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By O. E. Palasvirta

Several drum-type, low-intensity dry magnetic separators have recently been described 1,2,3,4 all of which share at least two generic similarities. The magnet consists of a multiplicity of poles of alternating polarity and, the speed of the drum shell, relatiw to the magnet, is such that the magnetics are agitated through rotation of the magnetic particles around their individual axes. The speed of the drum relative to the magnet (differential speed) determines the frequency of the field reversals. For effective agitation this frequency generally has to be above a specific value, which varies according to the mean particle size of the magnetics. With separators of small diameter, say less than 11/2 ft., a sufficient differential speed for treatment of fine magnetite can be attained only by rotating both the magnet and the drum separately; separators of large diameter may attain sufficiently high differential speeds with stationary magnets. Separators of large diameter thus have the advantage of simplicity of design. The capacity of a separator of this type is directly proportional to the speed of the shell. As the centrifugal force opposing the magnetic force increases at a slower rate than the peripheral speed of the shell when drum diameter is increased, large drums can be operated with higher peripheral speeds. Thus they have a higher capacity than smaller drums. Separation is also a statistical phenomenon, i.e. the grade of concentrate improves as the number of agitations or rotations of the magnetic particles per separation increases. As separators of large diameter have space for a large number of magnets they are best suited for production of optimum grade concentrate. The statements above are general clues For separator design. In the following an expression IS derived showing a more exact relationship between the pertinent separator variables. As both magnetic attraction and centrifugal forces are directly proportional to the volume of the affected bodies, complications in mathematical analysis, arising from variable particle size, are avoided by considering the force per unit volume of affected material. For the magnetic force per unit volume Runolinna (3) gives the following equation: V " 1 + N(ur, - 1) uo dr (1) where ur and uo stand for the relative permeability and the permeability of vacuum, respectively, N is the demagnetization factor, B the intensity of the magnetic field, and r the distance from the face of the magnetic pole. The permeability of a specific magnetite ore can generally be considered as a constant. For ground, liberated material N can also be treated as a constant, and the first simplification can be made by writing ur-1 1=k1. 1 + N(ur - 1) uD k1. Fig. 1 shows the field intensity curves for two U-magnets of different size, but of roughly similar geometry of cross-section as plotted against the distance from the plane of the pole faces. The curves

Jan 1, 1961

By E. H. Jr. Dix

THE use of magnesium as an alloying element in aluminum alloys has been limited, in general, to comparatively small quantities. In duralumin-type, strong-aluminum alloys, magnesium is present to the extent of ½ to ¾ per cent. and various grades of Magnalite and the "Y" alloy of the National Physical Laboratory of England contain up to 1 1/2 per cent. In this country small quantities of aluminum alloy sheet containing 4 per cent. magnesium are produced commercially. All commercial aluminum contains sufficient silicon to convert a portion of the magnesium added to the compound Mg2Si. It is well known that the solubility of both magnesium and magnesium-silicide decrease with decrease in temperature. It is, therefore, impossible to separate the age-hardening effect of the magnesium-silicide from that of magnesium, except by the use of aluminum of such high purity that the silicon content is negligible. The present paper is the fifth1, 2,3,4 of a series from the laboratories of the Aluminum Co. of America reporting the results of investigations of the equilibrium relations in aluminum-rich alloys made from the high purity aluminum manufactured by this company .5

Jan 1, 1929

By M. ROWE, H. E. Gilliland, L. BARNES

The authors of this paper are to be commended for a clear exposition of a timely subject. However, some important conclusions, in addition to those presented in the paper, can be drawn from the results of their elaborate and rather complete numerical computations. First of all, the major part of the calculations presented in the paper are for semi-infinite slabs of oil shale (the authors designate this as Model I) and a question must be posed — Are these elaborate computations needed to arrive at realistic estimates of the shale oil displaced. Consider the model of Lauwerier* that corresponds to the authors Model I if thermal conduction parallel to the fracture be neglected. If one also neglects the finite (but relatively small) heat capacity of the material in the fracture, it is easily shown from Lauwerier's solution that the cumulative oil production would be:

Jan 1, 1969

By D. B. Williams

The end of the war in Europe and the Pacific failed to curb the upward trend of production in Venezuela,- which easily surpassed that of any previous year. The total production for 1945 amounted- to 323,369, 430 bbl., which was 26 per cent over the total for 1944, the previous peak in the history of the oil industry of the country. This increase was caused mainly by the greater demand for petroleum in the last stages of the war; the fact that the danger from enemy submarines had been overcome, which allowed all oil companies to use increased shipping facilities, and the fact that more materials were available for drilling operations. However, the materials supplied were by no means adequate and considerable credit is reflected on the Venezuelan petroleum industry for the increased production obtained by utilizing all available equipment to its fullest extent.

Jan 1, 1946

Who's Who in Mineral Engineering 1977 - SME Membership Directory of the Society of Mining Engineers of AIME

Jan 7, 1977

By Zdzislaw Specht

THIS paper discusses elementary laws pertaining to seismic reflection methods and presents a general and simple criterion for determining the direction of dipping of a reflection horizon from observational data of distance and time. The important development of practical geophysics and the successful results obtained in America, Germany, and other countries, caused introduction of geophysical methods of prospecting in Poland. Of all methods, seismic prospecting has proved most successful in the area of the Carpathian foreland, where new oil reserves are to be expected. Because of the great depth of the sedimentary column in that area, rang-ing sometimes over 2000 meters, it was obvious that only the seismic reflection method could give reliable information regarding the structural features of these strata at such a depth. During the experimental surveys it appeared that the complicated geological conditions of that area do not always allow prediction of the depth and the angle of dipping of reflecting horizons, and for that reason information about the inclination of a given horizon has great importance in the determination of subsurface structure. Therefore the problem arises of obtaining from seismic reflection data reliable information as to the direction of dipping of reflecting strata, without any previous knowledge of the average velocity and depth of geologic horizons under consideration.

Jan 1, 1940

By T. G. Sieber, T. D. Tiemann

The extraction of quartz from siliceous iron ores by dissolution in sodium hydroxide solution has been described in detail in AIME Transactions. l923 data reported covered the temperature range from 230-416°F, where a continuous increase in the amount of silica extracted with increase in temperature was found. It is the purpose of this paper to describe some unexpected results of more recent work exploring principally the range of 500600°F where higher rates and greater amounts of silica extraction were antici-p ted. In brief, the experimental procedure consists in digesting the ore under pressure in solutions of sodium hydroxide, filtering the suspension and weighing and analyzing the dried residue for iron content. The amount of extraction is calculated from the weight loss or from the iron analysis of the residue and that of the original ore.

Jan 1, 1969

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral'iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,' while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By T. F. Witherbee

THE Fletcherville Furnace was built in 1864 and 1865, making its first blast from August until October of the latter year, when it was blown out to prevent its "bunging-up." Repairs were made in time to enable it to be blown in again December 12th, 1865, the blast ending October 7th, 1866. Total product 1921.15 tons iron, an average of 6.8.2.5 tons per day, from ores yielding 44.8 per cent. Consumption of charcoal 223.2 bushels per ton of iron. The furnace journal up to this time shows no record of furnace dimen¬sions, or temperature of the blast, but as near as can be ascertained, they were as follows, viz. Height of stack, 42 feet. Diameter of bosh, 11 feet. Angle of bosh, 7 1/2 inches to 12 inches rise, about 58°. Diameter of open tunnel head, 42 inches. Number of tuyeres 3; each 3 inches in diameter. Dam 15 inches high. Tuyeres 24 inches high. Tymp 22 1/2 inches high. Diameter of steam cylinder, 20 1/4 inches. Stroke 5 feet. Diameter of blast cylinder, 64 inches. The engine is direct-acting horizontal non-condensing. December 26th, 1.866, the furnace was again put in blast, having been considerably altered in the crucible; the height of stack, bosh, and tunnel head remaining as before. Six tuyeres were put in, three in each of the side arches. The hearth or crucible was rectangular in form, 3 feet wide x 32 feet long x 62 feet high. Inclination of bosh 58°. Height of tuyeres 26 inches ; nozzles 2 1/4 inches diameter. Temperature of blast estimated to be about 500°.

Jan 1, 1874

By D. E. Stephenson. Discussion by R. G. K. Morrison, L. Obert

R. G. K. Morrison (Chairman, Dept. of Mining Engineering and Applied Geophysics, McGill University, Montreal, Que., Canada) - The discing of drill core has been a recognized pressure phenomenon for many years but only recently has an interest been taken in the mechanism involved. The work of Jaeger and Cook is referred to in the text. The authors have now advanced the study to establish, within certain loading limitations, a direct relationship between axial and radial stress at failure. This is an important contribution. In mines generally, where pressure conditions result in the spalling of openings, the faces of drifts and crosscuts, on scaling, usually show a concavity with respect to the opening very similar to the face of the drill hole after the separation of the stub. The same holds for shaft sinks. This suggests a similarity between the mechanism of the discing of core and that of the spalling of an opening, under pressure, to develop a more stable outline. The latter, commonly regarded as shear, is the most conspicuous type of failure observed in

Jan 1, 1967

By M. N. Shetty

LARGE copper whiskers (-100 p) of 11111 orientation were tested in a floor-model Instron testing machine, at liquid nitrogen temperature. (Testing methods will appear elsewhere.) Whiskers deformed by twinning after some initial deformation. A load-elongation curve at the onset of twinning is reproduced in Fig. 1. Twinning was confirmed by taking a back-reflection Laue picture, using a slit colli-mator, which showed distinct splitting of reflections. The tensile stress reached just before twinning is about 1.4 x 107 g per sq cm (-7.0 x106 g per sq cm—resolved shear stress) which drops to 1.2 x107 g per sq cm (-6 x 106 g per sq cm—resolved). This twinning stress is about five to ten times larger than the value for bulk single crystals of copper deformed at 77°K (-106 g per sq cm—resolved). Twinning models based on Cottrell-Bilby's pole mechanism are discussed in detail by Venables.' In the present work a mechanism based on the idea of failure of a Lomer-Cottrell barrier by recombination will be proposed. An L-C barrier may fail either by recombination or by dissociation.3 Fig. 2 provides the necessary information. It shows that the stress necessary to break such a barrier is about 1.8 x 107 g per sq cm by recombination and 4 x 107 g per sq cm by dissociation at 77°K. The twinning stress reached by whiskers is comparable to the stress level required for failure of an L-C barrier by recombination. (Stroh himself points out that his calculations should not be taken too literally.) We consider a segment of the L-C dislocation which has recombined (AB in Fig. 3) over a length to form the total dislocation which then glides in the

Jan 1, 1965

By R. A. Wattenbarger, H. J. Ramey

The trend in gas well testing has been to rely more on the early-time flow data of drawdown and buildup tests than on stabilized flow tests. The stabilized testing methods often are not adequate for complicated modern gas reservoirs because many of these reservoirs have extremely low permeabilities and the transient flow period of a well test can last for days or weeks. It has become common to augment the flow capacity of gas wells by hydraulically fracturing their producing formations. In deep reservoirs the induced fractures are generally vertical and tend to follow a single plane of weakness. The presence of a vertical fracture at the wellbore complicates the transient flow behavior of a low permeability gas well. The flow is further complicated when turbulence occurs near the wellbore. Russell and Truittl published transient drawdown solutions for vertically-fractured liquid wells. They developed methods of drawdown and buildup testing utilizing these solutions, which were based on numerical simulation. Clark2 applied the basic Russell-Truitt solutions to analyze fractured water injection wells by falloff tests. Field examples were given to substantiate the method of analysis. The Russell-Truitt solutions and well testing methods can be extended to gas well flow. Millheim and Cichowicz3 presented the drawdown equations for *Now with Scientific Software Corp., Denver. ideal gas flow, including the effects of formation damage and turbulence. Two actual field cases were presented, both of which exhibited extensive fractures and turbulent flow. For the pressure range of these well tests, the use of ideal gas equations was acceptable. These field cases were significant in being the first published data showing the occurrence of turbulence in fractured gas wells. We, also, observed such cases in practice. Our purpose here is to extend the theory of fractured gas well testing to the flow of real gases. To determine the effects of wellbore storage and turbulence on well test interpretation, we developed a finite-difference model to simulate well test conditions. Since gas wells usually are widely spaced and have high compressibility, the emphasis has been put on the early transient behavior before the effects of the outer boundary are noticeable at the wellbore. The Mathematical Model The geometry of our mathematical model is similar to that used by Prats.4 The well is centered in a circular uniform reservoir. A vertical fracture of infinite flow capacity penetrates the formation and passes through the wellbore. The wellbore itself is not important. Fig. 1 shows a sketch of the problem. Fig. 2 shows the idealized model. The equation for the flow of real gas in a porous medium with uniform porosity, permeability and thickness is5-7

Jan 1, 1970

By L. B. Davidson

The petroleum literature contains many reports on the relative permeability properties of porous media. However, only recently have studies of relative permeability at elevated temperatures been made.1 -5 Each of these studies presents relative permeability data on water-oil systems in linear sandpacks or sandstone cores under isothermal conditions. The results of these investigations are dissimilar. Edmondsonl found that in Berea sandstone a temperature-dependent effect was present, while Shilobod,2 using the same material, found no temperature dependence after normalizing for initial water saturation. Workers at Texas A&M U.3-5 found that the ratio kw/ko was temperature dependent in an unconsolidated system. The differences in results of these studies are probably a consequence of differences in the material employed, in the experimental procedures followed, and in the properties of the porous systems used. This paper describes an experimental investigation of permeability ratio temperature dependence, conducted to clarify some of the results obtained by previous workers. Each experiment described in this paper involved the isothermal displacement of Chevron No. 15 white oil by either nitrogen, steam, or distilled water and displacement of water by nitrogen. All permeability ratios were calculated using the Welge procedure. Values of the water-oil permeability ratio were obtained over the temperature range 75OF to 540°F. Results indicate the ratio is temperature dependent at low water saturations, probably due to interfacial effects. However, as the saturation is increased, temperature dependence decreases until, above some minimum saturation, the ratio becomes insensitive to temperature. Previously published work indicates that the dependence reappears at very high water saturations, a region of the ratio curve not completely examined in the present study. It appears that water-oil permeability ratios are temperature dependent at the extremes of the ratio curve where changes in interfacial tension with temperature induce variations in residual saturations. Between the extremes, there is a region in which the permeability ratio is insensitive to temperature. The size and location of this region is probably a function of the characteristics of the porous system. Gas-oil permeability ratios calculated from nitrogen-white oil displacement experiments indicate a definite temperature dependence over the range 75OF to 500°F and over the entire gas saturation range studied. Evidence discussed in this report indicates that this dependence is a consequence of molecular slippage in the gas phase. This is an extension of the Klinkenberg effect6 to two-phase systems at high temperatures (the existence of slippage in two-phase systems at room temperature has been demonstrated7). Evidence for a similar source of temperature dependence in superheated steam-white oil experiments

Jan 1, 1970

By H. H. Stoek

MINE models have three distinct uses: 1. As exhibits in expositions and museums. 2. As exhibits in law suits. 3. As illustrations in teaching mining engineering. All three uses are in a sense educational. The third, or distinctively teaching function, has not been extensively developed in America as it has been abroad, chiefly because of the cost of the models and the scarcity of model makers. In connection with expositions, such as the Columbian, the Louisiana Purchase, and the Panama-Pacific, a number of very good mine and metallurgical models were prepared with funds furnished by State commissions, by mining organizations or mining companies. At the close of these, expositions, some of these models have been deposited in National or State museums or in educational institutions, but too many of them have been lost, or have been stored, away in some mining company's office or in the basement of some State building, where they have been lost sight of and have gradually fallen to pieces. A visitor to a German mining school is impressed by two facts: 1. The mining laboratories are in general inferior to those in America. 2. The mining museums are infinitely superior -to ours, particularly in models exhibited. One may reply to this comparison by saying that a museum is necessarily a work of time. From the historical standpoint this is, of course, true, but it is not necessarily true in connection with a working museum intended to illustrate current practice. For instance, the oldest mining school in Germany, that at Freiberg, has much excellent historical material, but very little on modern practice, while Berlin, one of the youngest German mining schools, has a most extensive and valuable collection of modern appliances and models. This is true in spite of the fact that one of the best-known model shops is at Freiberg, from which many of, the models to be seen in America have come. Because many of the models in American mining schools have come from

Jan 4, 1917

By J. M. Weehuizen

Complete details are given of the drilling method by which two shafts were sunk at the new Beatm'x mine of Staatsmijnen in the Netherlands. The nature of the rock strata in the Dutch mining district determined choice of the drilling rather than the freezing method. Data for each step and details of the equipment used are given in the illustrations. Staatsmijnen was founded in 1902 with government financial backing, but it is run as a private enterprise, on a commercial basis, with the normal fiscal obligations. The company now has four mines in operation with annual outputs amounting to 7 1/2 million tons of coal. In 1952 it was determined that a new mine—the Beatrix—would be opened. Details of the shaft-sinking operation are described in this paper. SHAFT LOCATION The coal-bearing carboniferous rock in the Dutch mining district is overlain almost completely by soft water-bearing strata, which at the site of the new shafts are about 1600 ft thick. The sinking of the new shafts through this soft water-bearing overburden (Fig. 1) is a costly and time-consuming affair. From the two availaible sinking methods: 1) Poetsch's well known freezing method or 2) the drilling method of Honigmann-de Vooys, the latter was preferred, not only because of its relative cheapness, under the prevailing conditions, but primarily because by using the drilling process, a special type of shaft lining of steel, concrete, and bitumen could be used. The new shafts, located 330 ft apart, have an inner diameter of 18 ft, 4 1/2 in. The boreholes, which have a diameter of 25 ft and which were drilled through nearly 1600 ft of overburden and some 100 ft of carboniferous, each contain more than 29,000 cu yd—by far the largest in the world. DRILLING METHOD The drilling method is based on the use of mud-flush—a thin mixture of clay and water—to keep the borehole filled during the entire drilling period and during insertion of the lining (Fig. 2). The pressure of the mudflush against the borehole wall is greater than that of the water in the surrounding

Jan 1, 1961

By Robert M. Funk, James E. Lawver

The development of a laboratory and pilot-scale high-tension electrostatic flowsheet for the production of iron-ore super concentrates having silica contents in the range of 0.1% is presented, A variety of hematite and magnetite ores were tested with this flowsheet, and the pertinent metallurgical data are given. The applications and limitations of this process are brought out in terms of both practical and theoretical considerations. There have been many new developments in the past few years that have required mineral beneficiation engineers to consider new techniques for iron-ore concentration. Developments in iron powder metallurgy, and particularly the making of sheet metal directly from high-purity iron-ore concentrates, and the concept of using metallized pellets as a substitute for scrap in electric-furnace steelmaking have created demands for what is commonly referred to as iron-ore superconcen-trates. In most cases, specifications for superconcentrates are that they contain less than 0.1% total gangue, with some applications requiring less than 0.05% gangue. To produce these concentrates, new and modified processes are being developed, and the three methods receiving attention as the primary concentrating methods are: 1) Magnetic separation in which dry rotor-type equipment is used for magnetite and the high-intensity magnets are used for hematite. 2) Amine flotation. 3) "High-tension" electrostatic separation (or, elec-trodynamic concentration). This paper examines the high-tension electrostatic process in terms of its limitations and abilities for the production of iron-ore superconcentrates. A technically effective and simple flowsheet was developed through laboratory and 5 and 100-ton pilot-plant studies for the production of concentrates containing from 0.02 to 0.20% SiO, with iron recoveries between 85 and 90%. The process is also shown to be economically feasible. Laboratory Test Program Separation Characteristics: The suitability of the electrostatic high-tension method for iron-ore supercon-centration stems from the fundamental mechanism governing the process, i.e., particles are separated on the basis of differences in electrical conductivities. This conductivity is a characteristic property of minerals, and if the difference between the conductivities of two min- erals is great enough, then their separation can be performed by a high-tension machine. As shown in Figs. 1 and 2, the critical factor is the time necessary for the particle charge density, which is established by a corona discharge field, to decay to a level such that the centrifugal force acting on the particle exceeds its electrostatic, or image, force. At this point, the particle can leave the rotor at some trajectory and fall into an appropriate product receptacle. This decay time is directly proportional to electrical conductivity, and the process variables, such as feed rate, rotor speed, electrode configuration, and rotor composition, are selected to optimize the ability of the separator to resolve different conductivities. Table 1 lists the measured conductivities for some of the iron and gangue minerals used in developing the flowsheet. These results were obtained by using the conductivity cell described by Lawver and Wright.' The discharge curve of most minerals that lend themselves to super concentration by high-tension is so fast that the

Jan 1, 1971

By R. P. Harvey, J. E. Walstrom, A. A. Brown

In view of the large number of wells directionally drilled from offshore platforms and urban drillsites, greater interest is being focused on the directional survey and on the uncertainty inherent in calculating the position of the bottom of the hole, or other benchmarks in the wellbore. Of the two methods presented here for evaluating this uncertainty, the first is analytical and uses the principles of probability and statistics. The second method uses Monte Carlo simulation to generate a pattern of the scatter of possible bottom-hole locations. Both methods are based on a model for which the usual assumption is made that the curvilinear axis of the wellbore is adequately represented by a large number, M, of linear segments joined end to end from the top to the bottom of the hole and closely following the course of the hole. The errors due to this approximation are assumed to be negligible and are not studied here. One form of the model is to consider that for a given hole there exists a perfect set of data describing it, of the above form. Each linear segment has an angle of inclination with the vertical 7, in radians, an azimuthal angle from true north xi in radians, and a length Si, in feet. The subscript variable, i, extends from 1 to M. Each of the M linear segments representing the axis of the wellbore has three components in the X, Y, and Z directions. These components are calculated from the equations: The bottom-hole coordinates as determined from the reference set of data for the wellbore are given by the following for i = 1 to M: X=SX, Y = Sy, Z=SZ; . (2) A directional survey instrument, lowered into the wellbore to the M segments, or stations, measures the values of the 7; and the 3,. In general, because of errors from various sources, the resulting angular measurements will not be precisely equal to the 7" and xi. Random variables l, and Ai are therefore considered with associated probability density functions fi(li) and gi(Ai), respectively, which represent the distributions of potential survey measurements for this hole. Since it is assumed that the values Si are accurately measured they are treated deterministically. The random variables corresponding to the surveyed bottom-hole coordinates are given, for i = 1 to M, by:

Jan 1, 1970

By R. D. Pehlke, J. V. Gluck

AS a portion of a general study of liquid-metal thermodynamics, high-temperature galvanic cells were used to study the effect of added dilute solutes on the activity of zinc in dilute solution with molten bismuth in the range 450° to 650°C. 1,2 The cells were of the type The experimental procedures have been described previously.1 In the course of studies conducted in the bismuth-rich corner of the systems Bi-Zn-Au and Bi-Zn-Cu, marked discontinuities were observed in the electromotive force-temperature relations for a number of the experimental compositions. Above the discontinuity temperatures, the relations, which were linear, exhibited slopes similar to the binary alloy of the same mole fraction zinc, as shown in Figs. I and 2. Below the discontinuity temperatures, the slopes were markedly different, but the relations remained linear. In general, as the amount of the third eletnent was increased, the slope of the lower portion of the relations tended to become less positive. The slopes of electromotive force-temperature relations reflect the entropy of mixing of zinc and, therefore, the occurrence of a discontinuity marks the transition between two different equilibrium situations involving the solution of zinc. A number of other investigators3-5 have used such observations to determine liquidus boundaries in binary alloys. Since the upper portions of the ternary electromotive force-temperature relations of this study had the same slopes as the binary alloys, the discontinuities are interpreted as marking the transition between the single-phase liquid region and the underlying two- and three-phase regions. Reference to the Zn-Bi equilibrium diagram6 confirms that the binary alloys were single-phase liquids at the experimental temperatures. Fig. I shows the electromotive force-temperature relations for the alloys containing Bi-Zn-Au and Fig. 2 shows similar relations for the Bi-Zn-Cu alloys. In the lower portion of each figure, the temperature of the discontinuity is plotted vs the mole fraction of the added solute at the various levels of zinc concentra- tion. Cross-plots from these curves at constant temperature permitted the construction of the partial liquidus surface isotherms shown in Figs. 3 and 4.

Jan 1, 1967

By F. D. Richardson

STAFF: Editor, Gerhard Derge Carnegie lnstitute of Technology Schenley Park Pittsburgh, Pa. 15213 Editorial Assistant, M. A. Redmerski Production Editor, Otto T. Johnson THE METALLURGICAL SOCIETY: Jack H. Scoff, President; Richard C. Cole, Past-President; Harold 0. Emerick, President-Elect; Ralph L. Hennebach, Treasurer; Robert W. Shearman, Secretary; Donald A. Parks, Assistant Secretary; Leslie S. Wilcoxson, Assistant Secretary. PUBLICATIONS COMMITTEE OF THE METALLURGICAL SOCIETY: R. E. Lund, Chairman; T. E. Dancy, H. O. Emerick, P. R. Gouwens, R. E. Grace, J. H. Jackson, H. H. Johnson, A. E. Lee, Jr., R. R. Nosh, R. D. Pehlke, and Paul Queneau. Review and selection of manuscripts is under the supervision of the following Publications Committees: Extroctive Metallurgy Division: R. E. Grace, Choirmon; G. M. Bell, D. W. Bridges, J. M. Cigon, G. W. Heoly, T. A. Henrie, R. D. (Holli-doy, C. E. O'Neill, C. S. Somis, A. W. Schlech-ten, and Charles Shull. Iron and Steel Division: R. D. Pehlke, Choirmon; T. P. Floridis, Arnulf Muon, G. R. St. Pierre, E. T. Turkdogan, L. H.Von Vlock, and J. M. Uys. lnstitute of Metals Division: H. H. Johnson, Jr., Chairman; J. B. Clark, Vice Choirmon; M. R. Achter, G. F. Bolling. J. O. Brittoin, G. P. Conard, II, R. S. Davis, L. A. Girifolco, G. T. Hohn, J. P. Hirth, L. Himmel, G.T.horn, George Krauss, J. D. Livingston, R. D. Manning, H. M. Otte, S. V. Rodcliffe, R. E. Reed-Hill, H. C. Rogers, E. ScaIa, O. Sherby, M. T. Simnad, G. R. Speich, E. A. Steigerwald, R. A. Swolin, W. A. Tiller, W. R. Upthegrove, J. B. Wagner, Jr., Derek Wolton, H. W. Weart, W. W. Webb, and D. Published seven times yearly in February, March, April, June, August, October, and December by the American lnstitute of Mining, Metallurgical, and Petroleum Engineers, Inc., 345 East 47th Street New York, N. Y. 10017. Telephone PLAZA 2 -6800. Subscription $30 per year for non-AtME members m United States and North, South, and Central America; $32, foreign; $7.50 for AlME members Single copies, $6.00, single copier foreign, $6.50. The AiME is not responsible for any statement made or opinion expressed in its publications . . . Copyright 1964 by the American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. . . . Registered cable address, AiME New York Indexed in Engineering Index, Industrial Arts Index, and Chemical Abstracts. Second dost postaas poid ot New York, N. Y.,ond Ann Arbor, Mich. Volume 230, Number 6.

Jan 1, 1964

By Hubert E. Risser

Although, for about a half-century the percentage of coal production provided through strip mining has steadily increased, recent trends indicate that a peak in percentage (not tonnage) is being approached, principally because of the decline in economic adrantage enjoyed by strip mining compared to underground mining. Factors contributing to the decline are the decrease in the margin of advantage in manpower requirements held by strip mining; an increase in depth and volume of overhurden, requiring larger equipment and capital investment; increasing lack of reserve land blocks large enough to support extensive strip mining operations; more stringent legislation for reclamation of stripped land, with increasingly higher costs of such reclamation; and the increasing costs of land surface rights for strip mining. Already there has been a peak and suhsequent decline in relative importance of strip mining insome major Eastern coal-producing states; trends indicate that a peaking for the whole Eastern region is on the way. Although, in the West the pressures are less severe, they will, nevertheless, reduce to an increasing degree the advantage that strip mining has possessed. For about half a century, strip mining has been providing an ever-increasing share of total coal output in the United States, and in the past 30 years this share has grown from less than 8% to 33.7%, as shown in Fig. 1. Fig. 1 also shows that strip mining is gaining faster in the West than in the East. From 1961 to 1967, output from strip mines grew 63.6 million toqs, or 52.2%. Certainly there is nothing in such performance to indicate any peaking in the level of strip coal-mine production. But the fact is that, if not in actual tonnage, strip mining appears to be reaching its peak in relative importance, at least east of the Mississippi River. And the area east of the Mississippi provides 90.0% of the strip and 94.9% of the total coal production of the nation. The relative economic advantage which spurred strip mining's growth for a third of a century has been diminishing markedly in recent years. Fig. 2 shows evidence of this decline. From 1947 until 1961, strip tonnage output remained fairly stable, at the end of the period showing only a 12.5% decline. Meanwhile, underground coal production fell 44.5%. As the result of the greater decline in underground coal, strip coal in 1961 furnished 30.3% of the total coal produced, compared to only 22.1% in 1947. In the succeeding six years, however, underground coal output increased by 76.5 million tons, while strip output increased only 63.6 million. Further evidence of the strengthening of underground coal's relative position — or if you will, the weakening of strip coal's position — can be found in the major coal stripping states: Illinois, West Kentucky, Ohio, Pennsylvania, Indiana, and West Virginia, which in 1966 provided 80% of the nation's strip coal. Fig. 3 shows what has been happening in three states lying in the Appalachian field and in the total output of these three states. In the figure, the column height represents the output of coal mined by all methods. The number at the base of each column is the percentage mined by stripping. In Pennsylvania and Ohio, the percentage of strip mining increased between 1956 and 1961, but by 1966 had declined from the 1961 level. In West Virginia, a decline occurred during the first five years but was followed by a rise. In January 1968, Coal Age published an article listing the locations and capacities of new large mines in the planning and construction stages that would be operating by 1968-1971. The plans for West Virginia and Pennsylvania indicated all the new mines would be underground. Except to the extent they might replace existing under-

Jan 1, 1970