Use of the geotechnical centrifuge as a tool to ... - AGU Publications

WATER RESOURCES RESEARCH, VOL. 38, NO. 8, 1159, 10.1029/2001WR000660, 2002

Use of the geotechnical centrifuge as a tool to model dense nonaqueous phase liquid migration in fractures Laurent C. Levy, Patricia J. Culligan, and John T. Germaine Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA Received 4 May 2001; revised 22 March 2002; accepted 4 April 2002; published 28 August 2002.

[1] We describe a study undertaken to investigate the potential of the geotechnical centrifuge as an experimental tool to study dense nonaqueous phase liquid (DNAPL) behavior in fracture systems. Scaling laws are developed that link observations made in a centrifuge model of a fracture system to the full-scale problem ( prototype). Centrifuge experiments carried out in synthetic fractures, described by smooth-walled vertical capillary tubes, demonstrate for the first time that the geotechnical centrifuge can be used to model DNAPL transport in a simplified system provided that inertial forces are negligible in both the model and the prototype. Experiments also confirm, as predicted by Kueper and McWhorter [1991], that DNAPL invades a smooth-walled, vertical fracture when the DNAPL pool height at its entrance reaches its entry pressure. A simple mathematical model describing the displacement of the DNAPL-water interface is also presented. The predictions of this model and the experimental data are in good agreement with each other in the lower half of an invaded fracture. However, at the early stages of DNAPL invasion into the fracture, our observed DNAPL-water interface velocities are slower than predicted by the model. We attribute this to an apparent dependence of the INDEX TERMS: 1829 local capillary pressure on the interface displacement velocity. Hydrology: Groundwater hydrology; 1831 Hydrology: Groundwater quality; 1832 Hydrology: Groundwater transport; KEYWORDS: fracture flow, geotechnical centrifuge, DNAPL contamination, scale modeling

1. Introduction [2] In recent years, contamination by dense nonaqueous phase liquids (DNAPLs), such as chlorinated solvents, polychlorinated biphenyls (PCBs), some pesticides, and coal tars, has become an important environmental concern in many industrialized nations. DNAPLs are used in a wide variety of industries and are produced in large amounts. The most common, such as 1, 2-dichloroethane, 1,1,1-trichloroethane or trichloroethylene, are, for example, produced in the United States at a rate of several hundreds of millions of kilograms per year [Pankow et al., 1996]. Accidental spills, poor storage facilities, and inadequate disposal practices are factors that contribute to the release of these chemicals into the subsurface environment. The solubility of DNAPLs in water varies from a few milligrams to a few grams per liter, depending on the compound [Huling and Weaver, 1991]. However, no matter how low, DNAPL solubilities are often larger than regulated drinking water limits by several orders of magnitude [Cary et al., 1989]. Thus DNAPLs pose a serious groundwater contamination problem when present, even in small quantities, in the subsurface environment. [3] In the United States the National Research Council [1994] has identified remediation of DNAPL-contaminated, fractured hydrogeological systems as an extreme technical challenge and has stated that the cleanup of such sites to drinking water standards is currently unlikely. Yet many Copyright 2002 by the American Geophysical Union. 0043-1397/02/2001WR000660

public water supplies and private homes rely on fractured bedrock aquifers for their water. For this reason the scientific and engineering community is showing growing concern regarding the remediation of DNAPLs in fractured media [e.g., Wickramanayake and Hinchee, 1998]. [4] Upon release at the ground surface, DNAPL is able to migrate through the vadose zone and the sand aquifer, following a complex path that is dependent on the DNAPL self-weight and the heterogeneities of the aquifer and generally uncoupled from the direction of groundwater flow [Kueper et al., 1992]. At the base of the aquifer, DNAPL can form a pool on top of a fractured bedrock system. If infiltration into the bedrock takes place, the DNAPL distributes itself throughout the fracture system in the form of DNAPL fracture pools, disconnected ganglia, and a dissolved aqueous phase species [Clarke et al., 1994]. [5] Once DNAPL enters a fracture system, the probability of encountering the nonaqueous phase liquid in a borehole where a sparse distribution of migration pathways exists will be very low [Kueper et al., 1992]. Thus the site investigation of a contaminated fracture system will rarely delineate an accurate distribution of DNAPL within the fracture network. With little information on the probable distribution of DNAPL at contaminated sites, the planning of an effective remediation strategy is rendered virtually impossible. For this reason the development and/or validation of models for DNAPL invasion of fracture systems is a critical step toward improving DNAPL remediation performances in these aquifers. Because experimental data involving DNAPL transport in full-scale fracture systems are scarce, observations from experiments that simulate

34 - 1

34 - 2

LEVY ET AL.: GEOTECHNICAL CENTRIFUGE AS A MODELING TOOL

Figure 1. Principle of centrifuge modeling. Gravity effects in a prototype are identical to inertial effects in a centrifuge model [after Schofield, 1980]. DNAPL behavior in fracture networks are a necessary companion to the successful evolution of these models. [6] This paper describes an investigation into the potential of the geotechnical centrifuge as an experimental tool to study DNAPL behavior in fracture systems. During geotechnical centrifuge testing, a scale geologic model is spun at high speeds in a geotechnical centrifuge, thereby increasing the body force that is acting on the model. A major advantage of this technique with respect to the investigation of subsurface transport phenomena is its ability to simulate large-scale field problems at a reduced scale and under controlled laboratory conditions. Examples of subsurface phenomena that have been successfully studied using this method include combined heat and solute transport around a buried, heat generating waste source [Hensley and Savvidou, 1993], unstable fluid infiltration in unsaturated soil [Griffioen and Barry, 1999; Culligan et al., 2002], DNAPL mobility in coarse-grained media [Pantazidou et al., 2000], and gas migration under the remediation technology of in situ air-sparging [Marulanda et al., 2000]. [7] To ascertain the potential of the geotechnical centrifuge for modeling DNAPL behavior in a fractured medium, experiments were carried out in synthetic fractures described by smooth-walled, vertically oriented capillary tubes of either circular or planar cross section. The use of a simplified fracture system allowed trends between experiments and the centrifuge scaling laws to be established with an initial confidence that would not be possible in a more complex system incorporating, for example, variable fracture aperture and surface wettability. [8] In this paper we introduce the principle of geotechnical centrifuge modeling and present the centrifuge scaling laws for reduced-scale, physical modeling of DNAPL behavior in a vertically oriented fracture. Next, we describe a series of centrifuge experiments that were performed to investigate the validity of these laws and to examine DNAPL behavior in synthetic fractures of varying aperture sizes and geometry. We then compare our experimental observations with a mathematical model describing twophase flow in a smooth-walled fracture. Finally, we use the

results of our study to draw some qualitative conclusions about DNAPL behavior in a simplified fracture system.

2. The Geotechnical Centrifuge 2.1. Introduction [9] During geotechnical centrifuge testing, a container housing a soil or rock experiment is spun around a central axis at a high rotational speed, thereby increasing the body forces acting on the medium and fluids within the container. At any given rotational speed w, the container and its contents will experience a centrifugal acceleration rw2, where r is the radial distance of the center of gravity of the container from the central axis. In the centrifuge modeling community it is customary to describe this acceleration as the product of the Earth’s gravitational acceleration g and a scaling factor N, often termed the ‘‘g-level’’ [Taylor, 1995]. [10] The geotechnical centrifuge can be used to perform reduced-scale modeling of a full-scale problem, usually termed the ‘‘prototype.’’ The scale model of the prototype is constructed from in situ materials where all macroscopic dimensions z are reduced by a factor N. It is then subjected to a centrifugal acceleration equivalent to Ng (Figure 1). Under these conditions the product r g z, where r is an in situ material density, will be the same at homologous points in the model and the prototype. Thus geologic stresses and fluid pressures in the model and the prototype will also be identical at homologous points. Because the mechanical behavior of geologic materials is heavily dependent on the in situ stress levels and fluid pressures [Lambe and Whitman, 1969], geotechnical engineers have for decades exploited the centrifuge for reduced-scale modeling of soil-structure interaction problems [Fahey et al., 1990]. [11] The ability to generate homologous stress and pressure conditions in a reduced-scale model of a prototype also has advantages when it comes to the experimental investigation of subsurface flow [see Culligan-Hensley and Savvidou, 1995]. For example, the equivalence of geologic stress levels is often required to obtain equivalence in material density (i.e., particle packing) between a model and its prototype

34 - 3


Figure 2. Schematic of single, vertical rough-walled fracture. Dense nonaqueous phase liquid (DNAPL) pool height is H. Total fracture length is l. DNAPL has penetrated z below fracture entrance where the local fracture aperture is e(z). Fluid conditions at the fracture exit are hydrostatic. [Berner, 1980]. Because particle packing effects microscopic dimensions, such as pore throat radii, material density equivalence between a model and its prototype has to be achieved to ensure that parameters such as fluid hydraulic conductivity and tortuosity are properly replicated in the model. [12] In problems involving multiphase flow, similitude of the product r g z, where r is the density contrast between the fluid phases, can also be preserved between a scale centrifuge model and its prototype. Hence the body forces acting to drive multiphase flow can be correctly replicated at a reduced scale in the geotechnical centrifuge. Because of the equivalence of microscopic dimensions between a centrifuge model and its prototype, the capillary forces acting to retard multiphase flow are also properly replicated. Thus the centrifuge testing allows the possibility of conducting realistic studies of field transport behavior in a scale model under well-controlled conditions. Note that multiphase flow observed during reduced-scale laboratory experiments might not describe properly what happens at a larger scale, because the body forces driving multiphase flow are not correctly reproduced in a scale experiment carried out under the Earth’s gravity, g. [13] Because it is not possible to reproduce the full complexity of field-scale heterogeneity in a reduced-scale experiment, centrifuge modeling, as per any other experimental modeling technique, will not generate data that lead on to direct predictions at a field site. Nonetheless, the use of the geotechnical centrifuge to identify macroscopic trends and phenomena at a field site can provide an insight that might not be gathered using alternate experimental techniques. 2.2. Centrifuge Scaling Laws [14] Centrifuge scaling laws connect the behavior observed in a 1/N-scale experiment conducted at Ng to the

behavior in the equivalent prototype. Culligan-Hensley and Savvidou [1995] summarize centrifuge scaling laws for modeling miscible fluid transport in a porous medium. Scaling for immiscible fluid transport in a porous medium is presented by Culligan and Barry [1998]. [15] To develop, for the first time, centrifuge scaling laws for DNAPL migration in fractured media, we considered conditions in the single rough-walled fracture shown schematically in Figure 2 and used a method known as ‘‘partial inspectional analysis’’ [Shook et al., 1998]. In doing so, we analyzed only a simplified set of governing equations for the problem that were based on the following assumptions: (1) the rock matrix itself is impermeable to fluids; (2) the DNAPL is nonwetting with respect to water; (3) the fracture can be described by average hydraulic properties; (4) the variations in fracture shape are small compared to the average fracture shape, so that longitudinal flow can be assumed to be independent of the longitudinal coordinates; (5) transverse flow in the fracture is negligible in comparison with longitudinal flow; (6) the fracture is initially water-saturated under hydrostatic conditions; (7) there is no mixing at the interface between the DNAPL and water phases; (8) both fluid phases are incompressible; and (9) the effects of the Coriolis acceleration can be neglected in the centrifuge model. In addition, we assumed a vertically oriented fracture, although it can easily be shown that the analysis is applicable for a fracture of any dip. [16] We performed the inspectional analysis by examining the governing equations for DNAPL invasion into the fracture and for DNAPL-water displacement following invasion. The scaling laws derived from this analysis are summarized in Table 1. Note that the DNAPL and water fluid properties in the centrifuge model were taken to be those in the prototype. 2.2.1. DNAPL Invasion of Fracture [17] Referring to Figure 2, the pressure discontinuity Pe(z) at depth z that can be sustained between DNAPL and water is given by [Longino and Kueper, 1999] Pe ðzÞ ¼

2es cos qs ; eð zÞ

ð1Þ

where s is the interfacial tension between water and DNAPL, qs is the static contact angle measured through water, e(z) is the local fracture aperture, and e is a dimensionless parameter that is equal to 1 for fractures of approximately planar cross section and to 2 for fractures of approximately circular cross section. For z = 0 the pressure Pe(0) is the so-called ‘‘fracture entry pressure’’ [Kueper and Table 1. Centrifuge Scaling Relationships Parameter

Prototype-Model Ratioa

Equivalent gravitational acceleration, g Macroscopic lengths, H, Hi, l, z Microscopic length, e Fluid pressures, Pe, Pc Fluid properties, rf, mf, s Static contact angle, qs Fluid permeability, kf Fluid velocity, uf Time, t

1/N N 1 1 1 1 1 1/N N2

a

N is the scaling factor.

34 - 4


McWhorter, 1991]. More generally, we refer to Pe(z) as the ‘‘local entry pressure.’’ [18] For similitude (i.e., equality) of the local entry pressure between a centrifuge model and its prototype, the ratio of model entry pressure to prototype entry pressure must be equal to 1. Hence

[24] At the DNAPL-water interface the fluid velocities on both sides of the interface will be equal and given by

e zp p ½ P ðz Þ ½2es cos qs m =½eðzm Þm e m m ¼ 1 ¼ ¼ ; P e zp p ½2es cos qs p = e zp p ½eðzm Þm

where z is the depth of the DNAPL-water interface below the fracture entrance, as shown on Figure 2. [25] For DNAPL-water displacement in the model fracture to correctly mimic the process of DNAPL-water displacement in the prototype, all of the terms in equation (5) must scale by the same factor. If we incorporate equation (6) into equation (5), and examine the scaling of the second term in equation (5), we find that

ð2Þ

where the subscripts p and m denote prototype and model, respectively. The interfacial tension, the static contact angle, and the parameter e have been taken to be identical in both the model and the prototype. [19] Equation (2) requires that the local fracture aperture in the centrifuge model be similar at homologous points to that in the prototype. This relationship is comparable to the requirement that microscopic dimensions must remain invariant between a centrifuge model and its prototype during modeling of porous media flow, in order to ensure that effects of capillarity are properly duplicated in a centrifuge test [see Culligan and Barry, 1998]. [20] Referring to Figure 2 and examining the case z = 0, DNAPL will invade the fracture when the additional fluid pressure exerted by the presence of the DNAPL pool is equivalent to the fracture entry pressure. Hence the criterion for DNAPL invasion of the fracture is given by H Hi ¼

Pe ð0Þ ; r g

ð3Þ

where r is the density contrast between DNAPL and water. The height Hi is the minimum invasion pool height. [21] From equations (2) and (3), ðHi Þm gp 1 ¼ ¼ ; ðHi Þp gm N

ð4Þ

where it has been assumed that the density contrast is the same in the centrifuge model and the prototype. [22] From equation (4) we conclude that the DNAPL pool height at invasion will be N times smaller in the centrifuge model than the prototype. Thus Hi correctly scales as a macroscopic dimension of the problem. 2.2.2. DNAPL-Water Displacement [23] Following invasion into the fracture, we assume that a sharp interface separates the DNAPL and water phases. Taking a small element of fracture located between depth z and depth z + dz, the momentum conservation for each fluid phase, f, can be written as rf

mf @uf @Pf ¼ rf g @t @z kf uf

ð f ¼ nw; wÞ;

ð5Þ

where Pf is the average fluid pressure at a section of the fracture, uf is the average fluid velocity through a section of the fracture, t is time, kf is the permeability of the fracture to the fluid, and nw and w denote nonwetting and wetting, respectively.

unw ¼ uw ¼

dz ; dt

rf g g m ¼ m ¼ N : gp rf g

ð6Þ

ð7Þ

p

This suggests that we should have the same scaling factor N for each term in equation (5), i.e., @Pf =@zm @Pf =@zp

m ¼ N ;

ð8Þ

p

mf dzm kf dtm m mf dzp kf dtp p

¼ N;

ð9Þ

2 rf ddtz2m 2m m ¼ N ; d z rf dt2p

ð10Þ

p

p

where we have assumed that the permeability of the fracture to the fluid phases will be similar in the centrifuge model and the prototype. Equation (8) can be verified if zm ¼ ð1=N Þzp ;

ð11Þ

which describes the centrifuge modeling requirement for the scaling of macroscopic length. [26] Equation (9) describes the scaling required for correct modeling of viscous pressure effects during a centrifuge test. For equation (9) to be valid, tm ¼ 1=N 2 tp :

ð12Þ

Equation (10) describes the scaling required for correct modeling of inertial effects during a centrifuge test. For equation (10) to be valid, tm ¼ ð1=N Þtp :

ð13Þ

Thus a conflict in the scaling of time will arise between the modeling of viscous pressure effects and the modeling of inertial effects during a centrifuge test that mimics DNAPL behavior in a fracture. The existence of this conflict in porous media studies is well known by the centrifuge


modeling community [Schofield, 1980]. For most porous media transport problems it is assumed that the effects of inertia are negligible, in which case equation (5) corresponds to the generalized Darcy’s law [de Marsily, 1986]. Hence the timescale factor is presumed to be 1/N2, as in equation (12). We have adopted this approach here, although we examine the validity of this decision in section 4.2. Note that in cases where the effects of inertia cannot be ignored in the prototype problem, for example, during earthquake loading of a soil, correct scaling between the centrifuge model and prototype can be achieved by using fluids in the model that are N times more viscous than those in the prototype [Steedman and Zeng, 1995]. When this approach is adopted, the timescale factor will be N. [27] In the above derivations we have taken for granted that the technique of geotechnical centrifuge modeling will lead to fluid pressures that are identical at homologous points in the centrifuge model and prototype. In fact, this will only be the case if DNAPL migration patterns in the centrifuge model do, on average, mimic the migration patterns in the prototype. In a natural fracture, accelerated transport of DNAPL via channeling might occur through large aperture regions of the fracture, while slow transport, or even entrapment of DNAPL, might occur in the smaller aperture regions due the influence of capillary, buoyancy, and viscous forces [Morrow et al., 1988]. Thus a key requirement of the centrifuge modeling process has to be that the aperture field histogram in the centrifuge model is geometrically similar to that in the prototype. Therefore the use of natural fracture specimens to construct a centrifuge model requires that the full aperture histogram of a fracture be representable in a 1/N-scale length of the fracture. If this is not the case, DNAPL behavior in the scaled section of the fracture might not, on average, represent that in the full fracture itself. The use of artificial fractures that mimic field aperture distributions at a smaller length scale is an alternative to the use of natural fractures. However, for this approach to be adopted, the field aperture distributions themselves must be known a priori. [28] Reduced-scale experiments performed in the laboratory (i.e., at 1 g) to investigate DNAPL behavior in a full-scale field system are an alternative to centrifuge testing. For these experiments the DNAPL pool height must be equivalent to that in the full-scale problem (prototype) to ensure entry of DNAPL into the fracture system [e.g., Chown et al., 1997; O’Hara et al., 2000]. Therefore, unlike centrifuge experiments, reduced-scale 1g experiments cannot properly mimic the ratio between the DNAPL pool volume and the fracture system volume that would exist in the field. For experiments that are designed to investigate DNAPL invasion into a fracture under a constant DNAPL pool height, this is not a problem. However, if DNAPL behavior in a fracture system under a diminishing pool height is to be investigated, geotechnical centrifuge modeling is more advantageous than laboratory testing.

3. Experimental Methodology [29] To investigate whether the geotechnical centrifuge is a useful tool with which to model DNAPL behavior in rock fractures, we conducted a series of centrifuge experiments using the balanced-arm centrifuge at the Massachusetts

34 - 5

Institute of Technology (MIT). A detailed description of this machine is given by Ratnam et al. [1996]. [30] To reduce any uncertainty in the experimental results that might be due to system heterogeneity, experiments were carried out in synthetic fractures described by smoothwalled, glass capillary tubes of either circular or planar cross section. In order to model a range of fracture sizes, we used circular capillary tubes of apertures (i.e., internal diameters) 0.66, 1.33, 2.2, and 2.7 mm obtained from McMaster-Carr. In addition, we used rectangular capillary tubes of apertures 0.2, 0.5, and 0.6 mm, with respective widths 2, 5, and 6 mm, obtained from G. Finkenbeiner Inc. (Waltham, Massachusetts). Because the widths of the rectangular capillary tubes were 10 times larger than their apertures, it was possible to assume the tubes had a planar section with negligible end effects. We computed the average aperture of all tubes used in the test series by measuring the volume of water that each tube could store. In some cases it became necessary to correct the nominal dimension supplied by the manufacturer. [31] For the DNAPL we used 4-chlorotoluene (4-CT). This chemical was selected because of its low solubility in water, low toxicity, and high flash point. To enable visual tracking of the DNAPL infiltration in a model fracture, the 4-CT was dyed red with Sudan IV hydrophobic dye (Aldrich) at a concentration of 0.2 g/L. The interfacial tension of 4-CT with water was not available in the literature. Thus we measured the interfacial tension of dyed 4-CT with water using two different methods. The first method used the shape of a pendant drop of 4-CT in water [Ambwani and Fort, 1979]. The second used a capillary rise method proposed by Rashidnia et al. [1992]. Rather than directly measuring the interfacial tension, the latter method measures the product s cos qs, where qs is the static contact angle of the liquid-liquid system with glass. In contrast, the pendant drop method gives a direct estimate of s, and is independent of the contact angle. No significant difference was found between s measured using the pendant drop method and s cos qs using the capillary rise method, suggesting that the resting (often referred to as the ‘‘static’’) contact angle [Dussan V., 1979] was very close to 0. Thus perfect wetting of the water was assumed in all tests. The fluid properties of 4-CT are summarized in Table 2. [32] Figure 3 illustrates the experimental setup. Several capillary tubes, of length varying from 40 to 120 mm and graduated every 10 mm, were set up vertically in a glassfronted box. The box was initially filled with distilled water. The upper part of each capillary tube was connected to a

Table 2. Relevant Properties of 4-Chlorotoluene (4-CT) and Watera 4-CT Density, g/mL Interfacial tension, N/m Solubility in water, g/L Viscosity, Pa s a

b

1.070 0.032 ± 0.004 1.06 103 d 0.9 103 e

All properties at 20C. Values from Budavari [1996]. c Values from Munson et al. [1994]. d Values from Howard and Meylan [1997]. e Values from Yaws [1995]. b

Water 0.998c 1.0 103

c

34 - 6


Figure 3. Experimental setup at rest. glass-reservoir tube having an internal diameter approximately 10 times larger than the internal diameter of the capillary tube. This connection was made using chemically resistant Teflon tape. To reduce the sensitivity of the measurements to cleanliness, the capillary and reservoir tubes were cleaned by first letting them stand overnight in a cleaning solution; next, successively rinsing them with distilled water, acetone, methanol, and distilled water; and finally, oven-drying them at 120C for an hour. This cleaning method was also used to rinse the glassware used to perform the interfacial tension measurements. [33] To avoid trapping air in either the capillary tube or the reservoir tube, de-aerated water was used as the wetting fluid. In addition, the setup was allowed to equilibrate overnight to dissolve any air bubbles trapped in the system during the test preparation. Prior to each centrifuge test a fixed amount of 4-CT was introduced into each reservoir tube with a syringe. The height from the top of the capillary tube to the top of the DNAPL phase was measured with an optical caliper (Titan Tool Supply Co., Buffalo, New York). Typical pool heights ranged from 10 to 50 mm and were less than the DNAPL pool height required for invasion, so that infiltration into the capillary tube would not take place before testing in the centrifuge. [34] During each test the g level was progressively increased at a rate of approximately 0.02 g s1. Upon accelerating, the centrifuge container in which the experiment was set up rotated freely about a trunnion such that the overall component of the Earth’s gravity and the centrifugal acceleration remained normal to the centrifuge platform. This is shown in Figure 4. At each increasing g level the DNAPL pool of the equivalent prototype increased until it reached the pool height required for invasion, Hi, given by equation (3). At this point, invasion took place. The displacement of the DNAPL-water interface in the capillary tube was monitored with time using a miniature video

camera (Panasonic Industrial Camera Division) mounted on the centrifuge platform. Because of the large difference in internal diameter between the reservoir tube and the capillary tube, displacement in the capillary tube took place with virtually no change in the DNAPL pool height. The DNAPL travel time through the capillary tube was of the order of seconds. Thus the g level acting on the centrifuge model could also be assumed constant throughout the invasion process. [35] To investigate the validity of the centrifuge scaling laws that we developed for DNAPL migration in fractures, we compared scaled data from centrifuge tests conducted on circular cross-section capillary tubes of apertures 0.66 mm and 1.33 mm, with data from experiments that we conducted on the full-scale systems, i.e., the equivalent prototypes. Note that when the centrifuge scaling laws are correct, scaled data from a centrifuge test should match the data obtained from the equivalent prototype. [36] We performed two full-scale (prototype) experiments in the laboratory: one on a circular cross-section capillary tube of length 1201 mm and diameter 0.66 mm, and a second on a circular cross-section capillary tube of length 610 mm and diameter 1.33 mm. Again, the upper part of each capillary tube was connected to a glass reservoir tube. The 4-CT was introduced into each reservoir tube with a syringe. Care was taken to ensure that the first droplets of DNAPL would sit on top of the capillary tube. As the height of the DNAPL pool increased, the needle was raised and kept in contact with the DNAPL phase, in order to avoid trapping of water droplets between the DNAPL pool and the capillary tube. This ensured the formation of a continuous DNAPL phase. During this process the height from the top of the capillary tube to the top of the DNAPL phase was measured with the optical caliper to accurately determine the pool height. DNAPL was slowly added until the pool reached a critical height. At this point, invasion took place.


34 - 7

Figure 4. Experimental setup during rotation. The container swings up such that the centrifugal acceleration is normal to the platform. The pool height immediately before invasion started was recorded as Hi. Following invasion, the displacement of the DNAPL-water interface in the capillary tube was monitored with time using a video camera.

4. Results and Discussion 4.1. Investigation of Centrifuge Scaling Laws 4.1.1. Scaled Tests on 0.66-mm-Aperture Capillary Tubes [37] For the full-scale ( prototype) experiment performed on the 1201-mm-long, 0.66-mm-aperture capillary tube, we observed invasion of the system at a DNAPL pool height of 305 mm. For a fracture of circular cross section having an aperture of 0.66 mm, the 4-CT pool height required for invasion is Hi = 275 ± 34 mm, using equations (1) and (3) and the 4-CT properties listed in Table 2. Therefore our observed value of 305 mm falls within the expected range. We then reduced the scale of the problem by a factor N = 10. Two circular capillary tubes of the same aperture, but having a scaled length of 119 mm, were set up in the centrifuge strong box. The 4-CT was pooled in the reservoirs above the capillary tubes at heights of 26 and 27 mm. We then accelerated the scale model and observed invasion of the capillary tubes at 9.7 and 10.4 g, respectively. From Table 1 we see that the equivalent prototype pool heights at invasion were therefore approximately 251 and 282 mm, respectively, which fall within our expected range of Hi and are in reasonably good agreement with the observed prototype height. [38] The depth of the DNAPL-water interface, z, versus time for the two centrifuge experiments and the prototype is given in Figure 5. Again, as discussed in section 2.2.2, depth is scaled by a factor N, whereas time is scaled by a factor N 2. Therefore an interface displacement test taking place over a

time period of a few seconds in the centrifuge at g level N = 10 corresponds to a timescale of the order of a few hundred seconds once it is scaled. In general, we note very good agreement between the scaled centrifuge data and the prototype data, especially in the lower region of the fracture. 4.1.2. Scaled Tests on 1.33-mm-Aperture Capillary Tubes [39] Next, we performed a full-scale (prototype) test on the 610-mm-long, 1.33-mm-aperture capillary tube. For a fracture of circular cross section and aperture 1.33 mm, the DNAPL pool height at invasion is expected to be 136 ± 17 mm, again using 4-CT properties given in Table 2. During

Figure 5. Depth of prototype interface versus time for 0.66-mm-diameter-aperture capillary tubes.

34 - 8


negligible during DNAPL transport in a fracture system. To explore the validity of this assumption for transport in the fracture system shown in Figure 2, we examine the solution to a theoretical model for DNAPL behavior in the fracture, which is developed below. 4.2.1. Theoretical Model Development [43] Starting with equation (5), recalling that z(t) is the depth of the DNAPL-water interface below the fracture entrance, and integrating from 0 to z(t) for the DNAPL phase, we obtain Pnw ð zÞ Pnw ð0Þ ¼

rnw g rnw

dunw mnw unw z: dt knw

ð14Þ

Likewise, integrating equation (5) from z(t) to l for the water phase gives Pw ðl Þ Pw ð zÞ ¼

Figure 6. Depth of prototype interface versus time for 1.33-mm-diameter-aperture capillary tubes. this test, invasion of the capillary tube was observed at a DNAPL pool height of 130 mm, which falls within the expected range. For the model tests we adopted two scale factors, namely, N = 5 and N = 10. Two 1.33-mm-aperture capillary tubes, one 120 mm long and the other 60 mm long, were placed in the centrifuge strong box. The 4-CT was pooled above the 120-mm-long tube at a height of 30 mm, while a pool height of 15 mm was formed above the 60-mm-long tube. We accelerated the tubes and observed their invasion at 4.6 and 9.5 g, respectively. The equivalent prototype pool heights at invasion were therefore approximately 138 and 142 mm, respectively. These values also fall within the expected range of Hi and are in good agreement with the observed prototype invasion height. [40] The average depth of the DNAPL-water interface versus time for the scale model tests and the prototype is given in Figure 6. From this figure we note a very good agreement between the prototype data and the scale test performed on the 120-mm-long capillary tube. However, we note a poor agreement between the prototype data and the data from the scale test performed on the shorter, 60-mmlong capillary tube. [41] To investigate further the effect of the model fracture length on the validity of the centrifuge scaling laws, we performed another centrifuge test at a scale factor N = 15. A 1.33-mm-aperture capillary tube of length 40 mm was placed in the centrifuge strong box. A 4-CT pool height of 10 mm was added to the reservoir tube above the fracture. The tube was accelerated and we observed its invasion at 11.7 g, suggesting a prototype invasion pool height slightly lower than anticipated. The average depth of the DNAPLwater interface versus time for this test is also plotted in Figure 6. From the figure we observe that the disagreement between the scaled centrifuge test data and the prototype increased as the length of the model fracture decreased.

rw g rw

duw mw uw ðl zÞ: dt kw

[44] Equations (14) and (15) are modified versions of Darcy’s law that include an acceleration term. In many theoretical models for DNAPL behavior in fractures, this term is neglected [see e.g., Chown et al., 1997]. [45] The permeability of the fracture to a fluid is the product of the intrinsic permeability of the fracture, ki and the relative permeability krf, which will be a function of the fluid phase saturation in the fracture [Longino and Kueper, 1999]. In what follows, we assume complete displacement of water by DNAPL. Under these conditions, krf = 1 and knw = kw = ki. This assumption is consistent with our observation in the full-scale experiments that the volume reduction of DNAPL in the reservoir tube was equal to the total volume of invaded capillary tube, suggesting that water was completely drained as the DNAPL front progressed. [46] Adding equation (15) to (14) and rearranging terms leads to Pnw ð zÞ Pw ð zÞ ¼ ðrw l þ r zÞ

d2z 1 dz ðm l þ m zÞ þ r g z dt 2 ki w dt

þ rw g l þ Pnw ð0Þ Pw ðlÞ;

ð16Þ

where m = mnw mw is the viscosity contrast between the DNAPL and water. [47] The left-hand side of equation (16) is the local capillary pressure in the fracture, described by Longino and Kueper [1999] as Pc ð zÞ ¼ Pnw ð zÞ Pw ð zÞ ¼

2es cos qa ; eð zÞ

ð17Þ

where qa is the advancing contact angle. [48] In addition, we note that the fluid pressures at z = 0 and z = l are hydrostatic and are given by Pnw ð0Þ Pw ðl Þ ¼ r g H rw g l;

4.2. Effects of Inertia [42] An important assumption of the centrifuge scaling laws presented in Table 1 is that the effects of inertia are

ð15Þ

ð18Þ

where we have assumed the DNAPL pool height remains static at H.


34 - 9

[49] Substituting equations (17) and (18) into (16) and rearranging gives ðrw l þ r zÞ

d2z 1 dz þ ðm l þ mzÞ r g z ¼ r g H Pc ð zÞ: dt 2 ki w dt ð19Þ

[50] Equation (19) has to be solved with the initial conditions z = 0 at t = 0 and dz/dt = 0 at t = 0. In general, there is no simple analytical solution to equation (19). However, if r and m are small with respect to the density and viscosity of water, as was the case in the investigation reported here (see Table 2), and if the local capillary pressure Pc(z) is approximately constant with depth, then equation (19) can be written as a second-order differential equation with constant coefficients, namely, d2 z m dz r g 1 z¼ þ w ð r g H Pc Þ: dt 2 ki rw dt rw l rw l

ð20Þ

Equation (20) can be solved analytically. Upon solving, it can be shown that the solution of equation (20) reduces to the solution of the first-order differential equation mw dz g 1 r z ¼ ð r g H Pc Þ; l l ki dt

ð21Þ

r rw g ki2

1: m2w l

ð22Þ

provided that

[51] Because equation (21) is (20) with no second-order term, equation (22) gives the theoretical condition under which the effects of inertia can be neglected for the problem. Note that the left-hand side of equation (22) is a dimensionless number, which we will term a, that is equivalent to the Archimedes number (ratio of buoyant force to viscous force). Equation (22) is specific to flow in fractures and extends the scaling laws developed by Culligan and Barry [1998] for immiscible flow in porous media. [52] Inspecting equation (22), we observe that r rw g ki2 =m2w lm m am ¼ N 2: ¼ ap r rw g ki2 =m2w lp p

ð23Þ

[53] Hence the magnitude of the inertia forces associated with a system will be much higher in a centrifuge model test than the prototype. For the developed centrifuge scaling laws to be correct, inertia must be negligible in both the scale model test and the prototype. Note that theoretical models that neglect the acceleration term when describing fluid flow in fractures are also only applicable for systems where a 1 (again, see e.g., Chown et al. [1997]). 4.2.2. Inertial Effects During Centrifuge Tests [54] For smooth-walled capillary tubes, ki ¼ e2 =d;

ð24Þ

where d = 32 for circular cross-section tubes, while d = 12 for planar tubes [de Marsily, 1986]. For the scaled tests on the circular cross-section, 0.66-mm-aperture tubes, the value of a for the prototype is given by ap = 1.1 104. Thus

Figure 7. Prototype DNAPL pool height versus fracture aperture from selected experimental results. am = 1.1 102 for the two centrifuge model tests conducted at N = 10. In this case the magnitude of the inertia forces remains small in both the centrifuge model and the prototype. The good agreement between the scaled centrifuge test data and the prototype data (Figure 5) indicates that the scaling laws given in Table 2 are, as assumed, valid under these conditions. [55] For the scaled tests on the circular cross-section, 1.33-mm-aperture tubes, we have ap = 3.5 103, giving rise to am = 8.75 102 for N = 5, am = 0.35 for N = 10, and am = 0.79 for N = 15. In this case the effects of inertia can only be neglected in the prototype and the scale test at N = 5. From Figure 6 we note that the scaling laws do appear valid for the test conducted on the longer capillary tube. However, the scaling laws are clearly not valid for the tests conducted using the shorter capillary tubes. Thus there is a limit to the centrifuge scaling factor N that can be used to model DNAPL transport in a fracture system. That this limit exists does not negate the utility of centrifuge testing in this area. Rather, it sets the bounds for the range of scale factors that can be used in the modeling of a specific prototype. For example, problems will not arise with modeling DNAPL behavior in a fracture of 2 m in length with an average planar aperture of 0.2 mm until N exceeds 160. Alternatively, for the same fracture aperture and a fracture length of 0.2 m, N cannot exceed 50. 4.3. Use of Centrifuge to Model DNAPL Behavior in Fractures [56] Because our investigations suggested that the geotechnical centrifuge could be used under certain conditions to model DNAPL behavior in a simplified fracture system, we performed approximately 50 model tests to investigate DNAPL behavior in fractures of both circular and planar cross section. In all tests, a 1 in the centrifuge model and the prototype. [57] Figure 7 presents the prototype DNAPL pool height at invasion versus the average fracture aperture predicted

34 - 10


intrinsic permeability ki. It represents the equivalent conductivity of a fluid of density r, having the viscosity of water and flowing in a fracture of permeability ki. [61] For small z, in other words, at early times, H cannot be neglected and is expected to affect the velocity of the interface, as shown by equation (25). Once the interface has invaded the simulated fracture to depth where z H, equation (25) is reduced to dz z K ; dt l

Figure 8. Prototype DNAPL-water interface displacement versus time. from a selection of our centrifuge test data. Our data have been compared with the theoretical relationship between Hi and e given by equations (1) and (3). From this comparison, we note that the data from our physical model confirm, as predicted by Kueper and McWhorter [1991], that DNAPL will invade a fracture system when the DNAPL pool height at the fracture entrance reaches the fracture entry pressure. [58] The depth of the DNAPL-water interface versus time from a selection of our centrifuge test data is given in Figure 8. For the prototype and the centrifuge model tests reported here, the height of the DNAPL pool remained at H Hi throughout the DNAPL invasion of the fracture. However, if the pool height was exactly Hi, the pool would be in a condition of critical equilibrium and invasion would not take place. Hence invasion is the result of an infinitesimal increment in pool height H. This increment is directly related to the rate of increase in g level during the centrifuge test. On the basis of this rate and the timescale of the test, we estimate that H = 0.01 Hi for our experiments. [59] Under drainage conditions, as investigated here, the advancing contact angle qa (see equation (17)) is less than the static contact angle qs [Dussan V., 1979]. Given that we have perfect wetting in our system, qa cannot be expected to decrease any further and is therefore assumed a constant equal to 0. For qa = qs = 0, equation (21) is reduced to dz z þ H ¼ K ; dt l

ð25Þ

H ¼ Hi þ H;

ð26Þ

K ¼ r g ki =mw :

ð27Þ

where

[60] The parameter K has dimensions of a velocity and is similar to the hydraulic conductivity of a system of

ð28Þ

meaning that the velocity of the DNAPL-water interface is proportional to the relative position of the interface with respect to the end of the tube, z/l. Equation (28) also shows that the exit velocity, i.e., the velocity when z = l, is independent of the length of the tube and equal to K. [62] A comparison between equation (25) and our experimental data is also given in Figure 8. As can be seen, agreement between equation (25) and the experimental data is good asymptotically, i.e., beyond a certain DNAPL invasion depth. In particular, the observed prototype exit velocity, which is given by the slope of the line tangent to the displacement profile at the exit point, is correctly predicted by equation (27). However, at the early stages of the DNAPL invasion, Figure 8 indicates that the observed DNAPL-water displacement velocity is less than that predicted by equation (25). This disagreement cannot be attributed to an overestimation of the value of H, because we still note a difference between equation (25) and our experimental data when z H. In other words, the length scale over which we observe disagreement is greater than the length over which H is important. That overestimation of H is not the cause of disagreement between equation (25), and our experimental data suggests that the capillary pressure term Pc (see equation (21)) might be increasing, rather than remaining constant, during the early stages of the DNAPL invasion process. An increase in Pc at this stage of the invasion would act to reverse the sign of H, which in turn would reduce the interface velocity given by equation (25). [63] Comparable deviations between experimental results and theoretical predictions of the displacement of water by nonwetting fluids have been reported before. A number of studies have examined the forced displacement of a wetting fluid by a nonwetting fluid in horizontal capillary tubes, i.e., where the interface velocity is controlled and the capillary pressure is measured [Blake et al., 1967; Blake and Haynes, 1969; Calvo et al., 1991]. These studies have concluded that the capillary pressure is generally not constant with interface velocity, at least for small velocities. Instead, the capillary pressure appears to increase with the interface velocity. [64] As pointed out by Blake and Ruschak [1997], the actual physics of dynamic wetting are still not understood. In the literature, observed capillary pressure dependence upon velocity has been attributed to one of two mechanisms. Blake [1993] claims that this dependence can be explained by a molecular rate process resulting from a disturbance of the thermodynamic equilibrium. Conversely, Cox [1986] claims that dependence of the capillary pressure on velocity arises from hydrodynamic shaping of the meniscus at the wettingnon wetting fluid interface. In either case, a unified quantitative relationship between Pc and dz/dt


during nonwetting displacement has not yet been provided in the literature. [65] At present, our observation of velocities slower than predicted by equation (25) at the initial stages of invasion, when capillary effects are important, cannot be quantitatively explained. However, it is consistent with previous studies, as cited above. A modification of equation (21) to include a dependence of Pc on dz/dt is needed to obtain agreement between our experimental data and the theoretical model. However, defining the exact relationship between Pc and dz/dt would require more detailed experimentation than described here.

5. Conclusions [66] This paper describes a study that was undertaken to investigate the potential of the geotechnical centrifuge as an experimental tool to study DNAPL behavior in fracture systems. Scaling laws linking observations made in a centrifuge model to the full-scale field problem ( prototype) demonstrated that the geotechnical centrifuge might be used to model DNAPL invasion and transport in a fracture, provided that the effects of inertia are negligible in both the centrifuge model and the prototype. Experiments carried out in synthetic fractures described by smooth-walled, glass capillary tubes of either circular or planar cross section were used to validate the centrifuge scaling laws. [67] A series of centrifuge experiments used to investigate DNAPL behavior in the idealized fractures confirmed that DNAPL will invade a smooth-walled, vertical fracture when the DNAPL pool height at the fracture entrance reaches the fracture entry pressure. Furthermore, it was shown that the DNAPL-water interface velocity in a smooth-walled fracture can be predicted in the lower half of the fracture by a model that was developed as part of this work. Both the model and our scaled centrifuge experiments show that the exit velocity of DNAPL in a smooth-walled vertical fracture is equal to the equivalent conductivity in the fracture of a fluid having the viscosity of water and a density equal to the density contrast between DNAPL and water. At the early stages of DNAPL invasion into a smooth-walled fracture, our experimental observations suggest that the DNAPL-water displacement is slower than anticipated. Such observations have been reported in prior studies investigating liquid-fluid displacements in capillary tubes and can be attributed to wetting dynamics processes. These effects are likely to be exaggerated in a real fracture system and will thus complicate the modeling of DNAPL migration in fracture systems if accuracy is required at the early stages of the DNAPL invasion process. [68] Although our experiments to date have only investigated DNAPL behavior in a simplified fracture system, their results still have utility in the development of models for predicting DNAPL behavior and remediation in complex fracture networks. Acquiring accurate descriptions of individual fracture properties, such as mean aperture size, aperture distribution, and fluid wettability, at the scale required by most fracture flow models still remains a challenge. Thus the coupling of a fracture system model [e.g., Wu and Pollard, 1992; Ivanova, 1998] that describes the orientation and distribution of a fracture network at a site with a fracture flow model that assumes smooth-walled fractures of constant average aperture is an alternative that

34 - 11

can practically be used at waste sites where information from outcrops, boreholes, and drilling cores can be used to infer average fracture properties. A combination of centrifuge experiments and theoretical development/validation, as presented in this paper, is one approach that can be used to advance the field in this direction. [69] Acknowledgments. The work presented here was supported by the Northeastern Hazardous Substance Research Center, an Environmental Protection Agency research center for federal regions 1 and 2. Funding for this research was also provided by the National Science Foundation Career grant CMS-9875883. The authors gratefully acknowledge the value of discussions with C. C. Mei and F.-J. Ulm of the MIT Department of Civil and Environmental Engineering in the preparation of this manuscript. In addition, we would like to acknowledge Stephen Rudolph for his help in conducting the centrifuge experiments and Kortney Adams for performing the tests using the planar fractures.

References Ambwani, D. S., and T. Fort Jr., Pendant drop technique for measuring liquid boundary tensions, in Surface and Colloid Science, vol. 11, edited by R. J. Good and R. R. Stromberg, pp. 93 – 119, Plenum, New York, 1979. Berner, R. A., Early Diagenesis: A Theoretical Approach, 241 pp., Princeton Univ. Press, Princeton, N. J., 1980. Blake, T. D., Dynamic contact angles and wetting kinetics, in Wettability, edited by J. C. Berg, pp. 251 – 309, Marcel Dekker, New York, 1993. Blake, T. D., and J. M. Haynes, Kinetics of liquid/liquid displacement, J. Colloid Interface Sci., 30(3), 421 – 423, 1969. Blake, T. D., and K. J. Ruschak, Wetting: Static and dynamic contact lines, in Liquid Film Coating, edited by S. F. Kistler and P. M. Schweizer, pp. 63 – 97, Chapman and Hall, New York, 1997. Blake, T. D., D. H. Everett, and J. M. Haynes, Some basic considerations concerning the kinetics of wetting processes in capillary systems, in Wetting, S.C.I. Monogr. Ser., vol. 25, pp. 164 – 173, Soc. of Chem. Ind., London, 1967. Budavari, S., (Ed.), The Merck Index: An Encyclopedia of Chemicals, Drugs, and Biologicals, 12th ed., Merck, Whitehouse Station, N. J., 1996. Calvo, A., I. Paterson, R. Chertcoff, M. Rosen, and J. P. Hulin, Dynamic capillary pressure variations in diphasic flows through glass capillaries, J. Colloid Interface Sci., 141(2), 384 – 394, 1991. Cary, J. W., C. S. Simmons, and J. F. McBride, Predicting oil infiltration and redistribution in unsaturated soils, Soil Sci. Soc. Am. J., 53(2), 335 – 342, 1989. Chown, J. C., B. H. Kueper, and D. B. McWhorter, The use of upward hydraulic gradients to arrest downward DNAPL migration in rock fractures, Ground Water, 35(3), 483 – 491, 1997. Clarke, J. H., D. D. Reible, and R. D. Mutch, Contaminant transport and behavior in the subsurface, in Hazardous Waste Site Soil Remediation, edited by D. J. Wilson and A. N. Clarke, pp. 1 – 49, Marcel Dekker, New York, 1994. Cox, R. G., The dynamics of the spreading of liquids on a solid surface, part 1, Viscous flow, J. Fluid Mech., 168, 169 – 194, 1986. Culligan, P. J., K. Banno, D. A. Barry, T. S. Steenhuis, and J.-Y. Parlange, Preferential flow of a nonaqueous phase liquid in dry sand, J. Geotech. Geoenviron. Eng., 128(4), 327 – 337, 2002. Culligan, P. J., and D. A. Barry, Similitude requirements for modelling NAPL movement with a geotechnical centrifuge, Proc. Inst. Civ. Eng. Geotech. Eng., 131(3), 180 – 186, 1998. Culligan-Hensley, P. J., and C. Savvidou, Environmental geomechanics and transport processes, in Geotechnical Centrifuge Technology, edited by R. N. Taylor, pp. 196 – 263, Blackie Acad. and Prof., New York, 1995. de Marsily, G., Quantitative Hydrogeology, 440 pp., Academic, San Diego, Calif., 1986. Dussan V., E. B., On the spreading of liquids on solid surfaces: Static and dynamic contact lines, Annu. Rev. Fluid Mech., 11, 371 – 400, 1979. Fahey, M., I. Finnie, P. J. Hensley, R. J. Jewell, M. F. Randolph, D. P. Stewart, K. J. L. Stone, S. H. Toh, and C. S. Windsor, Geotechnical centrifuge modelling at the University of Western Australia, Aust. Geomech., 19, 33 – 49, 1990. Griffioen, J. W., and D. A. Barry, Centrifuge modeling of unstable infiltration and solute transport, J. Geotech. Geoenviron. Eng., 125(7), 556 – 565, 1999.

34 - 12


Hensley, P. J., and C. Savvidou, Modelling coupled heat and contaminant transport in groundwater, Int. J. Numer. Anal. Methods Geomech., 17(7), 493 – 527, 1993. Howard, P. H., and W. M. Meylan (Eds.), Handbook of Physical Properties of Organic Chemicals, Lewis, Boca Raton, Fla., 1997. Huling, S. G., and J. W. Weaver, Dense nonaqueous phase liquids, Rep. EPA/540/4-91/002, Environ. Prot. Agency, Washington, D. C., 1991. Ivanova, V. M., Geologic and stochastic modeling of fracture systems in rocks, Ph.D. thesis, Mass. Inst. of Technol., Cambridge, 1998. Kueper, B. H., and D. B. McWhorter, The behavior of dense, nonaqueous phase liquids in fractured clay and rock, Ground Water, 29(5), 716 – 728, 1991. Kueper, B. H., C. S. Haase, and H. L. King, Leakage of dense, nonaqueous phase liquids from waste impoundments constructed in fractured rock and clay: Theory and case history, Can. Geotech. J., 29(2), 234 – 244, 1992. Lambe, T. W., and R. V. Whitman, Soil Mechanics, 553 pp., John Wiley, New York, 1969. Longino, B. L., and B. H. Kueper, Nonwetting phase retention and mobilization in rock fractures, Water Resour. Res., 35(7), 2085 – 2093, 1999. Marulanda, C., P. J. Culligan, and J. T. Germaine, Centrifuge modeling of air sparging: A study of air flow through saturated porous media, J. Hazard. Mater., 72(2 – 3), 179 – 215, 2000. Morrow, N. R., I. Chatzis, and J. J. Taber, Entrapment and mobilization of residual oil in bead packs, SPE Reservoir Eng., 3(3), 927 – 934, 1988. Munson, B. R., D. F. Young, and T. H. Okiishi, Fundamentals of Fluid Mechanics, 2nd ed., 893 pp., John Wiley, New York, 1994. National Research Council, Alternatives for Ground Water Cleanup, 315 pp., Natl. Acad. Press, Washington, D. C., 1994. O’Hara, S. K., B. L. Parker, P. R. Jorgensen, and J. A. Cherry, Trichloroethene DNAPL flow and mass distribution in naturally fractured clay: Evidence of aperture variability, Water Resour. Res., 36(1), 135 – 147, 2000. Pankow, J. F., S. Feenstra, J. A. Cherry, and M. C. Ryan, Dense chlorinated solvents in groundwater: Background and history of the problem, in Dense Chlorinated Solvents and Other DNAPLs in Groundwater, edited by J. F. Pankow and J. A. Cherry, pp. 1 – 52, Waterloo, Portland, Oreg., 1996.

Pantazidou, M., Z. S. Abu-Hassanein, and M. F. Riemer, Centrifuge study of DNAPL transport in granular media, J. Geotech. Geoenviron. Eng., 126(2), 105 – 115, 2000. Rashidnia, N., R. Balasubramaniam, and D. Del Signore, Interfacial tension measurement of immiscible liquids using a capillary tube, Contract. Rep. CR-189133, NASA, Washington, D. C., 1992. Ratnam, S., P. J. Culligan-Hensley, and J. T. Germaine, Modeling the behavior of LNAPLs under hydraulic flushing, in Non-Aqueous Phase Liquids (NAPLs) in Subsurface Environment: Assessment and Remediation: Proceedings of the Specialty Conference Held in Conjunction With the ASCE National Convention, Washington, D. C., November 12 – 14, 1996, edited by L. N. Reddi, pp. 595 – 606, Am. Soc. of Civ. Eng., New York, 1996. Schofield, A. N., Cambridge geotechnical centrifuge operations, Ge´otechnique, 30(3), 227 – 268, 1980. Shook, G. M., G. A. Pope, and K. Kostarelos, Prediction and minimization of vertical migration of DNAPLS using surfactant enhanced aquifer remediation at neutral buoyancy, J. Contam. Hydrol., 34(4), 363 – 382, 1998. Steedman, R. S., and X. Zeng, Dynamics, in Geotechnical Centrifuge Technology, edited by R. N. Taylor, pp. 168 – 195, Blackie Acad. and Prof., New York, 1995. Taylor, R. N., Geotechnical Centrifuge Technology, 296 pp., Blackie Acad. and Prof., New York, 1995. Wickramanayake, G. B., and R. E. Hinchee (Eds.), First International Conference on Remediation of Chlorinated and Recalcitrant Compounds, Monterey, California, May 18 – 21, 1998, 6 vols., Battelle, Columbus, Ohio, 1998. Wu, H., and D. D. Pollard, Propagation of a set of opening-mode fractures in layered brittle materials under uniaxial strain cycling, J. Geophys. Res., 97(B3), 3381 – 3396, 1992. Yaws, C. L., Handbook of Viscosity, Gulf, Houston, Tex., 1995.

P. J. Culligan, J. T. Germaine, and L. C. Levy, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA. ([email protected])