Role of Low Flow and Backward Flow Zones on Colloid Transport in

Jun 14, 2010 - Environmental Sciences, Peking University, Beijing, 100871, P. R. China, and ... vortices to colloid transport in real porous media, la...
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Environ. Sci. Technol. 2010, 44, 4936–4942

Role of Low Flow and Backward Flow Zones on Colloid Transport in Pore Structures Derived from Real Porous Media X I Q I N G L I , * ,†,‡ Z H E L O N G L I , ‡ A N D D O N G X I A O Z H A N G * ,‡ Laboratory of Earth Surface Processes, College of Urban and Environmental Sciences, Peking University, Beijing, 100871, P. R. China, and Department of Energy and Resources Engineering, College of Engineering, Peking University, Beijing, 100871, P. R. China

Received December 2, 2009. Revised manuscript received May 15, 2010. Accepted June 2, 2010.

To examine the relevance of low flow zones and flow vortices to colloid transport in real porous media, latticeBoltzmann (LB) simulations were combined with X-ray microtomography (XMT) to simulate flow fields in glass beads and quartz sand. Backward flow zones were demonstrated to be widely present in both porous media, with a greater volume fraction in the former relative to the latter porous media. Glass beads in the XMT images were approximated as spheres and their coordinates and radii were extracted to allow reconstruction of pore structures. LB simulations were again performed and the simulated flow fields in the reconstructed pore structures were coupled to a three-dimensional particle tracking algorithm. Particle tracking simulations demonstrated that significant amounts of colloids stayed in the simulated domains for long periods (up to 50 pore volumes). The percentages of colloids with long residence time increased as the depth of the secondary energy minimum increased. The majority of the colloids with long residence time were translated to low flow zones while being associated with grain surfaces via secondary minima. A small fraction of colloids entered low flow zones without being associated with the grains surfaces. Backward flow zones were also found to trap a small fraction of colloids for significantly long time (up to 10 pore volumes). In overall, however, backward flow zones trapped fewer colloids for shorter durations than low flow zones. In summary, this work demonstrates the importance of temporary trapping of colloids by the low flow and backward flow zones in real porous media. This trapping process can explain a number of intriguing experimental observations.

Introduction The colloid filtration theory (CFT) considers colloid removal by porous media as a two-step process: first, the mass transport of colloids to the proximities of grain surfaces; and second, the deposition of colloids to the surfaces (1). The transport step is characterized by the single-collector ef* Address correspondence to either author. Phone/fax: 86-1062753246 (X.L.); 86-10-62757432 (D.Z.). Fax: 86-10-62757427 (D.Z.). E-mail: [email protected] (X.L.); [email protected] (D.Z.). † College of Urban and Environmental Sciences. ‡ College of Engineering. 4936

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ficiency (η), which is the number of colloids colliding with the collector (i.e., the grain) divided by the number of colloids moving toward the collector. The equations correlating η to the parameters (e.g., fluid velocity, grain size) of the environmental conditions have been developed using trajectory analysis based on the Happel sphere-in-cell model (2-4). In this model, the porous medium is idealized as a collection of spheres, each surrounded by a concentric fluid shell (5). The deposition step is described by the collision efficiency (R), which is the number of collisions that result in deposition divided by the total number of collisions. The R is thought to be dependent on the interaction between grain and colloid surfaces (6). From η and R, the rate constant of colloid removal can be calculated and colloid concentrations at different transport distances predicted (1, 7). CFT predicts colloid transport in porous media fairly well in the absence of an interaction energy barrier between grain and colloid surfaces (conditions favorable for deposition) (e.g., ref 8). Under these conditions, every collision results in deposition (R ) 1). However, dramatic discrepancies between CFT predictions and experimental observations exist in the presence of an energy barrier (conditions unfavorable for deposition). CFT predicts that colloid deposition would be negligible at most (R ≈ 0) in the presence of even small barriers (e.g., >10 kT), whereas numerous laboratory and field studies demonstrated that significant colloid deposition occurs commonly (e.g., ref 9). The observed discrepancies were traditionally attributed to the neglect of grain and colloid surface charge heterogeneity and roughness which can locally reduce or eliminate the energy barrier (e.g., refs 10 and 11). Recently, increasing evidences suggest that the lack of incorporating correct mechanisms of colloid retention is another source of CFT failure under conditions unfavorable for deposition (12). Both direct observations and mechanistic simulations have demonstrated that colloids could deposit at grain-to-grain contacts (13-16), a feature that is not accounted for in the Happel model (5). Deposition and elution experiments in packed columns and impinging jet systems indicate that significant fractions of retained colloids under unfavorable conditions are associated with collector surfaces via secondary energy minima (17-19). These associated colloids are expected to translate along the grain surfaces due to the tangential hydrodynamic drag, until they reach low flow zones (e.g., rear stagnation zones) where the drag force is insufficient to overcome the forces that resist their further downgradient movement. Mechanistic simulations of colloid transport have confirmed this process (16). When enhanced colloid retention in low flow zones was accounted for in a kinetic model, superior fits to experimental breakthrough curves and retained profiles were obtained (20). More recently, Li and co-workers demonstrated another potential colloid removal mechanism, retention by flow vortices (where flow is in the opposite direction of the overall flow) (21). Colloids retained by flow vortices were tens of micrometers from grain surfaces, that is, they are not associated with secondary energy minima (which are typically less than 100 nm away from grain surfaces). Flow vortices near grain contact areas have also been demonstrated by Cardenas and Torkzaban et al. using the COMSOL software (22, 23) and by Biggs et al. using a lattice-gas automatabased method (24). However, these simulation studies and the mechanistic simulations that revealed retention in low flow zones by Johnson et al. (16) all dealt with unit cells of idealized packing systems. In addition, colloids retained by flow vortices were directly released into the vortices (21). Whether flow vortices are widely present in real porous media 10.1021/es903647g

 2010 American Chemical Society

Published on Web 06/14/2010

and whether colloids can get into the vortices have not been examined. As such, the role of low flow zones and flow vortices on colloid transport in real porous media is not well understood. In this work, LB flow simulations were performed based on X-ray microtomography-derived images of glass beads and quartz sand to verify the existence of flow vortices in real porous media. The glass beads were approximated as perfect spheres and their coordinates and radii were obtained from the images. Based on the extracted coordinates and radii, LB simulations were again conducted at a higher grid resolution. The derived flow fields were coupled to a three-dimensional particle-tracking algorithm to simulate the transport of colloids of various sizes under different flow and solution chemistry conditions. Based on the simulation results, the role of low flow zones on colloid transport in real pore media was elucidated.

Materials and Methods Acquisition of X-ray Microtomography Images. Soda lime glass beads (Cataphote Inc., Jackson, MS) and quartz sand (Fisher Scientific, Fair Lawn, NJ) had a size range of 710-850 µm (20-25 mesh, American standard). The porous media were packed in a borosilicate glass column (75 mm in length and 8 mm in inner diameter) and scanned using the conebeam X-ray microtomography system (Konoscope 40-130, Aracor Inc., Sunnyside, CA) at a spatial resolution of 20 µm. Images of the two porous media were reconstructed using a filter back projection algorithm. Details of the XMT system, the scanning procedures, and the reconstruction algorithm are available elsewhere (13, 25). Representative images of glass beads and quartz sand have been provided in a previous publication (13). LB Flow Simulation. For both porous media, five domains, each consisting of 220 × 220 × 220 pixels (4.4 × 4.4 × 4.4 mm), were randomly selected from the XMT images. A D3Q15 lattice-Boltzmann BGK model was used for flow simulations in the selected domains, with the voxel length exactly equal to the pixel length of the images (20 µm). Pressure boundaries were applied at the inlet and outlet planes (overall flow oriented in z direction). Solid (no-slip) boundaries were imposed at the x and y bounding planes and grain surfaces inside the domains. Details of the D3Q15 model and boundary conditions were described in a previous publication (21). To mechanistically elucidate the role of low flow zones and flow vortices on colloid retention, trajectory analysis of colloid movement needs to be performed. This requires the knowledge of colloid-grain interaction and other forces at each position. The interaction force depends on the separation distance between the colloid and grain surfaces. Since even the glass beads are not perfectly spherical (see representative images in ref 13), the grain surfaces and the separation distances can not be easily defined, disallowing calculation of the colloid-grain interaction force and subsequent trajectory analysis. To bypass this hurdle, the glass beads were approximated as perfect spheres in this work. Two 110 × 110 × 110 domains within two of the above 220 × 220 × 220 domains of glass beads were selected. The actual length in each dimension of the two domains was 2.2 mm. The coordinates of the centers and radii (in pixels) of the grains within the two domains were obtained from the XMT images using Image J. Both domains included 40 grains that fully or partly fell within the domains. Using the extracted coordinates and radii, the domains were reconstructed (denoted as Domain 1 and 2, respectively) and discretized to yield 220 × 220 × 220 voxels. LB simulations were again performed to obtain the flow fields in the two reconstructed domains. During LB simulations, the length of the domains was turned to a dimensionless value of 1. The

coordinates and radii were turned dimensionless accordingly and are provided in Table S1 and S2 in the Supporting Information (SI). The porosities of Domain 1 and 2 were 0.368 and 0.370, respectively, whereas the porosities before reconstruction were 0.367 and 0.324, respectively. The average diameter of the grains in the two domains was about 0.36 (corresponding to an actual size of 360 µm) (SI Table S1 and S2). Thus, the ratio of voxel size (1/220 ) 0.0045) to average grain diameter is about 0.0129 (0.0045/0.36), very close to the critical ratio at which simulated deposition converges at groundwater flow regimes for colloids down to 1 µm (21). Particle Tracking. The simulated flow fields of Domain 1 and 2 were coupled to a three-dimensional particle tracking algorithm. This algorithm tracked colloid trajectories in the pore spaces by performing complete force and torque balances to determine the colloid velocities in the three dimensions. The force and torque balances and the derivation of colloid velocities were described in detail in two previous publications (16, 21). A trilinear interpolation algorithm was used to obtain fluid velocities at any position in the pore space from the discrete flow fields derived from LB simulations. Details of this algorithm were provided in the recent publication (21). Simulation Conditions. Simulations were conducted for three sizes of colloids (0.5, 1.0, and 2.0 µm in diameter) at two superficial velocities in both domains (1.0 × 10-4 and 1.0 × 10-5 m s-1). At the higher velocity and in Domain 1, simulations were performed under four solution chemistry conditions: in the absence of an energy barrier (denoted as FAV); in the presence of energy barrier and with a secondary energy minimum of about 3 kT (UNFAV1), in the presence of an energy barrier and with a secondary minimum of about 0.5 kT (UNFAV2), and in the presence of an energy barrier and with a secondary minimum less than 0.1 kT (UNFAV3). The four solution conditions were created by assigning different ionic strengths and zeta potentials of colloid and grain surfaces (SI Table S3). At the low velocity in Domain 1 and at both velocities in Domain 2, simulations were performed under two conditions, FAV and UNFAV1. Under each simulation condition, four simulation runs using four different random seeds (the number used to generate particle entry positions) were carried out to allow a statistical analysis. For each simulation run, 500 colloids were simulated under UNFAV1 at the lower superficial velocity in Domain 1. Under the rest conditions, 1000 colloids were simulated. The colloids were released into the entry plane, z ) 0.1. Positions where the simulated fluid velocities were negative were excluded for entry. Colloids deposited at grain-to-grain contacts and at noncontact areas were recorded. Criteria for colloid deposition were provided in the previous paper (21). Also recorded were the colloids that stayed in the domains for more than 5 times of the mean residence time of water molecules at a particular superficial velocity. The mean residence time of water molecules is equivalent to the duration of a pore volume (PV). The duration of a pore volume can be calculated by dividing the displacement in z direction of an exiting water molecule (0.9 mm) by the fluid velocity. Simulation was terminated when the residence time of a colloid in the domain exceeded 50 PVs.

Results Backward Flow Zones in the Porous Media. LB simulations at the spatial resolution of the XMT images revealed that flow zones with negative z-direction velocities were widely present in both glass beads and quartz sand, as were in the unit cells (21). Representative flow fields of the z-direction velocities in glass beads and quartz sand are shown in Figure 1 and SI Figure S1, respectively. The white areas in the figures are grains, whereas the red areas represent pore spaces where VOL. 44, NO. 13, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Representative flow fields showing backward flow zones in glass beads. Shown in the figure is the x-z plane at y ) 0.464. The vector representation of the flow field in the boxed area is provided in SI Figure S2. The LB simulation was performed at a voxel length equal to the pixel length of the XMT image (20 µm). fluid velocity is positive (in the direction of overall flow). The yellow-green areas represent zones where z-direction fluid velocities are negative. Plotting the flow fields using vectors, however, indicates that the flow lines in the yellow-green areas are not closed (SI Figure S2). As such, flows in these zones do not form vortices, as opposed to the cases in unit cells (21, 22). These zones are hereinafter referred as backward flow zones to indicate that in these zones flows have backward components. Our previous definition in ref 21 that equated zones with negative z-velocity as flow vortices was incorrect, although flows in the zones of negative z-velocity in ref 21 do form vortices (flow lines are closed, vector plot not shown). The backward flow zones are typically located near the contact areas between grains, as demonstrated in previous simulation studies in unit cells (21-24). The volume of backward flow zones (derived by dividing the number of nodes with negative z-velocity by the total number of nodes in the pore space) took up 1.25 ( 0.33% (n ) 5) and 1.86 ( 0.14% (n ) 5) of the entire pore spaces in glass beads and quartz sand, respectively. The Student t test indicates that the volume fraction of backward flow zones in the quartz sand is significantly higher than in glass beads (t-probability ) 0.01). The largest negative dimensionless velocity in z-direction among the ten domains (five for each porous media) was -2.23 (the superficial velocity is 1). This velocity was used to normalize all the negative z-direction velocities in the two porous media. Numbers of nodes where the normalized velocities fell into specific ranges were summed up and compared to the total numbers of nodes in backward flow zones to derive the percentages. The majority of negative z-direction velocities (93.5% and 88.9% in glass beads and quartz sand, respectively) were less than 1/10 of the largest negative velocity (in magnitude) (SI Table S4). The percentage of nodes that had negative z-direction velocities greater than one tenth of the largest negative velocity was significantly higher in quartz sand than in glass beads (11.1% vs 6.5%). Simulated Colloid Retention in Reconstructed Pore Structures. Colloid Deposition and Retention in Domain 1. Under conditions favorable for deposition (FAV), simulated colloid deposition in Domain 1 increased with decreasing colloid size (ranging from 0.5 to 2.0 µm) and with decreasing fluid velocity (SI Table S5), consistent with filtration theory predictions (2, 3). The correlation equation developed by Tufenkji and Elimelech (2) predicts a η value of 0.0076, 0.0049, 4938

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and 0.0046 at a superficial velocity of 1.0 × 10-4 m s-1 for colloids with sizes of 0.5, 1.0, and 2.0 µm, respectively. At the same velocity and porosity (0.37), 10.3, 7.4, and 5.8% of the 0.5, 1.0, and 2.0 µm colloids were deposited, respectively (SI Table S5 and S6). The deposited percentages can not be directly compared with the η values, as the simulated domain consists of many grains, whereas η represents the probability of deposition onto a single grain under favorable conditions (R ) 1). At a porosity of 0.37, a domain of 1 × 1 × 1 mm corresponds to 12.3 full grains with a size of 360 µm. Using this number, the percentages of deposition translate to η values of 0.0084, 0.006, 0.0047, respectively, which differ from the corresponding theory-predicted values by a factor of 1.2 at most. At the low fluid velocity, the simulated and predicted η values differ by less than a factor of 2.5. Apparently, particle tracking based on the flow field simulated by the LB method does a fairly good job in simulating colloid transport in porous media under favorable conditions. Under the unfavorable conditions examined, no colloid deposition occurred at noncontact areas (SI Table S5 and S6), as the lowest energy barrier (14.5 kT) used in simulation was too high to cross by diffusion. However, at both superficial velocities, significant fractions of simulated colloid stayed in the domain for at least five PVs before they exited the domain or became deposited ( SI Table S5 and S6). For example, about 2.6% of the 1.0 µm colloids stayed in the domain for more than 10 PVs at the superficial velocity of 1.0 × 10-4 m s-1 and under UNFAV1. If these colloids were considered removed, this percentage would translate into an apparent collector efficiency of 0.0021 ()0.026/12.3) and an apparent collision efficiency of 0.35 ()0.0021/0.006, where 0.006 is the collector efficiency under FAV). The amount of these colloids decreased as their residence time increased (Figure 2, left). As deposition conditions become more unfavorable, the percentages of the long residence time colloids also decreased at the velocity of 1.0 × 10-4 m s-1. For example, under UNFAV1 and UNFAV2, a small fraction of 1.0 µm colloids stayed in the domain for more than 50 PVs (i.e., colloids remained in the domain throughout the maximum simulation duration), whereas under UNFAV3, all the simulated colloids exited the domain within 50 PVs (Figure 2, left). Under favorable conditions, the residence time of some simulated colloids also exceeded 5 PVs (but all less than 30 PVs) at both superficial velocities (SI Table S5 and S6). However, the percentages of these colloids were lower than those under UNFAV1 and UNFAV2 (Figure 2). In addition, significant fractions (up to 71.4%) of colloids with residence time longer than 5 PVs were deposited under favorable conditions, whereas only small fractions (typically less than 10%) of long residence time colloids deposited (at grain-to-grain contacts) under unfavorable conditions (SI Table S7). The causes and implications of the observation that colloids could stay in the domain for long time are discussed in details in the Discussion section. Colloid Deposition and Retention in Domain 2. Under favorable conditions, simulated colloid deposition in Domain 2 also increased with decreasing colloid sizes and with decreasing fluid velocities (SI Table S8), consistent with filtration theory predictions. In addition, at the same fluid velocity, the percentage of deposition in Domain 2 was very close to the percentage in Domain 1 for an identical colloid size (SI Tables S5-S7). This means that simulated deposition in Domain 2 also agreed well with theory predictions. Under unfavorable conditions, there were also colloids that stayed in the domain for over 5 PVs before exiting or depositing. The percentages of these colloids decreased as the residence time increased and when the deposition conditions became more unfavorable, as was observed in Domain 1 (Figure 2, right panel). The percentages of colloids with long residence time were significantly lower than those in Domain 1 under

FIGURE 2. Percentages of colloids with different residence time. Simulations were performed in both domains at a superficial velocity of 1.0 × 10-4 m s-1, under both favorable and unfavorable deposition conditions. Colloid size was 1 µm.

FIGURE 3. Time series of separation distance (H), z-coordinate (Z), z-direction fluid velocity (Vz), the nearest grains (J) of a representative colloid that experienced low fluid velocities (e.g., 16 PVs) while being associated with grain surfaces via secondary energy minima. otherwise identical simulation conditions (Figure 2 and SI Table S5-S7). The percentages of colloids with long residence time that were deposited were also lower than those in Domain 1 under identical conditions (SI Tables S7 and S9). It seems that the differences in domains of the same porous medium have a greater impact on colloid transport under unfavorable deposition conditions.

Discussion Role of Low Flow Zones on Colloid Transport. To reveal the mechanisms that caused certain colloids to stay in the domains for a very long time, the trajectories of the colloids with residence time longer than 5 PVs were examined. It was

found that the majority of these colloids were associated with the secondary energy minima for certain periods of time during their transport in the domains. Figure 3 shows the representative time series of the separation distance, the z-direction velocity, and the z coordinate of such a colloid. The colloid (1.0 µm) was simulated in Domain 1 under UNFAV1 at a superficial velocity of 1.0 × 10-4 m s-1. The colloid was released at a few to a few tens of micrometers from the grains (the 10th and 14th grain) and then became associated with the 25th grain via the secondary minimum (separation distance ) 16 nm) (Figure 3A and B). After about 10 s, it left the grain, moved toward the 34th grain and became associated again via the secondary minimum. This time the VOL. 44, NO. 13, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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association lasted for nearly 90 s (with a few short interruptions), followed by further downgradient movement. The total duration of association with the grain surfaces via the secondary minimum was more than half of its total residence time (about 150 s) in the domain. When the colloid was associated via the secondary minimum, its velocity in the z-direction (the direction of the overall flow) was typically low (Figure 3C). This is especially true for the time period between 50 and 110 s, where the velocity was lower than 1.0 × 10-6 m s-1, about 2-3 orders of magnitude lower than the average fluid velocity (2.7 × 10-4 m s-1). During the period of low z-direction velocities, the displacement rate of the colloid in the z-direction was minimal (Figure 3D). For example, during the time period from 41 to 115 s, the colloid only moved 35 µm in the z-direction, with an average rate less than 0.5 µm per second. During the same period, the displacements in the x and y coordinates were also quite small (less than 50 and 20 µm in x and y direction, respectively) (SI Figure S3). These observations confirm that translation of secondary minimumassociated colloids on grain surfaces to low flow zones, a mechanism operating in unit cells (16), is an important process that causes long residence time of colloids in real porous media. It is also clear that zones of complete stagnant flow are not needed for colloids to be retained for significantly long time (26). Examination of colloid trajectories also revealed that colloids of long residence time were not necessarily associated with secondary energy minima. For example, at the superficial velocity of 1.0 × 10-4 m s-1 and under UNFAV1, about 13% of the 1.0 µm colloids with residence time longer than 5 PVs did not reach the secondary energy minimum, that is, their separation distances throughout their residence in the domain were significantly greater than the separation distance of the secondary minimum. At separation distances of a few micrometers, some colloids also experienced low fluid velocities and stayed in the domain for up to 25 PVs (SI Figure S4). This indicates that association with secondary minima is not a prerequisite for long residence time. The existence of low flow zones in the pore domains seems to be more critical. Trapping in low flow zones without association via secondary minima is consistent with the observation that some colloids could also stay in the domain for a significantly long time (>10 PVs) under conditions favorable (FAV) or extremely unfavorable (UNFAV3) for deposition. Under favorable conditions, colloids reaching the proximities of grain surfaces will deposit due to the lack of an energy barrier. As a result, association with grain surfaces via secondary minima would not occur. Under conditions extremely unfavorable for deposition, the secondary minimum is too shallow to effectively keep the colloids from diffusing into the bulk solution. Finally, it is worth noting that some colloids that once became associated with grain surfaces via secondary minima exited the domains quickly (within 5 PVs) (data not shown), indicating that association via secondary minima alone is not sufficient for long residence time. Role of Backward Flow Zones on Colloid Transport. Simulations in this work also demonstrated that colloids could get into backward flow zones (i.e., they experienced negative z-direction fluid velocities) for certain periods of time during their transport in the domains. Less than 10% of the simulated colloids once entered the backward flow zones in Domain 1, whereas around 20% of the simulated colloids once experienced negative z-direction velocities in Domain 2 (SI Tables S10 and S11). In Domain 1, up to 55% of colloids that had residence time longer than 5 PVs once entered backward flow zones (SI Table S10). In Domain 2, the percentages were much lower (30% at most) under identical simulation conditions (SI Table S11), despite the fact that much more colloids experienced negative z-direction velocities in this 4940

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domain. Clearly, there is no strong correlation between entering backward flow zones and long residence time. The total time periods during which the colloids experienced negative z-direction fluid velocities were also recorded. A small fraction of these colloids could stay in backward flow zones for over 3 PVs (SI Table S12). More colloids stayed in these zones for over 1 PV under UNFAV1 than under FAV and UNFAV3, indicating that entering backward flow zones is dependent on solution chemistry. In a few cases, colloids stayed in backward flow zones for up to 10 PVs (data not shown), indicating that backward flow zones could potentially trap the colloids for significantly long periods of time. However, the number of such colloids is much lower than the total number of colloids of long residence time. Hence, low flow zones play a more important role in trapping the colloids in the domains. Occasionally, colloids in backward flow zones were a few micrometers from grain surfaces and could travel backward in z-direction (flow forward) for significant distances (Figure 4). In most cases, however, colloids experiencing negative z-direction fluid velocities were associated with grain surfaces via secondary minima (SI Figure S5). Such colloids did not move backward significantly in z-direction. This is consistent with the observation that the magnitudes of fluid velocities that colloids experienced were quite low. In this sense, backward flow zones can be regarded as special cases of low flow zones. Implications. Most laboratory and field studies on colloid transport in porous media at groundwater flow regimes typically involved elution of only a few pore volumes (e.g., ref 8). In these studies, colloids that remained in the porous media after elution were commonly considered as being removed from aqueous solutions due to deposition onto grain surfaces. Hence, if elution lasts for less than 5 PVs, the colloids with residence time longer than 5 PVs shown in this study would be considered to be deposited. However, the simulations in this work demonstrate that colloid removal may be due to temporary trapping (or more accurately, delaying of movement) of colloids in low flow and backward flow zones. Thus, the common practice in many previous papers that equated removal or retention to deposition is inappropriate. In addition, a number of experimental observations that have intrigued the research community of colloid transport for many years can be explained on the basis of the temporary trapping process. First, this process can explain colloid removal under conditions extremely unfavorable for deposition, without resorting to surface roughness and charge heterogeneities. As shown in Figure 2, there are still a small fraction of colloids trapped in low flow zones for over 10 PVs under such conditions (UNFAV3). Second, gradual increases in the numbers of trapped colloids with decreasingly unfavorable conditions is consistent with the previous observations that colloid removal gradually increased as deposition conditions becomes less unfavorable (e.g., ref 9). Under less unfavorable conditions, deeper secondary minima would keep more colloids at grain surfaces for longer time, allowing more of them to be translated into low flow zones. Third, colloids with long residence time shown in this study were loosely associated with or even quite away from grain surfaces. They would continue to move downgradient with flow, which could well explain the observation of low colloid concentrations during elution in the absence of macroscopic perturbations (e.g., refs 27 and 28). The downgradient movement of loosely associated colloids can also cause the downgradient movement of the mass center of retained colloids, leading to nonmonotonic profiles of retained colloid concentrations with the transport distance. Nonmonotonic retained profiles have been observed in many column experiments (e.g., refs 29-32).

have a significant impact on the simulated flow field and on subsequent particle tracking. Future work is required to extend simulations to larger domain sizes to allow quantitative comparisons between simulation results and experimental observations. Finally, it is also worth noting that our particle tracking approach did not explicitly consider colloid migration across multiple flow lines due to combined inertial and wall (grain surfaces) effects (e.g., refs 33 and 34). The fact that simulated η agreed well with theory-predicted values under favorable conditions indicates that neglect of colloid migration cross-flow lines may have a minor impact on the accuracy of the simulated deposition under such conditions. Further investigation will be conducted to examine how colloid migration across flow lines affects the simulated results under unfavorable deposition conditions (i.e., trapping of colloids by low flow zones).

Acknowledgments This material is based on work funded by the National Science Foundation of China (Grant No. 40772147 and 50688901). We thank Dr. C. L. Lin at the Department of Metallurgical Engineering of the University of Utah for providing the XMT images. We are also grateful to two anonymous reviewers for their critical comments.

Supporting Information Available Coordinates and radii of grains in the simulated domains, solution chemistry conditions, tabulated simulation results, and representative trajectories of colloids with long residence time. This material is available free of charge via the Internet at http://pubs.acs.org.

Literature Cited

FIGURE 4. Time series of z-direction fluid velocity (Vz), separation distance (H), and z-coordinate (Z) of a representative colloid that was carried backward in z-direction for significant distance. The simulation was performed in Domain 1 under UNFAV1 at a superficial velocity of 1.0 × 10-4 m s-1, with a colloid size of 1.0 µm. Shown in the insets are the fluid velocity, separation distance, and z-coordinate during the period when the colloid was within the backward flow zone. Throughout the duration within the backward flow zone, the colloid was away from the grain surface by at least a few micrometers. In summary, this work demonstrated that combination of XMT and the LB simulation is a powerful approach to study colloid transport mechanisms in porous media. The pore domains used in this work consisted of 3-4 grains in each dimension. At this scale, the solid wall boundaries applied at the x and y bounding planes of the domains may

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