Since the numerical model is seen to properly capture the main aspects of the infiltration behavior of water in soil, it can now be applied to the modeling of vapor intrusion. Regarding the contaminant vapor response to infiltration, the vapor intrusion modeling scenario is also simplified to be one-dimensional. A hypothetical soil column such as that described in the experiment in Section 2 above (and used in the validation of the infiltration model) was “expanded” from 0.935 m to 3 m deep. This model represents a groundwater contaminant source at 3 m below ground surface (as in , x = 0
refers to the groundwater surface). Loamy sand is arbitrarily selected, and the soil properties are again taken from the U.S. EPA Johnson & Ettinger model spreadsheet implementation (EPA, 2004
= 3.475/m, M*
= 0.427, θr
= 0.049, θt
= 0.39, and ks
]). Two events are modeled: rainfall intensities at 2.56 mm/h (moderate rain) for 24 h duration, and 20.5 mm/h (extreme rain) for 3 h duration. It is worth noting that the two events involve the same total amount of rain water. The rainfall intensity is classified as in Tokay and Short (1996)
. For simplicity, rainfall intensities used here are at the non-ponding condition for loamy sand (EPA, 1998
) and surface run off is not accounted for. The initial state of soil moisture distribution is chosen to be hydrostatic (Zhan and Ng, 2004
), and this is calculated using Equation (4)
3.1 Vapor Response to a Single Rainfall Event
presents the evolution of soil moisture and contaminant concentration profiles for the bounded bottom scenario of moderate (left panel) and extreme rain events (right panel). Both the fraction of organic carbon in soil foc and the evaportranspiration rate are assumed to be 0 in this calculation. show that depending upon the depth, the concentration of soil gas contaminant can change by an order of magnitude, as the process takes place. These changes will be looked at in more detail below. It needs to be recognized that the scenarios represented are intended to be illustrative for certain features, and not necessarily to represent “real-world” conditions. Regarding the evolution of the profiles, three main steps can be identified: infiltration, soil water redistribution and water lens formation. Although there is no distinct time division between these processes, to separate them into three steps might be helpful in understanding of the processes. The three steps are analyzed in chronological order below.
Figure 3 Modeling results for soil moisture (a) and (a′) and vapor concentrations (b) and (b′) at times 0, 3 h, 1 day, 1 week, 1 month, 1 year and final steady state. Left panel assumes rainfall intensity of 2.56 mm/h, duration: 24 h; right panel (more ...)
The initial height of the capillary fringe is about 0.47 m, calculated from the method given by Dexter and Bird (2001)
. The initial contaminant vapor concentration profile is obtained based on the initial state (I.C. [a]), which assumes hydrostatic distribution of realistic soil moisture (calculated from Equation 
), and this profile results in more than one order of magnitude drop in contaminant vapor concentration within the capillary fringe when the above is solved together with [3
] and [14
] at steady state. This results from the relatively large resistance to contaminant diffusion through the moist soil in the capillary fringe.
The first step can be characterized by water infiltration taking place during the rainfall. In this step, an obviously important factor is infiltration intensity. Comparing the 3 h soil moisture content lines for , it is obvious that the larger the infiltration intensity, the faster the wetting front propagates, and the more moist the soil becomes. To be more specific, shows the short term soil moisture and vapor concentrations at hypothetical shallow soil probes under these two rainfall events, where the infiltration steps (i.e.
actual rain periods) are shown in the shaded areas. These results are plotted for the top of the ground surface, where greater effect has been found as the wetting front moves through. are for soils without organic carbon, while (c) and (c′) are soils with 0.1 % organic carbon. The wetting front travels as a wave. The larger the infiltration intensity, the faster the wetting front propagates, and the faster contaminant concentration changes. The concentration first increases and then decreases, and its fluctuation is within 0.1~1.6 times of the initial value. Although the effective advection is downward (Equation 
), by virtue of water dissolving progressively more PCE, the contaminant vapor concentration first increases a small amount. This is partly because the wetting front acts as a boundary or capping to the upward transport of vapor, as discussed below. After increasing for a short time, the contaminant is washed out and concentration decreases. Note that at the “probe” position closest to the surface (0.1 m depth) the vapor concentration peak occurs well before the maximum in soil moisture content is achieved. In fact, if the movement of the infiltration front is taken to be characterized by when soil moisture content reaches 0.2, then this front moves at about 0.015 m/h (left) or 0.08 m/h (right), which is also close to the rate at which the peak in vapor concentration moves downward. Note that the velocity of this front is much greater than the value of the infiltration rate, because the open area for flow becomes quite small as pores fill with water (bearing in mind that reflect this filling). The upward gas flow velocity must become higher as pores become water filled, as of course Equation (15)
has been forced.
Figure 4 Short term soil moisture content (a) and (a′), and contaminant concentration (b), (b′), (c) and (c′), at 0.1, 0.2 and 0.3 m deep. Left panel assumes rainfall intensity: 2.56 mm/h, duration: 24 h; Right panel assumes rainfall intensity: (more ...)
To further understand the initially observed increase in contaminant concentration, two effects need to be considered. One is an upward displacement by water of more contaminated gas from deeper in the soil, and the other is the diffusion upward against the capping by the water layer. The latter contribution can be demonstrated by variation of the effective diffusivity (Equation 
); reduction of that diffusivity for the 2.56 mm/h, 24 hour rainfall case leads to smaller peaks, such as those that characterize the 20.5 mm/h, 3 h rainfall (shown in [b′]). This is because in the latter extreme rainfall case, the movement of the infiltration front, relative to diffusion, is much faster than in the moderate rainfall case, and concentration cannot build up as much beneath that “capping” front. The actual peak in concentration is itself a consequence of the dissolution of PCE vapor into the water phase. As the pores become water filled with passage of the infiltration front, PCE is scrubbed out of the soil gas phase, in maintaining Henry’s Law equilibrium. When no water partitioning is allowed (results not shown) the distinct peak behavior of disappears. Note also that for the extreme rainfall in , this scrubbing leads to lower ultimate levels of gas phase contaminant, over the time frame represented in this figure (longer times will be examined below). A similar phenomenon of concentration increase and decrease was found in experimental results presented by Illangasekare et al. (2011)
Soil that contains organic carbon absorbs PCE and this damps out the concentration change process (see [c] and [c′]). The fluctuation of vapor concentration never exceeds one order of magnitude of the initial value for both rainfall events even without organic carbon being present.
Immediately after the infiltration step, for the upper soil, the soil moisture content begins to decrease slowly--see . Meanwhile, the contaminant concentration ( [b]) starts to again increase slowly after the infiltration step, as the contaminant is released from the infiltrated water.
Following the initial infiltration step, the next step is termed a water redistribution step. There is no explicit time frame for the end of this step. At a depth of 1 m below the ground surface, for the above two rainfall events, the soil moisture and contaminant vapor concentrations after 1 month are virtually identical and thus only results for 20.5 mm/h rainfall events are shown in . As no more water is supplied at the soil surface during this stage, the downward flow rate of water greatly slows down. The wetting front is smoothed and thus, the wave type behavior becomes much less distinct. In deeper soil, the capping effect prevails over the washing effect, and contaminant concentration at 1 m below the ground surface increases slowly, though only by a small amount (about 30 %) compared to the short time effect seen in the upper soil. This agrees with recent soil gas field data and with previous radon literature (ITRC, 2007
) which indicated that the soil gas contaminant concentration variation is less than a factor of 2 within a season.
Figure 5 Soil moisture content (a) and (a′) and contaminant concentration (b) and (b′), at probes at 1, 1.5 and 2 m deep at 1 month after rainfall events of intensity: 20.5 mm/h, duration: 3 h, and foc = 0. Results (a) and (b) are at qevapo = 0, (more ...)
Evapotranspiration is added and included in . The evapotranspiration rate is chosen to be the same as used by Tillman and Weaver (2007)
, 58.42 cm/year. Other more complicated expressions for evapotranspiration rates are available (Grifoll and Cohen 1996
). During the infiltration step, the water upward flux by evapotranspiration is small compared to the infiltration rate (0.0667 mm/h
20.5 mm/h). At longer times, during the water redistribution step, the evapotranspiration rate decreases the amount of water available for distribution and accumulation. Considering mass conservation of water, all the infiltrated water can be lost to evapotranspiration after 39 days, at which point, the initial hydrostatic water distribution is recovered. In the presence of evapotranspiration, the influence of rainfall on vapor intrusion is shortened to include only the infiltration and water distribution steps; no water lens would accumulate above the groundwater table.
When evapotranspiration is set to zero, in a single rainfall event, the third and final step involves the formation of a water lens atop the groundwater and ends in a final steady state which is a new steady state, if that lens is not assumed to be absorbed into the original groundwater. The final groundwater and capillary zone height were shown in . However, the contaminant vapor concentration is still far from the steady state profile at 1 year. This implies that the contaminant vapor transport is approaching a new steady state over the course of years. Of course, it is unrealistic that there would be no further rain (or evapotranspiration), so this case is clearly hypothetical. But if the infiltrated water reaches the source and forms a water lens in this bounded bottom scenario, such a water lens behaves as a large resistance to contaminant vapor transport, and this would cause the vapor concentration to drop between the first several months and 1 year. This is shown in . The new steady state water distribution again reaches hydrostatic. The only difference between the initial steady state and the final steady state is that the groundwater level increased. It is important to note that the shape of the final steady state soil water retention curve remains the same. From mass conservation, based on the water infiltrated, the final groundwater height increase Δh
can be calculated by:
Figure 6 Vapor concentrations at the soil gas probes located 0.2, 0.5, 1, 1.5, 2, 2.5 and 2.8 m deep at long term conditions when qevapo = 0. Left panel: rainfall 20.5 mm/h for 3 h duration; right panel: simplified water lens model. In (a) and (a′) foc (more ...)
The total rainfall amounts, or the accumulated infiltration were 0.062 m (2.4 inches) for both of these two rainfall events, while the calculated Δh is 0.22 m which is larger because of the fact that the water must fill in available porosity.
A simplified water lens model is simulated, assuming an initial condition corresponding to the same water height as achieved in the infiltration model at long times. The simplified model solves Equation (3)
, without solving Equations (1)
, as neither the capping effect nor washout effect are considered. It determines the magnitudes of contaminant concentration due to the presence of a clean water lens atop the groundwater source. The result of this simplified model is shown at the right panel of , which is almost the same as the solution in the left panel which is that for the actual 20.5 mm/h rainfall events. Even though the infiltrated water (left case) dissolves some contaminant as it percolates towards the groundwater source, the water is still “clean” relative to the groundwater source, which is why the results of the two models are so similar to one another.
In either case while the vapor concentration steadily increases at a probe 2.8 m deep (0.2 m above the source), vapor concentrations at higher probes first decrease and then increase. Diffusion through the water lens in both models is the controlling, or rate limiting step, as PCE diffusivity in pure water is only 8.2×10−9 m2/s. The sorption to the organic carbon increases the time scale, comparing . The final states are the same for both models. In other words, addition of a thin clean water lens atop the original contaminant groundwater will have some effects of decreasing soil gas contaminant vapor concentrations, but the effects would be observed only over a very long time scale as compared to the initial infiltration step. A permanent change to groundwater contaminant concentration profile, as this illustration depicts, can have a dramatic influence on the potential for vapor intrusion. Keep in mind that only a 0.22 m thick lens was added atop a source 3 m beneath the soil surface. While it is of course not realistic to consider only a single rainfall event over the course of many years, the more significant aspect of the present analysis is that concentration profiles, near the top of the water table, can confound analysis of a situation in which the underlying bulk groundwater is not observed to change very much in contaminant concentration. This of course implies that where a monitoring well draws water can make a very large difference in predicted hazard posed by the contaminant in the water.
For an open bottom scenario, in which the groundwater (the source) completely mixes with infiltration water, and water drainage keeps the groundwater level the same, the contaminant concentration profile (results not shown) has the same shape as the bounded bottom scenarios discussed above, but the original steady state is recovered. The dynamics of any long-term process associated with infiltration affected water table levels are slow, and if the original water table height is recovered, will depend on how fast this recovery happens.
Vapor Response to Seasonal Rainfall Events
After discussion of the cases with one simple rainfall event, attention is turned to a “wet site” that is subject to seasonal rainfall characterized by a long series of small rainfall events. The modeling results are shown in . The hypothetical rainfall intensity is assumed to be described by:
which has a period of 1 day. The maximum rainfall of 0.26 mm/h can be classified as a very light rain. There are assumed to be 30 rainfall events over 30 days, then these stop for the rest of the year. Evapotranspiration is again set to be zero in order to see the maximum influence of rainfall. These events are modeled for the bounded bottom scenario. The accumulated rainfall is 0.094 m for 30 days; and it forms a water lens with a maximum thickness of about 0.33 m above the source at about 1 year after the events. The buildup of this lens takes place at later time than the single rainfall cases because water is added more slowly. From , superposition of rainfall events is obvious, as both soil moisture and vapor concentration in the upper soil changes continuously under a continuous rainfall over 30 days, with small fluctuation every day. The small fluctuation in vapor concentration results from the same effects as described before for the single rainfall events, but here reflects the gradual buildup due to cycling of rain. However, in soil deeper than 1 m below the ground surface, this kind of small soil moisture fluctuation is hardly visible ( [c]). The wetting front reaches the 1.5 m probe in a month. Therefore, in , soil moisture at probes 1 and 1.5 m deep show 30 % increase at 1 month. The capping and washing effect on contaminant concentration are also obvious ( [d]). It should be noted that the roughly one order of magnitude decrease of concentration after infiltration results not only from the washing effect, but also from the water lens effect as discussed for the single rainfall cases.
Soil moisture content (a) and (c), and vapor concentration (b) and (d) under seasonal rainfall conditions; foc = 0. Left panel: results for probes at 0.1, 0.2, and 0.3 m deep. Right panel: results for probes at 1, 1.5 and 2 m deep