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By J. W. Downey, A. E. Dwight, R. A. Conner

THE MgCu2 type Laves phase has been observed in the thorium-osmium and thorium-iridium systems. Two alloys corresponding to ThOs2 and ThIr, were prepared by arc melting a 5-g charge in a water-cooled copper. crucible. Both alloys were very brittle. X-ray diffraction patterns were obtained using filtered Cu and Co radiation with a Straumanis-type DeBye-Scherrer camera. The a,, values as shown in Table I were obtained by a Nelson-Riley extrapolation. The structure belongs to space group Oh7-Fd3m. Relative intensities for each of these compounds were calculated on the assumption that 8 thorium atoms occupy (a) positions and 16 osmium or irid-ium atoms occupy (d) positions. The calculated intensities are the product of the Lorentz-polarization factor, the multiplicity factor and F', the structure factor, neglecting the absorption and temperature

Jan 1, 1959

The 140th meeting* of the American Institute of Mining and Metallurgical Engineers was held in New York, Feb. 16 to 19, 1931. It consisted of the annual business session, twenty-six technical sessions at which 149 papers were presented, two round table discussions, two meetings of the Board of Directors, three meetings of Section Delegates, two formal lectures, four group dinners and 11 group luncheons, luncheon daily for members and guests, 20 committee meetings and conferences, the annual reception and dinner dance, an informal dance, a smoker-dinner, two meetings of the Woman's Auxiliary and a special program of entertainment for the ladies. Former members of the Rocky Mountain Club and friends lunched together at the Engineers Club on Tuesday. The proceedings of the Iron and Steel Division included four general technical sessions, an Iron Ore Round Table, the Howe Memorial Lecture, the Division luncheon at the Engineers Club Wednesday noon, a session each of the Executive Committee and the Committee on Nondestructive Testing, a luncheon each of the Committee on the Manufacture of Alloy Steel and the Blast-furnace Conference Group, and a dinner of the Committee on Physical Chemistry of Steelmaking. Dr. F. F. Lucas delivered the Howe Lecture, the title of which was "On the Art of Metallography." The Institute of Metals Division held three general sessions, its annual lecture, which was delivered by Dr. Arne Westgren and entitled "X-ray Determination of Alloy Equilibrium Diagrams," and a Division dinner at the Hotel New Yorker Thursday evening, at which Dr. G. W. Thompson was the principal speaker. The Executive Committee assembled at a luncheon on Thursday. A round table on Coal Land Valuations, a general technical session and a Division luncheon were held by the Coal Division. C. E. Bockus, President of the National Coal Association, made an informal talk at the luncheon which was held at the Engineers Club Monday noon. The Petroleum Division held six general sessions, including its annual production symposium. The annual dinner was held at the Engineers Club Thursday evening. A Gold Supply Symposium was the feature of the proceedings of the Committee on Mining Geology. This Committee also held a general session and a luncheon meeting. Sessions were held by other Technical Committees as follows: Mining Methods, 2; Mine Ventilation, 1 (besides which the Committee on Mine Ventilation Code held a meeting); Ground Movement and Subsidence, 1; Milling Methods, 1; Nonferrous Metallurgy, 1; Engineering Education, 1 (also a Committee luncheon); Non-metallic Minerals, 1, and Geophysical Prospecting, 2.

Jan 1, 1931

By V. B. Tare, H. Schmalzried

The use of solid electrolytes for determining kinetic paraneters at elevated tevnperatures is pointed out. The reaction rate constant k1 of the phase-boundary reaction during oxidution of iron to wiistite by CO2-CO gas mixtures has been deternined between 850 nnd 975C, using ZrOz(+CaO) as an electrolyte. Values are between 1.4 x 10-a and 5.2 x 10 ole per sq ctn atm. The tzain difficulty is due to mixed potentials arising from side reactions at the electrolyte inteyface. In a number of papers the calcium-doped zirconia electrolyte has been used for the determination of thermodynamic data from measured differences in oxygen activities (or potentials) between two electrodes. The purpose of this note is to suggest the use of this solid electrolyte for kinetic measurements as well. The principle can be seen from Fig. 1. A thin and compact phase II (electron conductor) is fixed on a plate of gas-tight, polished ZrO2(+CaO) (I), which separates two compartments with different oxygen potential. p, is a constant reference pressure of oxygen (1 atm). The electromotive force of this galvanic cell is given by E = RT5 In pep, and pe is the oxygen partial pressure at the interface electrolytephase 11. If phase I1 is in equilibrium with the surrounding gas phase, p, = DR. If pg changes sud- denly to a value pi, p, and therefore the electromotive force, E, change as a function of time according to the phase-boundary reaction rate at the gas phase I1 interface and the transport processes inside phase 11. It is assumed that local equilibrium is established at the boundary electrolytephase 11, that the gas phase shows no concentration gradients, and that the con-

Jan 1, 1967

By C. R. Pelley

This paper describes the analytical characteristics of Western subbituminous coal and the manner in which these characteristics apply to their use in a utility-sized steam generator. It compares these characteristics with those of typical Midwestern coal and Eastern bituminous coal. The paper also reviews in detail the design considerations that must receive attention when various blends of these three coals, or any combinations thereof, are planned to be used. This research paper describes variations in analytical and utilization characteristics when coals from different origins are blended in order to achieve a predetermined sulfur content for the purpose of predicting sulfur oxides emissions as they affect environmental regulations and the resulting alterations in utilization characteristics such blending would cause, and how such blends of coal would affect a utility-sized steam generator.

Jan 1, 1979

By Marion Rice

The copper-mining district of Jerome, Ariz., is of such economic importance that the following brief notes may be of interest. The ore deposits are said by Ransome1 to be pre-Cambrian, and are contained in the pre-Cambrian schists of the region. In the vicinity of the mine (the United Verde) the schist stands nearly vertical and strikes a little west of north. At least three varieties are distinguishable—(1) a green rock, schistose on its margins but grading into massive material, which is evidently an altered dioritic intrusive; (2) a rough gray schist with abundant pheno-crysts of quartz, apparently an altered rhyolite; and (3) a satiny, greenish gray, very fissile sericitic schist that may be a metamorphosed sediment. The ore occurs in varieties (2) and (3), the main belt of dioritic rock (1) lying just west of the orebodies. The ore is said to follow as a rule the layers of fine sericitic schist. T. A. Rickard2 Says that the ore at the United Verde Extension mine is found at the contact of diorite and schist, that both diorite and ore are earlier than the regional metamorphism, and that the quartz porphyry ("rhyolite" of Ransome) is of post-Cambrian age. The material considered here, a part of which was gathered by the writer, came from four of the mines of the district, and its study was undertaken at the suggestion of Dr. Berkey of Columbia University. The field relations and exact locations of the different specimens are not known, but a microscopic study of the thin sections gave some evidence as to the origin of the ore, which will be discussed below. The indications are that both ore and porphyry were introduced at the closing stages of the metamorphism, this being in accord with Ransome's view of the genetic relation of porphyry and ore rather than with the opinion that the ore is related to the diorite. Certain field occurrences mentioned in the literature also support this theory. Rickard, in the same article to which reference has been made, speaks of a vein of chalcocite several inches wide at the contact of one of the porphyry dikes, and Provot,3 although he regards the porphyry as subsequent to the ore, says: "Acid dikes encountered underground should be followed as they have been found in practice to lead to orebodies."

Jan 1, 1920

By J. D. Forrester

SINCE the introduction of the first percussion rock drill in about 1850, drilling equipment has undergone a progressive evolution so that a wide range of special classes of machines now are marketed by several manufacturers. Essentially all of the drilling machines presently employed for blasthole drilling are of the hammer-drill type. They are classified as hand-held hammers (jackhammers, sinkers, etc.), drifters (light or heavy), and stopers and are of many sizes; varying in weight and rotative and blowing power. Most makes of drill machines fundamentally are the same in principle of operation as they are designed to strike a blow on the end of a drill rod in the manner of early-day hand drilling. However, beyond this common characteristic, the similarity among different makes ceases. In choosing between similar machines of one make or another, it is important to remember that rock drill manufacturers have not attempted to standardize drill parts, the result being that a mine operator must approach, because of replacement parts, standardization by limiting the makes of machines used. The present-day selection of any particular drilling machine is dependent fundamentally on its inherent ability to make a hole, or series of holes, as speedily and as cheaply as is possible. Two categories of controlling elements become apparent in any analysis devoted to making the choice of a drill, namely: 1-Conditions under which the equipment is to be used, such as mining method practiced, type of labor available, character of rock material. 2-Physical characteristics or features of the given drilling machine. Regardless of the controls of class 1, above, the elements of this category are fixed by several factors. All of them are interrelated and, though some often are more important in one case than in another, an unfavorable variation of any-others being essentially equal-is sufficient to discredit the optimum applicability of the particular drill machine. The relative factors in the selection of a machine are as follows: First cost-This is not generally an important item on a comparative basis as the marketing of drill machines is highly competitive and most makes are priced closely.

Jan 1, 1952

The Murray Plant of the American Smelting & Refining Company is situated seven miles south of Salt Lake City, and has a fine view of the Salt Lake Valley with its fertile farms and orchards. It is located on the Los Angeles & Salt Lake and Denver & Rio Grande Western Railroads, and has a fine electric car service, cars running every 15 minutes. The beautiful and majestic Wasatch range lies about five miles to the east and the Oquirrh Range to the west, and from these mountains a large proportion of the ores treated are obtained.

Jan 1, 1925

By Robert E. Tally

CHAUNCEY L. BERRIEN, Butte, Mont. (written discussion).-Having had much actual experience with mine fires which have occurred or have been active in the mines of the Anaconda Copper Mining Co. during the past 4 years and having lately visited the fire zone of the United Verde mine with Mr. Tally, I wish to congratulate him for the success which he has had in controlling this fire and making the mine perfectly safe .for his miners. By this work he is not only keeping the property in operation but is reclaiming many lost orebodies. The ventilation system as described by him is practically the same as that used under my direction at the Mountain View mine fire in Butte in 1913 and at the Pennsylvania fire in 1916. This same system is at present being followed at the Leonard mine to extinguish a fire which has been active for 10 years although bulkheaded. The mining system in the Butte mine, at the origination of these fires was the same as that at the United Verde, namely, square setting .accompanied by the use of much timber bulkheading in the stopes owing to heavy ground. The pyritic content of the ore in Butte is not as high, but on the whole conditions have been the same, with the exception of actual location of the fire in the mine. I agree with Mr. Tally that flooding, the use of C02 or any gas, and the use of steam are all impracticable unless the fire zone can be absolutely sealed. His system of upcast escapement shafts in the fire zone, the use of bulkheads and fans to keep the gases away from the firemen, must be resorted to. By the method lie describes actual stoping may be carried on safely if started from the bottom of the fire and if the fire zone extends to the surface. In other words, the fire zone must be isolated from the rest of the mine by bulkheads and solid ground, with no ground above which can be damaged by spread of fire or caving. The serious fires in Butte have .occurred on or between levels in the mines where it was necessary to prevent their .extension upward, downward and laterally while the work of actually extinguishing them was in progress. This necessitated proper bulkheading should we lose control of the fire, the installation of ventilation similar to Mr. Tally's and the systematic drilling of holes with diamond drills for distributing water on the fire and around it.

Jan 12, 1916

By William S. Hannan, H. Rush Spedden

Flotation may be defined as a process whereby mineral particles are concentrated by selective adhesion to air-liquid interfaces. The process involves attachment of desired mineral particles to air bubbles, and removal of the mineralized air bubbles from the surface of the pulp as a mineral concentrate. Problem Although great strides have been made in understanding the principles of flotation, one part of the process which has not been adequately explained is the mechanism by which selected mineral particles become attached to air bubbles. A glance at the froth of an operating flotation cell demonstrates adequately that use of proper reagents and conditions mill result in such attachments; but how such attachment takes place is not definitely known. A better knowledge of this factor might lead to improved flotation practice either through altered machine design or the application of scientific innovations. Direct observation of the behavior of mineral particles and bubbles in an operating cell does not appear promising because of the complexity of the system. For this reason, conclusions concerning the problem must be deduced from theoretical considerations or from observation of simplified systems designed to reproduce conditions thought to exist in an operating cell. Present Theories Two mechanisms have been recognized as fundamental in particle-bubble attachment: gas precipitation and direct encounter. It is a simple matter to demonstrate in the laboratory that attachment can be brought about by either mechanism. As to the relative importance of the two in a particular flotation system, however, there is a divergence of views. Taggart1 states, Under exceptional circumstances sufficient force and time to effect attachment may conjoin in an ore pulp undergoing agitation, and a preformed bubble adhere to a collector-coated mineral particle, but the occurrence is rare. . . . Pulp-body froth flotation effects selection in the body of a conditioned pulp by causing gas bubbles to precipitate from solution in the liquid phase preferentially at the surfaces of collector-coated particles, and to cling to these particles, Gaudin2 states that, within the pulp body of an agitation machine, attachment of mineral particles to air bubbles occurs as a consequence of contact between the two. This theory has been supported by theoretical reasoning and much circumstantial evidence. Perhaps the most interesting bit of evidence in favor Of this theory js the difficulty in the flotation of fines. If attach-

Jan 1, 1949

By T. Egleston

For several years 1 have been engaged in studying the behavior of iron and steel under varying conditions of tension and compression, as well as of shock and abrasion. Some of these observations have been communicated to the Institute at various times. Within the past year I have been looking at the various observations that I have made as a whole, and have been led to the conclusion that there is a regular law of fatigue and refreshment of metals, and that the change which produces either the fatigue or refreshment, is a. chemical one, which is, however, in almost all cases accompanied by physical and molecular changes at the same time. That metals under conditions that were more or less well understood became worthless, has been known for many years. It has been known to blacksmiths that iron and steel, when improperly treated in their fires, become "burned," as they call it, and could no longer be used, and some of them have had a scrap heap into which such material was thrown. A few of them knew that after a period more or less long the iron or steel recovered some of its original properties and could, with many precautions, again be used, but that these phenomena followed any law has not to my knowledge been announced. My attention was first attracted to the varying conditions under which iron and steel rails break in service. It was not long before I became convinced that there was a general law applicable to all metals which allowed of their being used with safety within certain limits, and caused their rupture when the use extended beyond these limits, and this law I have called the law of fatigue- of metals. When me observe the causes of deterioration in iron and steel rails, we find that they are principally shocks, either slight and frequent, like those produced by the passing of a train over a road-bed in good order, which produces a vibration sensible to the ear laid on the rail, for very long distances, but distinctly audible for only a short one; or from sudden and heavy blows, like the descent of the locomotive and each car successively from a high to a low rail.

Jan 1, 1880

By C. C. Henning

IN any line of human activity logical handling requires an amount of attention to each phase that is in keeping with the importance of that phase. In the complex and rapidly changing field of modern ferrous metallurgy it is difficult to allot the proper degree of attention to the various subjects, and it is not surprising that one or more subjects of major importance should for a time be neglected. Bessemer steel is a good example of a neglected subject. It is largely taken for granted, inferior physical quality is assumed for it, and there is a lack of interest in its technical development and commercial application. Availability of supply is limited. In spite of this technical indifference, limited source and lack of commercial exploitation, bessemer steel constitutes a large volume of tonnage in daily use. There is a fairly prevalent idea even among technical people that bessemer steel survives mostly because of low cost and by reason of a dwindling residue of applications sufficiently common to permit of its use. The difference in cost between bessemer and open-hearth steel is governed largely by the relative cost of manufacture of pig iron and the market price of steel scrap. During the past four years there have been long periods of time during which the price of steel scrap was low enough so that open-hearth steel was considerably lower in manufacturing cost than bessemer. As to application, it may be pointed out that thousands of tons of this material in the form of bessemer screw steel are applied for moving parts in automotive and other equipment, Some forging work and considerable heat treating, particularly carburizing, is performed on this grade. From an economic standpoint the most effective contribution of bessemer steel lies in its free machining qualities. It is by far the freest

Jan 1, 1935

By A. W. Asman

An analysis is made of three different types of section production units that represent the manner in which most of the nation's bituminous coal is produced. The general delays and production characteristics of these sections are presented along with a method for evaluating section performance based on actual and theoretical production characteristics.

Jan 9, 1951

By L. S. Darken

In the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be represented satisfactorily by the simple equilibrium expression where (P) denotes the concentration of a product and (R) the concentration of a reactant in the reaction r1R1 + r2R2 + • • • D P lP1 + P 2P2 + • • • Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a component is not proportional to its true mol fraction. But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple components and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satisfactorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature— as ionization or the occurrence of polar and nonpolar molecules—are presumably less effective in inetal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

By L. S. Darken

In the study of reactions occurring in liquid iron, alone or in contact with a liquid oxide or slag phase, it has been found that the experimental data over a limited range of concentration can in some cases be represented satisfactorily by the simple equilibrium expression where (P) denotes the concentration of a product and (R) the concentration of a reactant in the reaction r1R1 + r2R2 + • • • D P lP1 + P 2P2 + • • • Some of the reactions for which it holds are listed in Table 1. For others, however, the simple equation apparently does not hold. This has been attributed to an improper method of expressing concentration (for instance, weight per cent instead of mol fraction); or it has been supposed that the solutions are not ideal in the sense that the activity of a component is not proportional to its true mol fraction. But it may be that the problem has been oversimplified by neglecting some molecular species actually present; that is, by considering only the ostensible simple components and thus leaving out of account possible compound formation. It is the purpose of the present paper to point out how, in a group of related cases, a reasonable consistent assumption relative to the presence of a compound makes it possible to express the experimental data satisfactorily by the simple equilibrium expression when this compound is taken into account, and to bring into harmony data referring to different reactions in liquid iron. There are several a priori reasons for believing that solutions in liquid iron should not deviate far from ideality, provided that the concentration of solute is not too great and is expressed in proper terms. The factors that commonly lead to nonideality in systems at ordinary temperature— as ionization or the occurrence of polar and nonpolar molecules—are presumably less effective in inetal and in slag systems at high temperature. Again, the type of equation commonly used to express the value of

Jan 1, 1940

By T. Egleston

FOR several years I have been engaged in studying the behavior of iron' and steel under varying conditions of tension and compression, as well as of shock and abrasion. Some of these observations have been communicated to the Institute at various times. Within the past year I have been looking at the various observations that I have made as a whole, and have been led to the conclusion that there is a regular law of fatigue and refreshment of metals, and that the change which produces either the fatigue or refreshment is a chemical one, which is, however, in almost all cases accompanied by physical and molecular changes at the same time. That metals under conditions that were more or less well understood became worthless, has been known for many years. It has been known to blacksmiths that iron and steel, when improperly treated in their fires, become "burned," as they call it, and could no longer be used, and some of them have had a scrap heap into which such material was thrown. A few of them knew that after a period more or less long the iron or steel recovered some of its original properties and could, with many precautions, again be used, but that these phenomena followed any law has not to my knowledge been announced. My attention was first attracted to the varying conditions under which iron and steel rails break in service. It was not long before I became convinced that there was a general law applicable to all metals which allowed of their being used with safety within certain limits, and caused their rupture when the use extended beyond these limits, and this law I have called the law of fatigue of metals. When we observe the causes of deterioration in iron and steel rails, we find that they are principally shocks, either slight and frequent, like those produced by the passing of a train over a road-bed in good order, which produces a vibration. sensible to the ear laid on the rail, for very long distances, but distinctly audible for only a short one; or from sudden and heavy blows, like the descent of the locomotive and each car successively from a high to a low rail. * Read at the Montreal Meeting, September, 1879.

Jan 1, 1880

By Charles Brush

THE general subject of accurate pyrometry, its great development in recent years, and the importance of its application in arts and manufactures is so ably treated in other papers that this paper will bee confined to a resume of some research work on certain temperature effects in carbon and other steels, some of which appear to, be new. The results of these researches are embodied in several papers presented to' various scientific societies during the last few years, most of them under the general title of Spontaneous Generation of Heat in Recently Hardened Steel.1 Several years ago, when studying the behavior, tinder certain conditions, of specimens of hardened tool steel, I observed that they all spontaneously generated a small quantity of heat, the rate of generation diminishing from day to day for several weeks before generation became imperceptible in the sensitive calorimeter used. In each case the steel had been hardened only a few days prior to its use. It seemed highly probable that the generation of heat was associated with some sort of "seasoning" or incipient annealing process, perhaps accompanied by slight changes of volume, and that it would be most rapid immediately after hardening. I subsequently investigated this curious phenomenon more fully. Twelve ½ in. round bars of tool steel, 5 in. long and with machined surfaces, were hardened by heating to high cherry red in a reducing atmosphere of a gas furnace and quenched in cold water. The bars then had a thin strongly adhering coating of black oxide. They were next stirred in a large quantity of water at room temperature, to acquire that temperature, wiped dry, and oiled with heavy, neutral mineral oil to prevent generation of heat by further surface oxidation, wiped free of excess of oil and placed in the copper cylinder of a heat-insulated box.

Jan 9, 1919

By W. H. Newhouse

DURING the past few years the writer has been impressed by the close relation of many epigenetic orebodies with anticlinal structures. In the literature on ore deposits there is occasional mention that an oreshoot or district is on an anticline, but in most of the descriptions no weight or significance is attached to the relation, and usually the fact is concealed in a mass of structural detail. A few writers have stressed the relationship in a few districts or on a certain type of deposit. Church, Spurr, Butler, Stahl and Schuette have called attention to certain features, but the general extent of such a correlation has not been made known in any publication that the author has seen. A recent article1 on the localization of ore deposits, by well-known geologists, does not consider this common association. The author has seen in the field a number of the structural features described, and in addition has made a fairly complete review of the literature. This paper presents enough of the examples found to show the frequency of the relation to anticlines, and since only a few deposits on synclines are known, all of these of any importance of which the writer knows are mentioned. With certain qualifications which are discussed later, epigenetic ore deposits of replacement or vein type are mostly found where local upwarps of the earth's crust have taken place. Where formations antedating the ore deposits are present in the proper attitude to demonstrate vertical warping (i. e., more or less horizontal beds) the structural feature on which a mineral district, or mineralized area is located is almost always anticlinal, or domelike in nature. Some or even most of the ore deposits in a given district may be on the flanks of the upwarp, but few major districts are located definitely on downwarped areas. Synclinal basins within certain limits of size appear to be unfavorable to the type of fracturing that admits ore-bearing solutions.

Jan 1, 1931

By H. F. Haller

COLUMBIA-SOUTHERN'S Barberton limestone mine, 8 miles southwest of Akron, Ohio, is a million-ton-per-year producer from a depth of over 2200 ft in a district where other underground mining at this depth is unknown. Mining extracts 46 of the top 51 ft from a formation of Devonian limestone discovered by drilling in the 1890's. The same drilling revealed extensive salt deposits below the lime- stone, which led to the location of the chemical plant at Barberton as a division of the Pittsburgh Plate Glass Co. in 1899. Soda ash was the principal product of the plant, and as production increased the demand for limestone increased. Columbia's first attempt to secure a reliable all-weather source of stone was the development of a quarry at Zanesville, Ohio, in 1919. Zanesville production eliminated some of the stock- piling required by the use of Michigan stone, avail- able only during the lake shipping season. Stone from some Zanesville horizons, however, was found to be more suitable for cement production than for soda ash, and rail transportation remained an important factor. As demand continued to increase, plans were made to develop the Barberton deposit.

Jan 12, 1954

By Loyd R. Kern

A procedure for determining the behavior of a reservoir under a gas or water injection program was reported by Buckley and Levertt in 1942.1 This method, which allowed the calculation of the phase saturation distribution behind the front of a displacing fluid, has been extended to apply to a more general situation. The reservoir may initially contain flowing quantities of the displacing fluid, or the fluid in the reservoir may be above saturation pressure SO that solution effects are present. Production may occur behind the front as in the case of a well which is produced after breakthrough of the displacing fluid. The calculating procedure is simplified in that the graphical integration necessary to determine breakthrough saturation is eliminated by performing a direct integration and the graphical differentiation necessary to determine saturation distribution is eliminated by representing the displacing phase fraction of the flowing stream by an empirical equation. This representation results in simple expressions for the producing gas or water/oil ratio and cumulative production. INTRODUCTION A method for the calculation of the saturation distribution behind the front (interface between the displaced and displacing phases in a gas injection or water flooding operation) was reported by Buckley and Leverett in 1942. The method leads to a curve for the saturation distribution which is double-valued; consequently, part of' the curve was interpreted to be physically meaningless. That part of the curve which has physical significance was determined by a graphical integra-tion (material balance). In this paper it is shown that the integration may be performed analytically with a resulting equation for the saturation of the displacing phase at the front. The case in which the displacing fluid is initially flowing and the case in which the reservoir is initially above the saturation pressure so that some injected gas goes into solution are included in the integration. The calculations are considerably simplified by representing the fraction of the flowing stream which is oil by an exponential function of saturation. The methods is extended to apply approximately to reservoirs in which wells located between the injection well and the front are produced. An illustrative example utilizing the methods presented is included. RESERVOIR BELOW SATURATION PRESSURE In the case of a water flooding operation or in the case of a gas injection operation in which no gas goes into solution in the displaced oil, the equation for saturation in a linear flow system as a function of time and position as given by Buckley and Leverett is where* q = total reservoir volume flow rate, rvb/day A = cross sectional area of system, sq ft / = porosity of formation x = distance from injection point, ft t = time, days Pj = saturation of the displacing phase /dx velocity of planes of constant saturation, ft/day *The nomenclature used here is not the same as that used by Buckley and Leverett A complete nomenclature is given in Appendix A.

Jan 1, 1952

By R. J. Borg, C. E. Birchenall

Vapor pressures of eight compositions of Mg-Cd have been determined by the Knudsen effusion technique. Measurements are made at several temperatures for each alloy and the results interpolated to a common temperature for the calculation of the activities. It is not possible to obtain values for the partial molar enthalpies because of the narrow temperature range spanned by the measurements. The results show less precision than those obtained for pure Cd which are also reborted. These alloys are extremely susceptible to corrosion which provides a possible explanation for the lack of precision. Nevertheless, the values of the activity are in good agreement with the results of electromotive force measurements previously reported for the Mg-Cd system. MAGNESIUM and cadmium are mutually soluble in all proportions in the solid state and form a single phase which has the hexagonal close-packed structure. X-ray investigations of this system1,2 have revealed a rapid variation in the relative dimensions of the unit cell occurring at approximately 50 at. pct. The rate of change of the c/a ratio with composition increases markedly for alloys containing more than 50 at. pct Cd. The purpose of this investigation was to determine the activity of Cd in the neighborhood of 50 at. pct and to discover whether or not the thermo-dynamic properties undergo a similar rapid change. The activities are calculated from vapor pressure data obtained by the Knudsen effusion method. Unfortunately the precision of the data from which the thermodynamic values are calculated is insufficient to establish unequivocally a departure from the normal trend. The results are reported primarily because they substantiate the only previously reported activity measurements3 and because they include values for pure Cd which in contrast to those of the alloys show excellent precision. The Cd-Mg system is known to contain several ordered phases. However, this investigation was made at temperatures considerably above the transition temperatures, and the alloys may be regarded as nearly random solid solutions. EXPERIMENTAL Apparatus—The effusion cells are machined from solid tantalum rod. The lids consist of threaded, flanged rings of tantalum onto which are welded shallow cups of 4 mil molybdenum foil. The orifice, which is located at its center, is made by grinding off a small dimple produced with a sharpened punch. Such an orifice has been mounted in plastic, sectioned, and the thickness of the orifice edge measured in a microscope. The maximum thickness is 0.00016 in., and the Clausing factor is consequently equated to unity. The area of the orifice is determined by tracing its projection on the screen of the metallograph at a known magnification and measuring the area of the tracing with a planimeter. Excellent temperature control is achieved with a 4 by 18-in. alundum core, gradient-wound, furnace

Jan 1, 1960