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where α1 and k1 are the van Genuchten parameter and the intrinsic permeability of the reference samples (Tabs. 4.3 and 4.4), respectively, α2 and k2 are the values to be determined in each cell, while γ is a fitting parameter, equal to 0.5 for the conventional Leverett function. To verify to what extent the spatial variability of intrinsic permeability plays a significant role in the numerical prediction of Hg0 _{DNAPL infiltration and} distribution, the γ parameter was subjected to a sensitivity analysis, assuming the value of 0.5 of the conventional Leverett function, and the very large values of 0.75 and 0.95, thus considering three different numerical scenarios.

The spatial domain was discretized in 1273 nodes and 2413 unstructured triangular cells, suitably refined in proximity of the DNAPL reservoir and of the top part of the medium glass beads layer. Across the whole domain, the water hydraulic head was set to 26.5 cm, and the boundary nodes on the top of the domain, outside the inlet, were constrained to this value assuming a Dirichlet boundary condition. Between the inlet walls, a volume of 10 ml of liquid Hg0 _{was injected into the domain with an average infiltration rate of 0.099 ml/s,} over a time of 101 s. On all other boundaries a no flux boundary condition was assumed for both water and elemental mercury. The solution was advanced over time with a variable time step ranging from 0.1 s to 2 s depending on convergence history, while convergence of the solution was ensured by an absolute tolerance of 10-5 _m.

5.2 Results and Discussion

5.2.1 PCE and Hg

Flow Container Experiments with Sands

The main difference between the two PCE and Hg0 _{infiltration experiments was found in} the early stage of the infiltration process. While PCE infiltrated and distributed within the water saturated porous sample, liquid Hg0 _{did not. When elemental mercury was poured} between the inlet walls, the sand particles of the top layer were displaced and started

mercury was added to build a sufficient head to overcome the sand entry head but, rather than infiltrating in the porous sample, Hg0 _{found a preferential pathway between the inlet} walls and the front walls of the container, thus spreading over the top surface of MS1. Then the experiment was stopped. Conversely, 12 ml of PCE infiltrated over a time of 436 s, under an initial head of 2.16 cm. Unfortunately, Bromophenol Blue did not allow the visualization of the PCE infiltration front within the stratified porous medium, hence no track of it over time is available. Nevertheless, PCE inflow rate and head variation over time (Fig. 5.4) were successfully measured.

Fig. 5.4. Measured PCE inflow rate and head over time.

The Pc(S) experiments (Chapter 4) showed that, in water saturated porous media, for the same sands, elemental mercury behaves like other DNAPLs, thus requiring to overcome an entry head to infiltrate. In terms of respective DNAPL heads, Hg0 entry head was lower than that of PCE (6.19 cm in MS1 and 12.51 cm in MS2 for Hg0_{, and 9.90 cm in MS1 and} 15.77 in MS2 for PCE), thus enhancing elemental mercury natural tendency to be more prone than PCE to infiltrate in water saturated porous media. Hence, the reason of such a sharp difference in the infiltration behaviour exhibited by the two DNAPLs in the flow container experiments is not immediately clear. Most probably, the difference in the intrinsic permeability field of the two flow container samples played a major role.

Dual gamma ray measurements of the porosity field (Figs. 5.5 and 5.6) revealed significant differences among the two samples. As a matter of fact, the sample used for the Hg0 _flow container experiment showed a porosity remarkably lower than the one used for the infiltration of PCE. Such a strong difference in porosity likely resulted in a sharp difference in intrinsic permeability, thus inducing differences in entry head. In particular, this difference in porosity was more pronounced in proximity of the inlet, namely where the infiltration should have occurred. Therefore, Hg0 _{did not infiltrate because it was} unable to build a sufficient head to overcome the higher entry head induced by a locally lower intrinsic permeability. Hence, the increase in DNAPL pressure, following the further addition of Hg0_{, resulted in the overcome of the resistance exerted by water between the} inlet and the front walls rather than that of water in the sand, thus inducing the Hg0 _escape through a preferential pathway.

The heterogeneity in the intrinsic permeability field played an important role also for the migration of PCE. This influence can be first noticed in Fig. 5.4, where the PCE inflow rate is depicted. Its maximum value occurred at the early stages of the infiltration, when the DNAPL head was at its maximum level and when the PCE front encountered the top layer of MS1, where porosity and intrinsic permeability were higher than the layers immediately underneath the inlet. Subsequently, for a short time interval, the inflow rate dropped dramatically, symptom of the fact that a small lower permeability lens was encountered. Then, it increased again and gradually reduced, with no particular variations, until the end of the infiltration process.

The discontinuity observed in the PCE saturation profile (Fig. 5.7) illustrates the dependency of the migration pattern with intrinsic permeability. The dual gamma ray detected the presence of PCE everywhere in the lowest part of the sample, with a maximum saturation of 0.094, while almost no PCE was detected in the top part. Most likely, the effect of micro heterogeneities was even more pronounced than macro heterogeneities. As a result, PCE migration probably developed under a gravitational instability regime, enhanced by the micro heterogeneities present within the sample, thus resulting in fingers formation (Poulsen and Kueper, 1992; Illangasekare, 1998). This would explain why the dual gamma ray system was not able to perform a continuous

measurement of the PCE front, in spite of the fine measurement grid adopted, and why PCE was found in the finer sand.

Fig. 5.7. Measured PCE saturation profile.

Fingers are expected to be thin, of the order of the pore sizes, hence, most probably, the dual gamma ray beam had locally either missed the fingers or smeared the saturation value through the whole thickness of the porous medium, thus resulting in an overall negligible measured PCE saturation in the top part of the sample. Fingers develop through preferential pathways dictated by the micro heterogeneities found during the migration (Mayer and Hassanizadeh, 2005). Therefore, under this flow regime and given the heterogeneity exhibited by the stratified sand sample, it is realistic to find PCE within the MS2 lens, despite the high entry head (15.77 cm of PCE) exhibited in the Pc(S) measurements (Chapter 4).