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By E. M. Wise

THE properties required of gold alloys for jewelry are not well standardized, due in part to problems peculiar to certain branches of the jewelry industry, in part to the individual preference of the fabricator and to his willingness to cope with certain difficulties in manufacture, which arise with the use of certain alloys. GENERAL REQUIREMENTS In general, the properties desired may be classed as follows: 1. Color should conform to the dictates of good taste and smart style. 2. Corrosion resistance and tarnish resistance should be good. This is to a considerable extent determined by the carat. Resistance to such corrosive agents as mercuric chloride as well as certain depilatories is unreasonable to expect and difficult to meet. 3. Strength and hardness must be adequate to maintain the delicate contours of finely modeled jewelry. 4. Wear resistance must be great enough to resist abnormal wear, such as is encountered by a wedding ring in a lifetime of wear. 5. Ductility must be sufficient to permit the fabrication of drawn shells, tubes and difficult shapes. Material having a yield point of not less than 60,000 lb. per sq. in., an ultimate strength of 100,000 lb. per sq. in., and an elongation of 40 per cent. is desirable. 6. Melting point should be between 800° and 1200° C.

Jan 1, 1928

By J. C. Draper

Duquesne Light Co.'s Portal No. 3 mine, in the Warwick group of mines in Southwestern Pennsylvania, was started in June 1965 with battery- powered tractor-trailer face haulage. The area as- signed to Portal No. 3 encompasses over 8000 acres of coal and will be developed by driving a set of main entries through the center of the tract in roughly a westerly direction, and sub mains on a 45º deflection angle in roughly a northerly direction (Figs 1 & 2). In the original planning these sub mains were to be at a 90º angle with the mains, but difficult roof conditions necessitated a change in plans. The entries and crosscuts are driven 18 ft wide in the normal Sewickley seam which varies between 46 and 56 in. high. The mine bottom is a strong shale and in average, cool or dry outside conditions stands up well for rubber-tired haulage equipment, but when the outside conditions are hot and humid, the bottom becomes soft and muddy. This condition lessens as the mine faces are advanced further from the portals because the condensation will then take place principally on the surfaces of intake entries outby the working areas. To aid the situation, an air cooling system was installed and is used as conditions dictate.

Jan 7, 1968

By J. C. Griffiths, D. W. Bennion

A mathematical model, which does not assume a priori that stratification exists, but was designed to test for the stratification was developed. The model segmented the reservoir horizontally into areas of common variance, then divided it vertically into strata (if strata were present). Next, trend surface techniques were used to determine the lateral extent and variation of each stratum. The model was tested on two reservoirs (sandstone and limestone) using porosity as the reservoir rock property. The sandstone reservoir contained approximately 60,000 samples from 2,000 cored wells, while the limestone reservoir had approximately 24,000 samples from 430 cored wells. Within the areas of common variance tested, the model was able to distinguish four separate lithological units or zones in the sandstone reservoir, four in the Marly section and seven in the Vuggy section of the limestone reservoir. INTRODUCTION To accurately predict the movement and production of fluids from a reservoir rock, it is necessary that the reservoir engineer have a knowledge of the rock properties and their distribution throughout the reservoir. For this study, a reservoir rock is defined as a solid containing interconnecting holes or voids which occur relatively frequently and are dispersed within the rock in a regular or random manner. The fraction of bulk volume that these interconnecting voids occupy is called porosity. The rock must also possess sufficient permeability to allow fluids to move through it and it may be composed of one or more strata or lithological units. A stratum or lithological unit as defined in this study is a body or volume of reservoir rock whose properties are so distributed that its lateral and vertical extent can be traced throughout or through a portion of the reservoir. Operationally, the existence of strata are question- able unless the variance within strata is less than among strata. Within the past few years computers have been widely used as a tool for calculating movement and production of fluids from reservoirs. Most prediction models require some type of a mathematical description of certain reservoir rock properties. In the past, most of these models have been relatively simple. Some have assumed vertical variation but no lateral variation, while others have assumed lateral variation but no vertical variation. In general, most of these models have not used functional relationships to predict reservoir rock properties as functions of position. The object of this study was to develop a model which would predict lateral and vertical variations of reservoir rock properties. Since samples are usually available from only a small portion of the total reservoir rock, it seemed logical that if measurements from these samples were to be used to infer the properties of the actual reservoir, the data should be treated statistically as a sample from the total population (reservoir). Therefore, the model developed in this study to predict reservoir rock properties was a stochastic model. The model was tested using porosity (a macroscopic reservoir rock property) measurements from two reservoirs — the first, a sandstone reservoir from which 60,000 samples were obtained; and the second, a limestone reservoir with 24,000 samples. Several investigators have proposed methods to determine the vertical and areal variation of a reservoir rock property. Stiles: Dykstra and Parsons 2 and Suder and Calhoun3 have all developed waterflooding prediction techniques which assume vertical variation but no lateral variation. Stiles developed a method to segment a reservoir arbitrarily using frequency distribution. Law4 suggested that porosity has a normal frequency distribution and that permeability has a log-normal frequency distribution. Elkins and Skov 5 proposed that when a reservoir is segmented vertically, the

Jan 1, 1967

By C. Goldberg, R. H. Wynne

WHEN using an optical goniometer to determine crystal orientation' it is advantageous to use a preferential etchant so that the etch pits have plane faces which are parallel to crystallographic planes, all of which are of the same "form." "Westinghouse Silver Etch" (WAg), a preferential etch for germanium, is made up as follows: 40 ml of 49.7 pct hydrofluoric acid, 20 ml of 70.7 pct nitric acid, and 40 ml of distilled water containing 2.0 g of silver nitrate. Examination of metallographs of WAg etched surfaces (Fig. 1, for example) indicates that, regardless of crystal orientation, the faces of the etch pits are (111) surfaces. Optical goniometer examination of these WAg etched surfaces also indicates that the faces of the etch pits are (111) surfaces, i.e., all bright reflections are from (111) planes. When using an optical goniometer of the type described by Barrett,' not only (111) reflections from a WAg etched germanium surface but also other reflections of lower intensity will be observed. These latter reflections can cause confusion. We have used an optical goniometer made from a war surplus astrocompass and a galvanometer lamp. The reflections are observed by using the goniometer in a darkened room and letting the reflected light be in- cident upon a piece of white paper. The resulting decrease of goniometer sensitivity enables (111) reflections only to be observed. This in turn permits the crystal orientation to be determined in a matter of minutes, since only two measurements are necessary. The authors wish to acknowledge the help received from R. E. Davis who assisted in making the metallographs and aided the authors in the interpretation of the metallographs.

Jan 1, 1954

By N. H. Muhlenberg

IT is often a tedious matter to get a solution of pig iron or steel, for the determination of phosphorus, which is absolutely free from silica. Where pig iron rich in silicon is dissolved in hydrochloric or nitric acid in the usual procedure, it is necessary, not only to evaporate the solution to complete dryness, but to heat the dry residue for some hours in an air-bath to a temperature of about 120° C. The oxide of iron is thus rendered insoluble in nitric acid, and is only slowly dissolved by hydrochloric acid. In the method of determining silicon by nitric and sulphuric acid, described in the Transactions of the Institute, Vol. VII, page 346, and Vol. VIII, page 508, we obtain in one or two hours a solution of the iron in the form of ferric sulphate entirely free from silica, and containing free sulphuric acid. It occurred to us that this solution might be made available for the determination of the phosphorus by the molybdate method. The following experiments were tried with unsatisfactory results. 1st. The iron was precipitated by ammonia, the precipitate filtered, washed, and dissolved in nitric acid. 2d. The iron was precipitated as basic acetate and dissolved in nitric acid. 3d. The solution was neutralized by ammonia, and nitric acid added in small excess. In all these cases the phosphorus obtained by precipitating by ammonium molybdate and magnesia-mixture was too low. The following method was then tried with success. The filtrate from the silica and graphite was evaporated to small bulk and heated in a porcelain dish on a sand-bath, until fumes of sulphuric acid ceased to escape. The dry residue was taken up with dilute nitric acid and the solution precipitated by ammonium molyhdate. The phosphorus was weighed as magnesium pyrophosphate. The results were satisfactory. To save time, the original solution of the iron in nitric and sulphuric acids was evaporated to dryness and heated as before until

Jan 1, 1882

By O. C. Wheeler

The slackening of activity in oil development in Colombia, which was noted in 1931, continued throughout 1932. In the producing fields output was further curtailed and active operations were substantially reduced. Exploratory work was at the lowest level reached in a good many years. Applications and Contracts for New Concessions The areas covered by the four applications accepted by the government in 1931 for concessions on national lands were not finally awarded the applicants, although the indications are that these will be granted during the coming year. iln application of Sr. Luciano Restrepo for a concession of 49,232 hectares located on the north side of the Sogamoso River in the Municipality of Bolivar, Department of Santander, was accepted by the Government toward the end of the year. The Government is expected to take action toward granting or denying this concession during 1933. The Richmond Petroleum Co. (Standard Oil Co. of California subsidiary) leased from Manuel Davila P. and Eduardo Villar a private tract known as the Fierro Arriba and Fierro Abajo lands located in the municipality of Victoria, Department of Caldas, near Honda. The terms of the lease provide for a cash rental and royalty. The company is allowed 10 years in which to start exploratory work. The lease covers a period of 15 years and is subject to renewal by periods of similar duration. Richmond Petroleum Co. The Richmond Petroleum Co. finally abandoned its Repelon No. 3 at 4312 ft., owing to drilling difficulties. No new hole was made on this well during the year. This was the only active drilling project in the country outside the Tropical Oil Company's concession, and with its abandonment all wildcat activities in the country ceased. South American Gulf Oil Co. This company did no drilling on its Colombian properties during the year. As in the preceding years, small amounts of oil, of no commercial

Jan 1, 1933

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By F. C. Farnham

In this paper it is shown that the vertical component of the earth's magnetic field for the area of the United States can be very closely approximated by assuming it to be the sum of the vertical components of two magnetic fields. The first of these is the field of the centered dipole described by J. Bartels,l the axis of this dipole intersecting the earth's surface at two antipodal points, the one in the Northern Hemisphere being at latitude 78.5°N. and longitude 69°W., and the dipole having such strength that the vertical component of its field at its axis pole is 0.63 oersted. The second field is that due to a second dipole situated halfway between the center of the earth and a point on the earth's surface at latitude 38.5°N., longitude 91.5°W., the axis of this dipole being along this radius, the south pole being toward the surface, and the dipole being of such strength that its field at the point on the surface mentioned above is 0.069 oersted. Using the field computed on this basis, tables of latitude and longitude correction factors were computed and are included in the paper. It is also shown that the secular variation in the earth's magnetic field may be roughly accounted for by assuming it to be due to motion of the second dipole described above. Although there is an error in the equation used for computing the strength of the field due to the second dipole, the distribution of the field computed is very nearly that of the assumed arrangement of dipoles. Subsequent work by the author reveals that minor changes can be made in the location of the second dipole, which will make the computed field fit the observed field even more closely. It has also been found2 that the vertical component of the field may be represented equally well by a purely empiric relationship.

Jan 1, 1940

By W. F. Tanner

A river delivers a given load of sand, and hence heavy materials, into the sea. The load is fixed by drainage basin characteristics and processes. Wave energy available for redistributing that load is fixed in an entirely different way. An equilibrium diagram of these two parameters (load vs energy) pennits a tentative prediction of what will happen to the heavy minerals. Alluvial rivers transport a mechanical load which consists essentially of wash load (finer than about 0.05 mm in particle diam), bed load (coarser than about 0.10 mm) and the transition sizes in between. A few rivers carry no appreciable mechanical load, and are excluded from this discussion. An example of the latter is the Suwannee River of Florida, which empties across an oyster bar into the Gulf of Mexico and does not build a delta despite the absence of significant waves or currents in that part of the Gulf. An alluvial river may deliver its load into a protected sediment trap (such as an estuary, sound or lagoon), onto a low-energy coast (where it builds a delta) or onto a high-energy coast (from which spot the river load is swept away). The nature and disposition of the load depends, obviously, on three sets of factors: 1) drainage basin characteristics and processes, which determine quantity and make-up of the load; 2) coastal structure and geomorphology, which determine the kind of river-sea coupling which

Jan 1, 1962

By J. T. Ryan

SiR Humphry Davy's epoch-making treatise delivered on Nov. 9, 1815, before the Philosophical Society of London, first announced and demonstrated a flame safety lamp for detecting methane in mine air. Coal mining was known in England as early as 1180, more than 600 years before the advent of a safe lighting and gas-detecting appliance. Mining, no doubt, took place first in outcrop coal, and danger from gas did not become apparent until the workings became deeper and more extensive. Davy's lamp did much to increase the safety of miners, and a modified Davy lamp is still widely used for detecting the presence and approximate amount of combustible gas in mine air. No factor in coal mining has improved more rapidly during the past 15 years than safety measures. This progress came about not only as a result of the workmen's compensation laws now in force in most of the states of the Union, but because the research work of the U. S. Bureau of Mines had demonstrated some dangers incident to coal mining which were not considered to be serious matters prior to that time. Electric power and explosives are necessary but potential hazards in American coal mines. A general mechanization program is now under way, while the mines are growing deeper and more extensive. Consequently ventilation problems are more complex and a demand has been created for positive detecting devices for carbon monoxide as well as methane. Scientists and manufacturers, working hand in hand during the past 10 years, have invented and developed appliances which make systematic and effective examination of mine air possible. The object of this paper is to describe briefly the approved testing devices in use today, with the hope that they may lead to the saving of life. Two Groups of Dangerous Coal Mine Gases Dangerous coal mine gases may be placed in two groups: (I) those that are dangerous because of their explosive properties, and (2) those that are dangerous because of their toxic properties. Methane (CH4) is the important gas of the first group, and in so-called gaseous mines constantly exudes from the coal and rock; it may accumulate and form an explosive mixture. The explosive range of methane-air mixtures is well defined. The low limit is 5 per cent., the high limit 15 per cent., and the most explosive

Jan 1, 1927

By I. E. Rosenzweig

THE problem considered in this paper is as follows: An arbitrary horizontally stratified area is given. The electrical properties of this area are characterized by a function p(z) (Fig. 1), which shows the relationship between resistivity p of thes oil and the depth z. For such general case the apparent resistivity p* will be computed, by FIG. 1.-GRAPH OF FUNCTION p(z) FIG. 2.-GRAPH OF p(Z) FOR n HOMO-GENEOUS LAYERS. earth-resistivity measurements carried out by any given configuration of electrodes. General solutions of this problem appear to be very important for interpretation of field results of resistivity measurements, concerning structural investigations. Such solutions have been given by many authors for the special case of a finite number of homogeneous layers (Fig. 2)1-4 as well as for the more general case of continuously rang-ing resistivities. 5-8

Jan 1, 1939

By S. Nenno, T. Saburi, Y. Mizutani, M. Yomarnoto, K. Komatsu

In the equilibrium phase diagram of the Ni-Mo sys-tem1,2 available at present, intermetallic compounds (or ordered phases)ß(Ni4Mo) and ?(Ni3Mo) are known to exist to the nickel rich side. In our recent investigations on Ni-Mo alloys, however, it has been found that the quenched alloys from the high temperature region containing more molybdenum than the Ni4Mo do not decompose directly into 0 and when annealed isothermally below the peritectoid temperature, i.e., 865°C. This note is to report the existence of Pt2Mo type superlattice (possibly ordered Ni2Mo) as a metastable phase in the early stage of decomposition. Alloys containing 20.1, 22.7, and 24.4 at. pct Mo were prepared by vacuum-melting electrolytic nickel of 99.9 pct purity and molybdenum powder of 99.9 pct purity in an alumina crucible. From the resulting ingots, sheets 0.3 mm thick were obtained by forging, hot-, and cold-rolling. The sheet specimens were water-quenched from ! region and subsequently annealed for various periods of time at temperatures below the peritectoid temperature. On these specimens were made optical-microscopic and transmis-sion-electron-microscopic observations. Fig. 1- Optical micrograph of the 22.7 at. pct Mo specimen annealed for 100 hr at 700°C after quenching. (ß + ?) region, B, nucleated along a grain boundaries are invading the preexisting (ß + Ni2Mo) region, A. Details of A are observable only by electron microscopy. Etchant: 60 pct HNO3-40 pct CH3COOH.

Jan 1, 1970

By Franklin J. Hill, Theodore D. Tiemann

Sized fractions of Wisconsin Gogebic taconite were reduced with hydrogen over the temperature range from 600° to 1000°C. In general, the degree and rate of reduction increase with temperature. Particle size has no observable effect except in the smaller fractions at 900°C and above, where reduction is impeded, possibly due to the siliceous nature of the ore. Gaseous diffusion appears to be significant as a rate controlling factor at certain stages. THE depletion of high grade iron ore reserves in the United States has established the need to utilize all available iron ore deposits, both in long range planning and from the viewpoint of national emergency. This has led to extensive research and development in this field. The beneficiation of Wisconsin Gogebic taconite ore has been previously studied by investigators at the University of Wiscconsin, 1 the United States Bureau of Mines,, Battelle Memorial Institute, 3 and others. Methods investigated have included concentration by flotation processes, magnetic and gravity separation, magnetic roasting and various combinations of them. The foregoing studies have been concerned with the production of an enriched ore suitable for blast furnace use. If the ore could first be reduced to metallic iron and then beneficiated, the product could be used directly in the open hearth or electric steel-making furnace. The by-passing of the blast furnace should enhance the economic feasibility of the beneficiating process. The work reported here,4 was undertaken to establish data on the hydrogen reduction of Wisconsin taconite that would eventually lead to the development of an economic direct reduction process for this and perhaps other low grade siliceous ores. The volume of work on direct reduction can be judged by the fact that 240 direct reduction processes were patented in the United States alone up to 1951, 5 and numerous additional processes have since been developed. Some of the factors contributing to direct reduction development are: 1) The increasing capital cost of the blast furnace and its accessory equipment. 2) The decreasing availability of high grade domestic ore. 3) The high cost of steel scrap for use in the open hearth and electric furnaces. In general, direct reduction processes can be divided into two types; those using a solid reductant (coal, peat, lignite) usually carried out in a kiln, and those using a gaseous reductant (H2, CO) in a shaft furnace or a fluidized bed retort. As there is no low cost coal readily available in northern Wisconsin but natural gas could be quite easily obtained, it is believed a gaseous reductant process would offer the greater feasibility for use on Wisconsin taconite. It is hoped that this preliminary work will beof interest to other investigators in this increasingly important field. TACONITE ORE The ore used in the investigation was obtained originally from the U. S. Bureau of Mines, and consisted of a representative composite made up from trench samples of the Norrie, Pabst, Plymouth, Pence, and Yale members of the Wisconsin Gogebic range iron formation. Chemically, the ore contains approximately 52 pct SiO, and 30 pct Fe. X-ray diffraction and other studies indicate the principal minerals to be quartz (SiO2), hematite (Fe2O3), and goethite (Fe2O3. H2O). Minor amounts of iron containing silicates, siderite (FecO3), and magnetite (FeO-Fe2O3) are present. The iron minerals and quartz are so finely disseminated that the ore requires grinding to less than 200 mesh (74 µ) for essential liberation.l,2 The iron content of each of the several size fractions studied is shown in Table I. EXPERIMENTAL METHOD The method used throughout the investigation was based on that developed by the U. S. Bureau of Mines in Minneaopolis6,7 in which the course of reduction is followed by the loss in weight of the ore sample. More specifically, a 100-g sample of the size frac-

Jan 1, 1962

By S. E. Haszko

Fused alumina or silica crucibles were used as the containing vessel. X-ray powder photographs were taken with CrKa radiation and the use of Straumanis type Norelco cameras of 114.6 mm diam. Crystallographic data for these compounds are shown in Table I. These results are in agreement with others of this series reported previousiy by Wernick and Geller.l The abnormally large atomic volume of Eu and Yb metal3 is manifested in EuA12 and YbAl2, when one compares them with the compounds reported in Ref. 1. However, the behavior of Yb in the Ni compound is the same as that observed in Ni5Yb having the Cu5Ca structure.4 Thus, it appears that Yb has a valence closer to 3 only in the Ni compounds; i.e.. the 2s and Id electrons are lost to the conduction band. 1,4 Europium in EuAl2, appears to have a valence closer to 2. In previous work.' X-ray patterns of ingots of NdCo2 indicated a multiphase material with faint indication of the presence of a phase having the MgCu2 structure. It was thought that NdCo2 formed peri-tectically from the melt, resulting in a multiphase system when cooled under nonequilibrium conditions. An X-ray pattern of a sample from a melt cooled more slowly than in past work showed that the major phase was NdCo2. The lattice constant, Table 1, is in excellent agreement with the value one can predict from the data of Ref 1. One of the other phases was identified as Co,Nd. The author wishes to thank J. H. Wernick for his guidance in this work, and D. Dorsi for the preparation of these compounds. 'J. H. Wernick and S. Geller: AIME Trans., in press. 'J. H. Wernick and S. E. Haszko: to be published. 'F. H. Spedding and A. II. Daane: Progress in Nuclear Energy, Series 5, Eds.: H. M. Finniston and J. P. Howe, McGraw-Hill Book Co., 1956. 'S. E. Haszko: to be published. 'J. H. Wernick and S. Geller: unpublished work. 6J. 11. Wernick and S. Geller: Acla Cryst., 1959, vol. 12, p. '162. The Influence of Hydrogen on the Lattice Parameters of Ti-Sn Alloys A. Coucoulas and H. Margolin A reinvestigation of the lattice parameters of Ti-Sn alloys by the present authors has revealed consistently higher c and a values than those obtained by Worrier. The difference is most pronounced in the c-parameters which are, therefore, used as a basis of comparison. This discrepancy was not due to air contamination, since precautions were taken to exclude this possibility. Specimens for Debye-Scherrer photograms were prepared by arc-melting 15-g buttons of Bureau of Mines titanium and 99.99 pct Sn, with compositions of 6, 8, 10, and 12 at. pct Sn. These buttons were forged under an oxygen-acetylene torch to 1/8-in. sq rods to produce relatively fine grained material. Scale and some surface were ground off, and the rods, after wrapping in molybdenum and titanium sheet, were vacuum annealed 15 min at 800 °C to remove hydrogen. Heat treatment of one of the samples at 875°C to produce ß and reveal a at the surface showed no surface contamination. Following the vacuum treatment, the specimens were wrapped in molybdenum and annealed for 1week at 800°C under two atmospheres of argon. After water-quenching, the rods were ground so that the thickness tapered to 0.1 mm at the tips. The ground specimens were then recapsuled as previously and reannealed 1 hr at 800°C to remove cold work. The

Jan 1, 1961

By L. Adler

Any design of a mine roof in bedded deposits which ignores differential deflections at the supports can quickly lead to dangerous overstressing. As illustrated by the typical case presented on page 1029, if one support deflects only 0.1 in. more than its neighbor, stresses 50 pct higher than anticipated will result. Previous studies1-3 have assumed that the mine roof acts like a beam clamped at both ends, with no deflection or slope' at the supports (Fig. 1). Essentially this assumes:5* ?A = ?, = ?b and dA = dB = 0. However, a host of conditions can cause differential sag or deflection at one support, and even an apparently trivial deviation can have major consequences in the beam: variations in spacing, size, and material of supports; local settlement due to floor heaving or lower mine openings; non-uniformity in wedging or bolt tensioning.8 In one particular instance concrete pillars, poured in place, shrank away from the roof upon setting.' When understood and controlled, differential sag becomes a definite advantage, permitting the transfer of loads from one support to another. Where one support is a bolt or prop and the other a pillar or rib, the load on the former can be reduced while the load on the pillar or rib is increased. This means two things: 1) savings can be effected by using smaller artificial supports such as props and bolts and 2) loads can be increased in the rib to induce eventual failure for longwall caving. In this last respect, another factor underlying coal bumps becomes understandable. The design of a mine roof by beam theory assumes that when a bedded formation is homogeneous, iso-tropic, and elastic, it will act like a uniformly loaded beam, fixed or clamped at both ends,6 s in Fig. 1.'" These are important assumptions. The uniform load is the weight of the beam itself or its body load. For a beam of unit width, this load becomes per foot: w = yhb. w = uniform load y = specific weight, lb per ft3 h = depth or thickness of beam, ft b = width of beam, ft Since b = 1, w - yh [ 1 ] A beam fixed at both supports is statically indeterminate to the second degree, that is, two equations in addition to those for static equilibrium are required to determine the reactions at the supports. These equations result from the geometry. From statistics: ^F,= 0;RA + RB — wL = 0 [2] wU S,M0 = 0 ; MB H------------MA — RBL = 0 [3] it Using superposition in which the left support is kept intact and the right one resolved into an active force and moment, we obtain from Fig. 2:" ?b = ?m + ? b2 + ?B3 = 0 dB = dB1 + dB2 + dB3 / wU Ma RBL \ V d°=(-r+-2—r)-zr [5] Where: Subscripts refer to position on axis of beam R = force, lb M = moment, ft-lb w = uniformly distributed load, lb per ft L = span, ft 0 = slope, radians d = deflection, ft E = Young's Modulus, lb per ft" 1 = Moment of inertia about the neutral axis, ft4 Solving Eqs. 2 through 5 for the four unknown reactions, we obtain: 2 L3 Fig. 3 is obtained by plotting MA and M, vs d, and then plotting RA and R, vs d, and adjusting their scales to coincide with MA and M, vs d,. It should be noted in Eqs. 6 and 7 that as dB increases, MA increases the same amount that Mn decreases. Eqs. 8 and 9 show a similar relationship between RA and R,. Proof that MA is the maximum absolute moment occurring in the beam is as follows: where M, = moment at x wx-When where M,., = maximum positive moment Eqs. 6 and 8 into above: For small dn: MA> M,,,

Jan 1, 1960

By J. A. Clum, R. W. Heins, T. D. Tiemann

The use of Na-montmorillonite clay hinders (Western Bentonite) in the pelletizing of iron ore concentrates is well established as is the idea that alternative binders must be found. 1-6 This note summarizes work done7 in evaluating a Wisconsin montmorillonite clay binder. The clay occurs in irregualr beds overlying the Prairie du Chien Dolomite and the St. Peters Sandstone near Hersey, St. Croix County. The raw Wisconsin clay contained 65% quartz and 35% clay minerals. The Na20to CaO ratio was 0.234. Suspension viscosity tests of the raw clay gave results only slightly better than water alone, even after treatment with activator materials. Sedimentation treatment reduced the quartz in the decantate to 5% after 240 min (four hours). Twenty minutes of sedimentation produced a decantate with 27.5% quartz which was found as effective as the 5% quartz decantate in pelletizing behavior. The 20 min decantate was used in subsequent tests. The decantate was filtered and dried at 110°(230°F). The minus 200 mesh portion of this was added directly to the magnetite concentrate. Pellets were made in a laboratory sized disc pelletizer from pastes consisting of ore concentrate, balling water (9%) and binder (clay, or clay + resins, or resins). The pastes were premixed in a Waring blender. The binders were: (1) 1% of a commercially used Western Bentonite; (2) 1 % or 3% of the Wisconsin clay (raw, or 20 min decantate); (3) 20 min decantate washed with activator solutions, (to exchange Na for Ca in the clay); (4) decantate with activator added in the balling water; (5) decantate with organic resins; (6) organic resins. Measurements of the 0.46 m (18 in.) Green Drop Number, the Dry Strength and the Fired Strength (fired at 1260°C (2300°F) for 30 min) were made. The dry and fired compressive strengths were determined on an Instron testing machine using a C-load cell and a F-load cell, respectively. The cross-head speed was 0.004 m/sec (0.1 in./min) for both. The results of each measurement were averaged for 15 pellets. A summary of those results is presented in [Table 1]. More detailed results and procedures are presented in another report.7 In addition to the effects on pellet strength due to various binders the effect of varying magnetite concentrate characteristics is noted in [Table l]. There, a few comparative data are shown for Cornwall, PA Magnetite, which has a generally liner particle size than the Black River Falls magnetite which was used for most of the tests.

Jan 1, 1979

By P. B. Baxendell, R. Thomas

Work on the calculation of vertical two-phase flow gradients by Cia. Shell de Venezuela has been based mainly on the "energy-loss" method proposed by Poett-mann and Carpenter in 1952. The "energy-loss-factor" correlation proposed by Poettmann and Carpenter was based on relatively low-rate flow data. This correlation proved inapplicable to high-rate flow conditions. In an attempt to establish a satisfactory correlation for high rates, a series of experiments was carried out at rates up to 5,000 BID in Cia. Shell de Venezuela's La Paz field in Venezuela, using tubing strings fitted with electronic surface-recording pressure elements. As a result of these experiments a correlation between energy-loss factor and mass flow rate was established which is believed to be applicable to a wide range of conduit sizes and crude types at high flow rates (e.g., above 900 BID for 27/8-in. OD tubing). It is anticipated that the resulting gradient calculations will have an accuracy of the order of % 5 per cent. At lower flow rates the energy-loss factor cannot be considered as constant for any mass rate of flow, but varies with the free gas in place and the mixture velocity. No satisfactory correlating parameter was obtained. As a practical compromise for low flow rates, a modification of the curve proposed by Poettmann and Carpenter was used. In practice this was found to give gradient accuracies of approxirnately ± 10 per cent clown to flow rates as low as 300 B/D in 27/8-in. tubing. INTRODUCTION Production operations in Cia. Shell de Venezuela's light- and medium-crude fields are principally concerned with high-rate flowing or gas-lift wells. Under these conditions the analysis of well performance, the selection of production strings and the design of gas-lift installations are vitally dependent on an accurate knowledge of the pressure gradients involved in vertical two-phase flow. Initially, attempts were made to establish the gradients empirically as done by Gilbert,' but the results were not reliable due to scarcity of data over a full range of rates and gas-oil ratios. Several methods of calculation based on energy-balance considerations were attempted, but the computations were cumbersome and the results cliscouraging. In 1952 a paper was published by Poettmann and Carpenter' which proposed a new approach. Their method was also based on an energy-balance equation. but it was original in that no attempt was made to evaluate the various components making up the total energy losses. Instead, they proposed a form of analysis which assumed that all the significant energy losses for mutiphase flow could be correlated in a form similar to that of the Fanning equation for frictional 1osses in single-phase flow. They then derived an empirical relationship linking measurable field data with a factor which, when applied to the standard form of the Fanning equation, would enable the energy losses to be determined. The basic method was applied in Venezuela to the problem of annular flow gradients in the La Paz and Mara fields" This involved establishing a new energy-loss-factor correlation to cover high flow rates and, also, some adaptation of the method to permit mechanized calculation using punch-card machines. The final result was 1 set of gradient curves for La Paz and Mara conditions which proved to be surprisingly accurate. With the encouraging results of the annular flow calculations, several attempts were made to obtain a corresponding set of curves for tubing flow. Here, unfortunately, little progress could be made. The original correlation of Poettmann and Carpenter was based on rather 1imited data derived from low-rate observations in 23/8- and 27/8-in. OD tubing. It did not cover the higher range of production rates, and extrapolation proved unsuccessful. A new correlation covering high flow rates was required, but this proved to be extremely difficult to establish since tubing flow pressure measurements at high rates did not exist—due to the difficulty of running pressure bombs against high-velocity flow. The necessity for reliable tubing flow data increased with the development of the new concessions in Lake Maracaibo, where high-rate tubing flow from depths of 10,500 ft became routine. Thus. it was decided to set up a full-scale test to establish a reliable energy-loss factor for tubing flow conditions. A La. Paz field light-oil producer with a potential of approximately 12,000 B/D on annular flow was chosen. To obtain full pressure gradients, a special tubing string was installed which was equipped with electronic surface-recording pressure measuring devices,

By R. A. Greenkorn, R. C. Smith

Hele-Shaw cells are used to model creeping flow through porous media (where Darcy&apos;s law is valid). The effects of inertia on flow about obstructions in a Hele-Shaw cell can be calculated by a perturbation method if one can determine a solution to Laplace&apos;s equation. Results of a computer solution for flow about circular, square and elliptical obstructions are presented. These results show that or a modified Reynolds number of less than I, the inertia terms are small; and for values of less than 3, the average streamline predicts the ideal flow. Therefore, the analogy might be used for studying flow in porous media up to a modified Reynolds number of at least 3. INTRODUCTION The nature of fluid flow in porous media is of interest in the fields of soil mechanics, ground water flow, petroleum production, filtration and flow in packed beds. Because it is very difficult to study the phenomenological behavior of flow in porous media, homologs and analogs are used to study flow characteristics. A Hele-Shaw model, made of two closely spaced plates - usually glass — is often used as an analogy to two-dimensional flow in porous media. Hele-Shaw2 showed experimentally that the streamline configuration for creeping flow around an obstacle located between two closely spaced parallel plates is the same as for two-dimensional, ideal flow about the same obstacle. Stokes7 verified these observations mathematically. The usual equation of motion for flow in porous media is Darcy&apos;s law. The form of the mathematical statement of Darcy&apos;s law is identical, within a multiplicative constant, to the expression for the average velocity over the plate gap in the plane of a Hele-Shaw model. These models may be used to describe flow in both homogeneous and heterogeneous porous media. In the mathematical proof of the Hele-Shaw analogy it is assumed that the convective terms in the Navier-Stokes equations are negligible and that the equations of motion degenerate to Laplace&apos;s equation, with pressure the dependent variable. Whenever a Hele-Shaw model is used as an analogy to flow in porous media, .the validity of this assumption is in question. Riegels5 showed that if convection is not neglected, the velocity distribution around a cylindrical obstruction in the flow field depends on a Reynolds number, the plate spacing, and a dimension characteristic of the obstacle. Riegels&apos; solution, a perturbation solution, uses the boundary condition that the flow rate into the obstacle averaged over the plate gap at any point on the obstacle is zero. The method requires that a solution to Poisson&apos;s equation for the perturbation pressure be found. Riegels evaluated this solution for the case of the cylindrical obstruction. His method may be simplified by eliminating the need for solving Poisson&apos;s equation for the perturbation pressure. Instead, an analytic expression for the perturbation pressure gradient is obtained (valid for arbitrary shapes) and used to eliminate pressure from the equations for the perturbation velocities. The results show, for symmetrical shapes, that if NRe < 1, the convective acceleration terms are small, and that the average velocities represent ideal flow up to at least NRe = 3, where: L is a characteristic dimension of the obstacle perpendicular to flow, b is the plate spacing, u is viscosity, v, is velocity of approach and p is density. THEORY* Incompressible fluid flow through a Hele-Shaw model and a porous medium are analogous because the equations for the average velocity components in two-dimensional flow are identical if:

Jan 1, 1970

By V. E. Elliott, C. L. Meyette

THE conditioning of semifinished steel products such as billets, blooms, and slabs to remove surface defects before further processing to finished products is a necessary accompaniment to steel mill rolling operations. A knowledge of the kinds of defects which occur and of the conditions in melting, teeming, and rolling that may lead to their occurrence is favorable to the production of quality products. Surface defects may be classed as either of mechanical origin such as those that occur in the heating and rolling operations and include breaks, tears, guide marks, mechanical laps and the like, or they may have been in the ingot before heating and rolling. Examples of the latter are ingot cracks, blow-holes, scabs, and inclusions which lead to the numerous known types of seams -and surface flaws. Most of the common types of surface defects and methods for their identification by visual examination or by the aid of macro-etch tests are well known. The conditions which caused their formation are also appreciably understood and this knowledge has been instrumental in the establishment of methods for metallurgical control. There are, however, defects of doubtful origin. In any endeavor to trace the causes for their occurrence, the question of first concern is: I. Whether they were formed in the rolling procedure. 2. Whether they existed in the ingot prior to rolling. In the case of semifinished products which are rerolled to finished products there is also the question of whether they were formed in the primary or in the secondary rolling. In metallurgical laboratories where numerous or routine examinations of the quality of rolled products are made over the course of time, there will doubtless be many puzzling cases of defect origin. Microscopic examination of the defects may, however, reveal a characterizing condition that can be used to classify them broadly with respect to their origin. Such a condition has been observed and, after detailed investigation, is described here with the thought that it may offer a useable and relatively simple solution to a bothersome problem. BASIS FOR CLASSIFYING In this discussion the term "mechanical type defects" will be used to designate those that have occurred as a result of the rolling operations such as in rolling from the ingot to billets, blooms, or slabs or in rerolling to finished products. The term "steel type defects" will he used to designate those that were present in the ingot prior to primary rolling or that were in the semifinished product prior to secondary rolling to finished product. The basis for distinguishing between the two types of defects lies in the relative degree of subscale formation surrounding them. Subscale is defined&apos; as a zone of

Jan 1, 1948

By B. M. Larsen

AN increasing amount of attention is being paid to the possible influence of oxygen, in its several modes of occurrence in steel, upon some of the properties of the metal; but clearly investigations along this line are unlikely to yield significant results until reliable analytical methods for the determination of oxygen have been established. This paper presents some results of a study of an improved Ledebur method which aims to determine a definite portion of the oxygen; namely; that which presumably is present in diffusible form in the. solid steel. These more or less preliminary results lead us to believe that the oxygen so determined has some significance; their presentation at this time will, we hope, stimulate discussion of, and focus attention upon, certain rather neglected aspects of the problem. Considerable work has been done recently on methods of estimating inclusions and on the vacuum-fusion method for oxygen; with results which, however, are of somewhat questionable significance. It is commonly presumed that the oxygen in a bath of molten steel in a furnace is present partly as a separate phase consisting of suspended particles of oxides or silicates, partly in solution, the latter being probably the more important. Upon addition of a deoxidizer, it reacts with some portion of the dissolved oxygen and precipitates it as additional suspended particles; the oxygen not eliminated in this way, which remains in solution in the liquid steel, may be regarded indifferently either as dissolved oxygen or as dissolved FeO. When the steel is poured, some of the suspended particles rise towards the surface, others remain trapped in the finished steel, appearing as nonmetallic inclusions in amounts corresponding usually to about 0.01 to 0.03 per cent 02 in the steel. The dissolved oxygen may be partly eliminated as CO during freezing of the ingot, but some remains either in solution or in part precipitated as FeO. Finished steels may thus contain oxygen in several forms: (1) In non-metallic inclusions which are probably quite insoluble in the solid metal at all temperatures; (2) in solid solution which at lower temperatures may be supersaturated; (3) in FeO particles produced by relief of this

Jan 1, 1932