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By F. D. Delve

RECENT studies by the author on the reduction of titanium from TiO2-bearing slags have been accompanied by difficulties that are attributed to

Jan 1, 1959

By E. H. Griswold

PETROLEUM production engineering is essentially the application of the laws of 'physics and mechanics to the production of oil. A true production engineer is one who can apply the principles of mechanics, hydraulics, thermodynamics, and other physical arts so as to facilitate' the efficient and economical recovery of oil. To this end he must have wide knowledge of practical field operations and a working knowledge of geology, with a thorough understanding of the underground state of the fluids which he seeks to control. Generally speaking, there have been two schools of production engineering, the California development and the Mid-Continent development. In California the preliminary production engineering was done by representatives of the U. S. Bureau of Mines and the State Mining Bureau, and was essentially subsurface work in regard to casing patterns, water shut-offs, and completion procedure, inasmuch as these were problems of the utmost immediate importance to the California industry. The oil companies were impressed with the value of such work and placed engineers, or more strictly speaking, engineering geologists on their field staffs. These men, realizing the need of further technical study in the mechanical phases of producing operations, added mechanical and mining engineers, and out of the blend developed what is now known as a production engineer.

Jan 1, 1932

By Sandford S. Cole

Manganese compounds occur in many mineral forms widely distributed throughout the crust of the earth. The most important of these commercially are the oxides which are usually found as irregular masses, but in some places (notably U.S.S.R.) occur as extensive beds of varying thickness and purity. The principal sources of ore have been U.S.S.R., Ghana (the Gold Coast of Africa), India, Union of South Africa, Belgian Congo, French Morocco, Cuba, Brazil, and Mexico. New developments of ore are being conducted in Brazil, British Guiana, French Equatorial Africa, and Northern Rhodesia. The production of the United States normally meets less than 10 pct of domestic manganese consumption. Manganese ore (35 pct or more Mn) is used principally by the ferrous metallurgy industry for production of manganese metal, ferromanganese, and other manganese alloys for use in production of steel ingots and castings. Some manganese is used in the nonferrous industry as an alloying element and cleanser in aluminum alloys, aluminum bronze, constantan, manganese bronze, Monel, Everdur, nickel-chromium resistance alloys, and nickel-silver. The metallurgical uses consume about 97 pct of the total manganese ore requirements of the United States. The balance goes principally for the manufacture of dry cells and for chemicals, with limited amounts for ceramic products, plastics, welding rods and varnish. The Materials Survey on Manganese, compiled in 1952 for Materials Office National Security Resources Board by the Bureau of Mines and Geological Survey, provides an excellent review of resources, reserves, specifications, uses, mining, beneficiation, metallurgical processes and deposits, and is worth referring to for greater details. Mineralogy and Geology The more common manganese minerals with typical characteristics are listed in Table 1 in order of importance. [ ]

Jan 1, 1960

By E. C. Burke, W. R. Hibbard

G. B. Craig (University of Toronto, Toronto, O,nt., Canada)—The advent of pyramidal slip at room temperatures in a magnesium crystal (M2,) and the very low value reported for the critical shear stress are puzzling. Table I1 shows the calculated values (approximate) for sin x cos I in this specimen if all the (10l) planes are considered. If So is the shear stress resolved in the direction of glide, on the glide plane, and U, is the stress operative in yield point tests, then: S,, — 325 (0.169) 55gpersqmm (approximately) for 1101: S,, = 325 (0.465) = 151 gpersqmm (approximately) for (0001): S,, — 325 (0.101) - 32.8 gpersqmm (approximately) Thus, we see the pyramidal plane in which the minimum shearing component operated. Barrett"' stated: "Experiments have repeatedly shown that, when there are several crystallographically equivalent slip systems in a crystal, the one having the greatest resolved shear stress will become active. ..." It does not appear to me that the measurements given are conclusive proof that pyramidal slip operated. E. C. Burke and W. R. Hibbard, Jr. (authors' reply) —Although the low value for the critical resolved shear stress for pyramidal slip may be puzzling, there does not appear to be any basis for questioning the validity of the measurements. Under the influence of constraints, slip systems having decidedly lower shearing components may become operative, e.g., "cross-slip" or the "forced glide" in magnesium reported by Bakarian. Since we believe that pyramidal slip occurred in the specimen because basal slip was inhibited, it is not too surprising to find an operative plane with a lower shear stress. -7 C. S. Barrett: Structure of Metals U94jl p. 2J6. New York. McGraw-Hill Book Co.

Jan 1, 1953

By S. E. Bretherton

Discussion of the paper of S. E. BRETHERTON, presented at. the San Francisco meeting, September, 1915, and printed in Bulletin No. 104, August, 1915, pp. 1595 to1599. ANTON EILERS, Brooklyn, N. Y. (communication to the Secretary*). While the advantages in the use of high-line siliceous slags in lead smelting which Mr. Bretherton discusses in this paper are obvious under certain economical conditions, he gives me credit for the introduction of such slags when it does not belong to me. It is true I did considerable experimental work, off and on, for the purpose of finding such slags, while at the Germania in 1877 and 1878, but I did not have occasion to introduce any such slags for regular work, because I had no ores which fitted the economical conditions for using high silica and high lime, except in isolated cases for very brief periods. On the contrary, the ores I had to treat were mostly very ferruginous and very low in silica, so that, economically, I was compelled to run nearly always on slags, which allowed me to use the abundant flux I had without cost. It was August Raht who first had occasion to establish and use for long periods a slag high in silica and line, and low in iron. This was when he was confronted with the task of smelting the. Horn-Silver ores at the smelting works at Franklin, Utah, with as little expenditure for fluxing material as possible. I was at that time in Leadville, Col., where, in the new works I had built, the Billings and Eilers smelters, I had occasion to use profitably many slags, but never anything as high in the earthy bases and in silica as Mr. Raht had to use.

Jan 12, 1915

By A. E. H. Bergmann

INTRODUCTION The Sachtleben Chemie GmbH in Duisburg, a subsidiary of the Metallgesellschaft AG, operates a new sulfuric acid plant that employs fluid bed roasting of pyrite concentrates. The plant produces about 300,000 tons per year of pyrite cinders from the fluid bed roasting unit. The cinder product consists of 58 percent iron and is about 80 percent by weight smaller than 50 microns. This cinder product was found to be a competitive source material for the cement industry as the iron-containing additive. However, the extreme fineness of the cinder and its dusting tendency were undesirable and an agglomerating technique became necessary. In order to keep the price of agglomerated pyrite-cinders at a competitive level, the agglomerating method must be chosen such a way the capital and operating costs are low. Initial experiments were carried out on a laboratory scale to make an appropriate choice of the agglomerating method. Major goals of agglomerating the cinders were to improve the transportation, storage, and proportioning and metering properties. Minimum specifications are put on the size, size distribution and shape of the product. Criterion for handling is that a minimum of minus one mm. fines are produced after several handlings, while for storage, it is also desirable for the agglomerated product to survive several months in open air. Thermal agglomeration processes such as sintering one known to produce excellent products, but are by far too expensive for our application. For the same reason, granulation, balling, and pelletizing tests with addition of organic binding agents, such as tylose, starch, sulfite wash, molasses, etc. were not continued. The costs for the binding agent was considerable, which is probably due to the high pore volume of our cinders (35 %). Furthermore, the pellets or granules

Jan 1, 1977

GEORGE F. KUNZ, New York, N. Y. (written discussion*).-We have been informed that the nickeliferous ores of Sudbury could furnish more palladium than the whole of the present world supply, together with a large amount of platinum. As the quantity of ore melted in Sudbury in 1916 totaled 1,521,689 tons, giving 80,010 tons of matte, and as the average of 3 years, up to 1915, are stated to show an average of 0.10 oz. of platinum and 0.15 oz. of palladium per ton of matte, this would indicate the presence of 12,000 oz. of palladium and 8000 oz. of platinum in the ore mined in 1916.1 Interest in the platinum situation is now more intense than it has ever been, and the great importance of this metal for many special uses is being increasingly appreciated. For munition manufacture, for chemical apparatus, in dentistry, and for jewelry, it has been and continues to be in great demand in spite of the phenomenal rise in its value. It is true that this has necessarily led to a search for substitutes, especially for dentistry and chemical uses, but while some of these have been found to answer the needs fairly well, for many 'other purposes platinum is still employed in spite of its great cost. As to the jewelry industry, the most public-spirited efforts have been made to restrict its use, and its employment in the manufacture of watchcases, purses, bracelets, and catches has been abandoned, gold being used in its place. The prime cause of the present shortage is, of course, the elimination of 'the Russian supply which, in normal times, constituted probably more than 90 per cent. of the world's production. This makes an intensive

Jan 4, 1918

By Henry M. Howe

IN discussing the classification of iron to-day, we are to leave out of consideration the general division into non-malleable or cast iron and malleable iron, as to the adequacy of which no question has been raised; and to confine ourselves to the subdivisions of malleable iron. This has been classified, according to the extent to which the properties imparted by carbon are present (viz., resilience, hardness, strength„ and, above all, the capacity for being hardened by sudden cooling from a high temperature), into (1) wrought iron which cannot be hardened, and (2) steel which can be hardened; and this classification I shall, for briefness, term the carbon classification. Until within a few years all authorities, both metallurgical and general,, have concurred in explicitly recognizing the carbon-given qualities, and preeminently the capacity for being hardened, as the essential qualities of steel ; this is laid down with clearness by every writer on the subject. For several years this old classification has not been sufficient to, meet all our needs, since the genius of Bessemer, Siemens, and, I may add, Holley, has produced wrought iron which has been perfectly melted, and thus freed from certain mechanical adhering impurities. This causes what we call homogeneousness for want of a better word, and gives rise to many important qualities which the old wrought iron had not;. qualities universally recognized, though not readily described. I shall, for briefness, style them the fusion qualities, and a classification based on them., a fusion classification. These qualities render the new product so vastly superior, for most purposes, to the wrought iron formerly known, that it is neces- * This paper was read in opening the discussion on the motion to adopt the report of the International Committee on the Nomenclature of Iron and Steel. At the conclusion of the discussion the resolutions on page 44 were adopted.

Jan 1, 1877

By George S. Rice

ARIAL maps of prospective mineral-bearing territory have become almost indispensable in all the branches of exploration, and have proved particularly useful in the great oil area of the Southwest. About nine years ago aerial photographic mapping in this area was begun. The early product was lacking in scale accuracy and other control features, which limited its effective use. Since then, the evolution of the technique of such mapping has been steady, with several mapping companies collaborating with five of the leading oil companies, and aerial maps have been prepared covering practically the entire area.Improvements in cameras, film, and developing equipment and practice have resulted in more uniform and clearer photographs, but the outstanding development has been the accuracy obtained with respect to scale and all other control features. Maps are no

Jan 1, 1936

By F. C. Greene

Development work in western Missouri was continuous during 1933, owing to the shallow depths at which production is obtained and the low operating costs. Unfortunately, no statistics covering the total production of oil and gas during the year are available. No new oil-producing pools were opened in 1933, but the Knoche area in 1.46 N., R.33 W., Cass County, was extended. There are probably less than 100 producing oil wells, all in Cass and Jackson counties, with a combined production of possibly around 150 bbl. daily. Several new gas areas were developed and there were several extensions of old areas, in 1933. Production was extended north by an entirely new pool—the Hammond pool, north of Plattsburg in Clinton Co. (sec. 18, T.55 N., R.31 W., and sec. 13, T.55 N., R.32 W.) where 13 wells were completed, the largest producing 2,332,000 cubic feet. In the Bartle and Marshall pool in secs. 3-4-9-10, T.47 N., R.33 W., Jackson County, four wells opened a new area. The largest well was 1,000,000 cubic feet. There were some small extensions near Independence, Jackson County. Two wells of about 300,000 cu. ft. were completed at a depth of 700 ft. in Kansas City and in a deeper sand than is usually productive. The Shaler area, in secs. 27-34, T.44 N., R.33 W. in Cass County, was extended with several wells, the largest of which was 300,000 cubic feet. The production in the pools mentioned is obtained chiefly from the Henrietta and Cherokee formations of the Pennsylvanian age.

Jan 1, 1934

By J. L. Huitt, D. K. Lowe

This laboratory flow study covers propping agent transporl in horizontal fractures as influenced by the characteristics of the propping particles, fluid and fracture. Correlations are presented for the transport of particles, deposition and fingering through dunes. For particles moving individually, the article velocity in some cases may be low compared to the hulk average fluid velocity; in other cases, the particle velocity may exceed the bulk average fluid velocity. At high propping agent concentration or low fluid velocity, the likelihood of particle deposition and dune formation increases. Fingering and channeling accompany dune formation. Dune formation can be limited to the outer region of tile fracture by adjustment of pump rate, fluid viscosity and particle concentration. A method is presented by which pump rate and fluid vircosity may he selected to control dune formation for given propping agent concentrations. INTRODUCTION The area and flow capacity of a fracture predominantly control the stimulation derived from hydraulic fracturing. Generation of fracture area exposes the rock matrix to a flow channel; the flow capacity of the fracture controls the flow through the channel to the wellbore under a given pressure gradient. This paper pertains to an important factor that affects the flow capacity of a fracture: the transport of the propping particles in the fracturing during the hydraulic fracturing treatment. With a better understanding of particle transport, fracturing treatments may be designed to obtain more effective distribution of the propping agent. RELATED STUDIES In recent years, the approach to obtaining high fracture flow capacity has been partial monolayer propping. Three papers1-3 have dealt with various facets of this concept. However, in some papers dealing specifically with particle transport, the results generally indicate that packing the propping particles within a fracture is inevitable. In early work&apos; with a sand slurry flowing in a pie-shaped flow cell, qualitative results showed that particle deposition in a fracture during transport should be expected. In other studies"" correlations based on slurry flow in vertical linear flow cells showed particle deposition was primarily a function of fluid velocity. In a recent paper the rate of sand advance (movement of dunes) in a horizontal linear flow cell was discussed. Subsequently, a method was given for designing fracturing treatments, based on the extent of sand advance during a treatment. In this work, particles whose diameter was small relative to the fracture width (i.e., dl W< 0.2) were primarily considered. The particle transport approaches that of sand transport in a stream bed. The industry trend, however, has been to use larger size propping agents. That is, particles with diameters approaching fracture widths predicted by Perkins and Kern.&apos;&apos; This trend has led to generally better fracturing treatments with particle relative sizes in the range 0.2 <d/W < 1.0. In all of the particle transport studies previously cited, the fluid characteristics were discussed. However, little or no attention was given to the parzicle characteristics. In this study the particles. as well as the fluid and fracture, are considered. VARIABLES AFFECTING PARTICLE TRANSPORT In the exploratory work to set LIP a program for this study, it was noted that particles within a batch moved at different velocities in a horizontal linear flow cell. In some cases the particles moved independently. In others there was particle interference. Also, particle deposition and fluid fingering occurred in some cases (Fig. 1). As a result of observing the easily distinguishab&apos;le types of particle movement, the particle variables as well as the fluid variables were included. In addition, the fracture width was included because the fluid velocity profile surely must affect the movement of the larger particles differently than that of smaller particles. Particle variables were density, diameter (based on a sphere of equal volumetric displacement), long and short dimensions, drag coefficient and velocity. Fluid variables were density, viscosity, yield shear strength and velocity. Fracture variables were the width and the angle between the plane of flow and a horizontal plane. Two factors which may prove to be important were omitted because of the complexity resulting from the parameters cited above. These are the fracture-surface roughness and gross irregularities that cause changes in the direction of flow. EXPERIMENTAL EQUIPMENT AND PROCEDURE A linear parallel-plate flow cell (Fig. 2) was used in the study. Lucite plates 1 in. thick formed the test section and permitted a viewing section 11 ft long and 10 in. wide. Spacing between the plates was adjusted with shims to give fracture widths 1/36 to 1/2 in. The model could be tilted to an angle of 45" with the horizonltal plane. Fluid flow was maintained with a Moyno positive displacement pump. Single particles were placed in the flow stream with a particle injector. A .4 - in. diameter plunger moving at a constant rate in a

Jan 1, 1967

By Francis M. Walters

IN spite of the war and the preoccupation of many physical metallurgists with work on secret or confidential problems, definite progress was made during 1944 in our understanding of the behavior of steel and of the effect of alloying elements. During the first two years of the war there was much concern over the possible unavailability of certain alloying elements; this period saw the development of the N.E. (National Emergency) steels. However, the measures taken eased the alloy situation and currently, highly practical problems under study are the graphitization of low-carbon steel and weld-cracking, while investigations of more theoretical interest have concerned hardenability, isothermal reactions, the effect of hydrogen and the interpretation of the notched-bar impact test.

Jan 1, 1945

By Luke L. Y. Chang, Bert Phillips

ThE tendency toward further oxidation of the intermediate oxides and the high volatilization rates of the higher oxides have prevented direct attainment of equilibrium data for the system tungsten-oxygen. As a result, St. Pierre et al.1 have proposed a phase diagram (to 800°C) based on thermody-namic data to 1200°C for the known tungsten oxides (WO2z, W18O49, W20O58, and WO3) and a report on a tungsten suboxide W3O.2 Recent modification of a technique previously described3 5 now permits adequate preservation of compositions of mixtures of metallic tungsten and metal oxides (e.g., of tungsten, cobalt, calcium, samarium, titanium) in order that condensed phase relations may be established to 1700 This method has been applied to study the high-temperature stability of tungsten oxides. In the method used, the desired compositions were sealed in nonreactive containers such that only a small gas volume remained. Each sample then established its own equilibrium atmosphere at temperature. This method has advantages in the study of systems of the W-0 type where knowledge of the condensed phases is desirable but for which composition and pressure of the gas phase are not readily attainable because of oxide volatility. Mixtures of 99.99 pct tungsten metal powder and purified tungsten anhydride (WO3) or in some cases W18O49* were equilibrated in pellet form in sealed

Jan 1, 1964

By J. K. Edgar

For a number of years the production and use of super-purity aluminum (better than 99.99 pct) has been steadily increasing. High-grade lots of. such aluminum show certain outstanding characteristics not found in lower grades containing principally silicon, iron and copper as impurities. One such characteristic is the so-called "self annealing," that is, the re-crystallization of the heavily cold worked metal at room temperature.&apos; Interest therefore is aroused as to the effects of the impurities. It is well known that the amounts of silicon and copper which occur in aluminum of better than 99.95 pct are completely soluble, at least at elevated temperatures (above 200°C). Iron, on the other hand, is known to be fairly insoluble in solid aluminum. Thus, a knowledge of the limits of this solubility would he of considerable use in studying the characteristics of the high purity metal. All investigators have agreed that iron has very low solubility in solid aluminum. Rosenhain, Archbutt and Hanson2 reported traces of an aluminum-iron phase in the "purest samples of aluminum obtainable." Gwyer and Phillips3 reported that an iron constituent was visible under the microscope in metal containing ".0088 per cent iron." Roth4 found that in the solid state the solubility of iron in high purity aluminum was 0.01, 0.01, 0.017 and 0.022 pct at 225, 320, 500 and 600°C respectively. Dix5 working with alloys containing less than 0.03 pct impurities, concluded from microscopic and chemical analyses of eutectic areas that the eutectic composition was close to 1.7 pct iron. Dix placed the eutectic temperature at 65s°C. Archer and Fink,6 using high purity aluminum-iron alloys, found that the hypoeutectic liquidus intersects the eutec-tic horizontal at 1.7 pct. This is in fair agreement with the investigation of the aluminum-iron system by Gwyer and Phillips who placed the eutectic at 1.89 pct iron with a freezing point of 653&apos;C. Preparation and Chemical Analysis oP Alloys Electrolytically refined aluminum (99.991 pct aluminum) and a high purity alumi-num-iron alloy (11.45 Pet iron) were used in the preparation of the alloys for this investigation. To aid in controlling the iron content of the experimental alloys, an alloy of lower iron content was prepared first from these materials. The high purity aluminum was melted and heated to about 700°C in a plumbago crucible coated with alundum cement and the aluminum-iron alloy was then added. The alloy was thoroughly stirred, fluxed and skimmed and then chill-cast into notch bars. The aIlalyses of the three materials are given in Table I. The alloys for the determination of the solid solubility of iron in aluminum were prepared by melting 600 g total of the aluminum plus the required quantity of the aluminum-iron alloy (No. 92531). These

Jan 1, 1949

By J. T. Ryan

WITH J. T. Ryan, of Pittsburgh, in the chair, 40 men on Monday afternoon were attracted to the first meeting of the new Health and Safety in Mines Committee. The speakers were well received and the discussion was good and virile. The field and scope of the new Health and Safety in Mines Committee was reviewed briefly, yet concisely, by Scott Turner. This committee is to cover the whole mining industry, in which much progress in reducing accidents has been made in recent years. Members of the A.I.M.E. can considerably assist in this important problem.

Jan 1, 1933

By Matti J. Saarivirta

The relative machinabilities of the precipitation-hardenable Cu-0.9 pct Cr, Cu-0.25 pct Zr, and Cu-0.9 pct Cr-0.25 pct Zr alloys are improved from 18 to 80 pct by 0.75 to 1.25 pct Pb. The Lead also improves the tensile strength, hardness, ad resistance to softening of the Cu-Cr and Cu-Cr-Zr alloys. When the alloy containing 0.7 to 2.2 pct Cr, 0.10 to 0.25 pct Zr, 0.75 to 1.25 pct Pb, and balance copper is solution-annealed at 1000°C (1830°F) and then aged at 525°C (Y75°F), tensile strength of 65,000 psi, 16 pct elongation, 62Rb hardness, and 84 to 87pct IACS electrical conductivity are obtained. The copper base Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys have high electrical and thermal conductivities, high strength and resistance to softening at elevated temperatures, but their machinability is poor, i.e., close to that of the pure copper. In the manufacture of various components such as welding electrodes or electrical and thermal conductors it is ofter desirable that the alloy have good machinability for high production rates and long tool life. Thus, alloys that combine these properties may be used not only for existing applications, but for new ones where good machinability is a requirement. This investigation was undertaken to improve machinability without impairing other desirable characteristics of the Cu-Cr, Cu-Zr, and Cu-Cr-Zr alloys. These commercial alloys contain about 0.4 to 1.2 pct Cr, 0.10 to 0.25 pct Zr, and balance copper. Lead was selected as an element that should improve the machinability and possibly other characteristics of the alloy. WORK PROCEDURE This investigation began with a study of the effect of lead on the hardness, tensile strength, electrical conductivity, and machinability of the binary alloy containing 0.10 to 1.30 pct Cr and balance copper. This was followed by an investigation of the effect of lead on the Cu-0.1 to 0.4 pct Zr and Cu-Cr-Zr alloys. The alloys were made from initially oxygen-free copper and for comparison some castings were made from phosphorus-deoxidized Lake Copper. Commercially pure chromium, zirconium, and lead were used for alloying. In melting the chromium was added to molten copper at 1400°C (2550°F), the heat held for 15 min at temperature, and the temperature then lowered to 1350°C (2460°F) when the other elements were added. The alloys were held for 15 min at this temperature and cast into a cast-iron mold. One-kilogram, 3-in.-diam castings were made. An argon cover was maintained during melting and casting to prevent oxidation. The chemical compositions of the alloys are shown in Table I. The micro structure and properties of the alloys were studied in the cast and wrought conditions prior to and after various solution-annealing and heat-treating cycles. The relative machinability was determined as a function of the lead content and compared with the free-machining Cu-lpct Pb alloy. To determine the machinability, 13/16-in.-diam cast specimens were cut by a machine hack saw using a constant cutting speed of 50 fpm, a fixed feed force, and a new blade for each alloy specimen. Molybdenum highspeed steel saw blades, 0.032 in. thick with 14 teeth per in., were used in all tests. No cutting fluid was used. Five tests were made on each specimen and the average elapsed time per test was taken as a measure of the relative machinability for that alloy. The variation of cutting time for each alloy was less than 110 pct.

Jan 1, 1969

By R. E. Goodman, M. A. Mahtab

The, state of stress around a vertical wellbore in rock following nonlinear stress-strain laws is examined by means of finite element analysis. The wellbore, is considered an axisymmetrier body with axisymmetric loading. The initial vertcal and borizontal stresses are "locked" in the rock elements around the wellbore and a new state of stress is generated by the displacements which occur around the borehole. A point-uise variation of the elastic moduli is made on the basis of the new stress state and the triaxial data. The initial stresses tire now reintroduced along with tile changed moduli and original boundary constraints. This procedure is repeatrd until convergent stresses are reached. The effect of nonlinearity on streases is examined for a 6,000-ft wellbore in a scbistose gnezss and Berea sandstone using results of laborratory triaxial compression tests. The results sbou that the effect is restrited to one well radius from the bottom periphery of the bole. Beyond a distance of one-quarter radius, the elfect of nonlinearity on stresscs IS almost always less than percent for the cases conszdered, The consideration of a static pressure inside the well does not magnify the effect of monlinearity on borehole stresscs. INTRODUCTION The terms " wellbore" and "borehole" here designate cylindrical openings in the ground with vertical axis and a circular cross-section. A knowledge of the stress redistribution that occurs on excavating a wellbore is important in understanding (1) the behavior of the lined or unlined hole, (2) hydraulic fracture response, and (3) the effect of stress redistribution on drillability; also it is important in predicting initial stresses in the virgin ground, and in analyzing the response of measuring instruments placed in the borehole. Our knowledge of the state of stress around a wellbore has been restricted to homogeneous, isotropic, elastic material and derives chiefly from the analysis by Miles and Toppingl and the photoelastic work of Galle and Wilhoit2 and Word and Wilhoit.3 In this investigation the state of stress is examined for a nonlinear elastic material by means of finite element analysis. Many rocks possess stress-strain curves that depart notably from straight lines in their initial or final portions. While the literature contains abundant stress-strain data from triaxial tests (axisymmetric loading) on cylindrical rock specimens, there is little information on rock deformability under nonaxisymmetric loading conditions such as occur at each point around the bottom of a wellbore. Although there is some knowledge of the effect of intermediate principal stress on rock strength, there is virtually nothing known about its effect on rock deformability; therefore, we have assumed here that the effect of intermediate principal stress can be ignored. A schistose gneiss4 and Berea sandstone5 were selected as representative rocks for this analysis. The traditional graphs of deviator stress (ol -o3) vs axial strain were reworked to give the tangent modulus as a function of the deviator stress for varying values of the minor principal stress. The result is a nesting family of skewed, bell-shaped curves for tile gneiss (Fig. 1A) and the sandstone (Fig. 2A). A similar replotting of the lateral strain data defines the variation of Poisson&apos;s ratio (v) with the deviator stress and confining pressure. These curves, shown in Fig. 1B for the gneiss and in Fig. 2B for the sandstone, are not so well ordered as the tangent modulus curves. However, all of these display an increase of v with deviator stress application, but the rate of increase diminishes with confinement. The ET and v curves for the two rock types are tabulated in Tables 1A and 1A for use in a digital computer so that material properties corresponding to a given state of stress can be assigned by interpolation. STATEMENT OF THE PROBLEM Given a state of stress in the ground prior to drilling a hole (initial stresses), we assume that

Jan 1, 1969

By Robert E. Green, T. Hinton

Expressions are derived for tke orientation factors appearing in the Grana to -Lucke theory of dislocation damping, for fcc crystals. The factors are given as functions of the elastic constants, the direction cosines of the specimen axis, atld the direction cosines of the particle displacemeizts, for darnping due to dislocation motion on each of the twelve possible slip systems as ixell as lor simultaneous dislocation rnotion on all twelve systems. RECENTLY Green&apos; has outlined the general procedure for calculation of the modes of wave propagation in a single crystal possessing a given crystallo-graphic orientation. In addition he has suggested how the results of such calculations along with calculations of the resolved shear-stress factors for slip enable the orientation-dependent factors (orientation factors) appearing in the Granato-Lucke theory of dislocation damping to be calculated. However, reen&apos; assumed that the maximum stress on dislocations was in the direction of the particle displacement of the elastic wave giving rise to the dislocation damping. The present cal&apos;culations show that this is an oversimplified approach appropriate only to special cases of high crystallographic symmetry. The exact calculation of stress on the dislocations can only be obtained by resolving the nine components of stress associated with the elastic wave into the appropriate slip direction and then summing. In this paper the general expressions for orientation factors are derived for fcc crystals in terms of the elastic constants, the direction cosines of the particle displacements, and the direction cosines of the specimen axis, bearing in mind the point mentioned above. Equations are presented which give the orientation factors for damping due to dislocation motion on each of the twelve possible slip systems as well as for simultaneous dislocation motion on all twelve systems arising from elastic-wave propagation. These orientation factors are appropriate to attenuation measurements made by the pulse-echo technique, where the elastic wave is a traveling wave. They will be compared with those for the case of a standing wave as derived by Granato and Lucke which are appropriate to measurements of internal friction by the resonance technique. The expressions for the orientation factors are compared with the five values given by insruch,&apos; based on unpublished work of Granato and Liicke, for positions of highest symmetry in the stereographic triangle. The various equations derived for modes of wave propagation and orientation factors have been evaluated for the case of aluminum crystals at 1-deg intervals throughout the stereographic triangle. These results will be presented in the form of contour diagrams in a subsequent paper3 and their relevance to ultrasonic measurements discussed. ORIENTATION FACTORS The coordinate system used for the calculations is shown in Fig. 1 and all specimen axes are taken to lie in the shaded standard triangle. The twelve slip systems are indexed according to Table I. Following the suggestion of lers, we may define the orientation factor Ok in the Granato-Liicke theory5 by the equation

Jan 1, 1967

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&apos; 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&apos;s commerce in such minerals. The U. S. Bureau of Mines has prepared charts showing the inter-

Jan 1, 1936

By J. W. Snavely

A practical mathematical treatment is presented for the determination and control of conveyor belt acceleration, particularly for conditions of starting where vertical curves are involved. A typical sample problem is analyzed, with required calculations, to clarify the procedure. THE part that acceleration plays in starting a belt conveyor and its effect on belt conveyor design are well understood in a general way. Its practical importance is easily overlooked, however, and under some conditions, it is absolutely necessary to give the problem of acceleration detailed study. Most handbooks on conveyor belting design adequately present basic data for the determination of acceleration values. This paper will only attempt to present practical thinking and a convenient method of treatment of acceleration in belt conveyor design. Mathematical Analysis In working out the various problems of conveyor belt acceleration, the starting point, as presented by the handbooks, is the familiar formula of "force of acceleration is equal to the mass times acceleration." By expressing these fundamental quantities in terms of belt conveyor design, it is possible to arrive at the unsuspected conclusion that the acceleration time for horizontal belt conveyors is independent of the load, and instead, dependent upon the belt speed, the type of drive arrangement and drive pulley, and the idler coefficient of friction. The mathematics leading to this conclusion are shown in Table I, which has been prepared to show this derivation. While at first the conclusion just given may not seem to be reasonable, further reflection indicates that obviously the type of drive pulley and the type of drive do affect materially the tension in the conveyor belt, and thus, as clearly shown, the time of acceleration is dependent upon the factors mentioned. Inasmuch as all of the factors except time are predetermined by the belt conveyor design, it becomes relatively easy to establish the accelerating time and to reduce further this time determination to a simple graph from which the time in seconds can be read directly. Such a graph is given in Fig. 1. The table appearing on Fig. 1 should be explained further. For a given belt speed, the time of acceleration can be expressed as a percentage of the belt speed. The time of acceleration is also dependent on the drive arrangement, and changes in the drive arrangement consequently change the time of acceleration. It further follows that for a given belt speed, the time expressed as a percentage of that belt speed also changes with the type of drive. Obviously then, it becomes possible to graph the percentage of speed for .each type of drive against the belt speed and accelerating time, after which, for a given belt speed and type of drive, the time can be read directly in seconds. Two constants were established for Fig. 1, the first one being the limiting of the maximum acceleration tension to 35 pct of the full load operating tension in the belt. The purpose of this is to limit the total tension imposed upon the belt during the acceleration period to 135 pct of the full load operating tension, &apos;which is the amount required to start or breakaway the fully loaded belt conveyor from rest. The other constant is the friction factor used for the idler equipment, which has been established as 0.022. For installations where it is necessary to establish the values of acceleration, invariably high grade idler equipment is used, and it has been established from field experience that 0.022 for the idler friction factor is amply conservative. The use of this friction factor for idlers must be tempered with judgment, of course, for occasions will arise where more power than indicated is required to start, even with the very best of equipment, such as low temperature operations that tend to congeal the grease in the bearings and thus produce additional friction drag. An inspection of the table in Fig. 1 affords a convenient rule of thumb method for determining the acceleration time, which conveniently can be 5 pct of the belt speed in seconds. The 5 pct of belt speed figure is close to the average for most types of drives. In using Fig. 1 it must be emphasized that it applies accurately to horizontal belt conveyors only.

Jan 1, 1953