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

Abstract

[1] In this paper, we study the influence of high log-conductivity variance ð 2 Y Þ and localscale 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 2 Y 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 (CV C ) as a function of the sampling position along a centerline, Peclet number, and 2 Y , as well as by higher-order moments, i.e., skewness and kurtosis. The parameter 2 Y 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 2 Y ¼ 8, the influence of local-scale dispersion is significant after five integral scales (I Y ) from the source for the connected (CN) field, while in case of a disconnected field, the local-scale dispersion effect is observed after 20I Y from the source. In the case of unit 2 Y , local-scale dispersion acts very slowly affecting concentration uncertainty at distances higher than 20I Y 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 2 Y and CN log-conductivity structure.Citation: Srzic, V., V. Cvetkovic, R. Andricevic, and H. Gotovac (2013), Impact of aquifer heterogeneity structure and local-scale dispersion on solute concentration uncertainty, Water Resour.

Concentration statistics of solute transport for the near field zone of an estuary

“…In the case of the concentration variance, the shape changes from bimodal to unimodal at large enough distances from the source ( Fig. 15 ), as previously observed ( Andricevic, 1998;2008;Schopflocher and Sullivan, 2002;Srzic et al, 2013;Sullivan, 2004 ).…”

“…8 . More results confirming this statement can be found in Srzic et al (2013) and Bellin and Rubin (1994) . Compared to the concentration mean, variance is shown to be sensitive on spatial scale (averaging scale) thus explaining the differences between numerically and analytically obtained concentration variance values shown in Fig.…”

“…Both effects vanish as one goes downstream (values of variance in core plume increase as peak values decrease) thus slowly progressing to a unimodal shape. Such behaviour in the near field zone was thoroughly discussed by ( Andricevic, 1998;2008;Sawford and Sullivan, 1995;Srzic et al, 2013;Sullivan, 2004 ). However, observed difference in shape between analytically and numerically obtained variance is due to the resolution of the numerical model, introducing an additional smoothness over the grid size.…”

Direct Breakthrough Curve Prediction From Statistics of Heterogeneous Conductivity Fields

“…In the other limit, extremely large values of “local‐scale” dispersion dominate any macrodispersive effects, and the macrodispersion equals the local‐scale dispersion. Literature studies have considered finite Pe that range from approximately 10 (Trefry et al, ) to 10,000 (Srzic et al, ), and some (e.g., Beaudoin & De Dreuzy, ; Janković et al, ) have considered no local‐scale dispersion, implying . Srzic et al () reported that that Pe was important for the time until the plume becomes ergodic (Dagan & Fiori, ; Fiori, ).…”

“…Literature studies have considered finite Pe that range from approximately 10 (Trefry et al, ) to 10,000 (Srzic et al, ), and some (e.g., Beaudoin & De Dreuzy, ; Janković et al, ) have considered no local‐scale dispersion, implying . Srzic et al () reported that that Pe was important for the time until the plume becomes ergodic (Dagan & Fiori, ; Fiori, ). However, for longitudinal macrodispersion, Dentz et al () considered local‐scale dispersion ranging 4 orders of magnitude above that of pure diffusion and and found only small sensitivity of the macrodispersion coefficient to the local‐scale dispersion strength.…”