Spatial moments for reactive transport in heterogeneous porous media

The transport of reactive chemicals through porous media is generally affected by multiple reactions with different rate constants. In this work, we investigate one-dimensional transport affected by rate-limited sorption, first-order mass transfer, and first-order transformation and derive analytical solutions for the spatial moments of the solute in the solution phase using an exponentially increasing dispersivity function to account for the spatial heterogeneity of hydraulic conductivity. Illustrative examples are used to discuss the effect of various rate constants on the travel distance, variance, and skewness. It is shown that the spatial heterogeneity of material properties can be satisfactorily accounted for by using an increasing macrodispersivity function. These solutions will be useful as a preliminary analysis tool for ascertaining the relative importance of various processes under given conditions. They may also be used to analyze the accuracy of various numerical techniques used for simulation of reactive transport through homogeneous and heterogeneous porous media.