Published online 25 February 2008
Published in Vadose Zone J 7:294-304 (2008)
DOI: 10.2136/vzj2006.0126
© 2008 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
SPECIAL SECTION: TOUGH2
Numerical Simulation of Field-Scale Contaminant Mass Transfer during Air Sparging
Darby J. VanAntwerpa,c,*,
Ronald W. Faltaa and
John S. Gierkeb
a Deps. of Geological Sciences and Environmental Engineering, Clemson Univ., Clemson, SC
b Dep. of Geological and Mining Engineering and Sciences, Michigan Technological Univ., Houghton, MI
c current address: RMT, Inc., 3754 Ranchero Dr., Ann Arbor, MI 48108-2771
* Corresponding author (Darby.VanAntwerp{at}rmtinc.com).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 31 August 2006.
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ABSTRACT
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Air sparging is a remediation technology for removing volatile organic contaminants (VOCs) from below the water table using air injection. Contaminant mass removal can be controlled by the mass transfer between liquid phases (aqueous and nonaqueous phase liquid [NAPL]) and the injected gas phase. Traditional multiphase flow numerical models ignore subgridblock-scale effects of gas channel flow on local mass transfer and assume local equilibrium between liquid and gas phases. This traditional, single-domain modeling approach tends to overpredict contaminant mass removal during sparging. A dual-domain multiphase flow approach for local interphase mass transfer may more accurately simulate contaminant removal, while still accounting for injected gas plume behavior. Mass transfer limitations are introduced through a numerical grid modification where each traditional single-domain gridblock is split into two domains: one with very strong capillary pressures that remains mostly water saturated and one with weak capillary pressures that becomes mostly gas saturated during sparging. The two domains are coupled through a first-order mass transfer expression. This simple model can then approximate the localized (subgridblock-scale) gas channel effects on mass transfer that are limited by liquid phase diffusion. In this study, data from a two-dimensional laboratory-scale experiment and a field-scale air sparging demonstration were used to test the capabilities of the dual- and single-domain approaches. It is the first time mass transfer has been simulated for air sparging at either of these scales using a multiphase flow kinetic interphase mass transfer model. Both experiments involved air sparging remediation of tetrachloroethylene, a NAPL. The single-domain local-equilibrium model resulted in an overprediction of mass removal rates in both cases. The dual-domain mass transfer approach provided a much better fit of the experimental data, and it is shown that the apparent interphase mass transfer coefficient becomes smaller with increasing scale.
Abbreviations: bgs, below ground surface • DNAPL, dense nonaqueous phase liquid • NAPL, nonaqueous phase liquid • PCE, tetrachloroethylene • PI, productivity index • SVE, soil vapor extraction • VOC, volatile organic contaminant
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INTRODUCTION
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Air sparging and soil vapor extraction (SVE) are in situ remediation technologies for removing volatile organic contaminants (VOCs) from the subsurface. During air sparging, air is injected into the saturated zone to volatilize dissolved and nonaqueous phase organic contaminants. The organic compounds partition into the advecting gases that migrate to the surface and vapor extraction wells are typically used to collect the contaminated vapors in the unsaturated zone. Although this technique has been successful in numerous laboratory and field-scale studies, the impacts of variables such as distribution and characteristics of contaminants, geological conditions, and methods of air sparging operation are still not fully understood. Numerical and analytical modeling can provide insight into the complex interactions that take place in the subsurface during air sparging.
Several previous studies have shown that multiphase flow codes can be effective in predicting gas plume shape and behavior (McCray, 1994; McCray and Falta, 1997; Hein et al., 1997). In those cases, the focus was on reproducing the gas flow patterns, and the chemical mass transfer was assumed to occur as a local-equilibrium process. While the flow field can be resolved with multiphase simulators, the grid elements typically are too large to account for gas channeling on the millimeter scale. This gas channeling may restrict the amount of contaminant in direct contact with gas, limiting the mass removal to the rate at which contamination can diffuse into the advecting gas channels. Falta (2000) successfully modeled air sparging removal of dissolved trichloroethylene from a column by incorporating first-order interphase mass transfer into a multiphase flow and transport code. This was accomplished by implementing a dual-domain mass transfer approach, which accurately resolved the contaminant removal tailing with time.
In the present work, comprehensive data from a laboratory and a field-scale experiment are examined using TMVOC, a multicomponent compositional multiphase flow simulator (Pruess and Battistelli, 2002). Many studies have used column data to examine mass removal, but it is important to assess how accurately processes at that scale represent larger field-scale processes. The laboratory and field air sparging studies that are simulated in this work were chosen because they both have comprehensive data sets and they were designed to complement each other.
The controlled two-dimensional laboratory sparging test was simulated first. The capabilities of the local equilibrium and dual-domain mass transfer approaches for representing the observed contaminant removal rates were assessed. Using the understanding gained from simulating the controlled two-dimensional experiment, the field experiment was simulated, and the applicability of the laboratory-scale mass transfer coefficient to a field-scale system was evaluated.
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Dual-Domain Approach to Modeling Kinetic Interphase Mass Transfer
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In a traditional numerical flow simulation, each element represents a single continuum. Within each element, local equilibrium is normally assumed, in which case there is no accounting for local mass transfer limitations that may occur due to fingering of gas channels. Multiphase simulations of sparging patterns show the gradational change in averaged gas saturation outward from the injection location during air sparging (Fig. 1
). A more-detailed representation may be that the air channel density is greater near the injection location and the air channel density decreases with distance from the sparge well. Air sparging studies have shown that channeling leaves some pore water relatively unaffected by the sparged gas (Ji et al., 1993; Elder and Benson, 1999). Contamination (NAPL or dissolved) that is isolated from the gas channels is not removed unless it diffuses through the water into the channels. In general, kinetic interphase mass transfer needs to be incorporated into a multiphase flow and transport model to accurately simulate contaminant removal by air sparging because it is not practical to resolve the individual gas channels in a field-scale simulation.
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FIG. 1. A simulated sparge zone in a single-medium multiphase flow model versus realistic channeling that occurs in air sparging. A modeled gas saturation distribution under constant mass injection of air is shown on the left. Illustrations of pore-scale channeling that occurs in a real system are shown on the right.
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Considering a two-phase gas–aqueous system, a first-order rate of kinetic interphase mass transfer can be described by
 | [1] |
where Qimt is the rate of chemical mass transfer from the aqueous phase to the gas phase per unit volume of porous media (kg m–3 s–1), Cw is the chemical concentration in the aqueous phase (kg m–3), Cg is the chemical concentration in the gas phase (kg m–3), H is the dimensionless Henry's constant for the chemical of interest in water (assumed to be constant), and kimt
(s–1) is the product of the mass transfer coefficient and the interfacial area. This equation could be implemented in a compositional multiphase flow model, but it would require separate mass balances of the contaminant in the gas and aqueous phases, rather than the global mass balance that is typically used.
An alternate method for implementing kinetic interphase mass transfer into a multiphase flow code uses a dual-domain approach (Falta, 2000). In this approach, the three-dimensional grid is divided into two volume fractions: one that represents coarser grained fractions of the porous media where gas channels are created, and one that represents finer grained materials that remain nearly saturated (Fig. 2
). Due to capillary forces (air entry pressure), gas will tend to preferentially flow through the coarser material when both are initially water saturated. The properties of these two volumes can be chosen so that the composite media behaves like a normal porous media. The two volume fractions are locally connected one dimensionally so that fluids and contaminant components can move between the two domains according to pressure and concentration gradients. In the present work, the fine-grained fraction tends to contain mostly water, so the mass transfer to the coarser grained fraction is limited mainly by aqueous diffusion.
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FIG. 2. Schematic of connections in a dual-media grid. Both media are globally connected and share a local connection. Also shown is conceptualization of dual-media processes in a gridblock. (Sg = gas phase saturation; Sw = aqueous phase saturation.)
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A suitable conceptual model of gas channel formation can be constructed using studies such as Elder and Benson (1999) to estimate interfacial areas for local connections, area fractions for global connections and diffusional distances for the dual-domain formulation. The mesh generation in TMVOC includes a subroutine that was modified for direct input of such quantities. This numerical approach allows for three-dimensional fluid and mass flow to occur globally in both volume fractions. This is also known as a dual-permeability formulation, to distinguish it from cases where global flows only occur in the coarse fraction (dual porosity formulations).
Denoting the coarse-grained volume fraction as material 1, and the fine-grained volume fraction as material 2, the first-order formulation of kinetic interphase mass transfer can be described as
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Comparing this equation with the multiphase diffusive flux between the coarse- and fine-grained media (domains), Falta (2000) showed that the dual-domain formulation produces a first-order rate-limited mass transfer between media with a mass transfer coefficient-interfacial area equal to
 | [3] |
where 
is the porosity, S is the phase saturation, 
is the phase tortuosity, D is the phase molecular diffusion coefficient, A12 is the specific interfacial area (interfacial area per unit total volume) between the coarse- and fine-grained volume fractions, and d12 is the average nodal distance between the two fractions. Braida and Ong (1998) observed that the mass transfer coefficient varies inversely with Henry's constant, which is also true for the above formulation.
The magnitude of the diffusion conductance between the two domains is determined, in part, by the ratio of interfacial area to diffusional distance, A12 to d12. As the ratio A12/d12 approaches infinity, the transport solution approaches that of local equilibrium (or of the single-domain approach). Mass transfer between the two domains also depends on the effective diffusion coefficients in the aqueous and gas phases, which are related to the relative phase saturations. When gas saturations in both domains are large, the rapid rate of gas diffusion tends to equalize the concentrations in the two volume fractions. However, when there is a contrast in gas saturation, the mass transfer tends to become limited by aqueous phase diffusion. Varying the contrast in the capillary pressures between the two domains along with adjusting the A12/d12 ratio are means of calibration, similar to calibrating a mass transfer coefficient to a system.
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Two-Dimensional Simulation of Bench-Scale Experiment
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Air sparging was studied in a 1-m-long by 0.5-m-high by 4-cm-thick laboratory apparatus to investigate removal rates and mobility issues of a dense nonaqueous phase liquid (DNAPL), tetrachloroethylene (PCE), during sparging in a controlled two-dimensional configuration (Heron et al., 2002). The general setup of the experiment is depicted in Fig. 3
. This laboratory experiment was designed to evaluate a field experiment planned for the Groundwater Remediation Field Laboratory at the Dover National Test Site (Taege, 2002), the results of which were also used to test the model discussed later in this paper. Reported system configuration, soil properties, and sparging conditions were used as the simulation input. Chemical input parameters were obtained from published properties. The sand–water–air characteristics and permeability parameters were selected to produce a sparge zone of similar size and shape to photographs of the initial sparging period based on preliminary two-phase (air–water) simulations. Modeled results were fit to observations of capillary rise and the formation of the sparge zone, as discussed below. Contaminant injection and redistribution were simulated using TMVOC along with the air sparging performance for varying injection rates, as reported in the study. Simulated PCE vapor concentrations and cumulative mass removed were compared with the experimental data.
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FIG. 3. Grid setup for simulating two-dimensional laboratory air sparging experiments including the sources and sinks. The relative location of the water table and capillary fringe are also shown. (ki = intrinsic permeability.)
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A DNAPL plume was created in the apparatus by rapidly injecting 100 mL of liquid PCE near the top of the box. Lowering and raising the water level produced a vertically smeared zone of PCE. Experimentally measured air sparging results from Heron et al. (2002) are summarized in Fig. 4
. Figure 4A shows the measured off-gas PCE concentration (open circles) during the experiment along with the cumulative mass of PCE removed (black line). The sparging rate (Fig. 4B) was varied and included three 8-h-long pulses of air and three 1-h pulses.
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FIG. 4. Summary of pulsed air sparging experiment. (A) Measured off-gas tetrachloroethylene (PCE) concentrations and interpolated mass removed. (B) Operational changes with pulsed air injection at later times.
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No soil permeability data were available for the medium sand used in the experiment, so it was assumed to have an intrinsic permeability between 10–7 to 10–6 cm2, which is a typical permeability range for a medium sand (Faybishenko, 2000). In an air sparging system with a constant injection rate, the lateral extent of the sparge zone primarily depends on the vertical permeability, with lower permeabilities producing a broader extent (McCray, 1994). Using the initial injection rate and selected capillary parameters (discussed below), the intrinsic permeability was adjusted to produce a sparge zone of similar size and shape to that appearing in photographs of the initial sparging period. These two-phase simulations showed that an intrinsic permeability of 3 x 10–7 cm2 produced a gas plume most similar to the pictures. The underlying silty-clayey soil has a reported hydraulic conductivity of 10–6 cm s–1, which corresponds to an intrinsic permeability of 10–11 cm2.
Moisture characteristic curve data were also not available for the media used in this study. Estimates of the sand capillary behavior were used to parameterize the two-phase van Genuchten formulation (van Genuchten, 1980), given below:
 | [4] |
where Pcgw is the gas–water capillary pressure (Pa), gw is an empirical constant related to air entry pressure (m–1), Sw is the aqueous phase saturation, Sm is an empirical constant related to residual saturation, 
w is the density of the aqueous phase (kg m–3), g is the gravitational acceleration [9.801 (m s–2)], and m is an empirically determined constant that determines the shape of the curve and equals (1 – 1/n). Values used in the study are listed in Table 1
. Adjustments were made to gw to produce a curve representative of a soil with an 8-cm capillary rise, as observed in the experiment (Heron et al., 2002). The n and Sm values were chosen to be within the range for a medium sand (Faybishenko, 2000).
For multiphase flow problems, such as air sparging, the effects of multiple phases in the pore spaces must be considered. Generally, the relative permeabilities are assumed to be a function of the saturation in the respective phase:
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where kr(g,w,n) are the relative permeabilities of the gas, water, and NAPL phases respectively; S(g,w,n) is the respective phase saturation, S(g,w,n)r is the residual phase saturation, and N is an empirical constant, usually between 2 and 3. A summary of soil and chemical parameters used in the initial single-medium air sparging simulations is included (Table 1). More details on the capillary function and relative permeability formulation are reported in VanAntwerp (2006).
In this modeling analysis of mass removal during air sparging, the two-dimensional grid consisted of 1624 elements (28 rows high, 58 columns long) to accurately resolve the initial distribution of PCE (Fig. 3). The element dimension perpendicular to the two-dimensional plane of the experiment was equal to the thickness of the apparatus. The exterior of the grid (exterior of box) is a "no-flow" boundary. The initial water saturation and pressure distribution are assigned by assuming gravity–capillary equilibrium.
A qualitative comparison of color photographs of the initial distribution of NAPL PCE, which was dyed red, to simulations of the NAPL redistribution patters after injection were used to obtain the residual NAPL saturation, since it was not measured. The residual NAPL saturation, used in the three-phase relative permeability function, was adjusted until the simulated spilled PCE distribution approximately matched the distribution inferred from the pictures. Air injection in the experiment occurred at a point approximately 12 cm above the top of the silt layer. An appropriately located element was used to inject air at a constant rate. TMVOC allows for tabular input of time-variable injection rates, which were obtained from the results shown in Fig. 4B.
Vacuum extraction was modeled using a well-on-deliverability condition in TMVOC, where fluid production occurs based on a specified flowing bottomhole pressure (Pwb) and a productivity index (PI) (Pruess and Battistelli, 2002). The production rate of phase β from a gridblock with phase pressure Pβ > Pwb is:
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where krβ is the relative permeability of phase β, and µβ is the viscosity of phase β. PI is calculated from the geometry and permeability of the system. For a two-dimensional cross-sectional model,
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where d is the distance from the outer boundary to the center of the producing element, A is the vertical cross-sectional area of the producing elements, and k is the intrinsic permeability; PI was assigned a value of 10–12 m3. A wellbore pressure of 99.5 kPa was used in the producing element as an atmospheric pressure boundary condition. The flow out of the producing well is driven by the over-pressure caused by the air injection in the otherwise closed system.
Simulations with a single-domain local-equilibrium model configuration overpredicted the contaminant mass removal rate (Fig. 5A
). Initial concentrations predicted by the model are similar to the experimental data; however, the single-domain model is unable to resolve the rapid decrease in concentrations after 1 d of sparging. The overprediction of the mass removal rates for the single-domain model is even more pronounced for the cumulative mass removal calculations. Within the first 4 d, the single-domain model predicts that 120 g of PCE were removed. Subsequently, another 20 g of PCE is predicted to be removed. In the experiment, only 90 g of PCE was actually removed. The differences in the cumulative mass removal between single domain and the experimental measurements (Fig. 5B) became smaller after 20 d because in the single domain simulation, nearly all of the mass of PCE in the sparge zone had been removed by Day 20, which is unrealistic. In the dual-domain simulation, however, there was still PCE present in the sparge zone beyond 20 d, as was the case for the laboratory experiment.
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FIG. 5. (A) Simulated effluent concentrations using a single- and dual-domain approach with a fine grid (28 x 58) along with the experimental data from a two-dimensional air sparging test. (B) Total mass removed as predicted by a dual-domain numerical simulation using a fine grid along with experimental mass removed from a two-dimensional air sparging test. The alpha ratio is representative of the capillary contrast between the coarse- and fine-grained media. (PCE = tetrachloroethylene.)
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For the dual-domain simulation, properties from the single-medium simulation were adjusted for the two domains following the logic presented in the Falta (2000) application of the dual-domain approach to air sparging. A similar sand was used in the Heron et al. (2002) experiment, as in the columns modeled by Falta (2000), so it was assumed that gas channels would form in approximately 20% of the sand during air sparging. A volume fraction of 20% of the original element was assigned properties of a coarse-grained media, and the remaining volume fraction (80%) was assigned properties of a fine-grained media to account for zones of stagnant pore water. Because the volume fraction in which gas channels form cannot be readily measured, it was a calibration variable.
The moisture characteristic properties of the sand need to be adjusted for the dual-domain approach. Capillary properties were chosen to allow for a contrast in water saturation between the two domains under capillary equilibrium (Fig. 6A
). The gw value in the van Genuchten capillary pressure equation was adjusted so that the volume-weighted average of the capillary properties from the two domains produces a curve similar to that used in the single-medium simulation as illustrated in Fig. 6B. The contrast in water saturation between the two domains allows for an aqueous phase diffusion limitation to the local mass transfer between the domains, but bulk processes within the model remain similar to that occurring in a single-medium simulation. Relative permeabilities for each domain can also be adjusted on the basis of original single-medium parameters. The global area fraction is used to weight the relative permeability values of the coarse and fine media, and the weighted average is a close match to the original single-domain curve (Fig. 7
). Parameters used in the capillary pressure and relative permeability functions for the dual-domain simulations are listed in Table 2
.
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FIG. 6. (A) the relative water distribution between the two media under local capillary equilibrium. Water saturations (Sw) of each media are plotted as a function of the overall volume-weighted average saturation. (B) Dual-media capillary pressures along with originally selected capillary pressures from single-medium simulation. The center curve is a volume weighted average of the two media curves. The dual-media capillary pressures were adjusted to produce a volumetrically weighted curve similar to the original pressure curve.
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FIG. 7. Flow area weighted average dual-media gas-phase relative permeability (krg) along with single-medium gas-phase relative permeability function. Dual-media parameters have been adjusted to produce a similar curve as the single-medium function.
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TABLE 2. Capillary pressure and relative permeability parameters used in the two-dimensional laboratory dual-domain simulation.
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Once capillary and relative permeability parameters were appropriately adjusted to accommodate the dual-domain grid, the simulation was run again with the same sources and sinks as with the single-medium simulation. Based on assumed gas channel geometry, the interfacial area (A12) value was set equal to 300 m2 m–3. The nodal distance between the channel and the domain interface (d1) was equal to 1 mm, and the diffusional distance (d2) was equal to 4 mm. Even though the dual-domain grid is based on a realistic gas channel geometry, some calibration for the mass transfer was needed. The contrast in water saturation between the domains, which is controlled by the capillary parameters, influences diffusive rate (Falta, 2000). Since there is not a unique set of dual-domain capillary curves when weighted according to the relative volume fraction of the material produce a curve similar to the single medium, some calibration is needed. Varying the contrast in the capillary parameters (gw) between the two domains is a method of calibration, similar to calibrating a mass transfer coefficient to a system. Sensitivity of the model to this variable can be tested by running simulations with varied contrast in capillary parameters.
After adjusting gw, the effluent concentrations from the dual-domain simulation were very similar to the laboratory data (Fig. 5B). As a result, the cumulative mass removal with time also closely matched the experimental data.
Using Eq. [3], an equivalent mass transfer value of 4.85 x 10–5 s–1 was calculated for this experiment, which is in the range reported by Braida and Ong (1998). This value is also close to what Falta (2000) calculated for the column studies, which was expected since the same ratio of A12 to d2 was used here. Since this laboratory-scale study was designed to complement the field-scale study, this A12/d2 ratio was used initially for the field-scale simulation.
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Three-Dimensional Simulation of a Field-Scale Air Sparging Experiment
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The next step was to use TMVOC to simulate a controlled air sparging field test. Both single- and dual-domain approaches were used in an attempt to model the observed removal rates. Only the first 57 d of operation, which included five operational changes (with three configurations and one shutdown), were simulated. During the second part of the test, which was not simulated, water was recirculated in the test cell. Simulating this condition would require some code modifications to TMVOC. This air sparging demonstration was conducted in one of two test cells as a part of the Groundwater Remediation Field Laboratory at the Dover National Test Site, Dover Air Force Base, Dover, DE (Taege, 2002). Each cell was nominally 4.6 m long by 3.0 m wide by 12 m deep (15 ft by 10 ft by 40 ft). Lateral boundaries (Fig. 8A
) were formed by sheet piles driven into the ground and into a clay layer 12.2 m (40 ft) below the ground surface, which acted as a lower boundary. Such constraints on the initial contaminant mass, injection–extraction flows, and the comprehensive data collection make this air sparging study well suited for testing models.
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FIG. 8. (A) The layout of the test cell. Numbers in circles represent volume of tetrachloroethylene (PCE) in liters injected at each release point. The four unlabeled wells were used for groundwater circulation and are not used in the model. (Adapted from Taege, 2002). (B) The model grid (scale equivalent to 8A) used for simulating air sparging in the test cell.
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The relevant details of the experimental design, setup, and conditions pertinent to the application and testing of TMVOC are provided below. Readers interested in the installation, equipment, instruments, sampling, and analyses are referred to Taege (2002).
Geology at the Dover site consists of fine- to coarse-grained sands containing varying silt, clay, and gravel content (Taege, 2002). Occasional clay and silt lenses are present, which is typical of a coastal plain depositional system. Subsurface characterization is important for assessing performance of remediation technologies. Heterogeneities in the soil may greatly control how effective air sparging can be at a site. Accurate estimates of soil properties and how they vary spatially, as well as estimates of initial contaminant distribution, are important for accurately modeling a remediation technology performance. A site characterization study (Applied Research Associates, 1996) reports some permeability measurements from the region where the test cell is located. Horizontal permeabilities ranged from 1 x 10–11 to 8 x 10–13 m2. Nonreactive tracer tests performed specifically in the test cell (Falta et al., 2003) indicated zones of varying permeability, but specific values of permeabilities in these zones were not determined.
The simulation model for this site assumes homogeneous geologic conditions. A homogeneous model is certainly an oversimplification of the geology, but assuming a homogeneous soil system allows for the calibration aspects to be performed more straightforwardly. Furthermore, detailed knowledge of local heterogeneities is usually not available at real field sites and was not at this site. Although the laboratory system described above was modeled as isotropic, the field site was assumed to have vertical anisotropy.
Since the injection and extraction gas flow rates were known and fixed in the simulation, the intrinsic permeability was adjusted using a preliminary multiphase flow simulation to produce air pressures in the wells similar to the measured values reported from the field. The modeled pressures were within 5% of observed pressures (25% of the observed vacuum pressure) when using an intrinsic permeability of 2 x 10–11 m2 in the horizontal (x,y) direction and 1 x 10–11 m2 in the vertical (z) direction.
Moisture-characteristic data was unavailable for the sediments in the test cell where sparging was performed. Some estimates of soil capillary characteristics were made for an adjacent test cell a few meters away (C. Enfield, personal communication, 2004). Since both test cells are in the same region, data from the adjacent cell was adopted for this study. These parameters are listed in Table 3
. The exponent (N) and residual gas saturation used in the relative permeability functions are values from previous studies in similar sandy media (McCray and Falta, 1996; Falta, 2000). Residual water saturation is determined from the capillary properties.
Although the lateral and bottom boundaries were somewhat irregular (Fig. 8B), a rectangular grid was used for the model simulations. Lateral variations from the flat rectangular boundary for the actual sheet-pile walls were less than a grid element dimension around the perimeter. Variations in the clay surface topography (vertical relief) were less than 0.3 m (1 ft) (Applied Research Associates, 1996). The entire top of the cell was capped with concrete except for a 20-cm-diameter (8-in-diam.) annulus around each of the 12 wells where the soil surface was open to the atmosphere. Each well was 5 cm (2 in) in diameter and screened from 6 m (20 ft) below ground surface (bgs) to 12.2 m (40 ft) bgs.
The three-dimensional finite difference grid (19 elements long by 15 wide by 40 high) was created to accurately resolve the locations of the air injection–extraction wells and contaminant injection points within the test cell. A plan view of the grid showing well locations as shaded blocks with numbers is also shown in Fig. 8B. Leakance of fresh air from the atmosphere was taken into account by connecting the 12 elements that contained a well to gridblocks assigned atmospheric conditions to provide a Dirichlet boundary condition.
The sparging system injected air into the lowest 30-cm (1-ft) interval of the well screen (11.9–12.2 m bgs or [39–40 ft bgs]). A point mass injection was used to simulate the injection of 80% relative humidity air. Measured flow rates from the experiment were specified as the model input. Three different configurations were modeled during the simulated 57 d (Fig. 9
). During the experiment, combined flows through the extraction vents (9.34 x 105 standard cubic cm min–1 [33 standard cubic feet min–1]) were kept at approximately twice the rate of injection to prevent the sparge well vapors from emerging through the cell surface. These wells were also modeled using a specified mass rate of extraction based on the measured rates. The extraction wells were screened from 6.1 to 12.2 m (20–40 ft) bgs; however, production of air occurs only from the screened interval above the saturated zone. Initially, this interval was 4.6 m (15 ft), but it shortened as the water table mounded upward as the sparging zone developed (around 0.4 m [1.2 ft], depending on injection–extraction well configuration).
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FIG. 9. Three operational configurations used in the model. The column on the left is a plan view of the injection (downward arrow) and extraction wells (upward arrow) with rates in standard cubic meters per minute indicated above or next to the arrows. The column on the right shows a conceptual cross-section for a given operational configuration.
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To model the wellbore effects, the gridblocks within the 4.6-m (15-ft) interval of well screen were assigned higher intrinsic permeability values to link the cells together (Fig. 10
). In this approach, water can flow into the bottom few feet of screen without being produced by the well. The cells representing the well screen were given a very high intrinsic permeability and a very low air-entry pressure. Gas was removed from the top two elements in the well screen by specifying a constant mass rate of extraction, and the individual components (air, water vapor, and contaminant vapor) were removed according to their concentration in the gas.
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FIG. 10. Grid configuration in the z direction, compared with a well schematic (adapted from Taege, 2002). All well grid cells are connected to an atmospheric boundary condition at the top. Constant mass extraction cells are used for the soil vapor extraction operation and cells within the screened interval of the well are assigned a higher permeability and lower capillarity than the bulk media. (bgs = below ground surface.)
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The USEPA researchers who organized the field studies were permitted to inject 107 kg of PCE into the test cell (Taege, 2002). The goal of the PCE release was to create a heterogeneously distributed, residual NAPL contaminated zone in the lower-most 1.5 m (5 ft) of the coastal sand deposits above the underlying clay layer. The PCE was injected into 3-mm-diam. tubing at a depth of 10.7 m (35 ft) according to the volumes and locations shown in Fig. 8A. To smear the contaminants vertically, the water table was lowered to approximately 11.9 m (39 ft) bgs after initial injection and then raised back to 10.7 m (35 ft) bgs. Because details of the resulting DNAPL structure are unknown, the PCE was emplaced in the system on the basis of known injection locations and mass.
For each injection location, the mass of PCE injected was known, but some assumptions about the initial DNAPL distribution were necessary. The PCE was assumed to occupy a roughly cylindrical zone beneath the release location, with some pooling at the sand–clay interface at the bottom of the test cell. The PCE injection well locations are used to represent the horizontal (x,y) coordinates for the center of the cylindrical zone of PCE. The vertical (z) position for the center of the cylinder is dependent on how far down the DNAPL migrated from the point of injection (the height of the cylinder). By developing a conceptual model for the NAPL distribution, these values can be estimated (Fig. 11
).
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FIG. 11. Realistic nonaqueous phase liquid (NAPL) spill and an idealized column of contamination used in the model.
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Approximately 20 kg of injected PCE mass was not observed in the initial partitioning tracer test analysis (Taege, 2002), so it was assumed that this was largely due to pooling of NAPL on the clay layer. Assuming that a DNAPL injected into each well at a constant rate would expand to a similar radius before migrating downward, the larger masses of PCE injected would penetrate deeper into the subsurface and possibly pool at the lower clay boundary. To account for the pooled mass of PCE, it was assumed that a mass of 8 kg of injected PCE would form a cylinder of contamination extending down to the clay layer and that any additional mass injected would form a pool on the clay. A mass of 8 kg, for example, would contaminate a height equal to the distance from the injection point to the clay layer (1.53 m [5 ft]). The remaining mass in excess of 8 kg was spread out laterally in the bottom 0.15 m (0.5 ft) of the grid. For PCE mass injections less than 8 kg, the height of the contaminated cylinder will be proportionally less. Using a diameter of contamination equal to the width of one gridblock, and the relative height and mass for each location, a soil mass fraction (xt) can be calculated as follows:
 | [9] |
where mPCE is the mass of contamination, 
t is the total volume of contaminated soil, b is the bulk density of the soil (kg m–3), 
x is the height of a gridblock, y is the width of a gridblock, nz is the number of contaminated blocks in the vertical (z) direction, and z is the height of a gridblock. This results in a NAPL saturation (Sn) of approximately 0.15, which can be calculated by
 | [10] |
where is porosity and n is the NAPL density.
A traditional single-domain, local-equilibrium model was tested based on the parameters, sinks, and sources described. As occurred for the laboratory experiment, the field-scale, single-domain simulation overpredicted mass removal (Fig. 12
). The overprediction is because subgridblock-scale mass transfer limitations are not taken into account in a single-domain approach. Simulated PCE removal (red line) for the first few days matches the experimentally derived mass removal rate fairly well, but after about 5 d, the simulation results diverge from the actual measurements. The simulation predicted the total mass removal over 57 d to be approximately 65 kg, whereas the actual mass removal was 39 kg. Some of the differences between the predicted and experimental results are likely the result of the initial contaminant distribution and soil heterogeneities, but a large part may be because local diffusive limitations were not taken into account. A dual-domain approach was implemented next.
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FIG. 12. Total experimental mass removal and simulated with TMVOC using a dual-media approach with the A12/d2 ratio from the laboratory-scale air sparging simulations (75,000) and the adjusted A12/d2 ratio (75), where A12 is the interfacial area and d2 is the diffusional distance.
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Properties from the single-medium simulation were adjusted for the dual domains in the same manner as in the laboratory simulation. The coarse-grained domain was again set equal to 20% of the total volume. Again, it is unknown whether precisely 20% of the sand volume would form gas channels, but the estimate is reasonable, based on Falta (2000). The dual-domain properties were based on the single-medium soil characteristics pertaining to the coastal sediments at the field site (Table 4
). A dual-domain model was run initially using the equivalent mass transfer rate (A12/d2) ratio as the laboratory experiment (75,000), but the model still overpredicted the PCE removal rate as shown in Fig. 12 (orange line).
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TABLE 4. Capillary pressure and relative permeability parameters used in the three-dimensional field demonstration dual-domain simulation.
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By reducing the ratio of A12/d2 to 75 (equivalent to increasing d2 and/or decreasing A12) to reduce the effective mass transfer coefficient, a better match of the total mass removal was obtained (Fig. 12, green line). Calibration of the model to the laboratory data depended greatly on the contrast in gas saturations between the two domains; however, in calibration of the field-scale model, the gas saturation contrast had a lesser effect than the A12/d2 ratio (VanAntwerp, 2006). The simulated mass removal using a dual-domain approach was similar to the actual data for the first flow configuration. At the first flow configuration change, occurring at 15 d, the model predicts a more abrupt increase in the mass removal rate than actually observed. The simulated mass removed from this time forward is approximately 5 kg higher than the observed. Flow configuration 2, which begins at Day 15, involves ceasing air injection into one well and doubling the flow rate at the other injection location.
The single-domain, local-equilibrium model predicts that almost all of the contaminant within the sparge zone will have been removed after approximately 15 d. A three-dimensional view of the DNAPL and gas saturation distribution at 15 d (Fig. 13
) shows that while the two simulation approaches predict similar overall gas flow patterns, the dual-domain model results in a slower removal of DNAPL from the sparge zone. The dual-domain contour plots are volume-weighted averages of the NAPL and gas saturations from the two domains at each node. The pooled PCE NAPL in the lower portion of the simulation remains unaffected throughout the course of both simulations.
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FIG. 13. Day 15 resulting gas saturations and nonaqueous phase liquid saturations for both single-medium and dual-media simulations at the end of configuration 1.
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Implementation of a dual-domain approach provided a better fit of the modeled data than the single-domain simulations. The calibration of an effective mass transfer coefficient allows one to accurately simulate how much NAPL is volatilized, but permeability structure and detailed NAPL distribution control which vents capture the volatilized mass. Slight differences in initial contaminant distributions were also examined in this study. In a homogeneous simulation, distance is a main control on the flow paths of air and contaminant, although in the field permeability and capillarity of the coastal plain sediments will also affect contaminant removal. Increasing the distance between an area of DNAPL contamination and an extraction vent in the modeled scenarios is similar to the extraction of the volatilized contaminant being retarded by an area of low permeability. It appears that even though the mass removed by Well 1146 was consistently underpredicted, the neighboring vent (Well 1141) was predicted to capture more mass than what was observed, so that the total mass removed was not greatly affected. Further details on this part of the analysis are included in VanAntwerp (2006).
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Discussion and Conclusions
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A multiphase numerical simulator was adapted to account for mass transfer limitations through a dual-domain approach. Using TMVOC as a single-medium model for contaminant removal scenarios overpredicted the mass removal rates due to a local-equilibrium assumption in each element. The dual-domain model–based simulation successfully matched data from the mass removal of a DNAPL at a laboratory and a field-scale air sparging operation.
Although moisture characteristics of the sand used in the laboratory were unknown, the constraints of the known capillary rise, photographs of sparge zone width response to injection rate, and initial contaminant distribution provided enough information to reasonably estimate soil parameters through model calibration. Contaminant mass removed during operational changes in air injection was accurately resolved in the dual-domain simulations but not in single-domain simulations assuming local equilibrium. During pulsed operation in the two-dimensional experiment, the dual-domain model could accurately predict the time for concentrations to tail off after a pulse of air, although exact matches of concentrations during the pulses could not be obtained.
The A12/d2 ratio that was fitted to the laboratory data, (which is analogous to fitting a mass transfer coefficient to a system) was 1000 times larger for the field-scale air sparging demonstration. This indicates that mass transfer rates measured at a bench scale may not be applicable to field-scale processes. One explanation for the difference in mass transfer coefficients may be a result of the formation of a relatively uniform sparge zone in the two-dimensional box that is directly in contact with the NAPL PCE. In the field system, many more heterogeneities affect the sparge zone formation, and larger zones may be excluded from gas flow.
The field-scale parameters had fewer constraints. The highly heterogeneous coastal plain sediments were assigned average bulk permeability and capillary value to model a homogeneous system for a more straightforward calibration of a mass transfer coefficient. Calibration of intrinsic permeability and A12/d2 ratio to the conventional sparging operation (flow configuration 1) provided reasonable matches of the simulated data to the actual data for the remaining sparging configurations modeled during the 57-d simulation. Simulated mass removal for individual vents was dependent on the initial NAPL distribution, although the total mass removed was less affected. The sensitivity of the model to initial contaminant distribution can be attributed in part to a lack of knowledge of where heterogeneities exist. Heterogeneities would affect the sparge zone formation and the flow paths to the extractions wells.
One drawback of this multiphase dual-domain approach to modeling mass removal in air sparging is the relatively large amount of site parameter data needed. However, as this study shows, a moderate amount of site information can still produce reasonable results if the data exist for model calibration at the field scale. Calibration of the model is important, and using laboratory-derived parameters may not be accurate.
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H.-H. Liu and T. H. Illangasekare
Preface: Recent Advances in Modeling Multiphase Flow and Transport with the TOUGH Family of Codes
Vadose Zone J.,
February 25, 2008;
7(1):
284 - 286.
[Abstract]
[Full Text]
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ABSTRACT
INTRODUCTION
