Quantitative analysis of experimental and synthetic microstructures for sedimentary rock

Abstract

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.

On the reconstruction of polycrystalline microstructures from two-point correlation statistics

“…The results are comparable to the previously published results from Monte Carlo simulations [9,10,11], so the method will not be discussed in detail.…”

“…Taking statistics from original structures avoided the irreconcilable situation of attempting to create structures from unrealizable statistics: given a set of two-point statistics in two or three dimensions there is no assurance that they can be realized as a structure [10]. A recent evaluation of techniques for reconstructing porous materials from local porosity statistics revealed shortcomings in current algorithms [11]. This investigation is intended for insights into the control of two-point statistics over structure, and not an analysis of what structures are realizable.…”

Machine learning framework for analysis of transport through complex networks in porous, granular media: A focus on permeability

“…What is still missing, however, are robust multiscale descriptors of pore connectivity and associated transmission pathways, and their relationship to macroscopic transport [13,[37][38][39][40][41][42]. Although techniques employing local percolation probabilities [22], the Euler characteristic [43] and n-point correlation functions [12,[44][45][46] have helped to fill this knowledge gap, studies continue to highlight a critical need for explicit, higher-order, threedimensional topology and connectivity descriptors to be incorporated in predictions of permeability and thermal conductivity [13,[37][38][39][40][41][42].…”

3D Stochastic Modelling of Heterogeneous Porous Media – Applications to Reservoir Rocks

“…Random 3D models are then generated in such a manner that they match the measured statistical properties, such as two-point correlation functions. Recent quantitative comparisons of these models with tomographic images of sedimentary rocks have shown that statistical reconstructions may differ significantly from the original sample in their geometric connectivity (Hazlett, 1997;Biswal et al, 1999;Manswart et al, 2000;Øren and Bakke, 2003).…”