Advertisement

The Relative Dispersion and Mixing of Passive Solutes in Transport in Geologic Media

Chapter
  • 116 Downloads

Abstract

The spreading of a contaminant in a heterogeneous aquifer depends on the scales of variability effectively explored by the plume. In particular, we observe two major contributions of the fluctuating velocity field in the contaminant movement: (i) the spreading caused by velocity variations of scales lesser than that of the plume size, which we will call ‘relative’ spreading, and (ii) the meander-like movement of the plume as a whole caused by velocity variations of scale larger than that of the plume size. The aim of this work is to consider the effects of the finite size of the contaminant plume on the local concentration moments 〈C〉 and σ C . In particular a ‘relative’ concentration, which depends on the scales of variability effectively explored by the plume, is defined. First, the mathematical formulation of the problem is developed along the Lagrangian framework. In particular, the expressions for the relative mean concentration and its variance are presented. Then, the methodology is applied to the regional transport problem, where the influence of the size of the plume and the pore-scale dispersion are quantitatively assessed.

Key words

aquifer transport groundwater quality solute dilution heterogeneous porous formation. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andricevic, R.: 1998, Effects of local dispersion and sampling volume on the evolution of concentration fluctuations in aquifers, Water Resour. Res. 34 (5), 1115–1129.CrossRefGoogle Scholar
  2. Andricevic, R. and Cvetkovic, V.: 1998, Relative dispersion for solute flux in aquifers, J. Fluid Mech. 361, 145–174.CrossRefGoogle Scholar
  3. Chatwin, P.C. and Sullivan, P. J.: 1979, The relative diffusion of a cloud of passive contaminant in incompressible turbulent flow, J. Fluid Mech. 91, 337–355.CrossRefGoogle Scholar
  4. Chu, S.Y. and Sposito, G.: 1980, A derivation of the macroscopic solute transport equation for homogeneous, saturated porous media, Water Resour. Res. 16, 542–546.CrossRefGoogle Scholar
  5. Dagan, G.: 1982, Stochastic modeling of groundwater flow by unconditional and conditional probabilities, 2. The solute transport, Water Resour. Res. 18 (4), 813–833.CrossRefGoogle Scholar
  6. Dagan, G.: 1984, Solute transport in heterogeneous porous formations, J. Fluid Mech. 145, 151–177.CrossRefGoogle Scholar
  7. Dagan, G.: 1989, Flow and Transport in Porous Formations,Springer-Verlag, 465 p.Google Scholar
  8. Dagan, G.: 1991, Dispersion of a passive solute in non-ergodic transport by steady velocity fields in heterogeneous formations, J. Fluid Mech. 233, 197–210.CrossRefGoogle Scholar
  9. Dagan, G. and Fiori, A.: 1997, The influence of pore-scale dispersion on concentration statistical moments in transport through heterogeneous aquifers, Water Resour. Res. 33, 1595–1606.CrossRefGoogle Scholar
  10. Fiori, A.: 1996, Finite-Peclet extensions of Dagan’s solution to transport in anisotropic heterogeneous formations, Water Resour. Res. 32, 193–198.CrossRefGoogle Scholar
  11. Fiori, A. and Dagan, G.: 1999, Concentration fluctuations in transport by groundwater: comparison between theory and field experiments, Water Resour. Res. 35 (1), 105–112.CrossRefGoogle Scholar
  12. Gelhar, L. W. and Axness, C. L.: 1983, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res. 19, 161–180.CrossRefGoogle Scholar
  13. Graham, W. and Mclaughlin, D.: 1989, Stochastic analysis of nonstationary subsurface solute transport. 1. Unconditional moments, Water Resour. Res. 25, 215–232.CrossRefGoogle Scholar
  14. Kapoor, V. and Gelhar, L. W.: 1994, Transport in three-dimensional heterogeneous aquifers: 1.Dynamics of concentration fluctuations, Water Resour. Res. 6, 1775–1788.CrossRefGoogle Scholar
  15. Kitanidis, P. K.: 1988, Prediction by the methods of moments of transport in heterogeneous formation, J. Hydrol. 102, 453–473.CrossRefGoogle Scholar
  16. Neuman, S. P., Winter, C. L. and Newman, C M 1987, Stochastic theory of field-scale Fickian dispersion in anisotropie porous media, Water Resour. Res. 23, 453–466.CrossRefGoogle Scholar
  17. Rajaram, H. and Gelhar, L. W.: 1993, Plume-scale dependent dispersion in heterogeneous aquifer: 2. Eulerian analysis and three-dimensional aquifers. Water Resour. Res. 29 (9), 3261–3276.CrossRefGoogle Scholar
  18. Richardson, L. F.: 1926, Atmospheric diffusion shown on a distance-neighour graph, Proc. Roy. Soc. Series A, 110: 709.CrossRefGoogle Scholar
  19. Selroos, J. 0.: 1995, Temporal moments for non-ergodic solute transport in heterogeneous aquifers, Water Resour. Res. 31, 1705–1712.Google Scholar
  20. Zhang, D. and Neuman, S. P.: 1996, Effect of local dispersion solute transport in randomly heterogeneous media, Water Resour Res. 32 (9), 2715–2724.CrossRefGoogle Scholar
  21. Zhang, Y. K., Zhang, D. and Lin, L.: 1996, Non-ergodic solute transport in three-dimensional heterogeneous isotropic aquifers, Water Resour. Res. 32 (9), 2955–2963.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  1. 1.Dipartimento di Scienze dell’Ingegneria CivileUniversita’ degli Studi di Roma TreItaly

Personalised recommendations