A semi-analytical solution for a two-dimensional capacitance model in solute transport

A two-dimensional capacitance model is presented for the analysis of solute transport in heterogeneous porous media where the transport processes are affected by mass transfer between the flowing volume in macropores and the stagnant volume in micropores. The semi-analytical solutions for both penetrating and nonpenetrating sources are obtained using double Laplace transforms and numerical inversions. The modeling results reveal the strong influences of dispersive and convective properties of porous media in the transverse direction on the overall transport that cannot be replicated by the current one-dimensional transport models. The solution may provide a useful tool to interpret some transport situations within common field geometries.