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Published in Vadose Zone Journal 2:368-381 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH PAPER

Modeling the Influence of Water Content on Soil Vapor Extraction

Hongkyu Yoon, Albert J. Valocchi* and Charles J. Werth

Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, 205 N. Mathews Ave., MC-250, Urbana, IL 61801
* Corresponding author (valocchi{at}uiuc.edu).

Received 14 November 2002.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 BACKGROUND AND MODEL DEVELOPMENT
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
We present a comprehensive model and simulation results to assess the impact of changing water content on nonaqueous phase liquid (NAPL) mass transfer, vapor phase retardation, and slow desorption during soil vapor extraction (SVE). Contaminant mass transfer and water and energy transport processes for a one-dimensional, nonisothermal, and single contaminant component system are considered. Literature-derived relationships are used to express the fraction of soil surface area exposed to the vapor phase and the NAPL–gas mass transfer rate expression as a function of water saturation. Simulations are presented for two scenarios: (i) low water saturation, where soil drying is expected and direct vapor sorption to soil may be important, and (ii) high water saturation, where NAPL mass transfer to the gas phase is rate-limited and the gas flow rate is very low. At low water saturation slow desorption controls long tailing in the effluent concentration and the cleanup time. Also, when dry air is purged through the system, water evaporation occurs, the temperature decreases, and hence, desorption rates decrease. The NAPL mass transfer rates were negligibly affected by water evaporation because time scales of the NAPL volatilization were much smaller than time scales of the water evaporation. At high water saturation, NAPL is trapped by water and NAPL mass transfer to the gas phase is limited by diffusion through water films. For this case, NAPL mass transfer is slow and thus controls concentration tailing and cleanup times.

Abbreviations: NAPL, nonaqueous phase liquid • RH, relative humidity • SVE, soil vapor extraction • TCE, trichloroethylene • VOC, volatile organic chemical


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
BACKGROUND AND MODEL DEVELOPMENT
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
SOIL VAPOR EXTRACTION is often used to remediate volatile organic chemicals (VOCs) from the vadose zone. During SVE a vacuum is applied and clean air is forced through the vadose zone to enhance volatilization of entrapped NAPLs (Hutzler et al., 1989; Johnson et al., 1995). Although SVE has been shown to remove large amounts of VOCs, high initial recovery periods are often followed by sustained periods of low recovery referred to as tailing (Crow et al., 1987; DiGiulio and Varadhan, 2001). This tailing behavior is evident at many field sites. A recent example is the large-scale SVE system used for carbon tetrachloride remediation at the Hanford Site, where low recovery rates were found to persist after several years of continuous operation (Rohay, 2000).

Nonaqueous phase liquid recovery rates during SVE are affected by many factors, including the properties, distribution, and mass transfer rates of NAPLs and the properties and heterogeneity of the porous media. Low recovery rates may result from the preferential bypassing of NAPL in unswept regions of low permeability (Kearl et al., 1991; Ho and Udell, 1992; Liang and Udell, 1999), the limited access of purge gas to NAPL trapped in high water saturation regions (Harper et al., 1998; Rathfelder et al., 2000; Yoon et al., 2002), slow NAPL dissolution and volatilization rates (Poulsen et al., 1996; Rathfelder et al., 2000), slow desorption from soil (Ball and Roberts, 1991), and high vapor phase retardation in low moisture soils (Chiou and Shoup, 1985; Batterman et al., 1995; Poulsen et al., 1998). Although this latter process (i.e., sorption of organic vapors on exposed mineral surfaces) is not generally expected to play a significant role in most cases (Armstrong et al., 1994; Abriola et al., 1999), it may potentially be important near the upper surface of the soil, in the vicinity of air injection wells, and in arid environments. In arid environments induced gas-phase advection is expected to enhance soil drying, and this may affect SVE performance since it is well-known that organic vapor sorption is enhanced under low water saturation conditions (Chiou and Shoup, 1985; Batterman et al., 1995). In field situations, these processes occur simultaneously and are interdependent.

Previous simulation studies have considered the impact of several of these processes on SVE. The effect of vapor sorption was incorporated into models of gaseous diffusion through the unsaturated zone, assuming the vapor sorption coefficient to be either constant (Shoemaker et al., 1990), or to be a prescribed function of soil water content (Culver et al., 1991; Ong et al., 1992). These studies concluded that VOC transport was significantly retarded for soil types having a high vapor sorption coefficient when the soil water content was low. The effect of vapor sorption was also incorporated into a two-dimensional SVE model with an assumption of local equilibrium partitioning among phases. Poulsen et al. (1998) developed a soil type–dependent relationship for predicting the trichloroethylene (TCE) vapor sorption coefficient as a function of soil water content. Simulation results showed that enhanced vapor phase sorption at low water content during SVE can increase the required remediation time.

The processes of slow desorption and NAPL evaporation have been incorporated into several SVE models (Rathfelder et al., 1991; Abriola et al., 1997; Ng et al., 1999), but none of these considered evaporative cooling. Glascoe et al. (1999) considered the effects of cooling on bioventing; however, the effects of cooling on NAPL volatilization and slow desorption, and the effect of water evaporation on retardation, were not considered.

Heterogeneity of the porous media can also have a significant effect on SVE cleanup time because air can flow preferentially into high permeability zones and bypass zones with high NAPL content. This has been studied by Ho and Udell (1992), Poulsen et al. (1996), and Massmann et al. (2000). However, they did not consider slow desorption processes. The effect of high water content on NAPL volatilization also has not been incorporated into SVE models. Recent experimental studies showed that NAPL entrapment in low permeability lenses can persist even following large infiltration events (Oostrom and Lenhard, 2003), and NAPL mass transfer can be significantly rate-limited in fine-grained soils with high water saturations (Harper et al., 1998; Yoon et al., 2002). Hence, this process should be accounted for in SVE simulations.

The objective of this study was to develop a comprehensive model that couples gas flow, water evaporation, water flow, and contaminant transport processes. The model will be used to determine the effects of water content on NAPL mass transfer, vapor phase retardation, and slow desorption during SVE and to assess the validity of simplified approaches that neglect water and heat transport processes due to water evaporation. To focus on the impact of water content and temperature, we consider a one-dimensional system. A conceptual model for predicting the vapor sorption coefficient and NAPL mass transfer as a function of water saturation is developed, and the desorption rate is expressed as a function of temperature using the Arrhenius relationship. Our goal is to test the hypothesis that as the purge gas becomes dry, NAPL and water will evaporate, the temperature will drop, and SVE efficiency will decrease because of increased vapor phase retardation and decreased slow desorption rates. Also, since entrapped NAPL may often be located in fine-grained layers having relatively high water content, the effect of water content on NAPL mass transfer rates will be studied to assess its impact on mass removal rate and mass removal pathways.


   BACKGROUND AND MODEL DEVELOPMENT
TOP
 ABSTRACT
 INTRODUCTION
 BACKGROUND AND MODEL DEVELOPMENT
RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES
 
A conceptual model of the processes affecting soil vapor extraction is shown in Fig. 1. Gas advects through the pore space containing NAPL and residual and/or hydrostatic water. Nonaqueous phase liquid directly in contact with the advecting gas volatilizes. Nonaqueous phase liquid directly in contact with water or water films and NAPL surrounded by water dissolve and diffuse through the water toward the advecting gas. Dissolved or volatilized NAPL components sorb to natural organic matter and mineral aggregates, creating another source of contamination that desorbs when gas phase concentrations decrease. While NAPL volatilizes readily, mass transfer from NAPL trapped or occluded by water is rate-limited due to slow diffusion through water. In arid environments, incoming air can be dry (<100% relative humidity [RH]), and thus water evaporation can occur during SVE. This results in soil drying and an increase in vapor phase retardation. These changes in soil moisture conditions give rise to capillary pressure gradients that can cause water flow. Evaporation also causes a decrease in soil temperature, which can result in changes to sorption equilibrium and kinetic parameters. In this section we briefly examine each of the mechanisms considered to affect SVE in this work, and the associated effects of moisture. Mathematical formulations and assumptions are presented. For more complex systems beyond the scope considered here, processes related to microbial activity, fluctuating air temperature and humidity, thermally enhanced SVE operation, infiltration, and multidimensional water movement due to high vacuum extraction can also affect water content and temperature.



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  		Fig. 1. Conceptual model of mass transfer processes during soil vapor extraction.

 
Mass Balance for Contaminant Transport
The NAPL phase is assumed to be immobile and at residual saturation, while water and gas phases are mobile. Water flow is caused only by capillary pressure gradients resulting from SVE-induced soil drying. Water and energy balance equations are presented later in the paper. The advective flux of contaminant in water caused by capillary pressure gradients is smaller than the gas flux by at least four orders-of-magnitude in the absence of infiltration and thus is ignored in the present work. In this system, the one-dimensional contaminant mass balance equations for a single component are expressed for the gas, solid, and NAPL phases:

[1]

[2]

[3]
where subscripts "s", "w", "n", and "g" designate the solid, water, NAPL, and gas phases; Cg, Cw (M L-3), and qs (M M-1) are the contaminant concentrations in the corresponding phases; n is the porosity; Sg, Sw, and Sn are the gas, water, and NAPL saturations; {rho}n is the density of the NAPL; {rho}b is the bulk density of solid phase (M L-3); Dh is the hydrodynamic dispersion coefficient (L2 T-1); q is the Darcy velocity of the gas phase (L T-1); and I{alpha}ß is the net interphase mass transfer rate to phase {alpha} from contiguous phase ß [M (L3 T)-1]. The Darcy velocity of the gas phase, q, is assumed constant; pore gas velocity changes are due to changes in the relative saturation of each phase during NAPL and water evaporation. The water–gas mass transfer process is approximated by equilibrium partitioning (Werth et al., 1997; Kaleris, 2002). Equations governing equilibrium partitioning are presented later. The hydrodynamic dispersion coefficient, Dh can be expressed as follows:

[4]
where {alpha}L is the longitudinal dispersivity (L), Dg is the molecular diffusion coefficient (L2 T-1), and {tau} is the tortuosity, here set equal to (nSg)10/3/n2 (Millington and Quirk, 1961).

NAPL Volatilization and Dissolution
Nonaqueous phase liquid mass transfer in unsaturated soils is influenced by a variety of factors, including NAPL properties, soil moisture, and the heterogeneity of porous media. As seen in Fig. 1, the NAPL phase may exchange mass with both the water and gas phases. Previous studies indicate that NAPL in direct contact with the purge gas is characterized by high NAPL mass transfer rates. This is especially true for spreading NAPLs that form thin films and thick layers at the air–water interfaces (Wilson et al., 1990; Hayden and Voice, 1993; Dong et al., 1995; Blunt et al., 1995; Wilkins et al., 1995; Fenwick and Blunt, 1998; Abriola et al., 1999). In contrast, NAPL trapped in low permeability regions or partially surrounded by trapped water may be characterized by slow volatilization rates. When NAPL is completely surrounded by water, mass transfer through water films controls NAPL removal. We approximate this mass transfer process with a dissolution rate constant. Rate-limited NAPL volatilization and dissolution are described with the commonly used linear driving force model based on Fick's first law (Miller et al., 1990; Powers et al., 1992; Wilkins et al., 1995):

[5]

[6]
where kgn is the lumped NAPL–gas mass transfer coefficient (1/T), kdis is the lumped NAPL dissolution rate constant into water (1/T), Csat is the saturation vapor concentration that is in equilibrium with the NAPL phase (M L-3), and Csol is the aqueous solubility (M L-3).

Nonaqueous phase liquid dissolution rates have been correlated to water velocity and NAPL saturation in water saturated porous media (Miller et al., 1998). Rate-limited dissolution has been observed at high water velocities and low NAPL saturation. In contrast to water saturated porous media, in unsaturated porous media water flow velocities are very small, even during water infiltration events, and interfacial area for NAPL dissolution is relatively high. Hence, the dissolution rate is assumed constant in time.

Nonaqueous phase liquid–gas mass transfer rates have been correlated to gas velocity and NAPL saturation. Rate-limited volatilization has been observed at high gas velocities (>0.5 cm s-1), and these rates were not affected by NAPL saturation in sandy soils (Wilkins et al., 1995; Abriola et al., 1999). In several column studies water saturations as high as 50% had almost no effect on NAPL–gas mass transfer (Hayden et al., 1994; Harper et al., 1998; Liang and Udell, 1999; Yoon et al., 2002). However, severe rate limitations for NAPL–gas mass transfer were observed at water saturations near 60% in fine-grained soils (Harper et al., 1998; Yoon et al., 2002). We model this rate-limited NAPL–gas mass transfer process by adopting the following power-law function for the volatilization rate coefficient (van der Ham and Brouwers, 1998; Yoon et al., 2002):

[7]
where kgn,i is the initial lumped NAPL–gas mass transfer coefficient, Sn,i is the initial NAPL saturation, and ß is a fitting parameter. In this model, the value of kgn,i controls the initial volatilization, whereas ß causes kgn to decrease as the fraction of NAPL trapped in high water content porous media increases with decreasing NAPL saturation (Yoon et al., 2002). We determined kgn,i using the Sh correlations in Table 1. We determined ß by fitting the NAPL volatilization part of our model to the experimental data of Harper et al. (1998) and Yoon et al. (2002). We found that ß ranged from near zero at low water saturations (i.e., below 15%) to values approaching 5 for water saturations >60%. The regression equation for ß is given below (r2 = 0.99):

[8]


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  		Table 1. Steady-state NAPL–gas phase mass transfer rates from laboratory experiments.{dagger}

 
Note that the NAPL–gas mass transfer coefficient, kgn is not sensitive to a reduction in NAPL saturation for ß < 1. At high water saturations when ß > 3, kgn decreases markedly as NAPL saturation decreases and NAPL volatilization becomes slower than NAPL dissolution. The change of NAPL–gas mass transfer rate is shown as a function of water saturation and NAPL saturation in Fig. 2. This is a unique aspect of our model, as the effect of water saturation on NAPL volatilization has not been considered before.



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  		Fig. 2. Ratio of nonaqueous phase liquid (NAPL)–gas mass transfer coefficient to initial mass transfer coefficient as a function of water saturation (Eq. [7] and [8]) at different remaining NAPL saturations.

 
Sorption and Desorption
Sorption and desorption of VOCs are controlled by the amount and type of minerals and soil organic matter. Mineral surfaces are primarily hydrophilic, while soil organic matter is primarily hydrophobic. At 100% RH, water covers the majority of mineral surfaces (Goss, 1992, 1993) and VOC sorption primarily occurs in organic matter (Karickhoff et al., 1979). As RH decreases, mineral surfaces lose sorbed water and sorb more VOCs. Previous investigators (Chiou and Shoup, 1985; Goss, 1992, 1993; Smith et al., 1990) have found that VOC sorption is orders of magnitude more favorable under dry than wet conditions.

The kinetics of VOC (de)sorption have been intensively studied at 100% RH and in water saturated systems. Under this condition, VOC sorption and desorption have been observed to occur on two distinct time scales, a fast time scale on the order of minutes to hours and a slow time scale on the order of weeks to months (Grathwohl and Reinhard, 1993; Farrell and Reinhard, 1994; Werth et al., 1997; Werth and Reinhard, 1997). Werth and Reinhard (1997) found that in sediments at 100% RH, fast desorption may be controlled by retarded diffusion through aqueous filled mesopores. The fast fraction of mass accounted for the majority of sorbed VOCs and is believed to control the bulk of retardation during SVE. Because fast desorption occurs in minutes, the corresponding mass transfer zone length is short compared with a typical field system size. Thus, we assume this fraction is at equilibrium. For the slow fraction, results from numerous studies (Luthy et al., 1997; Werth and Reinhard, 1997; Huang and Weber, 1998) suggest that diffusion through hydrophobic micropore spaces controls mass transfer. Slow desorption is typically modeled using either a single diffusion or mass transfer coefficient, or a distribution of these parameters.

Unger et al. (1996) developed an equilibrium partitioning model to predict the effect of water content on vapor phase sorption. The relationship between water saturation obtained from the soil pore size distribution and soil surface area was derived. We extend this model to account for slow desorption as well as equilibrium partitioning. The soil surface area consists of three classes of sites for sorption and desorption (see Fig. 1). Fractions of equilibrium partitioning are expressed as a function of water content to model retardation due to vapor phase sorption caused by water evaporation. The total sorbed mass concentration, qs (M M-1), can be expressed by the linear fractional approach, in a manner similar to that of a two-site model as follows:

[9]

[10]
where qweq is the concentration sorbed at a 100% water saturation (M M-1), qveq is the concentration sorbed at a 0% water saturation (M M-1), qmt is the concentration sorbed to the slow desorption sites (M M-1), fweq is the fraction of sorbed mass in equilibrium with the water phase, fveq is the fraction of sorbed mass in equilibrium with the gas (vapor) phase, and fmt is the fraction of sorbed mass that desorbs slowly.

Henry's Law and the Freundlich isotherm are used to represent equilibrium partitioning between gas, water, and aqueous phases:

[11]

[12]

[13]
where H is Henry's Law constant, KF1 and nF1 are Freundlich coefficients between water and solid phases, and KF2 and nF2 are Freundlich coefficients between gas and solid phases. The fraction of slow desorption (fmt) is assumed constant in time because data are not available and because water-filled micropores are not expected to empty even at low water saturation.

A first-order kinetics approach is used to represent mass transfers between water and slow desorption sites in the solid phase:

[14]
where kws is the mass transfer coefficient between water and solid (T-1). The rate of slow desorption (kws) changes with temperature according to the Arrhenius relationship (Werth et al., 2000):

[15]
where kws,ref is the water–solid mass transfer coefficient at 15°C, R is the ideal gas constant, and Eact is the apparent activation energy.

Water and Heat Transport
During soil drying capillary pressure gradients drive water flow from high to low water saturations (Rossi and Nimmo, 1994; Webb, 2000). The capillary pressure at any location in a system is determined from the water content and a capillary pressure–saturation profile. The well-known van Genuchten (1980) and Brooks and Corey (1966) relationships have been extended to model water flow in relatively dry porous media (Campbell and Shiozawa, 1992; Rossi and Nimmo, 1994; Fayer and Simmons, 1995; Morel-Seytoux and Nimmo, 1999; Webb, 2000).

Recently, Glascoe et al. (1999) explored the effect of advectively induced temperature and moisture changes on microbial activity during bioventing. They found that the flow of liquid water plays a crucial role because it acts to evenly redistribute soil moisture in a sandy soil. In turn this moderates the temperature drop in any one part of the system during SVE because warmer water flows to cooler zones where volatilization occurred. To what extent this occurs during SVE in lower permeability soils or in soils exposed to high advective gas velocities is not clear.

The one-dimensional mass and energy balance equations for nonisothermal multiphase flow and transport were developed assuming equilibrium partitioning between liquid water and water vapor and thermodynamic equilibrium among phases (Glascoe et al., 1999). According to the criterion presented by Milly (1982) the assumption of equilibrium water evaporation is reasonable. Thermal equilibrium has been shown to be a reasonable assumption in other experimental and numerical investigations of both normal and thermal venting systems (Lingineni and Dhir, 1992; Kaluarachchi and Mesbah-Ul Islam, 1995). The water balance equation is expressed as

[16]

[17]

[18]

[19]
where subscript "v" represents the water vapor, {rho}v and {rho}w are the densities of water vapor and liquid water (M L-3), and Jv and Jw are the flux of water vapor and liquid water (M L-2 T-1). In the water and energy balance equations the volumetric fraction of a phase ({theta}) is used instead of the saturation as in the transport equations. Kw({theta}w) is the effective hydraulic conductivity of liquid water (L T-1), {psi} is a matric potential (L), and Dv,g is an effective dispersion coefficient of water vapor as shown in Eq. [4].

The equation for the conservation of energy in the presence of NAPL without energy sinks and sources can be expressed as




[20]
where ci is the specific heat capacity of component i; T is the absolute temperature in the porous media (K); Tref is reference temperature (273.15 K); hLAT,w and hLAT,n are the latent heat of vaporization of water and NAPL, respectively; and kt,eff is the volume-averaged effective thermal conductivity of the soil–water–gas system (W m-1 K-1]. These equations are identical to the model developed by Glascoe et al. (1999) except for the NAPL term. The change in NAPL saturation can be obtained explicitly from the contaminant mass transport equations.

The vapor density can be calculated from the matric potential and soil temperature with a form of the Clausius–Clapeyron equation (Edlefson and Anderson, 1943):

[21]
where rh is the RH of the gas, g is the acceleration of gravity, and Rv is the water vapor gas constant (461.5 J kg-1 K-1).

The two-parameter junction model of Rossi and Nimmo (1994) and the relative permeability model of Mualem (1976) were used to simulate water and vapor flow simultaneously. A detailed description is given by Rossi and Nimmo (1994) and Glascoe et al. (1999).

Computational Approach
The contaminant mass transport equations (Eq. [1]–[15]) were solved numerically with a Crank–Nicolson finite difference scheme. The water mass and energy balance equations (Eq. [16]–[20]) were solved with an upstream finite difference scheme for the advective terms and a fully implicit finite difference scheme for the temporal terms. The two equation sets were decoupled and solved sequentially. First, the mass transport equations (Eq. [1], [2], and [14]) were solved, employing an alternating operator-splitting algorithm (Valocchi and Malmstead, 1992). The Thomas algorithm was employed for Cg in Eq. [1] and the fourth-order Runge-Kutta method was employed to solve two simultaneous first-order ordinary differential equations for Cg and qmt. Nonlinear coefficients (interphase mass transfer terms and terms that depend on NAPL saturation) are evaluated at the previous time step. The amount of NAPL volatilized was calculated from explicit solution of the mass balance Eq. [3]. Then, the water mass and energy balance equations (Eq. [16]–[20]) with the same primary variables (matric potential and temperature) given by Glascoe et al. (1999) were solved simultaneously, employing a Newton–Raphson iteration method. A convergence criterion of 10-8 in the absolute value of the change in the solution vector was used. Finally, time-lagged temperature and water saturation dependent properties (Eq. [15] for kws, Eq. [8] for kgn, Eq. [4] for Dh, fluid properties in Table 2, and Eq. [10] for fweq and fveq based on regression equations in Table 3) were then updated. To minimize numerical dispersion and oscillation, Peclet and Courant numbers were maintained at less than 2 and 1, respectively, and time steps varied depending on the transport conditions. The grid spacing was 0.05 m. The initial time step for contaminant mass transport was 0.001 s and increased up to Courant numbers of 1. The initial time step for water and energy balances was 1 s and was increased up to 0.01 d.


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  		Table 2. Fluid properties used in simulations.{dagger}

 

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  		Table 3. Regression equations between the fraction of soil surface area exposed to the gas phase (fveq) and water saturation (Sw).

 
For contaminant, water, and energy equations a third-type boundary condition was used at the inlet and a second-type (zero diffusive flux) boundary condition was used at the outlet. A detailed discussion of boundary conditions for the water and energy equations is given by Glascoe et al. (1999). The numerical model developed in this work was verified through comparisons of various simplified components of the model against available analytical solutions and mass balance computations. The numerical solution of the NAPL–gas mass transfer process in Eq. [1] with ß = 0 was verified using the analytical solution of Toride et al. (1993). Fractional desorption processes in Eq. [1] and [2] were verified through the two-site models of Toride et al. (1993) and Fry et al. (1993). For contaminant mass balance the error was maintained within 0.5% and <0.2% for the most of simulation cases. The water mass and energy equations were verified through comparisons with graphical results from Glascoe et al. (1999). Global water mass and energy balance errors were generally <0.5%.

Input Parameters for Simulations
This work was motivated from an assessment of the SVE system used to remove carbon tetrachloride (CCl4) from the vadose zone at the Hanford Site in Washington. Our goal was to study processes important at the site, but it is beyond the scope of this work to model actual site SVE operation. At this site the vadose zone is approximately 70 m thick and consists of strongly layered stratigraphic units that include an upper gravel and sand unit, overlying a finer-grained silty layer, overlying a carbonated-cemented Plio-Pleistocene (i.e., caliche) layer. Field moisture contents are very heterogeneous, with volumetric saturations in the range of 1.5 to 38.5% (Rohay, 2000).

Simulations for a 5-m distance are presented for two situations. Case I exhibits low water saturation in a high permeability soil where the gas flow rate is high, soil drying is expected and vapor sorption to soil may be important. Case II exhibits high water saturation in a low permeability soil, where the gas flow rate is low and NAPL mass transfer to the gas phase is rate-limited. Input parameters for Case I were based on the Hanford sandy soil, and input parameters for Case II were based on the Hanford silty sand and Plio-Pleistocene (caliche) soil (Khaleel and Freeman, 1995; Rohay, 2000). Gas flow rates were chosen in the range of 10 to 100 m d-1 at low water saturation and 0.5 m d-1 at high water saturation. These gas flow rates are similar to those encountered at the Hanford SVE site and many other sites (Gibson et al., 1993; Rohay, 2000; DiGiulio and Varadhan, 2001) beyond the vicinity of an extraction well. Capillary pressure–saturation data for the Hanford soils (Khaleel et al., 1995; Khaleel and Freeman, 1995) were used in a least-squares estimation of parameter values for the Rossi and Nimmo (1994) model. The saturation–capillary pressure curves for these soils are presented in Fig. 3.



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  		Fig. 3. Capillary pressure–saturation curves of Rossi and Nimmo model (RNM) fitted to experimental data of two Hanford soils for Case I and Case II.

 
The mass transfer model developed in this work was fit to the experimental data of Werth and Reinhard (1997) and Werth et al. (1997) for TCE and Livermore sand to obtain fmt and kws. To test the effect of kws on slow desorption, several values of kws ranging from 1.0 x 10-7 to 4.0 x 10-6 were chosen based on the literature (Rathfelder et al., 2000). Limited information is available regarding the CCl4 sorption parameters at the Hanford Site. Freundlich sorption parameters at both 0 and 100% water saturations were chosen from CCl4 sorption parameters at the Hanford Site (Yonge et al., 1996) and literature values for TCE sorption (Unger et al., 1996; Werth and Reinhard, 1997; Poulsen et al., 1998) because of the similarity between chemical properties of TCE and CCl4.

Correlations of Wilkins et al. (1995) and Yoon et al. (2002) shown in Table 1 were used to determine the initial NAPL–gas mass transfer coefficients for Case I and Case II, respectively. NAPL–gas mass transfer coefficients listed in Table 1 range from 0.025 to 2.63 s-1 for gas velocities from 20 to 2000 m d-1. These literature values are higher than values used in previous SVE modeling, which range from 1.2 x 10-6 to 1.2 x 10-3 s-1 (Rathfelder et al., 1991; Poulsen et al., 1996). A value of kdis of 1.5 x 10-7 s-1 was chosen from the value used in a TCE dissolution simulation (Sleep and Sykes, 1989). This value has been used in previous SVE modeling (Poulsen et al., 1998; Rathfelder et al., 2000). Also, this value adequately described the toluene experimental result of Harper et al. (1998) at a 22% water content. All transport parameters are given in Table 4.


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  		Table 4. Soil and transport parameters used in simulations.

 
Fluid properties used in simulations are given in Table 2. The saturated vapor pressure, Henry's Law constant, water solubility, and water vapor density are temperature-dependent variables.

Other chemical and porous media properties are considered constant within the temperature change considered in the present work (Kerfoot, 1991; Constantz, 1982). Correlations between fveq and Sw were regressed from adsorption data of Unger et al. (1996), as there are no data available for Hanford material. Coarser-grained Pequest and finer-grained Marcus Hook soils were chosen for Case I and Case II, respectively, to vary the fraction of surface area exposed to the vapor phase at low water saturation (<10%). The correlations are given in Table 3. The initial distribution of CCl4 among different phases was assumed to follow local equilibrium. For soil properties, mass transport parameters, and fluid properties, initial conditions were assumed constant and uniform throughout the domain.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 BACKGROUND AND MODEL DEVELOPMENT
 RESULTS AND DISCUSSION
SUMMARY AND CONCLUSIONS
 REFERENCES
 
Case I: Low Water Saturation
Effect of Water Evaporation and NAPL Volatilization
Simulation parameters varied in Case I are shown in Table 5. The relative effluent concentration and the normalized mass remaining for NAPL and sorbed phases are shown in Fig. 4 for Run 1. Run 1 was defined by intermediate values of all input parameters obtained from the literature. As shown, NAPL mass dropped quickly to zero, while the sorbed mass and effluent concentration dropped quickly at first, and then started to tail. Corresponding plots of the spatial mass remaining and concentration profiles at 4 d are shown in Fig. 5. In this figure both the fraction of equilibrium sorbed mass (feq = fveq + fweq) and the mass-transfer limited sorbed mass (fmt) are shown. The NAPL profile has a sharp front with a short mass transfer zone because NAPL volatilization was fast compared with advection. The feq profile and the concentration profiles are similar in shape, but they lag behind the NAPL profile. In contrast, the fmt profile has a broad front that decreases slowly. These results indicate that, as shown in Fig. 4, the effluent concentration was controlled by NAPL removal at early time and by slow desorption at later time. Mass in other phases (i.e., gas and water) did not noticeably affect the effluent concentration profile because NAPL and sorbed mass initially comprised 95.2 and 4.1%, respectively, of the total mass.


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  		Table 5. Parameters varied in low water saturation simulations (Case I).{dagger}

 


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  		Fig. 4. Predicted dimensionless mass remaining and effluent gas concentration with time (Case I, Run 1).

 


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  		Fig. 5. Spatial profile of mass remaining and concentration after 4 d (Case I, Run 1).

 
Spatial profiles for water saturation and temperature in Run 1 are shown in Fig. 6 and 7, respectively. A spatial profile for water saturation at 400 d in a material characterized by a large hydraulic conductivity (Kw, sat = 8.64 m d-1) is also shown. During SVE liquid water evaporated because the influent air was at 50% RH. As shown in Fig. 6, this caused a drying front to slowly propagate into the system. Note that the time scale for water evaporation to dry out the column is much longer than the time scale for NAPL volatilization; hence, the latter is not affected by water evaporation. For the case with large Kw, sat, water redistributed in the system fast relative to evaporation. Hence, the water saturation dropped more uniformly.



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  		Fig. 6. Spatial profile of water saturation at different times (Case I, Run 1).

 


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  		Fig. 7. Spatial profile of temperature at different times (Case I, Run 1).

 
Temperature profiles in Fig. 7 are affected by both water and NAPL volatilization. During the first 4 d of SVE, the temperature profile had a sharp front that corresponded to the NAPL volatilization front in Fig. 5. This result is similar to that by Lingineni and Dhir (1992), where the latent heat of vaporization for NAPL volatilization is provided by the incoming air and transferred from the soil system to the vapor phase. After NAPL was removed, the temperature continued to decrease toward the wet bulb temperature (9.3°C) as water evaporated. After 50 d, water evaporation near the system inlet stopped because equilibrium water saturation was reached (Fig. 6), and the temperature started to rebound (Fig. 7). For the high hydraulic conductivity case, the temperature was spatially uniform after 400 d because water was redistributed in the system fast relative to evaporation, and no additional drying occurred after this time.

The water content in a system was affected by the gas purge rate, the influent RH, and the initial water content. The effects of these parameters were evaluated by comparing Run 16 and Run 17 in Fig. 8. Relative to Run 1, Run 16 was characterized by a higher gas flow rate (100 m d-1) and a lower influent RH (25%), while Run 17 was characterized by a lower influent RH (25%) and a very low initial water saturation (4.56%). For both runs, a drying front slowly propagated through the system. For Run 16, the front propagated <1 m after 100 d, while for Run 17 the front propagated only 1.8 m after 100 d. These results indicate that even under extreme conditions, drying time is slow relative to NAPL mass removal (Fig. 4), and the two are essentially decoupled.



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  		Fig. 8. Spatial profile of water saturation at different times for Case I, Run 16 (symbols) and Case I, Run 17 (symbols with line).

 
Summary of Test Runs
Simulations were performed for 14 additional runs to illustrate the effect of mass transport, interphase mass transfer rates, and sorption parameters at low water saturation as presented in Table 5. As shown in Fig. 9, the time to remove NAPL, 95% of the sorbed mass, and 99% of the sorbed mass was calculated. Simulation results for each Run were compared with that of the reference run, Run 1. Summarizing, NAPL removal was not affected by water evaporation (Runs 1 and 2), slow desorption rates (Runs 1, 7–9), or equilibrium sorption parameters (Runs 1, 11–15), but it was prolonged when the gas purge rate was lowered (Runs 1 and 5) and when the NAPL volatilization rate was decreased (Runs 1 and 10). The time to remove 95 and 99% of the sorbed mass was slightly prolonged when water was allowed to evaporate (Runs 1 and 2), when the gas purge rate was lowered (Runs 1 and 5), when the fraction of slow desorbing mass was increased (Runs 1 and 11), and when the Freundlich capacity parameter was increased (Runs 1, 13, and 15), and markedly prolonged when the slow desorption rate was decreased (Runs 1 and 9).



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  		Fig. 9. Comparison of cleanup times in Case I.

 
Water evaporation causes the temperature to decrease and fveq to increase. The decrease in temperature causes kws to decrease. The decrease of kws resulted in a slight difference in the cleanup time between Runs 1 and 2. No soil drying effect on the cleanup time, however, was found because the development of the drying front takes approximately 100 d, as shown in Fig. 6, while the cleanup time is <100 d. Even at low RH (Run 4), vapor phase retardation caused by soil drying only marginally affected cleanup time. The cleanup time for NAPL was linearly proportional to the gas flow rate in Runs 1, 5, and 6. If the contaminated region is greater than the length of mass transfer zone, as shown in Fig. 5, the NAPL removal efficiency will depend only on the advective pore gas velocity. The effect of the magnitude of the NAPL–gas mass transfer coefficient will be discussed in the next section. The cleanup time for 95 to 99% of the sorbed mass in Runs 1, 5, and 6 was very similar, indicating the critical pore gas velocity for slow desorption may be lower than 10 m d-1 under the given conditions. The effect of slow desorption on SVE was simulated in Runs 7, 8, and 9. The strong dependence of the efficiency of SVE on the slow desorption rate is evident. The time to remove 99% of the sorbed mass ranged from approximately 20 to 600 d as the desorption rate varied from 4.0 x 10-6 to 1.0 x 10-7 s-1.

Finally, the effect of fveq was explored in Runs 13 through 15. As summarized above, only under an extremely dry condition (Sw = 1.76%) with high KF2 (Run 15) was desorption prolonged due to vapor phase retardation. The retarding effect of vapor sorption similar to that predicted in Run 15 was also found in other column experiments and simulations performed under dry conditions and with high sorption capacity soils (Grathwohl and Reinhard, 1993; Poulsen et al., 1998). Otherwise, contaminant removal was not affected (Runs 13 and 14). During NAPL removal, equilibrium sorption sites emptied fast relative to slow desorption sites. After NAPL removal, the gas concentration was very low. At this concentration level, vapor phase sorption had no significant role in retardation, while the slow desorption process controlled tailing. These results indicate that in most field conditions (including semiarid environments like the Hanford site), water content is greater than the very dry conditions for which significant vapor sorption will occur.

Case II: High Water Saturation
Effect on NAPL Volatilization
Simulation parameters varied in Case II are shown in Table 6. In contrast to Case I, gas flow is very slow because a high water saturation condition in a low permeability zone is considered. The relative effluent concentration and the normalized mass remaining for NAPL and sorbed phases are shown in Fig. 10 for Run 1. Again, Run 1 is defined by intermediate values of all input parameters obtained from the literature. As shown, NAPL mass decreased quickly at first, and then started to tail. The sorbed mass behaved similarly, except during tailing when there was a quasi-steady state. Effluent gas concentration was constant at first, dropped gradually until most of the mass was removed, and then dropped quickly.


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  		Table 6. Parameters varied in high water saturation simulations (Case II).{dagger}

 


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  		Fig. 10. Predicted dimensionless mass remaining and effluent gas concentration with time (Case II, Run 1).

 
Corresponding plots of the spatial mass remaining and concentration profiles at different times are shown in Fig. 11. As before both the equilibrium and mass-transfer fractions feq and fmt are shown for the sorbed mass. At 100 d, the length of mass transfer zone (Lmtz) was shorter than the system length of 5 m so that the effluent gas concentration equaled the saturated concentration. At 300 d Lmtz became greater than the system length, which led to a decrease in the effluent gas concentration. Lmtz increased because kgn decreased. At 300 d kgn was approximately 1.5 x 10-7 s-1 (Eq. [7]), which equals kdis used in Run 1. This shows that at 300 d both NAPL volatilization and dissolution control NAPL removal. After 300 d, kgn continued to decrease, and dissolution controlled NAPL removal. The presence of NAPL in the system controlled the gas concentration. This leads to the quasi-steady-state profile for sorbed mass. When all the NAPL was removed near the inlet boundary, Cg dropped sharply and the mass removal from the sorbed mass restarted, as shown in Fig. 11d. These results indicate that at high water saturation NAPL removal is slow and controls cleanup time. In contrast to the low water saturation runs, water evaporation had little effect on changing the temperature and water saturation. The temperature decreased <2°C even after 700 d because of the low gas flow rate and high initial water saturation.



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  		Fig. 11. Spatial profile at different times for Case II, Run 1 simulated in Fig. 10; (a) 100 d, (b) 300 d, (c) 600 d, and (d) 700 d.

 
Summary of Test Runs
Simulations were performed for six additional runs at high water saturation. Since the time scale required for the mass removal was similar for the NAPL and sorbed phases (Fig. 10 and 11), only the time to remove NAPL was calculated, as shown in Fig. 12. Summarizing, NAPL removal was affected dramatically by the magnitude of kdis (Runs 1–3) and ß (Runs 1, 4, and 5). Even for a 2-m length scale (Runs 6 and 7), NAPL removal was affected significantly by kdis.



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  		Fig. 12. Comparison of cleanup times in Case II.

 
As NAPL is removed, kgn decreases according to Eq. [7]. The decrease of kgn causes kdis to control NAPL mass removal at later time, depending on the magnitude of kdis. This decrease of kgn led to a big discrepancy in the NAPL removal times between Runs 1 and 2, indicating that the NAPL mass removal was significantly influenced below a dissolution rate of 1.5 x 10-6 s-1 under the given conditions.

Runs 1,4, and 5 with the same kdis showed that the NAPL removal time increased with increasing ß because kgn decreases dramatically as ß increases. The exponent ß in the power function model is used to describe the reduction of the interfacial area available for NAPL volatilization. As ß increases, the amount of water surrounding NAPL increases and dissolution becomes more important. Consequently, the time to remove NAPL markedly increases as ß increases. Increased cleanup time was found and discussed by Poulsen et al. (1996) and Rathfelder et al. (2000). Simulations of Poulsen et al. (1996) showed the dependence of NAPL removal efficiency on NAPL–gas mass transfer coefficients ranging from 1.2 x 10-6 to 1.2 x 10-3 s-1. They further suggested that rate-limited NAPL–gas mass transfer did not alter the NAPL removal mechanism, but influenced only the NAPL removal rate. In contrast, simulations conducted by Rathfelder et al. (2000) showed that NAPL removal was limited by diffusion through water as a result of water table upconing in the vicinity of an extraction well. This result suggested that water table migration can affect NAPL removal pathways as well as NAPL removal rate. The results in this work further indicate that the NAPL removal time was prolonged both due to the low gas flow rate through the low permeability soil and the small NAPL–gas mass transfer rate resulting from the water shielding effect on the entrapped NAPL. At the Hanford site, CCl4 was released more than 40 yr ago, and multiple wetting and drying cycles have occurred since this time. Much of the CCl4 is thought to be trapped in the caliche layer (Rohay, 2000). The water saturation in the caliche varies widely and is as high as 38.5% by volume (Rohay, 2000). Hence, the low permeability and high water saturations in this layer may shield NAPL from access to the advecting pore gas and subsequently increase the cleanup time.

The effect of the total simulation length scale was examined in Runs 6 and 7. If the cleanup time is proportional to the length, then mass transfer limitations are not significant. For Runs 2 and 7 with a high kdis (1.5 x 10-6 s-1) the cleanup time was nearly proportional to the length, while for Runs 1 and 6 with a lower kdis (1.5 x 10-7 s-1) the cleanup time differed by only 25%. With a low kdis Lmtz was longer than the length of the system (Fig. 11). These results imply that in many heterogeneous field situations, the cleanup time will be significantly influenced by diffusion through the water phase even for a short length of contaminant zones at high water saturation.


   SUMMARY AND CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 BACKGROUND AND MODEL DEVELOPMENT
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
REFERENCES
 
This paper presented a one-dimensional numerical model that assesses the influence of changing water content on NAPL mass transfer, vapor phase retardation, and slow desorption during SVE. Because water content changes due to evaporation cause changes in temperature and matric potential, the model also includes water and energy transport processes. Simulation results demonstrated the interdependence of these processes and their effects on the mass removal mechanisms and cleanup times. Two sets of simulations presented for cases of low and high water saturation revealed the following:

  1. At low water saturation, slow desorption controlled tailing in the effluent concentration and the cleanup time. Nonaqueous phase liquid mass was removed very fast relative to other processes because of high NAPL–gas mass transfer rates and high gas flow rates. High NAPL removal rates caused the temperature profile to have a sharp front that corresponds to the NAPL volatilization front. Water evaporation also caused the temperature to decrease, albeit at a longer time scale. The decrease in temperature caused the slow desorption rate to decrease, while slightly increasing the cleanup time. However, even at low RH (25%) and high gas flow rate, soil drying was slow relative to NAPL removal and the effects of water evaporation on NAPL removal were marginal.
  2. At high water saturation in lower permeability soils, the efficiency of mass removal was primarily controlled by NAPL removal. The prolonged cleanup time was most significant in runs having a low dissolution rate and high water saturation. For these cases, NAPL mass transfer was limited by diffusion through the water phase. Simulation results indicated that the limiting NAPL removal mechanism changed from volatilization to dissolution (i.e., diffusion through surrounding water) as soil moisture increased. This was accounted for in the parameter ß. It is important to note that the NAPL–gas mass transfer rate coefficients (kgn,i) estimated from laboratory column experiments (Table 1) are much greater than values used in previous numerical transport models (Poulsen et al., 1996). There was no justification for the small NAPL–gas mass transfer rate coefficients used in previous works. Hence, this work provides a more complete picture of when either volatilization or dissolution controls NAPL removal during SVE. There is a lack of data on the range of dissolution rate and the effect of the thickness of low permeability zones. Hence, more research is needed to evaluate the impact of water content on VOC vapor transport under a variety of conditions and its implications for soil vapor extraction.
  3. For all cases simulated, temperature and water content changes due to water evaporation were only marginally important in our one-dimensional system. Vapor sorption will play an important role in NAPL removal only under extremely dry conditions; otherwise, it can be neglected. It is possible that vapor sorption is important when modeling VOC flux to the atmosphere through the surface soil, or when determining the mass balance of NAPL components in a system. However, results in this study indicate that simplified models that neglect temperature change and water evaporation are valid under most field conditions.

There is currently little information available on the distribution of NAPL and water in heterogeneous systems with stratified lenses of low permeability and sandy soils. Recently, Oostrom and Lenhard (2003) showed that in a soil box experiment, NAPL remained in a low permeability zone surrounded by a high permeability zone even after significant water infiltration. This indicates that mass transfer from both low and high permeability zones is important, and that NAPL removal mechanisms proposed in our model must be applied to heterogeneous systems.


   ACKNOWLEDGMENTS
 
Support for this work was provided by the U.S. Department of Energy Environmental Science Management Program Project No. 70045. We thank Philip Meyer and Virginia Rohay for their assistance in obtaining the water retention data and other information about the Hanford site. We also acknowledge the effort of the Associate Editor and Reviewers, whose comments have led to significant improvement of our manuscript.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 BACKGROUND AND MODEL DEVELOPMENT
 RESULTS AND DISCUSSION
 SUMMARY AND CONCLUSIONS
 REFERENCES