Effect of Seepage Velocity on Pore Clogging Growth Behavior and Its Effect on Permeability Reduction During Fines Migration in Porous Media

Fines migration driven by fluid flows often causes pore clogging in porous media and thus reduces the permeability of the porous media. The clogging can pose serious problems in various practices, such as formation damage in hydrocarbon reservoirs, degradation of fluid withdrawal or injection efficiency, particle‐induced fouling in filtration membranes, or even a risk of sediment failure with geostructures. However, the effect of seepage flow velocity on the spatial growth pattern of fines‐induced pore clogging remains poorly identified. This study explores the pore clogging growth behaviors caused by flow‐driven fines migration and accumulation in porous media and the associated permeability reductions through a series of column experiments and concurrent X‐ray computed tomography imaging. Particularly, the X‐ray image analysis captures the spatial distributions of fines, and thus the homogeneous or heterogeneous (localized) clogging growth pattern under various seepage velocities. Our results reveal that an increase in the seepage flow velocity increases the likelihood of localized clogging growth, attributable to the direct interception of fines by the sand grains. The localized clogging growth causes a faster reduction in permeability than the homogeneous clogging growth. The presented study provides well‐controlled experiment data on fines distribution and associated permeability change, which gives insights into fines‐induced clogging behavior in porous media.

10.1029/2022WR033537 2 of 18 et al., 2012). Not only the quantity of deposited fines in a porous medium, but also the loci and growth pattern of clogging at a pore scale are required to estimate variations in fines-associated permeability (e.g., Herzig et al., 1970;Khilar & Fogler, 1998;Liu et al., 2019;Reddi et al., 2000). Particularly, it is critically important to understand and capture the spatial growth pattern of pore clogging during a transient stage even in a laboratory-scale samples (Pautz et al., 1989;Vetter et al., 1987).
Two extreme schemes are defined to describe the spatial patterns of clogging growth in the transient stage: dependent clogging (DC) growth and independent clogging (IC) growth (Liu et al., 2019). Let us imagine a pore clogged by fines deposition at the very early stage of fines clogging. On one hand, this clogged pore can serve as an initial clogging seed, and subsequent pore clogging occurs in the vicinity of this pre-existing clogged pore. This is referred to as the DC growth. On the other hand, subsequent pore clogging develops randomly and hence independently far from the pre-existing clogged pore, which is referred to as the IC growth. Therefore, DC yields a heterogeneous clogging distribution with locally concentrated clogged regions. By contrast, IC exhibits a relatively homogeneous clogging distribution.
Previous experimental studies have conducted to investigate clogging developments and some of their salient findings are as follows: (a) pore clogging causes redistribution of streamlines and complicates the clogging development (Brenner, 1961;Liot et al., 2018); (b) subsequently following-up fine particles are likely to be deposited in vicinity of the pre-existing or preceding clogging by fines deposition (Dersoir et al., 2015(Dersoir et al., , 2017; (c) the local clogging grows orthogonally to the flow direction (Sauret et al., 2018); (d) an interface between immiscible fluids facilitates localized clogging (Han et al., 2020;Jung et al., 2017;Wan & Wang, 2004); and (e) both the fine particle type and the interaction with the seepage velocity affect the occurrence of DC or IC in a convergent radial flow condition (Liu et al., 2019). Most studies investigate the clogging growth in two-dimensional (2D) porous media; however, it is challenging to estimate the permeability reduction in 2D porous media that cannot reflect flow path development due to the scale. To date, no experimental study in column scale that captures pore clogging development and simultaneously measures the permeability change during fines-induced pore clogging.
Therefore, this study explores the clogging growth in porous media and the associated reductions in permeability with the column scale experiment. In the column experiments, water with suspended fine particles are flown through a water-saturated sand pack, such that pore clogging is intentionally generated by migrating fine particles under a single-phase flow. The growth behaviors in uniformly packed beds are controlled with initial seepage velocity. A series of column experiments are conducted with X-ray computed tomography (X-ray CT) imaging while varying the flow velocity. Over the course of clogging, we visualize the growth patterns of clogging with X-ray CT imaging while monitoring the variations in permeability. The image analysis allows us to assess the spatial distributions of fines and thus homogeneous or heterogeneous localized clogging growth pattern. This study further examines the transition of clogging growth patterns from homogeneous to localized clogging growth associated with the dynamic evolution of preferential flow paths.

Materials
The clogging experiment uses a sand as a host sediment, powdered activated carbon (PAC) as fine particles, and water as a carrier fluid and a pore fluid. A uniformly graded, coarse sand with the mean grain size (D 50 ) of 722 μm is chosen as the host sediment (Ottawa 20/30; U.S. Silica, Frederick, MD, USA), as shown in Figure 1a. These sand grains have a fairly round shape (Roundness = 0.8; Cho et al., 2006) and they are uniformly graded with a low uniformity coefficient (Cu = D 60 /D 10 = 1.2), as shown in Table 1. Such uniformity in the grain size distribution and the spherical grain shape facilitate homogeneous packing across the column height and consistent packing between tests. These characteristics also provide consistency in porosity, pore structure, and pore size distribution.
As fine particles, the PAC (Yakuri Co., Kyoto, Japan) is used. The PAC shows a grain size distribution of 1-100 μm with the mean grain size (d 50 ) of 19 μm (Figure 1a) and has a platy shape similar to crushed silt (Table 1); both the size and shape characteristics are representative to silts among natural soils. In particular, PAC suspended in deionized water (DIW) shows the zeta potential value of −15 mV, which is slightly lower than silts but higher than most of clays. PAC is chosen as fine particles for their long suspension time. The lower grain density of PAC (1.4 g/cm 3 ) compared to the natural fine-grained soils (∼2.7 g/cm 3 ) results in the slower gravity-driven settling, and it facilitates examination of clogging growth, isolated from gravity-driven fouling. When natural fine-grained soils, such as silt, are used, the gravity-driven fouling can significantly affect the clogging growth behavior under the flow velocity regime used in this study. In addition, PAC is a microporous material, and it can be readily coated with metallic materials such as silver through chemical adsorption, which can result in better contrast in X-ray CT imaging (Kakavandi et al., 2014). However, this study uses PAC without chemical treatment.
Physicochemical characteristics of the carrier fluids, such as viscosity, interfacial tension, ionic strength (Kuhnen et al., 2000), salinity (Jang et al., 2020;Wan & Tokunaga, 2002), and pH (Khilar et al., 1983), heavily influence the fluid-fines interactions and hence the pore clogging phenomenon. The single-phase flow tests in this study use DIW as the pore fluid and the carrier fluid to minimize the effect of pore fluid chemistry on clogging associated with fluid-fines interaction, such as double diffuse layer repulsion. Table 1 summarizes the properties of host sediment grains (coarse sand) and fine particles (PAC). In this study, the size ratio of host sand particles to fine particles, D 50 /d 50 , is ∼38 (Figure 1a). The mean pore size is approximated to be 93-248 μm (d pore = 15-40% of D 10 ; Santamarina et al., 2001). The ratio of mean pore size to fine particle size, d pore /d 50 , ranges ∼5-13. Valdes and Santamarina (2006) have reported that d pore /d 50 < 1 causes sieving and filtering, and on the other hand, d pore /d 50 > 100 results in no clogging. While the condition with 1 < d pore / d 50 < 100 causes the retardation-type clogging, particularly, the bridge-type clogging is most likely to occur when 1 < d pore /d 50 < 20 and the migrating particle shape is platy (Valdes & Santamarina, 2006). Conclusively, our test condition with d pore /d 50 of 5-13 and platy PAC particles is expected to result in both retardation-type clogging and/or bridge-type clogging and it does not cause sieving nor filtering. The particle-to-particle size ratio, pore-to-particle size ratio, and low zeta potential indicate that the PAC is expected to represent silts rather than clays. Therefore, the experiments with the PAC are designed to examine size-relevant physical interactions between host grains and fine particles rather than chemical or electrostatic interactions.

Sample Preparation
The clogging experiments use a cylindrical, rigid-walled, polycarbonate column with an inner diameter of 20 mm, as depicted in Figure 1b. The coarse sand grains are packed inside the column up to a height of 79 mm by using the water pluviation method with hand tamping. The water pluviation method allows full saturation of pores with water, removing any trapped air bubbles, and this is critically important in postprocessing of X-ray images. Accordingly, the water-saturated sand packs are prepared while keeping the porosity consistently at 0.37-0.38. Screens with the opening size of 100 μm and springs are placed at the top and bottom of the sand pack to prevent the movement of sand grain during fluid flows.
In addition, a PAC suspension as the carrier fluid is prepared by rigorously mixing the PAC powder with DIW at a fines concentration of 0.5 wt%. This 0.5 wt% PAC suspension is injected to the water-saturated sand pack in the clogging experiments. The specific surface area of the sand was calculated by assuming a sphere with the mean grain diameter. b The specific surface area of the PAC was measured with the t-Plot method (De Boer et al., 1966). c The zeta potential was measured for the PAC suspension (0.5 wt% in DIW solution) which was used in the clogging experiments.

Column Setup
Two syringe pumps (500 HP, Teledyne ISCO, Lincoln, NE, USA) are connected to the column to inject fluids. One pump connected to the column through the transfer vessel provides feeds of the PAC suspension at constant flow rates to induce fines-induced pore clogging. In the transfer vessel, a magnetic stirrer constantly provides the PAC suspension mechanical mixing to keep the fines concentration consistent while feeding. The other pump directly connected with the column injects DIW at a constant flow rate, which is used to monitor the pressure response and measure the permeability of the sand pack. Pressure transducers (PX309 series, Omega Engineering, Stamford, CT, USA) are installed at two pressure ports on the column wall, one between the top screen and the sand pack, and the other below the bottom screen, to monitor the pressure difference across the column (differential pressure, ΔP). We use two types of pressure transducers: one pair for a high-pressure range (0-1.38 MPa), and another pair for a low-pressure range (0-103 kPa). When the fluid pressure reaches the maximum limit of the pressure transducer due to clogging, the low-pressure transducers are replaced by the high-pressure ones before continuing the subsequent injection. The discharge of PAC is confirmed with the effluent fluids during injection, but no additional examination of the effluent samples is conducted.

X-Ray CT Scan
The clogging experiments in this study exploit periodic X-ray CT imaging of the sand pack columns which enables monitoring of fines deposition and ensuing clogging growth in porous media. This study uses an industrial X-ray CT scanner (X-eye PCT, SEC, Korea) to capture fines-associated internal variations within the sand packs. X-ray CT scanning is carried out at the source voltage of 150 kV and the current of 1 A. The scan covers the center region of the vertical column from 23 to 54.7 mm high from the bottom; the total thickness of the scanned region is 31.7 mm. Single scan produces total 1,024 sliced images as one image set, and each sliced image has the pixel size of 37 μm and the depth of 31 μm. For the X-ray CT scans, all the plumbing lines are unmounted from the column and the valves are closed to ensure no mass flux during X-ray imaging.

Procedure of Clogging Experiments
Each clogging experiment involves several cycles of fines-induced clogging growth, followed by permeability measurement and X-ray CT imaging. Each cycle (or step) is comprised of the following activities in order: permeability measurement before clogging, injection of the PAC suspension (or fines suspension), permeability measurement after clogging, and X-ray CT scanning. Upon a water-saturated sand pack column prepared, the permeability of the sand pack is first measured by injecting DIW under a laminar flow regime with a flow rate of 1-5 mL/min (seepage velocity = 0.14-0.71 mm/s; Reynold number Re = 0.1-0.5). Then, the fines suspension is injected to the column until a significant increase in the differential pressure is observed. Figure 2 shows representative responses of differential pressure during the injection of fines suspension. As the migrating fines cause occlusion of pores within the sand pack, the differential pressure increases under a constant flow rate condition. Typically, the injected volume of the fines suspension ranges 25-265 mL, which corresponds to 3-30 times of the pore volume (3-30 PV; 1 PV = 9.17 cm 3 ). Once the injection of fines suspension is paused, we again measure the permeability by injecting DIW with a flow rate of 0.1-1 mL/min (seepage velocity = 0.014-0.14 mm/s; Reynold number Re = 0.01-0.1). Lastly, the column is imaged with X-ray CT. Thereafter, this cycle (fines suspension injection, permeability measurement, and X-ray CT imaging) is repeated by resuming fines suspension injection to induce further clogging growth, as depicted in Figure 2. The cycle is repeated until there is no significant change in the permeability reduction.
Total of six experiments is conducted while varying the flow rate from 3 to 30 mL/min. This corresponds to the initial seepage velocity of 0.43-4.3 mm/s for clean sand packs (Re = 0.31-3.1). Accordingly, three experiments with low-seepage velocities from 0.43 to 0.71 mm/s are grouped as the low-seepage group (Group LS; Re < 1), Figure 2. Representative pressure responses during the fines suspension injection. The result is obtained in Test 4 at Q = 30 mL/min (initial seepage velocity v = 4.3 mm/s). The injection was repeated for three steps. The inset figure depicts the differential pressure response during the first injection at Step 1.
6 of 18 and the others with high-seepage velocities from 2.15 to 4.3 mm/s are named as the high-seepage group (Group HS; Re > 1). Initial seepage velocity at the pore is estimated with the average cross-sectional area and injection rate, assuming the constant pore area throughout the sample. This is generally accepted for sand pack samples with uniform-sized particles as in our experiment. Table 2 summarizes the experiment program. Figure 3 illustrates the image analysis process, in which a sliced X-ray CT image acquired from Test 6 (Group HS with the seepage velocity of 2.15 mm/s) is shown as an example. Figure 3a shows a raw gray-scale sliced image of a cross-section in the sand column. The pixel size is 37 μm and the mean diameter of sand grains is 722 μm; the ratio of mean grain size to pixel size (D particle /L pixel ) is ∼20. Moreover, the contrast in X-ray attenuation between sand grains and water is sufficiently large. Such conditions allow the phase segmentation between sand grains and water-filled pores. This study uses the Niblack method (Niblack, 1985) to segment the pixels that represents pore spaces (pore pixel) and the pixels representing sand grains (grain pixel) from raw images. Figure 3b depicts the segmented pores within a clean sand column. Overall, we find that the resulting porosity from the Niblack threshold method better agrees with the measured porosity of the prepared sand packs than the other locally adaptive threshold methods (Sezgin & Sankur, 2004).

Segmentation of Pore Spaces
Accordingly, the gray-scale images of pore pixels are obtained by removing the grain pixels. Figure 3c displays a sliced image composed of the pore pixels after removal of the grain pixels, which shows the pore structure filled with water in a clean sand sample before Step 1. Note that the fine particles (PAC) are denser than pore water, and the deposition of fines in pores replaces water in the pore pixel. Therefore, the pixels with the fines deposition or clogging (color-coded with red color) have the higher attenuation than the pixels filled with the suspension (with light blue color). Thereafter, comparison in the pore spaces over the courses of multiple steps allows to capture clogging growth. Figure 3d highlights the fines-associated clogged pores, as illustrated with the red color. Figure 3e depicts that the subsequent injection of the fines suspension facilitates further growth of clogging from the previously clogged region, i.e., DC (or localized clogging).

Spatial Distributions of Fines Accumulation
Changes in CT numbers between steps can be used to capture the spatial distributions of accumulated fines and hence the fines-associated pore clogging growth pattern. We assume that the increase in CT number of a pore pixel, which is proportional to X-ray attenuation, is thus proportional to the mass of fine particles accumulated in the pore pixel. Thereby, we estimate the spatial distribution of fines accumulation along the height of the column.
One image set acquired at each step consists of total 1,024 sliced images (N = 1,024). The average CT number of each sliced image (X j , where j = 1…N and N = 1,024) is calculated by averaging all the CT numbers of the pore pixels in the given sliced image. These average CT numbers are obtained for all steps (X(step i) j , where step i indicates ith step). For given step i, changes in the average CT numbers of the corresponding slices are calculated Note. The initial seepage velocity is calculated using the following equation The Reynolds number is calculated using the following equation: Re = ρ f D p V s /μ, where ρ f is the water density (1,000 kg/m 3 ), D p is the mean particle diameter (722 μm), and μ is the dynamic viscosity of water (0.001 Pa s).
7 of 18 by subtracting the average CT numbers in previous step i − 1 from those in step i, i.e., the change in average CT number of Slice_j in step i, ΔX(step i) j . The image set when i = 0 (step 0) means the CT images acquired from a clean sand pack prior to injection of fines suspension. Then, this change in average CT value is correlated to the mass change at the same Slice_j, ΔM(step i) j , as follows: In the same manner, the total mass increase by fines accumulation for the entire scanned section is determined by summing the mass changes for all slices The mass variation at the slice in a certain step is normalized by the total mass increase to facilitate the comparison of changes among steps, i.e., ΔM(step i) j /ΣΔM(step i). This normalized mass variation is obtained by normalizing the change in average CT number with the total change in average CT number, i.e., ΔX(step i) j /ΣΔX(step i), which directly indicates the distribution of mass during injection. Figure 2 shows the representative differential pressure responses during repeated injections of the fines suspension, which are obtained from Test 4 with the flow rate Q of 30 mL/min. The injection of fines suspension causes Step 1, and (e) subsequent clogging growth around the initially clogged region. The attenuation (or material density) of the pore pixels is color-coded from blue to red. Red color indicates the highest attenuation due to fine particles in pores, and blue color indicates the lowest attenuation with no fines. The sand grains are segmented and expressed in black. These images are taken from Test 6. noticeable increases in differential pressure, of which magnitude evolves with clogging development. As the clogging grows more, the differential pressure elevates for a given flow rate. For an instance, during the first injection of the fines suspension (Step 1), the differential pressure increases to ∼0.3 kPa, which indicates the initiation of pore clogging. Subsequent injection in

Pressure Responses During Fines Migration and Clogging
Step 2 causes the greater differential pressure up to ∼6-7 kPa, which indicates the further growth of the pore clogging by fines. Thereafter, the differential pressure in Step 3 is kept at the same level to that in Step 2. Herein, the injected suspension volume differs among the steps (100 mL in Step 1 and 50 mL in Steps 2 and 3) because we stopped the injection in the instance of a sudden pressure rise. It is presumed that preferential flow paths are developed with the growth of pore clogging in Step 2. Therefore, in Step 3, the pore clogging barely grows as the introduced fines migrate through the preferential flow paths. This class of pressure responses are used to infer clogging growth behaviors. Figure 4 shows the variations in permeability during multistep fines suspension injection. The measured permeability is normalized by the initial permeability (K/K o ), i.e., normalized permeability. This is also called as the permeability reduction ratio associated with clogging. Fines-induced pore clogging reduces the permeability approximately by 99.5%-99.9% or more than 2 orders of magnitudes in all the cases, i.e., the permeability reduction ratio (K/K o ) less than 0.01. The normalized permeability (K/K o ) is leveled off to a consistent value of 0.001-0.005. The terminal permeability, which indicates the permeability after clogging, appears to be consistent, not affected by the initial seepage velocity. This result corroborates the previous finding by Wyss et al. (2006), in which they have reported that clogging probability is hardly influenced by the seepage velocity.

Permeability Reduction by Pore Clogging
The permeability decreases at a faster rate as the seepage velocity increases, as can be seen in Figure 4. Specifically, the permeability reduction ratios (K/K o ) per injected volume of the Group HS are greater than those of the Group LS. As the pore clogging probability increases with the number of migrating fine particles, the permeability reduction rate can be defined by normalizing the permeability reduction ratio with the injection volume. Therefore, the permeability reduction rate is computed by dividing the clogged permeability (K i+1 ) in the subsequent step (step i + 1) with the permeability (K i ) in the previous step (step i) and again normalized by the injected suspension volume between step i and step i + 1 with respect to the pore volume (PV), i.e., K i+1 /(K i · PV). Figure 5 compares the permeability reduction rates between the Group LS and Group HS. All the estimated permeability reduction rates are summarized in Table 3.
The permeability reduction process can be divided into three phases, as shown in Figure 5: clogging initiation phase (Phase I), clogging growth phase (Phase II), and terminal state (Phase III). In Phase I, the pore clogging initiates. Herein, the flow rate hardly affected the permeability reduction rates which show a similar range from 0.1 PV −1 to 3 PV −1 . In Phase II, the clogging grows subsequently with continued fines migration. In this clogging growth phase, the permeability reduction rates of Group HS (i.e., 10-60 PV −1 ) are significantly greater than those of Group LS (i.e., 0.7-3 PV −1 ) by approximately 1 order of magnitude. Note that Test 5 did not show the clogging initiation phase, but it showed a rapid clogging growth. Therefore, the permeability reduction rate from the first phase was assumed to correspond to Phase 2. Lastly, the clogging reaches to a terminal state in Phase III. At the terminal, the permeability reduction rates now decrease back to less than 1, regardless of the seepage velocity. Note that Test 3 in Group LS shows a relatively fast reduction during the clogging initiation phase (Step 1 and Phase I; Figure 4). Thereafter, in the clogging growth phase (Phase II), the permeability reduction rate or the slope of the curve of Test 3 is similar to those with the other two tests in Group LS (Tests 1 and 2).

X-Ray CT Image Analysis
The X-ray CT image sets which were acquired during fines migration and clogging are analyzed to identify changes in the internal pore structures and examine patterns of the pore clogging growth. The normalized permeability by its initial value is plotted with respect to the injected volume of the fines suspension. The red and blue lines indicate the low-seepage group (Group LS) and high-seepage group (Group HS), respectively. Figure 6 shows vertical distributions of fines accumulated along the column height, expressed as mass increments between Step 1 and Step 2 (Phase II) for all six tests with various seepage velocities. Herein, the vertical profile indicates the ratio of the mass increment at the given slice relative to the total mass increment ΔM(step i) j /ΣΔM(step i). Additionally, the standard deviations (SD) of this mass increment ratio intuitively portray the extent of variability in fines distribution, as shown in Figure 6. Table 3 lists the standard deviation values for each step in all tests. The vertical profiles of Group LS (Re < 1) show relatively flat profiles with low variations, and thus they have the mean value of 0.1% and the standard deviation value of ∼0.01%-0.02% (Figure 6a and Table 3). Such small standard deviations indicate homogeneous distributions of fines accumulated within a sand pack column. Whereas, the vertical profiles of Group HS (Re > 1) show significant fluctuations with the standard deviation value of ∼0.05%-0.07%, which is much greater than the LS group, while the mean values stay the same as 0.1% (Figure 6b and Table 3). Such high standard deviations indicate localized distributions of fines associated with pore clogging. Furthermore, Figure 7 clearly visualizes the vertical distributions of fines accumulated along the column height, in which the mass increment ratio is color-coded from blue to red. The higher color contrasts in Group HS (Tests 4, 5, and 6) imply the more localized distributions of fines than those in Group LS (Tests 1, 2, and 3). The vertical profile of Test 6 clearly shows such locally concentrated fines, which contrasts to the profiles of Group LS. Tests 4 and 5 in Group HS show more fines accumulations toward the bottom, though the standard deviations are still high. In these Tests 4 and 5, pore clogging appears to grow upwardly from the bottom region close to the outlet. It is noted that the localized clogging growth can be randomly initiated from anywhere within the sand pack, . The LS group shows gradual permeability reductions over phases. By contrast, the HS group shows abrupt permeability reductions at Phase 2. Here, the permeability reduction rate is defined as K i+1 /(K i • PV), where K i is the permeability at step i, K i+1 is the permeability at step i + 1, and PV is the injected fluid volume in pore volume during step i + 1. even under the same seepage velocity. Upon stochastic depositions of fines at some random locations, subsequently migrating fines continue to accumulate in the vicinity of those seeding locations, which leads to localized clogging growth or DC. Meanwhile, the location of initial seeding can be affected by various factors such as pore geometry, local velocities of carrier fluids and particles, and fines characteristics. Although the tests were conducted with the specimens composed of uniformly sized coarse sand in this study, the pore structure of each specimen is fairly unique, which is presumed to significantly affect the initial seeding location.

Image Analysis Result (I): Vertical Slices
Combined results of both the permeability reduction rate ( Figure 5) and the image analysis (Figures 6 and 7) demonstrate that an increase in seepage velocity, renders the greater likelihood of localized growth of pore clogging. Furthermore, our results also provide a clear evidence that the clogging growth behavior affects the permeability reduction rate. The localized clogging growth habit causes the greater extent to the permeability reduction by more than an order of magnitude than the homogeneous clogging growth habit. These observations corroborate 2D MFC experiment results by Liu et al. (2019). The clogging type is determined with the level of standard deviation σ for the clogging growth phase: homogeneous clogging when σ < 0.03 and localized clogging when σ > 0.05. b The high standard deviation values at the later steps in LS group are attributed to transition from independent clogging to dependent clogging behavior. More discussion can be found in Section 4.1. c In this step, the standard deviation value is estimated by comparing with Step 0.  The homogeneous mean value (0.1%) has the white color and each red or blue color indicate localized distribution along the slice.

Image Analysis Result (II): Horizontal Slices
In this study, the clogging growth is mainly attributable to fines retardation (or fines accumulation) owing to the slow settling velocity of the fine particles and the high-seepage velocity (Liu et al., 2019). Particularly the gravity-driven fouling has no or minimal effect on the clogging growth in the horizontal direction. As a result, the influence of seepage velocity on the clogging growth pattern is expected to be more pronounced in the horizontal slices. Therefore, in addition to the vertical profiles, spatial distribution of fines in the horizontal direction is analyzed by zoning a sliced X-ray image into 16 zones, as shown in Figure 8a. Then, the mass increment ratio at each zone is analyzed, as shown in Figures 8b and 8c. Here, we analyze Test 2 from Group LS and Test 6 from Group HS. As a result, the variation in Test 6 is much more significant among the 16 zones than that in Test 2, as shown in Figures 8b and 9c. Especially, the level of the standard deviation in Test 6 is remarkably greater than that in Test 2. In particular, the region at the column height from 31 to 39 mm shows severe local clogging growth, which is consistent with the observation in the vertical profile in Figures 6b and 7.

Characteristic Length of the Localized Clogging
The analysis above uses individual CT slices for fines distribution in which the slice depth (or thickness) is 31 μm. Meanwhile, several sliced images can be grouped as one slice sample to examine the mass variation or fines distribution for the given sample thickness. In fact, examining the change in standard deviation in the fines distribution with an increase in the sample thickness allows us to estimate the characteristic length of the clogged region. Figure 9a shows the standard deviations which are calculated for different sample thickness. The minimum sample thickness is 31 μm, which is the case using one sliced image. The standard deviation appears consistent until the sample thickness exceeds ∼1,000 μm. For more detailed analysis, Figure 9b shows the standard deviation normalized by the standard deviation at the minimum sample thickness, superimposed with the standard deviation from the six tests named as fluctuation of standard deviation. Interestingly, the normalized standard deviation result shows that the fluctuation becomes significant when the sample thickness exceeds ∼1,000 μm. This analysis suggests that the characteristic length of the clogged region is ∼1,000 μm or less.

Transitional Growth Pattern From Homogeneous Growth to Localized Growth
Continued fines deposition and ensuing pore clogging under a constant flow rate condition can raise the seepage velocity to a point where the homogeneous clogging growth evolves into the localized clogging growth. This class of the transition in growth pattern is confirmed in Test 3. Figure 10 shows the vertical profiles of fines distributions from Step 1 to Step 5, which was obtained from the X-ray CT image sets in Test 3. The degree of variations in the profiles indicates the homogeneous growth in Steps 1-3 with the SD of ∼0.015% and the localized growth in Steps 4 and 5 with SD of 0.048% and 0.066%, respectively. This clearly suggests that under a constant flow rate condition, the continued pore clogging can cause a transition in the clogging growth pattern from homogeneous growth to localized growth, due to the elevated seepage velocity. However, it still warrants further study on the critical seepage velocity (or threshold Reynolds number) over which the heterogeneous clogging (or DC) begin to prevail over the homogeneous clogging (or IC).

A Single Migrating Particle
This study examines the pore clogging during fines migration under a specific flow and clogging condition. Several dimensionless ratios can primarily represent our specific flow and clogging condition, which includes the ratio between the size of the constriction (or the mean pore size here d pore ) to the size of the migrating particle (here, the mean grain size of the fine particles d 50 ) and Reynolds number (Re).
• The ratio between the mean pore size and the migrating fine particle size, d pore /d 50 , ranges ∼5-13; such a condition excludes sieving and filtering, but satisfies the bridge-type clogging and deposition-type clogging conditions (Valdes & Santamarina, 2006). • Reynolds number (Re) characterizes a flow condition in porous media. Re of all the test conditions ranges 0.31-3.1, less than 10, as shown in Table 2. This indicates that the flow conditions were in the laminar regime with minimal turbulent. In such low Reynolds number conditions with high d pore /d 50 ratios, clogging can only be generated by gradual deposition of fine particles captured by host grains. It is because pore throats hardly filter a single fine particle, attributable to the high d pore /d 50 ratio; but the host grains (or solid walls in porous media) can capture a migrating fine particle. Figure 11 illustrates the possible capture mechanisms, which include the gravity-driven saltation (Figure 11a), collision of a migrating particle to obstacles (herein host grains; Figure 11b), direct interception of a migrating particle by host grains through van der Waals force, electrostatic force, and/or adhesion force (Figure 11c), and Brownian motion-based diffusive motion (Figure 11d).
These capture mechanisms are relevant to the forces that a fine particle experiences during fluid-driven migration in porous media. The relevant forces are the gravitational force (or buoyant weight of fine particles), viscous drag force, inertia force against motion change, electric attraction, and thermal diffusive force that drives Brownian motion of a fine particle. As the size of the fine particles ranges in micrometers, the advective transport is significantly greater than the diffusive transport driven by Brownian motion; the diffusive transport of the fine particles is thus negligible. Therefore, the relevant dimensionless ratios are the Archimedes number (Ar; gravitational force/viscous drag force) and Stokes number (Stk; inertial force/ viscous force), and for a spherical fine particle these are derived as follows: where v s is the seepage flow velocity, d 50 is the mean diameter of the fine particles, ρ f is the density of fines, ρ w is the fluid density (water in this study), μ is the fluid viscosity (water in this study), and D 50 is the mean diameter of the host sand.
Ar is the ratio between the terminal settling velocity of a particle and the flow velocity, which compares the gravitation-buoyancy-drag force associated with a free settling particle with the viscous drag force by advective fluid flow. Thus, it is proportional to the density difference between the fine particles and the fluid, and inversely proportional to the fluid velocity. Ar ranges 0.02-0.2 in all the tests; 0.02-0.04 for Group HS, and 0.12-0.20 for Group LS, of which level is relatively small, less than 1 in this study. Therefore, this Ar range less than 0.2 implies that the gravity-driven saltation is minimal. Furthermore, our test configuration with vertically placed sand pack columns and the downward PAC suspension flows facilitates to minimize the gravity-driven saltation effect.
Stk is the ratio between the inertial force of the moving particle and the drag force of the fine particles moved by the fluid, in other words, the ratio between the particle response time to the fluid field response time. While a particle with a low Stokes number follows fluid streamlines. When the Stokes number Stk is significantly greater than 1, the fine particle is dominated by inertia, thus a fine particle moves its own trajectory off the streamline of the fluid flow and can collide with the host grains (or solid walls in porous media) when the streamline is tortuous. On the other hand, when the Stokes number Stk is less than 0.1, a particle flows fluid streamlines, and thus it is unlikely to be captured by inertial collision (Tropea et al., 2007;Zhu et al., 2000). Stk ranges 1.3 × 10 −5 -1.3 × 10 −4 , lower than 0.01. Therefore, such a low Stk range indicates that in our test condition the migration paths of the fine particles are almost identical to the streamlines of the fluid flows.
Accordingly, owing to the low Re, Ar, and Stk regime of this study, the direct interception of migrating fines by the host grain through adhesive, van der Waals or electrostatic attraction is most likely the major capturing mechanism from a perspective of an individual migrating fine particle. The deposited fines via direct interception eventually causes pore clogging in porous media, either via IC or DC. Figure 10. Evolution of fines distributions with continued fines clogging from Step 1 to Step 5 in Test 3. Each profile is produced by comparing the X-ray image sets taken before and after the corresponding step. SD indicates the standard deviation. The resulting fines distribution implies that the clogging pattern evolved from homogeneous growth (Steps 1, 2, and 3) to localized growth (Steps 4 and 5). Figure 11. Pore-scale clogging mechanisms by migrating fine particle: (a) gravitational saltation, (b) inertial collision, (c) direct interception, and (d) diffusion.

Mechanism for Localized Clogging Growth
In the beginning of fines migration, the direct interception as the major mechanism for capturing fines takes place at any location throughout the media. Thereafter, the deposited fines reduce the size of pore throats (Li & Prigiobbe, 2018), and it hence increases the seepage velocity under a constant injection rate condition. Let us examine the question as to how the greater flow velocity increases the likelihood of the localized clogging growth (or DC).
The direct interception becomes more pronounced closer to the solid pore wall. This region is referred to as the sticking region (Wyss et al., 2006). This direct interception can be caused by physical contacts between the moving particles and the pore wall (Espinosa-Gayosso et al., 2012), adhesion force relevant to surface chemistry, van der Waals attraction, and/or electrostatic attraction (Ramachandran & Fogler, 1999). As the seepage velocity increases, the density of the streamlines increases. In turn, the outermost streamlines become closer to the impermeable solid boundary and some of them would be laid over the sticking region (Lin et al., 2009). Consequently, an increased seepage velocity increases the chance for fine particles migrating along those outermost streamlines to be directly intercepted by the sand grains, as shown in Figure 12. Once a pore is locally clogged, the seepage velocity increases in the vicinity of the clogged pore. Conclusively, the increased seepage velocity increases the chance of direct interception of migrating fine particles, and as a result, another clogging is also formed in the vicinity of the pre-existing clogged region.

Conclusion
This study proves the effect of seepage velocity on the clogging growth pattern, and its effect on permeability reduction. Particularly, our experiment condition corresponds to the regime with low Reynolds number (Re < 10), low Archimedes number (Ar < 0.1), low Stokes number (Stk < 0.01). Our results provide clear evidences that the localized clogging (or DC) causes faster reduction in permeability than the homogeneous clogging (IC), and second that an increase in the seepage flow velocity increases the likelihood of localized clogging growth. The high-seepage velocity with Re > 1 causes a localized distribution of the fines, which indicates the heterogeneous Figure 12. A schematic drawing of streamline distribution under a high-seepage velocity condition and under a low-seepage velocity condition, respectively. The shaded area indicates the sticking region on particle surfaces. Blue solid lines indicate the streamlines (or flow paths) closest to the fines and sand grains. Red solid lines indicate the center streamlines along which fine particles can migrate. pore clogging growth. The low-seepage velocity with Re < 1 induces a relatively uniform distribution of the fines, which implies the homogeneous clogging growth. The localized clogging growth reduces the medium permeability significantly faster than the homogeneous clogging development, by an order of magnitude. Under a particular initial seepage velocity, a transition from homogeneous growth to localized growth is observed as the local seepage velocity increases with continued fines accumulation. Spatial distributions of fines accumulation estimated by X-ray CT imaging well captures the clogging growth with the characteristic length of ∼1 mm and suggests that localized clogging develops in both vertical and horizontal directions. The pore-scale mechanism for localized clogging growth is explained with the direct interception mechanism, of which chance increases with the increased seepage velocity in the vicinity of the clogged pores. The presented results advance understanding on fines-induced clogging behavior in porous media, and provides well-controlled experiment data to develop formation damage models due to fines migration and clogging. The findings could be further extended to identify the clogging phenomena in various practices, such as aggregate layers in geostructures and pavement, formation damage in hydrocarbon reservoirs, and particle-induced fouling in filtration membranes.

Data Availability Statement
All of the X-ray CT raw images and analysis data used in the plots are available in Han and Kwon (2022).