Enhanced Mixing and Plume Containment in Porous Media under

Jul 22, 2009 - Department of Earth and Atmospheric Sciences, City College of New ... Graduate School and University Center, City University of New Yor...
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Environ. Sci. Technol. 2009, 43, 6283–6288

Enhanced Mixing and Plume Containment in Porous Media under Time-Dependent Oscillatory Flow P E N G F E I Z H A N G , * ,†,‡ STEPHANIE L. DEVRIES,† A N N E T T E D A T H E , †,| A N D AMVROSSIOS C. BAGTZOGLOU§ Department of Earth and Atmospheric Sciences, City College of New York, New York, New York 10031, Department of Earth and Environmental Sciences, Graduate School and University Center, City University of New York, New York, New York 10016, and Department of Civil and Environmental Engineering, University of Connecticut, Storrs, Connecticut 06269

Received March 21, 2009. Revised manuscript received June 28, 2009. Accepted July 8, 2009.

Solute transport experiments were conducted in a decimeter scaleflowcellpackedwithsandtostudythepotentialforenhanced mixing of solutes in porous media and improved containment of injected plumes under multiple pumping-well driven, timedependent oscillatory flow with respect to constant flow. Realtime imaging of the colorimetric reaction of Tiron (1,2dihydroxybenzene-3,5-disulfonic acid) and molybdate was used to quantify mixing, whereas fluorescein was used to better examine plume size. Results from the small scale experiments clearly demonstrated the enhanced mixing of solutes under low Reynolds number oscillatory flow (a factor of 2 with respect to constant flow in homogeneous sand and a factor of 3 in layered sand), as the result of increased contact interface for solute diffusion. Further, the injected solute plume was better contained under oscillatory flow (25% less area with respect to constant flow in homogeneous sand) due to the cancellation of advective transport at each well over time. Enhanced mixing under oscillatory flow may enhance the processes of chemical and biological remediation. Furthermore, improved plume containment under oscillatory flow may require smaller amounts of chemicals to be injected during aquifer remediation.

Introduction Aquifer remediation by injection of organic and inorganic compounds requires effective mixing between injected compounds and ambient groundwater. For instance, groundwater bioremediation can only occur where electron acceptors, electron donors, limiting nutrients, and microorganisms capable of contaminant degradation are simultaneously present (1, 2). In porous media where flow is laminar, mixing (in the absence of sorption) is achieved via dispersion: macroscopic dispersion leads to the deformation of a solute plume from its original shape (spreading), whereas pore-scale dispersion * Corresponding author e-mail: [email protected]; phone: (212) 650-5609; fax: (212) 650-6482. † City College of New York. ‡ City University of New York. § University of Connecticut. | Currently at Department of Horticulture, The Pennsylvania State University, University Park, Pennsylvania 16802. 10.1021/es900854r CCC: $40.75

Published on Web 07/22/2009

 2009 American Chemical Society

leads to the overlapping (mixing) of the compounds at the contact interface (3, 4). Ultimately, molecular diffusion at the pore scale causes direct mixing of reactants (3-5), while spreading indirectly enhances the mixing by increasing the contact area (3, 4). It is now generally recognized that transverse dispersion is the controlling mechanism for mixing of electron donors and acceptors at the narrow interface between a contaminant plume and ambient groundwater (6-12). Transverse dispersion is also the key process determining the dissolution rate of nonaqueous phase liquids in aquifers (13, 14). Unfortunately, under steady state flow, transverse dispersion is very small and only approaches an asymptotic value of the order of pore-scale dispersion coefficients (15). To enhance mixing in aquifers, Jones et al. (16) proposed a method of hydraulic manipulation, i.e., introducing temporal flow variability by repeatedly alternating extraction and injection of clean groundwater. Recent theoretical work by Cirpka and Attinger (15) and Dentz and Carrera (17) demonstrated that temporally fluctuating flow could significantly enhance transverse dispersion (and hence mixing) in heterogeneous media. Very recently, Bagtzoglou and Oates (18) proposed the use of chaotic advection for enhanced mixing and groundwater remediation. Chaotic advection refers to the complicated particle trajectories observed in the Lagrangian frame of reference under simple well-behaved velocity fields. In his pioneering work, Aref (19) noted that the stream function ψ in a twodimensional (2D) incompressible flow plays the role of a Hamiltonian. If ψ is time dependent, the 2D unsteady flow is generally nonintegrable and can produce chaotic particle motion under low Reynolds number (laminar) flow. The required time dependence of the stream function may be caused by some simple, external modulation of the flow system. Chaotic advection in fluids (without porous media) has been demonstrated by numerous theoretical and experimental studies in various flow systems, including blinking-vortex flow systems, tendril-whorl flow systems, pulsed source-sink systems, journal-bearing systems, and others (20-27). Chaotic mixing enhanced biological growth has also been demonstrated in a bench-scale apparatus consisting of two eccentrically placed cylinders by Bagtzoglou et al. (28). In contrast, chaotic advection in porous media received much less attention. A majority of these studies are related to chaos in hydrothermal flows (29-31), and only a handful are relevant to typical groundwater flow. At small pore scales, Metcalfe et al. (32) used the Hele-Shaw flow model and showed that time- and space-varying fluid injection from multiple sources/sinks could create many different kinds of chaotic flow patterns. Tsakiroglou et al. (33) performed solute transport visualization experiments on glass-etched pore networks and found that chaotic regimes were favored by low Peclet values and high pore-scale heterogeneities. At large field scales, Jones et al. (16) and Smith et al. (34), through numerical simulations, indicated that time-periodic oscillations in low Reynolds regimes could cause laminar flow to exhibit very complicated particle trajectories in aquifers, albeit the term chaotic advection was not mentioned. Later, theoretical work by Sposito (35) showed chaotic solute advection in the flow field near a recirculation well subject to time-dependent flow. He concluded that unsteady groundwater flow can, in principle and under certain conditions, induce chaotic advection. Theoretical work by Bagtzoglou and Oates (18) further demonstrated that time-dependent oscillatory flow (hereafter referred to as oscillatory flow) in a well triplet (arranged in a triangle with interwell distances VOL. 43, NO. 16, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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between 75 and 90 m) can cause chaotic advection and substantial mixing in the area within and around the well triplet. There is no experimental work to date, however, to verify enhanced mixing in porous media under oscillatory flow. The first objective of this study was, therefore, to experimentally verify enhanced mixing of solutes in porous media under oscillatory flow with respect to conventional constant flow, through real-time imaging of reactive tracers in a decimeter scale, quasi-2D flow cell packed with sand. The mass of product formed as the result of fluid-fluid mixing and the area of product distribution were used to assess the extent of mixing. The second objective was to verify the hypothesis that oscillatory flow with alternating injection and extraction in a set of wells would better contain injected solute plumes. This hypothesis stems from the fact that at each well the net flow would be zero over time under oscillatory flow (i.e., average large-scale advective transport would be canceled out) and dispersion would be the main mechanism for plume enlargement.

Materials and Methods Flow Cell. The flow cell is made of transparent acrylic and has internal dimensions of 180 mm (length) by 180 mm (width) by 10 mm (depth), with three inlets and three outlets evenly spaced on two sides (referred to as side ports, Figure S1 in the Supporting Information). Following the conceptual model of Bagtzoglou and Oates (18), a three-well pumping system was established via three additional pumping inlets/ outlets arranged in the shape of an equilateral triangle (with side lengths of 60 mm) in the center of the top of the flow cell (referred to as top ports, Figure S1 in the Supporting Information). The flow cell was packed homogeneously with 20-30 mesh translucent sand (Accusand, La Sueur, MN), in most cases, and was packed heterogeneously (3 layers with 20-30 mesh medium sand in the middle and 40-60 mesh fine sand above and below, see Figure S1 in the Supporting Information) in one set of experiments. The sand was thoroughly cleaned according to the procedures of Litton and Olson (36). Tracers and Imaging System. The colorimetric reaction of Tiron (1,2-dihydroxybenzene-3,5-disulfonic acid, Ti) and molybdate (Mo) was used to quantify mixing. Once in contact, the two colorless reactants rapidly form colored (yellow to dark red), stable, soluble product MoTi24-, which can be digitally imaged and quantified using light absorbance to study fluid-fluid mixing (4). The fluorescent dye fluorescein was used to better examine plume size. An imaging system with a charge-coupled device (CCD) camera (14-bit), originally developed for real-time monitoring of the transport of fluorescent solutes and colloids in porous media (37), was used in this study. A 535 nm emission filter was used to determine the light absorbance of MoTi24-, whereas a filter set of 465/535 nm (excitation and emission wavelengths, respectively) was used to determine the intensity of fluorescein. Calibrations. To calibrate absorbance vs MoTi24- mass in the packed flow cell, 0.05 M Tiron and 0.025 M molybdate (added as ammonium molybdate, (NH4)2Mo) stock solutions buffered to pH 6.1 in 0.13 M succinic acid were first prepared according to the procedures of Oates and Harvey (4). MoTi24solutions in dilute concentrations (0.00125, 0.00250, 0.00375, 0.0050, 0.0075, and 0.010 M) were then prepared from the stock solutions. A constant initial molybdate concentration of 0.010 M was used in the calibration here because at the beginning of reactive transport experiments the flow cell was saturated with 0.010 M molybdate solution. Our preliminary tests indicated that the presence of molybdate or Tiron solution alone in the flow cell did not cause any change in light absorbance (both solutions are clear), but the presence 6284

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of excess molybdate during the colorimetric reaction would cause slightly higher absorbance (∼20%), presumably due to the effect of excess molybdate on reaction kinetics. The packed flow cell was saturated with each MoTi24- solution via injection through the side ports at a total flow rate of 2.4 mL/min for 75 min (1.5 pore volumes) and then imaged. The packed flow cell was thoroughly rinsed with ultrapure Milli-Q water (Millipore Co., Billerica, MA) in between different calibration points. To calibrate light intensity vs fluorescein mass in the packed flow cell, fluorescein solutions of various concentrations (50.0, 100.0, 500.0, and 1000.0 µg/L) were prepared. The packed flow cell was then saturated with each of the fluorescein solutions and imaged. Transport Experiments. Two pumping schemes were used in this study: an oscillatory flow scheme and a constant flow scheme (control). To establish the oscillatory flow, one of the three wells was randomly assigned a pumping magnitude with realistic constraints and a direction (injection or withdrawal), and the magnitude was then randomly partitioned to the other wells, which were assigned the opposite flow direction of the first well (18). This configuration ensures that mass balance is conserved and no dewatering takes place. The mathematical expressions of the oscillatory flow scheme are as follows: qwell1 ) Mqsign(-0.5 + rand) + Sq(-0.5 + rand) qwell2 ) -qwell1rand qwell3 ) -(qwell1 + qwell2)

(1)

where qwelli is the flow rate at well i (i)1, 2, 3), Mq and Sq are constants, and “rand” is a random number between 0 and 1. In this particular study, Mq was set at 1.8 and Sq was set at 0.6, and the mean absolute flow at well 1 was around 1.8 mL/min. Estimation of the Reynolds number and Peclet number suggested that the flow system is laminar (creep flow) and is advection dominated (see details in the Supporting Information). The flow directions and rates were changed every 7.8 min, corresponding to about 1/20 of the total pore volume of the packed flow cell or 2.4 times the pore volume encompassed by the well triplet. For the control experiments, the flow direction and flow rate remained constant at the three wells, i.e., well 1 was always injecting (qwell1 ) 1.8 mL/min), and wells 2 and 3 were always extracting (qwell2 ) qwell3 ) -0.9 mL/min). Three digital peristaltic pumps with reverse flow capability were used. Each pump was connected via Tygon tubing (0.8 mm inner diameter) to a top port (i.e., “well”) of the packed flow cell, and all three pumps were connected to a reservoir. The pumps were calibrated frequently to maintain accurate flow rates at both directions. For transport experiments with the colorimetric reaction, the packed flow cell was first saturated with a 0.010 M molybdate solution buffered to pH 6.1 and a 0.020 M Tiron solution (also buffered at pH 6.1) was pumped into the flow cell via the well(s) from a reservoir using oscillatory flow or constant flow. Images of the resulting MoTi24- plume were collected every 1.3 min. To avoid mixing in the reservoir and reinjecting the product (MoTi24-) back into the flow cell, fluid extracted from the flow cell was directed to another container. For transport experiments with fluorescein, a reservoir with 60 mL of 1000 µg/L fluorescein was used, and extracted fluid was directed back to the reservoir. Triplicate transport experiments were conducted for each flow scheme. Between experiments, the flow cell was thoroughly flushed with Milli-Q water. Image Processing. All images were processed using the Kodak MI software 4.0 (Carestream Health, Inc., New Haven, CT). For experiments with the colorimetric reaction, the image of the packed flow cell saturated with 0.010 M

FIGURE 1. Calibration curves for MoTi24- (intensity loss vs mass) and fluorescein (intensity vs mass). Straight lines represent best linear-fit. Mass per pixel was obtained by dividing the total mass in the flow cell by the total number of pixels. (NH4)2Mo was used as the background. All images with MoTi24- present were then subtracted from the background using the Image Math function in the software, inverting the light intensity of the images for better visualization and easier subsequent image processing. The resulting images were then processed using software-generated ROIs (Regions of Interest) to isolate portions of the image whose intensity was greater than 500 (500-cutoff) and greater than 2300 (2300-cutoff, see examples in Figure S2 in the Supporting Information for the boundaries set by these cutoff values). The 500-cutoff (capturing over 95% of the total mass in the flow cell) was used to determine the size of the product (MoTi24-) distribution area, whereas the 2300-cutoff (corresponding to the boundary of the steepest intensity change) was used to represent the size of the interfacial area between the two plumes (Mo and Ti). For transport experiments with fluorescein, a cutoff value of 125 intensity levels (capturing over 90% of the total mass in the flow cell) was used to determine the size of fluorescein plumes.

Results and Discussion Calibrations. Light intensities are evenly distributed across the flow cell after illumination correction, so the mean intensity per pixel was used in calibration curves. For MoTi24-, light intensities decreased linearly as the amount of MoTi24in the packed flow cell increased from 0.00125 to 0.010 M. Therefore, light absorbance by MoTi24- was simply expressed as intensity loss obtained by subtracting raw image intensities from the background. Both MoTi24- calibration curves (expressed as intensity loss per pixel versus the mass of MoTi24- per pixel) show excellent linearity (r2 ) 0.983 and 0.974) in the range of the concentrations tested, with slightly more intensity loss (up to 30%) in the fine sand with respect to the medium sand (Figure 1). The calibration curve for fluorescein is also linear (r2 ) 0.999, Figure 1) in the concentration range tested. Enhanced Mixing under Oscillatory Flow. A few snapshots of the distribution of MoTi24- in the homogeneously packed flow cell are presented in Figure 2. MoTi24- formed rapidly at the interface between the molybdate solution originally present in the flow cell and the Tiron solution injected through the well(s) (Figure 2). As expected, the interface for the control exhibited a simple, narrow, ring-like structure. In contrast, the interface under oscillatory flow showed much more complex patterns as the flow direction and rate changed over time (Figure 2). The interfacial area under oscillatory flow increased rapidly for about 35 min

and then leveled off (Figure 3a, the dip around 75 min is the result of more MoTi24- being pumped out than being formed). In contrast, the interfacial area for the control increased rapidly only for the first 10 min and stayed relatively constant to about 60 min (Figure 3a). The slight increase after ∼60 min was caused by boundary effects as the flow approached the right side of the flow cell (Figure 2). After about 10 min, the interfacial area under oscillatory flow was consistently higher (average 2.2 times) than the interfacial area of the control (Figure 3a). This is in accordance with the chaotic advection theory which predicts that chaotic motion can stretch and fold the interface between two mixing fluids and significantly increase the interfacial area (38). The increased interface would provide more surface areas for solutes to diffuse, ultimately leading to enhanced mixing (39). The mass of MoTi24- within the interfacial area followed the same temporal trend as the interfacial area itself (cf. Figure 3a,b) and was also consistently higher (average 2.4 times) under oscillatory flow with respect to the control after about 10 min (Figure 3b). The mass of MoTi24- per area within the interfacial area was similar for the oscillatory flow (0.0109 ( 0.0010 mg/mm2) and the control (0.0102 ( 0.0005 mg/mm2), indicating that the increased amount of MoTi24- formed under oscillatory flow was mainly due to the increased interfacial area. Once MoTi24- was formed in the interface, it would be further distributed throughout the flow cell via advection and dispersion. The area of product distribution for the oscillatory flow experiments was again consistently higher (average 1.5 times) than that of the control after about 20 min (Figure 3c), albeit many data points are not considered statistically different (at 95% confidence level) due to the high standard deviations of the oscillatory flow experiments. The high standard deviations could be attributed to the fact that the three oscillatory flow experiments were not true replicates as the flow direction and flow rate were different (randomly generated for each experiment according to eq 1). Slight but variable changes in background illumination of the images may also have contributed to the large standard deviations on the total area (500-cutoff). The total mass of MoTi24- produced under oscillatory flow was about twice the mass of MoTi24- produced under constant flow (Figure 3d, notice that most data points are statistically different at 95% confidence level). Since MoTi24was formed as the direct result of mixing of Mo and Ti solutions, this result clearly demonstrated enhanced mixing in the homogeneously packed flow cell under oscillatory flow with respect to constant flow. A few snapshots of the distribution of MoTi24- in the heterogeneously packed flow cell (layered packing) are presented in Figure 4. For oscillatory flow, the interface of the Mo and Ti solutions in the layered packing showed even more complex patterns than that observed in the homogeneous packing (cf. Figures 2 and 4), presumably due to the refraction of flow between the boundaries of the fine and medium sand. For the control, the shape of interface in the layered packing was similar to that of the homogeneous packing, albeit the ring-like interface was slightly elongated in the horizontal direction due to a faster flow rate in the coarser sand layer in the middle. In fact, some boundary effects were evident at ∼50 min so the experiments had to be terminated at ∼60 min. After about 10 min, the interfacial area, mass of MoTi24- within the interfacial area, total area, and total mass of MoTi24- for the oscillatory flow experiments were all consistently higher than those of the control (Figure S3 in the Supporting Information). The difference in the extent of mixing between oscillatory flow and control in layered packing was even more pronounced than the difference in homogeneous packing. For instance, the ratio of the interfacial area between oscillatory flow and control (after 10 min) VOL. 43, NO. 16, 2009 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Snapshots of MoTi24- distribution over time in the homogeneously packed flow cell under time-dependent oscillatory flow (TDOF) and constant flow (control). Notice that MoTi24- was formed at the interface between the existing Mo solution and the injecting Ti solution. The approximate locations of the three wells are indicated as white dots on the last image.

FIGURE 3. Area and mass of MoTi24- distribution over time in the homogeneously packed flow cell: (a) area at 2300-cutoff; (b) mass at 2300-cutoff; (c) area at 500-cutoff; (d) mass at 500-cutoff. Error bars represent one standard deviation. Solid squares indicate that the area or mass for the time-dependent oscillatory flow (TDOF) is statistically higher (95% confidence level, see Table S1 in the Supporting Information for p-values associated with the t-statistic) than that of the control.

FIGURE 4. Snapshots of MoTi24- distribution over time in the heterogeneously packed flow cell under time-dependent oscillatory flow (TDOF) and constant flow (control). Dotted lines on the last image indicate the boundaries between the medium sand (20-30 mesh) in the middle and the fine sand (40-60 mesh) on the top and bottom. averaged 4.2 ( 0.9 for layered packing versus 2.2 ( 0.5 for homogeneous packing, and the ratio of the total MoTi24mass formed between oscillatory flow and control (after 10 min) averaged 3.2 ( 0.6 for heterogeneous packing versus 2.1 ( 0.4 for homogeneous packing. The refraction of flow at the boundaries of medium and fine sand under oscillatory flow appeared to cause even more mixing with respect to constant flow. Enhanced Plume Containment under Oscillatory Flow. Snapshots of the distribution of the fluorescent dye in the flow cell under oscillatory flow and constant flow (homogeneous packing) are presented in Figure 5. The size of the fluorescein plume under oscillatory flow is consistently 6286

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smaller (average 75%) than that of the control after about 10 min (Figure 6). For the control, well 1 (see Figure S1 in the Supporting Information for well locations) was constantly injecting and fluorescein was continuously pushed away from this well over the entire duration of the experiments (Figure 5). Although the extraction at wells 2 and 3 prevented the fluorescein from migrating toward the left side of the flow cell, fluorescein kept moving toward the right side of the flow cell (Figure 5). In this case, both advection and dispersion contributed to the enlargement of the fluorescein plume over time. In contrast, under oscillatory flow, fluorescein was pushed away from a particular well and then pulled back at this well as the flow direction reversed some time later. The

FIGURE 5. Snapshots of fluorescein distribution over time in the homogeneously packed flow cell under time-dependent oscillatory flow (TDOF) and constant flow (control). reductants for in situ redox manipulation or nutrients and electron acceptors for biostimulation) to effectively mix these compounds with contaminated groundwater. This technique could also be used to mix a contaminant plume depleted in electron acceptors with ambient groundwater rich in electron acceptors to promote attenuation of contaminants. Since chemical and biological reaction rates depend on the juxtaposition of reactants, these rates would consequently be more rapid under oscillatory flow. Therefore, oscillatory flow will likely accelerate aquifer remediation and reduce both exposure risks and cleanup costs. Improved plume containment under oscillatory flow will require smaller amounts of chemicals to be injected, further reducing costs for aquifer remediation. FIGURE 6. Area of fluorescein distribution (150-cutoff) over time in the homogeneously packed flow cell. Error bars represent one standard deviation. Solid diamonds indicate that the area for the control is statistically higher (95% confidence level) than that of time-dependent oscillatory flow (TDOF). net flow rate in each well was near zero over the duration of the experiments, i.e., advective transport of fluorescein through each well canceled out over time. Therefore, the enlargement of plume over time under oscillatory flow was mainly due to dispersion, not large-scale advection. It is noted that the better containment of injected solute plume under oscillatory flow does not conflict with enhanced mixing, as mixing is only occurring at the edges of an injected plume (cf. Figures 2 and 5). The plume size (solid white area in Figure 5) under oscillatory flow could be smaller with respect to constant flow, but the mixing zone (ring-like structure in Figures 2 and S2 in the Supporting Information) could be much larger. Implications for Aquifer Remediation. Results from the small scale experiments clearly demonstrated enhanced mixing of solutes under low Reynolds number oscillatory flow (a factor of 2 with respect to constant flow in homogeneous sand and a factor of 3 in layered sand), as the result of increased interfacial areas for diffusion. Further, the injected solute plume was better contained under oscillatory flow (25% less area with respect to constant flow in homogeneous sand) due to the cancellation of advective transport at each well over time. While more studies (e.g., larger scale, 3-dimensional flow fields, more complex heterogeneity, etc.) are needed to further exploit the oscillatory flow methodology, some postulations could be made regarding the potential of this technique for enhanced aquifer remediation. Extending oscillatory flow to the third dimension will increase the plume interfaces in the vertical dimension and will lead to additional mixing. It will also provide the opportunity to pump from different levels (packer intervals) in the wells, which will further increase mixing. Introducing more complex heterogeneity would likely lead to more spreading and stretching of solute plume interfaces (4) due to flow refraction and possibly flow focusing (40), resulting in more mixing. The oscillatory flow technique could be used in aquifer remediation where compounds are injected (e.g., chemical

Acknowledgments This work was partially funded by a PSC-CUNY grant. Constructive comments from three anonymous reviewers are greatly appreciated.

Supporting Information Available Schematic diagram of the flow cell (Figure S1), examples of boundaries set by various cutoff values (Figure S2), area and mass of MoTi24- distribution over time in the heterogeneously packed flow cell (Figure S3), p-values associated with the t-test (Table S1), and Reynolds number and Peclet number estimation. This material is available free of charge via the Internet at http://pubs.acs.org.

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