Published online 1 August 2007
Published in Vadose Zone J 6:458-470 (2007)
DOI: 10.2136/vzj2006.0125
© 2007 Soil Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
ORIGINAL RESEARCH
Water Behavior in Layered Porous Media with Discrete Flow Channels: Results of a Large-Scale Experiment
R. J. Lenharda,* and
P. Meakinb
a Southwest Research Institute, San Antonio, TX 78238-5166
b Idaho National Laboratory, Idaho Falls, ID 83415-2211
* Corresponding author (rlenhard{at}swri.org).
All rights reserved. No part of this periodical may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system, without permission in writing from the publisher.
Received 31 August 2006.
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ABSTRACT
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A meter-scale experimental system (2-m high by 2-m deep by 3-m wide) was used to investigate the behavior of water in a model system consisting of two unconsolidated sediment layers separated by a layer containing discrete flow channels. Stainless steel tubes were inserted vertically through a clayey matrix to represent the discrete flow-channel layer. The experimental system was well characterized, and results from water infiltration experiments were analyzed. A time series of water arrival at a network of 86 probes located in the unconsolidated sediment layers is presented, as well as water pressure histories at specific locations. Some probes were located at opposite ends of the flow channels to assess water migration through the discrete flow-channel layer. Analyses of the experimental results focused on capillary break phenomenon at the interface between the overlying unconsolidated layer and the underlying discrete flow channels. Dissimilar water pressure histories were measured at probes near the upper boundary of the discrete flow-channel layer, suggesting varied and complex water flow behavior. At some locations, a steady or periodic "leaking" of water through the discrete flow channels appeared to occur, contrary to capillary break theory. The authors advocate larger-scale experiments to advance our understanding and ability to model fluid flow across a wide range of spatial and temporal scales.
Abbreviations: INL, Idaho National Laboratory
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INTRODUCTION
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Small-scale physical models have been used for almost two centuries to investigate a wide range of large-scale subsurface processes (Hall, 1815; Daubrée, 1879; Cadell, 1888). In most cases, the experiments were not analyzed quantitatively, and the purported similarities between the model system and the full-scale system of interest are based on qualitative and/or visual characteristics alone. In many investigations, the characteristic length and time scales for the model system differ from those associated with the full-scale system by many orders of magnitude. If a model system is to accurately reproduce the behavior of the full-scale system, then the important dimensionless ratios associated with the model system must match those in the full-scale system (Buckingham, 1914; Hubbert, 1937; Langhaar, 1951; Sedov, 1993). In practice, it is not possible to construct a properly scaled model for a complex subsurface system because the limited range of material properties and practical experimental conditions do not allow all of the important dimensionless ratios to be matched. In many cases, the full-scale system is too complex for the effects of differences between the dimensionless ratios in the full-scale system and the model system to be assessed. These difficulties can be alleviated if the scale of the experimental system is increased. A related issue is that structures spanning a very wide range of length scales and processes taking place on a wide range of time scales often contribute to the behavior of a complex system, and it is not possible to construct a small-scale (laboratory bench-top) physical model that covers a correspondingly wide range of length and time scales.
Our interest in larger-scale experiments, which we refer to as "mesoscale experiments," is motivated by the need to better understand and predict the behavior of fluids in the subsurface and the concomitant transport of dissolved compounds and colloidal solids. In particular, we are interested in the behavior of organic, inorganic, and radioactive contaminants in the subsurface. The contamination of the subsurface by a variety of toxic substances is a widespread and important problem that threatens water quality and human health. The nature of the contaminated subsurface varies enormously from site to site, and, to a large extent, contaminated sites must be treated on an individual basis. For example, radioactive, organic (nonaqueous phase liquid—NAPL), and mixed wastes have been buried at shallow depths in surface sediments at the Idaho National Laboratory (INL) Site. There are indications that radionuclides and organic compounds from the buried wastes have penetrated through the deep (up to 200-m thick) vadose zone to the underlying Snake River aquifer (Holdren et al., 2002; Koeppen et al., 2004; Lenhard et al., 2004) much faster than originally predicted. At INL, the underlying stratigraphy consists of layers of fractured basalt separated by relatively thin unconsolidated sedimentary layers of both alluvial and aeolian origin.
One of the advantages of mesoscale experiments is that they can be used as surrogates for specific contamination scenarios to test computer models that predict fluid flow and contaminant transport behavior. Mesoscale experiments can provide "test beds" that can be used to evaluate the performance of various computer modeling approaches in systems with realistic complexity and scale. This test-bed approach is often not possible in typical laboratory-scale experiments because the size of the system may be on the order of or smaller than the intrinsic length scales associated with key physical processes and parameters. Mesoscale experiments have some significant disadvantages compared with typical laboratory experiments: they are relatively expensive, they take substantially more time to construct, and the experiments are usually of longer duration. Consequently, mesoscale experiments should be well planned and, if possible, they should be used to investigate a number of important issues simultaneously.
There are other reasons for using mesoscale experiments to investigate complex subsurface processes. For example, it is often necessary to embed devices in the experimental system to measure quantities such as pressure, temperature, the chemical compositions of fluids, and chemical potentials. Commonly, these devices, with their associated wires, tubes, and so on, are relatively large, and they can affect flow and transport behavior, despite continuing efforts to develop smaller devices. The effect of the devices and sensors on fluid behavior will be greater on smaller laboratory-scale experiments than on mesoscale experiments. Relative to field investigations, sensors can be placed with greater control, and a denser array of detectors and sensors is possible in mesoscale experiments. In the field, the expense of installing sensors and concerns about not perturbing the system too much have typically resulted in a relatively sparse array of detectors.
In this contribution, we describe mesoscale experiments that were performed to investigate the behavior of water in a model system consisting of two unconsolidated sediment layers (coarse sand) separated by a clayey layer in which vertical tubes were inserted to provide discrete flow channels. The range of tube diameters allows both capillary and noncapillary water flow to occur in the tubes. In several ways, the expected water flow behavior in this simple system will resemble that in a natural system in which a fractured, tightly consolidated rock underlies an unconsolidated porous layer. There are at least three similarities in the way that water behaves in the two systems. The first similarity is that water will move readily from the overlying unconsolidated layer into sufficiently small fractures or tubes due to capillary forces. Second, water will tend to accumulate above the interface between the two layers (i.e., the interface between the unconsolidated and fractured-consolidated layers or between the unconsolidated and discrete flow-channel layers) if the small fractures or tubes are unable to transmit all of the downward water flux or water will not enter large fractures or tubes because the capillary forces are stronger in the overlying unconsolidated layer, and the effects of gravity acting on the water (the hydraulic potential difference) is not sufficient to overcome the capillary pressure difference. The latter condition is referred to as a capillary break. Third, a negligible amount of water will be transferred from the tubes or from the fractures to the matrix of the tightly consolidated layer because of the very low permeability of the consolidated layer and the brief residence time of water at a given location along a fracture, especially during short-duration episodic events. In an elemental way, the vertical hollow tubes with varying diameters in an unstructured, low permeability, clayey matrix can be viewed as a surrogate fracture layer, recognizing that the complexity of natural systems is not fully captured.
Previous experimental investigations addressing fractured geologic media have focused on fluid flow in individual fractures (Nicholl et al., 1992; Kumar et al., 1995; Wan et al., 2000; Su et al., 2001), fracture intersections (Wood et al., 2002; Dragila and Weisbrod, 2004), and networks with a relatively small number of fractures (Sonnenborg et al., 1999; Glass et al., 2002; LaViolette et al., 2003; Wood et al., 2004). In addition, field tests designed to investigate systems in which fracture flow plays a dominant or important role have been performed on scales on the order of one meter (Dahan et al., 2000a, 2000b; Podgorney et al., 2000), on the order of a few meters (Nicholl and Glass, 2002; Salve et al., 2002; Faybishenko et al., 2003), on the order of ten meters (Abelin et al., 1985; Bussod and Turin, 1999; Faybishenko et al., 2000a), and on the order of hundreds of meters (Wood and Faybishenko, 2000). Even in the smallest field experiments (Dahan et al., 2000a, 2000b; Podgorney et al., 2000), the fracture network is difficult to characterize without a complete excavation of the site (Nicholl and Glass, 2002), which is usually not practical, and there is no way of reconstructing the site at a later date. In almost all cases involving field experiments, only the general characteristics of the fracture network are known, and they are typically determined from core samples taken near the site or from information obtained from nearby rock outcrops or analog sites. Another problem with field tests is that the system under investigation is not contained. Consequently, there is no mass balance in the instrumented region, and, quite often, most of the injected fluid leaves the instrumented region via unknown pathways, circumventing most of the installed sensors and detectors. To address some of these concerns, we advocate the use of large-scale laboratory experiments to test our understanding of governing flow and transport processes in complex porous media and to test our ability to predict such phenomena.
Although the water behavior is expected to be similar in our simple model system and in systems containing interfaces between unconsolidated porous media and fractured consolidated rock, our model system will not reproduce the full complexity of the water behavior found in natural systems because the heterogeneity of the sand layers in the model system is relatively small, and the vertical tubes do not have the complex geometry and wetting behavior of natural fractures. On the other hand, our experimental model does capture some major mechanisms by which water moves from an overlying unconsolidated layer to an underlying fractured medium, and the model is well characterized for possible detailed comparison with modeling investigations. We believe that the data presented in this paper is useful for investigating current conceptual models of water behavior at interfaces between overlying unconsolidated porous media and underlying fractured consolidated rock, and the computer modeling approaches based on them. Furthermore, we believe that water behavior in relatively simple systems, such as the one used in this work, must be understood before more complex and more realistic larger-scale experimental models are constructed and investigated. The experimental domain described in this paper was also used to investigate (i) gas phase migration of carbon tetrachloride down through the unconsolidated and discrete flow-channel layers, (ii) partitioning of carbon tetrachloride into underlying simulated groundwater flow, and (iii) bioaugmentation into the water-saturated region and characterization of resulting biotransformations of the dissolved carbon tetrachloride. The mesoscale experimental system was used for several studies. The materials and experimental design used in the studies were chosen to be suitable for all investigations. In this paper, we discuss only the water infiltration experiments that were conducted before the carbon tetrachloride transport and biotransformation investigations.
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Materials and Methods
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The mesoscale experimental system for the study consisted of a 2-m-high by 2-m-deep by 3-m-wide cell equipped with 86 probes connected to individual pressure transducers. The experimental cell was constructed of stainless steel with supporting cross ribs. A reinforced 2-m-deep by 2-m-high metal screen was secured to each end wall of the cell. The screens were rigid, and 10-cm-thick spacers were placed between the screens and the cell end walls to prevent bending of the screens when the cell was packed with porous media. The distance between the screens (i.e., the length of the packed porous media) was 280 cm. The open space between the screens and cell end walls served as water reservoirs to control boundary conditions. Large ports (>5-cm diam. openings) near the bottom of cell end walls were connected to small adjustable-height water reservoirs located outside of the cell via metal tubing. The small water reservoirs contained overflow tubes so that the heights of the small reservoirs could be used to control the water level inside the cell and simulate groundwater movement. Water could move freely between the packed porous media in the cell and the small water reservoirs outside the cell.
To conduct the study, a layer with vertical flow channels was constructed between two unconsolidated layers. The discrete flow-channel layer was designed to capture some major mechanisms by which water enters a fractured, tightly consolidated, porous medium from overlying porous media with smaller-sized flow conduits. In the first step of packing the experimental cell, an unconsolidated layer was created in the lower section of the cell by pouring coarse sand (Unimin 2075 from Emmett, ID) into the cell, which had been filled with water to a depth of 20 to 25 cm. Coarse sand was used to minimize the sorption of carbon tetrachloride onto the unconsolidated layers in the subsequent mesoscale experiments investigating carbon tetrachloride transport and biotransformations.
After the sand was poured into the cell, it was immediately raked to dislodge any trapped air and to establish enough grain-to-grain contacts to resist redistribution or shifting of the sand as the overburden was increased. The bulk density of the sand, determined from measurements following the experiments, varied from 1.51 to 1.57 g cm–3. The elevation of the upper surface of the lower unconsolidated layer was sloped from 102 cm above the horizontal bottom of the cell at one end to an elevation of 95 cm at the other end of the cell, a slope of 0.025 (see Fig. 1
). The interface was sloped because the interface between the upper unconsolidated layer and the discrete flow-channel layer was to be sloped, and we desired a constant discrete flow-channel layer thickness so that all tube sections could be cut to the same length.
In the second step of packing the experimental cell, the discrete flow-channel layer was created on top of the lower unconsolidated sand layer. The matrix of the discrete flow-channel layer was a 1:1 mixture (v/v) of fine sand and 95 to 98% kaolinite clay (McNamee clay, R.T Vanderbilt Co., Norwalk, CT). A nonswelling clay was used so that there would be no swelling or shrinking of the clay when the water pressure changed during the experiments. The sand and clay were thoroughly mixed to a liquid-like consistency and then gently poured over the lower sand layer. After placing approximately 1.5 m3 of the mixture into the cell, the water table was lowered to firm up the clayey mixture by creating a negative water pressure in the pores. The imposed water pressures prevented air from entering the water-filled pores (i.e., the air-entry capillary pressure was never approached). The final thickness of the clayey mixture was 25 cm. Approximately 907 kg of fine sand and 907 kg of clay was used to construct the clayey mixture.
The discrete flow channels were created by inserting stainless steel tubes through the clayey mixture. To prevent the clayey mixture from entering the interior of the tubes, a metal rod was placed in each tube, and both were inserted together through the clayey mixture until they contacted the underlying sand layer. Both the metal rod and tube were inserted slightly into the sand to prevent any clayey mixture from acting as a restricting water-flow layer at the bottom of the tubes. The metal rods were then removed, creating the apertures of the discrete flow channels, while keeping the tubes stationary. The diameters of the metal rods were only slightly less than the inside diameters of the tubes. A total of 635 tubes with inside diameters ranging from 1 to 17 mm were inserted through the clayey mixture. The range in tube sizes was chosen so that both capillary and noncapillary flow mechanisms would occur. In the small tubes, the entry of water and the flow of water through the tubes would be governed by capillary forces and to a lesser extent by gravity acting on the dense wetting fluid (water). In the large tubes, the entry of water and the flow of water through the tubes would largely be governed by gravity. Film flow or rivulet flow would be the likely mechanism for water motion in the large tubes. These general flow regimes are typical in fractured, tightly consolidated, porous media. Theoretically, capillary forces and viscous drag effects (the pressure gradients needed to drive the fluid through the granular porous media) near the entrances (upper ends) and exits (lower ends) of the tubes control the flow of water through the tubes.
The distribution of tube sizes were: 75 tubes with an inside diameter of 1 mm, 100 tubes with 2 mm, 100 with 3 mm, 100 with 4 mm, 75 with 5 mm, 75 with 6 mm, 50 with 8 mm, 50 with 10 mm, and 10 with 17 mm. This yielded a total of 166.6 cm2 (1.67 x 10–2 m2) of openings in the horizontal plane due to the tubes, which yielded a tube porosity of approximately 0.003. The tubes were positioned randomly in the horizontal plane with a correlation length of 50 cm, which yielded a clustered spatial distribution of tubes in the horizontal plane. The Sequential Indicator Simulator (SISIM.F) in the Geostatistical Software Library (GSLIB) by Deutsch and Journel (1998) was used to construct a map for the tube positions. The tube distribution was constrained to prevent overlaps. Figure 2
shows a top view of (a horizontal cut through) the random correlated tube pattern. The diameters of the tubes are not shown to scale.
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FIG. 2. A top view of the random correlated tube pattern. The discrete flow-channel layer interfaces are sloped downward from the left to the right.
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To ensure that the tubes were placed properly and their locations precisely known, holes only 1 mm in diameter larger than the outside diameter of the tubes were drilled through thin metal sheets using computer-assisted cutting machinery. The metal sheets were used as templates to guide insertion of the tubes into the clayey mixture. To support the templates, metal posts (25-cm high) were placed adjacent to the cell walls to minimize their impact on the experimental results. The slope of the metal templates was the same as that of the upper surface of the lower unconsolidated layer (0.025). The elevation of the metal templates was 127 cm above the bottom of the cell at one end and 120 cm at the other end (Fig. 1). Figure 3
shows two of the metal templates with the larger tubes inserted. The tops of all the tubes were flush with the metal templates before any sand was placed on top of the discrete flow-channel layer. The bottom of the tubes extended slightly into the sand below the clayey layer when the top of the tubes were flush with the metal templates. The metal templates were not removed before the experiments, thereby acting as additional barriers to downward water movement where tubes were not present. A metal screen with mesh openings slightly smaller than the diameter of the sand grains was placed over the metal templates and tubes to prevent sand in the unconsolidated layer, which would be placed above the discrete flow-channel layer in the next step of the packing process, from filling the tubes.
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FIG. 3. Stainless tubes inserted through metal template to create a simulated discrete flow-channel layer.
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In the third step of packing the experimental cell, an unconsolidated layer was placed above the discrete flow-channel layer. The same type of sand was used for the upper and lower unconsolidated layers. The water table was subsequently raised to form a 20- to 25-cm-deep pool on top of the metal templates, and the sand was packed using techniques similar to those used to prepare the lower unconsolidated layer. As the sand was added, water was added to maintain a water depth of 20 to 25 cm. The packing process was stopped when the upper unconsolidated layer surface reached an elevation of 180 cm above the bottom of the cell (Fig. 1). Approximately 13.6 metric tons of coarse sand was used to pack both unconsolidated layers.
We believe that the water-saturated clayey mixture penetrated by vertical, stainless steel tubes can be used to emulate major processes associated with water migration into a very low matrix permeability fractured rock layer. The rate of water movement though the clayey mixture (50% clay v/v) is negligible for the time scale of the experiments, because the permeability of the clayey mixture is very low. Gas migration would also be negligible, because it is extremely unlikely that continuous air-filled pathways would exist through the clayey mixture under the conditions used in the experiments; that is, the clayey mixture was always saturated with water. This corresponds to a situation in which the migration of gas and water through the consolidated rock matrix is negligible. Essentially all of the water and gas movement at the interface between the overlying sand and underlying discrete flow-channel layer is constrained to move laterally along the interface or to enter the tubes. Because of the range in tube diameters, water can enter the tubes under several mechanisms discussed above. The resulting water behavior is similar to that which would occur at an interface between overlying unconsolidated porous media and underlying fractured, tightly consolidated rock.
Theoretically, there should be a capillary break between the upper unconsolidated layer and the larger tubes. By using a screen with mesh openings similar to the sand grain diameters to prevent sand from entering the apertures of the vertical tubes penetrating the clayey layer, any capillary break effect due to the screen was minimized. Care was taken not to create a thin layer with capillary forces different from those in the sand, which can affect flow behavior observed in the experiments, by using a screen with openings significantly smaller than the pore sizes in the sand. Although the low permeability clayey mixture and open penetrating tubes can be used to capture the major flow processes at interfaces between unconsolidated porous media and fractured rock with very low matrix permeability, it is clear that this simple physical model will not capture the full complexity of fluid flow behavior at naturally occurring interfaces.
To measure water arrival at various locations in the unconsolidated layers, an array of 86 sensors (tensiometers) was designed. An increase in water pressure (i.e., an increase in the transducer voltage reading) was assumed to indicate the arrival of water. The tensiometers consisted of porous ceramic tips secured to copper tubing, which were connected to pressure transducers (Omega, Stamford, CT, PX240 series, part number PX243-05BG5V) located outside the cell via Teflon tubing. The ceramic tips had an outside diameter of 0.64 cm and were 3-cm long. The copper tubing also had an outside diameter of 0.64 cm. Swagelok fittings inserted through the cell wall were used to connect the copper tubing to the Teflon tubing. The pressure transducers were wired to a computer to permit automated recording of the pressure measurements. The ceramic tip, copper tube probes (pressure probes) were emplaced during packing of the sand described above (Fig. 4
).
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FIG. 4. A row of pressure probes being placed at an elevation of 60 cm from the bottom of the cell. The brass connectors on the left side of the cell are for additional pressure probes at higher elevations.
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The probes were placed to detect the downward water movement from the infiltration gallery and possible water migration down the sloped interface between the upper unconsolidated layer and the underlying discrete flow-channel layer. Two-dimensional views of the probe locations are shown in Fig. 5
. For discussion purposes, we label the z-coordinate as the height or elevation of the experiment domain, the x-coordinate as the width of the experimental domain, and the y-coordinate as the depth of the experimental domain (see Fig. 1). The line of probes below the discrete flow-channel layer (Fig. 5a) was placed to detect water movement through the discrete flow-channel layer. In Fig. 5b, which is an end view, all of the 86 probes are not evident because the projections of some of the probe positions onto the y–z plane are similar; that is, they overlap in Fig. 5b.
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FIG. 5. Locations of the pressure probes: (A) two-dimensional side view and (B) two-dimensional end view.
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All probes were flushed with water before calibrating the pressure transducers to ensure that the ceramic tips, copper tubing, and Teflon tubing were saturated with water. The tensiometers were calibrated by lowering the water table in the cell from an elevation of 160 cm to an elevation of 60 cm by 10-cm increments. Three or four measurements were taken at each elevation. Only pressures greater than –10 cm of water head were used in the calibration process. After each step, the water table elevation was held constant for at least 24 h before it was lowered another 10 cm. The water pressures were determined from the elevation of the water table assuming hydrostatic conditions.
Because of the coarseness of the sand and the relatively small ceramic probes, water contact between the probes and that in the sand was commonly broken (i.e., disconnected) when the water pressures were less than approximately –20 cm of water head. For tensiometers located at elevations of 160 cm and below, the coefficient of determination (R2) values from linear regression of voltage readings from the transducers and water pressures ranged between 0.9945 and 1.0, indicating a very good linear relationship. For tensiometers located above 160 cm (three at 175 cm and four at 170 cm), the relationship between transducer readings and water pressures was determined by using the average regression slope coefficient from the analyses of tensiometers at elevations of 160 cm and below. This approach was deemed adequate because the tensiometers were only used to detect water arrival at a location and not to measure water pressure or water content. For tensiometers above an elevation of 160 cm, there were insufficient data points (i.e., measurements of voltage and water pressures) to conduct robust regression analyses. Following the calibration of the tensiometers, the water table was lowered to 54 cm above the bottom of the cell. The water table remained at this elevation during the experiments.
A 10-cm square (100 cm2) infiltration gallery was created on the surface of the upper unconsolidated sand layer (180 cm elevation). The infiltration gallery size was arbitrary, but postexperiment sampling was considered. It was felt that a 10-cm square area could be reasonably characterized by a 5-cm inside diameter core sampler that could be used to collect samples for measuring hydraulic properties. The relatively small area of the infiltration gallery compared with the total cross-sectional area of the surface (0.18%) amplified the three-dimensional effects of infiltrating water. The position of the infiltration gallery was between 90 and 100 cm (x-direction) from the left side of the cell and 100 to 110 cm (y-direction) from the front of the cell toward the back wall (Fig. 1). A piston-displacement pump was used to supply water over the infiltration gallery. One experiment was conducted using a 50 mL min–1 infiltration rate, and another was conducted using a 150 mL min–1 infiltration rate. The 50 mL min–1 infiltration rate represents a low infiltration rate scenario, and the 150 mL min–1 infiltration rate represents a moderate infiltration rate scenario. Before both infiltration experiments, water was supplied with a garden hose to the surface of the upper unconsolidated layer to produce near-saturation conditions in the mesoscale cell. The water was subsequently allowed to drain for several days (3–4 d) before water was supplied to the infiltration gallery.
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Results
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The primary focus of this work was to conduct a mesoscale experiment to test our understanding of flow processes at and through interfaces between overlying unconsolidated porous media and underlying media with discrete flow paths and negligible matrix permeabilities. We were interested in the capillary break phenomenon at interfaces between overlying unconsolidated porous media and underlying fracture-dominated, low permeability media. The long-term goal of our research is to use the experimental data to test and improve modeling approaches for predicting the downward movement of contaminants through layers of unconsolidated and fractured-consolidated porous media. To understand the effects of small-scale flow behavior at larger spatial and temporal scales, the experimental domain needs to be relatively large. Because many contaminants commonly move downward with infiltrating water, we focused on measuring the migration of water. The time-dependent spatial arrival of water at a network of sensor locations, especially at the interfaces between the unconsolidated layers and the discrete flow-channel layer, provided data to test our understanding of governing flow processes in complex porous media. Water arrival at sensor locations was assumed if the water pressure head increased more than 1 cm of water. We chose this increment (i) because of our previous experience using similar transducers, and (ii) because an investigation using higher pressure increments did not result in significantly different interpretations of the experimental data.
To display the experimental results of the downward migration of water through the unconsolidated and discrete flow-channel layers in a simple manner, we show the results using a two-dimensional format, even though the experiment was three-dimensional. An argument supporting the use of a two-dimensional format is that a large majority (81%) of the sensors were located within a relatively narrow strip 20-cm wide under the infiltration gallery, from y = 95 cm to y = 115 cm (see Fig. 5b). The center of the water source area was at y = 105 cm. Therefore, 81% of the sensors were located within 5 cm from the boundary of the water infiltration gallery in the y-direction. The two-dimensional format we used is shown in Fig. 5a. The discrete flow-channel layer and the slope of the interfaces between the unconsolidated layers and the discrete flow-channel layer are evident.
In the analysis of the experimental data, a few sensors (seven) were considered to be unreliable because the recorded pressures were either positive or close to atmospheric. It is not clear why these sensors appeared to be unreliable during the water infiltration experiments. Only one of the seven sensors appeared to have a calibration error. These seven sensors are not included in the following figures or in the analysis of the experimental results.
Results of the 50 mL min–1 Infiltration Rate Experiment
A time sequence of water arrival at the sensors for the experiment with a 50 mL min–1 infiltration rate is shown in Fig. 6
. If water arrival was not detected by a sensor (the increase in water pressure head was less than 1 cm), then the sensor is marked black. If water arrival was detected by an increase in water pressure head of 1 cm of water or greater, then the sensor is marked light blue. The times shown in Fig. 6 are arbitrary, but they show the main features of water migration through the discrete flow-channel layer.
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FIG. 6. Results of water arrival for the 50 mL min–1 infiltration rate at sensor locations for times 1, 10, 50, 100, 150, and 167 h of experimental time. Light color (blue) indicates water arrival, and dark color (black) indicates no water arrival.
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After 1 h of infiltration, water approached the interface between the upper unconsolidated layer and the discrete flow-channel layer. Two anomalous readings indicated water arrival. There is no clear reason why these two sensors indicated water arrival. One sensor's reading (probe 69—below the discrete flow-channel layer) was slightly above the 1-cm water pressure head arrival detection criterion (an increase of 1.2 cm in the water head). The other sensor reading (for probe 41—above the discrete flow channels) showed an increased water pressure head of 2.1 cm. It is our assessment that these readings are anomalous, although it is possible that a narrow finger of water circumvented the other sensors. The heights (z coordinates) of the line of sensors above the interface between the upper sand layer and discrete flow-channel layer averaged about 2 cm above the interface, and the heights of the line of sensors below the interface between the discrete flow-channel layer and the underlying sand layer averaged 2 to 3 cm below the interface.
After 10 h of infiltration, the imbibing water plume widened and reached the interface between the upper unconsolidated layer and the discrete flow-channel layer. Again, there appear to be two anomalous readings below the discrete flow-channel layer. The measurements of both sensors were only slightly above the 1 cm of water head arrival detection criterion (probe 59 = 1.6 cm, and probe 67 = 1.3 cm).
After 50 h of infiltration, none of the sensors above the interface between the upper unconsolidated and discrete flow-channel layers indicated water arrival, but two more sensors below the discrete flow-channel layer indicated water arrival. At 100 h, almost all of the sensors above the discrete flow-channel layer indicated water arrival and the sensors below discrete flow-channel layer indicated that water broke through at a number of locations along the lower discrete flow-channel layer boundary, including locations that are "upslope" from the infiltration gallery. At 150 h, there were only slight differences in the pattern of water arrival from that at 100 h. At 167 h, the water arrival pattern was similar to that at 100 and 150 h, suggesting that a stable pattern emerged after 100 h, except for possible path switching. Because of the capillary break phenomenon between the sand and the larger flow channels, steady-state conditions may never occur, and this can lead to different channels (tubes) conducting water at different times (i.e., one cause for path switching).
During the 167-hour experiment, none of the lowest sensors indicated water arrival. This can be explained by the location of these sensors relative to the water table, which was at an elevation of 54 cm. The average water pressure head for the sensors located at the 60-cm elevation was slightly greater than –6 cm of water. At this pressure head, the water hydraulic conductivity is high enough to allow the infiltrating water to be transmitted downward without raising the water pressure gradient. Consequently, none of these sensors recorded an increase greater than 1 cm of water head, which is the cutoff we used for detecting water arrival.
Results of the 150 mL min–1 Infiltration Rate Experiment
A time sequence of water arrival at sensor locations for the experiment with a 150 mL min–1 infiltration rate is shown in Fig. 7
. Again, the times are arbitrary, but they show the general features of water behavior. After 1 h of infiltration, water had moved downward through the upper unconsolidated layer and reached the interface with the discrete flow-channel layer. Most of the sensors located approximated 2 cm above the interface indicated water arrival, even on the "upslope" side of the infiltration gallery. Sensors located below the discrete flow-channel layer had not yet indicated water arrival. After 10 h of infiltration, a number of sensors immediately below the discrete flow-channel layer indicated water arrival, one of which was on the upslope side of the infiltration gallery. After 50 h, most of the sensors below the discrete flow-channel layer indicated water arrival, four of which were upslope of the infiltration gallery. After 100 h, the pattern of sensors indicating water arrival was similar to that at 50 h. In fact, the patterns at 50, 100, 150, and 200 h were similar to each other, except for minor path switching. From 50 to 200 h of water infiltration, 13 to 16 of the 23 sensors under the discrete flow-channel layer always indicated water arrival. Only two of the sensors at the 60-cm elevation ever indicated water arrival. At 100 h, probe 74 measured an increase of 1.3-cm water head over the initial pressure. Also, the water pressure at probe 74 surpassed the 1 cm of water head water arrival criterion at other times not shown in Fig. 7. The only other probe at the 60-cm elevation to measure an increase greater than 1 cm of water head was probe 86, which is the sensor farthest to the right at the 60-cm elevation. The times at which these events occurred are not shown in Fig. 7. The increased infiltration rate (over the 50 mL min–1 experiment) caused a pressure change greater than 1 cm of water head at the locations of probes 74 and 86.
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FIG. 7. Results of water arrival for the 150 mL min–1 infiltration rate at sensor locations for times 1, 10, 50, 100, 150, and 200 h of experimental time. Light color (blue) indicates water arrival, and dark color (black) indicates no water arrival.
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Figures 6 and 7 provide only snapshots in time of water behavior in the model system. However, it is clear that water reaching the interface between the upper unconsolidated layer and the discrete flow-channel layer was readily transmitted downward. In both infiltration experiments, water broke through the discrete flow-channel layer earlier at some higher elevation locations than at some lower locations, suggesting that water breakthrough occurred under unsaturated conditions, not under near-saturated or saturated conditions.
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Discussion
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Detailed analyses of the experimental data reveal highly complex fluid flow behavior. Our expectation was that water would move downward through the upper unconsolidated layer to the interface with the discrete flow-channel layer and encounter a capillary break. Even for the smallest tubes (1-mm diam.), the infiltrating water should not enter the tubes until the water pressure head increased to at least –1.5 cm of water, assuming that the air phase is at atmospheric pressure. For the larger tubes (i.e., tubes with diameters greater than 5-mm diam.), the water pressure head must be approximately –0.3 cm or greater (almost saturated conditions) before water should enter. Because the water-saturated clayey mixture has a very low hydraulic conductivity, only a negligible amount of water will move through the mixture. It is well established that a structureless (i.e., dispersed) porous medium consisting of 50% clay-sized material will have a very low hydraulic conductivity. Therefore, the water saturation should increase along the lower boundary of the upper unconsolidated layer and begin to move in the x-direction (i.e., down the slope of the interface between the upper unconsolidated layer and the discrete flow-channel layer). After the water pressure head exceeds approximately –1.5 cm of water, water should enter the smallest tubes and move to the lower unconsolidated layer. Because of the hydraulic conductivity characteristics of the coarse sand, we expected the water to move significantly down gradient from the infiltration gallery before any breakthrough of water from the discrete flow-channel layer would occur. Our expectations are consistent with the concept of a capillary break at an interface where the overlying porous medium has smaller diameter flow paths than the underlying porous medium. However, the experimental results suggest that the water flow behavior may be more complex.
The capillary break effect can be investigated by observing the behavior of water pressure at probes with similar x–y coordinates located directly above and below the tubes (i.e., similar x–y coordinates, but different z coordinates). Probes 34 (above the discrete flow-channel layer) and 55 (below the discrete flow-channel layer) have identical x–y coordinates. Within ± 2 cm of each coordinate, there was one tube with a 10-mm diameter and one tube with a 4-mm diameter. Figure 8
shows the probe locations immediately above and below the discrete flow-channel layer. Because of the location of probes 34 and 55 relative to the tubes, it was expected that the water pressure behavior would reflect a capillary break phenomenon. In Fig. 9
, water pressures at probes 34 and 55 are shown for the 50 mL min–1 and 150 mL min–1 experiments. The water pressure behavior indicates that a capillary break was not operational. For the 50 mL min–1 experiment, water arrived at probe 34 at approximately 70 h. For the 150 mL min–1 experiment, water arrived in less than 1 h. The initial water pressure at probe 34 for the 150 mL min–1 experiment was approximately –12 cm of water. After water arrived at probe 34 for both experiments, there was little fluctuation of water pressure, especially for the 150 mL min–1 experiment. The water pressure head at probe 34 never approached –1 cm of water before water apparently moved downward through the tubes near probe 34. The minor fluctuations in water pressure at probe 55 suggest that the water flow through the nearby tubes may be periodic. Due to the slight increase in water pressure at probe 55, the nearby tubes likely transmitted only a minor amount of water. The slight decrease in water pressure from 0 to approximately 70 h at probes 34 and 55 for the 50 mL min–1 experiment is attributed to additional water drainage from the onset of the experiment. Apparently, equilibrium conditions with the water table elevation were not established at all locations when the experiment was initiated.
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FIG. 8. Planar positions of the probes immediately above (A) and immediately below (B) the discrete flow-channel layer.
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FIG. 9. Measured water pressure head at probes 34 and 55 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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Similar water pressure behavior is shown in Fig. 10
for probes 35 and 56 for both experiments. The x–y coordinates (Fig. 8) for probe 35 were (123, 95), and the x–y coordinates for probe 56 were (125, 95). Near both probes (± 2 cm of each coordinate), there were four tubes with a 10-mm diameter and one tube with a 4-mm diameter. For the 50 mL min–1 experiment, water arrived at probe 35 at approximately 70 h. As soon as the water arrived, the water pressure at probe 56 increased, indicating that water was being transmitted downward. The water pressure at probe 35 never exceeded –6 cm of water head. For a 4-mm diameter tube, water should not enter the tube from the overlying smaller pores unless the water pressure is above –1 cm of water head. For the 10-mm diameter tubes, water should not enter unless the water pressure is –0.15 cm of water head or greater. Clearly in both experiments (50 and 150 mL min–1), water entered the tubes at pressures less than that theoretically predicted. Water arriving near probe 35 was transmitted downward immediately because the water pressure history at probe 56 had a very similar pattern to that at probe 35. If water flowed to probe 56 from a location other than near probe 35 (i.e., from an outlet of other tubes further away from probe 35), then the pattern of water pressure changes at probe 56 should be dissimilar to that at probe 35—not almost identical. The slight fluctuations in water pressure at probes 35 and 56 again suggest that water was transmitted downward in a quasi-periodic manner.
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FIG. 10. Measured water pressure head at probes 35 and 56 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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A different type of water flow behavior is shown in Fig. 11
for probe 57, which was located below the discrete flow-channel layer and farther along the cluster of tubes containing probes 34 and 55 and probes 35 and 56 (Fig. 8). Within ± 2 cm of each x–y coordinate of probe 57, there were two tubes with a 10-mm diameter, one tube with a 2-mm diameter, and one tube with a 1-mm diameter. For both experiments, the water pressure increased slightly over time, indicating that water moved downward from nearby tubes in a more regular manner than near probes 34 and 55 and probes 35 and 56. This behavior may be attributed to the smaller diameters of the tubes near probe 57.
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FIG. 11. Measured water pressure head at probe 57 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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A still different type of water flow behavior was measured for a small grouping of tubes near probes 32 and 54, which were located in a direction from the infiltration gallery that is approximately orthogonal to the direction of probes 34 and 55, probes 35 and 56, and probe 57 (Fig. 8) from the infiltration gallery. The x–y coordinates of probe 32 were (103, 65), and the coordinates for probe 54 were (105, 65). Within ± 2 cm of each coordinate, there were two tubes with a 10-mm diameter, one tube with a 6-mm diameter, and two tubes with a 4-mm diameter. In contrast to the previously discussed probes, there were significant differences between the measured water pressures between the 50 and 150 mL min–1 experiments (Fig. 12
). For the 50 mL min–1 experiment, the water pressures at probe 32 varied significantly and periodically. For the 150 mL min–1 experiment, the water pressure at probe 32 was constant after the large initial water pressure increase at early times. Also in contrast to the previously discussed probes, there appeared to be very little, if any, water transmitted downward by the tubes. The water behavior at probes 32 and 54 appeared to be more consistent with effects resulting from a capillary break. For the 50 mL min–1 experiment, the water pressure increased at probe 32, but no water was transmitted to the probe immediately below the discrete flow-channel layer. Following the water pressure increases at probe 32, there were periods of water drainage, followed again by water pressure increases. Because the water pressure never approached a critical (entry pressure) value, determined from the Laplace equation for the capillary pressure difference across the air–water interface, water never was transmitted through the nearby tubes with 10-, 6-, and 4-mm diameters. For the 150 mL min–1 experiment, the water pressures also never approached the critical value for water to enter the nearby tubes. Consequently, water was not transmitted downward by the nearby tubes.
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FIG. 12. Measured water pressure head at probes 32 and 54 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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Complex water flow behavior was also observed at other locations where probes were positioned under and nearby tubes. In Fig. 13
, the water pressure histories at probe 60 are shown. The x–y coordinates of probe 60 were (155, 95). Within ± 2 cm of each coordinate, there were two tubes with a 6-mm diameter, one tube with a 5-mm diameter, and one tube with a 4-mm diameter. The tubes near probe 60 were generally smaller than those at the locations discussed above. For both experiments, the water pressure at probe 60 increased with only minor fluctuations occurring in the 50 mL min–1 experiment, indicating a constant slow supply of water.
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FIG. 13. Measured water pressure head at probe 60 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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Figure 14
shows that the water pressure histories at probe 64, with x–y coordinates of (193,75), were different than the pattern at probe 60. Furthermore, the histories for the 50 and 150 mL min–1 experiments were dissimilar. Within ± 2 cm of each coordinate, there was one tube with a 10-mm diameter and one tube with a 5-mm diameter. For the 50 mL min–1 experiment, the water pressures were constant for approximately 40 h from the onset of the experiment, and then drainage occurred until about 70 h of experimental time. Following approximately 70 h, the water pressures increased slightly, indicating water arrival. There were only minor fluctuations in the water pressures after 80 h. For the 150 mL min–1 experiment, a different pattern of water pressures was measured (Fig. 14). There was a significant increase in water pressure after 5 h. Thereafter, the pressures remained constant, indicating a steady supply of water through the tubes. Then on several occasions, there was a rapid decrease followed by a rapid increase in water pressures. We believe that this behavior results when flow through the nearby tubes ceases and then restarts later at a similar rate. Such behavior is consistent with path switching. We cannot ascertain if the flow path switching occurred in the 10-mm or the 5-mm tube or both. As with probes 57 and 60, there were no probes with similar x–y coordinates located above the discrete flow-channel layer. Therefore, the water pressure at which water entered tubes nearby probes 57, 60, and 64 are unknown.
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FIG. 14. Measured water pressure head at probe 64 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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In Fig. 15
, different water pressure histories are shown at probe 69 than probes at other locations. The x–y coordinates at probe 69 were (245, 85). Within ± 2 cm of each coordinate, there was one tube with a 10-mm diameter, four tubes with a 5-mm diameter, one tube with a 4-mm diameter, one tube with a 3-mm diameter, and one tube with a 2-mm diameter. The water pressure history pattern for the 50 mL min–1 experiment indicated that water was transmitted downward by nearby tubes in a periodic manner. The amount of water transmitted, as reflected by the magnitude of the water pressure changes, was greater than at other locations. For the 150 mL min–1 experiment, the water movement through the nearby tubes occurred at shorter intervals, which is reasonable given that the water flux is likely higher. It is difficult to assess whether a capillary break phenomenon occurred at the interface between the upper unconsolidated layer and the tubes because no probes were located at similar x–y coordinates above the discrete flow-channel layer. However, the water pressure histories for both experiments at probe 69 suggest that a capillary break phenomenon may be occurring. The water pressure changes for the 50 mL min–1 experiment before 75 h may be a result of additional water drainage from the upper unconsolidated layer during the early stages of the experiment.
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FIG. 15. Measured water pressure head at probe 69 for the 50 mL min–1 (A) and 150 mL min–1 (B) experiments.
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Conclusions
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A mesoscale experimental study was conducted to obtain a better understanding of the processes governing flow in heterogeneous porous media. The focus was a better understanding of water flow from unconsolidated porous media into porous media with very low matrix permeabilities and large flow conduits, such as fractures, that are the dominant flow paths. The capillary break phenomenon at the interface between overlying unconsolidated porous media and underlying fracture-dominated porous media was of particular interest. The mesoscale model system consisted of a layer of discrete flow channels between two unconsolidated layers. The model system was used to capture some major processes occurring at interfaces between overlying porous media with smaller flow conduits and underlying porous media dominated by large flow conduits. In the model, discrete flow channels were created by inserting stainless steel tubes through a low permeability clayey mixture. The tube diameters ranged in size from 1 to 17 mm to capture both capillary and noncapillary flow phenomena in the tubes. The unconsolidated layers were represented by coarse sand. Although the model system is much simpler than most natural systems, it can be used to capture some major mechanisms by which water enters a fractured, tightly consolidated, porous medium. A network of 86 probes was used to monitor water behavior.
Analyses of the water pressure data revealed that the water flow behavior was complex. At some locations, a steady or periodic "leaking" of water through the tubes was deduced from the water pressure measurements. At other locations, greater amounts of water were thought to be transmitted through the tubes. At still other locations, there was no evidence that water was transmitted downward through the tubes. There did not appear to be any strong relationship between the measured behaviors and the corresponding sizes of the nearby tubes. However, water conduction through the tubes appeared to be more uniform and steady when the tube diameters were smaller and more variable (often quasi-periodic) when the tube diameters were large.
A capillary break phenomenon was expected to occur at the upper interface with the discrete flow channels. According to Laplace's equation of capillarity, water should not have entered the smallest tubes until the water pressure head exceeded –1.5 cm of water and should not have entered the largest tubes until the water pressure head was almost atmospheric (
–0.2 cm of water). The movement of water into the discrete flow channels seemed not to always follow the capillary break theory. Water moved downward from the upper unconsolidated layer through the tubes at water pressures less than the critical values, as determined from Laplace equation of capillarity. A possible explanation is the weak capillarity of the coarse sand used in the unconsolidated layers. However, there should, theoretically, have been a capillary break at the upper apertures of the tubes because there were significant contrasts between the flow conduit sizes in the overlying sand and in the underlying tubes, except for the 1-mm inside diameter tubes. Another factor may be the complicated geometry at the interface between the overlying sand (and screen) and the underlying tube apertures. It is not unreasonable that rivulet flow or film flow may occur at some locations due to certain geometries of the sand along the circumference of the tubes coupled with wetting behavior. Changes (i.e., lowering) of the air–water interfacial tension and/or changes (i.e., increasing) of the water–solid contact angle are not plausible explanations for the observed behavior. An important result from our investigation is that factors other than just creating an interface where smaller diameter flow conduits overlay larger diameter conduits must be assessed when engineering and constructing a capillary break.
The varied water flow behavior patterns observed in our study, however, is not completely unexpected because multiphase fluid flow often results in complex spatiotemporal behavior. Even a dripping faucet exhibits complex and multiperiodic behavior (Shaw, 1984; D'Innocenzo et al., 2002). The unstable gravity-driven penetration of nonwetting fluid into a porous medium saturated with a wetting fluid also results in complex spatiotemporal behavior (Frette et al., 1992). Examples more relevant to the mesoscale experiments reported here include intermittent flow (Su et al., 1999) and path switching (Faybishenko et al., 2000b; Glass et al., 2002; and Wood et al., 2004) observed during the penetration of water into fractured systems. In light of these and other complex behavior in multiphase fluid systems (Nguen et al., 1996; Eggers, 1997; Barberon and Leblond, 2001), the complex behavior indicated by our measurements is not surprising. However, a detailed explanation would require extensive investigations covering a wide range of length and time scales, which is beyond the scope of the work reported in this paper.
Understanding flow and transport phenomena for the purpose of developing more accurate field-scale predictive models will require additional studies in which experimentalists and modelers can observe how small-scale physics manifest themselves at larger spatial and temporal scales. This will require larger-scale experimental studies, such as the one presented here, in which varied and complex behavior can be observed and measured. In our study, both local-scale effects (e.g., Fig. 9–15) and larger-scale behavior (e.g., Fig. 6 and 7) were measured. Our observations were not always consistent with the capillary break phenomenon as predicted from a conceptual model based on theory from the Laplace equation of capillarity. The experimental work demonstrates that complex behavior, which differs substantially from expected behavior, can occur even in a relatively simple and relatively well-characterized large-scale, experimental system. Behavior much more complex and more difficult to understand can be expected in natural systems. More research is needed using both mesoscale experiments and laboratory experiments to provide the information and understanding necessary to predict the behavior of multiple fluid phases in the subsurface. A better understanding of the behavior observed in simplified systems, such as that used in the mesoscale experiments described here, will build confidence in the conceptual models that are the foundation of many computer models used to predict the behavior of fluids in the vadose zone. Conceptual models that are based on our current understanding of flow processes in small-scale experimental efforts or from theoretical models may be inadequate for capturing, and predicting, the complex behavior observed in many large-scale investigations. There is a continuing need to test our understanding of flow behavior against larger-scale investigations.
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ACKNOWLEDGMENTS
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Dr. Hai Huang of the Idaho National Laboratory generated the correlated random distribution of tube positions in the horizontal plane. Drs. Gill Geesey of Montana State University and Alexandre Tartakovsky of Pacific Northwest National Laboratory helped with the experiments. The work described in this paper was supported through the Idaho National Laboratory Laboratory-Directed Research and Development Program under DOE Idaho Operations Office Contract DE-AC07-05ID14517. Acknowledgments are also extended to the Southwest Research Institute, where the lead author is currently employed.
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TOP
ABSTRACT
INTRODUCTION
