Gao MingLiang, He XiaoHai, Teng QiZhi, Zuo Chen, Chen DongDong
College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China and Northwest University for Nationalities, College of Electrical Engineering, Lanzhou 730030, China.
College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Jan;91(1):013308. doi: 10.1103/PhysRevE.91.013308. Epub 2015 Jan 26.
A random three-dimensional (3D) porous medium can be reconstructed from a two-dimensional (2D) image by reconstructing an image from the original 2D image, and then repeatedly using the result to reconstruct the next 2D image. The reconstructed images are then stacked together to generate the entire reconstructed 3D porous medium. To perform this successfully, a very important issue must be addressed, i.e., controlling the continuity and variability among adjacent layers. Continuity and variability, which are consistent with the statistics characteristic of the training image (TI), ensure that the reconstructed result matches the TI. By selecting the number and location of the sampling points in the sampling process, the continuity and variability can be controlled directly, and thus the characteristics of the reconstructed image can be controlled indirectly. In this paper, we propose and develop an original sampling method called three-step sampling. In our sampling method, sampling points are extracted successively from the center of 5×5 and 3×3 sampling templates and the edge area based on a two-point correlation function. The continuity and variability of adjacent layers were considered during the three steps of the sampling process. Our method was tested on a Berea sandstone sample, and the reconstructed result was compared with the original sample, using tests involving porosity distribution, the lineal path function, the autocorrelation function, the pore and throat size distributions, and two-phase flow relative permeabilities. The comparison indicates that many statistical characteristics of the reconstructed result match with the TI and the reference 3D medium perfectly.
通过从原始二维图像重建图像，然后反复使用结果来重建下一个二维图像，可以从二维图像重建随机三维（3D）多孔介质。然后将重建的图像堆叠在一起，以生成整个重建的3D多孔介质。为了成功执行此操作，必须解决一个非常重要的问题，即控制相邻层之间的连续性和变异性。与训练图像（TI）的统计特征一致的连续性和变异性可确保重建结果与TI匹配。通过在采样过程中选择采样点的数量和位置，可以直接控制连续性和变异性，从而间接控制重建图像的特征。在本文中，我们提出并开发了一种称为三步采样的原始采样方法。在我们的采样方法中，基于两点相关函数，从5×5和3×3采样模板的中心以及边缘区域依次提取采样点。在采样过程的三个步骤中考虑了相邻层的连续性和变异性。我们的方法在Berea砂岩样品上进行了测试，并使用涉及孔隙率分布、线性路径函数、自相关函数、孔隙和喉道尺寸分布以及两相流相对渗透率的测试，将重建结果与原始样品进行了比较。比较表明，重建结果的许多统计特征与TI和参考3D介质完美匹配。
