EXACT-SOLUTIONS FOR ONE-DIMENSIONAL TRANSPORT WITH ASYMPTOTIC SCALE-DEPENDENT DISPERSION

A general analytical solution is developed for one-dimensional solute transport in heterogeneous porous media with scale-dependent dispersio n. The solution assumes that the dispersivity, alpha, increases linear ly with distance, x, that is, alpha(x) = ax, until some distance x(0), after which alpha reaches an asymptotic value, alpha(L) = ax(0). The parameters a and x(0) characterize the nature of the scale-dependent d ispersion process. The general solution contains as special cases the solutions of the classical convection-dispersion equation (CDE) assumi ng a constant dispersivity, and a recent solution by Yates assuming a linearly increasing dispersivity with distance. A simplified solution is also derived for cases where diffusion can be neglected. In additio n, a solution for steady-state transport is presented. Results obtaine d with the proposed solutions demonstrate several features of scale-de pendent dispersion in nonhomogeneous media which differ from those pre dicted with the CDE model and the model of Yates.(1)