Evaluation of Thermal Effects on the Dissolution of a Nonaqueous

Nonaqueous−aqueous phase mass transfer rate coefficients measured for this system were put in dimensionless form (Sherwood number) and fitted to a p...
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Environ. Sci. Technol. 1997, 31, 1615-1622

Evaluation of Thermal Effects on the Dissolution of a Nonaqueous Phase Liquid in Porous Media PAUL T. IMHOFF,† ANGELA FRIZZELL,‡ AND CASS T. MILLER* Department of Environmental Sciences and Engineering, The University of North Carolina, CB 7400, 106 Rosenau Hall, Chapel Hill, North Carolina 27599-7400

Porous media contaminated with nonaqueous phase liquids (NAPLs) may serve as a long-term source of groundwater contamination. To remove NAPLs and thereby mitigate the potential impact to the environment and human health, it has been suggested that contaminated media be flushed with cosolvents, surfactants, hot water, or steam. In this study, hot water flooding was used to remediate a porous medium contaminated with tetrachlorethylene (PCE) at residual saturation in an otherwise water-saturated medium. The effect of temperature on the physical and chemical properties of the system was well characterized, and a quantitative assessment was made of the effect of temperature on PCE dissolution. A comparison of the results from the dissolution experiments with existing dimensionless correlations for NAPL dissolution in porous media elucidated the role of the aqueous-phase viscosity and the NAPL species aqueous-phase diffusivity. Nonaqueous-aqueous phase mass transfer rate coefficients measured for this system were put in dimensionless form (Sherwood number) and fitted to a power-law model. The Sherwood number was found to vary with the Schmidt number to approximately the 0.5 power, as suggested by previous investigators. This result is expected to apply to nonaqueousaqueous phase mass transfer in other systems where aqueous-phase properties are altered by the addition of chemicals.

Introduction Nonaqueous phase liquids (NAPLs) may enter the subsurface through spillage or leakage from pipelines, industrial processes, or storage facilities (1, 2). Although they are slightly soluble in groundwater, many NAPLs make groundwater impotable (3), even at concentrations far below their aqueousphase solubility. Thus, they often act as long-term sources of aquifer contamination. To mitigate this problem, several technologies have been advanced for removing NAPLs from the subsurface. Among them are flushing with cosolvents (4-6), surfactants (7-9), hot water (10), and steam (11). Cosolvent, surfactant, and hot water flushing either mobilize entrapped NAPLs (4, 8) or * Author to whom correspondence should be addressed. E-mail address: [email protected]. Fax: 919-966-7911. † Present address: 137 DuPont Hall, Department of Civil and Environmental Engineering, The University of Delaware, Newark, DE, 19716. ‡ Present address: ENSR, 2700 Wycliff Road, Suite 300, Raleigh, NC 27607.

S0013-936X(96)00292-1 CCC: $14.00

 1997 American Chemical Society

solubilize NAPLs into the aqueous phase (5, 8). Steam flushing either mobilizes NAPLs ahead of the steam front (11) or vaporizes volatile NAPL components behind the steam front, removing them in the vapor phase (12). Although considerable effort has been expended toward studying these processes in the laboratory and the field, many open questions remain. Two prominent concerns are mobility control and mass transfer resistance. Mobilized dense NAPLs may sink and be difficult to collect, and density and viscosity differences between the flushing solution and native groundwater may interact with geologic heterogeneities to hinder control of the flushing process. Mass transfer resistance may also significantly reduce the flushing efficiency because of diffusional resistance at the macroscale (8), a scale just above the pore scale where a representative elementary volume can be defined; the development of preferential flow paths or dissolution fingers through the contaminated zone (5, 13); or flow bypassing associated with geological heterogeneities. The objectives of this investigation were to explore the importance of mass transfer resistance at the macroscale during hot water flushing and to develop a phenomenological model for mass transfer in this setting. The effect of changing aqueous-phase properties on NAPL dissolution determined from this investigation is applicable to other flushing technologies.

Background Physicochemical Considerations. Hot water flooding has been used in the petroleum industry to improve recoveries of viscous oils by enhancing oil mobility (14). In treating groundwater contamination problems, hot water flooding has also been primarily considered as a mobilization technique for systems with high NAPL saturations (10, 15). Mobilization at increased temperatures is achieved through reductions in NAPL viscosity and interfacial tension. Dissolution of NAPL into the aqueous phase may also be improved by hot water flooding. NAPL dissolution is enhanced as elevated temperatures increase mass transfer across the aqueous-nonaqueous phase interface by decreasing the aqueous- and nonaqueous-phase viscosities, increasing the aqueous- and nonaqueous-phase diffusivities, and increasing aqueous-phase solubilities. In addition, increased temperatures typically lower the interfacial tension between aqueous and nonaqueous phases, which will affect the interfacial area for mass transfer (16). Conceptual Models for Nonaqueous-Aqueous Phase Mass Transfer. The two-resistance theory for mass transfer between two immiscible phases has been successfully used to describe gas-liquid mass transfer in trickle-bed reactors (17, 18), volatilization from surface waters (19, 20), and contaminant transfer between oil films and water (21, 22). For transport across an oil or NAPL interface into the aqueous phase, the flux is

Ji )

kia Pi kin

(

Cin

Pi kin + kia Pi

- Cia

)

(1)

where Ji is the mass flux of species i into the aqueous phase; kia is the aqueous-side mass transfer coefficient; kin is the nonaqueous-side mass transfer coefficient; Pi is the nonaqueous-aqueous phase partition coefficient; Cin is the bulk nonaqueous phase concentration of species i; and Cia is the bulk aqueous phase concentration of species i.

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TABLE 1. Mass Transfer Correlationsa reference

formulation

model type

Miller et al. (35)

Shai ) 12(φ - θn) Re0.75 θ0.60 Scai 0.5 a n

Powers et al. (37)

Shai ) 4.13 Re0.598 a

( ) d50 dM

0.673

0.369 Uin

lumped domain

() θn θni

β

lumped domain

β ) 0.518 + 0.114(d50/dM) + 0.10Uin

Imhoff et al. (39), model 4

Shai ) 340θ0.87 Re0.71 n a

( )

Geller and Hunt (27)

Shai

Sn5/9 i i

Powers et al. (38)

Shdi,m ) 36.8 Re0.654 a

) 70.5

Re1/3 a

θ4/9 n

z d50

-0.31 b

φ

lumped domain

-2/3

( ) d50 dni

5/3

c

sphere

multiple sphere

a Parameters are defined in the Notation section. b z/d c 50 ) 7 for conditions without dissolution fingering; Imhoff and Miller (13). Imhoff et al. (39).

The partition coefficient of species i depends on the composition of the nonaqueous and aqueous phases (23, 24). For sparingly soluble organic substances that form ideal nonaqueous phase solutions, the partition coefficient can be assumed to be (23-25)

Cin

Pi )

(2)

xin Sia

where xin is the mole fraction of species i in the nonaqueous phase, and Sia is the solubility of species i in the pure aqueous phase. This form has been used to model the dissolution of mixtures of benzene and toluene (26) as well as the partitioning of aromatic hydrocarbons (27) and polycyclic aromatic hydrocarbons (24) from gasoline and diesel fuel into the aqueous phase in porous media systems. However, the simplifying assumptions leading to eq 2 were not appropriate for the dissolution of mixtures of dissimilar solvents (28). In this case, models for Pi require activity coefficients for the nonaqueous phase that may not be estimated accurately with existing techniques (28). Most models for multiple species NAPL dissolution have neglected resistance in the nonaqueous phase under the premise that aqueous-side resistance dominates. For example, if Pi kin is 50 times larger than kia, then there is only a 2% error in the computed flux if a simplified flux law is used:

Ji ) kia

(

Cin Pi

- Cia

)

(3)

This form was assumed in the dissolution studies involving gasoline (29), mixtures of benzene and toluene (26), and mixtures of dense solvents (28) as well as in the transport of solutes through porous media contaminated with residual decane (30). However, semirigid skin-like films developed at coal tar-aqueous phase interfaces after the interface aged for as little as 3 days (31). Similar films have been reported in the petroleum literature (32, 33) and may occur in the case of NAPLs composed of high molecular weight organic compounds. Such films reduce kin (31) and have been suggested as the reason why kin were three times smaller for coal liquids than aromatic hydrocarbons (21). Significant

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mass transfer resistance within the nonaqueous phase was also observed in a study of creosote dissolution (34). Finally, diffusional resistance within the nonaqueous phase away from the aqueous-nonaqueous phase interface may affect mass transfer. Existing models for NAPL dissolution neglect this resistance, primarily because previous studies have examined the dissolution of isolated NAPL ganglia, and diffusional limitations within these ganglia were presumed to be negligible (26, 30). However, for pooled NAPLs or for particularly viscous NAPLs such as coal tars, this resistance could be significant. Remediation techniques that reduce diffusional resistance within the nonaqueous phase may be beneficial. Empirical Models for Nonaqueous-Aqueous Phase Mass Transfer. While many investigators have examined nonaqueous-aqueous phase mass transfer (26, 35-39), models relating mass transfer coefficients to system properties are few. Available models were developed for NAPLs trapped as isolated ganglia in sands or glass beads, where mass transfer resistance was dominated by resistance in the aqueous phase. Consequently, the models express the aqueous-side mass transfer coefficient, kia, as a function of system parameters. Here, though, the interfacial area for mass transfer is not easily measured, and three types of models have been used: sphere (26), multiple sphere (38), and lumped domain models (35-37, 39). The sphere and multiple sphere models approximate the NAPL ganglia as spheres with the specific interfacial area for mass transfer between the immiscible phases, ana, estimated from this geometry, where ana ) Ana/V, Ana is the interfacial area between the nonaqueous and aqueous phases, and V is the bulk volume or, in some cases, the aqueous-phase volume. Alternatively, lumped domain models combine kia and ana together into a single unknowns the aqueous-side mass transfer rate coefficient, Kia ) kia ana. A summary of these models is given in Table 1, where the bulk volume of the porous medium is used for V. These models were developed from water flushing experiments that were conducted at laboratory temperatures between 20 and 25 °C. The molecular diffusivities of the organic compounds in the aqueous phase, Dia, varied by less than 10%, and the aqueous-phase kinematic viscosities, νa, varied by less than 5% between these experiments. Thus, while the models shown in Table 1 scale Kia or kia with Dia and νa to various powers, these scalings have not been verified.

Instead, they were inferred based on dimensional arguments and experimental measurements of mass transfer in other engineered systems (35, 36). Groundwater temperatures may be significantly different from the experimental conditions examined in the above laboratory studies: native groundwater is typically cooler (40), while hot water or steam flushing will result in elevated temperatures (41). Under these conditions, Dia and νa may be significantly different from values encountered in these earlier studies. The addition of surfactants and cosolvents for enhanced remediation will also alter Dia and νa and thus affect the aqueous-side resistance to mass transfer. In this investigation, the effect of temperature on mass transfer was measured, and the appropriateness of existing correlations for scaling mass transfer with Dia and νa was examined.

Experimental Methods Chemicals. Water was deionized and distilled. HPLC grade PCE (Sigma Chemical Co., Milwaukee, WI) was selected as the NAPL and was used without further purification. HPLC grade methanol (Mallinckrodt Specialty Chemicals Co., Paris, KY) was used as a solvent for aqueous PCE samples, and spectroanalyzed grade methylene chloride (Fisher Scientific, Pittsburgh, PA) was used to extract PCE from the porous media. Interfacial Tension, Kinematic Viscosity, and Molecular Diffusion Coefficient. The effect of temperature on several system properties was first determined experimentally, taken from published measurements, or estimated from existing correlations. The PCE/aqueous-phase interfacial tension was measured between 5 and 40 °C using a drop-volume tensiometer (Model DVT-10, Kru ¨ ss USA, Charlotte, NC). Measurements were made after the PCE/aqueous-phase mixture had been shaken on a mechanical shaker for 6-8 days. The effect of temperature between 5 and 40 °C on the kinematic viscosity of water was taken from Lide (42). The effect of temperature on the PCE molecular diffusion coefficient was estimated using the correlation of Tyn and Calus (43). Errors using this correlation have been reported to be less than 10% (44). Aqueous Phase Solubility. The aqueous-phase PCE solubility was measured between 5 and 40 °C using a generator column technique (45). A 2.5-cm i.d. jacketed glass column (Model 5819, Ace Glass, Inc., Vineland, NJ) was packed with glass beads (d50 ) 0.0277 cm; uniformity index, Uin ) 1.2 ) to a length of 20 cm and saturated with the aqueous phase. The plunger tips were constructed of Teflon; the lower plunger tip was covered with stainless steel screens to hold the beads in place, while a layer of fine glass beads was placed against the top plunger to act as a capillary barrier. PCE was then established at residual saturation (NAPL saturation, Sn, ≈ 0.15) using methods similar to those in previous investigations (36, 39). The experimental setup is shown in Figure 1. A water bath adjustable to (1 °C was used to maintain water at a desired temperature as it was recirculated through a glass jacket surrounding both the inner glass column and a jacketed beaker. Influent water flowing through tubing submerged in the jacketed beaker was preheated or precooled by the recirculating water before it entered the inner glass column. The temperature of the column influent and effluent were monitored with an Omega Model HH21 thermometer and attached thermocouples that were accurate to within (0.1%. Column temperatures were maintained to within (1 °C of the specified temperature for the experiment. Similar temperature control was achieved for the mass transfer experiments described below. Clean water was pumped up through the PCE-contaminated media at a Darcy velocity of 2.9 m/day for the solubility experiments. Ten effluent samples were collected within 1 cm of the porous medium by inserting a glass syringe with

FIGURE 1. Experimental setup for solubility and mass transfer experiments. The configuration shown is for the mass transfer experiments. The length of the porous medium was greater for the solubility experiments, and the column was inverted from what is depicted. a stainless steel needle into the effluent line. In this way, samples were removed before they cooled or warmed to room temperature. Effluent samples were diluted into methanol, and the diluted samples were analyzed for PCE using a Hewlett Packard (HP) Model 5890 Series II gas chromatograph. Standards were prepared in an identical manner as the samples except that PCE was added to the methanol before dilution with water. Effluent samples were also collected at a Darcy velocity of 14.7 m/day. A two-sample t-test was used to test the hypothesis of equal population means for samples collected at the two velocities. At a significance level of 0.05, the mean PCE concentration did not differ between both sets of samples for each temperature examined. This indicates that equilibrium was achieved between the PCE ganglia and the aqueous phase, since contact time between the PCE and the aqueous phase differed by a factor of 5 for experiments at the two flow rates while measured aqueous-phase concentrations were the same. For this reason, data collected at both aqueous-phase velocities were combined and used for analysis. Mass Transfer Rate Coefficient. The experimental setup used to determine the aqueous-phase solubility was modified slightly for determination of the mass transfer rate coefficient. To create a capillary barrier at the top of the media, instead of using a fine layer of glass beads a nylon filter with 0.2-µm pores to inhibit PCE breakthrough was glued to the upper plunger tip with solvent-resistant sealant. A glass fiber filter disc (grade G6, Fisher Scientific, Pittsburgh, PA) was inserted between the nylon filter and the glass beads to maintain a hydraulic connection. The lower plunger and associated tubing that were in place during the creation of the PCE residual were replaced with a clean plunger and tubing that had not contacted PCE. The column was also inverted from the configuration used to determine the aqueous-phase solubility, the column length shortened to 1.0 cm, and the aqueous-phase velocity increased to 42-51 m/day. Effluent samples were diluted into methanol and analyzed for PCE using a UV spectrophotometer (either Model U-2000 or U-3300, Hitachi Instruments, Inc., Danbury, CT) at a wavelength of 225 nm. Standards were prepared in an identical manner as the samples except that PCE was added to the methanol before dilution with water. For this shorter column and these higher velocities, effluent PCE concentrations were below the solubility limit, Cis : Cia was never greater than 74% of Cis. It is assumed in the analysis that follows that a column length of 1.0 cm (porous medium volume ) 5.1 cm3) is sufficient to define an REV for NAPL saturation with this medium. REV analyses performed with glass bead media have been used to estimate the deviation of Sn from a well-

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defined mean, if the averaging volume is too small (46). However, a similar analysis has not been performed for the porous medium used in this investigation, which precludes a definitive statement about the size of an REV for this medium. There are similar concerns about the existence of an REV for Sn for other NAPL dissolution experiments, particularly those in media with wide ranges in particle sizes (37). Four independent mass transfer experiments were conducted in this investigation. At least two, and at most nine, measurements of the effluent concentration were made at 5, 20, and 40 °C for each mass transfer experiment. Sufficient time was allowed for the system to come to thermal equilibrium between each change in temperature. Experiments were not conducted at temperatures greater than 40 °C because the Teflon plungers on the column ends did not seal effectively at higher temperatures. At the end of each mass transfer experiment, the PCE remaining in the column was extracted with methylene chloride. The upper plunger was removed, and 1 mL of methylene chloride was added to the column, mixed with the porous medium and pore fluids, and then sampled. PCE concentrations in the methylene chloride samples were determined using a UV spectrophotometer at a wavelength of 240 nm. The extraction technique was tested by spiking a column with a known mass of PCE and comparing this mass with the extracted mass; the error was approximately 2%, demonstrating the accuracy of the method. The initial Sn was determined by adding the mass eluted to that determined by extraction. Losses of PCE through elution from the column during the mass transfer experiments ranged between 1.4 and 4.0% of the initial mass, indicating that Sn changed by a small amount. In the analysis that follows Sn was assumed to be constant during the dissolution stage, and an average Sn over the duration of each experiment was used in all calculations.

FIGURE 2. Interfacial tension between PCE and the aqueous phase versus temperature. For data from this study, 95% confidence intervals are the size of the data symbols. Solubility data required in the correlations included solubility of the aqueous phase in PCE, taken from Stephenson (48), and solubility of PCE in the aqueous phase, taken from this study or from Stephenson (48) for temperatures outside of 5-40 °C. Pure phase interfacial tensions required by Antonov (58) and Girifalco and Good (59) methods were taken from AIChE (60). Other parameters required for Antonov’s method were computed following procedures recommended by Lyman et al. (61). Empirical parameters required for Donahue and Bartell (62) and Fu et al. (63) were taken from Demond and Lindner (47).

Results Interfacial Tension, Kinematic Viscosity, and Molecular Diffusion Coefficient. Interfacial tension measurements are shown in Figure 2 along with data collected from other investigations and four empirical correlations. The data from this study indicate that the interfacial tension decreased by 7% between 5 and 40 °C, from 42.80 ( 0.15 (95% CI) to 39.84 ( 0.08 (95% CI). This is consistent with interfacial tension changes on the order of 0.1 dyn/cm per °C measured for other organic/aqueous phase systems (47). For PCE at residual saturation, interfacial tension changes of this magnitude are expected to have a minor effect on PCE/aqueous phase interfacial area. Based on literature data (42) and the correlation of Tyn and Calus (43), the kinematic viscosity of water decreases by a factor of 2.3 between 5 and 40 °C, while the molecular diffusion coefficient of PCE in water increases by a factor of 2.6. Aqueous Phase Solubility. The PCE solubility data shown in Figure 3 suggest a decrease in solubility as temperatures increase from 5 to 20 °C, followed by increasing solubility up to 40 °C. The solubility at 5 °C (258 (2 mg/L, 95% CI) is higher than at 40 °C (242 (6 mg/L, 95% CI). Data are shown from Stephenson (48), as is a correlation by Horvath (49), which was developed using recommended data selected from a comprehensive literature search; note that Stephenson’s results are in better agreement with those from this study than Horvath’s. At 20 °C though, Stephenson’s results differ significantly from this study’s. However, the measured solubility at 20 °C (221 (3 mg/L, 95% CI) is nearly the same as that reported in a recent investigation (5) that also used the generator column technique (225 mg/L). The generator column technique is preferred by several workers for saturat-

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FIGURE 3. Aqueous-phase PCE solubility versus temperature. ing the aqueous phase with sparingly soluble organic solutes (50). PCE solubilities measured from this study were used in the mass transfer calculations. Mass Transfer Rate Coefficient. Effluent PCE concentration measurements were used for subsequent analysis of Kia using an equation developed by Miller et al. (35) for steady-state dissolution and transport, modified so that Kia was defined in terms of the bulk volume of the porous medium

(φ - θn) Kia )

[[

va -

(

)] ]

2Dl Cia (z) ln 1 z Ci 4Dl

s

2

- v2a

(4)

where φ is the porosity, θn ) φSn is the NAPL volume fraction,

TABLE 2. Results from Mass Transfer Experiments 5 °C exp

O

Sn

4 6 10 12

0.38 0.39 0.38 0.38

0.25 0.25 0.11 0.11

a

va (cm/s) Na Cai (z)b (mg/L) 0.059 0.058 0.050 0.049

Number of samples.

b

4 5 7 9

107.9 ( 2.3 116.6 ( 5.3 67.2 ( 9.4 50.5 ( 8.4

20 °C

40 °C

Kai b (1/day)

Na

Cai (z)b (mg/L)

Kai b (1/day)

795.3 ( 22.8 878.8 ( 56.1 445.5 ( 73.6 316.0 ( 60.6

2 5 5 9

117.2 ( 2.8 1120.4 ( 40.6 129.1 ( 9.2 1300.9 ( 149.7 67.5 ( 11.5 540.9 ( 114.7 86.9 ( 6.8 732.6 ( 75.1

Na Cai (z)b (mg/L) 5 5 3 4

168.0 ( 0.8 175.2 ( 4.5 81.9 ( 0.7 105.8 ( 1.4

Kai b (1/day) 1786 ( 17.2 1931.5 ( 103.6 610.4 ( 6.2 843.4 ( 15.9

Mean ( 1 SD.

z is the distance from the column inlet, va is the average interstitial aqueous-phase velocity, and Dl is the longitudinal dispersion coefficient. For the high velocities encountered in these experiments, Dl was estimated from

Dl ) Rlva

(5)

where Rl is the longitudinal dispersivity and was estimated as Rl ) 1.5d50, based on findings of other investigations in granular porous media where Rl varied between d50 and 2d50 (51). Because transport was dominated by advection in this investigation, computed Kia changed by less than 1% when Rl was varied between d50 and 2d50. Kia was determined at three temperatures in four dissolution experiments. Experimental conditions for these experiments, effluent concentration data, and computed Kia are shown in Table 2. For comparison with the work of other investigators, Kia were put into dimensionless form and fit to a power-law model with a statistical software package (52), using linear regression of the log-transformed model and nonlinear regression. The mean aqueous-phase Sherwood number, Shia ) ( Kia d250 )/ Dia, at each temperature from each experiment was regressed using the sample variance of Shia as regression weights. The log-transformed model fitted to the data was i ln (Shia ) - ln (Re0.75 θ0.9 a n ) ) ln (β* 0) + β* 1 ln (Sca )

(6)

with

ln (β*0) ) 0.533 ( 1.112 β*1 ) 0.468 ( 0.151

((95% CI) ((95% CI)

and the nonlinear model was i β1 Shia ) β0 Re0.75 θ0.9 a n Sca

(7)

with

β0 ) 1.340 ( 1.499

((95% CI)

β1 ) 0.486 ( 0.173

((95% CI)

where Rea ) (vad50)/νa is the aqueous-phase Reynolds number, and Scia ) νa/Dia is the aqueous-phase Schmidt number. Attempts to simultaneously fit exponents for Rea, θn, and Scia did not result in meaningful solutions. Changes in νa due to temperature affected both Rea and Scia, and θn did not vary significantly during these experiments. For this reason, exponents on Rea and θn were taken from the literature. An exponent of 0.75 was selected for Rea because of agreement with other researchers: Miller et al. (35) and Imhoff et al. (39) found exponents of 0.75 and 0.71, respectively, although Powers et al. (37) determined a best-fit value of 0.61. In transient dissolution experiments, the exponent on θn was

FIGURE 4. Comparison of the Sherwood number, Shai , determined from this study with that predicted from existing correlations. The Sherwood number was normalized with the Schmidt number, Scai , to the 0.5 power, to account for temperature variations in this investigation. 0.87 (39) or varied between 0.75 and 0.96 (37); here, 0.90 was selected. The log-transformed and nonlinear models resulted in coefficients of multiple determination of 0.96 and 0.98, respectively, indicating that much of the variability in the data was accounted for. The parameters ln (β*0) and β0 were negatively correlated with β*1 and β1, respectively, with a correlation coefficient of -0.996 in both models. Best estimates of the fitted parameters were sensitive to the exponents selected for Rea and θn. However, varying the exponent for Rea between 0.60 and 0.90 and for θn between 0.60 and 1.0, ranges that encompass fitted exponents from all previous investigations, resulted in model-estimated parameters that fell within the 95% confidence intervals given above. Based on these results, we conclude that the best estimate of the exponent on Scia from this investigation is 0.5, although confidence in this particular value is not great considering the assumptions in the analysis and the large confidence intervals above. For comparison with data from other investigations, the fitted correlation for the nonlinear model is plotted in Figure 4 with correlations from other investigations (35, 37, 39) using representative conditions from these experiments (θn ) 0.04). Data were normalized with Scia 0.5 because of the significant change in this parameter for the experiments in this study. The data collected from this study fall below those from the other investigations. They are closest to those of Powers et al. (37) and Imhoff et al. (39). This similarity is to be expected, since the procedure for creating the NAPL residual was most like that used in those studies. These displacement techniques were intended to imitate the NAPL-emplacement processes occurring in real groundwater systems.

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FIGURE 5. Maximum potential mass flux of PCE, Kai Cis , and several other NAPLs versus temperature for representative conditions. Predicted Kai were found from eq 7. Parameters required for predicting Kai and estimating Cis came from the following sources: molecular diffusion coefficient estimated using Tyn and Calus (43) for PCE and Wilke and Chang (64) for all other compounds, viscosity data from Lide (42), molar volume at normal boiling point estimated using Tyn and Calus (65), and aqueous-phase solubility estimated using empirical correlations developed by Horvath (49). The most important observation from the regression analysis is the fitted exponent on Scia . An exponent of 0.5 indicates that Kia ∝ Dia 0.5. Chemical engineering investigations of mass transfer from single spheres (53-55) or packed beds of spherical particles (56, 57) suggest that Shia should vary with Scia to a power between 0.33 and 0.67. Miller et al. (35) selected a value of 0.5 for their model based on these published data. However, molecular properties were not varied in the experiments of Miller et al. (35) or in other experimental investigations of NAPL dissolution. Thus, the correct functional relationship between Shia and Scia has not been established for the dissolution of NAPL ganglia in porous media. With the exception of Miller et al. (35), the published correlations shown in Figure 4 do not include Sc0.5 and instead indicate Kia ∝ Dia. Molecular properties for the aqueous phase vary significantly with temperature: in this study, Scia for PCE decreased by a factor of 6 as temperature increased from 5 to 40 °C. Because of this variability, it was possible to assess the relationship between Shia and Scia .

Discussion Hot water had a small effect on the nonaqueous-aqueous phase interface, altering the interfacial tension by 7% over the temperature range examined. Interfacial tension changes of this magnitude were judged to have a minor effect on the interfacial area for mass transfer. There was also no resistance to mass transfer in the nonaqueous phase, since a singlespecies NAPL was used. However, the aqueous phase properties varied significantly in this system, and data indicated Shia ∝ Scia β1, where β1 ≈ 0.5. This result should be applicable to the dissolution of NAPL ganglia in porous media for other systems where aqueous-phase properties are altered. Flushing with hot water had a small effect on the solubility limit of PCE, but increased Kia by a factor of approximately 2 as the aqueous-phase temperature was increased from 5 to 40 °C. The actual mass flux per unit bulk volume of the porous medium is Kia ( Cis - Cia ). The maximum potential mass flux is Kia Cis , which is plotted in Figure 5 for PCE and representative conditions in the experiments, using the best-fit model

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from nonlinear regression. The data are extrapolated to 60 °C, and the maximum potential mass flux increases by a factor of 3 as temperature increases over this range. The best-fit model was used to predict KiaCis for several other NAPLs of environmental interest, which are also shown in Figure 5. Hot water flushing over this temperature range may increase the maximum potential mass flux for these compounds by up to a factor of 5. The rate of mass transfer for the compounds shown in Figure 5 does not increase by orders of magnitude because of hot water flushing. However, hot water flushing may be an attractive remediation technique if the aqueous-phase solubility of a contaminant increases significantly with temperature or if there are significant mass transfer limitations in the nonaqueous phase because of high viscosity, e.g., coal tars. In this case, hot water flushing may decrease resistance to mass transfer within the nonaqueous phase through viscosity reduction. Hot water flushing may also be used to heat volatile NAPLs before air sparging or air venting. Vapor extraction processes are more effective if the volatile NAPLs are at elevated temperatures, and hot water is a much more effective medium for heat transfer than air; the thermal conductivity of water is 1 order of magnitude larger than that of air (44).

Acknowledgments Helpful discussions and assistance in conducting the experiments was provided by John F. McBride. The authors also thank Oliver Pau for performing the PCE solubility measurements and Clint Willson for conducting the interfacial tension measurements. The work upon which this paper is based was supported by Grant 5 P42 ES05948-02 from The National Institute of Environmental Health Sciences; Grants DAAL0391-G-0155 and DAAL03-92-G-0111 from The Army Research Office, Research Triangle Park, NC; and Grant UNC-788 from The North Carolina Water Resources Research Institute, Raleigh, NC.

Notation ana

specific interfacial area for mass transfer between the nonaqueous and aqueous phases (L-1) interfacial area between the nonaqueous and Ana aqueous phases (L2) i equilibrium concentration of the NAPL species Cs i in the aqueous phase (M L-3) i bulk aqueous-phase concentration of species i Ca (M L-3) i bulk nonaqueous-phase concentration of species Cn i (M L-3) dM diameter of a “medium” sand grain assumed as 0.05 cm (L) d10, d50, particle diameter such that 10%, 50%, or 60% of d60 porous media are finer by weight (L) molecular diffusivity of species i in the aqueous Dia phase (L2 T -1) Dl aqueous-phase longitudinal dispersion coefficient (L2 T -1) i mass flux of species i from the nonaqueous to J the aqueous phase (M L-2 T -1) i aqueous-side mass transfer coefficient for speka cies i (L T -1) i nonaqueous-side mass transfer coefficient for kn species i (L T -1) i aqueous-side mass transfer rate coefficient for Ka species i (T -1)

N Pi Rea Sia Sn Sni Scia

Shia Shi,m a Uin va V xni z Rl β0, β1 β*0, β*1 νa φ θn θni

number of effluent samples (-) species i nonaqueous-aqueous phase partition coefficient (-) aqueous-phase Reynolds number ) (d50va)/νa(-) solubility of species i in the pure aqueous phase (M L-3) nonaqueous-phase saturation (-) initial nonaqueous phase saturation (-) aqueous-phase Schmidt number for species i ) νa/Dia (-) aqueous-phase Sherwood number for species i ) (Kiad250)/Dia (-) modified aqueous-phase Sherwood number for species i ) (kiad50)/Dia (-) uniformity index ) d10/d60 (-) interstitial aqueous-phase velocity (L T -1) bulk volume of the porous medium (L3) mole fraction of species i in the nonaqueous phase (-) distance from the column inlet (L) longitudinal dispersivity (L) fitted parameters in the nonlinear model for Kia (-) fitted parameters in the log-transformed model for Kia (-) kinematic viscosity of the aqueous phase (L2 T -1) porosity (-) volumetric fraction of the nonaqueous phase (-) initial volumetric fraction of the nonaqueous phase (-)

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(67) Demond, A. H. Ph.D. Dissertation, Stanford University, Stanford, CA, 1988.

Received for review April 1, 1996. Revised manuscript received January 14, 1997. Accepted January 16, 1997.X ES960292X

X

Abstract published in Advance ACS Abstracts, March 15, 1997.