Evaluation of analytical solute discharge moments using numerical modeling in absolute and relative dispersion frameworks

Abstract

Two-dimensional numerical simulations are used to validate the analytical solutions for the solute discharge moments. In addition to the analysis of classical absolute dispersion we also consider relative dispersion whereby plume meandering (deviation from mean flow path caused by velocity variations at scales larger than plume size) is removed. The numerical simulations are used within a Monte Carlo framework to assess the accuracy and robustness of the analytical predictions of the solute discharge moments (mean and variance). Results show that the analytical predictions deviate from the numerical simulations as the log conductivity variance increases. Deviation occurs for the mean as well as the variance of the solute discharge. The absolute dispersion formulation, however, shows better agreement with the numerical simulations than does the relative dispersion for strong heterogeneity and vice versa for small variability. The relative dispersion results, however, depend on the prediction of the ensemble mean of the plume arrival time, which differs between simulations and analytical solution. Using the first-order analytical estimate for this parameter leads to a much better agreement between the numerical and the analytical results for solute discharge moments in the relative dispersion case.