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By B. H. Caudle, A. R. Khan

The oil production performance of thin-oil-column type reservoirs producing entirely by natural water drive are discussed in this paper. The dimensionless production histories were obtained in a series of scaled porous-medium laboratory-model tests under varying effects of rate of production, mobility ratio across moving boundary, ratio of oil- and water-sand thickness and mobility ratio across fixed boundary including the effects of different residual oil saturations in the water-invaded regions. This scaled-model study of thin oil columns indicated that greater recovery of oil results for lower values of the following: rate of production, mobility ratio across the moving boundary, water-sand thickness relative to the oil-sand thickness, and mobility ratio across the fixed boundary or residual oil saturation in the water-invaded region of oil sand The results of the study are given as dimensionless production history plots which may be used to predict the performance of the field they represent. INTRODUCTION Oil fields producing under natural water drive can be classified into two major groups: (1) an "edge-water drive" reservoir group in which the water is encroaching from the reservoir periphery, and (2) the group of reservoirs in which the oil-sand is entirely underlain by an aquifer. Reservoirs in the second group are further subclassified as "bottom-water drive" reservoirs and "thin-oil-column" reservoirs. The latter reservoirs are characterized by their relatively equal oil- and water-sand thicknesses and by having both the oil and water zone relatively thin. When oil is produced from a water-drive reservoir by a partially penetrating well, water breaks through sooner or later before all of the displace-able oil is recovered. Many analyses of this general situation have been made with varying degrees of realism in their approaches, both theoretical and experimental5.6 in nature. Pertaining to the scaled laboratory model studies of natural water drives using porous media, detailed investigations have been made by Henley, et al.7 on bottom-water drive and by Caudle8 on edge-water drive reservoirs. No laboratory model studies, however, have been made to investigate the performance characteristics of thin-oil-column reservoirs. This paper presents the results of a study on scaled models of thin-oil-column reservoirs, operated under varying conditions corresponding to the actual field practices. SCALING PARAMETERS The object of scaling is to produce a one-to-one relationship between physical and dynamic parameters of the model -and prototype. The most comprehensive treatment of scaling techniques for oil reservoirs is given by Geertsma, et a1.,9 which covers two methods for arriving at dimensionless groups for scaling. Table 1 lists the scaling parameters suitable for creating kinematic and dynamic similarities between the model and the prototype in the variables considered for the thin-oil-column reservoirs. In order to achieve similarity it is essential that the dimensionless groups listed in Table 1 have equal values in the model and the protorype simulated. Since it has been established that the role of interfacial forces is neglible in gross fluid movement in a reservoir no attempt was made to scale capillary forces- Although there are reports describing Scaling criteria for these forces,10,ll consideration of the necessary but restrictive conditions for

Jan 1, 1970

By C. K. Leith

Conservation, narrowly and strictly considered, means the preservation in unimpaired efficiency of the resources of the earth; or in a condition so nearly unimpaired as the nature of the case, or wise exhaustion, admits. And broadly considered, it means more than the word itself implies, for it naturally includes an examination of methods whereby the natural inheritance of the human race may be improved; and still more broadly considered. and as used in popular discussion, it includes a treatment of the effects of productive conservation methods upon distribution. "Conservation means a sacrifice of the present generation to the future generations whenever it is carried too far. There is a sharp limit to the economic sacrifice that we may reasonably ask the private person to make for even the present welfare, and the limit is still sharper when we come to consider the interests of future generations." In a paper on the iron ores of America, presented to the Pan-American Scientific Congress at Washington, I have emphasized the fact that the reserves of iron ores in the two Americas are enormously in excess of the requirements of the present generation, in fact, so large that no shortage is to be anticipated for many generations in the future; that a large part of the value of iron ores is put into them by man's efforts to make them available. This fact is fundamental for the intelligent consideration of policies of conservation as applied to iron ore. As I interpret it, this fact makes it practically unnecessary that the present generation should make any especial sacrifice for future generations in the way of conservation of its iron-ore resources. Even if we were disposed to look forward to a period of 100 or 200 years, with a view to insuring the welfare of the people living at that time, it is doubtful whether any procedure we could now formulate would materially help them in the matter of iron ores, so large are the reserves available. In order that an appeal for conservation may be effective it must obviously favor the welfare of the present or immediately following generations; it must promise benefits to general and individual welfare during a period within the range of comprehension of the average man.

Jan 1, 1916

By T. E. Scott, R. P. Zerwekh

The charactevistics of the deformatiotz of fcc thorium were examined between 78 and 473 K. Activation energy, actiuation volume, and the temperature dependence of the flow stress were determined and conlpared uith several theories for the rate-controlling mechnnistn of the tempemture-dependent component of the flou~ stress. It was established that the Cottrell-Stokes law does not hold, even approximately, for thorium. Through consideration of the above factors and other parameters, it was concluded that the vandom solute barrier theory proposed by Friedel demonstrates the best agreement with experimental observations of the deformation of thorium below ambient temperature. THORIUM, the first metal in the actinide series of rare-earth elements, is interesting and important from two points of view. In the more practical vein, it is a potential reactor fuel. As such, it is important to know its properties. Of specific interest here are the mechanical properties of thorium. Second, no detailed information concerning the deformation characteristics of the actinide elements has been gathered to date. In view of the interesting physical and chemical properties of these metals, their mechanical behavior might reveal characteristics which could improve our understanding of the mechanisms controlling deformation of the more common metals. For example, it has been shown1 that thorium exhibits a yield point which is greatly enhanced by interstitial solute elements such as carbon. This is not a normal occurrence in fcc metals. The goal of this investigation, therefore, was to characterize the deformation of polycrystalline thorium. MATERIAL AND PROCEDURES Thorium, made by the magnesium intermediate alloy process described by Peterson et al.,2 was rolled and swaged to 0.065-in.-diam wire. The metal analysis is given in Table I. After preparation, the oxygen and nitrogen contents had risen to 308 and 60 ppm, respectively. The 0.065-in.-diam wires were cut into 2-in. lengths and annealed in a vacuum of lo-' Torr at 750°C for 1 hr, producing a grain size of 2735 grains per sq mm. The ends of the 2-in. sections were masked off so that a 1-in. gage length could be electropolished. Specimens were polished at 35 v in a solution of 6 pct perchloric acid in methanol which was maintained at 0°C . The gage diameters after polishing were about 0.0625 in. The tests were run on a screw-driven tensile machine at a constant crosshead speed corresponding to a strain rate of 0.005 min-'. The strain rate was changed rapidly after each 0.01-in. extension between 0.005 min-' and one of three higher strain rates which were selected in order to achieve strain-rate ratios of 5, 10, and 20. Tests were run at several temperatures from 78" to 473°K; most were tested at 423", 300°, 215", and 78°K. EXPERIMENTAL RESULTS Flow Stress vs Strain and Temperature. Typical true stress-true strain curves for thorium are shown in Fig. 1 for several temperatures over the range 473" to 78°K. The curves for 78", 215", 300") and 423°K were obtained from strain-rate change tests using the lower (0.005 min-') or base strain-rate values of stress. Additional tests, using the same base strain rate at different strain-rate ratios, gave curves which virtually superposed on those shown, indicating that strain-rate changes did not materially influence the work-hardening characteristics at the base strain rate. The curves for 273") 373") and 473°K were standard tensile tests at 0.005 min-'. The behavior of the flow stress with temperature is

Jan 1, 1968

AT THE beginning of September, the French eased their pressure against Germany and allowed the latter to, be granted an arrangement for its reparation payments in kind according to the Lubersac-Stinnes agreement. The whole arrangement as to the German reparations is, however, but temporary. The Greeks suffered a disastrous defeat at the hands of the Turks in Anatolia, which rapidly resulted in the expulsion of the Greeks from Asia Minor, the Turks occupying Smyrna about Sept. 10. A few days after entering Smyrna the Turks sacked the city and finally set it afire, creating one of the most terrible destructions in history. At the same time their advance on Constantinople, together with their demands on the Allies, brought them directly in, con-flict with the latter and Great. Britain prepared for a new war, with doubt as to the support of France, whose political interests in the Near East are as different as their economic interests with respect to ;Germany. The Turkish situation became thus a threat against the peace of Europe. A revolution in Greece, followed by the abdication of King Constantine and the return of Venizelos to a function in the Government was one of the conse-quences of the defeat in Asia Minor. Civil war continued in Ireland, with more or less -bloodshed. Economically there has been no change for the better in Europe. In Great Britain there, are no signs of an -important trade revival. In Germany and Austria things are worse. French, Italian and Spanish affairs continue in a bad way. In the United States business is represented as "booming," but many people are inquiring where is the boom? About the middle of September Congress passed the tariff and the soldier bonus bills. The President signed the former and vetoed the latter, with a strong message that won praise among people who understand condi-tions. Congress tried to pass the bill over the veto, but failed. The President signed the tariff bill, which became effective Sept. 21. A severe handicap was thus imposed on American economics.

Jan 10, 1922

By H. H. Rachford

This work presents a first-order analysis of the instability underlying viscous fingering in adverse viscosity-ratio water floods. It extends previous analyses of frontal instabilities, which were carried out with equations for parallel plate models, by including effects of the saturation transition zone observed behind the front in water floods in water wet systems. This zone tends to insulate incipient fingers from the high-mobility watet;. thus conditions for the onset of fingering differ from those in the parallel plate theory. Finite-difference solutions of the two-dimensional equations of displacement in porous media exhibited the predicted stability characteristics in six hypothetical field- and laboratory-scale floods in rectangular reservoirs. In contrast to results with parallel plate systems, this paper concludes that for waterwet reservoirs, laboratory models scaled by the usual criteria are also correctly scaled for frontal instability. Further, fingering in the systems studied can occur in any saturation range behind the front, and may occur at an intermediate saturation even though stability obtains both at the saturation corresponding to the Buckley-Leverett front and near residual oil saturation. Other points of contrast are that the likelihood of occurrence of fingering may not increase as flow rate or viscosity difference increases, but my be sensitive to changes in he relative permealdlity and capillary pressure functions. INTRODUCTION The recovery of oil by water flooding frequently involves displacing the oil by water of a lower viscosity. Displacement of a fluid by a less viscous one may lead to gross channeling or fingering like that observed in solvent floods, in which it severely lowers recovery efficiency.1 In addition to adverse effects on recovery, it has been suggested that the unstable move- ment causing fingering may interfere with interpretation of scaled model studies of proposed water floods, since the instability in the model might not be faithfully scaled to that in the reservoir prototype. In view of the serious implications of this possible breakdown of widely used scaled model techniques4-6 it is the purpose of this paper to examine the question further. Instabilities in the solutions of systems of differential equations imply a loss of smooth dependence on initial and boundary conditions. Thus, the possibility exists that in using models whose scaling is based on the differential system there may arise size- and rate-dependent factors which are not properly scaled. This possibility was examined in detail by Chouke et al., who analyzed the instability of frontal advance in a related problem, water-oil displacement in parallel plate models,2 in which a moving interface separates two regions of constant, unequal mobilities. First-order perturbation theory predicts the existence of a critical wave length for the growth of perturbations: and a wave length of maximum instability of A, = The interpretation is that wave lengths in a perturbation which are longer than A, will grow. Thus, if the width of a two-dimensional channel is greater than A,, fingers will grow, and the spacing of the fingers which grow at the maximum rate will be approximately It is important that the higher the velocity and/or the difference in flow resistance, the lower is A,, and thus the greater the number of fingers that can grow in a given model. In applying these conclusions to porous media, a pseudo-interfacial tension, , was assumed for the invasion front. Since this would not necessarily be equal to the liquid-liquid interfacial tension, an unknown constant was substituted for the foregoing expression for A, This was determined

Jan 1, 1965

By E. W. Davis

ABOUT a year ago several carloads of magnetite ore from New York state were sent to the Mines Experiment Station at the University of Minnesota for grinding and concentration tests. The flowsheet used minus ½ -in. ore as feed to a 3 by 3-ft. overflow cylindrical ball mill operating at 37 r.p.m. in closed ciruit with a vibrating screen. The screen oversize was returned to the mill for further grinding and the screen undersize was concentrated magnetically. Several different screens, between 8 and 35 mesh, were used and it was desired to determine the capacity of the ball mill operating in closed circuit with each screen. From earlier tests using this flowsheet and equipment, it was known that when comparatively coarse screens were used it was necessary to increase the grinding dilution in the mill beyond that ordinarily used when grinding in closed circuit with classifiers. It was also known that after the circulating load had passed about zoo per cent of the original feed it tended to increase rapidly in amount, and grinding conditions appeared to become unstable. These conditions may be peculiar to this small ball mill but they were very marked in this series of tests. If conditions were not right, the mill would suddenly "go dead," and it was found desirable to operate so that the occasional rattle of balls against the lining of the mill could be detected. As the test proceeded, it was found that the cure for almost any difficulty that developed in the grinding circuit was to add more water to the mill feed. To begin with, the mill was operated at pulp densities of from 60 to 65 per cent solids but gradually it was found that with higher dilutions grinding conditions were more stable and the ball-mill power per ton of screen undersize decreased. Actually, the most satisfactory operating conditions were secured with a pulp density of about 40 per cent solids. The ore was hard but it was possible to grind ½ in. feed so that all would pass an 8-mesh screen with a power expenditure in the ball mill of less than 2 1/2 kw-hr. per ton and with a circulating load of less than 50 per cent. With so high a dilution in the feed to the mill, it was feared that steel wear would be very high. However, the mill was not noisy, and in order to find exactly the grinding conditions, a special test was made at the end of the main series of tests. After the mill had been in operation for several hours and grinding conditions had become balanced, the power to all the equipment was shut off at a given signal. The ball mill made about one revolution after the power was turned off, and just as soon as the mill stopped, a spout was placed at the discharge trunnion and all of the pulp that flowed out of the mill was caught in tanks. The manhole in the mill was then opened and the whole mill charge dumped into other tanks. Both of these products were weighed, dried, and weighed again. The balls were screened out and weighed, and the dry solids were sized. In this way it was possible to determine the nature of the pulp and the ore within the mill under actual grinding conditions.

Jan 1, 1945

By Robert B. Hall, Charles W. Bauer

Alunite, KA13(SO4)2(OH)6, was used from the 15th century until early in the present century as a source of potash alum and aluminum sulfate. Since early in this century its use for this purpose has declined to virtually nil with acid treatment of bauxite or clay replacing alunite as a source of alum. During the First World War alunite served as an emergency source of potassium sulfate fertilizer in the United States and Australia. More recently, alunite has been investigated as a nonbauxite ore of aluminum, with potassium sulfate and sulfuric acid as recoverable byproducts. The Soviet Union established a commercial-scale plant in the mid-1960s producing cell-grade alumina from alunitic ore and recovering byproduct potassium sulfate and sulfuric acid. Interest in nonbauxite ores, including alunite, is expected to continue in countries that presently are dependent on imports of bauxite or alumina to support their aluminum industries. The US has the largest aluminum producing and fabricating industry in the world but imports more than 90% of its aluminum-bearing raw materials. This chapter reviews the status of alunite as a potential source of aluminum with byproduct fertilizer, and the resources available to support this industry, whenever this becomes economically feasible. Historical Background Alunite has received little attention until recently, yet for centuries it held a higher place than many of the industrial minerals considered essential today. The deposits of alunite at Tolfa, northwest of Rome, were mined almost continuously from 1462 until about the middle of the present century (DeLaunay, 1907; Lombardi, 1977). The potash alum made from the alunite, called Roman alum, was a valued commodity in international trade, being used in the making of paper, in tanning leather, and as a mordant in textile dyeing. The industry at Tolfa is said to have been controlled by the Vatican and was a source of revenue for the Papal State until fairly recent times (Lombardi et al., 1977). Since early in the present century, the preferred method for making alum has been by acid treatment of bauxite, clay, or other aluminous material, so that alunite has fallen into near-total disuse as a source of alum chemicals. Appreciable quantities of mixed alunite-kaolin rock still are quarried in the Tolfa district for use by the Italian cement industry (Lombardi and Mattias, 1979), but the role of this material in the making of Italian cement is not clear. A large deposit of alunite-bearing rock in Chekiang province, mainland China, is said to have yielded a "great quantity" of alum over a period of several centuries (Yih, 1931). During the 19th century, alunite deposits in France, Spain, Australia, and other countries were exploited as raw material for making potash alum and aluminum sulfate. Interest in alunite was revived during the First World War, not for alum, but as an emergency source of potassium sulfate fertilizer. Large veins of nearly pure alunite had just been discovered on Alunite Ridge, 11 km southwest of Marysvale in Piute County, Utah (Butler and Gale, 1912), and these were quickly brought into production for making potash fertilizer to replace supplies cut off from the famous deposits at Stassfurt, Germany. An estimated 225 kt of Marysvale alunite was mined and processed at that time (Callaghan, 1973). Similarly, Australian alunite deposits were mined as a source of potash fertilizer during both world wars (Hall, 1978).

Jan 1, 1983

By Donald Ofte, L. J. Wittenberg

The absolute viscosity coefficients and activation energies for viscous flow of bismuth, lead, and zinc are reported. The viscosities were measured in an oscillating cup viscosimeter from nearly 1000°C to within 1 deg of the melting point of zinc; 2 deg of the melting point of lead; and in the supercooled condition of bismuth, 9 deg below the melting point. Two methods of relating the change in the viscosity coeflicient with temperature were compared. From the plot of the logarithm of viscosity (77) as a function of reciprocal absolute temperature (1/T), the equations of the lines which fit the data are: AS a part of the Reactor Fuels and Materials Research program at Mound Laboratory, precise measurements of the physical properties of liquid metals are of interest because the desirability for a low vapor pressure liquid coolant in high-temperature nuclear power plants has focused attention on the properties of the liquid metals.' Also, a clearer understanding of the liquid metal state can be achieved when better measurements are available. For these reasons, the viscosity values of certain liquid metals have been determined. The viscosities of the liquid metals, bismuth, lead, and zinc are measured in an oscillating cup viscosi-meter. In this apparatus the liquid is sealed in a right-circular cylindrical cup which is attached to a torsion fiber so that the system forms a torsion pendulum. The damping effect of the molten metal upon the normal oscillations of the torsion pendulum is a function of the viscosity of the liquid. This method is advantageous because of the small amount of sample required (8 to 10 cc), the ease of remote operation of the apparatus in a vacuum system, and the containment of the liquid metal in a hermetically sealed, nonreactive, tantalum crucible. With the liquid metal sealed in the crucible, loss of liquid by vaporization and chemical reactions with atmospheric gases are prevented. Additionally, an absolute viscosity determination is obtained which avoids the sources of possible error in a relative measurement. The difficulties in a relative method include the repetitious cup calibrations, and the uncertainty inherent in the practice of calibration of the apparatus at room temperature and extrapolation to the high temperatures necessary for the investigation of most liquid metals. The oscillating cup viscosimeter was first described by Meyer in 1891.2 The first complete mathematical treatment offering an absolute measurement of viscosity with this type of apparatus was proposed by Andrade and chiong3 in 1936 for an oscillating sphere filled with a liquid. This solution was modified to include a right circular cylinder by Hopkins and Toye4 in 1950, and R. Roscoe5 in 1958. Roscoe's treatment for the calculation of the viscosity of a liquid at a particular temperature from the logarithmic decrement and period of oscillation of the torsion pendulum was used in this investigation. A detailed description of the method of calculating the viscosity from these measurements has been reported earlier.' This calculation has been programmed for the IBM 704 and IBM 1620 computers for expedition of the otherwise laborious calculations. APPARATUS The cutaway view of the apparatus in Fig. 1 shows the suspension system within the high vacuum enclosure. The low residual gas pressure. maintained between 1 x 10-4 and 5 X 10-6 mm Hg during a determination, avoided both air drag on the pendulum and

Jan 1, 1963

By Donald E. Grimes

In conjunction with Inland Steel&apos;s development of lead-bearing steels possessing improved machin-ability because of tellurium and/or selenium additions, it was decided to determine liquidus and solidus temperatures in the Pb-PbTe-PbSe sub-ternary system. With the exception of alloys in the PbTe-PbSe system, it is believed that no previous study of this subternary has been performed. Thermal analysis was employed in a general survey of the subternary. In addition to PbTe, PbSe, and pure lead, ten ternary compositions were selected at intervals of ten at. pct. Sixty-gram alloys were prepared by sealing an appropriate mixture of the elements in quartz crucibles with a central thermocouple-well under a vacuum of less than 10 p. All three elements were 99.999+ pct pure with only trace impurities detected by spectroscopic examination. After the alloys had been heated at least 20°C above the liquidus in a Kanthal furnace, cooling and heating curves were obtained. Two or more cooling curves were employed both for the determination of each alloy liquidus and for the solidus of those al- loys containing greater than 50 at. pct Pb. Cooling rates were 0.5° to 3.5°C per min during the 5 min immediately prior to the start or end of solidification. For those ternary alloys containing 50 at. pct Pb, the solidus was determined from heating curves. Temperatures were measured with a Pt/Pt-10 pct Rh thermocouple which was calibrated in the same apparatus against the freezing points of zinc (A. D. MacKay—99.999 pct), antimony (A. D. MacKay-99.999 pct), and copper (ASARCO—99.999+ pct) both before and after the experimentation. The only interruptions in the continuous strip-chart recording of the temperature occurred for brief periods at significant points of interest when direct readings were made with a Rubicon Type B potentiometer sensitive to * 1 µv. The average liquidus and solidus temperatures obtained in this investigation are listed in Table I together with probable errors based on the accuracy of the thermocouple calibration and the reproduci-bility of the data. No chemical analyses of the alloys were performed because the synthetic or as-charged compositions were felt to be reliable. The melting points obtained for PbTe (924.7° ± 0.7°C) and PbSe (1084.0° ± 0.6°C) compare favorably with recent findings of other investigators.&apos;-&apos; As indicated in Table I, both the liquidus and solidus temperatures increase as selenium replaces tellurium for a constant atomic percent lead. As a result, the ternary liquidus and solidus temperatures for a given percent lead lie between the corresponding binary temperatures published in the literature. It should be noted that those ternary alloys containing 50 at. pct Pb exhibit a relatively narrow liquid-plus-solid region (<80°C) when compared with alloys containing greater than 50 at. pct Pb. Alloys with 60, 70, or 80 at. pct Pb not only have a much wider liquid-plus-solid region (>500°C) but also exhibit considerably lower and approximately constant solidus temperatures which thus form a virtually isothermal solidus "plane" slightly below the melting point of pure lead (327.3°C). For these alloys

Jan 1, 1965

By W. L. Kerlie, J. H. Richards

The variation in hydrogen content of basic open-hearth steels during refining and the effect of changing from steam to air atomization were studied. The water content of the furnace atmosphere, the slag basicity, and the degree of oxidation of the slag-metal system largely control the hydrogen in the steel. SMALL amounts of hydrogen have an adverse effect on the ductility of steel and a wide range of hydrogen contents has an adverse effect on the internal soundness of both ferrous and nonferrous castings. This has been of major concern to the metal industry, both manufacturers and fabricators, for many years. As one of the results of continuing investigations of the hydrogen problem, much has been learned about methods of reducing the hydrogen content of liquid metals below the relatively high levels that are normally associated with such phenomena as rising ingots and excessive porosity in sand casting. However, it was not until a reliable and simple method for sampling and analyzing liquid metal was developed that much progress was possible in quantitatively evaluating the effect of steelmaking practice on hydrogen contents at levels below 6 to 8 ppm. Throughout all the work described in the following presentation the Geffner pintube technique was used to obtain samples of liquid metal1 * and the tin-fusion method, developed at Massachusetts Institute of Technology,2 was used to analyze the samples. Before attempting a systematic experimental program for minimizing the hydrogen content of open-hearth steels, it was necessary to determine the variation in hydrogen in the open-hearth bath during the normal processing of a heat. The logs of ten heats are illustrated in Figs. 1 through 7. The number at each point on the graphs refers to the number of pintube samples analyzed for hydrogen. An increase in the hydrogen content of the liquid metal during the early period of refining is apparent in all heats. There is evidence of a decrease in hydrogen later in the refining period, see Fig. 2, for example. Therefore, the existence of a maximum hydrogen content at some intermediate time during the refining period is anticipated. To test for the existence of a maximum, the data illustrated in Figs. 1 to 5 were grouped together so that they could be examined on a collectively comparable basis. The grouping was effected, as illustrated in Fig. 8, by superimposing Figs. 1 to 5 so that the apparent hydrogen maxima coincided at a fixed position, indicated by the zero on the time axis. Also, by vertical adjustment until the graphs appeared to the eye to be superimposed, the hydrogen scale was made to show the change in hydrogen content. That is, a standard amount was subtracted from the hydrogen values for each heat. Therefore, Fig. 8 represents a generalized presentation of the data and, for this reason, cannot be used to predict the actual hydrogen content of the bath during refining, but rather to show the probable rate of change in hydrogen during refining. Statistical examination of the grouped data in Fi.g. 8 shows that the apparent. increase and suhsequent decrease in hydrogen are real and confirms the existence of a maximum in general. The average increase In hydrogen during the early period of refining is between 0.8 and 1.3 ppm per hr, and the

Jan 1, 1958

By C. L. Sollenberger, Will Mitchell, Ford F. Miskell

Heat treatment of ore prior to comminution reduces power requirements for grinding, reduces grinding media wear, and improves recovery of iron values from a typical Minnesota magnetic taconite. Test data demonstrating this, as well as an analysis of the economics of commercial application of the technique, are presented. THE taconites in general are hard, tough ores, difficult to grind. Liberation of iron mineral constituents usually is accomplished by grinding the ore through at least 100 mesh, and often it has been found necessary to grind substantially through 325 mesh to achieve satisfactory recovery and grade in the concentration process. Because of the fineness of grind required and the enormous tonnages of material contemplated for treatment in the future, costs resulting from grinding media wear and power consumption, together with capital investment required for comminution, approach astronomical figures. Economy in any one of these elements per ton of material ground could very well reflect a considerable saving to the ferrous industry in yearly costs. With this in mind, the Research Laboratories of Allis-Chalmers Manufacturing Co. have launched a program to discover means of effecting this economy. The initial phase of the work as described here deals with a heat treatment of crushed raw ore, followed by thermal shock in cooling, for the preparation of rod mill feed. Several investigators1-" ave noted an improvement in the grindabilities of ores treated in this manner. One investigator2 subjected low grade iron ores to heat treatment in an electric furnace. Basing his conclusions on screen analyses of crushed products, he observed that treated ore was more easily crushed than the untreated. He reported that observation of the treated and untreated ore through a microscope revealed cracks following the grain boundaries in treated ore, whereas no cracks were present in untreated ore. However, few if any have quantified the improvement in terms of total hp hours saved, reduction of wear of grinding media, or reduction of capital costs of grinding equipment involved. By means of Bond rod mill and ball mill grindabilitiesh nd by comparative wear tests, the conditions maintained during this investigation have been definitely evaluated. Heat treatment experiments have been made on a batch scale in a muffle furnace, followed by continuous scale experiments in a rotary kiln under various conditions of temperature, atmosphere, retention time, and quenching to determine the combination that would give the greatest improvement in the grindability of a taconite without affecting adversely the magnetic susceptibility of the magnetite. From these data, relative costs have been calculated for grinding both untreated and heat- treated ore on a basis of plant capacity of 120 tons per hour. Heat requirements for a rotary kiln, as well as the kiln capacity required for the treatment, have been estimated. For these tests 50 tons of ore were obtained from the Aurora mine of the Erie Mining Co., Hibbing, Minn. The ore was reported7 to have been selected from the magnetic portion of the lower chert horizons. An average chemical analysis of&apos; this portion is shown in Table I and an approximate mineralogi-cal analysis is shown in Table 11. No attempt was made to differentiate between the various silicates because the compositions vary widely on the different horizons and depend on the degree of oxidation. Minnesotite, however, is the predominant silicate. The siderite grains were dispersed throughout the ore but were essentially associated with the rock-forming minerals. In a series of preliminary tests in which batches of —6 mesh ore were heat-treated in a muffle fur-

Jan 1, 1953

By Will Mitchell, Ford F. Miskell, C. L. Sollenberger

Heat treatment of ore prior to comminution reduces power requirements for grinding, reduces grinding media wear, and improves recovery of iron values from a typical Minnesota magnetic taconite. Test data demonstrating this, as well as an analysis of the economics of commercial application of the technique, are presented. THE taconites in general are hard, tough ores, difficult to grind. Liberation of iron mineral constituents usually is accomplished by grinding the ore through at least 100 mesh, and often it has been found necessary to grind substantially through 325 mesh to achieve satisfactory recovery and grade in the concentration process. Because of the fineness of grind required and the enormous tonnages of material contemplated for treatment in the future, costs resulting from grinding media wear and power consumption, together with capital investment required for comminution, approach astronomical figures. Economy in any one of these elements per ton of material ground could very well reflect a considerable saving to the ferrous industry in yearly costs. With this in mind, the Research Laboratories of Allis-Chalmers Manufacturing Co. have launched a program to discover means of effecting this economy. The initial phase of the work as described here deals with a heat treatment of crushed raw ore, followed by thermal shock in cooling, for the preparation of rod mill feed. Several investigators1-" ave noted an improvement in the grindabilities of ores treated in this manner. One investigator2 subjected low grade iron ores to heat treatment in an electric furnace. Basing his conclusions on screen analyses of crushed products, he observed that treated ore was more easily crushed than the untreated. He reported that observation of the treated and untreated ore through a microscope revealed cracks following the grain boundaries in treated ore, whereas no cracks were present in untreated ore. However, few if any have quantified the improvement in terms of total hp hours saved, reduction of wear of grinding media, or reduction of capital costs of grinding equipment involved. By means of Bond rod mill and ball mill grindabilitiesh nd by comparative wear tests, the conditions maintained during this investigation have been definitely evaluated. Heat treatment experiments have been made on a batch scale in a muffle furnace, followed by continuous scale experiments in a rotary kiln under various conditions of temperature, atmosphere, retention time, and quenching to determine the combination that would give the greatest improvement in the grindability of a taconite without affecting adversely the magnetic susceptibility of the magnetite. From these data, relative costs have been calculated for grinding both untreated and heat- treated ore on a basis of plant capacity of 120 tons per hour. Heat requirements for a rotary kiln, as well as the kiln capacity required for the treatment, have been estimated. For these tests 50 tons of ore were obtained from the Aurora mine of the Erie Mining Co., Hibbing, Minn. The ore was reported7 to have been selected from the magnetic portion of the lower chert horizons. An average chemical analysis of&apos; this portion is shown in Table I and an approximate mineralogi-cal analysis is shown in Table 11. No attempt was made to differentiate between the various silicates because the compositions vary widely on the different horizons and depend on the degree of oxidation. Minnesotite, however, is the predominant silicate. The siderite grains were dispersed throughout the ore but were essentially associated with the rock-forming minerals. In a series of preliminary tests in which batches of —6 mesh ore were heat-treated in a muffle fur-

Jan 1, 1953

By M. R. Tek, M. L. Katz

The flow of fluids in stratified porous systems, in which adjacent layers of the system are in communication over part or all of their common interface, in many instances involves crossflow between layers. A theoretical study has been made of the unsteady-state flow of slightly compressible fluids during depletion of bounded stratified porous systems. Consideration has been restricted to single-phase flow, with negligible capillary and gravity effects. Analytical expressions have been derived for pressure distribution and for (luxes at the producing face in two-layer systems with complete fluid communication between layers. These expressions occur in the form of double Fourier and Fourier-Bessel series. The method of extending the solution to any number of layers is demonstrated by deriving the equation for pressure distribution in a three-layer system. On the basis of the exact results for two-layer systems, certain generalizations regarding the behavior of stratified systems in general are presented. The performance of stratified systems, in terms of cumulative flux as a function of time, is shown to lie at all times between bounds established from single-layer theory. The upper bound is given by treating the system as a single layer with arithmetic average physical properties. The corresponding lower bound is the summation of the fluxes from each layer as treated individually. Variation in performance of stratified systems between the upper and lower bounds is determined by the extent to which crossflow occurs in the system. The principal parameters affecting the amount of crossflow are the vertical permeability of the system, the ratio of system thickness to "radius of drainage" and, for radial systems, the ratio of system thickness to interior radius. At very early times, the system performance is near the lower bound. As time and the radius of drainage increase, the per- formance tends toward the upper bound. INTRODUCTION One of the principal problems confronting the reservoir engineer today is the incorporation of the effect of reservoir heterogeneity into predictions of reservoir performance. The first part of this problem is the characterization of the actual reservoir heterogeneity in a mathematically useful manner.1, 2 It is then necessary to calculate the effect of this heterogeneity on the system performance. It is frequently possible to estimate this effect by comparison with the known behavior of an idealized system. One such idealized system is the stratified or "layer-cake" model. Many studies have been made of the behavior of stratified systems, from both a theoretical and experimental standpoint. The great majority of the theoretical studies have been concerned with systems of separated layers, with no fluid crossflow. Among the more noteworthy of such theoretical papers is that recently published by Lefkovits, et al,3 in which a comprehensive analysis was presented for the behavior of bounded stratified systems which are unconnected except at the wellbore. Three recent references have dealt with stratified systems including the effect of crossflow. Jacquard4 has presented mathematical derivations pertaining to depletion of two layer systems producing at constant rate. A doctoral dissertation by Katz5 contains analytical solutions and tables of results for pressure distribution and fluid flux during constant-terminal-pressure depletion of two-layer and three-layer systems with crossflow, together with tables of eigenvalues necessary in the computations. The dissertation also presents results from experimental studies of stratified systems using a heat-transfer analog model. This paper is largely based on the material in this dissertation. A third paper has been presented by Russell and Prats6 since completion of the work resented herein, containing mathematical derivations for and discussion of the behavior

By H. L. B. Gould, Jr. Wenny D. H.

TO date there has been but limited interest in alloys of 80 to 95 pct Co and Fe with or without other additions. In 1932, S. R. Williams&apos; reported practically zero magnetostriction for the 90 pct Co-10 pct Fe alloy. This same composition was used for pole pieces to control the magnetic field in magnetrons operating at high temperatures.&apos; In 1947, a 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn composition was investigated3 for use in ballast lamps because of its high temperature coefficient of resistance. Recently, as part of a survey of ductile and malleable magnetic alloys capable of being processed to thin gages for possible applications in memory devices, the high Co-Fe alloys have been re-examined to determine their fabricating and magnetic characteristics. Alloys from 80 up to 95 pct Co and Fe with and without additions such as vanadium were prepared. In general these all had excellent ductility and malleability. Wire was drawn to thin gages without difficulty and fine hard-drawn wires flattened to 2) The phenomenon may have potential in estimating the carbon content of molybdenum. A given solution-treating temperature and cooling rate could perhaps be calibrated so that the area fraction of surface covered by carbide could be interpreted in terms of carbon concentration. By segregating to the surface, a big "magnification" of the carbon content is obtained, which should make the method cheap, direct, and sensitive and, therefore, perhaps of interest to the molybdenum industry. This work was conducted at Battelle Memorial Institute. Financial support by the Aeronautical Systems Division, United States Air Force, under Contract No. AF 33(657)-7376, is gratefully acknowledged, and the writer is thankful for the experimental assistance of Miss Marjorie Cantin. ribbon without splitting. Similarly, strip was cold-rolled as much as 99.75 pct reduction to a 0.25 mil thickness without intermediate anneals. Samples of round and flat wire and foil, in the severely cold-worked and annealed states, were checked for magnetic characteristics. The alloys exhibited widely divergent magnetic characteristics depending on the processing and heat-treating procedures used in preparing the samples. Direct-current hysteresis loops showing the different magnetic characteristics of 90 pct Co, 9.5 pct Fe, and 0.5 pct Mn alloys are shown in Figs. 1 to 8 inclusive, while Figs. 9 and 10 show the loops for an alloy of 82 pct Co, 11.75 pct Fe, 5.6 pct V, and 0.65 pct Mn. Figs. 1 and 2 show the high remanence and exceedingly square-loop characteristics of the hard-drawn wire and ribbon roll flattened therefrom. With the change in processing from roll flattening to flattening by drawing through flat diamond dies the resultant change in texture is accompanied by the drastic change in the shape of the loop as shown in Fig. 3. This skewed loop on annealing reverts to a more normal loop as shown in Fig. 8. The most unique loops are obtained with flat rolled strip. These are shown in Figs. 4 and 5. In the case of the hard-rolled material, Fig. 4, there is little change in induction until the magnetizing force reaches 50 oe. From 50 to 60 oe there is a sharp increase in induction to over 15,000 gauss, which for all practical purposes is saturation. The induction remains at a constant value while the magnetizing force decreases to 40 oe. At this point the

Jan 1, 1965

By Theodore A. Blake

At the Chicago meeting of the Institute, May, 1884,I had the pleasure of announcing the introduction of a new machine for fine crushing, or The Blake multiple-jaw crusher, which, in combina tion with the ordinary Blake breaker, could be used in the reduc tion of ores or any hard and brittle substance to almost any degree of fineness. I am now able to give some practical results derived from its use on an extensive scale, on the gold ores of South Caro lina and the iron ores of Lake Champlain, together with some accurate and detailed statistics of the cost of crushing over one hundred thousand long tons of magnetic iron ores of the Chateaugay Ore and Iron Company at Lyon Mountain, Clinton County, N. Y., about thirty miles west of Plattsburgh. The construction of the multiple jaw-crusher, since the date of my first paper, is the same, except in the substitution of main swinging, instead of main sliding, or toggle jaw,—thus doing away with the upward thrust on the tension rods and the wear incident thereunto. (See Fig. 1.) It has also been found, in case of the fine crusher, that is, in machines of not over 4 inch width of opening, that the use of several small machines with a series of jaw openings, say 15 inches by 4 inch, is better than one large machine with a series of openings 24 by 4 inch, or 36 inches by 4 inch, as at first constructed. Many details of the method of holding in jaw-plates, etc., have been perfected. Without giving any details with respect to the different mills built upon the Blake &apos;system, let me state that, although it has proved possible to carry any hard and brittle material with crushers alone to a fineness such that all particles will pass a 30-mesh wire screen, still the economical limit of such crushing will be found somewhere between 14 and 20. If it is necessary to carry all the material to a fineness greater than this, the system must be supple

Jan 1, 1888

By J. S. Aronofsky, J. P. Heller

This paper presents a mathematical analysis of the fluid mixing which occurs during flow through porous media. The analysis is based on the well-known diffusion equation with mass transfer term. It is pointed out that the use of this equation is justified by a single general assumption which does not specify any particular mechanism for the mixing process. Formulas are given for tracer fluid concentrations for two different boundary and initial conditions. Calculated numerical values compare closely with some published results of experiments in which no viscosity or density difference existed between displaced and displacing fluids. INTRODUCTION A phenomenological theory of the mixing and diffusion process is presented for the flow in a porous medium of two miscible liquids of equal viscosity and density. This is based on the classical diffusion equation which has been used to explain such processes as Brownian motion and heat conduction. More recently, this same differential equation has been derived (in a manner analogous to the work in this paper) for the problem of heat transfer during fluid flow in porous media.&apos; The purpose of this paper is to show that the available experimental evidence justifies the use of this simple diffusion equation. The recent data of Koch and Slobod&apos; and of von Rosenberg&apos; are used to test this diffusion model by comparing concentration curve shapes and calculating "effective diffusion coefficients". The same differential equation for miscible displacement, as well as some experimental confirmation, has been published in Japan by K. Yuhara,4 and recently in this country by Day.5 Yuhara arrives at his con-clusions through analogy with turbulent diffusion, de- scribing the microscopic velocities in terms of "eddy motion" — although unlike the ordinary eddies of hydraulics. Day proceeds directly from Scheidegger&apos;s6 concept of the dispersion of velocities. After a very clear description of Scheidegger&apos;s theory, he applies it to calculate the motion first of a drop and then of a thin layer of brine into a bed of sand. For the latter case, Day derives and solves the same differential equation as Eq. 1. In our presentation no detailed assumptions are made as to the mechanism of displacement. In fact, several microscopic processes may well be involved—the only general assumption made is that their cumulative microscopic effect may be described by the addition of a second-order term to the differentirl equation of continuity. DERIVATION OF EQUATIONS Let us consider the displacement in one spatial dimension of Liquid A from a sample of porous media by Liquid B. A and B are assumed completely miscible and of the same viscosity and density. Both fluids are also assumed to be incompressible and it is specified that the total flow is the same for any cross section. It is evident that the rate at which Liquid B would be carried across such a section would be given by the product of the fluid velocity, u, and the concentration, C, of B in the fluid mixture assuming the constancy of u and C over the cross section. Since the volume of Fluid B is conserved, this leads to the one-way wave equation - u ?C/?x = ? ?C/?l where x increases in the direction of u—the "Darcy velocity", Q/A (or velocity flux per unit area), and 9 is the fractional porosity. Consider the case where fluid B is displacing Fluid A and the concentration distribution is represented by a step funcLon (with a vertical discontinuity). The solution of Eq. 1 predicts no mixing

Jan 1, 1958

By P. A. Beck, S. Kohara, M. N. Parthasarathi

IT has been shown1,3 that many observed phenomena related to annealing textures in f.c.c. metals can be adequately accounted for, at least in a qualitative way, by considering the orientation dependence of the boundary mobility, without any hypotheses concerning preferred orientation of nuclei. It was noted1 that this approach is particularly successful in the common cases of primary recrystallization in highly cold-worked polycrys-talline metals, where nuclei occur in great abundance, and that in the other extreme case, where the number of nuclei is very limited, or even only a single crystal is grown, the orientation dependence of boundary mobility has only a small effect, or none at all, on the orientations resulting from annealing. Recently Dunn described examples3-6 where observed secondary recrystallization textures apparently cannot be accounted for on the basis of oriented growth alone, but also require oriented nuclei, or at least the absence of nuclei in certain orientation ranges. In general, the great difficulty in correlating the preferred orientation of recrystallized grains with that of nuclei is inherent in the fact that nuclei are by nature very small, and that they are usually identifiable as "nuclei" only after growth, i.e., after they have already been subject to growth selectivity. An investigation was carried out by Liebmann and Lücke,&apos; and also a very similar one by Graham and Cahn,&apos; to obtain quantitative information on the orientation depend- ence of boundary migration rates in the recrystallization of slightly deformed aluminum single-crystal rods or plates, in which artificially nucleated recrystallized grains of predetermined orientation were grown. Liebmann and Lücke foupd maximum boundary mobility for boundaries across which the misorientation corresponded to a rotation of 40 deg around a common [Ill] axis, in accordance with earlier conclusions.9,1 Also, they confirmed that such an orientation relationship predominates among crystals growing into slightly extended single crystals from presumably random artificial nuclei. On the other hand, Graham and Cahn found no preferred orientation among crystals grown in a similar manner. It is not as yet known how these observations may be reconciled with each other. The view has been expressed in various papers5&apos;10,21 that selective growth based on the orientation dependence of boundary mobility is not in itself sufficient to account for the formation of sharp re-crystallization textures, such as those often observed in highly deformed polycrystalline metals after annealing. The present work was undertaken to ascertain whether or not it is possible to obtain a sharp re-crystallization texture in a case where random nuclei are assuredly present in large numbers. It was previously found1&apos; that high-purity aluminum crystals rolled 80 pct on the (110) plane in the [1T2] direction, when suitable precautions are taken, may be annealed for periods of about 1000 sec at 350°C without recrystallization. It was also found that the reluctance to recrystallize in this case is due to the scarcity of material in sufficiently deviating orientations to serve as nuclei. By using such a matrix,

Jan 1, 1959

By T. S. Lundy, R. E. Pawel, F. R. Winslow, C. J. McHargue

The volume-diffusion coefficients of Nb-95 and Ta-182 in niobium have been measured over the temperature range 878° to 2400°C. High-temperature specimens (T 21500°C) were sectioned by conventional lathe and grinding techniques while low-temperature specimens were sectioned by an anodizing and stripping technique previously described. Over a range of more than ten orders of magnitude in diffusivity, the self-diffusion data is well-represented by the equation: D = (1.1+ 0.2) exp [- (96,000 * 900)/RT ] cm2/sec Upward deviations from this line are explained by short-circuit diffusion in combination with the loss of resolution of the sectioning techniques. Oxygen contamination within the range 100 to 450 ppm was found to have little or no effect on the self-diffusivitj 01 niobium. In a limited number of measurements, the diffusivity of Ta-182 in niobium was found to be about half that of Nb-95 in niobium. These data may be described by D = (I.0+0.90.5)exp [- (99,300 * 2400) /RT ] PREVIOUSLY reported studies of self-diffusion in niobium were by Resnick and Castleman1 and Peart, Graham, and Tomlin.2 The data of Resnick and Castleman over a temperature range 1585" to 2120°C show considerable scatter but. can be represented by D = (12.4 *0.8) exp [-(105,000+3OOO)/RT] cm2/sec The limited data of Peart, Graham, and Tomlin follow the equation D = 1.3 exp (-95,00O/RT) cm2/sec In view of recent diffusion data for ß zirconium3 and 0 titanium4 in which Arrhenius-type plots do not yield straight lines and of the potential high- temperature uses of niobium and its alloys, we thought it important to investigate the diffusion behavior of this bcc refractory metal over a large temperature range. This has recently been done for molybdenum,5 chromium,6 vanadium,"" and tantalum.9 Niobium was a particularly suitable material for this study largely because of the development of an anodizing and stripping sectioning technique which enables diffusivities as small as l0-19&apos; sq cm per sec to be determined accurately.10 In addition to self-diffusion data, data were obtained for the diffusion of Ta-182 in niobium and for the effect of varying oxygen content on self-diffusion. I) EXPERIMENTAL PROCEDURE Materials. The niobium was obtained from three sources: 1) melting stock from Shieldalloy Corp., 2) electron-beam melted single crystals, 1/2 in. diameter, from Semi-Elements, Inc., and 3) oxygen-doped, electron-beam melted single crystals from Materials Research Corp. The melting stock was electron-beam melted and specimens 5/8 in. diameter by 1/2 in. long were machined from the center of the bar. The analysis supplied by the vendor and an interstitial analysis of one of the specimens are given in Table I. The single crystals (type 2 above) were cut with a jeweler&apos;s saw to specimens about 3/8 in. long. The interstitial analysis of this material is given in Table 11. This material was used

Jan 1, 1965

By A. G. Guy

Zinc vapor from a reservoir of liquid zinc maintained at lower temperatures was diffused into sets of copper-zinc alloys at 759° and 870° C and into sets of silver-zinc alloys at 650° and 700° C. Each set of ,four copper-zinc alloys consisted of pure copper and 90/10, 80/20, and 70/30 brass. Similarly the set of silver-base alloys consisted of specimens containing 0, 7, 15, and 20 pct Zn. Natural markers at the initial surfaces of the specimens ware "trapped" under a thin electroplate and their depth of burying was measured after diffusion. The ratio of diffusivities of the two components determined from these data and the chemical diffusion coefficient calculated by the Matano method agreed with previously reported results. The line of markers was irregular and was often discontinuous when a grain boundary was crossed. TECHNIQUES involving the vapor phase have been widely employed in studying diffusion phenomena in metals. Many investigators have evaporated the more volatile component from an alloy, but it is generally believed that the porosity created under these conditions interferes with adequate interpretation of the experimental results. The extensive work of Gertsriken6 has been criticized on this score. Accary1 found that the diffusion coefficient for de-zincification of brass is larger by a factor of five than that for zincification, although he attributed the difference to a higher vacancy concentration under conditions of dezincification. Balluffi and siegle2 thoroughly investigated the technique of adding a more volatile component to a less volatile base metal as a means for studying diffusion. They verified that no porosity forms in a brass under these conditions and that the diffusivities of the two components can be determined from observations of the motion of markers originally placed on the surface of the specimen. The mathematical analysis that they developed for treating the experimental data was modified in a later note, but essentially it involved using the graphical Boltzmann-Matano method that is customarily applied to solid-solid diffusion couples. The experimental method used in the present research was similar to that employed by Balluffi and Siegle except for two modifications. Balluffi and Siegle used alloy chips as the source of metal vapor. This procedure has the disadvantage that the concentration of solute at the surface of the specimen changes during the diffusion experiment as the alloy content of the chips is gradually decreased. This disadvantage was overcome by employing liquid zinc as the source of zinc vapor in a manner similar to that described by Herasymenko.9 There was then no limitation on the amount of solute usefully available, and several relatively large specimens could be diffused in a given experiment. The second modification was the use of natural markers on the surface of the specimen rather than larger, artificial markers, such as the alumina powder employed by Balluffi and Siegle. It was expected that the fine, natural markers would permit more precise measurement of the buried interface as in the case of ordinary sandwich specimens.10 EXPERIMENTAL The experiments were designed so that zinc from the vapor phase would maintain a constant zinc content at the surface of pure copper (or silver) and

Jan 1, 1960

By D. W. Fuerstenau, J. H. Brown

The paper by Professors Sun and Mitchell illustrates the value of ultrasonics as a tool for the mineral engineer. In particular, it opens up a number of possibilities to those interested in the field of comminution. The provision of desliming technique, which is thorough as well as rapid, is a distinct contribution, but the data of the paper suggest applications beyond desliming, in that the same treatments may be useful for size determination purposes. Fig. 1 shows that a marked dependence exists between particle size and the height to which it can be elevated by ultrasonic vibrations. While the curves are only extended down to a size of about 100 u, the fact that they appear to be increasing in slope in this range suggests that the separation may be even more marked here. This, we feel, is very strong evidence that a nlethod for fine sizing could be developed to use ultrasonic waves as the separating force. Professors Sun and Mitchell indicate that floccula-ti~n will present no difficulty: "During the investigation it was found that ultrasonic waves were able to dislodge the adhering gangue particles from the min- era1 surfaces and to disintegrate the soft particles into fine sizes." Thus, it appears that the use of ultrasonic waves as the power behind a size separation process may eliminate the problem of flocculation encountered in most wet sizing techniques. It would be interesting to size a fine material under conditions in which particles are known to be flocculated and under conditions where they are known to be dispersed. Use of a sizing technique of this nature may solve several problems that have long persisted in the fine sizing field. The flocculation problem may be overcome; the continuous production of closely sized fractions may be possible with a device similar to the one described; and with photoelectric methods, rapid analyses in the subsieve sizes may be possible. In general, we suggest that this paper be followed by a study of the sizing applications of the apparatus described. We feel that such a study would not only be rewarding in providing a new sizing technique, but also that the present paper almost requires such work to complete the picture of particle motion in a field of ultrasonic waves.

Jan 1, 1958