Published online 2 June 2005
Published in Soil Sci Soc Am J 69:990-995 (2005)
DOI: 10.2136/sssaj2003.0208
© 2005 Soil Science Society of America
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Soil Physics Note
GAS TRANSPORT OF VOLATILE ORGANIC COMPOUNDS IN UNSATURATED SOILS
QUANTITATIVE ANALYSIS OF RETARDATION PROCESSES
Heonki Kima,*,
Seungjae Leea,
Ji-Won Moonb and
P. Suresh C. Raoc
a Dep. of Environmental System Engineering, Hallym Univ., Chuncheon City, Gangwon-do, 200-702, Korea
b Environmental Sciences Division, MS-6036, Oak Ridge National Lab., Oak Ridge, TN 37831
c School of Civil Engineering, Purdue Univ., West Lafayette, IN 47907-2051
* Corresponding author (heonki{at}hallym.ac.kr)
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ABSTRACT
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Knowledge of the gas transport of volatile organic compounds (VOCs) through unsaturated soils is important for understanding the fate of these contaminants. However, studies have not been performed for examining the retardation of VOCs, based on quantitative analyses of processes contributing to retardation as the function of water content during gas flow through unsaturated soils. No investigations have evaluated whether different factors that contribute to VOC retardation during gas transport have an additive effect, such that the sum of different effects can be used to predict overall transport velocity. A series of gas transport experiments was conducted in a soil column over a range of water contents, using a soil with low organic carbon content (approximately 0.1%), and tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA) as representative VOCs. Three phase-partitioning processes (partitioning into soil water, adsorption at the soil particles, adsorption at the air–water interface) were evaluated independently. The sum of retardation effects from these processes was then compared with the observed VOC retardation factors. Measured retardation factors for PCE and TCA were in good agreement with those predicted over the range of water contents (0.02–0.24) examined in this study, supporting the additive nature of different phase-partitioning processes for the gas transport of VOCs in soils. Also, the relative contribution of each phase-partitioning process to the total retardation of VOCs during gas transport was a strong function of water content.
Abbreviations: BTC, breakthrough curve • PCE, tetrachloroethene • TCA, 1,1,1-trichloroethane • VOC, volatile organic compound
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INTRODUCTION
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VOLATILIZATION AND ADVECTIVE gas transport of VOCs are the basis for remediation technologies, such as soil vapor extraction, soil venting, and air sparging, that remove VOCs from subsurface source zones of nonaqueous-phase liquid (NAPL) wastes (USEPA, 1991, 1992). Diffusive mass transfer of VOCs across interfaces between phases (NAPL–water, NAPL–air, water–air) and transport through the mobile gas phase are the primary rate-limiting processes. During gas transport through soils, VOC molecules may interact with various physical domains. The following four primary VOC phase-partitioning processes have been identified for unsaturated soils that do not contain NAPLs (Okamura and Sawyer, 1973; Conklin et al., 1995; Kim et al., 2001): (i) adsorption at the air–water interface, (ii) partitioning or dissolution into the bulk aqueous phase, (iii) sorption by the solid phase of the soil from the aqueous phase, and (iv) sorption at the solid surface from the gas phase. These processes affect VOC transport in the gas phase, and the extent of the impact from each process depends on the quantity and distribution of the interacting physical domains involved, as well as the chemical properties of the VOC.
Phase-partitioning processes result in retardation of VOC transport through the gas phase, as in the following one-dimensional, advective–dispersive transport equation (e.g., van Genuchten et al., 1974):
 | [1] |
where Rt is the total retardation factor (dimensionless) that accounts for all phase-partitioning processes, Cg is the VOC concentration (mol/cm3) in the gas phase, vg is the pore-gas velocity (cm/min), Dg is the dispersion coefficient (cm2/min), t is time (min), and x is distance (cm). Note that Eq. [1] is applicable for homogeneous flow domains and for local equilibrium conditions for phase partitioning.
Direct sorption of VOCs from the gas phase to polar solid surfaces is unlikely when the soil contains bulk water (Okamura and Sawyer, 1973; Dorris and Gray, 1981; Ong and Lion, 1991; Kim et al., 2001; Goss and Schwarzenbach, 2002; Roth et al., 2002). Thus this sorption process is considered negligible, and removed from further consideration in this study. Assuming linear additivity effect of each phase-partitioning process (Conklin et al., 1995; Brusseau et al., 1997; Kim et al., 2001), the Rt for VOCs during gas transport through soils with water-wetting solid surface property and with bulk water present can be expressed as follows:
 | [2] |
where ß represents the partial retardation factor with the subscripts g, w, i, and d referring to VOC retention in the gas phase, in the aqueous phase, at the air–water interface, and sorbed at the solid domain of the soil from aqueous phase, respectively. The terms on the right hand side of Eq. [2] are defined as follows:
 | [3] |
with:
 | [4] |
where 
w and g are the volumetric water and air contents [dimensionless, volume of water (or air)/volume of bulk soil], respectively; ai is the specific air–water interfacial area (cm2/cm3 bulk soil); 
b is the soil bulk density (g/cm3 bulk soil); KH is the Henry's law constant [dimensionless, cm3(aqueous phase)/cm3(gas phase)]; Ki is the interfacial adsorption coefficient [cm3(gaseous phase)/cm2(air–water interfacial area)]; Kd is the sorption coefficient [cm3(aqueous phase)/g(soil)]; Cs is the VOC concentration (mol/g) adsorbed by the solid phase; Cw is the VOC concentration (mol/cm3) in the aqueous phase; and 
i is the VOC concentration (mol/cm2) adsorbed at the air–water interface. Note that all concentrations here (Cw, Cs, i) are equilibrium concentrations.
The quantitative relationship between the phase-partitioning, retardation, and the gas transport of VOCs has been the focus of several investigations (Okamura and Sawyer, 1973; Conklin et al., 1995; Popovicova and Brusseau, 1998; Kim et al., 1999, 2001). Although factors contributing to VOC retardation during gas transport have been examined (Okamura and Sawyer, 1973; Conklin et al., 1995), the evaluation of all of the phase-partitioning processes shown in Eq. [3] had not been possible until the interfacial tracer technique was introduced (Brusseau et al., 1997; Kim et al., 1999), allowing for ai measurement, and thus the estimation of ßi in Eq. [3]. The effect of adsorption at the air–water interface on the gas transport of VOCs was previously either neglected (e.g., Conant et al., 1996), or incorporated with Ki values (e.g., Conklin et al., 1995). With experimentally measured ai values, the analysis of Rt according to Eq. [3] was conducted at a single water content (Brusseau et al., 1997; Popovicova and Brusseau, 1998), while the functional relationship between ai, w, and Rt was investigated for the case of negligible sorption by soil (Kim et al., 1999, 2001). Here, we extend this experimental analysis to VOC retardation over a range of water contents and for a case when VOC sorption from the aqueous phase onto soil is important. The dynamic nature of water content in the vadose zone and the attendant changes in the air–water interfacial area necessitate an understanding of the effect of varying water content on VOC transport in unsaturated soils.
The first objective of this study was to evaluate all of the phase-portioning processes shown in Eq. [3] and their relative contributions to Rt as a function of w for VOCs with different sorption coefficients (e.g., different Kd values). The second objective was to examine the validity of the linear-additive model (Eq. [2] and [3]) for predicting VOC retardation during gas transport in unsaturated soils by comparing the Rt values predicted from independently determined ß values to those experimentally measured.
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Materials and Methods
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Materials
Compressed methane gas (99% purity) from Aldrich Chemical (St. Louis, MO) was used as the nonreactive tracer. Reagent-grade tetrachloroethene (PCE), 1,1,1-trichloroethane (TCA), n-hexane, and n-decane were also purchased from Aldrich Chemical and used as received. Tetrachloroethene and TCA were used as representative VOCs, while n-hexane was used as the interfacial tracer for ai measurement, and n-decane was used as the VOC-extraction solvent for the Kd measurement experiments. Ultra-pure nitrogen (N2) was used as the carrier gas for the gas transport experiments. The chemical properties of the VOCs relevant to this study are listed in Table 1.
A sample of surface soil was collected from an agricultural field in Chuncheon City, South Korea. The soil contains 0.1% of organic carbon, as measured by the Walkley–Black method (Walkley, 1947). The soil was mostly sand (62%) and silt (33%) with a small fraction of clay (5%), as measured using a particle-size analyzer (Mastersizer 2000; Malvern Instrument Co., Malvern, UK). The surface area of dry soil, measured using the N2 adsorption method (Nova 2000; Quantachrome Instruments, Boynton Beach, FL), was 5.1 x 104 cm2/g. Mineral composition of the soil was analyzed using an X-ray diffractometer (Model MXP-3; MAC Science, Japan) and found to consist of quartz and feldspar with kaolinite and smectite as the minor constituents.
Experimental Methods
For gas transport experiments, a stainless steel column (1.0-cm i.d., 6.0-cm length, 4.7-cm3 total volume) was packed with dry soil. The packed soil had a dry bulk density (b) of 1.5 g/cm3, a porosity of 0.44, and a specific solid surface area of 7.6 x 104 cm2/cm3, calculated based on the soil surface area measured by N2 adsorption. Double-distilled water was injected at both ends of the soil-packed column. To achieve a homogeneous distribution of water along the column, both ends of the column were sealed, and the column was heated at 110°C for 24 h, then cooled to room temperature. The w achieved for the first set of gas transport experiments was measured to be 0.021 by the weight of the column.
The soil column was then installed in a modified gas chromatograph (GC) (Model M600D; Yong Lin Instrument Co. Ltd., Anyang City, Korea) for the VOC transport experiments (Fig. 1)
. Methane was decompressed to atmospheric pressure before injection into GC using a gas-tight syringe (5 µL). About 5 mL of each liquid was placed in separate 20-mL glass vials, and the vapor from the headspace was withdrawn with a gas-tight syringe (10 µL), and injected through the GC injection port. The injected masses of VOCs were estimated to be 1.3, 3.5, 1.6, and 4.4 µg for CH4, n-hexane, PCE, and TCA, respectively, based on the vapor pressures and injected volumes. Each VOC was injected separately to avoid possible interactions between VOCs during transport if introduced as a mixture. The VOC concentration in the column effluent was monitored using a flame ionization detector (FID) connected directly to the column. The obtained VOC concentration–elapsed time relationship since a VOC injection, or breakthrough curve (BTC), was then processed to estimate the Rt value (see next section, Method of Moments).
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Fig. 1. Experimental setup for the gas transport experiments for volatile organic compounds (VOCs). GC, gas chromatograph.
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After the first set of gas transport experiments, the column was detached from the GC and a predetermined amount of water was injected through both ends of the soil column for experiments at a higher w level; the heating and cooling cycle was repeated to ensure homogeneous water distribution before VOC transport experiments. The experimental protocol for VOC injection and detection at higher w was identical to that of the first set of experiments. This step was repeated to achieve incremental changes in w up to 0.24. The w value of the column was determined from the total column volume and the weight difference between dry-packed and wet soil column.
A bubble humidification flask was installed between the gas cylinder and VOC injection port to preclude drying the soil column during the experiment (Fig. 1). A constant pore-gas velocity of about 2 cm/min was achieved, using a needle valve, for a set of experiments performed at given w. Throughout the experiments, the detector (FID) temperature was set at 250°C, while the temperature of soil column and at the VOC injector was maintained constant at 22 ± 2°C. The suite of gas transport experiments was performed in duplicate.
The KH and Ki values of the VOCs used in this study were obtained from literature (Mackay and Shiu, 1981; Hoff et al., 1993). KH values at 22°C estimated using thermodynamic parameters (heat of vaporization and molar excess enthalpy of dissolution in aqueous phase) and KH values at 25°C (from the literature) were used in this study (Table 1). The difference in Ki values at different temperature (22°C experiment temperature and 25°C temperature for literature values) was found not to cause significant error on ßi predictions, and thus literature values were used.
Sorption coefficients (Kd) for PCE and TCA were measured in batch experiments (at 22 ± 2°C) as follows. A known amount of dry soil (about 4 g for PCE, 8 g for TCA) was mixed with aqueous solutions of PCE (approximately 7.3 mL) and TCA (approximately 3.0 mL) at five different concentrations. In capped vials with no headspace, soil was equilibrated with the aqueous VOC solutions for at least 12 h using a shaking rotator (20 rpm; Glas-Col, Terre Haute, IN). After centrifugation, 1 mL of the supernatant in each vial was transferred to an empty vial, and equal amount of n-decane was added to extract PCE or TCA. Standard solutions of PCE and TCA made in n-decane also contained about 10 µg/mL of chloroform as an internal standard. Extracted samples and standards were analyzed using an analytical GC system (Model 6890; Hewlett-Packard, Palo Alto, CA), equipped with a capillary column (HP-5; Hewlett-Packard) and an electron capture detector (injector 200°C, oven 80–300°C, detector 350°C, sample injection volume 5 µL, injector split ratio 100:1).
The ai value was measured at each w using the interfacial tracer method (Brusseau et al., 1997; Kim et al., 1999, 2001) with n-hexane as the interfacial tracer. The n-hexane transport experiment was repeated at least three times at each water content. From the measured Rt value for n-hexane, the ai value was calculated using Eq. [2] and [3], assuming ßw and ßd are negligibly small (i.e, very large KH value) given the low water solubility of n-hexane (Table 1).
Method of Moments
Mean residence times for VOCs in the soil column for each transport experiment were calculated by analyzing the temporal moments of the measured breakthrough curves (BTCs). The normalized, first temporal moment (µ1) for a VOC pulse displacement, which corresponds to the mean residence time in the column, was calculated as (Suzuki and Smith, 1971; Valocchi, 1985):
 | [5] |
where m0 and m1 represent the absolute zero-th and first moments, respectively, estimated from the BTCs. Here, it is assumed that the injected VOC pulse size is sufficiently small (i.e., Dirac pulse) compared with the gas pore volume of the column and that no VOC mass was lost (i.e., m0 represents the injected mass). The Rt value of a VOC was estimated from the ratio of mean residence time (µ1) of the VOC to that of methane, used here as the nonreactive tracer:
 | [6] |
where the superscripts v and m refer to VOC and methane, respectively. At the gas flow rate used in this study, displacement of one pore volume of the soil column took about 3 min, while it took less than an hour to complete a breakthrough curve for the VOC with the largest retardation factor (Rt = approximately 17) measured in this study.
Biodegradation of PCE or TCA under N2 atmosphere during one hour (maximum VOC residence time in the column during transport) is unlikely, especially because the soil column was repeatedly heated up to 110°C for several hours to promote water redistribution. The GC, including the soil column, was a completely closed system with no possibility of VOC mass loss due to leaks. All components of the system, including the column, that contacted with the vaporized VOC were stainless steel, with no plastic parts exposed to the carrier gas. Preliminary experiments with an empty stainless steel column showed that the sorption of PCE and TCA at the system was negligible [Rt values for both chemicals measured for the empty column were 1.04 ± 0.05 (standard deviation)]. Therefore, the VOC mass loss was assumed to be minimal and not to affect the temporal moments and Rt values estimated from BTC.
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Results and Discussion
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Evaluation of Phase-Partitioning Processes
The Kd values for PCE and TCA sorption by soil from aqueous phase were determined from the linear sorption isotherms (Fig. 2) . The Kd value for PCE was about five times larger than that for TCA, while the KH and Ki values for both chemicals were fairly close to each other (Table 1). Thus, at a given w, sorption by soil (as represented by ßd in Eq. [3]) was the primary factor contributing to greater Rt values for PCE than for TCA. The measured Kd values for PCE and TCA were found to be directly related to their hydrophobicities; measured Kd values are inversely proportional to aqueous solubilities and follow a similar trend as the octanol–water partition coefficients [Kow = Co/Cw, where Co is the equilibrium VOC concentration (mol/cm3) in the octanol phase] (Table 1). Also, Kd values predicted (0.85 cm3/g for PCE and 0.34 cm3/g for TCA) based on Kow and soil organic carbon content (Rao and Davidson, 1980) are in fair agreement with the measured Kd values.
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Fig. 2. Sorption isotherms at the soil from aqueous-phase tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA) measured at 22°C. The term Cs is the volatile organic compound (VOC) concentration adsorbed by the solid phase, and Cw is the VOC concentration in the aqueous phase.
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Another important factor that determines ßi values in Eq. [3] is the ai value, measured in this study at different w using n-hexane as the gaseous interfacial tracer. The BTCs measured for n-hexane at different w (Fig. 3a)
shift to the right with decreasing water content, implying longer residence time due to increasing retardation from adsorption at the air–water interface. Note that while the BTCs shown were truncated at five pore volumes, the entire BTC was monitored down to the detection limit of the detector; these complete data were used for the temporal moment analyses and for calculating Rt values (Eq. [5] and [6]). As w decreased, the ai value estimated using n-hexane increased (Fig. 3b). The largest ai measured, 6.6 x 104 cm2/cm3 at w = 0.021, approached the N2–measured solid surface area of 7.6 x 104 cm2/cm3.
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Fig. 3. Measurement of specific air–water interfacial areas (ai). (a) Breakthrough curves (BTCs) for methane and n-hexane at different water contents (w). The pore volume scale is the total volume of column effluent after volatile organic compound (VOC) introduction divided by the gas volume in the column, and the term Cg is the concentration normalized by the total area of the BTC. (b) Measured mean total retardation factor (Rt) values for n-hexane and calculated ai values.
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At the lowest w of 0.021 achieved in this study, the mean thickness (
) of the water film formed on the surface of soil was estimated to be 4.0 nm (about 13 layers of water molecule), based on w and ai values ( = w/ai). This result suggests that when the mean thickness of water film approaches zero, the air–water interface follows the microtopography of the dry soil surfaces, and that the resulting ai value is close to that of the specific surface area of the soil. Therefore, the contribution to retardation of VOC adsorption at the air–water interface becomes relatively more important at lower w.
Direct sorption of VOCs from the gas phase to the solid surface was considered to be insignificant for the system used in this study. The mineralogical composition of the soil was analyzed to be mostly quartz and feldspar, which are typically water-wetting. Thus, over the w range achieved in this study, and considering that the carrier gas was water-saturated, it is very unlikely that patches of completely dry surface existed allowing for direct contact of the gaseous VOCs. The sorption capacity of "dry" soil is known to be orders of magnitude larger than that of "wet" soil, and will significantly retard the travel velocity of VOCs (Kim et al., 2001). Such an anomaly was not observed in this study even at the lowest w. This justifies our use of Eq. [2] with no term for solid sorption through the gas phase.
Gas Transport of Volatile Organic Compounds
Since PCE and TCA have similar KH values (Table 1), they should have similar ßw values at a given water content. Because the Ki values for PCE and TCA are also similar, both VOCs should have similar ßi values under the same condition. Thus, for soils that do not have significant aqueous-phase sorption capacity to their solid domain for PCE and TCA (i.e., negligible ßd values in Eq. [3] compared with ßw and ßi values), these two VOCs should show similar Rt values (Kim et al., 2001). In contrast, very different Rt values for PCE and TCA were observed for the surface soil used in this study (Fig. 4)
. This difference in Rt values is primarily due to the difference in ßd (or Kd) values, reflecting different extents of sorption of these VOCs by soil from the aqueous phase (Fig. 5)
.
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Fig. 4. Breakthrough curves for methane, tetrachloroethene (PCE), and 1,1,1-trichloroethane (TCA) at the water content of 0.154. The term Cg is the concentration normalized by the total area of the breakthrough curve (BTC).
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Fig. 5. Retardation factors for tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA). The rectangles (first replication) and triangles (second replication) represent measured total retardation factor (Rt) values; solid lines represent predicted total (Rt) and partial (ß) retardation factors; and vertical solid lines represent the standard deviation of predicted Rt values.
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For TCA, at high w all three VOC retention processes contributed equally to Rt (Fig. 5). However, as w decreased, interfacial adsorption (ßi term) became the primary contributor to total retardation factor (Rt) as a result of increased ai values. Without a significant increase in ai values with decreasing w, the functional relationship between ßi and w would be similar to those for ßd and ßw. At the lowest w, the partial retardation factor (ßd) due to sorption by the soil from the aqueous phase contributed only a small fraction (<20%) to Rt, but as w increased ßd was an increasingly larger component of the Rt.
For PCE, over the w range examined in this study, ßd was the primary contributor to the retardation during gas transport (Fig. 5). The magnitude and changes with w for the other partial retardation factors (ßi, ßw, and ßg) were similar to those for TCA. Although ßd and ßi showed similar values at the lowest w achieved in this study, ßd increased with increasing w while ßi decreased, resulting in large gap between ßd and ßi at high w.
These observations indicate that VOC sorption by soil from the aqueous phase can be the dominating process controlling retardation during gas transport, particularly at high w (as shown with PCE). Other processes, such as adsorption at the air–water interface, may play a significant role at low w (as shown here for TCA). The value of w was found to be a key factor that affects the value of Rt and the relative contribution of the partial retardation factors (ß). Thus, a careful assessment of both the retention processes (Kd, Ki, KH) and the extent of sorption sites (b, ai, w) of the soil of interest has to be conducted for correct prediction of VOC transport through gas phase. The uncertainty associated with the predicted Rt values (shown as vertical lines in Fig. 5) was found to be mostly from ßd and ßi. The relative contributions of measurement errors for ßd and ßi to the compounded standard deviations (2
) of the predicted Rt values are shown in Fig. 6
.
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Fig. 6. Ranges of standard deviations (2) for partial retardation factors (ßi and ßd) and predicted total retardation factor (Rt) for tetrachloroethene (PCE) and 1,1,1-trichloroethane (TCA).
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The Rt values for PCE and TCA measured in gas transport experiments are in reasonable agreement with the Rt values estimated based on Eq. [2] and [3] (Fig. 5). This agreement implies that the assumption of linear additivity of ß values was valid for the experimental conditions used in this study. This observation also supports the local equilibrium assumption that was necessary to use Eq. [1] to [4]. If the VOCs did not reach equilibrium during gas transport, the measured Rt values of VOCs would be smaller than the Rt values predicted based on local equilibrium assumptions (i.e., Eq. [4]) in proportion to the degree of nonequilibrium. Volatile organic compound sorption by the soil from the aqueous phase is likely to be the most rate-limited among the three sorption processes because the sorption site (soil particle surface) is the farthest from the mobile gas phase. In order for a gaseous VOC to access the surface of soil, it first has to cross the air–water interface, and to partition into the aqueous phase. Since no significant experimental underestimation of Rt values, particularly at high w range, was observed in this study, the validity of the local equilibrium assumption was confirmed.
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ACKNOWLEDGMENTS
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This research was supported by the Korea Science and Engineering Foundation (Grant R01-2000-000-00057-0). This work was also supported by a research grant from Hallym University, South Korea.
Received for publication August 8, 2003.
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ABSTRACT
INTRODUCTION
