Reconstruction of a digital core containing clay minerals based on a clustering algorithm

It is difficult to obtain a core sample and information for digital core reconstruction of mature sandstone reservoirs around the world, especially for an unconsolidated sandstone reservoir. Meanwhile, reconstruction and division of clay minerals play a vital role in the reconstruction of the digital cores, although the two-dimensional data-based reconstruction methods are specifically applicable as the microstructure reservoir simulation methods for the sandstone reservoir. However, reconstruction of clay minerals is still challenging from a research viewpoint for the better reconstruction of various clay minerals in the digital cores. In the present work, the content of clay minerals was considered on the basis of two-dimensional information about the reservoir. After application of the hybrid method, and compared with the model reconstructed by the process-based method, the digital core containing clay clusters without the labels of the clusters’ number, size, and texture were the output. The statistics and geometry of the reconstruction model were similar to the reference model. In addition, the Hoshen-Kopelman algorithm was used to label various connected unclassified clay clusters in the initial model and then the number and size of clay clusters were recorded. At the same time, the $K$-means clustering algorithm was applied to divide the labeled, large connecting clusters into smaller clusters on the basis of difference in the clusters’ characteristics. According to the clay minerals’ characteristics, such as types, textures, and distributions, the digital core containing clay minerals was reconstructed by means of the clustering algorithm and the clay clusters’ structure judgment. The distributions and textures of the clay minerals of the digital core were reasonable. The clustering algorithm improved the digital core reconstruction and provided an alternative method for the simulation of different clay minerals in the digital cores.

Figure 1

Schematic diagram of the size of sediment grains. $R_I$ is the radius of the initial grain, $R_S$ is the radius of the sediment grain (considering the clay content), $V_I$ is the volume of the red grain (the initial grain), $V_C$ is the volume of the blue ring (the clay mineral), $V_S$ is the volume of the sediment grain (considering the content of clay), where $V_S=V_I+V_C$.

Figure 2

Digital core reconstructed by the PB method. (a) The initial grain size distribution. (b) Casting thin section of the reference model. (c,d) The 2D slices of sedimentation and compaction process by the PB method. (e) The 3D digital core reconstructed by the PB method.

Figure 3

Digital core based on the hybrid method. (a) The process of the reconstructed model by the hybrid method (2D slices). (b) The 3D digital core reconstructed by the hybrid method.

Figure 4

Distribution patterns of clay clusters on the surface of the grain after division of rock matrix and unclassified clay minerals. (a) Surface indentation of the grain. (b) Interactive filling between clay cluster and grains. (c) Intergrain filling between two grains. (d) Intergrain filling among multiple grains. (e) Surface filling of strati form cluster on the grain. (f) Scattered distribution on the grain. The black parts represent the rock matrix and the grayish parts represent the unclassified clay minerals.

Figure 5

Cluster identification by the HK algorithm. (a) 2D slice after division of rock matrix and unclassified clay minerals. (b) Cluster identification by the HK algorithm (different colors represent the labeled clay clusters).

Figure 6

Schematic of clustering algorithm. (a) Initial system. (b) System labeled by the HK algorithm. (c) System labeled and divided by the HK and $K$-means algorithms.

Figure 7

Structural features of clay clusters in the digital cores and scanning electron microscope (SEM). (a,c,e) SEM of surface filling of the grain, intergrain filling, and metasomatic texture. (b,d,f) textures of surface filling of the grain, intergrain filling, and metasomatism in the digital core.

Figure 8

Digital core containing different clay minerals. (a) The 3D digital core containing clay minerals. (b) 2D slices of digital core containing clay minerals.

Figure 9

Comparison of statistical functions in the digital core and the reference model in both pores and matrix. (a) AC and LP function of pores; (b) AC and LP function of matrix; (c) fractal dimension.

Figure 10

The process of division of clay clusters by the clustering algorithm. (a) The 2D slices of the reconstructed model by the hybrid method. (b) The 2D slices after division of rock matrix and unclassified clay clusters. (c) The 2D slices of clay clusters in the reconstructed model. (d) The 2D slices after applying both HK and $K$-means algorithm.

Figure 11

Size distribution of clay clusters in the reconstructed model.

Figure 12

Distribution of different textures of clay clusters in the digital core.

Figure 13

Distribution of the different clay clusters in the digital core.

Figure 14

Configurations and distributions of different clay minerals in the digital core. (a–d) The 3D configurations of montmorillonite, chlorite, kaolinite, and illite. (e–h) The amount and number distributions of clay clusters in the digital core.