In this paper, we introduce a stable-phase approach for hierarchical annealing which addresses the very large computational costs associated with simulated annealing for the reconstruction of large-scale binary porous media images. Our presented method, which uses the two-point correlation function as the morphological descriptor, involves the reconstruction of three-phase and two-phase structures. We consider reconstructing the three-phase structures based on standard annealing and the two-phase structures based on standard and hierarchical annealings. From the result of the two-dimensional (2D) reconstruction, we find that the 2D generation does not fully capture the morphological information of the original image, even though the two-point correlation function of the reconstruction is in excellent agreement with that of the reference image. For the reconstructed three-dimensional (3D) microstructure, we calculate its permeability and compare it to that of the reference 3D microstructure. The result indicates that the reconstructed structure has a lower degree of connectedness than that of the actual sandstone. We also compare the computation time of our presented method to that of the standard annealing, which shows that our presented method of orders of magnitude improves the convergence rate. That is because only a small part of the pixels in the overall hierarchy need to be considered for sampling by the annealer.
SUMMARYTo predict the macroscopic properties (e.g., transport, electromagnetic, and mechanical properties) of porous media, it is necessary to have a three-dimensional (3D) representation of porous media. We reconstruct the geologically realistic 3D structure of Fontainebleau sandstone based on the two-dimensional (2D) thin sections by using the multiple-point statistics method. For this method, the size of template is an important parameter that reflects the perceived scale of spatial structure of porous media. In this paper, we take advantage of entropy method to obtain the appropriate size of the template, which is proven to be correct and feasible. The reconstruction method proposed by us combines successive 2D MPS simulations as well as 3D MPS simulation, which takes account into the pore structure information (e.g., heterogeneity and connectivity) both intralayer and interlayer. This reconstruction method is tested on Fontainebleau sandstone for which 3D images from micro-CT scanning are available. Applying local percolation theory analysis, this new approach can depict the expected patterns of geological heterogeneities. In addition, it also can well reproduce a high degree of connectivity of the pore space better than other reconstruction methods based on lower-order statistics.
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