Solute transport in random composite media with uncertain dispersivities

Characterization of dissolved chemical migration in porous media requires knowledge of the fluid velocity field and parameters governing solute dispersion within the diverse geomaterials constituting the internal architecture of the system. Several studies have been focused on the assessment of the impact on solute concentrations of an incomplete knowledge of the fluid velocity field, typically a result of the effects of uncertain hydraulic properties of the hosting media (e.g., permeability). Limited attention has been devoted to analyze propagation of the uncertainty associated with spatial distributions of local dispersivity values to solute concentration fields. Here, we address this issue by focusing on a random composite medium, where the location of the boundary between two distinct geomaterials is uncertain as well as their associated dispersivity values. We derive and solve the equations satisfied by the (ensemble) mean and variance of solute concentration and investigate the relative impact on these moments of the two sources of uncertainty considered. Our results suggest that, in the investigated set-up, the temporal and spatial evolution of ensemble moments of the solute concentration depends on (i) the overall dispersive length scales encompassed by the solute during its migration and (ii) the actual sequence of the materials traversed by the solute.