Spatial moments for colloid-enhanced radionuclide transport in heterogeneous aquifers

We consider colloid facilitated radionuclide transport by steady groundwater flow in a heterogeneous porous formation. Radionuclide binding on colloids and soil-matrix is assumed to be kinetically/equilibrium controlled. All reactive parameters are regarded as uniform, whereas the hydraulic log-conductivity is modelled as a stationary random space function (RSF). Colloid-enhanced radionuclide transport is studied by means of spatial moments pertaining to both the dissolved and colloid-bounded concentration. The general expressions of spatial moments for a colloid-bounded plume are presented for the first time, and are discussed in order to show the combined impact of sorption processes as well as aquifer heterogeneity upon the plume migration. For the general case, spatial moments are defined by the aid of two characteristic reaction functions which cannot be expressed analytically. By adopting the approximation for the longitudinal fluid trajectory covariance valid for a flow parallel to the formation bedding suggested by Dagan and Cvetkovic [Dagan G, Cvetkovic V. Spatial Moments of Kinetically Sorbing Plume in a Heterogeneous Aquifers. Water Resour Res 1993;29:4053], we obtain closed form solutions.For illustrative purposes, we consider the case when sorption/desorption between solution and moving colloids is a linear non-equilibrium process, whereas sorption onto the soil-matrix is a linear equilibrium process. Based on the flow and transport parameters pertaining to the alluvial aquifer at the Yucca Mountain Site (Nevada), we investigate the potential enhancing role of colloidal particles by comparing radionuclide spatial moments with and without colloids, and mainly investigate the sensitivity to the reverse rate parameter. The most potentially significant effects are obtained when radionuclide attachment to colloidal particles is irreversible. The simplicity of our results makes them suitable for quick assessments of the potential impact of colloids on contaminant transport in heterogeneous aquifers.