An analytical solution for one‐dimensional transport in porous media with an exponential dispersion function

Abstract

An analytical solution describing the transport of dissolved substances in heterogeneous porous media with an asymptotic distance‐dependent dispersion relationship has been developed. The solution has a dispersion function which is linear near the origin (i.e., for short travel distances) and approaches an asymptotic value as the travel distance becomes infinite. This solution can be used to characterize differences in the transport process relative to both the classical convection‐dispersion equation which assumes that the hydrodynamic dispersion in the porous medium remains constant and a dispersion solution which has a strictly linear dispersion function. The form of the hydrodynamic dispersion function used in the analytical solution is , where α(x) = a L[1 − e−bx/L] and is the average pore water velocity. The proposed model may provide an alternate means for obtaining a description of the transport of solutes in heterogeneous porous media, when the scale dependence of the dispersion relationship follows the behavior given by α(x). The overall behavior of the model is illustrated by several examples for constant concentration and flux boundary conditions.