Analysis of nonlinearly reactive transport by means of temporal moments

Modeling coupled reactions and flow in porous formations is extremely important for predicting the fate of chemicals in groundwater. Once in the geological medium, pollutants are advected by water and in most cases may undergo to chemical and physical processes. In this note we extend the Lagrangian approach developed by Dagan & Cvetkovic (1996) for nonlinearly reacting solutes by accounting for a finite pulse of solutes that are supposed to obey to Freundlich isotherm. In line with previous works (see, for instance, Dagan 84), we assume that groundwater takes place due to a fixed pressure drop applied to the boundary of the porous medium. Moreover, owing to the slow changes in time of flow patterns, the resulting saturated flow field is regarded steady and its statistics is assumed to be given. Solute is injected at a constant concentration C0 when 0<t<T0, while C0=0 for t>T0. The field scale transport problem consists into characterizing an erratic plume along distinct random flow paths that do not interact between them (high Peclet number). Using the conceptual framework developed by Cvetkovic & Dagan (1994), reactive transport along three-dimensional flow paths is transformed into one-dimensional Lagrangian-Eulerian domain. By the aid of the linear theory, temporal moments of flux concentration through a large control plane (CP) are derived. For purposes of illustration, the first two temporal moments are computed for a few parameters values in order to discuss the relative impact of nonlinearity and heterogeneity upon transport.