Tahmasebi Pejman, Sahimi Muhammad
Department of Mining, Metallurgy and Petroleum Engineering, Amir Kabir University of Technology, Tehran 15875-4413, Iran.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 Jun;85(6 Pt 2):066709. doi: 10.1103/PhysRevE.85.066709. Epub 2012 Jun 29.
The purpose of any reconstruction method is to generate realizations of two- or multiphase disordered media that honor limited data for them, with the hope that the realizations provide accurate predictions for those properties of the media for which there are no data available, or their measurement is difficult. An important example of such stochastic systems is porous media for which the reconstruction technique must accurately represent their morphology--the connectivity and geometry--as well as their flow and transport properties. Many of the current reconstruction methods are based on low-order statistical descriptors that fail to provide accurate information on the properties of heterogeneous porous media. On the other hand, due to the availability of high resolution two-dimensional (2D) images of thin sections of a porous medium, and at the same time, the high cost, computational difficulties, and even unavailability of complete 3D images, the problem of reconstructing porous media from 2D thin sections remains an outstanding unsolved problem. We present a method based on multiple-point statistics in which a single 2D thin section of a porous medium, represented by a digitized image, is used to reconstruct the 3D porous medium to which the thin section belongs. The method utilizes a 1D raster path for inspecting the digitized image, and combines it with a cross-correlation function, a grid splitting technique for deciding the resolution of the computational grid used in the reconstruction, and the Shannon entropy as a measure of the heterogeneity of the porous sample, in order to reconstruct the 3D medium. It also utilizes an adaptive technique for identifying the locations and optimal number of hard (quantitative) data points that one can use in the reconstruction process. The method is tested on high resolution images for Berea sandstone and a carbonate rock sample, and the results are compared with the data. To make the comparison quantitative, two sets of statistical tests consisting of the autocorrelation function, histogram matching of the local coordination numbers, the pore and throat size distributions, multiple-points connectivity, and single- and two-phase flow permeabilities are used. The comparison indicates that the proposed method reproduces the long-range connectivity of the porous media, with the computed properties being in good agreement with the data for both porous samples. The computational efficiency of the method is also demonstrated.
任何重建方法的目的都是生成二相或多相无序介质的实现，这些实现要符合有限的数据，以期这些实现能为那些没有可用数据或测量困难的介质属性提供准确预测。这类随机系统的一个重要例子是多孔介质，重建技术必须准确地表示其形态——连通性和几何形状——以及其流动和传输特性。当前许多重建方法基于低阶统计描述符，无法提供关于非均质多孔介质属性的准确信息。另一方面，由于多孔介质薄片的高分辨率二维（2D）图像可用，同时完整的3D图像成本高、计算困难甚至无法获得，从2D薄片重建多孔介质的问题仍然是一个悬而未决的突出问题。我们提出一种基于多点统计的方法，其中由数字化图像表示的多孔介质的单个2D薄片用于重建该薄片所属的3D多孔介质。该方法利用一维光栅路径检查数字化图像，并将其与互相关函数、用于确定重建中使用的计算网格分辨率的网格划分技术以及作为多孔样品非均质性度量的香农熵相结合，以重建3D介质。它还利用一种自适应技术来识别可在重建过程中使用的硬（定量）数据点的位置和最佳数量。该方法在Berea砂岩和碳酸盐岩样品的高分辨率图像上进行了测试，并将结果与数据进行了比较。为了进行定量比较，使用了两组统计测试，包括自相关函数、局部配位数的直方图匹配、孔隙和喉道尺寸分布、多点连通性以及单相和两相流渗透率。比较表明，所提出的方法再现了多孔介质的长程连通性，计算得到的属性与两种多孔样品的数据吻合良好。该方法的计算效率也得到了证明。
