Semianalytical Model Predicting Transfer of Volatile Pollutants from

Jul 19, 2010 - III-CNRS, Case 29, 3, Place Victor Hugo,. F-13331 Marseille Cedex 3, France. Received November 17, 2009. Revised manuscript received...
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Environ. Sci. Technol. 2010, 44, 6228–6232

Semianalytical Model Predicting Transfer of Volatile Pollutants from Groundwater to the Soil Surface O L I V I E R A T T E I A * ,† A N D ¨ HENER‡ PATRICK HO Universite´ de Bordeaux, EGID, 1 Allee Daguin, 33607 Pessac Cedex, France, and Laboratoire Chimie Provence, UMR 6264, Universite´s d’Aix-Marseille I, II et III-CNRS, Case 29, 3, Place Victor Hugo, F-13331 Marseille Cedex 3, France

Received November 17, 2009. Revised manuscript received May 20, 2010. Accepted May 21, 2010.

Volatilization of toxic organic contaminants from groundwater to the soil surface is often considered an important pathway in risk analysis. Most of the risk models use simplified linear solutions that may overpredict the volatile flux. Although complex numerical models have been developed, their use is restricted to experienced users and for sites where field data are known in great detail. We present here a novel semianalytical model running on a spreadsheet that simulates the volatilization flux and vertical concentration profile in a soil based on the Van Genuchten functions. These widely used functions describe precisely the gas and water saturations and movement in the capillary fringe. The analytical model shows a good accuracy over several orders of magnitude when compared to a numerical model and laboratory data. The effect of barometric pumping is also included in the semianalytical formulation, although the model predicts that barometric pumping is often negligible. A sensitivity study predicts significant fluxes in sandy vadose zones and much smaller fluxes in other soils. Fluxes are linked to the dimensionless Henry’s law constant H for H < 0.2 and increase by approximately 20% when temperature increases from 5 to 25 °C.

Introduction The pollution of groundwater by volatile organic compounds (VOCs) such as chlorinated solvents, petroleum hydrocarbons, or freons is a worldwide problem, and the processes acting on these pollutants and leading to natural attenuation of the pollutant plumes have been studied intensively. Much work has been focused on dispersion, dilution, chemical or biological degradation, and sorption, but relatively little work has been devoted to mass loss by volatilization to the atmosphere. Many VOCs have relatively high Henry’s law constants, and it is well-known that VOC signatures in soil vapors can be related to the extension of the underlying plumes (1-4). Knowledge of an accurate mass flux from groundwater is critical for both assessing a mass balance for the natural attenuation capacity of the aquifer and the analysis of risk due to human exposure to vapors at sites with buildings. The following processes governing the mass flux from groundwater to soil have so far been identified: gas-phase * Corresponding author e-mail: [email protected]. † Universite´ de Bordeaux, EGID. ‡ Laboratoire Chimie Provence, Universite´s d’Aix-Marseille. 6228

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diffusion (5), dissolved-phase advective and dispersive transport, gas-phase advection by barometric pumping (6), water table fluctuations (7, 8), advective displacement of soil air due to water infiltration (9), and vapor density effects in the presence of VOCs in free phase (10, 11). Two experimental studies, both on the laboratory scale, investigated in detail which processes control the VOC flux between groundwater and soil surface. McCarthy and Johnson (7) measured the TCE flux in a laboratory tank with horizontally flowing groundwater either at constant or fluctuating groundwater table, and published the vertical concentration distribution of TCE in the unsaturated zone. Werner and Ho¨hener (8) studied the volatilization fluxes of 4 different freons from laboratory columns with fluctuating groundwater tables and found a dependency of the fluxes with the Henry’s law constant. From these studies, it is concluded that a model for predicting volatilization fluxes must include the moisture distribution in the capillary fringe. The most complete field mass flux measurements were performed at the Picatinny arsenal, New Jersey, where TCE fluxes have been measured using flux chambers at the soil surface under natural conditions during 12 months (12) and later during 9 concurrent measurement and simulation events (13). The measurements frequently gave fluxes that were orders of magnitude higher than fluxes that would be calculated based on a linear concentration gradient with depth and Fick’s first law (12). A numerical transient, onedimensional gas flow and transport model incorporating the effects of gas-phase diffusion, equilibrium air-water partitioning of organic vapors, and unsaturated zone airflow caused by atmospheric pressure changes (i.e., barometric pumping) has been developed (14) and compared to the data (13). Parker (6) presented a simple Fickian model for diffusive/ dispersive transport and barometric pumping. The transport across the capillary fringe was modeled using an aquifercapillary fringe nonequilibrium factor, but it would be preferable to use better-defined parameters like the transversal vertical dispersivity and the van Genuchten parameters for soil moisture distribution in the capillary fringe (15). Other simple models are used for risk assessment in connection with vapor intrusion into buildings (16-18). In summary, the models currently available for predicting mass fluxes of VOCs in the unsaturated zone are either too simple and poorly calibrated, or too data-intensive (13). The aims of this study were to develop a semianalytical model for quantifying the volatilization of pollutants from groundwater plumes based on classical soil hydraulic parameters, and to validate it by comparing model simulations to experimental data and to simulations obtained by a numerical model. The semianalytical model should include barometric pumping, while still being able to run using simple spreadsheet software.

Model Development Description of Modeled Scenario and Major Assumptions. The model developed in this work describes the flux of a volatile pollutant from a groundwater plume through the unsaturated zone to the atmosphere. The pollutant is dissolved in groundwater at a constant concentration, and does not undergo any degradation, mass transfer is considered between the soil, air and water phases. Its atmospheric concentration is negligible. The horizontal velocity of groundwater in the plume obeys Darcy’s law. Dispersion and variation of horizontal velocity are considered in the capillary fringe. Where barometric pumping is negligible, 10.1021/es903477f

 2010 American Chemical Society

Published on Web 07/19/2010

the pollutant’s flux is at steady state, and therefore sorption is not an issue; in the contrary sorption is considered. In the unsaturated zone, the aqueous phase does not undergo vertical advection. The considered scenario is a large plume extension and thus an approximately constant concentration in groundwater in the horizontal plane, allowing a 1-D vertical calculation of vapor fluxes in the soil. The vertical flux is governed by diffusion in both the aqueous and gaseous phase, and by advection caused by barometric pumping. The present version of the model considers a homogeneous soil. Soil Moisture and Velocity Distribution in the Profile. We use the soil moisture distribution from Van Genuchten (15) equations:

Where D0a is the diffusion coefficient in free gas and n is the total porosity. It is possible to write the same equations for diffusion in the water phase. Assuming equilibrium of pollutant concentrations between water and gas phase and using the nondimensional Henry’s law constant (H) yields

θ ) θr + (θs - θr)[1 + (RH)1/(1-m)]-m

Sorption to solid phases is not included here as we consider steady state but could be readily linked to this equation. This formula is the classical formulation for volatile pollutant transfer in the soil (e.g., 5). The originality of our approach comes from the use of the Van Genuchten soil moisture distribution in the soil profile and the consideration of the horizontal water velocity in the capillary fringe, which leads to the following equation, using eqs 4, 7 and Millington’s formulation for diffusion in water:

(1)

where θr is residual water content, θs is saturated water content, H ) |Hp| water pressure, and R and m are unitless Van Genuchten (VG) parameters. As we assume steady state, there is a hydraulic equilibrium between groundwater and soil, and the total head of water is constant in the soil profile. Therefore, the pressure head, H, is equal to the altitude of the considered point vs the piezometric level. This property is used to calculate θ as a function of depth. In the capillary fringe, water is moving horizontally (19), with the horizontal gradient being similar to the one existing in the groundwater. However, within the capillary fringe the hydraulic conductivity may decrease when saturation is decreasing. The hydraulic conductivity is given by the Van Genuchten equations as K(θ) ) Ks√Se[1 - (1 - Se1/m)m]2 Se ) (θ - θr)/(θs - θr) (2) where Ks is the saturated hydraulic conductivity. The velocity is proportional to the hydraulic conductivity and gradient. As we consider that the head gradient in the capillary fringe is null in the vertical direction and equal to the gradient of the groundwater in the horizontal direction, we can write v* ) v0k*(z) ) v0K(θ)/Ksat

(3)

where v0 is the groundwater velocity, v* is the velocity in the capillary fringe, and k*(z) is the ratio of hydraulic conductivity at altitude z to saturated hydraulic conductivity. Dispersion in the capillary fringe (Dj w) obeys the same laws as in the groundwater (20), we can thus write j w ) Dw + Rzv* ) Dw + Rzv0k* D

(4)

where Rz is the vertical dispersivity and Dw is the effective diffusion in unsaturated media. Calculation of the Pollutant Flux. Assuming a steady state system, the vertical gas flux is stationary and is constant at any depth in the soil. Dispersion in the gas phase can be written using Fick’s law, by analogy to diffusion ja Ja ) -D

dCa dz

(5)

where Ja is the flux of pollutant in the gas phase, Dj a is the dispersion coefficient in the soil gas, and Ca is the concentration in the gas phase. We use the classical Millington (21) formulation for diffusion (although recent papers like 22 use different exponents that give slightly different values for the diffusion coefficient): j a ) Da ) D0a D

θa10/3 n2

(6)

Ca ) H · Cw

(7)

The total flux is then written as follows: J ) -Da

[

J ) - D0a

θa10/3 n

2

dCa dCw dCa - Dw ) - (Da + Dw /H) dz dz dz

(

+ D0w

10/3 θw

n

2

) ]

+ Rzv0k* /H

(8)

dCa dCa ) -A(z) dz dz (9)

To our knowledge this type of equation cannot be solved analytically. However, it is possible to integrate it numerically as it is explicit and depends only on the depth z, although the link between θ and z is quite complex (van Genuchten equations). To integrate it numerically we use the following approach: dCa )

-J dz or Ca ) c + J · I(z) with I(z) ) A(z)

1 dz ∫ A(z) (10)

I(z) is integrated with respect to z by the rectangle approximation. We use very thin intervals in the capillary fringe due to important variations of θ and k*. The number of intervals is fixed to 200; thinner intervals are obtained close to the water table by the use of an exponential function. The boundary conditions are generally as follows: Ca ) 0 at z ) 0 (soil surface) Cw ) C1 at z ) L (water table depth vs soil surface) C1 is the concentration in the groundwater. However a nonzero concentration can be specified at the surface. The value of the flux being independent of z, one can write: J)

HC1 I(L)

(11)

When J has been calculated one can obtain the value of the pollutant concentration in the soil air with Ca(z) ) J · I(z)

(12)

Barometric Pumping. Barometric pumping in the soil is due to cyclic variations of atmospheric pressure, which may generate air movement within the soil porosity. These movements are cited by some authors to be one of the sources of increased pollutant fluxes to the atmosphere (12). The analytical method to calculate barometric pumping, which is considered in the model by adding a supplementary term in dispersion, is given in the Supporting Information. However, the generated fluxes are negligible for most VOL. 44, NO. 16, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Left: Relative TCE content in the air phase: experimental (points) and semianalytical (lines) data for various values of dispersivity. Right: water content in the same experiment: experimental (points) and fit of VG parameters (line). situations, except for large barometric variations (weather change) over saturated soils (see SI).

Model Validation Comparison with Experimental Data. McCarthy and Johnson (7) made a very detailed experiment where they measured TCE in horizontally flowing water and in gas phase in the unsaturated zone in a 1-m scale tank. The parameters of this experiment are detailed in Table 1 of the Supporting Information. We used their experimental data to test our model (devoid of the extension for barometric pumping). We directly fitted the VG parameters on the published water content profile. The only remaining fitting parameter is the vertical dispersivity in the sand. McCarthy and Johnson (7) also use this parameter as a fitting parameter and found a value of 1 mm. This value is satisfying as it is close to the mean grain size, a good approximation of the true vertical dispersivity in small scale experiments (23). As the authors of the experiment, we find a value of 1 mm as the best estimate of the dispersivity. The fit of the vertical profile is fairly good (see Figure 1). Comparison with Numerical Model. We used Hydrus3D (24) in a steady state mode to simulate the Johnson and McCarthy experiment. Hydrus 3D is one of the few commercial numerical codes that is able to simulate groundwater movement, transfer from water to gas phase, and diffusion in the gas phase. It has been difficult to reach the correct profile because of the important effect of boundary conditions. In fact, a fixed water flux condition (equal to the measured one) at the input of the saturated region tended to overpredict concentrations and fluxes (see Figure 2). The results are correct only when the boundary conditions are set in terms of water head.

Results and Discussion The presented model is able to simulate experimental data with the same or even better accuracy than a numerical model, having the advantage of ease of manipulation and instantaneous results. The required data include VG parameters for the soil and pollutant properties. The major unknown is the vertical dispersivity. Literature data suggest that transverse dispersivity is often close to the size of the soil grains for the capillary fringe scale (23). The equations for barometric pumping, included in the model, are detailed in the Supporting Information. The analytical solution used in this work gives the same results as numerical calculations of Massman and Farrier (9). These 6230

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FIGURE 2. Comparison of measured data and the semianalytical calculation with two different numerical simulations with Hydrus. First test: head boundary conditions; and second test: flux boundary conditions. results show that barometric pumping becomes important only for very deep unsaturated zones (>20 m) and large pressure variations (>50 mbar). Choi and co-workers (25) confirm these results in field data modeling. Sensitivity Study. Several parameters were varied to assess their importance on the overall flux of the pollutant to the atmosphere. All conditions are described in the Supporting Information. The concentration of the volatile organic compound in the groundwater is set to 1 µg · L-1 in every case. Since the flux is proportional to the concentration in groundwater, one can calculate the flux directly for any other concentration in groundwater. The first sensitivity test examined variations of the VG parameters. We simply use common values of the VG parameters for typical soil classes (26). We use the saturated hydraulic conductivity of the soil as the discriminating parameter between soil classes. Figure 3 clearly shows that the “sand” soil type leads to a much higher volatilization than any other soil. The sandy soils encircled in Figure 3 are clayey and silty sands and yield only 14-39% of the flux in sand, and all other soils less than 11%. The groundwater velocity plays some role in the volatilization flux that varies by a factor of 3 for a velocity

FIGURE 3. TCE flux according to the soil type for C ) 1 µg · L-1 of TCE in groundwater. multiplied by a factor of 25 for the “sand” soil. The relative importance of each diffusion/dispersion process is given in the SI. In a second sensitivity analysis, we use the “sand” soil but vary the contaminant type, by changing the diffusion coefficient and the Henry’s law constant. Henry’s law constant varies much more than the diffusion coefficient in free air, when substances are varied. The volatilization flux shows an interesting pattern: when the H value (dimensionless air/water coefficient) is higher than 0.2 the H constant is not limiting any more and all compounds have similar volatilization fluxes. Thus if the contaminant has a high Henry’s law constant, an error on the H value or the diffusion coefficient will not modify the volatilization flux significantly. Among other factors temperature has been claimed to be important in volatilization studies (12, 13, 27). Soil temperature influences the values of H and of the diffusion coefficients (air and water). We used EPA online calculation tools for this purpose: H variations are based on the classical Clausius-Clapeyron relationship and the variation of the vaporization enthalpy with temperature; Da variations were computed by using a formula considering the molar volume of the substance (see Supporting Information). For these sensitivity analyses, the pollutant under consideration is TCE. The variation of J is smaller than a factor of 2 for temperature varying from 5 to 25 °C. This effect seems to be slightly smaller than the values cited by Tillman et al. (13). But these authors did not give the formula to understand the origin of differences. The difference may originate from the calculation of the variation of the Henry’s constant with temperature. Use and Limits of the Model. The major interest of the proposed model is its simple use through a spreadsheet (download at http://perso.egid.u-bordeaux3.fr/~atteia/ PagePerso/Software.htm). Of course, this model has less possibilities than a numerical model. In contrast, the accuracy was better than the numerical model run with a coarse grid. Instantaneous calculation allows testing the influence of each parameter in a minute. The results underline the importance of a correct description of the capillary fringe to calculate volatilization fluxes. For this, the use of VG approach seems to be more adapted than a Brooks and Corey (27) approach that includes an abrupt change of water content vs suction slope at the top of the capillary fringe. The broad use of the VG approach will help the user to get the correct parameters and thus a satisfying estimation of fluxes. The non linearity of the water content close to the upper boundary of the capillary fringe leads to low volatilization fluxes. A simple calculation shows that a linear approach considering a homogeneous water content along the profile may lead to an overestimation of the volatilization fluxes of a factor higher than 6 compared to the presented approach.

FIGURE 4. Variation of the volatilization flux for various typical groundwater pollutants discriminated by their non dimensional Henry’s law constant (soil type: sand; C1 in groundwater: 1 µg · L-1).

FIGURE 5. Role of temperature on the pollutant flux (soil type: sand; concentration in groundwater: 1 µg · L-1). The high concentration at the capillary fringe top also leads to significant fluxes generated by a groundwater level decrease. This effect, although not considered here as the model is developed for steady state, has been demonstrated experimentally (8) and must be considered when interpreting field data. Because of the assumptions used for the formulation of the model, two important limitations must be communicated. At first, the model does not take under consideration volatile substances existing as a liquid organic phase in the unsaturated zone. In unsaturated zones containing only traces on nonaqueous phase liquid, the volatilization flux will be much higher (28). The major use of the model is thus in areas downgradient of identified source zones. Second, the advection of the aqueous phase due to rainfall or evaporation is not taken under consideration. The data from Rivett (4) for instance show a very steep gradient (2 orders of magnitude) of the concentration at the top clean infiltration of groundwater, below the capillary fringe, that may be due to clean infiltration water that reaches the groundwater. The model results are thus only applicable to periods of low rainfall. It can also be considered that due to recharge, the model result will generally overestimate the volatilization flux. In contrast, if water advection is upward due to high evaporation rates, the model will underestimate pollutant fluxes. Future work should incorporate vertical advection of water, especially also dynamic changes such as when the groundwater level fluctuates.

Supporting Information Available Model formulation for barometric pumping and calulated examples, data of the Johnson and McCarthy experiment, VOL. 44, NO. 16, 2010 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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parameters for the sensitivity study, formulas for temperature dependence of H, and diffusion coefficients. This material is available free of charge via the Internet at http:// pubs.acs.org.

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