Pore-corner networks unveiled: Extraction and interactions in porous media

Generalized network models (GNMs) serve as powerful tools, bridging the intricate gap between pore- and continuum-scale multiphase transport in porous media. An essential step in the development of these models is to extract pore-corner networks from actual porous materials. In this paper, we present a pore-corner-network extraction method involving two steps. In the first step, pore networks, comprising pore bodies interconnected by pore throats, are extracted based on the omnidirectional Euclidean distance concept. Subsequently, corners within each distinct pore unit, consisting of a pore body and half of the connected pore throats, are identified by sweeping the pore unit with a sphere. The radius of the sphere corresponds to the minimal corner radius within the cross-sections at the centers of pore throats within the pore unit. To extract pore-corner networks from three-dimensional images of porous materials efficiently, we introduce a domain decomposition approach. In this approach, the porous material of interest is divided into multiple subdomains, each enveloped by a protective layer. To validate our proposed extraction method, a GNM is developed to simulate evaporation in a porous medium composed of packed spherical beads. This model is systematically compared with microcomputed tomography experimental data. Encouragingly, the modeling results are in good agreement with the experimental data, particularly in terms of the variation of liquid distribution over time. Our proposed extraction method not only contributes to disclosing the structures of pores and corners in real porous media but also benefits the development of GNMs that can be employed to understand in detail the multiphase transport in porous media from the pore-scale perspectives.

Figure 1

Steps to extract a pore-corner network. (a) Void space of 12 packed spheres illustrated in Fig. S2 in the Supplemental Material [54]. (b) Medial axis of the void space. (c) Regions of pore bodies and of pore throats. (d) Extraction of corners in void space. (e) Identification of corners in pore bodies and pore throats. (f) Extracted pore-corner network.

Figure 2

Steps to extract a pore network from a two-dimensional (2D) porous medium. (a) A 2D voxelized porous medium. (b) The anchored void voxels at the inlet and outlet surfaces of the medium. (c) Hierarchical levels of void voxels inside the voxelized porous medium. (d) Medial axis and the centers of pore bodies and of pore throats. (e) Pore-body regions (shown in red) and pore-throat regions (shown in blue). (f) Extracted pore network.

Figure 3

Steps to obtain the anchored void voxels at the inlet and/or outlet surfaces of porous media. (a) The inlet and/or outlet surface of a porous material composed of packed spheres. (b) Hierarchical levels of void voxels. (c) Extracted medial axes (green lines) and the neck void voxels (black voxels). (d) Void clusters and the anchored void voxels (yellow voxels).

Figure 4

Steps to extract corners in a pore unit: (a) The structure of a pore unit composed of a pore body (red zone) and void space between this pore body and centers of neighboring pore throats (blue zones). (b) Corner radius of the two-dimensional (2D) cross-section of a pore throat. (c) The pore unit (shown in white) is swept by a sphere (shown in yellow) with the radius equal to corner radius of this pore unit. (d) Extracted corners (orange zone) in the pore unit.

Figure 5

Schematic of the transformation of (a) a three-dimensional (3D) cross-section into (b) a two-dimensional (2D) representation at the center of a pore throat.

Figure 6

Steps to extract a corner network. (a) Corner void voxels in pores (shown in green in the pore bodies and yellow in the pore throat). (b) Clusters of corner void voxels. (c) Omnidirectional Euclidean distance (OED) of corner void voxels in the pore throat. (d) Extracted corner network.

Figure 7

Schematic of the domain decomposition method to calculate the omnidirectional Euclidean distance (OED) map of a large porous material. (a) A large two-dimensional (2D) digital porous material of 100 × 100 voxels and four subdomains. (b) Protective layers of subdomain (shown in red). (c) Hierarchical levels of void voxels in subdomains. (d) Hierarchical levels of void voxels in the whole domain.

Figure 8

Schematic of pore-corner-network extraction from a real porous medium composed of packed spheres. (a) Three-dimensional (3D) binary image of the sphere packing obtained by micro-CT techniques. (b) Corners in the sphere packing. (c) Corner network of the sphere packing. (d) Extracted pore-corner network of the sphere packing.

Figure 9

Experimental setup for evaporation of sphere packing used in the micro-CT experiment.

Figure 10

Liquid distribution profile in the sphere packing along the $z$ direction, obtained from micro-CT experiment and generalized network model (GNM) simulation, at total liquid saturations of (a) 0.77, (b) 0.52, (c) 0.10, and (d) 0.03.

Figure 11

Distributions of liquid in the sphere packing at various total liquid saturations $S_t$ obtained from (a) micro-CT experiment and (b) generalized network model (GNM) simulation.

Figure 12

Variation of the total liquid saturation $S_t$ in the packing sphere with evaporation time $t$ obtained from micro-CT experiment and generalized network model (GNM) simulation.