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By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967

By H. B. Pulsifer

ONE of the most common basic open-hearth furnace products is a simple carbon steel with a carbon range from 0.05 to 0.15 per cent. The material is widely used for sheets, tubes, bars, wire and the innumerable special objects of secondary fabrication. The properties of the material vary over wide ranges, depending on the more exact composition and details of manufacture or treatment that affect its structure. The present paper is a review of those properties and structures that have been found by studying this steel as used in the cap screw industry. At first glance this might be thought a narrow application of the steel, but, since the industry uses the material in the cold-worked, annealed and heat-treated conditions, the title of the paper may be excused for its comprehensiveness. Yet, in studying the wide ranges of properties and structures that preclude a more specific title, there can be no suggestion of completeness or finality. Even a summary of a few years' work is no more than a preliminary survey of a field that will be fertile in scientific data and industrial products for many years to come. An outline of the structures will be given first, then a list of the previous contributions that are at hand and finally some details of the work and related problems, especially concerning this low-carbon steel in the surface-hardened condition.

Jan 1, 1931

By K. J. Gill, P. Chiotti

Thermal, metallographic, and vapor pressure data were obtained to establish the phase diagram for the thorium-zinc system. Four compounds corresponding to the stoichiometric formulas Th2Zn, ThZn2, ThZn4, and Th2Zn17 were observed. The melting points of these compounds under constrained vapor conditions were found to be 1055°, 1105°, 1095°, and 1015°C respectively. Four eutectics exist in this system with the following eutectic temperatures and thorium contents in wt pct: 1040°C, 89 Th; 945°C, 79 Th; 1045°C, 55 Th; and 995°C, 35 Th. The standard free energy, enthalpy, and entropy of formation for the compounds were determined from zinc vapor pressure data. ALTHOUGH the thorium-zinc system has been of technical importance in the commercial production of thorium and more recently of interest to some proposed pyrometallurgical separations processes for reactor fuels or blanket materials no detailed investigation of this system has been made in the past. Some previous work has been reviewed by Hanssen.1 The existence of four compounds, Th2Zn17, ThZn4, ThZn2, and Th2Zn has been established and their crystal structures have been studied by X-ray diffraction techniques.2-4 Smirnov et al.,5 determined the solubility of thorium in zinc and investigated the two-phase region between Th2Zn17 and zinc. They calculated some of the thermodynamic properties for these alloys from emf measurements on the cells Th/ThCl4(fused)/Cl2, C and Th2Zn17(s)+ Zn (l)/ThCl4(fused)/Cl2, C. The possibility of reaction between the anode materials and fused thorium tetrachloride to produce a lower valent thorium salt would have to be resolved in order to evaluate the results obtained. The purpose of the present investigation is to establish the phase diagram for the thorium-zinc system and to determine the standard free energy, enthalpy, and entropy of formation for the compounds formed. MATERIALS AND EXPERIMENTAL PROCEDURES The metals employed in the preparation of alloys were Bunker Hill slab zinc, 99.99 pct pure and Ames Lalboratory thorium. The major impurities in the thorium in parts per million were oxygen—1250, carbon—350, iron—100, nitrogen-75, and silicon—70. The metals in the form of several small massive pieces, total weight about 30 g, were cleaned with acid, washed with water and acetone, and dried just prior to their use for alloy preparation. Tantalum containers were found to be suitable for all the alloys studied and were used throughout this investigation. The metals were sealed inside of small 1-in.-diam tantalum crucibles by welding on preformed tantalum covers. A small thermocouple well made from 1/8-in.-diam tantalum tubing was welded in the bottom of each crucible. These crucibles were enclosed in

Jan 1, 1962

By W. L. Saunders

WHEN work was begun in September, 1910, on the rock excavation for the foundation of the gigantic dam at Valhalla, N. Y., which is to convert Kensico lake into an important storage reservoir of the Catskill Aqueduct system, one of the first steps taken by the contractor, H. S. Kerbaugh, Inc., was the development of a quarry to supply the stone needed in the construction work.The importance of a bountiful supply of suitable rock in an accessible location is apparent when it is considered that nearly a million cubic yards of cyclopean masonry will be contained in the completed structure, not to mention dimension and facing stones, concrete blocks, and mass concrete. The dam structure will be over 1800 ft. long and about 170 ft. above the present river bed. However, for a distance of some 800 ft., it will be carried down to solid ledge rock, which will make the finished structure about 300 ft. in maximum height. It will be about 200 ft. thick at the base and directly beneath the coping it will be 28 ft. thick. This dam will raise the reservoir surface 110 ft. above old Kensico lake. The reservoir capacity will be 29,000,000,000 gal.-equal to New York's total needs for over two months. The contract price for this work is nearly $8,000,000 and is second only in amount to the cost, over $12,600,000, of the Ashokan Reservoir work. Fig. 1 is a view of the dam site.

Jan 2, 1914

By L. H. Simons, H. H. Spain

I NT RODUCTION Theory indicates that linear water-floods should exhibit scaling and stabilization properties in both oil-wet and water-wet porous media'. Experimental verification of these proper-ties in oil-wet media was obtained some time ago', and more recently, Perkins', employing a high permeability unconsoli dated sand and a low oil-to-water viscosity ratio, has obtained flooding data in a water-wet medium which follow the pattern of scaling and stabilization. Also, Root and Calhoun3 have found similar trends in the displacement of gas by liquids from unconsolidated sands. In general, however, the experimen-tal evidence appears still somewhat conflicting since scaling and stabilization of water floods in water-wet media has not been observed in most of the studies to date'.".'. The purpose of this paper is to provide a more comprehensive picture of waterflood behavior in water-wet media and to corroborate the validity of the scaling and stabiliza-tion concepts. The need for differentiating between the intrinsic nature of water-oil displacements inside a porous medium and perturbating secondary end effects is discussed, pertinent experimental procedures are outlined and the results of flooding tests conducted at low and at high oil-to-water viscosity ratios on con- solidated, water-wet Alundum cores are analyzed. END EFFECTS IN WATER-WET MEDIA Outlet End Effects The peculiar feature of the outlet end effect in water-wet cores is that it not only results in an excessive wetting phase saturation at the outflow face,'.' but that it also retards the moment of water breakthrough: i.e., causes an undue delay in the appearance of water in the produced effluent. Conditions existing in a water-wet core when water first arrives at the outflow face are schematically shown in Fig. 1. At this flooding stage the saturation distribution, Fig. la, has not yet been distorted by the outlet end effect. A water-invaded pore at the outlet core face, opening into the oil-filled void space between the end of the core and the end plate of the flooding cell, is illustrated in Fig. lb. The curvature of the water-oil interface is concave toward the outlet, and the pressure on the water side of the interface is lower than on the oil side by an amount equal to a certain capillary pressure (Fig. lc). Before the water (of this particular pore) can be produced from the core, it is apparent that the pressure in the water phase must exceed that in the oil outside the core. Accordingly. when water first reaches the outlet face, it will not leave the core but will accumulate inside, and only oil will be produced. Eventually, as the water injection is continued. sufficient pressure is built up in the water to reverse the curvature of the interfaces in the outlet pores, and only then will water be produced from the core. This stage, illustrated in Fig. 2. corresponds to the conventional "water breakthrough" observed in flooding experiments. For purposes of discussion, it is convenient to distinguish between the flooding stage at which water first arrives at the outlet face of a core (Fig. 1) and the stage at which water is first produced from the core ( Fig. 2). The former will be referred to as "water arrival" and the latter water breakthrough. In oil-wet media

By Charles E. Wait

IT is said by some that the occurrence of a deposit of sulphide of antimony in Southwestern Arkansas has been known for fifteen or twenty years. Whether or not such is the case I am not prepared to say, but I am not able to find any record of such a discovery, or any analysis of antimony ore obtained from that section, published at so early a period. The present discoveries, that seem to be attracting some attention, date back to the winter of 1873-74. At that time a vein of ore was found by Mr. Robert Wolf, in honor of whom the vein was named, and still is called, "the Wolf lode." At the time of the discovery the ore was unknown to the prospector, and its composition was not thoroughly understood in that locality until samples were sent to several analytical chemists, who pronounced it sulphide of antimony-stibnite. Since the discovery of this ore there have been three mines opened, and a number of interesting minerals of the antimonial series have been found. I have had an unusually good opportunity to collect specimens from these mines; and it is owing to the constant inquiry concerning the character of these ores that I have collected for publication the results of quite a number of analyses, sufficient I trust to clearly point out their composition. This is one of the few localities in the United States where antimony ore is found in workable quantities; I say workable quantities, because two different shipments of ore have been made to English reduction works, and in both cases excellent returns were made. The discovery of these deposits will, it is hoped, give rise to a prosperous and remunerative industry at no distant day, and when fully developed they may yield ore in sufficient quantity to supply the regulus for the home demand, thus adding wealth not only to those interested, but also to the State of Arkansas. The three mines are situated in the northern part of Sevier County, and may be reached by the St. Louis, Iron Mountain and Southern Railway to Fulton, thence by wagon-road to Columbus, Nashville, Centre Point, and to the mines. During most seasons of the year the

Jan 1, 1880

By L. D. Keller

The application of hydraulic concentration to large scale operations has been effectively accomplished by the use of the SiphonSizer. Operation has been simple, automatic and essentially trouble free. The use of the primary desliming SiphonSizer on magnetic taconites has shown an improvement in grade of concentrate and an increase in recovery over conventional hydroseparators. Magnetic concentrates have been further deslimed and upgraded in SiphonSizers by floating a coarse middling product away from the heavier concentrate. The application of the Siphon-sizer to closed circuit grinding has met with only partial success to date. Hydraulic concentration of minerals has been practiced for a good many years. Until recently, however, the practice has been limited to equipment using a multiplicity of small pockets and relatively low tonnages and flows. The adaptation of the SiphonSizer to the concentration and classification of magnetite has changed this concept. Some fifty commercial units varying in size from a 16-ft diam circular unit to a 25x100-ft rectangular unit are currently in operation on magnetic taconites. Additional units up to 38 ft diam are under construction. Depending upon the application in the flowsheet, upgrading varies from 0.75% to 14% Fe in a single stage. To those not familiar with taconite processing, the importance of the struggle to remove economically as much silica as possible may not be fully appreciated. Perhaps some figures pertaining to transportation costs will underscore this important process. If the silica content of the concentrate from a 10,000,000 ton per year plant could be reduced by I%, a savings in boat freight, at $2.00 per ton, would amount to $200,000 annually! THE SlPHONSlZER The SiphonSizer, as illustrated in Figs. lA, 1B and 2, is a hydraulic classifier in which the hydraulic water is distributed uniformly across the bottom of the vessel by means of a system of headers (1 and 2), jet pipes (3), and nozzles (4). The depth of the teeter bed is automatically maintained by the siphon-float assembly. The feed is introduced through a feed well (5) and separated into two fractions by the effects of rising water and the density of the teetered bed. The magnetite fraction is discharged by the siphon (12) while the fine slime and light middling overflow a peripheral weir (9) to the overflow launder (6). The bed depth is controlled automatically by float valves (7), which are responsive to changes in the height of clear water supported in the superelevation tubes (8) by the density of the teetered bed. On top of the float (7) is a needle valve (10) which permits

Jan 1, 1963

By Albert Sauveur

It is delightful to read a technical paper like that of J. E. Johnson, The Effect of High Carbon on the Quality of Charcoal-Iron, presented in October, 1912, at the Cleveland meeting of the American Institute of Mining Engineers.' The clear, simple, and straightforward manner in which he describes his experiments and results makes you feel as if you had been, so to speak, at his elbow during the course of his investigations, while his method of procedure is so rational that you can fairly anticipate each step in the logical sequence of the tests performed. The following notes suggested by Mr. Johnson's paper are presented here in the hope that they may help, if only a mite, towards the final solution of a problem of considerable scientific and industrial importance. Physical Properties of Cast-Iron us. Its Ultimate Composition. Mr. Johnson writes that " an investigation along the lines of consumption showed that different irons have different characters totally independent of their analyses," and he declares that " the presence or absence of these elements [meaning carbon, phosphorus, silicon, and manganese] alone will not account for all, scarcely for a half, of the facts which have long been known." He further tells us that some foundries have " proved, by the most irrefutable tests, that they could take a certain iron of a given analysis and produce certain results," while with " another iron of the same analysis they could not produce these results at all." I feel confident that every experienced and thinking metallurgist will readily believe Mr. Johnson's statements and will share his views in regard to the hopelessness of inferring the

Jan 1, 1914

By R. P. Rothwell

IN January last I published in the Engineering and Mining Journal a table giving, with a considerable degree of accuracy, the production of anthracite coal for the year 1874. At that time it was impossible to give any correct estimate of the production of bituminous coal, for the returns I had been able to secure from such distant and scattered districts were not always forwarded punctually, and the work of -obtaining anything like a true estimate of the coal mined in districts from which I was unable to obtain official returns was both laborious and tedious. As will be seen from the detailed reports furnished herewith, I have succeeded in obtaining tolerably accurate returns of 20,093,704 tons; and upon careful revision by numerous well-informed local authorities, my first estimate of the amount of coal not officially returned to me has grown very considerably; indeed, as I get more information on the subject I find that our bituminous coal production greatly exceeds the amount we have been accustomed to hear it placed at, aggregating as it does, 26,465,704 tons. Mr. Andrew Roy, State Inspector of Mines for Ohio, has reported the production of Ohio at 4,168,445 tons, while his first estimates were but 3,820,000 tons; and similarly, in other cases, the more full the returns direct from the mines the more incorrect do I find all previous reports. I am able now to furnish, not an accurate statement, indeed, but by far the most full and reliable one that has yet been published of our coal production. The amount of labor involved in obtaining this admittedly imperfect report has been simply enormous. In the following tabular statement it will be perceived that Pennsylvania produces nearly one-half of all the bituminous coal mined * Since this paper was read fuller reports from some of the States whose production had been "estimated" have modified the figures given. The most serious error is in California, which produces probably 200,000 tons less than these figures. Oregon and Washington territories also yield smaller amounts than here reported; but these reductions are probably fully compensated by fuller reports from other States that were here underestimated. The correct aggregate amount will not vary much from that here given. Early in 1876 I will be able to give a fuller and more accurate report for the year 1875.

Jan 1, 1875

By E. H. Herron, J. H. Perry

Mathematical simulation of reservoir behavior may be used to help understand reservoir processes and to predict reservoir behavior, thereby leading to the most economically desirable form of exploitation. In addition, simulation can be used as a tool for reservoir description to learn more about the physical nature of the reservoir and the mode of primary recovery. This use is essential in most reservoir studies and represents one of the more significant applications of simulation. Prediction of reservoir behavior provides information concerning displacement efficiency, optimum well locations, and the comparison of alternative producing processes. Since oil, water and gas all commonly occur in many reservoirs, a simulation that takes into account the simultaneous flow of three immiscible phases is a prerequisite for obtaining such information. Furthermore, a simulation that describes this flow in two dimensions provides the capability of evaluating combination gas- and water-drive reservoirs with either an areal or a cross-sectional description. Many reservoir problems require such a simulation. The objective of the research described here was to develop a mathematical model and associated computer program for accurate, efficient, and economical prediction of the reservoir flow of three phases in two-dimensional geometry. Several authors have discussed multidimensional reservoir simulation of two phases.l-3 Gottfried et al.' presented an analy- sis of three-phase simulation in one dimension. Fagin and Stewart" and Garrett6 have discussed the simulation of three-phase flow in two dimensions, but their solution techniques were different from the method discussed in this paper. In particular, previous models and computer programs have usually involved either fewer capabilities or inefficient and less rigorous descriptions resulting in limited applicability. In the following sections, we present a description of the model, an evaluation of the method, and the application to reservoir problems. Additional and supporting material is presented in the Appendix. The Three-Phase Model General Description The three-phase model consists of the mathematical description of the flow of oil, water and gas in a reservoir. Conceptually this description considers flow in all three space dimensions, but in the subject simulator it is assumed that no flow occurs in the third dimension. The model includes the effects on reservoir behavior of fluid and rock compressibility, viscosity, gravity, capillary pressure, relative permeability and gas solubility. Within the two-dimensional restriction, the reservoir considered may be completely heterogeneous and anisotropic. The differential equations governing multiphase, multidimensional flow in a reservoir are too complex to be solved analytically, so they are approximated by a system of finite difference equations and solved

Jan 1, 1970

By A. E. Anderson, H. J. Hilll

Laboratory data for 155 field muds and 77 .shales have been used to develop correlations to estimate the net streaming potential component of the SP. Analysis of these data and comparison with field tests show that streaming potential corrections must be made to obtain an accurate estimate of the electrochemical potential for use in the determinntion of formation water resi-iiviy. The self-potential curve is related to formation water resistivity, and considerable effort within the oil industry has been directed toward clarifying this relationship. The Schlumbergers and Leonardon1,2 recognized that two types of potentials, electrochemical and electro-kinetic, resulted in the net potential variation in the borehole. Most of the later papers have dealt with the electrochemical component and its controlling parameters. The investigations of Wyllie,2" Salisch' and Moore5 provide the most extensive sources of data on streaming potentials across mud cakes. These authors observed streaming potentials of sufficient magnitude to be of critical importance in SP interpretation, if it is assumed that streaming potentials develop only opposite permeable beds. Streaming potentials across shales have been reported by Schenck and by Gondouin, et al.7 Since SP magnitude is the difference in potential opposite shale and sand beds, these authors suggested that the net streaming potential component may be negligible. The present investigation was initiated to evaluate empirically some of the parameters controlling the magnitude of the net borehole streaming potential and to determine whether useful relations between mud properties and net streaming potential could be established. Field muds were used in this investigation. These muds were characterized by the amount and type of chemical treatment utilized for five days before Sampling. Filter loss, mud resistivity, mud density and filtrate resistivity were determined for each mud with conventional methods and apparatus. Mud filtrate pH was estimated with Hydrion pH paper for the appropriate range. Streaming PotentIals Across MuD Cakes Commercial calomel-saturated KC1 electrodes are subject to potential changes attributed to contamination of the very small fiber-tip bridge by particles of clay from the drilling mud.3 To minimize this difficulty, a large diameter bridge (Fig. 1) was constructed with saturated KC1-agar gel and a filter disc of microporous porcelain. Experiments showed that streaming potentials across this bridge are less than 0.2 mv at pressure dif-

By W. D. Johnston, T. P. Thayer

THE minerals that collectively are known as chromite form an isomorphous series of the general formula (Mg,Fe) 0. (Cr,Al,Fe) 203. So wide is the range in chemical composition in this group that chrome ore consisting entirely of the mineral chromite may range from less than 30 pct to more than 60 pct Cr203. The most comprehensive published data on the chemical com- position of chromite are by Stevens,62 who made complete analyses of 52 samples of chromite concentrate from many localities in North, Cen- [ ] tral, and South America. These samples were mechanically purified to remove associated silicates and might be regarded as the cleanest chromite that could be obtained by any mechanical milling process. Fig 1 shows the predominant zone of isomorphism, within the triangular prism of composition defined by the mineralogical end members of the series, wherein his analyzed samples fell.

Jan 1, 1949

By D. Turnbull, H. N. Treaftis

Precipitation of tin from Pb-Sn alloys (lead-rich) occurs by the nucleation and growth of hemispherical cells which consist of tin lomelloe interspersed in the depleted solid solution. Nucleation and growth of these cells and the tin interlamellar spacing at various compositions and temperatures have been investigated. The interlamellar spacing increases approximately as the reciprocal of the logarithm of the supersaturation ratio. For constant initial tin concentration the concentration of cell nuclei increases with decreasing temperature to a limiting temperature-independent value. The kinetic results support the view that the cell growth rote is governed by the diffusion of tin along the cell boundary. In the main, the results confirm the authors' earlier deductions, drawn from resistometric and calorimetric data, about the precipitation mechonism. IT has been shown1, 2 that tin (ß) precipitates from lead-rich (a) PbSn solutions by the nucleation and growth of cells (cellular or discontinuous precipitation). These cells consist of tin lamellae, with a spacing 1, interspersed in a depleted a solution. Reorientation of a also accompanies cell growth. The kinetics of cellular precipitation of tin from lead have been measured by resistometric2, 3 and ca1orimetric1, 3 techniques. The time-transformation isotherms (t equals time; x, volume fraction of specimen transformed) of the initial rapid precipitation, which drains about 60 pet of the tin from solution, have been described by a kinetic law having the form x = 1 —exp (—bt n) [I] where n usually has the value 3.0. It was shown" that this law and the other kinetic facts can be explained satisfactorily if it is assumed that the cells grow at a constant rate and that all the cells nucleate in a time negligible in comparison with the period of cell growth before impingement. Thus, for hemispherical cells b = (2/3)pNG3 [21 where G is the rate of cell growth in cm per sec, and N is the number of cell nuclei per unit volume. The rapid rate of cell growth at low temperatures can be accounted for"' if it is assumed that the dissolved tin drains to the lamellae edges by diffusion along the sweeping cell boundary rather than by diffusion through the a crystal (volume diffusion). For cell growth governed by cell boundary diffusion it was shown, approximately G=2(X° - X° / X° ) DBA / l2 where A equals the thickness of the cell boundary; D R, the coefficient of diffusion of tin atoms within the boundary; and X° and X, are the atom fractions of tin in the supersaturated and saturated solutions, respectively. Zener8 had already shown that, where

Jan 1, 1959

By V. N. Cox, C. H. Grant

Both the underwater method and the rock cratering method contribute useful information in evaluating and comparing new explosive compositions. Results indicate that metallized explosive systems which contain no high explosives can be formulated to offer more energy and to do potentially more work than other slurry explosive systems. Commercial field trials are presently being conducted with a metallized explosive that does not contain any high explosive. Although there have been only a few commercial blasts to date, the results are encouraging. The Dow Chemical Co. has been engaged in explosives research since 1953. The incentive for this research was based on the desire to find additional markets and uses for magnesium metal of which DOW is a heavy producer. The thermodynamic calculations for explosives incorporating light metals indicate energies approximately twice that of nonmetallized explosives currently being used. Early in 1960, additional patent rights were acquired from independent inventors and a development station at Virginia, Minn., was set up to conduct a commercial testing and market evaluation program with this new product. The actual manufacturing of the explosive was to take place in the boreholes. Due to the complexities involved in controlling the manufacture of the explosive in the borehole, performance was sometimes in doubt. Furthermore, experience indicated that the metallized explosive systems could not be evaluated by the standard laboratory methods then being used, and it was necessary for us to look for more suitable research methods. Tests were conducted on several known methods for explosive evaluation. The most promising were the Navy underwater method for energy evaluation and a modified Livingston crater method intended to compare explosive performance in rock. After shooting over 2000 charges of 8 to 60 lb under water and in taconites and granites with many types of explosives, a metallized explosive was developed which is now being manufactured at a pilot plant in Virginia, Minn. and is being evaluated commercially. UNDERWATER METHOD An underwater method of evaluating explosives has a number of advantages. A permanent site can be established and operated indefinitely. A large number of charges may be fired in a short length of time. The medium in which the explosive is shot is exactly the same for successive shots. Data are recorded electronically minimizing human judgment. A disadvantage of the underwater method is the lack of confinement provided by the water medium. Many explosive compositions require a greater degree of confinement to develop good energy release. Although the relative significance of the two components of energy release that are usually measured, the shock energy and the bubble energy, and their relationship to breaking rock are not clearly understood, the underwater method is a valuable research tool for screening explosive compositions and gaining an insight into the manner in which explosives release their energy. Fig. 1 shows schematically the underwater apparatus. The piezoelectric gages are calibrated tourmaline crystals which convert the shock wave to an electrical impulse which is transmitted to an oscilloscope and recorded on Polaroid film. The shock traces are picked up by scopes 1 and 2. Scope 1 is timed to pick up the full trace whereas scope 2 is timed to cover the first increment of the shock trace expanded, and therefore allows full inspection of the propagation and peak pressures. Scope 3 records the bubble trace. When the explosion occurs, a bubble of gaseous detonation products is formed. The outward momentum of the water keeps expanding the bubble even after

Jan 1, 1963

By R. A. Bosch, F. V. Lenel, G. S. Ansell

RECENTLY, Ansell and aenel' proposed a dislocation model to account for the yielding behavior of dispersion-strengthened alloys. The criterion for yielding used in this model was that yielding occurs when the shear stress due to arrays of piled-up dislocations fractures or plastically deforms the dispersed second-phase particles. Calculations based on this model predict that the yield strength, uysof a dispersion-strengthened alloy containing particles whose geometry permits them to be considered as straight, i.e. not curved, barriers to dislocations follows the relation where and are the shear moduli of the matrix and dispersed phase respectively, b is the Burger vector of a dislocation in the matrix, A is the mean free path between dispersed phase particles and C is a constant. This yield stress, ys, is closely approximated in polycrystalline alloys by the proportional limit. The offset yield stress, uoy, is the yield stress, uys, plus the increase of stress due to strain hardening in the offset strain increment. Previous investigation1 has shown that Eq. [I] describes the yielding behavior of several different dispersion-strengthened alloys as a function of the mean free path between dispersed phase particles at a constant temperature. The purpose of this investigation was to investigate the temperature dependence of the yielding behavior of dispersion-strengthened alloys. The alloys studied, MD2100 and MD5100, are SAP-type alloys containing flake shaped aluminum oxide particles dispersed in a matrix of commercial purity aluminum. The proportional limit and 0.2 pct offset stress of both of these alloys were determined as a function of temperature over the temperature range from -190" to 500 C. All tests were conducted on an Instron tensile testing machine. Stress was measured by means of the Instron load cell. Strain was measured by means of SR-4 strain gages attached to the tensile specimens. Stress sensitivity was 80 psi. Strain sensitivity was 2 x 10F Fig. 1 shows the values received for the proportional limit and 0.2 pct offset yield stress plotted as a function of homologous temperature for both the MD2100 and MD5100 alloys. Inspection of Eq. [I] shows that of the terms which determine the theoretically predicted yield stress, uy,, only the shear moduli have an appreciable temperature dependence. From Eq. [I] the yield stress at any temperature T, UT, may be predicted from the yield stress at any arbitrary reference temperature, in this case 25 OC, u25, by the relation where the subscripts T and 25 refer to the values of the property at test temperature and at 25"C, respectively. The temperature dependence of the yield stress predicted by Eq. 121, based on the observed value for the proportional limit at 25OC, is also shown in Fig. 1. In evaluating Eq. [2] the following data was used. The values for the shear modulus of

Jan 1, 1962

Jan 1, 1959

By Frank Rieber

THE study of earthquakes long ago developed the fact that by studying the travel times of the various groups of waves from the same earthquake, as received on seismographs at varying distances, major discontinuities in the earth's crust could be reasonably well defined. Using this original discovery, and adapting the mathematical methods originally devised in seismology for determining the depth below the surface at which such discontinuities occur, other investigators were able to develop a new branch of seismology which promises to be extremely useful in extending the boundaries of our information on local conditions below the earth's surface. As an outstanding example of the applications of this work, we have the so-called "seismograph" exploration of the Gulf Coastal region, which has resulted in the discovery of a large number of salt domes, from many of which oil fields may be developed. The original seismological investigations, from which different major discontinuities in the earth's crust were deduced, as well as these later successful experiments in locating salt-dome structures, involve relatively simple problems. In each case we are dealing with surface materials in which elastic waves will be propagated with a fairly definite velocity. Under this material we have something quite different, in which the elastic waves will be propagated with a much higher velocity. The transition from one medium to the other is likewise relatively abrupt. For example, in the Gulf Coastal region the sedimentary formations have a velocity of 6000 or 7000 ft. per sec., while the velocity of elastic waves in the cap rock of a salt dome may exceed 15,000 ft. per sec. Under such conditions, delineation of the formation is a relatively simple matter, and, furthermore, there is very little opportunity for ambiguous results.

Jan 1, 1928

By J. B. Fletcher

The Miami mine first started operations in 1910. For convenience, the history of the orebody can be divided into the following categories (Fig. 1): 1) 1910 to 1925: 24.4 million tons of high grade ore, mined by top slicing, sublevel caving, etc. 2) 1926 to 1954: 102 million tons of low grade ore, mined by block caving.

Jan 1, 1961

By R. F. Shurtz

The problem of estimating the precision of systematic samples from a mineral deposit is attacked by interpolating the quality, or other attribute measured, by using Fourier approximation. Such approximation using trigonometric functions yields a particularly simple expression for the variance of the mean value of the attribute sampled. The increasing volume of publication in which the science of statistics has been applied to the problem of predicting the quality of an ore deposit from sets of samples taken from it might lead one to believe that engineering judgment can be replaced by statistics. There is, in fact, an implicit application of the principle of indifference or of "no advance knowledge" which has been discredited in modern statistical theory and practice. These pages will show that it is not always advantageous, efficient, or safe to apply this principle. This problem will be dealt with by using series of orthonormal functions to describe the distribution of the quality of ore in space as contrasted with the more commonly used distribution of quality as a frequency function. Mining engineers are rarely well acquainted with the use of such series or of the functions comprising them. These uses are commonplace in the fields of communication and information theory and it is not surprising that applications taken from these fields should be found appropriate for the analysis of the information contained in a set of samples from an ore deposit. It is hoped that presentation of the following basic, but incomplete, results will generate wider interest in this method and a fuller development of it as well as of the necessary computational techniques. FUNDAMENTAL PREMISES Random variables in the strictest sense are not very common in mine sampling. The sets of samples are almost always taken systematically and are, hence, not subject to all the laws governing random events. Therefore, unless there is indeed random experimental error in the determinations of quality, the treatment of systematic samples of n members as though they were random samples of n members often leads to calculation of confidence limits for the mean quality which are larger than they should be with the result that unnecessary additional sampling is done. The reason for this will emerge in the following discussion leading to Eq. 24 and its generalization. In order to inquire into such questions on a rigorous basis and at the same time avoid arithmetic complications that would obscure the concepts involved, a one dimensional distribution of quality will be assumed. The quality, Q, in suitable units is expressed as a function of the distance, x, along some straight traverse of the deposit. Such a function

Jan 1, 1967

By W. J. Verner, J. R. Lucas

Billions of tons of bulk solid materials are processed through our industrial plants each year, and the tonnage is steadily rising. It has been estimated that for every dollar spent in industry as a whole, approxinlately 30 cents is consumed in the handling of bulk solid materials. It is in this category that tremendous savings are possible through the use of improved techniques. Since World War 11, the mining, steel, chemical, and grain industries, among others have made use of increased materials-handling automation in order to gain some of these savings. However, in a chain of automatic operations, every link must be completely reliable, for if there is a single failure, the whole system immediately becomes ineffective. Only too often the weak link in the chain proves to be the flow of bulk solids from bins. To contribute to the fundamental knowledge in this area, a research study has been continuing at The Ohio State University. The principal objective of the investigation has been to study the internal stresses existing in confined bulk solids. LITERATURE SURVEY Literature studies have revealed that many outstanding people have made contributions to the field of bulk solids. For instance, C. F. Jenkin,1 suggested: a. The pressure on a bin wall is not directly proportional to the depth beneath the surface of material in the bin. b. The vertical pressure distribution on the base of a bin is not actually uniform but is a variable. c. Arches form in bins as a result of very small deformations of the material in the bin. This deformation causes a series of gaps to appear, and consequently causes the disappearance of diagonal forces that cannot act across these gaps. The removal of the diagonal forces causes horizontal forces to be introduced which seem to be the chief cause of arching. 11. A. Janssen,4 in 1895 in connection with his experiments on bins, derived a differential equation to describe both the lateral and vertical pressure in bins with vertical sides. This represents a significant contribution to bulk solid theory, and thus its solution is reproduced as follows: L = KV = RW/U' [l-e -U'KY/R] I where L is the lateral pressure of the bulk solid in psf., V is the vertical pressure of the bulk solid in psf., K is the ratio of the lateral pressure to the vertical pressure at any point, R is the hydraulic radius of the bin in feet, W is the density of the bulk solid in lbs. per cubic feet, U' is the coefficient of friction between the stored material and the bin wall, and Y is the head of material above the point in question in feet. In 1903, Jamieson,6 in an elaborate series of experiments on full sized bins measured vertical and lateral pressures by hydraulic diaphragms. He determined many values for mediums of corn, wheat, peas, and flaxseed. In 1951, Caughey, Tooles, and scheer3 measured both lateral and vertical pressure in deep bins by using strain guages on steel bands. Values were calculated for cement, gravel, sand, soy beans, shelled corn

Jan 1, 1961