Published online 27 April 2006
Published in Vadose Zone J 5:539-553 (2006)
DOI: 10.2136/vzj2005.0079
© 2006 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Transport of a Mixture of Chlorinated Solvent Vapors in the Vadose Zone of a Sandy Aquifer
Experimental Study and Numerical Modeling
Martine Bohy,
Lotfi Dridi,
Gerhard Schäfer* and
Olivier Razakarisoa
Institut de Mécanique des Fluides et des Solides de Strasbourg, Institut Franco-Allemand de Recherche sur l'Environnement (IFARE), UMR 7507 ULP-CNRS, 23 rue du Loess, BP 20, F-67037 Strasbourg Cedex, France
* Corresponding author (schafer{at}imfs.u-strasbg.fr)
1 Controlled Experimental Research Site for Water and Soil Remediation. 
2 At 9°C, 1 ppmv 
5.68 10–3 mg L–1 for TCE; 1 ppmv 7.16 10–3 mg L–1 for PCE.
Received 4 July 2005.
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ABSTRACT
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Experimental and modeling studies were performed to investigate the simultaneous transport of trichloroethylene (TCE) and perchloroethylene (PCE) in the vadose zone of a large (25 by 12 by 3 m) well-instrumented artificial aquifer called SCERES. The experimental facility, made up of a 1-m-thick saturated zone and a 2-m-thick unsaturated zone, allowed direct measurements of the contaminants in both the liquid and gas phases. Main objectives of the study were to obtain a better understanding of the fate and transport of chlorinated solvents in the subsurface and, more specifically, to compare simultaneously measured TCE and PCE volatilization rates from the soil surface with predictions obtained with both a comprehensive multiphase multicomponent numerical model (SIMUSCOPP) and a quasianalytical approach based on Fick's first law. The numerical and quasianalytical results generally agreed very well with the observed data. Transient PCE and TCE vapor phase concentrations calculated with the numerical model were found to be close to the observations, which indicated applicability of Raoult's Law. A comparison of observed and calculated TCE and PCE concentrations in the capillary fringe showed more impact of water infiltration on the simulations as compared with the observed data, which may reflect a lack of equilibrium between the gaseous and aqueous phase during leaching for the given experimental flow conditions. A sensitivity analysis showed that the adopted source boundary condition (a fixed nonaqueous phase liquid [NAPL] saturation distribution instead of an injected DNAPL source) did not have much influence on the concentration breakthrough curves, but that temperature can be an important factor influencing the results.
Abbreviations: DNAPL, dense nonaqueous phase liquid • NAPL, nonaqueous phase liquid • PCE, perchloroethylene • REV, representative elementary volume • TCE, trichloroethylene • VOC, volatile organic compound
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INTRODUCTION
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SUBSURFACE POLLUTION by volatile organic compounds (VOCs) such as TCE and PCE represents a serious environmental problem in many industrial areas (Fried et al., 1979; Cohen and Mercer, 1993; Pankow and Cherry, 1996). These dense nonaqueous phase liquids (DNAPLs) are immiscible and denser than water. During their transport in the subsurface, a significant part of these pollutants can be retained by capillary forces in the unsaturated zone as residual saturation, and as such may contaminate the soil gas phase due to their high vapor pressure. Contaminants in the gas phase can potentially propagate rapidly in the vadose zone, thereby significantly increasing the polluted area (Falta et al., 1989; Mendoza and McAlary, 1990; Mendoza and Frind, 1990a, 1990b; Jellali et al., 2001).
The processes governing VOC transport in the unsaturated zone are volatilization of the pure pollutant phase, gas–water partitioning, advective transport, aqueous and gaseous diffusion, hydrodynamic dispersion, and dispersion in the gas phase. The contribution of each of these processes to mass transfer depends both on the properties of the pollutant itself, and on the physical and chemical properties of the subsurface (Falta et al., 1989; Mendoza and Frind, 1990a, 1990b; Lenhard et al., 1995; Rivett, 1995; Thomson et al., 1997; Hippelein and McLachlan, 2000). Since gaseous diffusion is one of the key processes involved, much research work has been performed on stationary and transient diffusive mass fluxes using Fick's first and second laws of diffusion and on measurement of gas diffusion coefficients in soils (Grathwohl, 1998; Moldrup et al., 2000; Wang et al., 2003; Werner and Höhener, 2003; Werner et al., 2004). In the case of a mixture of DNAPLs, volatilization of the components depends on their mole fraction in the mixture and their vapor pressure. Raoult's Law expresses the equilibrium vapor pressure of each component k in the mixture, provided vapor behaves as an ideal gas, as follows (Smith and van Ness, 1987)
 | [1] |
where Pk is the vapor pressure of component k in the mixture (L–1 M T–2), Xk is the mole fraction of component k, and Po is the vapor pressure of pure component k (L–1 M T–2), the latter being a function of temperature. Equation [1] assumes an ideal DNAPL mixture, implying an activity coefficient of the compounds of one. Under these conditions, the equilibrium vapor concentration of compound k, Cg,k (M L–3) can be described as
 | [2] |
where MWk and Cg,ksat denote the molecular weight (M mol–1) and the saturation concentration in the gas phase (M L–3) of the individual pure compound. R and T are the gas constant (8.3144 Jmol–1 K–1) and temperature (K). As a result of continuous changes in the mole fraction of each component in the mixture (enrichment or depletion in time with regard to the other compounds), a selective preferential volatilization process will take place, beginning with the most volatile compound, which has the higher vapor pressure (Gioia et al., 1998).
In the absence of advective transport, the assumption of equilibrium partitioning between the gaseous and aqueous phases appears to be valid (Miller et al., 1990; Powers et al., 1992; Cho et al., 1993). This partitioning can be described with Henry's Law as
 | [3] |
where Cg,k is the concentration of component k in the gaseous phase (M L–3), KH,k is Henry's Law constant of component k, and Cw,k is the concentration of component k in the aqueous phase (M L–3). The tendency of a component to volatilize increases with higher Henry's constants.
Vapor plume spreading and phase partitioning will indirectly cause the contamination of soil aqueous and solid phases. Contamination of groundwater can occur by advective–dispersive transport of dissolved contaminants in the aqueous phase across the capillary fringe, or by downward vapor transport caused by infiltrating water or water table fluctuations. This mass transfer is generally evaluated using numerical models (Falta et al., 1989; Sleep and Sykes, 1989; Mendoza and McAlary, 1990; Pankow et al., 1997; Thomson et al., 1997; Baehr et al., 1999; Gaganis et al., 2002; Altevogt et al., 2003), or by means of small laboratory experiments in conjunction with numerical models (McCarthy and Johnson, 1993).
To better understand the mechanisms governing mass transfer from the vadose zone to groundwater, particular attention must be paid to the dynamic behavior of the interface between the saturated and unsaturated zones, commonly referred to as the capillary fringe (De Marsily, 1981; Castany, 1998). This interface between the saturated and unsaturated zones is defined by McCarthy and Johnson (1993) as the region covering both the tension-saturated region above the water table where the water pressure is less than atmospheric, and the lower part of the unsaturated zone where the soil moisture content is such that significant horizontal flow can occur. Silliman et al. (2002) defined the capillary fringe as simply that region above the water table where the water content remains at or close to saturation. Water content variations in the capillary fringe affect the area available for mass exchange, the tortuosity of the air and water phases, and the relative permeability of the medium to air and water. While many studies have focused on mass transport across the capillary fringe, they are often limited by the reduced observation scale (Barber et al., 1990; Bishop et al., 1990; McCarthy and Johnson, 1993; Rivett, 1995; Thomson et al., 1997; Rivett et al., 2001).
Field experiments have long been recognized as important in evaluating the risk of groundwater pollution by VOC vapors, testing numerical transport models, and devising remediation strategies (Falta et al., 1989; Sleep and Sykes, 1989; Thomson et al., 1997; Rivett et al., 2001). To gain a better understanding of the different subsurface mass transfer processes and to test predictive models, the French-German Institute of Environmental Research (IFARE) recently constructed a large outdoor research facility SCERES (Site Contrôlé Expérimental de Recherche pour la réhabilitation des Eaux et des Sols1) (Zilliox et al., 1996; Jellali et al., 2003; Benremita and Schäfer, 2003). This study is a followup of previous investigations dealing with residual TCE sources in the vadose zone of SCERES. The mass transfer of TCE from the unsaturated zone to both the atmosphere and groundwater and the overall mass balance were previously analyzed by Jellali et al. (2003). Numerical simulations of their experiment using the multiphase multicomponent code SIMUSCOPP developed by the Institut Français du Pétrole (IFP) indicated that the simplifying assumption of local equilibrium was appropriate to describe gas–water mass transfer processes (Benremita and Schäfer, 2003).
This paper focuses on (i) an experimental study of the transport of a mixture of TCE and PCE in the unsaturated zone and in the capillary fringe of the SCERES research facility, (ii) numerical modeling of the experiment using SIMUSCOPP, and (iii) comparing simultaneously measured TCE and PCE volatilization rates with calculated fluxes using both SIMUSCOPP as well as a quasianalytical approach based on Fick's first law.
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MATERIALS AND METHODS
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The SCERES Facility
The SCERES experimental setup (Jellali et al., 2003) comprises a water-tight buried basin 25 m long, 12 m wide, and 3 m deep, filled with two sand layers which function to recreate an alluvial aquifer (Fig. 1
). Hydraulic gradients, flow rates, water table locations, and sampling could be managed and monitored by means of two instrumented galleries at the upstream and downstream ends of the basin. The bottom 50 cm of the basin consists of a drainage layer made up of coarse quartz sand having a median particle diameter of 1 mm, a hydraulic conductivity of 6 x 10–3 m s–1, and a total porosity of 0.38. The bulk of the facility consisted of a 2.5-m-thick medium quartz sand layer with a hydraulic conductivity of 8 x 10–4 m s–1, a mean grain size diameter of 0.4 mm, a total porosity of 0.4 and a uniformity coefficient of 2.1. The aquifer contained a 1-m-thick saturated zone and a 2-m-thick unsaturated zone. The hydraulic gradient was fixed to about 0.009 m m–1, which produced an average flow velocity in the facility of close to 1.5 m d–1 and a total flow rate of about 1.36 m3 h–1. A more detailed description of the experimental setup is given by Jellali et al. (2003).
DNAPL Source Zone
Based on an average residual saturation value of about 0.03 for the TCE–PCE mixture in the unsaturated zone, and to avoid DNAPL reaching the saturated zone, 2.64 L of the TCE–PCE mixture was injected as a pure phase 0.35 m beneath the soil surface using a special injection device as described in Jellali et al. (2003). The device consisted of a stainless-steel reservoir of 56-cm diameter with a capacity of 37 L, which supplied DNAPL through 50-cm-long hollow tubes each containing four 0.2-mm-diameter holes near their bottom. The pollutant, injected over a 8-min time period, consisted of 63% TCE and 37% PCE. The source injection was assumed to occur at time t = 0.
The source zone was located 11 m from the downstream part of the basin and 6 m from the lateral walls (Fig. 1). The experiment was conducted under stationary flow conditions with fixed water levels at the inlet and outlet of the basin. The average temperature in the upper part of the unsaturated zone was about 7°C and approximately 11°C at a depth of 1.7 m. Water saturation as measured with time domain reflectometry (Imko probes, Micromodultechnik GmbH, Ettlingen, Germany) 11 m from the downstream outlet and 4 m from the lateral walls, was about 20% near the ground surface and 30% at a depth of 1.7 m (Fig. 2
). To study the impact of rainfall on the fate and transport of the pollutants, the soil surface above the injected vapor plume was sprinkled with water at t = 34 d for 6.5 h at a rate of 221 mm d–1.
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Fig. 2. Measured and simulated relative water saturation profiles and sampling depths in the vadose zone of SCERES.
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Soil Gas Sampling
The transport of TCE and PCE vapor was monitored using 73 gas samplers installed at depths of 0.25, 0.50, 1.00, 1.30, and 1.70 m and different distances from the DNAPL source (Fig. 1 and 2). The gas samplers consisted of 1-cm-i.d. hollow tubes fitted at their tip with a 4-cm-long screened head and covered with textile membranes. The TCE and PCE gas samples were pumped through a fine Teflon tube (2-mm i.d.) connected to the samplers. The samples were analyzed directly using a multigas monitor equipped with a photo-acoustic infrared detector (Innova Type 1312, Air Tech Instruments, Ballerup, Denmark). The detection limit of this apparatus was <1 ppmv, with a measurement uncertainty of about 1% of the measured value.2
In spite of the fact that the gas sampling tubes had a relatively large internal diameter of 0.01 m, we estimated that only 4.5% of the injected TCE mass (corresponding to 117 g) and 3% of the injected PCE mass (equivalent to 40 g) was lost during purging and sampling. These estimates are based on average sampling volumes (e.g., the measurements at a depth of 1.7 m required 170(0.5)2
= 133.5 cm3) and using a purging volume equivalent to three times the internal volume of the sampling tubes.
Flux Measurement at Soil Surface
The volatilization rate from the soil surface into the atmosphere was measured using a flux chamber made of a high-density polyethylene 30-cm cubic box, installed 10 cm below the soil surface. A complete description of the chamber is given by Jellali et al. (2003). The flux chamber works in a closed-circuit manner with recirculation of the vapors to avoid forced suction of soil gas. The suction holes were connected to pressure holes via a charcoal tube, a flow meter, and a pump. The solvent vapors trapped by charcoal were analyzed using gas chromatography with flame ionization detector. The TCE or PCE vapor flux density per unit surface 
k (M L–2 T–1) for component k during a given time period was calculated using the expression
 | [4] |
where Mres,k (M) is the residual TCE or PCE vapor mass remaining in the chamber measured with the multigas monitor, Mads,k (M) is the TCE or PCE mass adsorbed on the charcoal trap, A (L2) is the measurement area at the soil surface and 
t (T) is the monitoring interval. Experimental uncertainties of the measured flux due to the calibration of the gas chromatograph were estimated to be about 15% for TCE and 18% for PCE.
Several locations along the longitudinal x axis above the source and at distances of 1.5, 2.5, 3.5, and 5.5 m from the source center were monitored to estimate the volatilization rate from the soil interface. To verify symmetry of the mass fluxes, two measuring points were added in the lateral direction at distances of 1.5 and 3.5 m downstream of the source.
Capillary Fringe Sampling
Water samples were taken from the capillary fringe using suction cups installed at depths of 1.85 and 1.95 m (Fig. 1 and 2). The suction cups were made of a special Teflon–quartz mixture (Prenart Equipment ApS, Denmark) (Jellali et al., 2003). Seventeen suction cups were installed 0.75 and 2 m laterally and downstream of the pollution source. Samples were obtained using a vacuum pump connected to the cups and applying a suction of 100 mbars. Concentrations of the dissolved solvents were analyzed by gas chromatography with flame ionization detector (Chrompack, Varian, Les Ulis, France) after liquid–liquid extraction with hexane. Analytical uncertainties as estimated from chromatographic calibration were about 5% for each component.
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RESULTS
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TCE and PCE Vapor Concentrations
The maximum theoretical concentrations of the TCE–PCE mixture at 9°C are about 27816 ppmv for TCE at a mole fraction of 63% and 3574 ppmv for PCE at a mole fraction of 37% (values of saturation concentrations in the gas phase, see Table 1). Because of considerable TCE volatilization during the first few days of the experiment, the mole fraction of TCE decreased substantially and became in time smaller than the mole fraction of PCE. The maximum vapor concentrations of TCE and PCE measured 0.75 m downstream from the source were higher at a depth of 1.7 m than at 0.25 m, as shown on Fig. 3a
and 3b. The high density and volatility of the components influences vapor phase transport by inducing high vapor losses to the atmosphere and significant concentration gradients. Similar effects were observed by Jellali et al. (2003) in their single-component TCE experiments.
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Fig. 3. Measured TCE and PCE vapor concentrations at (X = 0 m; Y = 0.75 m) and (X = 0.75 m; Y = 0 m), at depths of (a) 0.25 m and (b) 1.7 m.
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The vapor plume stretched out laterally near the source zone to a distance of 6 m. The plumes for both compounds were radially nearly symmetric near the source as shown in Fig. 3, particularly at a depth of 1.7 m. Even during leaching of the vapor at t = 34 d, the TCE vapor concentration did not decrease much more rapidly, while the PCE vapor concentrations remained almost constant (Fig. 3). The TCE component started to decrease at about the 12th day after injection since not enough pure phase of TCE was left in the source to supply the TCE vapor plume after leaching with water. The PCE vapor concentrations still increased at the time of watering, but then slightly decreased due to the infiltrating water (Fig. 3). Four days after leaching, the PCE concentrations reached the same values as before rainfall at all depths, thus indicating that the source zone may still have contained pure PCE phase.
TCE and PCE Concentrations in the Capillary Fringe
Average water saturations measured in the capillary fringe near the source zone were about 80 and 98% at depths of 1.85 and 1.95 m, respectively (Fig. 2). Relatively low dissolved TCE and PCE concentrations were observed at a depth of 1.85 m 1 d after injection of the solvents and at a depth of 1.95 m after 3 d (Fig. 4
). Figure 4 shows very rapid concentration changes between depths of 1.85 and 1.95 m. At a lateral distance of 0.75 m from the source and a depth of 1.85 m, the maximum aqueous TCE and PCE concentrations were 280 and 35 mg L–1, respectively, whereas at a depth of 1.95 m the maximum TCE and PCE concentrations were all <5 mg L–1 (Fig. 4).
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Fig. 4. TCE and PCE water concentrations measured at (X = 0 m; Y = –0.75 m) at depths of 1.85 and 1.95 m.
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Using results shown in Fig. 3b and 4, dissolved TCE and PCE concentrations monitored in the capillary fringe at a depth of 1.85 m can be correlated with the vapor concentrations measured at a depth of 1.7 m. The temporal mean ratio of measured dissolved concentrations to equivalent vapor concentrations in the water phase using Henry's Law is about 1.15 for TCE and 0.41 for PCE. These values indicate that a concentration equilibrium may exist between the gaseous and aqueous phases in the lower part of the vadose zone for TCE, but that it takes much more time for equilibrium to be achieved in the case of PCE (ratios of 0.7 only after 62 d). The depletion of the solvent vapors in the unsaturated zone was faster due to the high vapor diffusion coefficients, whereas mass transfer through the capillary fringe was limited because of slow diffusion in the aqueous phase.
Measured Vapor Fluxes across Soil Surface
Figure 5
shows that 9 d after injection of the DNAPL mixture, the TCE flux measured above the source was about 5 g m–2 d–1 and after 29 d about 2.3 g m–2 d–1. The measured PCE flux above the source was about 2.1 g m–2 d–1 at the beginning of the experiment, but then increased to 4 g m–2 d–1 at approximately t = 20 d. The depletion of the TCE source was clearly noticeable up to a distance of 3.5 m. The mass fluxes themselves decreased in time, faster near the source zone than at a distance of 3.5 m.
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Fig. 5. Evolution of the TCE and PCE fluxes measured at different distances from the source on the flow axis.
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The TCE and PCE vapor fluxes 1.5 m downstream the source still represented 66% and 29%, respectively, of the fluxes measured above the source, while at a distance of 3.5 m they represent only about 22% and 9% of the source values for TCE and PCE, respectively. The PCE fluxes hence decreased faster with distance from the source than TCE. Being less volatile than TCE and having a higher density, PCE was not expected to spread out laterally as fast as TCE in the vadose zone. Finally, we note that the upward volatilization fluxes were found to be relatively constant laterally radius around the source. This finding was supported by measurements taken at a distance of 1.5 m, both at the flow axis and laterally.
Prediction Vapor Fluxes Based on a Quasianalytical Approach
For stationary vapor phase diffusion conditions (i.e., assuming a constant concentration gradient between depths of 0.25 and 1 m, as shown in Fig. 6
, and a constant relative air saturation of the porous medium), the vertical vapor flux of TCE and PCE due to diffusion can be calculated using a one-dimensional approach based on Fick's first law. The measured concentration gradients between depths of 0.25 and 0.5 m hence can be used to estimate the mass flux per unit surface. We used the empirical relationship of Millington and Quirk (1961) to estimate the diffusion coefficient of each component from the porosity, and relative air saturation (Shoemaker et al., 1990; Mendoza and Frind, 1990a). The vertical diffusive mass flux per unit surface for each component k is then given by
 | [5] |
where 
is the porosity, Sg is the air saturation, dCmes,k/dz (M L–4) is the measured vertical concentration gradient of component k, and Dair,k (L2 T–1) is the free-air diffusion coefficient of component i. Uncertainties in the predicted fluxes using Eq. [5] were calculated using
 | [6] |
which follows from Eq. [5] using a total derivative expansion, and assuming no errors in the diffusion coefficients. Using our experimental data, we obtained uncertainties of about 13 and 11% for the TCE and PCE vapor phase mass fluxes, respectively.
The fluxes calculated using the above quasianalytical approach only slightly underestimated the measured fluxes measured 1.5 m downstream of the source up until 35 d (Fig. 7
). Infiltration of water temporarily decreased the volatilization rates due to an increase in the water content in the first few centimeters of the unsaturated zone. Once the water front passed, the PCE flux increased again near the source since enough pure DNAPL phase was present in the source to supply the unsaturated zone with vapors.
Mass Distribution
The experimental data collected at the downstream instrumentation gallery and in the unsaturated zone of the SCERES facility allowed us to establish a mass balance of the injected solvents. Most of the 2429 g pure TCE and 1585 g pure PCE injected in the porous medium ended up in the vapor phase and eventually volatilized into the atmosphere. The amount of dissolved solvents remaining in the aquifer was <1% for both TCE and PCE at the end of the experiment. Integration of the upward diffusive mass flux over the entire facility would give an estimate of the total amount of mass volatilized into the atmosphere. For an average relative water saturation of 21% and an average temperature of 9°C, Table 2 presents the mass of TCE–PCE vapors volatilized into the ambient air at different times. Notice that 89% of the mass of TCE and 85% of the mass of PCE volatilized from the unsaturated zone into the atmosphere over a period of 104 d.
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Table 2. TCE and PCE volatilized masses as calculated with a quasianalytical approach based on Fick's Law. Percentages pertain to the total amounts of TCE (2459 g) and PCE (1585 g) injected in the SCERES facility.
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NUMERICAL ANALYSIS
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In this study we used the numerical code SIMUSCOPP (SIMUlation des Sites COntaminés par des Produits Pétroliers), which is a three-dimensional industrial simulator designed for three-phase flow and transport in porous media (Le Thiez and Ducreux, 1994). SIMUSCOPP is based on a finite-difference discretization scheme with local subgridding features. Nonlinearities are solved using Newton's method, while the solution of linear systems is obtained by means of direct or iterative methods (e.g., conjugate gradient with various preconditioning schemes). The primary variables are air pressure and air and water saturation for flow, and the phase compositions for transport. Since the code is discussed at length elsewhere (Le Thiez and Ducreux, 1994), only the most essential parts are briefly summarized here.
Governing Transport Equations
General equations for the simultaneous flow of three immiscible fluid phases p in a porous medium at the scale of a representative elementary volume (REV) have been introduced in petroleum reservoir engineering (Aziz and Settari, 1979). In the case of mass exchange between fluid phases, the general mass conservation equation for each component k in the three fluid phases and adsorbed on the solid phase is obtained by summing up across the Np phases (Sleep and Sykes, 1993) as follows
 | [7] |
where p refers to the gas (g), NAPL (n), or water (w) phases, respectively; is porosity as before; 
p (M L–3) is the mass density of phase p; Sp is the volumetric saturation of phase p; 
p (L T–1) is the specific discharge of phase p; xkp is the mole fraction of component k in phase p, qkr is the mole fraction of component k adsorbed on the solid phase; r (M L–3) is the mass density of the solid phase; Qk (M L–3 T–1) is the injection or withdrawal rate of component k; and 
kp (M L–2 T–1) represents the mass flux of component k in phase p due to hydrodynamic dispersion given by
 | [8] |
The dispersion tensor of component k in phase p is assumed to be given by (Bear, 1972):
 | [9] |
where 
L (L) and T (L) are the longitudinal and transverse dispersivities of the medium, respectively; vpi (L T–1) and vpj (L T–1) are components of the mean flow velocity vector of phase p; 
ij is the Kronecker symbol; Dkpm (L2 T–1) is the molecular diffusion coefficient of component k in phase p, and 
p is the tortuosity factor. The specific discharge of phase p is assumed to be adequately expressed by the generalized Darcy's Law, which may be written as (Bear, 1972)
 | [10] |
where 
(L2) is the intrinsic permeability tensor, krp is the relative permeability of phase p, µp (M L–1 T–1) is the dynamic viscosity of phase p, Pp (M L–1 T–2) is the pressure of phase p, 
(L T–2) is the gravity acceleration vector. The nonlinear system of equations given by Eq. [7] is closed by the totality conditions
 | [11] |
and by specifying constitutive relationships describing the interactions of the fluids at the REV scale with respect to the physical processes of capillarity and immiscible viscous displacement. We note that the distribution of component k between the various fluid phases is based on the local thermodynamic equilibrium assumption (see Eq. [2] and [3]).
Constitutive Relationships
We assume in our simulations that in three-phase systems, the diphasic capillary pressure remains a function of one saturation only (e.g., gas saturation for a gas–water and gas–NAPL system, and water or NAPL saturation for a NAPL–water system). Since the gas phase pressure is the reference pressure for our calculations, the water and NAPL phase pressures are derived from diphasic capillary pressures as follows (Le Thiez and Ducreux, 1994):
 | [12] |
 | [13] |
where Pcgn is the capillary pressure in a gas–NAPL system, Pcnw is the capillary pressure in a NAPL–water system, and Pcgw is the capillary pressure in a gas–water system, Pcnw,min is the minimum capillary pressure in a NAPL–water system obtained at residual NAPL saturation, Snc is the critical saturation of the NAPL phase, under which NAPL is considered as a discontinuous fluid phase and its pressure is supposed to be equal to water pressure.
The relative permeabilities of the water and gas phase are assumed to be a function only of relative water and gas saturation, respectively:
 | [14a] |
 | [14b] |
In our study we express the three-phase relative permeability–saturation relationship for the NAPL phase in terms of a geometric system based on relative permeabilities of NAPL in a two-phase NAPL–water system (krnw) and in a two-phase NAPL–gas system (krng) leading to linear NAPL isopermeabilities as follows (Le Thiez and Ducreux, 1994):
 | [15] |
with
 | [16] |
where Swr is the irreducible water saturation, and Snrw and Snrg are residual NAPL saturations in a NAPL–water system and NAPL–gas system, respectively.
Numerical Implementation and Model Parameters
Our computational grid comprised only one-half the width of the SCERES facility so as to limit PC memory requirements and computer time. The numerical grid used in SIMUSCOPP was a three-dimensional Cartesian mesh with local refinements using subgrids around the pollution source and in the capillary fringe (Fig. 8
) where the highest NAPL gradients were expected.
Vapor transport in our simulations was calculated using capillary pressure curves of diphasic gas–water systems and relative permeabilities of water, gas, and NAPL. The diphasic capillary pressure–saturation relationships of the gas–water system were obtained using van Genuchten parameters ( and n) determined for the given porous medium using a two-phase gas–water system (van Genuchten, 1980). For saturations between Swr and (1 – Snr), we used the Mualem–van Genuchten model (Parker et al., 1987) for the relative permeability of the water phase. The same model was used for relative permeabilities of the gas phase for gas saturations between Sgr and (1 – Swr – Snr). For values above (1 – Snr) and (1 – Swr – Snr), krw and krg were calculated by linear extrapolation up to krw = 1 and krg = 1, respectively (Fig. 9
).
Porous media and DNAPL properties, boundary and initial conditions, as well as parameters for the constitutive relationships are presented in Tables 1 and 3. The hydrodynamic and physical properties of the medium in Table 3 were obtained from preliminary studies on laboratory columns and previous experiments performed on the SCERES facility. The constitutive relationships were estimated using the Mualem–van Genuchten parameters (, n) derived from observed relative water saturation profiles in the SCERES facility. The pollution source was created in the unsaturated zone by infiltrating 2.64 L of the TCE and PCE mixture on 15 injection points distributed as in the experiment over a 56-cm-diameter zone. We emphasize here that the mole fraction of each component in the DNAPL mixture is one of the primary variables in SIMUSCOPP and, thus evolves with time during the numerical simulations.
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Numerical RESULTS
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In this section we compare measured and calculated concentration breakthrough curves. We focus in particular on one representative sampling location 0.75 m laterally of the source (X = 0 m, Y = 0.75 m).
Vapor Phase Concentrations
Calculated TCE concentrations were found to be in good agreement with the measured data, albeit with a systematical overestimation (Fig. 10
), especially immediately before watering at a depth of 1.7 m where the maximum relative deviation was up to 60%. The PCE measured concentrations were well matched by the calculations at a depth of 0.25 m, but they substantially underestimated (up to 5 times) observed concentrations at a depth of 1.7 m, particularly before 20 d.
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Fig. 10. Observed and simulated (a) TCE and (b) PCE gas concentrations at (X = 0 m; Y = 0.75 m) at depths of 0.25 and 1.7 m (sim = simulated, meas = measured).
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The effect of rainfall was in general more visible on the simulated breakthrough curves as compared with the measured data for both components. The measured TCE concentration curves decreased continuously at both depths, while the calculations showed a strong decrease in concentrations immediately after watering. The effect of infiltration was well reproduced for PCE. At a depth of 0.25 m, the measured and calculated curves both decreased after watering, whereas at a depth of 1.7 m the concentration increased because of enrichment of the vapor plume.
After 50 d, the numerical simulations predicted higher vapor concentrations and a longer persistent vapor plume in the aquifer than observed, particularly for PCE. One possible explanation may be the use of a too low air diffusion coefficient of TCE next to the source. Since the diffusion coefficient is strongly dependent on temperature, a higher temperature would lead to a more persistent TCE vapor plume (see Fig. 10a) and, consistent with Raoult's Law, to more depletion of PCE from the unsaturated zone.
Dissolved Solvent Concentrations in the Capillary Fringe
The shapes of the simulated dissolved TCE and PCE breakthrough curves agreed satisfactorily with the measured data at a depth of 1.85 m, except for a tendency to somewhat overestimate the measurements. The numerical model also predicted an earlier arrival time of the DNAPLs in the water phase than was observed, until about 2 to 3 d. We emphasize that all numerical simulations were conducted using model input parameters (see Table 3) based on preliminary laboratory studies (Bohy, 2003; Razakarisoa et al., 2004). Additional numerical studies have shown that the early arrival of TCE (Fig. 11
) may have been caused by underestimating TCE sorption onto the solid phase, rather than by more rapid advective vapor phase transport or more diffusive transport of dissolved components within the capillary fringe. For example, a 30 times increase in the sorption constant for TCE produced a breakthrough curve where dissolved TCE was first observed after 1 d instead of nearly immediately (see also Fig. 14b). However, increasing sorption did not produce an overall better fit to the measured data.
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Fig. 11. Simulated and measured dissolved TCE and PCE concentrations at (X = 0 m; Y = 0.75 m) at a depth of 1.85 m.
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Fig. 14. Sensitivity analysis: influence of (a) source zone definition and (b) the adsorption coefficient on calculated aqueous concentrations at (X = 0 m; Y = 0.75 m).
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Comparisons of the numerical results with observed TCE and PCE concentrations at a depth of 1.85 m also showed that the impact of water infiltration on the dissolved concentrations was more significant in the simulation than in reality (Fig. 11), as was already apparent for the vapor concentrations near the capillary fringe (Fig. 10). This result may reflect a lack of instantaneous concentration equilibrium between the gaseous and aqueous phase during and immediately after the infiltration in our experiment when the advective downward transport rates where highest.
Calculated Vapor Flux across Soil Surface
We used the SIMUSCOPP code to calculate the vapor flux at a distance of 1.5 m from the source zone for comparison with both the direct measurements and the approximate Fickian-based calculations (Fig. 12
). The numerical simulation was close to the experimental data, except between 20 and 30 d where the simulation produced vapor fluxes that were only 80 and 60% of the measured TCE and PCE values, respectively. The maximum relative difference between the simulation and the Fickian-based fluxes after 14 d was about 18% for TCE and 40% for PCE. After water infiltrated into the medium, the simulated TCE flux decreased much faster than the calculated flux, while the PCE flux seemed to remain constant for a longer period than that calculated analytically.
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Fig. 12. Measured, analytically calculated (Fickian_based) and numerically simulated volatilization rates into the atmosphere at (X = 1.5 m; Y = 0 m).
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Mass Balance
A detailed mass balance is presented in Table 4. The simulations predicted that 70 d after injection of the mixture of TCE and PCE, 68% of the TCE mass and 40% of the PCE mass had volatilized into the atmosphere. At the same time, 25 and 7% of the injected TCE and PCE masses had reached the model outlet, which is more than what was observed (0.1 and 0.08% of the injected TCE and PCE masses).
Up to about 20 d, the amounts of TCE and PCE volatilized into the atmosphere as calculated with SIMUSCOPP (Table 4) were very similar to those estimated using the quasianalytical approach (see Table 2) based on measured concentrations at depths of 0.25 and 0.5 m. After 20 d, however, the quasianalytical approach overestimated the numerical results, most likely we think because of a lack of symmetry in the distribution of the vapor plume.
Sensitivity Analysis
To obtain a better understanding of some of our experimental results, we performed a sensitivity analysis with the numerical model to evaluate (i) the impact of a modified DNAPL initial condition (i.e., initially fixed residual TCE and PCE saturations) and (ii) the possible effect of soil temperature on the numerical results.
Pollution Source Formulation
Instead of simulating the infiltration of the DNAPLs as separate fluid phases, the mixture of TCE and PCE was introduced by assuming an average residual saturation of 3% within the presumed source covering a zone 0.5 m long and 0.5 m wide, and located between depths of 0.35 and 1.25 m. Calculated TCE and PCE vapor and aqueous concentrations obtained with this fixed source zone are compared with the experimental data and our earlier results assuming DNAPL infiltration (reference case), as shown in Fig. 13
and 14
.
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Fig. 13. Sensitivity analysis: Influence of the source zone definition on calculated gaseous concentrations at (X = 0 m; Y = 0.75 m).
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Simulated TCE and PCE concentrations at a depth of 0.25 m showed the same shape as the measured data, with a maximum relative difference of 4 and 30% for the fixed source and reference cases, respectively (Fig. 13). At a depth of 1.7 m, between 5 and 25 d, the measured TCE concentrations were underestimated with the fixed source simulation but overestimated by about 6% by the reference simulation (Fig. 13). However, after 25 d the monitored TCE vapor data were mostly overestimated with the two modeling approaches, reaching a maximum deviation of about 100% after 40 d.
Both numerical simulations (the fixed source and the reference case) markedly underestimated measured PCE vapor concentrations at a depth of 1.7 m until 15 d. As was discussed earlier and further shown in Fig. 13, the predicted PCE vapor plume was much more extensive than the observed distribution.
At a depth of 1.85 m, the shapes of the measured dissolved TCE and PCE breakthrough curves were well represented by both modeling approaches (Fig. 14a), with some overestimation of especially the PCE data near the end of the experiments. For TCE, the fixed-source simulation was very close to the observed data, while the reference case overestimated the measurements by up to about 25%. The measured PCE concentrations were overestimated up to 30% after 30 d by both calculations. The results in Fig. 13 and 14 are important in that they suggest that exact delineation and modeling of the DNAPL injection process is not necessarily that critical for accurate simulation of the fate and transport of a DNAPL mixture, at least for experimental conditions similar to those of our study.
Temperature Effects
To show the influence of temperature on vapor transport, we performed three simulations using average temperatures of 7, 9, and 11°C. Results are shown in Fig. 15
. The choice of temperatures was motivated by our measurements, which indicated average temperatures of 7°C between the soil surface and a depth of 0.9 m, 9°C between 0.9 and 1.5 m, and 11°C below 1.5 m. Among the temperature-dependent parameters used in the numerical model, the gas–NAPL equilibrium coefficient was the most sensitive to temperature. In view of results about the source zone and to reduce the calculation time, we performed the temperature sensitivity analysis using only the fixed source modeling approach.
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Fig. 15. Sensitivity analysis: influence of average temperature on calculated vapor concentrations at point (X = 0 m; Y = 0.75 m).
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For both components, at a depth of 1.7 m, a temperature elevation of only 2°C increased the calculated maximum vapor concentrations by up to 1000 ppmv for TCE and 500 ppmv for PCE. The best match of the observed TCE and PCE data at this depth were obtained assuming a temperature of 11°C. At a depth of 0.25 m, a better fit of the observed concentration was obtained for temperatures of 7 or 9°C. These temperatures are very much in agreement with the measured temperature profile in the experimental facility. The temperature sensitivity study suggests that future versions of SIMUSCOPP should be able to account for a nonuniform vertical temperature profile, which is not possible with the current version.
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CONCLUSIONS
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The transport of DNAPL vapors from a pollution source consisting of TCE and PCE located in the vadose zone was studied in a large, well-instrumented outdoor experimental facility, SCERES. The facility allowed multidepth gas samples to be taken from the unsaturated zone, as well as samples of dissolved solvents from the capillary fringe, thus providing a valuable database for testing numerical transport models.
Measured transient vapor concentrations of TCE and PCE were found to agree with concentrations predicted using Raoult's Law. The controlled experiment confirmed that the transport of TCE and PCE vapors in the vadose zone occurred mostly by diffusion and that the capillary fringe constitutes a significant barrier to pollutant transfer to groundwater, as was previously also shown by Jellali et al. (2003) for a single component TCE system.
Volatilization and transport of the TCE and PCE components were predicted reasonably well using the numerical code SIMUSCOPP, leading to close agreement with observed vapor fluxes. The comparisons also showed that simple one-dimensional calculations from observed observations using Fick's first law were adequate for estimating volatilization rates into the atmosphere. A comparison of measured and predicted vapor and dissolved DNAPL concentrations indicated that the assumption of local concentration equilibrium may be invalid during rainfall periods when large soil water fluxes may occur.
Results of our sensitivity study further suggest that exact representation of the DNAPL source injection process is not essential to accurately reproducing the fate and transport of TCE and PCE mixtures for conditions similar to our experiments. However, temperature variations of as little as 2°C were found to result in a maximum change of 15% of predicted vapor concentrations. Hence, field-scale simulations of PCE and TCE vapor phase transport may need to include the effects of a nonuniform temperature profile versus depth, thereby considering the nonisothermal effects of such temperature-dependent parameters as the gas–NAPL equilibrium coefficient.
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ACKNOWLEDGMENTS
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Financial support for this research from the "Contrat de Plan Etat-Région Alsace" (ULP, CNRS, Ministère de l'Aménagement du Territoire et de l'Environnement), the pluri-formation program "Institut Franco-Allemand de Recherche sur l'Environnement" (IFARE), the Programme National de Recherche en Hydrologie (INSU-CNRS), the Agence de l'Eau Rhin Meuse (AERM), and the Agence De l'Environnement et de la Maîtrise de l'Energie (ADEME) is gratefully acknowledged. Furthermore, the authors would like to thank M.Th. van Genuchten for additional reviews of the manuscript and for his valuable comments and suggestions that helped to improve the paper significantly.
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TOP
ABSTRACT
INTRODUCTION
