Abstract
An analytical solution in closed form of the advection-dispersion equation in one-dimensional contaminated soils is proposed in this paper. This is valid for non-conservative solutes with first order reaction, linear equilibrium sorption, and a time-dependent Robin boundary condition. The Robin boundary condition is expressed as a combined production-decay function representing a realistic description of the source release phenomena in time. The proposed model is particularly useful to describe sources as the contaminant release due to the failure in underground tanks or pipelines, Non Aqueous Phase Liquid pools, or radioactive decay series. The developed analytical model tends towards the known analytical solutions for particular values of the rate constants.
Highlights
The study of contaminant transport in porous media is of great importance for scientists working in environmental engineering, hydrology, geology, soil physics, chemical, and petroleum engineering
Leij et al and Wang et al [17,18,19] provided a series of multi-dimensional analytical solutions by using the Green Function Method (GFM) [20] for various plane and linear sources
We propose here a closed form analytical solution of the one-dimensional advection-dispersion equation (ADE) in semi-finite domain for a reacting solute under first order decay and linear sorption described by a retardation factor
Summary
The study of contaminant transport in porous media is of great importance for scientists working in environmental engineering, hydrology, geology, soil physics, chemical, and petroleum engineering. Leij et al and Wang et al [17,18,19] provided a series of multi-dimensional analytical solutions by using the Green Function Method (GFM) [20] for various plane and linear sources With this method, under some particular initial and boundary conditions, a more complex solution can be constructed by combining the single directional solutions. The solution so proposed is of simple use, is written in an analytical form that includes the Van. Genuchten solutions [25] for specific boundary conditions, and is adoptable for developing multi-dimensional analytical solutions by using the Green Function Method
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