Advertisement

Transport in Porous Media

, Volume 30, Issue 1, pp 57–73 | Cite as

On the Influence of Pore-Scale Dispersion in Nonergodic Transport in Heterogeneous Formations

  • Aldo Fiori
Article

Abstract

Flow of an inert solute in an heterogeneous aquifer is usually considered as dominated by large-scale advection. As a consequence, the pore-scale dispersion, i.e. the pore scale mechanism acting at scales lower than that characteristic of the heterogeneous field, is usually neglected in the computation of global quantities like the solute plume spatial moments. Here the effect of pore-scale dispersion is taken into account in order to find its influence on the longitudinal asymptotic dispersivity D11we examine both the two-dimensional and the three-dimensional flow cases. In the calculations, we consider the finite size of the solute initial plume, i.e. we analyze both the ergodic and the nonergodic cases. With Pe the Péclat number, defined as Pe=Uλ/D, where U, λ, D are the mean fluid velocity, the heterogeneity characteristic length and the pore-scale dispersion coefficient respectively, we show that the infinite Péclat approximation is in most cases quite adequate, at least in the range of Péclat number usually encountered in practice (Pe > 102). A noteworthy exception is when the formation log-conductivity field is highly anisotropic. In this case, pore-scale may have a significant impact on D11, especially when the solute plume initial dimensions are not much larger than the heterogeneities' lengthscale. In all cases, D11 appears to be more sensitive to the pore-scale dispersive mechanisms under nonergodic conditions, i.e. for plume initial size less than about 10 log-conductivity integral scales.

groundwater nonergodic transport dispersion heterogeneous formations hydrogeology 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams, E. E. and Gelhar, L. W.: 1992, Field study of dispersion in a heterogeneous aquifer, 2, Spatial moments analysis, Water Resour. Res. 28, 3293-3307.Google Scholar
  2. Dagan, G.: 1982, Stochastic modeling of groundwater flow by unconditional and conditional probabilities 1. Conditional simulation and the direct problem, Water Resour. Res. 18, 813-833.Google Scholar
  3. Dagan, G.: 1984, Solute transport in heterogeneous porous formations, J. Fluid Mech. 145, 151-177.Google Scholar
  4. Dagan, G.: 1986, Statistical theory of groundwater flow and transport: Pore to laboratory, laboratory to formation and formation to regional scale, Water Resour. Res. 22, 120S-135S.Google Scholar
  5. Dagan, G.: 1989, Flow and Transport in Porous Formations, Springer-Verlag, New York.Google Scholar
  6. Dagan, G.: 1990, Transport in heterogeneous porous formations: Spatial moments, ergodicity, and effective dispersion, Water Resour. Res. 26, 1281-1290.Google Scholar
  7. 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.Google Scholar
  8. Fiori, A.: 1996, Finite Péclet extension of Dagan's solutions to transport in anisotropic heterogeneous formations, Water Resour. Res. 32, 193-198.Google Scholar
  9. Freyberg, D. L.: 1986, A natural gradient experiment on solute transport ina sand aquifer, 2, Spatial moments and dispersion of nonreactive tracers, Water Resour. Res. 22, 2031-2046.Google Scholar
  10. Garabedian, S. P., LeBlanc, D. R., Gelhar, L. W. and Celia, M. A.: 1991, Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 2, Analysis of tracer moments for a nonreactive tracer, Water Resour. Res. 27, 911-924.Google Scholar
  11. Gelhar, L. W. and Axness, C. L.: 1983, Three-dimensional stochastic analysis of macrodispersion in aquifers, Water Resour. Res. 19, 161-180.Google Scholar
  12. Gelhar, L. W.: 1993, Stochastic Subsurface Hydrology, Prentice-Hall, Englewood Cliffs.Google Scholar
  13. Kitanidis, P. K.: 1988, Prediction by the methods of moments of transport in heterogeneous formation, J. Hydrol. 102, 453-473.Google Scholar
  14. Neuman, S. P., Winter, C. L. and Newman, C. M.: 1987, Stochastic theory of field-scale Fickian dispersion in anistropic porous media, Water Resour. Res. 23, 453-466.Google Scholar

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Aldo Fiori
    • 1
  1. 1.Dipartimento di Scienze dell'Ingegneria CivileUniversità di Roma Tre, RomaRomaItly

Personalised recommendations