An Analytical Solution Evaluating Steady-State Plumes of Sequentially Reactive Contaminants

A steady state version of an analytical solution of the reactive flow and transport problem is derived. This solution allows a better understanding of the steady-state plume characteristics, and allows the prediction of the effectiveness of natural attenuation of sequentially reactive contaminants. The sequential reactions are assumed to be first order. Using spatial moments as compact information of plume characteristics, the total mass, plume centroids, and extents of each contaminant plume are derived as functions of dispersivity, velocity, and reaction rates. The steady-state plume centroids and extents are independent of stoichiometric coefficients. The solution is demonstrated for a four-species sequentially reactive transport in a one-dimensional column. The extension to three dimensions is easily made and does not change the basic functions.