Super-dimension-based three-dimensional nonstationary porous medium reconstruction from single two-dimensional image

Abstract Nonstationary porous media widely occur in nature, and a means of determining their three-dimensional (3D) structure can be highly significant for various objectives, such as seepage analysis and physical property investigation. The super-dimension (SD) reconstruction concept can be used to reconstruct the 3D structure of a stationary porous medium from a single two-dimensional (2D) reference image, which is referred to as the training image. In this study, we applied the SD reconstruction concept to a nonstationary porous medium. By introducing a probability-based image block selection mechanism into the SD reconstruction method, we established the statistical relationship between the number of “0” pixels (grain phase) in the 2D and 3D image blocks of the real core stored in the SD dictionary. We employed this identified relationship for the selection of dictionary elements to maintain the nonstationary information of the core during the reconstruction. In addition, we proposed relevant strategies for "block matching", "template selection", "element storage" and "pixel filling" in the reconstruction process. On this basis, we developed an original nonstationary medium reconstruction algorithm. To verify the accuracy of reconstruction results through experiments, we employed statistical similarity analysis methods based on the two-point correlation function and morphological similarity analysis tools for determining the pore radius and pore volume distributions. Finally, the seepage characteristics were analyzed. The proposed method was confirmed to be effective for reconstructing a nonstationary structure with statistical and morphological features consistent with the samples. The universality of the algorithm proposed here was also verified by its successful application to the stationary porous medium.

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