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Strongly correlated and complex random geometries abound in
natural porous media. In fact, porous media can be considered
as interface dominated materials exhibiting strongly correlated
random geometries over many decades in length. The talk will
give an overview of methods for geometric characterization and
analysis of physical properties for random geometries as they
occurr in natural porous media [1,2]. Recently stochastic
multiscale media have attracted considerable interest [3].
A method to generate stochastic morphologies for multiscale
media is presented [3,4]. The method is particularly suited for
modeling carbonate rocks occurring in petroleum reservoirs
that exhibit porosity and grain structure covering several
decades in length scales. The mathematical model reproduces
correlations with primordial depositional textures, scale
dependent intergranular porosity over many decades, vuggy
porosity, a percolating pore space, a percolating matrix
space, and strong resolution dependence of both physical and
morphological descriptors such as permeability or Minkowski
functionals. The continuum based model allows discretization
at arbitrary resolution and provides synthetic micro-CT images
for resolution dependent simulations, morphological analysis
or tests of multiscale models and methods.
[1] R. Hilfer, in: Statistical Physics and Spatial Statistics (Lecture Notes in Physics, vol554), Springer, Berlin, p. 203 (2000) [2] C. Lang et al., Journal of Microscopy 203, 303 (2001) [3] B. Biswal et al., Phys.Rev.E, vol 75, 061303 (2007) [4] B. Biswal et al., Image Analysis and Stereology 28, 23-34 (2009) |
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