Modeling of scale‐dependent dispersion in hydrogeologic systems

Abstract

An approach for handling scale‐dependent dispersion using a finite element (linear triangular) solute transport model was developed. Dispersivity is allowed to vary temporally as a function of the mean travel distance of the solute from an input source. Various scale‐dependent dispersivity relationships were presented including types which approach continuously to a maximum or asymptotic value. The finite element model results were verified for a one‐dimensional case by comparison of the theoretical variances of the solute distribution for a given dispersivity‐travel distance function with the variances calculated from the finite element model concentration distributions. The model was applied successfully to the results of several tracer tests reported in the literature that have exhibited a scale effect. For systems that exhibit a constant (asymptotic) dispersivity at large times or mean travel distances, the importance of scale‐dependent dispersion at early times or short travel distances was shown to be minimal in long‐term predictions of solute transport.