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  • 1
    Language: English
    In: Advances in Water Resources, 2011, Vol.34(2), pp.314-325
    Description: ► Stochastic reconstruction with a combination of multi-point statistics. ► Good rendition of connectivity with Minkowski functions and Chord length distributions. ► Transport behavior compares well between reference media and reconstructed media. ► Pressure field tends to bridge local discontinuities within highly conductive regions. Flow and transport in porous media is determined by its structure. Beside spatial correlation, especially the connectivity of heterogeneous conductivities is acknowledged to be a key factor. This has been demonstrated for well defined random fields having different topological properties. Yet, it remains an open question which morphological measures carry sufficient information to actually predict flow and transport in porous media. We analyze flow and transport in classical, two-dimensional random fields showing different topology and we determine a selection of structural characteristics including classical two-point statistics, chord-length distribution and Minkowski functions (four-point statistics) including the Euler number as a topological measure. Using the approach of simulated annealing for global optimization we generate analog random fields that are forced to reproduce one or several of theses structural characteristics. Finally we evaluate in how far the generated analogons reproduce the original flow and transport behavior as well as some more elaborate structural characteristics including percolation probabilities and the pair connectivity function. The results confirm that two-point statistics is insufficient to capture functional properties since it is not sensitive to connectivity. In contrast, the combination of Minkowski functions and chord length distributions carries sufficient information to reproduce the breakthrough curve of a conservative solute. Hence, global topology provided by the Euler number together with local clustering provided by the chord length distribution seems to be a powerful condensation of structural complexity with respect to functional properties.
    Keywords: Simulated Annealing ; Solute Transport ; Minkowski Functionals ; Chord Length Distribution ; Local Percolation Probability ; Pair Connectivity Function ; Engineering
    ISSN: 0309-1708
    E-ISSN: 1872-9657
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  • 2
    Language: English
    In: Advances in Water Resources, August 2012, Vol.44, pp.101-112
    Description: ► New averaging approach that conserves hydraulic non-equilibrium during rapid infiltration of water. ► New indicators to describe hydraulic non-equilibrium quantitatively. ► Direct link between front morphology and hydraulic non-equilibrium. ► Insights into how structural connectivity affects hydraulic non-equilibrium. ► Shortcomings of an upscaled Richards model extended by hydraulic non-equilibrium. Water infiltration into heterogeneous, structured soil leads to hydraulic non-equilibrium across the infiltration front. That is, the water content and pressure head are not in equilibrium according to some static water retention curve. The water content increases more rapidly in more conductive regions followed by a slow relaxation towards an equilibrium state behind the front. An extreme case is preferential infiltration into macropores. Since flow paths adapt to the structural heterogeneity of the porous medium, there is a direct link between structure and non-equilibrium. The aim of our study is to develop an upscaled description of water dynamics which conserves the macroscopic effects of non-equilibrium and which can be directly linked to structural properties of the material. A critical question is how to define averaged state variables at the larger scale. We propose a novel approach based on flux-weighted averaging of pressure head, and compare its performance to alternative methods for averaging. Further, we suggest some meaningful indicators of hydraulic non-equilibrium that can be related to morphological characteristics of infiltration fronts in quantitative terms. These methods provide a sound basis to assess the impact of structural connectivity on hydraulic non-equilibrium. We demonstrate our approach using numerical case studies for infiltration into two-dimensional heterogeneous media using three different structure models with distinct differences in connectivity. Our results indicate that an increased isotropic, short-range connectivity reduces non-equilibrium, whereas anisotropic structures that are elongated in the direction of flow enforce it. We observe a good agreement between front morphology and effective hydraulic non-equilibrium. A detailed comparison of averaged state variables with results from an upscaled model that includes hydraulic non-equilibrium outlines potential improvements in the description of non-equilibrium dynamics including preferential flow in simplified, upscaled models based on Richards equation.
    Keywords: Transient Flow ; Upscaling ; Pressure Head Averaging ; Hydraulic Non-Equilibrium ; Preferential Flow ; Connectivity ; Engineering
    ISSN: 0309-1708
    E-ISSN: 1872-9657
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