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Experimental study and analytical modeling of preferential flow and partitioning dynamics at unsaturated fracture intersections
  • Torsten Noffz,
  • Marco Dentz,
  • Jannes Kordilla
Torsten Noffz
University of Göttingen, Geoscientific Centre (GZG), Göttingen, Germany

Corresponding Author:[email protected]

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Marco Dentz
Institute of Environmental Assessment and Water Research (IDAEA), Spanish National Research Council (CSIC), Barcelona, Spain
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Jannes Kordilla
University of Göttingen, Geoscientific Centre (GZG), Göttingen, Germany
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Unsaturated fractured aquifer systems offer a domain for complex gravity-driven flow dynamics leading to the development of preferential flow along fracture networks that often strongly contributes to rapid mass fluxes. This behaviour is difficult to recover by volume-effective modeling approaches (e.g. Richards equation) due to the non-linear nature of free-surface flows and mass partitioning processes at unsaturated fracture intersections. The application of well-controlled laboratory experiments enables to isolate single aspects of the mass redistribution process that ultimately affects travel time distributions across scales. We use custom-made acrylic cubes (20 cm x 20 cm x 20 cm) in analogue percolation experiments to create simple fracture networks with single or multiple horizontal fractures. A high precision multichannel dispenser produces gravity-driven free surface flow (droplets; rivulets) at flow rates ranging from 1 ml/min to 5 ml/min. Hereby, total inflow rates are kept constant while the fluid is injected via 15 (droplet flow) or 3 inlets (rivulet flow) to reduce the impact of erratic flow dynamics. Normalized fracture inflow rates (Q_f/Q_0) are calculated and compared for aperture widths d_f of 1 mm and 2.5 mm. A higher efficiency in filling an unsaturated fracture by rivulet flow observed in former studies can be confirmed. The onset of a capillary driven Washburn-type flow is determined and recovered by an analytical solution. In order to upscale the dynamics and enable the prediction of mass partitioning for arbitrary-sized fracture cascades a Gaussian transfer function is derived that reproduces the repetitive filling of fractures, where rivulet flow is the prevailing regime. Results show good agreement with experimental data for all tested aperture widths.