Analytical modeling of diffusion-limited contamination and decontamination in a two-layer porous medium

Diffusion of dissolved contaminants in multilayer porous media is an important phenomenon affecting both contamination and remediation in natural aqueous environments, including diffusion in groundwater aquitards and contaminated bed sediments. This study presents a new analytical solution for solute diffusion in a semi-infinite two-layer porous medium for arbitrary boundary and initial conditions. The solution was obtained by using the Green's function approach in the Laplace domain with the application of the binomial theorem to facilitate inversion back to the real time domain. Results based on this solution were found to be simple both in form and ease of calculation and to be in good agreement with those obtained using numerical calculations based on the Crank-Nicolson finite difference method. Applications of the solution are presented in the context of a contaminated groundwater aquitard to demonstrate how different boundary and initial conditions can greatly affect the contamination and decontamination of porous media, and to illustrate how diffusion modeling might be used in a forensic sense.