Channeling, channel density and mass recovery in aquifer transport, with application to the MADE experiment

Channeling effects in heterogeneous formations are studied through a new quantity denoted as channel density a(x,t). Focusing on advection only, a(x, t) is defined as the relative number of streamtubes (or channels) containing solute between x and x1dx at a given time t, regardless of the mass that they carry. The channel density generally differs from the widely employed longitudinal mass distribution m(x, t), and their difference increases with time and the degree of heterogeneity. The difference between a and m reflects the nonuniformity of mass distribution relative to the plume geometry. In particular, the fast channels typically carry a larger fraction of mass than their share in their relative volume, which in turn can be rather small. Detecting such channels by a network of monitoring wells may be a challenging task, which might explain the poor solute recovery of some field experiments at increasing times. After application of the proposed concepts to the simple case of stratified formations, we model the channel density and mass distribution pertaining to the MADE experiment, which exhibited poor mass recovery at large times. The results presented in this study emphasize the possible channeling effects at MADE and the general difficulty in sampling the leading edge of the plume, which in turn may contain a significant fraction of the plume mass.