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Dispersion in Ground Water Flowing Through Heterogeneous Materials Dispersion in Ground Water Flowing Through Heterogeneous Materials GEOLOGICAL SURVEY PROFESSIONAL PAPER 386-B Prepared on behalf of the U.S. Atomic Energy Commission Dispersion in Ground Water Flo wing Through Heterogeneous Materials By H. E. SKIBITZKE and G. M. ROBINSON CONTRIBUTIONS TO PROBLEMS OF RADIOACTIVE WASTE DISPOSAL GEOLOGICAL SURVEY PROFESSIONAL PAPER 386-B Prepared on behalf of the U.S. Atomic Energy Commission UNITED STATES GOVERNMENT PRINTING OFFICE, WASHINGTON : 1963 UNITED STATES DEPARTMENT OF THE INTERIOR STEWART L. UDALL, Secretary GEOLOGICAL SURVEY Thomas B. Nolan, Director For safe by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D,C, CONTENTS Page Abstract. ________________________________ Bl Introduction ___..__ _____________________ 1 Dispersion phenomena-_________________ 1 Effects of heterogeneity______________-____ 2 References cited________________________ 3 ILLUSTEATIONS Page PLATE 1. Typical dispersion of dyes in model with heterogeneity.----- Facing B2 FIGUBE 1. Typical cross section of sandstone models__________--_---_----------- 2 2. Section showing theoretical flow lines near region of high premeability 3 m 668729 63 CONTRIBUTIONS TO PROBLEMS OF RADIOACTIVE WASTE DISPOSAL DISPERSION IN GROUND WATER FLOWING THROUGH HETEROGENEOUS MATERIALS By H. E. SKIBITZKE and G. M. KOBINSON ABSTRACT then very little knowledge has been gained about rela­ Laboratory studies of dispersion in water flowing through tions between direction of flow and hydraulic gradient. porous media show that the heterogeneity of the medium is the Recently, many investigators have studied dispersion dominant dispersive factor. All other factors have insignificant in ground water. They have observed the spread of effects on dispersion. waste liquids in the vicinity of waste-disposal wells, for INTRODUCTION example, and have found that the spread far exceeds that which would be predicted by classical hydrody­ Man has always discharged wastes on or in the namics. One notion is that chemical diffusion, com­ ground, so contamination of ground water by wastes is not a new problem. The amount of wastes of all kinds, pounded by flow around sand grains in an aquifer, however, is increasing rapidly. This increase and the causes dispersion. Experiments by the writers, how­ recent appearance of radioactive wastes, which are being ever, show that such is not the case. disposed of directly or indirectly into ground-water In many of the recent laboratory experiments the dis­ systems, make it essential to learn in detail the nature persion was much too great to be accounted for by diffu­ of ground-water movement and the rates and directions sion and flow around sand grains. This conclusion of flow at specific locations. necessitates analysis of the precise meaning of the per­ The direction of ground-water flow, according to meability coefficient in Darcy's law. Many writers have classical concepts, is perpendicular to the equipotential noted that the permeability coefficient actually is a ten­ lines (lines connecting points of equal head) in an sor quantity, though it is generally applied as a scalar. aquifer. This is literally correct, however, for only Permeability being a tensor, rather than a scalar, would perfectly homogeneous granular, porous materials. In account for a difference between the direction of flow real aquifers, all of which contain inhomogeneities, the and the direction of the maximum hydraulic gradient. actual microscopic flow pattern is very complex in de­ However, the explanation of extensive dispersion is tail, and the directions of flow diverge from the hydrau­ more involved because streamlines do more than simply lic-potential gradients. This causes wide dispersion of bend; they also diverge. Divergence of streamlines is water-soluble and -miscible liquids that enter an the principal concern in this discussion. aquifer. In most laboratory tests reported in the literature, Determination of equipotential lines is relatively observed dispersion in homogeneous media can be simple compared to the determination of real flow lines, attributed to disturbing unnatural factors, such as dif­ because the principles by which equipotential values ferences in the chemical composition and physical char­ may be determined are much simpler than those which acteristics of the tracer and the liquid, or to the physical govern the direction of flow. Ground-water hydrolo- and physico-chemical properties of the permeable mate­ gists generally have concerned themselves largely with rial used in the experiments. Tracers having greater lines of equal potential, but the advent of waste-disposal viscosity than the liquid (such as colored glycerin) or problems requires a change of emphasis. tracers of greater density (such as an aqueous solution of dye) seem to introduce excessively disturbing condi­ DISPERSION PHENOMENA tions in the experiments. To overcome difficulties of Many investigators have used tracers to determine di­ that sort, we used a radioactive-tracer solution which rections of ground-water flow. As early as 1899, Slich- had the same viscosity, density, and other properties as ter (1899) reported experiments with tracers, but since the liquid (Skibitzke and others, 1961). Bl B2 CONTRIBUTIONS TO PROBLEMS OF RADIOACTIVE WASTE DISPOSAL In the experiment, a dilute solution of nonradio- the model (fig. 1). Glass plates, cemented along the top active phosphoric acid was allowed to flow through a and bottom of the sandstone model, permitted direct ob­ porous block of artificially cemented homogeneous sand­ servation of saturated flow. By cementing the glass to stone. Flow was maintained for about 1 month to bring the sand, we avoided the boundary effects that have dis­ the solution into ion-exchange equilibrium with the torted the flow patterns in many experiments. Liquid solid block. A tracer solution then was introduced was permitted to flow through the completed model, through a small hollow needle near the input end of the and small streams of dye were injected in the flow field block. The tracer was phosphoric acid which contained at upstream points. Although physical properties of a radioactive phosphorous but was otherwise physically dye may cause some dispersion, dye tracer permits and chemically identical with the liquid flowing through visual comparison of phenomena in homogeneous and the block. By isotropic exchange along the filament of heterogeneous materials. Flow velocities approximat­ tracer solution downstream from the point of injection, ing 20 feet per day were within the range of velocity of radioactive phosphorus replaced some of the stable ground water under average natural conditions in phosphorus which had been adsorbed on the sand similar materials. grains. After 6 weeks of continuous flow with the A typical example of wide dispersion caused by he­ tracer present, the block was cut into several slices and terogeneity is shown in plate 1. The model was about the distribution of radiophosphorus was determined. 4: feet long and about 1 foot wide. In cross section, the Analysis with radiographic film and with radiation shape of the embedments was much like those illustrated counters showed that the sand grains actually retard in figure 1, and they were much higher in permeability diffusion rather than accelerate it. That is, diffusion than the matrix. The two dye-injection points were was less than would be expected in a body of free water. near the inflow edge of the model. Eed dye was intro­ Thus, strong dispersion in porous material does not duced at one point and green at the other. During the seem to be caused by diffusion. experiment, dye spread through nearly the whole width of the model by the time it reached the downstream end. EFFECTS OF HETEROGENEITY The process by which the dye spreads is analogous In additional experiments, we observed dispersion in to the process by which an influent stream recharges an models of heterogeneous media. Several hydraulic aquifer, or by which effluent ground water feeds a models, having various sizes and width-to-length ratios, stream (fig. 2). The position of the streamline which were built by cementing sand with epoxy resin to form separates recharge flow from through flow (represented an artificial sandstone. All the finished models were by the heavy line in figure 2) depends on the rate of less than 4 feet long and 2 feet wide and were about 2 recharge or discharge in the region of high permeability inches thick. Heterogeneity was introduced before compared to the rate of flow in the part of the matrix cementing the blocks by embedding bodies of coarse with through flow. The curve representing any stream­ sand in a matrix of fine sand or by embedding bodies line is asymptotic to a straight line parallel to the direc­ of fine sand in a matrix of coarse sand. Most of the em­ tion of through flow. Highly permeable channels in bedments were sinuous channels, U-shaped in cross sec­ the model shown in figure 1 carried liquid at a much tion, and with depths less than one-third the thickness of higher velocity than did the adjoining less permeable Artificial sandstone (matrix) Contrasting permeability Glass plate Epoxy seal Glass plate FIGURE 1. Typical cross section of sandstone models used for studying effects of heterogeneity on dispersion. Section transverse to direction of fluid movement. UNITED STATES DEPARTMENT OF THE INTERIOR PROFESSIONAL PAPER 386-B GEOLOGICAL SURVEY PLATE 1 .-$&^ '"' ""^^%S*... ^ £i-:::Wi*S:i: Direction of flow Injection/ points INTERIOR GEOLOGICAL SURVEY. WASHINGTON. D. C. 62293 TYPICAL DISPERSION OF DYES IN A MODEL WITH HETEROGENEITY DISPERSION IN GROUND WATER FLOWING THROUGH HETEROGENEOUS MATERIALS B3 Dividing streamline x , Region of high permeability FIGURE 2. Section showing theoretical flow lines near a region of high permeability. General direction is to the right if head is relatively high or to the left if relatively low in the region of high permeability. matrix. Liquid flowed from the model matrix into dye entered a region of contrasting permeability, dis­ the channel and from the channel into the matrix. persion was widespread.
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