Improved algorithm for estimating pore size distribution from pore space images of porous media

Pore size distribution (PSD), which is defined as the percentage of the pores of each size to the total volume of the pores, is a key parameter to characterize the microstructure of porous media. Based on the pore geometry definition of three-dimensional (3D) maximal ball and two-dimensional (2D) maximal disk in discrete space, an improved algorithm is proposed to obtain PSD from pore space images of porous media. To validate the accuracy of our algorithm, a synthetic porous medium with a known PSD is generated by computer simulation. In addition, other 2D and 3D images of various types of samples, including sandstones, carbonates, and man-made materials, were also used to obtain PSD. The PSDs were compared quantitatively with that obtained by using the existing state of the art algorithm. The results show that our algorithm is more accurate in characterizing the pore structure and more consistent with the direct visual identification. In addition, the efficiency of our algorithm was also evaluated by calculating the PSD of large-scale 3D images, the results of which indicate that all calculations can be completed in a relatively short time.

Figure 1

Illustration of digital (a) circles and (b) spheres. From left to right: $R^2=0$; $R^2=1$; $R^2=2$.

Figure 2

Variation of the difference degree of circle and sphere with the radius.

Figure 3

Schematic of padding 2D image array. (a) The original image array with a size of 3 × 3: 0 denotes pore pixel and 1 denotes matrix pixel; (b) the padding image array with a size of 9 × 9.

Figure 4

Program flow chart of maximum radius calculation.

Figure 5

Program flow chart of labeling pore region.

Figure 6

Reconstruction of (b) synthetic porous medium with (a) specific PSD information.

Figure 7

3D and 2D views of the internal pore structure in the studied samples. (a) Berea; (b) C1; (c) S1; (d) M1; (e) M2; (f) M3.

Figure 8

Comparison of PSD results between the calculated value of different algorithms and theoretical value.

Figure 9

Comparison of PSD calculated by different algorithms.

Figure 10

Results of (a) PSD and (b) cumulative PSD for M2 sample (Note: the symbols represent the real measurement data, and there are no pore radius data for the line segment between the two symbols.)

Figure 11

Results of PSD (left) and cumulative PSD (right) for (a) M3, (b) Berea, (c) C1, and (d) S1 sample. (Note: the symbols represent the real measurement data, and there are no pore radius data for the line segment between the two symbols.)