Solute transport in highly heterogeneous media: The asymptotic signature of connectivity

The connectivity of the more conductive hydrofacies strongly determines flow and transport in heterogeneous media. Here we study solute transport in 3D binary isotropic samples with a proportion ������of a high hydraulic conductivity facies (������+), and (1 - ������) of a low (������-) one. The ������+ facies is characterized by two connectivity parameters: a connectivity structure type (no, low, intermediate and high), that controls how well the ������+ facies is connected, and an integral scale ������������, that controls the heterogeneity characteristic lengthscale. Under ergodic conditions, and in the asymptotic Fickian regime that arises only very far from the injection plane, we analyze two transport quantities: the normalized mean solute arrival time (������*������), and the longitudinal dispersivity ������������. As ������reaches the percolation threshold ������������(������������ depends on the connectivity parameters), ������+ channels spanning the sample along the mean flow direction appear, giving rise to fast flow pathways . A sharp decrease of (������*������), and a sharp increase of ������������, occur when ������ & RARR; ������������. As ������exceeds ������������, a subsequent minimum of (������*������) and a maximum of ������������are observed. This result is in contrast with previous ones by other authors that found a maximum of ������������at ������= ������������. On the other hand, ������kept fixed, ������������decreases as the connectivity of the ������+ facies increases. We conclude that the connectivity features sampled by the solute particles during their trajectories are retained in the transport quantities even after the asymptotic regime is attained. Also, that connectivity mainly affects ������������through a shift or displacement of ������������. Finally, the existence of a spatial connectivity structure may imply early, but also late, arrival times, compared with the absence of structure.

Automated summary

This study investigates solute transport in 3D binary isotropic samples and finds that the connectivity of the high conductivity facies directly affects the flow pathways and the transport properties of the system. The results show that as the percolation threshold is reached, fast flow pathways are formed, leading to a decrease in solute arrival time and an increase in longitudinal dispersivity.