A general two-dimensional analytical solution for solute transport in anisotropic porous media with time-varying velocity field, different contaminant sources, and initial contamination

This study presents a novel two-dimensional analytical solution for solute transport in homogeneous porous media accounting for the effects of anisotropy in presence of adsorption and decay. The solution is derived using Green’s function for an infinite domain and extends existing analytical formulations by relaxing several simplifying assumptions commonly adopted in literature. In particular, the proposed analytical solution accounts for the effects of mechanical dispersion along the non-principal direction of groundwater flow as well as for the dependency of the dispersion tensor on the actual groundwater velocity field, without simplifications or convenient orientations of the model domain. The solution is also general as allows to account for: i) bi-directional groundwater velocity field and its variation over time; ii) source terms of different geometries (e.g., point, line, and surface sources) and temporal variability; iii) general initial concentration distributions of the contaminant concentration. The proposed analytical solution is also tested over benchmark problems conceived with a well-known numerical model for flow and transport in porous media (COMSOL Multiphysics®), and the agreement between the two is excellent.