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Three-Dimensional Modeling of the Scale- and Flow Rate-Dependency of Dispersion in a Heterogeneous Unsaturated Sandy Monolith

^a Agrosphere, ICG-IV, Forschungszentrum Jülich, D-52425 Jülich, Germany
^b Dep. of Environmental sciences and Land Use Planning, Université Catholique de Louvain, Croix du Sud, 2 Bte 2, B-1348 Louvain-la-Neuve, Belgium

View larger version (40K): [in a new window]   Fig. 1. Macrostructure (red: stones, yellow: clay) in the monolith and position of the TDR probes. TDR of the first transect (cyan), second transect (green), and third transect (blue).

View larger version (22K): [in a new window]   Fig. 2. Experimental and modeled auto- and cross-variograms of the four scaling factors.

View larger version (62K): [in a new window]   Fig. 3. Horizontal cross sections in the monolith showing distribution of the four scaling factors.

View larger version (56K): [in a new window]   Fig. 4. Comparison of the pressure head (first column), water content (second column), logarithm of the local flow velocity and streamlines (third column) under steady state with jw0 = 2.19 x 10–7 (Exp. 2) for the three cases: Case I, only macrostructure (first row); Case II, macrostructure plus sand hydraulic parameter variability (second column); and Case III, macrostructure plus sand hydraulic variability and anisotropy for hydraulic conductivity (third row). Streamlines (in blue) were computed from linear interpolations of the velocity field.

View larger version (42K): [in a new window]   Fig. 5. Pressure head profiles at steady state for the nine flow rates (Table 2): observed data (open circles) and average pressure head profiles for Cases I (red line), II (green line), and III (blue line). Color-similar filled areas give the extent of the pressure head variability.

View larger version (47K): [in a new window]   Fig. 6. Vertical and horizontal cross sections of relative solute concentration distributions in the monolith for a flow rate jw0 of 1.64 x 10–6 m s–1 (Exp. 5) after an irrigation dose of 13.16 cm. Upper right: depth-averaged relative concentration for Case I (red line), Case II (green line), and Case III (blue line). The dotted white lines show the cutting planes.

View larger version (50K): [in a new window]   Fig. 7. Vertical cross sections of relative solute concentration distribution in the monolith for a flow rate jw0 of 2.63 x 10–6 m s–1 (Exp. 7) after an irrigation dose of 10.51 cm. Each column represents one different stochastic simulation. First line is for the isotropic media (Case II) and the second line for the anisotropic medium (Case III).

View larger version (27K): [in a new window]   Fig. 8. Apparent velocity obtained from TDR-probe BTCs of the first profile versus depth for Case I (red lines), Case II (green lines), Case III (blue lines), and observations (black lines) for five flow rates.

View larger version (23K): [in a new window]   Fig. 9. The TDR-scale L–depth relationships for Case I (top, in red), Case II (middle, in green), and Case III (bottom, in blue). Observed L distributions are given in black. Probes from Profile 1 are represented by open squares, Profile 2 with open circles, and Profile 3 with open triangles (see Fig. 1 for a description of probe locations). Error bars show the standard deviation due to flow rate.

View larger version (21K): [in a new window]   Fig. 10. Effective longitudinal dispersivity estimated from simulated outlet breakthrough curves for Case I (red), Case II (green), Case III (blue), and experiments (dots).

View larger version (81K): [in a new window]   Fig. 11. Steady-state log-relative velocity cross sections for five different flow rates.

View larger version (15K): [in a new window]   Fig. 12. Monolith-scale dispersivity profile. Crosses or circles represent the average of the dispersivity obtained at a given depth for all flow rates; error bars give the standard deviation. Data, Case I, Case II, and Case III are in gray, red, green and blue, respectively.

View larger version (22K): [in a new window]   Fig. 13. Mechanical retardation factor at the outlet for Case I (red circles), Case II (green circles), Case III (blue circles), and experiments (+).