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By R. T. DeHoff

A new approach to the measurement of the size distribution of particulate structures imbedded in opaque bodies is developed. The method is based upon the assumption of a general two-parameter distribution curve, and the estimation of these two parameters from three well-known counting measurements made upon metallogvaphic sections. The total number of particles in the system is also a product of the analysis. Application of the method with the assumption of the logarithmiconorma1 disfribution function is developed in detail. A complete description of the geometry of a particulate structure requires the determination of the size distribution of particles. The problem of estimating the size distribution of particles of a particular phase in a multiphase system, or the grain-size distribution in a homogeneous system, has been approached by many investigators.'-'0 All of the solutions proposed by these investigators share the following characteristics. a) A minimum of several hundred particle sections in the microstructure must be examined, and some characteristic dimension recorded, such as area,3'5 intercept length,6"9 or diameter.1'2'4'10 b) The resulting data must undergo a series of fairly complex calculations to generate the empirical histogram which describes the size distribution in three dimensions. c) In order to manipulate the result, the histogram must be fitted to some assumed mathematical formula, using the attendant statistical procedures. d) With two notable exceptions,8,10 the particles must be spherical. The measurements and calculations involved are in general very tedious and time-consuming, with the logical result that much effort has been expended in the development of equipment which will perform these tasks automatically and semiautomati-cally.9,11-15 considerable success has been achieved in this area, but the equipment is in general expensive, and usually places stringent requirements On the quality of microstructure which can be reliably analyzed. In laboratories which do not possess such equip- ment, the analysis of geometry is usually limited to measuring total properties of the microstructures, such as volume fraction and interfacial area, because the measurements required are much simpler to make. The determination of size distributions rarely is undertaken. The development which is presented in this paper permits the estimation of size distributions of three-dimensional structures from the same simple counting measurements which are required to determine the surface area and volume fraction of the particulate structure, and one other counting measurement. The basic approach that is used is to assume a general mathematical form for the distribution, which is described by two parameters (as the normal distribution is described by assigning values to the mean and the standard deviation), and then estimate these two parameters from the results of the counting measurements. The introduction of a third counting measurement also permits the evaluation of the number of particles per unit volume, Nv.

Jan 1, 1965

By W. H. Somerton

The effects of drilling variable on rotary drilling rates and efficiencies have been studied by a series of laboratory drilling tests. TWO-cone 1.25-in. diameter hits were used to drill vertically upwards into rock samples at corltrolled weights and rates of rotation. Shale, sandstone and specially prepared concrete samples were used in this study. Power input to the ririllirig systeln was measured and drilling chips collected for energy — .size reduction studies. Reasouably good correlations between drilling variables and rates of penetrotion were found. Qrrantities that are difficult to evaluate include rock strength parameters and the effects of bit wear. Effects of bit size and geormetry require further investigation. Analysis of the drilling chips confirmed the premise that, for rocks containing two or more mineral constituents of diflerent strengths, a greater amourrt of rock breakage occurs in the weaker constituent. Drilling conditions which required greater amounts of energy produced finer drilling chips. As bit tooth wear progressed, drilling chips became finer. Efficiency of rotary drilling as a rock breakage mechanism was extremely low. Comparison was made with theoretical energy requirements and with energy requirements for size reduction by comminution methods. INTRODUCTION Many technological developments and innovations have made possible the successful drilling of oil wells by the rotary method to depths exceeding 20,000 ft. Bigger, more powerful rigs, better steels, improved bit design and more careful control of the circulating system have all contributed to this success. Despite these advances comparatively little is known regarding the basic mechanism of rock breakage by the rotary drilling process. Future improvements and, in particular, reduction of drilling costs will undoubtedly require a clearer understanding of the variables controlling effectiveness and efficiency of rotary drilling. Rotary drilling is inherently an inefficient means of producing rock breakage. Loss of energy in transmission from the surface to the cutting mechanism may be large, thus limiting the total amount of energy which may be applied to rock breakage. Increased efficiency may be realized by improved energy transmission methods such as the turbodrill. Conversion of transmitted energy to rock breakage by use of rotating cutter teeth is likewise inefficient. Improvement of cutter efficiency has been obtained essentially by empirical means —changes in bit tooth size, shape and spacing, and tooth deletion to give clean bottom-hole patterns. The present work was undertaken to investigate the factors controlling rates of bit penetration under laboratory drilling conditions. Laboratory drilling apparatus is shown in Fig. 1. The effects of rock strength and bit wear on drilling rates were investigated. Drill cuttings were analyzed to determine the character of breakage and to compare this with other methods of producing rock breakage. VARIABLES INVOLVED IN ROTARY DRILLING Some of the variables controlling bit penetration rates can be studied conveniently by dimensional grouping. R/DN f(F/D2S) or

By E. E. McGinley, L. D. Woodworth

DURING the past several years has occurred what, in the light of future events, may aptly be called the rebirth of the acid Bessemer process. The increased attention given to the technical and metallurgical details involved in the production of Bessemer steels has been exceedingly fruitful, and indicates the value of further research and plant development. In times like these, when the steelmaking capacity of the country is operating at a maximum rate to supply materials for the national defense program, it behooves the Bessemer operator not only to strive to increase production but also to maintain a high standard of quality. The opportunity is ripe, it seems, to recapture fields of application once considered the birthright of Bessemer steels, but supplanted in recent years by open-hearth grades. This involves cooperation all along the line, from the blast-furnace operator to the metallurgical contact man and salesman. The metallurgist's part in this program involves the study of the many steelmaking variables and the measures necessary to ensure constancy in the finished product. It is equally important that the knowledge gained be disseminated widely to ensure the wise application of Bessemer steels in new fields. The merits of Bessemer steels for certain work are well understood. The combined properties of good weldability, machinability and stiffness are unique and fully explain the strong entrenchment of Bessemer steels in certain fields; e.g., skelp for small butt-weld conduit, screw steels machined in automatics, and certain tinplate applications. It is the purpose of this paper to review briefly the physical properties of Bessemer steels as contrasted with those of open-hearth steels, to discuss control measures now employed in the making of Bessemer steel, and to consider the advantages derived from the use of these control measures. PHYSICAL PROPERTIES OF BESSEMER VS. OPEN-HEARTH STEELS A number of Bessemer blows and open-hearth heats were tested for tensile strength, ductility and impact strength. The steels selected were confined to sections from ¾ to 1 ¼ -in. diameter, inclusive, and the carbon content covered was sufficient to yield parallel ranges in ultimate strength for the comparison. Other factors, such as the extent of deoxidation of the steel and variations in chemistry, were kept as comparable as possible. Machined test pieces of 0.505-in. diameter with an 8-in. gauge length were pulled. The data obtained are shown in Fig. 1, ultimate strength being plotted against carbon content. This graph shows that for equivalent carbon content Bessemer steel has on the average 15,000 lb. per sq. in. greater tensile strength and, conversely, for the same tensile strength Bessemer steel requires on the average 0.14 per cent less carbon. The average phosphorus content for the Bessemer steel was 0.090 per cent,

Jan 1, 1941

By Donald W. Scott, Adam Wesner

This paper describes the study of 23 nonmagnetic iron-formation samples from the Mesabi Range and shows the significance of their chemical, mineral, and physical properties in terms of their concentration. Data presented here resulted from a research project carried out from 1942 to 1952 by 10 major producers of iron ore, working in conjunction with Battelle Memorial Institute. THE inevitable depletion of Mesabi direct-shipping iron ores, hastened by recent wars, has increased the importance of developing methods to concentrate iron-formation materials. Many mining companies, independent research organizations, chemical companies, and equipment manufacturers are devoting attention to this important work. It is only natural that magnetic iron-formation materials have received major emphasis, since magnetic recovery methods apply and reserves of Mesabi magnetic taconites are large. However, the nonmagnetic* iron-formation materials are likewise believed to represent a large reserve and their study has not been neglected. tions over the years have shown that in addition to the unenriched taconite, which is dense and hard, and the direct-shipping ore, there are transition taconites grading into the friable wash, or intermediate ores. The transition taconites are less massive than the unaltered taconites and usually coarser-grained. This variation, coupled with the fact that there were no extensive drillings in the unaltered taconite, posed a most difficult problem of obtaining samples that would be representative of large tonnages of the fresh rock. The problem was increased by the tremendous extension of the nonmagnetic formation materials on the Mesabi and by the question of their accessibility to mining. A drilling program was evolved that would surmount these difficulties. Selection of samples was made by a committee representing producers in the area. The samples were procured from 1—taconite walls near bodies of stripping burden or wash ore and 2—from shafts in the process of being sunk through taconite for drainage or mining operations. Most of the samples were obtained from the cherty horizons because it became obvious early in the program that the slaty horizons represented an exceedingly difficult concentration problem, owing to the character of the gangue minerals and the fine grind required for liberation of the valuable minerals. More samples were procured from the lower cherty horizon than from the upper cherty because it was more accessible to mining. It is not known how well the samples selected represent the nonmagnetic iron-formation material. However, they were chosen by people Well acquainted with the geology of the Mesabi range and the mining problems involved. It is believed that they represent a fair cross-section of the types of materials that will be encountered. Table I gives data on the origin of the 23 samples and the horizon footages from which they were obtained. Samples 1 through 10, and 15 and 16

Jan 1, 1955

By P. Chaudhari, Michael B. Bever

The heat of solution at infinite dilution of selenium in bismuth, the heat of mixing of selenium and bismuth, and the limit of solubility of selenium in bis~rzuth have been determined at 573, 623; and 663°K by metal solution calorimetry. The heat of forrrzation of the compound Bi2Se at these temperatures has been determined from the heat effects associated with the precipitation of the compound from a saturated solution oj selenium and bismuth. The published information on the thermodynamic properties of the system Bi-Se is limited. The heat of solution at infinite dilution of selenium in bismuth at 623°K has been measured.' The heat of formation at 273 K1 and room temperature2 and the heat capacity at 80 K3 of the compound Bi2Se3 have been reported. An estimate of the heat of formation of the compound BiSe at room temperature has been published.2 Information on the phase relations in the system Bi-Se is available.' In the investigation reported here the following quantities have been determined at 573", 623", and 663°K: 1) the heat of solution at infinite dilution of selenium in bismuth, 2) the heat of mixing of selenium and bismuth in bismuth-rich solutions, 3) the limit of solubility of selenium in bismuth, and 4) the heat of formation of the compound BizSe. These quantities were determined by the addition of selenium to bismuth-rich solutions in a metal solution calorimeter. The determination of the heat of formation at the tem- perature of the calorimeter bath involved the precipitation of the compound from a saturated solution in the calorimeter. 5,6 This method differs from that commonly used which requires the addition of the compound and of a mechanical mixture of its components and yields the heat of formation at the temperature from which the additions are made (273 K EXPERIMENTAL PROCEDURE AND CALCULATIONS The solution calorimeter has been described in detail.' Pure bismuth (99.999+ pct) was used as the bath at the start of a run. The calorimeter was calibrated with small amounts of bismuth added from 273°K; the differences of the heat contents of bismuth at 273°K and the temperatures of the baths are listed in Table I. After the calibration, additions of hexagonal selenium (99.999+ pct) were made. Loss of selenium by evaporation was negligible. No unusual experimental difficulties were encountered.9 The differences in the heat contents10 of selenium at 273°K and the temperature of the bath, listed in Table I, were subtracted from the measured heat effects to give the "adjusted heat effects". The methods by which the heat of solution at infinite dilution, the

Jan 1, 1968

By Irving Lipkowitz

While the light metals are recognized generally as a distinct group in technical literature, economic classifications and data usually still treat them as part of the nonferrous group of metals. However, the economic characteristics of the light metals also differ markedly from those of other nonferrous metals. The distinctiveness of the light metals, as, a group and individually, becomes evident when their growth, since World War II is compared with that of other metals, as in Table 14.3.1. The growth of light-metals production has been much sharper than that of other metals. A weighted average for the light metals shows an increase of 112% during the 1958 to 1968 period. This compares with a 62% increase in the "All Primary Metals" component of the Federal Reserve Board Index of Industrial Production. The contrast was even sharper during the next six years (1968-1974), with light metals production up another 50% as against a 21 % increase in the FRB Primary Metals production index. The most important reason, however, for considering light metals separately is the trend and pace of technological change and not their distinctive statistics. Technology both creates and demands increasingly sophisticated materials. As technology advances and as all the world makes more extensive use of advanced technology, the importance of the light metals is likely to accelerate rapidly. There may be a profound clue to the future in the fact that light metals were predominant among the materials used in the construction of the Apollo 11 spacecraft. In determining what materials to use for the spacecraft and its equipment, the National Aeronautics and Space Administration (NASA) has explained that it did not look to "some of the more exotic metals" and relied instead on "generally proven materials." Accordingly, it apparently used a wide variety of metals, including precious metals, rare earths, special steels, copper, and light metals. What seems particularly significant is that, in seeking performance, NASA relied as heavily as it did on the light metals. Materials breakdown estimates show that aluminum accounted for over 75% of the materials used, titanium for another 5%, and magnesium was also used. Thus, light metals accounted for over 80%' of the materials used for the Apollo 11 spacecraft. The light metals are also unique in their availability. They rank high in abundance among the elements in the earth's crust. Aluminum is the third most abundant element, after oxygen and silicon, with magnesium ranking eighth, and titanium ninth. Among the structural metals, aluminum is the most abundant in the earth's crust, iron is second, magnesium third, and titanium fourth. This potential availability of light metals provides strong incentives for continuing improvements in process technology, because of two major national problems: (1) there is

Jan 1, 1976

The Carol concentrator of the Iron Ore Company of Canada was completed in 1962 and through expansions .has become one of the largest iron ore beneficiation plants in the world with a new feed capacity of 147,000 It (149,350 mt) per day. The Carol ore contains specular hematite and magnetite having a bulk density of 166 lb/cu ft (2660 kg/m3) It is crushed to 7 in. (178 mm) for feeding to autogenous mills for subsequent concentration by Humphrey’s s spirals. Mine ore is loaded into 150 It (152 mt) trucks by 10 cu yd (7.65 m3) shovels and then, at a transfer station, is loaded into side-dump rail cars of 100 It (101.6 mt) capacity. Each train is composed of twenty cars and operates completely automatically as it hauls the ore to the primary crushing station, dumps its loads, and returns to the loading station, a 11.5 mile (18.5 km) round trip. The primary crushing station is composed of two 60 in. by 89 in. gyratories installed in 1962 and 1972. Neither crusher has a grizzly ahead of it. Rail cars are dumped into 300 It (305 mt) pockets which contain splitters for spider protection. What few oversize boulders which do not go through the crushers are drilled and blasted. Liners in the dump pocket and the crushed ore pokcet under the crusher are manganese steel. Both crushers are direct driven by 700 hp (5 15 kw) motors, and the hardness of the ore causes them to pull almost their full power. Crushed ore drops into a 160 It (163 mt) pocket equipped with radioactive level control units for low-intermediate, and high level indications. The low level unit stops and starts the apron feeder, the intermediate unit controls the feeder speed, and a high-level reading stops the car dumping. Apron feeders are 72 in. (1. 82 m) wide and are variable speed from 12 to 52 fpm (3. 7 to 15. 8 mpm). They discharge to 60 in. (1.52 m) wide takeaway belts. Crushing capacity, nominal and maximum for each crusher, is 4, 000 ltph (4. 064 mtph) and 4,600 ltph (4,674 mtph). The crusher eccentric is removed by a conventional cart which travels on removable rails. Mainshaft removal and maintenance is done by 65 and 75/10 ton cranes. Mainshaft replacement requires eight hours, a usual time, but concave replacement requires only sixteen hours, a result of a fine maintenance organization. Mantle relining is done at grade next to a repair track. Zinc is used for backing both mantles and concaves. Both the electrical rooms and the dust collectors are located below grade,

Jan 1, 1978

By J. T. Shimmin

THE past twenty-five years has been a period of unparalleled improvement in all lines of mining and metallurgical equipment, but probably none has undergone greater refinement and development than the vacuum filter. Beginning a quarter of a century ago, there has been steady advancement in the art of vacu-um filtration until today its use has become virtually standard practice for dewatering throughout the entire metallurgical industry as well as in important parts of the chemical and industrial processing fields. The credit for the first successful application of vacuum filtration 'at the Consolidated Mercury mines in Utah in 1902 undoubtedly belongs to George Moore. There, it is said, his filter reduced the loss of gold in the slime and sand from $1.25 to 40c. per ton. Successful applications were subsequently made by Mr. Moore at the Liberty Bell mines, Telluride, Colo., the Lundberg, Dorr &Wilson mill at Terry, S. D., and elsewhere. E. L. Oliver is generally credited with, having done the most to work out the necessary continuity of op-eration exemplified in the well-known continuous vacu-um filter which bears his name. Others made improve-ments also, but in my opinion all the new ideas advanced in recent years are modifications of the fundamental principles originated by the two pioneers, Moore and Oliver. Considerable interest has been shown recently in the new type of continuous internal-type vacuum filter which is associated with my own name1. In response to frequent inquiries regarding it and the steps which led up to its invention, I am giving herewith a brief account of the early history of this development and some of the more important installations which have been made during the last year or so. A. M. Nicholas (now deceased), an Australian engi-neer, conceived the idea, several years ago, of manu-facturing a continuous vacuum filter with the filter medium applied upon the inside of the drum, as con-trasted with existing drum filters in which the medium is applied externally. Nicholas recognized that a ma-chine of this type would be simpler than one with a tank and would overcome some of the difficulties en-countered with tank filters on certain classes of pulps, and he appreciated the value of having filtration take place in the same direction as the gravitational settle-ment of the solid particles in the pulp, the pulp being retained within the drum instead of being held against the outside surface. The ease of starting up after a shut down was likewise realized by Nicholas. It was tried in the United States, but was not entirely success-ful primarily due to mechanical defects.

Jan 5, 1928

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K'K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K', and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943

By Arthur F. Taggart

This paper proposes two units (believed to be new) for designating, respectively, capacity and efficiency for primary and intermediate crushers. Capacity Operators know that the tonnage of rock that can be put through a particular crusher in a given time depends primarily upon the crusher setting (open setting for jaw and primary gyratory types; closed setting for cones and rolls), and secondarily on the lithological character of the feed, its maximum size, the amount of fines that it carries, its moisture content, and the method of feeding. The proposed capacity formula states a relationship between all of these factors in one empirical equation, as follows: Tr = TR80K'K" [I] in which Tr, called "reduction tons per hour" is the new capacity unit; T = tons of feed per hour requiring crushing; R80 = "80-per cent reduction ratio"; and K, K', and K" are constants that approximate quantitatively lithological character, moisture content and method of feeding, respectively. T is the hourly weight of material in the feed that is coarser than the coarsest discharge of the crusher. (For marked departures from the normal specific-gravity range—2.5 to 2.7—T should be adjusted to corresponding volumes.) In the crushers under consideration, discharge from the crushing zone is limited by the minimum dimension of a particle. Passage of the particle through a square-mesh screen is limited by its intermediate dimension. Sheppardl has shown that the ratio of maximum: intermediate: minimum average dimensions of broken rock fragments may be taken as about 1.5:=:0,6 for nonslabby rocks such as are normally crushed, while for slabby rocks, such as thin-bedded sedimentaries, foliated schists and gneisses, and the blocky metamorphics, the ratio is of the average order I.3:I:o.3, with the possibility of an even smaller relative value for the thickness. Gaudin2 finds the corresponding ratio for —I50 + 200-mesh pyrite to be I.4: I:0.6. The hourly tonnage of crusher-plant feed, therefore, should be diminished by the amount thereof that would pass a square-mesh screen of which the aperture is S times the crusher setting, where S is a shape factor with the value 1.7 for rocks that break exceptionally cubic; 2 for ores and rocks that exhibit no appreciabie tendency to slabbiness; and 2.5 to 3, or, in exceptional cases, even larger, when the tendency to slabbiness is marked. R80 is the quotient of the theoretical square-mesh aperture that would pass 80 per cent of the feed, divided by the aperture that would pass 80 per cent of the product. It is best determined from screen tests. If, as is usual with primary crushers, a sizing test of feed is not available, the

Jan 1, 1943

By C. W. Haworth, M. G. Hall

THE diffusion of copper in silver has been studied by Sawatzky and Jaumot1 and Cahoon and Youdelis.2 Sawatzky and Jaumot measured tracer diffusion in single crystal specimens but the 12.9 h half-life of CU64 limited the time of the diffusion anneal to about 50 hr, and in consequence the minimum temperature of the investigation was 716°C. Cahoon and Youdelis employed polycrystalline diffusion couples, and measured the interdiffusion coefficient over the range 0 to 2 at. pct Cu. These experiments were performed at temperatures down to 630°C and a discontinuity in the Arrhenius plot was observed at -700°C. The high D-values at lower temperatures were attributed to the effect of grain boundary diffusion. The present experiments were undertaken to investigate this anomaly and study the low temperature region of the diffusion of copper in silver. The method employed single crystal samples and a plated source of copper. Silver single crystals 2½ by 4 in. sq were grown from zone-refined silver bar (>99.99 pct Ag) by the Bridgeman technique, and $ in. thick slices were cut by spark machining. The specimens were electro-polished, and a 2 µm layer of copper was electroplated on to the planar surface at one end of each specimen using a potentiostatic voltage source. The following solution was used for plating: CuSO4 . 5H2O 125 gm H2SO4 (S.G. 1.8) 53 ml H2O 1000 ml The diffusion couples were sealed in capsules, in an argon atmosphere, and were annealed at either 701, 597, or 498°C. The temperature measurements were made to an accuracy of *l°C After the anneal, the penetration of copper into the silver was determined using an electron probe micro-analyzer. 100 sec scaler measurements of the intensity of Cu Ka! X-radiation were performed at 2 to 5 µm intervals along a line normal to the source, with a beam potential of 25 kv. Allowances were made for the background radiation, and the dead-time of the counting system in the normal way, and the intensity ratios were corrected to weight concentration by the method of Duncumb & de-Casa.3 For the analysis of the diffusion profiles, it was first observed that the copper layer did not completely dissolve in the host crystal for the specimens annealed at 498 and 591 whereas for the specimen annealed at 701°C, a single phase solid solution was formed. For the 498" and 597°C specimens, the concentration of copper in the silver at the interface was therefore constant throughout the anneal and the analysis for a

Jan 1, 1970

By J. H. Henderson, J. Naar

The displacement of a wetting fluid from a porous medium by a non-wetting fluid (drainage) is now reasonably well understood. A complete explanation has yet to be found for the analogous case of a wetting fluid being spontaneously imbibed and the non-wetting phase displaced (imbibition). During the displacement of oil or gas by water in a water-wet sand, the porous medium ordinarily imbibes water. The amount of oil recovered, the cost of recovery and the production history seem then to be controlled mainly by pore geometry. The influence of pore geometry is reflected in drainage and imbibition capillary-pressure curves and relative permeability curves. Relative permeability curves for a particular consolidated sand show that at any given saturation the permeability to oil during imbibition is smaller than during drainage. ' Low imbibition permeabilities suggest that the non-wetting phase, oil or gas, is gradually trapped by the advancing water. This paper describes a mathematical image (model) of consolidated porous rock based on the concept of the trapping of the non-wetting phase during the imbibition process. The following items have been derived from the model. 1. A direct relation between the relative permeability characteristics during imbibition and those observed during drainage. 2. A theoretical limit for the fractional amount of oil or gas recoverable by imbibition. 3. An expression for the resistivity index which can be used in connection with the formula for wetting-phase relative permeability to check the consistency of the model. 4. The Iimits of flow performance for a given rock dictated by complete wetting by either oil or water. 5. The factors controlling oil recovery by imbibition in the presence of free gas. The complexity of a porous medium is such that drastic simplifications must be introduced to obtain a model amenable to mathematical treatment. Many parameters have been introduced by others in Iprogressing" from the parallel-capillary model to the randomly interconnected capillary models independently proposed by Wyllie and Gardner3 and Marshall4. To these a further complication must be added since an imbibition model must trap part of the non-wetting phase during imbibition of the wetting phase. Like so many of the previously introduced complications, this fluid-block was introduced to make the model performance fit the observed imbibition flow behavior. THE IMBIBITION MODEL ASSUMPTIONS The following assumptions are common to many two-phase models previously described. 1. The wetting characteristics of the medium are clearly defined. 2. When two fluids co-exist in the medium, the wetting phase will fill the smaller pores and the non-wetting fluid the bigger ones. 3. The pores have a circular cross section. 4. Apparent pore radii are related to the capillary pressure (drainage) by

By J. D. Rice, H. H. Rachford, G. H. Bruce, D. W. Peaceman

The problem of unsteady-state gas flow through porous media leads to a second-order non-linear partial differential equation for which no analytical solution has been found. In this paper a stable numerical procedure is developed for solving the equation for production of gas at constant rate from linear and radial systems. An electronic digital computer is used to perform the numerical integration using an implicit form of an approximating difference equation. Solutions are presented in graphical form for various values of dimension-less parameters. The solutions are compared with the laboratory study of gas depletion in a linear system. INTRODUCTION Production of fluids from porous rock reservoirs is essentially a transient process. Transient gradients develop as soon as production begins, and further withdrawals continue to cause disturbances which propagate throughout the reservoir, each adding in some way to the prior ones. A correct mathematical analysis of this behavior is complicated by the fact that the transient or unsteady-state flow of compressible fluids must be described by difficult second-order partial differential equations. As a practical matter, three distinctly different cases arise: 1. Flow of single-phase liquid 2. Flow of gases 3. Multiphase flow The first of these has been found to give a linear second-order equation similar to the well-known heat flow equation. where 7 is fluid density, 8 is time, and a a constant for the system, provided d 7 = r cdp, where the compressibility, c, is constant over the range of pressure, p, considered. Solutions of Equation (1) for both linear and radial flow are available in several forms.2'3' On the other hand. the second case, which is the flow of gas, gives a non-linear second-order equation, the solution of which is not known. Although a number of approximate solutions have been proposed, each is limited in value by the associated simplifying assumptions. Inasmuch as the analysis of transient flow is limited to liquid systems, a solution of the second case is necessary if further progress is to be made in studying underground fluid movement. For this reason a solution of Equation (2) was undertaken by means of numerical integration of approximating difference equations. BASIC DIFFERENTIAL EQUATION Equation (2; is derived by combining the equation of continuity, the perfect gas law, and Darcy's law to give the basic differential equation Strictly speaking, the fluids present in a gas reservoir are not perfect gases. Furthermore, there are indications that over certain velocity ranges, Darcy's law is not applicable. It would not be practicable. however, to attempt to obtain numerical solutions which would take into account all the possible variations from these laws which could occur in actual systems. The

Jan 1, 1953

By J. D. Clark

ONE'S lifetime does not usually offer the oppor-tunity to observe and be a part of the commercial development of an entirely new material. Petalite has been known for over a century, but at first it was presumed rare. However, it was found to be so abundant that it has become a new and extremely useful industrial tool. Mineralogy Petalite is a lithium-aluminum-silicate mineral. It was from petalite that J. A. Arfwedson first discovered lithium in 1818. The theoretical composition of Li2O • A12O8 • 8SiO2 is equivalent to 78.4 pct silica, 16.7 pct alumina and 4.9 pct lithia. The mineral in its known commercial occurrence is colorless to white and rarely gray, transluscent and rarely transparent. It is brittle, has a vitreous luster, and occurs usually in cleavable masses (fig. 1). It is classified as a di-silicate, but is similar in composition to the metasilicate spodumene, Li2O.-Al2O8-4SiO2 (table I). However, their specific gravities are quite different (3.13 to 3.20 for spodumene, 2.39 to 2.46 for petalite). Occurrence Petalite specimens have been reported in many localities; however, there are only three known countries having occurrences of commercial significance. The classic locality is Sweden's Utö Mines, which, although reportedly still containing considerable petalite, have been closed and are not expected to be operated in the near future. At Varuträsk, in northern Sweden, petalite carrying 4 pct lithium oxide is the main ore. In 1946 there was reported about 1000 tons on hand. However, the iron content was 0.60 pet too high for other than chemical use. Petalite has been reported in western Australia. At the Cottesloe mine, where small quantities have been reported available, it is produced in conjunction with feldspar. Petalite occurs in considerable quantity in the feldspar quarry at Londonderry, and it was estimated1 in 1943 that over 3700 tons might be available. The petalite in South West Africa was first discovered by F. J. Jooste, a lawyer by profession, in 1938. The following year he discovered a much larger deposit, and in 1948 another important discovery was made. These deposits occur near Kari-bib and constitute the only known commercial deposits. Their full extent has not yet been determined, but huge massive blocks of petalite of the purest grade, running into many thousands of tons, can be seen in all these deposits. To date, 60,000 tons of high grade, low iron containing ore has been blocked out in the major bodies. Mining for years to come will be confined to simple quarrying. Selection from accessory minerals has proved

Jan 1, 1951

By J. D. Clark

ONE'S lifetime does not usually offer the oppor-tunity to observe and be a part of the commercial development of an entirely new material. Petalite has been known for over a century, but at first it was presumed rare. However, it was found to be so abundant that it has become a new and extremely useful industrial tool. Mineralogy Petalite is a lithium-aluminum-silicate mineral. It was from petalite that J. A. Arfwedson first discovered lithium in 1818. The theoretical composition of Li2O • A12O8 • 8SiO2 is equivalent to 78.4 pct silica, 16.7 pct alumina and 4.9 pct lithia. The mineral in its known commercial occurrence is colorless to white and rarely gray, transluscent and rarely transparent. It is brittle, has a vitreous luster, and occurs usually in cleavable masses (fig. 1). It is classified as a di-silicate, but is similar in composition to the metasilicate spodumene, Li2O.-Al2O8-4SiO2 (table I). However, their specific gravities are quite different (3.13 to 3.20 for spodumene, 2.39 to 2.46 for petalite). Occurrence Petalite specimens have been reported in many localities; however, there are only three known countries having occurrences of commercial significance. The classic locality is Sweden's Utö Mines, which, although reportedly still containing considerable petalite, have been closed and are not expected to be operated in the near future. At Varuträsk, in northern Sweden, petalite carrying 4 pct lithium oxide is the main ore. In 1946 there was reported about 1000 tons on hand. However, the iron content was 0.60 pet too high for other than chemical use. Petalite has been reported in western Australia. At the Cottesloe mine, where small quantities have been reported available, it is produced in conjunction with feldspar. Petalite occurs in considerable quantity in the feldspar quarry at Londonderry, and it was estimated1 in 1943 that over 3700 tons might be available. The petalite in South West Africa was first discovered by F. J. Jooste, a lawyer by profession, in 1938. The following year he discovered a much larger deposit, and in 1948 another important discovery was made. These deposits occur near Kari-bib and constitute the only known commercial deposits. Their full extent has not yet been determined, but huge massive blocks of petalite of the purest grade, running into many thousands of tons, can be seen in all these deposits. To date, 60,000 tons of high grade, low iron containing ore has been blocked out in the major bodies. Mining for years to come will be confined to simple quarrying. Selection from accessory minerals has proved

Jan 1, 1951

By S. Feuerstein, J. M. Galligan

SURFACE effects in the deformation of metal single crystals have been noted by a variety of workers.&apos; A large majority of these experiments have used surface roughening or a second chemical constituent at the surface. We performed the following experiment to see how the presence of a fine polycrystalline layer influenced the stress-strain behavior of single crystals of zinc. Spherical single crystals oriented for single slip were acid-machined into cylindrical dumbbell-shape shear specimens having a gage length of 3.2 mm and a cross section of 20 sq mm. The crystals were then deformed varying amounts at the surface of the gage section with emery paper. Following this treatment, the crystals were heated for approximately 8 hr at 200°C. This resulted in a polycrystalline surface layer, with an observed grain size of approximately 1/10 mm in diameter. Deformation of these crystals was undertaken at 78°K in pure shear, the shear direction <1120> lying in the basal plane. The deformation apparatus has been described elsewhere.2 The presence of a polycrystalline layer markedly raises the first observed plastic deformation, as can be seen from Fig. 1. This yield stress is then followed by a region of low work hardening comparable to that observed in shear tests on similar untreated zinc single crystals. However, the extent of easy glide is quite seriously curtailed, and is followed by a more rapid increase in work hardening, reminiscent of Stage II observed in the deformation of fcc crystals. The higher yield can probably be attributed to the difficulty of penetrating the grain boundaries by dis locations from sources interior to the boundaries. If we associate this yield stress with this breakthrough, then we might expect that more dislocations would be trapped in the crystal than is normally the case. If there is an increased density of trapped dislocations, this could lead to an increase in the amount of trapping with increasing strain, giving a larger strain hardening in the crystal. Although other explanations can be given, it is quite tempting to characterize the region of increased work hardening as a manifestation of Stage II-type deformation. This seems reasonable if the polycrystalline layer is quite efficient in holding up a large number of dislocations. In zinc crystals, since it is well-known that the slip distance can be as large as the specimen dimensions, one would only expect to entrap a large number of dislocation with very large crystals or by applying surface layers. If this interpretation of increased strain hardening is correct, it might present a method of studying Stage II in single crystals of zinc. This research was supported, in part, by the Office of Naval Research (1959). The encouragement and stimulation given by Professor E. R. Parker is gratefully acknowledged.

Jan 1, 1965

By Richard Hodgson

FMC Corporation, at their mine and soda ash refinery near Green River, Wyoming, currently mines in excess of 3 million tons per year of trona. Upon completion of the current expansion, the mine will be producing in excess of 4.0 million tons per year. The single level mine, approximately 1,500 feet in depth, is currently serviced by five (5) concrete lined circular shafts varying in diameter from 12 ft. to 24 ft. A sixth shaft is complete, but not yet operational and the seventh is currently being sunk. Two of the shafts are equipped with single drum hoists. The original production shaft is equipped with a double drum hoist. The newest production shaft and the main service shaft are both equipped with ground mounted friction hoists. These friction hoists have given excellent service and another will soon be installed as a man and material hoist at No. 7 Shaft. There are a number of advantages that the ground mounted hoist has over a tower mounted hoist. There are also operating problems common to both. FMC&apos;s original experience with ground mounted friction hoists began in 1962 with the conversion of a single drum hoist to a friction hoist. The converted hoist was an Ottumwa with a 5 ft. diameter drum and a 4 ft. face. This hoist had been installed at the No. 3 Shaft for some years prior to its conversion to a friction hoist. At the time the conversion of this hoist was made, there were no friction hoists in service in Wyoming. Wyoming mining laws required that all conveyances carrying men be equipped with safety dogs. Since it was desired that wire rope guides be used, safety dogs were impractical. Agreement was reached with the State Mine Inspectors that safety dogs would not be necessary provided that recommended rope safety factors for hoisting men would still be maintained if one hoisting rope was broken. Since-the shaft is approximately 1,500 ft. deep, the recommended safety factor is 6.0 so that this installation has a safety factor in excess of 8.0 for hoisting men when new ropes have been installed. The hoist conversion was engineered by Lake Shore, Incorporated. The friction ring was made in halves and bolted over the original drum face which had been machined to remove the grooves. The ring provided for four 3/4 in. diameter ropes on 8 inch center to center spacing. The pitch diameter of the modified drum was 72 inches. The grove liners are hald in place by hard-wood wedges bolted to the drum. The other modification required by the conversion was an increase in size of bearing caps and the hold-down bolts because of the increased force tending to lift the drum.

Jan 1, 1975

By Charles Prasky, Robert K. Zahl, John C. Nigro

Bench scale and pilot plant research was conducted using dolomitic (CaO - MgO) lime as the basic additive in the preparation of self-fluxed pellets from a typical magnetic taconite concentrate (5.5% SiO2). The specific objective of this investigation was to ascertain the viability of the magnesia lime pellets in high temperature oxidizing and reducing atmospheres. Pellet basicity and induration temperature were major parameters affecting fired pellet quality; temperatures ranging from 1200° to 1250°C appeared to be the most favorable for production of self-fluxed pellets with basicities (B) above 1.0. Comparison of the mechanical and metallurgical properties of regular (acid) and self-fluxed pellets (B = 1.55) produced under similar conditions in a modified grate pelletizing machine showed that the selffluxed pellets were more resistant to abrasion and to high and low temperature reduction disintegration, an important consideration in commercial application. The +3 mesh Linder index increased from 68% (regular pellets) to over 90% (self-fluxed pellets). The reducibility and swelling indices of the self-fluxed pellets were found to be comparable to the regular pellets.

Jan 1, 1974

By L. S. Darken, H. A. Wriedt

The equilibria at 1 atm total pressure and 600° to 1300°C (1112° to 2372°F) between gas mixtures with various partial pressures of the reactive constituents (principally sulfur dioxide, carbon dioxide, water vapor, oxygen or carbon monoxide, and hydrogen) and coexisting solid phases (groups variously including calcium oxide, calcium carbonate, calcium sulfide, calcium sulfate, iron, ferrous sulfide, and the iron oxides) are examined. Tables and charts show the combinations of temperature, oxygen activity, and carbon dioxide partial pressure under which the various groups of the solid phases coexist and the corresponding sulfur dioxide pressures. In the presence of calcium sulfide, calcium sulfate, and calcium oxide, the partial pressure of sulfur dioxide has a peak value at each temperature which increases from 101 atm at about 800°C (1472°F) to 1 atm at about 1200°C (2192°F). With water vapor present, hydrogen sulfide may predominate among gaseous sulfur compounds, particularly at low temperatures and oxygen activities; under all other circumstances considered, sulfur dioxide is the dominant gaseous sulfur-bearing species.

Jan 1, 1974

By A. W. Schlechten, R. P. Abendroth

Equilibrium H2S/4 ratios were determined as functions of temperatunz and composition in a hydrogen recirculation apparatus. A high-temperature solid solution exists in the range two-phase regionfrom TiS 1.96, to TiS1.30, Various thermodynamic quantities were calculated from the data. COMPOUNDS in the titanium -sulfur system have not receiyed much attention in the past, probably because they do not occur naturally in the earth&apos;s crust. However, titanium-sulfur compounds have been used in various metallurgical processes. The U.S. Bureau of klines&apos; studied the formation of ti- tanium-sulfide mattes from charges composed of rutile, pyrite, and carbon, with the resulting sulfide matte being chlorinated to form titanium tetrachlo-ride. Fishel, Roe, and Ellis&apos; investigated the de-sulfurizing action of titanium in steels, and Schwarz and Koster studied the preparation of metallic titanium from the sulfide using aluminum and magnesium reduction. The thermodynamic properties of some of the compounds present in the titanium-sulfur system may prove to be of some use in the consideration of future processes using these sulfides, and would

Jan 1, 1960