The impact of local diffusion on longitudinal macrodispersivity and its major effect upon anomalous transport in highly heterogeneous aquifers

Igor Janković, Aldo Fiori*, Gedeon Dagan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

22 Scopus citations

Abstract

Flow and transport are solved for a heterogeneous medium modeled as an ensemble of spherical inclusions of uniform radius R and of conductivities K, drawn from a pdf f (K) (Fig. 1). This can be regarded as a particular discretization scheme, allowing for accurate numerical and semi-analytical solutions, for any given univariate f (Y) (Y = ln K) and integral scale IY. The transport is quantified by the longitudinal equivalent macrodispersivity αLeq, for uniform mean flow of velocity U and for a large (ergodic) plume of a conservative solute injected in a vertical plane (x = 0) and moving past a control plane at x ≫ IY. In the past we have solved transport for advection solely for highly heterogeneous media of σY2 ≤ 8. We have found that αLeq increases in a strong nonlinear fashion with σY2 and transport becomes anomalous for the subordinate model. This effect is explained by the large residence time of solute particles in inclusions of low K. In the present work we examine the impact of local diffusion as quantified by the Peclet number Pe = UIY / D0, where D0 is the coefficient of molecular diffusion. Transport with diffusion is solved by accurate numerical simulations for flow past spheres of low K and for high Pe = O (102 - 104). It was found that finite Pe reduces significantly αLeq as compared to advection, for σY2 ≳ 3 (Pe = 1000) and for σY2 ≳ 1.4 (Pe = 100), justifying neglection of the effect of diffusion for weak to moderately heterogeneous aquifers (e.g. σY2 ≤ 1). In contrast, diffusion impacts considerably αLeq for large σY2 due to the removal of solute from low K inclusions. Furthermore, anomalous behavior is eliminated, though αLeq may be still large for Pe ≫ 1.

Original languageEnglish
Pages (from-to)659-669
Number of pages11
JournalAdvances in Water Resources
Volume32
Issue number5
DOIs
StatePublished - May 2009

Keywords

  • Groundwater hydrology
  • Random media
  • Stochastic processes

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