Environ. Sci. Technol. 2003, 37, 4481-4486
Application of Waves for Remediation of Contaminated Aquifers AMIT GROSS,† ALEXEY BESOV,‡ DAMIANA DIAZ RECK,† S H A U L S O R E K , * ,†,§ G A B I B E N - D O R , § ALEXANDER BRITAN,§ AND EUGENE PALCHIKOV‡ Department of Environmental Hydrology & Microbiology, Institute for Water Sciences and Technologies, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev Sede Boqer Campus, 84990, Israel, Lavrentyev Institute of Hydrodynamics, Novosibirsk, 630090, Russia, and Department of Mechanical Engineering, Pearlstone Center for Aeronautical Studies, Ben-Gurion University of the Negev, Beer Sheva 84105, Israel
A theory developed suggested that significant displacement of solute in saturated porous media results from the propagation of compression waves. Four independent onedimensional experimental setups and a variety of laboratory methods were used to confirm the predictions of the theory, specifically aimed at developing a novel method of inducing compression waves for use in remediation of contaminated aquifers. Compaction and shock waves were emitted through granular porous media saturated with saline water. The changes in solute concentration at observation points along the propagating wave were used to verify the validity of theory. The first setup was designed mainly to provide a qualitative assessment (i.e., changes in pressure due to the propagating wave were not recorded). In situ quantitative measurements of the pressure and electrical conductivity profiles along a sand column were done with the second and third experimental setups, respectively, to short and long shock waves. In the fourth setup, solute displacement was visualized by X-ray absorption. The findings were consistent with the theory in all experimental setups.
Introduction Aquifers are often contaminated by various sources such as pesticides and fertilizers from agricultural runoff, wastewater from domestic and/or industrial spills, and contamination due to the mishandling of oil products. Restoration of contaminated aquifers makes use of complicated processes, and in most cases the achievement of complete reclamation is impossible. In recent years, we had developed the theoretical basis for wave propagation in multiphase deformable porous media (e.g. refs 1-3), following an abrupt pressure change. This is expressed in the form of macroscopic balance equations of mass, momentum, and energy for * Corresponding author phone: 972 (0)8 6596902; fax: 972 (0)8 6596909; e-mail:
[email protected]. † Institute for Water Sciences and Technologies, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev. ‡ Lavrentyev Institute of Hydrodynamics. § Department of Mechanical Engineering, Pearlstone Center for Aeronautical Studies, Ben-Gurion University of the Negev. 10.1021/es026297d CCC: $25.00 Published on Web 08/28/2003
2003 American Chemical Society
compressible Newtonian fluids within a thermoelastic solid matrix. In ref 4 we demonstrated the superiority of this theory over various other models appearing in the literature. The basis of our mathematical modeling (1) is in averaging the microscopic balance equations over a representative elementary volume yielding macroscopic representation of these equations, accounting for the interaction between fluid and solid phases and the solute being transported through the porous medium. Nondimensional analysis (1) of the phases’ macroscopic balance equations yields four evolution periods governed by different dominant balance equations of the phases. During the second evolution period, the fluid momentum balance equation conforms to a nonlinear wave equation. In ref 2 we followed a similar procedure accounting also for solute migration, demonstrating that during the second evolution period solute is being displaced by compression waves even if the fluid is almost stagnant. The onedimensional (1D) formulation conforms to a pressure traveling wave equation accounting for the fluids mass and momentum equations decoupled from the solute transport equation. The latter is excited by a source-like term obtained after solving the pressure wave. Based on the theory (2), a simple analytical solution (5) of the 1D case was developed, for a range of various physical parameters such as different matrix stiffness and adsorption. The analytical solution predicts (Figure 1) significant withdrawal of solute in response to introduction of an expansion wave (associated, e.g., with pumping) or inward displacement of the solute due to the action of a compaction wave (associated, e.g., with injection). In the case of the compaction wave, we note significant displacement of mass that is accumulated in the direction of propagation while decrease of the solute mass at preceding depth, while maintaining mass balance. The unique significance of introducing pressure waves into an aquifer as well as its economic potential is in the ability to focus on cleaning groundwater at localized sites; mobilize trapped contaminants; and guide the motion of a contaminant plume by controlling the intensity and direction of the applied pressure. Following our theoretical findings (2, 5), the aim of this study was to qualitatively validate the theory (1) and its analytical 1D solution (5) through 1D experimental setups.
Materials and Methods Based on the theoretical model and its analytical solution, the theory was experimentally tested in four independent setups and a variety of laboratory methods, described below. First Setup. The apparatus was composed of two compartments (Figure 2): The first was a cylindrical pressure chamber 60 cm long and 10 cm in diameter. The top cover of the cylinder was connected by tubing to a high-pressure tank of nitrogen gas. A pressure gauge was located on the chamber’s sidewall and a membrane covered its bottom. The second compartment was a PVC tube (“shock tube”) 80 cm long and 1.5 cm in diameter, filled with quartz sand (Table S1, Supporting Information). The shock tube was connected to a water supply and to the pressure chamber via a valve. Three 13-mm filter holders were attached 20, 40, and 50 cm from the top of the tube. Syringes of 5 mL were inserted into each filter holder. The lower end of the tube was supported with a 200 µm screen to allow water flow. Experimental Procedure. The sand in the shock tube was saturated with a saline solution of known concentration, and continuous flow was maintained through it. After displacement of 2-3 pore volumes, the salinity was similar in all the measuring stations and was recorded as the initial VOL. 37, NO. 19, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. An example to the dimensionless graphic results of the 1D analytical solution (5) for both expansion waves (A) and compression waves (B). C0 denotes initial solute concentration prior to application of abrupt pressure change. “t” denotes time level postapplication of abrupt pressure change.
FIGURE 2. Experimental apparatus used as the first setup for generating abrupt pressure changes through a saturated porous medium. salinity. The salinity was measured in terms of electrical conductivity (EC) (corresponding to solute concentration) with an EC meter (CDM210 Radiometer, Copenhagen). The water flow was then stopped, the valve between the pressure chamber and the shock tube was opened, and pressure was emitted into the pressure chamber. After the membrane broke (when the pressure reached 1.2-2.0 atm in the chamber), the valve between the pressure chamber and the tube was immediately closed, samples were withdrawn with the syringes, and the EC was measured. The elapsed time between the water flow cutoff and the sampling did not exceed 30 s. The experiment was replicated 7 times with a range of salinities between 200 and 10 000 ppm NaCl. We repeated the procedure with uranine, a water-soluble fluorescent dye, and measured the fluorescence in an SFM 25 fluorometer (Kontron Instruments Zurich, Swiss). The initial concentration of the uranine was 0.25 mg/L, equal to 40 fluorescence units of the fluorometer (excitation at 450 nm, emission 400 nm). This experiment was replicated 7 times. The same procedure was repeated 4 more times but without the plastic membrane that separated the pressure chamber from the shock tube. This was to verify that the abrupt pressure change is the trigger causing the changes in the solute concentration. The latter experiment was repeated with a moderate change in the pressure to establish a control experiment. A statistical “t” test was used to compare the absolute changes in the concentration in these control 4482
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FIGURE 3. The shock tube and peripheral accessories used in the second setup. The shock wave was generated by the abrupt release of a magnetic field. Electrical conductivity was measured at channels located at various distances from the bottom of the saturated sand medium. Index numbers are as follows: 1. metal wall of the tube; 2. saturated sand; 3. upper surface of sand; 4. electrical conductivity gauge or pressure gauges; 5. electromagnetic shock-wave generator; 6. sine-wave generator; 7. decoupling transformer; 8. receiving transformer; 9. amplitude detector with doubling, which converts the amplitude of the alternating voltage of the signal to direct voltage of positive polarity; 10. noninverting operational amplifier; 11. output terminal; 12 and 13. compensating amplifiers; 14. input to a recorder. experiments with the absolute changes after an abrupt change in the pressure at each sampling station. Second Setup. A 250-mm metal column (40 mm diameter) filled with saturated sea sand (average grain size 0.8 mm) was attached to an electrical shock wave generator located at the bottom of the column (6). A membrane was accelerated by a pulsed magnetic field to generate the shock wave. Three electrical conductivity (EC) gauges (details in the subsequent Discussion section) were located in the column (Figure 3) along the direction of wave propagation. Saturated sand was introduced into the column in a manner that minimized the possibility of accumulation of trapped bubbles between the sand grains. The final accumulated volume of air in the tube did not exceed 0.2% of the total column volume, as determined by measuring the speed of sound in the saturated column. Similarly to the first setup, the saline solution was not flowing through the column during the application of the shock waves or during the following EC measurements. Experimental Procedure. Forty short high-pressure shock waves (∼70 atm), traveling at the speed of sound in the saturated sand mixture (>1500 m/s), were applied every 30 s, and the EC was recorded every 60 µs at all three locations throughout the experiment with a ACL8112 ADLINK record-
FIGURE 4. Seven replications of the first setup, using NaCl. The NaCl concentration was measured as electric conductivity (including standard errors) at four sampling stations along the shock tube’s length. ing device. EC changes relative to the initial EC were calculated. Third Setup. The third setup (Figure S1, Supporting Information) was a simple shock tube, 5-m long (40 mm diameter) composed of two sections: (A) a 2.5 m long highpressure tube that was separated from (B) the low-pressure tube by an instant-opening pneumatic valve with an electric starter (ISTA Inc. Petersburg, Russia). Detailed description of the setup can be found in the section “Third setup”, Supporting Information. Experimental Procedure. Air pressure was increased to 8 atm in the high-pressure chamber before releasing the instant-opening electrical valve. This created a shock wave that propagated downward through the low-pressure tube. Immediately, after the application of the shock, the pressure was released from the entire shock tube. Then the pressure chamber was repressurized and another shock was applied. Each EC measurement was made after five applications of shocks. The total number of shock applications was 40-60. The time between consecutive shocks (loads) did not exceed 3 min. Fourth Setup. Sea sand with an average grain size of 0.8 mm was mixed with potassium iodide (KI) solution at a concentration of 50 g/L. The saturated sand was placed in a shock tube similar to the one described for the second setup, and the initial distribution of the KI was examined by X-ray absorption (7). Four shock loadings were emitted through the tube, and a second X-ray photo was taken
FIGURE 5. Seven replications of the first setup, using uranine. The uranine concentration was measured as fluorescence units (including standard errors) at four sampling stations along the shock tube’s length. immediately afterward. The X-ray photos were digitized, and the gray scale intensities were reclassified on a 20 colors scale using Erdas Imagine geographic imaging software (8). The spread of KI through the column before and after the shock wave applications was determined and compared (8).
Results and Discussion Following refs 1 and 2, our experiments were conducted to verify whether solute displacement is plausible upon introducing compaction waves into a tube of saturated porous medium. Several processes affect the extent of solute displacement and the ability to detect it: (1) the steepness of the pressure gradient, (2) the amplitude of the pressure rise, (3) the solute concentration, (4) the elapsed time between pressure excitation and EC measurement, and (5) the location of the measuring stations. Since the measurements were not temporally and spatially continuous along the propagated wave, it was difficult to capture the instant in-situ changes in solute concentration. Moreover, to install such continuous measurements was technically impossible. Hence, the phenomenon was demonstrated in four different setups using a variety of methods. This approach minimized the possibility of artifacts. First Setup. The experiments resulted in a significant change in solute concentration compared with the control study. In most replicates, the solute concentration decreased at the first measuring station (channel 1, Figures 4 and 5) and increased at the second and/or third measuring station. VOL. 37, NO. 19, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 7. Typical pressure change at the measurement channels after application of a shock wave in the second setup.
FIGURE 6. Uranine concentration, as measured fluorescence units, at four sampling stations along the shock tube after application of continuous pressure of 1.5 atm (with no abrupt change in pressure).
TABLE 1. Average Absolute Change and Range of Change in NaCl and Uranine Concentrations after Abrupt Increase in Pressure in a Tube Containing Saturated Porous Mediuma location
solute
range of percent concn change
average concn change ( StE
20
NaCl uranine control NaCl uranine control NaCl uranine control
0.3-10.0 1.8-26.0 0.0-1.0 -1.1-15.3 0.3-10.7 0.3-2.1 -9.2-1.5 0.0-10.0 0.0-2.0
3.2 ( 1.6 7.6 ( 2.4 0.3 ( 0.2 3.3 ( 2.3 5.4 ( 1.7 1.0 ( 0.4 2.6 ( 1.6 4.2 ( 2.0 0.8 ( 0.3
40 50
a Samples were taken from three locations down the tube (20, 40, and 50 cm below the surface of the sand) before and after the abrupt change in pressure, and the percent difference was calculated. In “control” experiments the change in uranine concentration was measured after a slow pressure increase, with no abrupt pressure change.
Similar patterns were found for both NaCl and uranine. This pattern of solute displacement was in line with the theory predictions (Figure 1), in which there is a displacement of mass that is accumulated in the direction of propagation while decrease of the solute mass at preceding depth. An argument can be made that the lessening of salinity (at channel 1) near the point at which pressure originated was due to downstream advection of water parcels, while solute adhered to or was caught in the granular matrix. However, we noted less salinity at the first measuring station and, at times, accumulation downstream (Figures 4 and 5). This indicates that solute was shifted, rather than parcels of saline water. Moreover, in the control study we applied high pressure without executing an abrupt pressure rise and found no significant change in EC throughout the column (Figure 6). These findings support the theory that an abrupt pressure change is necessary to cause the displacement of solute. The differences in solute concentration (Table 1) ranged from 0.3% to 10% (positive or negative changes indicate withdrawal or accumulation, respectively) for NaCl and 1.8% 4484
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to 26% for uranine at the first measuring station. The average difference was 3.2% and 7.6% for NaCl and uranine, respectively. At the second measuring station, the change in NaCl concentration ranged between 1.1% and 15.3% with an average of 3.3%, and for uranine between 0.3% and 10.7% with an average of 7.6%. At the third measuring station, the change in NaCl concentration ranged between -9.2% and -1.5% with an average of -2.6%, and for the uranine it ranged from 0% to -10% with an average of -4.2%. As expected, the EC changes in the control experiment were minor, indicating that solute displacement occurs only after an abrupt pressure change. The main drawback with this setup was that we could not follow the profile of the propagating pressure change in the shock tube. Nevertheless, using a membrane, we managed to generate an abrupt change of pressure assumed to propagate as a sharp front. Second Setup. A short shock wave is suitable for small laboratory installations, since the propagation distance (which is usually not more than 10-20 wavelengths of the shock) has a limited effect. In the second experimental setup (Figure 3) the short shock wave propagated toward the free surface of the wet sand (Figure 3, index 3) and passed the measuring gauges (Figure 3, index 4). The pressure profile of the shock wave was recorded with custom-made piezoelectric transducers (9) located along the shock tube (Figure 3, index 4). The shock wave characteristics shown in Figure 7 demonstrate that the wave velocity between the second and third channels was higher than between the first and second channels. Upon entering the tube, the shock wave travels through the sand matrix and propagates, after several shocktube diameters, into the tube’s metal walls at a speed exceeding 5000 m/s, which is higher than its speed in the saturated sand (approximately 1500 m/s). Since the wave reflects back into the sand from the wall, we note that it travels faster between the second and third channels. Moreover, the loss of wave energy due to its travel through the wall is indicated (Figure 7) by a 50% decrease in the shock wave amplitude and a deformed shape at a distance less than three tube diameters. This phenomenon, however, did not affect the changes and direction of solute displacement, as proposed by the theory (2) and Figure 1, and shown in Figure 8. Since the water remained stagnant, the argument of displacing water parcels due to application of the wave cannot apply. Besov and Kedrinskii (9) demonstrated that the reproducibility of pressure amplitude and shape was greater than 98%. It was therefore possible to replace the piezoelectric transducers with electrical conductivity gauges and to record the salinity profile. Changes in the solute concentration were minor after one application of the shock wave, and therefore more shocks were applied. The observed EC in the first channel increased slightly and then decreased as the numbers of loads increased and salt was displaced in the direction of the wave. The same
FIGURE 8. Cumulative relative (to the initial level) changes in electric conductivity at the different channels after a set of shock wave emissions in the second setup. Channels 1, 2, and 3 were located 5.5, 12.5, and 18.5 cm, respectively, from the shock source. phenomenon is shown in the second and third channels, except that the maximum change in the solute conductivity was less than at channel number 1. Salinity measurements made by withdrawing liquid from the tube (as performed in the first setup) are problematic because of the minimum volume (5-10 mL) of water needed for external EC measurements. We found that the maximum volume of water that can be withdrawn with a syringe from the saturated sand is approximately 10% of the saturated sand volume because of surface tension. Point-wise syringe measurement for the second and third setups was not feasible, since a withdrawal of 10 mL would affect 8-cm length of the sand column (assuming an effective porosity of 40%).
We are not aware of means to allow instant direct in-situ measurement of salt concentrations in water. We therefore used in-situ EC measurements, since the range of salinities used in the experiments is linearly correlated with the EC. The EC meter that was used was based on application of constant-amplitude voltage between two electrodes and measured the EC as the change in electric current between the electrodes. In situ EC measurements along a metal shock tube can cause several difficulties: (a) both electrodes must be disconnected from ground to prevent electrical shorts; (b) electrodes can become coated by impurities in the water when an electrical current is applied for a prolonged time; and (c) compaction and rearrangement of the sand grains as well as the appearance of bubbles can also affect EC measurements. To circumvent these phenomena we used, respectively, the following procedures: (a) Differential electric amplifiers prevented electrical shorts. (b) Application of a voltage difference with a frequency of 25 kHz eliminated coating of the electrodes and extended the area from which EC could be recorded. (c) Compaction of the granular medium (quartz sand) was assumed negligible after several applications of the shock waves. Moreover, X-ray visualization suggested that changes in the porous medium’s volume are negligible after application of four sequential shock waves with a pressure of 65 atm (see below). The formation of microbubbles and their effect could not be evaluated in this setup. The first and forth setups were based on direct salinity measurements (i.e. withdrawal of solution from the tube)
FIGURE 9. A. X-ray photo of shock tube containing a practically uniform distribution of potassium iodide (KI) salt along the center axis (red area), before application of shock wave. B. X-ray photo of the shock tube after application of four shock waves (shock wave propagated from left to right). The displacement of KI in the direction of the propagating wave is demonstrated by the intensity of the colors (see scale) near the source of the shock wave (left). C. Displacement of KI along the central axis of the tube postapplication of shock waves. VOL. 37, NO. 19, 2003 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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and spectral methods (i.e. fluorescence and X-ray visualization) that were not affected by possible formation of micro bubbles. Third Setup. Long shock waves are suitable for field applications, because their influence extends to longer distances, and therefore they were tested in this setup. Changes in salt concentration along the shock tube in the third setup were generally consistent in pattern and magnitude (Figure S1A, Supporting Information) with the results obtained with the second setup (Figure 8). However, some of the patterns of change in EC, obtained under presumably similar initial conditions (salinity, pressure conditions, sand arrangement, etc.), deviated (Figure S2B, Supporting Information) from the expected pattern. It is possible that the cause for the deviation was that the sand was not replaced between trials, and the initial conditions were actually not so similar (e.g., possible adsorption on the sand grains). Fourth Setup. Based on the absorption of X-rays by heavy ions (7), iodide (atomic number 53) was used to evaluate relative changes in the distribution of the KI solute concentration. Because of the cylindrical geometry of the tube, X-ray absorption is not uniform crossing the diameter of the tube. We, therefore, analyzed the intensity distribution along the central axis of the tube (Figure 9C). Figure 9A depicts that, before application of the shock wave, the distribution of KI along the center of the column (red color) was fairly uniform. After the application of four shocks, KI was displaced in the direction of the propagating wave, as described in Figure 9B. This is indicated by less X-ray absorption where the shocks were applied, indicating a lower KI concentration. Figure 9C delineated the solute shift along the central axis of the tube prior and postapplication of the wave. It can be seen that the KI was displaced about 3.5 cm in the direction of the propagating wave where there was a decrease in KI concentration near the source of the shock wave (left-hand side) and some accumulation toward the far end of the tube (right-hand side). Mass balance was confirmed by calculating the intensities throughout the whole cross section area of the tube; we note that the total intensity was similar prior
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and postapplication of the shock waves, suggesting no loss of the KI mass.
Acknowledgments The authors gratefully acknowledge the assistance of Vladimir Shlimak and Moshe Poizner from the Ben-Gurion University of the Negev, Israel for the design and construction of the shock tube of the third setup and to Dr. Arnon Karnieli and his team, Ben-Gurion University of the Negev, for their assistance in processing the X-ray photos.
Supporting Information Available Properties of the sand that was used in the first setup (Table S1), detailed description and photo (Figure S1) of the third setup, and its performance in displacing salt postapplication of shock wave (Figure S2). This material is available free of charge via the Internet at http://pubs.acs.org.
Literature Cited (1) Bear J.; Sorek S. Transp. Porous Media 1990, 5, 169-185. (2) Sorek, S. Transp. Porous Media 1996, 22, 271-285. (3) Levy, A.; Sorek, S.; Ben-Dor, G.; Bear J. Transp. Porous Media 1995, 21, 241-268. (4) Sorek, A.; Levy, G.; Ben-Dor, G.; Smeulders, D. Transp. Porous Media 1999, 34, 63-100. (5) Burde, I. G.; Sorek, S. In Computational Methods in Water Resources, Proceedings of the XIII Interence Conference, Bentley, L. R., Sykes, J. F., Brebbia, C. A., Gray, W. G., Pinder, G. F., Eds.; 2000; Vol. 1, pp 339-344. (6) Besov, A. S.; Berngardt, A. R.; Kedrinskii, V. K.; Pal’chikov, E. I. J. Acoust. Soc. Am. Suppl. 1985, 1(77). (7) Palchikov, E. I.; Sukhinin, S. V.; Besov, A. S.; Akhmetov, D. G.; Kondratenko, D. A. X-PMFLAGS: 34078848 0 “iso-8859-1” National Library of Scotland Legal Deposit and Donations Unit 31, Salisbury Place, Edinburgh EH9 1SL, Scotland, UK, 1998. (8) Erdas. Erdas Imagine geographic imaging software 8.5, Erdas Inc., Atlanta GA, 2001. (9) Besov, A.; Kedrinskii, V. Proceedings of Bubble Dynamics and Interface Phenomena, Birmingham, UK, 1994.
Received for review November 3, 2002. Revised manuscript received April 29, 2003. Accepted July 14, 2003. ES026297D
