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By A. Chakravarti, C. C. Harris

First-order kinetics adequately describe the recovery of a single floatable species. The conditions under which cell behazior can be simulated by a single-phase model are discussed; deviations from the multiphase model are accountable. The rate coefficient depends upon operating conditions besides particle size and mineralogy and the physicochemical properties of the pulp constituents. The model for a real flotation system combines the first -order, single-phase model with a distribution of noninteracting species. Methods for determining the distributions are discussed. Applications of the procedure to flotation studies are outlined. The mathematical description of flotation as a rate process can be traced to Garcia1 who reported cases in which the fraction of solid remaining in a cell in semi-batch operation, F (for Notation used throughout, see Table l), decays exponentially with experimental time T. F = e-k>r. (1 The differential equation leading to Eq. 1 is dF ----= -k,F (2) dT which is recognized as the algebraic analog of the chemical kinetics first-order reaction equation.' This has led to suggested mechanisms for flotation and mathematical relationships other than first order: with very little foundation other than analogy. The flotation rate coefficient kl can be accounted for as the product of several probabilities concerning bub-ble-particle attachment and detachment, aggregate entry from pulp into froth and return from froth to pulp, and removal from froth as concentrate. These factors clearly contribute to the magnitude of the overall flotation rate, and there are others also, but describing flotation merely as the overall probability of consecutive gross events hardly appears a significant advance in understanding. More recently, it has been described in terms of a stochastic process, which promises to provide a more satisfactory approach? The present paper will be more concerned with a phenomeno-logical description of the flotation process than with an account of the internal mechanics of the process. This is not a statement of priorities, or a judgement of the relative importance of these options but rather an assessment of what is presently possible. Previous investigators'" have developed methods for interpreting semi-batch flotation data in terms of species distribution. These methods have been used in an attempt to explain flotation behavior in response to changes in operating conditions." Inspection of examples given in the literature" reveals discrepancies between theory and experiment, and data obtained in the Colum-

Jan 1, 1971

By J. T. Eash, N. B. Pilling

As a group, the alloys of iron, nickel and carbon are, in application, one of the most versatile of the ferrous alloy family, and while many investigations have been made of their properties and structure only a few attempts have been made to show the microstructural relation over a wide range of composition. It is neccssary at once to be clear about the kind of structural relation with which we are concerned. The equilibrium diagram provides quantitative data regarding structural make-up and its variation with temperature, but equilibrium structures often are far different from the technologically significant ones. This is particularly true of steels and cast irons, and some of the most important cornponents of their structure may have no place in the diagram of equilibrium. The fugitive phases that result from transFormation are dealt with in a highly detailed and descriptive manner in. the S-curves originated by Bain. The present effort lies in a still different field, which is to portray the relation between sweeping changes in composition and in resultant structure, under controlled but nonequilib-rium conditions of thermal treatment. The Guilletl diagram presented in 1903 was the initial attempt at such a correlation and frequent references to this diagram can be found in the literature even though later work has shown it to require considerable modification. Kase2 published in 1925 a diagram that was based upon observations of furnace-cooled melts: At low carbon contents this diagram agreed fairly well with experience in showing pearlite to exist in alloys containing up to 6 per cent nickel, and completely austenitic steels at 24 to 28 per cent nickel. At high carbon contents, however, irons were indicated as being martensitic at around 2 per cent nickel and austenitic at 12 per cent nickel; these interpretations are open to serious question. Based upon experience with steels and cast iron, Wickenden3 suggested a diagram that agreed fairly well with Kase's in the steel range but which presented a wide departure from it in the higher-carbon, high-nickel regions. In its broad picture, the Wickenden diagram is an approach to "practical" structures. Reference may be made at this point to the efforts of Marsh5 to construct an iron-nickel-carbon equilibrium diagram by the coordination of scattered data, which are described at length in the monograph cited. None of these preceding attempts has appeared to meet the need for an exposition of the structural sequence that is encountered in traversing the nickel-steel nickel-cast-iron range under what might be called ordinary departures from equilibrium. ExperimentaT. Conditions Since the intent has been to establish structures developed under arbitrary conditions, experimental details have perhaps more than usual importance. Three of these conditions should particularly be noticed: (I) the material was cast and not subjected

Jan 1, 1942

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 R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained the isothermal growth of the phase follows a simple parabolic equation: X2 = kt [I] where X is the thickness of the alloy layer, k the reaction rate constant, and t the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such. a plot has been con¬sidered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation k = Ae-Q/RT [2] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative, thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase .4 The reaction layers tend to have a

Jan 1, 1942

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 A. G. Preban, R. J. De Angelis, J. B. Cohen, P. Gordon, D. C. Brillhart

Changes in stored energy, resistivity, density, X-ray line broadening, and dislocation arrangements (from transmission electron microscopy) have been mensured on copper specimens shock-loaded at 75 to 435 kbars. The stored energy in shock-loaded copper and changes in density and resistivity are larger than those after conventional deformation. A high density of twins makes an appreciable contribution to all the measured quantities. Dislocation densities rise to values of 1011 lines per sq cm at the highest pressure. The resistivity, density, and X-ray In a study of the effects of shock loading on copper, changes in stored energy, resistivity, density, hardness, lattice parameter, line broadening, and dislocation structure have been examined after subsequent annealing of specimens shocked to various pressures. This paper presents certain aspects of the data, taken by two groups, one at the Illinois Institute of Technology, and the other at Northwestern University, and compares the changes in these properties, and what they indicate about the effects of shock deformation. measurements yield dislocation densities in substantial agreement at all pressures, after correcting for the effects due to the twins. At the higher pressures, electron microscopy yields dislocation densities that are lower by a factor of about 5 to 10. Dislocation densities from stored -energy measurements are high; this finding can be rationalized by the consideration that the deformation twin boundaries present are largely incoherent. There is no evidence for homogeneous dislocation nucleation during shock loading. Shock loading any metal or alloy, such as copper, causes a large increase in yield strength, with dimensional changes of the order of only a few percent."' Other properties have not been extensively studied, but this result clearly indicates the importance of examining the substructure. Previous studies of the substructure of conventionally deformed specimens have been made using electron microscopy,3-6 X-ray diffraction,7,8 and etch pitting.9,10 The dislocation density can reach values of about 10" per sq cm; and the dislocations are arranged in cells approximately 0.15 in size. The substructure varies widely, however, from point to point in the specimen. The substructure of explosively loaded copper consists of cells of about the same dimensions6,11 but their size is more uniform.6 Profuse twinning occurs12,13 and the twins are often too small to be detected optically.6,13 The boundaries outlining these twins appear to be incoherent.14 There is now ample evidence 13-15 that twinning is a strengthening mechanism in fcc metals but this is only part of the strengthening effect in shock-loaded copper.* From the twinning systems which operate in shock-loaded single crystals,13 and from changes in texture on shock loading,17 it has been shown that both the

Jan 1, 1968

By J. T. Eash, N. B. Pilling

As a group, the alloys of iron, nickel and carbon are, in application, one of the most versatile of the ferrous alloy family, and while many investigations have been made of their properties and structure only a few attempts have been made to show the microstructural relation over a wide range of composition. It is neccssary at once to be clear about the kind of structural relation with which we are concerned. The equilibrium diagram provides quantitative data regarding structural make-up and its variation with temperature, but equilibrium structures often are far different from the technologically significant ones. This is particularly true of steels and cast irons, and some of the most important cornponents of their structure may have no place in the diagram of equilibrium. The fugitive phases that result from transFormation are dealt with in a highly detailed and descriptive manner in. the S-curves originated by Bain. The present effort lies in a still different field, which is to portray the relation between sweeping changes in composition and in resultant structure, under controlled but nonequilib-rium conditions of thermal treatment. The Guilletl diagram presented in 1903 was the initial attempt at such a correlation and frequent references to this diagram can be found in the literature even though later work has shown it to require considerable modification. Kase2 published in 1925 a diagram that was based upon observations of furnace-cooled melts: At low carbon contents this diagram agreed fairly well with experience in showing pearlite to exist in alloys containing up to 6 per cent nickel, and completely austenitic steels at 24 to 28 per cent nickel. At high carbon contents, however, irons were indicated as being martensitic at around 2 per cent nickel and austenitic at 12 per cent nickel; these interpretations are open to serious question. Based upon experience with steels and cast iron, Wickenden3 suggested a diagram that agreed fairly well with Kase's in the steel range but which presented a wide departure from it in the higher-carbon, high-nickel regions. In its broad picture, the Wickenden diagram is an approach to "practical" structures. Reference may be made at this point to the efforts of Marsh5 to construct an iron-nickel-carbon equilibrium diagram by the coordination of scattered data, which are described at length in the monograph cited. None of these preceding attempts has appeared to meet the need for an exposition of the structural sequence that is encountered in traversing the nickel-steel nickel-cast-iron range under what might be called ordinary departures from equilibrium. ExperimentaT. Conditions Since the intent has been to establish structures developed under arbitrary conditions, experimental details have perhaps more than usual importance. Three of these conditions should particularly be noticed: (I) the material was cast and not subjected

Jan 1, 1942

By K. A. Semlak, F. N. Rhines

NFILTRATION is a term used to designate that i- process by which the pores of a metal powder are filled with a relatively low-melting liquid metal through the action of capillary forces. This is accomplished in practice either by heating the porous body in contact with the solid infiltrant metal above the melting point of the latter, or by preheating the porous body separately and then dipping it into the liquid metal. The liquid, as it sweeps through the porous body, replaces the gases progressively, thus yielding a relatively dense product in a short time.' Liquid-phase sintering, which is related to infiltration, is a process by which a mixture of two or more metal powders is sintered at a temperature between the liquidus and solidus of the ultimate alloy.' According to Cannon" liquid-phase sintering can be divided into three stages which he calls liquid flow, accommodation, and solid sintering. The largest density increase occurs during the first stage, where the lower melting component melts and, driven by capillary forces, flows among the particles of the higher melting component, where, after dissolution of the bonds between the solid particles, it moves them into close packing. This happens so quickly that little has yet been learned of its mechanism. A study of the rate of capillary rise of a liquid metal in a higher melting metal-powder compact may be expected, therefore, to contribute not only to a firmer understanding of the process of infiltration as such but also to a more extensive knowledge of what occurs during the initial stage of liquid-phase sintering. Theoretical Basis In order to derive a mathematical expression of the rate of infiltration, it has been assumed that a powder compact consists of a great many parallel capillary tubes and that the rate of rise of a liquid in an average capillary channel represents the rise in the entire compact. For a straight capillary, assuming that Poiseuille's law obtains for the non-stationary state and that wetting is very rapid, Ligenza and Bernstein' have derived the following differential eauation of motion where h is the height of rise of the column of liquid at time t, R, is the radius and 1 the length of the capillary, t) and 7, the viscosities of liquid and air, respectively, p and p, the density of the liquid and air, respectively, y the liquid-gas surface tension, 0 the liquid-solid contact angle, and g the acceleration due to gravity. The term on the left of Equation [I] represents the rate of change of momentum of the contents of the capillary tube. On the right the terms represent, respectively, the forces due to a) surface tension, b) viscous resistance, c) gravity, and d) end-drag effect. Equation [I] is not amenable to explicit solution, but for a tube of sufficiently small radius, the rate of rise may be slow enough so that the rate of change of momentum and end-drag terms may be neglected. The validity of this simplification was established by Ligenza and Bernstein' by graphical differentiation of observed data obtained from organic liquids rising in glass tubes. The solution of this simplified case is:

Jan 1, 1959

By Leah L. Naugle, H. G. Landau, H. H. Lowry

EVIDENCE has been accumulating in recent years, in part from the work of the Coal Research Laboratory, that coals belong to a family of natural polymers and that even in complex reactions the differences between coals are quantitative and not qualitative. This point of view leads to the expectation that if a series of coals were subjected to a closely controlled set of experimental conditions the results obtained should be related to the chemical analyses of the individual coals. The data accumulated over the past 10 years by the Bureau of Mines in its "Survey of Coke-, Gas-, and By-Product-Making Properties of American Coals," in what has come to be recognized as the Bureau of Mines-American Gas Association (BM-AGA) carbonization assay test,1-12 offer an unusual opportunity to check this conclusion. The present paper reports an analysis of the data on the first go coals and coal blends-including coals numbered I to 55b, inclusive -which have been carbonized according to a standard procedure at intervals of 100°C. from 500° to 1100° in either or both 13 or I8-in. cylindrical retorts." In Table I are given the name of the seam from which the sample was obtained, the analytical data used, and the reference to the original publication of the Bureau of Mines. The coals range in fixed carbon from 46.2 to 79.0 per cent, in volatile matter from 15.4 to 41.3 per cent, in ash; from 2.1 to 15.9 per cent, in moisture from o.8 to 19.7 per cent, and in total sulphur from 0.40 to 4.44 per cent; therefore the entire gamut of bituminous coals is represented. The petrographic nature of the individual coals is not considered in the following analysis, although both "normal" bright coals and splint coals are included in the samples studied. For information on the petrography of the coals and for further information characterizing the coals the original papers should be consulted. Although the coals that are included extend over the whole range of bituminous coals, they do not cover this range entirely adequately. In particular, only 13 of the go coals have moisture contents greater than 3 per cent. This concentration at low moisture values means that the effect of moisture, which is an important factor, cannot be determined with as much certainty as would be desirable. All the coals were not tested at every temperature and in both retort sizes. Only the first 30 coals were tested at 1100°, and only about 50 at the other temperatures, except at 900°, where nearly all of them were included. In the accompanying tables the actual number of observations entering into each correlation is given. In this study equations are given for calculating analyses, yields, and properties of coke and by-products from the coal analyses. To decide whether these equations are satisfactory it is necessary to know the accuracy with which these quantities were measured in the assay tests.

Jan 1, 1941

By Frank H. Macpherson

Few people realize the tremendously important part that Saline and Pulaski Counties in central Arkansas have played in the winning of the war The present favorable war situation might have been very different if we had not had the bauxite produced during the past two years from these two small areas, a total Of about 15 square miles. As a general statement, it can be said that the Arkansas bauxite deposits are, individually, relatively small, irregular in thickness, somewhat scattered and, therefore, compared with coal or iron-ore or open-pit copper deposits, relatively ill adapted to a rapid and drastic expansion in output. A few years ago it would have seemed an impossibility for these two counties to produce over six million long dry tons of bauxite in one year. However, with the cooperation of the operators, that is what happened in 1943, when the state of Arkansas achieved the seemingly impossible with a production of 6,020,684 1 long tons (dried equivalent) of bauxite ore during the calendar year, compared with an average annual production of 323,7252 tons in the period 1931 to 1941. It became apparent early in the year '94' that the united States soon might be drawn into the war, and, therefore, that an immediate study of the domestic metal situation was necessary. Aluminum is by far the most important metal used in the manufacture of aircraft and many other implements of war and it was evident that there would have to be a tremendous increase in the domestic production of bauxite, which is practically the only present source of this metal. AS more than 95 per cent of the known bauxite reserves of the United states was in Arkansas, careful preliminary studies were made in that state by representatives of the united States Bureau of Mines, the United States Geological survey and the War Production Board in the summer of 1941 Reserves in other states also were studied. The result of these studies was a recommendation by the War Production Board that mining in the bauxite.producing areas of Arkansas be geared for maximum production, in order to supply sufficient ore for this country's war requirements and, if necessary, to supply the war needs of Canada as well. The annual goal of eight million long tons (dry weight) set for Arkansas by the war Production Board was exceeded in 1943, when in August the output reached a rate equivalent to more than 8,300,000 long tons, dry basis. Because of the comparatively small tonnage of bauxite reserves, Congress appropriated funds for an extensive drilling program to be carried out by the Bureau of Mines in cooperation with the Geological Survey. Drilling began in May 1942 but owing to delay in delivery of drills, and trucks upon which the drills were mounted the program did not get into peak operation until early in 1943. By the end of July 1944, the Bureau of Mines records indicated an addition to the Arkansas reserves of 10,000,000 long tons (wet basis) in place,

Jan 1, 1946

By G. C. Rauch, T. H. Courtney, J. Wulff

The superconducting behavior of Nb-Ti alloys containing 40 and higher wt pct of Nb and variable oxygen content was studied as a function of thermomechanical processing. Critical current density (Jc) us applied transverse magnetic field (H) data were obtained for 0.010 in. diam wires at 4.2° Kin steady fields up to 120 kOe. The precipitate responsible for increase in Jc in each of the alloys studied was related to niobium and oxygen content. In alloys containing 40 to 60 wt pct Nb with less than about 1600 ppm of oxygen, w precipitation in the range 350° to 450°C appears to be responsible for the maximum value of Jc observed. In alloys of higher oxygen content (-2500 ppm), the oxygen-enriched a phase which precipitates in the temperature range 450° to 550°C is a more effective fluxoid pinner. Maximum Jc in low oxygen (350 ppm) 80 wt pct Nb alloys was achieved by 600°C aging heat treatments. Measurements of resistive critical field also reflect the changes in composition accompanying precipitation in these alloys. It is well known that the superconducting critical current density, Jc, of solid solution superconducting alloys can be increased by precipitation heat treatments.1-4 The precipitate, to serve as an effective superconzlucting fluxoid pinner and increase Jc, must be of proper size and spacing.' Its electronic properties must also be different from those of the matrix.6 As in age-hardenable systems, optimum temperature and time of aging are dictated by the composition and history of the particular solid-solution alloy under consideration. The alloy diagram of Ti-Nb7-9 shown in Fig. 1 is typical of ß-stabilized Ti alloys. Precipitation to achieve high Jc in Ti-Nb and Ti-Ta alloys is usually carried out in what is believed to be a two-phase a + ß region.1,2,4,10 Previous work on Ti-Nb4,11 and on other ß-stabilized systems such as Ti-V, Ti-Mo,12-14 has shown, however, that the first precipitate to appear is not necessarily (Y. Under specific conditions the meta-stable w phase is precipitated instead. A further complication arises in such alloys from the strong influence of contained oxygen on the phase stability and on the kinetics of precipitation.15,16 The superconducting critical current density of Nb-Ti alloy containing less than 36 wt pct Nb has been studied by Vetrano and Boom1 and Kramer and Rhodes.4 The most effective aging temperature was found to be about 425°C; fluxoid pinning was attributed to the precipita- tion of a by Vetrano and Boom and of w by Kramer and Rhodes. Although the latter workers used recrystal-lized material and the former cold-worked, studies carried out in our laboratory lead us to believe that the type of precipitate responsible for increased Jc is unaffected by prior cold-work.17 That other types of precipitates may also be effective, especially in higher oxygen-containing alloys, has been demonstrated by Reuter, et al.2 in this laboratory with the aid of electron microscopy. Reuter et al. found that at an aging temperature of 600°C, fee-TiO is precipitated, resulting in high values of Jc. Even higher values of Jc were observed after heat treatment at 500°C, but the precipitate could not be indexed as fee-TiO. Whether the precipitate was oxygen-rich w or a could not be clearly distinguished. The work nevertheless indicates that appreciable amounts of oxygen alter the nature of the phases precipitated at different temperatures, at least in alloys containing more than 36 wt pct Nb. Since such compositions are more readily worked into suitable wire than lesser niobium content alloys, it was decided to study the response to aging of the alloy compositions reported in the present paper with the hope of clarifying the effect of composition on the precipitation processes responsible for high values of Jc. I. EXPERIMENTAL Nb-Ti alloys containing 40, 50, 60, and 80 wt pct Nb were prepared by are-melting 35 g ingots of iodide crystal bar titanium and electron-beam melted niobium.

Jan 1, 1969

By W. A. Walker, G. W. Ostroot

An increase in the number of deep wells being drilled where extreme bottom-hole temperatures are encountered, and the anticipated drilling of wells where temperatures in the range of 500°F or higher may occur, has brought about a comprehensive investigation of cementing materials and of the techniques involved in their proper usage at these elevated temperatures. Included are developments in cements, retarders, weighting materials and other cement additives which make it possible to formulate a variety of compositions to help resolve the cementing problems of these extreme well conditions. The problems associated with the selection and testing of cements are discussed, and a resume of field results is included. Previous studies on strength retrogression indicate that caution should be exercised in the selection of a cementing composition for use in high-temperature wells. It now appears that, by the addition of silica flour as a stabilizing additive to certain cements, compositions covering a wide range of slurry densities can be designed to meet extreme well conditions without strength retrogression. Improvements in cement retarders make it possible to produce a four-hour thickening time at static temperatures up to 500°F. This temperature is considerably higher than conditions presently being encountered in drilling and completion work. Inert weighting materials, used to produce 20-lb/gal or heavier cement slurries, are reviewed. INTRODUCTION As the search for oil continues, the number of wells being drilled to depths of 10,000 ft or below has continued to increase over the past decade. During 1959, there were 50,893 wells drilled in the United States for a total of 209 million ft of hole. Of this total, approximately 4.45 per cent were drilled below 10,000 ft and 0.30 per cent below 15,000 ft, with a record depth of 25,340 ft recorded (Table 1). With the drilling of this record-shattering hole comes the question, "How deep can wells be drilled?".' Limitations with respect to equipment (surface and subsurface), cementing materials and techniques would cause some concern; however, a panel of experts have agreed that the U. S. oil industry has the equipment and know-how to drill a 50,000-ft hole. The greatest deterrent would be the 700°F temperature they would anticipate encountering at this depth. Although the number of wells drilled under what is generally considered hot-hole conditions (230°F and higher) has been relatively high, each well often presents distinctly individual problems and requires separate consideration and selection of special materials, techniques and equipment. At the present time there are over 30 additives and special cements available for use in "tailoring" a cementing composition for a specific well. It is not uncommon to use three or four different additives with the basic cement to produce the desired slurry characteristics. A generally accepted procedure is to make laboratory tests on selected cementing compositions prior to pumping them into wells deeper than 12,000 ft, or where static temperatures are in the range of 260°F or higher. In some instances, it is recommended that laboratory tests be made where less severe well conditions are encountered. Prior to selecting a cementing composition for a particular well, key personnel representing the operator, drilling contractor and service company should meet to determine that each individual is acquainted with every detail which might influence cementing results and to discuss the execution of the job. For cementing hot-holes, a number of factors must be evaluated before proceeding with the operation. Consideration must be given to the following. 1. Thickening time—The slurry must remain fluid for a sufficient length of time to allow displacement down the casing and up the annular space in a primary cementing job or, in squeeze-cementing, adequate thickening time for both the build-up of a satisfactory squeeze pressure and the reversing out of excess cement. The thickening time of standard retarded cements will often be too short under extreme temperature conditions, thus involving special formulations and requiring laboratory tests to determine the proper amount of additional retarder to obtain the desired pumpability.

By R. E. Jenkins

The Bell Canyon member of the Delaware Mountain group has yielded quite a large number of fields in which completion and production problems have been numerous and complex. Reserves are difficult to estimate due to the problem of evaluating the formation water saturation, and the feasibility of water flooding is questionable. Extensive laboratory investigations were undertaken to determine if normally measured rock and contained fluids properties could account for many of the peculiar characteristics of the formation. A statistical study or routine core-analysis data was made. Capillary-pressure data were obtained by several techniques. Fresh-water and brine permeabilities were measured and relative permeabilities of oil, water and gas were determined. Some qualitative wetta-bility tests were performed, and the petrography of a few thin sections was studied. The results of this work are presented, with typical or average data shown for each test. The permeability -to- water characteristic of the Delaware was found to be abnormally poor. Correlations of laboratory and field performance data indicate high water saturations in much of the formation. Pore geometry is highly uniform. INTRODUCTION The Delaware formation has undergone extensive exploration and development in the past few years. This has resulted in the discovery of quite a number of fields—producing oil for the most part. A large percentage of the productive wells have produced water along with the oil. Often there is no apparent pattern for the percentage of water cut experienced. In several instances vertical displacments of over 200 ft have been established between communicating wells in which the formation appears to be about the same, yet the structurally high wells yield a much higher water cut than the lower wells. Drill-stem tests have contributed little to well completion because they nearly always show small amounts of water (usually mud filtrate), regardless of what is produced later in the life of the well. Other formation evaluation methods have had no more than limited success in indicating ultimate productivity. Consequently, predicting the type of fluid productivity of Delaware wells has been very difficult. Hydraulic fracture treatments are almost universal, and unstimulated Delaware wells have not exhibited the productivity that normally would be expected of wells with the specific permeabilities encountered. Some operators have indicated that their Delaware wells need frequent re-stimulation. The uncertainty of reservoir water saturations reported for the Delaware has made difficult the task of evaluating oil in place in the reservoirs and estimating primary recovery. The unreliability of this data also will cause feasibility studies for water flooding or other secondary-recovery methods to be problematical. Several opinions have been voiced to explain why the Delaware performs as it does. Chronically poor well completions, dynamic water and tilted water tables, capillary inequi-libria, peculiar relative permeability characteristics and oil-wetness are among the suggested reasons. The dual purpose of this paper is (1) to describe the principal rock characteristics, and (2) to present an evaluation of those characteristics so that approaches can be made to explain the irrational behavior of wells completed in the Delaware. STUDY OF ROUTINE CORE-ANALYSIS DATA A statistical study of routine core-analysis data has been made to relate fundamental rock properties and characteristics of the formation to well productivity. For the most part, well production data were obtained from operators and augmented by production data from commercial information services. Only data which were available in detail and which were considered to be accurate were used. The core data used were obtained on samples from the perforated or open interval only and, thus, may not always represent the total productive interval in a well. All the core-analysis data included in this study are from the Bell Canyon member of the Delaware and were obtained by "plug-type" techniques, as opposed to whole-core or full-diameter techniques. Porosity values were obtained by the summation-of-fluids technique, permeability values are air permeabilities corrected for slippage to an equivalent liquid permeability, and the oil and water contents were determined by means of a high-temperature downdraft retort. All the procedures used are discussed at length in Ref. I. The core-analysis data were sorted

A. G. Cockbain—The paper by Burlingame, Bitsianes and Joseph is of great interest in extending the work done on high grade sinters, particularly that of Hessle, and the development and application to them of the technique of McBriar, Johnson, Andrews and Davies on ironstone sinters. In this laboratory the work of McBriar et al. has also been continued and extended to cover high grade sinters, and a sectioning technique similar to that used by McBriar et al. was attempted on sinter cakes made in the laboratory sinter unit, using magnetite concentrates (containing 64 pct Fe). In these experiments no attempt was made to flush out the products of combustion with nitrogen before cooling. It was considered that free air penetration would occur on only a limited scale with the size of sinter cake made (14 in. sq x 12 in. deep). Chemical analyses of the zones showed generally similar features of those described by Burlingame et al. and especially the FeO rich region at and just behind the flame front, i.e. zones of ignition and combustion. This seems to indicate that the nitrogen atmosphere does not materially affect the states of oxidation in the sinter cake or at least that special care is not required unless the sinter cake is small. Burlingame et al. consider that FeO present has some significant part to play in the mechanism of sintering. This view does not find favor with the author. The reduction of iron oxides in the presence of red hot coke is a well known phenomenon, whether conducted in an atmosphere of nitrogen or in a crucible in air, and in view of the presence of some carbon in the hot sinter, especially just at the ignition zone, cessation of the progress of the flame front will in no way affect the reduction of iron oxides near hot coke. Even in a nitrogen atmosphere some CO and CO, will be generated by reduction and by continual oxidation and reduction of CO as the transfer agent, the oxidation state of the iron oxides can be lowered quite rupidly so long as free carbon exists with enough heat. Knowing the composition of the gas at the flame front (obtainable by probes), it would be possible to calculate the static oxidation state of Fe2O3/Fe3O2 in equilibrium with it and hence obtain a check on the chemical analyses to see if in fact direct reduction of the Fe2O3/Fe2O1 to FeO has taken place. Have the authors attempted this? It appears to this writer that what is required is some means of reducing rapidly the heat content of the ignition zone and immediately behind, and at the same time insuring no oxidation by the air. In ironstone sinters the difficulty of oxidation state of the iron did not arise on account of the very large slag bulk. However, in high grade sinters knowledge of this, and also the mechanism whereby high oxidation states can be obtained in the final sinter, is of great interest. R. D. Burlingame (author's reply)—The question has been raised as to whether the high FeO content found in high-fuel sinters is due to actual reduction at the advancing flame front or due to unavoidable direct reduction during the quenching period. For such direct reduction to have taken place in the freshly-formed sinter, a considerable amount of solid carbon would have had to escape combustion and be available throughout the hot sinter zone during the quenching period. A simple stoichiometric calculation with the limited data available indicates that a zone of freshly-formed sinter over 2 in. wide must have averaged roughly 2 pct C to accomplish the amount of reduction found. Furthermore, the presence of this amount of carbon would indicate that the fuel in the charge had not burned over a narrow front but over a zone at least 2 in. thick. In contrast to such a condition, the data of the present investigation indicate that the combustion of fuel is confined mainly to a narrow front in which high temperatures and reducing conditions favor. the formation of excess ferrous iron.

Jan 1, 1959

By W. D. Kruger

Methods for analyzing flooding or cycling projects by means of two-dimensional flow calculations are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The accuracy of such analyses depends on the basic reservoir data employed, especially the absolute permeability distribution in the reservoir; however, absolute permeability data normally are determined from well flow tests and/or core measurements and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. A calculation procedure is presented for determining the areal permeability distribution in the reservoir. Use of the procedure allows verification of the basic reservoir data through the matching of past reservoir conditions, thereby providing proper data for reliable predictions of future operations. The calculation procedure is a numerical technique based on a mathematical model of the reservoir and is designed for solution by means of an electronic digital computer. Results from field application of this procedure are presented. Permeability distributions from measured data are compared to those calculated to indicate the need for the analysis. Comparisons of field-measured and calculated pressure distributions are given to establish the validity of the calculation procedure. The conclusions of this paper are (I) use of the calculation provides data that allow a match of past reservoir conditions and thus reliable prediction of future operations; and (2) the procedure should, where applicable, be used to provide adequate reservoir data for use in two-dimensional flow calculations and related reservoir analyses. INTRODUCTION One means of providing more precise engineering control over reservoir operations during all stages of depletion is to develop some type of model to simulate the reservoir, using information developed from the behavior of the prototype to predict the performance of the actual reservoir. The use of mathematical rather than physical models for this purpose has been gaining in importance recently because of the application and availability of electronic computers. Mathematical models avoid instrumentation difficulties and allow easier handling of large-scale problems. At present, analyses employing two-dimensional models are common, and thought is being given to the use of models in three dimensions. The use of multi-dimensional models is necessary to show not only what is occurring in the reservoir, but also where in the reservoir the phenomena of interest are taking place. Methods for analyzing flooding or cycling projects by means of two-dimensional numerical models are presented in the literature. The use of these methods allows the determination of optimum operating conditions for such projects and provides information on pattern efficiencies, relative flow rates, pressure distributions and floodout histories. The applicability of numerical models and the results of using such analyses have been presented through field examples. The references indicated here discuss fully the data necessary to build the mathematical reservoir model and the way the model is used to study or predict the future performance of the reservoir. The accuracy of the analysis of such projects depends on the basic reservoir data employed in the construction of. the model. In order to be sure the model represents the reservoir, it must be used to match some known set of reservoir conditions, i.e., to match past reservoir performance. The accuracy of the model is directly dependent upon the absolute permeability distribution in the reservoir; however, absolute permeability data are normally determined from well flow tests and/or core measurements, and are so limited in quantity and quality that they do not adequately describe the reservoir flow properties. There is always the need for better data and for verification of existing data. The purpose of this paper is to show the use of the mathematical model to match past performance in flooding or cycling projects, the use of numerical techniques to adjust the basic absolute permeability data if necessary so that a match is obtained, and in this way to generate the effective areal permeability distribution of the reservoir. A review of the basic concepts of the numerical model will be given, followed by a discussion of the data-adjusting technique for matching past performance. TWO field examples will be cited to show

By Paul J. Fopiano

SOME relationships between the flow characteristics of iron single crystals of 99.9 pct purity and the behavior of imperfections have been investigated. X-ray rocking-curve measurements and etch-pit counts were made as a function of plastic strain, and compared to the stress-strain curve obtained on a modified Polyani tensile machine. Crystals grown from rolled strips of vacuum-melted iron by the strain-anneal method1 had a high preference for a (110) longitudinal direction and a (211) face normal. The tensile specimens were prepared from 2 by i by 0.040 in. single crystals having a gage area of 3 by \ in. Rocking-curve measurements were carried out with a highly perfect germanium monochromating crystal in which the dazz spacing was matched to that of the dZl1 in the ir0n.l Well-collimated CuKal radiation was used throughout. These procedures practically eliminated errors due to geometrical and wavelength resolution. Inasmuch as the rocking-curve half breadth may vary markedly from point to point in the specimen being irradiated, the crystals were strained in place by mounting a hydraulic loading device on the double-crystal spectrometer. The rocking curves were taken after each increment of strain in the unloaded condition, since no observable difference was found in the rocking-curves between the loaded and unloaded states. The rocking-curve half breadths of the as-grown specimens were in the range 90 to 120 sec of arc when the beam irradiated an area of about -£ by -& in. on the specimen. DeMarco and weiss3 have shown that, for a well-colli- mated X-ray beam, irradiating about 10"! sq in. of the very same material, half breadths within 10 pct of the Darwin natural half breadth were observed. Since the rocking-curve specimens were stressed by the load-unload technique, the strain achieved at any given stress depended on the time of holding because of low-temperature creep. Fig. 1 shows the rocking-curve half breadth (also area/peak height) as a function of plastic strain for a relatively short holding time (2 to 5 min) at each stress level. For strains less than 0.1 pct the rocking-curve breadth is essentially constant; it is only for larger strains that there occurs a significant increase in this breadth. Where the holding times at each stress level were longer (by well over an order of magnitude) there occurs a significant increase in the rocking-curve breadth only after plastic strains of the order of 0.6 pct had been introduced into the specimen. This observation is related to the time dependence of creep phenomena and emphasizes the difficulty in comparing data obtained by two such different straining methods. Etch-pit results were obtained using a 2 pct nital etch on specimens strained in the range of 0 to 1 pct. Prior to etching, all specimens were annealed for 3 hr at 150°C, the carbon content being sufficient to decorate the dislocations for strains of at least 1 p~t.~ The data points were all taken from parts of the same single crystal which had been strained with short holding times at stress in increments of strain of the order of tenths of 1 pct. The (211) plane is particularly difficult to etch-pit in vacuum-melted iron and therefore it is felt that these values are as much as an order of magnitude low. Fig. 2 shows the etch-pit density as a function of plastic strain. The smooth curve passing through the data points is not meant to infer a quantitative correlation with the rocking-curve data. What is of interest, however, is the change in etch-pit density in the region of 0.2 pct plastic strain. The first three increments in strain (points 2,3, and 4) did not produce a measurable change in the etch-pit density while subsequent increments did produce a measurable change. While the absolute values of these results do not appear to be cor-

Jan 1, 1967

By C. Gatlin, N. E. Garner

Results of impulsive wedge penetration tests on two synthetic, plastically deforming rocks are presented. Basic data obtained were force-time, displacement-time, and force-displacement curves for the impacts, plus the crater geometry. Wedge geometry and blow frequency were varied over a considerable range. The synthetic rocks consisted of wax-sand mixtures; two waxes of diflerent ductilities were used to provide variable "rock" characteristics. Conventional triaxial tests showed that these synthetic rocks exhibited force-deformation curves and Mohr envelopes quite similar to real rocks, except that strengths were much lower. Measured forces from static penetration tests agreed closely with theoretical values; however, dynamic force values were much higher than the static. These latter disparities are attributed to the viscous nature of the waxes. Thus the utility of these or similar rock models must depend on the scaling of rock viscosity, which is as yet unknown for impulsive loadings at elevated stress states. It appears, however, that some macroscopic, static phenomena may be studied with wax-sand rock models. INTRODUCTION The resistance of solid materials to indentation or perforation by projectiles or other penetrators has been studied by workers in many areas. Despite these efforts no universally accepted laws or formulas are available for describing experimental observations. In the metals field the force-deformation behavior of impacting bodies is often analyzed by the Hertz law for elastic collisions, the Meyer law if plastic deformations occur, or some combination of both.' The similarities of these expressions to empirical drilling formulas of the oil industry are apparent. Beginning with the basic contributions of Simon and co-workers at Battelle,' a number of experimental papers concerning the reaction of rocks to vertical impact have appeared in the U. S. mining and petroleum literature.'-' Most published data have, to date, been obtained at atmospheric pressure, although some early high pressure information was reported by Payne and Chippendale.8 Maurer" has recently utilized available brittle impact data to develop a drilling rate equation based on the experimentally observed proportionality between crater volume and blow energy. His result agreed with earlier efforts by both Somerton, who used dimensional analysis, and Outmans, who used plasticity theory. It has long been known that rocks exhibit different modes of failure depending on the state of stress. The literature in this area is considerable; however, papers by Bredthauer, Handin and Hager,13 nd Robinson", are adequate to illustrate the point. Since rocks flow plastically at certain triaxial stress conditions, the mathematical theory of plasticity has been used to analyze the rock drilling problem. Cheatham'" has altered the wedge identation solution of Randtl to rocks, and has developed useful equations for penetrator forces under a variety of conditions. Outmans" has utilized Hill's solution in a similar manner to develop a drilling rate equation. Both Cheatham and Outmans used the linear Mohr-Coulomb rule to relate rock strength and confining pressure. The actual stress at the hole bottom is not easily ascertained, although photoelastic studies by Galle and Wil-hoit," plus the analytical treatment of Cheatham and wilhoiti8 provide some insight. Consequently it is not clear to what extent the highly idealized rheological model of a perfectly plastic solid can be realistically applied to the rock drilling problem. This paper is the first report on a long range experimental study of crater formation in rocks at elevated stress states. The data presented here are from the first phase of the project. Data obtained from impulsive wedge impacts on two synthetic, plastically deforming rocks are presented. MODEL ROCKS Geologists have long been faced with modelling the behavior of the earth and, as a consequence, have studied scaling problems in some detail.' In general, their main problem is handling the wide disparity between laboratory and geologic time. In our studies the time effects (blow velocity or rate of loading, blow duration, etc.) were essentiafly the same for both. model and prototype, as were were geometry and tooth penetration. Thus application of available scaling laws suggests that Similarity is obtained if the stress-strain curves of model and prototype are similar." For this reason Hubbert and Willis''

By R. Q. Shotts

This paper is a review of recoverable reserves of bituminous coal in the Southern Appalachian area, according to the latest published estimates. A few comparisons are made, some apparent trends are discussed, and some comments are made regarding the limitations of present estimates. The definition of Southern Appalachian area used in this report is somewhat arbitrary. It includes all the bituminous coal deposits of Alabama, Georgia, and Tennessee. All of West Virginia has been excluded. The East Kentucky and Virginia counties included were selected in connection with a literature study the writer made in 1959 of possible coal supply areas for the Tennessee Valley Authority. The selected counties were considered to be the only ones from which TVA might expect to obtain coal. The availability of coal from some of these counties is doubtful, but no other East Kentucky counties were considered more than remote possibilities. With these limitations, the Appalachian area covered is that from which producers of electric power and steel and commercial coal users, located in the Southeastern U. S., may expect to obtain their supplies of coal. Of course, it is recognized that coal from the eastern interior fields is also available to many of these same organizations. RANK AND QUALITY OF THE COALS Practically all the coals in the Southern Appalachian region are of high volatile A bituminous rank. An occasional sample indicates a slightly lower rank, but such samples may be oxidized or otherwise not representative. Some thin beds in Lookout Mountain and Sand Mountain in Alabama and Georgia, are low volatile bituminous coals, but they have not been mined extensively in modern times. There is a possibility that some of the deeper beds along the southeastern edge of the Warrior field of Alabama are near the Low-medium volatile bituminous dividing line. The Sewanee bed and some other minor ones of the Southern Tennessee field, some of the lower beds in Virginia, many beds in Sand and Lookout Mountains in Georgia and Alabama, one or more beds in the Coosa field, possibly some lower beds in the Cahaba field, and most of the beds along the southeastern edge of the Warrior field and the southern end of the Sequatchie anticline of Alabama, are of medium volatile bituminous rank. The quality of the Southern Appalachian coals is highly variable. Some of them, particularly such prevailingly thin ones as the Black Creek bed of Alabama and the Straight Creek bed of Kentucky, are unusually low in mineral matter— probably the lowest in the U. S. With the exception of certain beds and local areas, Alabama and East Kentucky coals probably have as low average ash and sulfur content as can be found in any sizeable coal area in the country. The sulfur content of Southern Appalachian coals is also variable, but few beds are consistently high in sulfur. In Alabama, sulfur generally increases from southeast to northwest across the Warrior field, but this trend is not quite as clear in the other states. A few beds in Northern Tennessee are prevailingly high in sulfur. All Southern Appalachian coals are potential coking coals if they can be prepared to meet chemical requirements. Only a comparatively small part of the medium volatile A bituminous coal, but most of the medium volatile bituminous coal mined is actually used for coking purposes. An estimate of reserves of coking coal under the requirements of present practice, could be compiled comparatively easily, but this probably has never been done. The reserve of coal that can be coked as an ingredient of a suitable blend is probably many times the size of the reserves of coal that will yield suitable blast furnace and foundary coke without blending. WHAT CONSTITUTES ECONOMICALLY RECOVERABLE COAL RESERVES? When one first realizes the vast extent of the coal-bearing rocks in the Southern Appalachian area, (see Fig. 1) the thought is likely to occur that the supply of coal is inexhaustible. This is particularly true on realizing that in some of the basins of thicker coal-

Jan 1, 1962

By E. D. Gardner

FIFTY years ago the Utah Copper enterprise at Bingham was just getting under way. An epic in metal mining was in the making. Throughout the West the bonanza deposits were approaching exhaustion and most ore still went direct to smelter. But concentrators were shortly to be constructed for treating milling grade ores, and most important, the pilot plant for the Utah Copper enterprise was being built that year at the mouth of Bingham Canyon. The same decade was to see development at the Inspiration mine in Arizona of the most important new mining method for 50 years to come—undercut block caving. Although the average grade of ore being mined has been declining for 50 years, and wage rates and prices of supplies have been greatly increased, the mining industry has continued to grow and to prosper. Technology has advanced to a point where minerals can be mined under the most severe conditions. The hardest rock can be drilled and broken and the heaviest ground handled. Large or small, an ore-body can be mined successfully, at any desired rate of production. It is possible to pump great volumes of water and to ventilate the most extensive workings; air conditioning has made practicable the mining of ore where the rock temperatures are beyond those that can be borne by man. Mining today in the U. S. is a huge earth-moving operation. In 1953 nearly 2 billion tons of material were mined for direct use or for processing. Stripping at open-cut mines totaled about 1.7 billion cu yd. Table I gives relative tonnages of the branches of the mineral industry in 1953. In addition to the solid materials moved, 350 million tons of petroleum and 340,000 tons of gas were produced in 1953. Fifteen million tons of salt and 5 million tons of liquid sulphur were pumped from wells. An appreciable amount of copper was recovered by leaching old mine workings and dumps. Total value of minerals produced in 1953 was $14.4 billion: oil and gas $7.6 billion, coal $2.6 billion, nonmetallics $2.4 billion, and metals $1.8 billion. Formidable problems face some branches of the industry today, especially pertaining to increased output tons per manshift. The time has come when these problems should be reappraised. With current wage rates, the industry no longer can afford to pay men to do manual labor. It should be recognized, also, that the miner is a skilled worker; efforts to promote the dignity of his calling and his pride of accomplishment have yielded beneficial results. Mineral deposits occur under widely varying conditions. In most instances the degree of support needed by the roof and walls is the deciding factor in selection of an underground mining method. The degree of support needed, in turn, is governed by natural physical characteristics of the ore and its enclosing rocks. Mine operators, of course, learn to judge ground by observation, and an experienced mine boss generally can anticipate what will happen following any given mining operation. A more scientific approach, however, would be advantageous in most cases. More should be known about the strength of the ore and the enclosing rocks, more about stresses set up in the ground when ore is removed, and more about the mechanics of moving ground. Better understanding would work both ways: first, favorable rock conditions could be fully utilized for more efficient mining, and second, hazards of rock falls could be minimized, loss of ore in mining reduced, and expenses caused by ground pressures and subsidence lowered. In general, mining comprises breaking the ore or rock in place, supporting the mine workings, and transporting the ore to the surface. This latter is a materials handling problem. Ventilation, of course, must be provided, and the mines must be kept free of water. Development work at some places is the most important cost item in extracting ore. Drilling and blasting remain the usual practice for breaking ore or rock from place except, of course, at block-caving mines. The drilling and blasting practice at a mine must fit the mining method. In laying out mining procedures attention is being given to

Jan 1, 1956

By Louis P. Gignac

INTRODUCTION The selection of trackless equipment for underground mining can be a complex engineering problem due to the wide range of equipment sizes and operating modes. Computer simulation is particularly useful in estimating the performance of different systems for specific rock- handling problems. A hybrid simulator, incorporating some of the features of deterministic and stochastic simulation, was developed in order to handle not only queuing delays at loading and dumping points, but a1 so traffic interferences. Any number of vehicles can operate in any one of four basic modes (LHD, LAF, FEL, HFC) in parallel or in series. If the units use common roadways, loading and dumping points, certain operating delays will occur and be registered by the simulator and thus give a better evaluation of the marginal productivity of each additional unit. Based on a typical layout of drawpoints and ore passes for the sub-level stoping method, productivity and operating costs of different rock-handling systems will be examined. 1 . COMPUTER SIMULATION Numerous applications of computer simulations are reported in the 1iterature for various mining problems. Depending on the complexity of the system to be studied, simulation models were conceived with different degrees of sophistication. Three different types of simulators are generally recognized: stochastic, deterministic, and hybrid. Stochastic or Monte Carl o simulation randomly generates items, transactions, or events from some population defined by a frequency distribution and produces some expected future situations. Because this type of simulation is governed by the input of probability distributions, it requires a detailed knowledge of the system to be simulated; it implies expensive and time-consuming studies and reports to gene- rate this input information. A major short- coming of stochastic techniques is in new equipment evaluation, where the lack of data is unavoidable, and in new system design where the conditions are outside the range of the known historical behavior of the equipment. However, probabilistic simulation is almost essential for the study of cyclic queues and traffic problems. Deterministic simulation studies a system by generating performances on the basis of the mechanical capabilities of the vehicles and the physical limitations of the mining scheme. It is based on the engineering principle that the engine converts its energy into a rimpull at the wheels, which is in turn opposed by the rolling resistance and the grade of the ground; the machine is accelerated or decelerated until the tractive and resistive forces are in equilibrium, at which point it moves at constant speed. The information required by this technique, such as rimpull charts and equipment weight, is readily available from equipment suppliers. However, equipment performance at the mining site is also dictated by human and environmental conditions and changes with time and usage. For this reason, deterministic simulation generally overestimates the system capabilities; these must then be adjusted by efficiency factors based on observation and experience. Recently, hybrid simulation models, using both stochastic and deterministic techniques, have been built with some of the events generated stochasticly and others being deterministic. This compromising approach originated at the Pennsylvania State University. O'Nei1 (1966) designed a simulator for truck-and- shovel operations that allows for transportation from multiple faces to mu1tiple destinations. Each truck performs according to its mechanical capabilities while its loading and dumping time and its load fluctuate according to specific probability distributions. A major advance in the simulation of mining systems is due to Sanford's model (1969) of underground coal mining operations. The originality of the model is in the use of an Executive System Control which sets up the initial system, de- fines the operation conditions , and instructs continuously four sub-assemblies representing shuttle cars, trains, continuous miners , and conveyors, which in turn generate a feed-back of their movement to the Executive Control System for further instructions. The model has enough flexibility to simulate simultaneous and sequential jobs that characterize any dynamic system. Sanford's early work evolved slowly to what is known today as the Under- ground Materials Handling Simulator for coal mining (Manula, 1974).

Jan 1, 1981