(E22) Nine participants undertook the calculations related to the aquatic pathway as a result of infiltration through the overlying unsaturated soil layer on the basis of Scenario 1.4. These results are presented below. The transport processes and the general modelling approaches have been described in Section E3.1 and E3.2. A brief comparison of modelling approaches can be found in Table E1. Detailed descriptions of individual models are given in Annex I–B.
(E23) Figures E1 and E2 show the vertical profile of HTO concentration in groundwater 1 km downstream from the source, with the boundary condition of a prescribed constant flux at the watertable, for low and high dispersivity respectively:
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In the case of a low vertical dispersivity of 0.05 m (Figure E1), the concentration of tritium just within the entrance of the aquifer at z = 0, is not very different from the concentration of tritium in the entering vertical stream. All the curves obtained lie close together within a factor of two, and show concentrations decreasing by a factor of one thousand at a depth of about 40 m below the watertable, which indicates a low vertical mixing rate. Three of these curves are based on very elaborate numerical models and four of them are based on relatively simple analytical models that have been adapted to the conditions of the scenario (cf. Table E1).
In the case of a high vertical dispersivity of 0.5 m (Figure E2), there is a significant decrease of concentration at the passage of the watertable, owing to the predominance of dispersion over convection. As in the previous case, the curves lie close together and give similar values within a factor of two, but show a reduction in concentration of only ten at the bottom of the aquifer. This indicates a very high vertical mixing rate, as could be expected from the high vertical dispersivity that was assumed in the calculation.
(E24) Figures E3 and E4 refer to the vertical profiles of HTO concentration in groundwaters, with the boundary condition of a prescribed constant concentration at the watertable, for respectively the same low and high dispersivity as considered above. With this new boundary condition, the concentration is strictly the same on each side of the watertable at z = 0, for any value of the vertical dispersivity:
In the case of low dispersivity (Figure E3), five curves lie close together. An isolated curve diverges appreciably from the others, by showing a much reduced vertical mixing.
No explanation can be found for the divergence between this curve and the others. The five grouped curves are very similar to those previously obtained for low dispersivity for the case of a prescribed-flux condition.
In the case of high dispersivity (Figure E4), there are also five curves that lie close together and, as above, two curves that differ appreciably from the others due to some error that has not been identified until now. The five consistent curves are quite different from those obtained for the case of high dispersivity with a prescribed-flux condition.
This dissimilarity is explained in the next paragraph.
(E25) In the calculations above, two ways of defining the watertable boundary condition have been addressed, which leads to very dissimilar results in the case of high dispersivity. The main difficulty then consists in choosing, among the two different boundary conditions, the one that is the most suitable to describe adequately a real situation. This problem was formerly considered by Kreft and Zuber (1978). These authors studied the physical meaning of the dispersion equation and its solutions for different boundary conditions. They have shown that the different boundary conditions correspond to different ways of measuring the solute concentration. The prescribed-flux condition corresponds to a measure of the solute in the resident fluid at a given fixed point, while the prescribed concentration condition corresponds to a measure of the solute in the fluid passing through a given cross section. If one wishes to estimate the concentration of tritium in the resident fluid of the aquifer, which is the quantity one tries to measure in the field, it is more appropriate to use the prescribed flux boundary condition rather than the prescribed concentration boundary condition.
(E26) It appears from the results that the shape of the vertical profiles of tritium concentration in the aquifer is very sensitive to the value of the vertical dispersivity. For the high dispersivity values used herein, appreciable amounts of tritium invade the aquifer down to its
bottom. In contrast, for the low dispersivity values, the vertical mixing of tritium appears to be very limited, even after a few decades of atmospheric releases, which leads to a stratification of most of the tritium in the upper part of the aquifer. In a real situation, the vertical mixing of tritium in an aquifer will depend greatly on the dispersive properties of the aquifer. In a critical review of data on field-scale dispersion in aquifers, Gelhar et al. (1992) insist on the fact that very low vertical dispersivities have been observed at many sites, and that the high values sometimes advanced should be considered with caution.
E5. CONCLUSIONS
(E27) This model-model intercomparison research exercise concerning HTO infiltration to groundwaters, has shown that the results were dependent on the choice of the boundary condition at the watertable, and of the dispersivity of the medium. It was agreed that it was appropriate to choose a prescribed flux boundary condition, rather than a prescribed concentration boundary condition. It was shown that the results were very sensitive to the dispersivity parameter, and that the value of this parameter must be selected very carefully from the data available in the literature. In the simple yet realistic conditions of the scenario, it was verified that many numerical or analytical models arrived at similar results. But this did not mean that both approaches could be used equivalently in any situation, since it was evident that certain heterogeneities encountered in real situations could only be treated by numerical simulation. The experience gained in the model-model intercomparison showed that the correct use of numerical models for this specific problem was rather sensitive, and full attention had to be paid to the time and space discretisation used in the model.
TABLE E1. COMPARISON OF MODELLING APPROACHES USED IN THE MODEL-MODEL INTERCOMPARISON EXERCISE BASED ON SCENARIO 1.4 (GROUNDWATER TRANSPORT)
Institution (Modeller)
Steady Water Flow in Unconfined Aquifer determined from:
HTO Transport in Aquifer determined from:
ANDRA
Not considered IMPACT code: 1D vertical transport equation
solved by an explicit finite difference technique. Constant concentration at watertable.
Consultant (Y. Belot)
Analytical approximations of the horizontal and vertical velocities (flow conservation)
2D analytical solution of the transient transport equation, obtained by integration of impulse responses.
CEA (G. Guinois)
METIS code (Ecole des Mines) 3D finite-element module
METIS code.
Transient transport finite-element module.
FZK (W. Raskob)
Analytical approximation of the horizontal velocity Vertical velocity assumed negligible
2D Gaussian solution of the steady state transport equation.
NIPNE (D. Galeriu)
Analytical approximations of the horizontal and vertical velocities (flow conservation)
Analytical solution.
STUDSVIK (O. Edlund)
Analytical approximations of the horizontal and vertical velocities (flow conservation)
2D analytical solution of the transient transport equation, obtained by integration of impulse responses.
VNIIEF (A. Golubev))
Analytical solution of the hydraulic equation Transport equation solved by a finite-difference method.
ZSR
(M. Täschner)
Analytical approximation of the horizontal velocity Vertical velocity equal to infiltration velocity
1D analytical solution of the transient transport equation.
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