Abstract
Dilution of solute in two-dimensionally periodic heterogeneous porous media is assessed by numerically simulating advection-dispersion. The concentration fluctuations, created by advective heterogeneity, are destroyed by local dispersion, over a characteristic variance residence time (VRT). For an impulse introduction of solute, initially, plumes become increasingly irregular with time—the coefficient of variation (CV) of concentration grows with time. A priori, the spatial second moment and mean concentrations are insufficient measures of dilution, because concentration fluctuations can be large. At large times (t > VRT) the relative concentration fluctuations weaken—the concentration CV was observed to slowly decrease with time. At the center of mass the general trend of the decreasing CV follows VRT/t (predicted by Kapoor and Gelhar). The VRT is found to be an increasing function of the log hydraulic conductivity microscale. In employing effective dispersion coefficents to model the mean concentration, it needs to be recognized that excursions of concentrations around the mean are singularly determined by local dispersion.
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Kapoor, V., Kitanidis, P.K. Concentration fluctuations and dilution in two-dimensionally periodic heterogeneous porous media. Transp Porous Med 22, 91–119 (1996). https://doi.org/10.1007/BF00974313
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DOI: https://doi.org/10.1007/BF00974313