Analytical model for 1-D contaminant diffusion through clay barriers

Abstract

Studies on diffusion transport of contaminants through clays are vitally important for performance assessment of waste disposal facilities. Laboratory through-diffusion (double-reservoir) experiment represents a well-established and routinely used technique for the determination of design mass transport parameters in a single test. Availability of accurate and simple theoretical models is valuable for simulating diffusion transport of contaminants through clays for the design and evaluation processes of many waste disposal facilities. The theoretical solutions for this problem are commonly obtained by numerically solving the governing diffusion equation in combination with finite mass boundary conditions. The lack of analytical solutions to this problem encouraged the development of numerical solutions. However, a high computational cost is associated with such time-marching numerical solutions. Closed-form analytical solutions are proposed, in this work, for one-dimensional (1D) transient through diffusion transport of sorptive contaminants through homogeneous clays. Proposed analytical solutions are compared with the solution obtained using existing methods on experimental data. The proposed analytical solutions are simple and accurate for theoretically estimating transient diffusion transport of sorptive contaminants through clays. The proposed model has ready application for analysing routine laboratory through-diffusion experimental data.