On the reconstruction of structural and functional properties in random heterogeneous media

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.