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Title: Exact analytical solutions for contaminant transport in rivers 2. Transient storage and decay chain solutions

item VAN GENUCHTEN, MARTINUS - Universidade Federal Do Rio De Janeiro
item LEIJ, FEIKE - California State University
item Skaggs, Todd
item TORIDE, NOBUO - Mie University
item Bradford, Scott
item PONTEDEIRO, ELIZABETH - Universidade Federal Do Rio De Janeiro

Submitted to: Journal of Hydrology and Hydromechanics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/23/2013
Publication Date: 9/1/2013
Citation: Van Genuchten, M.T., Leij, F.J., Skaggs, T.H., Toride, N., Bradford, S.A., Pontedeiro, E.M. 2013. Exact analytical solutions for contaminant transport in rivers 2. Transient storage and decay chain solutions. Journal of Hydrology and Hydromechanics. 61(3):250-259.

Interpretive Summary: The fate of contaminants in the environment depends on a host of contaminant transport phenomena that govern the movement of contaminants in water, soil, and air. Transport processes such as diffusion can be modeled mathematically using partial differential equations, and mathematical solutions to those equations can be used to predict the migration and impact of contaminants released into the environment. In this work (presented as a two-part series), we discuss a class of transport equations known as advection-dispersion equations (ADE). The equations take on different forms depending on what processes are thought to be operating in a given environment. In this part 2 of the series, we present several solutions for relatively complex formulations of the ADE which can be used to model transport in streams, lakes, and other surface water bodies. Many of the presented solutions were obtained by adapting solutions that were developed for groundwater systems and which were scattered across the scientific literature. By adapting these solutions and compiling them all in one place, this research will assist scientists and engineers in predicting or analyzing contaminant transport in rivers and other surface water bodies.

Technical Abstract: Contaminant transport processes in streams, rivers, and other surface water bodies can be analyzed or predicted using the advection-dispersion equation and related transport models. In part 1 of this two-part series we presented a large number of one- and multi-dimensional analytical solutions of the standard equilibrium advection-dispersion equation (ADE) with and without terms accounting for zero-order production and first-order decay. The solutions are extended in the current part 2 to advective-dispersive transport with simultaneous first-order mass exchange between the stream or river and zones with dead water (transient storage models), and to problems involving longitudinal advective-dispersive transport with simultaneous diffusion in fluvial sediments or near-stream subsurface regions comprising a hyporheic zone. Part 2 also provides solutions for one-dimensional advective-dispersive transport of contaminants subject to consecutive decay chain reactions.