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By W. J. Skewes, C. T. Holland

Properly constructed stopes are necessary underground for proper ventilation and safe, healthful working conditions. Mining companies are concerned with providing the best possible stoppings at an economic cost. It is important to consider 1) proper materials, 2) construction that ensures maximum performance from the material used, and 3) keeping costs within reasonable limits for the unit operation—stopping—involved. The authors investigated all aspects of the problem and have attempted to layout a study program to provide information on all phases. Mining companies every year purchase huge amounts of material for the construction of ventilation stoppings. This material by the time it is in place in the stoppings will cost the company many thousands of dollars. In addition and more importantly these stoppings are supposed to confine air travel along certain well defined paths into areas where it is needed to provide safe and healthful atmospheres for workmen. The cost of forcing this air through the mine is large and in general increases as the total quantity increases. Consequently, if the stoppings leak, increased cost results and in addition unsatisfactory ventilation may prevail in the mine. Therefore, it is essentia1 to provide the best possible stoppings at an economic cost. When attempting to provide the best stoppings possible at an economic cost, three aspects of the problem must be considered. These are 1) getting the most suitable material for stopping constructions, 2) constructing the stopping so as to get the best performance from the material used, and 3) keeping the cost of stopping construction to a minimum for a suitable stopping. This investigation is concerned with all phases of the problem and has attempted to lay out a study to provide information on all of them. In order to develop information on the best stopping material available it seemed wise, after con- sidering the job a stopping must do, to investigate the following aspects of material used for stoppings: 1) strength in compression, 2) compressibility or yield under load, 3) porosity, and 4) permeability. To provide information on the best manner of construction the following aspects of air leakage through the stopping were investigated: 1) when the stopping is built of dry stacked materials—i.e., the joints are not mortar-laid (See Fig. 1); 2) when the stopping is built of dry stacked material and then plastered on one side (see Fig. 2); 3) when the

Jan 1, 1961

By William E. Galloway, Gary E. Smith, Christopher D. Henry

INTRODUCTION Studies relating to the Oakville aquifer as presented in this report and by Henry et al. (this volume), are part of a larger , comprehensive examination of regional and local stratigraphic, hydro- geologic, and geochemical parameters within the Oakville Formation recently completed by the Bureau of Economic Geology. The Oakville serves both as a major Gulf Coast aquifer and an important uranium host (Fig. 1). Regional and local controls on hydrodynamics and hydrochemistry have important implications for hydrochemical exploration, the establishment of premining baseline parameters, and the design of post mining restoration procedures. Investigations of the Oakville Formation were de- signed for the purpose of determining the response of the aquifer to uranium extraction and were funded by the U.S. Environmental Protection Agency under grant numbers R-805357-01 and R-805357-02. Physical Stratigraphy Physical stratigraphic analysis shows that the Oakville Sandstone, a lithostratigraphic unit deposited by a major coastal-plain f luvial system, consists of five mappable, component depositional elements (Figs. 2 and 3). Each major component element is the product of one or more rivers traversing the Miocene coastal plain. In turn, each river possessed a unique sediment load, discharge characteristics, and source terrane. Consequently, each element exhibits distinguishing geometric and compositional parameters that potentially influence the flux and hydrochemical evolution of contained ground waters (Galloway, Henry, and Smith, in preparation). The Oakvil le Sandstone, as mapped and interpreted as a lithostratigraphic unit in the study area, corresponds closely to the Jasper aquifer system, an equally well-defined Gulf Coastal Plain hydrogeologic unit (Baker, 1978). Principal surrounding hydrogeologic units include the underlying Catahoula confining system, the Jasper aquifer system itself, and the overlying Burkeville confining system (lower Fleming mudstones). The Evangeline aquifer system includes much of the Fleming Formation. The Jasper aquifer system is bounded above and below by relatively less transmissive, finer grained confining systems, although absolute transmissivity varies greatly within both the Jasper and confining units. Lithostratigraphic and hydrogeologic boundaries coincide almost exactly within the Hebbronville flu- vial axis (Fig. 3). Correspondence of geologic and hydrostratigraphic boundaries is good within the George West axis; farther to the northeast the correlation of the Jasper aquifer with units mapped as Oakville Formation diverges to varying degrees. A complete analysis of these trends and a study of the depositional facies comprising the Oakvillle are included in Galloway, Henry, and Smith (in preparation). REGIONAL HYDROGEOLOGY The stratigraphic, compositional, and structural framework of the Oakville Formation and the mosaic of interrelated depositional facies that are combined in this framework play a key role in defining the hydrogeology of the Oakville. Furthermore, a combination of climate and hydrogeology, as well as past and present socioeconomic conditions, has determined water and land use patterns within the region of Oakville outcrop. Utilization of Oakville Ground Water Stratigraphic control for determining which wells produce ground water from the Oakville aquifer was established by preparing structural and isopach maps of the Oakville Formation using regional electric log cross sections. Surface elevation and screened interval data (or total well depth, if open-hole completion techniques were used) from each water well, combined with the stratigraphic data, allowed accurate assessment of the producing aquifer for individual wells. Information on well and screen depths, water levels, and usage of water from

Jan 1, 1980

By H. Schwartzbart, J. R. Low

Annealed, .Poly crystalline, low carbon steel exhibits a phenomenon known as the "yield point." If such a steel is loaded in tension, the load increases steadily with elastic strain, drops suddenly, fluctuates about some constant load value for a time and then rises with further strain. The load at which the sudden drop occurs is called the "upper yield point"; the load at which deformation proceeds at constant load is known as the "lower yield point"; the amount of elongation at constant load is termed the "yield point elongation." Deformation which occurs during the yield point elongation is heterogeneous in nature, deformed metal existing next to undeformed metal. The drop in load from the upper yield point is concurrent with the formation of a band of deformed metal which usually appears at a stress concentration such as a fillet and at an angle of approximately 45" with the direction of pull. As deformation proceeds during the yield point elongation, the deformed region grows until the entire specimen has been strained an amount equal to the strain in the first band. A phenomenon very often associated with the yield point is that of strain aging. Aging in steels may be of two types: quench aging, or precipitation hardening, and strain-aging. Strain aging differs from precipitation hardening in that if the metal is merely strained instead of given a solution anneal and quenched, it then undergoes changes in properties similar to those observed in quench aging. The yield point effect and strain aging are most markedly exhibited by low carbon steel, but have been observed in other alloys. Numerous explanations for the mechanisms of both phenomena have been advanced, but the evidence for the acceptance of any of the hypotheses is incomplete. One of the explanations of the yield point phenomenon frequently proposed is that there exists a honeycomb of grain boundary material that supports the load above the yield strength of the ferrite and that when this network ruptures, the ferrite flows with no increase in load. This notion was first advanced by Dalbyl in 1913 and has been since put forward in more concrete form by many investigators. The testing of this hypothesis was, in part, the object of the present investigation. Similarly, the mechanism by which strain aging occurs remains to be explained. Presumably, it is a precipitation hardening phenomenon similar to quench aging, the precipitation being initiated by strain. However, it is not known whether the process is a solution and precipitation effect or a change in solubility due to strain. One obvious method of determining whether or not the yield point is a grain boundary phenomenon is to determine if single crystals exhibit a yield point. Low and Gensamer2 have shown that carbon and nitrogen are responsible for the yield point and aging in steel and that these effects can be eliminated by the removal of these elements through wet hydrogen purification. Single crystals that have been grown in wet hydrogen treated material must then be recarburized or re-nitrided in order to evaluate the effect of grain boundaries. In the present investigation, single crystals of iron which had been annealed in wet hydrogen to remove the carbon and nitrogen were cut into two specimens having the same orientation with respect to the tension axis. Of these, one specimen was pulled in tension in the wet hydrogen treated state and the other was carburized or nitrided and tested similarly. All the crystals were examined for a yield-point and strain aging. The grain boundary hypothesis for the explanation of the yield point in steel has been tested only indirectly previously. Arrowsmith,3 Andrew and Lee,4 Edwards and Pfeil,5 Fell,6 Ludwik and Scheu,7 Winlock and Leiter8 and others found a decrease in proportional limit and yield point effect with an in-

Jan 1, 1950

By Y. C. Liu, R. H. Richman

From rolling textures of polycrystalline AgCl determined as a function of temperature, changes in the amounts of the individual textural components are correlated with temperature-dependent changes in glide geometry. The preferred orientations are influenced by the slip behavior as follows: 1) pencil glide, characterized by (110) slip directions and a greater participation in the deformation the higher the temperature, leads to a(012) fiber texture; 2) low-temperature deformation, primarily on (110) (110) systems, generates the {237}-(11, 9, 7) component; and 3) slip on {111}(110), comprising a significant portion of the room-temperature deformation, generates the {135}(211) and {110}(112) components. Typical re crystallization textures are also presented and briefly discussed. SPECIFIC relations between flow mechanisms in crystals and the individual orientations or components in deformation textures are necessary for a thorough understanding of the origin of such textures. Within each ordinary class of crystal struc- tures there is insufficient variety in the observed preferred orientations to permit direct and unambiguous correlation between flow mechanism and texture. A second approach to this problem is the correlation of textural changes with some known variation in glide geometry within one substance,1 In this paper, the latter approach is applied directly to a material in which there are distinct changes in the character of glide with changes in temperature. Silver chloride, although a nonmetal, is reported to exhibit slip,2,3 fiber textures,4 and rolling textures5,6 crystallographically similar to those of the well-studied fcc metals;7,8 in addition, there is a marked temperature sensitivity of the glide planes upon which flow occurs.3 Previous investigations of textures in AgCl unfortunately did not employ methods sufficiently sensitive to define possibly important minor components in the texture, nor did they utilize the temperature dependence of the glide systems. Thus, in order to clarify the effects of changes in slip mechanism, this paper reports a survey, using semiquantitative methods, of preferred orientations in rolled AgC1. Inasmuch as the influence of prior deformation texture upon preferred orientations after annealing is also of interest, some representative annealing textures are presented.

Jan 1, 1965

By C. M. Wayman, R. Bullough

The rediffraction of Bragg diffracted beams by differently oriented regions (such as twins) of a crystal may give rise to "extra" reflections or reciprocal lattice points. These two papers are concerned with predicting these additional reflections which result from twin related regions of a lattice. Analysis is made for {111}fcc twins, (112)bcc twins, and {hkil}hcp twins. It is first required, knowing the specific variant of the twinning plane in each case, to predict the positions of the twin reflections relative to the matrix reciprocal lattice. Once this is done, the positions of the "extra" multiply diffracted reflections may be deduced. Part I is devoted to establishing "selection ru1es" for twinning, i.e., the necessary and sufficient conditions for the existence of twinned reciprocal lattice points. 1. INTRODUCTION. Transmission electron diffraction patterns are frequently complicated by multiply diffracted beams. Pashley and stowell1 have recently demonstrated that certain extra reflections in evapo- rated films of gold result from the rediffraction of matrix Bragg diffracted beams by (111) microtwins in the gold. It was previously (and erroneously) suggested 2,3 that observed "irrational" reflections in fine-grained gold were due to the presence of some hcp gold. A similar situation exists, apparently, for some bcc materials; fine (112) twins in bcc martensite in Fe-Ni alloys4 give rise to extra reflections. There are many other examples. The number of transmission electron microscopic investigations is continually increasing, and because of the importance of double (and multiple) diffraction in the interpretation of diffraction patterns, it was judged that a detailed elaboration of the principles involved is desirable, as well as the extension of these principles in reasonably closed form to other crystal structures, particularly bcc and hcp. The present analysis considers double diffraction caused by (111) twins in fcc metals, (112) twins in bcc metals, and {hkil} = {hkl) twins in hcp metals. For each case of twinning, the various possible (variants of) twins give rise to a set of interpenetrating reciprocal lattices. The relative spatial arrangements of these reciprocal lattices can be deduced (Part I) and are expressed in terms of simple "selection rules". The resulting sets of interpenetrating reciprocal lattices are then analyzed for possible doubly diffracted reflections (Part II). The notation used, and some important formulas are given in Appendices I and 11.

Jan 1, 1967

By J. J. Gilman

Examination showed that characteristic cleavage step patterns are observed on the cleavage surfaces of undeformed, slipped, bent, twinned, compressed, and indented zinc crystals; and the effect of temperature is discussed. Dimples were seen to produce cleavage steps in a treelike pattern in otherwise undeformed crystals. The steps seem to originate when cracks intersect screw dislocations. IT has been known for a long time that the path of fracture in polycrystals may be discontinuous (see Jaffe, Reed, and Mannl for review). Recently, Kies, Sullivan, and Irwin2 have proposed, and given evidence, that crack propagation is discontinuous within individual crystals as well. Other evidence has been given by Low.' When discontinuous cracks within a crystal join together to make a macrocrack, the lamellae between each set of two cracks are torn somewhere, forming small cliffs. These cliffs appear as lines when the cleavage surface is observed microscopically.4,5 The lines have been called vein, tree, and riverlike markings by various authors, and they have sometimes been mistaken for fissures. The descriptive term cleavage steps is used in this paper. Cleavage steps vary in height over a wide range of values, from molecular dimensionsG to lor. and larger. Kies, Sullivan, and Irwin,2 as well as George,' have shown that the gross cleavage step patterns for plastics, polycrystalline metals, and for mono-crystals are sometimes similar. Thus, they depend mostly on the mechanical variables that prevail during cleavage and are relatively insensitive to the structure of the material. For example, parabolic markings2,7,8 sometimes result when cracks open up ahead of, and not coplanar with, the main crack front. If the advance crack has the same velocity as the main crack, their intersection line is a parabola, otherwise it is a hyperbola or an ellipse. The patterns are strongly affected by differences in crack velocities. This results in chevron patterns which point to the place of origin of the main crack. It is the purpose of this paper to demonstrate the existence of a mechanism of cleavage step formation which is a continuous rather than a discontinuous process. Also, certain characteristic step patterns are described, and the strong effect of temperature is shown. The specimens were zinc monocrystals (grown from 99.999+ pct pure metal). These were cleaved at room temperature and at — 196°C. Results and Discussion Cleavage step patterns are highly variable from point to point on a given specimen, as well as from one specimen to another. Although the patterns shown in the photographs are typical, they have been selected for graphic illustration. Figs. la and lb compare undeformed crystals that were cleaved at —196 °C and room temperature, respectively. Cleavage at room temperature (Fig. lb) resulted in a higher density of high steps (dark black lines) and enhanced the visibility of the fine background markings. Deformation by simple slip caused no marked change in the step patterns until the glide strain reached about 1.0. But, as Fig. lc shows, the density of high cleavage steps was greatly increased by large glide strains. Corrugations lying perpendicular to the slip direction may also be seen in Fig. lc. These are caused by deformation bands. The cleavage resistance of the crystal of Fig. lc was very high compared to undeformed crystals (estimated by the force on a needle required for cleavage). Striking and varied cleavage step patterns were observed on bent crystals. Two characteristic patterns that were observed on crystals bent at 25°C, and cleaved by reverse bending at —196°C, are shown in Figs. 2a and 2b. The first, Fig. 2a, consists of V-shaped lines similar to the parabolas of other materials2,7 Fig. 2b shows a pattern that is the equivalent of Fig. la, consisting of faint background lines with a few higher step markings. Cleavage of bent crystals at room temperature resulted in Figs. 2c and 2d. Now, the cleavage step lines show a strong tendency to follow one of two perpendicular paths. In Fig. 2c (bent once), many of the cleavage step components that lie parallel to the bend axis are assembled into irregular lines. In Fig. 2d (bent twice), the cleavage steps again tend to consist of two perpendicular components, but neither of the components is assembled into lines. Also, the step density is higher.

Jan 1, 1956

By J. J. Rutledge

I. Description of the Clinton Ores and Associated Rocks. The Clinton rocks in Stone valley comprise (1) thick layers of deep-red shale, (2) layers of reddish-gray shale interspersed with beds of sandstone and thin beds of extremely fossiliferous limestone, and (3) yellowish-gray shales alternating with thin layers of olive-colored shales. These layers of shale are all very thin and are at no point massive.' A bed of gray-white sandstone varying in thickness from 12 to 30 ft. occurs in the upper portions of the Clinton shales. This is called the ore sandstone, a name given to it by Rogers and adopted also by the Second Pennsylvania Geological Survey. It is the surest guide to the presence of the iron-ore bed, which lies below its lower edges at distances varying from 10 to 20 ft. This ore sandstone, in the valley, lies generally at very low inclinations, but often is locally subjected to considerable changes in dip. At its outcrop this ore sandstone weathers very easily and yields a rather sparse crop of stone, composed of dirty, iron-stained boulders. Upon the roads these boulders are quite well rounded, and bear fragments of crinoid stems and other fossil forms. The ore sandstone exhibits at many points evidences of former movements in this very great thickness of the shales, and as it is the only stratum in this series competent to transmit and record stresses due to structural movements, its evidence is of considerable importance in determining the occurrence of movements in times past.

Jan 1, 1910

By M. G. Corson

INFORMATION regarding the use of manganese alloys has hitherto been incomplete and available only from widely scattered sources. This paper attempts a systematic description of properties and uses of alloys other than manganese bronze, manganin and duralumin, which are probably the only non-ferrous alloys associated with manganese in the minds of most metallurgists.1 PROPERTIES OF MANGANESE Manganese can react either acid or basic; it is hard to obtain in the pure state; it has two different crystalline lattice structures, both of the cubic system, one stable above 850° C. and the other below 650° C., both coexisting in the intermediate range. Although the commercial product is hard and brittle, the pure metal seems to be ductile. In fact Zhemchuzhny, in Russia, was able to obtain ductile manganese and draw it to fine wires by the simple expedient of adding about 3 per cent. copper to the alumino-thermic product. Copper most probably brings the silicides, aluminides, nitrides and carbides present in the commercial product into a much less harmful form of distribution. One industrial use that can be foreseen for wrought manganese articles is as anodes for electrolytic processes in sulfate and nitrate solutions, particularly with high voltages. A practically insoluble skin of manganese peroxide is likely to form in such cases and an insoluble and strong anode material will be available. MANGANESE AS A SCAVENGER Because of its activity manganese might become the most efficient scavenger and refiner of copper, were it not for the fact that 0.01 per cent.

Jan 1, 1928

By S. Kado, G. Derge, L. Yang

Self-diffusion coefficients of silver in molten silver have been measured by means of the capillary-reservoir method in the temperature range 1002" to 1105°C. The results can be .represented by the equation D = (7.10 i 0.06) X 10-4 exp [(—8150 ± 1130)/RT]. The heat of activation agrees within the limit of experimental uncertainty with that for the viscous flow. The validity of the Eyring and the Stokes-Einstein equations are examined on the basis of the self-diffusion coefficients obtained and the known viscosity data of molten silver. MEASUREMENT of the self-diffusion coefficient of silver in molten silver was made in the temperature range 1275° to 1378°K, using the capillary-reservoir method and &"' as the radioactive tracer. The experimental arrangement is shown in Fig. 1. Silver of 99.99 pct purity (fine silver), was melted and degassed in vacuum in a graphite crucible situated inside a McDanel vacuum jacket. The crucible (4 in. tall and 1 in. ID) was protected both at the top and at the bottom with graphite shields and contained about 220 g of silver. The sample holder was a piece of graphite rod (1 in. long and 1/2 in. diam) with 4 capillaries drilled longitudinally into it. The holder was screwed onto a long graphite rod (12 in. long and 74 in. diam) which was connected to a steel disk hanging on a nylon string through a glass pulley. The steel disk kept the sample holder at the center of the McDanel tube and was heavy enough to overcome the buoyancy when the holder was lowered into the molten silver. By turning a handle connected to the pulley through a tapered glass joint, it was possible to raise or lower the sample holder without breaking the vacuum. Two such arrangements were constructed, sitting side by side in 2 Kanthal furnaces. One with non-radioactive silver in its crucible was used for the diffusion run and the other with radioactive silver in its crucible was used for filling the capillaries. To fill the capillaries with radioactive silver, the sample holder was degassed first and then lowered into the radioactive molten silver in vacuum. Purified argon gas was then admitted into the system to push the liquid silver into the capillaries. After cooling in argon, the filled capillaries were polished on emery paper to expose the top of the rod and used immediately as samples for the diffusion run which was carried out at the same temperature as that used for filling the capillaries. During the diffusion run, the samples were degassed in vacuum and lowered slowly into the nonradioactive molten silver before purified argon was admitted into the system. After a predetermined period of time, the samples were raised out of the melt and cooled in argon. The temperature of the melt was measured before and after the run with a chromel-alumel thermocouple inside a McDanel protection tube. Another chromel-alumel thermocouple attached to the outside wall of the McDanel vacuum jacket was used to indicate any fluctuation in the temperature of the furnace during the run, which was found to be less than ± 2°C for the longest run made (93 min). The temperature gradient inside the molten silver was found to be negligible. No significant difference was observed in the results obtained whether the melt was stagnant during the run or was stirred by raising and lowering the sample holder slowly a few times a minute for a distance of about 1/4 in. inside the melt.

Jan 1, 1959

By M. T. Simnad, R. F. Mehl, L. Yang

Techniques for studying marker movement in K-Rb interdiffusion have been worked out. The results indicate that Rb diffuses faster than K and that the ring mechanism of diffusion cannot be the dominant one operating in this case or probably in cases involving other alkali metals, despite their low ion core repulsive energies. SEVERAL theoretical attempts have been made in the past decade to elucidate the mechanism of diffusion in body-centered-cubic metals. No general agreement, however, has been reached by different authors. Zener,1 and later LeClaire,2 on the basis of a correlation between the entropy of activation for self-diffusion and the temperature dependence of the elastic constants, predicted that a ring mechanism should operate in the diffusion of body-cen-tered-cubic metals. Paneth3 calculated the activation energies of various ring, vacancy, and interstitial mechanisms for the self-diffusion in alkali metals and concluded that the most likely one was based on the linear motion of "crowdions," which is in fact a different form of interstitial diffusion. Fumi,1 however, showed that the experimental values of the activation energies for self-diffusion in the alkali metals could be better accounted for if the diffusion process in these metals was assumed to follow a vacancy mechanism. The same conclusion was reached by Kojima5 for the self-diffusion in lithium. Experimental evidences published during the past few years seem to exclude the ring mechanism as the predominating one in the diffusion of body-centered-cubic metals. For instance, maker movement has been observed in ß-brass, first in this laboratory" and later by Resnick and Baluffi.5 Shewmon and Bechtoldh also found marker movement in the body-centered-cubic system Ti-Mo and showed that the argument which led Zener and LeClair to favor a ring mechanism was not incompatible with a vacancy mechanism. In spite of this, it seemed to the authors that further experimental tests should be made by studying the Kirkendall effect in body-centered-cubic systems that characteristically have small ion core repulsion, such as the alkali-metal systems. Since the ion core repulsion term constitutes the main part of the activation energy needed for the rotation of a ring, such a test should be the most critical of all. The system K-Rb was chosen for experimental study because these metals form a continuous series of solid solutions. Experimental Investigation Owing to the extremely active nature of these two metals, a brass dry box (18 x 11 x 10 in.) was built for making the diffusion couple. It had a big lucite window on top, two side ports through which neo-prene-rubber gloves were inserted, and another side port covered with an optically flat-glass window for microscopic examination of the sample. Inside the box there were a circulating fan driven with a rotating horse-shoe magnet located outside the box, a heater used to generate potassium vapor for getter-ing the box, and a cold trap for keeping the inside of the box cool. Chemically pure grade K and Rb were triple distilled before they were transferred in vacuum into cylindrical steel molds kept in pyrex-glass ampules, Fig. 1. The latter together with the tools needed for making the diffusion couple were put into the dry box. After the box was flushed with purified argon and gettered with potassium vapor, generated from a heated steel crucible inside the box, the glass ampules were broken and the mound on the top of the alkali-metal ingot was cut off with a razor blade to yield a flat surface. To make the diffusion couple, one K ingot and one Rb ingot were pushed out of the molds together with their steel supports by screwing a metal plunger into the bottom of each mold. They were then laid on a brass cradle inside the assembling carriage (shown separately in Fig. 2) with the flat faces opposite to each

Jan 1, 1959

By J. S. Aronofsky

The results of polentiometric model studies and numerical computations are described. The purpose of these studies was to determine the influence of the mobility ratio on flooding efficiencies during water encroachment in petroleum reservoirs, in systems of regular well geometry. The direct line drive well pattern having relative spacing distances of one and one-half to one was investigated for water to oil mobility ratios of 10. 1. and 0.1. The results of these studies indicate that the pattern Sweep efficiency i.; very dependent upon the mobility ratio. INTRODUCTION The almost universal occurrence of water in the immediate neighborhood of oil-hearing sands lends considerable emphasis to the desirability of having a rational analysis of water encroachment into petroleum reservoirs. This problem has 1)become increasingly important with the accelerated use of water injection for secondary recovery operations. The water encroachment problem has been studied from both the theoretical and experimental viewpoints by Muskat.' He has formulated, in a precise manner, differential equations to express flow in a water encroachment system, and rigorous analytical solutions have been developed for the linear, radial, and spherical cases.' However, it becomes exceedingly difficult to solve the encroachment problem rigorously for any general two-dimensional system in which the shape of the two-fluid interface is not immediately evident from the geometry of the system. The difficulty lies in the fart that a rigorous analytical solution requires that the shape of the two-fluid interface be known simultaneously with its instantaneous posititon and with the pressure distribution on both sides of the interface. Although this paper concerns the study of the two-fluid system of oil and water. the methods described in the paper are generally applicable to other systems of incompressible and immiscible fluids in which the displacing fluid sweep-the displaced fluid down to a residual value. In each region it is assumed there is only one mobile fluid and its mobility is constant throughout the region. The Same procedure. with minor alteration, is applicable for gas injection systems provided the assumption can be made that both the displaced and displacing gases can be described by steady state formulas. For the particular two-fluid problem considered in this paper, there is a relative permeability. K, and a viscosity. p. associated with the water zone, and a different permeability and viscosity associated with the oil zone. The K/p (mobility value associated with a particular volume element of the porous medium. at any instant of time. will depend upon whether the element is ahead of. or behind the advancing interface. It is assumed that all volume elements ahead of the interface are characterized by the K/p value for oil, while all the elements behind the interface are characterized by the K/p value for water. That is. the K/p value in the oil zone is constant throughout the oil zone. and the K/p value in the water zone is also constant but different from the value in the oil zone. The symbols are defined at the end of the paper. The well pattern chosen for initial study is the direct line drive; the swept-out area at breakthrough was determined by two different methods which are described in the section on theory. These are: 1. Potentiometric analyzer 2. Numerical computation The use of the potentiometric analyzer for studying water flooding problems is adequately described in the literature, particularly for cases where the mobility in the water zone is assumed equal to the mobility in the oil zone." ' 5

Jan 1, 1952

By H. H. Rachford, D. W. Peaceman

A system of partial differential equations describing miscible displacement of fluids in porous media is derived The system takes into account the influence of gravity, the spatial distribution of permeability, diffusion, and fluid viscosities and densities. A numerical procedure for approximating solutions to the differential systems has been tested for a horizontal two-dimensional geometry. In end-to-end displacements of oil with less-viscous solvents, the numerical solutions exhibited fingering qualitatively similar to that observed in laboratory models. Small random spatial variations in permeability about the mean value are sufficient to initiate fingering. Quantitative comparisons of computed results with laboratory data show good agreement. INTRODUCTION Miscible flooding of oil by solvent is receiving increasing consideration for field use.1-4 Unfortunately, such floods potentially present severe problems in loss of recovery through the by-passing of oil by expensive solvent. Consequently, their economic evaluation requires sound techniques for predicting recovery. The purposes of this work are to present a finite-difference method for calculating the multidimensional displacement of oil by solvent and to investigate the validity of the method by comparing results of calculations with data from displacements in laboratory models.5 The formulation of the method to simulate the model experiments treats a case of limited scope in the description of solvent flooding in the reservoir. The model experiments were carried out with fluids that were assumed to form an incompressible, ideal, two-component system with constant diffusivity. Establishing the validity of the method even in its present form provides a major step toward the goal of quantitatively evaluating individual solvent flooding projects. First, it demonstrates the fea- sibility of calculating the course of displacements which are dominated by an inherent macroscopic instability, i.e., viscous fingering. In addition, the method provides almost the only practical means of examining the effect of the size and extent of reservoir inhomogeneities on the development and propagation of the fingers, taking into account the important influences of diffusion and gravitational segregation. It might be inferred that such studies cannot yield results of practical value because in displacements dominated by macroscopic instability the pattern of finger development and the resulting performance should depend critically on small variations in the geometric distribution of reservoir inhomogeneities. The present method offers the capability inherent in computational techniques of predicting performance reproducibly with any arbitrary distribution of reservoir properties and, as such, provides a means of evaluating the sensitivity of behavior to uncertainties in reservoir definition and, thus, assessing the reliability of prediction of performance. THE PHYSICAL PROBLEM DATA USED FOR QUANTITATIVE TESTS OF CALCULATIONS In this work, a calculation for treating the miscible-displacement process is tested by comparing calculated results with experimental data. The experiments chosen for comparison have been described in detail,5 and the quantitative features are summarized in a later section. Briefly, oil was flooded by solvent of equal density from a thin rectangular channel in Lucite packed with uniform Ottawa sand. Under these conditions, two-dimensional geometry is considered adequate to represent the process. Inasmuch as the present work is concerned with testing of the method by comparison with specific two-dimensional data, the system of equations presented in the succeeding section will be oriented to defining the physical system specifically. THE DIFFERENTIAL EQUATIONS Suppose x, y to be a Cartesian co-ordinate system and define h(x, y) to be the height of a point above a horizontal reference plane. It will be assumed

By L. A. Wilson, N. H. Harrison, R. R. Clay, R. L. Reed. D. W. Reed

Experiments have been performed in a linear near-adiabatic system for the purpose of extending data on reverse and forward combustion from atmospheric pressure to 1,000 psig. Results obtained from reverse combustion appear to conform qualitatively with the existing description of the process when reaction kinetics are suitably modified to account for the increase in pressure, i.e., increasing tbe pressure decreases the peak temperature and increases the combustion zone velocity. Forward combustion appears to be a fuel dominated process wherein peak temperature and combustion zone velocity are not very sensitive to changes in pressure. The moderate effects of pressure that do exist at low flux virtually disappear at high flux providing all oxygen is consumed. With this provision. increasing the pressure decreases the frontal velocity and increases the peak temperature. Results me shown graphicaIIy which demonstrate the effects of presswe on peak temperature, rate of advance, oil recovery, air/oil ratio, carbon oxides produced and temperature distributions. INTRODUCTION Numerous field tests of oil recovery using the technique of underground combustion are now in progress. Operating pressures used are always substantially in excess of atmospheric pressure. Nevertheless, the literature contains no laboratory data pertaining to the effects of pressure except for those of Martin, Alexander and Dew.1 Unfortunately, these data appear to reflect heat losses which may have obscured some of the effects of increased pressure. The underground combustion processes are exceedingly complex, and general concepts relating to them have necessarily been described in relatively simple terms. Particularly with regard to forward combustion, the interaction between multiphase fluid flow, heat transport and various rate mechanisms is so involved that to date a rigorous treatment is not available. In this paper a linear near-adiabatic system is described which was found capable of operating at pressures up to 1,000 psig and temperatures of at least 1,100 F. Using this equipment, experiments on both forward and reverse combustion were accomplished at elevated pressures and the data presented as a function of air flux or temperature. It will be assumed that the reader is familiar with the papers of Wilson, Wygal, Reed, Gergins and Henderson on forward combustion and that of Reed, Reed and Tracht3 on reverse combustion, so that it is not necessary to repeat the details of the two processes. EQUIPMENT AND PROCEDURE It was decided to study the effects of pressure over the interval 0-1,000 psig using a near-adiabatic system. Since satisfactory operation of such a system requires very thin tubing walls, it proved necessary to insert the entire combustion tube and heater assembly into a high pressure jacket in such a way that the internal tube pressure could be counterbalanced by pressurizing the annulus. This meant that the numerous heater and thermocouple wires had to pass through gas-tight seals that required considerable effort to maintain effective. An unexpected difficulty arose in connection with the nature of the annulus pressuring gas. It turned out that the composition of this gas critically affected the functioning of the adiabatic control system. Operation of the equipment at elevated pressures was not particularly difficult. The problems that did arise were a direct consequence of the large numbers of connections and seals involved. EQUIPMENT The equipment consisted of the combustion tube which fitted within the pressure jacket. This jacket was in turn mounted on a wheeled carriage which facilitated movement and provided for rotation of the

By R. J. Teitel

The Pb-U system has been investigated by X-ray, thermal, and microscopic analyses. Two pyrophoric intermetallic compounds were found; UPb3 and UPb. The crystallographic structure of UPb3 is reported. A phase diagram was drawn for the system showing three eutectic and one syntectic reaction. AS a result of the interest in uranium metallurgy, the Pb-U system has been investigated. Practically no quantitative data appears in the literature concerning this system. Chips were machined from bars of high-purity uranium obtained from Ames Laboratory and the lead was 99.9 pct high-purity grade from Bel-mont Smelting & Refining Co. The chips were pickled in a dilute solution of nitric acid, washed in water and then alcohol, and dried prior to use for alloy preparation. The lead was simply sheared from the pig with no chemical treatment. Lead and uranium were placed in graphite crucibles and loaded into an induction furnace. In order to insure good alloy formation, the lead was loaded above the uranium to wash the uranium chips into the melt. After the charge was held at the desired preparation temperature for 15 to 30 min, it was allowed to cool in the crucible. The entire melting operation was accomplished in an atmosphere of helium (double charcoal refined grade with no further treatment). The procedure was to outgas the furnace by first evacuating it to 10-% m Hg, admitting helium to 8 psi gage and sealing the furnace off. An optical pyrometer focused on the charge through a hole in the crucible cover was employed for thermal measurements. Usually a 50° to 70°C correction had to be added to the instrument value. The most suitable alloy preparation temperature range was found between 1220° and 1280°C. The reason for this is explained by the phase diagram, Fig. 7. Above this temperature range two liquids separate preventing alloy formation upon cooling at a reasonable rate. On the other hand, below this range the uranium was coated with a layer of both compounds and the rate of reaction was diminished by diffusion processes. The fastest reaction rate occurred in this narrow range of temperature because only UPb coats the uranium and it evidently does not protect the uranium as well as UPb,. Apparatus and Procedures The development of apparatus and techniques was determined by the peculiar properties of the alloys. All the alloys were pyrophoric, and, consequently, the alloys had to be protected from oxidation by handling them in a dry box or inert atmosphere furnaces. Other operations performed outside of this equipment had to be done as quickly as possible. Thermal analyses were conducted in a furnace and arrangement similar to that described by the author.' Graphite crucibles having a thermocouple well in the bottom were used to contain the prepared alloy, while a helium atmosphere protected the melt from oxidation. The furnace was outgassed by pumping a 10-3 mm Hg vacuum until the furnace had been heated to 400°C. Then helium was admitted and the furnace sealed under 8 psi gage pressure. Chromel-alumel thermocouples were used for thermal analysis and the accuracy of thermal measurements was judged to be k 5°C. At first, an attempt was made to use platinum-platinum-rhodium thermocouples, but evidently lead vapors attack it at high temperatures forming low melting alloys. These lead vapors had direct access to the thermocouple because the graphite crucible was porous. A differential temperature control was used to regulate thermal analyses. The thermal gradient across an alundum tube placed between the windings and the crucible was maintained constant by a controller.

Jan 1, 1953

By J. Spotts McDowell

Preparation and Use.-Magnesite is an important refractory in open-hearth, heating, and electric furnaces for steel-making and in many of those employed in the metallurgy of copper and lead. It is sold in the form of brick, finely ground "furnace magnesite" for brick-laying, and dead-burned grains for making and repairing furnace bottoms. The latter are a mixture of granules varying in size from pieces of about 5/8 in. (1.6 cm.) diameter to very fine but sandy particles. Dead-burned magnesite results from calcining 'the crude or lightly burned mineral at a temperature that will not merely drive off practically all the CO2, but will also cause sintering of the particles. During this process the pieces shrink considerably and become hard, dense, and inert to atmospheric moisture and C02; under-burned material, on the other hand, will hydrate on exposure to the air. A small percentage of ferric oxide seems to be necessary for the production of a satisfactory sinter; from 4.5 to 8 per cent. in the dead-burned grains is considered the most desirable amount. Dolomite has been little used for brick-making in the United States, but it is prepared for use in the granular condition calcined or "double-burned" and is the principal ingredient of several materials offered for sale under various trade names for refractory purposes. Dolomitic refractories are almost wholly confined to the open-hearth and electric furnaces, where they are used for fettling and as substitutes for magnesite. Much more magnesite and dolomite are used for basic open-hearth steel-making than for all other refractory purposes. The hearth of the furnace is usually built up of magnesite brick and dead-burned grain magnesite so laid that the brick base is protected by a working bottom of the granular material. The latter is sintered into place in layers 1 to 2 in. (2.5 to 5 cm.) thick to a total depth of 12 to 18 in. (30 to 45 cm.) at the center of the furnace. After each heat, burned dolomite is thrown against the banks as high as it will stick, and all holes in the bottom are filled. At most plants such holes, at the end of each week, are also

Jan 2, 1919

By Oscar Johnson

The industry has been canvassed for information on methods of handling grinding steel at milling plants, an important subject overlooked in most descriptive articles on milling plant arrangements. The data collected are offered in this paper as a guide to designers and planners who have loading and storage problems to solve. WITH capacities of milling plants expanding from a few hundred tons per day to many thousand, replenishment of grinding media is an important phase of mill operation. Information on this aspect of milling procedure, solicited from several mining companies, is summarized here. At International Nickel's Copper Cliff concentrator the normally strenuous job of changing rods is considerably simplified by the use of the Garrow rod charging machine, Fig. 1. The overhead crane, Fig. 2, brings a bundle of rods, weighing four to a ton, to the loading platform of the machine, positioned in front of the mill. The rods roll one by one down the slight incline of the platform onto a conveyor which sends them into the mill. A modified version of the Garrow machine, Fig. 3, is used at the Federal mill of St. Joseph Lead Co. An overhead crane places the portable steel structure in position in front of the discharge end of any one of the five 9x12-ft rod mills. It then raises a bundle of about twenty 3-in. rods to the discharge platform of the charging machine. The rods are 11 ft 7 in. long and weigh about 278 lb. By tripping a lever the operator allows one rod at a time to roll onto the inclined rollers. A slight push by the operator sends the rod smoothly into the mill. The Union Miniére du Haut Katanga rod charging machine, Fig. 4, is mounted on a pair of wheels at the forward end with swiveling castors at the back for steering it to position for use or storage. Wheels are equipped with locking brakes to maintain the machine in position while it delivers rods to the mill. The device is made in two parts. The first consists of the base, which carries the supporting wheels, grooved rollers, and drive. The other part serves as the rod deck, which can carry up to six 3-in. x 12-ft rods. A short boom built integral with the base reaches through the mill trunnion and delivers the rods into the mill barrel. Three grooved guide rollers ,are provided to receive the rods from the sloping charging deck. One rod at a time is fed to the rollers and thus delivered into the mill. Two of the rollers are driven by 11/2-hp motor through a V-belt drive. The third roller is driven off the first by a single V belt in a groove below the rod groove and on the same center line. Rods are delivered to the charger by an overhead crane in bundles of three to six as needed. The power is supplied by cables plugged into power outlets, suitably located near the rod mill discharge end. The Oliver Iron Mining Co. uses a rod charger, Fig. 5, suspended from a monorail by cables. It is constructed .of structural steel and has two decks, each capable of carrying five rods of 4-in. maximum diameter. The rods ride in grooved free-turning rollers. Legs extending down from the mill end of the mechanism act as supports when the unit is ex-

Jan 1, 1955

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry's law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2'= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,' using Laitinen and Liu's' value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,' and the equations of Wagner and Werner,' the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O' and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies' have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969

By G. A. Vissac

The only fine coal washer with proved automatic controls, the feldspar jig is capable of good efficiencies even at low separating gravities, handles a variety of products, and treats 150 tph and over. IN continental Europe the feldspar jig is used almost exclusively for cleaning the fine sizes of coal; it operates with an artificial bed, made up generally of pieces of feldspar or of any other hard and heavy rock with good cleavages. A primitive form of this machine requiring close supervision was used in this country years ago, but output was small. The modern machines are generally air-pulsated Baum-type jigs, with capacities up to 150 tph, and treat sizes from % in. to 0, usually previously dedusted or deslimed. These jigs are equipped with very accurate and sensitive automatic controls insuring satisfactory operation even at low separating gravity and with feeds irregular in quality and quantity. This paper will deal more particularly with coal cleaning separation, but the technical studies apply equally to all minerals. Theory of the Feldspar Jig To understand fully the operation of the feldspar jig and to appreciate its potential value, it is necessary to measure and analyze the motion of small particles of various specific gravities, falling in various media, under various conditions. As no practical formulas were available for that purpose, the writer has developed new theories and established new sets of formulas, which cannot be demonstrated here. They are applicable to all minerals and to many problems of coal or mineral concentration. These formulas do not pretend to absolute accuracy, but results, tested by comparison with experimentally recorded data, are sufficient for practical purposes, as they give definite indications of trends, relative values, and order of magnitude of the many factors involved. For pulsating motions no earlier formulas are available. In the case of continuous currents or motions, such formulas as Rittinger's, Allen's, or Stokes', over a hundred years old, apply only to special shapes and sizes of particles, involve factors and coefficients difficult to measure or appreciate, and deal only with free motions. They are of little use in solving practical problems. Units used with the formulas presented here are in the CGS system. Lateral friction and suction have been taken into account according- to methods currently used in aerodynamics, and only hindered motion is dealt with. As the feldspar jig is primarily intended to create a fluid bed condition, the mixture of fluids and solids obtained is homogeneous, and the apparent specific gravity of the separating medium is calculated accordingly. For instance, if 20 pct of the volume is coal and shale, with an average of 1.60 sp gr, in a liquid of 1.10 sp gr, the actual specific gravity of the separating fluid is 0.80 x 1.1 + 0.20 X 1.6 = 1.20. The fundamental equations are as follows: The general motion of a particle falling in a medium of specific gravity equal to u, hindered motion. is dv/dt = g/Ls [ L (s-u) - u/g v2 [1] g = 981 cm per sec, acceleration of gravity, and L = thickness of the particle of specific gravity (s) and velocity (v). The initial acceleration dv/dt = g (1-u/s ) [2] is a function of the specific gravity of the particle, only for a given medium, and independent of its dimensions—an ideal separating condition. The terminal velocity Vt = gxL- (s-u)/u, [3] for a given value of u, is a function of s and L. Two particles, L, s, and L2 s2, are said to be equivalent if they have the same terminal velocity, and accordingly L1/L2=s2-u/s1-u. [4] Two such particles cannot be separated by continuous currents, in any concentrating device. Because the initial accelerated motion, which provides for efficient separation, is followed by a constant velocity, which has a limiting effect, it is essen-

Jan 1, 1956

By P. A. Beck, Hsun Hu

It has been known for many years that in cold drawn polycrystalline aluminum the recrystallization texture is practically identical with the deformation texture.l,2,3 V. Goeler and Sachs4 stated that in cold rolled polycrystalline aluminum, too, the deformation texture is retained upon recrystallization. This behavior was interpreted by Dehlinger9 as an indication that each recrystallized grain inherits the orientation of the matrix in which it grew. However, Burgers and Basart showed6 that in deformed aluminum single crystals the orientation of the recrystallized grains strongly deviates from that of the matrix. Barrett demonstrated8 that even in deformed polycrystalline aggregates the local orientation within each deformed grain changes on recrystallization. No explanation has as yet been offered of how the aggregate texture can be retained, while the local texture is everywhere changing. According to Burgers and Louwerse6 the orientation change on recrystallization in compressed and rolled aluminum single crystals corresponds to a rotation around [112] axes lying in the active slip planes and perpendicular to active slip directions. This orientation change was rationalized by them on the assumption that the orientation of the recrystallized grains is determined by the orientation of the available nuclei, and that these nuclei are small fragments of the deformed crystal, rotated in the deformation process. Barrett pointed out,? however, that these assumptions were by no means proven, and that the total volume of material necessary for the nuclei is so small, that it must be available in any orien- tation whatever. It is, therefore, unlikely that an "oriented nucleation" theory could satisfactorily explain the orientation changes in recrystallization of a deformed crystal. Furthermore, in contradiction to Burgers and LOU-werse's conclusions, Barrett's results for the orientation change could be best expressed in terms of rotations around. [Ill] axes. Thus agreement is lacking not only in the interpretations but apparently even in the experimental results contributed by the various investigators. The orientation relationships on coarsening* in a highly oriented polycrystalline matrix were first investigated by Burgers and Basart.5 They produced a fine grained highly oriented matrix by the recrystallization of a compressed or rolled single crystal of aluminum, and studied the orientation relationships in three successive generations of crystals: the "deformation texture" in the single crystal, the recrystallization texture, and the coarsening texture. Burgers24 showed that the preferred orientation of each successive generation was almost always widely different from that of the preceding one, but that the coarse grains often approximately reverted to the orientation of their grandparent, the deformed single crystal. This observation, and the idea that the orientation of the coarse grains is determined by that of the available "nuclei," led to the concept that the coarse grains are nucleated by the remnants of the deformation texture.12,15 On the other hand, Bowles and Boas16 found, in a carefully conducted experiment, that in recrystallized fine grained copper of cube texture coarse grains grow in orientations which can be derived from the orientation of the recrystallized matrix by rotation around a [lll].] direction: the coarsening texture here does not appear to be related in any simple manner to the original rolling texture from which the cube texture had been obtained by recrystallization. It may be assumed that in a recrystallized material, even with a strong texture, there always are present some grains of practically any orientation. These may serve as "nuclei" for the coarse grains, provided that the conditions are favorable for their growth. The existence of a coarsening texture may be considered as an indication that grains with certain relative orientations with respect to the preferred orientation of their neighbors can grow much faster than others. This "oriented growth" theory was briefly suggested by van Arkel, as early as 1936,13 and it was mentioned by Burgers." Recently, C. G. Dunn produced direct

Jan 1, 1950

By S. R. Mitchell, M. Weissman, J. H. Brown

It has been demonstrated that for fine grinding operations, the energy input (E) and the product size modulus (k) are related by an equation of the form E = Ak1-n (1) where "A " and "n" are constants.(1) Also, it was suggested that "A" is determined by the comminuting device and that "n" depends primarily on the rock. It was the purpose of this investigation to study these constants by determining the form of an energy-size reduction relationship over an extreme range of energy inputs, and at the same time, to evaluate the minimum particle size produced during grinding. The comminution system consisted of a stainless steel laboratory ball mill in which quartz was ground at 60% solids for times ranging from 1 minute to 700 hours. The mill which measured 10" diameter by 12" long was loaded with about 60 pounds of balls ranging in diameter from 3/8" to 1-1/8" and was driven at 55 r.p.m. Quartz was selected for the tests because it is a brittle material for which size distribution data were expected to show a constant distribution coefficient regardless of product size.(1) This permitted specification of product size by a size modulus alone. The quantities measured were the time of grind (measure of energy input) and the specific surfaces of the products. Since no accurate method is available yet for determining particle size directly in the very fine size ranges specific surface data were used for this purpose. The relationship between these two quantities may be expressed as where Cis a constant which includes a shape factor, p is the specific gravity of the solid,_S is the specific surface and D is an equivalent particle diameter. For a material in which the distribution coefficient does not change with size the term (l/S) may be substituted for k in equation L if the proportionality constant "A" is changed correspondingly. This substitution was made in this work but in addition, screen analyses were made on several products to verify the equivalence of the two methods of size specification. EXPERIMENTAL DETAIL QUARTZ Quartz from two sources was tested. One series of tests was made on a clear, high purity crystalline quartz from Brazil and Arkansas, and another series was run on massive quartz fromNewHampshire. Grinding charges of the high purity material consisted of 2000 gram samples of -3-8 mesh particles, while the charges of the New Hampshire quartz were 500 gram samples of a -35+48 mesh screen fraction. The difference in the sizes of these two series of charges was not significant in view of the extreme size reduction accomplished, and the New Hampshire samples were smaller to permit ginding to finer sizes in shorter times than required for 2000 gram lots. SAMPLING AND ANALYSIS Separate charges were ground for all tests in which the grinding times were less than one hour and for all tests on New Hampshire quartz since these products were difficult to sample accurately without affecting the entire charge. During the long time grinding tests the mill was

Jan 1, 1961