AN ANALYTICAL SOLUTION FOR ONE-DIMENSIONAL TRANSPORT IN HETEROGENEOUS POROUS-MEDIA

An analytical solution for describing the transport of dissolved substances in heterogeneous porous media with a distance‐dependent dispersion relationship has been developed. The analytical solution can be used to characterize differences in the transport process relative to the classical convection‐dispersion equation which assumes that the hydrodynamic dispersion in the porous medium remains constant. The form of the hydrodynamic dispersion function used in the analytical solution is D(x) = α(x(v¯ + diffusion, where α(x) is the distance‐dependent dispersivity and v¯ is the average pore water velocity. It is shown that for models which differ only in how the dispersion function is expressed, erroneous model parameters may result from parameter estimation techniques which assume a constant hydrodynamic dispersion coefficient if the porous medium is more accurately characterized by a distance‐dependent dispersion relationship. For such situations, the proposed model could be used to provide an alternate means for obtaining these parameters. The overall features of the solution are illustrated by several examples for constant concentration and flux boundary conditions. Copyright 1990 by the American Geophysical Union.