6 M ay 1 99 9 Microstructure analysis of reconstructed porous media

We compare the quantitative microstructural properties of Berea Sandstone with stochastic reconstructions of the same sandstone. The comparison is based on local porosity theory. The reconstructions employ Fourier space filtering of Gaussian random fields and match the average porosity and two-point correlation function of the experimental model. Connectivity properties of the stochastic models differ significantly from the experimental model. Reconstruction models with different levels of coarse graining also show different average local connectivity. Recently a number of stochastic models have been proposed for reconstruction of the microstructure of porous media(see [1,2] and references therein). To assess the quality of the reconstruction, it is neccessary to have quantitative methods of comparison for such microstructures. General geometric characterization methods normally include porosities, specific surface areas and correlation functions [4]. Here we follow a more general quantitative characterization for stochastic microstructures which is based on local porosity theory (LPT) [3,4]. Our analysis allows to distinguish quantitatively between three different microstructures all of which have identical porosities and correlation functions. The three microstructures are an experimental sample of Berea Sandstone obtained by computerized microtomography and two stochastic models of the same sandstone obtained through the Gaussian filtering method [1]. Consider a three-dimensional sample S = P ∪ M (with P ∩ M = ∅) where P is the pore space, M is the rock or mineral matrix. ∅ denotes the empty set. The porosity φ(S) of such a two component porous medium is defined as the ratio φ(S) = V (P)/V (S) where V (P) denotes the volume of the pore space, and V (S) is the total sample volume. For the sample data analysed here the set S is a cube with sidelength M in units of the lattice constant a of a simple cubic lattice. Let K(r, L) denote a cube of sidelength L centered at the lattice vector