Markov prior-based block-matching algorithm for superdimension reconstruction of porous media

A superdimension reconstruction algorithm is used for the reconstruction of three-dimensional (3D) structures of a porous medium based on a single two-dimensional image. The algorithm borrows the concepts of “blocks,” “learning,” and “dictionary” from learning-based superresolution reconstruction and applies them to the 3D reconstruction of a porous medium. In the neighborhood-matching process of the conventional superdimension reconstruction algorithm, the Euclidean distance is used as a criterion, although it may not really reflect the structural correlation between adjacent blocks in an actual situation. Hence, in this study, regular items are adopted as prior knowledge in the reconstruction process, and a Markov prior-based block-matching algorithm for superdimension reconstruction is developed for more accurate reconstruction. The algorithm simultaneously takes into consideration the probabilistic relationship between the already reconstructed blocks in three different perpendicular directions ($x, y$, and $z$) and the block to be reconstructed, and the maximum value of the probability product of the blocks to be reconstructed (as found in the dictionary for the three directions) is adopted as the basis for the final block selection. Using this approach, the problem of an imprecise spatial structure caused by a point simulation can be overcome. The problem of artifacts in the reconstructed structure is also addressed through the addition of hard data and by neighborhood matching. To verify the improved reconstruction accuracy of the proposed method, the statistical and morphological features of the results from the proposed method and traditional superdimension reconstruction method are compared with those of the target system. The proposed superdimension reconstruction algorithm is confirmed to enable a more accurate reconstruction of the target system while also eliminating artifacts.

Figure 1

Process of building the dictionary.

Figure 2

Reconstruction process.

Figure 3

Schematic of neighborhood matching.

Figure 4

Schematic of the Markov chain.

Figure 5

Strategy for adding hard data to the algorithm reconstruction.

Figure 6

Schematic of (a) reference CT image, (b) target system, and (c) reconstruction results.

Figure 7

The $xy, yz$, and $zx$ cross sections of the reconstruction results obtained by the Markov algorithm (a)–(c) without and (d)–(f) with the two proposed blocking-artifact removal strategies, respectively.

Figure 8

Comparison of the (a) $x$-, (b) $y$-, and (c) $z$-direction ACF curves of target systems reconstructed using the traditional SD algorithm and the SD algorithm with the Markov-matching process.

Figure 9

Comparison of the (a) average size of pore radius, and (b) average size of throat radius of target systems and reconstructed results by the SD algorithm with the Markov-matching process for ten different core samples (a)–(j).

Figure 10

Comparison of the pore diameter and pore volume distributions.

Figure 11

Comparison of the local pore distributions.

Figure 12

Comparison of the drainage and imbibition relative permeability curves for the target system (solid line) and the reconstructed model (dotted line). (a) drainage and (b) imbibition.