1. bookVolume 23 (2015): Issue 3 (November 2015)
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
access type Open Access

Solute transport in aquifers with evolving scale heterogeneity

Published Online: 22 Apr 2017
Volume & Issue: Volume 23 (2015) - Issue 3 (November 2015)
Page range: 167 - 186
Received: 01 Dec 2014
Accepted: 01 Feb 2015
Journal Details
License
Format
Journal
eISSN
1844-0835
First Published
17 May 2013
Publication timeframe
1 time per year
Languages
English
Abstract

Transport processes in groundwater systems with spatially heterogeneous properties often exhibit anomalous behavior. Using first-order approximations in velocity fluctuations we show that anomalous superdiffusive behavior may result if velocity fields are modeled as superpositions of random space functions with correlation structures consisting of linear combinations of short-range correlations. In particular, this corresponds to the superposition of independent random velocity fields with increasing integral scales proposed as model for evolving scale heterogeneity of natural porous media [Gelhar, L. W. Water Resour. Res. 22 (1986), 135S-145S]. Monte Carlo simulations of transport in such multi-scale fields support the theoretical results and demonstrate the approach to superdiffusive behavior as the number of superposed scales increases.

Keywords

[1] Attinger, S., Dentz, M., H. Kinzelbach, and W. Kinzelbach (1999), Temporal behavior of a solute cloud in a chemically heterogeneous porous medium, J. Fluid Mech., 386, 77-104.Search in Google Scholar

[2] Bellin, A., M. Pannone, A. Fiori, and A. Rinaldo (1996), On transport in porous formations characterized by heterogeneity of evolving scales, Water Resour. Res., 32, 3485-3496.Search in Google Scholar

[3] Cintoli, S., S. P. Neuman, and V. Di Federico (2005), Generating and scaling fractional Brownian motion on finite domains, Geophys. Res. Lett. 32, L08404, doi:10.1029/2005GL022608.Search in Google Scholar

[4] Dagan, G. (1994), The significance of heterogeneity of evolving scales and of anomalous diffusion to transport in porous formations, Water Resour. Res., 30, 33273336, 1994.Search in Google Scholar

[5] Dagan, G. (1987), Theory of solute transport by groundwater, Annu. Rev. Fluid Mech., 19, 183-215.Search in Google Scholar

[6] Dagan, G. (1988), Time-dependent macrodispersion for solute transport in anisotropic heterogeneous aquifers, Water Resour. Res., 24, 1491-1500.Search in Google Scholar

[7] Dentz, M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2000), Temporal behavior of a solute cloud in a heterogeneous porous medium 1. Point-like injection, Water Resour. Res., 36, 3591-3604.Search in Google Scholar

[8] Dentz, M., H. Kinzelbach, S. Attinger, and W. Kinzelbach (2000), Temporal behavior of a solute cloud in a heterogeneous porous medium 2. Spatially extended injection, Water Resour. Res., 36, 3605-3614.Search in Google Scholar

[9] Di Federico, V., and S. P. Neuman (1997), Scaling of random fields by means of truncated power variograms and associated spectra, Water Resour. Res., 33, 1075-1085.Search in Google Scholar

[10] Fiori, A. (1996), Finite Peclet extensions of Dagan's solutions to transport in anisotropic heterogeneous formations, Water Resour. Res., 32, 193 198.Search in Google Scholar

[11] Fiori, A. (2001), On the inuence of local dispersion in solute transport through formations with evolving scales of heterogeneity, Water Resour. Res., 37, 235242.Search in Google Scholar

[12] Fiori, A., and G. Dagan (2000), Concentration fluctuations in aquifer transport: A rigorous first-order solution and applications, J. Contam. Hydrol., 45, 139 163.Search in Google Scholar

[13] Gelhar, L. W. (1986), Stochastic subsurface hydrology from theory to applications, Water Resour. Res., 22, 135S-145S.10.1029/WR022i09Sp0135SSearch in Google Scholar

[14] Gelhar, L. W., and C. L. Axness (1983), Three-dimensional stochastic analysis of macrodispersion in aquifers, textitWater Resour. Res., 19, 161-180.Search in Google Scholar

[15] Gradshteyn, I. S., and I. M. Ryzhik (2007), Table of Integrals, Series, and Products, Elsevier, Amsterdam.Search in Google Scholar

[16] Jeon, J.-H., and R. Metzler (2010), Fractional Brownian motion and motion governed by the fractional Langevin equation in confined geometries, Phys. Rev. E 81, 021103, doi:10.1103/PhysRevE.81.021103.Search in Google Scholar

[17] McLaughlin, D., and F. Ruan (2001), Macrodispersivity and large-scale hydrogeologic variability, Transp. Porous Media, 42, 133154.10.1023/A:1006720632173Search in Google Scholar

[18] Papoulis, A., and S. U. Pillai (2009), Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York.Search in Google Scholar

[19] Radu, F. A., N. Suciu, J. Hoffmann, A. Vogel, O. Kolditz, C-H. Park, and S. Attinger (2011), Accuracy of numerical simulations of contaminant transport in heterogeneous aquifers: a comparative study, Adv. Water Resour. 34, 47-61.10.1016/j.advwatres.2010.09.012Search in Google Scholar

[20] Ross, K., and S. Attinger (2010), Temporal behaviour of a solute cloud in a fractal heterogeneous porous medium at different scales, paper presented at EGU General Assembly 2010, Vienna, Austria, 02-07 May 2010.Search in Google Scholar

[21] Schwarze, H., U. Jaekel, and H. Vereecken (2001), Estimation of macrodispersivity by different approximation methods for ow and transport in randomly heterogeneous media, Transp. Porous Media, 43, 265 287.10.1023/A:1010771123844Search in Google Scholar

[22] Suciu N. (2010), Spatially inhomogeneous transition probabilities as memory effects for diffusion in statistically homogeneous random velocity fields, Phys. Rev. E, 81, 056301, doi:10.1103/PhysRevE.81.056301.Search in Google Scholar

[23] Suciu, N. (2014), Diffusion in random velocity fields with applications to contaminant transport in groundwater, Adv. Water Resour. 69, 114-133.10.1016/j.advwatres.2014.04.002Search in Google Scholar

[24] Suciu, N., C. Vamo_s, J. Vanderborght, H. Hardelauf, and H. Vereecken (2006), Numerical investigations on ergodicity of solute transport in heterogeneous aquifers, Water Resour. Res., 42, W04409, doi:10.1029/2005WR004546.Search in Google Scholar

[25] Suciu N., C. Vamos, F. A. Radu, H. Vereecken, and P. Knabner (2009), Persistent memory of diffusing particles,Phys. Rev. E, 80, 061134, doi:10.1103/PhysRevE.80.061134.Search in Google Scholar

[26] Suciu, N., S. Attinger, F.A. Radu, C. Vamos, J. Vanderborght, H. Vereecken, P. Knabner (2011), Solute transport in aquifers with evolving scale heterogeneity, Preprint No. 346, Mathematics Department, Friedrich-Alexander University Erlangen-Nuremberg (<http://fauams5.am.uni-erlan-gen.de/papers/pr346.pdf>).Search in Google Scholar

[27] Suciu, N., F.A. Radu, A. Prechtel, F. Brunner, and P. Knabner (2013), A coupled finite element-global random walk approach to advectiondominated transport in porous media with random hydraulic conductivity, J. Comput. Appl. Math. 246, 27{37.Search in Google Scholar

[28] Suciu, N., F.A. Radu, S. Attinger, L. Schüler, Knabner (2014), A Fokker-Planck approach for probability distributions of species concentrations transported in heterogeneous media, J. Comput. Appl. Math., in press, doi:10.1016/j.cam.2015.01.030.Search in Google Scholar

[29] Vamoș, C., N. Suciu, H. Vereecken, J. Vanderborght, and O. Nitzsche (2001), Path decomposition of discrete effective diffusion coecient, Internal Report ICG-IV. 00501, Research Center Jülich.Search in Google Scholar

[30] Vamoș, C., N. Suciu, and H. Vereecken (2003), Generalized random walk algorithm for the numerical modeling of complex diffusion processes, J. Comput. Phys., 186, 527-544, doi:10.1016/S0021-9991(03)00073-1.Search in Google Scholar

[31] Vanderborght, J. (2001), Concentration variance and spatial covariance in second-order stationary heterogeneous conductivity fields, Water Resour. Res., 37, 1893-1912.Search in Google Scholar

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