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

Abstract

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 p of a high hydraulic conductivity facies (k+), and (1−p) of a low (k−) one. The k+ facies is characterized by two connectivity parameters: a connectivity structure type (no, low, intermediate and high), that controls how well the k+ facies is connected, and an integral scale Ib, 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 〈ta∗〉, and the longitudinal dispersivity αL. As p reaches the percolation threshold pc (pc depends on the connectivity parameters), k+ channels spanning the sample along the mean flow direction appear, giving rise to fast flow pathways. A sharp decrease of 〈ta∗〉, and a sharp increase of αL, occur when p→pc. As p exceeds pc, a subsequent minimum of 〈ta∗〉 and a maximum of αL are observed. This result is in contrast with previous ones by other authors that found a maximum of αL at p=pc. On the other hand, p kept fixed, αL decreases as the connectivity of the k+ 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 αL through a shift or displacement of pc. Finally, the existence of a spatial connectivity structure may imply early, but also late, arrival times, compared with the absence of structure.