Elsevier

Powder Technology

Volume 362, 15 February 2020, Pages 635-644
Powder Technology

Pore-throat characterization of unconsolidated porous media using watershed-segmentation algorithm

https://doi.org/10.1016/j.powtec.2019.12.026Get rights and content

Highlights

  • Watershed method to identify pore−throat of various unconsolidated porous media

  • Spherical particles generate smaller throat but larger pore than angular particles.

  • Comparison to medial axis method shows similar trend but larger pore and throat.

  • Relationship of pore volume and surface area demonstrated a fractal behavior.

  • Normalized pore size distribution demonstrated a single Gaussian function.

Abstract

Pore-throat characteristics of porous media play important roles in various flow processes. However, pore size distribution (PSD) and throat size distribution (TSD) of various porous media have rarely been reported. Watershed-segmentation (WS) is a promising pore-throat identification method. To avoid over- and under-segmentations, a trial-and-error method was devised and validated using artificially ordered packings. Afterwards, we analyzed porous media with various characteristics, and comparisons with artificially ordered packing were made. More angular particles generated larger pores and throats. TSD of spherical particles was bimodal, whereas other particles resembled a normal distribution. Pore surface area and volume relation demonstrated a fractal behavior. Compared with medial axis (MA) method, PSD and TSD from WS method were larger but exhibited similar distribution trends. Normalizing the PSD with the median pore size yielded a single Gaussian model, demonstrating a possible PSD model. However, normalization to TSD data does not produce a single Gaussian model.

Introduction

In porous media, pore-throat characteristics influence various flow processes. In the case of a single fluid flow, pore-throat characteristics define the permeability and tortuosity, which are crucial in the applications of water-filtration beds and the biofilm developments [1]. As water flows through a filter bed, permeability and tortuosity control the flow rate and ensure sufficient retention time for water filtration. Permeability is controlled by the throat size of the porous media, whereas tortuosity is affected by the pore networks of the media. However, in the filtered bed, biofilm and residual filtered material thicken after a prolong operation time. As a result, the throats could be closed, and the pore networks could be altered. Resultantly, permeability decreases with an increase in tortuosity, and thus filter-bed performance is affected. Therefore, investigating these characteristics is important for understanding the limitations of filter bed operations [2]. For multiphase flow, pore-throat characteristics affect capillary trapping [3]. Since capillary trapping mainly occurs inside the pores, the size and shape of the pores determine the trapped phase. These characteristics define the stability of the trapped phase and its exposure to the surrounding fluid. Stability governs the possible displacement of the trapped phase from the pore [4], and exposure influences the mass transfer of the trapped phase [5,6]. Therefore, it is important to understand these interrelations as they are studying filter bed [1], soil science [7], powder technology [8], enhanced oil recovery [9], and geological carbon sequestration [10].

In spite of its importances, void space inside porous media cannot be observed directly; therefore, measuring it requires a special approach. Owing to the advancements in computed-tomography (CT) technology, especially X-ray micro-tomography (micro-CT), CT has become the main technology to study pore-scale phenomena in porous media [11]. CT is capable of measuring void space in various porous media with a sufficient and uniform image resolution.

In addition to special approach for void measurement, the identification of pore-throat involves complex processes. In general, there are four types of approaches of pore-throat identification: (i) Delaunay tessellation (DT) [8,12,13] identifies pore and throat from tetrahedral spaces contained in four spheres that are close to each other; the pores are approximated from the spheres inscribed inside the tetrahedral spaces, whereas the throats are approximated from spheres inscribed inside the connections between the tetrahedral. However, this method is limited to spherical particles because if non-spherical particles were used, the tetrahedral spaces would become unpredictable. (ii) The maximum-ball (MB) method [14,15] is performed by inscribing a maximum-sized ball at the middle of a pore network. The largest sphere is defined as the pore, whereas the smallest sphere, which connects larger spheres, is defined as the throat. However, the MB method was computationally extensive. As reported by Taylor et al. [16], it required the longest time to identify the pore-throat. (iii) The medial-axis (MA) [17,18] method detects a series of points, which generates a line that defines the void topological structure, in the middle of the void structure. By applying this concept to a porous medium, the structure of the porous medium can be derived, resulting in pore-throat identification and separation. For throat definition, the minimum inscribed circle along the MA line is determined, and then throat size is assumed to be the total void area perpendicular to the medial axis line at the center of minimum inscribed sphere. Pore is then defined as the void volume between throats. However, Al–Raoush and Willson [19] combined the concepts of MB with MA by modifying pore- and throat-size definitions as maximum and minimum inscribed spheres at the MA node (junction among MAs). However, the MA method poses a limitation for pores with high coordination numbers. Since a pore is identified as an MA node, a large pore could be segmented to be more than one pore because of the separation of medial axis line junctions. Although a merging parameter can be introduced [[17], [18], [19]], the selection of this value could be problematic for large pores with high aspect ratios. Resultantly, this method could cause an over-segmentation of pores. (iv) The watershed segmentation (WS) [20,21] method was originally a method used for separating geographical catchment basins using a distance map [22]. The application of this method to porous media, however, yields satisfactory results in pore-throat identification [20,21]. Also, the WS method directly delivers segmented pore-throat images in shorter computational time than other methods, providing easier access for inspections and post-processing procedures [16]. Although Wildenschild and Sheppard [11] found that WS is prone to errors in the presence of noises, Rabbani et al. [20] showed that WS delivers acceptable results and coordinate numbers similar to those by MB method in the absence of noise interferences. One of the limitations associated with WS is that an arbitrary parameter to avoid pore-throat over- and under-segmentations needs to be specified. However, no discussion regarding the optimum selection of this parameter has been made. Moreover, the WS method has been used primarily for consolidated porous media [20,21]. To the best of our knowledge, the performance to process porous material with high porosity, i.e., unconsolidated porous media, with various characteristics has not been reported yet.

Given these pore-throat identification methods, there are two kinds of method to calculate pore and throat sizes. First, as given by the DT, MB, and combined MB-MA methods, pores and throats sizes are calculated through approximation of the inscribed ball by excluding the volume or area outside the maximum inscribed ball. Second, as given by the MA and WS methods, pore and throat sizes are calculated based on actual shape and size. The volume is usually represented by the equivalent sphere diameter to retain the total volume as well as the cross-sectional area of the pore and throat. In the case of fluid flow and fine-particle trapping in porous media, the first of these two kinds of method is acceptable because the initial capillary pressure, permeability, and mechanical trapping are mainly controlled by the radius of inscribed ball within the network [12,16,23]. However, for capillary trapping, the shape of the trapped phase tends to follow the pore and throat shapes [3]. Thus, the pore and throat shapes affects the surface area of the trapped phase, which controls the exposure to surrounding fluid. Therefore, for capillary trapping, this type of calculation is more appropriate.

Owing to our interest in capillary trapping inside various unconsolidated porous media, we previously used the MA method to perform pore-size distribution (PSD) analyses of porous media characterized by various particle sizes and shapes and developed an empirical model to approximate PSD based on particle characteristics [3]. By normalizing with the median pore size (dp,median), PSD formed a single Gaussian function, which can be used as an underlying concept to develop an approximation model for PSD in various unconsolidated porous media. However, there are several questions that still remain unanswered: is this result also applicable to methods other than the MA method? What if this result is just the effect of the used pore-throat identification method? Furthermore, what about throat-size distribution (TSD)? Can a similar tendency be found by normalizing the TSD with the median throat size (dt,median)?

Herein, micro-CT was used to scan various porous media with diverse particle characteristics, and then pore and throat characteristics were investigated using WS. To validate the WS method, we generated three porous media by artificially ordered packing of mono-sized spherical particles, which the pore and throat sizes can be calculated analytically, and processed them using the WS method. The PSD, TSD and, their shape in relation to various particle characteristics were also discussed. We also compared pore-throat identification using MA method obtained from our previous work [3]. Furthermore, we investigated the tendency of PSD and TSD to form single Gaussian functions after normalization using median size values.

Section snippets

Experimental methods

Granular particles of various sizes and shapes were used. The type of particle, range of size, median diameter (d50), sphericity, roundness, and the generated porous media porosity are listed in Table 1. Particle-size ranges were based on sieve-size classification used by the American Society for Testing and Materials. Sphericity and roundness were measured using the method by Patmonoaji et al. [3]. In general, glass beads (GB), plastic beads (PB), and Toyoura sands (TS) represent spherical

Image processing methods

The stacks of cross-sectional images had to be processed by a series of image processing techniques to derive the quantitative data, such as porosity, pore size, pore surface area, and throat size, and the qualitative data, such as 3D images of solid, void, segmented pores, and segmented throats.

First, void space and solid needed to be distinguished through binarization. Several automatic thresholding methods, such as Otsu, Bernzen, Median, and Phansalkar, were tested. By comparing the porosity

Ordered packing and close random packing of 600–710 μm glass beads

By processing the artificially generated ordered packing, we could validate the WS method because the size and shape of both pores and throats could be calculated analytically, and the results serve as benchmarks for pore and throat segmentation process. Also, since all the ordered packings have the same d50 with GB 600–710 μm (d50= 655 μm) and the particle shapes are also spherical, a comparison between the ordered packing and CRP can be done. Through such comparison, we could determine CRP

Conclusions

We tested the WS method for pore-throat identification in unconsolidated porous media having different particles sizes and shapes. We minimized possible under- and over-segmentations by finding the optimum value of the initial-flooding parameter by trial and error method. WS method performance to process ordered packings provided satisfactory agreement with the analytical solution. MA method [17,18] performance to process CRP with different sizes and shapes also yielded the same trends for PSD

Declaration of Competing Interest

There is no conflict of interest to declare. The study was supported by a grant from JSPS KAKENHI with the grant number of 17H00790.

Acknowledgements

This work was supported by JSPS KAKENHI with grant numbers 17H00790.

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