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DATE DUE MTE DUE MTE DUE .JULrfi’i i999 1“ WM“ WATER TRANSPORT DUE TO CAPILLARY PHENOMENA OVER AN IMPERMEABLE BARRIER IN UNSATURATED SAND By Geofi‘rey Stephen Salthouse A THESIS Submitted to Michigan State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE Department of Agricultural Engineering 1997 ABSTRACT WATER TRANSPORT DUE TO CAPILLARY PHENOMENA OVER AN IMPERMEABLE BARRIER IN UNSATURATED SAND By Geoffrey Stephen Salthouse Capillary rise is an important mechanism in the movement of liquid through unsaturated porous media. Wastewater treatment systems can utilize this process to provide aerobic conditions while transporting the eflluent to subsequent treatment or final disposal. Experiments were conducted to investigate the influence of the efl‘ective size and uniformity of sand media on capillary siphoning, defined as the transport of water by capillarity over an impermeable barrier. U-shaped siphon tubes were filled with graded sand media of difl‘erent efl‘ective sizes (0.1, 0.2 and 0.4 mm) and difl‘erent unifonnity coemcients (1.5, 2.5 and 4.5), capped with porous endcaps and inverted so that one leg could saturate in water. The capillary rise distance from the saturation level to the tube invert was varied stepwise to achieve steady state flow through the siphon at rise distances ranging from 2 to 10 cm. Siphon outflow was measured before the rise distance was incrementally increased. Maximum capillary flux of 15.5 cm/hr was delivered by the 0.2 mm effective size media at a rise distance of 5 cm. Minimum flux of 0.2 cm/hr was delivered by the 0.4 mm media at 10 cm capillary rise. Media uniformity results indicate that a wide range of particle sizes may provide less capillary transport capacity under certain conditions. Further research into the influence of media uniformity on capillary siphoning is needed. To my parents, Arlen Ross and Patricia May Salthouse, for their ever-present and unconditional support, and who have taught me the value of perseverance in task, and dedication to purpose. I would also like to commemorate this work to Audrey Krajkovich who continues to be of particular inspiration. ”The knowledge of man is as the waters, some descending from above, and some springing from beneath.” -Francis Bacon iii ACKNOWLEDGEMENTS I would like to express my sincere appreciation to my major professor, Dr. Ted Loudon, for his guidance, his patience, and most of all for his endless and contagious energy. I also recognize the support of all my friends and colleagues who have helped to make this a rewarding and enjoyable endeavor, particularly Andy Fogiel, Amy Abler and Andrew Wedel. iv TABLE OF CONTENTS LIST OF TABLES ....................................................................................................... vii LIST OF FIGURES ................................................................................................... viii LIST OF SYMBOLS .................................................................................................... ix INTRODUCTION ......................................................................................................... 1 REVIEW OF THEORY AND LITERATURE ............................................................. 4 CHARACTERIZATION OF A POROUS MEDIA FLOW SYSTEM ............................................. 4 Media ...................................................................................................................... 4 Fluid ...................................................................................................................... l4 TRANSPORT PHENOMENA IN POROUS MEDIA .............................................................. 17 Energy And Potential ............................................................................................. 17 Fluid Movement ..................................................................................................... 21 Saturated F low ....................................................................................................... 27 Unsaturated Flow .................................................................................................. 28 UPWARD FLOW THROUGH POROUS MEDIA ................................................................. 32 Evaporation ........................................................................................................... 32 Capillarity ............................................................................................................. 33 Capillary Siphoning ............................................................................................... 37 Application to Wastewater Treatment ..................................................................... 39 EXPERIJVIENTAL PROCEDURES ............................................................................ 42 TRANSPORT MEDIA .................................................................................................... 42 Media Preparation ................................................................................................. 43 Geometric Description ........................................................................................... 44 CAPILLARY SIPI-ION .................................................................................................... 45 Design ................................................................................................................... 45 Construction .......................................................................................................... 45 LABORATORY SETUP .................................................................................................. 47 Experimental Design .............................................................................................. 48 WATER SUPPLY SYSTEM ............................................................................................. 49 WATER DISPOSAL SYSTEM .......................................................................................... 52 SAMPLE PREPARATION ............................................................................................... 52 Vacuum Saturation. ................................................................................................ 53 System Equilibration .............................................................................................. 54 DATA COLLECTION ..................................................................................................... 54 COLLECTION CONTAINERS .......................................................................................... 56 DETERMINATION OF CAPILLARY FLUX ........................................................................ 56 RELATED EXPERIMENTATION ...................................................................................... 57 Time to Equilibrium ............................................................................................... 57 RESULTS AND DISCUSSION ................................................................................... 58 EFFECTIVE SIZE .......................................................................................................... 58 UNIFORMlTY .............................................................................................................. 65 APPLICATIONOPRESULTS ........................................................................................... 67 SUMMARY AND CONCLUSIONS ........................................................................... 70 APPENDIX A ............................................................................................................... 74 CAPILLARY FLUX LABORATORY DATA FOR SIPHON SET 0125 (D10 = 0.1 MM U = 2.5) APPENDIX B ............................................................................................................... 76 CAPILLARY FLUX LABORATORY DATA FOR SIPHON SET 0225 (BM = 0.2 MM U = 2.5) APPENDIX C ............................................................................................................... 78 CAPILLARY FLUX LABORATORY DATA FOR SIPHON SET 0425 (D10 = 0.4 MM U = 2.5) APPENDIX D ............................................................................................................... 80 CAPILLARY FLUX LABORATORY DATA FOR SIPHON SET 0215 (BM = 0.2 MM U = 1.5) APPENDIX E ............................................................................................................... 82 CAPILLARY FLUX LABORATORY DATA FOR SIPHON SET 0245 (Dm = 0.2 MM U = 4.5) LIST OF REFERENCES ............................................................................................ 84 LIST OF TABLES TABLE I. MICHDOT GRADING SPECIFICATIONS FOR 2N8 SAND. .................................. 42 TABLE 2. GRAIN SIZE DISTRIBUTIONS FOR ALL TREATMENTS BY PERCENT PASSING THROUGH SIEVE. ................................................................................................... 44 vii LIST OF FIGURES FIGURE 1. CROSS-SECTION OF A SAND-FILLED CAPILLARY SIPHON. .................................. 46 FIGURE 2. GRAIN-SIZE DISTRIBUTIONS FOR EXPERIMENTAL MEDIA OF VARIOUS EFFECTIVE SIRS. .......................................................................................................................... 47 FIGURE 3 . GRAIN-SIZE DISTRIBUTIONS FOR EXPERIMENTAL MEDIA OF VARIOUS UNIFORMITIES .............................................................................................................. 49 FIGURE 4. SCHEMATIC DIAGRAM OF CONSTANT LEVEL WATER SUPPLY SYSTEM. ............... 51 FIGURE 5. MEAN STEADY-S'I‘ATE CAPILLARY FLUX OVER AN IMPERMEABLE BARRIER AT VARIOUS RISE DISTANCES WITH STANDARD DEVIATION BARS (D,o= 0.1 MM; U = 2.5). ..59 FIGURE 6. MEAN S‘I'EADY-STATE CAPILLARY FLUX OVER AN IMPERMEABLE BARRIER AT VARIOUS RISE DISTANCES WITH STANDARD DEVIATION BARS (D,o= 0.2 MM; U = 2.5). ..60 FIGURE 7. MEAN STEADY-STATE CAPILLARY FLUX OVER AN IMPERMEABLE BARRIER AT VARIOUS RISE DISTANCES WITH STANDARD DEVIATION BARS (Dlo= 0.4 MM; U = 2.5). ..61 FIGURE 8. EXPONENTIAL PREDICTION CURVES FROM MEASURED CAPILLARY FLUX OF WATER THROUGH POROUS MEDIA OF THREE DIFFERENT EFFECTIVE SIZES (U = 2.5). ....... 63 FIGURE 9. MEAN STEADY-STATE CAPILLARY FLUX OVER AN IMPERMEABLE BARRIER AT VARIOUS RISE DISTANCES WITH STANDARD DEVIATION BARS (Dlo= 0.2 MM; U = 1.5). ..56 FIGURE 10. MEAN STEADY-STATE CAPILLARY FLUX OVER AN IMPERMEABLE BARRIER AT VARIOUS RISE DISTANCES WITH STANDARD DEVIATION BARS (D,o= 0.2 MM; U = 4.5). ..67 FIGURE 1 l. ADJUSTED MEAN STEADY-STATE CAPILLARY FLUX OVER AN IMPERMEABLE BARRIER AT VARIOUS RISE DISTANCES WITH STANDARD DEVIATION BARS (D10: 0.2 MNI; (1" 4.5). ..................................................................................... 68 LIST OF SYMBOLS N‘smaeoww'xmwgb KM KW) Pa D . . D . . Area [L2] Specific moisture capacity [L'l] Maximum particle dimension [L] Diflixsivity [L’TJ Media efl‘ective size (10% finer than dimension) [L] 60% finer than dimension [L] Void ratio [1] Pore formation factor [1] Water-filled porosity [1] Body forces [MLT'Z] Acceleration due to gravity [MLT'Z] Pore shape factor [1] Distance above datum [L] Capillary pressure head [L] Pressure head [L] Difl‘erence in free-water surface elevations [L] Permeability [L2] Saturated hydraulic conductivity [LT'] Unsaturated hydraulic conductivity (moisture) [LT'] Unsaturated hydraulic conductivity (tension) [1.1“] Distance [LI Pressure [IVIII'T'z] Atmospheric pressure [ML'lT'Z] ix R V: N 6&9‘9-9 Bubbling (air-entry) pressure Capillary pressure Pressure in soil water Volumetric flux Volumetric flow rate Radius Pore equivalent radius Reynold’s number Effective saturation Residual (irreducible) saturation point Time Tortuosity at saturation Tortuosity at efl‘ective saturation Tortuosity of the wetting phase Coefficient of uniformity Specific discharge Thickness of media perpendicular to barrier Linear velocity Mass flux Work Horizontal space coordinate Horizontal space coordinate Vertical space coordinate Capillary rise distance Distance above free-water surface Solid-liquid contact angle Porosity Gravitational potential - per unit mass Total (hydraulic) potential - per unit mass X [MU'TZI [ML'lTZI [ML'sz] ILT'] [13'1"] [L] [L] [1] [1] [1] [T I [1] [1] [1] I 1] [11"] [L] [1'1"] [Ml-QT'I M’T’] [1] I1] [1] [L] [L] [°] [1] [L’F’] [L714] spbpgmhpsw < Surface tension Total (hydraulic) head Pore-size distribution index Dynamic viscosity Moisture content (mass basis) Initial moisture content Volumetric water content Fluid density Bulk density of media Matric suction (moisture potential) head Del mathematical operator [M72] [L] [1] [MU‘T’] [1] [1] [1] [ML'3] [Mrs] [L] none Chapter 1 INTRODUCTION Water is among the most basic necessities of Virtually all life on our Earth. Its specific and peculiar characteristics allow human existence to flourish as part of a complex and remarkable ecosystem. We even dare to speculate whether life could exist on distant worlds based on possible evidence of water. It lies at the base of our subsistence and our culture. Wars are fought over it; peace is made across it. It can isolate societies, andcan symbolize baptism and societal introduction. It hangs above us and runs below us. And yet its simple molecular structure—two hydrogen atoms and one oxygen atom—belies the impact that decline in quality or quantity ean have on our technologically complex, and yet often aloof, society. A clean and plentiful supply of water for current and future uses is becoming more scarce as a naturally-propagated resource. Population stresses across the globe, and even in previously remote rural communities, have mandated consideration of water treatment systems and conservation programs. Large, centralized wastewater treatment plants have been marginally successful in handling increasing purification needs, but can be economically prohibitive or practically unjustifiable. Smaller scale and localized systems are receiving greater attention and support in numerous areas, although many of these 2 systems are still being regarded critically in the private and public arenas. This is often due to the perception of unreliability of these “alternative” systems, although improper design, installation and/or management are more frequent causes of failure than the inherent technology. Emulating the mechanisms of the hydrologic cycle and the myriad of physical, biological and chemical processes which commune to efliciently recycle the Earth’s water resources is a challenging, yet crucial task. It is imperative that scientists work to understand and apply the pathways through which water can be reclaimed and reused in order to meet the needs—let alone satisfy the demands—of an increasingly sophisticated human population. Biological systems typically are not easily characterized and reproduced, yet they often provide the most eflicacious solutions and reliable schemes. Working in consort with water to sustain life is the “living mantle” of the planet: the soil. The interaction of these two vital resources provides us with crops, protects against flooding, even moves mountains. Much has been done, particularly in the agricultural realm, to promote and actualize investigation into the static and dynamic interchange between soil as a porous media, and water as a permeating substance. From oil reserve extraction to aquifer remediation to crop subirrigation, examples of human attempts to understand and afi‘ect porous media flow mechanisms and characteristics are numerous and diverse. The movement of water (and other fluids) through soil takes many courses as part of the hydrologic cycle. Infiltration and redistribution are two such courses which serve to transport water according to the governing laws of potential, and the natural quest for the elusive state of equilibrium. Capillary rise, or the increase in elevation due to a potential 3 gradient, is another unsaturated flow mechanism which been the subject of research over the years. Some water treatment systems, such as sand filters, take advantage of unsaturated flow in order to provide an aerobic environment for the propagation of organisms beneficial to treatment. Coupled with physical and chemical processes, this biological activity can efl‘ectively provide a level of treatment which helps to ensure proper management of animal, domestic and, to some degree, commercial wastes. One such wastewater treatment system relies upon capillary siphoning, or transport over an impermeable barrier in unsaturated media, to provide an aerobic treatment zone following anaerobic treatment. A version of the upflow filter is now commercially available and approved for use in a limited area of the United States. In order to optimize the functionality and economics of this type of system, a need was identified for research into the hydraulic characteristics of the media specified for the capillary upflow matrix of the system. This research serves as a partial response to that need. To that end, the specific objectives of the research described herein are to: l) Quantify the efl‘ect of capillary rise distance (2 cm < z < 10 cm) on the volumetric flow rate of water over an impermeable barrier in unsaturated sand media; and 2) Study the relationship between the geometric properties (effective size and uniformity) of the transport media and the rate of capillary siphoning over an impermeable barrier in unsaturated sand. Chapter 2 REVIEW OF THEORY AND LITERATURE Characterization of a Porous Media Flow System In order to understand and optimize flow through porous media, it is important to properly describe the firndamental components of the flow system. These components are 1) the media itself and 2) the fluid (or fluids) in motion through it. Complete and accurate descriptions of these parts allow for better comprehension and application of any given flow system. Additional components, such as an organic fraction, may also exist and may afi‘ect flow through the system, but these are outside the scope of this discussion. Media A complete discussion of fluid transport through a porous media system would be quite extensive, considering the wide range of related fields from rock bed oil extraction to crop water requirements to wastewater treatment. While some of the concepts are common to most or all situations, it would be dificult to cover all aspects of porous media flow. Therefore this discussion will be conducted within some necessary restrictions: 1) the non-solid space in the media must be interconnected and large enough to allow entry of fluid particles; and 5 2) the media primarily being considered will be of unconsolidated, granular structure. Many of the concepts related herein hold true for other types of porous media systems such as wood, textiles, building and filter materials. This is also true for other types of porous earth materials such as those where the pore space was formed by evolution of gases during crystallization, or vugular limestone where soluble constituents of the rock have been dissolved by water forming channels (Corey, 1986). SOLID MATRIX The portion of the media system being considered which does not allow the entry of any fluid, even under pressure, can be described as the solid Won. The particles of this fi'action constitute the solid matrix. This matrix can also be in a continuous form, such as limestone. A comparative and descriptive measure of the material being examined is the bulk density, p5,. This is the ratio of the mass of dried material to the sample’s total volume. In soils p, can range fi'om about 1.1 grn/cm3 in clay soils to 1.6 grn/crn3 for sandy soils (Hillel, 1982). Bulk density is afl‘ected by the structure of soils, or by the degree of compaction of the media. The solid matrix can be considered to be either consolidated or unconsolidated. An example of a consolidated porous media is limestone which maintains an overall structure. Sand is an example of an unconsolidated media, where the individual particles make up the solid matrix and exert a stress on neighboring particles if an external force is applied. 6 Hillel (1982) defines structure as the “arrangement and organization” of particles, and describes three general categories: single-grained, massive and aggregated. Most granular media have a single-grained structure with little tendency to adhere to neighboring particles. The arrangement of these grains can vary widely, and depends upon their relative sizes and shapes as well as the way they were deposited. Tightly packed media in large cohesive blocks are referred to as having massive structure. An example of this is dried clay. Aggregated structure results fi'om the primary particles grouping together in “quasi-stable clods”; these clusters acquiring their own structural characteristics (Hillel, 1982). This category is considered desirable in typical agricultural applications. Many texts are available which comprehensively cover media characteristics, particularly soils (Terzaghi and Peck, 1967; Lambe and Whitman, 1969; Hillel, 1982). This discussion focuses primarily on sand-like materials of single-grained structure. A number of different methods have been adopted by various disciplines to describe the geometrical makeup of a given granular media sample. One method used in soil science is the statement of relative amounts of sand, silt and clay in the sample. The commonly used USDA method defines these portions as 2 mm 2 d 2 0.05 mm, 0.05 m > d > 0.002 mm, and d 5 0.002 mm respectively, where d represents the largest dimension of a particle (Hillel, 1982; Singer and Munns, 1987). Engineers generally define unconsolidated media particles using two variables: efi‘ective size, D10, and uniformity coeficient, U. The efi‘ective size is defined as the particle size for which ten percent of the total mass of the air-dried media is finer. The 7 uniformity is a measure of how much the particle sizes vary within a media sample. It is defined as the ratio of the D60 to the D10, where the D60 defines the particle size for which sixty percent of the total mass is finer (Terzaghi and Peck, 1967). PORE NETWORK The pore space within any porous media is considered to be either efi‘ective or isolated. Effective pore space is interconnected and forms a continuum, or network, within the media. This includes dead-end, or blind, pores. On the other hand, some of the non- solid space within the sample is not interconnected and therefore considered to be isolated fiom the effective pore network. These isolated pores do not contribute to fluid transport through the media. Pore space can exist within individual grains of a porous media (primary pore space) as well as between aggregates of the material (secondary pore space). The presence of aggregates implies some amount of particle cementation, although secondary pore space can exist without it. The total volume of pore space, relative to mass, of media with aggregated structure is typically greater than that which is not. (Corey, 1986). Significant parameters which are used to describe the non-solid space contained within a sample of porous media are porosity, bubbling pressure, permeability, and tortuosity. Descriptions in the literature of this pore space range from idealized models of unconnected bundled tubes (Morel-Seytoux, 1969) to complex network systems (Dullien, 1972). 8 One of the primary descriptors of efl‘ective pore space is the porosity ¢. Porosity can be defined as the ratio of the interconnected, non-solid volume to the total volume of the sample of media being considered. As a ratio, d is dimensionless and is theoretically bounded by 0 and 1, although practical values in granular porous media range fi'om about 0.3 to 0.6. The volumetric water content a” defined as the water-filled portion of the total volume of a media system, can approach ¢ under saturated conditions. An alternate description of the void space in a media is the void ratio e which is defined as the ratio of the volume of voids to the volume of solid substance (Terzaghi and Peck, 1967). Media with structure will have higher porosities than those without. The shape of the grains can have an effect on porosity, as plate-shaped particles could be oriented in such a way as to create porosities lower than that of spheres, although the opposite is also possible. Porosity is usually minimized for media containing grains of widely varying sizes as the smaller particles can move into the spaces between the larger particles. It is also possible for organic and mineral cementing materials (and other precipitates) to reduce porosity. This means that consolidated sandstones generally have lower porosities than unconsolidated sand. Corey ( 1986) gives some approximate porosities for various typical materials: Consolidated sandstones 0.10-0.30 Uniform spheres packed to theoretical minimum porosity 0.26 Unconsolidated sands 0.39-0.40 Soils with structure 0.45-0.55 9 The “size” of a pore is a dificult thing to define exactly. Unlike a capillary tube, a pore typically does not have any discreet diameter or length, but rather has a variety of interconnections with other pore space through throats or constrictions (Dullien, 1972). The average pore size of a reference volume in a sample is defined by Corey (1986) as the ratio of the porosity of the sample to its specific surface. The specific surface is defined in his text as the ratio of internal solid surface area to the total volume, although henotesthatinsomecasesitisconsideredtheratio ofthisareatothemass ofthe solid. Average pore size is analogous to the concept of hydraulic radius in hydraulics in that it refers to the ratio of the volume of the pore to the surface area bounding it. Pore size is therefore associated with grain size and distribution in that smaller grains generally mean smaller pores. Porous media with structure can, however, have larger pores associated with the secondary pore space (Corey, 1986). Malik et al. (1984) discussed the shape factor G as a means of describing a pore’s geometry. These authors proposed that G could be written as 8 G=—+E f where f is the water-filled porosity (or efl‘ective saturation S.) and E is their formation factor. This formation factor accounts for the tortuosity, shape and continuity of the flow pathways in the porous media, and was empirically related to the permeability k of the media as E = 126 - 166280k". The proposed shape factor formula is valid for a capillary tube where f = 1 and E = 0. Therefore G is equal to a value of 8 for circular, uniform diameter capillaries. 10 Porous media was also compared by the authors to a “group of communicant tubes” which can be characterized by an equivalent radius r.. This parameter is defined as the radius of a capillary tube which would exhibit equivalent behavior. Transmission constants derived fi'om the results of capillary rise experiments were used to predict the pore geometrical properties E, G and r. (Malik et al., 1984). These predicted values for r. were later found by Kumar and Malik (1990) to be higher and linearly related to the mean pore radius determined from soil water desorption curves. Lawrence (197 7) calculated r. fiom desorption curves assuming cylindrical pores and applying the classic capillary rise equation in the form where pgh is the applied suction, yis the surface tension of the fluid and a is the solid- liquid contact angle. The breakdown of the pore space-within an element into various ranges of pore size is defined as the pore-size distribution. This is somewhat related to the grain-size distribution in that generally a greater variation in grain sizes means a greater range of pore sizes. An exception can be found in the case of a sample which has been mixed to the point that the pore-size distribution is fairly uniform even with a wide grain-size distribution. Brooks and Corey (1964) state that the pore-size distribution index 2. evaluates the distribution of sizes of the flow channels within a particular porous media. They present experimental evidence that (for isotropic media) this parameter, along with the bubbling 11 pressure p1,, can be used to describe the functional relationships among saturation, capillary pressure and the air and water permeabilities. The pore-size distribution index is defined by the authors as the slope of the log- log graph of effective saturation S. as a firnction of capillary pressure head (pJpg). The A s. E [2.] Pc where p. is the capillary pressure at which desaturation of the media begins. ,1 was found empirically derived equation is to range fiom a value of less than 2 inmedia with well-developed structure (less uniform) to values of 5 for some sands (more uniform). There is a tendency for finer materials to have smaller values of pore—size distribution index, although thorough mixing and dense packing can cause It to increase. It was determined experimentally that l varies inversely with d (Corey, 1986). Hillel (1982) also states that the pores in coarse-textured soils are usually more uniform in size. However, Laliberte and Brooks (1967) found that pore—size distribution is changed only slightly over a wide range of porosities (Varied by changes in bulk density) while the hydraulic conductivity and bubbling pressure of a given media may change several-fold over the same range. Brooks and Corey (1964) discuss how, under certain conditions, A and Pb can be used to describe the requirements for sirnilitude between any two flow systems in porous media. Laliberte and Brooks (1967) later stated that for modeling purposes, one requirement for sirnilitude between model and prototype is identical values of pore-size 12 distribution index. The size reduction of the model is determined by the ratio of the bubbling pressures in the model and the prototype. Evidently, the bubbling pressure of the model medium may be adjusted to suit the size of the model by changing the bulk density and hence the porosity of the medium without appreciably changing the pore-size distribution index. Bubbling pressure pr, or air-entry pressure, has been defined by Brooks and Corey (1964) as the lowest capillary pressure at which a continuous gas phase can exist within the media. They state that the bubbling pressure is related to the maximum pore-size forming a continuous network of flow- channels within the medium. They also present experimental evidence that (for isotropic media) this parameter, along with the pore-size distribution index 2., can be used to describe the firnctional relationships among saturation, capillary pressure and the air and water permeabilities. Stakrnan (1966) used the air bubbling pressure to determine the equivalent pore diameter, from which he calculated the mean particle size of the sand separates and thereby determined the hydraulic conductivity of the sample. He compared these estimates to the values calculated from the Kozeny-Carman equation and the Brinkman formula. Air entry into media with coarse texture is ofien more distinct than finer media due to the more uniform pore sizes which usually exist in the coarser media (Hillel, 1982). More rapid desaturation will occur at this critical pressure due to the large fiaction of pores which begin to drain as pb is reached. The permeability It is the portion of the hydraulic conductivity K of a media flow system which is a factor only of the media itself, independent of the fluid properties and 13 the flow mechanism. Permeability is measured in darcys where one darcy is equal to a flow rate of one cubic centimeter per second of a fluid with a Viscosity of one centipoise through a cube having sides one centimeter in length under a pressure difference of one atmosphere. Permeability, sometimes referred to as specific, or intrinsic permeability, is related to K as Rs a K: where p is the fluid density, g is the acceleration due to gravity, and p is the dynamic viscosity of the fluid (Corey, 1977). Canaan (1941) speculated that media permeability could be calculated fiom particle size and porosity, while more recently Malik et al. (1984) state that the intrinsic permeability of porous media is determined by the geometrical properties of the pores, such as equivalent radius r. and the shape factor G. This shape factor accounts for porosity, tortuosity, shape and continuity of conducting channels in the media. Suter (1964) declared that the capacity of a soil to store fluid is proportional to its porosity, but porosity has little efl‘ect upon permeability. However, the usefulness of this storage capacity is dependent upon permeability, which in turn depends upon continuous passageways through the media. The introduction of finer particles reduces permeability by increasing tortuosity with minimal changes to porosity (Suter, 1964). Fluid particles of the wetting phase must travel an increasingly tortuous path as the media desaturates. This is because the particles can no longer travel across the center of pore spaces where the non-wetting phase now exists. Corey (1986) determined that (for l4 isotropic media) the tortuosity of the wetting phase T w is inversely proportional to [II-9.] _=_ Se2 Tse w where T [,0 is the tortuosity of the wetting phase at saturation (S. = 1.0). Effective effective saturation S, as saturation represents the fluid available above the “irreducible” or residual saturation point 8,. Below this point the moisture is considered to contribute negligibly to flow (Corey, 1986) Fluid The other major component of the porous media flow system, in addition to the media, is the fluid which is being transported through it. The characteristics of the flow system depend upon both the media properties and the fluid properties. The fluid can be in a liquid or a gas phase, or in a combination of these. If more than one fluid, or more than one phase of the same fluid, occupies the pore space concurrently the system is said to be“ ’ unsaturated with respect to the specified fluid. Some primary parameters of the fluid which affect its ability to move through the media system include the surface tension rand the viscosityp. These parameters are in turn afl‘ected by such variables as temperature and impurities in the fluid. The molecules on the surface of a liquid experience an unbalanced force due to their attraction to molecules in the interior of the liquid. This net inward force causes a tension to be created in the surface which can be measured. The molecules in the interior are in a lower energy state than those at the surface so molecules attempt to move into the 15 liquid’s interior. Surface tension 7 is a measure of the energy required to increase the surface of the liquid, and is inversely afi‘ected by temperature. For water at 25°C, r= 7.20 x 10'2 J/mz. For liquid to spread across the surface, or wet, another material a small amount of energy must be expended. Whether the liquid will wet the surface or retain its spherical shape depends on how the cohesive forces between like molecules compare to the adhesive forces between unlike molecules, such as those of a liquid and those of the surface. The liquid will wet the surface as long as the adhesive forces are suficiently strong. Otherwise a liquid drop will be maintained on the surface. Adding a detergent to water lowers the surface tension of the water. A decrease in surface tension corresponds to a decrease in the energy required to spread the drop into a film. Substances which reduce the surface tension of water are known as wetting agents (Petrucci, 1985). In the area of contact between the two-fluid surface and the solid surface, the interfacial forces act along the planes of contact between the three phases. It is dificult to measure the interfacial force which exists at the solid-liquid interface, although it is important in unsaturated systems. This force controls the contact angle a of the interface between the two fluids in contact with the solid. This angle, which is measured through the denser fluid, determines which is the wetting or the non-wetting fluid (Corey, 1986). Using glass beads and water, Laroussi and De Backer (1979) measured contact angles ranging from 41° to 66° for wetting and drainage respectively, supporting results of previous work by other authors. 16 Wettability describes how fast a fluid will spread over a surface, and is inversely related to surface tension and Viscosity (Corey, 1986). Young’s equation states that for the interfacial forces to be in equilibrium, 7w cos or + 731. = 765 where the subscripts refer to the liquid-gas (LG), the solid-liquid (SL) and the gas-solid (GS) interfaces. The first term on the left side of the equation is referred to by Bear (1979) as the adhesion tension. This determines which fluid will preferentially wet the solid surface by adhering to it and spreading out over it. For a < 90° the denser fluid is considered to wet the solid (ie. water and air), while for a > 90° the denser fluid is said to be the non-wetting fluid (ie. mercury and air). Viscosity p is also a function of intermolecular forces of attraction. It is related to shear force and deformation rate, and can be thought of as a fluid’s resistance to flow. Temperature increase will generally cause a reduction in p as the strength of molecular forces of attraction are lowered (Petrucci, 1985). Newtonian fluids—such as air, water and oil—exhibit direct proportionality between shear stress and the velocity gradient of the fluid near the shear surface (Potter and Wiggert, 1991). The flow mechanism which consists of two distinct fluids displacing each other without mixing is called immiscible displacement. In miscible situations there is no distinct interface between the fluids, such as flesh and salt water in an estuary, or aquifer intrusion (Freeze and Cherry, 1979). Irnmiscible fluids are characterized by this boundary across which discontinuities in density and pressure exist (Corey, 1986). 1 7 Transport Phenomena in Porous Media Energy And Potential Classical physics defines energy in two principal forms: kinetic and potential. Movement of water through unsaturated media is generally at very low velocities, and because kinetic energy varies with the square of velocity this form is generally considered to be negligible. This leaves the potential energy of the water in the media as the predominant form. The difl‘erence in this potential between two zones becomes the driving force for water movement through the media as it attempts to reach and maintain an equilibrium condition (Hillel, 1982). . Water in a porous media is difl‘erent fijom pure, flee-standing water in that it is influenced by force fields in addition to those due to body forces such as gravity. These include the attraction of the solid matrix and the efi‘ect of dissolved constituents. TOTAL POTENTIAL The energy state of water in soil or other porous media can be described relative to its fiee energy per unit mass, or potential (Hillel, 1982). It is necessary to discuss the concept of potential in order to describe flow through porous media as it is the gradient of this energy field which is the driving force for flow. This is true for both saturated and unsaturated media conditions, the difference being the individual factors which make up the total, or hydraulic, potential. This potential is of more importance as a relative measure of energy level rather than as an absolute quantity. According to the International Soil 18 Science Society (Aslyng, 1963 in Hillel, 1982), the formal definition of “total potential” of soil water is “. . .the amount of work that must be done per unit quantity of pure water in order to transport reversibly and isothermally an infinitesimal quantity of water fi'om a pool of pure water at a specified elevation at atmospheric pressure to the soil water (at the point under consideration)” In actual practice the potential is determined by measuring some other property, such as pressure or elevation, which has a known relationship to the potential. The total potential consists of contributions from various factors, such as the gravitational potential, the matric potential, the osmotic potential and possibly others. These other factors exist under conditions which vary according to each individual case being examined, and in many cases are of negligible influence on the total potential (Klute, 1952). In this discussion, the total potential (Dwill be considered to be the sum of two components: the pressure potential (“matric” potential for unsaturated flow), d... and the gravitational potential, pg. There may be other potentials, such as osmotic and adsorptive potentials, depending upon whether or not the pertinent force fields are present and act upon the water in the porous medium. The total water moving field is given by -Vd>= -V(¢m +45). Freeze (1969) wrote that the existence of continuous saturated-unsaturated flow domains implies the existence of this potential field, with the potential quantity defined in 19 such a way that it is valid both above and below the water table. He referred to the quantity as the hydraulic potential ‘1’ = 92+(P'Po) /P where 4) is the hydraulic (or total) potential (cm’lsec’), g is the acceleration due to gravity (cm/secz), z is the elevation above the datum (cm), p is the pressure (dynes/cmz), pa is the atmospheric pressure (dynes/cmz), and p is the density of the fluid (glcm’). If pa is taken to bezeroandwerecallthatp=ng, weobtain <1> = g(z+H). With the hydraulic or total head o defined as dilg, we note that ¢=2+H where z is the elevation head and H is the pressure head (substituting the moisture tension head V for unsaturated conditions). MATRIC POTENTIAL The complex air-water interfaces in an unsaturated medium are important in determining the pressure in the water. The forces acting in the air-water and solid-water interfaces are responsible for the soocalled capillary phenomena and originate in the cohesive and adhesive forces between molecules. These forces attract and bind water in the soil and lower its potential energy below that of bulk water (Hillel, 1982). 20 The pressure potential in an unsaturated medium is usually called the capillary or matric potential. In 1907 Buckingham defined the capillary potential by assuming a conservative field of force, the gradient of which is the capillary potential (Novak, 1972). Gardner et al. (1922, in Richards, 1931) later noted that this potential was related to the pressure in the water films, and showed that porous clay apparatus could be used for its measurement. Richards (1931) describes experiments which show that the pressure in the liquid films is less than atmospheric and is a firnction of the quantity of liquid present in the medium. He stated that “(t)he forces acting in the boundary surfaces of liquids are directly responsible for all capillary phenomena and have their origin in the cohesive and adhesive attractions which are exerted between molecules.” CAPILLARY PRESSURE As previously stated, when two immiscible fluids are in intimate contact, an interface is developed across which there is a discontinuity in pressure. There is a tendency for this interface to assume a configuration which minimizes the area of contact between the fluids. This is due to the flea energy possessed by the molecules of the liquid lying on the interface (Richards, 1931). This is what causes the curved nature of the interface, as a sphere has the smallest proportion of molecules at the surface (Petrucci, 1985). In a vertical capillary standing in water, a curved surface or meniscus is formed, and capillary rise takes place until the hydrostatic pressure balances the pressure difference due to curvature. Across the curved interface the pressure difference at any given point is described by 21 ..A - — (l+_l_) Pc- P-Pz PI-‘l’ r’ r” where p, and p; are the pressures in the fluids taken as the interface is approached from their respective sides, yis the surface tension, and r’ and r " are the radii of curvature of the interface at the point (Carman, 1941). The magnitude of the pressure difference depends, therefore, on the curvature of the interface which is a firnction of saturation. This is known as the Laplace formula for capillary pressure, p, (Bear, 1979). When the two fluids being considered are air and water, the air is often considered to be at atmospheric pressure (p; = 0) which defines the capillary pressure as a negative value, leading to the use of the terms “suction” and “tension” in much of the literature, primarily that of soil scientists. A related term is pF which is the logarithm to the base 10 of the matric suction in centimeters of water (Stakman, 1966). Pressure head is defined as the pressure divided by the specific weight of the fluid, which allows the use of units of length, greatly simplifying calculations (Potter and Wiggert, 1991). The matric suction in a sample can be measured with a tensiometer, and is often referred to as capillary pressure head he, defined by Bear (1979) as hc=Pc/Pg=-Pw/PQ; Pw=0. Fluid Movement Fluid flow in porous media can occur in either a steady state or transient flow condition. Flux, gradient and water content remain constant with time in a steady state flow system, while they can vary in a transient flow system. Steady flow measurements are generally less difficult to obtain and more accurate than transient flow (Hillel, 1982). 22 CONSERVATION LAWS The flow of fluid is a mechanical process which must obey the laws of physics. The Navier-Stokes equation for the motion of a fluid, which relates the viscous, inertial, body and pressure forces involved in the flow, can be written 92. -92. a .1. ) dt-F p+(p13VV v+V Vv where p is the fluid density, v is the linear velocity, F denotes the body forces, ie. acceleration due to gravity, P is the pressure in the fluid, and ,u is the Viscosity. The solution of this equation is diflicult even in he space where the boundary conditions may be known and easily stated. Use of this equation in heterogeneous, unsaturated media is limited due to the difficulty in describing the boundary conditions. Therefore, an alternate expression must be used to describe the motion of a fluid in such cases (Klute, 1952). The flow of a fluid must obey the principle of conservation of mass. This is usually expressed for free space as: "the net excess of mass flux per unit time into or out of any infinitesimal volume element in the fluid is equal to the time rate of change of the fluid density in the volume element multiplied by the free volume of the element”. This is stated mathematically as where p is the fluid density and V is the mass of fluid flowing through unit cross section in unit time. This must be modified for porous media where the entire pore volume is not available for fluid flow. For unsaturated media we may write 23 d gt-(pbgl = 'V -V where n, is the bulk density and 9 is the moisture content on a mass basis. Replacing the mass flux V (=qp) with the volume flux q (as defined below by Darcy’s law) yields %IP,OI=V-(pKVd>) where p is the fluid density. This is the general equation of unsaturated flow (Klute, 1952). EQUATIONS OF FLOW H. Darcy was the first to model the movement of water through porous media in 1856. In studying the flow of water through an early sand filter for the town of Dijon, France, he came up with the empirical equation .. ._ A_P 9-..- L) to predict the volumetric flow rate through sand under saturated, isothermal, and steady state conditions. This relationship indicates that the flow rate Q is proportional to the change in pressure Ap over the distance L by the product of the hydraulic conductivity K and the cross-sectional area of the column A (Novak, 1972). Darcy’s law is analogous to Fourier’s law in the flow of heat, to Ohm’s law in the flow of electricity, and to Fick’s law in difi‘usion (Klute, 1952). Darcy's law was also found to hold true for unsaturated flow if the driving force is changed fi'om a pressure gradient (Ap) to a potential gradient (A (D). Darcy’s law is valid 24 for unsaturated media at a given moisture content because in the unsaturated medium there are pores which are wholly or partly filled with air. Since air inclusions efl‘ectively prevent liquid flow through themselves, they could theoretically be replaced by a solid phase and the result would be a saturated medium (Richards, 1931; Corey, 1986). It is assumed that the compressibility of air is negligible in this analogy. Itmaybeseenthenthatthepresenceofairintheporeshastheefi‘ect ofreducingthe volume of medium available for flow of the fluid and does not of itself invalidate Darcy's law. Due to the fact that the effective cross-section available for flow of the fluid is reduced in an unsaturated medium as compared to that of a saturated medium, the conductivity of an unsaturated medium is a function of moisture content, K( 6), and will decrease with decreasing moisture content of the medium (Klute, 1952). Some limitations do exist for the application of Darcy’s Law in porous media. Cases in which the flow rate is high enough to cause non-laminar flow, such as some limestones or cracked rock, preclude the use of the law. Reynolds number R., based on average grain diameter of the media, must be less than 10 when defined as _P_%‘l R" u where p and p are the density and viscosity of the fluid, d is the grain diameter and v, is specific discharge, defined as volumetric flow rate over area (Freeze and Cherry, 1979). Darcy's law for flow in the x-direction of an x, y, z coordinate system can be written as - 92 qx - le9 yr 29 W) ax - 25 Flow in the other two coordinate directions can be described with similar expressions (Freeze, 1969). In this case the hydraulic conductivity is expressed as a function of position and matric suction head. The equation of continuity for unsteady flow of a compressible fluid, is 3(pvx) 300v!) atpvz) _ a -[ ax + By + 32 ]’a—/”9)' Substituting the appropriate form of Darcy's law into this equation and expanding the right-hand term, the continuity equation becomes %[PK(x. y. z. V0333] +%[pl<(x.y. avg—3] +%[PK(X.)’. ZJI’laa—r] = P 33—? + '3;- From this generalized equation of flow it is possible to develop the one-, two-, or three- dimensional forms of the steady or unsteady flow equations for saturated or unsaturated flow of a compressible or incompressible fluid through non-homogeneous, porous media. The terms on the right-hand side of this ecjuation represent the de—watering of an elemental cube within the media, both from changes in the moisture content 0, and fi'om changes in the fluid density p. Any variation in hydraulic conductivity K with position in saturated flow results fiom the inhomogeneity of the porous medium, while in unsaturated flow, K varies with position even in homogeneous soils, due to the firnctional relationship between K and moisture content (Freeze, 1969). The flow equation for water in unsaturated soils was first formulated in 1931 by Richards who approached the problem of capillary flow measurement using methods 26 which were theoretically and experimentally analogous to those used in the study of conduction of heat and electricity. Water is usually assumed to be incompressible for unsaturated unsteady flow, that is p is constant and é‘p’o't = 0. For a homogeneous soil, K(x, ,z, w) becomes Kai) and the one-dimensional, vertical form reduces to Richards' equation a 22 -29. Elxmlazll‘ at' The uI-based form of this equation for one-dimensional, vertical, unsaturated, unsteady flow becomes (Freeze, 1969) a 31’. _ 21’. ifwe recall that ¢=z + wand with the specific moisture capacity C defined as d9 C(yl) = a. The corresponding 6-based equation was derived by Philip (195 7) using the concept of difl‘usivity D where The derived equation is 27 where wand K are single-valued firnctions of 0(ie. hysteresis is ignored), and z is the vertical dimension, positive upwards. The corresponding one-dimensional horizontal form is 39 a 39 3:37.095) where x is the horizontal space coordinate (Philip, 1991). Poiseuille’s Law applies to capillary flow fiom a tension-free source, and is stated Irr‘p = 8141 Q where Q is the volumetric flow rate, r is the tube radius, p is the pressure difl‘erence driving flow, L is the tube length and p is the fluid Viscosity. The flow into capillary tubes can be modeled using the force pulling the fluid (2m ycos or) acting on the cross-sectional area (102). The equation then becomes _ may cosa Q - 4141 and can easily be solved for capillaries of various radii (Swartzendruber et al., 1954). This law also fails when high pressure gradients exist in the system (Richards, 1931). Saturated Flow Hydraulic conductivity is defined fiom Darcy’s law as the proportionality constant K which contains media and fluid components as xJ—P’i. u 28 Traditionally, determination of K involves applying Darcy’s law to results of laboratory testing. Saturated conductivity is also somewhat affected by temperature as p is inversely temperature-dependent (Swartzendruber, 1969). Malik et ai. (1984) estimated the hydraulic conductivity fiom capillary rise experiments. The primary advantage cited by these authors was the great reduction in time necessary to obtain conductivity data as compared to standard methods which require complete saturation of the sample before testing. They referred to their method as the “Quick Capillary Rise” or QCR method. The validity of this approach was verified a few years later (Kumar and Malik 1990) who found that the values obtained using QCR matched those determined by traditional methods. Unsaturated Flow When the efi‘ective pore space of a porous medium is no longer completely filled with a given liquid, the medium is said to be unsaturated with respect to that liquid. The type of unsaturated system, however, depends upon the nature of the second fluid occupying the vacated pore space. If the second fluid is another liquid, heterogeneous saturation results if the two liquids are immiscible. Ifthe second fluid is a gas, or a mixture of gases such as air, then the resulting three-phase system describes what is commonly considered unsaturated flow. The process of water flow in such an unsaturated system could also be described as a two-fluid problem in immiscible displacement, where water and air are the fluids (Swartzendruber, 1969). 29 Unsaturated media exhibits adsorption in addition to capillary phenomena which causes the formation of hydration “envelopes” over the surface of the particles. Particularly under greater suction conditions, the. primary water retention mechanism is adsorptive rather than capillary. In this case retention capacity depends more on media texture than structure (Hillel, 1982). The movement of a fluid along a solid surface depends upon both adhesive and cohesive forces. The initial wetting of the solid by the liquid depends primarily upon adhesive forces. Ifthe surface densities of fiee energy for the air-liquid, air-solid and liquid-solid interfaces for a given three-phase system are n, 72 and m respectively, it may be shown that 7, +7, -y,, =W =yr(l+cosa) where Wis the work necessary to separate a unit area of liquid from solid and a the contact angle between the liquid and the solid. If W< 27,, a may vary anywhere between 0 and 180 degrees. If, however, W 2 27, then a is zero and the liquid will spread over the surface of the solid and is said to wet the solid. Once the solid is wetted adhesive forces primarily hold the liquid film firmly in contact with the solid surface and are no longer efi‘ective in producing liquid motion. Additional liquid outside the adsorbed films is flee to move as a result of unbalanced forces (Richards, 1931). In a liquid-saturated porous media system the process of water transport is one of bulk flow. However, the existence of the gaseous phase in an unsaturated system allows also for the possibility of water transport in vapor form. It is generally felt that vapor- phase transport is relatively insignificant compared with the liquid-phase transport, unless 30 the soil water content is very low or when temperature variations or salts induce significant vapor-pressure gradients (Gardner, 1958; Swartzendruber, 1969). Klute (1952) credits Childs and George with establishing the method of calculating the functional relationship K(Q between conductivity and moisture content of an unsaturated system fiom the moisture characteristic curve. This curve is a plot of the matric potential versus the moisture content of the transport medium. They related the conductivity of an unsaturated medium to the geometry of the void space using a pore size distribution curve as a measure of the latter. Some of the factors which canafl'ect flow in unsaturated media are entrapped air which may go into or come out of solution, dispersion of aggregates in the fluid, bacterial growth and action during the flow period plus the variation due to moisture content (Klute, 1952). The temperature dependence of surface tension, which plays a role in the moisture state of unsaturated media, has some efl‘ect on the V-a relationship and thereby also on conductivity (Swartzendruber, 1969). Wind (1966) used evaporation from a saturated column to determine unsaturated hydraulic (”capillary”) conductivity. The total weight of the column was determined daily along with changes in the moisture content and tension at various depths fiom the column surface. He found that measurement of K0,!) determined with the aid of Bouyoucos' electrical nylon units, are fairly accurate at moisture tensions between 0.1 and 20 atmospheres. Below 0.1 atmospheres they lack accuracy. He calculated the velocity of flow at different depths from the changes in moisture content and weight. For every day, at every depth the velocity of flow is known; it equals 31 the amount of moisture lost by the soil below. The potential gradient belonging to this flow was calculated fi'om the moisture tension readings, thereby allowing calculation of K(r//) with the formula q=x(w)[-‘-;;,'”--1) where q is the velocity of flow in mm/day, and duddx is the potential gradient in chcm. It is known that the hydraulic conductivity becomes a firnction of matric potential (and thus water content) in unsaturated media. The relationship between V and 0 is described functionally in the moisture characteristic (or moisture retention) curve. This curve is not single-valued, but rather dependent upon the moisture history of the sample, such as whether fluid is draining fi'om or being added to the media. This multi-valued functionality is referred to as hysteresis, and afl‘ects interfacial tension and wettability depending upon whether the fluid-fluid interface is advancing or receding. A higher saturation level can be obtained at a given value of tension for a sample being drained than for one during irnbibition. Air can also be entrapped during irnbibition, which will not permit the complete saturation of pore space. During the draining cycle, once the local pressure has increased to allow fluid movement through a constriction or neck, adjoining larger pores will desaturate almost immediately (Bear, 1979). Refilling the same pores requires less pressure as the pressure is dictated by the size of the pore, not the neck (Parlange, 1980). This phenomenon is often referred to as the “ink-bottle” efl‘ect. Other authors have attempted to account for the hysteresis phenomenon in their modeling of unsaturated flow (Miller and Miller, 1955; Philip, 1964). As stated by Philip (1991), hysteresis does not invalidate the use of the equations of flow as long as the M6) 32 firnction chosen is appropriate to the flow being studied; a wetting curve is appropriate for absorption or infiltration, while a drying curve is appropriate for water removal processes. Upward Flow Through Porous Media Evaporation Thaeisgaraalagreananmmngsdarfistsflmmerateofevaporafionfiomasoflis wnnofledbydthaflecapadtyofamwsphaemevaporatewatambyflremfl'scapadtym nansnhmmdwanface.Atrdafivdyshdlowdepthsflwamwspimistypicaflyflw lirnitingfactor(Corey,1986).Uptoalimitingratethesteadyupwardflmrfiomawatertable wfllmeddnpdarfidratedidfiedbyfiwannowhaeflnsmeisdefimdbyflwwflhydraufic wnducfivhympafiesmdmnbemladfledudngflnDamy—Bwldnglmnequafimforaady mflwflaflchlfisrequheshrowledgeofKMbwhichnnynmbehmwnmdcanbedifimR toobtain Alexander(1982)examinedamurrbaofmethodsofpredicfingfluoforavarietyof soils. Anatetal. (1965) studied steady upward flow fiom water tabiasrelatedtoevaporation Theyfowsedonsoflpmmnaaswlfichdaamimthenmdnmmmeofupwudflowaswdlas theefi‘ectofthemoisturehistoryofthesoil(risingvs. fallingwatertable).Theyfoundthatthe flow rate following a drainage cycle can be 100 times greater than following irnbibition into a drysoil. Thepamnetasmdudedmflrdresfimafionequafionwaeporesindisuihrfionmdag depth from surface and bubbling pressure. 33 Capillarity A difl‘erence in pressure between two points in a liquid film, such as that found in unsaturated media, causes the liquid to move in the direction of lower pressure. The term capillarity was used by Richards (1931) to describe “liquid systems where the pressure distribution is determined by the surface tension and curvature of a gas-liquid interface.” Capillary rise can be defined as the movement of a liquid in an upward vertical direction due to molecular forces of attraction and adsorption. It can be clearly demonstrated by lowering a small-diameter tube into standing water and observing the level of the water in the tube. This level will be at some distance above the fi'ee water level of the water supply (for tube diameters smaller than a critical value). This rise is a result of attraction between the tube and the molecules of water, and the surface tension characteristics of the water. The upper surface of the water assumes a curved shape and is referred to as the meniscus. This surface meets the tube surface at an angle called the contact angle. This angleis dependent upon the material of the wall, impurities on the wall surface and the surface tension of the liquid. The contact angle can approach 0° for chemically clean tubes, which allows for the maximum rise height distance. In such an unsaturated three-phase system, the curved meniscus obeys the following equation of capillarity .. —A — l+_l- p0 p.- p- ,1 r2 34 where pa is the atmospheric pressure, usually considered to be zero, p, is the pressure of the water, 7is the fluid’s surface tension, and r, and r; are the principal radii of curvature of a point on the meniscus (Hillel, 1982). At equilibrium the vertical forces on the water column in a small-diameter tube must be equal. This can be described by the equation httr2 pg = 2m cosa where h is the height of capillary rise, p is the density of the water, g is the force of gravity, yis the surface tension of the fluid and a is the contact angle (Baver, 1956; Terzaghi and Peck, 1967). The lefl-hand term describes the downward force due to gravity acting on the volume of the water column, while the right-hand term indicates the upward force holding the column in the tube. The surface tension force acts on the tube wall along the surface of the meniscus formed at the fluid-fluid interface. This surface meets the tube at an angle equal to the contact angle, so the vertical component of this force is equal to room which acts over the perimeter of the meniscus. The theoretical maximum height of capillary rise for a liquid in a tube can be determined by solving for h in the above equation. The rise tends to occur as the liquid molecules are attracted to the solid surface and the contact angle a is close to zero. A column of liquid is then pulled upward by these adsorptive forces. The liquid will continue to rise into the tube until the downward forces on the liquid column equal the upward forces, with h increasing as cosa decreases toward a value of zero. In the case of capillary rise in a porous media such as soil or sand, the tube is replaced by an interconnected network of voids between the particles. This pore space is 35 almost impossible to completely describe in size and direction, although it acts similarly to a bundle of tubes in its ability to raise a liquid through capillarity. In this case the liquid is transported in a film which exists above a layer of liquid one or two molecules thick which is adsorbed to the solid surface of particles. This layer is sometimes called a hydration envelope (Hillel, 1982). The transport fihn becomes thicker in areas of contact between two particles where hydration envelopes intersect. Cannan (1941) declared the height of capillary rise to be an important indication of a media’s relative capillary potential in comparing any two soils or sands. He showed that the maximum height of capillary rise could be estimated fi'om the particle size and porosity of a fine sand, and determined that, although the force driving capillarity is much greater for a fine sand than for a coarse one, water enters the coarse sand at a faster rate. He provided theoretical calculations of upward capillary movement of water into initially dry sands. Wladitchensky (1966) suggested that the height ofcapillary rise is also dependent on the hydrophilic character of the pore walls. Wadsworth and Smith (1926) studied the efi‘ect ofthe cross-sectional area ofsoil columnsoncapillaryrise. Squarecross-sectionalcohunnsusedvariedfi'om 1 inchto 12inches, mdthenwdiausedwasdassifiedasYdofimsmdybmnwlfichpassedfiuoughaan mesh Theyfoundthatingenerai largecolumns showagreaterriseafteragiventimethan smallcolumns. Theyfoundfliatthesizeofthecomaina'wasofgreatesthnponanceincolunms withacross—sectional areaoflessthantwenty-fivesquareinches. Theyalsofoundthatafairly urfifommrdmnsistanmoisuuewmanedstsataflpohnsmmyhonmmalpmwiflnnflre column 36 Someofthefactorswhichhaveanefi‘ect oncapiliaryriseincludetheinitialmoisture content and the degree ofcompactness ofthe media Capillary rise height increases as initial moisture content increases (Ijjas, 1966; Wladitchensky, 1966). As the compactness of the mediawasinaeased,themardnmmcapillaryriseheiglnalsowasmcreased. Ijjas(1966) manedflredischargeduetocapiflmyacfionoveranhnpameablebarfier. Hefoundthatat capillary rise heights greater than 6 cm this volumetric discharge was greater for a compact soil than for a loose soil. He surmised that this was due to the greater role of media permeability at shorter rise distances. Early studies speculated that the rate of capillary rise in loam soil increased with temperature, with looseness of packing, and with original moisture content of soil. It was also observed that rise was more rapid in columns of sand particles of mixed sizes than for particles of uniform size. Ijjas (1966) found that the rate of capillary rise into an initially dry soil was greater for a less compacted soil, but only within the first 100 minutes. Malik et al. (1989) used saturated hydraulic conductivity and wilting point to obtain soil constants which gave maximal capillary rise flux as a function of rise height 2. In an earlier study Malik et al. (1984) used the rate ofcapillary rise in (dry) porous media columns during the first time segment (t < 2 hours) to validate Poiseuille’s law by the straight line relationship between dz/dt and l/z. This allowed the quick estimation of pore geometrical properties (formation factor, shape factor and equivalent pore radius) and capillary constants for a flow system, including hydraulic conductivity. A zone exists above the saturation or fiee water level in a soil which has been referred to as the capillary fiinge, or tension-saturated zone. The pores in this zone are saturated, but the capillary pressure is less than atmospheric. This anomalous situation 37 exists due to the existence of the air entry or bubbling pressure in the moisture characteristic curve. The media will remain saturated until this pressure is reached, at which point the largest continuous pore will desaturate. This pressure corresponds to a height above the flea water level, so below that height the media will remain saturated. The capillary fiinge height affine-grained media will extend higher than that ofa coarse- grained media due to the greater negative value of bubbling pressure (Freeze and Cherry, 1979) Capillary Siphoning Capillary siphoning, or wicking, can be defined as the movement due to capillarity of a fluid over an impermeable barrier in unsaturated media. The siphoning phenomenon was described briefly by Terzaghi and Peck (1967), but without reference to other work in the area. That text states that capillary siphoning was the cause of losses fi'om twelve miles ofcanals in Germany in the range of450 ganin at a rise distance of12 inches. This was reduced to 100 gal/min when the rise distance was increased to 16 inches. Studies were done in Hungary on the losses fi'om canals due to seepage over impermeable barriers, but only some of this work has been translated into English (Ijjas, 1966). It has been possible, however, to glean some information fi'om the data reported in Ijjas' Hungarian-language paper (Ijjas, 1965). In his papers Ijjas looked at the seepage over an impermeable barrier in a canal wall for both a medium (A; D10 .=. 0.13 mm, U= 2.3) and a fine (B; 010 s 0.08 mm, U= 2.7) sand. He confirmed the generally accepted fact that the height of capillary rise 38 increased with initial moisture content 00, and determined that the ultimate rise height was greater with decreased media porosity ¢. However, during the initial period of wetting (<100 minutes) the rate of capillary rise was greater in a more porous media. He also examined the “(e)fi‘ect of the vertical distance (2) between the upper edge of the sealing and the canal watersurface on the magnitude of capillary losses” (Ijjas, 1965). Ijjas’ work found that system outflow Q decreased logarithmically as 2 was increased. He measured values of Q ranging fi'om 4.5 Usec km (27.8 gpd/fi) at z = 2 cm to 1 L/sec km (6.9 gpd/ft) at z = 10 cm. While he did not state specifically, it is behaved that these results were from the medium sand (A) media. Ijjas firrther examined the dependence of the capillary outflow upon the vertical distance H. between the fi'ee-water surface elevations upstream and downstream of the barrier. Hefound that Qincreasedby20% atz=2 cmand 50%atz=10cmwhenH.. was increased from 65 cm to 115 cm. The outflow increased with H. (at a given value of 2), more dramatically at smaller values ofz, with the greatest rate of increase for H. less than 65 cm. For example, when 2 = 5.0 cm Q increased from 1 IJsec km (6.9 gpd/fi) at H. =10 cm to 2.5 L/sec km (17.4 gpd/ft) at H. = 50 cm. He found that for z > 6 cm the outflow was greater from media with less pore volume (¢ = 37.6%), while at z < 6 cm the outflow was greater for media with more pore volume (,0 = 43.0%). He attributed this to the efl‘ects of media permeability on unsaturated conductivity. The effect of the thickness of media (v...) protecting (perpendicular to) the impermeable barrier on the outflow from the system was also examined by Ijjas. His study 39 found that maximum outflow occurred at greater values of v... as 2 increased. The greatest amount of seepage was measured when v... was about 13 cm for z = 5 cm, while at z = 0 cmitwasrecordedwhenv,=9cm(H.=20 cm). Maximum seepage for0 6.2cm ‘— L /—J Porous Membrant} ’1', __'__ —\— Perforated Endcap Figure 1. Cross-section of a sand-filled capillary siphon. bonded together with PVC cement and all joints sealed with silicone caulking compound for watertight construction. Each siphon was later filled with water in order to test for leaks. The siphons were filled with the appropriate media as described under Sample Preparation later in this chapter. Once the siphon had been filled with media the ends were capped. The caps consisted of tubing accessory pieces which fit tightly over the straight ‘legs’ of the siphon, and then reduced to a size which could fit inside the straight tubes. This reduction allowed for the placement of a rigid plastic end-plate which provided structural containment of the siphon media. These plates were adequately perforated to allow free movement of water into and out of the siphon. The granular media was actually contained within the siphon by a fibrous goo-membrane typically used as a porous wrap around agricultural drainage tile. 47 This was placed between the media and the perforated end-plate before the endcap assembly was caulked in place. Once this construction was completed, the siphons could be inverted so the legs were oriented downward for final placement on the support structure. At this point taps were installed at the midpoint of the top of the horizontal section for vacuum saturation and to provide atmospheric pressure within the siphon container. Laboratory Setup Experimentation for this study was conducted in the Soil and Water Laboratory of the Department of Agricultural Engineering in A. W. Farrall Hall on the campus of Michigan State University in East Lansing, Michigan USA Tests were run between late March and mid-June 1996 with measured ambient temperatures ranging fi'om 23 .5° C to 250° C and relative humidity between 15% to 77%. +IX10)-0.l m; U=2.5 3 —I- 'D(10)-0.2rrrnr;U-2.5 g - -O - -D(10)-0.4rrln;U-2.5 h l 3 E . 4 E ‘ I E ‘5 i flu 0.01 0.10 1.00 10.00 Grain Size,rrlrr Figure 2. Grain-size distributions for experimental media of various efl‘ective sizes. 48 Experimental Design The distribution treatments chosen for comparison consisted of three difl‘erent efl'ective sizes, all with similar uniformity (DM = 0.1, 0.2 and 0.4 m; U = 2.5), and three difi‘erent uniformities, all with similar effective sizes (U = 1.5, 2.5 and 4.5; D10 = 0.2 mm). Grain-size distributions for these media can be seen in Figures 2 and 3, respectively. Three replicated samples of each treatment were established for statistical purposes. This results in a total of fifteen difl‘erent siphons which were built and filled with the appropriate media distributions (the distribution with D10 = 0.2 mm and U = 2.5 being common to both comparisons). The siphons were coded according to the distribution parameters with the first two numbers signifying the effective size, the second two numbers signifying the uniformity, and the fifth character signifying the replicate sample code (decimal points were dropped). For example, the siphon code “0145A” signifies an efl‘ective size of 0.1 mm, a uniformity coefficient of 4.5, with the sample being in the first (‘A’) set of replicate units. Support Structure A structure was designed and built which served to provide support for the siphons as they were used in this study. The structure consisted of three identical wooden racks upon which the siphons were placed and separated into the three replicate groups (A, B and C). The racks were constructed so that the upflow legs of each siphon hung down into a plastic reservoir tub so that almost the entire upflow leg could be kept in a saturated state. The siphons would then remain stationary throughout the experimentation as the 49 -—o—D(10)-0.2 nan; U315 .. —|— -n(ro)-o.2mu-2.s I? - -O--D(10)-0.2rran;U-4.5 3 ~ g : . s '5’ a“. 0.0] 0.10 1.00 10.00 GrdrrSizemlrr Figure 3. Grain-size distributions for experimental media of various uniforrnities. level of the water in the tubs was lowered incrementally, and system outflow readings obtained. The structure kept the outflow leg of the siphons about 10 cm above the benchtop so that either the water disposal tub or a flow sample collection container could be placed under the outflow leg when needed. The reservoir tubs, on the other hand, were elevated by the structure so that the upflow legs were about 1 cm above the bottom of the tub. This made possible a range of capillary rise distances of 1 to 12 cm. Water Supply System Water was supplied to the reservoir tubs and kept at constant elevations in all three tubs through the use of supply bottles combined with a constant head chamber system (ie. Marriotte bottle). The constant head chamber (CHC) was a glass cylinder with an inside 50 diameter of about 5 cm which was supported vertically above the benchtop. The bottom of the chamber tapered to a connection with Tygon tubing which was manifolded to the three reservoir tubs. The top of the chamber was plugged with a rubber stopper containing three holes. One hole held a rigid plastic tube which extended fiom about 5 cm above the stopper to about 5 cm above the bottom of the chamber; the bottom of this tube provided the elevation of atmospheric pressure which defined the constant elevation of water in the reservoir tubs. The second hole contained tubing which also extended to about 5 cm fiom the bottom of the chamber and provided water to the chamber fi'om the supply bottles. The third hole also contained tubing which only extended to the bottom of the rubber stopper; this tube connected the air space in the chamber with the air space in the two supply bottles. The two 20-liter glass supply bottles were connected to the constant head chamber so that separate, continuous air and water lines existed between all three pieces of the system. This allowed the CHC to supply water on demand to the reservoir tubs as the siphons moved water out of the tubs. This mechanism worked as follows: as water was siphoned out of the tubs the water level in the tubs was lowered; this caused the water level in the CHC to also decrease creating a vacuum in the air space of the supply system. As this vacuum increased in the charnber’s air space, air was drawn through the atmospheric pressure tube and bribbled up into the air space of the chamber. This temporarily equalized the pressure in the constant head system. Figure 4 shows a schematic diagram of the constant head supply system. The continuous air and water lines between the CHC and the supply bottles 51 CSCI'VOII' Figure 4. Schematic diagram of constant level water supply system. increased the amount of time before the system needed to be refilled. This had to be done before the CHC water level lowered to a critical elevation—the bottom of the atmospheric pressure tube—when air could enter the water line, thereby destroying the integrity and utility of the constant head device. For the primary experimentation of this study distilled water was used exclusively in the supply system in order to eliminate unwanted variables possibly associated with minerals contained in municipal water supplies. This supply water was also disinfected on a weekly basis with the addition of 5.25% Sodium Hypochlorite (NaOCl ) solution3. This reduced the possibility of biological grth both within the siphon media and throughout 3 Household Bleach, Clorox Corporation 52 the supply system. The NaOCl solution was added to achieve a concentration of 10 ppm C12 in the supply water which was deemed adequate to inhibit biological growth’. Water Disposal System A collection and disposal system was also designed and built in order to handle the water which had already passed through the siphons. This system consisted of six collection tubs: two for each of the three replicate groups. Each of these tubs was equipped with a drainage port near the bottom of the tub which drained the water into flexible tubing which was then manifolded so that all of the tubs’ water eventually ran through a single hose which emptied into a floor drain. The design of this system allowed for continuous, unattended disposal of the water as it moved through the siphons. The drainage ports were constructed from quick-release tubing connectors which allowed the tubs to be easily removed so that the flow volume measurement containers could be placed under the siphons for data collection. Sample Preparation In order to obtain usefirl comparative data across the various treatments, all siphons were subjected to the same preparation before data collection was begun. A protocol was followed which could be reproduced by others attempting to confirm, or build upon, the data described in this work. The three replicates within each treatment were prepared simultaneously and identically. " Correspondence with Dr. Blaine Severin, Michigan Biological Institute, East Lansing, MI USA 53 Care was taken when packing the siphons with the granular media as it was important to achieve similar bulk densities between siphons, and cross-sectional uniformity throughout the length of each siphon. Similar bulk density was desired to reduce the chance of porosity difl‘erences between replicated samples of any given treatment, and to eliminate density as a variable between treatments. Since each siphon was physically similar, resulting in the same volume (1370 crn’) for all siphons, the same mass of dry sand (2200 g) was packed into each unit. This results in a bulk density of 1.6 g/cm3 which corresponds to a porosity of 0.38, described by Corey (1986) as normal for unconsolidated sand media. Uniform cross-sectional makeup was achieved by filling each siphon fi'om both of the open ends alternately using a 30 cm long pipe with 4 cm inside diameter. This pipe was placed into the open end of the siphon and filled with media through a funnel. As the pipe was slowly removed, the sand filled the siphon and was settled by light tapping on the outside of the siphon with a hammer. This procedure was continued until the prescribed mass of sand had been packed into the siphon container. Vacuum Saturation The siphons were all vacuum saturated so that a definite starting point could be defined before data collection was started. This is very important given the efi‘ect that the moisture content of the transport media has been shown to have on capillary rise phenomena. Vacuum saturation was utilized in order to best evacuate air fiom within the 54 All three replicates within a treatment were placed in a water-filled tub so that both the upflow and the downflow ends were submerged, but the vacuum taps kept above the water surface. The replicates were then all connected to a single vacuum pump using a manifolded tubing system. This tubing was connected to a 500 ml laboratory vacuum flask which acted as a water trap to keep moisture out of the vacuum pump. The pump was run at a vacuum pressure of 25 mm of Hg until Virtually no air was observed moving out of the siphons through the transparent vacuum taps. System Equilibration The vacuum hoses were then removed and the siphons were placed on the support structure with only the upflow leg immersed in water contained by the reservoir tubs. Air which may have been trapped in the submerged upflow endcap was completely evacuated to eliminate the chance of air movement into the siphon media in the saturated portion of the upflow leg. The downflow leg of the siphons were allowed to drain freely (into the disposal tubs) which initiated the siphoning mechanism within each unit. The CHC height was initially set so that the water in the reservoir tubs was maintained at a level which corresponded to an capillary rise distance of 2.0 cm. Once all of the siphons were properly prepared and set on the support structure, they were allowed to equilibrate at this initial rise distance for 11 days before data collection commenced. This idle time was found to be necessary in order to allow the water movement through the system to reach a point of constant outflow. 55 Data Collection The purpose of the primary data collection in this study was to quantify how the transport media chosen for transmission of water over an impermeable barrier afl'ects the rate of water movement through the system by capillary phenomena at various rise distances. Therefore, the primary data measurement parameter was the amount of water which collected over a set period of time for each treatment at each capillary rise distance. In some instances this volume of water was relatively small, leading to possible errors in measurement. The mass of water was determined to be a more accurate account than the volume due to more accurate instnrmentation. Collection of data was begun once a constant volumetric outflow rate fiom the system was achieved. The data were collected from all siphons within a treatment set simultaneously, and fi'om all treatments sequentially. Containers were. placed under the downflow leg of each siphon and the time noted. The tare weight of each container was previously recorded and the containers numbered. When the collection containers were close to being filled, they were removed and weighed on a laboratory balance. This time varied from 10 to 55 minutes depending upon the flow rate of the system. The gross weights were recorded and the process repeated twice more for a total of three consecutive readings for each of three replicate samples of each treatment. The only adjustment which was made in the system configuration between sets of readings was a successive, step decrease in the water level in the reservoir tubs (which corresponds with an increase in the capillary rise distance). After each set of readings were taken at a given rise distance, the CHC was lowered by 1 cm which allowed the level in the reservoirs to lower as water moved through the siphons. An equilibration period of at 56 least five days was allowed once the CHC was adjusted to a new level (as determined from preliminary experimentation described below). Collection Containers Collection containers were carefirlly designed and built in order to minimize the possibility of evaporation of the water during the collection period. The end of the siphons’ downflow legs were tapered to allow a tight fit with the collection container. The body of the container was constructed from sections of the same material as the siphon body. At the beginning of a collection period the rim of the container was slipped up over the end of the taper and a block inserted under the container to hold it snug against the siphon’s endcap while still providing adequate ventilation. The containers had a maximum capacity of 350 ml of water. Determination of Capillary Flux A spreadsheet was created which converted the raw collected data into a measure of the capillary flux through the siphons. The flux in this case is defined as the volume of water which passes through a unit cross-section of upflow media area per unit time (dimensions: [Ls/{L2 " T}] = [LIT] ). The input to the spreadsheet consisted of the beginning and end times of the run, the final weight of each container holding the individual flow volumes, and the container number. From this information the flow rate was calculated, then divided by the cross-sectional area of the capillary upflow zone, with the resultant being the capillary flux which was reported in units of centimeters per hour. Copies of these spreadsheets can be found in the Appendices. 57 Related Experimentation Time to Equilibrium A steady state was required by the active capillary siphons before flow measurements were taken in order to accurately compare the capillary flux through the various treatments. This means that all of the siphons remained flowing at the same capillary rise distance for long enough after any disturbance so that negligible change in flow rate was occurring. A preliminary experiment was completed earlier and provided experience for the time necessary to reach steady state. A 4-inch diameter PVC pipe was used to construct a siphon similar to the experimental units described above. This siphon was filled with air-dried MichDOT 2NS sand which contained no particles larger than 3.36 mm in diameter and contained negligible amounts of fines. This siphon was filled and capped as previously described before being placed on a support structure with the upflow leg submerged in water. The siphon was allowed to run for thirty days before the flow volume was measured at a rise distance of 8 cm. After this initial flow reading the water level was lowered by one centimeter to a rise distance of 9 cm. From this point in time flow volume readings were taken about every four hours for 10 days at a constant rise distance of 9 cm. The results of this experiment indicated that, after an initial decrease, the flow volume through the siphon reached a constant state after five days. Based on these findings the primary experimentation siphons were allowed to remain constantly running at a set rise distance for at least 5 days after each increase in the capillary rise distance. Chapter 4 RESULTS AND DISCUSSION Effective Size Three difl‘erent particle-size distributions of sand media were used to compare capillary flux over an impermeable barrier as a function of the media’s efl‘ective size, or D10. The efl‘ective sizes considered were 0.1 mm, 0.2 mm and 0.4 mm. The media distributions were all pre-deterrnined and mixed so that a consistent uniformity coeficient of 2.5 was maintained across all three treatments. The capillary siphons were also packed to the same bulk density (p, = 1.6 g/cm’) in order to ensure consistent total pore volumes, thereby eliminating porosity as a variable between treatments. These siphons were then subjected to the experimental procedure described elsewhere in this thesis, and data were collected according to the protocol defined therein. The resulting data are shown graphically in Figures 5, 6 and 7. Each of the data points shown in these figures is the average of nine individual measurements of system outflow: three replicate siphons for each treatment from which three consecutive outflow measurements were taken. Each data point is accompanied by bars which indicate the standard deviation of the nine averaged measurements. The intermediate efi‘ective size (D10 = 0.2 mm) delivered the greatest outflow at all 58 59 20 18 16 I4 Ca‘rylhanth 3 O 0 1 2 3 4 5 6 7 8 9 10 l 1 Callllary Rise Dlstanee, an Figure 5. Mean steady-state capillary flux over an impermeable barrier at various rise distances with standard deviation bars (D,a= 0.1 mm; U = 2.5). capillary rise distances (2) examined. The maximum averaged flux for this media was 15.5 cm/hr at z = 5 cm with a standard deviation (SD) of 2.94 chhr. The outflow fiom this intermediatemediadecreasedto4.9cm/hr(SD=0.54 cm/hr)atz= 10cm. Atz< 5 cm the measured outflow was found to decrease to 7.0 chhr (SD = 3.52 cm/hr) at z = 2.0 cm. The smallest media examined (D10 = 0.1 mm) delivered the second highest flux values at all rise distances examined. The maximum outflow of this media was measured at z = 3 cm where the flux was 5.6 cm/hr (SD = 0.81 cm/hr). The outflow decreased to a minimum flow of 1.63 cm/hr (SD = 0.13 cm/hr) as 2 increased to 10 cm. The initial outflow atz= 2 cm was measured tobe 3.8 cm/hr (SD = 1.09 cm/hr). The capillary flux values were smallest at all rise distances for the largest media examined (D10 = 0.4 mm). These values ranged from 5.2 cm/hr (SD = 2.08 chhr) at z = 3 20 18 16 I4 Caplarthcrrrtlrr O 0‘ 0 1 2 3 4 5 6 7 8 9 10 1 1 Caflllary [Use Distance, cm Figure 6. Mean steady-state capillary flux over an impermeable barrier at various rise distances with standard deviation bars (Dm= 0.2 m; U = 2.5). cmtoalowof0.2 cm/hr(SD=0.11 cm/hr) atz= 10 cm. Thefluxatz=2 cmwasfound to be 2.2 cm/hr with SD equal to 1.31 cm/hr. ItcanbeseeninFiguresS,6and7thattheresultantfluxat2cmrisedistanceis lower than the trend implied by the other data. Disinfectant was not added to the water supply until after the 2 cm data were measured. This is suspected to have resulted in inaccurately low flow rates at 2 cm due to the possible buildup of microorganisms in the media which could impede the flow of water by blocking some of the pore space pathways. Therefore these 2 cm data were not included in the following data analysis and discussion. It is well acknowledged in the literature (Moore, 193 9; Suter, 1964; Terzaghi and Peck, 1967; Hillel, 1982) that under typical saturated conditions the permeability should 61 20 18 16 I4 CaplerthLeIMu' 8 O 0 l 2 3 4 5 6 7 8 9 10 11 Caflllary Rise Distance, arr Figure 7. Mean steady-state capillary flux over an impermeable barrier at various rise distances with standard deviation bars (Dm= 0.4 m; U = 2.5). be greater for larger-grained media than for media made up of smaller grains, i.e. [cm > 19;... This can describe the movement of water over an impermeable barrier in porous media fi'om an upstream phreatic elevation greater than that of the barrier rim, to a downstream water level below the rim elevation. As the upstream level is lowered to some elevation below this rim, the flow system parameters change to those of an unsaturated flow condition. In this unsaturated flow condition the matric potential gradient of the media becomes the dominant driving force for water movement rather than the gravitational potential. Upward capillary flux has been examined by soil scientists (Alexander, 1982; Malik et. al. 1989) in order to model the movement of water fiom a subsurface water table to the root zone of plants, and/or to the ground surface where evaporation can take place. As the water table elevation is lowered beyond some critical point, larger-grained media 62 (ie. coarse sand) can move less water a given rise distance than a finer-grained material. This implies a cross-over in the Flux vs. Rise Distance curves for any two systems which vary only in the effective size of the media. At a capillary rise distance equal to zero the flow over the barrier can be expected to be saturated as the tension-saturated zone, or capillary fiinge, will extend to some elevation above the barrier. In this situation the coarse sand media (DM = 0.4 mm) should provide the greatest outflow, followed sequentially by the intermediate (Du; = 0.2 mm) and fine sand (Dm= 0.1 mm). As the capillary rise distance is increased (by lowering the phreatic level upstream of the barrier), the system outflow will be controlled by the limiting zone of water movement. In unsaturated homogeneous media this can be expected to occur in the zone with the lowest moisture content. In the upflow leg of the siphon system this will be in the area of the barrier rim. The limiting flow for the overall system should occur in this upflow leg where the water must move against the gradient of gravitational potential. The ability of any given media to transmit water decreases as air replaces the water in the pore space. This occurs first in the larger pores as the media is desaturated. A coarse-grained material will generally possess a greater proportion of large pores than will a finer material. The outflow from the coarser media will therefore drop off more rapidly as the rise distance is incrementally increased due to desaturation of the larger pores in the limiting flow zone. Conversely, the flow rate through the finer material will decrease more slowly over the same rise distance increase. Because fewer of these large pores exist in the fine media, their contribution to the total flow is smaller as the relative matric volume dewatered by the rise distance increase is less. 63 This means that the system outflow should be the same at some point for any two media of different efl‘ective sizes as they are changed from a saturated to an unsaturated or semi-saturated flow condition. Before this point the larger media (and associated large pores) will have greater outflow, while beyond this point the smaller media will have a greater proportion of pore space contributing to the flew and therefore the outflow will be greater (assuming that the porosity and other variables are kept constant). Figure 3 represents exponential prediction wives generated fiom the Flux vs. Rise 1 Distance data collected for the three difl‘erent efl‘ective sizes. This graph confirms that the 0.4 mm efi‘ective size has the greatest initial slope (ie. change in flow vs. head), and the 0.1 mm media curve has the least slope. The graph also shows the cross-over points for the ‘70 ,0 “ — D(lO)-o.lnm __, r r s , — — IXIO)=0.2nln 50 \ “ .— ~\\ - - ' - D(10)=0.4rnn % x. 40 —t E '~‘~ L__' s. \ Actual Data Range —-> 30 s \ i . n, 5 ‘\‘ \‘ 20 :'\ 5“ {\‘k ~~~~ .. ~‘ 10 ‘- R-— —__ -— ..F~o..-. T...‘ 0 T . . . . . Z. '. '.' 'W -3 -2 -l 0 I 2 3 4 S 6 7 8 9 10 ll Capillary Rise Distanee,ern Figure 8. Exponential prediction curves from measured capillary flux of water through porous media of three difl‘erent effective sizes (U = 2.5). 64 0.1 mm and 0.2 mm curves with the 0.4 mm curve. The corresponding cross-over point for the 0.1 mm and 0.2 mm curves should occur at some greater rise distance as expected from theory and literature related to capillary rise from finer media at greater distances. The cross-over for the 0.2 mm and 0.4 mm media occurs at some small distance above the siphon invert as the transport media becomes saturated, given that the saturated hydraulic conductivity of larger media allows greater flow. The cross-over for the 0.1 mm and 0.4 mm media occurs while the system is nearly saturated and capillary fiinge efl'ects allow the flow rate of the larger media to increase more rapidly than the finer media. This graph supports the theory that media with an intermediate efl‘ective size can deliver the greatest system outflow over a specified range of capillary rise distances. Results similar to these were indicated in the work of Ijjas (1965) and Malik et al. (1989) although under different experimental conditions. Ijjas measured the capillary discharge over an impermeable barrier for a medium (Dm = 0.13 mm) and a finer (D10 = 0.08 mm) grained sand at various rise distances. He reported that the capillary discharge curves crossed at an elevation slightly above the barrier, with the finer media delivering greater outflow as the rise distance was increased. Malik et al. (1989) measured the maximal capillary rise as a function of height from the water table for a number of soils ranging fi'om a sand to a silt clay loam. They reported that the slope of their curves decreased more steeply for coarse textured soils, and indicated cross-over points for these curves. While the range of heights from the water table studied by Malik and his colleagues were generally greater than 20 cm, the theoretical basis for their results was confirmed at smaller heights by Parlange et al. (1990) and is firrther confirmed empirically by this work. 65 Uniformity The second part of this work was designed to examine the efl'ect of grain size uniformity on capillary outflow from a siphon system. The uniformity coefiicient U is a measure of the variation in grain sizes present in a given unconsolidated media system. Sand separates were mixed so that three difl'erent uniforrnities could be studied: 1.5, 2.5 and 4.5. A smaller value of U indicates a more uniform distribution of grain sizes. The effective size for all systems was kept the same (D10 = 0.2 mm), while bulk densities of 1.6 g/cm3 were maintained. At the same efl‘ective size for all three mixes, a higher uniformity coeficient indicates more particles of larger size in the mix and likely some larger pores as well. The most uniform media (U = 1.5) delivered the greatest outflow of 16.4 cm/hr (SD = 1.68 cm/hr) at a rise distance of 3 em, but this was the only instance where this media exceeded both of the other treatments. The data for this treatment can be seen in Figure 9. The intermediate media (U = 2.5) generally delivered the highest outflows at rise distances of 4 cm and greater (see Figure 6). The least uniform media (U = 4.5) was found to deliver the least outflow at z 2 7 cm and, as discussed later in this section, even these numbers may be artificially high. The data for this treatment can be seen in Figure 10. The efi‘ect of media uniformity on capillary flux is not clearly evident from these results. This may be due to the fact that even distribution of particles within the U-shaped siphon is dificult to control, even under careful packing procedures. This is particularly true for the least uniform media which contains a wide range of particle sizes. These particles can end up in any number of various configurations which may have a great efl‘ect 0 1 2 3 4 5 6 7 8 9 10 1 l Calliiary lass “stance. cm Figure 9. Mean steady-state capillary flux over an impermeable barrier at various rise distances with standard deviation bars (D10 = 0.2 m; U = 1.5). upon the performance of the system. For example, the pore space can be radically difl‘erent depending upon whether the smaller particles find their way into the spaces between the larger particles. This would lead to smaller average pore sizes and a more uniform pore- size distribution, thereby affecting capillary rise. Evidence of this efl‘ect can be seen in the large variability in measured outflows of the three siphons containing the least uniform media (U = 4.5). The standard deviations for this treatment range fi'om 38% to 83% of the mean flux values with the majority greater than 50% of the mean. This is due to the measured outflow of one of the three treatment siphons which consistently delivered more than twice the outflow of the other two. If this individual siphon is excluded, the standard deviations for this treatment range fi'om 2% to 23% of the mean for the data being analyzed. In this case the least uniform 67 0 1 2 3 4 5 6 7 8 9 10 11 Caflliary Rise “stance, cur Figure 10. Mean steady-state capillary flux over an impermeable barrier at various rise distances with standard deviation bars (Dm= 0.2 mm; U = 4.5). media system consistently delivered the lowest outflows for z 2 3 cm. This adjusted data is shown in Figure 11. Application of Results The results stated and discussed above can help in a better understanding of the effects of some media parameters on capillary movement of water over an impermeable barrier in porous media. This information can be helpful to the study of upward movement fi'om a water table to construction foundations, plant roots or the ground surface. The data is even more relevant when applied to systems which utilize flow over an impermeable vertical barrier. In the case of water retention structures, such as canals and dikes, the goal is typically to minimize the flow over the barrier. For this situation it appears that a larger 68 0 l 2 3 4 5 6 7 8 9 10 11 Caflllary Rise Distance, can Figure 11. Adjusted mean steady-state capillary flux over an impermeable barrier at various rise distances with standard deviation bars (D10 = 0.2 mm; U = 4.5). media efi‘ective size should minimize outflow, particularly if the vertical distance fi'om the free water surface to the barrier rim is maximized. The data appears to indicate that outflow may also be minimized if the media particle sizes vary over a large range, although this result should be confirmed by firrtherresearch. Another important application of these results is the use of unsaturated flow over a barrier to create an aerobic phase in an upflow filter for wastewater treatment. In this case the goal is more likely to maximize the movement of the fluid over a barrier or to provide an appropriate residence time in an aerobic zone. This is in fact the application which instigated this research, specifically the range of rise distances and the media size which were investigated. Of course, there would be a number of other variables which would apply to that application which were not included in this study. Primary among these would be the use of wastewater instead of distilled water as the transported fluid. 69 Wastewater contains numerous constituents which could afl‘ect surface tension characteristics, pore clogging by suspended solids, the buildup of a biological layer on the media matrix, and other factors. To maximize system outflow, the data support the use of an intermediate particle size (D10 is 0.2 mm) at a rise distance which ranges fi'om 3 to 5 cm. The data also seem to support the use of a fairly uniform media distribution (U A: 2.5) to maximize outflow, although this was not definitively supported and needs firrther study. Chapter 5 SUMMARY AND CONCLUSIONS The phenomenon of capillary siphoning was studied and experimentation designed and executed to obtain data which could be used to better understand and quantify this process. Capillary siphoning has been defined as the natural transport due to capillary forces of a fluid over an impermeable barrier in unsaturated media. In this case the fluid was distilled, disinfected water, and the media was unconsolidated sand. The primary impetus for this work was the use of capillary siphoning in the aerobic treatment zone of a decentralized wastewater treatment system which has recently been developed. This system relies upon capillary action to raise partially treated water up from a phreatic surface and into the unsaturated zone for final treatment before discharge. In order for the treated water to exit the system it must move up and over an impermeable barrier. It is this capillary rise and horizontal movement through the unsaturated media which provides the aerobic treatment. The media which is contained in this portion of the treatment system should be chosen so that it provides adequate hydraulic capacity in addition to proper treatment. The capillary siphoning process must be able to discharge the volume of influent to the system while maintaining aerobic capillary flow without the barrier perimeter being excessive. 7O 71 This can be achieved by choosing the optimal media based upon its capillary hydraulic characteristics. The primary goal of this work was to determine how the effective size and uniformity of the media particles influence the capillary discharge, and to quantify the flow rates which can be expected through these media over a range of rise distances. The steady state capillary flux through media with three different effective sizes— 0.1 mm, 0.2 mm and 0.4 mm—was measured in the laboratory. Measurements were obtained at capillary rise distances ranging fiom 2 to 10 cm. The greatest outflow at all rise distances was obtained from the intermediate (0.2 mm) treatment. The maximum flux was 15.5 cm/hr at 5 cm rise distance for this media, decreasing to 4.9 cm/hr at 10 cm. This was greater than both of the other treatments which ranged fi'om 5.6 cm/hr at 3 cm to 1.63 cm/hrat 10 cmforthe0.1mmtreatment, and fiom 5.2 cm/hrat 3 cmto 0.2 cm/hrat 10 cm for the 0.4 mm treatment. The larger media can be expected to show the greatest outflow under saturated conditions due to its higher hydraulic conductivity, although once the transition is made to an unsaturated state the larger pores associated with this media will desaturate rapidly at small values of matric tension. This causes a sharp decline in the slope of the rise distance- capillary flux curve with a large percentage of the efl'ective pore space making little contribution to flow even at small rise distances. This decline can be seen in the 85% decrease in flux as the rise distance was increased from 3 cm to 6 cm. On the other hand, the smallest media studied will have the lowest saturated hydraulic conductivity, but as the media desaturates with increased rise distance a larger percentage of pores will continue to contribute to flow. Therefore the slope will decline at a slower rate, indicated by the less than 40% decrease in flux over the same range. 72 Therefore, media with an intermediate size can be expected to provide greater capillary discharge at these shallow rise distances. This is because it will have a greater conductivity at saturation than the smaller media, and decrease less rapidly with increased suction than the larger media. This was confirmed by the data collected in the laboratory, although firrther testing would be needed to determine whether the intermediate grain size selected—0.2 mm with a uniformity coeficient of 2.5—is the precise optimal size. In the experiments conducted with uniformity as the variable, differences were not as apparent. Media having an efi‘ective size of 0.2 mm were prepared with three difl‘erent coeficients of uniformity—1 .5, 2.5 and 4.5. The capillary rise distances ranged fiom 2 cm to 10 cm. The most uniform media delivered the greatest flux: 16.4 cm/hr at a rise distance of3 cm, decreasing to 4.6 chhr at 10 cm. The intermediate media ranged fiom 15.5 cm/hr at 5 cm to 4.3 chhr at 10 cm, while the least uniform media ranged fi'om 15.6 cm/hrat3 cmto4.0cm/hrat 10cmofcapillaryrise. It shouldbenotedthattherewasa great deal of variability in the readings of the individual treatment replicates for the least uniform media. As the results above imply, it is difficult to determine how particle uniformity influences the capillary hydraulics of this granular porous media. The pore space contained within a uniform media can also be expected to be fairly uniform, with the extreme case being a media made up of identical spheres. As particle size variability is increased, a greater chance exists for smaller particles to fill in the larger spaces between particles. This introduces packing as a crucial variable in media with less uniformity, with the possibility of widely difl‘ering pore space configurations contained within replicates of similar media. 73 In conclusion, the objectives of this research as stated above have been met. The capillary flux at rise distances between 2 and 10 cm has been quantified for a number of different media mixtures. The influence of media efl‘ective size on flow rate at these rise distances has been studied, and a conclusion drawn regarding the importance of selecting the prOper intermediate size for maximum flow. The influence of media uniformity on flow rate has also been studied. While no definitive conclusions could be drawn from the experimental data collected, results suggest that the variability of packing could be a significant factor affecting the flux through a system containing a wide range in particle sizes. Further research needs to be done to extend this work to examine how media size and uniformity affect the transport of wastewater. The long term efi‘ects of capillary movement of wastewater through sand media should be researched, with particular emphasis on changes in the pore space. The efl‘ect of media packing on fluid transport also needs to be studied, particularly for less uniform media. APPENDICES APPENDIX A APPENDIX A Capillary Flux Laboratory Data for Siphon Set 0125 (D10 = 0.1 m U = 2.5). 74 13.52.9111 Siphon A Siphon B Siphon C Average Mlmmum Maximum Run #1 3.076 3.809 5.108 3.998 3.076 5.108 Run #2 2.645 3.839 5.375 3.953 2.645 5.375 Run #3 2.134 3.252 4.509 3.298 2.134 4.509 Average 2.618 3.633 4.997 3. 7fll Minimum 2.134 3.252 4.509 I 2.134l Maximum 3.076 3.839 5.375 | 5.375l Run #1 4.639 5.896 6.397 5.644 4.639 6.397 Run #2 4.526 5.847 6.264 5.545 4.526 6.264 Run #3 4.560 6.023 6.443 5.675 4.560 6.443 Average 4.575 5.922 6.368 5. 622I Minimum 4.526 5.847 6.264 | 4.526 Maximum 4.639 6.023 6.443 ‘ 6.443| Run #1 4.450 4.920 5.309 4.893 4.450 5.309 Run #2 4.095 4.563 4.854 4.504 4.095 4.854 Run #3 4.386 4.923 5.183 4.830 4.386 5.183 Average 4.310 4.802 5.115 4.743I Minimum 4.095 4.563 4.854 | 4.093 Maximum 4.450 4.923 5.309 | 5.309| Run #1 4.288 4.170 4.574 4.344 4.170 4.574 Run #2 4.499 4.443 4.789 4.577 4.443 4.789 Run #3 4.214 4.141 4.533 4.296 , 4.141 4.533 Average 4.334 4.251 4.632 4.406l Minimum 4.214 4.141 4.533 [ 4.141 Maximum 4.499 4.443 4.789 , 4.789| Run #1 3.065 3.324 3.686 3.359 3.065 3.686 Run #2 3.164 3.418 3.779 3.454 3.164 3.779 Run #3 3.253 3.455 3.838 3.515 3.253 3.838 Average 3.161 3.399 3.768 3.443I Minimum 3.065 3.324 3.686 I 3.065I Maximum 3.253 3.455 3.838 3.838 75 APPENDIX A Capillary Flux Laboratory Data for Siphon Set 0125 (D10 = 0.1 m U = 2.5) - cont. IO Carrillmfllntsmlhr Si honA Si honB Run #1 2.822 . . 2.813 3.167 Run #2 2.815 2.817 3.144 2.925 2.815 3.144 Run #3 2.835 2.828 3.169 2.944 2.828 . 3.169 Average 2.824 2.820 3.160[ 2.934I Minimum 2.815 2.813 3.144 [ 2.813l Maximum 2.835 2.828 3.169 | 3.169| Run #1 2.441 2.470 2.826] 2.579 2.441 2.826 Run#2 2.372 2.391 2.719 2.494 2.372 2.719 Run #3 2.390 2.388 2.733 2.504 2.388 2.733 Average 2.401 2.417 2.759l 2.526] Minimum 2.372 2.388 2.719 | 2.372I Maximum 2.441 2.470 2.826 | 2.826| Run #1 2.151 2.042 2.369 2.187 2.042 2.369 Run #2 2.138 2.055 2.368 2.187 2.055 2.368 Run #3 2.164 2.052 2.362 2.192 2.052 2.362 Average 2.151 2.049 2.366[ 2.1M Minimum 2.138 2.042 2.362 I 2.042] Maximum 2.164 2.055 2.369 2.369 Run #1 1.621 1.492 1.795 1.636 1.492 1.795 Run #2 1.618 1.494 1.778 1.630 1.494 1.778 Run #3 1.627 1.492 1.794 1.638 1.492 1.794 Average 1.622 1.493 1.789L 1. 6351 Minimum 1.618 1.492 1.778 [ 1.492l Maximum 1.627 1.494 1.795 | 1.795| APPENDIX B APPENDIX B Capillary Flux Laboratory Data for Siphon Set 0225 (Dm = 0.2 m U = 2.5). Capillary WWW Siphon A Siphon B Siphon C Average Minimum Maximum Run#1 4.308 7.125 11.719 7.717 4.308 11.719 Run #2 3.300 6.918 11.774 7.331 3.300 11.774 Run #3 2.341 5.675 10.103 6.040 2.341 10.103 Average 3.316 6.573 11.199 7.029I Minimum 2.341 5.675 10.103 l 2.3m Maximum 4.308 7.125 11.774 | 11.774| Run #1 12.426 13.121 15.489 13.679 12.426 15.489 Run #2 11.640 12.906 15.079 13.208 11.640 15.079 Run #3 11.421 13.268 15.594 13.428, 11.421 15.594 Average 11.829 13.099 15.387 13.438l . Minimum 11.421 12.906 15.079 11.421l Maximum 12.426 13.268 15.594 | 15.594| Run #1 16.483 13.379 14.495 14.786 13.379 16.483 Run #2 14.855 12.635 13.482 13.658 12.635 14.855 Run #3 15.704 13.259 14.015 14.326 13.259 15.704 Average 15.681 13.091 13.997 14.2571 , Minimum 14.855 12.635 13.482 12.63H Maximum 16.483 13.379 14.495 | 16.483| Run #1 19.406 12.045 14.874 15.442 12.045 19.406 Run #2 19.470 12.679 15.733 15.961 12.679 19.470 Run #3 17.862 12.032 14.990 14.961 12.032 17.862 Average 18.912 12.252 15.199 15.455 Minimum 17.862 12.032 14.874 12.032l Maximum 19.470 12.679 15.733 | 19.470| Run #1 8.933 9.615 12.352 10.300 8.933 12.352 Run #2 9.809 10.577 13.485 11.290 9.809 13.485 Run #3 9.289 10.036 12.793 10.706 9.289 12.793 Average 9.344 10.076 12.877 10. 765] Minimum 8.933 9.615 12.352 8.933I Maximum 9.809 10.577 13.485 | 13.485| 76 77 APPENDIX B Capillary Flux Laboratory Data for Siphon Set 0225 (Dm = 0.2 m U = 2.5) - cont. 10 Capillanr 13111842111611 Siphon A Siphon B Siphon C Average Minimum Maximum Run #1 11.271 8.111 10.145 9.843 8.111 11.271 Run #2 11.008 8.067 10.057 9.711 8.067 11.008 Run #3 10.829 8.053 10.119 9.667 8.053 10.829 Average 1 1.036 8.077 10.107 9. 740] Minimum 10.829 8.053 10.057 | 8.053I Maximum 11.271 8.111 10.145 | 11.271| Run #1 3.489 7.073 8.895 6.486 3.489 8.895 Run #2 3.380 6.854 8.652 6.295 3.380 8.652 Run #3 3.337 6.808 8.615 6.253 3.337 8.615 Average 3.402 6.911 8.721 6345| Minimum 3.337 6.808 8.615 [ 3.33fl Maximum 3.489 7.073 8.895 | 8.895| Run #1 4.116 5.794 7.033 5.648 4.116 7.033 Run #2 4.005 5.780 6.929 5.571 4.005 6.929 Run #3 4.002 5.790 6.912 5.568 4.002 6.912 Average 4.041 5.788 6.958 5. 596I Minimum 4.002 5.780 6.912 | 4.002 Maximum 4.116 5.794 7.033 7.033 Run #1 4.885 4.298 5.564 4.916 4.298 5.564 Run #2 4.769 4.308 5.532 4.870 4.308 5.532 Run #3 4.660 4.323 5.536 4.839 4.323 5.536 Average 4.771 4.310 5.544 4.875 Minimum 4.660 4.298 5.532 4.298l Maximum 4.885 4.323 5.564 | 5.564| APPENDIX C APPENDIX C Capillary Flux Laboratory Data for Siphon Set 0425 (Dm = 0.4 m U = 2.5). Canillm rim 2 Qanillm Elmmllu Siphon A Siphon B Siphon C Average Minimum Maximum - Run #1 1.249 4.187 1.987 2.474 1.249 4.187 Run #2 0.825 3.869 1.847 2.180 0.825 3.869 Run #3 0.605 3.225 1.562 1.797 0.605 3.225 Average 0.893 3.760 1.799 2151| Minimum 0.605 3.225 1.562 I 0.605] Maximum 1.249 4.187 1.987 | 4.187| Run #1 2.507 5.687 7.105 5.100 2.507 7.105 Run #2 2.439 5.770 7.013 5.074 2.439 7.013 Run #3 2.569 6.223 7.277 5.356 2.569 7.277 Average 2.505 5.893 7.132 5.1 77[ Minimum 2.439 5.687 7.013 [ 2.4391 Maximum 2.569 6.223 7.277 , 7.277| Run #1 1.721 2.831 4.371] 2.975 1.721 4.371 Run #2 1.718 2.656 4.076 2.817 1.718 4.076 Run #3 1.833 2.818 4.334 2.995 1.833 4.334 Average 1.757 2.768 4.260I 2. 9291 Minimum 1.718 2.656 4.076 1.718 Maximum 1.833 2.831 4.371 4.371|‘ Run #1 0.538 0.752 2.736 1.342 0.538 2.736 Run #2 0.604 0.829 2.903 1.446 0.604 2.903 Run #3 0.645 0.762 2.732 1.380 0.645 2.732 Average 0.595 0.781 2.790I 1.389 Minimum 0.538 0.752 2.732 0.538 Maximum 0.645 0.829 2.903 2.1%] Run #1 0.420 0.309 1.562 0.764 0.309 1.562 Run #2 0.428 0.323 1.563 0.771 0.323 1.563 Run #3 0.429 0.317 1.555 0.767 0.317 1.555 Average 0.425 0.316 1.5601 0. 767] Minimum 0.420 0.309 1.555 | 0.309I Maximum 0.429 0.323 1.563 | 1.563| 78 79 APPENDIX C Capillary Flux Laboratory Data for Siphon Set 0425 (Dm = 0.4 m U = 2.5) - cont. lO Camilla Elnzumlhr Siphon A Siphon B Siphon C IAverage Minimum Maximum Run #1 0.537 0.264 1.126 0.264 1.126 Run #2 0.533 0.259 1.105 0.259 1.105 Run #3 0.543 0.252 1.119 0.252 1.119 Average 0.538 0.258 1.117L o. 6381 1 Minimum 0.533 0.252 1.105 0.252I Maximum 0.543 0.264 1.126 1.126 Run #1 0.368 0.145 0.734 0.145 0.734 Run #2 0.364 0.153 0.732 0.153 0.732 Run #3 0.365 0.143 0.725 0.143 0.725 Average 0.366 0.147 0.730L 0.414I , Minimum 0.364 0.143 0.725 0.143] Maximum 0.368 0.153 0.734 0.734 Run #1 0.272 0.126 0.505 0.126 0.505 Run #2 0.285 0.132 0.505 0.132 0.505 Run #3 0.277 0.132 0.501 0.132 0.501 Average 0.278 0.130 0.504l Minimum 0.272 0.126 0.501 0.1%] Maximum 0.285 0.132 0.505 0.505 Run #1 0.186 0.079 0.317 0.079 0.317 Run #2 0.187 0.083 0.310 0.083 0.310 Run #3 0.192 0.066 0.332 0.066 0.332 Average 0.188 0.076 0.320I Minimum 0.186 0.066 0.310 0.066] Maximum 0.192 0.083 0.332 | 0.332| APPENDIX D APPENDIX D Capillary Flux Laboratory Data for Siphon Set 0215 (Dm = 0.2 m U = 1.5). Camila Qaniflafl Eluzumlhr Siphon A Siphon B Siphon C IAverage Minimum Maximum Run #1 1.109 6.758 9.845 5.904 1.109 9.845 Run #2 0.957 6.048 9.429 5.478 0.957 9.429 Run #3 0.823 4.909 7.988 4.573 0.823 7.988 Average 0.963 5.905 9.088] 5.319] Minimum 0.823 4.909 7.988 ] 0.823] Maximum 1.109 6.758 9.845 l_9~£1§l Run #1 17.568 17.927 14.323 16.606 14.323 17.927 Run #2 17.033 17.962 14.208 16.401 14.208 17.962 Run #3 16.911 17.520 14.070 16.167 14.070 17.520 Average 17.171 17.803 14.200] 16.391 1 Minimum 16.911 17.520 14.070 14.070] Maximum 17.568 17.962 14.323 | 17.962] Run #1 9.522 14.921 9.765 11.403 9.522 14.921 Run #2 8.264 13.765 8.997 10.342 8.264 13.765 Run #3 8.542 14.565 9.647 10.918 8.542 14.565 Average 8.776 14.417 9.470] 10.888 Minimum 8.264 13.765 8.997 8.264] Maximum 9.522 14.921 9.765 | 14.921] ‘* Run #1 12.700 15.303 9.832 12.612 9.832 15.303 Run #2 13.064 15.994 10.568 13.209 10.568 15.994 Run #3 11.377 14.165 9.489 11.677 9.489 14.165 Average 12.380 15.154 9.963 12. 499] , Minimum 11.377 14.165 9.489 9.489] Maximum 13.064 15.994 10.568 | 15.994] Run #1 7.086 12.579 4.366 8.010 4.366 12.579 Run #2 7.897 14.129 5.059 9.029 5.059 14. 129 Run #3 7.371 13.312 4.748 8.477 4.748 13.312 Average 7.451 13.340 4.724 8.503] Minimum 7.086 12.579 4.366 ] 4.366] Maximum 7.897 14.129 5.059 | 14.129] 8O 81 APPENDIX D Capillary Flux Laboratory Data for Siphon Set 0215 (Dm = 0.2 m U = 1.5) - cont. 911121111111 mm m Siphon A Siphon B Siphon C [Average Minimum Maximum 7 Run #1 7.832 9.911 6. 504 8. 082 6. 504 9. 911 Run #2 7.747 9.877 6.564 8.063 6.564 9.877 Run #3 7.558 9.798 6.578 7.978 6.578 9.798 Average 7.712 9.862 6.549] 8.041] Minimum 7.558 9.798 6.504 | 6.504] Maximum 7.832 9.911 6.578 | 9.911] 8 Run #1 3.464 8.039 5.713 5.739 3.464 8.039 Run #2 3.288 7.701 5.509 5.499 Run #3 3.242 7.732 5.503 5.492 Average 3.331 7.824 5.575] 5.577] Minimum 3.242 7.701 5.503 | Maximum 3.464 8.039 5.713 | 8.039] 9 Run #1 4.810 5.932 4.446 5.063 Run #2 4.730 5.880 4.675 5.095 Run #3 4.654 5.870 4.746 5.090 Average 4.731 5.894 4.622] 5.082] Minimum 4.654 5.870 4.446 ] Maximum 4.810 5.932 4.746 | 5.932] 10 Run #1 4.908 5.218 3.495 4.540 Run #2 4.885 5.229 3.580 4.565 Run #3 4.866 5.237 3.645 4.583 Average 4.887 5.228 3.574] 4. 563] Minimum 4.866 5.218 3.495 ] Maximum 4.908 5.237 3.645 APPENDIX E APPENDIX E Capillary Flux Laboratory Data for Siphon Set 0245 (D10 = 0.2 m U = 4.5). mailing: 1152.501 2 WWW Siphon A Siphon B Siphon C Average Minimum Maximum Run #1 6.973 17.078 7.763 10.604 6.973 17.078 Run #2 4.257 16.182 7.640 9.360 4.257 16.182 Run #3 2.785 12.840 6.658 7.428 2.785 12.840 Average 4.672 15.367 7.354 9.131] Minimum 2.785 12.840 6.658 I 278$ Maximum 6.973 17.078 7.763 | 17.078] Run #1 8.999 28.617 10.443 16.020 8.999 28.617 Run #2 8.618 27.469 10.238 15.442 8.618 27.469 Run #3 8.338 27.142 10.438 15.306. 8.338 27.142 Average 8.652 27.743 10.373 15.589] Minimum 8.338 27.142 10.238 | 8.338 Maximum 8.999 28.617 10.443 28.617 Run #1 4.828 21.665 7.206 11.233 4.828 21.665 Run #2 4.545 20.949 7.008 10.834 4.545 20.949 Run #3 4.865 22.120 7.509 11.498 4.865 22.120 Average 4.746 21.578 7.241 11.188] Minimum 4.545 20.949 7.008 ] 4.545 Maximum 4.865 22.120 7.509 22.120] “ Run #1 7.144 27.499 6.418 13.687 6.418 27.499 Run #2 7.594 28.821 6.919 14.445 6.919 28.821 Run #3 7.487 28.434 6.940 14.287 6.940 28.434 Average 7.408 28.252 6.759 14.140] Minimum 7.144 27.499 6.418 | 6.418] Maximum 7.594 28.821 6.940 | 28.821] Run #1 4.866 23.198 5.045 11.036 4.866 23.198 Run #2 5.462 26.121 5.725 12.436 5.462 26.121 Run #3 5.182 24.628 5.378 11.729 5.182 24.628 Average 5.170 24.649 5.383 11.734 Minimum 4.866 23.198 5.045 4.866 Maximum 5.462 26.121 5.725 26.12“ 82 83 APPENDIX E Capillary Flux Laboratory Data for Siphon Set 0245 (D10 = 0.2 m U =4.5) - cont. 10 Canines: mam Siphon A Siphon B Siphon C [Average Minimum Maximum Run #1 4.515 15.352 4.397 8.088 4.397 15.352 Run #2 4.616 15.517 4.494 8.209 4.494 15.517 Run #3 4.556 15.129 4.435 8.040 4.435 15.129 Average 4.562 15.333 4.442] 8.112] , Minimum 4.515 15.129 4.397 ] 4.397] Maximum 4.616 15.517 4.494 | 15.517] Run #1 3.535 8.396 3.779 5.236 3.535 8.396 Run #2 3.544 8.338 3.780 5.221 3.544 8.338 Run #3 3.524 8.403 3.783 5.237 3.524 8.403 Average 3.534 8.379 3.781] 5.231] Minimum 3.524 8.338 3.779 | 3.524] Maximum 3.544 8.403 3.783 I 8.403] Run #1 3.259 6.551 3.170 4.327 3.170 6.551 Run #2 3.290 6.575 3.193 4.353 3.193 6.575 Run #3 3.282 6.448 3.172 4.301 3.172 6.448 Average 3.277 6.525 3.178] 4.327] Minimum 3.259 6.448 3.170 ] 3.170] Yaximum 3.290 6.575 3.193 * I 6.575] Run #1 2.358 7.525 2.269 4.051 2.269 7.525 Run #2 2.338 7.526 2.277 4.047 2.277 7.526 Run #3 2.336 7.445 2.272 4.017 2.272 7.445 Average 2.344 7.499 2.273] 4.038] Minimum 2.336 7.445 2.269 ] 2.26] Maximum 2.358 7.526 2.277 * [ 7.52—6] LIST OF REFERENCES LIST OF REFERENCES Alexander, L. 1982. 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(Hungarian; Summary in English) Ijjas, I. 1966. Effect of Compactness and Initial Moisture Content of the Soil on the Process of Capillary Rise. UNESCO Symposium on Water in the Unsaturated Zone. 11:547-559. Klute, A. 1952. Some Theoretical Aspects of the Flow of Water in Unsaturated Materials. Soil Sci. Soc. Am. Proc. 16:144-148. Kumar, S. and R. S. Malik. 1990. Verification of Quick Capillary Rise Approach for Determining Pore Geometric Characteristics in Soils of Varying Texture. Soil Sci. 150:883-888. Laak, R 1982. On-Site Soil Systems, Nitrogen Removal. In W ' - - ‘ -. ..Eds A S. Eikum and R. W. Seabloom. D. Reidel Publishing Co., Boston. Lambe, T. W. andR. V. Whitman. 1969. W. John Wiley and Sons, Inc., New York. Laliberte, G. E. and R H. Brooks. 1967. Hydraulic Properties of Disturbed Soil Materials Afl'ected by Porosity. Soil Sci. Soc. Am. Proc. 31:451-454. Laroussi, C. and L. W. De Backer. 1979. Relation Between Geometrical Properties of Glass Beads Media and their Main Ma Hysteresis Loops. Soil Sci. Soc. Am. J. 43:646-650. Lawrence, G. P. 1977. Measurement of Pore Sizes in Fine-Textured Soils: A Review of Existing Techniques. J. of Soil Sci. 28:527-540. Malik, R. S., S. Kumar and I. S. Dahiya. 1984. An Approach to Quick Determination of Some Water Transmission Characteristics of Porous Media. Soil Sci. 137:395-400. Malik, R S., S. Kumar and R K. Malik. 1989. Maximum Capillary Rise Flux as a Function of Height fi'om the Water Table. Soil Sci. 148:322-326. 86 Miller, R D. and E. E. Miller. 1955. Theory of Capillary Flow: 11. Experimental Information. Soil Sci. Soc. Am. Proc. 19:271-275. Moore, R E. 1939. Water Conduction from Shallow Water Tables. I-Iilgardia. 12:383- 426. Morel-Seytoux, H. J. 1969. Introduction to Flow of Irnmiscible Liquids in Porous Media. In W. Ed. R J. M. De Wiest. Academic Press, New York. 456-515. Novak, L. J. 1972. Transport Phenomena in Porous Media with Emphasis on Water Movement in Soils. PhD. Thesis. Michigan State University. East Lansing, MI. Otis, R J. 1985. Soil Clogging: Mechanisms and Control. In On-Site Wastewater Treatment; Proceedings of the Fourth National Symposium on Individual and Small Community Sewage Systems. ASAE. 238-250. Parlange, J. -Y. 1980. Water Transport in Soils. Annu. Rev. Fluid Mech. 12:77-102. Parlange, J. -Y., R Havercamp, J. L. Starr, C. Fuentes, R S. Malik, S. Kumar and R K. Malik. 1990. Note - Maximal Capillary Rise Flux as a Function of Height fiom the Water Table. Soil Sci. 150:896-898. Petrucci,RH..1985 ° ' ' Edition. Macmillan Publishing company, New York. Philip, J. R 1957. The Theory of Infiltration: 1. The Infiltration Equation and its Solution. Soil Sci. 83:345-357. Philip, J. R 1964. Similarity Hypothesis for Capillary Hysteresis in Porous Materials. J. Geophys. Res. 69: 1553-1562. Philip, J. R. 1991. 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John Wiley and Sons, Inc., New York. USEPA 1980 0- °. ' ~ .r Office of Research and Development, Municipal Enviro. Research Lab. Cincinnati, Ohio. USEPA 625/ 1-80-012 Wadsworth, H. A. and A Smith. 1926. Some Observations upon the Efi‘ect of the Size of the Container upon the Capillary Rise of Water through Soil Columns. Soil Sci. 22:199-211. Wind, G. P. 1966. Capillary Conductivity Data Estimated by a Simple Method. UNESCO Symposium on Water in the Unsaturated Zone. 181-191. Wladitchensky, s. A 1966. Moisture Content and Hydrophility as Related to the Water Capillary Rise in Soils. UNESCO Symposium on Water in the Unsaturated Zone. 360- 365. "I711111111]11111111111“