Exposure concentration statistics in the subsurface transport

The concentration fluctuations resulting from hazardous releases in the subsurface are modeled through the concentration moments. The local solute exposure concentration, resulting from the heterogeneous velocity field and pore scale dispersion in the subsurface, is a random function characterized by its statistical moments. The approximate solution to the exact equation that describes the evolution of concentration standard moments in the aquifer transport is proposed in a recursive form. The expressions for concentration second, third and fourth central moments are derived and evaluated for various flow and transport conditions. The solutions are sought by starting from the exact upper bound solution with the zero pore scale dispersion and introducing the physically based approximation that allows the inclusion of the pore scale dispersion resulting in simple closed-form expressions for the concentration statistical moments. The concentration moments are also analyzed in the relative and absolute frame of reference indicating their combined importance in the practical cases of the subsurface contaminant plume migration. The influence of pore scale dispersion with different source sizes and orientations are analyzed and discussed with respect to common cases in the environmental risk assessment problems. The results are also compared with the concentration measurements of the conservative tracer collected in the field experiments at Cape Cod and Borden Site.