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United States Department of Agriculture

Agricultural Research Service

Research Project: Effects of Agricultural Water Management and Land Use Practices on Regional Water Quality Title: Exact analytical solutions for contaminant transport in rivers 1. The equilibrium advection-dispersion equation

Authors
item Van Genuchten, Martinus -
item Leij, Feike -
item Skaggs, Todd
item Toride, Nobuo -
item Bradford, Scott
item Pontedeiro, Elizabeth -

Submitted to: Journal of Hydrology and Hydromechanics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: February 23, 2013
Publication Date: June 1, 2013
Repository URL: http://www.ars.usda.gov/SP2UserFiles/Place/53102000/pdf_pubs/P2405.pdf
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 1. The equilibrium advection-dispersion equation. Journal of Hydrology and Hydromechanics. 61(2):146-160.

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 1 of the series, we present several solutions for relatively simple 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: Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present a series of one- and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective-dispersive transport with mass exchange in dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.

Last Modified: 7/22/2014
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