An analytical solution for one-dimensional advective–dispersive solute equation in multilayered finite porous media

Abstract

A general analytical solution for the one-dimensional advective–dispersive–reactive solute transport equation in multilayered porous media is presented. The model allows an arbitrary number of layers, parameter values, and initial concentration distributions. The separation of variables technique was employed to derive the analytical solution. Hyperbolic eigenfunctions, as well as traditional trigonometric eigenfunctions, were found to contribute an important part to the series solution and were not included in some existing solutions. The closed-form analytical solution was verified against a numerical solution from a finite difference-based approach and an existing solution derived from general integral transform technique (GITT). The solution has several important advantages over the GITT technique and other existing solutions. The limitations of existing solutions and the ability of the current solution to address those limitations are identified. Among other applications, the current analytical solution will be useful for modeling the transport of contaminants in sediments and, particularly for the design of layered caps as a remedial approach. The analytical solution also has significant advantages over numerical solutions for sensitivity analyses and the solution of inverse problems.