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Title: Analytical solution for multi-species contaminant transport in finite media with time-varying boundary conditions

item PEREZ GUERRERO, JESUS - Brazilian Nuclear Energy Commission
item Skaggs, Todd
item VAN GENUCHTEN, MARTINUS - Universidade Federal Do Rio De Janeiro

Submitted to: Transport in Porous Media
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 2/17/2010
Publication Date: 10/1/2010
Citation: Perez Guerrero, J.S., Skaggs, T.H., Van Genuchten, M.T. 2010. Analytical solution for multi-species contaminant transport in finite media with time-varying boundary conditions. Transport in Porous Media. 85(1):171-188.

Interpretive Summary: In soils and groundwater, some environmental contaminants undergo chain reactions that transform the contaminant from one chemical species to another. Examples include nitrogen, pesticides, and radionuclides. 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 that incorporates more flexible boundary conditions and thus permits the simulation of more realistic contamination scenarios. The research will benefit scientists and engineers seeking to prevent or remediate groundwater and soils contamination.

Technical Abstract: Most analytical solutions available for the equations governing the advective-dispersive transport of multiple solutes undergoing sequential first-order decay reactions have been developed for infinite or semi-infinite spatial domains and steady-state boundary conditions. In this work we present an analytical solution for a finite domain and a time-varying boundary condition. The solution was found using the Classic Integral Transform Technique (CITT) in combination with a filter function having separable space and time dependencies, implementation of the superposition principle, and using an algebraic transformation that changes the advection-dispersion equation for each species into a diffusion equation. The analytical solution was evaluated using a test case from the literature involving a four radionuclide decay chain. Results show that convergence is slower for advection-dominated transport problems. In all cases the converged results were identical to those obtained with the previous solution for a semi-infinite domain, except near the exit boundary where differences were expected. Among other applications, the new solution should be useful for benchmarking numerical solutions because of the adoption of a finite spatial domain.