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By Nathaniel Arbiter, Norman L. Weiss

Factors now accelerating the trend to larger concentrators and larger equipment units are reviewed. After almost 40 years of stability with unit sizes less than 100 cu ft, 200 and 300-cu-ft flotation-cell units are now operating and a 500-cu-ft machine is being built. The design of these cells is considered, as is the design and operation of flotation circuits against the background of the need to achieve greater process efficiency while holding down operating and investment costs. Particular attention is paid to the scale-up problem. With the newer cells having five to ten times higher unit capacities, the advantages resulting from this in sampling, mill operation nnd control, testing and plant layout are indicated, as well as the broad direction for changes in the overall design of 50,000 to 100,000-tpd concentrators. A comparison is given of the available larger cells of U.S. manufacture with analysis of differences and similarities. After almost 60 years of application in this country, froth flotation is still by far the most important process for concentrating metallic ores as well as a number of nonmetallic ores including fluorspar, phosphate rock, and potash. Its use on iron ores and coal is increasing. In the metals groups, the largest plants and the greatest progress are found in copper and molybdenum mills, and the section of this paper that deals with applications will be found most pertinent to that field. During its long reign, the flotation process has passed through several phases of evolution and has achieved progress in economy, efficiency. and simplicity of operation. Much of today's success in the flotation of low-grade ores can be attributed to that progress. Even more important to us than our ability to cope with today's conditions are tomorrow's problems, which we can contemplate with some prescience and confidence. Our annual production of copper, lead, zinc, and molybdenum—to mention only the most important metals occurring in the U.S. as sulfides- must be held at a high level in the face of a declining grade of ore. It is probable that the tonnage of such ores mined and processed will double in this country before the turn of the century. Not only will many of the existing flotation mills be enlarged again and again, but larger mills will be built here and abroad to meet our needs. At this moment, in fact, there are at least three proposed new foreign mills or expansions that envision 100,000-tpd milling rate on copper ores. Table 1' shows the trend in copper ore grades in U.S. in recent years. Table 2' shows the projected annual growth rate of consumption 1966-1985. A study by one of the authors 25 years ago showed that of 32 copper mills in North America with more than 100-tpd capacity, only eight had capacities exceeding 10,000 tpd. The average for these eight was 25,000 tpd. These included the three giants of that day, Magna, Arthur, and Morenci; the other five averaged a little over 10,000 tpd. Today instead of the eight mills with capacities exceeding 10,000-tpd capacity we have 25, and the mill with less than 1000-tpd capacity is fast becoming extinct. Much less range is found in lead and zinc mills, which are still generally small except for the few with over 1000-tpd capacity in Missouri, Utah, and Idaho, and a few zinc ore mills in the same size category. Molybdenum and potash operations are the fastest growers in North America today, but when one considers the projected increase in consumption of copper together with the projected decrease in grade of ore (3% annually), he can foresee that copper ore milling will soon lead the list. Technological improvements to meet the challenge of lower-grade ores have taken the wholly predictable path toward bigger equipment. In mining, shovels, draglines, scrapers, and trucks have led the way; in ore processing, we have seen a rapid increase in size of grinding mills, flotation cells, and pumps. Twenty-five years ago, for example, the 10-ft-diam ball mills treating 2000 tpd at Morenci were considered the giants, but today some grinding mills in similar service have five times that capacity. The specific matters to be dealt with in this paper are 1) the underlying principles that affect flotation-machine design, and the conditions required to produce

Jan 1, 1971

By H. W. Meyer, H. N. Lander, F. D. Delve

A method of calculating the changes in blast-furnace performance brought about by burden and/or blast modifications is presented. Essentially the method consists of three simultaneous equutions derived from materials and heat balances. These equations can be used not only to evaluate quantitatively the effect of changes in process operating variables on furnace performance, but also to provide a useful means of evaluating changes in process variables which cannot be measured directly. It has been customary for a number of years to use simple heat and materials balances as a basis for assessing blast-furnace practice. A good example of the method used to set up these balances is that proposed by Joseph and Neustatter.1 This approach to process assessment has limited utility, however, in that it cannot be used to predict the furnace coke rate or production under new operating conditions. Using an approach based on multiple correlation of blast-furnace variables, R V. Flint2 has developed an equation which may be used to predict the change in coke rate that will result from some changes in operating conditions with a reasonable degree of accuracy. Although this equation has useful applications in production planning, it cannot be used to study the relationships between the operating variables and the fundamental thermochemi-cal characteristics of the process. In attempting to analyze the blast-furnace process quantitatively, the idea of dividing the furnace into zones3 may at first appear attractive. In our present state of knowledge, however, it is not possible to define with any accuracy the physical limits of such zones in relationship to their temperatures or to the reactions which may occur in them. Although its application is restricted, the zonal approach to blast-furnace analysis is useful in some instances. For example, the change in the calculated flame temperature in the "combustion zone" caused by injecting steam constitutes information which is helpful in understanding why the addition of steam to the blast is best accompanied by an increase in blast temperature. The zonal approach cannot, at the present time, be used to establish the relationships between process variables and process performance if the whole process rather than part of it is to be considered. One of the earliest approaches to the problem of relating blast-furnace operating variables to pro- duction and coke rate was that developed by Marshall.4 Essentially Marshall's work showed that it was possible to estimate the performance of a furnace by solving three simultaneous equations which consisted of rudimentary carbon and heat balances plus a further equation relating the production, wind rate, and the carbon burned at the tuyeres. Although these equations did not include all of the chemical and thermal variables of the process, their derivation and application seems to be the earliest attempt which achieved any success in relating prior furnace operating data to the calculation of furnace performance under different blast conditions. Work carried out in Germany has been directed mainly towards prediction of coke rates using material and thermal balances rather than statistical methods. wesemann5 used prior furnace operating data as part of the basis for predicting the change in coke rate accompanying a change in burden composition. This author employed a method of successive approximations to estimate the secondary changes in slag volume and stone rate brought about by the change in coke rate. The most recent analysis, which seems to have been developed concurrently with the thermochemical model presented in this paper, has been described by Georgen.6 This author has succeeded in improving on Wesemann's approach by expressing the total changes in the slag volume and stone rate in terms of the change in coke rate itself. This is accomplished in a manner similar to that used in the thermochemical model described in this paper. Although Georgen makes use of a calculated furnace heat loss, he does not relate the heat loss per unit of hot metal to the production rate as is done in the present work. Georgen's approach may be used to calculate the changes in materials requirements accompanying changes in furnace operation; it cannot be used to assess the resulting changes in production. The fact that blast-furnace behavior can be interpreted by consideration of the heat requirements of the process was demonstrated by Dancy, Sadler, and Lander.7 In the analysis of blast-furnace operation with oxygen and steam injection these authors showed that it was possible to account for the changes in production and coke rate

Jan 1, 1962

By C. G. Dunn

It is well known that plastic deformation alters many of the properties of a metal and subsequent heat-treatment partially or completely restores these properties.l In the deformed or strained state, the metal is unstable and tends to change toward a condition called a "strain-free state." The transformation occurs through recovery, recrystallization, and grain growth—processes that may take place singly or in combination. The distortion of the lattice of an individual grain of a metal in a state of strain may be rather complex in nature, because plastic deformation produces: (I) dislocations within mosaic blocks; (2) elastic variations of the lattice spacings; and (3) gross alterations throughout the lattice, especially along slip planes, along composition planes between a grain and its mechanical twins, and along boundaries of deformation bands. These gross alterations are of the nature of bent planes or rotated regions of the crystal lattice and are revealed by a spread in the orientation of the grain. Although we cannot describe these strains and their formation accurately because of insuffcient knowledge, we can, nevertheless, use the information as well as possible to obtain a better understanding of recovery processes. In recovery, the lattice of a grain is not made anew as it is in recrystallization, but is improved or mended in such a way that the basic structure remains unaltered: Until recatly observations were .that recovery produced no marked changes in the shapes of spots in Laue diffraction patterns, whereas recrystallization did, but now it is known for silicon ferrite2 that Laue spots may become quite sharp entirely through recovery. Consequently, the shape of Laue spots alone would not be a suitable test to distinguish between recovery and recrystallization. There is considerable evidence that the micro-structure usually does not change visibly during recovery. Absence of a visible change in the microstructure, therefore, provides a sufficient test of recovery in many cases. However, including this observation in a definition of recovery as a necessary condition (this is usually done) is unfortunate, because recovery may, as will become evident later, produce new grain boundaries that are visible not only in the microstructure but also in the macrostructure. For the present, therefore, let us say that a necessary condition for a process to be one of recovery is that the principal orientation or orientations of a deformed grain be essentially unchanged throughout the transformation toward the strain-free state. Several transformations may occur that fulfill this condition, and the nature of the distortion in a grain indicates what these must be if the lattice is to be mended in part or fully. Consequently, it will be convenient as well as

Jan 1, 1947

By C. G. Dunn

It is well known that plastic deformation alters many of the properties of a metal and subsequent heat-treatment partially or completely restores these properties.l In the deformed or strained state, the metal is unstable and tends to change toward a condition called a "strain-free state." The transformation occurs through recovery, recrystallization, and grain growth—processes that may take place singly or in combination. The distortion of the lattice of an individual grain of a metal in a state of strain may be rather complex in nature, because plastic deformation produces: (I) dislocations within mosaic blocks; (2) elastic variations of the lattice spacings; and (3) gross alterations throughout the lattice, especially along slip planes, along composition planes between a grain and its mechanical twins, and along boundaries of deformation bands. These gross alterations are of the nature of bent planes or rotated regions of the crystal lattice and are revealed by a spread in the orientation of the grain. Although we cannot describe these strains and their formation accurately because of insuffcient knowledge, we can, nevertheless, use the information as well as possible to obtain a better understanding of recovery processes. In recovery, the lattice of a grain is not made anew as it is in recrystallization, but is improved or mended in such a way that the basic structure remains unaltered: Until recatly observations were .that recovery produced no marked changes in the shapes of spots in Laue diffraction patterns, whereas recrystallization did, but now it is known for silicon ferrite2 that Laue spots may become quite sharp entirely through recovery. Consequently, the shape of Laue spots alone would not be a suitable test to distinguish between recovery and recrystallization. There is considerable evidence that the micro-structure usually does not change visibly during recovery. Absence of a visible change in the microstructure, therefore, provides a sufficient test of recovery in many cases. However, including this observation in a definition of recovery as a necessary condition (this is usually done) is unfortunate, because recovery may, as will become evident later, produce new grain boundaries that are visible not only in the microstructure but also in the macrostructure. For the present, therefore, let us say that a necessary condition for a process to be one of recovery is that the principal orientation or orientations of a deformed grain be essentially unchanged throughout the transformation toward the strain-free state. Several transformations may occur that fulfill this condition, and the nature of the distortion in a grain indicates what these must be if the lattice is to be mended in part or fully. Consequently, it will be convenient as well as

Jan 1, 1947

THE Institute met on Wednesday evening, May 22d, in the parlor of the Stanton House, Dr. T. Sterry Hunt, President, in the chair. The President delivered an introductory address on the Brown Hematite Deposits of the Great Valley, after which the following papers were read and discussed : Note on the Result of an Experiment with the Wheeler Process of Combining Iron and Steel in the Head of a Rail, by W. E. C. Coxe, of Reading, Pa. On the Jenks Corundum Mine, Macon County, N. C., by Dr. R. W. Raymond, of New York City. On Wednesday afternoon, previous to the opening session, the members who had already arrived in Chattanooga, were taken by the Local Committee to the works of the Roane Iron Company, and Chattanooga Iron Company, and then to the top of Lookout Mountain, where, at the request of the members present, Dr. Hunt described the geological and geographical features of the Chattanooga region, with the magnificent panorama spread out before them as a map. On Thursday morning an excursion was made by steamboat down the Tennessee River as far as Shellmound. Here cars were taken to the coal mines of the Dade Coal Company, where the members were courteously received by Mr. E. B. Wells, the Superintendent. After a trip through the mines the party partook of a collation provided by the company. South Pittsburgh, on the Tennessee River, was next visited, where the Southern States Coal, Iron and Land Company have a large blast-furnace plant in the course of erection. After conducting the party through the works, shops, etc., Mr. James Bowron, the manager, entertained the members with graceful hospitality at dinner. The second session was held on Thursday evening for the transaction of business. The President, Dr. T. Sterry Hunt, appointed Messrs. W. E. C. Coxe, R. H. Richards, and F. J. Slade, scrutineers, to examine the ballots for officers for the ensuing year.

Jan 1, 1879

By Jacques Steininger, Robert E. England

Single crystals of ZnTe and ZnTe1-,Sex with x up to 0.13 have been grown from the elements by temperature gradient solution zoning using excess tellurium as a solvent. Best results have been obtained with charges with the compositions 45/55 at. pct Zn, Te, for ZnTe and increasing amounts of selenium for ZnTe1-xSex. The temperature in the molten zone was maintained at about 1070°C with a gradient of about 10°C per cm. Chemical analyses of quenched ZnTe ingots show tellurium concentrations in the molten zone as high as 70 pct with concentration differences across the zone of 1 to 2 at. pct Dark dots which are observed by transmitted light microscopy in as-grown crystals can be removed by annealing in zinc vapor at 900 C. INTEREST in wide band gap semiconductors has led to a new study of ZnTe and ZnTel-xSex crystal growth. ZnTe is the only II-VI compound with a wide band gap (2.3 ev) that can be made p type with low resistivity. Attempts to make it n type with low enough resistivity to be useful for p-n junctions have so far been unsuccessful.1 ZnSe has a band gap of 2.65 ev but can be made n type only. However, ZnTel-xSex solid solutions with x as low as 0.36 have been made both highly n and p type2 with a minimum band gap around 2.12 ev3 at room temperature and appear to hold the best promise for efficient injection electroluminescence in the visible. ZnTe has the lowest melting point of the zinc chal-cogenides (1295°C) and consequently attempts have been made to grow crystals from both the liquid and the vapor phase.4 Complicated apparatus is required for growth from stoichiometric melts because of the high vapor pressures of the elements at the melting point of ZnTe and because of the problem of quartz devitrification. Small crystals have thus been grown in high-pressure equipment by Fischer5 and by Narita et a1.6 with pressures of the order of 50 atm of argon to prevent excessive evaporation from the melt. Large crystals of ZnTe can be obtained by growth from the vapor phase4 but they often present numerous dislocations and inclusions. An improvement in the quality of vapor- grown ZnTe crystals was reported by Albers and Aten7 by equilibration of mixtures of small crystals with compositions lying on either side of the solid single-phase field at fixed temperature. The same technique was later applied by Aten8 to the growth of ZnTe1-xSex crystals with less than 1 pct inhomo-geneity. Because of the higher liquidus temperatures of the solid solutions and the high vapor pressure of selenium, previous attempts to grow ZnTel-xSex from the melt have been limited and unsuccessful.9 The phase diagram of the Zn- Te system is reproduced in Fig. 1, based on data from Kobayashi10 and Kulwicki.11 Carides and Fishher12 have reported lower liquidus temperatures on the tellurium-rich side, but their data would require confirmation. The liquidus temperature on the tellurium-rich side decreases rapidly with increasing tellurium concentration and the Te2 vapor pressure over the liquidus also decreases accordingly.'3 The decrease in liquidus temperature and vapor pressure therefore makes it possible to use conventional apparatus if there is a sufficient excess of tellurium in the melt. Single crystals of ZnTe have thus been grown by Kucza,14 in a modified Bridgman technique, from solutions containing up to 60 at. pct of Te by lowering unsupported quartz ampoules through a temperature gradient at about 1200°C. Under these conditions, the phase diagram indicates that the entire charge is initially molten. Crystal growth can therefore proceed by normal freezing and rejection of excess tellurium into the melt. The modified Bridgman technique has several major limitations. Because of the rejection of excess tellurium into the melt during freezing, the melt composition and the temperature at the growth interface vary continuously. They tend to follow the liquidus until the eutectic which is very close to pure tellurium (447°C, >99 pct Te). Since the solidus composition also varies with temperature,15 crystals grown by this method are inhomogeneous. They present small variations from stoichiometry which may affect their structure and physical properties. The simultaneous increase in tellurium content and decrease in melt temperature also combine to reduce the rate of diffusion of tellurium away from the growth interface, thereby causing constitutional supercooling and possibly dendritic growth. To minimize these effects, the initial melt composition is in practice kept relatively close to stoichiometry (less than 60 pct Te). This however limits the possibilities of operating at low temperatures and pressures. This paper describes a modified method of crystal growth by temperature gradient solution zoning (TGSZ) which is an adaptation of the temperature gradient zone-melting technique developed by pfann16 and of the traveling solvent method of Mlavsky and weinstein.I7 The TGSZ method now applied to the growth of ZnTe and ZnTel-xSex crystals is characterized by its very simple experimental arrangement and sample preparation technique. Unlike the modified Bridgman technique, there is no increase in the tellurium concentration in the melt and therefore it is possible to operate at lower temperatures and pressures. This method is also suitable for maintaining a constant temperature at the growth interface.

Jan 1, 1969

By C. G. Dunn

IT is well known that plastic deformation alters many of the properties of a metal and subsequent heat-treatment partially or completely restores these properties.1 In the deformed or strained state, the metal is unstable and tends to change toward a condition called a "strain-free state." The transformation occurs through recovery, recrystallization, and grain growth-processes that may take place singly or in combination. The distortion of the lattice of an individual grain of a metal in a state of strain may be rather complex in nature, because plastic deformation produces: (I) dislocations within mosaic blocks; (2) elastic variations of the lattice spacings; and (3) gross alterations throughout the lattice, especially along slip planes, along composition planes between a grain and its mechanical twins, and along boundaries of deformation bands. These gross alterations are of the nature of bent planes or rotated regions of the crystal lattice and are revealed by a spread in the orientation of the grain. Although we cannot describe these strains and their formation accurately because of insufficient knowledge, we can, nevertheless, use the information as well as possible to obtain a better understanding of recovery processes. In recovery, the lattice of a grain is not made anew as it is in recrystallization, but is improved or mended in such a way that the basic structure remains unaltered. Until recently observations were that recovery produced no marked changes in the shapes of spots in Laue diffraction patterns, whereas recrystallization did, but now it is known for silicon ferrite2 that Laue spots may become quite sharp entirely through recovery. Consequently, the shape of Laue spots alone would not be a suitable test to distinguish between recovery and recrystallization. There is considerable evidence that the micro- structure usually does not change visibly during recovery. Absence of a visible change in the microstructure, therefore, provides a sufficient test of recovery in many cases. However, including this observation in a definition of recovery as a necessary condition (this is usually done) is unfortunate, because recovery may, as will become evident later, produce new grain boundaries that are visible not only in the microstructure but also in the macrostructure. For the present, therefore, let us say that a necessary condition for a process to be one of recovery is that the principal orientation or orientations of a deformed grain be essentially unchanged throughout the transformation toward the strain-free state. Several transformations may occur that fulfill this condition, and the nature of the distortion in a grain indicates what these must be if the lattice is to be mended in part or fully. Consequently, it will be convenient as well as

Jan 1, 1946

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

H. S. COE, St. Louis, MO. (written discussion *)-I feel much gratified that Mr. Mishler has confirmed those principles of slime settlement expressed by Mr. Clevenger and myself. I wish to state that, when we wrote the article referred to by. Mr. Mishler we had not seen his earlier article in which he gave a formula to be applied to the settling rate off feed pulp for determining thickener area required at El Tigre. It has been my experience that in cyanide work the settling area required is determined by the settling rate of the feed pulp for perhaps 20 per cent. of all of the ores to be encountered. For the other ores, the area required is greater than that indicated by the settling rate of the feed and corre-sponds to the settlement of a somewhat thicker free-settling pulp. Mr. Mishler, in his paper, has thoroughly outlined a set of tests for determining thickener capacity, which, if carefully carried out, should be entirely reliable, provided allowance is made for changes in the mill feed from time to time. Two features of his paper, I, believe; need comment. In speaking of the time required for slime to flocculate after being fed, Mr. Mishler quite properly states that the actual settling rate for the feed pulp can-not be that of completely flocculated pulp because of this time lost in flocculation. It seems to me, however, that this feature cannot be of very great importance, for the following reason: The upper zones of pulp in a thickener may be, and often are, as thin as the feed pulp. If, therefore, the feed be introduced at sufficient depth below the pulp surface to prevent agitation at the surface, there will be ample time for it to become flocculated before it becomes the surface layer, and it, will

Jan 1, 1918

By R. D. Carter

Methods are presented for calculating the performance of multiwell gas reservoirs. These methods account for two-dimensional, unsteady-state flow of a non-ideal gas through a heterogeneous formation. The performance can be obtained for gas reservoirs with known physical properties and configuration subjected to specified development and production schedules. These methods may prove helpful in optimizing the exploitation of gas reservoirs. The numerical solrrtion procedures given for this non-linear problem are extensions of known techniques for the linear diffusion equation. Two of these procedures are based on a new difference equation given by Saul'ev. Limitations and advantages of these procedures are discussed. An example solution is presented and is used to compare the calculation methods. INTRODUCTION Li planning the operation of a multiwell gas reservoir, it is desirable to predict its performance for each alternate development and producing schedule under consideration. This paper presents three numerical procedures that can be used to calculate such gas reservoir performance using a digital computer. These methods account for two-dimensional transient flow of a non-ideal gas within the reservoir. Extension of these methods to three-dimensional flow is possible. The paper is divided into three parts. The first describes the problem for which a solution is wanted and three numerical procedures that can be used to obtain solutions. The second discusses the information necessary to set up a problem. This part will be of greatest interest to the field engineer. The third gives data and results for an example problem. PROBLEM AND SOLUTION METHODS In the following development, a gas reservoir is regarded as a sealed, porous, permeable, heterogeneous body in which a single, non-ideal gas phase is flowing. Flow is permitted in the x- and y-horizontal directions, but is considered to be negligible in the vertical or z-direction. The reservoir can be tapped by one or more wells. Methods to be described provide a basis for calculating the complete performance of the reservoir, including rates and cumulative production from the wells, and pressure distribution and decline in the reservoir. If the isothermal flow of a non-ideal gas obeying Darcy's Law occurs in two dimensions in a region R, the governing equation in this region is:

Jan 1, 1967

By G. Y. Chin, W. F. Hosford

It has long been recognized that, for a crystal to undergo an arbitrary shape change by crystallographic shear, at least five independent shear systems must be activated. Taylor1 analyzed the deformation of fcc crystals by {111}<110> slip and showed that the principle of minimum work could be used to determine which combination of slip systems might act to produce a given shape change. Later Bishop and Hi112 attacked the same problem by first identifying the state of stress which could physically activate five or more {111)(110) systems simultaneously and then invoking the principle of maximum virtual work to determine which combination would act for a given shape change. Taylor&apos;s general approach has been used to calculate the active slip systems and the relative strengths during axisymmetric flow of cubic crystals with other deformation modes, including {112}<111> slip3 and {111}<112> twinning.&apos; It is the purpose of this note to identify the stress states capable of activating simultaneously five or more of these systems. {111}<112> Twinning. The {111}<112> systems are defined in Table I and illustrated in Fig. 1. The sense of the shears are those for twinning in fcc crystals. The shear stress on any system may be written in terms of the stress components expressed relative to the 1,2,3 cube axes. For example, the stress For five or more of the systems ij to be activated simultaneously, it is necessary that Tij/T be equal to unity in at least five of the expressions [3], while Tij < T for the remainder. (These restrictions assume that the same shear stress T is required to activate each system and that the shear stress on any system cannot exceed that for its activation.) The discrete values of the stress components A through H which can satisfy these restrictions are listed in Table II together with the values of Tij/T for all systems. It may be noted that Tij/ T is not necessarily zero on all nonactive systems as found by Bishop and Hill for <110> {111} slip. In fact, for the case of twinning Tij/T may reach negative values as large as -2 for shear stress in the reverse direction, Table 11. This means that, if those stress states are to be valid, the shear stress to activate reverse twinning must be greater than twice that for forward twinning. Such stress states are probably valid in view of the directionality of the twinning process. There has been no documentation of reverse twinning thus far. It may be noted that the stress states fall into four classes, which may simultaneously activate eight, six, six, and five twin systems respectively. These solutions may be applied to the {112}(111)

Jan 1, 1970

By J. de la Vergne, L. O. Cooper

The hydrostatic steel mine shaft liner (HSL) Provides a permanent wall lining for drilled shafts. It is watertight and suitable for bad ground conditions. After a shaft has been drilled to its full depth, the HSL is lowered into it and secured in place with cement grout. The liner consists of a cylindrical steel shell usually reinforced with exterior stiffening rings. The shell is basically designed for compressive strength and the rings are provided to give the shell added resistance to buckling. There are no published standards for the correct procedures to design an HSL. This paper gives a method that appears logical. A design solution can be complex with increased opportunity for error. This paper presents simple formulas to produce sufficient accuracy for construction design. Two new concepts are presented, referred to as transition pressure and critical pressure. An example demonstrates use of the formulas and concepts presented. To facilitate comprehension and use of the formulas, Greek letters are avoided and most of the English alphabet symbols used refer by association to their definitions. An appendix shows derivation of the formulas.

Jan 1, 1984

By A. J. Miller, G. R. Brophy

THE Grossmann principle1 for the calculation of hardenability of steel from composition is attractive because of its simplicity. It postulates that the hardenability of a steel for any particular grain size may be expressed in terms of an ideal critical diameter, which is the product of an ideal critical diameter for a "pure" iron-carbon base multiplied by a succession of factors for each element of composition contained, including the incidentals. It infers that the multiplying factor for a given quantity of an element is constant for all combinations of composition. Grossmann has stated that in the great majority of cases the experimental values of hardenability are found to be well within 10 per cent of the calculated values. The validity of the scheme has been confirmed in principle by Crafts and Lamont2,3 and by Kramer et al .4 Their results differ from the original in the magnitude of the effect of some elements but, since they accepted the product concept and followed its direction, it is to be expected that similar results would be obtained. Crafts and Lamont, in their second paper, recognized that the factor relations for manganese and nickel were not continuously linear, but beyond certain critical amounts increase sharply. Austin, Van Note and Prater5 demonstrated nonlinear relations between hardenability and alloy contents. Their curves for chromium, silicon, manganese and nickel were all convex upward to show decreasing incremental effects. They concluded that Grossmann&apos;s factors underevaluate the hardening effect of low percentage additions of these elements, and overevaluate the larger additions. [ ] More recently W. Steven6 has found that the factor method fails when applied to complex steels containing two or three principal alloying elements other than carbon. Multiplying factors derived from his results bear a complex relation to composition and are not constant for a given amount of an element as the base composition varies. C. A. Liedholm7 found that, using either the Grossmann or the Crafts-Lamont multiplying factor values, not only were

Jan 1, 1945

For the third year in a row total value of the Nation&apos;s mineral production broke all previous records. A new peak of $20.4 billion was reached in 1964. So says the U. S. Bureau of Mines. The Bureau&apos;s preliminary estimate for 1964 is $800 million higher than the value reported for 1963, and $1.6 billion greater than the 1962 figure. The unprecedented demand for minerals, has stimulated development of new mines and expansion of processing capacity in many parts of the country.

Jan 2, 1965

By G. R. Smithson, John E. Hanway

This paper, the first of two papers covering the development of a metallurgical process for the treatment of a complex ore, describes the bench-scale experimental Program undertaken as a basis for initial process design. The results of using various potentially applicable process steps are detailed and the basis for selecting certain of these steps for Pilot-plant development is outlined. A process consisting of the steps of sulfate roasting, leaching, copper recovery, solution purification, zinc electrolysis, and brine leaching for lead recovery was recommended for further study. THIS paper describes the bench-scale development of a sulfate roasting process designed to recover copper, lead, and zinc from a complex ore. The extrapolation of the bench-scale results to pilot-plant design and the results of pilot-plant operation will be described by Lund, et al.&apos; in a subsequent paper. Several years ago, the research divisions of the St. Joseph Lead Co. became responsible for the development of a metallurgical procedure to treat a complex sulfide ore containing copper, zinc, and lead sulfides. The primary objective was to devise a procedure which would permit economic recovery of the nonferrous values. As could logically be expected, the study of conventional flotation procedures was undertaken; in addition, however, because the physical nature of the mineral association in the complex ore indicated that physical methods of ore beneficiation might not prove to be entirely satisfactory, a program also was established to investigate alternative methods of direct metallurgical treatment for recovery of the metal values. Exploratory test work by the St. Joseph Lead staff led to the conclusion that a sulfate roasting technique represented the most attractive approach for a direct metallurgical process. Sulfate roasting would provide for the selective conversion of the nonferrous values to forms soluble in conventiona1.1 leaching agents and would permit their efficient separation from the insoluble iron and other gangue materials. It should allow efficient utilization of the thermal energy available from oxidation of the sulfide raw material, and might provide an opportunity for recovering byproducts such as iron and sulfur. The decision to evaluate a selective sulfation procedure as a basic processing step also was influenced by the excellent results obtained by the St. Joseph Lead Co. in using this procedure for the recovery of cadmium from zinc sulfide concentrates. The choice of selective sulfation as a major processing step served as a basis for an extended experimental investigation of the process with bench- and pilot-scale equipment to prove its feasibility. St Joseph Lead Co., aware that Battelle Memorial 1nstitute had participated in the development of several fluidized-bed sulfate roasting procedures, asked Battelle to undertake the bench-scale development of a suitable sulfation process. This paper describes the procedure used and the results obtained at Battelle in the treatment of the complex sulfide ore. EXPERIMENTAL WORK Nature of the Raw Material. The sulfide ore deposits of interest are essentially a massive sulfide, with the indivudual ore minerals being extremely fine grained and intimately intergrown with each other and with the associated gangue. The zinc in the ore is present mainly as sphalerite (ZnS), the lead as galena (PbS), and the iron either as pyrite (Fes2) or as pyrrhotite (FeS). Table I shows the chemical analysis of various individual samples of the ore. These analyses illustrate the variability of the ore body and impose a rather severe requirement on any type of metallurgical process—that of being able to tolerate probable wide variations in the assay of the head ore. The tentative flowsheet designed to serve as a guide for the initial experimental investigation of

Jan 1, 1962

By M. S. Seltzer

High temperature steady-state creep rates have been determined jor lead sulfide single crystals whose defect concentrations were fixed by equilibration under controlled sulfur pressure. The activation energy of creep, Qc , for undoped lead sulfide, is a function 01 composilion, decreasing from 2.9 to 2.2 ev as the carrier concentration increases from 9 x 1016 to 8 1018 electrons cm-3 for lead excess crystals, and increasing from 1.7 to 2.3 ev as the concentration of holes increases from 4 x 1017 to 1 x 1018 cm-3 in sulfur excess material. For five different composilions, Qc for undoped and bismuth-doped crystals has been found to be equal to Qpb + Qs, the self-diffusion activation energies for lead and sulfur in PbS. It is well-established1 that high-temperature steady-state creep of pure metals is a diffusion-controlled process, where the activation energy of creep is equal, within experimental error, to the activation energy of self-diffusion. The relationship between the activation energy for steady-state creep and those for self-diffusion in binary compounds is more complicated, however, because two different diffusing species must be considered, and becayse the activation energies may be influenced by compositional variations and by foreign atom additions.2-4 In some cases experimentally determined creep activation energies are correlated with those for self-diffusion of the slower-moving species, but such agreement is by no means universal. Interpretation of experimental results is difficult because few investigations include measurements of creep rates and self-diffusion coefficients of both diffusing species on single crystals of similar composition and foreign atom concentration. The objective of this investigation, therefore, is to determine the influence of stoichiometric defects and foreign atoms on steady-state creep and self-diffusion for a well-characterized binary compound. Lead sulfide, a compound semiconductor which crystallizes in the NaC1-type structure, and whose homogeneity range includes compositions on either side of the 1:l atom ratio, was chosen for study in this investigation. The pressure-temperature-composition relations for PbS are available,5,3 and deviations from stoichiometry may be monitored by electrical measurements.7 Single-crystal specimens are available to allow observation of effects due to bulk phenomena without interference from grain-boundary effects. These crystals have been employed to determine steady-state creep rates under compressive stress for "pure" and bismuth-doped PbS as a function of sulfur pressure and temperature as well as crystal orientation and applied stress in order to establish the relationships between defect concentrations and creep rates. EXPERIMENTAL PROCEDURES Crystal Growth. Lead sulfide crystals, prepared by the Bridgman method, are grown in evacuated quartz crucibles, filled with almost equal atomic proportions of high-purity (99.999 pct) lead and sulfur, and heated to a temperature above the melting point of PbS (about 1127°C) so that the lead and sulfur react to form molten PbS. The crucible and melt are dropped through the hot zone of the crystal-growing furnace at the rate of 1 cm per hr. The maximum melting point of PbS is slightly on the lead-rich side of the 50:50 composition; hence crystals grown from a near stoichiometric melt are usually n-type semiconductors containing excess lead atoms. Typically the lead excess concentration in solid solution with the PbS is 3 x 1018 atoms cm-3. Crystals containing either 1/20 or 1/2 mole pct Bi2S3 were prepared by addition of the foreign atoms prior to crystal synthesis. Preparation of Specimens of Controlled Stoichiom-etry. Since it is difficult to grow crystals of desired composition, the process of crystal growth and control of stoichiometry are separated into two distinct operations. Equilibration of as-grown PbS to a desired composition is most easily accomplished by first annealing the n-type crystals under high sulfur pressure (about 1 atm) at temperatures above 700°C. This process serves to put excess lead precipitates into solution, yielding 0 -type crystals upon quenching to room temperature. Inter diffusion occurs readily in crystals so treated, and the methods described by Bloem may then be employed to obtain crystals of controlled stoi-chiometry. For the creep measurements made in this study, this involves heating crystals in mixtures of H2 and H2S The equilibrium constant for H2S is given by: Thus the sulfur partial pressure is obtained from knowledge of the H2/H2S ratio and Kh2S for the temperature in question. Fig. 1 shows the p-T-x diagram for PbS. It can be seen that, within the stability limits for single-phase lead sulfide, desired compositions may be obtained by equilibrating under a specified sulfur pressure and temperature. Characterization of Crystals. The principal methods for evaluating PbS crystals include measurement of electrical properties and mass-spectrographic analysis. The measured electrical parameters include Hall coefficient, conductivity type, and electrical resistivity Bloem7 has shown that there is a 1:l relation between the defect concentration and carrier concentration obtained. Hence, if the contribution to the carrier con-

Jan 1, 1968

By W. David Leyshon

This paper compares the general characteristics of Florida phosphate rock for the manufacture of fertilizers and phosphoric acid. The subjects covered are relative reactivity for superphosphate manufacture and various properties of the rock for use in phosphoric acid production, including gypsum filterability, sulfuric acid consumption, foaming, relative cor-rosiveness, chemical composition, and others. Comprison will include rocks of North Africa, the western U.S., and other locations. This paper reviews some of the important properties of phosphate rock, giving particular attention to a comparison of Florida phosphate with some of the major phosphates produced in the world. It also discusses some of the techniques available for evaluatine Phosphate. rock for phosphoric. acid and fertilizer use. The use of Florida rock outside the U.S. has been increasing steadily, evidence in itself of certain desirable properties of this rock. Table I is a list of the major producers and exporters of phosphate rock as of 1965. Florida, meaning in this case Central Florida, was the largest producer of phosphate rock and the largest exporter of rock. Of a total world production estimated at 60 million tons, about 50 million tons were produced during 1965 by the areas listed in Table I. One major producing area omitted from Table I and from subsequent evaluations in this paper comprises Nauru, Ocean, and Christmas Islands, whose output totaled about three million tons in 1965. This phosphate is marketed entirely by the British Phosphate Commissioners, primarily in Australia and New Zealand, and does not get into the world market elsewhere to a significant degree at the present time. South Africa, Egypt, Israel, and North Vietnam also produce lesser quantities of rock for the international market, and these materials are also excluded from this review. The phosphate industry is now seeing the introduction of several new areas that will be significant factors in the rock market in the future. The North Carolina and North Florida areas each have capacity at present or in the near future for producing about three million tons per year. The Djebel Onk mine in Algeria has a potential of about 800,000 tons per year. In addition, announcements have been made of significant development of deposits in Peru and in the Spanish Sahara, and sizable expansions are planned in several of the existing areas that are now of minor importance. Competition for the rock market appears to be increasing so that more attention will probably be paid to evaluating phosphates available from different areas. It is not possible here to go into all the properties of even a few of the materials listed in Table I. However, it is practical to discuss some comparative properties important for making phosphoric acid and fertilizers, and to touch on the techniques used for the evaluation of various phosphate rocks. Table II gives typical analyses of the major phosphate rocks available in the world as of 1965. There is, of course, an inherent danger in labeling any analysis as typical, but it appears that variations between two samples of rock within one given area are generally less than between two samples from different areas. The analyses listed were compiled from several years of data so they may not be representative of the present output of any particular area. The range of grades represented by these analyses goes from 66 BPL for Gafsa rock to 85 BPL for Kola

Jan 1, 1968

By C. D. Hall

This paper may be divided into two main parts: (1) analysis and data to show that Eq. 6 adequately correlates the authors&apos; experimental data, and (2) the assertion that Eq. 20 "should permit scale-up with data taken from one pipe diameter for Newtonian, inelastic non-Newtonian, and viscoelastic fluids, such as dilute polymer fracturing fluids, which produce considerable pressure reductions." The authors might well recommend that this broad grouping of fluid types could be correlated by using Eq. 6 (requiring data from at least two pipe diameters). On the other hand, Eq. 20 is only shown to be adequate for conditions within the range of the present data set. Specifically, predictions by Eq. 20 for diameter scale-up to casing sizes would give larger deviations than implied in Table 2, and scale-up for some other fluids that give large drag reduction could be grossly in error. The description of a class of fluids "which produce a diameter family of straight parallel lines on a log (d?p/4L) vs log (8 v/d) plot. . ." defines a necessary condition for using Eq. 6; i.e., that s shall be constant for each fluid. The proposal that Eq. 20 is applicable to turbulent flow of such fluids is equivalent to saying that the spacing of these parallel lines, with A being constant, will be found to correspond to m = -1.20 for all such fluids. Table 1 shows the values of m derived from data on 16 non-Newtonian fluids. The key statement of this paper is that the diameter exponents "do not vary significantly from . . . -1.20." In statistical terms, this says that the m value for each fluid, which was obtained from all the measurements made on that fluid. has not been shown to be different from the arithmetic mean of the m values for the 16 fluids tested. This implies that the group mean, -1.20, is a more reliable value to use for an individual fluid than is the m value derived from the data on that fluid alone. No statistical test is described to support the key statement that the diameter exponents do not vary significantly from -1.20. Such a test would have to take into account that each individual m value is shown to correlate the pressure gradients for its fluid, with only about 3 percent standard deviation over the diameter range covered. That is, the m value is not the result of a single independent measurement. Thus, it would not be sufficient, or valid, to compare the deviation of one of the m values with the variance of the 16 values of m about their mean. An alternative interpretation of the key statement is that the diameter exponents do not vary appreciably from -1.20; i.e., that using -1.20 does not cause serious inaccuracy. Table 2 seems to be offered in support of such an assertion. However, such a statistical treatment (1) is unnecessary and (2) cannot lead to any valid scale-up generalization. The amount of error introduced by using a 1"wrong" value of diameter exponent — i.e., -1.20 instead of m — is determined by Eq. 6. The ratio of the pressures predicted by Eqs. 6 and 20 for scale-up from ds in small pipe to d, in casing is The pressure for 30-percent calcium carbonate slurry (m = -1.112) in 10-in. ID pipe would be predicted 30 percent higher by Eq. 6 than by Eq. 20, if based on tests in 0.5-in. ID pipe. The data set tested in Table 2 represents only a limited sample of pipe diameters (ratio of about 4:l) out of the population of diameters that would

Jan 1, 1970

By H. Dykstra

Calculated wellbore pressures were obtained for parameters of radilcs ratio and permeability. In all cases bur two, after-production was allowed to occur for one day. The calculated pressure build-up data were compared with actual pressure build-up data from a condensate well. The paper discusses the comparison, gives reasons for, inability to match calculated (2nd actual data, and presents conc1usions derived from the comparison. INTRODUCTION Considerable information has been published on the decline in wellbore pressure for oil and gas fields resulting from production of fluids. Considerable information also has been published on pressure build-up for oil fields, but relatively little has been published for gas and condensate fields. Perrine&apos; summarized the equations derived for pressure build-up in oil wells and showed how the different methods could be applied. On the other hand, very little theoretical information has been published on pressure build-up in gas or gas-condensate wells.2-4 Tracy,&apos; by pointing out the similarity between the equation describing oil wellbore pressure decline and the equation describing gas wellbore pressure decline, showed how methods of pressure build-up analysis could be applied to a gas well. In analyzing pressure build-up data for gas or gas-condensate wells, it would be very desirable to compare actual pressure build-up data with calculated pressure build-up data. Such a comparison would lead to a better feeling for the quantitative picture of gas-well build-up curves and would help to establish a degree of confidence in a given build-up curve. This paper discusses the comparison and presents conclusions made from it. Calculated wellbore pressures are given for parameters of radius ratio and permeability. In all cases but two, after-production was allowed to occur for one day. The work was done in an attempt to evaluate the reserves of a gas-condensate field. As will be discussed later, it was not possible to make an evaluation. METHOD OF CALCULATION The method used for solving the depletion and pressure build-up behavior for a gas-condensate well was that developed by West, Garvin and Sheldon.5 or the IBM 704 computer program used, it was assumed that liquid condensing out of solution would have only a minor effect on the flow behavior. Therefore, the field was treated as having single-phase flow, with the gas saturation S, remaining constant at unity minus the connate-water saturation Sw. As will be discussed later, this may not have been a good assumption. It also was assumed that oil production could be considered as equivalent gas production by using a conversion factor based on an analysis of the liquid produced. An outer boundary condition of no-flow was assumed. BASIC DATA The data required for the study were reservoir properties, fluid properties and production data. Reservoir properties included the following: thickness h, 179 ft; porosity, 0.194; connate-water saturation, 0.43; gas saturation, 0.57; permeabilities k, 1.0, 0.5, 0.25 and 0.15 md; radius ratios re/rw, 800, 1,000 and 2,000; wellbore radius rw, 5 in.; initial reservoir pressure P, 6,529 psia; and reservoir temperature, 272°F. The selection of permeabilities was based on core-analysis data showing an average air permeability of about 2 md. With a relatively high connate-water saturation, the average effective gas permeability would be about one-half, or less, of the air permeability. The selection of radius ratios was based partly on the observed rapid decline in wellbore pressure during production and partly on the fact that the well was believed to be located in a relatively small fault block. Reservoir fluid properties were obtained from a reservoir fluid study on a recombined sample of gas and condensate. Gas formation-volume factors were calculated from pressure-volume measurements made at reservoir temperature. Gas viscosities were calculated by the method of Carr, et al,G from an analysis of the re-combined sample. These data are shown as a function of pressure in Table 1. The production schedule from the gas-condensate

By WALTON H. HAMILTON

THE demand for "production control" has, like the poor, been with us always. With the development of the nation, the accumulation of business experience, and a maturing understanding of how our many and varied industries work, it is increasingly evident that an uncontrolled output is a source of great mischief and that order and performance demand a control of production. To see clearly the demand for "production control" we must look in detail at the ways in which industries operate. General pictures, grand aggregates, situations as "wholes," and smoothed curves are likely to be deceptive. An industry may seem to keep the even tenor of its ways, and yet the establishments which made it up may experience a great range of fortunes. A nice bundle of statistics may show in the aggregate a lovely regularity which is not shared by the firms which make up a trade. An industry may appear to be reasonably profitable, and yet the profits may be very unevenly distributed. The people in an industry, and dependent on it, are managers, laborers, stockholders, creatures of flesh and blood, such as you and I. General pictures and abstract statements must not blind us to what is happening to firms, corporations and individuals.

Jan 1, 1929