Experimental and Numerical Validation of the Total Trapping Number

Received April 09, 2007. Revised manuscript received Sep- tember 18, 2007. Accepted September 20, 2007. The total trapping number (NT), quantifying th...
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Environ. Sci. Technol. 2007, 41, 8135–8141

Experimental and Numerical Validation of the Total Trapping Number for Prediction of DNAPL Mobilization YUSONG LI,† LINDA M. ABRIOLA,† THOMAS J. PHELAN,‡ C. ANDREW RAMSBURG,† AND K U R T D . P E N N E L L * ,§,| Department of Civil and Environmental Engineering, Tufts University, 200 College Avenue, Medford, Massachusetts 02155, Geosyntec Consultants, 289 Great Road, Suite 105, Acton, Massachusetts 01720-4766, School of Civil and Environmental Engineering, Georgia Institute of Technology, 311 Ferst Drive, Atlanta, Georgia 30332-0512, and Department of Neurology, Emory University School of Medicine, 615 Michael Street, Atlanta, Georgia 30322

Received April 09, 2007. Revised manuscript received September 18, 2007. Accepted September 20, 2007.

and (b) reduce the interfacial tension (IFT) between the nonaqueous and aqueous phases, facilitating immiscible DNAPL displacement or “mobilization” (7). Mobilization holds potential for more efficient removal of contaminant mass (8, 9), particularly in source zones containing regions of high DNAPL saturation. The implementation of low-IFT surfactant-based remediation strategies, however, requires careful design to avoid uncontrolled downward migration of mobilized DNAPL and to minimize DNAPL entry into lowerpermeability media (10–12). Regardless of the specific remediation design objective, the ability to predict the onset of DNAPL mobilization and subsequent migration of mobilized DNAPL is essential. At the pore scale, capillary forces act to retain entrapped NAPL ganglia, while viscous and gravity forces may act to promote displacement. Pennell et al. (7) derived a dimensionless total trapping number (NT) expression that quantifies this force balance NT ) √NCa2 + 2NCaNB sin R + NB2 where, the capillary number (NCa) is defined as NCa )

The total trapping number (NT), quantifying the balance of gravitational, viscous, and capillary forces acting on an entrapped dense nonaqueous phase liquid (DNAPL) droplet, was originally developed as a criterion to predict the onset and extent of residual DNAPL mobilization in porous media. The ability of this approach to predict mobilization behavior, however, has not been rigorously validated in multidimensional systems. In this work, experimental observations of residual tetrachloroethene (PCE) mobilization in rectangular columns are compared to predictions obtained using a multiphase compositional finiteelement simulator that was modified to incorporate the dependence of entrapped residual, flow, and transport parameters on the total trapping number. Consistent with calculated NT values (1.21 × 10-3–1.10 × 10-2), residual PCE-DNAPL was mobilized immediately upon contact with a low-interfacial tension (IFT) surfactant solution and rapidly migrated downward to form a bank of mobile DNAPL. The numerical model accurately captured the onset and extent of PCE-DNAPL mobilization, the angle and migration of the DNAPL bank, the swept path of the surfactant solution, and cumulative PCE recovery. These findings demonstrate the utility of the total trapping number for prediction of DNAPL mobilization behavior during low-IFT flushing.

Introduction Surfactant-enhanced aquifer remediation (SEAR) has been demonstrated to be an efficient remediation technology for removal of dense nonaqueous phase liquids (DNAPLs) from the subsurface (1–4). Surfactants can be used to (a) increase the aqueous-phase solubility of DNAPL constituents, a process commonly referred to as micellar solubilization (5, 6), * Corresponding author phone: 404-894-9365; fax: 404-894-8266; e-mail: [email protected] or [email protected]. † Tufts University. ‡ Geosyntec Consultants. § Georgia Institute of Technology. | Emory University School of Medicine. 10.1021/es070834i CCC: $37.00

Published on Web 11/03/2007

 2007 American Chemical Society

(1)

qaµa σan cos θ

(2)

and the Bond number (NB) is defined as NB )

∆Fgkkra σan cos θ

(3)

Here qa is the Darcy velocity of the aqueous phase (positive upward) [L/t], R is the angle of flow relative to the horizontal, µa is the dynamic viscosity of the aqueous phase (M/L t), σan is the IFT between the aqueous and nonaqueous phases [M/t2], θ is the contact angle between the aqueous/nonaqueous interface and the porous medium (deg), ∆F is the density difference between the aqueous and nonaqueous phases [M/L3], g is the gravitational constant [L/t2], k is the magnitude of the intrinsic permeability tensor of the isotropic porous medium [L2], and kra is the relative permeability to the aqueous phase. Equation 1 reduces to NT ) √NCa2 + NB2 for horizontal flow (R ) 0°) and NT ) |NCa + NB| for vertical flow (R ) 90°). In one-dimensional column experiments, the onset of DNAPL mobilization corresponded to NT values ranging from 2 × 10-5 to 5 × 10-5, while complete ganglia displacement was observed at NT values approaching 1 × 10-3 (7). These critical NT values are similar to the threshold NCa values reported for oil desaturation curves in the absence of buoyancy effects (13), supporting the consistency of the total trapping number approach with previous work reported in the petroleum literature. The total trapping number provides a unique criterion for a priori prediction of residual DNAPL mobilization and has been used in the design and interpretation of surfactant floods at both the laboratory and field scales (14, 15). Furthermore, quantification of capillary, viscous, and buoyancy forces has been key to the development of novel remediation techniques based on DNAPL mobilization, including the surfactant gradient approach (16), dense brine injection (17), and density modified displacement (10, 18). To facilitate remedial design and system performance predictions, the total trapping number has been incorporated into compositional multiphase flow simulators (19, 20). VOL. 41, NO. 23, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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TABLE 1. Relevant Properties of 20–30 Mesh Ottawa Sand and Wurtsmith Aquifer Material soil property

Wurtsmith aquifer material

20–30 mesh Ottawa sand

mean grain size, d50 (mm) intrinsic permeability, k (m2) solid density, Fs (g/cm3) organic carbon content, foc (% wt.) Van Genuchten R (1/Pa) Van Genuchten n estimated residual aqueous phase saturation, Sar estimated maximum residual PCE saturation, Snr linear PCE sorption coefficient, KD (mL/g)

0.35 4.2 × 10-11 2.65 0.02 1.67 × 10-4 5.31 0.125 0.15 0.17

0.71 3.9 × 10-10 2.65 nd 9.59 × 10-4 7.42 0.07 0.12 0.08

TABLE 2. Flushing Parameters, Dimensionless Analysis, and PCE Recoveries for the Wurtsmith (WS-1) and Ottawa Sand (OS-1 and OS-2) Displacement Experiments displacement experiment experimental parameter porosity, φ total pore volume, pv (mL) initial PCE-DNAPL saturation, Sn (%) effective aqueous-phase permeability, ke (m2) aqueous phase flow rate, Qa (mL/min) aqueous phase Darcy velocity, qa (cm/min) capillary number, NCa bond number, NB total trapping number, NT angle of mobilization, τ PCE recovered as NAPL (mL) PCE recovery as NAPL (% vol)

Although these numerical models have been used to simulate surfactant floods at laboratory and field scales (21, 22), their implementation of the total trapping number concept to predict DNAPL mobilization behavior has not been rigorously tested. The objective of this study was to evaluate the utility of the total trapping number concept by directly comparing predictions of the theory to observations from well-controlled, two-dimensional DNAPL displacement experiments. The total trapping number concept was implemented in a multiphase compositional simulator, the Michigan subsurface environmental remediation (MISER) model (23, 24) that has been extensively validated for applications to surfactantenhanced solubilization (15, 25). Low-IFT mobilization experiments were conducted in horizontal rectangular glass columns containing uniform distributions of residual DNAPL. Comparisons of observed displacement fronts and effluent recovery data with numerical simulations of the mobilization are used to explore the validity of the total trapping number approach.

Laboratory Experiments Materials and Methods. Three displacement experiments were conducted in rectangular glass columns with internal dimensions of 14.8 cm (length) × 5.2 cm (height) × 2.6 cm (width). Two columns (experiments OS-1 and OS-2) were packed with 20–30 mesh Ottawa sand (U.S. Silica) and one column (experiment WS-1) was packed with aquifer material obtained from Wurtsmith Air Force Base located in Oscoda, MI. Relevant properties of the two porous media are summarized in Table 1. Tetrachloroethene (PCE) (99.5%+, Sigma Aldrich) was selected as the DNAPL because of its prevalence at contaminated sites and its relatively large density contrast with water. At 20 °C, PCE has a liquid density of 1.625 g/cm3, a dynamic viscosity of 0.89 cP, an aqueous solubility of 200 mg/L, and an interfacial tension with water of 47.8 dyne/cm (7, 36). To facilitate visual observation, PCE8136

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WS-1 0.38 76.0 12.9 1.72 × 0.96 0.07 4.54 × 1.12 × 1.21 × 67.9 9.92 101.4

10-11 10-4 10-3 10-3

OS-1 0.36 71.2 12.4 1.76 × 0.96 0.07 4.54 × 1.15 × 1.15 × 87.7 9.30 105.2

10-10 10-4 10-2 10-2

OS-2 0.36 72.3 13.8 1.64 4.95 0.36 2.33 1.07 1.10 77.7 9.07 91.2

× 10-10 × 10-3 × 10-2 × 10-2

DNAPL was dyed with Oil-Red-O (Fisher Scientific), an organic-soluble dye, at a concentration of 1 × 10-4 M. In previous studies, the addition of Oil-Red-O to PCE at this concentration has been shown to have no significant effect on the viscosity, interfacial tension, and density of PCE (7). The surfactants, sodium diamyl sulfosuccinate (Aerosol AY) and sodium dioctyl sulfosuccinate (Aerosol OT), were obtained from American Cyanamid (now Cytec) and were used as received from the manufacturer. All aqueous surfactant solutions were prepared with distilled water that had passed through a Nanopure analytical purification system (Barnstead/Thermolyne Corp.). The rectangular columns were packed with either air-dry Ottawa sand or Wurtsmith aquifer material. A uniform residual saturation of PCE-DNAPL was established following the procedures described in ref 7 (see Supporting Information, Experimental Methods). The columns were oriented horizontally and flushed with an aqueous solution consisting of a 4% (wt) 1:1 mixture of Aerosol AY and Aerosol OT containing 500 mg/L of CaCl2. The liquid density of the 4% Aerosol AY/OT solution at 20 °C was determined to be 1.03 g/cm3 using calibrated 25 mL glass pycnometers (Ace Glass). The dynamic viscosity of the 4% Aerosol AY/OT solution was determined to be 3.5 cP at 25 °C and a shear rate of 200 s-1 using a Rheostress R-75 rheometer (Haake). At 22 °C, the 4% 1:1 Aerosol AY/OT solution has an apparent PCE solubility of 71 720 mg/L and an IFT with PCE of 0.09 dyne/cm (9). The critical micelle concentration of Aerosol AY/OT was calculated to be approximately 1200 mg/L (27). Experimental conditions for each column, including the capillary, bond, and total trapping numbers, are summarized in Table 2.

Numerical Model Development Numerical simulations were conducted using a modified version of an existing two-dimensional Galerkin finite element multiphase compositional simulator, MISER (23, 24).

This model solves a coupled system of flow and species transport equations, incorporating the effect of temporally and spatially variable phase composition on multiphase flow parameters (e.g., capillary pressure-saturation, relative permeability, density). For this work, the trapping number concept was implemented in MISER to predict the onset of DNAPL mobilization and to quantify the relation between NT and the multiphase flow constitutive equations. To improve model performance under low-IFT conditions, a mixed method approach (28) was implemented in MISER to solve the pressure-based phase mass balance equations, and near-zero capillary pressures were replaced by a linear function with very small capillary pressure values to maintain numerical stability thereafter (29). Trapping Number Implementation. The value of NT was computed using eq 3, with IFT represented as a linear function of surfactant concentration below the CMC. In previous implementations, NT has been correlated with DNAPL residual saturation, based on experimental data for n-decane (19) or on a critical NT value of 5 × 10-5 and a maximum residual DNAPL saturation for a hypothetical water–DNAPL system when NT ) 0 (20). Experimental data from ref 7 were used to derive a functional relationship between NT and DNAPL residual saturation by fitting the following expression to measured PCE-DNAPL desaturation data for each sand type min max min Snr ) Snr + (Snr - Snr )[1 + (T1NT)T2]1⁄T2–1

(4)

max the residual where Snr is the residual DNAPL saturation, Snr min DNAPL saturation before mobilization, Snr is the residual DNAPL saturation after full mobilization, and T1 and T2 are fitting parameters. In eq 4, T1 controls the onset of DNAPL mobilization; as T1 decreases, mobilization occurs at a higher NT. T2 controls the desaturation curve shape; a higher T2 is associated with a steeper desaturation curve (Table S1, max Supporting Information). To implement eq 4 in MISER, Snr was assumed to be equal to the initial DNAPL saturation, min was assumed to be equal to 0.015, which represents and Snr the observed residual saturation at complete mobilization (7). Parameter fits for PCE-DNAPL desaturation in 20–30 mesh Ottawa sand were directly used for the Ottawa sand experiments (T1 ) 1.31 × 104 and T2 ) 7.81), while parameters for the Wurtsmith aquifer material (T1 ) 2.17 × 104 and T2 ) 3.53) were determined by linear interpolation of sand grain size and uniformity index. Constitutive Relationships. Capillary pressure–saturation relations for the aqueous-nonaqueous system in this study were represented by the van Genuchten functional form (30) (see Table S2, Supporting Information). The influence of IFT on the capillary pressure-saturation relationship was incorporated using Leverett scaling (31). Two widely used parametric models, the Mualem (32) and Burdine (33) models, were incorporated for estimation of the relative permeability (Table S2). In these two models, changes in entrapped DNAPL residual and IFT will affect both the integrand and limits of integration in the relative permeability expressions. Interphase mass exchange of the organic component between the nonaqueous and aqueous phases is modeled as a rate-limited process that was driven by the difference between aqueous phase concentration and solubility (Table S2). The solubility of PCE in the surfactant solution was represented as a linear function of surfactant concentration at a concentration above CMC and remained as the PCE water solubility when the surfactant concentration fell below the CMC. The lumped mass-transfer coefficient was estimated from the correlation of Mayer et al. (34) (Table 2S), which was developed for a similar surfactant–DNAPL system.

Results and Discussion Displacement Experiments. Three rectangular column experiments were conducted to evaluate the mobilization and subsequent migration of residual PCE-DNAPL in Wurtsmith aquifer material (experiment WS-1) or 20–30 mesh Ottawa sand (experiments OS-1 and OS-2) (Table 2). The initial residual PCE-DNAPL saturations ranged from 12.4 to 13.8%, which could be visually observed as entrapped droplets and ganglia, uniformly distributed throughout the columns. The effective permeability to water (ke ) kkra) of the Ottawa sand columns (OS-1 and OS-2) was approximately 1.70 × 10-10 m2, while the corresponding value for the Wurtsmith column (WS-1) was one order-of-magnitude lower (1.72 × 10-11 m2), consistent with the differences in intrinsic permeability (Table 1). On the basis of the measured properties of the 4% Aerosol AY/OT flushing solution (µa ) 3.5 cP; Fa ) 1.03 g/mL; IFT ) 0.09 dyn/cm), applied Darcy velocities (0.07 or 0.36 cm/min) and effective permeability values, the capillary, bond, and total trapping numbers were computed using eqs 1–3 (Table 2). The resulting values of NT ranged from 1.21 × 10-3 (WS-1) to 1.10 × 10-2 (OS-2), which are greater than the experimental value (1 × 10-4) corresponding to nearly complete displacement of PCE-DNAPL from one-dimensional soil columns packed with various size fractions of Ottawa sand (10). Thus, mobilization of the entrapped PCE-DNAPL was expected during flushing with the 4% Aerosol AY/OT solution. In addition, the bond numbers calculated for each experiment were 2.5–25 times larger than their corresponding capillary numbers, indicating that gravity will have a greater impact on mobilization than viscous forces, and therefore, downward migration of mobilized PCE-DNAPL is likely to occur. In the first displacement experiment (WS-1), mobilization of residual PCE-DNAPL was observed immediately after introduction of the 4% Aerosol AY/OT solution into the column at a flow rate of 0.96 mL/min. After it was flushed with 0.13 PV of surfactant solution, a sufficient volume of mobilized PCE-DNAPL had migrated downward to form a 10 cm high bank of mobile DNAPL above the lower boundary of the rectangular column (Figure 1a). As flushing proceeded, an angled bank of PCE-DNAPL formed along the lower portion of the rectangular column (Figure 1b, 0.38 PV), which moved toward the column outlet at an average pore velocity of approximately 0.17 cm/min, calculated from the location of the x-axis centroid of the bank over time. The observed bank angle at 0.38 PV was at least 60° from vertical, as shown in Figure 1b, with the region of the bank 20–80 cm from the inlet forming an angle of approximately 70°. The expected angle of this DNAPL bank displacement relative to the x-axis (τ) can be obtained from the ratio of the bond and capillary numbers (7, 12) τ ) arctan

( ) NB NCa

(5)

where a τ value of 0° corresponds to a vertical bank (perpendicular to flow) and a value of 90° indicates a horizontal bank (parallel to flow). Based on eq 5, the estimated bank angle is 68°, which compares favorably with the experimental observations (Table 2). Hence, the onset, extent, and angle of PCE-DNAPL mobilization observed during lowIFT surfactant flushing of Wurtsmith aquifer material were consistent with behavior expected on the basis of total trapping number analysis. Note that the bank behavior is also consistent with previous studies in two-dimensional aquifer cells containing residual TCE-DNAPL, where injection of a low-IFT Aerosol MA surfactant solution (NT ) 2.0 × 10-3) resulted in the formation of TCE-DNAPL banks with angles of approximately 65 and 85°, similar to the values (76 and 87°, respectively) predicted using eq 5 (35). VOL. 41, NO. 23, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Comparison of observed and simulated PCE-DNAPL saturation profiles after flushing Wurtsmith aquifer material with (a) 0.13 and (b) 0.38 pore volumes (PV) of 4% 1:1 Aerosol AY/OT at a rate of 0.96 mL/min (experiment WS-1).

FIGURE 2. Comparison of observed and simulated PCE-DNAPL saturation profiles after flushing 20–30 mesh Ottawa sand with (a) 0.43 and (b) 0.76 pore volumes (PV) of 4% 1:1 Aerosol AY/OT at a rate of 0.96 mL/min (experiment OS-1). Close inspection of the upper portion of the Wurtsmith displacement experiment photographs (Figure 1) indicates that a milky-white region formed in the vicinity of the surfactant front, extending from the upper surface of the PCE-DNAPL bank to the top of the column. This behavior was attributed to macroemulsion formation, which has been observed during surfactant flushing of soil columns containing residual PCE (9, 36) and in batch systems containing PCE-DNAPL and aqueous surfactant solutions (6). Macroemulsion formation may have negative impacts, including sequestration of surfactant, leading to lower contaminant solubility in the aqueous phase (6), pore clogging, and reduced effective permeability caused by increased solution viscosity and droplet deposition (37). In the Wurtsmith experiment (WS-1), however, the macroemulsion flowed through the column with minimal impediment, and complete PCE recovery (mass balance ) 101.4%) was achieved after flushing with only 1.6 PV of the 4% Aerosol AY/OT solution (Table 2). The observations of macroemulsion transport and enhanced PCE recovery are consistent with studies employing emulsion-based delivery techniques (18). In the second set of displacement experiments, the effect of the flow rate on PCE-DNAPL mobilization behavior was explored in a higher permeability medium, 20–30 mesh 8138

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Ottawa sand (k ) 3.9 × 10-10 m2). In the first Ottawa sand experiment (OS-1), the 4% Aerosol AY/OT solution was introduced at a flow rate of 0.96 mL/min. Representative images of the column after flushing with 0.43 and 0.76 PV of the surfactant solution are shown in Figure 2. Mobilization of residual PCE-DNAPL was observed immediately after introduction of the surfactant solution. Individual PCE droplets migrated downward and accumulated along the lower boundary of the rectangular column to form a bank of mobile DNAPL approximately 6 cm thick (Figure 2). The rapid downward migration of mobilized PCE-DNAPL droplets resulted in an inverted front (i.e., approximately 45° from horizontal) between the advancing surfactant solution and the zone of residual PCE, with the fastest migration of the surfactant solution immediately above the bank of mobile DNAPL. This behavior was attributed to the high permeability of the clean Ottawa sand, the greater density of the surfactant solution containing solubilized PCE relative to the resident aqueous solution, and the shorter vertical travel distance for the PCE droplets located near the bank. This phenomenon can be thought of as “mobilization fingering” and is analogous to the dissolution fingering process where the removal of entrapped DNAPL via dissolution leads to increased effective permeability and fingered patterns of clean media (38). The

FIGURE 3. Comparison of observed and simulated PCE-DNAPL saturation profiles after flushing 20–30 mesh Ottawa sand with (a) 0.50 and (b) 0.68 pore volumes (PV) of 4% 1:1 Aerosol AY/OT at a rate of 4.95 mL/min (experiment OS-2). bank of mobile DNAPL was nearly horizontal along the upper surface, consistent with the 88° bank angle computed using eq 5. The mobile PCE-DNAPL bank migrated steadily toward the effluent end of the column at a pore velocity of approximately 0.19 cm/min, resulting in the recovery of 91.2% of the initial PCE volume after flushing with 2.0 PV of 4% Aerosol AY/OT (Table 2). In the second Ottawa sand displacement experiment (OS2), the flow rate was increased to 4.95 mL/min in an effort to create a more vertical advancing surfactant front (i.e., smaller bank angle). Photographs of the resulting displacement profile after injection of 0.50 and 0.68 PV of 4% Aerosol AY/OT solution are shown in Figure 3. Despite the increased flow rate, the surfactant solution again advanced more rapidly immediately above the 6 cm thick bank of mobile DNAPL located along the lower boundary of the column. The bank of mobile DNAPL migrated steadily along the bottom of the column at an average velocity of 1.1 cm/min, an increase that was approximately proportional to the increase in applied aqueous flow rate between experiments OS-1 and OS-2 (Table 2). Complete recovery (105% mass balance) of PCE-DNAPL was achieved after flushing with 2.0 PV of 4% Aerosol AY/OT (Table 2). Despite the 5-fold increase in aqueous flow rate (viscous force), the angle of the mobile DNAPL bank decreased only slightly compared to the first Ottawa sand experiment (OS1). An 80° angle (from vertical) is superimposed on the 0.50 PV panel (Figure 3b), and shows that the bank angle of 78° calculated based on a force balance (eq 5) overpredicted the effect of increased flow rate (viscous force). The formation of relatively flat mobile DNAPL banks along a lower confining boundary during low-IFT surfactant flushing was also observed by Willson et al. (39). These observations suggest that the bank angle concept provides accurate estimates of the DNAPL migration trajectory at early time. At later time, the angle of the upstream portion of the bank became smaller (steeper), which may have been caused by (a) the greater pressure required to displace the continuous pool that formed along the lower boundary of the column and (b) the increased viscosity of the displacing surfactant solution because of macroemulsion formation. Numerical Simulations. The numerical model was implemented for the three low-IFT displacement experiments. The rectangular columns were discretized using a herringbonetype finite element mesh, with 2 mm vertical and horizontal spacing. Finer discretizations did not yield substantially different results and required much longer computation time.

The initial time step was set as 0.001 s, which was later automatically adjusted based on the solution convergence history. A no-flow boundary condition was established for both aqueous phase and nonaqueous phase on the left, top and bottom boundaries of the column domain. The aqueous surfactant solution was uniformly supplied to the column inlet through a series of source terms. At the column outlet, the total flow rate was set equal to the aqueous phase inflow rate (incompressible assumption). The distribution of aqueous and nonaqueous flow rates at the outlet was determined by the ratio of relative permeability of the two phases. No dispersive flux conditions were enforced for all components on all boundaries in both phases, except that a constant flux boundary condition was prescribed for the aqueous phase components at the column inlet. For all three experiments, cumulative mass balance errors for the components were less than 0.5%. The applicability of a relative permeability model to the low-interfacial tension displacement system was evaluated first by comparison of experimentally derived effluent recovery curves to simulations based on either the Mualem (32) or Burdine (33) models. Simulations of cumulative PCEDNAPL volume collected in the column effluent are shown in Figure 4 for experiments WS-1 and OS-2. In both experiments, predictions based on the Mualem relative permeability model closely matched the observed effluent PCE volumes. For example, in the Wurtsmith experiment (WS-1), the Mualem model captured the initial rise of the PCE-DNAPL recovery curve and predicted a total effluentfree PCE volume of 9.6 mL, which is only slightly less than the measured value of 9.92 mL (Figure 4a). In contrast, simulations based on the Burdine model underpredicted the rate of PCE-DNAPL flow in the column, resulting in delayed breakthrough of PCE-DNAPL at the column effluent. On the basis of these observations, the Mualem relative permeability model was selected for use in the simulations described below. Simulated and experimentally measured PCE-DNAPL saturation profiles are compared at several time points for each column experiment in Figures 1–3. Numerical simulations of the entire mobilization process are provided as timelapse animations in Supporting Information (Figures S1– S3). Inspection of these figures reveals that the formation, location, and migration of the mobile DNAPL bank observed in the experiments was generally well reproduced by the numerical simulator. The angle of the simulated mobile DNAPL bank in experiment WS-1 (Figure 1b) at 0.38 PV was VOL. 41, NO. 23, 2007 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 4. Comparison of observed (data points) and simulated cumulative effluent PCE-DNAPL recovery curves for experiments (a) WS-1 and (b) OS-2 based on the Burdine (dashed line) and Mualem (solid line) relative permeability models. 68°, which is identical to the value estimated using eq 5 (Table 2) and similar to the observed bank angle of approximately 60°. In both of the experiments conducted with Ottawa sand (OS-1 and OS-2), the numerical model accurately predicted the formation of a relatively flat mobile DNAPL bank along the bottom of the rectangular column (Figures 2 and 3). This behavior is consistent with the large contribution of the gravitational force (NB) in the higher permeability 20–30 mesh Ottawa sand (ke ) 1.7 × 10-10 m2) relative to the viscous force (NCa) (Table 2). In the numerical simulations, the NT value was calculated at each time step for all the points within the rectangular column domain to identify the onset of PCEDNAPL mobilization. Representative plots of the total trapping number profile in the column are provided for all three experiments after injection of 0.5 PV of the 4% Aerosol AY/OT solution (Figure S4, Supporting Information). In regions of the column accessed by surfactant solution, the total trapping numbers exceeded 1 × 10-4, which is consistent with the observed complete displacement of residual PCE-DNAPL. The boundaries between the clean region, mobile NAPL bank, and zone residual PCE-DNAPL are delineated by total trapping numbers that are similar to the critical value required for the onset of DNAPL mobilization (i.e., 2 × 10-5–5 × 10-5) and are shown as yellow regions in Figure S4 (Supporting Information). Thus, incorporation of NT to describe the onset of mobilization allowed the simulator to reproduce the general shape of the mobile DNAPL bank and regions of clean soil in all three experiments. Within the mobile DNAPL banks, the simulated PCE-DNAPL saturations were greater than 0.3 and reached a maximum value of 0.9, which corresponds to the minimum residual water saturation of 0.1 (Figures 13). These high PCE-DNAPL saturations result in low aqueous phase relative permeability, and thus, the simulated trapping number values computed in the mobile DNAPL bank are small (Figure S4, Supporting Information). To quantitatively compare simulated and observed mobile DNAPL bank migration, the centroids of PCE-DNAPL banks were calculated for each experiment and compared with the center of mass of the simulated PCE-DNAPL banks. The position of the simulated and measured x-axis centroids for the PCE banks versus the pore volumes of 4% Aerosol AY/OT introduced are presented in Figure S5 (Supporting Information). In all three experiments, the simulated mobile DNAPL bank migration rate closely matched the observed centroid migration values, with maximum discrepancies of 0.6, 0.7, and 1.6 cm for experiments WS-1, OS-1, and OS-2, respectively. The experimental data and numerical simulations presented here provide the first detailed validation of the trapping number in a two-dimensional system. Successful reproduction of PCE-DNAPL bank formation, migration, and surfactant transport confirm the validity of the total trapping number approach, and support the use of this approach for 8140

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a priori predictions of DNAPL mobilization and implementation in multiphase flow and transport simulators used in the design of low-interfacial floods for treatment of DNAPL source zones.

Acknowledgments The authors thank Drs. Eric Suchomel and Jed Costanza for digitizing photographs of the displacement experiments, Mr. John Pennell for milling the stainless steel endplates, Ms. Laura Loverde for measuring the viscosity of the Aerosol AY/ OT solution, and American Cyanamid (Cytec) for providing the aerosol surfactants. Support for this research was provided by the Strategic Environmental Research and Development Program (SERDP), Project ER-1293 “Development of Assessment Tools for Evaluation of the Benefits of DNAPL Source Zone Treatment”, under contracts DACA72-02-C0018 and W912HQ-04-C-006. This work has not been subject to SERDP review, and no official endorsement should be inferred.

Supporting Information Available Description of the column saturation methods, PCE desaturation curve parameters (Table S1), equations for calculating constitutive relationships (Table S2), time-lapse simulation sequences for the three displacement experiments (Figures S1–S3), total trapping number plots (Figure S4), and the evolution of x-centroids of the PCE mobile DNAPL banks (Figure S5). This material is available free of charge via the Internet at http://pubs.acs.org.

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