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Measurement of pore connectivity to describe diffusion through a nonaqueous phase in unsaturated soils
Journal of Contaminant Hydrology 40 Ž1999. 221–238 www.elsevier.comrlocaterjconhyd
Measurement of pore connectivity to describe diffusion through a nonaqueous phase in unsaturated soils Charles E. Schaefer 1, Rolf R. Arands, David S. Kosson
)
Chemical and Biochemical Engineering, Rutgers The State UniÕersity of New Jersey, 98 Brett Road, Piscataway, NJ 08854-8058, USA Received 3 July 1998; received in revised form 30 April 1999; accepted 18 May 1999
Abstract Contaminant diffusion through a nonaqueous phase liquid ŽNAPL. in unsaturated soils may often be an important transport mechanism. A diffusion tube technique was used to measure the effective diffusivity through NAPL in unsaturated soils as a function of soil type Žor pore size distribution., water saturation Žmilliliter waterrmilliliter void., and NAPL saturation Žmilliliter NAPLrmilliliter void.. Results indicated that the effective diffusivities depended on the ‘connectivity’ of the NAPL. This ‘connectivity’ increased with NAPL saturation, but was shown to have a more complex relation to the water saturation and pore size distribution of the soil. A series of mercury intrusion and extrusion experiments was also carried out to characterize the pore size distribution and pore ‘connectivity’ of the model soils. Using this characterization of the pore size distribution, along with a previously developed diffusional resistance model, the effective diffusivity was reasonably predicted for the soils and saturations examined in this study. q 1999 Published by Elsevier Science Ltd. All rights reserved. Keywords: NAPL; Porous media; Diffusion; Soils; Pore size distribution
1. Introduction Nonaqueous phase liquids ŽNAPLs. may migrate downwards due to gravity and eventually become immobilized as a heterogeneously dispersed phase in the soil )
Corresponding author. Fax: q1-7324452637; E-mail: [email protected] Currently at Stanford University, Department of Petroleum Engineering, 367 Panama St., Rm. 65, Stanford, CA 94305-2220. 1
0169-7722r99r$ - see front matter q 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 9 9 . 0 0 0 5 3 - 4
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subsurface as a result of fuel spills, solvent spills, or other releases ŽCohen and Mercer, 1993.. The NAPL can be composed of several constituent hydrocarbon components, a fraction of which may be volatile and partially water-soluble organic contaminants ŽMalone et al., 1993.. Heavy hydrocarbon components of the NAPL may serve as a source of slow release for these diffusively mobile organic contaminants ŽBouchard et al., 1990; Guiguer, 1991; Zalidis et al., 1991.. If the NAPL exists in quantities large enough to form a continuous phase, a concentration gradient of constituent components may occur in the NAPL itself. This would result in diffusional transport of constituent organic contaminants through the NAPL. In low-permeability porous media, where the fluid velocity is very low, the primary transport mechanism can often be diffusion. Since the bulk NAPL often contains much higher concentrations of hydrophobic contaminants than either the aqueous or air phases, the bulk NAPL can serve as a significant diffusion pathway. There have been extensive studies on aqueous phase diffusion through unsaturated soils ŽRobin et al., 1987; Ryan and Cohen, 1990; Schaefer et al., 1995., as well as vapor phase diffusion through unsaturated soils ŽNielson et al., 1984; Collin and Rasmuson, 1988; Schaefer et al., 1997.. Vapor phase diffusion with NAPL present has also been recently studied ŽSchaefer et al., 1998.. However, examination of diffusion through a NAPL in unsaturated soils has not been examined. Models have incorporated solute diffusion through the oil phase, but the parameter Deff Žthe effective diffusivity through the bulk oil phase. was not investigated ŽKaluarachchi and Parker, 1990; Sleep and Sykes, 1993.. Several additional attempts have been made to model diffusion through a porous media using a detailed pore network. However, these attempts have all incorporated an empirical geometric factor or specific packing arrangement to account for pore connectivity ŽChatzis and Dullien, 1985; Sahimi and Stauffer, 1991.. Use of mercury intrusion data to describe and characterize connectivity in a porous catalyst has been suggested ŽHollewand and Gladden, 1992.. Based on their simulation results, broad pore size distributions lead to increases in tortuosity due to shielding of large pores by smaller pores. However, obtaining accurate pore distribution results via mercury intrusion analysis is difficult due to large pores being accessed via small pore openings ŽDullien, 1992.. Attempts have been made to correct mercury intrusion data to account for this phenomena, but once again, a specific correction for the unknown pore connectivity must be determined ŽConner and Horowitz, 1988.. Recent work by Schaefer et al. Ž1997; 1998. has incorporated mercury intrusion and extrusion analyses to determine pore connectivity at threshold penetration Ži.e., the pore diameter where mercury first penetrates the porous media.. This technique was able to predict the insular saturation of gas-filled voids, and led to development of a model to predict the gas phase effective diffusivity through unsaturated soils. Understanding and characterizing the porous network are essential to the prediction of the effective diffusivity through the NAPL in unsaturated soils. In this study, the effective diffusivity through the NAPL is examined. Experiments to measure the effective diffusivity through a model NAPL are carried out as a function of moisture content and NAPL content for three unsaturated soils. A procedure using mercury intrusion and extrusion is also described to characterize the porous media. Results are
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used to develop and validate a model to predict effective diffusivity through the NAPL as a function of these variables. Prediction of the effective diffusivity through NAPL will improve contaminant transport models, and will provide more accurate information on the costs, clean-up time scales, and technical feasibility of selected remediation techniques.
2. Model development The diffusional resistance through the NAPL is defined as follows: R s D 0rDeff ,
Ž 1.
where R s diffusional resistance wdimensionlessx D 0 s free diffusivity of solute through the NAPL wcm2rsx Deff s effective diffusivity through porous media wcm2rsx. D 0 was determined by the capillary method using a dodecane 14 C-radiolabeled tracer ŽCussler, 1984.. The value obtained was 1.1 = 10y5 cm2rs. Previous work describing the gas phase diffusional resistance through unsaturated soils may be extended to describe diffusional resistance through the NAPL ŽSchaefer et al., 1997, 1998.. Changes consist of redefining the interparticle and macropore regimes in terms of the NAPL: Rs
ž
1
1 q
R1
Ž R2 q R3 .
y1
/
Ž 2.
where R 1 s Ž ´ inter , NAPL2r3´ inter , NAPL 2r3 .
y1
R 2 s Ž volume fraction of ´ macro , d filled with NAPL. R 3 s Ž ´ macro , 2r3 d ´ inter , NAPL
2r3 y1
.
Ž 3. y4 r3
s1
Ž 4. Ž 5.
´ inter, NAPL s volume of NAPL in the interparticle pore regime per bed volume wmlrmlx s ´ total, NAPL y ´macro, d ´macro, d s volume of NAPL-filled macropores per bed volume at the largest pore diameter Ž d . that the NAPL fills wmlrmlx ´ total, NAPL s total NAPL volume per bed volume wmlrmlx. It is important to note that this model will apply to NAPLs which are nonspreading Žwill not spread between air and water down to molecular thickness. and will have a measurable residual saturation ŽZhou and Blunt, 1997.. The difficulty in Eqs. Ž2. – Ž5. lies in the determination of ´ macro, d , the NAPL-filled macropore porosity. This parameter is the volume of NAPL Ždivided by the total bed volume. which becomes discontinuous and immobilized in the porous medium. The
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Fig. 1. Mercury intrusion into a porous soil bed is used to estimate the relation between pore diameter and pore volume. Darkened areas represent NAPL regimes. Since water will preferentially fill small pores before NAPL in most soils, the amount of water in the soil will determine in what pore regime the NAPL will lie. Relative saturation is defined as milliliter liquid per milliliter total void volume. The pore size distribution curve shown here is for Quakertown soil Žporosity s 40%..
NAPL-filled macropore porosity is a function of the porous media geometry. Measurement of this macropore porosity allows for an estimate of pore connectivity. Unlike the previous gas phase diffusion model which measures the macropore volume only at threshold penetration Žinitial penetration of mercury into the soil bed., the macropore volume Ž ´macro, d . now must be determined at all pore diameters. A NAPL in a multi-phase porous media will occupy a specific pore regime. For a NAPL spill invading unsaturated soil initially at a low moisture content, the NAPL will reside in pores smaller than it would in soils initially at a higher moisture content ŽFig. 1. because of preferential wetting by the aqueous phase ŽFig. 2.. Similar pore models and fluid configurations to those shown in Fig. 2 have been proposed ŽZhou et al., 1997; Kawanishi et al., 1998.. The amount of water initially in the porous medium Žand thus the location of the NAPL in the porous medium. may determine the connectivity or continuity of the NAPL. It is necessary to determine the volume of pores which will remain filled with NAPL after the phase has become discontinuous at every pore diameter Žnot just at the threshold diameter.. In order to calculate this, the difference in mercury intrusion volume at every pore diameter between a primary and secondary intrusion must be determined. This may be represented by the log differential intrusion volume Žincremental volumerDlogŽdiam... at each pore diameter. Log differential intrusion volume is used to determine soil pore size distribution ŽFies, ` 1992.. The following equation, which employs mercury intrusion results of two sequential intrusions, is used to determine the macropore volume of the NAPL:
´macro , d s Ž ´macro , thresh . Ž dVintr 1 y dVintr 2 . r Ž dVthresh , 1 y dVthresh , 2 . ,
Ž 6.
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Fig. 2. Fluids in a pore corner. Assuming the porous medium is water wet, the water will reside in the smallest pores. NAPL will follow next, then air. The two simplified pores shown here contain the same NAPL content, but the pore on the right has a higher water saturation. This causes the NAPL to lie in a different location Žin larger diameter regimes..
where ´ macro, d s volume of NAPL-filled macropores per bed volume at the largest pore diameter Ž d . that the NAPL fills wmlrmlx ´ macro, thresh s macropore volume calculated by the difference in intrusion volumes at threshold penetration wmlrmlx dVintr 1 s log differential intrusion volume at the largest pore volume in which the NAPL resides determined from an initial mercury intrusion wmlrlog mmx dVintr 2 s log differential intrusion volume at the largest pore volume in which the NAPL resides determined from a second mercury intrusion wmlrlog mmx dVthresh, 1 s log differential intrusion volume at threshold penetration of mercury into the soil bed wmlrlog mmx dVthresh, 2 s log differential intrusion volume at threshold penetration of mercury into the soil bed for the secondary intrusion wmlrlog mmx. As mercury is extruded after an initial intrusion, mercury-filled pores which are only surrounded by smaller pores become detached and the mercury becomes entrapped in the porous media ŽLenormand et al., 1983.. Such pores can contain a fluid phase, but cannot by themselves provide a complete and continuous diffusive pathway across a porous medium. For the case of NAPL migrating downward through unsaturated soil, these pores Ž ´macro, d . would contain NAPL, but all pores which surround and connect them would contain either water or air. Eq. Ž6. allows the volume of pores surrounded only by smaller pores to be calculated at every soil pore diameter. At threshold penetration, a direct measurement of ´macro, thresh is attainable because all the pores with a diameter greater than that at the threshold diameter are macropores ŽSchaefer et al., 1997.. Direct measurement of the macropore porosity at pore diameter d Žwhere d - d thresh . may be determined by comparing the differential intrusion volumes. If dVintr 1 is calculated at the threshold penetration diameter, then dVintr 1 s dVthresh, 1. The same applies to dVintr 2 and dVthresh, 2 . Thus, the bracketed term in Eq. Ž6. has a value of 1. The difference dVintr 1 y dVintr 2 in
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Eq. Ž6. is the change in differential intrusion volume due to the presence of mercury in previously trapped soil pores. For example, if the difference dVintr 1 y dVintr 2 at soil pore diameter d is half of the value of dVthresh, 1 y dVthresh, 2 , then the macropore value at diameter d is half the volume of the macropore volume measured at threshold penetration Ž ´macro, thresh .. Some approximations are made to obtain an estimate of ´ macro, d . Hidden pores Žpores which are surrounded by smaller pores. are not directly considered in determining the actual pore size distribution. Pores which fill at a given capillary pressure of mercury may not be accessible until smaller pores, which fill at a higher capillary pressure, become mercury-filled. However, this pore volume is accounted for as the ‘trapped’ mercury volume in the secondary intrusion Ž dVintr 1 y dVintr 2 .. Assuming that the capillary pressures needed to gain access to these smaller pores are relatively close to the larger blocked pores Ži.e., only pores with slightly smaller diameters must be accessed to enter the ‘hidden pores’., hidden pores do not cause a significant error in the overall analysis. Large differences in the intrusion volumes between the primary and secondary intrusions will occur at pore diameters where the hidden pores exist and ´ macro, d will have large values. Eq. Ž6. measures the connectivity, not the precise topology, of the pores. Pore classes which are highly connected will remain continuous, and will have low values of ´macro, d . Pore classes which are less connected will have a larger value of ´macro, d . Thus, NAPL residing in the more highly connected pore classes will remain continuous at lower NAPL saturations. This will cause lower effective diffusivities. By making these simplifications and only considering the connectivity of pores, precise geometric or topological data are not needed to provide an analysis of diffusive transport in uniform porous media. However, these assumptions may limit the application of the described model to only a limited number of porous media applications. 3. Experimental design Three different soils were examined with varying physical and chemical characteristics ŽTable 1.. Soil analyses were carried out at Rutgers Soil Testing Laboratory ŽCook College, New Brunswick, NJ.. Diffusion tube experiments to measure Deff ŽEq. Ž1..
Table 1 Physical and chemical properties of selected soils
Sand Ž%. Silt Ž%. Clay Ž%. Texture Specific surface area ŽBET — N2 adsorption. Žm2 rg dry soil. Organic matter Ž%.
Quakertown
Pequest
Adelphia
20 60 20 Silt loam 9.75
44 44 12 Loam 15.4
72 14 14 Sandy loam 6.4
3.9
2.1
1.4
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were carried out on each soil. Dodecane served as the model NAPL, with 14 C-labeled dodecane used as the diffusing solute. Dodecane was chosen because of its low vapor pressure and water solubility. In addition, dodecane is a common component of gasoline and fuel oil ŽUSEPA, 1995. and will not spread as thin films on water ŽDemond and Lindner, 1993.. Several different dodecane and water relative saturations Žmilliliter liquidrmilliliter bed void volume. were examined. Dodecane relative saturations ŽRS. examined ranged from 0.02 to 0.60. Water relative saturations examined ranged from 0.10 to 0.90. Experiments were designed so as not to exceed 0.95 total Žwater and dodecane. relative saturation. This ensured that some air-filled pores were present in all experiments. The effective diffusivity through the NAPL, and subsequently, the diffusional resistance, was calculated as a function of soil type, moisture content, and NAPL content. A separate set of experiments was also carried out to determine the pore size distribution data used in Eq. Ž6.. A series of mercury intrusion and extrusion experiments on packed soil was performed to determine the porous media parameters in the calculation of ´macro, d . Thus, NAPL residing in the more highly connected pore classes. Eqs. Ž2. and Ž6. were used to calculate the diffusional resistance and compared with the diffusional resistance obtained from the experimental data. 4. Experimental methods 4.1. Mercury intrusion and extrusion Mercury intrusion and extrusion experiments to determine the pore size distribution and ´ macro, thresh were carried out as previously described ŽSchaefer et al., 1997.. Mercury intrusion has been shown to be a good method to predict the residual saturation for NAPL in porous media ŽDullien, 1992.. A Micromeritics ŽNorcross, GA. Pore Sizer 9320 porosimeter was used for the analysis. Soils were packed in the glass penetrometer cup to obtain porosities similar to those used in the diffusion experiments. In order to measure ´ macro, d . Thus, NAPL residing in the more highly connected pore classes, a full Žup to 30,000 psi. mercury intrusion experiment was carried out Žto obtain dVintr 1 ., immediately followed by an extrusion Žor, withdrawal of the mercury from the soil pores. and full intrusion Žto obtain dVintr 2 . on the same packed soil sample. The differential intrusion was calculated as follows ŽFies, ` 1992.: dVintr 1 s DVrD Ž log d . , Ž 7. where DV d
s incremental intrusion volume wmlx s pore diameter wmmx. The same calculation is used for dVintr 2 .
4.2. Dodecane diffusion tube experiments A modified method of the diffusion tube technique was used to examine diffusion of C-dodecane through unlabeled dodecane in unsaturated soils ŽSchaefer et al., 1995.. Two 20 g samples of oven-dried soil Ž1058C. were placed in beakers. Measured amounts 14
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of 0.005 M CaCl 2 aqueous solution and dodecane were added to each beaker. One beaker contained 14 C-labeled dodecane, while the other contained only unlabeled dodecane. Both beakers were mixed by hand until they appeared completely homogenized. The beakers were then covered to prevent any evaporation. While premixing of the liquids with the soil may not provide the exact pore scale fluid configuration obtained via gravity drainage Žwhich would occur in the field., the general fluid configuration Žas shown in Fig. 2. was still assumed. Experiments carried out in which uniform saturations were obtained by gravity drainage yielded similar results Žsimilar values of the measured effective diffusivity. to experiments in which the saturations were obtained by premixing of the fluids. Thus, premixing of the fluids with the soil provided a reasonable replication of the fluid configuration and connectivity obtained during gravity drainage. The unlabeled soil then was packed into the diffusion tube ŽFig. 3.. The diffusion tube consisted of a plastic 60 ml syringe Ži.d. of 2.65 cm. with both ends cut and resealed with rubber stoppers. The diffusion tube was weighed and the bed height measured to determine the mass and bed height of the unlabeled soil. The labeled soil was then packed into the tube, with the final mass and bed length recorded. Next, the tube was sealed and the 14 C-labeled dodecane was allowed to diffuse for a measured time interval. The diffusion tube was placed horizontally to minimize gravitational effects. To ensure that moisture loss was minimal during the diffusion period, the ends were wrapped in Parafilme. Diffusion times varied from 1 to 4 days, depending on the moisture content and dodecane content used. Diffusion times had to be long enough to allow formation of a
Fig. 3. Diffusion tube experimental method. Extruded soil slices were approximately 1 g each.
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diffusion profile, but short enough so that the profile do not reach the ends of the tube. The soil then was carefully extruded from the diffusion tube and sliced orthogonally to its axis in approximately 1 g slices. All slices were weighed to determine the exact mass. These slices then were placed into scintillation vials with 1.5 ml of Cytoscint w scintillation cocktail. A Beckman scintillation counter was used to measure the counts per minute Žcpm. of each sample. Counts were taken over a period of 3 min. Initial experiments using controls Ž14 C-dodecane with scintillation cocktail. and labeled soil slices indicated that the soil did not have any measurable quenching effects on the 14 C counting. In addition, a background sample was included with each experiment to ensure that there was no significant 14 C contamination of the soil prior to sample preparation. Also, no measurable sorption to the soil was observed. An effective diffusivity was calculated by regression of the experimental data. For diffusion times such that the diffusion profile did not reach the end of the diffusion tube, the following transport equation may be used ŽCussler, 1984.: C y Cavg Cinf y Cavg where C Cinf z t Deff Cavg Cyinf
s erf
z
ž( / 4 Deff t
,
Ž 8.
s measured cpm at position Z of tube wcpmrg dry soilx s high boundary cpm wcpmrg dry soilx s distance from interface wcmx s diffusion time wsx s effective diffusivity through the NAPL wcm2rsx s Ž Cinf q Cyinf .r2 s low boundary cpm Žequal to background. wcpmrg dry soilx.
In order to solve Eq. Ž6., the soil bed porosity Ž ´ . as well as the relative saturation of each liquid ŽRS i . had to be calculated. Mercury intrusion data were then used to estimate the location of the liquid in the soil pores ŽUnger et al., 1996.. The parameters were computed as follows:
´
s 1 y Ž rrrsolid . , U
RS i
s milliliter liquid ir Ž ´ V bed . ,
ViX
X s RSUi V Hg ,
Ž 9. Ž 10 . Ž 11 .
where ´ s bed porosity wmlrmlx r s soil bed bulk density Ždry basis. wmgrcm3 x rsolid s soil solid density determined by the pycnometer method ŽBlack, 1965. wmgrcm3 x RS i s relative saturation of liquid i in the soil bed Ž i s water or NAPL. wmlrmlx V bed s soil bed volume wcm3 x ViX s volume of liquid i wcm3rg dry soilx X VHg s total intrusion volume of mercury for a given soil sample wcm3rg dry soilx.
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Eq. Ž11. allowed the location of water and NAPL in the soil pores to be determined ŽFig. 1..
5. Results and discussion 5.1. Mercury intrusion and extrusion Mercury intrusion and extrusion results on the three soils are shown in Figs. 4–6. Table 2 lists the bed porosities and threshold macropore volumes Ž ´macro, thresh . obtained for each soil. Duplicate experiments carried out on Quakertown soil verified that the mercury intrusion results were reproducible. The difference between the initial and secondary intrusion was due to trapping of mercury in pores which were only accessible through smaller pores. For Quakertown and Pequest soils, which both exhibited broad pore size distributions, the percentage difference between the two intrusions was large near threshold penetration. Not until the pore diameter decreased by nearly one order of magnitude did the difference between initial and secondary intrusions decrease by a factor of 2. In Adelphia soil, which had a much narrower pore size distribution than the other soils, the percentage difference between the primary and secondary intrusion near threshold penetration was not nearly as large as for the other soils. There is little difference between primary and secondary intrusions for Adelphia soil between pore diameters of 30 and 8 mm. In contrast, Quakertown and Pequest soils show significant differences between primary and sec-
Fig. 4. Log differential intrusion vs. diameter for Quakertown soil. Threshold penetration is at approximately 11 mm. Also shown are the graphical calculations of dVthresh, 1 and 2 , dVintr 1 , and dVintr 2 for a soil water relative saturation of 20% and an NAPL relative saturation of 20%. The small discontinuity at 7 mm is due to transfer of the sample from a low-pressure to a high-pressure port on the analytical equipment.
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Fig. 5. Log differential intrusion vs. diameter for Pequest soil. Threshold penetration is at approximately 9 mm. The small discontinuity at 7 mm is due to transfer of the sample from a low-pressure to a high-pressure port on the analytical equipment.
ondary intrusion for up to two orders of magnitude less in pore diameter following threshold penetration.
Fig. 6. Log differential intrusion vs. diameter for Adelphia soil. Threshold penetration is at approximately 50 mm. The small discontinuity at 7 mm is due to transfer of the sample from a low-pressure to a high-pressure port on the analytical equipment.
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Table 2 Summary of mercury intrusion results
Soil bed porosity Ž%. Total intrusion volume Žmlrg. Pore diameter at threshold penetration Žmm. Ž ´ma cro, thresh . Žmlrml bed.
Quakertown
Pequest
Adelphia
39 0.31 11 0.036
38 0.21 13 0.038
36 0.23 55 0.017
In all three soils, little difference between initial and secondary intrusions was exhibited in pores less than 0.1 mm. This indicated that the value of ´ macro, d was small in this pore regime. Due to the pore topology, there was very little mercury which became trapped in these pores during the extrusion. Fig. 4 also shows the graphical calculation of the differential intrusion parameters used in Eq. Ž6.. Results are shown for a system containing 20% relative saturation of water and 20% relative saturation of NAPL ŽFig. 1.. Threshold penetration is at approximately 11 mm. The difference between the log differential intrusion volumes of the primary and secondary intrusions Ž dVthresh, 1 y dVthresh, 2 . may be measured at this point. In addition, the macropore volume at threshold penetration Ž ´ macro, thresh . may be measured at this pore diameter ŽSchaefer et al., 1997.. The difference in log differential intrusion volumes between dVintr 1 and dVintr 2 is also shown at 1.0 mm. This is the largest pore diameter in which the NAPL resides ŽFig. 1.. Fig. 7 shows the calculated value of ´macro, d as a function of pore diameter for Quakertown and Adelphia soils. This value is largest at the threshold diameter for each soil, and approaches a value close to
Fig. 7. ´ma cro, d as a function of pore diameter for Quakertown and Adelphia soils. The vertical line represents threshold penetration.
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Fig. 8. Diffusion profile obtained for Quakertown soil at 45% dodecane relative saturation and 33% water relative saturation. The dashed line is the regression ŽEq. Ž8.. to obtain the effective diffusivity Ž Deff ..
Fig. 9. Diffusional resistance through the NAPL as a function of water and NAPL relative saturation in Quakertown soil. Vertical lines represent the point where the NAPL becomes discontinuous and diffusional resistance becomes infinite. Model simulations are carried out at 10 and 80% RS of water. Symbols represent varying water relative saturations Ž10–30%, v; 40–60%, `; 70%, ^; 80%, '.. Soil bed porosity is approximately 50%.
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zero as the pore diameter approaches 0.01 mm. Larger values of ´ macro, d are shown for Quakertown soil than for Adelphia soil near threshold penetration. 5.2. Diffusion tube experiments A typical diffusion profile showing Eq. Ž8. regressed to the experimental data is shown in Fig. 8. Diffusion profiles were typical of those obtained in previous studies examining aqueous phase effective diffusivities ŽSchaefer et al., 1995.. Analysis of both the water and 14 C-dodecane saturations as a function of column length showed that neither a gradient of dodecane nor a gradient of water existed across the soil bed. Results of the diffusion tube experiments are shown for each soil in Figs. 9–11, along with the corresponding model simulations at the designated water relative saturations. The repeatability of the experimental data was verified by examining four data points on Quakertown soil at 36% dodecane relative saturation and 20% water relative saturation. Results gave an average diffusional resistance of 8.2 " 1.0 at a 95% confidence interval. Vertical lines in the figures represent the point at which the model predicts infinite resistance Žno diffusion. due to the NAPLs becoming discontinuous across the soil bed. Data points lying at approximately 10 4 represent experiments in which no diffusion was measured. Quakertown and Pequest soils exhibited a significant difference in diffusional resistance as a function of water content at low dodecane relative saturations. In contrast, Adelphia soil showed minimal effects of moisture content at low dodecane
Fig. 10. Diffusional resistance through the NAPL as a function of water and NAPL relative saturation in Pequest soil. Vertical lines represent the point where the NAPL becomes discontinuous and diffusional resistance becomes infinite. Model simulations are carried out at 10 and 80% RS of water. Symbols represent varying water relative saturations Ž10–30%, v; 40–60%, `; 70%, ^; 80%, '.. Soil bed porosity is approximately 45%.
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Fig. 11. Diffusional resistance through the NAPL as a function of water and NAPL relative saturation in Adelphia soil. Vertical lines represent the point where the NAPL becomes discontinuous and diffusional resistance becomes infinite. Model simulations are carried out at 10 and 80% RS of water. Symbols represent varying water relative saturations Ž10–30%, v; 40–60%, `; 70%, ^; 80%, '.. Soil bed porosity is approximately 39%.
relative saturations. The Adelphia data support the assumption that only diffusion through the NAPL is significant. If vapor phase diffusion was significant at low dodecane and water saturations, the 80% water relative saturation data would show diffusional resistances about two orders of magnitude greater than the 10–30% water relative saturation data ŽSchaefer et al., 1998.. This is not the case for Adelphia soil, even at low dodecane saturations. Thus, the differences in diffusional resistances as a function of water saturation observed in Quakertown and Pequest soils are due to NAPL phase diffusion, not vapor phase diffusion. The model ŽEq. Ž2.. was able to predict the trend in the data based on the mercury intrusion analysis and calculation of ´ macro, d Žwhich incorporates pore size distribution and pore connectivity. for all three soils. In Quakertown and Pequest soils, the difference between the various moisture contents was large near threshold penetration. This difference was most noticeable at the high moisture contents. High moisture contents forced dodecane to reside in large pores ŽFig. 1.. As shown in Figs. 4 and 5, the large pores showed the greatest differences between primary and secondary intrusions, and thus had the largest ´ macro, d . The large value of ´ macro, d indicated that these pores were very ‘unconnected’. For a given dodecane saturation, lower connectivity caused a higher diffusional resistance Žor, lower effective diffusivity.. This difference diminished in the small pores Ž- 0.1 mm., indicating a greater extent of pore ‘connectivity’.
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The difference between moisture contents at low dodecane relative saturations was much smaller in Adelphia soil. This is also explained by the mercury intrusion analysis. Fig. 5 shows a much smaller percentage difference between primary and secondary intrusions in the large pores than what is shown in Quakertown and Adelphia soils. Less mercury was entrapped in Adelphia soil pores during the extrusion process, which means that the NAPL in the Adelphia soil pores was not discontinuous and connected only by water or air-filled pores. This effect produced a smaller value of ´ macro, d ŽFig. 6.. Significant differences between primary and secondary intrusions do exist for Adelphia soil between approximately 7 and 1 mm. The value of ´ macro, d is larger in this regime. However, the larger value of ´ macro, d does not have a significant effect on the diffusional resistance because the value of ´ inter is much larger than ´macro, d at these pore diameters ŽEqs. Ž2. – Ž5... Thus, moisture content does not effect the diffusional resistance of Adelphia soil because Eq. Ž2. is unaffected by changes in ´ macro, d with pore diameter. Quakertown and Pequest soils exhibited a broad pore size distribution in pores with diameters greater than 8 mm. Adelphia soil had a much narrower pore size distribution in this regime. The broader pore size distributions of Quakertown and Pequest soils led to increased trapping of mercury in soil pores during the mercury extrusion experiments, and subsequently larger values of ´ macro, d in this regime. Adelphia had less trapping of mercury in soil pores, and subsequently, smaller values of ´ macro, d in the same pore regime. Higher values of ´ macro, d caused higher diffusional resistance values at high water contents Žwhich caused the NAPL to reside in pores close to the threshold penetration. in these soils. Thus, pore regimes with broad pore size distributions have higher diffusional resistances than pore regimes with a narrow pore size distribution. This conclusion is in agreement with previously performed simulations ŽHollewand and Gladden, 1992..
6. Conclusions The use of mercury intrusion and extrusion analyses may be used to describe the continuity or ‘connectivity’ of pores. In some porous media, pore continuity may be a measurable function of pore topology. Soil pore size distribution was shown to have a significant effect on diffusional transport. The presented model, which incorporates a measure of the trapped or ‘macropore’ volume Ž ´macro, d ., was able to reasonably describe diffusion through porous soil media as a function of dodecane and water relative saturation, as well as pore size distribution.
Acknowledgements The authors gratefully appreciate Vivian Guirguis, William Chen, and Stanley Karunditu for their assistance in carrying out the experiments. This work was supported in part by the U.S. Department of Defense, Office of Naval Research and Advanced
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Research Projects Agency, University Research Initiative program ŽGrant N00014-92-J1888, R and T a4Or41ruri. and the U.S. Environmental Protection Agency Northeast Hazardous Substance Research Center, Project a R-49. References Black, C.A., 1965. Methods of Soil Analysis — Part 1. American Society of Agronomy, Madison, WI. Bouchard, D.C., Mravik, S.C., Smith, G.B., 1990. Benzene and naphthalene sorption on soil contaminated with high molecular weight residual hydrocarbons from unleaded gasoline. Chemosphere 21 Ž8., 975–989. Chatzis, I., Dullien, F.A.L., 1985. The modeling of mercury porosimetry and the relative permeability of mercury in sandstones using percolation theory. International Chemical Engineering 25, 47–66. Cohen, R.M., Mercer, J.W., 1993. DNAPL Site Evaluation. CRC Press, Boca Raton, FL. Collin, M., Rasmuson, A., 1988. A comparison of gas diffusivity models for unsaturated porous media. Soil Sci. Soc. Am. J. 52, 1559–1565. Conner, W.C., Horowitz, J., 1988. Correcting porosimetry data to obtain the actual pore and throat size distributions. AICHE Symposium Series 84, 29–34. Cussler, E.L., 1984. Diffusion: Mass Transfer in Fluid Systems. Cambridge University Press. Demond, A.H., Lindner, A.S., 1993. Estimation of interfacial tension between organic liquids and water. Environ. Sci. Technol. 27, 2318–2331. Dullien, F.A.L., 1992. Porous Media: Fluid Transport and Pore Structure, 2nd edn. Academic Press, New York. Fies, ` J.C., 1992. Analysis of soil textural porosity relative to skeleton particle size, using mercury porosimetry. Soil Sci. Soc. Am. J. 56, 1062–1067. Guiguer, N., 1991. Numerical modelling of the fate of residual immiscible fluids in saturated porous media. Water Sci. Technol. 24, 261–270. Hollewand, M.P., Gladden, L.F., 1992. Modelling of diffusion and reaction in porous catalysts using a random three-dimensional network model. Chemical Engineering Science 47, 1761–1770. Kaluarachchi, J.J., Parker, J.C., 1990. Modeling multicomponent organic chemical transport in three-fluid-phase porous media. J. Contam. Hydrol. 5, 349–374. Kawanishi, T., Hayashi, Y., Roberts, P.V., Blunt, M.J., 1998. Fluid–fluid interfacial area during two and three phase fluid displacements in porous media: a network study. Proceedings of International Conference and Special Seminars on Groundwater Quality: remediation and Protection, Tubingen, Germany. Lenormand, R., Zarcone, C., Sarr, A., 1983. Mechanisms of the displacement of one fluid by another in a network of capillary ducts. J. Fluid Mech. 135, 337–353. Malone, D.R., Kao, C.M., Borden, R.C., 1993. Dissolution and biorestoration of nonaqueous phase hydrocarbons: model development and laboratory evaluation. Water Resour. Res. 29, 2203–2213. Nielson, K.K., Rogers, V.C., Gee, G.W., 1984. Diffusion of radon through soils: a pore distribution model. Soil Sci. Soc. Am. J. 48, 482–487. Robin, M.J.L., Gillham, R.W., Oscarson, D.W., 1987. Diffusion of strontium and chloride in compacted clay-based materials. Soil Sci. Soc. Am. J. 51, 1102–1108. Ryan, P.A., Cohen, Y., 1990. Diffusion of sorbed solutes in gas and liquid phases of low-moisture soils. Soil Sci. Soc. Am. J. 54, 341–346. Sahimi, M., Stauffer, D., 1991. Efficient simulation of flow and transport in porous media. Chem. Eng. Sci. 46, 2225–2233. Schaefer, C.E., Arands, R.R., van der Sloot, H.A., Kosson, D.S., 1995. Prediction and experimental validation of liquid-phase diffusion resistance in unsaturated soil. J. Contam. Hydrol. 20, 145–166. Schaefer, C.E., Arands, R.R., van der Sloot, H.A., Kosson, D.S., 1997. Modeling of the gaseous diffusion coefficient through unsaturated soil systems. J. Contam. Hydrol. 29, 1–21. Schaefer, C.E., Arands, R.R., Kosson, D.S., 1998. Modeling of the gaseous diffusion coefficient in the presence of NAPL. J. Contam. Hydrol. 33, 431–437. Sleep, B.E., Sykes, J.F., 1993. Compositional simulation of groundwater contamination by organic compounds: 1. Model development and verification. Water Resour. Res. 29, 1697–1708.
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Unger, D.R., Lam, T.T., Schaefer, C.E., Kosson, D.S., 1996. Predicting the effect of moisture on vapor-phase sorption of volatile organic compounds to soil. Environ. Sci. Technol. 30, 1081–1091. USEPA, 1995. Review of Mathematical Modeling for Evaluating Soil Vapor Extraction Systems. EPAr540rR-95r513. Zalidis, G.C., Annable, M.D., Wallace, R.B., Hayden, N.J., Voice, T.C., 1991. A laboratory method for studying the aqueous phase transport of dissolved constituents from residually held NAPL in unsaturated soil columns. J. Contam. Hydrol. 8, 143–156. Zhou, D., Blunt, M., 1997. Effect of spreading coefficient on the distribution of light non-aqueous phase liquid in the subsurface. J. Contam. Hydrol. 25, 1–19. Zhou, D., Blunt, M., Orr, F.M. Jr., 1997. Hydrocarbon drainage along corners of noncircular capillaries. J. Colloid Interface Sci. 187, 11–21.
Measurement of pore connectivity to describe diffusion through a nonaqueous phase in unsaturated soils Charles E. Schaefer 1, Rolf R. Arands, David S. Kosson
)
Chemical and Biochemical Engineering, Rutgers The State UniÕersity of New Jersey, 98 Brett Road, Piscataway, NJ 08854-8058, USA Received 3 July 1998; received in revised form 30 April 1999; accepted 18 May 1999
Abstract Contaminant diffusion through a nonaqueous phase liquid ŽNAPL. in unsaturated soils may often be an important transport mechanism. A diffusion tube technique was used to measure the effective diffusivity through NAPL in unsaturated soils as a function of soil type Žor pore size distribution., water saturation Žmilliliter waterrmilliliter void., and NAPL saturation Žmilliliter NAPLrmilliliter void.. Results indicated that the effective diffusivities depended on the ‘connectivity’ of the NAPL. This ‘connectivity’ increased with NAPL saturation, but was shown to have a more complex relation to the water saturation and pore size distribution of the soil. A series of mercury intrusion and extrusion experiments was also carried out to characterize the pore size distribution and pore ‘connectivity’ of the model soils. Using this characterization of the pore size distribution, along with a previously developed diffusional resistance model, the effective diffusivity was reasonably predicted for the soils and saturations examined in this study. q 1999 Published by Elsevier Science Ltd. All rights reserved. Keywords: NAPL; Porous media; Diffusion; Soils; Pore size distribution
1. Introduction Nonaqueous phase liquids ŽNAPLs. may migrate downwards due to gravity and eventually become immobilized as a heterogeneously dispersed phase in the soil )
Corresponding author. Fax: q1-7324452637; E-mail: [email protected] Currently at Stanford University, Department of Petroleum Engineering, 367 Panama St., Rm. 65, Stanford, CA 94305-2220. 1
0169-7722r99r$ - see front matter q 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S 0 1 6 9 - 7 7 2 2 Ž 9 9 . 0 0 0 5 3 - 4
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subsurface as a result of fuel spills, solvent spills, or other releases ŽCohen and Mercer, 1993.. The NAPL can be composed of several constituent hydrocarbon components, a fraction of which may be volatile and partially water-soluble organic contaminants ŽMalone et al., 1993.. Heavy hydrocarbon components of the NAPL may serve as a source of slow release for these diffusively mobile organic contaminants ŽBouchard et al., 1990; Guiguer, 1991; Zalidis et al., 1991.. If the NAPL exists in quantities large enough to form a continuous phase, a concentration gradient of constituent components may occur in the NAPL itself. This would result in diffusional transport of constituent organic contaminants through the NAPL. In low-permeability porous media, where the fluid velocity is very low, the primary transport mechanism can often be diffusion. Since the bulk NAPL often contains much higher concentrations of hydrophobic contaminants than either the aqueous or air phases, the bulk NAPL can serve as a significant diffusion pathway. There have been extensive studies on aqueous phase diffusion through unsaturated soils ŽRobin et al., 1987; Ryan and Cohen, 1990; Schaefer et al., 1995., as well as vapor phase diffusion through unsaturated soils ŽNielson et al., 1984; Collin and Rasmuson, 1988; Schaefer et al., 1997.. Vapor phase diffusion with NAPL present has also been recently studied ŽSchaefer et al., 1998.. However, examination of diffusion through a NAPL in unsaturated soils has not been examined. Models have incorporated solute diffusion through the oil phase, but the parameter Deff Žthe effective diffusivity through the bulk oil phase. was not investigated ŽKaluarachchi and Parker, 1990; Sleep and Sykes, 1993.. Several additional attempts have been made to model diffusion through a porous media using a detailed pore network. However, these attempts have all incorporated an empirical geometric factor or specific packing arrangement to account for pore connectivity ŽChatzis and Dullien, 1985; Sahimi and Stauffer, 1991.. Use of mercury intrusion data to describe and characterize connectivity in a porous catalyst has been suggested ŽHollewand and Gladden, 1992.. Based on their simulation results, broad pore size distributions lead to increases in tortuosity due to shielding of large pores by smaller pores. However, obtaining accurate pore distribution results via mercury intrusion analysis is difficult due to large pores being accessed via small pore openings ŽDullien, 1992.. Attempts have been made to correct mercury intrusion data to account for this phenomena, but once again, a specific correction for the unknown pore connectivity must be determined ŽConner and Horowitz, 1988.. Recent work by Schaefer et al. Ž1997; 1998. has incorporated mercury intrusion and extrusion analyses to determine pore connectivity at threshold penetration Ži.e., the pore diameter where mercury first penetrates the porous media.. This technique was able to predict the insular saturation of gas-filled voids, and led to development of a model to predict the gas phase effective diffusivity through unsaturated soils. Understanding and characterizing the porous network are essential to the prediction of the effective diffusivity through the NAPL in unsaturated soils. In this study, the effective diffusivity through the NAPL is examined. Experiments to measure the effective diffusivity through a model NAPL are carried out as a function of moisture content and NAPL content for three unsaturated soils. A procedure using mercury intrusion and extrusion is also described to characterize the porous media. Results are
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used to develop and validate a model to predict effective diffusivity through the NAPL as a function of these variables. Prediction of the effective diffusivity through NAPL will improve contaminant transport models, and will provide more accurate information on the costs, clean-up time scales, and technical feasibility of selected remediation techniques.
2. Model development The diffusional resistance through the NAPL is defined as follows: R s D 0rDeff ,
Ž 1.
where R s diffusional resistance wdimensionlessx D 0 s free diffusivity of solute through the NAPL wcm2rsx Deff s effective diffusivity through porous media wcm2rsx. D 0 was determined by the capillary method using a dodecane 14 C-radiolabeled tracer ŽCussler, 1984.. The value obtained was 1.1 = 10y5 cm2rs. Previous work describing the gas phase diffusional resistance through unsaturated soils may be extended to describe diffusional resistance through the NAPL ŽSchaefer et al., 1997, 1998.. Changes consist of redefining the interparticle and macropore regimes in terms of the NAPL: Rs
ž
1
1 q
R1
Ž R2 q R3 .
y1
/
Ž 2.
where R 1 s Ž ´ inter , NAPL2r3´ inter , NAPL 2r3 .
y1
R 2 s Ž volume fraction of ´ macro , d filled with NAPL. R 3 s Ž ´ macro , 2r3 d ´ inter , NAPL
2r3 y1
.
Ž 3. y4 r3
s1
Ž 4. Ž 5.
´ inter, NAPL s volume of NAPL in the interparticle pore regime per bed volume wmlrmlx s ´ total, NAPL y ´macro, d ´macro, d s volume of NAPL-filled macropores per bed volume at the largest pore diameter Ž d . that the NAPL fills wmlrmlx ´ total, NAPL s total NAPL volume per bed volume wmlrmlx. It is important to note that this model will apply to NAPLs which are nonspreading Žwill not spread between air and water down to molecular thickness. and will have a measurable residual saturation ŽZhou and Blunt, 1997.. The difficulty in Eqs. Ž2. – Ž5. lies in the determination of ´ macro, d , the NAPL-filled macropore porosity. This parameter is the volume of NAPL Ždivided by the total bed volume. which becomes discontinuous and immobilized in the porous medium. The
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Fig. 1. Mercury intrusion into a porous soil bed is used to estimate the relation between pore diameter and pore volume. Darkened areas represent NAPL regimes. Since water will preferentially fill small pores before NAPL in most soils, the amount of water in the soil will determine in what pore regime the NAPL will lie. Relative saturation is defined as milliliter liquid per milliliter total void volume. The pore size distribution curve shown here is for Quakertown soil Žporosity s 40%..
NAPL-filled macropore porosity is a function of the porous media geometry. Measurement of this macropore porosity allows for an estimate of pore connectivity. Unlike the previous gas phase diffusion model which measures the macropore volume only at threshold penetration Žinitial penetration of mercury into the soil bed., the macropore volume Ž ´macro, d . now must be determined at all pore diameters. A NAPL in a multi-phase porous media will occupy a specific pore regime. For a NAPL spill invading unsaturated soil initially at a low moisture content, the NAPL will reside in pores smaller than it would in soils initially at a higher moisture content ŽFig. 1. because of preferential wetting by the aqueous phase ŽFig. 2.. Similar pore models and fluid configurations to those shown in Fig. 2 have been proposed ŽZhou et al., 1997; Kawanishi et al., 1998.. The amount of water initially in the porous medium Žand thus the location of the NAPL in the porous medium. may determine the connectivity or continuity of the NAPL. It is necessary to determine the volume of pores which will remain filled with NAPL after the phase has become discontinuous at every pore diameter Žnot just at the threshold diameter.. In order to calculate this, the difference in mercury intrusion volume at every pore diameter between a primary and secondary intrusion must be determined. This may be represented by the log differential intrusion volume Žincremental volumerDlogŽdiam... at each pore diameter. Log differential intrusion volume is used to determine soil pore size distribution ŽFies, ` 1992.. The following equation, which employs mercury intrusion results of two sequential intrusions, is used to determine the macropore volume of the NAPL:
´macro , d s Ž ´macro , thresh . Ž dVintr 1 y dVintr 2 . r Ž dVthresh , 1 y dVthresh , 2 . ,
Ž 6.
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Fig. 2. Fluids in a pore corner. Assuming the porous medium is water wet, the water will reside in the smallest pores. NAPL will follow next, then air. The two simplified pores shown here contain the same NAPL content, but the pore on the right has a higher water saturation. This causes the NAPL to lie in a different location Žin larger diameter regimes..
where ´ macro, d s volume of NAPL-filled macropores per bed volume at the largest pore diameter Ž d . that the NAPL fills wmlrmlx ´ macro, thresh s macropore volume calculated by the difference in intrusion volumes at threshold penetration wmlrmlx dVintr 1 s log differential intrusion volume at the largest pore volume in which the NAPL resides determined from an initial mercury intrusion wmlrlog mmx dVintr 2 s log differential intrusion volume at the largest pore volume in which the NAPL resides determined from a second mercury intrusion wmlrlog mmx dVthresh, 1 s log differential intrusion volume at threshold penetration of mercury into the soil bed wmlrlog mmx dVthresh, 2 s log differential intrusion volume at threshold penetration of mercury into the soil bed for the secondary intrusion wmlrlog mmx. As mercury is extruded after an initial intrusion, mercury-filled pores which are only surrounded by smaller pores become detached and the mercury becomes entrapped in the porous media ŽLenormand et al., 1983.. Such pores can contain a fluid phase, but cannot by themselves provide a complete and continuous diffusive pathway across a porous medium. For the case of NAPL migrating downward through unsaturated soil, these pores Ž ´macro, d . would contain NAPL, but all pores which surround and connect them would contain either water or air. Eq. Ž6. allows the volume of pores surrounded only by smaller pores to be calculated at every soil pore diameter. At threshold penetration, a direct measurement of ´macro, thresh is attainable because all the pores with a diameter greater than that at the threshold diameter are macropores ŽSchaefer et al., 1997.. Direct measurement of the macropore porosity at pore diameter d Žwhere d - d thresh . may be determined by comparing the differential intrusion volumes. If dVintr 1 is calculated at the threshold penetration diameter, then dVintr 1 s dVthresh, 1. The same applies to dVintr 2 and dVthresh, 2 . Thus, the bracketed term in Eq. Ž6. has a value of 1. The difference dVintr 1 y dVintr 2 in
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Eq. Ž6. is the change in differential intrusion volume due to the presence of mercury in previously trapped soil pores. For example, if the difference dVintr 1 y dVintr 2 at soil pore diameter d is half of the value of dVthresh, 1 y dVthresh, 2 , then the macropore value at diameter d is half the volume of the macropore volume measured at threshold penetration Ž ´macro, thresh .. Some approximations are made to obtain an estimate of ´ macro, d . Hidden pores Žpores which are surrounded by smaller pores. are not directly considered in determining the actual pore size distribution. Pores which fill at a given capillary pressure of mercury may not be accessible until smaller pores, which fill at a higher capillary pressure, become mercury-filled. However, this pore volume is accounted for as the ‘trapped’ mercury volume in the secondary intrusion Ž dVintr 1 y dVintr 2 .. Assuming that the capillary pressures needed to gain access to these smaller pores are relatively close to the larger blocked pores Ži.e., only pores with slightly smaller diameters must be accessed to enter the ‘hidden pores’., hidden pores do not cause a significant error in the overall analysis. Large differences in the intrusion volumes between the primary and secondary intrusions will occur at pore diameters where the hidden pores exist and ´ macro, d will have large values. Eq. Ž6. measures the connectivity, not the precise topology, of the pores. Pore classes which are highly connected will remain continuous, and will have low values of ´macro, d . Pore classes which are less connected will have a larger value of ´macro, d . Thus, NAPL residing in the more highly connected pore classes will remain continuous at lower NAPL saturations. This will cause lower effective diffusivities. By making these simplifications and only considering the connectivity of pores, precise geometric or topological data are not needed to provide an analysis of diffusive transport in uniform porous media. However, these assumptions may limit the application of the described model to only a limited number of porous media applications. 3. Experimental design Three different soils were examined with varying physical and chemical characteristics ŽTable 1.. Soil analyses were carried out at Rutgers Soil Testing Laboratory ŽCook College, New Brunswick, NJ.. Diffusion tube experiments to measure Deff ŽEq. Ž1..
Table 1 Physical and chemical properties of selected soils
Sand Ž%. Silt Ž%. Clay Ž%. Texture Specific surface area ŽBET — N2 adsorption. Žm2 rg dry soil. Organic matter Ž%.
Quakertown
Pequest
Adelphia
20 60 20 Silt loam 9.75
44 44 12 Loam 15.4
72 14 14 Sandy loam 6.4
3.9
2.1
1.4
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were carried out on each soil. Dodecane served as the model NAPL, with 14 C-labeled dodecane used as the diffusing solute. Dodecane was chosen because of its low vapor pressure and water solubility. In addition, dodecane is a common component of gasoline and fuel oil ŽUSEPA, 1995. and will not spread as thin films on water ŽDemond and Lindner, 1993.. Several different dodecane and water relative saturations Žmilliliter liquidrmilliliter bed void volume. were examined. Dodecane relative saturations ŽRS. examined ranged from 0.02 to 0.60. Water relative saturations examined ranged from 0.10 to 0.90. Experiments were designed so as not to exceed 0.95 total Žwater and dodecane. relative saturation. This ensured that some air-filled pores were present in all experiments. The effective diffusivity through the NAPL, and subsequently, the diffusional resistance, was calculated as a function of soil type, moisture content, and NAPL content. A separate set of experiments was also carried out to determine the pore size distribution data used in Eq. Ž6.. A series of mercury intrusion and extrusion experiments on packed soil was performed to determine the porous media parameters in the calculation of ´macro, d . Thus, NAPL residing in the more highly connected pore classes. Eqs. Ž2. and Ž6. were used to calculate the diffusional resistance and compared with the diffusional resistance obtained from the experimental data. 4. Experimental methods 4.1. Mercury intrusion and extrusion Mercury intrusion and extrusion experiments to determine the pore size distribution and ´ macro, thresh were carried out as previously described ŽSchaefer et al., 1997.. Mercury intrusion has been shown to be a good method to predict the residual saturation for NAPL in porous media ŽDullien, 1992.. A Micromeritics ŽNorcross, GA. Pore Sizer 9320 porosimeter was used for the analysis. Soils were packed in the glass penetrometer cup to obtain porosities similar to those used in the diffusion experiments. In order to measure ´ macro, d . Thus, NAPL residing in the more highly connected pore classes, a full Žup to 30,000 psi. mercury intrusion experiment was carried out Žto obtain dVintr 1 ., immediately followed by an extrusion Žor, withdrawal of the mercury from the soil pores. and full intrusion Žto obtain dVintr 2 . on the same packed soil sample. The differential intrusion was calculated as follows ŽFies, ` 1992.: dVintr 1 s DVrD Ž log d . , Ž 7. where DV d
s incremental intrusion volume wmlx s pore diameter wmmx. The same calculation is used for dVintr 2 .
4.2. Dodecane diffusion tube experiments A modified method of the diffusion tube technique was used to examine diffusion of C-dodecane through unlabeled dodecane in unsaturated soils ŽSchaefer et al., 1995.. Two 20 g samples of oven-dried soil Ž1058C. were placed in beakers. Measured amounts 14
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of 0.005 M CaCl 2 aqueous solution and dodecane were added to each beaker. One beaker contained 14 C-labeled dodecane, while the other contained only unlabeled dodecane. Both beakers were mixed by hand until they appeared completely homogenized. The beakers were then covered to prevent any evaporation. While premixing of the liquids with the soil may not provide the exact pore scale fluid configuration obtained via gravity drainage Žwhich would occur in the field., the general fluid configuration Žas shown in Fig. 2. was still assumed. Experiments carried out in which uniform saturations were obtained by gravity drainage yielded similar results Žsimilar values of the measured effective diffusivity. to experiments in which the saturations were obtained by premixing of the fluids. Thus, premixing of the fluids with the soil provided a reasonable replication of the fluid configuration and connectivity obtained during gravity drainage. The unlabeled soil then was packed into the diffusion tube ŽFig. 3.. The diffusion tube consisted of a plastic 60 ml syringe Ži.d. of 2.65 cm. with both ends cut and resealed with rubber stoppers. The diffusion tube was weighed and the bed height measured to determine the mass and bed height of the unlabeled soil. The labeled soil was then packed into the tube, with the final mass and bed length recorded. Next, the tube was sealed and the 14 C-labeled dodecane was allowed to diffuse for a measured time interval. The diffusion tube was placed horizontally to minimize gravitational effects. To ensure that moisture loss was minimal during the diffusion period, the ends were wrapped in Parafilme. Diffusion times varied from 1 to 4 days, depending on the moisture content and dodecane content used. Diffusion times had to be long enough to allow formation of a
Fig. 3. Diffusion tube experimental method. Extruded soil slices were approximately 1 g each.
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diffusion profile, but short enough so that the profile do not reach the ends of the tube. The soil then was carefully extruded from the diffusion tube and sliced orthogonally to its axis in approximately 1 g slices. All slices were weighed to determine the exact mass. These slices then were placed into scintillation vials with 1.5 ml of Cytoscint w scintillation cocktail. A Beckman scintillation counter was used to measure the counts per minute Žcpm. of each sample. Counts were taken over a period of 3 min. Initial experiments using controls Ž14 C-dodecane with scintillation cocktail. and labeled soil slices indicated that the soil did not have any measurable quenching effects on the 14 C counting. In addition, a background sample was included with each experiment to ensure that there was no significant 14 C contamination of the soil prior to sample preparation. Also, no measurable sorption to the soil was observed. An effective diffusivity was calculated by regression of the experimental data. For diffusion times such that the diffusion profile did not reach the end of the diffusion tube, the following transport equation may be used ŽCussler, 1984.: C y Cavg Cinf y Cavg where C Cinf z t Deff Cavg Cyinf
s erf
z
ž( / 4 Deff t
,
Ž 8.
s measured cpm at position Z of tube wcpmrg dry soilx s high boundary cpm wcpmrg dry soilx s distance from interface wcmx s diffusion time wsx s effective diffusivity through the NAPL wcm2rsx s Ž Cinf q Cyinf .r2 s low boundary cpm Žequal to background. wcpmrg dry soilx.
In order to solve Eq. Ž6., the soil bed porosity Ž ´ . as well as the relative saturation of each liquid ŽRS i . had to be calculated. Mercury intrusion data were then used to estimate the location of the liquid in the soil pores ŽUnger et al., 1996.. The parameters were computed as follows:
´
s 1 y Ž rrrsolid . , U
RS i
s milliliter liquid ir Ž ´ V bed . ,
ViX
X s RSUi V Hg ,
Ž 9. Ž 10 . Ž 11 .
where ´ s bed porosity wmlrmlx r s soil bed bulk density Ždry basis. wmgrcm3 x rsolid s soil solid density determined by the pycnometer method ŽBlack, 1965. wmgrcm3 x RS i s relative saturation of liquid i in the soil bed Ž i s water or NAPL. wmlrmlx V bed s soil bed volume wcm3 x ViX s volume of liquid i wcm3rg dry soilx X VHg s total intrusion volume of mercury for a given soil sample wcm3rg dry soilx.
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Eq. Ž11. allowed the location of water and NAPL in the soil pores to be determined ŽFig. 1..
5. Results and discussion 5.1. Mercury intrusion and extrusion Mercury intrusion and extrusion results on the three soils are shown in Figs. 4–6. Table 2 lists the bed porosities and threshold macropore volumes Ž ´macro, thresh . obtained for each soil. Duplicate experiments carried out on Quakertown soil verified that the mercury intrusion results were reproducible. The difference between the initial and secondary intrusion was due to trapping of mercury in pores which were only accessible through smaller pores. For Quakertown and Pequest soils, which both exhibited broad pore size distributions, the percentage difference between the two intrusions was large near threshold penetration. Not until the pore diameter decreased by nearly one order of magnitude did the difference between initial and secondary intrusions decrease by a factor of 2. In Adelphia soil, which had a much narrower pore size distribution than the other soils, the percentage difference between the primary and secondary intrusion near threshold penetration was not nearly as large as for the other soils. There is little difference between primary and secondary intrusions for Adelphia soil between pore diameters of 30 and 8 mm. In contrast, Quakertown and Pequest soils show significant differences between primary and sec-
Fig. 4. Log differential intrusion vs. diameter for Quakertown soil. Threshold penetration is at approximately 11 mm. Also shown are the graphical calculations of dVthresh, 1 and 2 , dVintr 1 , and dVintr 2 for a soil water relative saturation of 20% and an NAPL relative saturation of 20%. The small discontinuity at 7 mm is due to transfer of the sample from a low-pressure to a high-pressure port on the analytical equipment.
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Fig. 5. Log differential intrusion vs. diameter for Pequest soil. Threshold penetration is at approximately 9 mm. The small discontinuity at 7 mm is due to transfer of the sample from a low-pressure to a high-pressure port on the analytical equipment.
ondary intrusion for up to two orders of magnitude less in pore diameter following threshold penetration.
Fig. 6. Log differential intrusion vs. diameter for Adelphia soil. Threshold penetration is at approximately 50 mm. The small discontinuity at 7 mm is due to transfer of the sample from a low-pressure to a high-pressure port on the analytical equipment.
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Table 2 Summary of mercury intrusion results
Soil bed porosity Ž%. Total intrusion volume Žmlrg. Pore diameter at threshold penetration Žmm. Ž ´ma cro, thresh . Žmlrml bed.
Quakertown
Pequest
Adelphia
39 0.31 11 0.036
38 0.21 13 0.038
36 0.23 55 0.017
In all three soils, little difference between initial and secondary intrusions was exhibited in pores less than 0.1 mm. This indicated that the value of ´ macro, d was small in this pore regime. Due to the pore topology, there was very little mercury which became trapped in these pores during the extrusion. Fig. 4 also shows the graphical calculation of the differential intrusion parameters used in Eq. Ž6.. Results are shown for a system containing 20% relative saturation of water and 20% relative saturation of NAPL ŽFig. 1.. Threshold penetration is at approximately 11 mm. The difference between the log differential intrusion volumes of the primary and secondary intrusions Ž dVthresh, 1 y dVthresh, 2 . may be measured at this point. In addition, the macropore volume at threshold penetration Ž ´ macro, thresh . may be measured at this pore diameter ŽSchaefer et al., 1997.. The difference in log differential intrusion volumes between dVintr 1 and dVintr 2 is also shown at 1.0 mm. This is the largest pore diameter in which the NAPL resides ŽFig. 1.. Fig. 7 shows the calculated value of ´macro, d as a function of pore diameter for Quakertown and Adelphia soils. This value is largest at the threshold diameter for each soil, and approaches a value close to
Fig. 7. ´ma cro, d as a function of pore diameter for Quakertown and Adelphia soils. The vertical line represents threshold penetration.
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Fig. 8. Diffusion profile obtained for Quakertown soil at 45% dodecane relative saturation and 33% water relative saturation. The dashed line is the regression ŽEq. Ž8.. to obtain the effective diffusivity Ž Deff ..
Fig. 9. Diffusional resistance through the NAPL as a function of water and NAPL relative saturation in Quakertown soil. Vertical lines represent the point where the NAPL becomes discontinuous and diffusional resistance becomes infinite. Model simulations are carried out at 10 and 80% RS of water. Symbols represent varying water relative saturations Ž10–30%, v; 40–60%, `; 70%, ^; 80%, '.. Soil bed porosity is approximately 50%.
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zero as the pore diameter approaches 0.01 mm. Larger values of ´ macro, d are shown for Quakertown soil than for Adelphia soil near threshold penetration. 5.2. Diffusion tube experiments A typical diffusion profile showing Eq. Ž8. regressed to the experimental data is shown in Fig. 8. Diffusion profiles were typical of those obtained in previous studies examining aqueous phase effective diffusivities ŽSchaefer et al., 1995.. Analysis of both the water and 14 C-dodecane saturations as a function of column length showed that neither a gradient of dodecane nor a gradient of water existed across the soil bed. Results of the diffusion tube experiments are shown for each soil in Figs. 9–11, along with the corresponding model simulations at the designated water relative saturations. The repeatability of the experimental data was verified by examining four data points on Quakertown soil at 36% dodecane relative saturation and 20% water relative saturation. Results gave an average diffusional resistance of 8.2 " 1.0 at a 95% confidence interval. Vertical lines in the figures represent the point at which the model predicts infinite resistance Žno diffusion. due to the NAPLs becoming discontinuous across the soil bed. Data points lying at approximately 10 4 represent experiments in which no diffusion was measured. Quakertown and Pequest soils exhibited a significant difference in diffusional resistance as a function of water content at low dodecane relative saturations. In contrast, Adelphia soil showed minimal effects of moisture content at low dodecane
Fig. 10. Diffusional resistance through the NAPL as a function of water and NAPL relative saturation in Pequest soil. Vertical lines represent the point where the NAPL becomes discontinuous and diffusional resistance becomes infinite. Model simulations are carried out at 10 and 80% RS of water. Symbols represent varying water relative saturations Ž10–30%, v; 40–60%, `; 70%, ^; 80%, '.. Soil bed porosity is approximately 45%.
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Fig. 11. Diffusional resistance through the NAPL as a function of water and NAPL relative saturation in Adelphia soil. Vertical lines represent the point where the NAPL becomes discontinuous and diffusional resistance becomes infinite. Model simulations are carried out at 10 and 80% RS of water. Symbols represent varying water relative saturations Ž10–30%, v; 40–60%, `; 70%, ^; 80%, '.. Soil bed porosity is approximately 39%.
relative saturations. The Adelphia data support the assumption that only diffusion through the NAPL is significant. If vapor phase diffusion was significant at low dodecane and water saturations, the 80% water relative saturation data would show diffusional resistances about two orders of magnitude greater than the 10–30% water relative saturation data ŽSchaefer et al., 1998.. This is not the case for Adelphia soil, even at low dodecane saturations. Thus, the differences in diffusional resistances as a function of water saturation observed in Quakertown and Pequest soils are due to NAPL phase diffusion, not vapor phase diffusion. The model ŽEq. Ž2.. was able to predict the trend in the data based on the mercury intrusion analysis and calculation of ´ macro, d Žwhich incorporates pore size distribution and pore connectivity. for all three soils. In Quakertown and Pequest soils, the difference between the various moisture contents was large near threshold penetration. This difference was most noticeable at the high moisture contents. High moisture contents forced dodecane to reside in large pores ŽFig. 1.. As shown in Figs. 4 and 5, the large pores showed the greatest differences between primary and secondary intrusions, and thus had the largest ´ macro, d . The large value of ´ macro, d indicated that these pores were very ‘unconnected’. For a given dodecane saturation, lower connectivity caused a higher diffusional resistance Žor, lower effective diffusivity.. This difference diminished in the small pores Ž- 0.1 mm., indicating a greater extent of pore ‘connectivity’.
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The difference between moisture contents at low dodecane relative saturations was much smaller in Adelphia soil. This is also explained by the mercury intrusion analysis. Fig. 5 shows a much smaller percentage difference between primary and secondary intrusions in the large pores than what is shown in Quakertown and Adelphia soils. Less mercury was entrapped in Adelphia soil pores during the extrusion process, which means that the NAPL in the Adelphia soil pores was not discontinuous and connected only by water or air-filled pores. This effect produced a smaller value of ´ macro, d ŽFig. 6.. Significant differences between primary and secondary intrusions do exist for Adelphia soil between approximately 7 and 1 mm. The value of ´ macro, d is larger in this regime. However, the larger value of ´ macro, d does not have a significant effect on the diffusional resistance because the value of ´ inter is much larger than ´macro, d at these pore diameters ŽEqs. Ž2. – Ž5... Thus, moisture content does not effect the diffusional resistance of Adelphia soil because Eq. Ž2. is unaffected by changes in ´ macro, d with pore diameter. Quakertown and Pequest soils exhibited a broad pore size distribution in pores with diameters greater than 8 mm. Adelphia soil had a much narrower pore size distribution in this regime. The broader pore size distributions of Quakertown and Pequest soils led to increased trapping of mercury in soil pores during the mercury extrusion experiments, and subsequently larger values of ´ macro, d in this regime. Adelphia had less trapping of mercury in soil pores, and subsequently, smaller values of ´ macro, d in the same pore regime. Higher values of ´ macro, d caused higher diffusional resistance values at high water contents Žwhich caused the NAPL to reside in pores close to the threshold penetration. in these soils. Thus, pore regimes with broad pore size distributions have higher diffusional resistances than pore regimes with a narrow pore size distribution. This conclusion is in agreement with previously performed simulations ŽHollewand and Gladden, 1992..
6. Conclusions The use of mercury intrusion and extrusion analyses may be used to describe the continuity or ‘connectivity’ of pores. In some porous media, pore continuity may be a measurable function of pore topology. Soil pore size distribution was shown to have a significant effect on diffusional transport. The presented model, which incorporates a measure of the trapped or ‘macropore’ volume Ž ´macro, d ., was able to reasonably describe diffusion through porous soil media as a function of dodecane and water relative saturation, as well as pore size distribution.
Acknowledgements The authors gratefully appreciate Vivian Guirguis, William Chen, and Stanley Karunditu for their assistance in carrying out the experiments. This work was supported in part by the U.S. Department of Defense, Office of Naval Research and Advanced
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