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Title: Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients

Author
 PEREZ GUERRERO, J - Brazil Nuclear Energy Commission Skaggs, Todd

 Submitted to: Journal of Hydrology Publication Type: Peer Reviewed Journal Publication Acceptance Date: 6/18/2010 Publication Date: 8/20/2010 Citation: Perez Guerrero, J.S., Skaggs, T.H. 2010. Analytical solution for one-dimensional advection-dispersion transport equation with distance-dependent coefficients. Journal of Hydrology. 390(1-2)57:65. Interpretive Summary: Mathematical models are often used in investigations of contaminant migration in soils and groundwater. For example, a model might be used to predict the likelihood that a chemical released into the soil environment will reach a drinking water well. Soils and aquifers are rarely uniform over long distances; accounting for the natural variability of soils and aquifers in mathematical models is a challenge for scientists and engineers. In this work, we formulated a new mathematical model for contaminant transport in non-uniform soils and aquifers. The model will allow for 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: Mathematical models describing contaminant transport in heterogeneous porous media are often formulated as an advection-dispersion transport equation with distance-dependent transport coefficients. In this work, a general analytical solution is presented for the linear, one-dimensional advection-dispersion equation with distance-dependent coefficients. An integrating factor is employed to obtain a transport equation that has a self-adjoint differential operator, and a solution is found using the generalized integral transform technique (GITT). It is demonstrated that an analytical expression for the integrating factor exists for several transport equation formulations of practical importance in groundwater transport modeling. Unlike nearly all solutions available in the literature, the current solution is developed for a finite spatial domain. As an illustration, solutions for the particular case of a linearly increasing dispersivity are developed in detail and results are compared with solutions from the literature. Among other applications, the current analytical solution will be particularly useful for testing or benchmarking numerical transport codes because of the incorporation of a finite spatial domain.