This research was part of the master thesis "Solute Transport in Heterogeneous Porous Media" by Lisa Feustel.

Experiment

The experimental setup developed in former studies by Jens Buchner and Steffen Heberle is used to analyze tracer movement in an unsaturated, heterogeneous, layered porous medium with stationary water flow. The structure of the medium consists of approximately uniform, horizontal layers of glass beads that come in three different sizes.

Solute transport is observed in this experiment by adding a pulse of the food dye Brilliant Blue at the top of the cell during constant water infiltration. The range of diameters of the beads leads to strongly different hydraulic properties, so a strong influence of the layer structure on the transport is expected. The experiment is repeated with a number of infiltration rates to study the influence of the hydraulic structure that changes with the mean water content.

The dominant influence of the medium's structure on the pathway of the pulse is illustrated for three positions.

  • At about 0.01 m distance from the surface of the medium a long layer of fine material is located. For low infiltration fluxes, the tracer passes straight through this layer. At higher infiltration rates the layer causes a wide detour for parts of the pulse (see Figure 1.1).
  • At about 0.05 m depth, a coarse layer causes for low infiltration rates a detour, while with increasing flux the part of the tracer, that passes this coarse layer straight, increases (see Figure 1.2). For high fluxes all of the tracer passes the layer straight.
  • At about 0.13 m depth, a large lens-shaped coarse layer is located. For low infiltration rates, is causes a detour of this layer. Depending on the details of the pathway above the lens, it is bypassing at one or both sides. With increasing flow rate, parts of the tracer pass the lens till all tracer goes straight through it (see Figure 1.3)

Figure 1.1

  • Time sequence of detour due to fine layer at 0.01 m in experiment at flow rate 3.5e-5 m/s (upper picture) and 75e-5 m/s (lower picture). Tracer is colored black, coarse to fine material is colored from bright to dark gray.



Figure 1.2

  • Time sequence of detour of coarse layer at 0.05 m in experiment at flow rate 3.5e-5 m/s (upper picture) and 75e-5 m/s (lower picture).

Figure 1.3

  • Time sequence of pulse behavior at lens structure at 0.13 m in experiment at flow rate 18.7e-5 m/s (upper picture), 33.7e-5 m/s (middle picture) and 75e-5 m/s (lower picture).

These observations lead to qualitative constraints of the hydraulic conductivity functions. The preferred pathway through the finer material for low flow rates can be associated with a higher hydraulic conductivity of this material at low water content. For higher fluxes the coarse material is the preferred pathway. Therefore the conductivity of the coarse material is assumed to be higher than the conductivity of the other materials at high water content. Thus, a crossing point of the hydraulic conductivity functions of the fine and the coarse material must exist.

Simulation of Experiment

Based on the experiments, simulations with the same structured medium and boundary conditions are run. They are realized with $\mu \phi$, a numerical solver of the Richards equation and the convection-dispersion-equation, developed by Olaf Ippisch. The hydraulic properties are parametrized after Mualem-van Genuchten. A set of parameters was found to imitate the experimental observations, with a much larger conductivity of the fine material than of the coarse for low water content, a larger conductivity of the coarse material for high water content, and a crossing point somewhere in between. The resulting simulation is able to reproduce the behavior and the pathway of the tracer pulse qualitatively.

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