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Stochastic Continuum Transport Equations for Field-Scale Solute Transport

Overview of Theoretical and Experimental Results

Agrosphere, ICG-IV, Forschungszentrum Jülich GmbH, D-52425 Jülich, Germany

View larger version (17K): [in a new window]   Fig. 1. Normalized equivalent dispersivity due to spatial variability of local flow velocity, (eq – dL)/(2f1), as a function of normalized travel distance, x1/1, in media with isotropic structures (1 = 2 = 3), elongated structures parallel (1/2,3 = 5,) and perpendicular (1/2,3 = 0.2) to the direction of the mean flow. Full lines: 1/dL = 500. Dashed line: 1/dL = 50.

View larger version (19K): [in a new window]   Fig. 2. Variance of stream tube velocities, vs2 (red), and dispersivities that characterize: the spreading of an averaged breakthrough curve, equivalent dispersivity, eq (black), the spreading of locally measured breakthrough curve, stream tube dispersivity, s (blue), and the pore-scale dispersivity d (green), in reference planes at different distances from the injection surface in an heterogeneous aquifer with f2 = 1, 1 = 2 = 5 m, 3 = 1 m, dL = 0.1 m, dT = 0.01 m. Thick lines are first-order predictions; symbols refer to parameters derived from a numerical experiment in a realization of the conductivity field.

View larger version (52K): [in a new window]   Fig. 3. Maps of simulated concentrations distributions in a heterogeneous two-dimensional saturated flow field (f2 = 1, 1 = 2 = 10 cm, dL = 0.2 cm, dT = 0.02 cm, s = 0.5) of three different tracers: inert tracer (top panel), a nonlinearly sorbing reactive tracer (kf = 1, nf = 0.67), and a strongly nonlinearly sorbing tracer (kf = 0.6, nf = 0.3). Concentration maps are shown when the center of mass of the plume is at 40 cm below the injection surface (x1 = 60 cm in the plots).

View larger version (18K): [in a new window]   Fig. 4. Breakthrough curves of flux averaged concentrations at two depths, 0.5 and 0.8 m, below the injection surface in a heterogeneous two-dimensional saturated flow field (f2 = 1, 1 = 2 = 10 cm, dL = 0.2 cm, dT = 0.02 cm, s = 0.5) of two different tracers: a nonlinearly sorbing reactive tracer (kf = 1, nf = 0.67) (left panel), and a strongly nonlinearly sorbing tracer (kf = 0.6, nf = 0.3) (right panel). Solid lines are numerically simulated breakthrough curves in realizations of the conductivity field, dashed lines are the predictions by the equivalent CDE (Eq. [42]) and symbols are predictions by a STM (Eq. [41], [43], [44], [45]).

View larger version (18K): [in a new window]   Fig. 5. Effect of (a) the travel time/distance and (b) the local-scale dispersion (Pe = 1/dL) on the spatial correlation in the direction transverse to the mean flow direction of the local concentration, CC (open circles), and stream tube velocities, vsvs (solid circles). First-order predictions in a heterogeneous aquifer with f2 = 1, 1 = 2 = 5 m, 3 = 1 m, dL = 0.1 m, dT = 0.01 m are shown.

View larger version (74K): [in a new window]   Fig. 6. Transport in a layered soil profile. Top panel represents the spatial distribution of the hydraulic conductivity in the profile [f2 = 1, dL = 0.2 cm, dT = 0.02 cm, s = 0.5, 1 = 2 = 10 cm (top layer), 1 = 20 cm, 2 = 2 cm (bottom layer)], middle panel the simulated vertical component of the pore water velocity, vx1, and the bottom panel the concentration profile when the center of mass of the plume is at 50 cm below the injection surface. In the areas between the two top and two bottom horizontal lines, the spatial correlation in the horizontal direction of the concentrations was calculated (see Fig. 7).

View larger version (15K): [in a new window]   Fig. 7. Spatial correlations of (a) concentrations, CC, and (b) stream tube velocities, vsvs, in the direction perpendicular to the mean flow direction in a layered soil profile (see Fig. 6). Symbols refer to correlations derived from numerical simulations and lines from first-order predictions. Correlations of concentrations were derived at 30 cm below the injection (top layer; solid circles, dashed lines) and at 70 cm below the injection (bottom layer; open circles, solid lines) when the center of mass of the plume is at the boundary of the two layers. Correlations of stream tube velocities were derived at the 40-cm depth (top layer; solid circles, dashed lines) and at the 80-cm depth (bottom layer; open circles, solid lines).

View larger version (12K): [in a new window]   Fig. 8. Simulated breakthrough curves of spatially averaged solute fluxes at two depths in a realization of a two-dimensional heterogeneous soil profile. Averaged fluxes are plotted vs. the cumulative amount of leachate. Solid circles represent simulated breakthrough in a steady-state flow field; open circles are the results for a transient flow field simulated for climatic boundary conditions.