General analytical solutions for one-dimensional diffusion of degradable organic contaminant in the multi-layered media containing geomembranes

Abstract

In practical engineering construction, multi-layered barriers containing geomembranes are extensively applied to retard the migration of pollutants. However, the associated analytical theory on pollutants diffusion still needs to be further improved. In this work, general analytical solutions are derived for one-dimensional diffusion of degradable organic contaminant (DOC) in the multi-layered media containing geomembranes under a time-varying concentration boundary condition, where the variable substitution and separated variable approaches are employed. These analytical solutions with clear expressions can be used not only to study the diffusion behaviors of DOC in bottom and vertical composite barrier systems, but also to verify other complex numerical models. The proposed general analytical solutions are then fully validated via three comparative analyses, including comparisons with the experimental measurements, an existing analytical solution, and a finite-difference solution. Ultimately, the influences of different factors on the composite cutoff wall’s (CCW, which consists of two soil-bentonite layers and a geomembrane) service performance are investigated through a composite vertical barrier system as the application example. The findings obtained from this investigation can provide scientific guidance for the barrier performance evaluation and the engineering design of CCWs. This application example also exhibits the necessity and effectiveness of the developed analytical solutions.

Keywords

general analytical solutions / degradable organic contaminant / diffusion behavior / multi-layered media containing geomembranes / composite barrier system

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