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By C. L. Sollenbeger, R. B. Greenwalt

PERHAPS the most widely used dispersants or gangue depressants in nonmetallic flotation are sodium silicates, which vary in silica-to-soda ratio from 1 to 3.75. Typical manufactured silicates in order of decreasing solubility and increasing amounts of silica are Metso, silica-to-soda ratio of 1.00; D, 2.00; RU, 2.40; K, 2.90; N, 3.22; and S-35, 3.75.* References in flotation literature1,2 to the use of sodium silicates are often weak because they fail to mention the type of silicate used. Metso and silicate N have occasionally been mentioned, but when the type of silicate is not mentioned, it is usually assumed to be N, the cheapest of the soluble silicates and the one recommended by sodium silicate manufacturers as a flotation agent. In the All is-Chalmers Research Laboratories a systematic study was made of the effect of different alkali-silica ratios on the concentration by flotation of two scheelite ores. One of these was a high grade ore from the Sang Dong mine in Korea. The effect of such factors as pH; addition agents; and conditioning time, temperature, and pulp density on the flotation efficiency of this ore have been described previously. The other ore was a low grade ore from Getchell Mines Inc., Nevada. The mineralogy and techniques of concentrating this ore have been described by Kunze. Hereafter these ores will be referred to as the Korean and Nevada ores. Experiments were made with both to determine the effect of three factors—-type of silicate, concentration of silicate, and pH of the pulp—on recovery and grade of tungsten in a rougher concentrate. Average WO, content of the Korean ore was 1.50 pct and of the Nevada ore 0.27 pct. The predominant tungsten mineral in both ores was scheelite, which was accompanied by a small amount of powellite. The powellite and scheelite were finely disseminated through both ores and required a —200 mesh grind for liberation. Major gangue minerals in the Korean ore, in decreasing order of abundance, were amphi-boles, quartz, biotite, garnet, fluorite, and calcite. Bulk sulfides composed about 3 pct of the total weight. Gangue in the Nevada ore, in descending order of abundance, was garnet, alpha quartz, calcite, phlogopite, wollastonite, and amphiboles. Sulfide minerals were 3 to 4 pct of total weight. Batch flotation experiments were made with 500-g samples of ore, each sample wet-ground to 90 pct passing 200 mesh. The finely ground ore was floated in a Fagergren batch cell at 25 pct solids. The natural pH of the Nevada ore was 8.9 and of the Korean ore, 8.5. The D, RU, K, N, and S-35 sodium silicates were obtained in colloidal dispersions with varying amounts of water. The most alkaline, Metso, was in dry powdered form. For convenience in addition, 5 pct solutions by weight were prepared from each of the silicates, on the basis of dry sodium silicate dissolved in the correct amount of distilled water. Chemical analyses of the various silicates are given in Table I, together with the pH of the 5 pct solutions. A preliminary bulk sulfide float was made with secondary butyl xanthate as the collector and pine oil as the frother. The WO] analysis of the sulfide concentrate was nearly 1 pct for the Korean ore and about 0.1 pct for the Nevada ore. The tungsten contained in the sulfide concentrate constituted about 3 pct of the total tungsten in each ore. No effort was made to recover these tungsten values. The scheelite was floated with oleic acid. Adjustments in pH were made with sulfuric acid or sodium carbonate. A 1 pct solution of 85 pct Aerosol OT was sprayed on the froth and sides of the cell during the scheelite float to aid in dispersing the minerals and to decrease the entrapment of gangue particles. Six tests were planned for each of the six types of silicate in which concentrations of 1, 2, and 4 1b of silicate per ton of dry ore were investigated at both 6.5 and 10 pH. All tests were made at room temperature. The performance of each silicate was judged from the grade and recovery of WO, in the scheelite rougher concentrate. Tungsten recovery was calculated on the basis of the scheelite remaining in the ore after the preliminary sulfide float. Testing of each silicate at three levels of concentration and two levels of pH required 36 tests with each scheelite ore. Variance analyses were performed on the concentrate grades and recoveries to determine whether or not the type of sodium silicate, the concentration of sodium silicate, or the pH significantly affected recovery or grade. Results Concentrate Grade: A variance analysis of the concentrate grades for the Korean ore showed that concentration of the silicate and pH of the ore pulp were major factors in producing a high grade concentrate. Also, the silica- to-so da ratio was important as an interaction with pH. The concentrate grade vs silica-to-soda ratio is plotted in Fig. 1. The curves show that the concentrate grade improved with an increase in concentration of sodium silicate and also

Jan 1, 1959

By W. T. Cardwell

Physically absurd, triple-valued saturations appear in the straight-forward solution of the Buckley-Leverell equations for the displacement of oil by water or gas. From an engineering viewpoint, the triple value causen no difficulty. It is well known how it may be compensnted in order to obtain physically meaningful, numerical results. From a scientific viewpoint, the question still arises: What did the triple value mean? This paper explains how and why the triple value arose in non-capillary Buckley-Leverett theory. The discussion should serve as a background for the understanding and use of the modern method of characteristics in di.~pkzc(>ment theory. INTRODUCTION Displacement theory was introduced to petroleum technologists in 1 941 by Buckley and Leverett.' Their first equation, which they wrote down without derivation, was equivalent to the following: ?s/?t= - qr/F ?f/?r (1) where S = saturation of displacing fluid (a fraction) r = time q,. = total volumetric velocity of both the displacing phase and the phase being displaced (usually, but not necessarily, assumed to be a constant) F = porosity (a fraction) f - fraction of the total volumetric velocity that is the volumetric velocity of the displacing phase (assumed to he a function of S only x = distance. Buckley and Leverett called Eq. I "a material balance equation". Actually it is derived from both a continuity equation, or material balance equation, and Darcy's law. Buckley and Leverett jumped from their Eq. 1 immediately to their Eq. 2, which was the equivalent of the following: (?x/?t)x = qr/F df/ds = qr/F f'(s) (2) The jump from Eq. 1 to Eq. 2 involves apparently simple mathematics, but in that apparently simple mathematics lies a subtle point that is part of the key to the meaning of the triple value to be discussed here. Eq. 2 may be readily interpreted as saying that a point of constant saturation (on a saturation-vs-dis-tance curve) moves with a constant velocity that is proportional to the total volumetric rate, inversely proportional to the porosity, and is otherwise a function of the saturation itself. So that if one knows the derivativc with respect to saturation of the fractional flow function, f(S), for each saturation, one knows the velocity of each point of the moving saturation-vs-distance curve. The function f(S) can he determined experimentally and its derivative f'(S) can be calculated. It turns out that the experimentally derived f'(S) is not a monotonic function of S, but instead it has a definite maximum and declines away at both high and low saturations. This in turn means, in accordance with Eq. 2, that on a moving saturation-vs-distance curve, ccrtain intermediate saturations will travel faster than the saturations either higher or lower. The result is indicated in Fig. 1. In Fig. 1, the abscissas represent distances along a column of porous medium, which column is assumed to be uniform in cross-section perpendicular to the ab-scissal direction. The ordinates represent fractions of pore space occupied by the displacing phase, which may be either water or gas. It is assumed that the saturation is uniform over all planes perpendicular to the abscissal direction. The saturation is a function only of time and one space variable. Time variation of the saturation is represented by change in shape of a curve such as curve AGJ, which represents the initial saturation-vs-

By L. W. Pommier, F. B. Brien, A. K. Bhasin

The diflerential movement of solid particles through solid-liquid suspensions is very important to many branches of engineering. The flow of suspensions around immersed bodies is mainly of a turbulent nature. Problems are encountered when attempts are made, as is the general practice, to extrapolate the velocity and resistance relationships of Newton, pertaining to Newtonian systems, into non-Newtonian solid-liquid suspensions. The conventional velocity and resistance relationships for turbulent flow in fluids when applied to suspensions, do not take into consideration the two very important variables: suspension particle size and solid volume fraction. A study of the effect of suspension particle size (dgb) on the velocity of falling balls leads to the concept of a critical particle size (dgc) at which the suspensions will be Newtonian. This leads to the classification of static suspensions into two types: suspensions consisting of particle of diameter dgh > dgt, and those with dgh, < dgr. Separate velocity and resistance equations for these two types of suspensions have been proposed, taking into account both the solid particle size and solid volume fraction. The agreement between the velocities predicted from the proposed equations and the measured velocities, confirms their validity. The resistance force offered by suspensions to the movement of immersed bodies has been calculated from the proposed equations, and the effects of suspension particle size and solid volume fraction on the resistance force and velocity have been examined. The movement of immersed bodies in solid-liquid suspensions is of great importance in many areas of engineering such as minerals processing, oil well drilling, suspension flow in pipelines, and hydrometallurgy. A number of mineral dressing processes deal essentially with the movement of solids in suspensions—in particular, classification, thickening, filtration, ore washing, and gravity concentration—thus a study of the fluid characteristics of suspensions is of theoretical and practical interest.&apos; A rigorous analysis of the mechanisms of momentum transport of a solid-liquid system is complex indeed. The rheological properties of the suspensions deviate from those of liquids, varying, for example, with density, solid volume fraction, size and shape of the solid phase of the suspension, and with the density and viscosity of the liquid phase. The flow of suspensions around immersed bodies is mainly of a turbulent nature and hence studies of the turbulent flow characteristics of suspensions are of par- ticular importance. Problems are encountered when attempts are made to extrapolate the velocity and resistance relationships of Newton, pertaining to Newtonian systems, into non-Newtonian solid-liquid suspensions. Due to the numerous variables present in a suspension, certain limitations and assumptions become necessary in order to produce quantitative relationships for predicting their effects. The solid particle size and the solid volume fraction are two of the more important variables. By comparing the measured and calculated Newtonian velocities of falling balls in simple static suspensions, the existing velocity and resistance relationships have been modified to take these variables into account. In order to keep the study less complex, all other variables such as the characteristics of suspending liquid and shape of the particle are maintained constant. Objective The objective of the present investigation is to modify the Newtonian velocity and resistance equations in order to take into account the suspension particle size and solid volume fraction. Theory Liquids are classified on the basis of viscosity, which may be defined as the relationship between applied shear stress and resulting rate of shear.&apos; pure single-phase fluids composed of small light molecules behave as Newtonian liquids, having a single viscosity pa-

Jan 1, 1971

By H. L. Hartman

The estimation of the magnitude of pressure changes which occur in mine ventilation circuits is of primary importance to the mining engineer in making changes in an existing mine or in projecting the ventilation requirements of a new mine. It is a formidable task in many cases, because no adequate theory is available and empirical data are unreliable or even lacking. The common practice of increasing one&apos;s estimate of the mine static pressure by an arbitrary "safety factor" to compensate for the unknown is a poor substitute for accuracy. Generally little difficulty is encountered in calculating friction losses in mine airways. As long as the friction factor can be reliably estimated, the well-known Atkinson formula gives accurate results. However, it is in the determination of shock losses that the ventilation engineer encounters difficulty and is apt to resort to an arbitrary allowance. Shock losses may constitute as little as five or as much as twenty-five percent or more of the overall pressure drop in the mine, and such allowances are generally completely unsatisfactory. Since other shock losses have been covered by McElroy (1), this paper deals with a long-neglected source of shock and pressure change in ventilation circuits, divergence and convergence of airflows, here referred to by their more common mining terms, splits and junctions. PREVIOUS WORK There is practically no fundamental information available in ventilation literature on the splitting and junction of airflows, either in mining or mechanical engineering periodicals or handbooks. Fluid mechanics textbooks seemingly avoid the subject of divergence and convergence, except for brief empirical treatment. The only investigation reported for mine ventilation systems was by Weeks, et a1 (21), in 1933. Although applicable to the case of line brattices in coal mines, it cannot be applied to the general case of mine splitting and junctions involving change of direction with little or no area change. In dealing briefly with the subject of shock losses at splits and junctions, McElroy (1) suggests only that they be considered comparable to bends, with losses at junctions being increased 50 pct to allow for interference of merging streams. He recognizes the importance of quantity ratio but concludes that exact quantitative data are lacking to compute losses at splits and junctions. A very capable summary and analysis of the state of knowledge in industrial ventilation and fluid mechanics regarding losses due to divergence has recently been reported by Gilman (3). In considering all earlier work dealing with both air and water as fluids, he compares results on a common basis and obtains good empirical agreement. For divergent flow, the controlling variable in each branch is the quantity ratio, although the deflection angle is of secondary importance. Empirical equations are presented for straight and 90-deg branches with varying velocity ratios, assuming branches smaller than the main duct. These formulas are modifications of the Borda equation for abrupt contraction and expansion. The only information available on shock losses in convergent flow are approximate experimental data presented by Alden (4) and the Manual of Recommended Practice for Industrial Ventilation of the American Conference of Governmental Industrial Hygienists. Alden considers the effects of both quantity ratio and deflection angle. The data indicate an effect opposite to that observed in divergence, the shock loss varying directly with quantity ratio. SHOCK LOSS THEORY Because pressure losses due to shock have been found to bear a constant relation to the mean velocity of flow in a given conduit, they are frequently expressed as a dimensionless function of the velocity head, termed the shock loss factor. For airflow in ducts and mine airways, the shock loss may be represented by the formula (1): Hx - XHv, (1)

Jan 1, 1961

By Waldemar Lindgren

CONTENTS. [ ] I. INTRODUCTION. THE precious metals, gold and silver, are the basis of the monetary systems of the world. It is, therefore, natural and inevitable that widespread interest should be manifested in their production and in the various classes of deposits in which they are contained. At times a great scarcity of the precious metals has prevailed; at other times the production has seemed so abnormally large that fears have been entertained regarding their ultimate retention as standards of value. Since most nations have adopted the gold standard, and the remaining ones appear likely to do the same in the near future, the question of available supply of gold for the present and future very naturally arises. This necessarily involves a consideration of the characteristics of the gold-deposits. After the absorption of the gold treasures of the New World by the conquistadores, the gold-placers of Brazil and Russia

Jan 1, 1913

By M. E. Wadsworth, R. L. Pearson

THE dissolution of UO, in carbonate solutions can occur only il the tetravalent uranium is oxidized to the hexavalent state. The carbonate system is of particular interest because it provides a means whereby the oxidized uranium may be dissolved by forming the complex ion UO,(CO3)3-1. In the presence of oxygen the over-all reaction may be written UO+1/2O,4CO3T+2HCO2UO,(CO4)11+H2O [1] UO, was used in this study because it could be obtained in high purity and also because it is representative of the most refractory of the primary uranium minerals. The mineral ulrichite is the natural counterpart of the synthetic UO, used. The kinetics of the leaching of UO, should be similar for any of the uraninite type minerals. A pressurized system was used not with the hope it could be extended to commercial systems as a primary purpose but simply to provide the means whereby important temperature and pressure parameters could be varied for the evaluation of the kinetic processes. The importance of such pres-

Jan 1, 1959

By R. G. Hawthorne

This report is concerned with fluid displacement in porous media, in those cases where viscous and gravitational forces control the displacement. Such a system would usually be found in a sand body of large physical dimensions such as an oil reservoir, although it is possible to create such a system in the laboratory. It is shown that the position of the fluid interface can be predicted by numerical calculations using a basic idea presented by Dietz. Fluid flow is considered in a vertical plane in a homogeneous, porous medium of sufficient thickness that the capillary transition zone is small in comparison with the total reservoir. A theory developed by Dietz&apos; is used to make numerical calculations of the position of the fluid interface. The results for several conditions are compared with scaled model experiments. The results show that, for gas drive in a reservoir of steep dip, a relatively low flow rate can displace large volumes of oil before gas breakthrough. On the other hand, water injection at favorable mobility ratio and low dip may show best performance at high rates. Water tends to underride the oil and, given sufficient rime, will break through without much oil displacement. For certain conditions, which include relatively low flow rate, the interface is a straight line and its behavior is simple to calculate. At higher flow rates, the interface is unstable, and a numerical solution was programed for an automatic computer. In general, good agreement is shown between the fluid model and the computed results so long as gravitational forces have control. For a water drive at very unfavorable mobility ratio, many small water fingers appear. These viscous fingers are not controlled by the relatively small gravitational forces. When viscous fingering becomes the controlling factor, the mathematical model is oversimplified, and results do not check the fluid flow model. INTRODUCTION Present methods of reservoir analysis depend upon certain simplifying assumptions to obtain mathematical descriptions of practical use. Material-balance methods (Muskat2 or Tarner2) assume uniform fluid saturations in the entire reservoir, or in a few subdivisions of the reservoir. An unsteady-state flow calculation by West, er at considered pressure and saturation changes in flow to a well during solution gas drive, and neglected gravity effects. Results showed only a 4 per cent difference for ultimate oil recovery by the Muskat method, even though the case chosen for study was one in which unsteady-state effects should be high. The Buckley-Leverett5 method commonly assumes a one-dimensional flow system. It is applicable at high flow rates where viscous forces predominate over gravity forces. Simultaneous, parallel flow of the two fluids is assumed, and the concept of a fluid interface is not introduced. Permeabilities to each fluid for a given saturation must be known. The method is not applicable for a two-dimensional system where cross flow becomes possible. Less well known is the displacement equation derived by Dietz. This method is designed for two-dimensional flow systems and assumes a definable fluid interface within the porous medium. Dietz showed that, for a range of low flow rates, the interface would be stable. straight and at an angle of inclination which could be simply calculated. At a certain critical flow rate, the calculated interface tilt would equal the formation dip. For higher flow rates, a finger of displacing fluid would invade the displaced fluid. Dietz indicated that his method applied only to macroscopic reservoir behavior, while the Buckley-Leverett method applied to the small transition zone at the fluid interface. The examples worked out in this report are based on the fluid-displacement theory of Dietz. It is shown that the Dietz theory may be used to derive equations analogous to the Buckley-Leverett equations. In contrast to the Buckley-Leverett method, flow is considered in a plane rather than being limited to a line. Rather than a frontal advance, the movement of a fluid interface is followed. For flow rates substantially exceeding the critical rate and for high viscosity ratio, many fingers of invading fluid occur-—rather than the single finger assumed by Dietz. On the other hand, so long as some gravitational influence remains, the flow is not entirely parallel to the bedding planes as assumed by Buckley and Leverett; therefore, both methods fail to give an adequate descrip-

By B. J. Bayles, J. A. Ford, M. J. Salkind

Unidirecltonally sulidijied AL-A13Ni was found to exliibit excellent microstructural stability to 508°C. Above this temperature the transverse micvostructure coarsened in a manner analogous to "Ostwald Ripening", but the A13Ni whiskers did not spheroidize or foreshorlen. The coarsened whiskers reinforced the matrix as effectirely as the finer whiskevs and no reduction in room-temperature tensile strength mas noled after exposure for 90 hr at 96 pel 0-1 the absollite melling temperature of the eulectic. The slability was auribucted to the presence of low-index (and presurrlably lor-energy) cvystallographic interjaces between phases. The driving force for microstructural coursening was presumed to be the reduction of interfacial energy between the phases. Finer micvoslructures were found to coarsen more rapidly than those which weve imitally coarser. FIBER-reinforced metals have been shown to exhibit good short-time tensile properties at elevated temperatures.1-4 However, many elevated-temperature applications require long-time property retention which dictates the necessity for microstructural stability. Two types of instability are common to fiber composities. The first, chemical instability, is due to chemical reaction between the matrix and the relnforcing phase. Petrasek and weeton5 have shown that chemical reaction between tungsten wire and several copper alloy matrices resulted in degradation of the reinforcing phase and reduction in strength of the composite materials. Kreider and Leverant4 have noted similar behavior for boron-reinforced aluminum above 400°C. The second type of instability arises in systems in which the phases are essentially chemically stable with respect to each other and is characterized by spheroidization and/or agglomeration of the reinforcing phase. parratt6 has reported this type of degradation to occur relatively rapidly at moderate temperatures for nickel and cobalt alloys containing whiskers of silicon nitride, aluminum oxide, and silicon carbide and has identified it as "physicochemical" instability. Although both types of instability are the result of the differences in the chemical potential between the fibrous phase and the matrix, they may be differentiated by the fact that the second type, "physicochemi-call&apos; instability, results in little or no net change in the composition or amount of each phase present. It does, however, result in a morphological change which profoundly affects the strengthening mechanism. Chemical interaction. on the other hand, results in a change in the composition and amount of one or more of the phases present, or the appearance of a new phase. In the latter case, the appearance of the mi-crostructure, that of a fibrous phase aligned in a matrix, may remain essentially unchanged, but the chemical degradation of the fiber results in markedly reduced composite strength. This investigation was initiated in an attempt to evaluate the microstructural and related mechanical property changes of a whisker-reinforced eutectic composite after elevated-temperature exposure. The composite system chosen for this study was the uni-directionally solidified A1-A13Ni eutectic which Lemkey. Hertzberg, and Ford7,8 demonstrated to behave as a whisker-reinforced composite. The microstructure of the unidirectionally solidified material consists of aligned needles of A13Ni in a matrix of aluminum. EXPERIMENTAL PROCEDURE Eutectic ingots having a nominal composition of 6.2 wt pct Ni were produced by melting 99.99+ pct A1 and 99.99 pct Ni in recrystallized alumina crucibles in an argon atmosphere. The analyses of the starting materials are listed in Table I. These master heats were cut up? melted by induction heating, and unidirectionally solidified vertically in 1/2 -in.-ID. 6-in.-long graphite crucibles, in a dynamic argon atmosphere. Therma1 gradients in the liquid were determined by measuring the temperature in the melt as a function of apparatus travel distance, as discussed by Kraft and Albright.9 The rate of solidification was assumed to be equal to the uniform rate at which the crucible assembly was withdrawn from the furnace. Ingots representative of nominal growth rates of 2, 5, and 11 cm per hr were produced and the solidification parameters are summarized in Table 11. Ingots used for met allographic analysis were pre-

Jan 1, 1968

By J. H. Brophy, S. J. Michalik

A constitution diagram for the system Mo-Ir has been determined. The maximum solubility of iridium in molybdenum is 16 at. pct at 2110ºC and decreases to less than 5 at. pct at 1500°C. The solubility of molybdenum in iridium is 22 at. pct. Three intermediate phases appear in the system: 8 MoJr, having the p-tungsten structure; a phase, a cornplex tetragonal structure; and the hcp ? phase. Metallography, melting point determinations, X-ray diffraction and fluorescence, and electron micro-probe unalyses were employed in establishing the diagram. PREVIOUS to the present investigation, the intermediate phases in the Mo-Ir system were identified, but no detailed account of the phase diagram has been reported in the literature. Raub1 investigated alloys of Mo-Ir over an extensive range of composition between the temperatures of 800º and 1600°C. The in-termetallic compound MosIr was found to exist with nearly pure molybdenum, as the solubility of iridium in molybdenum was not detectable parametrically in this temperature range. MO3Ir was found to be iso-morphic with a ß-tungsten type structure, having a parameter of 4.959Å. An intermediate hcp phase, designated as the ? phase, ranged in composition from 52 to 78.5 at. pct at 800ºC, and from 41 to 78.5 at. pct Ir at 1200°C. Parameters noted for the ? phase were as follows: at 42.7 at. pct Ir, a = 2.771i0, c = 4.4366, c/a = 1.601; at 78.5 at. pct Ir, a = 2.736A, c = 4.378A, c/a = 1.600. Molybdenum was found to be soluble in iridium up to 16.5 at. pct Mo (83.5 at. pct Irj, with the parameter of iridium increasing to 3.845A at the solubility limit. Knapton,2 who investigated alloys between 15 and 85 at. pct Ir, essentially agreed with Raub&apos;s data, but, in addition, found a a phase in as-melted alloys near 25 at. pcto Ir. The oaphase lattice parameters were a = 9.64Å, c = 4.96Å, c/a = 0.515. The a phase was replaced by the 8 -tungsten phase on annealing at 1600°C. Knapton concluded that the a was stable only at elevated temperatures, and placed the composition of the a phase at approximately 30 at. pct Ir. The intermetallic compound Mo3Ir, with a lattice parameter of 4.965A, was included among the 8-tungsten structures reported by ~eller.&apos; Matthias and Corenzwit,4 and Bucke15 studied the superconducting nature of MosIr, and reported a superconducting transition temperature of 8.$K. The present investigation describes the phase relationships in the Mo-Ir alloy system determined by melting point measurements, X-ray diffraction and fluorescence, and metallography. EXPERIMENTAL PROCEDURES Alloys for the determination of the phase diagram were prepared from powders. Commercial 99.9 pct Mo from Fansteel Metallurgical Corp. and 99.9 pct Ir powder from J. Bishop and Co. Platinum Works were used. The powders were weighed to nominal compositions, mixed, and then pressed, without binder, into compacts weighing 4 to 6 g. These were presintered in uacuo between 1200&apos; and 1400°C for 1 hr, to reduce the degree of spattering during subsequent arc-melting. The compacts were arc-melted in a nonconsumable tungsten electrode furnace six times on alternate sides on a water-cooled copper hearth in an atmosphere of zirconium-getter ed argon at 500 mm of mercury pressure. In almost all cases, this procedure yielded buttons of satisfactory homogeneity. The composition of all melted buttons were confirmed by X-ray fluorescent analysis using the experimentally determined ratio of the iridium La1 line intensity to that of the molybdenum Ka1 line as a function of composition. In this determination four alloys analyzed by wet chemical methods were used as standards. An uncertainty range of ±1 at. pct has been attributed to all indicated compositions. All heat treatments and solidus measurements were carried out in tantalum resistance heating elements in vacuum conditions of 10-4 to 10-5 mm of mercury. A detailed account of this procedure has been reported by Schwarzkopf and Brophy.8 In the heat treatment and solidus measurements of iridium-rich alloys (50 at. pct Ir or greater), a tungsten lining was inserted into the tantalum resistance heating element because of a eutectic reaction which occurs between iridium and tantalum at 1948ºc.7 Heat treatments and solidus measurements carried out at compositions less than 40 at. pct Ir both with and without tungsten linings within the resistance

Jan 1, 1963

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.&apos; Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.&apos;.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949

By E. P. Burtchaell

A method is presented for evaluating the effect of gravity drive upon the reservoir performance of a high relief pool. Conventional forms of reservoir analysis do not consider the alterations in the basic material balance data caused by gravity segregation of reservoir fluids. A procedure is outlined for structurally weighting physical and chemical data for use in the material balance equation. It is demonstrated how actual pool performance data can be utilized to evaluate the future reservoir performance of a gravity drive pool. INTRODUCTION Conventional reservoir engineering. procedure is inadequate for the analysis of an oil pool which has considerable structural relief, steep dips, and good permeability development. In, pools of this type, gravity drainage has an important part in the movement of oil to the wells and the effects of gravity on the overall pool performance should be included in any analysis of reservoir behavior. Many engineers have the opinion that the force of gravity in the movement of oil is not important until the later life of a pool.&apos; Probably the basis for this belief is that gravitational effects may not be readily discernible until a pool is nearing depletion. This would be especially true for pools not having a high degree of structural relief and permeability development. Actually the effects of gravitational forces are at a maximum when the pool pressure is high, for during this period the hydrostatic head of the oil column is at a maximum and the viscosity of the oil is at a minimum. Oil recoveries from pools having favorable gravity drive characteristics may equal or even exceed recoveries which might be expected from water displacement. Field evidence indicates that in some reservoirs gravity drive has resulted in recoveries greater than that which could have been expected from gas expansion or water drive.&apos;.3 Unfortunately, the possible effects of gravity drive on pool performance have been underestimated and other reasons have been sought to explain the high recoveries obtained. There are unquestionably many reservoirs to which the principles of gravity drainage can be effectively applied. It is the purpose of this paper to illustrate one method whereby gravity drive is included in the reservoir analysis of an oil pool. A hypothetical pool, typical of many California reservoirs, is used as an example. As used in this paper, "gravity drive" is defined as the overall effect of gravitational influences on the recovery of petroleum from the reservoir; "gravitational segregation" as the gravity separation of oil and gas within the reservoir; and "gravity drainage" as the downward movement of oil as caused by the force of gravity. SAND VOLUME DATA Fig. 1 presents a structural contour map of the pool under study. Maximum closure is 1950 feet with dips on the south flank approaching 45". The original gas-oil interface was set at -5200 feet. Average thickness of the producing sand was 200 feet. For use in subsequent calculations ill this paper, the pool was subdivided into 100-foot vertical increments and the sand-volume content of each increment was obtained. If the gross sand thickness is small, under 100 feet, the sand-volume content can be obtained by superimposing an isopachous map upon a structural contour map and planimetering the average thickness of each 100-foot increment. For sand thicknesses over 100 feet, one approacli would be to construct a sufficient number of cross-sections of the pool from which the weighted sand-volume of each 100-foot increment could be obtained. Variations in the sand body with depth, as determined by core data, can also be included in the above process. Table I presents a summary of sand-volume calculations, core data, and the original distribution of reservoir hydrocarbons in the pool. Fig. 2 illustrates the structural distribution of the sand-volume content. A total of 171,398 acre-feet is contained within the productive limits of the pool. Assuming an average porosity of 25% and an interstitial water content of 20%, the original hydrocarbon content was computed to be 227,075,000 barrels. DEPTH-PRESSURE DATA The determination of the initial vertical pressure arrangement in the pool is necessary for PVT and material balance calculations. Whenever sufficient data are available, a plot of pressure versus subsea depth of measurement should be made. From this plot a representative fluid pressure gradient can be established. Lacking sufficient initial pressure data, an initial pressure gradient may he estimated or calculated from avail-

Jan 1, 1949

TO THE BOARD OF DIRECTORS AND MEMBERS OF THE AMERICAN INSTITUTE OF MINING AND METALLURGICAL ENGINEERS GENTLEMEN: Submitted herewith are the report of the Treasurer for the year 1939 and reports for the same year of the following standing committees: Admissions, Membership, Papers and Publications, Mining and Metallurgy (Magazine), Library, Speakers for Local Sections and Student Societies, and Student Relations. These reports present additional details. Membership.-For the second year in Succession membership reached a new high level for all time, as indicated in the accompanying tabulation in which "Members" includes all categories except Student Associates. [END 1938 END 1939 NET GAIN Members9, 57 610, 163 587 Student Associates 2,898 3,760 862 12,474 13,923 1,449] Net gain in membership (aside from Student Associates) was 587 compared with 744 in 1938, despite the fact that applications received in 1939 exceeded those received in 1938 (1271 against 1162). The smaller net gain is accounted for in three ways: (1) A greater lag in enrollment of those elected in the last quarter of the year; (2) an increase in the number of applications involving change of status from Junior Member to Member; and (3) an increase of 167 in the loss by death by resignation and by suspension in 1939 as compared with 1938. Experience shows that at the end of a year of less prosperous conditions in the mineral industries, and, therefore, among engineers engaged in these industries, resignations and suspensions are more numerous. Business and industrial indexes all show 1938 to have been somewhat less prosperous than 1937; but the improvement in 1939 should be reflected in the record for 1940.

Jan 1, 1940

By Be Van Presley

There has been developed at Latouche a rather unusual system of mining which, for want of a better name, has been called the "Latouche system of mining." It is a modified form of shrinkage stoping applicable to orebodies of large or fairly large size where the ground is such that timbering would not be required in stoping. Mention has been made of this method of mining by Birchll who gave no details as it had been in use only a short time and the final outcome undetermined. The system, however, has proved to be entirely successful and it is thought that a paper covering it might be of general interest. Before proceeding with a detailed description of the Latouche system a brief description of the property and the various mining methods previously used will be given. Location The Beatson mine of the Kennecott Copper Corpn. is situated on the west coast of Latouche Island, in Prince William Sound, Southwestern Alaska, 45 miles east of Seward, the coast terminus of the U. S. Government Railroad. It is a regular port of call for ships on the Southwestern Alaska run. The island is about 12 miles long and 3 miles wide. A ridge of mountains runs the entire length with a maximum elevation of 2500 feet. Climate Latouche has to contend with possibly the greatest amount of precipitation on the North American continent. The annual average precipitation for the past 4 years has been 188 in., with 248 in. for the year 1926. A rainfall of 4 in. per day is not uncommon. In the winter the thermometer rarely falls below +20° F. and the snowfall is usually heavy during the months of March and April.

Jan 1, 1928

By N. M. Levine, W. M. Fassell

In this laboratory study the problem of aerative conditioning to separate chalcopyrite and pyrite from cobaltite was simply effected with a sulfy-drate collector and pH by proper choice of mixing variables. It was shown that for a given impeller type and geometry, selectivity is governed by a relation between the Froude number and a modified power number multiplied by impeller tank-diameter ratio wherein the power factor is expressed as power intensity or horsepower per unit volume of contained pulp. In applying this approach to other systems, other criteria would be used in place of selectivity. The purpose of this paper is to show how solutions to problems of aerative conditioning of pulps may be enhanced by development of mixing parameters in a given system through application of a fundamental approach to agitation. The term aerative conditioning refers to a combination of processes which include mechanical gas dispersion, gas solution in the liquid phase, transport of dissolved gases and other reactants to the reaction zone, physico-chemico interaction within the liquid phase and/or at the solid surface, and, finally transport of products away from the reaction zone. Important elements of these processes are: 1) Air-Liquid Contact Area: This area limits the rate at which a given gas may dissolve in a given liquid. Thus, an aerative conditioning system should be designed for optimum gas dispersion. 2) Diffusional Factors: Such factors as concentration gradient, diffusion film thickness, and diffusivity may govern the rate at which dissolved constituents are transferred to the zone of interaction at a particle surface and the rate at which reaction products are transported therefrom. Thus, such systems would be designed for maximum turbulence to effect good mixing and to minimize diffusion film thickness. 3) Solids-Turbulent Liquid Contact Time: Sufficient time should be provided for interactions to take place at solid-liquid interfaces. The region of maximum turbulence for mechanical systems being in the impeller zone, it is important that the number of passes through this zone be optimized. This means that a proper balance should be struck be- tween flow and turbulent power to achieve optimum conditioning time. Too high a flow rate and insufficient turbulence may be improper if the reactions are diffusion limited. On the other hand, too much turbulent power and too little time in the reaction zone due to insufficient flow power may also be limiting. 4) Geometry and Impeller Design: The design of the conditioning vessel and the type of impeller employed are important factors in determining the relative distribution between flow and turbulent power and the degree of gas dispersion. Maximization of power input would be to no avail if the distribution between flow and turbulent power were improper or gas dispersion insufficient. 5. Physical Chemistry: The reactions between dissolved gases and solid surfaces may be limiting if gas solubility, activation energies and/or free energies are not favorable. J. H. Rushton, E. W. Costich, and H. J. Everett&apos; have summarized the mechanical elements of the combination of processes listed in a fundamental mixing equation. This equation was derived by dimensional analysis and relates the physical variables for a single impeller, centered in a cylindrical, vertical axis, flat-bottomed tank. It is, where T is tank diameter in feet; H is liquid depth in feet; C is height of impeller off tank bottom in feet; S is pitch of impeller; L is length of impeller blades; W is width of impeller blades; R is number of baffles; D is impeller diameter in feet; Np is the power number, pg/dN3D5; P is power in foot-pounds per second; g is the gravitational constant, feet per second; J is width of baffles; B is number of im-

Jan 1, 1961

By A. Lubinski, J. L. Logan, W. S. Althouse

A4ost gas twells and flowing oil wells are completed and treated through a string of tubing and a packer. Changes in temperature and in pressure inside or outside the tubing will: (I) if free motion of the tubing inside the packer is permitted, increase or decrease the length of the rubing; or (2) if free motion is prevented, induce forces in the tubing and on the packer. If pressure inside the tubing is greater than outside, the tubing may buckle helically even in the presence of a packer-to-tubing tension. The tubing will always buckle, and much more severely, if free motion is permitted. The buckling may be prevented by pulling the tubing in sufficient tension. The prediction of these forces and tubing movement has here to fore been based upon calculations that did not inciude helical buckling. This paper preseitts means with which these length or force changes can be calculated while taking into account the effect of helical buckling. To avoid damaging formations, failure of remedial operations, or damage to the tubing or packer, application is made to practical problems involving calculations of the required length of seals, amount of sluckoff or tension, and prevention of permanent corkscrewing. INTRODUCTION Leakage of a packer may result in costly failures of such operations as squeeze cementing, hydraulic fracturing, etc. To avoid such failures, the authors are often asked questions pertaining to the length of necessary seals, the amount of necessary slackoff, etc. Published work&apos; does not take into account helical buckling of tubing. Investigation of helical buckling was prompted by the fact that allowance must be made for this phenomenon in order to provide relevant answers. In the past, theoretical work on helical buckling was confined to conditions for which such buckling does not The mathematical treatment of behavior in a buckled condition, given in the Appendix, is novel. Assumptions upon which this investigation is based are listed and discussed in a special section. The following are a few of the many kinds of problems which may be solved with this paper. 1. Consider a packer in which tubing may move. Such movement will occur after pressures and temperature are changed. The paper provides means for: (a) calculating the amount of such movement and, therefore. the required length of seals; and (b) calculating the necessary amount of initial slackoff, for which there is no danger of unsealing the packer, if the length of seals is given. Such calculations, as well as those which follow, tully take into account the fact that part of the movement ib due to elastic helical buckling of the lower part of the string. This buckling may occur even in tubing under tension. Insufficient initial slackoff for a given length of seals, or insufficient length of seals for a given slackoff, may result in costly failures. A field case of such a failure will be given further in this paper. 2. In the case in which tubing cannot move in the packer, changes of pressure and temperature result in tubing-to-packer forces and forces in the tubing above the packer, both of which may be calculated. This knowledge is important because, if these forces are too large, the) could damage the packer or the tubing. 3. For wells in which wireline tools are to be run through the tubing, the paper provides means to keep the tubing from buckling, thereby permitting free passage of tools. 4. In deep wells, mainly in the presence of large casing, tubing may become "corkscrewed", i.e., take a permanent helical set. A field case is described further in the text. Using this paper, one may calculate in advance conditions under which permanent corkscrewing would occur, and then take preventive steps. HELICAL BUCKLING Consider a string of tubing, freely suspended in the absence of any fluid inside casing, as shown in Fig. I(a). Now consider an upward force F applied at the lower end of this tubing. This force compresses the string; and if the compression is large enough (which is always the case in actual problems), the lower portion of the string will buckle into a helix, as shown in Fig. 1 (b). The lower end of the tubing is subjected to a compression F. This compression decreases with the distance from the bottom and becomes nil (neither compression nor ten-

By J. K. Elliott, P. H. Kelly

Many engineering functions such as surface metering work and laboratory compressibility check points involve the use of liquid densities of light hydrocarbon mixtures at various pressures and temperatures. However, at the present time, no simple reliable method exists for determining density variation, particularly if the composition of the liquid is unknown. Consequently, a study was undertaken to develop and present a simple and accurate method of predicting density variation of a light hydrocarbon liquid with pressure and temperature, knowing only the density of the liquid at some condition. The experimental liquid compressibility data from API Project 37 by Sage and Lacey&apos; have been considered to be accurate within 0.5 per cent and cover a wide range of pressure (14.7 to 10,000 psia), temperature (100" to 400°F) and molecular weight (up to 150). From these data, a set of liquid density curves, which relate density to pressure, temperature and molecular weight, was developed. These curves make it possible to predict density variation with pressure and temperature. Compared to extensive laboratory compressibility data on a complex, light hydrocarbon liquid, the use of the liquid density curves resulted in an average error of less than 0.5 per cent. Based on the results of this analysis, it is concluded that the set of liquid density curves developed from the data of Sage and Lacey provides an accurate and simple method for predicting the density variation of light hydrocarbon liquids when the density at some condition is known. These curves should be very helpful in many engineering calculations, particularly in the surface metering of light hydrocarbon liquids. INTRODUCTION Many situations arise in field and engineering laboratory work, such as reservoir engineering studies, check of experimentally determined laboratory data and orifice flow-meter formulas, where liquid density factors at various pressure-temperature conditions are required. Also, the need for accurate light hydrocarbon liquid information has become more important with the advent of miscible-type displacements for secondary recovery purposes in oilfield operations. Several reliable methods are available1 - "or determining the density of liquid hydrocarbons if the composition of the liquid is known. However, there is a definite lack of methods for accurately determining the variation of density when the composition of the liquid is unknown. The purpose of this study is to review the various methods for determining hydrocarbon liquid densities and to develop a simple and reliable method of determining variation in density of light hydrocarbon liquids with pressure and temperature when the compositio~n of the liquid is unknown. METHODS FOR DETERMINING DENSITY OF LIQUIDS OF KNOWN COMPOSITION Sage, Lacey and Hicks&apos; have proposed a method to predict the density of light liquid hydrocarbons by using partial molal volumes. Data are available on experimentally developed partial liquid volumes of hydrocarbons over a rather limited range of temperature, pressure and composition. The partial mold volume method has proved satisfactory for determining the density of some hydrocarbon liquids when the composition is known. Within the range covered in the Sage, Lacey and Hicks1 data, the results agree within about 3 per cent of the experimental values. Hanson mentions the limitation of this method to a composition range of approximately 10 per cent by weight of methane, which will not allow this correction to cover most low molecular weight-light hydrocarbon liquids. Standing and Katz2 studied data on light hydrocarbon-liquid systems containing methane and ethane at high temperature and pressure and have presented a method for determining liquid densities, assuming additive volumes for all components less volatile than ethane and using apparent densities for methane and ethane. The compressibility and thermal-expansion curves used by Standing are based on assumptions that compressibility of a hydrocarbon liquid at temperatures below 300°F is a function of the liquid density at 60°F and that thermal expansion of the liquid is affected little by pressure. The information required to use this technique with an example problem is furnished by Standing.&apos; Hanson eports an average error of - 0.5 per cent using the method of apparent densities in calculating liquid densities of several volatile hydrocarbon mixtures. However, as implied, the apparent density method is not applicable for liquid density calculations when the composition of the liquid is unknown. Watson- as presented a method

By A. I. Blank, S. E. Maddigan

Many experimental and theoretical investigations have been made on the processes involved in annealing and recrystallization of metals. Most of these, however, have treated the time element as constant and heat-treatments used have been for relatively short times. Aside from the early work by Carpenter and Elam,&apos; the few that have investigated the effect of time on the processes have usually done so for fairly short time periods. During recent years the growing interest in long-time creep properties of metals and alloys under stress has made increasingly important a better knowledge of the recrystallization during prolonged heating. The recrystallization temperature of 70-30 brass given by Clark and White" in 1932 was somewhat above 400°F. (204°C.) but under 500" (260°C.), whereas in our laboratory recrystallization has been observed in creep specimens at 204°C., the lowest temperature of Clark and White&apos;s range. Since the creep properties are quite different above and below the recrystallization temperature, erroneous conclusions can readily be drawn by the application of short-time recrystallization data to creep problems. It was thus considered of both practical and theoretical value to make long-time annealing studies near the minimum recrystallization temperature. In this way useful additions could be made to data on recrystallization temperatures and, since the reactions in this range are relatively slow, additional insight could be obtained into the factors involved in annealing. Several comprehensive reviews of recrystallization processes have been written,3-6 therefore only a brief review of the generally accepted facts will be given here. Though the effects of heat-treatment usually are expressed as related to observations with varying temperatures, it is logical to assume that the same order of occurrence will exist with time as a variable. Thus, we may postulate that with increasing time we mill observe the following

Jan 1, 1940

By S. E. Maddigan, A. I. Blank

Many experimental and theoretical investigations have been made on the processes involved in annealing and recrystallization of metals. Most of these, however, have treated the time element as constant and heat-treatments used have been for relatively short times. Aside from the early work by Carpenter and Elam,&apos; the few that have investigated the effect of time on the processes have usually done so for fairly short time periods. During recent years the growing interest in long-time creep properties of metals and alloys under stress has made increasingly important a better knowledge of the recrystallization during prolonged heating. The recrystallization temperature of 70-30 brass given by Clark and White" in 1932 was somewhat above 400°F. (204°C.) but under 500" (260°C.), whereas in our laboratory recrystallization has been observed in creep specimens at 204°C., the lowest temperature of Clark and White&apos;s range. Since the creep properties are quite different above and below the recrystallization temperature, erroneous conclusions can readily be drawn by the application of short-time recrystallization data to creep problems. It was thus considered of both practical and theoretical value to make long-time annealing studies near the minimum recrystallization temperature. In this way useful additions could be made to data on recrystallization temperatures and, since the reactions in this range are relatively slow, additional insight could be obtained into the factors involved in annealing. Several comprehensive reviews of recrystallization processes have been written,3-6 therefore only a brief review of the generally accepted facts will be given here. Though the effects of heat-treatment usually are expressed as related to observations with varying temperatures, it is logical to assume that the same order of occurrence will exist with time as a variable. Thus, we may postulate that with increasing time we mill observe the following

Jan 1, 1940

By H. F. Yancy

PooR results in coal washing and in ore concentration are sometimes attributed to the shape of the particles in the feed. It is well known that the shape of a particle influences its rate of fall in water. This is evidenced by the value of the constant C in the Rittinger equation for the velocity V of settling in water, V = C-D(d- z ), where C has the following values: 2.73 for roundish grains, 2.37 for long grains and 1.92 for flat grains. This report, which is based upon data obtained during the course of coal-washing investigations conducted by the U. S. Bureau of Mines in cooperation with the College of Mines of the University of Washington, gives the results of a method or procedure of screening in which the particles are separated into three shapes and shows the deportment of these shapes when coal is treated on a coal-washing table. The method consisted in first screening the coal with Tyler standard square-hole sieves, followed by screening tests of each of these products with screens of rectangular opening. For this purpose Tyler "Ton-Cap" screens were used; each square-hole product was subsequently sized with two Ton-Cap sieves so selected that their shortest dimensions were approximately 75 and 50 per cent., respectively, of the opening of the square-mesh sieves. For example: A product which is through 8 mesh (0.093 in.) and on 10 mesh (0.065 in.) is screened on slotted sieves which have openings 75 and 50 per cent. of the 0.065-in. opening in one direction and an opening of not less than 0.065 in. in the other direction. For convenience in discussion, the particles retained on the first slotted screen are termed "cubical"; those retained on the second slotted screen are termed "prismatic" and those passing the second screen are called "flat." (See Fig. 1.) The square-mesh screens separate particles according to two dimensions, length and breadth; the slotted screens divide them further according to the third dimension, or thickness. Prismatic particles have a mass of about two-thirds, and flat particles of about one-half, that of cubical particles of the same square-mesh size. The screen-

Jan 1, 1931

By Rex B. McLellan

Studies of the eyuilibrzum between ferrite and austenite with gas mixtures (CO + CO2 and H2 + CHe) have been used as a means of deducing the energy and vibrational entropy of carbon atoms in dilute interstitial Fe-C solutions. A simple model for dilute interstitial solutions is given which enables a solubility equation for the equilibrium between the gas mixtures and the solid to be deduced. This solubility equation is used to estimate the partial In this work measurements of the equilibrium between dilute solid solutions of carbon in iron and gaseous mixtures of CO2 + CO and CH4 + Hp have been analyzed using theoretical solubility equations deduced from a knowledge of the thermodynamic parameters of the gas mixtures and an appropriate model for the solid solution. The solubility equations are deduced by equating the chemical potential of carbon atoms in the gas thermodynamic functions of dilute Fe-C solutions from the measured equilibrium between the solid and the gas mixtures. It is shown that the vibra-tional entropy of a carbon atom in a and y iron is smaller than the corresponding entropy 01. a nitrogen atom in solid solution inferrite or austenite and that there is little difference between the vibrational entropies of both nitrogen and carbon atoms in ferrite and austenite. and solid phases. The chemical potential of carbon in the gas is found from a simple statistical mechanical analysis of the gas mixtures utilizing spec-troscopic data while that for carbon in the interstitial solution is found from a model in which the carbon atoms act as bound oscillators distributed in a random fashion in the solution. The solid solution is dilute enough to enable solute-solute interactions to be ignored. Thus the configurational entropy of the solution is ideal but the mixing entropy contains additional excess terms due mainly to the vibrational changes occurring on solution formation. The partial excess entropies (and the partial energies) do

Jan 1, 1965