Environ. Sci. Technol. 2005, 39, 7208-7216
Magnetic Resonance Imaging and Quantitative Analysis of Particle Deposition in Porous Media TAL AMITAY-ROSEN, ANDREA CORTIS, AND BRIAN BERKOWITZ* Department of Environmental Sciences and Energy Research, Weizmann Institute of Science, Rehovot 76100, Israel
Measurements of particle deposition and mobilization in water-saturated porous columns were performed using nuclear magnetic resonance imaging (MRI). The use of MRI enabled the acquisition of detailed, noninvasive measurements that quantify spatial and temporal evolution of particle transport patterns and porosity changes due to particle deposition. Measurements indicate that for the considered particle sizes and flow conditions significant particle deposition occurs at some distance into the column. Because identification of unique parametrizations for processes of particle straining, deposition, and detachment is complex and nonunique, a simple phenomenological model of particle deposition and porosity reduction is suggested. This model captures the essential features of the experimental measurements on spatial and temporal flow and deposition patterns.
Introduction The transport and deposition of colloidal particles in porous media have significant influence on a wide variety of natural and engineering processes, including water purification, colloidal sedimentation, and the limiting of liquid loss during oilfield drilling. Colloids (including bacteria and viruses) are generally regarded as particles up to 10 µm in diameter, which tend to remain suspended in an aqueous solution (1). In addition to being contaminants themselves, they play a significant role in contaminant mobility because they can migrate considerable distances, carrying a variety of highly sorbing groundwater pollutants such as hydrophobic organics and toxic metals (2, 3). Deposition and mobilization of these particles can cause significant changes in medium properties such as porosity and permeability (4). The transport of suspended particles in porous media is controlled by several processes, including advection, dispersion, straining (trapping), physicochemical filtration (deposition), and detachment. Depending on the size of the suspended particle, a number of mechanisms may be responsible for physicochemical filtration: (i) gravitational sedimentation, where the gravitational forces acting on the particle cause it to settle onto a sediment grain (collector), (ii) interception, where the particle size and trajectory are such that it encounters the collector grain while flowing past, and (iii) Brownian diffusion, where the particle is brought into contact with a collector due to its Brownian motion (5, 6). Geometrical models (7, 8) suggest that straining could have a significant influence when the ratio of the particle * Corresponding author phone: 972-8-9342098; fax: 972-89344124; e-mail:
[email protected]. 7208
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diameter to the median grain diameter of the porous medium is greater than 0.05. Similarly, a limiting ratio of 0.154 for predicting straining of particles in constrictions has been proposed (9). However, recent experimental evidence suggests that straining could be important at much smaller particle to grain size ratios (10). Mobilization (detachment) of deposited particles is also a key process governing colloid transport and fate. Mobilization can take place following drastic changes in pore water chemistry and when the hydrodynamic forces overcome the adhesive forces between particles and the medium grains (11). Detachment processes are usually modeled by first-order kinetics; however, heterogeneity of the surface may result in more than one removal rate coefficient (12). Laboratory works to date have focused mainly on column experiments that measure colloid breakthrough times; some have also measured colloid deposition by destructively opening packed columns after fixed time intervals (1, 10, 13-20). Many such studies do not consider significant reductions in porosity and permeability as a result of particle deposition. While these studies have enabled the understanding of many aspects of particle deposition in saturated porous media, the macroscopic patterns of deposition are still not well understood. This is due at least in part to a lack of measurements that can provide spatial-temporal measurements of deposited particles along a porous column. Here, we explore particle transport behavior in porous media by visualizing the real-time evolution of particle deposition and mobilization patterns, using nuclear magnetic resonance imaging (MRI). MRI is capable of noninvasive measurements of porosities and flow velocities inside opaque, threedimensional porous media in a laboratory setting (22). Existing and future theoretical models that predict the essential features of these spatial and temporal flow and deposition patterns can then be compared to these data. We also propose a phenomenological model that captures the temporal evolution in porosity along the columns.
Experimental Analysis Apparatus. Particle transport, deposition, and mobilization behaviors were studied by injecting a solution containing 1 or 12 µm in diameter poly(tetrafluoroethylene) (PTFE) particles through a horizontal, cylindrical column (inner diameter and length of 25.2 and 76 mm, respectively) packed with monodisperse, polystyrene beads. The polystyrene beads and PTFE particles are chemically inert, and their magnetic susceptibilities resemble those of aqueous phases. Whether particles and aggregates are deposited by straining and/or attachment is not specifically investigated here. Full details on the apparatus are provided in the Supporting Information. Methodology. Particle transport experiments using a MRI system were divided into two stages. First, deposition was measured during colloid suspension injection for a period of, generally, about 180 min. Mobilization of deposited particles was then examined by pumping colloid-free solution (at the same volumetric flow rate) through the column for about 120 min. Porosity and velocity measurements were obtained for the first 37.2 mm length of the column. This length was divided into (usually) nine vertical slices, in the xy-plane (perpendicular to the principal flow direction); slices were 2 mm in width, with a distance of 2.4 mm between them. Velocity and porosity measurements were taken every 30 min. Full details on the methodology are provided in the Supporting Information. Porosity Measurements. During each porosity measurement, the fluid flow was stopped for ∼6 min of imaging time 10.1021/es048788z CCC: $30.25
2005 American Chemical Society Published on Web 08/17/2005
FIGURE 1. Selected axial images of the porous medium at several distances from the inlet, for an experiment with 12 µm particles: (a) 0, (b) 120, (c) 180 min. The column was oriented horizontally, with the reference tube (white spot) positioned at the top. to increase the signal-to-noise ratio of the images. Possible disruptions to the deposition pattern caused by stopping and restarting the fluid flow were not considered. A regular spin-echo pulse sequence that allows visualization of twodimensional (2-D) density images was used (22). The images were acquired with a field of view of 30 mm in the xy-plane, an echo time of 15 ms, a repetition time of 400 ms, and four averages. The resulting density images are composed of a 256 × 256 voxel matrix; thus, a spatial resolution of ∼0.12 mm was achieved. The signal-to-noise ratio obtained in the images was ∼30. The brightness in the images is a measure of the amount of protons, i.e., the amount of fluid. Porosity values for each slice were obtained by averaging the intensities of each voxel to the maximum value in the reference tube. Porosity measurements were corrected to account for the influence of the transverse relaxation time (22), background noise, and the reference tube. The measurement error, calculated from the standard deviation of the background noise, was less than 0.01 and 0.02, for 1 and 12 µm particles, respectively.
Velocity Measurements. Motion in the presence of magnetic field gradients causes phase shifts in the MRI measurements that are directly proportional to the flow velocity. A classical two-dimensional phase-sensitive (i.e., flow-encoded spin-echo pulse sequence) MRI pulse sequence with bipolar gradients was applied (22) to obtain 2-D flow velocity images of the aqueous phase in the xy-plane, in the direction of the principal flow direction (z), with an imaging time of ∼2 min. The images were acquired with a field of view of 30 mm in the xy-plane, a repetition time of 1000 ms, and an echo time of 41.5 ms, which is longer than the echo time used for the porosity measurements and therefore causes a reduction in the image intensity. The measurement error was obtained by computing the standard deviation of no-flow images; this error was found in all cases (for all slices) to be less than 0.17 mm s-1, which is ∼30% of the average measured velocity. All phase images were corrected from phase shifts caused by the magnetic field and radio frequency field inhomogeneities. VOL. 39, NO. 18, 2005 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 2. Porosity of an experiment with 1 µm particles. (a) Porosity vs distance from the column inlet for different times. (b) Porosity vs time for different distances from the column inlet.
FIGURE 3. Porosity of an experiment with 12 µm particles. (a) Porosity vs distance from the column inlet for different times. (b) Porosity vs time for different distances from column inlet.
Results and Discussion
the MRI-apparent porosity. It is important to note that the aggregate porosity defines a volume that precludes flow, deposition, and mobilization of particles; the model developed below accounts naturally for this MRI-apparent porosity. Figure 1 shows axial images of the porous medium, from the MRI measurements, at three distances along the column, and at three different times. The white spot in each image is the reference tube that is filled with aqueous solution, considered to have unit porosity. The particle accumulation along the column as well as the cross-sectional heterogeneity in deposition patterns are clearly evident. Typical sets of porosity values for the 1 and 12 µm particles are given in Figures 2 and 3, respectively; by comparison of these figures, the porosity changes are seen to display similar behavior. The porosity of the imaged portions of the column decreases as the experiments proceed. For the particle sizes, porosity, and flow rates used in the experiments, the tendency for greater changes in porosity to occur deeper into the imaged portion of the column evidently arises because particles entering the column travel some distance before being deposited. In other words, particles entering the porous column, which are smaller than many of the pores and channels, have sufficient inertia to travel with the liquid until they deposit by either straining or physicochemical filtration; as noted elsewhere, particles can also deposit as aggregates. This behavior was found to be consistent and reproducible in all of the experiments. In mechanistic terms, a positive feedback can arise wherein regions with some deposited particles tend to trap more particles until the local flow paths change and deposition is focused elsewhere. A direct
Deposition and mobilization experiments were conducted by pumping an aqueous solution containing either 1 or 12 µm PTFE particles through packed columns. The column was emptied and packed uniformly with new beads after each experiment. Several of the experiments were used to determine suitable operating parameters, including measurement times and protocols (duration and density of images). Deposition and mobilization behaviors were found to be qualitatively similar in all experiments; porosity measurements at similar distances or times were found to vary by 10-20% in the different experiments (but using the same size PTFE particles). As mentioned above, detailed mass balance calculations were not possible. However, estimates of the mass of deposited particles, based on the available porosity images, were consistent (i.e., less than the total mass of particles injected into the column). We note that particles deposit looselysindividually and as aggregatesswithin the bead column pore space, partly because of their negative surface charge (Apparatus subsection). As a consequence, the particle aggregates themselves as well as the deposits of particles around the beads are porous. Visual examination of the aggregates and the column during unpacking at the conclusion of each experiment indicated this porosity to be significant (apparently > 50%; see also, e.g., ref 23). Because of limitations in the signal-to-noise ratio and resolution of the MRI, this pore space appears as solid matter (i.e., darker voxels) in the images and hence causes the MRI-based estimates of reduction in pore space to be larger than they actually are. The estimated porosity reported here refers to 7210
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FIGURE 4. Autocorrelation curves of porosity values, experiment with 1 µm particles (from Figure 1): (a) spatial autocorrelation, (b) temporal autocorrelation.
FIGURE 5. Porosity vs time at different distances from column inlet: (a) 1 µm particle experiment, (b) 12 µm particle experiment.
demonstration of this behavior is given below in terms of porosity autocorrelation functions (discussion of Figure 4 below). The decrease in porosity is not an immediate process. Moreover, the porosity changes are not homogeneous throughout the column, and minor fluctuations arise particularly at earlier times. For example, in reference to Figure 2b, the decrease in porosity is enhanced after 120 min, especially further along the column; near the inlet, the net porosity change is ∼15%, while further into the column the net porosity change approaches 50%. After 180 min, the porosity decreased to 50% of its initial value for the slices closest to the column inlet (and also for the slice at 30.8 mm from the inlet); a decrease of 70% was observed for the slices situated at 17.6 and 22 mm from the inlet. We note also that identical experiments on longer columns (i.e., 150 mm rather than 76 mm) showed the same particle deposition patterns over the first ∼36 mm of the column (i.e., the study region of interest). After the porosity reaches some minimum value, particles begin to be remobilized (Figure 2, at times of 150 and 180 min). Particle remobilization was also observed in the 12 µm particle experiments (Figure 3, at a time of 240 min). As porosity decreases in any given column cross section (slice), the fluid velocity in this region increases (recall the constant volumetric flow rate inlet boundary condition), thus enabling particle mobilization and migration. Spatial and temporal porosity autocorrelation curves are shown in Figure 4, for the 1 µm particles. The autocorrelation provides a measure of the correlation of a variable with itself through space or time. If there is any systematic pattern in the spatial/temporal distribution of the porosity, then it is
said to be spatially/temporally autocorrelated; random patterns exhibit no autocorrelation. If nearby or neighboring sections have similar porosity (“persistent behavior”), then the (spatial/temporal) porosity autocorrelation is positive. Negative (spatial/temporal) porosity autocorrelation describes patterns in which porosities are dissimilar (“antipersistent behavior”). From Figure 4, the overall correlation is seen to be weak after short distances (
