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a Dep. of Earth and Planetary Sciences, Univ. of Tennessee, Knoxville, TN 37996-1410
b 1463 Oxford Place, Cookeville, TN 38506
c Institute for Hydraulics and Rural Water Management, BOKU, Muthgasse 18, A-1190 Vienna, Austria
d Dep. of Agronomy and Soils, Auburn Univ., Auburn, AL 36849-5412
* Corresponding author (eperfect{at}utk.edu).
Received 19 January 2004.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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w(hc), close to saturation on an 18-cm-long by 10-cm-diameter undisturbed column of interbedded sandstone and clayshale saprolite. The Campbell empirical model was fitted to both w(hc) relations. The resulting best-fit parameters were 19.54 and 30.10 cm of H2O for the displacement capillary pressure head (h0) and 0.029 and 0.045 for the pore-size distribution index (1/b), for the air–water and Fluorinert–water data, respectively. Corresponding model parameters corrected for the hydrostatic fluid distribution within the column were 14.08 and 15.96 cm of H2O for h0, and 0.026 and 0.034 for 1/b. The correction procedure had a large effect on the Fluorinert–water w(hc) relation and relatively little impact on the air–water w(hc) relation. Parameters from the air–water relations were used to predict Fluorinert–water w(hc) relations using the expression: (h0)2 = (
2/1)(h0)1, where (h0)1, (h0)2 and 1, 2 are the capillary displacement pressure heads and interfacial tensions with water for air and Fluorinert, respectively. These analyses showed that direct measurements of the Fluorinert–water w(hc) relation need to be corrected for column height. The corrected Fluorinert–water w(hc) relation was accurately predicted (R2 
0.99) by both the fitted and corrected (h0)1 values. Thus, the error in prediction introduced by not considering column height or contact angle effects was relatively small. Our results show that scaled air–water w(hc) relations can be used to predict DNAPL intrusion into water-saturated saprolite at a physical point.
Abbreviations: DNAPL, dense nonaqueous phase liquid • SWSA, Solid Waste Storage Area
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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Because DNAPL migration and distribution are largely controlled by capillarity, any attempt to predict DNAPL behavior in a porous medium requires determination of the capillary pressure–saturation relationship, hereafter denoted by w(hc), where w is the volumetric content of the wetting fluid and hc is the capillary pressure head. The standard procedure for measuring w(hc) consists of introducing a nonwetting fluid at a known pressure into a porous medium, waiting for an equilibrium condition, and then determining the wetting phase saturation of the sample (Corey, 1994; Lenhard et al., 2002). This procedure produces one pressure–saturation data pair. Additional data pairs are produced by incrementing the nonwetting fluid pressure. The data pairs are then used to construct a static equilibrium drainage curve that describes the capillary behavior of the sample. Such curves are often parameterized using empirical expressions for the w(hc) relation such as the Brooks and Corey (1964) equation, the Campbell (1974) equation, and the van Genuchten (1980) equation.
The majority of pressure cell studies involving DNAPL–water systems have been performed on homogeneous porous media (e.g., Lenhard and Parker, 1987; Demond and Roberts, 1991). Relatively little is known about the capillary behavior of DNAPLs in heterogeneous porous media (Kueper et al., 1989; Hinsby et al., 1996; Illangasekare, 1998). The large column sizes required for adequate representation of such materials mean that traditional procedures for measuring the w(hc) relation may not be directly applicable.
If the densities of the nonwetting and wetting fluids are different, the capillary pressure will vary with height within the pressure cell (Dane et al., 1992; Liu and Dane, 1995a). Because pressure varies with height, one pressure value cannot represent pressure conditions everywhere within a tall column, but is only representative of one elevation in the sample. Because of this limitation, the standard procedure for measuring capillary behavior suggests that samples should be <2 cm tall. The variation of capillary pressure with height in a sample of this height is negligible in comparison to the relatively large pressures needed to drain the wetting fluid from small pores (Dane and Hopmans, 2002). Thus, little error is introduced by assuming that capillary pressure measured at one elevation within the sample is representative of values throughout the sample.
This height constraint presents a problem for samples containing fractures or macropores. Large undisturbed columns are often needed to obtain a representative sample of the heterogeneity that is present. In these cases, capillary pressure variations with height may be significant in relation to the lower capillary pressures at which fractures and macropores drain; hence, the height of the sample cannot be neglected.
Additionally, equilibrium saturations within tall columns may not be representative of the entire sample. In a homogeneous material, pores are uniformly distributed throughout the sample, and the displaced fluid comes from all parts of the sample. Thus, the saturation value at any equilibrium step applies to the whole volume of material. In a heterogeneous material, however, the elevation of the interface between immiscible phases within each fracture or macropore will be a function of the aperture size and pressure conditions at each equilibrium step. Thus, it cannot be assumed that the wetting fluid is displaced uniformly from the whole volume of the sample.
Liu and Dane (1995a) developed a computational procedure and a FORTRAN program (Liu and Dane, 1995b) to account for variations of hc and w with column height. Their approach corrects the parameters of the Brooks and Corey (1964) equation for the height of the experimental column given information on the pressure cell configuration and densities of the wetting and nonwetting fluids. Schroth et al. (1996) used a similar method to correct the parameters of the van Genuchten (1980) equation for column height. More recently, Jalbert and Dane (2001) proposed a correction procedure that does not require a model for the w(hc) relation; the method was validated against a simulated data set. Unfortunately, our experience suggests that it is highly sensitive to small fluctuations and does not work well with experimental data. To our knowledge, none of the above methods has been applied to correct the capillary behavior of a DNAPL in a tall column of heterogeneous material. The advantage of such an approach is that once the local parameters are obtained, then the w(hc) relation can be upscaled to any column height of interest.
It is possible to predict DNAPL entry into water saturated voids by scaling the air–water w(hc) relation (Leverett, 1941; Parker et al., 1987; Demond and Roberts, 1991). If the capillary displacement pressure head, h0, at which an immiscible phase first enters a porous medium is known, then the size of the drained void can be estimated by (Corey, 1994)
 | [1] |
is the pore radius in the case of capillary tube models or the space between two fracture surfaces in the case of parallel plate models, is the interfacial tension between the nonwetting and wetting fluid phases, 
is the contact angle between the nonwetting fluid and solid phases, 
w is the density of water, and g is strength of the gravitational field. It follows that the entry pressure at which another immiscible phase would enter the same material can be predicted from
 | [2] |
1 and 2 are the interfacial tensions of Fluids 1 and 2 with water, and 1 and 2 are the contact angles with the solid phase for Fluids 1 and 2.
Working with homogeneous porous media, Dumore and Scholls (1974) and Lenhard and Parker (1987) demonstrated that the w(hc) relation of one immiscible fluid can be scaled by the ratio of interfacial tensions to give a good approximation of relations for other immiscible fluids in the same material. This implies that does not change significantly and that for equivalent saturations, the capillary pressure relation between two different immiscible fluids in the same material can be approximated by
 | [3] |
Equation [3] suggests that the capillary behavior of a hazardous DNAPL such as trichloroethylene can be predicted from the measured capillary behavior of a nonhazardous immiscible fluid such as air. This approach does not appear to have been tested on a heterogeneous porous medium. Moreover, since Eq. [3] is based on h0, it is likely that not correcting for column height will have a significant impact on the accuracy of the scaling procedure in the case of such materials.
The objectives of this study were to (i) experimentally determine capillary pressure–saturation relations for DNAPL and air intrusion into an initially water-saturated heterogeneous porous medium, (ii) correct these relations for finite column height effects, (iii) evaluate the impact of this correction on the prediction of the DNAPL–water w(hc) relation from the air–water w(hc) relation, and (iv) compare pore-size distributions inferred from the capillary pressure–saturation relations with those observed in thin section.
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MATERIALS AND METHODS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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A column of saprolite (
10 cm in diameter) was excavated in the field using procedures developed by Jardine et al. (1993) and Cumbie (1997) to minimize sample disturbance. The column was carved so its long axis was oriented parallel to both bedding (which dipped at 69° to the southeast) and the in situ subsurface water flow direction. Bedding strike was N34E. The sample was excavated from a depth of 90 to 108 cm below ground surface.
In the laboratory, the saprolite sample was trimmed to fit inside an 18-cm-long, 10-cm-diameter PVC casing. Epoxy was then poured into the annulus to prevent fluid flow between the sample and casing, and end caps with influent and effluent connections were attached. Trimmings from the column were used to estimate bulk density (b) using the clod method (Grossman and Reinsch, 2002). Total porosity (
) was calculated from b assuming a particle density of 2.67 g cm–3 as described by Flint and Flint (2002).
After assembly the column was saturated with degassed 0.005 M CaCl2 solution. This solution (hereafter referred to as water) was used as the saturation fluid throughout the study. It was chosen to minimize dispersion of pedogenic clays within the sample. The saturation fluid was applied to the bottom of the column by raising the applied head in 1- to 2-cm increments for several days to minimize air entrapment. The saturated hydraulic conductivity (Ksat) was measured using the steady-state flow method after complete saturation was achieved (Dane et al., 2002).
Before conducting the capillary pressure–saturation experiments, the effluent end cap was temporarily removed and a water-saturated porous ceramic plate, with an air-entry value of 500 cm, was placed in direct contact with the sample and firmly attached with epoxy. After reassembly, the column was flushed with water. The completed pressure cell did not leak when tested at pressure heads of up to 290 cm.
Capillary Pressure–Saturation Measurements
Air was the first immiscible fluid introduced into the pressure cell. After that experiment the column was slowly rewetted with water to bring the sample back to complete saturation. The second immiscible fluid introduced was Fluorinert FC-40, a clear, colorless, multipurpose, nonhazardous perfluorocarbon (3M Specialty Materials, 1999). Fluorinert was employed as a surrogate DNAPL because of its physical similarity to common hazardous contaminants such as perchloroethene. Selected physical properties of the fluids used are given in Table 1.
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Because air is less dense than water, it was injected from the top of the column (i.e., zn = 17.9 cm). The effluent tubing was open to the atmosphere at an elevation of zw = 18.6 cm, so the pressure head of the wetting fluid at this elevation, Pw(zw), was constant at 0 cm (Fig. 1). During air injection, 84 pressure targets were set over a head range of 0 to 220 cm. The average target increment was 2 cm, and equilibrium times varied from a few minutes up to 21 h. The air injection experiment lasted 13 d.
Fluorinert was injected from the bottom of the column because it is denser than water (i.e., zn = 0 cm). The pressure cell was inverted so the flow direction was the same as during the air injection (Fig. 1). The effluent tubing was open to the atmosphere at an elevation of zw = 18.25 cm, so Pw(zw) was constant at 0 cm. A total of 153 pressure targets were set during the Fluorinert injection. The average target increment was 1.4 cm, and equilibrium times varied from a few minutes to 184 h. The Fluorinert injection experiment lasted 54 d.
Saprolite Petrography
After the capillary–pressure saturation experiments were completed, the column was dismantled, and hand specimens approximately 2.5 cm thick were sawed from both the inlet and outlet ends and allowed to completely air dry. These samples were first coated and impregnated with Hillquist (Fall City, WA) epoxy while heated on a hot plate, then cut (while dry) with a diamond trim saw into 5 by 8 cm diameter billets, and finally polished to 600 grit using wet–dry industrial sandpaper. The billets were glued to large-format commercial glass slides with Hillquist epoxy, and after 24 to 48 h were cut off (while dry) with a diamond trim saw to about 3- to 5-mm thickness. Thin sections were prepared (while dry) to standard optical thickness (30 µm) using progressively finer grades of sandpaper, as described in Mora et al. (1993). Quartz has a first-order gray interference color in thin sections that are prepared to this thickness. Micromorphological analysis was conducted using standard geological and soil petrographic techniques (Brewer, 1976; Pettijohn et al., 1987; FitzPatrick, 1993).
Data Analysis and Scaling
The capillary pressure head at the influent level, hc, was calculated using the expression (Liu and Dane, 1995a):
 | [4] |
w, was calculated from and the measured volume of water displaced from the sample during each pressure increment. For the Fluorinert–water experiment, w was calculated from and the measured volume of Fluorinert injected into the sample. The volume of Fluorinert injected was used in place of the volume of water displaced because a power interruption caused a partial loss of data for the volume of water displaced. Because Fluorinert is virtually incompressible and insoluble in water, the volume of Fluorinert injected was assumed to approximate the volume of water that was displaced. Capillary pressure-saturation relations were then constructed by plotting w vs. hc.
The w
relations were parameterized using the Campbell (1974) empirical model:
 | [5a] |
 | [5b] |
Equation [5] was fitted to the w vs. hc data using segmented nonlinear regression analysis based on the Newton iterative procedure (SAS Institute, 1997). The h0 and 1/b parameters were treated as fitted values, while was fixed to be the measured value. Convergence was achieved for both fits according to the SAS Institute (1997) default criterion. Best estimates of the Campbell (1974) parameters obtained in this manner are referred to hereafter as fitted values.
In the capillary pressure–saturation relations determined above, hc corresponds to a specific elevation, whereas w is an average value for the entire column. Multiphase fluids in heterogeneous porous media often produce nonuniform distributions of hc and w in a column of finite height (Dane et al., 1992). Thus, the fitted Campbell (1974) parameters may not represent the true behavior of the porous medium at a physical point. Liu and Dane (1995a) showed that the local w is related to the average w by
 | [6] |
Inserting Eq. [5] into Eq. [6] and performing the integration yields three analytical expressions relating w to w for the conditions: w = n, w < n, and w > n, where n is the density of the nonwetting fluid. For a given pressure cell geometry and fluid density pair, the unknown parameters in these expressions are the point estimates of h0 and 1/b. Thus, by fitting the analytical expressions for w to the measured capillary pressure–saturation relationship, best estimates of the local Campbell (1974) parameters can be obtained. We used TrueCell (Jalbert et al., 1999), a Windows interface based on the Liu and Dane (1995b) Fortran program, to perform this fitting procedure. Input values for the fluid densities and pressure cell characteristics used in TrueCell are given in Tables 1 and 2, respectively. The was fixed to be the measured value, and since TrueCell is based on the Brooks and Corey (1964) equation, residual saturation was set to zero. Best estimates of h0 and 1/b obtained in this manner are referred to hereafter as corrected values.
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2/1 = 0.72. |
RESULTS AND DISCUSSION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The remaining 10 to 20% of the saprolite consisted of horizontally bedded and bedding-perpendicular clayshale layers and lenses that varied from 0.05 to 2 mm in thickness. Depositional clayshale (i.e., originally deposited as part of the parent material) was a characteristic greenish-gray color and showed some evidence of ductile flow related to tectonic deformation of the bedrock. Pedogenic clays constituted 10 to 15% of the saprolite and appeared distinctly different from the depositional clayshale. They were reddish-colored in transmitted light, and exhibited a strong birefringence fabric in cross-polarized light.
A continuous distribution of void sizes was present, consisting of root pores, partially infilled fractures, and matrix pores in both the sandstone and clayshale beds. Each thin section contained between one and three fresh root pores (filled with undecayed root tissue) that ranged from 0.5 to 2 mm in diameter, plus partially to completely clay-filled old root pores. All of the root pores were circular and occurred in clay-rich seams, often bedding-parallel fractures infilled with pedogenic clay.
The fractures were geometrically complex and were partially to completely infilled with pedogenic clays. Bedding-parallel fractures typically followed primary depositional clay layers; these fractures ranged from 0.05 to 1.5 mm wide, as judged from the thickness of pedogenic clay infillings. Orthogonal bedding-perpendicular fractures typically cross-cut the sandstone beds at very high angles (60–90° with respect to bedding orientation). These fractures ranged from 0.05 to 1 mm wide, although most were <0.3 mm wide, as judged from the thickness of pedogenic clay infillings, and were spaced between 0.3 and 1.5 cm apart. The amount of open fracture porosity (i.e., unoccluded by pedogenic clay) was impossible to quantify from the thin sections, because nearly all of the clay infillings experienced desiccation-induced shrinkage to varying degrees. The sandstone beds contained relatively large matrix pores while those in the clayshale layers were much smaller. Variations in the amount of infilling of the sandstone matrix, fracture network, and old root pores probably contributed to the wide range of voids present.
The total porosity () of the column was 0.54 m3 m–3. This value is consistent with previous investigations of the saprolite at the SWSA 7 site, which report 0.39 
0.55 (Wilson et al., 1992; Jardine et al., 1993; Cumbie, 1997; Driese et al., 2001). Despite the high , the saturated hydraulic conductivity (Ksat) of the column was only 4.0 x 10–6 m s–1, probably due to partial blockage of pores and fractures by pedogenic clays. This value falls within the range of previously measured Ksat values for saprolite at this site, which are summarized in Fig. 2
of Driese et al. (2001).
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w relations were similar. Once the displacement pressure head was exceeded, the pore volume invaded increased gradually, confirming the wide range of pore sizes observed in the thin sections. There was no evidence of rapid drainage from the fracture network and root pores. There are at least two possible explanations for this behavior. First, it is possible that fracture drainage was impeded by the presence of the pedogenic clay infillings. Thus, drainage from matrix pores would be hard to distinguish from fracture drainage. Alternatively, because there was a distribution of capillary pressures with height within the column, fracture drainage could have occurred from parts of the sample even when other parts of the fracture network had ceased draining. The most likely explanation is some combination of both effects.
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= 36%), indicating a significant effect of column height on the estimated pore-size distribution index. The predicted curves from these fits are shown in Fig. 2 and 3. The Campbell (1974) model normally produces a sharp displacement entry pressure at a physical point. Thus, close to saturation there is some discrepancy between the observed and predicted values of w in both experiments (Fig. 2 and 3). Model predictions also deviated somewhat from the observed w values at hc > 175 cm in the air intrusion experiment (Fig. 2). The reasons for this discrepancy are unclear, but the fact that the Fluorinert intrusion data did not show a similar trend suggests it was not related to drainage of a distinct fracture or pore domain.
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= 24%), as they should be. Moreover, based on Eq. [1] with = 0 and w = 1 g cm–3, the corrected h0 values yielded more consistent estimates of the maximum fracture width () than the fitted values. Results for the fitted h0 values were 75 µm for air intrusion and 35 µm for Fluorinert intrusion, a discrepancy of = 53%. In contrast, the difference between the maximum fracture widths based on the corrected h0 values ( = 104 and 66 µm for the air–water and Fluorinert–water data sets, respectively) was only = 37%. The improved equivalencies obtained for the corrected 1/b and values as compared with the fitted values demonstrate the value of Liu and Dane's (1995a) computational procedure.
The mass fractal dimension (D), a physically based geometric measure of the range of void sizes present, was calculated from the corrected 1/b values using the expression (Giménez et al., 1997):
 | [7] |
For both the air–water and Fluorinert–water data sets, D 2.97. The fact that D is so close to three indicates a medium dominated by small pores and a slow drainage regime. We are unaware of any previous estimates of D for saprolite. However, comparison of our result with D values for different textured soils (Brakensiek and Rawls, 1992) suggests that the void-size distribution in this material is analogous to that of clay. Thus, the thin interbedded clayshale layers and pedogenic clay infillings appear to dominate the hydrologic properties of the saprolite even though it was derived mainly from sandstone.
Predicted capillary pressure–saturation relations based on the corrected Campbell (1974) model parameters in Table 3 are included in Fig. 2 and 3. Except for a slight decrease in the displacement capillary pressure head, the correction procedure had relatively little impact on the overall form of the air–water relation. In contrast, there were major changes to the form of the Fluorinert–water relation: the displacement pressure head was almost halved, and the slope of the drainage curve was reduced (Fig. 3).
To evaluate the potential for predicting DNAPL intrusion into water-saturated saprolite based on air intrusion data, scaled volumetric water contents were calculated from the Campbell (1974) air–water parameters using Eq. [3] and compared with those obtained from the Fluorinert–water experiment (Fig. 4 and 5)
. The scaling procedure was unable to reproduce the fitted Fluorinert–water relation; the predictions underestimated high values of w and overestimated lower values (Fig. 4). In contrast, both the fitted and corrected scaled air–water parameters resulted in approximately 1:1 regression lines (intercept = 0.05, slope = 0.90 and intercept = 0.08, slope = 0.84 for the fitted and corrected predictions, respectively) that explained approximately 99% of the total variation in the corrected Fluorinert–water relation (Fig. 5).
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Contact angles were not measured for the fluid pairs used in this study. Demond and Roberts (1991) showed that such measurements can improve scaling of capillary pressure–saturation relations in the case of homogeneous porous media. However, Fig. 5 suggests that the error introduced by assuming a = b = 0 in Eq. [2] was negligible for the more heterogeneous material used in this study.
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CONCLUSIONS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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The Campbell (1974) equation provided a good fit to the measured air–water and Fluorinert–water capillary pressure–saturation relations. Our results indicate that for DNAPL–water systems the parameters of this model are very sensitive to the hydrostatic fluid distribution within a tall column and require correction for this effect. Failure to do so can result in significant overestimation of the displacement pressure, which determines if a nonwetting fluid will enter a finer layer or not.
From a practical perspective our most significant result is the demonstration that air intrusion measurements can be successfully employed, in conjunction with Eq. [3], to predict DNAPL entry into a water-saturated heterogeneous porous medium at a physical point. Under the conditions of this study, the magnitude of the error introduced by not correcting the air–water parameters used in the scaling procedure for column height effects or differences in contact angle was relatively small.
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONCONCLUSIONSREFERENCES |
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for the different experiments.
