On macrodispersion in uniform ? radial divergent flow through weakly heterogeneous aquifers

Abstract

The transport of instantaneously injected conservative solute through a well in the formation of random conductivity is analyzed. The solute is advected by the recharging well flow with the uniform background gradient. The longitudinal trajectory variance is derived for the central mean streamline. It is shown that the solute is spread as in a radial flow at small travel distances and as in a uniform flow far from the well. Closed form expressions of the longitudinal trajectory variance and macrodispersivity are derived for the case of small scale heterogeneity. It is shown that the macrodispersivity is bounded between the asymptotic macrodispersivities pertinent to the well and uniform flows.