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Geosciences and Environmental Engineering Group, Environmental Science Division, Oak Ridge National Laboratory, P.O. Box 2008, Oak Ridge TN 37831-6036
* Corresponding author (parkerjc{at}ornl.gov)
Received 23 December 2002.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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Abbreviations: NAPL, nonaqueous phase liquid • PCE, perchloroethene
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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Volatile contaminant transport in the vadose zone under natural conditions is often attributed to vapor phase molecular diffusion and dissolved phase advective–dispersive transport (e.g., Jury et al., 1990; Ravi and Johnson, 1997). Measurements of vapor fluxes from contaminated groundwater, however, have been reported to significantly exceed those attributable to diffusion (Smith et al., 1996). Other processes that may induce vapor phase transport include barometric pressure changes, water table fluctuations, air displacement due to water infiltration, and vapor density variations (Scotter et al., 1967; Camp Dresser and McKee, 1986; Mendoza and Frind, 1990; Massmann and Farrier, 1992; Nilsen et al., 1991; Rohay et al., 1993; Auer et al., 1996; Conant et al., 1996; Ellerd et al., 1999). Of these phenomena, gas phase advection induced by water infiltration is expected to be of minimal importance in most cases, because average induced airflow rates are small and will usually dissipate close to the ground surface (Camp Dresser and McKee, 1986).
This paper investigates contributions of barometric pumping and periodic water table fluctuations to vapor transport in the vadose zone relative to molecular diffusion. Simplified models are presented to assess volatilization losses from contaminated groundwater and residual NAPL depletion from soil, while considering vapor diffusion, aqueous advection, and dispersive vapor transport due to periodic air pressure fluctuations.
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VAPOR TRANSPORT PROCESSES |
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TOPABSTRACTINTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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 | [1] |
 | [2] |
is total soil porosity, a is air-filled porosity, and Da,o is the free air diffusion coefficient (Millington and Quirk, 1961). For a layered soil with transport perpendicular to layering, the effective diffusion coefficient may be computed as the weighted harmonic average of the layer values (i.e., 
xi/xi/
i).
Dispersive Vapor Transport
It has been recognized for many years that barometric pressure fluctuations induce cyclic airflow in and out of the ground surface and wells (e.g., Scotter et al., 1967; Kimbell and Lemon, 1972; Clements and Wilkening, 1974; Petersen et al., 1987; Nilsen et al., 1991). This phenomenon, commonly referred to as "barometric pumping," has been shown to affect radon and volatile organic chemical entry into buildings (Clements and Wilkening, 1974; Camp Dresser and McKee, 1986; Parker, 2002) and vapor emissions from the ground surface and from wells (Nilsen et al., 1991; Massmann and Farrier, 1992; Auer et al., 1996; Rossabi and Falta, 2002; Neeper, 2001). Transient air pressure fluctuations induced by water table fluctuations have been shown to induce similar effects (Camp Dresser and McKee, 1986), although typically of lesser magnitude unless the fluctuations are of high frequency (e.g., in tidal influenced zones).
Numerical and analytical models of natural vapor pumping of have been documented by a number of authors (Camp Dresser and McKee, 1986; Nilsen et al., 1991; Massmann and Farrier, 1992; Auer et al., 1996; Rossabi, 1999; Neeper, 2001; Parker, 2002). These studies indicate that at long time scales relative to the frequency of periodic pressure fluctuations, as the net volumetric airflow rate approaches zero, vapor phase contaminant mass fluxes will be induced by irreversible mass loss to the atmosphere due to out-gassing that may be modeled as a Fickian dispersive transport process described by
 | [3] |
 | [4] |
Many theoretical and experimental studies have shown that dispersivity may increase with travel distance due to the tendency of variance in soil permeability to increase as the observation volume increases (e.g., Greenkorn, 1983; Gelhar et al., 1992). A study by Gelhar et al. (1985) of vertical aqueous phase transport in the unsaturated zone at a number of sites showed increases in longitudinal dispersivity for vertical flow as a function of travel distance. The results can be approximated by the empirical relation
 | [5] |
We are unaware of any experimental studies of dispersion induced by cyclic air pressure fluctuations. However, since hydrodynamic dispersion is predominantly due to large-scale permeability variations rather than pore-scale phenomena, it is reasonable to assume that the dispersivity for vapor phase transport will be similar to that for aqueous phase transport for the same mean flow orientation (i.e., vertical transport in the unsaturated zone). Indeed, this assumption is nearly universally assumed by multiphase transport models used in subsurface hydrology and reservoir engineering applications. We will follow this same approach, while noting that there is a need for field-scale research of gas phase dispersive transport to better understand these processes.
For periodic water table fluctuations characterized by a fluctuation range xwt for a full cycle period, twt, the mean absolute air velocity will be equal to
 | [6] |
a is the average air-filled porosity.
For barometric pressure fluctuations, the mean airflow may be derived from the ideal gas law (e.g., Camp Dresser and McKee, 1986; Auer et al., 1996). For a pressure fluctuation range P about a mean air pressure Po with a fluctuation period tbp, air in the soil will be compressed (or decompressed) by an average relative amount P/2Po for a time interval tbp/2. Therefore, the mean absolute Darcy velocity due to barometric pressure fluctuations will be
 | [7] |
 | [8] |
xi/ xi/ki) and average porosity may be computed as the weighted arithmetic mean (i.e., xii/xi).
A transient analysis of barometric pressure fluctuation induced flow by Auer et al. (1996) indicated that for katbp > 1 Darcy day, pressure perturbations propagate to a depth of at least 10 m. Employing other parameter values used by Auer et al. (i.e., P/Po = 0.015, a = 0.35) in Eq. [8] yields the same result. Barometric pressure fluctuations may be expected to propagate to significant depths in soils that are at least moderately permeable.
From Eq. [4] through [7], the magnitude of dispersion induced by barometric pressure fluctuations and water table fluctuations, respectively, will be
 | [9a] |
 | [9b] |
These equations are equivalent to models derived by Camp Dresser and McKee (1986) and Auer et al. (1996).
It is evident from Eq. [9] that a variety of dispersion coefficients may be computed for different processes inducing airflow, as well as for fluctuations with different magnitudes and periods. Since the various perturbations are likely to be out of phase, effects will not generally reinforce. It is therefore suggested to identify the process and period that induces the greatest dispersion and to disregard others when using the Fickian approach. For example, if diurnal pressure fluctuations of 0.5 kPa (0.005 atm) and weekly fluctuations of 2 kPa (0.02 atm) were observed, the diurnal period would have the dominant effect (i.e., 0.005/1 > 0.002/7) and should be employed for computing dispersion due to barometric pumping. From Eq. [9a] and [9b] and noting that P/Potbp is generally in the range 0.002 to 0.02 d-1, it is evident that barometric pumping will predominate over the effects of fluctuating groundwater unless xwt/twt is greater than 0.001 to 0.01 d-1 times the water table depth. This condition is likely to be met only if the period of water table fluctuations is short, for example, due to tidal effects.
Vapor transport in unsaturated soil is commonly assumed to be diffusion-controlled. To assess the potential error that may arise from this assumption, we may define the dispersive diffusive flux ratio, Da,disp/Da,dif computed from Eq. [2] and [9]. Consider first the dispersive transport induced by water table fluctuations. Two fluctuation scenarios are considered: (i) seasonal fluctuations of 3.6 m with a 1-yr period (xwt/twt = 0.01 m d-1) and (ii) tidal fluctuations of 0.5 m per 12-h period (xwt/twt = 1 m d-1). Each fluctuation scenario is analyzed for air saturations of 0.05, 0.50 and 0.95. For all cases, Da,o = 0.7 m2 d-1, = 0.4, and ß = 0.02 are assumed. The results (Fig. 1) indicate that dispersive fluxes induced by low-frequency (e.g., annual) fluctuations are less than diffusive fluxes, except at very low air saturations. In contrast, dispersive fluxes induced by high-frequency (e.g., tidal) fluctuations may substantially exceed those due to diffusion, especially if air-filled porosity is low and/or groundwater is relatively deep.
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P/Po, between 0.01 and 0.03 are typically observed with periods, tbp, of 1 to 7 d. As previously noted, the dispersion parameter ß is expected to be between 0.002 and 0.1. The foregoing indicate a probable range for the parameter group ßP/Potbp between 10-5 and 10-3 d-1. The ratio of dispersive fluxes induced by barometric pressure fluctuations to diffusive fluxes is computed for upper and lower ßP/Potbp values and for air saturations of 0.05, 0.5, and 0.95. It is assumed that the dispersive travel distance, Ldisp, is equal to the propagation depth of pressure fluctuations, xbp (e.g., volatilization from groundwater with pressure perturbation propagation unlimited by soil permeability). It is also assumed that Da,o = 0.7 m2 d-1 and = 0.4 for all cases.
Computed dispersive diffusive flux ratios for barometric pumping increase with depth more strongly than for the case of water table pumping (Fig. 2). This is expected from Eq. [9a], which indicates that dispersion due by barometric pumping increases with the square of depth when xbp = xdisp. For systems with low air-filled porosity, barometric pumping dominates transport across the range in ßP/Potbp. Near the upper range of ßP/Potbp, barometric pumping dominates transport for fairly shallow soils (i.e., >5 m) with moderate air-filled porosity and for deep soils (>15 m) with high air-filled porosity.
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VOLATILIZATION OF CONTAMINANTS FROM GROUNDWATER |
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TOPABSTRACTINTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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 | [10] |
 | [11] |
For steady-state, one-dimensional transport, mass balance requires
 | [12a] |
 | [12b] |
 | [12c] |
 | [13a] |
 | [13b] |
 | [14a] |
 | [14b] |
For vapor diffusion from the ground surface to the atmosphere across a boundary layer of thickness 
, the volatilization rate at the ground surface will be
 | [15] |
<< xcf (e.g., Jury et al., 1990) and Da,o > Deff, the atmospheric boundary layer impedance, /Do, will normally be much less than the upper limit soil impedance, xcf/Deff (see Eq. [14b]). For steady-state conditions with Jo = Jsoil, we therefore note from Eq. [14] and [15] that Ccf - Co >> Co - Catm will generally prevail and assuming Catm 
0, the atmospheric emission rate may be closely approximated by
 | [16a] |
 | [16b] |
The vapor concentration distribution in the soil for x >> 0 may be similarly estimated from Eq. [13] substituting Co 0. However, to obtain accurate estimates of steady-state concentrations near the ground surface, Eq. [13] must be solved subject to Eq. [14] and [15] such that Jo = Jsoil.
Further attention to the boundary condition at the capillary fringe is warranted, since the vapor concentration just above the capillary fringe is often unknown. More commonly, information is available on the groundwater concentration at or below the water table (i.e., depth of zero capillary pressure). Let us assume that the groundwater concentration is Cgw at a depth xgw below the water table or xgw + Lcf below the top of the capillary fringe, where Lcf is the capillary fringe thickness. The contaminant flux in the saturated zone from the point below the water table to the capillary fringe may be approximated as
 | [17] |
 | [18] |
Using Eq. [16] and [17] and assuming steady state such that Jsat = Jsoil indicates
 | [19a] |
sat is a nonequilibrium factor defined by
 | [19b] |
 | [20a] |
 | [20b] |
 | [20c] |
Note that if Isoil >> Isat, then Ccf HCgw, which corresponds to equilibrium between soil vapor above the capillary fringe and water at the measurement depth.
From the perspective of groundwater, volatilization represents a mass loss to the system. We may formulate this loss in the mass balance equation
 | [21] |
is the volatilization rate per porous media volume. The volatilization losses integrated over a finite thickness of the aquifer, Laq, must equal the volatilization flux at the capillary fringe. Assuming steady-state volatilization, this yields
 | [22] |
If we take the average groundwater concentration to be represented by the concentration at the midpoint of the integration range and use Eq. [19] to define Cw and Eq. [16] for Jo, we find
 | [23a] |
is an apparent first-order decay coefficient defined by
 | [23b] |
 | [23c] |
sat is defined by Eq. [19b] with xgw + Lcf = Laq/2. Note that Laq may represent the entire aquifer (e.g., in a vertically integrated model) or only a fraction of the aquifer (e.g., the upper layer in a numerical groundwater model). As Laq 0, the vertical nonequilibrium term sat 1. Equation [23] indicates that volatilization from the groundwater and ultimately to the ground surface has the form of a first-order decay phenomenon from the standpoint of the groundwater.
To assess the behavior of the foregoing model, consider the volatilization from groundwater of PCE, which has a Henry's coefficient of about 0.5 at a temperature of 10°C. We further assume relative barometric pressure fluctuations (P/Po) of 0.01 with a period (tbp) of 1 d, a total porosity () of 0.4, an aquifer thickness (Laq) of 10 m, and a vertical saturated zone dispersivity (Avsat) of 0.1 m. Three soil types with different air permeabilities (ka) and air saturations (Sa = a/) are considered:
Groundwater permeability is assumed equal to air permeability multiplied by the horizontal/vertical anisotropy ratio and divided by air relative permeability. The latter is taken to be equal to air saturation, which is a good approximation for high air saturations, and the anisotropy ratio is assumed to be 10, which is typical for many sites. A horizontal groundwater gradient of 0.01 is assumed. First-order decay coefficients for groundwater volatilization are computed as functions of groundwater depth (xcf) for various soil conditions and unsaturated zone hydraulic fluxes (Fig. 3).
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For the moderate permeability case (ka = 10-11 m2 [10 darcy], Sa = 0.7), apparent decay coefficients decrease to between 0.0005 and 0.005 d-1. Minimum decay rates shift to a depth of about 10 m, and volatilization exhibits somewhat greater sensitivity to hydraulic flux than for the high permeability case. Otherwise, the behavior is qualitatively similar to that for the high permeability case.
For the lowest permeability case considered (ka = 10-10 m2 [1 darcy], Sa = 0.5), computed decay coefficients are <0.001 d-1 for water depths greater than about 1 m. Minimum decay rates further shift to slightly lower depths, and volatilization rates exhibit pronounced sensitivity to the unsaturated zone hydraulic flux. A secondary maximum in volatilization rate occurs at a depth of about 22 m, which corresponds to the maximum propagation depth of barometric pressure fluctuations for these soil conditions.
Vertical mixing within the saturated zone has a significant influence on predicted volatilization rates, as evidenced by the high sensitivity to saturated zone vertical dispersivity (Avsat) (Fig. 4), which has been reported to vary between approximately 0.001 and 1 m (Gelhar et al., 1992). Identical sensitivity will occur with respect to groundwater velocity (groundwater dispersivity and velocity occur only as a product in the model; see Eq. [18]). The assumed relationship between unsaturated and saturated zone parameters in the foregoing example is reasonable, but certainly not universally applicable. The results should be regarded as illustrative and not as generic. Site-specific conditions must be considered.
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VOLATILIZATION AND LEACHING OF SOIL NAPL CONTAMINATION |
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TOPABSTRACTINTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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 | [24] |
is soil dry density, qu is unsaturated zone hydraulic flux (we limit the current analysis to qu 
0), and H is Henry's coefficient. Assuming pseudo steady-state conditions and negligible boundary layer impedance at the ground surface, the vapor flux may be estimated by Eq. [16], using xn in lieu of the groundwater depth, to obtain
 | [25a] |
 | [25b] |
 | [26a] |
 | [26b] |
As an example, consider the volatilization of residual PCE initially at an average soil concentration of 1000 mg kg-1 from the ground surface to groundwater at a depth of 10 m. Perchloroethene has a saturated vapor concentration, Cn, of 75 mg L-1 and a Henry's coefficient of 0.5 at an assumed average subsurface temperature of 10°C. The soil is assumed to have an air-filled porosity of 0.2, an air permeability of 10-10 m2 (1 darcy), and a density of 2000 kg m-3. The fraction of initial mass lost (= xn - xo/xb- xo) as a function of time is computed from Eq. [26] for qu of 0.0, 0.003, and 0.01 m d-1 (Fig. 5). Computed times for complete NAPL depletion from the soil are 123, 52, and 31 yr, respectively.
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 | [27] |
 | [28a] |
 | [28b] |
 | [28c] |
The foregoing solutions are not applicable to NAPL mixtures that contain chemicals with disparate solubilities and vapor pressures. For such systems, equilibrium total vapor phase and dissolved phase concentrations will decrease with time (as more volatile and soluble species are preferentially lost), while equilibrium concentrations of individual species may increase or decrease with time depending on whether their mole fractions in the mixture increase or decrease. For such systems, Eq. [27] may be integrated numerically for the multispecies mixture using equilibrium vapor concentrations computed for each time step on the basis of the current mixture composition.
If more refined flux estimates or spatial distributions of concentrations are needed, partial differential equations for transient vapor and dissolved transport must be solved. When such recourse is necessary, use of the Fickian approximation to account for air pumping effects will greatly reduce the computation burden compared with an explicit modeling approach, while providing a more accurate representation of the physical processes governing field-scale transport.
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APPENDIX |
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TOPABSTRACTINTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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, soil–atmosphere boundary layer of thickness.
, volatilization rate from aquifer per porous media volume.
, total soil porosity.
a, air-filled porosity.
, first-order groundwater volatilization coefficient.
sat, aquifer–capillary fringe nonequilibrium factor.µa, dynamic air viscosity (approximately 2 x 10-5 kg m-1 s-1).
, soil dry density.a, source depletion rate factor.
Aal, longitudinal (vertical) air phase dispersivity.
Avsat, vertical dispersivity in the saturated zone.
Catm, vapor concentration in the air above the boundary layer.
Cgw, groundwater concentration at depth xgw below the water table.
Cw, groundwater concentration.
Cs, contaminant mass per mass of dry soil.
Cn, vapor concentration at NAPL front.
C*s, soil concentration above which NAPL must occur.
C*n, initial aqueous phase concentration.
Ca, vapor phase concentration.
Cw, dissolved phase contaminant concentration.
Co, vapor concentration at the ground surface.
Ccf, vapor concentration just above the capillary fringe.
Deff, effective diffusion–dispersion coefficient (= Da,dif + Da,disp).
Da,disp, vapor phase dispersion coefficient.
Da-dif, effective soil vapor diffusion coefficient.
Da,o, free air diffusion coefficient.
Dsat, saturated zone vertical dispersion coefficient.
Dosat, effective diffusion coefficient in the saturated zone.
H, dimensionless Henry's coefficient.
Isat, mass transport impedance in the saturated zone.
Isoil, mass transport impedance in the unsaturated zone.
Jwi, contaminant flux density in groundwater in the i direction.
Jo, vapor flux density at the ground surface.
Jsat, vertical dispersive contaminant flux density in the saturated zone.
Jsoil, vertical contaminant flux density in unsaturated zone (positive upward).
Ja,disp, dispersive vapor flux density.
Ja,dif, diffusive vapor flux density.
ka, air permeability.
Laq, thickness of aquifer or upper layer from which volatilization occurs.
P, barometric pressure fluctuation range.
Po, mean atmospheric air pressure.
qsat, groundwater Darcy velocity.
qu, unsaturated zone hydraulic flux.
Sa, air saturation (= a/).
twt, period of water table fluctuations.
tbp, period of barometric pressure fluctuations.
x, depth.
xj, j-direction coordinate.
xcf, depth to capillary fringe.
xdisp, vertical travel distance.
xbp, depth of barometric pressure propagation.
xo, initial depth to top of NAPL source.
xb, initial depth to bottom of NAPL source.
xn(t), depth to top of NAPL zone at time t.
xgw, depth below the water table at which Cgw is known.
xwt, magnitude of water table fluctuation.
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REFERENCES |
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TOPABSTRACTINTRODUCTIONVAPOR TRANSPORT PROCESSESVOLATILIZATION OF CONTAMINANTS...VOLATILIZATION AND LEACHING OF...APPENDIXREFERENCES |
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