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United States Department of Agriculture

Agricultural Research Service

Research Project: IMPROVED KNOWLEDGE AND MODELING OF WATER FLOW AND CHEMICAL TRANSPORT PROCESSES IN IRRIGATED SOILS Title: Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media

item Pérez Guerrero, J -
item Skaggs, Todd
item Van Genuchten, M -

Submitted to: Transport in Porous Media
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: February 18, 2009
Publication Date: March 19, 2009
Repository URL:
Citation: Pérez Guerrero, J.S., Skaggs, T.H., Van Genuchten, M.T. 2009. Analytical Solution for Multi-Species Contaminant Transport Subject to Sequential First-Order Decay Reactions in Finite Media. Transport in Porous Media. 80(2):373-387.

Interpretive Summary: In soils and groundwater, some environmental contaminants undergo chain reactions that transform the contaminant from one chemical species to another. Examples of such contaminants include nitrogen, radionuclides, and pesticides. The concentration of these contaminants in the subsurface can be estimated for different scenarios using mathematical models that calculate the chemical transformations. In this work, we developed a new mathematical model for making such calculations. The research will benefit scientists and engineers seeking to prevent or remediate groundwater and soils contamination.

Technical Abstract: Transport equations governing the movement of multiple solutes undergoing sequential first-order decay reactions have relevance in analyzing a variety of subsurface contaminant transport problems. In this study, a one-dimensional analytical solution for multi-species transport is obtained for finite porous media and constant boundary conditions. The solution permits different retardation factors for the various species. The solution procedure involves a classic algebraic substitution that transforms the advection-dispersion partial differential equation for each species into an equation that is purely diffusive. The new system of partial differential equations is solved analytically using the Classic Integral Transform Technique (CITT). Results for a classic test case involving a three-species nitrification chain are shown to agree with previously reported literature values. Because the new solution was obtained for a finite domain, it should be especially useful for testing numerical solution procedures.

Last Modified: 8/27/2016
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