ARS | Publication request: Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions

Submitted to: Chemical Engineering Journal
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: January 30, 2013
Publication Date: April 1, 2013
Repository URL: http://www.ars.usda.gov/SP2UserFiles/Place/53102000/pdf_pubs/P2420.pdf
Citation: Perez-Guerrero, J.S., Pontedeiro, E.M., Van Genuchten, M.T., Skaggs, T.H. 2013. Analytical solutions of the one-dimensional advection-dispersion solute transport equation subject to time-dependent boundary conditions. Chemical Engineering Journal. 221:487-491.

Interpretive Summary: The fate of contaminants in the environment depends on a variety 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, we demonstrated a technique for solving transport equations which include time varying boundary conditions. Time variable boundary conditions permit the analysis of a wider range of contamination scenarios than constant boundary conditions, and allow for more realistic simulations. The research will benefit scientists and engineers seeking to prevent or remediate groundwater and soils contamination.

Technical Abstract: Analytical solutions of the advection-dispersion solute transport equation remain useful for a large number of applications in science and engineering. In this paper we extend the Duhamel theorem, originally established for diffusion type problems, to the case of advective-dispersive transport subject to transient (time-dependent) boundary conditions. Generalized analytical formulas are established which relate the exact solutions to corresponding time-independent auxiliary solutions. Explicit analytical expressions were developed for the instantaneous pulse problem formulated from the generalized Dirac delta function for situations with first-type or third-type inlet boundary condition of both finite and semi-infinite domains. The developed generalized equations were evaluated computationally against other specific solutions available from the literature. Results showed the consistency of our expressions.