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By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush's work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By E. W. Pehrson, J. W. Furness

NONMETALLIC MINERALS, exclusive of fuels, may be divided into three groups: Building materials, fertilizer minerals, and miscellaneous minerals. Building materials, such as sand, gravel, slone, lime, and the ingredients of cement and clay products, occur widely in nature and are thus available near consuming centers at relatively low prices. Cost of transportation over great distances deters any' substantial movement in world trade. On the other hand, fertilizer minerals, such as phosphate rock, potash, nitrates, sulfur, and pyrite, and the miscellaneous nonmetallic minerals, such as long-fiber asbestos, mica, graphite, fluorspar, and china clay, do not have such widespread occurrence and consequently contribute the major part of the world's commerce in such minerals. The U. S. Bureau of Mines has prepared charts showing the inter-

Jan 1, 1936

By Robert Stefanko

With passage of the Clean Streams Act of the Commonwealth of Pennsylvania and its impact on the coal industry, considerable research has been conducted to explore various approaches to the problem, including deep-well disposal. Available drillhole data from gas and oil wells were used to develop cross -sectional maps for various portions of the state and potential disposal zones were evaluated. Bethlehem Mines Corp., faced with a severe water problem at its Marianna operation in Washington County, cooperated with the Dept. of Mining at The Pennsylvania State University in establishing a 1500-ft well into the Salt Sands for the purpose of determining the feasibility of mine water disposal. The thickness, porosity, and permeability of the formation at the well site proved to be below what had been anticipated from drillhole data. Further, subsequent hydraulic fracturing did not improve the flow characteristics of the well; pumping pressures remained in the range of 1800-2000 psig for disposing of water at the rate of 150 gpm. The legal problems of disposal at the site were very formidable. When the Salt Sands proved to be less than satisfactory, permission could not be obtained to dispose in other promising formations. The paper details many of the problems associated with the experimental well and makes an assessment of the potential for deep-well disposal of mine water. The concept of disposing of liquid industrial wastes by deep-well injection is not a new one. Brines associated with crude oil long have been disposed of in this manner, with the additional benefit of aiding secondary oil recovery. More recently, with the expansion of nuclear energy, the lethal, highly radioactive wastes which are by-products of the fission process have created severe disposal problems. During the past ten years, a variety of industries have resorted to subsurface disposal, some of the details of which are given e1sewhere.l,2 The list reveals wide variations in injection rate, pumping pressure, cost, and waste disposition. Included are successful installations in Western Pennsylvania. Enactment of more restrictive clean-water legislation in Pennsylvania recently had a great impact on the coal industry. Among its provisions was the reclassifica-tion of most mine water as industrial waste whose dis-posal is prohibited in any stream of the Commonwealth. This had the effect of accelerating research in a variety of areas, although treatment methods still retained primary interest. When a feasibility study of deep-well disposal was proposed to the Pennsylvania Dept. of Mines and Mineral Industries, the Coal Research Board (CRB) approved it. This paper summarizes the efforts on this project. Acid mine water is a chemically complex liquid. having no definite quantitative relationship among its constituents. However, it is the iron disulfide (FeS2) associated with practically all coal seams that produces the objectionable products present in acid mine water when combined with air and water. The principal contaminants are sulfuric acid (H2SO,) and ferric hydroxide (Fe(OH)2. Ferric hydroxide is a rust-colored gelatinous precipitate that coats stream bottoms and destroys aquatic life. However, other ions and bacteria are present in acid mine water in varying amounts.

Jan 1, 1971

By C. H. Lieb

ONE astounding fact in the production of petroleum is the comparatively recent realization by producers that flowing production is the cheapest crude produced. About 1910 or even later, operators actually endeavored to get a producing well to pumping as quickly as possible after completion. A well was not really considered to be completed until it was operating on the pump. Remarkable progress has been made since then. It was not until about 1920 that producers began to take a serious interest in pressures and to think a little about proper methods of handling oil wells. Pressure gauges were installed, and records of pressures maintained, which was quite an innovation. Desultory experiments were made with tubing of different sizes, as well as experiments with placing the bottom of the tubing string at different levels in the well. Probably the first important departure from customary procedure was about 1926, during the Seminole development, when gas lift

Jan 1, 1936

By N. H. Emmons

An interesting development of copper blast-furnace construction has been brought about in adapting the blast-furnace to be a "burner" for sulphuric acid making. When the Tennessee Copper Co. first decided to construct an acid-plant, the standard type of brick-top furnace, supported by structural steel, was the only one in use at its plant. All the tests for temperature and strength of gas had been made on these furnaces, and had been satisfactory. When, however, the acid-plant was put on the flue, and the flue had to have a damper put in it to force the gas into that plant, troubles began. The furnaces were fairly tight, and for a few months the work was quite satisfactory. Fig. 1 shows the old type of furnace-top used at the start. It was soon found that this top would not stand the temperatures, particularly when dampered back, as was necessary to force the gas into the Glover towers. The structural steel, of which the furnace skeleton was constructed, warped and twisted so badly that it was not safe to use the furnaccs. This effect is shown by Fig. 2, which is a photograph of old No. 4 furnace, after the brick-work had been removed. It became apparent that a new type of top mas necessary and the engineering force was started on the design of a new furnace-top, with the result that a low top, with brick-lined flues at each end below the feed-floor, leading to the main concrete dust-chamber, was constructed. This furnace, No. 7, is shown in Fig. 3. The charging-doors are made of cast-iron sections, three sections to a door, and three doors to a side. A door to the furnace was made of east copper, but the heat was great that the copper bent readily, due to the jarring of its

Jan 1, 1911

By P. C. Hodges

WHILE there is very little romance connected with the operation of a stone quarry, yet to those who have participated in the growth and development of a business that has been a pioneer in its field and that FIG. 1.-LOCATION OF PROPERTY OF MARBLE CLIFF QUARRIES COMPANY. has been in continual operation two-thirds of a century there is bound to be a background of experience, which if properly capitalized, brings progress as well as satisfaction in its accomplishment.

Jan 1, 1936

By F. Julius Fohs

CENTRALLY located with relation to the largest iron- and steel-producing districts of the United States, the fluorspar-deposits of Kentucky possess increasing interest and importance. As typical of the numerous fluorspar-mines of Kentucky and Illinois, I have selected for description the Memphis., because it and others of its immediate group exhibit the conditions characteristic of all. I. THE MEMPHIS MINE. This mine lies 5 miles NW. of Marion, in Crittenden county, Kentucky, a station on the Chicago and Nashville division of the Illinois Central R. R. For the first mile and a half out of Marion we see only Birdsville or Middle Chester sandstones of Mississippian age. Then we cross a fault of some 350 ft. displacement, and the Ste. Genevieve oolite sets in. Beyond the fault, oolite is the predominant rock, except that the bills to the north have a capping of Cypress or lowest Chester sandstone, 80 ft. below which is an outcrop of from 6 to 10 ft. of Ste. Genevieve (Rosiclare) sandstone. Occasional sink-holes are noticed, and as the mines are approached evidence of faulting is again seen.. A line of crude head-frames and open-cut dumps, extending for more than a quarter of a mile, marks the Klondike vein. The open-cuts are from 15 to 20 ft. deep, and in most of them, from the surface down, was found the reddish gravel which is really fluorspar-some of it white or purple and crystal-clear (if the red clay is washed off), and some carrying iron and silica, and stained by waters from the decaying limestone walls. In one of these cuts, at a depth of 20 ft., white and purplish honey-combed fluorspar was found, in which the larger cavities are due to limestone and calcite leaching, and the minute ones to the leaching of zinc-blende.

Apr 1, 1909

By E. J. Ripling, M. W. Toaz

Tensile tests were conducted on pure magnesium and on four commercial alloys over a variety of temperatures and strain rates. The high positive slope of the ductility vs testing temperature curves that is found over a short range of testing temperatures for these materaturerials was shown to result from the fact that the microstructure was not stable at these testing temperatures. Pure magnesium did not display a transition temperature, although its sub-room temperature ductility was low. This poor ductility resulted from a grain boundary weakness. The aluminum-bearing commercial magnesium alloys had a higher ductility than the pure magnesium. ness.Thealuminum-bearingcommercialThese alloys did exhibit a transition temperature and grain boundaries that were stronger than the grain material. Both pure magnesium and the commercial alloys began initiating cracks at strains equal to one half of their fracture strain. MAGNESIUM base alloys' enormous potential as structural materials lies in their high strength to weight ratios. At present, the high strength magnesium base alloys such as AZ-80, which will be discussed later, have about as high a tensile strength to specific gravity ratio as the highest strength wrought aluminum alloy, 75s-T6, and, of course, a much higher strength to weight ratio than structural steel. Further, since the magnesium base alloys develop their high strength to weight ratios with moderate strengths and extremely light weights, the ratio of load carrying capacity to the weight of many structures is relatively higher for the magnesium base alloys than their strength to weight ratios would indicate. This results because judicious increases in section size, such as increasing the depth of bending members or adding reinforcing ribs, can frequently increase the weight of a structure linearly while the strength and stiffness increase as the second or third power of the added weight. Strength and rigidity must be designed into lightweight structures by those techniques which establish multiaxial stress states. Consequently, strong, lightweight structures frequently also possess a greater propensity toward brittle failures. In order to insure against these catastrophic failures, an extra premium must be placed on ductility and toughness in light alloys. Current knowledge of the ductility and toughness behaviors—notched behaviors—of magnesium base alloys is limited.* Most of the magnesium base alloys * The state of present knowledge regarding the effect of testing temperature on mechanical properties has recently been summar-ized by Pritchard.' crystallize in the hexagonal system, so that they are expected to exhibit a tough and ductile to brittle transition temperature. Actually, a transition temperature behavior has been reported for commercially pure magnesium in the literature, but the characteristics of this transition temperatureh uggest that it may not be a transition in the usual meaning, but simply the onset of some thermal softening, a performance much like that which face-centered-cubic lead might exhibit slightly below room temperature. If transition temperatures do exist, such important questions as the manner in which they are affected by internal variables such as chemical composition and grain size, or the effect of external variables such as rate of straining or notch severity have never been investigated. The investigation reported upon herein was undertaken in order to define some of the mechanical behaviors of the magnesium base alloys better, to gain a better understanding of the influence of some of the above listed variables, and particularly to understand their effect on ductility and toughness better. Material and Procedure Material-—Pure magnesium and four commercial alloys were used in this investigation. The alloys were selected so that chemically they made up a series with approximately the same minor alloying

Jan 1, 1957

By Frank L. Hess

BERYLLIUM is demanding more of the limelight, and the output of beryllium copper (containing 2% to~ 3 per cent of beryllium) seems to have grown 60 per cent above that of 1936, which was double that of 1935. There is increasing interest in beryllium-aluminum alloys and small quantities are being marketed at $50 per lb. for the contained beryllium. Other alloys also can be produced. Further price decreases for beryllium copper (now $23 per lb. for the contained beryllium) seem , possible and desirable. No difficulty has been experienced in obtaining beryl and a 'reserve stock has been built up. One supplier heretofore found reliable has offered to furnish 200 tons per month. Supplies during 1937 have come from the Black Hills in South Dakota, Colorado. India, and South America

Jan 1, 1938

By E. C. Lee

THE safety of mine workers has received more attention from both State and Federal law-making bodies than any other industry, a fact that shows clearly the hazardous nature of the industry. The last, but by no means the least, of the measures adopted for the protection of mine workers, is workmen's compensation legislation. This is proving to be a powerful instrument for greater safety in the industries, from the fact that special stress is laid not on how the accident happened or who may have been responsible for it, but on how badly the employee is hurt by it. The injured person does not have to employ lawyers to prove his case, because the mere fact of his employment is proof of his right to compensation. The immediate effect of such legislation is the certainty confronting the mine operator that he must pay out large sums for every accident, regardless of its cause, thus adding materially to the cost of the production of his coal. This fact furnished to the operator the strongest incentive to reduce the causes of accidents; not that the operator has ever lacked reasonable consideration for the welfare of his employees and a proper humane interest in their safety, but his engrossment in earning his daily livelihood has been so great that he has not felt that he had the time to devote to the safety of the operation. This time he must now find because of the actual-cash value of the prevention of accidents in his mines. This agency alone proved inadequate to bring about a material improvement because operators have always been willing enough to improve safety conditions when possible to do so within reasonable limits of their financial ability. The requirement in the Workmen's Compensation Laws of several of the States, that the mine operator shall insure as a guarantee of his ability to meet his compensation obligations, has furnished the needed incentive, moral and financial, necessary to the prompt and effective dissemination of a more general knowledge of the causes and

Jan 10, 1917

By AIME

THE wind howls almost incessantly over the mining engineers working in the near desert that is the Division of Namaqualand, the upper Atlantic coastal corner of South Africa's Cape of Good Hope Province. But when these men at the U. S.-owned mines called Nababeep South and East O'okiep (pronounced Oh-keep) tell you about their achievements, they can be heard above the wind. For their O'okiep Copper Co. Ltd. now produces over half the Union of South Africa's annual output of 30,000 tons of copper metal. Moreover, it is a very decent sample of U. S. geotechnical imagination. financial daring, and managerial skill, all operating successfully in a

Jan 1, 1947

The income of the Institute is derived mainly from dues, advertising in MINING AND METALLURGY and sale of publications. These sources are fortunately supplemented by the interest from invested funds now amounting to over $500,000, a considerable portion constituting endowments for especial purposes. Aside from the medal funds the principal endowments are the James Douglas Fund for support of the Library, the Rocky Mountain Fund and the Seeley W. Mudd Memorial Fund. The income from the two last named is available for the support of research and a variety of other purposes. It is allocated by the Board of Directors upon recommendation of standing committees in each case. An active effort is being made to increase the endowments of the Institute, it being felt that unusual opportunities exist for research and public and professional service through the organization.

Jan 1, 1939

By René de Batz

From 1754 to the end of 1895 the production of gold in Russia had been approximately as follows: Kilogrammes. Russia proper (Finland and the Caucasus),. .. 890 The Ural Region,........505,386 Western Siberia,........116,937 Eastern Siberia,........1,218,372 Total,.........1,841,085 of the value of more than $1,200,000,000.

Jan 1, 1899

By G. B. Pryde, R. M. Magraw

In laying out a new mine, provision should be made for the ultimate recovery of as much coal in any given bed as is consistent with safety and economic mining. Though each mining district, if not each individual mine, has problems that make the adoption of any hard and fast rule impossible, certain basic principles are adapted to practically all conditions. One of the most vital is the provision for barrier pillars of ample dimensions to protect all haulage and permanent airways during the life of the property. Where conditions permit, room or butt entries should be driven on the strike or slightly to the rise, and rooms turned at right angles to these entries. The width of rooms and room pillars is governed by conditions prevailing in the mines under consideration. A safe rule is: In advancing, extract not more than 25 to 35 per cent. of the entire seam; in exceptionally thick seams, considerably less than 25 per cent. should be taken. Rooms usually vary in length from 250 to 350 ft. (76 to 106 m.) with a barrier pillar of not less than 80 ft. between the last crosscut. in rooms and the back entry of the level above. All entries, rooms, and entry-and-room crosscuts should be driven .on sights and room crosscuts should be driven at, right angles to the direction of the rooms. In mines under excessively heavy cover or where roof conditions are bad, rooms should be driven narrow and a barrier pillar left at every fifth to tenth room. This barrier should be of such dimensions that one or more rooms, with pillars of usual dimensions, may be turned through it when the barrier is no longer required. Two of the advantages of such a barrier are the protection of the panel against peaking of roof load during pillar extraction and the easy closing of the entry in case of fire. Where economic conditions permit, it is preferable to follow the retreating panel system of mining. In the case of coal that outcrops, and even in cases where no outcrop is exposed, it is preferable to commence pillar extracting on the high side of the mine. Where the retreating

Jan 1, 1922

By V. O. Struebing, K. A. Johnson, F. H. Ellinger, C. C. Land

The system Pu-Ce-(Pu,Ce)Co2 has been investigated by thermal, micrographic, and X-ray diffraction methods. The principal characteristics of this system were found to be: 1) a "eutectic" valley extending across the phase diagram from the 6 Pu/Pu3 Co eutectic at 408°C to the 7 Ce/Ce24Co11 eutectic at 42Z°C, the maximum temperature in the valley being 443°C; 2) three ternary inter mediate phases, each having an appreciable mutual solid solubility for plutonium and cerium; 3) eleven four-phase equilibria comprising one eutectic, four peritectics, and six Class II reactions; 4) a pseudobinary section between the ternary phase A and the y Ce solid solution, and another such section between the 6 Pu solid solution and the 77 phase (Pu3 CO) containing cerium in solid solution. ALLOYS of plutonium that are completely molten at temperatures in the vicinity of 500°C are of interest for use in the liquid state as fast reactor fuels. Since exploratory work1,2 on Pu-Ce-Co alloys had indicated that a "eutectic" valley extended across the ternary system between the Pu-co[6 Pu/n (Pu3co)] and the Ce-CO[? Ce/? (ce24co11)] binary eutectics, thus allowing alloys of any plutonium concentration to be selected within the temperature limitation, the present investigation was begun for the purpose of accurately defining the "eutectic" valley. However, when the existence of three ternary intermediate phases and the consequent complexity of the liquid-solid equilibria were discovered, the investigation was expanded to cover the complete system, except for the corner between the isomorphous series PuCo2-CeCo2 and pure cobalt. 1) EXPERIMENTAL The purities of the alloy components are given in Table I. Alloy buttons, each weighing about 5 g, were prepared by arc melting the accurately weighed components (±0.1 mg) under a purified He-Ar atmosphere. Weight loss as a result of melting was usually less than 1 part in 1000; therefore, the buttons were not chemically analyzed. One half of each button was re-melted by induction heating in vacuo in a magnesia crucible and furnace-cooled, so as to produce a somewhat coarser microstructure than that of the rapidly cooled arc-melted button. About 20 g of each alloy to be examined by thermal analysis were remelted in vacuo in a tantalum crucible of the inverted thermocouple well type. The thermal, X-ray diffraction, heat treating, and micrographic methods used in this investigation were essentially the same as have been described in earlier reports.3,4 Two etchants for these alloys were found to be satisfactory: A) 8 (parts by volume) orthophosphoric acid, 5 ethanol, and 5 glycol; B) 7 tetraphosphoric acid, 36 water, and 57 2-ethoxyethanol. Etchant A was used at 5 to 6 v for 15 to 20 sec, and etchant B was used at 10 v for 10 sec. 2) THE LIMITING BINARY SYSTEMS 2.1) Plutonium-Cerium. The phase relationships of this system have been investigated by Ellinger, Land, and Cramer,5 and by Selle and Etter.6 The over-all agreement of their phase diagrams is good, but there are some discrepancies in the positions of some phase

Jan 1, 1967

The fundamentals of blasting involve both the properties of explosives and of the rock being blasted. Four of the most important explosive properties appear to be energy density, bulk density, rate of energy release and the pressure- time history of the gases produced. Important rock properties are density and porosity, strength, and energy absorption including the effective moduli of elasticity. Rock structure also has a marked effect on its properties: for example, joints, bedding, and fracture alteration. Several mechanisms enter into rock fragmentation by blasting. These include slabbing, radial fracturing, crushing and bursting by the gas bubble. All of these factors are closely related to properties of both explosives and rock. Slabbing depends upon the first generated stress wave, whose shape and magnitude are a result of the pressure generated by the explosive, its time history and the resultant response of the rock, including its ability to sustain the stress wave. Actual slabbing, in turn, is a function of the magnitude and shape of the pressure pulse and the tensile strength of rock. Further fragmentation depends to a great extent upon the amount of gas in the bubble and its energy and pressure.

Jan 10, 1967

By William F. Brace, Howard R. Pratt, Wayne S. Brown

In many engineering structures, the mechanical properties of large volumes of rock must be considered. Typically, such properties are assumed to be the same as those of small laboratory samples, although it is clear that the laboratory samples do not contain the joints, faults, and other natural planes of weakness of the rock mass. A cheap, convenient testing procedure is needed with which the engineer can more accurately assess the strength and elastic properties of natural jointed rock. As a first step in this direction, a test has been developed capable of determining mechanical properties of large samples in their natural undisturbed state. In the present paper, some preliminary experiments on relatively unjointed material are described. Numerous attempts have been made to measure the deformation modulus of rock masses with varying degrees of success. Rocha (1), Grimm (2), and Alexander (3) have placed flat jacks in a slot in the rock and measured the pressure required to deform the slot. Bonnechere (4) has grouted large flat jacks in granite masses and performed similar experiments using a variety of strain measuring techniques. The U. S. Bureau of Mines has conducted radial jacking tests in which a uniform radial stress is applied to the inside of a tunnel of circular cross section and radial deformation is measured by extensometers located at various depths in the tunnel fall. Plate jack tests (Rocha (5), Shannon and Wilson (6)), pressure chamber tests, and cable jacking tests (Zienkiewicz and Stagg (7)) have all been used to determine in-situ deformation modulus. Several bore hole techniques have also been used to measure rock deformation. These include bore hole jacks (Goodman (8)), bore hole dilatometers using expandable membranes (Menard (9)) and bore hole penetrometers. Most of the above tests except the radial jacking test have an unknown stress distribution and require considerable approximation to calculate a deformation modulus. These approximations include the use of elastic theory for solutions of rigid plates, thick-walled cylinders, etc., and determination of values for Poissons

Jan 1, 1971

By C. T. Young, J. L. Lytton

In recent investigations,1,2 the strength and thermal stability of dislocation substructures prepared by 5 to 25 pct room temperature tensile straining and recovery annealing at 120°, 160°, and 200°C have been studied in randomly oriented polycrystalline high purity aluminum. The techniques of transmission electron microscopy revealed that a major source of the strength and stability of dislocation substructures was the formation, during room temperature straining, of well-defined cells bounded by dislocation tangles which rearranged into nearly perfect dislocation networks during recovery, forming the boundaries of subgrains. The strength of such substructures increases with decreasing cell or subgrain size,2"6 and the formation of fine subgrain structures can provide thermally metastable strength at low temperatures and can favorably alter the course of primary creep at elevated temperatures.7'8 For maximum benefit, however, sub-grain growth should be reduced or eliminated. It was, therefore, decided to investigate the use of heterogeneous precipitation on dislocation networks as a means of imparting increased strength and thermal stability to subgrain structures through effective pinning. C.T. YOUNG, STUDENT MEMBER AIME, and J. L. LYTTON, Member

Jan 1, 1970

By P. K. Guerrero, N. Arbiter

The correlation of power consumed by a tumbling mill with the dimensions, speed, and load has been attempted by three principal methods. One of these, the torque formula, has been reviewed critically elsewhere.' This approach, while analytical, disregards the individual motion and speed of the tumbling bodies and assumes that the gross geometry of the entire load is sufficient to establish the power requirement. A more general approach, using dimensional analysis, has been applied in this laboratory by the present authors1'1, and more recently by Rose.3 This disregards the internal conditions within the mill entirely and in effect is an empirical procedure for correlating data. Finally, the complete analysis of tumbling mill dynamics as first made by Davis' attempts to develop the power requirement from individual ball and rod paths and velocities. Although Davis' result is applicable only at a single speed for a given size and load it could be useful, since his optimum speed is at the upper limits of conventional tumbling mill practice. Where power values predicted by the Davis equation were compared with actual mill requirements, they were found too low for small mills and much too high for the largest mills. This suggested that the agreement with actual intermediate range requirements might be fortuitous, and the development of the equation was examined critically. The probable source of error was found to lie in an erroneous assumption made by Davis in converting the energy of ball or rod motion to power. With the same approach, but with different assumptions, a modified equation has been obtained which predicts results that are usually consistently high. This is to be expected, since it is assumed that there is no slip between load and shell and no interference among tumbling bodies. Both these effects should account for the difference. Development of Equation: When a cylindrical shell charged with a substantial weight of rods or balls is slowly rotated about a horizontal axis, the load surface first assumes an inclination that gradually increases to a maximum. Continued rotation results in failure within the load, characterized by a sliding of the top layers down the slope and a reduction in the angle of inclination. Further rotation again increases the angle, and the cycle repeats. If the speed is increased, there is continuous load failure and build-up and a continuous stream of rods or balls descends over the upcoming mass, which moves in circular arcs. At higher speeds the up-

Jan 1, 1961