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Published in Vadose Zone Journal 2:692-701 (2003)
© 2003 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA

ORIGINAL RESEARCH PAPERS

Volatile Organic Compounds Volatilization from Multicomponent Organic Liquids and Diffusion in Unsaturated Porous Media

Guohui Wang, Sayonara Brederode F. Reckhorn and Peter Grathwohl*

University of Tübingen, Center for Applied Geoscience, Sigwartstrasse 10, 72076 Tübingen, Germany
* Corresponding author (grathwohl{at}uni-tuebingen.de).

Received 9 December 2002.



   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Vapor phase diffusion is an important transport process in the unsaturated zone affecting evaporation of volatile organic compounds (VOCs) from pure and multicomponent organic liquids. To evaluate some widely used empirical relationships for the estimation of effective diffusion coefficients in the unsaturated zone and to assess the validity of Raoult's Law during aging of organic mixtures, two series of laboratory-scale column experiments were performed using pure toluene, pure methyl tert-butyl ether (MTBE), and two multicomponent "kerosene-type" liquids containing four to seven compounds. The analytical one-dimensional solution of Fick's Second Law described the diffusion process of pure compounds very well in two sands with different water contents. The effective diffusion coefficients obtained correspond well to a recently published empirical relationship (Moldrup et al., 2000); the capacity factors fitted indicate equilibrium partitioning of the solute between gas phase and water. A one-dimensional numerical model based on the combination of Fick's Second Law and Raoult's Law was used to predict the volatilization and the diffusion process from multicomponent organic liquids. Both the vapor phase diffusion process of the VOCs and the aging of the organic mixtures were predicted very well solely on the basis of effective diffusion coefficients estimated from the empirical relationship and assuming an ideal mixture (e.g., an activity coefficient of 1 in Raoult's Law).

Abbreviations: CS, medium to coarse sand • FS, fine sand • MTBE, methyl tert-butyl ether • NAPL, nonaqueous phase liquids • PCE, tetrachloroethene • PMQ, Penman–Millington–Quirk model • TCE, trichloroethene • VOC, volatile organic compound • WLR, Water-Induced Linear Reduction model • 1,1,1-TCA, 1,1,1-trichloroethane


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
GROUNDWATER CONTAMINATION by VOCs is one of the major subsurface environmental problems of our time. With increasing use of the underground space (e.g., landfills, fuel, and solvent storage), subsurface contamination with VOCs occurred at many sites. Recently, it was estimated that 7% of the ambient groundwater resources of the USA contain VOCs above the reporting level of 0.2 µg L-1 (Squillace et al., 1999). In most cases subsurface contamination occurred due to accidental releases of nonaqueous phase liquids (NAPL) to the unsaturated zone. During downward migration, parts of the NAPL are trapped in pores by capillary forces, resulting in a residual saturation of about 2 to 20% of the available pore space (Boulding, 1995). The NAPL can also reach the groundwater table or accumulate on layers of low permeability, forming pools of high residual saturation. Volatile organic compounds will evaporate from the residual phase due to vapor phase diffusion. In multicomponent organic liquids the more volatile compounds evaporate first resulting in changing composition of the mixtures ("aging"). The lateral migration of the VOCs from the source can result in large areas of contamination (Mendoza et al., 1996). The vapor phase transport in the unsaturated zone has been identified as a potentially important mechanism for groundwater contamination (Baehr, 1987; Washington, 1996; Baehr et al., 1999; Klenk and Grathwohl, 2002). The spreading of the vapors depends on diffusion, density, or pressure gradients in general and on the partitioning of the VOCs between gas and water as well as water and solids. Many studies show that for migration of VOCs in the unsaturated zone diffusion is the dominating transport process (Jury et al., 1984; Baehr and Corapcioglu, 1987; Silka, 1988; Mendoza et al., 1996; Hughes et al., 1996; Pasteris et al., 2002). Since vapor diffusion is commonly a rapid process, contamination may occur much more quickly than by infiltration of seepage water (Mendoza et al., 1996). According to Falta et al. (1989), density-driven flow is only important for highly volatile compounds with relatively high Henry's Law constants and in highly permeable soils. They concluded that contaminants such as toluene and ethylbenzene are not likely to be affected by density-driven flow.

Vapor phase diffusion depends on the soil porosity, water content, organic C content (sorption), and temperature (Lyman et al., 1982). The dominant parameters affecting diffusion fluxes of VOCs in the unsaturated zone are the vapor pressure and the effective diffusion coefficient (Mercer and Cohen, 1990). Diffusion of single compounds in the unsaturated zone is well understood, and several empirical relationships for determination of effective diffusion coefficients have been developed for different soils (e.g., Penman, 1940; Marshall, 1959; Millington, 1959; Millington and Quirk, 1960, 1961; Sallam et al., 1984; Moldrup et al., 1997, 2000).

For multicomponent organic liquids, however, the current knowledge concerning the aging of the residual organic phase during the diffusion dominated volatilization process is still limited. Baehr and Corapcioglu (1987) modeled the vapor phase transport in the unsaturated zone from a fuel hydrocarbon mixture of eight constituents, which were divided into three classes according to the magnitude of Henry's Law constant, by averaging the thermodynamic properties of individual hydrocarbons in each class. Pasteris et al. (2002) observed the concentration profile of each compound volatilized from an artificial mixed NAPL source in a large-scale lysimeter experiment and found the fuel compounds were transported upward and downward at almost same rate, indicating transport by vapor phase diffusion only. Broholm et al. (2003) conducted a well-controlled field experiment with an emplaced kerosene NAPL source in the unsaturated zone and showed that NAPL aging corresponded well to Raoult's Law.

The objectives of this study were (i) to predict the changing composition ("aging") of NAPLs in the unsaturated zone during the volatilization of its constituents; (ii) to validate a simple, spreadsheet-based numerical model describing the diffusion process from organic mixtures based on the combination of Fick's Second Law and Raoult's Law; and (iii) to evaluate the different empirical relationships for the prediction of the effective diffusion coefficients for coarse and fine sands at different water contents.

Two series of laboratory-scale column experiments were conducted to identify and quantify vapor phase diffusion of VOCs volatilized from pure and multicomponent organic liquids in the unsaturated zone. The columns were filled with two different sands at various water contents to simulate a wide range of environmental conditions. Two single compounds (toluene and MTBE) were used to determine effective diffusion coefficients under steady-state condition and to validate the equilibrium partitioning between gas phase and water in the transient part of the experiments. Two organic mixtures consisting of MTBE, methylcyclohexane, toluene, ethylbenzene, trichloroethene (TCE), 1,1,1-trichloroethane (1,1,1-TCA), and tetrachloroethene (PCE) were chosen to investigate the aging of NAPL sources.


   THEORY
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Volatilization from Multicomponent Organic Liquids—Phase Partitioning
Partitioning between the organic liquid phase and the vapor phase is described by Raoult's Law:

[1]
where Cg, {chi}, and {gamma} denote the equilibrium vapor concentration (g L-1), the mole fraction, and the activity coefficient of the compounds in the mixture. Csatg, po, MW are the saturation concentration in the gas phase (g L-1), the vapor pressure (kPa), and the molecular weight (g mol-1) of the individual pure compound. R and T are the gas constant (8.3144 J mol-1 K-1) and temperature (K), respectively. In a first approximation {gamma} can be assumed to be one, if the interactions between the compounds with similar structure are assumed to be insignificant as shown, for example, for polycyclic aromatic hydrocarbons in coal tar (Eberhardt and Grathwohl, 2002) and hydrocarbon constituents in gasoline (Cline et al., 1991).

The equilibrium partitioning of compounds between water and air is described by Henry's Law:

[2]
here Cg and Cw denote the equilibrium concentration (mg L-1) in air and water phases, respectively, and H is the Henry's Law constant.

The water–solid partitioning of hydrophobic organic compounds is described by the distribution coefficient Kd (L kg-1).


[3]

Cs is the compound concentration in solid phase (mg kg-1); Koc and foc denote the water–organic C partitioning coefficient (L kg-1) and the fraction of organic C in the soil, respectively.

Molecular Diffusion
Molecular diffusion describes mass transport due to the random thermal motion of molecules and atoms, which will cause a net mass flux down a concentration gradient and thus the spreading of a concentration peak with time. Ideally, vapor phase diffusion in multicomponent gaseous systems is based on the Stefan–Maxwell equation (Baehr and Bruell, 1990), but in practice, Fick's Law appears to be a reasonable approximation under a wide range of conditions (Mendoza et al., 1996), especially if the partial pressures of the VOCs are low compared with other gases in the unsaturated zone (e.g., N2, O2). Transient diffusion through a soil layer can be described by Fick's Second Law:

[4]
where Deg is the effective diffusion coefficient (cm2 s-1), {alpha} is the capacity factor, C is the concentration in the soil air (mg L-1), and x and t are the distance (cm) and time (s). {alpha} accounts for the distribution of a compound in the three-phase system: soil solids, air, and water (Grathwohl, 1998):

[5]
where ng, nw denote the air- and water-filled soil porosities (volumetric air or water content), and {rho} denotes the dry bulk density (g cm-3) of the soil. The ratio Deg/{alpha} is known as apparent diffusion coefficient (Grathwohl, 1998).

The effective diffusion coefficient (Deg) is usually determined from steady-state vapor phase diffusion experiments in unsaturated porous media. Several empirical relationships have been developed to predict Deg on the basis of the ratio of the soil air-filled porosity ng and the total porosity n. The most well-known empirical relationships (see Table 1) were developed by Penman (1940), Marshall (1959), Millington and Quirk (1960)(1961), Sallam et al. (1984), and recently by Moldrup et al. (1997)(2000). Penman (1940) originally proposed a general relationship for both dry and moist porous media for a range of air-filled porosities up to 0.6. Millington and Quirk (1960)(1961) proposed two models for gas diffusion. The second model (1961) is often used in transport simulation studies whereas the first model (1960) is less common. Sallam et al. (1984) proposed a similar model for low air-filled porosities, that is, higher water saturation in the soil. Moldrup et al. (1997) derived additional empirical relationships for undisturbed as well as sieved and repacked soils by combining the Penman and Millington–Quirk models (PMQ model). More recently, they proposed the Water-Induced Linear Reduction (WLR) model based on Marshall (1959) which gives better accuracy in predicting Deg compared to the PMQ model (Moldrup et al., 2000).


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  		Table 1. Comparison of some empirical relationships for calculation of Deg, air-filled porosity (ng), and total porosity (n).

 
Modeling of Diffusion Fluxes in Porous Media
An analytical solution to Fick's Second Law exists to calculate the diffusive flux of a compound from a constant concentration (C0) through a soil layer of thickness d initially free of the contaminant and zero concentration at the upper boundary (Crank, 1975):

[6]

At steady-state conditions Eq. [6] reduces to Fick's First Law:

[7]
where Fstat denotes the steady-state diffusion flux (g cm-2 s-1).

During volatilization of a multicomponent organic liquid, its composition and thus the equilibrium vapor phase concentration of its constituents (Cg) change with time according to Raoult's Law (aging). The time-dependent boundary condition requires to solve Fick's Second Law numerically, for example, by a finite difference method (Grathwohl, 1998):

[8]
where Cjk denotes the solute concentration in the soil air at the grid node j at the time step k and {Delta}x and {Delta}t denote the grid size and the time increment between time steps. The dimensionless group (Deg/{alpha})({Delta}t/{Delta}x2) has to be smaller than 0.5 (stability criterion).

In this study, the analytical solution was first used to obtain the effective diffusion coefficients for the pure compounds (toluene and MTBE) by fitting the diffusion fluxes measured in the steady-state region by adjusting Deg. In addition, the equilibrium assumption for compound partitioning between the air, water, and soil phases was validated. Deg values fitted were then compared with existing empirical relationships. For organic mixtures, a numerical model based on the combination of Fick's Second Law and Raoult's Law was used to predict the aging of the multicomponent organic liquids solely based on independently determined parameters (Deg and {alpha}).


   MATERIALS AND METHODS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 
Materials
The compounds selected for this study are typical constituents of kerosene, gasoline, and solvents, which frequently occur at subsurface spills. Pure toluene and MTBE were obtained from Merck Chemical Corp. Two mixtures were prepared in the laboratory as shown in Table 2 along with selected compound properties. Mixture 1 consisted of four compounds (MTBE, methylcyclohexane, toluene, and ethylbenzene) and Mixture 2 consisted of seven compounds (MTBE, methylcyclohexane, toluene, ethylbenzene, 1,1,1-TCA, TCE, and PCE). The chlorinated compounds were included because they would not be affected by aerobic biodegradation.


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  		Table 2. Physicochemical properties of the investigated compounds at 20°C.{dagger}

 
The experiments were conducted with two different sandy materials: medium to coarse sand (CS) from a gravel pit in the Rhine Valley (Germany) and fine sand (FS) from a homogeneous glacial melt water sand deposit (Værlose Air Force Base, Denmark). The lithology of the sands comprises mainly silicates (quartz and feldspar) with a minor fraction of carbonates and very low organic matter contents. The carbonate contents of the CS and FS sands were 2.8 and 1.8%, and the fractions of organic C foc were 0.0001 and 0.00016, respectively (as determined by dry combustion). Before the experiments the sands were sieved to a grain size smaller than 2 mm and dried at 105°C for 24 h to minimize potential microbial growth. The average grain sizes (50% value taken from the standard gravimetric sieve analysis) of the CS and FS were 0.7 and 0.125 mm, respectively. After cooling down to ambient temperature (25°C), deionized water was added to get the desired water contents. The wet sand was mixed intensively and put into plastic bags for at least 24 h at a temperature of 10°C to obtain a uniform water content before preparing the columns for the diffusion experiments. Dry samples were not used to avoid strong adsorption of VOCs to mineral surfaces, which is not representative for the subsurface environment in humid areas. The three toluene column experiments with different water contents were packed with similar overall porosity to elaborate the influence of the water content on the vapor phase diffusion. The physical properties of the columns and the measured values for Deg and {alpha} are summarized in Table 3.


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  		Table 3. The physical properties of the soil columns including values for Deg and {alpha} determined from the pure compound diffusion experiments.

 

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  		Table 4. Parameters used for forward modeling the organic mixture experiments.

 
Equation [5] and the data listed in Table 3 show that {alpha} values for toluene and MTBE depend on the compound-specific H values and the water contents. For the low-foc samples employed in this study Kd becomes important only if the water content (w) is low and H as well as Koc are relatively high. The compounds specific difference in values for Deg depends on their molecular size and therefore is only minor for the compounds employed.

Laboratory Column Experiments
The schematic of the experimental system is depicted in Fig. 1. The sandy samples were packed into stainless-steel columns 25 cm long with 10.43-cm inner diameter and kept in place by means of a fine-meshed stainless-steel screen 2 cm above the bottom. The thickness (height) of the packed sample was 20 cm. The bottom endcap below the steel mesh served as a reservoir containing the NAPL. Direct contact between the organic liquid and the sandy soils was avoided. A small port sealed by a Teflon-lined septum allowed the injection of organic liquids by a syringe. The entire apparatus was installed inside a temperature controlled room with 20 ± 0.5°C. Nitrogen gas was used to purge the top surface of the soil to keep the concentration reasonably close to zero. The N2 flow rates were adjusted to achieve compound concentrations in the headspace above the soil surface to 1 to 2% of the saturated vapor concentrations existing at the lower boundary of the soil columns. The flow rates were 150 mL min-1 for pure toluene and mixture 1, 1000, and 620 mL min-1 for pure MTBE and Mixture 2, respectively. The purge gas flow was kept constant by an electrically controlled flow meter. Nitrogen was wetted through a humidifier before the column to prevent the drying of the soil sample. Gas samples of up to 1.0 mL were taken using a gas-tight syringe from a T-connection at the N2 outlet tube with a diameter of 6 mm. Sampling time intervals ranged from 10 min to hours. The concentration of the hydrocarbons was determined by capillary gas chromatography: HRGC 5160, Carlo Erba, Milan, Italy; WCOT fused silica, 50-m-long column; N2 flow rate of 5.0 mL min-1 equipped with a FID detector (flame ionization detector).



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  		Fig. 1. Schematic of the experimental system.

 
The diffusive fluxes (g m-2 h-1) were calculated from the measured concentration at the column outlet Cg,d (g m-3) and the flow rate of the N2 Q (m3 h-1):

[9]

A denotes the cross-sectional area of the soil column (m2).


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
CONCLUSIONS
 APPENDIX
 REFERENCES
 
Diffusion Experiment with Pure Compounds Toluene and MTBE
The measured fluxes obtained in the pure source columns are plotted in Fig. 2. The curve shapes of the two compounds are similar, but MTBE shows more retarded and approximately 10 times higher fluxes than toluene as expected from the differences in vapor pressure (Table 2).



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  		Fig. 2. Comparison of measured fluxes with the analytical solution of Fick's Second Law (Eq. [6]) for (a) pure toluene and (b) MTBE vapor diffusion in unsaturated soil with different water contents; fitted values for Deg and {alpha} are given in Table 3.

 
The time lag before reaching the plateau indicating steady-state fluxes depends on the capacity factor. The transport of MTBE is much more retarded than that of toluene due to its much lower Henry's Law constant. Figure 2 illustrates that the diffusive fluxes are in addition very sensitive to the soil water content. It influences both the steady-state diffusive fluxes and the time lag. The curves show that with increasing soil water content, the steady-state diffusion fluxes decrease whereas the time lag increases. This is because the effective diffusion coefficient and the capacity factor are both functions of the soil water content. For a soil with a certain porosity, a higher water content would increase the time lag (increased {alpha}) and decrease the steady-state fluxes (decreased Deg). Values determined for Deg and {alpha} are listed in Table 3. Deg was determined from the pure toluene (Tests 1, 2, and 3) and from pure MTBE columns (Tests 5, 6, and 7) by Eq. [7]. Fstat was determined by averaging the flux data in the plateau regions in Fig. 2. {alpha} was determined by minimizing the mean square error between analytical solution and measured fluxes in the preplateau region. As listed in Table 3, the values expected for {alpha} correspond well to measured ones. In the case of MTBE, the experimental value (0.026) for Henry's Law constant was used in the model prediction because of uncertainties of the Henry's Law constant in literature values, which range from 0.013 to 0.057 at 25°C (OSTP, 1997). The experimental value of Henry's Law constant was calculated from the fitted {alpha} values by Eq. [5] and corresponds well with the measurements by Callender and Davis, who reported a value of 0.023 at 20°C (Callender and Davis, 2001). Sorption to the sand samples was insignificant because of the small values of Kd.

More tailing was observed in the measured toluene fluxes than predicted from the independently determined capacity factors, especially in the columns of low water contents (w = 0.47 and 1.88%). The fact that only low water contents and toluene but not MTBE showed this behavior indicates that adsorption to the water–air interface may take place as an additional process. In the case of toluene, the differences between measured and predicted {alpha} values were 41, 28, and 1% at water contents of 0.47, 1.88, and 4.72%, respectively (Table 3). For MTBE this effect was not observed because of its low Henry's Law constant.

Figure 3 compares measured and predicted values for Deg. The Penman (1940) model can give good predictions at very low water contents, but overestimates Deg at increased water contents. The Millington and Quirk (1961) model fits at relatively high water contents but overestimates Deg at lower water contents. The Moldrup et al. (2000) relationship fits almost perfectly and was subsequently used to predict Deg of the compounds in the multicomponent organic liquid experiments.



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  		Fig. 3. Comparison of the experimental effective diffusion coefficients of toluene (filled symbols) and MTBE (open symbols) with values predicted by different empirical relationships (Table 1).

 
Volatilization from Multicomponent Organic Liquids
Both the predicted and experimentally measured vapor phase diffusion breakthrough curves from the two organic mixtures are presented in Fig. 4. Table 4 lists the parameters used in the numerical modeling of the two organic mixture experiments. Deg was predicted by the empirical relationship of Moldrup et al. (2000) (see Fig. 3); {alpha} values were predicted with Eq. [5] since the measured and predicted values were in good agreement for toluene and MTBE (as shown in Table 3, especially under relatively high soil water contents). Kd was estimated from Koc and foc (Kd = Kocfoc), assuming that organic matter is responsible for sorption. Adsorption to mineral surface can play a significant role if the relative humidity in the soil is lower than 90% (Chiou and Shoup, 1985). According to Kleineidam et al. (1999) organic matter is solely controlling the sorption of hydrophobic organic compounds in moist natural soils and sediments even at extremely low foc values. Although there is quite some uncertainty in estimating Koc, the comparison of measured and calculated capacity factors of Tests 3 and 7 in Table 3, which have similar water contents as in the mixture columns, shows that the {alpha} values are almost the same. That implies the Kd values used in the prediction of {alpha} are adequate. In most cases Kd is not significant compared with the water content in Eq. [5] (even if Kd is increased by a factor of 2, only ethylbenzene shows a significant effect of a 43% increase of {alpha}).



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  		Fig. 4. Diffusion breakthrough curves from organic mixtures. Measured data (symbols) and predictions by the numerical model (lines).

 
Model predictions and experimental data compare very well for Mixture 2 and Mixture 1. In all cases the first arrival of the compounds at the column outlet was predicted very well. The tailing of the diffusive fluxes of the more sorbing compounds was overestimated by the model, especially for Mixture 1, indicating a mass balance problem in the end of the experiment as discussed below. The numerical model accuracy was checked by calculating mass balances for each compound. The cumulative masses of each compound are plotted in Fig. 5. The graphs in Fig. 5 illustrate that for all compounds, the modeled m/M values finally are equal to 1, which indicates that the mass balance is modeled correctly. The experimental measured m/M values (i.e., the total diffused mass) was less than expected from the model. For Mixture 2, about 10% of the injected source mass was not recovered. For Mixture 1, for ethylbenzene and toluene only, 30 to 50% was recovered from the column. The reason for this is due to losses in the experimental system. In the Mixture 1 column two rubber seals were used that absorbed the compounds. In Mixture 2 they were replaced by Teflon seals, which improved the mass balance in the experiment significantly. Some other sinks in the system may still exist, which the model does not take into account. Biodegradation can probably be excluded because no additional peaks were observed in the gas chromatograms, which could be an evidence for this assumption. Since the system was free of O2 (purging with N2), the more favorable aerobic degradation of aromatics is not likely. The chlorinated compounds, which can degrade under anaerobic conditions, show the same loss as the hydrocarbons, and no biodegradation products (e.g., vinyl chloride or dichloroethene) were observed in the chromatograms. The experimental running time (100 h) was probably too short to establish a microcosm able to significantly biodegrade VOCs in these low organic C content samples.



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  		Fig. 5. Comparison of normalized cumulative masses predicted by numerical modeling (lines) and experimental data (symbols). m denotes the cumulative mass diffused from the columns, and M is the mass of each compound initially present in the organic mixtures.

 
Figure 6 shows the change in composition of the organic mixtures with time (aging) according to the model prediction. Figure 6 indicates that for volatilization of NAPL to the air, the vapor pressure is the dominating factor. The more volatile compounds evaporate first; therefore, the mass in the liquid source will deplete first and the molar fraction will correspondingly decrease in the order: MTBE > 1,1,1-TCA > TCE > methylcyclohexane > toluene > PCE > ethylbenzene. In contrast, the compounds with relatively low vapor pressure will become enriched in the source with time (i.e., the mole fraction will increase).



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  		Fig. 6. Change of the mole fraction of each compound in the multicomponent organic liquids as simulated with the model: (a) Mixture 1, (b) Mixture 2.

 
The calculations shown in Fig. 4 through 6 are based on the assumption of ideal conditions in the organic mixtures, that is, an activity coefficient of 1 in Raoult's Law. Activity coefficients as estimated by UNIFAC indicate values within 20% of unity for the hydrocarbons used in this study (for chlorinated compounds, the interaction parameters between subgroups in UNIFAC were not available). The excellent agreement of modeled and measured flux data in the plateau region (Fig. 4) supports the assumption of activity coefficient close to 1.

Implication Scenario for the Field Scale
The experiment and numerical simulations discussed above address the scenario where a layer of NAPL evaporates. For the field scale the question arises whether this scenario is still appropriate or whether other mass transfer limitation arise. The evaporation in the column can be characterized by a double-film diffusion model, where diffusion occurs through a film in the NAPL in series with a film in the air (flux in air film = flux in NAPL film):

[10]
where {delta}NAPL and {delta}g denote the film thickness in the NAPL and in the gas phase, CNAPL is the concentration of the compound in the NAPL, and KNAPL is the partition coefficient of the compound between NAPL and gas phase. If we make a number of assumptions, then the mass transfer resistance is clearly limited by diffusion in the air:

  1. KNAPL is large (e.g., >1000; in a first approximation = 1/Csatg; 1011 for MTBE, 4296 for methylcyclohexane, 9395 for toluene, 24510 for ethylbenzene, 1385 for 1,1,1-TCA, 2616 for TCE, and 7738 for PCE, respectively).
  2. In the given scenario {delta}g corresponds to the length of the packed bed in the column (=20 cm).
  3. DNAPL is estimated to be approximately 1 x 10-5 cm2 s-1.
  4. Deg is 1 x 10-2 cm2 s-1.
  5. {delta}NAPL is <1 cm.

At the field scale {delta}g is even larger and evaporation of NAPL pools floating on top of the groundwater table is expected to be limited by vapor phase diffusion.

If we consider evaporation from a zone of residual NAPL (dispersed droplets of NAPL trapped in pores in a "smear zone"), then the size and thickness of that zone ({delta}NAPL) compared with the distance to the atmosphere ({delta}g) will determine whether aging (change in composition) of the NAPL occurs simultaneously across the source. For thick smear zones close to the atmosphere ({delta}g -> 0), we expect concentration gradients to develop within the residual NAPL whereas for large values of {delta}g (meters) the NAPL source could be considered as completely mixed.


   CONCLUSIONS
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
APPENDIX
 REFERENCES
 
Comparison between model and experiment for pure toluene and pure MTBE vapor sources in two different sandy soils indicates that the Moldrup et al. (2000) model more accurately predicts the effective diffusion coefficient Deg for a wide range of soil water contents for the experiments presented in this study than the Penman (1940) and Millington and Quirk (1961) models. The experiments also indicate that the spreading rates of VOCs in the unsaturated zone are strongly influenced by the soil water content, especially for highly soluble compounds.

Volatilization and subsequent vapor phase diffusion of constituents of the multicomponent organic liquids are described reasonably well by the one-dimensional numerical diffusion model based on the combination of Fick's Second Law and Raoult's Law with an activity coefficient of 1 (indicating ideal conditions). Therefore, this simple approach can be used to simulate the aging process of an organic mixture during diffusion dominated volatilization process.


   APPENDIX
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
REFERENCES
 
Notation
The abbreviations shown in parentheses represent the dimensionality of the variables being used, with M = mass, L = length, L3 = volume, and t = time.


   ACKNOWLEDGMENTS
 
The financial support for this work was provided by the EU project GRACOS (contract-number EVK1-CT-1999-00029) and the DAAD (Deutscher Akademischer Austausch Dienst). The authors thank Bernice Nisch and Renate Riehle for their technical assistance in the hydrogeochemistry laboratory.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 THEORY
 MATERIALS AND METHODS
 RESULTS AND DISCUSSION
 CONCLUSIONS
 APPENDIX
 REFERENCES
 




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Vadose Zone J., April 25, 2005; 4(2): 225 - 239.
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D. Werner, P. Grathwohl, and P. Hohener
Review of Field Methods for the Determination of the Tortuosity and Effective Gas-Phase Diffusivity in the Vadose Zone
Vadose Zone J., November 1, 2004; 3(4): 1240 - 1248.
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