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By S. R. B. Cooke, Y. S. Kim, I. Iwasaki

lron oxides or the gangue minerals of iron ores can be made to float, depending upon the choice of collector. The selectivity of the separation is controlled by the accompanying chemical and operating conditions. In this report the findings on the general flotation characteristics of magnetite are summarized and the results are compared with those obtained for other iron oxides. Depending upon the choice of collector, either the iron oxides or the gangue minerals of iron ores can be made to float, the selectivity of the separation being controlled by the accompanying chemical and operating conditions. The mechanism by which a collector exerts preferential affinity for either group of minerals has been a subject of extended discussion. Previous investigations on the electrokinetic properties and flotation characteristics of hematite,' goethite,2 and quartz3 have demonstrated the electrical nature of the interaction of the collector with these oxide surfaces; anionic collectors are effective on positively charged surfaces and cationic collectors on negatively charged surfaces. Thus, from the differences in the electrokinetic properties of the above-named oxides, a theoretical basis has been provided for their separation by some typical collectors. Examination of the results reported for hematite and goethite shows that their electrokinetic properties and flotation characteristics are remarkably similar. It is of considerable interest, therefore, to examine similar information for magnetite, another common iron oxide, in order to consolidate the flotation characteristics of the three principal minerals of oxide iron ores. Such information is practically significant in the up-grading of both natural and artificial mag- netite produced from taconite, and in the treatment of partially oxidized magnetite ores. Information on maghemite and lepidocrocite, polymorphs of hematite, and goethite, respectively, is also of some theoretical interest in ascertaining the effects of crystal structure and of hydration in the iron oxide group. This article reports the findings on the general flotation characttxistics of magnetite, and compares the results with those obtained for other iron oxides. Experimentally, tlhe surface properties of magnetite were investigated by electrophoresis, and by measurement of the aclsorption of some typical flotation collectors. Its flotation behavior was tested by contact angle measurements and by simple flotation tests using a modified Hallimond tube. The basic information thus gathered was shown to be directly applicable to the interpretation of the results of batch flotation tests made on an artificial mixture of magnetite and quartz. EXPERIMENTAL MATERIALS Magnetite: Magnetite concentrate from Port Henry, N. Y., was further purified by fine crushing and magnetic separaiion, and was used throughout this investigation. For flotation tests the 150/200 mesh fraction was iso1ated and was cleaned by leaching briefly with warn 0.1 N HC1 followed by repeated washing with demineralized water. The final sample analyzed 71.71 pct Fe, 22.37 pct Fe" and 0.47 pct insoluble, and was stored in demineralized water. For e1ectrophoresis and adsorption measurements, the —400 mesh fraction of the magnetite concentrate was ground dry in a pebble mill. The surface area of the ground sample, as determined by the gas permeability method, was 70,000 sq cm per g. Since artificial magnetite has been reported to possess somewhat different physical properties than those of natural magnetite, it also was briefly examined. Preliminary flotation tests on a sample of artificial magnelite, prepared by reducing Brazilian hematite in a C0/CO2 mixture and analyzing 71.94 pct Fe and 23.78 pct Fe'', gave, however, nearly identical results with those using natural magnetite. It was concluded that artificial magnetite behaves similarly to natural magnetite. Samples which had been magnetically separated showed a tendency to cluster together due to residual

Jan 1, 1962

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

By S. Weinig, E. S. Machlin

IN a previous study of the grain boundary stress relaxation phenomenon,&apos; the authors had arrived at the conclusion that two successive steps were involved in the complete relaxation of stress at a grain boundary. These two steps were grain boundary migration and grain boundary slip. It was further suggested that the slower of these two processes is rate controlling. In an attempt to ascertain the validity of the above, a study of grain growth kinetics on the same alloys used for the previous study was undertaken. Separate wire specimens, 0.030 in. diam, in the same as-deformed state (99 pct reduction in area) as in the previous investigation were heated to the various temperatures for a sequence of times. The compositions used and the temperatures of testing are summarized in Table I. A statistical determination of grain size was then made on each specimen, using the average length of traverse between boundaries as a measure of the grain size. Examples of typical results obtained are shown in Figs. &apos;1 and 2. The grain growth law D = ktn was found to fit most of the data. Using this relation, values of the grain growth exponent n were calculated and the inter -esting dependence of n on solute content shown in Figs. 3 and 4 was then obtained. Also, it was found that the constant K which was obtained from extrapolation is roughly independent of solute content. (K is uncertain to within ±25 pct.) An estimate of the activation energy for grain growth was made using the technique of Burke? This method utilizes the plot of the reciprocal of time necessary for the grain size to increase from a definite starting size Do, to a final size D, for each isothermal heat treatment. The slope of this curve corresponds to the heat of activation for the process. In Fig. 5 the rate of grain growth is plotted against the reciprocal of absolute temperature. The activation energies were obtained from these curves and are summarized in Fig. 6. Discussion It is interesting to note that the same saturation in the variability with concentration has been found for the grain growth exponent n in this research as was found in the previous researches on both grain boundary stress relaxationa and internal friction of dislocation origin." The significant feature is that saturation in the variation of these properties has been found to occur at about the same level of solute concentration, namely, between 0.1 and 0.5 atomic pct. The only characteristic common to these different quantities is that solute adsorption at grain boundaries and dislocation can take place and affect these values in a similar fashion. Thus, it is concluded that the grain growth exponent n depends upon solute adsorption at the grain boundaries. It appears, therefore, that theoretical considerations leading to the contrary conclusions5,6 have not treated the real process by which solute atoms exert their effect on grain growth. Prior to the analysis of the observed activation energies, certain of the aspects of the aforementioned grain boundary stress relaxation investigation will be briefly reviewed. It was found that with the addition of solute atoms the grain boundary stress relaxation peak (internal friction vs temperature) decreased in intensity. Simultaneously a second peak was observed which increased with increasing solute atoms. Both of these peaks were shown to be the result of grain boundary stress relaxation. They have been termed, respectively, poire peak and solute peak. It was suggested that the solute peak was dependent upon grain boundary migration, whereas the pure peak was a manifestation of grain boundry slip. Activation energies for both peaks were obtained as a function of Solute content. The value of the activation energy in the temperature range corresponding to the solute peak was

Jan 1, 1958

By Robert M. Lewis

Can wet-ground mica be produced from mica schist ores, and if so, would its properties be comparable with products now on the market? This was the problem which prompted the development of a flowsheet for the beneficiation of mica schist. The fine-ground mica industry relies on weathered pegmatites and alaskite ores as sources of raw material. The mica concentrates obtained from these ores are relatively clean and require moderate beneficiation to meet color and bulk-density specifications. Mica obtained from mica schist is iron-stained and decrepitated and requires additional beneficiation to produce a wet-ground mica product. Despite these adversities, there are several advantages to be gained by mining and processing mica schist ores. The mica content of these ores is considerably higher than that of the pegmatites and alaskite ores now being mined, often containing in excess of 40% mica. This higher-grade mica feed should promote a lower mining and milling cost. The mica schist ores with their higher mica content would mean less tailings to handle; however, there would have to be a means for disposing of acid and sulfate wastes. A flowsheet was developed whereby mica could be recovered from mica schist ores and beneficiated in a way that would result in a high-quality end product.&apos; The essential phase of the process involves using reducing reagents to increase the magnetic susceptibility of iron contaminants which then can be removed with a magnetic separator. General Treatment Procedure The mica is floated by either of two methods, an amine float in an acid circuit&apos; or the U.S. Bureau of Mines (USBM) amine-fatty acid float in an alkaline circuit&apos; The flotation mica is ground in a pebble mill to liberate contaminated particles and expose iron-stained surfaces. The concentrate is then conditioned with a reducing reagent and passed through a Frantz Ferrofilter for the removal of magnetic material. The nonmagnetic product is acid-leached to further reduce the iron contamination. The leached material is then ground to product size and checked for specifications. Discussion of Flowsheet and Its Development Flotation: The mica is concentrated by flotation using either of two methods: an amine float in an acid circuit, or the USBM amine-fatty acid float in an alkaline circuit.&apos; The writer does not wish to elaborate on the relative merits of the two flotation procedures; however, after investigating ores from various localities, it was felt that the amine float in an acid circuit was more consistent when using a standard procedure. Iron Reduction and Magnetic Separation: This phase of the flowsheet may be considered the key to the process. It was developed when it became apparent that hot acid leaching had just about reached its maximum effective¬ness for color improvement. S. C. Sun and William Hirsh in "Hydrochloric Acid Leaching of Iron From Pennsylvania Aluminous Clays,"` reported iron extraction for -20-mesh minerals of 82.20% for hematite and only 33.46% for magnetite. The test procedure employs a 19% hydrochloric acid solution, 104°C temperature, and 10% solids. It was felt that magnetic removal of some of the iron contaminants before leaching therefore would be advantageous. Since the iron minerals present as contaminants vary in magnetic susceptibility, it was decided to experiment with reducing reagents as a means of influencing their magnetic properties. Zinc hydrosulfite or sodium hydrosulfite were the reagents used throughout the tests. The procedure developed consists of conditioning the mica concentrate in a closed container at approximately 5% solids with a reducing reagent. Approximately 10.0 lb of zinc hydrosulfite per ton of mica concentrate is used. The ferric iron is reduced to the ferrous state (magnetic) and oxidation is retarded by isolation from the atmosphere in a closed container. After the desired conditioning time has elapsed, the material is passed through a Frantz Ferrofilter where the magnetic particles are retained and discarded as

Jan 1, 1972

By H. W. Mead, C. E. Birchenall

SELF-DIFFUSION in pure gold has been studied by Sagrubsky,1 McKay,2 Gatos and coworkers,3,4 and Okkerse.5 Sagrubsky used a sectioning technique but reported results far lower than any of the others. The work seems to be carefully done, and it appears that a factor of 60 must have been omitted in his calculations or the units misstated by an equivalent amount. McKay used a surface activity method, and Gatos and Kurtz, following Gatos and Azzam, applied autoradiography to the measurement of activity on an oblique section through the diffusion zone. These two investigations agree well with each other but give results below those reported here. Okkerse employed a very careful sectioning technique. Chemical interdiffusion in Au-Ag alloys has been measured under several concentration conditions. Average values of the diffusion coefficient for the range of 0 to 18 atomic pct Au were obtained by Braune.6 since the diffusion coefficient probably varies markedly over this range, the values may not be too useful. Also, a plot of these data suggests that grain boundary contributions may have been appreciable at the lowest temperature employed. Ebert and Trommsdorf7 give average values for 0 to 9 atomic pct Ag, and Johnson8 reports average values for 45 to 55 atomic pct Au. Johnson also measured silver and gold self-diffusion coefficients in 49.2 atomic pct Au alloys, and self-diffusion in pure silver. The self-diffusion of gold in pure silver has been determined by Jaumot and Sawatsky.10 Other measurements which do not cover a range of temperature or are of low precision are not mentioned in this account since a review by Kubaschewski is available." This contribution reports diffusion coefficients for self-diffusion in gold, self-diffusion of gold in Au-Ag alloys, and chemical diffusion in Au-Ag alloys. Although it had been intended to obtain silver self-diffusion data in the alloys it now appears unlikely that these measurements can be done soon, so a table has been worked out for a self-consistent scheme of diffusion coefficients which should not be too far from the true values. Experimental Details Experiments on pure metals were conducted using fine gold of 99.99+ pct Au and silver of the same purity. Alloys were prepared by melting the two metals together in a graphite crucible in vacuo and allowing the slug to solidify in the crucible. After machining to a cylinder about 0.85 in. diam each slug formed one half of a diffusion couple. Compositions were determined later by analyzing chips taken from the extremities of the diffusion zones. The gold used in the preparation of alloys was sometimes pure gold but was normally either in the form of clean pickled alloy from previous experiments or gold recovered by oxalic acid precipitation from warm aqueous solution. Chips from the various stages of experimentation were dissolved in aqua regia and the solution taken to low bulk, diluted with water, and again taken to low bulk before diluting for the precipitation. This precipitated gold contained a small amount of silver as the only impurity detectable by spectrographic analysis. Disks for use in diffusion couples had opposite plane faces abraded on emery paper as far as zero grit, were annealed for 12 hr at 900°C in argon, and had one face of each disk polished to 000 emery paper. Radioactive gold was plated at about 2 ma per sq cm from a small volume of cyanide solution containing 1 mg of inactive gold as a carrier. Specimens , were freshly abraded on 4/0 emery paper immediately prior to plating. In the case of the active couples disks of a similarly prepared but unplated alloy or pure metal were placed on top and welded to the active disk. With the concentration couples disks of different compositions were welded. Welding was performed after a pressure of 5,000 lb had been applied at

Jan 1, 1958

By C. E. Gregor

Current modern trends in mining show that hoisting shafts are being expected to fulfill an important ventilation function. However, where rigid guides and supporting structures are mandatory, ventilating power costs will be high, unless the transverse structures (shaft sets) are streamlined. In the complex configurations of hoisting shaft furniture patterns, either for original design purposes, or for the adjustment of an existing shaft, a useful degree of aerodynamic optimization, by reduction of overall resistance, can only be effectively evaluated by model studies in a special purpose wind tunnel, as described herein. The author has shown that, in one particular case, an annual power cost saving of more than $50,000 was indicated, mainly by the selection of buntons and dividers of improved aerodynamic profile. Mining companies are now realizing the advantages that can accrue through proper attention to the aerodynamic aspects of mine shaft design. With progressive demands of civilization for an ever greater supply of coal and metals, and with greater depths of working, higher rates of extraction, advanced degrees of mechanization, and improved standards of environmental health and work comfort, shaft design is becoming an extremely important aspect of mining operations. In addition, because the cost of sinking, equipping, maintaining, and operating a mine shaft is continually increasing, there is a greater incentive to use a shaft for the maximum duty, consistent with economy. The current natural tendency is therefore to sink multi-purpose shafts, to install as much equipment as is safely and effectively possible to operate; and then, over and above all these functions, to use the shaft to its maximum possible ventilating capacity, as a major, or auxiliary, airway. Clearly, this latter additional function can only be employed at a significant cost, since the most economic operating airways are smooth-lined and devoid of internal rigid furniture. It is true that hoisting functions can be carried out in such shafts if rope guides are used, but only under restricted conditions. Where a manway must be provided, fixed guides and supporting structures are mandatory, and ventilation costs become accentuated. It is generally recognized that the prime element of cost in ventilating a mine can be represented by the power required to drive the fan unit. It is also known that the largest component of total mine resistance is that of the downcast shaft, where this shaft is equipped with rigid guides for hoisting purposes. The pressure loss varies directly as the resistance of the shaft, in accordance with a modification of the Atkinson equation p = RQ2/3600. Furthermore, the air horsepower drawn is given by the equation AHP = (p x 0/33000. Therefore, the power required to drive the fan unit varies as the resistance of the shaft and the cube of the air quantity. Clearly, if Q is a specified minimum, then the only way to minimize the pressure loss (and the power costs) is to reduce the shaft resistance R. (See Table I for a list of symbols.) The resistance to airflow of a shaft equipped with rigid guides and supporting structural sets consists of two components which, for the sake of analytical simplicity, can be regarded as additive. 1) Frictional resistance, represented by the viscous frictional forces within the boundary layer, as air flows along the surfaces of the walls and the periphery of the vertical elements (guides, pipes, cables, ropes, etc.) of the furniture. The friction loss can be readily calculated by the Atkinson equation, after selection of a suitable value for the friction factor K from the McElroy compilation.&apos; KxLxO xQ2 5.2 xA3 Friction loss can be minimized by lining the shaft walls (particularly if of circular or elliptical cross-section) with a smooth continuous lining of monolithic concrete.

Jan 1, 1968

By Robert E. Brand, Strathmore R. B. Cooke

For a study of the bonding that occurs in magnetite pellets during oxidation, cubes of magnetite, hematite, and quartz were prepared, each with one surface polished and nearly optically plane. These faces were fired together under pressure and at various temperatures to determine whether bonding would occur. Sections of surfaces that bonded were examined microscopically. An attempt was made to measure the strength effected by this treatment. EARLIER work1,2 has shown that the strength developed by fired magnetite pellets containing silica or silicates is due to three separate effects. Two of these are associated with the formation of slag in the interior of each pellet at temperatures above 1000°C, where the atmosphere is substantially though temporarily neutral. The third is independent of the silica content and is responsible for the development of a hard shell around the pellet during the initial stages of firing, a condition which permits the pellet to assume the increasing load of the overlying burden and prevents extrusion of the slagged and semi-liquid interior. Pellets made from hematite concentrates do not show these effects unless specific additives are incorporated, and it is these differences in behavior which in large part account for the difficulty in producing satisfactory pellets from such concentrates. Elsewhere it has been stated that "the most important factor responsible for the development of strength in fired magnetite pellets containing no additive is the oxidation of magnetite to hematite and the subsequent recrystallization and grain growth of this constituent."&apos; The object of the investigation reported in the present paper was to study in detail the mechanism described above and to evaluate its contribution to the strength of the fired pellet compared with other possible mechanisms, excluding slag bonding. This was effected by placing together polished faces of two cubes prepared from specific minerals and then heating them under constant pressure at different temperatures both in air and in nitrogen. The materials used were magnetite, hematite, and quartz. The magnetite was coarsely crystalline material from western Montana, the hematite was Itabira ore from Brazil, and the quartz was of optical grade but of unknown origin. A high-grade Lebanon (Pennsylvania) magnetite concentrate was used to prepare briquets for the investigation of bonding strength. Analyses of the iron oxide materials are given in Table I. The specimens for furnace treatment were prepared with a carborundum cut-off wheel, which cut the minerals into cubes approximating % in. along each edge. Care was taken to make the sides as parallel as possible. The edges of the faces to be polished were beveled, and the cubes were mounted in brass rings with sealing wax, this being essential to prevent the specimens from rocking during polishing. To prevent excessive friction, the wax was recessed so that only the brass ring and the face of each specimen would be in contact with the polishing lap. Each specimen was then ground with No. 600 carborundum to produce a level surface before polishing. The Graton-Vanderwilt process was not used for polishing because of the long time required by this method, but several other methods were tried. Cloth laps using levigated alumina or chromium oxide did not produce the desired polish. Satisfactory results were obtained by means of a pitch lap: which was used for all the mineral cubes, with levigated alumina as the polishing medium. The lap was operated in a machine similar to those used in the preparation of single optical surfaces. It was run at low speeds and moderate pressures, and polishing was stopped occasionally to prevent overheating of the lap. A good polish with flat surfaces could be obtained in about 5 min. After polishing the sealing wax was removed either in hot water or in a solvent such as turpentine.

Jan 1, 1955

By A. W. Schlechten, C. M. Hsiao

The apparent vapor pressures of a number of metal sulphides were determined by measuring their rate of weight loss when they were heated under vacuum. The calculated pressures are due in some instances to the volatility of the sulphide and in others to the decomposition pressure. FIE direct reduction of metallic sulphides, as in the precipitation method for lead or antimony, is not a widely used process today. However, it might be employed for the production of a number of metals if the operation were carried out under reduced pressures. Two general procedures are possible; the reducing agent could form a stable nonvolatile sulphide from which the valuable metal could be removed by volatilization or liquation. The other approach would be to choose a reducing agent which would form a sulphide that could be volatilized away from the valuable metal. A vacuum operation would serve to protect the sulphides and metals from oxidation and would increase the evaporation rates. A related process is the separation of metallic sulphides by selective volatilization either at atmospheric pressure or under vacuum. This procedure is already used commercially for the elimination of lead and cadmium as PbS and CdS from zinc calcines; it might well have other applications. To predict such processes it is necessary to know the relative volatilities of the metallic sulphides and to know whether they volatilize as sulphides or whether the predominant weight loss is due to decomposition. Such data would also be of value in studying problems such as the use of sulphides for refractories, as described by Brewer,] or in the evaluation of the theory of ore deposition from the vapor state, as proposed by Brown.&apos; Qualitative statements concerning the volatility of metallic sulphides can be found frequently in the literature and are well summarized by Mellor, but accurate determinations of rates of evaporation or vapor pressures are very scarce. Kelly" lists vapor pressure data only for PbS; his reference being to the work of Schenck and Albers,4 who measured the vapor pressure of PbS by a dynamic method between 850" and 995°C. More recently Veselovskii5 has determined the vapor pressures of the sulphides of antimony, lead, cadmium, and zinc at temperatures ranging from 360" to 1000°C using Knudsen&apos;s method. A second Russian worker, Pogorelyi,6 determined the vapor pressures of CdS and ZnS at temperatures from 900" to 1250°C. The results obtained by these workers are shown in subsequent graphs in comparison with the data of this paper. Brewer and coworkers1 have studied some of the metallic sulphides to determine their suitability as refractories in vacuum. Veselovskii&apos;s determinations on PbS checked well with those of Schenck and Albers, and his determinations of CdS check almost exactly with Pogo-relyi. For the vapor pressure of ZnS the data of Veselovskii and that of Pogorelyi are in fair agreement, as shown in Fig. 1, but it should be pointed out that Lumsden7 has discovered that the equation given by Veselovskii for the vapor pressure of ZnS: - 14,200 log P9.495 is in error by a factor of ten when compared to the experimental data. In contrast with the scarcity of data on vapor pressures, the decomposition pressures of many metal sulphides have been determined and are summarized by Smithells.8 Theoretical Considerations The experiments described in this paper consisted of determinations of the rate of weight loss of certain metallic sulphides under very low pressures at different temperatures. These data plus observation and analyses of the products reveal the mechanism of the weight loss and also provide a basis for the calculation of the vapor pressure or apparent vapor pressures of the sulphides.

Jan 1, 1953

By R. Schuhmann

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) In his excellent paper, Dr. Schuhmann has proposed a mechanism for conlrninution which can be utilized to explain a number of phenomena which have been observed in the size reduction of solids. The difference between the product obtained from a ball mill and from a rod mill can readily be explained by Dr. Schuhmann&apos;s hypothesis. Consider that the size distribution of the product from each comminution event is given by y; - 100 (x/ki) (1) where Yi is the cumulative percent finer than size x, ki is the size modulus, and is the distribution modulus for the single comminution event. The total product from a cornminution operation will be the summation of the products from all of the individual cornrninution events. If the size moduli from the various comminution events range from kl to kn , the size distribution of the total product will be a straight line on a log-log plot only to a particle size equal to k ,. Considering 100 volurnes of feed, the value of y for x equal to kl is Riven by where y is the cumulative percent finer than size kj, z is the number of comminution events of kind i, and vi is the volume of each particle crushed. y=z1 qv1+z2 qv2 (k1/k2) +.............zn qvn (k1/kn) (3) F or particle sizes greater than k1 7 e. 6. x = k3, the value of y will be given by k3 A y = z1 qv1 + z2bv2 + Z3uV3 + zn zn qvn (k3/kn)(4) Only when x is equal to k, will y equal 100. &apos;Thus, the total product from a comminution operation will be a straight line on a log-log plot strictly up to a particle size equal to kl and above that size the line will curve so that y will equal 100 for the coarsest particle or k, (see Fig. 1). The actual shape of the size of distribution curve will depend upon the relative number of conmninution events of different kinds. In the case of ball milling, the ratio kn/kl may be pite large and there will be considerable deviation at the coarse sizes in a Schuhmann plot. kIowever, the grinding action in a rod mill is such that fine particles are protected from the rods by the coarse particles. Consequently, kn/kl will be quite small and the product from a rod mill will give a straight line Schuhmann plot almost to y equal 100%. In his paper, Dr. Schuhmann also has presented a very straightforward definition of grindability derived from the basic energy equation E = Ak-a (5) where E is the energy required to comminute a material to a size modulus of k and A is a constant. According to Dr. Schuhmann, the grindability of a material is the volume of material comminuted finer than unit size per unit of energy expended, this being 1/A. For comparison of grindabilities at any size two numbers are required, both = and 1/A, and anyone tabulating grindabilities should give both of these numbers. Concerning the experimental determination of grindabilities, if the material being comminuted possesses distinct cleavage, the energy re quired for comminution is given by E = Ak-(a-y) (6) where y is small number less than = . Because of cleavage, less energy will be required for comminution. To be certain that cleavage does not affect the gindability of the material being tested, it is suggested that the method used by Dr. Charles for determining grindability be used to ascertain if the deviation exponent y is zero or finite. R. Schuhmann, Jr. (Author&apos;s Reply) Dr. Fuerstenau&apos;s interesting comparison of rod milling and ball milling

Jan 1, 1961

By F. J. Fayers, J. W. Sheldon

A theoretical discussion is presented of the behavior of the interface between two fluids of different physical properties when displacement is occurring along a thin tilted bed. An approximate equation of motion is deduced for the motion of the interface, suitable boundary conditions are derived and the conditions necessary for the approximation to be valid are determined. Steady-state behavior and the circumstances under which a steady-state interface can develop are discussed. Finite-difference solutions of the equation of motion for two characteristic water-drive problems are presenled. The theory of displacement in a thin bed may be regarded as being the porous-medium-equivalent of the classical "shallow-water wave" theory of hydrodynamics. INTRODUCTION The solution of moving interface problems are important in predicting the behavior of oil reservoirs under various conditions of production. Kidder4,5 has obtained analytic solutions for the fingering problem and for another particular case of the motion of the interface between two immiscible fluids of unequal density in a porous medium. In the present analysis, we analyze the problem of the motion of an interface along a slightly dipping bed whose length is long compared with its thickness. The requirement of a thin bed is necessary in order to give a simple differential equation for the motion. The two fluids are of unequal density and mobility. In the derivation of the equation of motion, it is assumed that the lighter fluid is being injected at constant rate at the high end of the porous layer, while heavy fluid is produced at the low end of the layer. The analysis applies equally well, however, to the reverse procedure in which the heavier fluid is injected at the low end of the tilted layer. It will be shown that the behavior of the system is critically dependent on which fluid has the higher mobility and that the interface can in certain circumstances achieve a simple progressive steady-state shape. The fluids may be considered to be immiscible or miscible. It is assumed, however, that the thickness of the interface region is negligible in comparison with other dimensions of the system, and that the strength of the saturation or concentration discontinuity remains constant during the motion. In conjunction with Buckley-Leverett theory and areal sweep-out calculations, the tilted interface problem is one of the fundamental problems of reservoir engineering; it defines the very important underpassing and overpassing phenomena associated with water-drives, gas-drives and secondary recovery operations. The tilted interface problem has been dealt with previously by Dietz.2 In the present paper, we endeavor to derive the pertinent mathematical results more rigorously, and in doing so we obtain modifications in both the differential equation and boundary conditions for those given by Dietz. We also attempt to show the connection between these results and some of the recent work on the stability of interfaces. Finally, we attempt to demonstrate the practical importance of the thin bed theory by showing the difference in behavior of two characteristic waterflood problems. In the favorable mobility case recovery is improved by increasing production rate, while in the unfavorable case undercutting or overcutting is minimized by reducing the displacement rate. PROPERTIES OF THE EQUATION OF MOTION Fig. 1 illustrates a porous layer of constant thickness H and tilt 8 with Fluid 1 of mobility ?l and density pl below Fluid 2 of mobility ?2 and density p2. The fluids are incompressible and flowing with volumetric flux q along the layer. Both the slope a of the interface with respect to the bed and the curvature of the interface are assumed to be small. What is meant by "small" is indicated in the derivation given in Appendix A of an approximate equation of motion for the interface. Other symbols are defined in the "Nomen-

By B. Ancker, E. R. Parker

The small-angle dislocation-boundary density of nickel and some of its alloys was investigated as a function of strength. It was found that the strength is a linear function of the density for pure nickel and for Ni-Ti alloys, but not for Ni-Co alloys. The results are interpreted in terms of dislocation theory. THE processes by which metals deform are still poorly understood, even though there has been a concentrated research effort in this field during the past fifteen years. Single crystals and individual grains in polycrystalline aggregates often develop a subgrain structure when deformed. Substructure formation occurs as a result of local plastic bending and its development is augmented by annealing at moderate temperatures.&apos; Investigations made to date, largely qualitative in nature, have shown that the substructure is composed of a network of small-angle boundaries. The purpose of the present paper is to present some quantitative data on substructure (obtained by X-ray techniques) and to correlate the results with the strength of the metal in which the substructure existed. Nickel and some of its alloys were used for the experiments. The presence of certain kinds of foreign atoms greatly alters the formation and effect of the substructure. Polycrystalline tensile specimens were prepared from high purity nickel, two Ni-Ti alloys, and two Ni-Co alloys; the composition of these materials is given in Table I. Tensile specimens having a reduced section 1/4 in. diam by 3 in. long were machined from materials which were refined, cast, forged, and swaged in the authors&apos; laboratories. The specimens were annealed for 1/2 hr at 1150°C, a treatment which produced grains having a diameter of approximately 0.5 mm. This rather large grain size was used to facilitate later examination of the substructure. Duplicate specimens of pure nickel and of each alloy were strained various controlled amounts in tension at room temperature and recovered for 1 hr at 800°C. (This strain induced prior to recovery will be referred to hereafter as the "prestrain.") One of each of the recovered specimens was pulled in tension at room temperature to obtain the stress-strain curves. The other bar was cross-sectioned in the gage length, carefully polished, and deeply etched to remove all cold-worked material. This specimen was then examined by the X-ray microscopic technique2 to determine the nature and magnitude of the substructure. The use of duplicate specimens permitted a direct correlation between tensile properties and substructure characteristics. X-ray microscopic studies were made with an apparatus constructed to have an average resolving power of about 4 microns. The monochromatic radiation reflected from grains which were oriented favorably was recorded on fine-grain photographic plates. These were examined at Xl00 which represents the true magnification, since there was essentially none in the X-ray system. This permitted detection of angular differences between subgrains of as little as 10 min. A very large number (over 100) of grains for each specimen was examined at this magnification and the number of substructure boundaries per grain was tabulated. An accurate relative measure was obtained under fixed experimental conditions, e.g., same grain size, resolving power, magnification, etc. The greatest source of error lay in counting the subboundaries, but this proved to be surprisingly small when repeated counts were made by different investigators. Furthermore, as the subsequent analysis indicates, whatever human error was introduced was not significant. Analysis of the Substructure Data When the number of substructure boundaries per grain was plotted against the frequency, skew (asymmetrical) distribution curves of the type shown in Fig. 1 were obtained. These are smoothed curves for the 1 atomic pct Ti in nickel alloy subjected to various prestrains and are representative of the curves obtained with all the metals. Since skew-distribution curves cannot be analyzed by elementary statistical methods, detailed investigations were undertaken in order to 1—test the consistency

Jan 1, 1955

By J. H. O’Dette

BLISTER formation on wrought aluminum products has been a matter of concern to aluminum fabricators for many years. The fact that blisters make their appearance during the final stages of fabrication means that much time and effort have been expended before it is evident that the material must be scrapped. This and the loss of production are ample reasons for embarking on a research program to find out more about blistering and possible methods of control. Many excellent papers on this subject have appeared in the technical literature in the last few years. In one of the more recent papers, Kostronl gives a fairly complete review of the problem of gas in aluminum and blistering in general. From the work of the various investigators, a general mechanism for the formation of blisters has evolved and may be summarized briefly as follows: Hydrogen gas is usually present in the cast ingot, in the atomic or ionic state, in excess of the solid solubility. At room temperature the gas atoms are relatively immobile, but at elevated temperatures they become mobile and diffuse to free surfaces where they associate to form molecules. If these free surfaces are discontinuities within the ingot then the associated gas molecules collect and build up considerable pressure until equilibrium is reached with the dissolved gas around the discontinuity. Since the solubility of the gas is proportional to the square root of the partial pressure it is evident that large pressures may be built up at the discontinuities. When the metal is rolled to sheet the pressure of the gas in these, discontinuities is sufficient to deform the surface of the sheet and form a blister, particularly when the strength of the material is reduced during the annealing. Although the mechanism of the formation of blisters was fairly well known, the actual impor- tance of the individual roles played by the gas and the discontinuities was not so well established that positive methods for control of blistering were at hand. It was the object of the investigation to learn more about the nature of the discontinuities giving rise to blistering and to develop methods of control. The investigation was carried out in three stages as follows: a) A study of the more commonly used methods of removing hydrogen from aluminum, such as fluxing and holding, and their effects on blistering. b) Location of the discontinuities giving rise to blistering. c) A study, by indirect methods, of the movement of gas in the metal and its effect on blistering, and the development of methods of blister control during fabrication. Removing Gas and Reducing Blistering by Fluxing or Holding-—The work of removing gas and reducing blistering by fluxing or holding was carried out on metal of Alcan 2s (1100) composition with an artificially high gas content. The high gas content was obtained by introducing water into the melt prior to casting; the water reacted with the aluminum forming A12O3 and hydrogen. The procedure was to raise the gas content by introducing water into an aluminum melt and using half the melt to cast one ingot immediately. The remaining metal was treated again with water to make up for the reduction in gas content during holding, while the first ingot was being cast, and then given a fluxing or holding treatment and cast into an ingot. Samples for gas determination were cast from the molten metal before and after the gassing operation; before, after, and during fluxing, and while casting. Samples were also cut from sections of the ingots. Gas determinations were made on these samples using the well known vacuum fusion technique. All ingots were hot rolled at 500°C to 0.250-in. slab which, in turn, was cold rolled to 0.040 in. sheet. The sheet was coiled and annealed for 2 hr at 500 °C and then cut into 5-in. squares which were inspected for

Jan 1, 1958

By F. A. Crossley

The additions: o, Sn, Zr, Cb, Mo, and V were studied for their effects on the a/a + Ti3A1 boundary of Ti-A1 base ternary alloys. These additions were chosen because of their importance to commercial titanium alloy practice—oxygen as the major impurity (in terms of influence on mechanical properties) and the others as major alloying additions. The composition and temperature ranges of investigation varied according to the system as shown in Table I. The principal means of investigation was light-microscopy. The basis of the ternary studies was the recently determined titanium-rich end of the Ti-A1 system.&apos; MATERIALS, METHODS, AND PROCEDURES Ingots were prepared in 15 g size for all alloys except those of the Ti-Al-Mo and Ti-A1-V systems which were prepared in 20 g size. These alloys were prepared from high-purity, electrolytically refined titanium obtained from the Bureau of Mines, Boulder City Metallurgical Laboratory, Boulder City, Col., and Chicago Development Corp., Riverdale, Md., for the 15 g and 20 g ingots, respectively. The alloying additions were obtained from commercial sources, and were at least of 99.9 pct purity, except the V-15 wt pct A1 master alloy for vanadium additions. This alloy was of 98.2 pct purity; the major impurities were 0.37 wt pct Fe and 0.38 wt pct Si. The ingots were prepared by multiple melting in a nonconsum-able-electrode arc furnace. The ingots were covered with Markal coating "CR-T22" (Markal Co., Chicago) to protect them from scaling. Markal coating is applied as a slurry of solids in a volatile carrier liquid. The coated article is air dried. Upon heating to the hot working temperature the coating fuses to form a glassy, protective film. The ingots were heated to 1000°C and rolled to 0.16 in. thickness, reheating after each pass. The glassy film was removed by sand blasting. Ten mils were removed from all surfaces by grinding and/or pickling (3 pct HF, 30 pct HN03, balance water). Grinding was always followed by pickling to remove traces of the grindmg medium. Hydrogen removal was accomplished by vacuum annealing at 1000°C for 2 hr to a final pressure of about 0.02 µ Hg. This was followed by annealing in evacuated Vycor bulbs (800°C, 2 hr, ice brine quenched (IBQ)) in order to maximize ductility. The materials were then lightly pickled and cold rolled to 0.12 in. thickness or cracking, whichever occurred first. After rolling, 1/2 by 1/4 in. specimens were cut for the equilibration anneals given in Table 11 and carried out as previously described.1 Final polishing of the specimens for metallographic examination was done by electrolytic means. Specimens were first examined without etching under bright field and polarized light illumination, for this is the only means of detecting the "two-phase" phenomenon.1,2 The term "two-phase syndrome" refers to Ti-A1 al-loys which appear on the bases of their chemical, phys-ical, and mechanical properties, to be two-phase, but are actually single phase and inhomogeneous in composition. Since processing and heat treatment of the alloys of the first group were completed before the two-phase syndrome was discovered, a number of the specimens were found to exhibit this phenomenon—80 pct of those of the Ti-Al-Zr system, 5 pct of those of the Ti-Al-Sn system, 30 pct of those of the Ti-Al-Zr system. The affected specimens were homogenized by heating above the ß transus temperature and quenching. The heat treatment and working schedules to accomplish this are given in Table 111. After rolling, specimens were pickled (3 pctHF, 30 pct HNO3 in water) to remove 1 to 2 mils from the

Jan 1, 1970

By Wolfgang O. Gluschke

INTRODUCTION Virtually all countries have general legislation covering most aspects of mining and mineral processing, including investment and tax laws, safety and health regulation, and specific rules applying to exploration reporting procedures. Yet most developing countries negotiate individual agreements with foreign investors for major mineral projects, in particular when all or part of the expected output is exported. Such agreements are known under several different names, as for example concession agreement; technical assistance agreement or service contract; management agreement; production sharing contract; joint venture; or contract of work. The objectives and conditions governing such contracts are as diverse as these titles are. While a mining project is only one among a large mumber of similar undertakings in industrial countries, in most developing countries such projects usually have a dominating position within the country&apos;s economy. The general legislation is often inadequate and insufficiently detailed to cover all aspects of large projects with extensive foreign inputs and international markets. Therefore, the need for specific arrangements. Specific arrangements may also become necessary due to the complexity of markets for mineral products, the large number of participants - equity partners, suppliers, financial institutions, buyers, etc. - or economic and political conditions in the host country and fiscal regulations in the home country of the investors. Most agreements are concluded between governments, or government agencies, in developing countries and private industry headquartered in developed market economies - Canada and the United States of America in North America, Western European countries, Japan, South Africa and Australia - or, in some instances, with state-owned firms in these countries. There are fewer agreements between developing countries and the centrally planned economy countries - Eastern Europe and the USSR - which cannot be considered here because of absence of adequate information. Agreements can be concluded at any of the different stages from exploration through closing of a mine. While most contracts are negotiated at the time when a potentially viable ore body has been delineated and investigated sufficiently to anticipate a realistic time for commencement of production, other agreements start with "grass-roots" exploration, during operation of a mine, smelter or refinery or, exceptionally, after a temporary shutdown. While several major provisions are included in all types of agreements, others are covered in much more detail (or not at all) in some contracts reflecting the specific work programme of each project. While it is realized that subdivision and classification of complex contractual relations is necessarily arbitrary to a certain extent, such grouping is useful in practical terms, especially for the non-specialist. The following discussion, therefore, will start with a description of the major forms of contractual relation - concession, investment contract, joint venture, management agreement, service and production sharing contracts. Major issues covered in all, or almost all, agreements will then be dealt with. These include stages of development, corporate structure and control, fiscal arrangements, infrastructure development and environmental law, and dispute settlement and renegotiation. FORMS OF CONTRACT RELATIONS There has been marked change in the type of agreement entered into during the 1960s (and before) and the early 1970s and the period thereafter. While straight "concessions" - granting of exclusive rights to foreign investors over a certain deposit or areas with little restriction or well-defined obligations - were the rule during the first half of this century, more complex agreements have evolved since. Some of these cover every conceivable aspect, foreseen or only possible, and define rights and obligations of all partners to the last detail. Over the years, agreements have without doubt become more beneficial for the developing host countries, in part as a result of well-publicized nationalizations, as for example in Chile, and in part due to changed attitudes in all countries

Jan 1, 1985

By G. H. Enzian

THE effects of phosphorus and nitrogen on the properties and behavior of low carbon steels are important considerations to both the manufacturer and the user of such material. For one thing, these two elements are the principal points of distinction between the chemical compositions of Bessemer and open-hearth grades. Further, open-hearth steels themselves may vary considerably in nitrogen content depending on the raw materials and ..practice used. In addition, appreciable amounts of rephosphorized open-hearth steels are being used at the present time in some low alloy, high strength grades and in certain other cases. For these and other reasons, it was felt desirable to obtain more complete knowledge of the effects of simultaneous small variations in phosphorus and nitrogen content on such properties of low carbon steel as tensile strength, impact toughness, sensitivity to cold work, and strain aging. A long range investigational program designed to furnish such information, was carried out, and the present paper summarizes some of the data currently obtained. General Discussion The strengthening effect of relatively small amounts of phosphorus in steel has been recognized, and to some extent utilized, for many years. A number of investigators have pointed out, from time to time, that under proper conditions of control, phosphorus can be a useful alloying element in low carbon steels.1-3 Nevertheless, in spite of the volume of data on the subject, the use of phosphorus for this purpose has always been handicapped by widespread feeling that its presence makes the steel brittle, difficult to cold work, and unreliable at low temperatures. This belief on the part of some steel users is not entirely justified in many cases, and often stems from early experience with acid Bessemer steels which have appreciably higher phosphorus (and nitrogen) contents than basic open-hearth grades. Nitrogen in steel, and its effect on properties, has also received considerable attention in the literature.4 In 1906, Braune5 ascribed the brittleness of Bessemer rails to the nitrogen content, and proposed a schedule of nitrogen limits for steels for various uses. This was one of the first papers to recommend directly the use of nitrogen content as a quality control measure, but it did not meet with much favor or support; as a matter of fact, the Jernkon-toret was rather sharply criticized for publishing the paper. In the intervening years a number of papers have been published on the subject of nitrogen in steel. As a result, it is now generally recognized that nitrogen can have an important effect on the properties and behavior of steel and that the presence of this element should be considered in any systematic study of factors affecting steel quality. In 1932, Graham6 introduced the concept that the quality of various steels could conveniently be evaluated and compared in terms of "sensitivity", which was defined as "the characteristic reaction rate of a piece of steel toward brittleness or hardness." This concept formed the basis for a broad research program into factors causing variations in the quality of commercial steels. At an early stage of this work, it became apparent that the observed effect of either phosphorus or nitrogen on the sensitivity of steel depended, in no small measure, on how much of the other of these two elements was also present. Indeed, the combined effect of phosphorus and nitrogen in steel may often be more important than the specific effect of either. With a few exceptions, it is not possible to predict accurately the effect on steel properties of a change in the amount of either phosphorus or nitrogen in the steel without also specifying the approximate amount of the other element. It seems desirable, at this point, to discuss briefly the distinction between strain-sensitivity and strain aging as used in this paper. In the early stages of its development, the work-brittleness test7 (which will be described in more detail later) was used

Jan 1, 1951

By D. C. Hilty, W. Crafts

A qualitative pseudoternary solidification diagram for the Fe-S-O system modified by manganese is proposed and supported by experimental derivation of an isothermal section at 1475°C and substantially 1 pct Mn in the solid-metal phase. The solubility of oxygen in liquid iron containing 1 pct Mn and sulphur contents up to 0.9 pct has been measured at 1600°C and found to increase as the sulphur content exceeds 0.15 pct. AS has been pointed out previously,&apos; all oxide and sulphide inclusions in steel, excluding mechanically entrained matter, result from modifications of the basic Fe-S-O system. Therefore, one method of attack on the problem of the mechanism of deoxida-tion and inclusion formation is to examine the influence of deoxidizers on the Fe-S-O liquidus diagram. This approach has been adopted in work on the subject being carried out at the Metals Research Laboratories of the Electro Metallurgical Co. and has resulted in the postulation of types of solidification diagrams for the Fe-S-O system modified with common deoxidizers. This method has been of considerable assistance in interpretation of the factors affecting the formation of inclusions.&apos; For the most part, however, these diagrams have been highly speculative. They were constructed primarily by inference from the pertinent binary and ternary systems and from the appearance of inclusions produced by specific deoxidizers. Moreover, since the systems contain four or more components, simplifying assumptions and qualifications were necessary in order to permit their representation as modifications of the Fe-S-O diagram. Consequently, experimental confirmation of the type of construction employed for these diagrams is desirable, and the present paper is concerned with such evidence. The addition of manganese to the Fe-S-O system was selected for initial investigation. Manganese is an important component of practically all steel and is, therefore, of fundamental interest. Because of its great affinity for sulphur, manganese has a more profound effect on the sulphide side of the Fe-S-O diagram than any of the other common deoxidizing eletments. In addition, more quantitative information pertaining to the contiguous binary and ternary systems involving iron, manganese, sulphur, and oxygen is available than for the other deoxidizers. Fe(Mn)-S-O Solidification Diagram Many of the side diagrams of interest in connection with this system are known. The Fe-Mn binary has been well established by several investigators;% the Fe-O system has been clarified by Darken and Gurry;&apos; and FeO-MnO diagrams have been published by Herty,5 Andrew, Maddocks, and Howat,6 and by Hay, Howat, and White.7 The Mn-O diagram does not appear to have been derived experimentally, but the portion of &apos;it that is of interest can be visualized easily from a consideration of the melting points of Mn and MnO and the fact that a broad miscibility gap must exist between them. The ternary Fe-Mn-O diagram has been discussed by Benedicks and Löfquist,8 Wentrup,9 and by Körber and Oelsen.10 Experimental study of the Fe-Mn-O system has been carried out by Körber and Oelsen and to a lesser degree by Chipman, Gero, and Winkler,11 Hilty and Crafts," and others. On the basis of published information, then, an outline of the Fe-Mn-O liquidus diagram can be constructed as illustrated by Fig. 1. In this, as in all succeeding diagrams, transformations such as the ?-? reaction in iron have been ignored for purposes of simplification. The arrows denote falling temperature. The distinguishing feature of this diagram is the broad region of liquid immiscibility extending

Jan 1, 1955

By Walter Crafts, D. C. Hilty

The liquidus diagram for the iron field of the Fe-S-O system has been derived experimentally. The solubility of oxygen in molten Fe-S alloys has been measured at several temperatures and found first to decrease slightly and then increase rapidly with increasing sulphur content. IT is well-known that the types, distribution, and amount of inclusions in any given steel are closely allied with the oxygen and sulphur contents of the metal, so that the term "deoxidation" as conventionally applied in steelmaking refers not only to the control of oxygen and oxide inclusions but to collateral modification of sulphide inclusions as well. Inclusions commonly occur in steel as mixtures of oxides and sulphides, sometimes closely associated and sometimes apparently completely divorced. Their effects on the properties of the metal may vary widely depending on their types and distribution as well as on their quantity. The mechanism by which inclusions form, however, and the means for controlling it are exceedingly complex and not well understood. Nevertheless, as described by Benedicts and Lofquist&apos; and by Wentrup&apos; all oxide and sulphide inclusions, excluding mechanically entrained matter, must result from specific modifications of the basic equilibria of the Fe-S-O system. In an investigation of the mechanism of deoxidation and inclusion formation being carried out at the Union Carbide and Carbon Research Laboratories, it became evident that quantitative data for the fundamental Fe-S-O system were essential to a better understanding of the problem. Consequently, the liquidus surface of the portion of the Fe-S-O diagram of interest in steelmaking has been determined, and the solubility of oxygen in liquid iron containing sulphur has been measured. Fe-S-O Diagram The portion of the Fe-S-O diagram of specific interest in steelmaking is the Fe-FeS-FeO corner. Of the contiguous binary diagrams for this partial system, only those for Fe-FeO and Fe-FeS are known with reasonable certainty.3 Several attempts to derive the FeO-FeS diagram have been made, chief among them being the work of Giani as reported by Oberhoffer,4 and, more recently, that of Vogel and Fulling." Although both Giani and Vogel and Fulling published diagrams for the FeO-FeS system, their observations indicated that the oxide component approximated Fe3O4 rather than FeO, so that there is doubt whether the system is truly binary. Benedicts and Lofquist and also Wentrup published qualitative sketches of the ternary diagram based on the assumption that it was of the type described by Marsh for a ternary system in which two of the contiguous binary systems are simple eutectic systems and the third exhibits a solubility gap in the liquid. Apparently, however, the only previous effort to establish the diagram experimentally was that of Vogel and Fülling whose results are reproduced in Fig. 1. Although defining approximately the limits of the miscibility gap and the location of the ternary eutectic, point E in Fig. I, Vogel and Fülling&apos;s diagram must be considered only semiquantitative. It was derived from a limited number of observations mainly along two quasi-binary sections, and the directions of the tie-lines and the location of the critical point, K in Fig. 1, were estimated by computation. Experimental Procedure The experimental technique employed for the present investigation involved melting mixtures of ferrous sulphide and ferric oxide in contact with iron. Since it was considered that in this part of the system the vapor pressures of sulphur and SO, are so low that they would not affect the results significantly, the melting was carried out in a current of argon to sweep out products of any initial re-

Jan 1, 1953

By F. W. Jessen, N. Mungan

The plastic flow characteristics of clay water suspensions were first recognized by Binghaml in 1916 and further studied by Ambrose and Loomis&apos; in 1931-1932. Many physical and chemical properties of clay suspensions are deeply influenced by particle size distribution as well as by the exchange cation. Separation of a number of fractions is particularly helpful in making a detailed study of a suspension. A limited amount of work has been conducted on the effects of particle size on specific properties of mud drilling fluids. A knowledge of particle size distribution is essential for a better understanding of fundamental properties of clay suspensions, particularly viscosity and gel strength. The purpose of this investigation was to study the effect of particle size on the viscosity and gel properties of clay suspensions and to determine any changes in mineral composition accompanying variation in size. EXPERIMENTAL PROCEDURE Numerous methods may be used to fractionate a poly-dispersed clay suspension into nearly mono-dispersed systems. Particles larger than 44 micron (325-mesh) may be obtained by wet screening. For sizes from 44 to 1 micron, the fractionation may be accomplished by sedimentation, elutriation plus microscopy,&apos; or turbidimetry.6 When dealing with systems which contain a major portion of particles below l-mi-cron size, slit ultramicroscopy,7 centrifuge methods of Svedberg,5 eams,9 and McBain,l0 and X-ray methods" may be employed. The Sharples super centrifuge has been proved suitable for the economical separation of suspended particles of submicron range.12,13,14 Three-hundred and forty-five gal of 1 per cent by weight Aquagel suspension was mixed in a high-speed 5-gallon mud mixer and the suspension was allowed to stand in 5-gal glass bottles for 30 days to assure full hydration. All particles larger than 44 microns were removed by wet screening. Five fractions in the range of 44 to 1 micron were obtained by sedimentation. The Sharples super centrifuge method described by Hauser and Reed.13 Norton and Speil,14 Ha user and Lynn,15 and Hauser and Schachman,10 as employed to yield five fractions of submicron size. A super centrifuge operation chart prepared by Fancher, Oliphant, and Houssierre12 was used to determine operating conditions for the desired particle ranges. The clay suspension, after removal of all material above 1-micron size, was centrifuged. During rotation of the bowl, the particles were deposited on a thin plastic liner which fit closely inside the bowl. After passing 5 gal of suspension through the centrifuge, the liner was removed and the particles on the liner were scraped off, remixed and recentrifuged. This was repeated five times. Thus, Fractions H, I, K, and L were obtained. The finest fraction, M, remained in an approximately 0.4 per cent suspension. Water was evaporated under reduced pressure from this suspension to yield the finest particles. Results of the fractionation are included in Table 1. In order to achieve proper orientation and humidity conditions for X-ray diffraction analysis, the following procedure was employed. The dilute suspensions were placed on glass slides and allowed to dry at room temperature. This was repeated several times. Previous to measurement each sample first was placed in a water desiccator for half an hour and then allowed to stand for 15 minutes at room temperature. thus yielding an equilibrium condition of about 52 per cent relative humidity. The relative humidity of the room in which the X-ray diffraction was carried out was maintained at approximately 50 per cent so that there was no change in the spacings during the X-ray examination. Samples

By A. J. Griest, A. P. Young, P. D. Frost

A study was made of the effect of ß grain size on the tensile ductility of a-ß titanium alloys haet treated to strengths in the range 165,000 to 180,000 psi. It was concluded that the primary cause of $ embrittlement is the large grain size which is obtained so rapidly in many a-ß titanium alloys when heated into the ß field. It was also found that grain-boundary a and acicular intragranular a in the microstructure are not necessarily detrimental to the tensile ductility if the prior ß grain size is sufficientlv fine. BETA embrittlement occurs in a-ß alloys when the finish hot-working or stages of the subsequent heat treatment have been done at temperatures in the ß field. In order to avoid this embrittlement, for-gings must be finished at temperatures under the ß transus. For better workability, it would be desirable to forge at temperatures in the ß field. For this reason, research has been conducted to determine the cause of ß embrittlement. Although ß grain size has been considered as a possible contributing factor to ß embrittlement, only limited research has been done to evaluate its effect. The effect of addition elements on ß grain growth in unalloyed titanium has been studied by Liu.&apos; Complete mechanical property data, however, were not obtained for correlation with grain size. Ogden and coworkers2 have investigated the effect of both a and ß grain size and grain shape in Ti-Cr-Mo alloys. Their data indicated that tensile ductility was relatively insensitive to ß grain size at annealed strength levels (140,000 psi ultimate). No study has apparently been made to determine the relationship between ß grain size and ß embrittlement in a-ß alloys heat treated to high strength (180,000 psi ultimate). The high-strength condition is that in which ß embrittlement is particularly severe. Beta grain size is not easily varied through the use of a range of annealing times and temperatures in the ß field, because of the rapidity with which ß grain growth occurs. Short-time heating techniques are needed to obtain the smallest ß grains. EXPERIMENTAL PROCEDURE In this research, the experimental procedure was as follows: 1) Tensile and microimpact specimen blanks were resistance heated to produce a range of ß grain sizes. 2) The tensile and microimpact blanks were then solution-treated in the a-ß field and aged to produce predetermined ultimate tensile strengths in the range 165,000 to 180,000 psi. Tensile and impact ductility were then correlated with a grain size for constant strength levels. Materials—The alloys Ti-6A1-4V, Ti-4A1-4Mn, and Ti-16V-2.5Al are representative of the heat-treatable a-ß types in which ß embrittlement can be severe. The compositions and ß transi of the heats studied are given in Table I. The Ti-16V-2.5Al heat was melted and fabricated to 1/4 in. round at Battelle; the other alloys were obtained as 1/4 in. round rolled from commercial heats. The micro-structures of the as-rolled alloys were fine a-ß mixtures. This structure is typical of titanium alloys hot-worked extensively in the a-ß field. Resistance-Heating Treatments to Establish ß Grain Size—For direit resistance heating, a 1/4-in.-diam s~ecimen was heated with a 3000-watt transformer rated for 1000 amp with adjustable secondary voltage. The apparatus included a spray quench fixture. Both heating and quenching periods could be automatically controlled. For temperature measurements, 28-gage Chromel-Alumel wires were tack-welded to the specimen at its midpoint. A high-speed recorder-controller was used to control the heating cycle.

Jan 1, 1960

By R. J. Wagner, Jim Douglas Jr., P. M. Blair

The calculation of the behavior of an oil reservoir during a water flood has long been an important problem to reservoir engineers. Buckley and Leverett derived the differential equation which describes the displacement of oil from a linear porous medium by an immiscible fluid, but this equation could not be solved by the methods of classic mathematics. Consequently, in order to integrate the equation over the length of the reservoir, they neglected the effects of capillary pressure. In the present paper, a numerical method has been developed for determining the behavior of a linear wafer flood with the inclusion of capillary pressure. The differential equation which was derived for the case of incompressible fluids is second order and non-linear. This differential equation was approximated by an implicit form of difference equation which is second order correct in both time and distance. An electronic digital computer was used to perform the numerical solution of the difference equation. INTRODUCTION The problem of calculating the flow and distribution of fluids in an oil reservoir subjected to a water flood has long challenged the reservoir engineer. The ability to solve this problem would provide a valuable tool for the design and study of field waterflooding programs. One of the first contributions in this field was made by Buckley and Leverett,&apos;.&apos; who developed a method of calculating waterflood performance in a linear reservoir. Their technique was limited by the practical necessity of excluding quantitative consideration of capillary pressure. It is the purpose of this paper to describe a method for calculating the behavior of a linear water flood with capillary pressure considered. This method, although limited to the linear case, should serve as a step toward the solution of the two- or three-dimensional waterflooding problem which would better describe actual reservoirs. The treatment of the problem has assumed that the reservoir is linear and homogeneous, that both oil and water -are incompressible, and that gravitational forces may be neglected, and that water is injected into one end of the reservoir and oil and water are produced from the other. Though these assumptions may not be directly applied to natural reservoirs, they are closely approached in many laboratory core tests. The physical problem has been represented mathematically by means of a differential equation and suitable boundary conditions. The inclusion of capillary pressure effects causes the differential equation to be second order and non-linear, and it is not amenable to solution in terms of known functions. Nevertheless, the problem may be solved by numerical methods. The authors have successfully calculated several cases from the start of water injection through to depletion of the hypothetical reservoir using realistic capillary pressure and relative permeability characteristics that were chosen so as to put the method to a test. DIFFERENTIAL EQUATION In two- or three-dimensional problems involving the two-phase flow of incompressible fluids through a porous medium, the equations describing the flow can be combined until only two dependent variables remain, the pressure in one phase, and the saturation of one phase. These variables appear in two simultaneous partial differential equations which are derived on the basis of the conservation of mass and Darcy&apos;s law as applied to two-phase flow. For a linear reservoir, this system of differential equations can be reduced to a single, nonlinear, second order, parabolic differential equation for one dependent variable, the saturation of one phase. For incompressible water and oil, it can be shown that the conservation of mass for the two phases requires that Where q, and q, are the water end oil flow rates per unit cross-section, s, and so their saturations, +, the porosity, and [ and T, dimensional space and time variables. Darcy&apos;s law, as extended to two-phase flow including the effect of capillary pressure,&apos; is as follows: