Model with Measured Values of DOC

The profile described in Section 10.2 was chosen for modelling, since it provided most of hydrogeological and geochemical data and because of its orientation in flow direction. Both top partial graphs (a and b) of Fig. 10.6 present the field of velocities, just as it results from the product of gradient of water table and the hydraulic conductivity kf in each cell. For the hydraulic gradient we used different values at the coordinates in x-direction, which were interpolated between the measured values of the piezometers. 

This quite arbitrary method of two-dimensional transport ignores the components of vertical flow and thus underestimates the transversal dispersion thereby induced. On the other hand we tested a simple non-reacting case with the same hydraulic conditions against an analytical solution and found that the longitudinal dispersion is not influenced by numerical dispersion, whereas the numerical solution overestimates the transversal dispersion by approximately 10 %. The influence of the boundary conditions for top and bottom of the aquifer (no gradient, no flux) is more important in terms of an increased transversal dispersion for these cells. All these effects are negligible compared to the influences of inhomogeneities of hydraulic conductivities onto the modelled transversal dispersion. 

The estimated values for the total amount of iron in the solid phase, based on an empirical relation to hydraulic conductivity - as described in Section 10.2, were used as start condition for iron(III)-concentration in the solid phase of the aquifer. 

Since we wanted to model the reaction between DOC and iron(III)oxides in this system, there is only the reaction rate of this reaction left for a calibration of the model. Our example shows a satisfactory fit with the measured values for DOC in the ground-water of the flow field when we use a reaction kinetic of the first order and a rate constant of 3.3E-10 mol/m s (see Table 10.1). For calibration, we compared measured and modelled (250 years of modelling time) DOC concentrations at 600 m distance to the river with each other. There are two pairs of piezometers in shallow and deep parts of the aquifer in 600 m distance to the river that were used for comparison (9560 T and 9561 F plus 12/99 F and 12/99 T, compare Chapter 11). Measured values indicate that 

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