Soil-to-indoor air exposure models for volatile organic compounds: The effect of soil moisture^†

Hypothetical environmental scenario

A building foundation (including the zone of influence [7], discussed below) was assumed to be 1.83 m (6 ft) above a contaminated zone of soil that was 1.22 m (4 ft) thick. The contaminated zone was assumed to contain a model volatile organic chemical at an initial concentration of 1 μg/g. The soil between the foundation and the contaminated zone was assumed to be initially contaminant-free. The soil texture was assumed to be sandy loam. Base values for soil properties were taken as follows: bulk density of soil, 1,300 kg/m³; total porosity, 0.41 (v/v); soil organic carbon content, 0.1%. Additional soil properties, used only by the IMPACT model, are shown in the appendix. The area of the zone of influence subject to contaminant entry was assumed to be 52 m², and the building ventilation rate was 46 m³/h. Physicochemical properties for the model contaminant were set at representative values for VOCs. The K_oc was 100 ml/g and the dimensionless Henry's law constant was set at 0.222. These values correspond to those reported for benzene; they were also close to median values for 30 environmentally significant VOCs [17]. Air and water diffusion coefficients were set at representative values of 5 × 10⁻⁶ and 5 × 10⁻¹⁰m²/s, respectively [6]. The chemical half-life in soil, when used, was set at 16 or 180 d. The shorter half-life has been reported for benzene in soil, and is representative of rapidly degrading VOCs, such as nonhalogenated chemicals [18]. The longer half-life is more representative of halogenated chemicals [18].

Calculation of volatilization flux—Jury model

The indoor air exposure model previously presented by Sanders and Stern used a simplified form of the volatilization model of Jury et al., which assumed no soil moisture movement [1]. In this study, the full Jury model (Equations 18, 21, and A2, see Jury et al. [6]) was used, which allowed determination of the effect of soil moisture advection. The model of Jury et al. calculates a time-dependent volatilization flux of a chemical from the soil surface, assuming that a finite source of the chemical is originally contained within a specified depth range beneath the soil surface [6]. First-order degradation of the chemical can also be included. Transport of chemical is accomplished via both diffusive and advective processes. The diffusive component is controlled by a soil diffusion coefficient, which is a function of the Henry's law constant, the diffusion coefficient of the chemical in both air and water, the adsorption coefficient of the chemical to the soil, soil water content, porosity, and bulk density [2]. Partitioning of chemical between the vapor, aqueous, and sorbed phases is assumed to be at equilibrium at all times. The advective component is controlled by a user-specified soil moisture flux rate, which is held constant as a function of time.

Calculation of volatilization flux—IMPACT model

The IMPACT model is specifically designed for the calculation of soil cleanup criteria for hazardous waste sites as controlled by the soil-to-groundwater pathway [14-16]; however, the model also includes, as a mechanism of contaminant loss, the volatilization pathway.

The IMPACT model incorporates equilibrium partitioning, diffusive, degradation, and mass-balance processes equivalent to those employed by the Jury model, but includes the additional process of hydrodynamic dispersion. These processes are assembled into an advection-dispersion equation representing contaminant transport through the soil column, expressed in terms of the aqueous phase concentration [13, 15, 16]. The equation is similar to that of Baehr [19]. The most significant capability included in the IMPACT model that is not available in the Jury model is the ability to simulate soil moisture contents and moisture transport on a day-to-day basis. This is done using the moisture form of the Richards equation to describe moisture transport [20], and Darcy's law to describe moisture flux [21]. To evaluate these equations, the hydraulic conductivity expression of Campbell is used [22], and soil moisture retention and soil diffusivities are calculated according to the empirical expression proposed by Clapp and Hornberger [23]. To solve the contaminant transport and moisture flow equations, the soil column is divided into imaginary layers (0.30 m thick in this study). The moisture flow equation is solved using a fully implicit finite difference technique [24]. The advection-dispersion equation is solved numerically using Hamming's modified predictor/corrector method [24]. A 1-d time step was used in this study.

The IMPACT model was executed in two modes. First, soil moistures and moisture advection rates were held constant at various levels to allow comparison of the output of this model with that of the Jury model, which can only accomodate constant soil moisture advection. Second, the model was run in the default simulation mode, using actual daily temperature and rainfall records for Newark, New Jersey, USA, from 1959 to 1989 [13]. When run in this mode, initial net infiltration was calculated using a mass balance expression accommodating evapotranspiration, precipitation, and surface runoff. Evapotranspiration rates were calculated using Thornthwaite's method [25, 26]. Potential evapotranspiration was first calculated as a function of temperature and percentage sunshine [25]. Actual evapotranspiration was then calculated by the water balance method of Thornthwaite and Mather [26]. Surface runoff rates were calculated using the Soil Conservation Service runoff curve number [27]. Recharge (advection) of soil moisture to the water table was then transiently calculated using the net infiltration as a boundary condition at the top of the soil zone [13]. A limitation of the one-dimensional hydrologic approach used in this study is that it does not take into account shielding of impacting precipitation by the building, which may reduce recharge rates directly under the structure. To more realistically determine absolute moisture advection rates from a specific climate or rainfall history, a two-dimensional model would be required.

Seasonal and short-term temperature fluctuations in nearsurface soil would affect the magnitude of some contaminant chemical parameters, particularly the Henry's law constant and the first-order degradation constant. The IMPACT model does not allow for adjustment of contaminant properties as a function of temperature; daily temperature and rainfall data were used only for calculating moisture transport. The model may therefore underestimate the fluctuations in near-surface contaminant transport and degradation processes when it is used in the natural environmental simulation mode.

Transformation of volatilization flux values into air concentrations and doses

In his discussion of transport of VOCs into buildings, Little et al. suggested that the rate-limiting step in the transport process is the diffusion of the chemical through the soil to a zone of influence around the building foundation [7]. The zone of influence is a region of soil surrounding the foundation in which significant soil gas advection into the building occurs. Contaminants entering this zone are immediately removed from it by being swept into the building airspace by advection, with the foundation offering little resistance to contaminant entry. Research on the entry of radon and VOCs into buildings supports this assumption [7, 28]. As discussed previously by Sanders and Stern [1], this assumption matched the soil surface boundary condition of the model of Jury et al. for chemicals with high Henry's law constants, in which contaminants rapidly pass through a stagnant air layer located at the soil surface [3]. No accumulation of contaminant vapor occurs in either the zone of influence or in Jury's stagnant air layer. This allowed the direct use of the volatilization flux calculated by the Jury model as the contaminant flux into the building airspace. An equivalent mechanism was implemented in the IMPACT model by setting the top boundary condition to maintain zero contaminant concentration in the liquid phase, thus forcing contaminant to immediately volatilize upon reaching the soil surface, with no contaminant vapor accumulation. Therefore, IMPACT flux calculations could also be used directly as flux rates into the building airspace. Flux values, J(t), of the contaminant entering the building airspace were converted to indoor basement air concentrations as a function of time by multiplying them by the ratio of the flux area A (52 m²) to the building airflow rate, Q (46 m³/h)

(1)

To calculate cumulative doses, C(t) is multiplied by an indoor-specific inhalation rate I (15 m³/d) to obtain a dose rate as a function of time. By integrating the dose from time 0 to time t, a cumulative dose as a function of time is obtained

(2)

Analytical solutions are available for Equation 2 when the Jury model is used. In the absence of soil moisture advection, the solution presented by Sanders and Stern may be used [1]. When soil moisture movement is involved, the integral portion of the above equation may be evaluated using the analytical solution reported by Jury et al. [6]. When using the IMPACT model, Equation 2 was evaluated using numerical integration. Cumulative doses were calculated for a 30-year exposure period, based on United States Environmental Protection Agency (U.S. EPA) estimates of a reasonable upper percentile of the time an individual will live in a single residence [29]. For carcinogens, it is assumed that the cumulative dose is the relevant metric for risk assessment [29].

Sensitivity analysis of the model of Jury et al.—No soil moisture advection

Soil moisture contents vary considerably, ranging from <0.05 (v/v) to nearly saturation values (approximately 0.5 [v/v]), depending on soil texture and environmental conditions. The sensitivity of indoor air concentrations and cumulative inhaled doses to soil moisture content, in the absence of soil moisture movement or chemical degradation, was investigated using the Jury model (Figs. Fig. 1., Fig. 2. and Table 1). The magnitude of the indoor air concentration peak, and the time at which this peak occurred, varied significantly with soil moisture. As soil moisture was increased from 10 to 30% (v/v), peak indoor air concentrations decreased from 450 μg/m³ to 9 μg/m³, and the time of the peak concentration increased from 25 d to 1,100 d (Fig. 1 and Table 1). Because cumulative dose is proportional to the area under the indoor air concentration curve with respect to time, the soil moisture variation also had a substantial effect on cumulative dose in the early stages of exposure (Fig. 2). However, the effect of soil moisture on the long-term 30-year cumulative dose was less dramatic, varying by less than a factor of two (Table 1). The model of Jury et al. predicted that all chemical would eventually volatilize into the building foundation if chemical degradation and soil moisture advection are not modeled (Fig. 2). If the exposure period entirely brackets the entire volatilization time-course of the chemical, the total dose of inhaled chemical will remain constant. If the exposure time period is shorter than the time for complete volatilization, the total dose will be dependent on soil moisture.

When chemical degradation was included, the dose accumulation curve reached a final plateau quickly relative to long-term exposure periods (Fig. 3). When compared to simulations without degradation, peak indoor air concentrations occurred earlier, were lower, and decreased more dramatically as the soil moisture was increased (Table 1). The 30-year cumulative doses, relative to doses obtained without degradation, were reduced by as much as seven orders of magnitude relative to the dose inhaled with 10% soil moisture and no chemical degradation (Table 1). Clearly, the soil moisture content and the chemical degradation rate are critical factors to be considered when assessing the indoor air exposure pathway using an environmental scenario similar to that employed in this study.

Sensitivity analysis of the model of Jury et al.—Soil moisture advection included

When soil moisture is present at a level above field capacity, advection of moisture towards the water table will occur. Using a sandy loam soil texture and soil moisture contents of 19, 21, and 24%, hydrologically appropriate steady-state rates of soil moisture flow were calculated using the IMPACT model as described below (Table 1). This range of soil moisture contents spanned most of the normal annual range of soil moisture for this soil texture. The paired moisture contents and moisture flow rates were then used in the Jury model. At a lower moisture content (19%), the downward advection of soil moisture had little effect on the time course and magnitude of indoor air concentrations, or on the dose accumulated (Table 1). Under these conditions, diffusive transport was the dominant transport mechanism because of the relatively large volume of airspace available in the soil and the low rate of soil moisture advection (0.016 cm/d). As the soil moisture was increased to 24%, advection of soil moisture increased by over a factor of 10, to 0.27 cm/d (Table 1). The increased advection and the reduced pore space for available diffusive transport significantly reduced the peak indoor air concentration of the chemical in the building airspace and the long-term dose inhaled (Table 1). These results indicate that the moisture content of the soil should be compared to its field capacity and saturation volume when deciding whether or not to model soil moisture movement.

Comparison of the model of Jury et al. to the IMPACT model under steady-state soil moisture conditions

The IMPACT simulation model was designed to calculate daily and seasonal variations in soil moisture movement and soil moisture content. However, the model could also be executed in a mode that allowed for constant soil moisture content and advection, thus allowing comparison with the model of Jury et al. under equivalent conditions. Through trial and error, the steady-state downward moisture flux that matched a given constant soil moisture profile was determined, as controlled by the Richards equation and Darcy's law (Table 1). The range of volumetric soil moisture contents modeled (19, 21, and 24% [v/v]) spanned the range predicted for a sandy loam soil when the IMPACT model was run in the default simulation mode, in which daily and seasonal variations in soil moisture properties were modeled as a function of daily precipitation and temperature records (Fig. 4).

The volatilization of the model contaminant into indoor air was calculated using both the Jury and IMPACT models, using the three steady-state soil moisture conditions described above. The models were also run at a soil moisture content equal to the soil's field capacity (10% [v/v]), to determine their behavior when no soil moisture advection occurred. Simulations were initially conducted in the absence of chemical degradation. Under field capacity conditions, peak indoor air concentrations were nearly the same for both models, although the peak time for the IMPACT model was slightly later (Fig. 5a). This is attributed to the value of the spatial increment used in the numerical solution scheme. Calculated long-term doses using each model were nearly the same (Table 1). At the annual average moisture for this soil (21%), when both advection and diffusive transport of the model contaminant were significant, the IMPACT model yielded a peak indoor air concentration that was one-half that predicted by the Jury model, and which occurred at a substantially later time-point (Fig. 5b). However, the long-term estimated doses were nearly the same for both models (Table 1). At a moisture content near the upper limit of the range predicted for this soil (24%), in which advection dominates, the time of the peak indoor air concentration was nearly the same for both models, whereas the magnitude of the peak indoor air concentration was lower using the IMPACT model (Fig. 5c). The cumulative long-term dose, although quite small for both models, was lower using the IMPACT model (Table 1).

The Jury and IMPACT models both incorporate similar assumptions regarding the contaminant diffusion process (the Millington and Quirk model [30]), and soil moisture advection was matched between the two models. Additionally, assumptions regarding the overall contaminant transport process were similar for both models, in that diffusion of chemical through the soil to the zone of influence around the building foundation was considered to be the rate-limiting step. However, important differences exist between the two models. First, mechanical dispersion is not modeled in the Jury model. This may partly explain the observation that the IMPACT model gave peak concentrations that were somewhat lower and broader than those observed using the Jury model. Second, although most transport assumptions were similar for both models, the assembly of these processes into an overall transport equation varied. The Jury model is an analytical solution containing the advection and diffusion transport assumptions described by Jury et al. [2, 6], whereas the IMPACT model uses an advection-dispersion equation, incorporating an additional term for mechanical dispersion [13, 15, 16]. Finally, it is possible that the numerical methods used in the IMPACT model may have introduced some perturbations in predicted results. The IMPACT model output has been compared to an analytical solution of the advection-dispersion equation in the case of steady-state flow conditions, and agreement was found to be excellent [13]. However, the comparison was restricted to predicting the concentration profile of the contaminant in the soil zone.

When comparing model predictions with environmental measurements, an order of magnitude agreement is frequently considered to be adequate [31]. The same criterion could be applied when determining whether or not there is adequate agreement between different models [17]. Using this criterion, the models gave comparable results, because peak heights, peak times, and calculated doses agreed to within a factor of three, and were nearly equivalent in several cases. From this perspective, either model could be used for investigating the soil-to-indoor air pathway under constant soil moisture flow conditions.

The Jury model and the IMPACT model were also compared when chemical degradation was included, with the half-life for the model contaminant set at 16 or 180 d. Degradation assumptions differed between the two models, in that the Jury model considers degradation to occur in all three phases, whereas the IMPACT model assumes that degradation occurs in the liquid phase only, an assumption that is probably more realistic. Given the partitioning assumptions of this study, significant levels of contaminant will exist in both the sorbed and aqueous phases (at 20% soil moisture, about 60% in the aqueous phase and 40% in the sorbed phase). Therefore, when a given half-life is entered for the two models, the overall degradation rate will be somewhat lower for the IMPACT model, depending on the level of soil moisture. At the field capacity (10%), the IMPACT model doses became progressively higher than the Jury model doses as the half-life was decreased (Table 1), because the low soil moisture restricted the amount of possible aqueous phase degradation. At an intermediate soil moisture (21%), doses using the IMPACT model were one-third of those determined using the Jury model when a 16-d half-life was used, whereas the doses were nearly equivalent between the two models in the absence of degradation (Table 1). The reason for this observation is that the significantly longer transport time for the model contaminant using the IMPACT model (Fig. 5b) allowed more time for chemical to degrade before volatilizing, despite the slower overall rate of degradation of the model relative to the model of Jury et al. At the highest soil moisture (24%), transport times using both models were similar, and the IMPACT model dose again increased relative to the Jury model dose as the half-life decreased, becoming equal at a 16-d half-life (Table 1). Despite the mechanistic differences in the degradation process between the two models, peak times, peak concentrations, and calculated doses still agreed to within a factor of three (with one exception) when a 180-d half-life was used, and to within a factor of three (with two exceptions) when a 16-d half-life was used (Table 1), indicating that the models were roughly comparable.

IMPACT simulation under natural environmental conditions

When the IMPACT model was run under natural environmental conditions, using daily temperature and precipitation records for Newark, New Jersey, USA, soil moisture levels and soil moisture movement varied considerably both day-today and seasonally (Fig. 4). The short-term peaks and valleys resulted from particular storm events and were a function of the magnitude and duration of rain storms. The longer term rises and falls were due to seasonal variations in soil surface temperatures. In winter, evapotranspiration decreases and soil moisture contents and moisture movement increase. An opposite effect occurs during the warm season.

When indoor air concentrations were investigated under natural environmental conditions, similar day-to-day and seasonal variations can be seen, although the magnitude of these effects taper off with time as the bulk of the chemical is volatilized from the soil (Fig. 5d). Volatilization increased during periods of low soil moisture and moisture advection, and decreased when moisture levels and moisture advection increased (Figs. Fig. 4., Fig. 5.), with shorter term spikes and troughs corresponding to individual storm events.

Although the concentration trace of the natural environmental simulation is difficult to compare directly to the simplified moisture runs, it was observed to fall within the range of concentration traces predicted using simplified moisture conditions that span the annual range of moisture calculated for this soil (Table 1 and Fig. 5). Over the longer term, the accumulated dose should be comparable to a run under steady-state conditions using average soil moistures. The average soil moisture simulated using the IMPACT model was 21%, which could be maintained using a steady-state soil moisture advection of 0.056 cm/d. However, the average soil moisture advection was calculated to be about 0.12 cm/d, which under steady-state conditions required a constant soil moisture of 22%. Although this 1% difference in soil moisture seems small, it corresponded to a doubling in the soil moisture advection rate, and a significant decrease in the calculated total dose (Table 1). When steady-state simulations were run at a soil moisture of 22%, the Jury model dose decreased relative to the dose at 21% moisture by a factor of two to three (from 661 to 310 mg, in the absence of degradation, Table 1). The IMPACT model dose decreased by a factor of three to seven (from 700 to 90 mg, in the absence of degradation, Table 1). This illustrates the extreme sensitivity of predicted indoor air concentrations and exposures to even small variations in soil moisture behavior. Under the conditions of this study, the dose resulting from the simulation carried out under natural environmental conditions fell in between the two doses predicted by the IMPACT model using the average moisture content of 21% or the average moisture advection of 0.12 cm/d (Table 1). When chemical degradation was not considered, the IM-PACT model dose under natural environmental conditions was within a factor of two of those calculated using the Jury model under average soil moisture advection conditions (0.12 cm/d). When degradation was included, the doses were nearly the same (Table 1).

Comparisons with steady-state conditions are more difficult to interpret when contaminant degradation is included. Because the IMPACT model assumes that degradation is first-order with time, the effect of degradation will be somewhat dependent on the season in which the simulation is started. The simulation in this study began in January, during a period of low volatilization, so degradation was able to act upon the initial mass of contaminant for 2 to 3 months before significant volatilization occurred. Nonetheless, over the longer term, this effect appeared to be minimal.