VOC Accumulation and Pore Filling in Unsaturated Porous Media

A series of unsaturated column experiments was conducted to study different grain-scale accumulation mechanisms affecting total uptake of volatile org...
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Environ. Sci. Technol. 1996, 30, 2884-2891

VOC Accumulation and Pore Filling in Unsaturated Porous Media TIMOTHY L. CORLEY,† JAMES FARRELL,‡ BEI HONG,† AND M A R T H A H . C O N K L I N * ,† Department of Hydrology and Water Resources and Department of Chemical and Environmental Engineering, University of Arizona, Tucson, Arizona 85721

A series of unsaturated column experiments was conducted to study different grain-scale accumulation mechanisms affecting total uptake of volatile organic compounds (VOCs) onto a model solid and subsequent removal of VOCs from the porous media. Experimental variables included VOC (benzene, methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene), moisture content (primarily water-unsaturated conditions), and influent VOC concentration. Calculations of the mass distributions of benzene indicated that it was primarily in the aqueous and air phases with a small fraction at the airwater interface. Similar calculations for the other VOCs indicated that greater than 50% of the accumulated mass of these VOCs was located within intraparticle pores and on the substrate surface. Analysis of the sorption data in terms of a pore-filling model support the hypothesis that a capillary phase separation (CPS) process occurred within the pores and produced a neat, separate VOC phase. We suggest that CPS will become more critical in materials with small mesopores or micropores, and that it is partly responsible for the existence of a resistant fraction of VOCs present within water-filled intraparticle pores.

Introduction A more fundamental understanding of the physical and chemical processes that affect the uptake of volatile organic compounds (VOCs) by uncontaminated natural materials (soils and sediments) and the removal of VOCs from contaminated natural materials is continuing to be developed. Under water-saturated conditions, a VOC is distributed between the bulk aqueous phase, external to the individual grains, and the solid phase, which includes both intraparticle, water-filled pores and the internal and/or external surfaces of the grains. In addition to these two ‘storage compartments’ accumulation of a VOC at the air* Corresponding author telephone: (520) 621-5829; e-mail address: [email protected]. † Department of Hydrology and Water Resources. ‡ Department of Chemical and Environmental Engineering.

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water interface can define another compartment that can significantly affect the distribution of a VOC under waterunsaturated conditions (1-5). Although moisture content and the fraction organic content (foc) of the natural material are two factors that strongly influence the importance of this process relative to aqueous- or solid-phase accumulation (2, 5), the magnitude of accumulation at the air-water interface is controlled by the hydrophobicity of a VOC (4, 5). Sorption to these individual compartments must be considered in detail to understand the uptake and final distribution of a VOC under water-unsaturated conditions. As the experimental data base has grown, it has become increasingly apparent that both interparticle and intraparticle grain-scale mass transfer phenomena have critical roles in determining the rate of VOC removal and, ultimately, the fraction of VOC removed from contaminated media (5-17). The existence of a fraction of the initial VOC present that slowly desorbs from contaminated media has been recognized for over a decade and has been labeled the ‘resistant’ fraction (6). This resistant fraction is apparently associated with slow diffusional processes controlling VOC removal rates from water-filled intraparticle pores and has been observed in studies with natural materials under both water-saturated and water-unsaturated conditions (5, 7-12, 14-17). Although retarded diffusion through pores due to pore geometry and solute size effects (18) coupled with adsorption to the surface has often been cited as a possible causative mechanism responsible for the observation of a resistant VOC fraction (7, 10, 16, 17), analyses of recent studies of trichloroethene, tetrachloroethene, and trichloromethane desorption from columns packed with microand mesoporous silica gels or glass beads (15) strongly suggest that retarded diffusion does not provide a complete explanation of the desorption-resistant fraction. The near equivalence of normalized desorption rates that was observed for these VOCs is inconsistent with a release of the resistant VOC fraction that is limited by sorption retarded aqueous diffusion. In addition, the normalized desorption rates of trichloroethene from four different silica gels and the glass beads were essentially equivalent, even though the pore- and particle-size distributions of the solids were markedly different. Farrell and Reinhard (15) suggested that an explanation more consistent with their data would be that the resistant fraction is due to the presence of a separate, neat VOC phase formed within small capillaries. The purpose of the research reported here was to determine the distributions of a homologous series of VOCs among the three bulk phases (air, water, and solid), the air-water interface, and intraparticle pores. Our working hypothesis was that accumulations at the air-water interface and within pores were the dominant storage mechanisms for VOCs in low foc porous media under waterunsaturated conditions. We investigated VOC sorption onto and desorption from glass beads (zero foc) under watersaturated and water-unsaturated conditions to test this hypothesis. Moisture content, hydrophobicity of the VOC (benzene, methylbenzene, 1,4-dimethylbenzene, and 1,3,5trimethylbenzene were used), and initial concentration of the VOC were the primary experimental variables.

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TABLE 1

Initial Conditions for Column Experimentsa experiment

θa

θw

Co (µg cm-3)

-1 Pv P v,sat

pulse pv

B1a B1b B2a B2b T1a T1b T3a T3b T4a T4b T2a T2b X1a X1b X3a X3b X2a X2b TMB1a TMB1b TMB3a TMB3b TMB4a TMB4b TMB2a TMB2b

0.305 0.305 0.225 0.225 0.305 0.305 0.265 0.265 0.245 0.245 0.225 0.225 0.305 0.305 0.265 0.265 0.225 0.225 0.305 0.305 0.265 0.265 0.245 0.245 0.225 0.225

0.09 0.09 0.17 0.17 0.09 0.09 0.13 0.13 0.15 0.15 0.17 0.17 0.09 0.09 0.13 0.13 0.17 0.17 0.09 0.09 0.13 0.13 0.15 0.15 0.17 0.17

30.9 23.9 8.48 2.65 2.03 4.99 9.25 9.25 10.2 11.0 3.14 5.94 2.43 2.75 4.00 5.61 2.08 1.43 1.32 2.43 3.58 4.47 2.93 2.93 4.07 3.63

0.077 0.059 0.021 0.007 0.014 0.036 0.065 0.065 0.071 0.077 0.022 0.042 0.046 0.053 0.077 0.107 0.040 0.027 0.076 0.141 0.213 0.267 0.173 0.173 0.240 0.213

8.43 8.62 16.48 18.16 16.38 15.09 33.20 23.78 32.44 28.57 21.78 36.03 20.97 22.54 29.96 33.20 36.31 39.81 29.09 30.40 44.21 43.34 40.57 41.15 41.22 48.46

a Capital letters refer to benzene (B), methylbenzene (T), 1,4dimethylbenzene (X), and 1,3,5-trimethylbenzene (TMB). a and b denote -1 is fraction of saturated vapor pressure replicate experiments. Pv Pv,sat of VOC in inlet stream. Pulse is the number of pore volumes of VOCcontaminated air passed through column.

Materials and Methods Unsaturated Column Experiments. The experimental apparatus and protocols used in these studies differ from those described in Conklin et al. (5) only by the means used to produce a VOC-containing airstream. A custom-built batch distillation unit equipped with a condenser was used to saturate an airstream with benzene, methylbenzene, 1,4dimethylbenzene, or 1,3,5-trimethylbenzene. The VOCcontaminated airstream (2-4% of the total air flow into the column) was then introduced into the main humidified air flow upstream of the column inlet to produce the final influent mixture. Inlet VOC concentrations did not vary by more than (2% with this system. Replicate experiments were run for all conditions, and good reproducibility was obtained. The glass columns used (30 cm in length and 2.5 cm in diameter, Kontes) were packed with glass beads to yield a dry bulk density (Fb) of 1.60 ( 0.01 g cm-3 and a total porosity (θT) of 0.395 ( 0.005 (cm3 of void volume divided by total volume of the empty column, cmT3). Variables studied included moisture content (θw ) cm3 water per cmT3) and initial VOC concentrations (see Table 1). Total volumetric air flow was held constant at 0.417 cm3 s-1 for all experiments and yielded interstitial velocities of 0.278, 0.320, 0.346, and 0.377 cm s-1 at θw equal to 0.09, 0.13, 0.15, and 0.17, respectively. Gas sampling and analyses were as described in Conklin et al. (5). Saturated Column Experiments. Water-saturated column experiments were conducted to provide values of the distribution coefficients between the glass beads and water

for each VOC. Each experiment consisted of introducing a finite pulse (0.218 pore volume) of VOC-contaminated aqueous solution into a stainless steel column packed with glass beads (Fb ) 1.590 g cm-3 and θT ) 0.370). The VOC concentration in the pulse ranged from 10 to 15 ppm by mass and resulted in a total mass of each VOC introduced into the column of about 10 µg. Total volumetric flow rate through the column was varied by a factor of 30 to determine whether the measured retardation factors exhibited any dependence on interstitial velocity. This range of flow rates yielded interstitial velocities from 0.0052 to 0.156 cm s-1. The final sets of experiments were conducted at the lowest velocity of 0.0052 cm s-1. Data acquisition and analyses for VOC and tracer experiments were as described in Conklin et al. (5). Materials. The glass beads used were soda-lime beads. The beads were dry sieved, and the fraction that passed through a 90-µm screen and retained on a 63-µm screen was used after additional processing to remove possible organic contaminants from the external surfaces and to remove alkali metals (Na, Ca, and Mg). This processing involved (1) rinsing the beads with 1 M NH4OH, followed by rinsing with distilled, deionized water until the pH of the wastewater was less than 11; (2) refluxing in 2 M HCl for 4 h followed by rinsing with distilled, deionized water; (3) refluxing in 2 M HCl for 2 h, draining off the spent solution, and refluxing in fresh 2 M HCl for an additional 2 h; (4) rinsing with distilled, deionized water until the pH was greater than 4, then refluxing for an additional 1 h in distilled, deionized water; (5) a final rinsing until achieving a neutral pH in the wastewater; and (6) oven-drying at 180 °C for 12 h. The specific surface area and internal porosity of the glass beads from this batch processing were determined from N2 adsorption at 77 K using the Brunauer-EmmettTeller (BET) multipoint method (19). Although it is recognized that Kr or Xe adsorption at 77 K offers the possibility of higher precision in the actual measurement of adsorption for materials with specific surface areas less than about 5 m2 g-1, N2 was used because of costs and instrument capabilities. In addition, it does not necessarily follow that the resultant value of the surface area using either of these alternate gases will have a higher accuracy than that obtained with N2 (20). The N2 BET isotherm exhibited type II isotherm character with a type H3 hysteresis loop (20). A value of 0.083 m2 g-1 was determined for the specific surface area, and a value of 0.00021 cm3 g-1 was determined for the cumulative pore volume of pores between 1.7 and 300 nm in diameter. The BET specific surface area is about a factor of 3 higher than the external specific surface area of the beads calculated from an average bead diameter (75 µm), the known θT, and correlations available in the literature (21). A standard t-plot analysis of the isotherm did not yield positive evidence for the presence of micropores (the intercept of the t-plot was not statistically different from zero), although the value of the constant c in the BET equation (c ) 52) suggests the presence of micropores (22). An average pore size of 10 nm was derived from the BET analysis. Benzene, methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene were purchased from Aldrich Chemical Company and were used as received. Physical properties of these VOCs are listed in Table 2. Pressurized gases directed to the columns were breathing-quality air and ultra-

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TABLE 2

Physical Properties of VOCsa VOC

KH 3 (cmw cm-3 a )

KIA (µm)

KD,sat 3 -1 (cmw gs )

benzene methylbenzene 1,4-dimethylbenzene 1,3,5-trimethylbenzene

0.222 0.27 0.286 0.358

0.443 1.12 2.6 5.9

0.00373 ( 0.0004 0.00538 ( 0.0009 0.00809 ( 0.0005 0.010 ( 0.001

a Henry’s constant benzene, methylbenzene, and 1,4-dimethylbenzene (59) and 1,3,5-trimethylbenzene (60); the air-water interface coefficient (3); and KD,sat (this work) at 25 °C.

TABLE 3

Experimental Results and VOC Mass Distributions experiment

Rexp

mload (mg)

ma (mg)

mw (mg)

mIA (mg)

B1a B1b B2a B2b T1a T1b T3a T3b T4a T4b T2a T2b X1a X1b X3a X3b X2a X2b TMB1a TMB1b TMB3a TMB3b TMB4a TMB4b TMB2a TMB2b

2.35 2.43 4.56 4.54 5.18 5.16 7.17 7.12 8.07 8.31 9.98 9.72 5.87 5.98 7.92 7.82 13.23 12.87 6.17 6.34 8.43 8.57 10.74 11.29 12.27 12.74

3.50 2.72 1.35 0.40 0.46 1.11 2.43 2.47 3.00 3.25 1.08 1.93 0.58 0.63 1.21 1.68 0.97 0.65 0.35 0.64 1.26 1.52 1.11 1.10 1.63 1.50

1.39 1.07 0.281 0.088 0.091 0.224 0.361 0.361 0.368 0.397 0.104 0.197 0.109 0.124 0.156 0.219 0.069 0.047 0.059 0.109 0.140 0.174 0.106 0.106 0.135 0.120

1.84 1.43 0.956 0.298 0.10 0.245 0.657 0.657 0.835 0.899 0.353 0.551 0.113 0.127 0.268 0.375 0.182 0.125 0.049 0.090 0.191 0.239 0.181 0.181 0.285 0.253

0.147 0.114 0.050 0.016 0.024 0.060 0.124 0.125 0.145 0.156 0.047 0.088 0.068 0.077 0.125 0.176 0.072 0.049 0.083 0.154 0.254 0.318 0.219 0.219 0.319 0.284

high-purity helium (Liquid Air Corporation) for the tracer studies. Data Analysis. Breakthrough curves were constructed from data collected during each of the unsaturated column experiments. Mass-balance calculations were performed by integrating areas under the sorption and desorption limbs of the breakthrough curves; these calculations also provided values for the total mass loaded onto each column. Experimentally defined retardation factors (Rexp) were obtained by integrating areas above sorption limbs and below desorption limbs. The overall uncertainty of the retardation factor for each experiment is less than 5%. The response curves from the water-saturated experiments were used to calculate the first normalized moment of each data set, which is equal to Rexp (23-25).

Results Results from the unsaturated column experiments are presented in Table 3. All 26 experiments gave breakthrough curves in which C/Co (C is the measured effluent concentration, and Co is the initial concentration) reached 1.0 after 5-50 pore volumes of VOC-containing air passed through the clean column. The number of pore volumes required for C/Co to equal 1 increased with increasing hydrophobicity

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of the VOC, as illustrated for θw ) 0.17 in Figure 1. Massbalance calculations for all of the experiments listed in Table 3 indicated mass closure to within (2% and indicated that the total uptake and release of each VOC were reversible. Also, there was no experimental evidence of hysteresis due to previous exposure of a column to VOCs. No effect of concentration on the shape of the breakthrough curves was observed after normalization of the effluent concentration measurements by Co. The apparent displacement of the desorption limbs in Figure 1 is the result of different pulse lengths (see Table 3) and disappears after a simple translation of the abscissa coordinate values. The rising limbs of the breakthrough curves were not symmetrical about C/Co ) 0.5 for any of these VOCs, and the observed asymmetry increased with increasing hydrophobicity, suggesting increased mass transfer resistance with increasing VOC hydrophobicity. Increased desorption limb tailing was also observed with increasing VOC hydrophobicity. Tailing in the desorption limb may be due to isotherm nonlinearity or result from mass-transfer limited desorption rates. In either case, this tailing suggests the importance of intragranular processes on VOC retention. Experimentally derived retardation factors Rexp for vapor transport indicated that Rexp increased with moisture content for all VOCs (see Table 3 and Figure 2). The values for each VOC were not dependent on Co or the length of the pulse as the entries for experiments T2a and T2b in Tables 1 and 3 demonstrate. Also, values of Rexp derived from the sorption and desorption limbs agreed to within experimental error [Rexp,desorp ) (1.018 ( 0.030) × Rexp,sorp]. As anticipated, the value of Rexp at a fixed value of θw increased with the hydrophobicity of the VOC, but the most significant difference among Rexp values was between benzene and the other three VOCs. Rexp values for benzene were a factor of 2-3 lower than Rexp values for methylbenzene, 1,4-dimethylbenzene, or 1,3,5-trimethylbenzene. The maximum difference among the more hydrophobic compounds was 40%. The overall increase of Rexp for each VOC as θw increased from 0.09 to 0.17 was approximately the same as the ratio of these two moisture content values. The total mass loaded onto the column (mload, mg) determined from each breakthrough curve normalized by the total mass of beads is the total specific mass loaded onto each column (qtot, µg g-1), which is assumed to be the sum of the specific masses sorbed to the individual storage compartments:

qtot )

mload ) qa + qw + qIA + qint FbVT

(1)

where VT is the volume of the empty column (cm3) and the superscripts refer to the air phase (a); the bulk, external aqueous phase (w); the air-water interface (IA); and the solid (int). The specific mass sorbed to the aqueous and solid phases and at the air-water interface was calculated by subtracting the specific mass of VOC in the air phase from qtot:

qsorb ) qtot -

CoVTθa FbVT

(2)

where θa is the air-filled porosity at each moisture content (cma3 cmT-3). As shown in Figure 3, qsorb was approximately a linear function of the fractional saturation of the vapor phase with each VOC. The specific uptake of benzene and

FIGURE 1. Breakthrough curves at θw ) 0.17 for (a) benzene; (b) methylbenzene; (c) 1,4-dimethylbenzene; and (d) 1,3,5-trimethylbenzene.

FIGURE 2. Rexp values increase with moisture content for all VOCs.

methylbenzene were similar over a common range of Co/ Csat values and were significantly greater than that for 1,4dimethylbenzene or 1,3,5-trimethylbenzene. Retardation factors measured in the saturated column experiments were similar for all adsorbates and were only marginally greater than 1 (Rexp ) 1.015, 1.023, 1.035, and 1.043 for benzene, methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene, respectively). No significant differences in values of Rexp were observed over the range of interstitial velocities included in the test matrix (0.00520.156 cm s-1). The tailing observed for the more hydrophobic VOCs did not contribute significantly (less than (3%) to the values of the integrands required to calculate the first normalized moments of the data and, therefore, did not affect the values of Rexp. The effective saturated watersolid distribution coefficient is referred to as KD,sat (Rexp ) 1 + FbKD,sat/θT).

FIGURE 3. Specific mass uptake to aqueous and solid phases and at air-water interface increases with fractional saturation of air phase.

Discussion The distribution of each VOC among the different storage compartments as a function of θw is of primary interest. One compartment that may increase in importance with an increase in the value of θw is the aqueous phase external to the individual particles (13.25 g of water was loaded onto the column at θw ) 0.09 versus 25.03 g at θw ) 0.17). A comparison of the total intraparticle volume (N2 BET data yields 0.048 cm3 for the entire column) with the total volume of water loaded onto the column at each moisture content indicates that most of the aqueous phase resides on the external surfaces of the grains (0.048 cm3 represents less than 0.5% of the total water at any θw). In addition, the depth of this liquid film can be estimated to increase from 0.08 µm (270 monolayers) at θw ) 0.09 to 0.16 µm (520 monolayers) at θw ) 0.17. This means that the external

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(about 22% at θw ) 0.09 versus about 31% at θw ) 0.17) and that the air and aqueous phases accounted for 41 ( 1.3% of mload at all θw. Smaller fractions of 1,4-dimethylbenzene and 1,3,5-trimethylbenzene were present in the aqueous phase than for benzene or methylbenzene. These results indicate that at a fixed θw the fraction of mload in the air and water phases decreases with increasing hydrophobicity of the VOC (benzene is included in describing this trend). Because the surface area of pendular rings formed by water on the external surface of the grains increases linearly with θw over the range of moisture contents investigated (27), it is also possible that accumulation at the air-water interface will increase in importance with increased θw. Based on the values of the adsorption constant (KIA, cm) in Table 2 and an estimated value of the specific surface 2 area of the air-water interface (AIA, cmIA cmT-3) at each θw, the mass of each VOC adsorbed at the air-water interface (mIA, mg) is calculated from the following:

mIA ) qIAFbVT ) CoVTKIAAIA

(5)

and is used to derive values for the specific mass sorbed by the solid (onto the surface and within previously waterfilled pores):

qint ) qia,p - qIA

FIGURE 4. Specific mass sorbed depends on VOC and fractional saturation: (a) total sorption to solid phase and at air-water interface; (b) total sorption within intraparticle pores and onto solid surface.

water layer should have properties consistent with a bulk water phase (26) and, therefore, that the aqueous-phase concentration of each VOC within the external water film should not exceed that calculated from Co and KH (the 3 dimensionless Henry’s constant, cmw cma-3) for the specific VOC. Based on the physical constants for each VOC listed in Table 2, the mass of VOC in the external aqueous phase (mw, mg) can be calculated from the following:

θw mw ) qwFbVT ) CoVT KH

(3)

and can be used to determine values for the specific mass sorbed to the air-water interface and the solid phase:

qia,p ) qIA + qint ) qsorb - qw

(4)

Values for mw are listed in Table 3, and qia,p is plotted versus Co/Csat in Figure 4a. It is apparent from the entries for mload, ma, and mw in Table 3 that benzene was present predominantly in the aqueous phase (52.6% at θw ) 0.09 versus 71-75% at θw ) 0.17). Although the fraction of benzene in the air phase decreased with increased θw, the air and external aqueous phases accounted for greater than 91% of the benzene loaded onto the column at both moisture contents. The values for methylbenzene indicate less than 33% accumulated in the aqueous phase for all θw

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(6)

The values for AIA were estimated from relationships for the specific surface area of pendular rings as a function of θw (27) and correlations for the specific external surface area of randomly packed media (21), and they varied linearly 2 2 from 463 cmIA cmT-3 at θw ) 0.09 to 572 cmIA cmT-3 at θw ) 0.17. Values for mIA are listed in Table 3, and qint is plotted versus Co/Csat in Figure 4b. The entries for benzene indicate that less than 4.2% of mload was present at the air-water interface and less than 4.7% accumulated within the glass beads at all θw. Relatively small changes in the fractions present in these two compartments occur with increased θw. In addition, the values of qint and Cw ()Co/KH) for each benzene experiment yield values of 0.0038, 0.0042, and 0.0071 cmw3 gs-1 for the slope, in reasonable agreement with the value of KD,sat listed in Table 2 for benzene. This finding is of particular significance because it is a strong indication that the estimates of AIA as a function of θw are close to the correct values. Results of the calculations for methylbenzene, 1,4dimethylbenzene, and 1,3,5-trimethylbenzene indicate that for a fixed value of θw, accumulation at the air-water interface increases in importance with increased hydrophobicity of the VOC. As observed for benzene, the fractions of mload of these VOCs in the air phase and at the air-water interface decreased with increased θw. Absorption of the more hydrophobic VOCs into the bulk, external aqueous phase increased with increased θw but not to the same extent as benzene. In direct contrast to the results obtained for benzene, the largest fractions of mload for methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene were associated with sorption to the solid surface and within intraparticle pores. That this solid phase accumulation exhibited a very weak dependence on θw is due to the presence of completely water-filled pores at all values of θw. It is important to note that plots of qint versus Cw for these VOCs yield slopes that are much greater than the corresponding values of KD,sat listed in Table 2 (ratios of 33,

FIGURE 5. Pore-filling model correlates sorption of methylsubstituted benzenes by glass beads with water-filled pores.

FIGURE 6. Pore-filling model applied to trichloroethene desorption from borosilicate glass beads.

31, and 38 were obtained for methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene, respectively), indicating that the sorption isotherms for the more hydrophobic VOCs exhibit nonlinear uptake. A capillary phase separation (CPS) process within the intraparticle pores of the glass beads is consistent with the results summarized in Table 3 and Figure 4b. The uptake not accounted for by qw, qIA, and adsorption onto the solid surface (qads) may be the result of the formation of a separate, neat VOC phase within previously water-filled pores. To test this hypothesis, we have recast the calculated values of qint versus Co/Csat in terms of coordinates associated with a pore-filling model that is based on an adaptation of the Polanyi adsorption potential theory to adsorption from dilute solutions and uses a Dubinin-Radushkevich-type isotherm equation (28, 29):

filled pore volume of 5.4 ( 2, 4.4 ( 2, and 2.0 ( 0.5 µL from the data for methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene, respectively. The apparent decrease in VOC-filled pore volume with increasing hydrophobicity of the VOCs may be indicative of different degrees of pore filling, or different size ranges of pores being filled, as a consequence of molecular structure or sorbate/sorbent and sorbate/sorbate interactions. Conversely, differences in Vo may reflect inaccuracies in the derived values of qint for each VOC. It should be noted that the data for benzene are consistent with values of ∆G ) -19.38 kJ mol-1 (the absolute magnitude of ∆Ghyd benzene is 19.33 kJ mol-1) and Vo ) 0.5 µL. The pore-filling model adopted for analysis of the methyl-substituted benzene data may be useful in interpreting sorption data for other compounds. Farrell and Reinhard (15) measured the desorption of trichloroethene from borosilicate glass beads under water-unsaturated conditions (210 µm bead diameter; Fb ) 1.41 g cmT-3; θw ) 0.105; θa ) 0.323; 303 K). N2-BET data for this material indicated a low specific surface area (0.060 m2 g-1) and yielded no positive evidence of micropores in agreement with later isotherm data using Kr. A set of calculations as reported here has been applied to this data for trichloroethene, and the results are shown in Figure 6. Based on eqs 7 and 8, ∆G ) -22.9 ( 1.5 kJ mol-1 (absolute magnitude of ∆Ghyd of trichloroethene is 21.7 kJ mol-1) and Vo is approximately 0.6 µL. These results further support our hypothesis that CPS is an important mechanism affecting accumulation of VOCs in porous media. The possibility of a VOC phase separation within intraparticle pores can be explored based on thermodynamic considerations. The thermodynamics of confined fluids differ from those of bulk fluids as a result of two additional contributions to the internal energy of the system. For an adsorbing solution between two parallel plates separated by a distance H (a slit geometry), the total differential of the internal energy (dU) can be expressed as (30, 31)

ln V ) ln Vo -

[ ]

Csat B 2 T ln 2 Co β

2

(7)

The ordinate value, V (µL of pure VOC), is based on qint, the mass of glass beads, and the bulk density of the VOC (Fvoc, g cm-3); Vo is the volume filled with neat VOC at saturation (Csat/Co ) 1); and, B/β2 (K-2) is a function of the pore structure and sorbate/sorbate and sorbate/sorbent molecular interactions. This pore-filling model naturally leads to the following relationship that allows values of the Gibb’s free energy change for the process (∆G, kJ mol-1) to be estimated from experimental sorption measurements:

∆G ) -

( )

Csat Rβ2 + RT ln 4BT Fvoc

(8)

As Figure 5 shows, data for methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene are correlated satisfactorily by eq 7 over the range of concentrations used in these experiments. The slopes of the lines in Figure 5 yield values of ∆G of the pore-filling process of -22.4 ( 1.0, -23.5 ( 4.5, and -25.9 ( 0.4 kJ mol-1 for methylbenzene, 1,4-dimethylbenzene, and 1,3,5-trimethylbenzene, respectively. These values are approximately equal in magnitude to the free energies of hydration (∆Ghyd) of these VOCs (+22.7, +25.8, and +29.2 kJ mol-1, respectively) and strongly suggest that the principal mechanism for sorption of these VOCs into the glass beads involves CPS. The intercepts obtained from linear regression yield values for the VOC-

dU ) -p dV + T dS +

∑µ dn + 2γ dA - Af dH i

i

(9)

i

where p, V, T, S, µi, and ni represent pressure, volume, temperature, entropy, chemical potential of component i, and mole number of component i, respectively. The

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standard (bulk phase) terms are supplemented by a surface work term that accounts for changes in internal energy due to changes in interfacial area (dA) and interfacial energies (2γ is the total wall-fluid interfacial tension) and a second term (Af dH) that arises from solvation forces (31-33) and represents the energy changes due to changes in the separation (dH) of interfaces of area A. The variable f in eq 9 is the solvation force and contributes directly to the cavity work needed to insert a solute molecule into a pore (32). It has a major role in determining stratification and phase separation in small pores (30-33). This force is a function of wall-fluid and fluid-fluid intermolecular forces and is related to the interfacial energy by

f ) -2

∂γ (∂H )

T,µi

(10)

Evans and Marconi (31) extended the thermodynamic analysis of Ash et al. (30) to determine conditions required for phase separation of a binary mixture. A key result of this work is that within a pore, a pure solute phase can be in equilibrium with a solution that has a solute concentration less the bulk phase saturation concentration. Specifically, the reduction in solubility of a VOC arising from confinement is given by

-2γvm cos θ C ) exp Csat rRT

(11)

where C is the aqueous VOC concentration within the pore, Csat is the solubility in bulk water, γ is the interfacial surface tension of VOC and water, vm is the molar volume of the VOC, θ is the contact angle, and r is the pore radius. This relationship has been derived by others (34, 35), and it has been used to accurately describe the adsorption of aromatic compounds by mesoporous, carbonaceous materials (3537). If applied to our alkylbenzene data for glass beads, eq 11 indicates that for the experimental values of Co/Csat, CPS of benzene would occur only in pores of 1-2 nm in diameter (about 2-3 molecular diameters). However, CPS of the other compounds could occur for pore diameters of 4-6 nm (about 5-10 molecular diameters). These numbers should be viewed as estimates only because of questions regarding the range of pore sizes over which eq 11 can be applied (31, 33), the range of contact angles of the VOCs on water-wet glass (38), and the hydrophobicity of the glass surfaces (39-44). The two additional energy contributions in eq 9 (interfacial and solvation terms) affect the phase behavior of confined fluids and are responsible for capillary condensation from the gas phase and CPS from the liquid phase. Interfacial forces may promote CPS in pores of any size, but solvation forces are significant only where interfaces are separated by distances less than about 20 molecular diameters (35-37, 45-47). For interfacial energy changes to promote CPS of a neat solute phase from aqueous solution, the solute phase must preferentially wet the solid, i.e., the solute-solid interfacial energy (γs-s) must be less than the water-solid interfacial energy (γw-s). Replacement of the water-solid interface by a solute-solid interface leads to a decrease in free energy (G) per area of interface replaced given by

∂G ) γs-s - γw-s ∂A 2890

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CPS promoted by changes in interfacial energy has been experimentally observed between mica sheets confining organic solvents containing trace amounts of water (48). Water condensed from an organic solvent to form bridges between the sheets when the separation was about 6-8 nm (49). The lower interfacial energy between water and mica compensated for the entropy decrease associated with condensation at a water concentration below saturation. In contrast, interfacial energy changes would oppose CPS of a hydrophobic solute in an aqueous system with mineral solids, because most mineral solids are preferentially waterwet (γs-s > γw-s), and replacing the water-solid interface by a VOC-solid interface would cause an increase in G. CPS of the hydrophobic solute could still occur if solvation and hydrophobic energy changes were of sufficient magnitude to compensate for the increase in interfacial energy. Solvation forces arise from unfavorable packing geometries between surfaces separated by distances that are nonintegral multiples of the molecular diameter. For most liquids, these solvation forces decay in a damped, oscillatory manner about the mean van der Waals force and extend up to separations of 20 molecular diameters (45, 46, 50). Results from molecular dynamics and Monte Carlo simulations of fluids in microcapillaries indicate that the oscillatory behavior of the solvation force is strongly correlated with enhanced partitioning of a solute within the pore (32). However, for water and other associating liquids, effects of hydrogen bonding cause an additional monotonic force that is superimposed on the oscillatory component (46, 51). This monotonic force is repulsive for water between hydrophilic surfaces and attractive if the surfaces are hydrophobic (47). Again, simulations of fluids confined by solid surfaces indicate that the increased energy associated with these repulsive forces may lead to phase separations in molecular-sized pores (52-58). Experimental measurements indicate that this additional monotonic force component associated with water-filled pores may exceed 30 mJ m-2 at separation distances less than 1 nm (47). Therefore, CPS may be promoted by the reduction in potential energy accompanying replacement of waterfilled micropores with hydrocarbon-filled micropores. Our experimental results with methyl-substituted benzene compounds and our re-analysis of sorption data for trichloroethene suggest that the proposed pore-filling mechanism is relevant to the transport of VOCs through porous media under both water-unsaturated and watersaturated conditions. Because the thermodynamic favorability of the overall process is determined by consideration of liquid-liquid and liquid-solid processes occurring within small pores, the CPS mechanism identified in this study may also occur in water-saturated systems. Pore filling as a dominant mechanism for VOC accumulation would also suggest that intraparticle diffusion would be the rate-controlling step in both saturated and unsaturated systems. The approximate agreement ((5%) of the CPS ∆G values and the values of ∆Ghyd for the VOCs is strong evidence supporting the model described in eqs 7 and 8. Additional experimentation with a variety of mesoporous and microporous materials and hydrophobic organic compounds is necessary to clarify the influence of sorbate and sorbent properties on CPS.

Acknowledgments The research was supported in part by the U.S. Environmental Protection Agency Grant R 816282-01 and by Grant

ES04949 from the National Institute of Environmental Health Sciences, NIH. The contents of this paper are solely the responsibility of the authors and do not necessarily represent the official views of the U.S. Environmental Protection Agency or the National Institute of Environmental Health Sciences.

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Received for review August 31, 1995. Revised manuscript received May 6, 1996. Accepted May 20, 1996.X ES950644K X

Abstract published in Advance ACS Abstracts, July 15, 1996.

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