Generalized semi-analytical solution for coupled multispecies advection-dispersion equations in multilayer porous media

TL;DR

This paper presents a new semi-analytical solution for multispecies contaminant transport in layered heterogeneous porous media, accommodating complex reactions, multiple layers, and boundary conditions, validated against numerical methods.

Contribution

It introduces a generalized semi-analytical approach that handles multiple species and layers with complex boundary conditions, extending previous limited solutions.

Findings

Solution agrees with published results and numerical simulations.

Applicable to arbitrary numbers of species and layers.

MATLAB code provided for implementation.

Abstract

Multispecies contaminant transport in the Earth's subsurface is commonly modelled using advection-dispersion equations coupled via first-order reactions. Analytical and semi-analytical solutions for such problems are highly sought after but currently limited to either one species, homogeneous media, certain reaction networks, specific boundary conditions or a combination thereof. In this paper, we develop a semi-analytical solution for the case of a heterogeneous layered medium and a general first-order reaction network. Our approach combines a transformation method to decouple the multispecies equations with a recently developed semi-analytical solution for the single-species advection-dispersion-reaction equation in layered media. The generalized solution is valid for arbitrary numbers of species and layers, general Robin-type conditions at the inlet and outlet and accommodates both distinct retardation factors across layers or distinct retardation factors across species. Four test cases are presented to demonstrate the solution approach with the reported results in agreement with previously published results and numerical results obtained via finite volume discretisation. MATLAB code implementing the generalized semi-analytical solution is made available.