Topological Characterization of Porous Media

It is an attractive approach to predict flow and in based on direct investigations of their structure. The most crucial property is the of the structure because it is difficult to measure. This is true both at the pore scale, which may be represented as a binary structure, and at a larger scale defined by continuous macroscopic state variables as phase density or. At the pore scale a function is introduced which is defined by the as a function of the pore diameter. This function is used to generate of the porous structure that allow to predict bulk hydraulic properties of the material. At the continuum scale the structure is represented on a grey scale representing the porosity of the material with a given resolution. Here, topology is quantified by a connectivity function defined by the Euler characteristic as a function of a porosity threshold. Results are presented for the structure of natural soils measured by. The significance of topology at the continuum scale is demonstrated through numerical simulations. It is found that the effective permeabilities of two heterogeneous having the same auto-covariance but different topology differ considerably.

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