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Impact of aquifer heterogeneity structure and local-scale dispersion on solute concentration uncertainty

In this paper, we study the influence of high log- conductivity variance and local-scale dispersion on the first two concentration moments as well as on higher-order moments, skewness, and kurtosis, in a 2-D heterogeneous aquifer. Three different heterogeneity structures are considered, defined with one and the same global isotropic Gaussian variogram. The three structures differ in terms of spatial connectivity patterns at extreme log-conductivity values. Our numerical approach to simulate contaminant transport through heterogeneous porous media is based on the Lagrangian framework with a reverse tracking formulation. Advection and local-scale dispersion are two competing and controlling mechanisms, with a relative ratio defined by the Peclet number (Pe) ; hydraulic log-conductivity variance in the simulations is assumed to be one or eight. The term local-scale dispersion is used as a combined effect of molecular diffusion and mechanical dispersion. Uncertainty of the concentration field is quantified by the second-order moment, or the coefficient of variation (CVC) as a function of the sampling position along a centerline, Peclet number, and log-conductivity variance, as well as by higher-order moments, i.e., skewness and kurtosis. The log-conductivity variance shows a strong influence on the concentration statistics, while the three different structures have a minor impact in the case of low heterogeneity. The results also indicate that for log-conductivity variance equal to 8, the influence of local-scale dispersion is significant after five integral scales (IY) from the source for the connected (CN) field, while in case of a disconnected field, the local-scale dispersion effect is observed after 20IY from the source. In the case of unit log-conductivity variance, local-scale dispersion acts very slowly affecting concentration uncertainty at distances higher than 20IY from the source. Our inspection of Monte Carlo concentration skewness and kurtosis with the ones obtained from the Beta distribution show the discrepancies for high log-conductivity variance and CN log-conductivity structure.

heterogeneity structure ; advection ; local-scale dispersion ; concentration uncertainty ; skewness ; kurtosis

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