probabilities as memory effects for diffusion in statistically homogeneous random velocity fields. Phys. Rev. E 81, 056301 (2010)

    Article  Google Scholar 

  18. Suciu, N., Knabner, P.: Comment on ‘Spatial moments analysis of kinetically sorbing solutes in aquifer with bimodal permeability distribution’ by M. Massabo, A. Bellin, and A. J. Valocchi. Water Resour. Res. 45, W05601 (2009)

    Google Scholar 

  19. Suciu, N., Vamoş, C.: Comment on “Nonstationary flow and nonergodic transport in random porous media” by G. Darvini and P. Salandin. Water Resour. Res. 43, W12601 (2007)

    Google Scholar 

  20. Suciu, N., Vamoş, C.: Ergodic estimations of upscaled coefficients for diffusion in random velocity fields. In: L’Ecuyér, P., Owen, A.B. (eds.) Monte Carlo and Quasi-Monte Carlo Methods 2008, pp. 617–626. Springer, Berlin (2009)

    Chapter  Google Scholar 

  21. Suciu, N., Vamoş, C., Vanderborght, J., Hardelauf, H., Vereecken, H.: Numerical investigations on ergodicity of solute transport in heterogeneous aquifers. Water Resour. Res. 42, W04409 (2006)

    MATH  Google Scholar 

  22. Suciu, N., Vamoş, C., Eberhard, J.: Evaluation of the first-order approximations for transport in heterogeneous media. Water Resour. Res. 42, W11504 (2006)

    Google Scholar 

  23. Suciu, N., Vamos, C., Vereecken, H., Sabelfeld, K., Knabner, P.: Ito equation model for dispersion of solutes in heterogeneous media. Rev. Anal. Numer. Theor. Approx. 37, 221–238 (2008)

    MathSciNet  MATH  Google Scholar 

  24. Suciu, N., Vamoş, C., Vereecken, H., Sabelfeld, K., Knabner, P.: Memory effects induced by dependence on initial conditions and ergodicity of transport in heterogeneous media. Water Resour. Res. 44, W08501 (2008)

    Article  Google Scholar 

  25. Suciu, N., Vamos, C., Radu, F.A., Vereecken, H., Knabner, P.: Persistent memory of diffusing particles. Phys. Rev. E 80, 061134 (2009)

    Article  Google Scholar 

  26. Suciu, N., Attinger, S., Radu, F.A., Vamoş, C., Vanderborght, J., Vereecken, H., Knabner, P.: Solute transport in aquifers with evolving scale heterogeneity. Preprint No. 346, Mathematics Department—Friedrich-Alexander University Erlangen-Nuremberg (2011)

    Google Scholar 

  27. Suciu, N., Attinger, S., Radu, F.A., Vamoş, C., Vanderborght, J., Vereecken, H. Knabner, P.: Solute transport in aquifers with evolving scale heterogeneity. An. Sti. U. Ovid. Co-Mat. 23(3), 167–186 (2015)

    MathSciNet  MATH  Google Scholar 

  28. Vamoş, C., Suciu, N., Vereecken, H., Vanderborght, J., Nitzsche, O.: Path decomposition of discrete effective diffusion coefficient. Internal Report ICG-IV 00501, Research Center Jülich (2001)

    Google Scholar 

  29. Yaglom, A.M.: Correlation Theory of Stationary and Related Random Functions, Volume I: Basic Results. Springer, New York (1987)

    Book  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Friedrich-Alexander University of Erlangen-Nürnberg, Erlangen, Germany

    Nicolae Suciu

  2. Tiberiu Popoviciu Institute of Numerical Analysis, Cluj-Napoca Branch of the Romanian Academy, Cluj-Napoca, Romania

    Nicolae Suciu

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  1. Nicolae Suciu
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Suciu, N. (2019). Monte Carlo GRW Simulations of Passive Transport in Groundwater. In: Diffusion in Random Fields . Geosystems Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-15081-5_5

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