Numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7.5 µm. One of the samples is a microtomographic image of Fontainebleau sandstone. Two of the samples are stochastic reconstructions with the same porosity, specific surface area, and two-point correlation function as the Fontainebleau sample. The fourth sample is a physical model which mimics the processes of sedimentation, compaction and diagenesis of Fontainebleau sandstone. The permeabilities of these samples are determined by numerically solving at low Reynolds numbers the appropriate Stokes equations in the pore spaces of the samples. The physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately, while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude. This finding confirms earlier qualitative predictions based on local porosity theory. Two numerical algorithms were used in these simulations.One is based on the lattice-Boltzmann method, and the other on conventional finite-difference techniques. The accuracy of these two methods is discussed and compared, also with experiment.

A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and "pore size" distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples.

A quantitative comparison of the pore space geometry for three natural sandstones is presented. The comparison is based on local porosity theory which provides a geometric characterization of stochastic microstructures. The characterization focusses on porosity and connectivity fluctuations. Porosity fluctuations are measured using local porosity distributions while connectivity fluctuations are measured using local percolation probabilities. We report the first measurement of local percolation probability functions for experimentally obtained threedimensional pore space reconstructions. Our results suggest to use local porosity distributions and percolation probabilities as a quantitative method to compare microstructures between models and experiment.

A quantitative comparison between the experimental microstructure of a sedimentary rock and three theoretical models for the same rock is presented. The microstructure of the rock sample (Fontainebleau sandstone) was obtained by microtomography. Two of the models are stochastic models based on correlation function reconstruction, and one model is based on sedimentation, compaction and diagenesis combined with input from petrographic analysis. The porosity of all models closely match that of the experimental sample and two models have also the same two point correlation function as the experimental sample. We compute quantitative differences and similarities between the various microstructures by a method based on local porosity theory. Differences are found in the degree of anisotropy, and in fluctuations of porosity and connectivity. The stochastic models differ strongly from the real sandstone in their connectivity properties, and hence need further refinement when used to model transport.

A simulated annealing algorithm is applied to the reconstruction of two-dimensional porous media with prescribed correlation functions. The experimental correlation function of an isotropic sample of Fontainebleau sandstone and a synthetic correlation function with damped oscillations are used in the reconstructions. To reduce the numerical effort we follow a proposal suggesting to evaluate the correlation functions only along certain directions. The results show, that this simplification yields significantly different micro-structures as compared to a full evaluation of the correlation function. In particular we find that the simplified reconstruction method introduces an artificial anisotropy that is originally not present.