## 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 I_{Y}. The transport is quantified by the longitudinal equivalent macrodispersivity α_{Leq}, 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 ≫ I_{Y}. In the past we have solved transport for advection solely for highly heterogeneous media of σ_{Y}^{2} ≤ 8. We have found that α_{Leq} increases in a strong nonlinear fashion with σ_{Y}^{2} 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 = UI_{Y} / D_{0}, where D_{0} 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 (10^{2} - 10^{4}). It was found that finite Pe reduces significantly α_{Leq} as compared to advection, for σ_{Y}^{2} ≳ 3 (Pe = 1000) and for σ_{Y}^{2} ≳ 1.4 (Pe = 100), justifying neglection of the effect of diffusion for weak to moderately heterogeneous aquifers (e.g. σ_{Y}^{2} ≤ 1). In contrast, diffusion impacts considerably α_{Leq} for large σ_{Y}^{2} due to the removal of solute from low K inclusions. Furthermore, anomalous behavior is eliminated, though α_{Leq} may be still large for Pe ≫ 1.

Original language | English |
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Pages (from-to) | 659-669 |

Number of pages | 11 |

Journal | Advances in Water Resources |

Volume | 32 |

Issue number | 5 |

DOIs | |

State | Published - May 2009 |

## Keywords

- Groundwater hydrology
- Random media
- Stochastic processes