Impact of particle size on colloid transport in discrete fractures

Transcription

1 Click Here for Full Article WATER RESOURCES RESEARCH, VOL. 42, W12S08, doi: /2006wr004873, 2006 Impact of particle size on colloid transport in discrete fractures Ori Zvikelsky 1,2 and Noam Weisbrod 1 Received 9 January 2006; revised 18 May 2006; accepted 3 July 2006; published 28 November [1] The impact of particle size on colloid transport was explored in two saturated, naturally discrete fractured chalk cores, with equivalent hydraulic apertures of 183 and 380 mm. Tracer experiments were carried out using negatively charged fluorescent latex microspheres (FluoSpheres 1 : 0.02, 0.1, 0.2, and 1.0 mm diameter) as well as Li + and Br as the soluble tracers. In both fractures, FluoSpheres exhibited earlier arrival times than the solutes and a complete lack of tails in their breakthrough curves, proving that their transport is advection-dominant. In all experiments the 0.2-mm FluoSpheres were recovered to a much greater extent than the 0.02-mm FluoSpheres and to a slightly greater extent than the 1.0-mm FluoSpheres. Similarly, the highest maximum C/C 0 values were found for 0.2 mm, then for 1.0 mm, while the maximum C/C 0 values for the 0.02-mm colloids were significantly lower. The insignificant contribution of settling relative to Brownian motion (diffusion) as an efficient deposition mechanism was demonstrated for all sizes of FluoSpheres in both fractures. Citation: Zvikelsky, O., and N. Weisbrod (2006), Impact of particle size on colloid transport in discrete fractures, Water Resour. Res., 42, W12S08, doi: /2006wr Introduction and Background 1.1. Fractures as Favorable Pathways for Colloids [2] The factors affecting transport of colloidal particles in fractured porous media are of increasing interest because of the potential role of fractures as pathways for pollutant migration [e.g., Chrysikopoulos, 1999; Weisbrod et al., 2002; James and Chrysikopoulos, 2004; McCarthy and McKay, 2004]. A fundamental understanding of particle behavior in discrete fractures is essential for predicting migration rates of contaminants attached to mobile colloids, as well as pathogen transport through fractured networks. Fractures are likely to be favorable conduits for colloids for several reasons: (1) large flow paths, (2) high-flow velocities relative to the surrounding matrix, (3) lack of diffusion from the fracture aperture to the matrix, especially in lowpermeability rocks where the pore size is usually small, and (4) as both colloids and fracture surfaces are likely to be negatively charged at most natural phs, the colloidal particles will tend to stay midstream, away from the fracture walls [Chrysikopoulos, 1999; McKay et al., 2002]. Possible sources for the existence of a colloidal phase in fractures include: (1) dust storms, especially in arid and semiarid environments, and land spread waste [McCarthy and Shevenell, 1998; McGechan and Lewis, 2002], (2) erosion of fracture fillings, coatings and fracture walls, especially in the upper vadose zone where wetting and drying cycles take place [Weisbrod et al., 1999, 1 Department of Environmental Hydrology and Microbiology, Zuckerberg Institute for Water Research, J. Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede-Boqer, Israel. 2 Department of Geological and Environmental Sciences, Ben-Gurion University of the Negev, Beer-Sheva, Israel. Copyright 2006 by the American Geophysical Union /06/2006WR004873$09.00 W12S b], (3) precipitation of minerals due to changes in geochemical conditions [Dijk and Berkowitz, 1998], and (4) in situ chemical or physical perturbations in the unsaturated or saturated system due to changes in ph, ionic strength, organic compound content or flow velocities [McCarthy et al., 2002; McKay et al., 2002]. Once colloids exist within a fracture, different factors may control their potential to become mobile, including the surface properties of the colloids and the matrix, ph and chemistry of the flowing solution, flow velocities, etc. [Vilks and Bachinski, 1996; McCarthy and Shevenell, 1998; Becker et al., 1999; McKay et al., 2000, 2002; Chinju et al., 2001; McCarthy et al., 2002; Weisbrod et al., 2002; Becker et al., 2003] Laboratory Experiments in Fractures [3] In a series of experiments in which artificial fractures were simulated by inserting small tubes into columns of sand, Toran and Palumbo [1992] examined the effect of fractures on colloid transport. They showed that the presence of fast flow paths, such as fractures, significantly enhances colloid breakthrough in comparison with conservative solutes and decreases colloid retention. In a study with synthetic colloids (microspheres) in saturated fractured tuff, Reimus [1995] showed that microspheres always migrate faster than iodide. He attributed the phenomenon to Taylor dispersion, matrix diffusion of the iodide, size exclusion of the microspheres (being too large to diffuse) and/or the fact that colloids migrate through a smaller effective volume in the fractures because they diffuse too slowly to enter the stagnant zones along the fracture walls. Vilks and Bachinski [1996] studied colloid mobility as a function of particle size, water velocity, flow direction, and flow path in a large naturally fractured granite block. A number of conclusions could be drawn from their study: (1) There is no size impact on colloidal migration within the size range of to mm. (2) Colloid transport is 1of12

2 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 Table 1. Fracture s Physical Dimensions and Equivalent Hydraulic Aperture Core Diameter, cm Fracture Length, cm Core Length, cm Fracture Width, cm Equivalent Hydraulic Aperture, mm Core Core very sensitive to flow path and flow direction, i.e., colloids exhibit different recovery rates in the same pair of boreholes. (3) Colloid transport is significantly decreased below a critical velocity. (4) In most cases, the colloids elute before and recover less than conservative tracers. Fast transport rates (retardation factor <1) of colloids in various fractured materials have also been reported by Hinsby et al. [1996], Becker et al. [1999], Cumbie and McKay [1999], Chinju et al. [2001], McCarthy et al. [2002], and McKay et al. [2002]. It should be noted that R < 1 is just a special case in which fast transport can be observed. [4] Several field experiments have been performed to evaluate the potential of colloidal transport on large scales [e.g., McKay et al., 1993a, 2000; Vilks et al., 1997; Becker et al., 1999, 2003; Weisbrod et al., 2002; Mori et al., 2003]. In most cases, recovery of colloids was generally low, highly dependent on water velocity, and a consistent optimal size for colloid recovery was not always found. Because of the large distances and therefore long traveltimes, diffusion and colloid charge were found to be very important [McKay et al., 2000; Becker and Shapiro, 2003]. It should be noted that in natural systems, colloid particles can range in diameter over several orders of magnitudes (polydisperse). It is often assumed that the realistic distribution of sizes of naturally occurring colloids is lognormal [Ledin et al., 1994]. James and Chrysikopoulos [1999, 2000, 2003a] ran transport simulations of a polydisperse colloid suspension with lognormal size distribution in a single fully saturated fracture with uniform aperture. They showed that polydisperse solutions exhibit greater spreading than monodisperse and variably sized colloid suspensions (two or more well-defined size populations). The smallest particles of the distribution tend to travel at velocities close to the mean and are greatly affected by matrix diffusion due to large molecular diffusion coefficients, whereas the largest particles are transported faster and further along the fracture due to the large Taylor dispersion coefficient, which may lead to early breakthrough of the larger colloids in the distribution. It should be noted that increased retardation of colloid plumes with higher variance of colloid diameter distribution is due to both the slower average velocity of the smallest particles and their tendency to diffuse into the solid matrix. Similarly, Oswald and Ibaraki [2001] used a numerical simulation that takes into account advective-dispersive transport of colloids, filtration and remobilization of colloids in discretely fractured porous media. The primary results of the analysis showed that matrix porosity and the process of colloid filtration in fractures are directly related and play important roles in controlling colloid migration. [5] The impact of colloid size on colloidal transport in fractures has been directly and indirectly explored in several studies [Becker et al., 1999; Cumbie and McKay, 1999; McCarthy et al., 2002]. Several authors have managed to define an optimum colloid size for transport through a specific fractured system. Cumbie and McKay [1999] observed greater recovery for 0.5-mm colloids in fractured saprolite with respect to 0.05-, 0.1- and 1.0-mm particles. In the same fractured material, McCarthy et al. [2002] found that colloid diameter has less effect than the solution chemistry, but their findings showed that 0.5-mm particles exhibit the highest recovery rates relative to 0.1-, 1.0- and 2.1-mm particles. Becker et al. [1999] demonstrated that 0.36-mm particles recover to a greater extent than 0.83-mm particles in a fractured granite block. On the other hand, Vilks and Bachinski [1996] reported an insignificant effect of colloid size on its transport in the same aforementioned granite block. Under certain conditions, size exclusion may also contribute to the dispersion of colloids and may lead to earlier breakthrough [Chrysikopoulos and Abdel-Salam, 1997]. James and Chrysikopoulos [2003b] have shown that the finite size of a particle excludes it from the slowest moving portion of the parabolic velocity profile that develops within a fracture. Consequently, the effective particle velocity is increased, while the overall particle spreading (dispersion) is reduced. [6] In this study, we examined the simultaneous transport of three sizes of colloids, 0.02, 0.2 and 1.0 mm, in two naturally discrete fractured chalk cores. The main objectives of this study were to (1) experimentally explore the role of colloid diameter on its transport in a low-permeability, natural, discrete, porous fractured chalk; (2) quantify the differences between colloid (FluoSphere) and solute (Li + and Br ) transport in fractured chalk cores; and (3) investigate the main processes responsible for colloid deposition inside the fractured chalk. Colloid-transport behavior and recovery rates within each fracture were interpreted and analyzed with respect to the fracture s physical and hydraulic properties. 2. Materials and Methods 2.1. Rock Samples and Experimental Apparatus [7] Two fractured chalk cores were obtained from the chalk formation of the Eocene Avdat Group in the northwestern Negev desert of Israel. The two cores were drilled along a vertical single fracture that bisects the entire core length. The dimensions of the cores and fractures are presented in Table 1. The two pieces of each core were cleaned of loose particles using airflow, and placed back together to mimic their natural configuration. Each fractured core was wrapped with Teflon tape before it was fixed with epoxy cement (Duralite) inside a PVC casing. Teflon inlet and outlet chambers were attached to each side of the flow boundaries of the fracture while the other two boundaries were sealed with epoxy cement to make them no-flow (Figure 1). The chamber s volume was relatively large (20 ml) to prevent clogging [Arnon et al., 2005]. [8] The cores were saturated under vacuum using degassed artificial rainwater (ARW). The chemical composition of the ARW (major ions in mg/l) before addition of the tracers was Ca , Cl 12.7, SO , Na , Mg , HCO 3 35, NO , with ph 7.3 ± 0.1 and an ionic strength of M. This composition is similar to that of the average chemical composition of rainwater in the 2of12

3 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 [Snow, 1968]. The flux measurements for any given hydraulic gradient were taken under steady state conditions and were measured gravimetrically at 1- to 10-min intervals (±0.02 ml/min). The hydraulic head differences were measured with a Foxboro 1 differential pressure transducer (IDP10, Foxboro, MA), calibrated for hydraulic head differences of 0 to 12 mm (±0.05 mm). These measurements were taken both prior to and following the tracer experiments to see whether colloidal deposition and/or dissolution-precipitation processes had changed the hydraulic aperture. The accuracy of the calculated hydraulic aperture was ±5%. Figure 1. Schematic configuration of the experimental setup for flow and tracer experiments. The differential pressure transducer (PT) was connected to the inflow and outflow ends for hydraulic tests only. northern Negev, Israel [Livshitz, 1999]. The saturation process was carried out in a customized vacuum system [Zvikelsky, 2005], and was terminated once the processes of water imbibition into the chalk core stopped (approximately 2 days). The amount of water imbibed into the chalk cores was similar to the chalk cores void volume based on an estimated 40% for porosity [Weisbrod et al., 1999]. [9] To ensure chemical equilibrium between the ARW and the salty chalk matrix and to initiate the experiments with a chemical steady state, the cores were flushed for 300 days with ARW at a flow rate of 2500 ml/d. The effluent was sampled throughout flushing and analyzed periodically, and dissolution or precipitation was found to be insignificant during the flushing and experimental stages [Zvikelsky, 2005]. The insignificant effect of dissolutionprecipitation on the fracture s hydraulic properties, as well as the steady state chemical conditions, were confirmed by periodical measurements of the equivalent hydraulic aperture and outflow chemical analysis. To prevent biofilm formation within the fracture void, which might alter the fracture s hydraulic and/or surface properties [Arnon et al., 2005], the cores were flushed periodically (between tracer experiments) with a biocide (sharomix-mci 30 mg/l). Prior to and following the biocide injection, the cores and ARW vessel were sampled and the microorganisms were enumerated by plate count on R2A media Flow Experiments [10] Flow experiments were conducted to calculate the equivalent hydraulic aperture, based on the cubic law 2.3. Tracer Experiments [11] To explore the impact of colloid size on its transport, four types of carboxilate-modified latex (CML) microspheres (negatively charged surfaces) were selected (Fluo- Sphere; Molecular Probe #, Eugene, OR). Their specific physical and chemical properties, as well as those of the crushed chalk, are given in Table 2. The criterion for FluoSphere selection was that one size of FluoSphere with specific excitation and emission wavelengths would show no artifact response (emission) when excitation wavelengths of the rest of the FluoSpheres (different sizes) in the tracer solution were projected. A linear calibration curve (without mutual interference) was observed when FluoSpheres with wavelengths (excitation/emission) of 365/415, 540/560, and 580/605 were used together. [12] Before conducting each of the tracer experiments, the fractured chalk cores were flushed at a low flow rate (1 ml/min) with background ARW for at least 4 h. Overall, 12 tracer injections were performed on the cores, with the fractures in horizontal orientation (Tables 3 and 4). In each experiment, simultaneous injection of ARW with differentsized FluoSpheres and LiCl or LiBr was performed. The colloid conservative tracer solution was injected into the fracture through the inlet chambers by a low-pulsation peristaltic pump (Minipulse 3, Gilson, Middelton, WI), and was collected at the outlet of the fracture at 2- to 3-min intervals in 10-mL vials. (Spectra/Chrom CF-1 Fraction Collector, Spectrum Laboratories, Houston, TX, Figure 1). The duration of the injection period of tracer solution was 384 and 183 min, in cores 1 and 2, respectively. This duration was determined according to the calculated fracture volume. [13] At the end of the injection step, the tracer solution in the inlet chambers was switched to background ARW solution for 1100 to 1600 min (>50 fracture volumes). Finally, the fracture was flushed with a dispersive solution (0.001 M NaCl) in both directions to remove any colloids deposited within the system. The M NaCl, combined with a flow rate 20 times faster than that used during the Table 2. Physical and Chemical Properties of the FluoSphere Colloids a Particle Diameter d p, mm Tracer Number of Particles Concentration, mg/l r p, g/cm 3 per Milliliter Excitation/Emission Wavelength, nm Zeta Potential x, mv Fl E / Fl E / Fl E / Fl E / crushed chalk a Here d p denotes the diameter of the Fluospheres, r p is the particle density ( and x is the zeta potential as measured using ZetaMaster (Malvern Instruments LTD). ARW was the solution used in all experiments. Fl. stands for FluoSpheres. Read 3.59E+06 as of12

4 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 Table 3. Results of Tracer Experiments in Core 1 Experiment Tracers a First Arrival Time, min 0.5 C/C 0 Arrival Overall Mass Time, min Max C/C 0 Recovery, % E E E E-1 Li E E E E-2 Li E E E E-3 Li E E E E-4 Li E E E E-5 Li E-5 Br Average (±0.6) 53(±6.8) 0.92(±0.02) 90.6(±1.6) Average (±0.6) 57(±4.4) 0.96(±0.02) 93.2(±1.3) Average (±0.6) 65.5(±5.4) 0.76(±0.02) 76.8(±1.8) Average Li (±0.9) 171(±17) 0.65(±0.01) 97(±1.2) Average Br a FluoSphere diameter in mm. Table 4. Results of Tracer Experiments in Core 2 Experiment First Arrival Number Tracers a Time, min 0.5 C/C 0 Arrival Time, b min 0.35 C/C 0 Arrival Mass Recovery, Time, b min Max C/C 0 % E E E-6 Li + 32 NA E E E-7 Li + 24 NA E E-8 Li + 23 NA E E-9 Li + 24 NA E E E E-10 Li + 26 NA NA E-10 Br E E E E-11 Li + 28 NA NA E-11 Br E E-12 Li + 27 NA NA E-12 Br Average (±0.25) 27.6 (±2.51) 18.3 (±3) 0.90 (±0.03) (±4.8) Average (±0.35) 30.6 (±3.39) 19.9 (±5.8) (±1.4) Average Average (±0.27) 48 (±18.6) (±8.8) 0.76 (±0.08) 75.2 (±8.9) Average Li (±3) NA (±9) 0.36 (±0.04) 96.3 (±1.3) Average Br 11 (±1) 50.4 (±1.04) 34.3 (±1.5) 0.86 (±0.01) (±0.76) a FluoSphere diameter in mm. b NA: Li + relative concentration did not reach the value listed in the column heading. 4of12

5 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 experiments (i.e., 20 ml/min) in the final flushing stage provided maximum remobilization of colloids deposited within the fracture. [14] Five multitracer experiments were carried out in core 1: the first four experiments were repetitions with the same multitracer solution (1.0-, 0.2-, 0.02-mm FluoSpheres and LiCl). In the fifth experiment, LiBr was added to the ARW instead of LiCl (Table 3). [15] Seven transport experiments were carried out in core 2 (Table 4); the first two were identical repetitions (1.0-, 0.02-mm FluoSpheres and LiCl), and the third was the same experiment with three sizes of FluoSpheres, 1.0, 0.2, 0.02 mm, and LiBr instead of LiCl. In other experiments (E-8, E-9, and E-12), only one type of FluoSphere (0.1, 0.02 or 1.0 mm) was used at a time with all other conditions identical to the multitracer experiments Analytical Measurements [16] The effluent colloid concentration (mg/l) was determined using a fluorometer (Cary Eclipse Fluorescence Spectrophotometer, Varian, Palo Alto, CA). Li +, Ca 2+, Mg 2+, and Na+ concentrations were analyzed using AA (Atomic Absorption, Perkin-Elmer 1100B, Wellesley, MA). SO 4 2,NO 3 and Cl were analyzed by spectrophotometer and Dionex 4500i ion chromatography. Br concentrations were measured using a modified version of method Br B[American Public Health Association, 1995] with a Hitachi U-2000 spectrophotometer (±5%). Zeta potential of the FluoSpheres 1 and the ground chalk was measured with a ZetaMaster (Malvern Instruments LTD, Worcestershire, UK) Data Analysis [17] The total recovery rate for each experiment was determined by integrating the colloid concentration from the breakthrough curves (BTCs) plus the colloid concentration from the last stage, in which the fracture was flushed with M NaCl at a high flow rate. [18] The average flow velocity was calculated based on the calculated equivalent hydraulic fracture apertures, by dividing the discharge by the cross-sectional flow area (V = Q/2Wb) [Neuzil and Tracy, 1981; Silliman, 1989], and the average water traveltime was calculated by dividing the fracture length by the average water velocity. [19] The equivalent hydraulic aperture (2b) can be calculated from the linear slope obtained by plotting the lefthand side of equation (1) against the hydraulic gradients [Lapcevic et al., 1999]. Q 12m W r f g ¼ ð2bþ3 Dh L where 2b is the fracture aperture (L), Q is the flow rate (L 3 /T), m is the dynamic viscosity (M/LT), W is the width of the fracture (L), r f is the fluid density (M/L 3 ), g is the acceleration of gravity (L/T 2 ), Dh is the hydraulic head drop along L (L) and L is the fracture length (L). [20] Four mechanisms can cause colloid deposition: straining, Brownian motion (diffusion), interception and sedimentation [e.g., Elimelech et al., 1995]. Each of these mechanisms affects the different sizes of FluoSpheres differently. Brownian motion is inversely proportional to the particle diameter in the Stokes-Einstein equation (equation (2)), ð1þ whereas the square of the particle diameter is directly proportional to the rate of Stokes settling (see equation (3)). D ¼ kt 3mpd p where D is the Stokes-Einstein diffusion coefficient (L 2 /T), T is the water temperature (K), k is the Boltzmann constant ( erg/k) and d p is the particle diameter (L). [21] According to Becker et al. [1999], the relative influences of Brownian motion and sedimentation can be analyzed by comparing their characteristic transport length scales over a time interval. The length scale of sedimentation, L S, is defined for a spherical particle by multiplying the rate of Stokes settling by the time interval (equation (3)), which is the calculated residence time of water in the fracture: L s ¼ 1 18m r p r f gd 2 p t where r p is the density of the particles (M/L 3 ), and t is the time interval (T). [22] The Brownian motion length scale is p L D ¼ ffiffiffiffiffiffiffiffi 2Dt where D is calculated from equation (2). [23] The ratio of L s /L D represents the relative influence or dominance of one of the two aforementioned deposition mechanisms (Brownian motion or settling/sedimentation). When the ratio is about 1, the two mechanisms are expected to be relatively balanced (both have a similar effect). Values much greater than or lower than 1 over the time interval will support assumptions of the particles tendency to settle or diffuse, respectively. In addition to L s /L D > 1, particle settling will be significant only if the lower boundary (such as a fracture wall) is accessible during the time interval. For the case of fractured rocks, the ratio of L s /b (where b is half the fracture aperture) must be greater than 1 for settling to occur. This value represents accessibility of the colloids to the lower boundary (wall) of the fracture [Becker et al., 1999]. [24] The impact of Brownian diffusion can be demonstrated using the solution for a 1-D solution of Fick s second law: M x ¼ erfc p M 0 2 ffiffiffiffiffiffi Dt where M/M 0 is the relative concentration of FluoSpheres at a distance x from a constant concentration source, at time t. To demonstrate the maximum impact of colloid size differences on the probability of collision with the fracture walls, it is assumed that there is a constant concentration of colloids at the center of the fracture; the concentration near the fracture walls is then calculated. The actual concentration profile in the fracture is unknown, but this simplification is expected to provide an indication of the relative importance of diffusion on the retention of colloids of different sizes [Cumbie and McKay, 1999]. ð2þ ð3þ ð4þ ð5þ 5of12

6 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 Figure 2. Comparison of the BTCs of 1.0-, 0.2-, and 0.02-mm FluoSpheres, Li +, and Br in core 1 between (a) 0 and 1500 min and (b) 0 and 80 min (further details are in Table 3, E-5). [25] Enhanced transport velocity of colloids, as observed by several authors [McKay et al., 1993b, 2000, 2002; Reimus, 1995; Hinsby et al., 1996; Becker et al., 1999; McCarthy et al., 2002; Keller et al., 2004], could be explained by a combination of different mechanisms. The first is charge exclusion: electrostatic repulsion between the negatively charged FluoSpheres and the negatively charged chalk surface (Table 2) forces the colloids to travel midstream rather than near the fracture walls and in small channels. Second is the effect of size exclusion: the size of the FluoSpheres (significantly larger than solutes) forces the colloids to migrate through large flow channels only. Additionally, colloids travel in the center of streamlines, leading to faster velocities, fewer detours and thus a shorter range of traveltimes [James and Chrysikopoulos, 2003a; Auset and Keller, 2004]. The third effect is Taylor dispersion: Taylor dispersion results from the mixing induced by velocity variations across the fracture aperture. An increased particle diameter-to-fracture aperture ratio implies a narrower range of velocities for a colloidal plume, thereby decreasing the dispersive effect of the velocity gradient. If a plume is subjected to a single velocity, it spreads by molecular diffusion alone (equation (2)). The Taylor dispersion coefficient (D Taylor ) (equation (6)) depends on the flow and fracture properties: D Taylor ¼ D þ 2 Vmax 2 ð2bþ2 ð6þ 945 D Equation (6) was modified from Adamczyk and van De Ven [1981] and has been used recently by James and Chrysikopoulos [1999, 2003b]. V max is the maximum velocity occurring along the centerline of the fracture: here, the V max values used are calculated from the values of the time at which the first FluoSpheres arrive at the outflow (V max = L/Fluo. first arrival time). It should be noted that the Taylor dispersion coefficient is a limiting case of the effective dispersion coefficient, D eff [James and Chrysikopoulos, 2003b, equation 19]. It can be used when the particle diameter becomes very small (d p!0) as well as when the particle diameter is comparable to the fracture aperture (d p!2b). As the diameter of the particle become infinitesimally small, the effective velocity with which the particle plume travels is reduced to the mean flow velocity. According to the calculations made by James and Chrysikopoulos [2003b], if d p /2b is smaller than 0.05, D eff D Taylor can be assumed. In the systems explored in this paper, the maximum d p /2b ratio was (minimum 5E-5). [26] The dominance of each transport mechanism, advection or diffusion, on the tracers (colloids and solutes) in both fractures can be estimated by comparing the Peclet (Pe) number of each tracer. The Pe number in a parallel plate aperture [Detwiler et al., 2000] is defined as Pe ¼ V Ave2b D 3. Results 3.1. Flow Experiments in the Fractured Cores [27] The average calculated equivalent fracture apertures were 380(±4) and 183(±7) mm for cores 1 and 2, respectively. No significant changes in the calculated equivalent hydraulic apertures (±1 4%) were observed in either core in more than a year of experiments. Thus it is assumed that no significant deposition, precipitation or dissolution occurred within the fractures during the experiments or between them. The water traveltimes were 29.7(±1) and 14.1(±1) min in cores 1 and 2, respectively Tracer Experiments [28] Very good repetitions were observed in the tracer experiments in both fractures (Tables 3 and 4), and therefore only one experiment from each core (E-5 in Figure 2 and E-10 in Figure 3) is graphically shown while the average values from all the experiments (Tables 3 and 4) were used to analyze the data Core 1 Experiments [29] The BTC (E-5, Figure 2) shows early first arrival (defined as C/C 0 = 0.01) of all three sizes of FluoSpheres (18.8 min) relative to Li + and Br (31.5 and 30.7 min, respectively) and to the mean calculated water traveltime (29.7 min). The later arrival time of the ions is discussed further on. The maximum C/C 0 obtained for each of the different FluoSphere tracers varied according to their size, with average values of 0.96, 0.92, and 0.76 for the 0.2-, 1.0-, and 0.02-mm FluoSpheres, respectively (Table 3). The maximum C/C 0 value of Li + (0.65) was lower than that of the FluoSpheres, while that of Br (no repetitions) was similar to ð7þ 6of12

7 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 Figure 3. Comparison of the BTCs of 1.0-, 0.2-, and 0.02-mm FluoSpheres, Li +, and Br in core 2 between (a) 0 and 1500 min and (b) 0 and 80 min on a semilogarithmic scale to emphasize (c) the tailing of the solutes relative to the lack of tailing of the colloids (further details are in Table 4, E-10). the 1.0-mm FluoSpheres. Despite similar first arrival of the different FluoSpheres, arrival of the center of mass (0.5 C/C 0 ) increased with decreasing size (53, 57, and 65.5 min for 1.0, 0.2, 0.02 mm, respectively). Br and Li + arrived to the center of mass at much later times (74 and 171 min, respectively). Relative concentrations of all FluoSpheres decreased to low values, below 1% of their injected concentration, 370 min after cessation of tracer injection, while at the same time the relative concentrations of Li + and Br were 10 and 2%, respectively. Even at the end of the experiment (1600 min after injection), the Li + concentration was still above 1% of the tracer solution. The average overall mass recovery was 93.2, 90.6, and 76.8% for the 0.2-, 1.0- and 0.02-mm FluoSpheres, respectively (same order as observed for the maximum C/C 0 ). The overall mass recovery of Li + and Br was 97 and 93%, respectively. Detailed results of each experiment and the standard deviations from the averages are given in Table Core 2 Experiments [30] The average arrival time for all FluoSphere sizes was 4.2 min (4.0 min for the single 0.1-mm run). The arrival time for Li + was 24.6 min, and for Br, 11 min. Average values of maximum C/C 0 for 1.0-, 0.2-, 0.1- and 0.02-mm Fluo- Spheres, Li +, and Br were 0.90, 0.99, 0.85, 0.76, 0.36 and 0.86, respectively (Table 4). Note the initial rapid breakthrough of FluoSpheres compared to the solutes and to the calculated average traveltime of water in the fracture (14.1 min; Figure 3b). [31] The relative concentration of the FluoSpheres rapidly decreased to values lower than 1% of the influent tracer concentration after the tracer solution was switched back to ARW. On average, FluoSpheres reached values lower than 1% at 244 min, while at the same time the solutes (Li + and Br ), particularly Li +, showed very moderate declines in concentration, creating a smooth and steady tail on the Li + BTCs and a fluctuating tail on the Br BTCs (C/C 0 = and 0.054, respectively). [32] The average overall mass recovery was 99, 90.6, 89.9 and 75.2% for the 0.2-, 1.0-, 0.1- and 0.02-mm Fluo- Spheres, respectively. Again, this follows the order observed for the maximum C/C 0 values. As in core 1, despite the delayed center-of-mass peak and longer tails, the overall mass recoveries of Li + and Br were high (96.3 and 97.8%, respectively). Detailed results of each experiment and the standard deviations from the averages are given in Table 4. In the last stage of the experiments (flushing), in both fractures, the mass of colloids in the NaCl effluent could be considered negligible. 4. Discussion 4.1. Impact of FluoSphere Size on Mass Losses and Deposition [33] The maximum mass recoveries and C/C 0 values were for the 0.2-mm FluoSpheres while the lowest values were for the 0.02-mm FluoSpheres. Values for the 1.0-mm FluoSpheres were always slightly lower than those of the 7of12

8 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 Figure 4. Influence of particle size on their recoveries during the tracer experiments. Given are mean ± SD based on five and seven experiments in cores 1 and 2, respectively (data appear in Tables 3 and 4). Note that the data for the 0.1-mm FluoSpheres in core 2 is from Zvikelsky [2005] and not discussed in this paper. 0.2-mm FluoSpheres (Tables 3 and 4 and Figure 4). This behavior is not related to the surface charge of the FluoSpheres, as the measured zeta potentials were the same order of magnitude for all of them (Table 2). Therefore it seems that the most efficient size for colloidal transport in our system is less than 1 mm, and probably close to 0.2 mm. The most efficient particle size for transport in fractures is highly dependent on the fracture properties as well as on the properties of the matrix (details in the introduction) [Vilks and Bachinski, 1996; Becker et al., 1999; Cumbie and McKay, 1999; McCarthy et al., 2002]. [34] In most reported studies of colloid transport, the recovery rates were much lower than 30% [Toran and Palumbo, 1992; Vilks and Bachinski, 1996; Cumbie and McKay, 1999; McCarthy et al., 2002]. Although recovery rates higher than 50% for colloid migration in fractures have been observed in a few other studies [Reimus, 1995; Becker et al., 1999; Knapp et al., 2000; Chinju et al., 2001], these were for colloids of 0.3 to 1.0 mm in tuff and granite. The recovery rates observed in this study (90, 95, 75% for the 1.0-, 0.2-, and 0.02-mm colloids) are extremely high. [35] The maximum C/C 0 values observed in this work for colloid sizes ranging from 0.02 to 1.0 mm are also among the highest measured in fractured rocks. For colloids smaller than 0.3 mm, C/C 0 values reported in the literature were always much smaller than the values observed in this work, in both laboratory experiments [Hinsby et al., 1996; Vilks and Bachinski, 1996; Cumbie and McKay, 1999; McCarthy et al., 2002; McKay et al., 2002] and field studies [McKay et al., 1993b, 2000; Vilks et al., 1997; Becker et al., 1999; Mori et al., 2003]. The reason for the high recovery rates and maximum C/C 0 values in this work is probably related to the characteristics of the host rock, chalk. The chalk matrix has very narrow pore throats and the discrete fractures have relatively large apertures Dominance of Deposition in Transport Mechanisms [36] The common explanation for colloid retention is deposition on the fracture surfaces or inside the matrix voids. The colloid sizes used here ( mm) were two to four orders of magnitude smaller than the equivalent fracture hydraulic apertures of the chalk cores (183 and 380 mm). Therefore it is unlikely that the flow trajectories would cause straining (physical filtration due to size) or interception (colloids moving along a streamline coming into contact with the fracture wall). Particle interception is highly dependent on the fluid approach velocity of the colloids to the fracture surface (collector) as well as on particle size [Elimelech et al., 1995]. The different average fluid velocities (1.46 and 2.73 cm/min in cores 1 and 2, respectively) inside the fractures did not demonstrate differences in deposition rate, and therefore interception as a deposition mechanism is likely to be insignificant. Straining is more important in porous media when the ratio between colloid diameter and grain diameter is greater than about 0.2 [Herzig et al., 1970]. Assuming that the pore size is about 10% of the grain size, straining is important if the ratio between colloid and grain size is larger than In our system, the ratio between the largest colloid and small aperture (maximum ratio) was about Therefore straining is not likely to play a significant role in colloid deposition within the fracture aperture (along the flow direction). [37] It should be noted that the calculated equivalent hydraulic fracture aperture integrates the effects of larger and smaller aperture regions and neglects the complicated internal fracture structure. Fracture structure heterogeneities on all scales are well documented [e.g., Weisbrod et al., 1998, 2000a; Dahan et al., 2000; Knapp et al., 2000; Chinju et al., 2001; Arnon, 2004]. [38] Therefore some local straining and/or interception zones could be present, even within a fracture of large calculated equivalent hydraulic aperture. However, the M NaCl solution used to flush the fractures in both directions at high velocity following the experiments did not yield any significant release (remobilization) of FluoSpheres. Therefore it appears that no FluoSpheres were strained within the system, regardless of potential channeling. [39] The last two mechanisms that may significantly contribute to colloidal deposition are sedimentation and Brownian motion. Sedimentation acts in the direction of gravity whereas Brownian motion acts in all directions. Both mechanisms are highly dependent on particle size. According to the length scale analysis [Becker et al., 1999], FluoSphere deposition was significantly more affected by Brownian motion than by sedimentation over the time interval studied in the fractured chalk. For the to 0.1-mm FluoSpheres, both L S /L D and L S /b were significantly less than 1 in both cores (Table 5). For the 1.0-mm FluoSpheres the L S /L D values were around 1, suggesting balance between the settling and Brownian motion forces. However, because the L S /b values were smaller than 1 (Table 5), it is assumed that Brownian motion was the governing deposition mechanism in this case as well. The similarly high mass recovery rates and maximum C/C 0 values observed for the 0.2- and 1.0-mm FluoSpheres suggest that indeed the same mechanism is controlling their deposition inside the fracture aperture. The fact that there is no attenuation of large FluoSpheres compared to the smaller ones implies that there is no significant settling 8of12

9 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES Table 5. Summary of the Length Scale Ratios and the Simulation of FluoSphere Diffusion a Particle Diameter, mm t, min b, mm D, cm 2 /s L S,cm L D,cm L S /L D L S /b M/M 0 Core E E E E E E E E E E E E E E E E-7 Core E E E E E E E E E E E E E E E-4 a L S and L D are the settling and Brownian motion length scales, respectively, t is time interval of water residence time in the fracture, b is half fracture aperture, and D is the diffusion coefficient of particles based on the Stokes-Einstein equation. M/M 0 is the relative concentration of FluoSpheres due to diffusion near the fracture walls at the calculated residence time of water in the fractures. W12S08 within the fractures. Furthermore, the small density difference (0.055 g/cm 3 ) between the FluoSpheres and ARW does not support settling (equation (3)), and thus a naturally buoyant scenario appears plausible. Brownian motion of colloids is known to be an effective deposition mechanism for particles smaller than 1.0 mm. Several studies have confirmed that the retention of colloids smaller than 1.0 mm in fractures can be attributed to deposition due to Brownian motion [Becker et al., 1999; Cumbie and McKay, 1999; McCarthy et al., 2002; McKay et al., 2002]. [40] Assuming that there is a constant concentration of colloids at the center of the fracture and assuming equivalent hydraulic aperture values, equation (5) was solved for the different-sized colloids. It was found that for the smallest-sized FluoSpheres (0.02 mm), the relative concentration at the fracture walls would be high while for the larger-sized FluoSpheres, the relative concentration values would be very low (Table 5). This would increase the collision probability of the small colloids with the fracture walls and result in their increased deposition and attenuation. Although the exact values will vary as a function of distance from the fracture wall, this calculation demonstrates the large differences between the collision probabilities of small versus large colloids. Increasing collision will increase the deposition of small colloids onto the fracture walls. [41] In addition, there is the possibility of small-sized FluoSpheres penetrating the matrix voids. The loss of colloids from the fracture aperture to the matrix due to diffusion needs to be considered when the FluoSpheres are small enough to penetrate the matrix pores. The probability of penetration into the pores is highly dependent on the rock matrix porosity as well as on the pore size distribution. The average measured porosity values of the chalk were 40% [Weisbrod et al., 1999]. Thus, when a FluoSphere collides with the fracture walls, its average probability of contacting a pore is 40%. The maximal and minimal measured values of pore throat diameter in the chalk are 0.30 and mm, respectively, with an average value of mm [Nativ and Adar, 2001]. These values suggest that the likelihood of the smallest FluoSpheres (0.02 mm) penetrating into the matrix is significantly greater than that of the larger ones in each collision. Furthermore, as already noted, the likelihood of collision between the smallest colloid and the fracture wall is significantly larger than for the large colloids. The threshold ratio of pore throat to colloid is about 1.5 [Sirivithayapakorn and Keller, 2003]; below this value, colloids may penetrate the matrix Colloid Transport [42] The FluoSpheres displayed extremely rapid arrivals at the outflow of the cores compared to the calculated water velocity (based on the equivalent hydraulic aperture), regardless of FluoSphere size (Tables 3 and 4). Early arrival was defined as the appearance of C/C 0 = 0.01 at the outflow point. On the basis of these data, the fastest FluoSpheres traveled at a front velocity that was 1.58 and 3.51 times greater than the average velocity of water in cores 1 and 2, respectively. Accelerated arrival times of microspheres, bacteria and viruses have been observed in other experiments in fractured porous media [Toran and Palumbo, 1992; McKay et al., 1993a, 1993b; Hinsby et al., 1996; Becker et al., 1999; Knapp et al., 2000], although in most cases this acceleration was not as significant as observed in the experiments reported here [e.g., McKay et al., 2002]. Again, the combination of large apertures, high porosity and small pore throats of the fractured chalk increases the differences between colloid and solute traveltime. [43] The low diffusion coefficients of the FluoSpheres ( cm 2 /s to cm 2 /s for the 0.02 to 1.0 mm FluoSpheres, respectively, Table 5) compared to solutes ( cm 2 /s and cm 2 /s for Li + and Br, respectively [Newman, 1973]) and the lift forces due to the finite size of the colloid could keep it centered in the high velocity streamline. Although a comparison between the hydraulic apertures and channeling within the cores was not the focus of this study, it is interesting to note the similarities in the observed behavior of the colloids and the impact of size on colloid transport, despite the differences in the internal properties of the cores. The calculated Taylor dispersion coefficients decreased significantly with reductions in colloid size (Table 6). The differences might explain the order of appearance of C/C 0 = 0.5 for the FluoSpheres (large to small (Figures 2 and 4 and Tables 3 and 4)). [44] Bromide (Br ) is often treated as a nonreactive, conservative solute tracer. Using Br s first arrival time, it should be possible to obtain a second estimate (in addition to the average water velocity deduced from the flow experiments) of the water velocity in the fractures. A comparison 9of12

10 W12S08 ZVIKELSKY AND WEISBROD: COLLOID TRANSPORT IN DISCRETE FRACTURES W12S08 Table 6. Summary of Taylor Dispersion Coefficients Colloids, mm of first arrival times for Br and colloids enables us to estimate the ratio of the fracture volume accessed by the two tracers (Br and FluoSpheres, Table 7). The data in Table 7 suggest that the colloids experienced only about 64% and 35% of the fracture volume (core 1 and 2, respectively) experienced by Br. These data may support the aforementioned assumption of enhanced fast flow in core 2 based on the D Taylor calculations. These findings support recent works and are persuasive evidence for the existence of favorable pathways in the studied fractured chalk [Dahan et al., 2000; Weisbrod et al., 2000b; Arnon et al., 2005; Kurtzman et al., 2005] Colloid Versus Solute Transport [45] The early arrival of colloids compared to solutes (Li + and Br ) may again be explained by a combination of the aforementioned effects (size exclusion and charge exclusion). As already noted, colloids are expected to be transported mainly by advection through the fractures. Previous studies have supported the theory of advection dominance on colloids (microspheres) while migrating in fractures [Cumbie and McKay, 1999; McCarthy et al., 2002]. [46] On the other hand, the solutes (Li + and Br ) are more subject to diffusion due to their high diffusion coefficients. High diffusion rates between fractures and the chalk matrix have been reported by several authors [Polak et al., 2002; Bernstein, 2003; Arnon, 2004], as expected in high-porosity materials such as chalk. The role of matrix diffusion in the fractured chalk cores is confirmed by the attenuation of both solutes (Br and especially Li + ) compared to colloids or even to the calculated water residence time in the fracture. Despite the lower diffusion coefficient of Li + compared to that of Br,Li + is significantly retarded compared to all tracers and exhibits long back-diffusion tails (Figures 2a and 3a and Tables 3 and 4). Table 7. Comparison Between the First Arrival Times (C/C 0 = 0.01) of the FluoSpheres and Br in the Fractured Chalk Cores Br First Arrival Time, min Colloid First Arrival Time, min D Taylor, a cm 2 /min Core Core a D Taylor is calculated with V max values based on the FluoSpheres early arrival velocity. Arrival Time Ratio (Colloids/Br ) Core 1 E Core 2 E E E Table 8. Peclet Number (Pe) Calculations on the Basis of l and Diffusion Coefficient Values for Solutes and Colloids FluoSphere Diameter, mm FluoSphere Pe Solutes Solutes Pe Core E+3 Li E+4 Li E+4 Br E+5 Br Core E+3 Li E+4 Li E+4 Br E+5 Br This phenomenon might be explained by the inverse electrical charges of the positive Li + and the surrounding negatively charged matrix (the chalk being negatively charged at the experimental ph; Table 2). While the Br is influenced by charge exclusion that rejects it from the fracture walls, the Li + is attracted to the walls. Nevertheless, the overall mass recovery of Li was close to 100%, and Zvikelsky [2005] observed no sorption of Li + to ground chalk. The lower overall mass recovery of Br compared to Li + in core 1 (Table 3) could be due to: (1) inaccuracy of the Br analysis technique and only one repetition for Br ; (2) the higher diffusion coefficient of Br (relative to Li + ) could result in its lower overall mass recovery. It should be noted that the overall mass recovery of Br in core 2 was higher than that of Li + (Table 4). However, the residence time of the solution in that core was about half that in core 1. Nevertheless, a detailed exploration of the mass recovery of Li + and Br was beyond the scope of this paper. [47] Focusing on the late stages of the colloid BTCs shows a lack of tailing for all colloid sizes, even the smallest, which has a relatively high diffusion coefficient (Figure 3c and Table 5). The lack of tailing suggests that there is no back diffusion of colloids of any size. As already noted, in theory the small-diameter colloids (0.02 mm) could penetrate the matrix pores. The combination of relatively low recovery and the lack of back diffusion suggests that their penetration into the matrix is irreversible. This is probably due to the complexity of the tortuous pore interconnections. [48] Table 8 summarizes the Pe values for colloids, Li + and Br. For small Pe values (1), molecular diffusion dominates, whereas for large Pe values (>1), advection dominates. Obviously, from the data in Table 8, the transport within the fractures is advection-dominant, although diffusion plays a major role in solute attenuation relative to colloids. Note the three to four order of magnitude difference between Pe for solutes and colloids in both cores. This difference is proportional to the influence of diffusion on solute and colloid transport under the applied hydraulic conditions. 5. Summary and Conclusions [49] Tracer tests were carried out in two fractured chalk cores. FluoSpheres ( mm) were used as the model colloids in all of the experiments either alone, or simultaneously with the solute tracers LiCl or LiBr. This study shows that very rapid colloid transport with high mass 10 of 12