### Abstract

In advective transport through weakly heterogeneous aquifers of random stationary and isotropic three-dimensional permeability distribution, transverse macrodispersivity α_{T} is found to be zero. This was determined in the past by solving the transport equation at first order in the log conductivity variance σ^{2}_{γ}. However, field findings indicate the presence of small but finite α_{T} . The aim of the paper is to determine α_{T} for highly heterogeneous formations using a model that contains inclusions of conductivity K, submerged in a matrix of conductivity K_{0}, for large κ = K/K_{0}. In the dilute medium approximation, valid for small volume fraction n, but arbitrary κ, and for spherical inclusions, it is found that α_{T} = 0 because of the axisymmetry of flow past a sphere. A medium made up of rotational ellipsoids of arbitrary random orientation, macroscopically isotropic, and of the same κ and n is devised as a counterexample. It is found that because of the intertwining of streamlines α_{T} > 0, being of order (κ - 1)^{4} for κ » 1. These findings are confirmed by accurate numerical simulations of flow through a large number of interacting inclusions; for κ = 10 and n = 0.2 (jamming limit), the large value α_{T}/α _{T}≃ 0-15 is attained. The numerical simulations display the strong permanent deformation of stream tubes responsible for this phenomenon, corned as "advective mixing." The two-point covariance, used in practice in order to characterize the aquifer structure, is not able to detect the structures that produce advective mixing. Nevertheless, the presence of high-conductivity lenses inclined with respect to the mean flow may explain the occurrence of finite α_{T} in field applications.

Original language | English (US) |
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Article number | W08415 |

Journal | Water Resources Research |

Volume | 45 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1 2009 |

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## Cite this

*Water Resources Research*,

*45*(8), [W08415]. https://doi.org/10.1029/2009WR007741