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By M. H. Gaskell, D. M. Kehn, G. T. Pyndus

A correlation of the bubble point pressure for black oil systems is developed using the standard physical-chemical equations of soiutions. The correlation is based on 158 experimentally measured bubble point pressures of 137 independent systems and is expressed in terins of the usually measured field pnrameters— flash separation gm-oil ratio, rank oil gravity, total gas gravity, and reservoir temperature. The data were obtained on systems produced in Canada, Western and Mid-Continent01 United States, and South America. The average error (algebraic) in the representation is 3.8 per cent, and the maximum error encountered is 14.7 per cent. INTRODUCTION In the absence of experimentally measured properties of reservoir fluids, it is often necessary for the field engineer to make estimates regarding the fluid properties based on the usually measured producing parameters. To aid in these estimations, various correlations have appeared in the literature in recent years. Among the pertinent properties of interest is the bubble point pressure. A correlation for this parameter has been reported by Standing'. However, this correlation was based essentially on California produced crudes and this limitation was pointed out with its presentation. The correlation presented in this paper utilized data on crude oil systems from Canada, Wes- tern and Mid-Continental United States, and South America. CORRELATION DEVELOPMENT The basic assumption used in this development is the same as employed by Standing', There is a wide variety of ways to combine these parameters; however, in this instance the combination was made on the basis of Henry's law2. Accordingly, the relationship proposed is Although Eq. 2 defines an individual system, it is of limited value since H' is a function of gas-phase composition and the system temperature. It was observed that for the systems where the bubble point was measured at several temperatures that the ratio of the bubble point pressures and the ratio of the corresponding absolute temperatures (R) were practically identical. Thus, for correlation purposes the bubble point pressure may be taken as a direct function of the absolute temperature. This relation is valid only for those systems that are not near the critical point. Accordingly, this correlation will be inadequate for systems in the region of the critical point. The solubility of the various hydrocarbons found in the gas phase increases with the molecular weight. Thus, the saturation pressure should be inversely related to the gas gravity. Applying these principles to Eq. 2 and rearranging terms gives: The variables 02 the left side of Eq. 3 were designated as the "hubble point pressure factor". The number of mols of tank oil per barrel is a function of the "mclecular weight" of the tank oil. Although the tank oil is a complex mixture, it was assumed for the purposes of this correlation that a unique molecular weight could be assigned to a given oil. This was designated as the "effective molecular weight", and was related to the oil gravity, This empirical relationship was developed simultaneously with the correlation by assuming values of M,. and working to obtain a smooth curve for both the correlation and the effective molecular weight. The relationship between the oil gravity and the effective molecular weight used in this correlation is shown in Fig. 1. The effective molecular weight is somewhat higher than the molecular weight of the C fraction. The difference between these values is largest for the low-gravity systems. It is noted that this effective molecular

By B. O. Pickard

WITH more than a score of shafts and numerous stope openings to the surface, all inter-connected underground; with underground temperatures high, often exceeding 100° wet bulb; with an ore presenting a dust health-hazard; with certain rocks giving off inert gases; with an altitude of 6000 ft. above the sea level and a dry desert climate, the Tonopah mines offered an interesting, problem to the student of metal-mine ventilation. Tonopah is not an old mining district relatively speaking. It was discovered in 1900 and Tonopah soon was a boom camp. By 1910 the mines of this district had paid many millions of dollars in dividends. At the time of the 1921 ventilation study, mining had passed its peak of production and the operators were striving to reduce costs, to discover new ore bodies, and to attract desirable workmen. In 1925, the camp was operating on a still less prosperous basis, but the several managements had not relaxed in their efforts to keep the mines on a paying basis, neither had they lost their faith in the ability of the mines and the price of the silver to "come back." Early in the fall of 1921 the Bureau of Mines was invited by the mine operators at Tonopah, Nevada, to make a detailed study of the under-ground air conditions in the Tonopah silver district. D. Harrington,? who was then directly supervising the ventilation studies of the bureau, detailed district engineer B. 0. Pickard, mining engineer E. D. Gardner, surgeon C. E. Kindall, and petrographer H. Insley to carry on the study. G. S. Rice, as chief mining engineer of the Bureau of Mines, was in general charge of the work. Upon the completion of the study each operator was furnished a report on conditions in his mine.

Jan 2, 1927

By Edmund Kirby

THE results to come from the application of cheap oxygen to industry in general will be so great that it is not possible to enumerate them beforehand and still less to estimate them. We naturally think first of the fuel to be saved; yet this is only a minor item. The main results will be changes in methods of manufacture or of operation. The speed of operation will be greatly increased, with consequent savings in labor and fixed charges, and also, in most cases, in the cost of fuel. High temperature will be brought within the reach of every manufacturer, whereas it is now available only to those operating expensive electric furnaces located within reach of large water power. New speeds and new temperatures mean improvements and processes not thought of at present. Incidentally the changes in methods will probably change the location of important world industries, the tendency being to concentrate at the fuel centers. The whole subject is so new that most of the data which an engineer requires for definite estimates do not exist. All that is possible now is to obtain a general view of the subject with rough and fragmentary estimates for some of the industries with which we are specially concerned. Most of the figures presented deal with fuel saving merely because there are available no data from which to estimate the effect on speed of operation. When working out the practical problems involved in substituting oxygen for air, in most cases the change will be made step by step; by trying out air enriched with increasing percentages of oxygen. Such partial applications of oxygen will be temporary expedients during the transition and there will be no stopping place short of the complete substitution of air by oxygen. This final stage is therefore the one discussed in this paper.1

Jan 11, 1924

By Henry M. Howe

The object of the present paper is to suggest injecting into the hearths of iron blast furnaces, whose temperature has become unduly lowered, some form of fuel whose calorific intensity, under the peculiar conditions existing there, is considerably higher than than of liquid petroleum, the rose of this substance for melting out chills having grievonsly disappointed the high hopes which were at first entertained of it. A chill being a fall of the temperature below that needed for the complete liquefaction of the slag, which requires, according to Plattner, about 1800' C., one would suppose that the chief thing to be accomplished in curing it would be to raise the temperature in the crucible of the furnace. The most obvious ways of doing this seem to be to raise the temperature of the blast, and to increase the amount of fuel in the crucible itself. Simply increasing the rate at which the blast enters the furnace, if carried beyond a certain point, should lower the temperature in the crucible. The existence of a chill shows that the fuel is arriving too slowly at the tuyeres. If air be introduced so rapidly as to he in excess of that required for the combustion of the fuel, all that excess will simply lower the temperature around the tuyeres, carrying the region of intense heat upwards, and weakening its intensity by increasing its size. Up to a certain point, increasing the rate of introducing the blast will increase practically pari passu the rate at which the fuel reaches the tuyeres. But when mechanical obstructions, which so often accompany chills, retard the descent of the fuel, there must be a point beyond which this does not hold good, and beyond which farther

Jan 1, 1883

By I. Fatt

Relative permeability and relative electrical resistivity curves are obtained for networks of tubes with a tube radius distribution by means of a network of resistors used as an analog model. These curves are similar to those obtained from real porous media. The effects of pore size distribution and network structure on relative permeability and resistivity are demonstrated. INTRODUCTION Study of the dynamic properties of networks of single size tubes in paper IT' of this series has shown that the network model has flow properties similar to those observed on real porous media. The comparison of properties of single size tube networks with those of real porous media cannot be carried far because very few porous media have uniform size pores. The capillary pressure curve from most porous materials such as soil, sandstone, and sintered glass indicate that these materials have pore size distribution similar to those shown in Figs. 5-1, 9-1, and 10-I.† To properly test the network model, it is therefore necessary to compare the dynamic properties of real porous media with those of networks of tubes in which the tube radii are distributed accord- ing to the distributions in the aforementioned figures. A network in which the tube sizes are distributed cannot be treated in the same manner as a network of single size tubes. In the single size tube network, the relation between tube geometry, flow resistance, and tube volume did not have to be known if the assumption was made that whatever relation did exist was the same for all tubes in a particular network. In a network of distributed tube size, the relation between tube geometry and flow resistance must be known or assumed in order to replace the tubes by equivalent electrical resistors. Relation of Tube Geometry to Flow Resistance The interchangeability of tubes and electrical resistors in the network model is possible because of the analogy between Poiseuille's law and Ohm's law. Poiseuille's law for a cylinder is q= pr4/8µl ?P.........(1) where q is the volumetric rate of flow, µ is the viscosity, ?P is the pressure gradient, r is the tube radius, and 1 is the tube length. Ohm's law is I=1/R?E..........(2) where I is the flux and is equivalent to the volumetric rate in Poiseuille's law, R is the resistance, and ?E is the voltage gradient. Both laws give the flux as a function of the potential drop and the resistance of the medium. By analogy then, 1/R=pr4/8µl ?P...........(3)

Jan 1, 1957

By W. R. Ingalls

I WAS led some time ago to draft a statement of economic principles immediately affecting our national welfare from the standpoint of the engineer. It was the intention to offer this to the American Engineering Council as a resolution to be adopted, or a declaration to be made, of course after suitable con-sideration and debate. The presentation has not been . formally made, but I have been asked to let it be made to the mining engineers through the medium of MINING AND METALLURGY, the American Institute of Mining and Metallurgical Engineers being a constituent part of the Federated American Engineering Societies. I shall welcome any expressions of opinion that this statement may inspire. The statement follows: The engineers of, the United States, functioning through the American Engineering Council of the, Federated American Engineering Societies, feel it their duty to advise the American people respecting the present state of economic affairs in the nation, just as an individual engineer would his client. The people of the United States constitute a great corpora-tion, whose business affairs are analogous to those of a commercial company -multiplied many times. The engineers feel constrained to offer their opinion owing to the responsibility to do things which rests upon them. Confronted by the steady impoverishment of natural resources and the operation of the economic law of diminishing returns it devolves upon management, functioning through the engineering profession aided by scientists, to make such improvements leading to increased production and such elimination of wastes as to offset the increasing adversities of nature merely to hold our own; and to do more than offset them in order to improve the scale of living of the people. The engineers accept this responsibility, but in so doing they demand attention to their advice respecting fundamental economic matters, lest they be unduly hampered in the performance of the professional duties, which they acknowledge. The American Engineering Council therefore declares the following as the advice of engineers to the American people:

Jan 8, 1923

By L. A. Rapoport, W. J. Leas

The original Burkley-Leverett theory has been extended and a more detailed formulation of the waterflood behavior in linear horizontal systems is presented. Particular consideration has been given to the evaluation of capillary pressure effects and differential equations permitting an explicit evaluation of these effects have been derived. On the basis of the developed theory it is recognized that the flooding behavior is dependent upon the length of the system and the rate of injection. At the same time it has been determined that systems of different lengths yield the same flooding behavior if the injection rates and or the fluid viscosities are properly adjrrsted or "scaled." It has also been found that the sensitivity of the flooding behavior with respect to rate and length decreases as any one of these {actors increases in value and that for sufficiently long systems and high rate.; of water injection the flooding behavior becomes independent of rate and length. or "stabilized." To such stabilized conditions the theory formulated by Buckley and Leverett is applicable. A number of laboratory flooding tests have been made and good agreement Iraq been found between theory and experimental observations. The experimental results are discussed and it is shown that under field conditions the flooding behavior is usually stabilized. As a result of these finding; a procedure is indicated for evaluating field performances either on the basis of tests performed with commonly available core samples or by means of calculations using relative permeability data INTRODUCTION In recent years the development of methods for evaluating oil recovery by waterflooding has been the object of considerable research. A theoretical analysis of the mechanisms involved in the displacement of immiscible fluids was originally established by Buckle!- and Leverettl and experimental investipatio~~s have been made by numerons workers." Many of the experimental results are in mutual agreement and bear out several significant features of the flooding mechanism as predicted by theory. Thus it lias been generally recognized that a flood corresponds to the movement of a steep saturation hank or "front" (primary phase), followed by additional gradual oil displacement (subordinate phase). It has also been found that for any porous medium the flooding behavior is largely dependent upon the oil-water viscosity ratio and that for increasing values of this ratio the relative importance of the primary displacement phase decreases while that of the subordinate phase becomes more pronounced. Although the studies to date have clarified certain aspects of the flooding process. they have given rise to observations of a somewhat contradictory nature that cannot he explained in terms of the original theory. These observations pertain mainly to the effect of injection rate or pressure gradient upon recovery. Some investigators report laboratory tests that indicate incresing oil recoverieq with increasing rates of water injectill, others find the flooding behavior to be independent of and other. mention lower oil recoveries with increased injection rates.3 The conflicting evidence indicated above creates considerable uncertainty with respect to laboratory testing procedures and the utilization of the resulting data for field evaluations. The principal purpose of this paper, then, is to resolve these Uncertainties by means of a comprehensive theoretical and experimental investigation of the flooding meanism. THEORETICAL DEVELOPMENT Derivation of Flooding Equations The mathematical description of transient flow phenomena is based upon the consideration of the various processes occurring during an infinitesimal time interval in an infinitesimal volume element and upon the correlation of these processes with those occurring in the adjacent elements. The volume elements are defined as being infinitesimal in comparison to the overall dimensions of the porous system, yet each sufficiently large so aS to encompass the full range of pore openings encountered throughout the system. If a porous system can arbitrarily be subdivided into an infinite number of volume elements all possessing the same distribution of pore openings and if this distribution is unformly continuous. the system may be said to be homogeneous. Such a homogeneous porous medium is considered in the present studivs. It is furthermore postulatecl that only oil and water are present in the pornu wediu. that they act a- totally incompressible and immiscible fluids. and that gravity effects are negligible. In n linear flow system of unit cross sertional area. as treated here. the infinitesimal volume element.; to he considered are cylindrical ".slices" of thickness dx. oriented perpendicularly to the direction of flow. The equations applicable to any such volume element. at my time. describe the movement. of oil and water across the element:

Jan 1, 1953

By W. K. Hardy, H. H. Stadelmaier, L. J. Huetter

The ternary system Co-Sn-C was studied in the cobalt-rich region. The liquidus projection ulas established and two fonr -phase reactions were found. An isothermal section at 950°C was worked out. In the region studied the following phases were observed: cobalt-rich solid solution, graphite, binary compound y -cobalt-tin, and a ternary compound. As a result of the limited solubility of carbon in liquid cobalt-tin alloys, the investigation was limited to the cobalt-rich region. Tin contents up to 32 at. pct were studied. Cobalt of 99.99 pct purity, tin of 99.97 pct purity and synthetic graphite of 99.93 pct minimum purity prepare the alloys. Carbon determinations of all alloys were obtained by gas volumetric analysis. Samples were investigated microscopically and by X-ray diffraction using CoK, and FeK, radiation. Cooling curves were obtained with a number of alloys to determine the temperature of the four-phase reactions. The thermocouple was calibrated with the melting points of high-purity silver and copper. In the region studied the following phases were observed: Cobalt-rich solid solution (face-centered cubic) Graphite. Binary compound y (solidifies congruently at composition Cop~n)'. Ternary compound k which is face-centered cubic with superlattice and nonferromagnetic.' In Fig. 1 the fields representing the projections of the liquidus surfaces were determined by microscopic investigation and are labled by their primary phase. In the field labled C graphite is the primary phase. During solidification in this field much of the primary graphite was expelled through the surface of the melt. It could not always be established microscopically whether the remaining graphite was primary or purely eutectic. Therefore it was not possible to determine accurately the boundary curve which drops from the binary eutectic el at 1309 "~~ to the point of the four-phase reaction at F. The ter-nary carbide is the primary phase in the field labled k. To the right of this field the primary graphite is consistently nodular whereas flake graphite is observed at tin contents somewhat below F. The ternary carbide does not appear to solidify congruently. The graphite is attacked in a peritectic reaction along the boundary between k and C. Thus no graphite is observed in alloys in the k field. In alloys right of the boundary between k and C the graphite nodules are located in the center of the k crystallites, further documenting the peritectic nature of the reaction with the graphite. A four-phase reaction was found at F and 1120 &3"C. The most likely reaction is L+ CY-Co + C — k. Below the temperature of the binary eutectic ez at 1112" a second four-phase reaction was observed at E and 1100 lt3"C. It is the ternary eutectic L — CY-Co + k + y. Figs. 2(a ) to (e) show microstructures of the ternary alloys in the as-cast condition. Fig. 2(a) shows the eutectic a-Co + C (with some primary graphite) with the carbide k in the grain boundaries. Fig. 2(b) shows primary cobalt (dark areas) and the eutectic a-Co + k which is formed along F-E.

Jan 1, 1961

By William L. Fink, Dana W. Smith

Approximately two years ago the authors obtained data that indicated that initial precipitation could not be detected by change of lattice parameter in the aluminum-rich aluminum-magnesium alloys. Some of these data were first published in a brief note in Mining and Metallurgy'. Cast specimens were used at that time and they showed initial precipitation relatively sooner than sheet material of the same composition. For this reason a more thorough investigation has been carried out using a homogenized aluminum-magnesium sheet corltairling approximately 10 per cent magnesium. Materials.—The aluminum used in the preparation of the aluminum-magnesium alloy was of high purity, containing less than 0.01 per cent each of iron, silicon and copper. The magnesium was high-purity sublimed magnesium. Preparation of Alloy.—Approximately 4 kg. of the aluminunl was melted in a plumbago crucible in an electric furnace and the magnesium was added. The melt was thoroughly stirred with a graphite rod and fluxed with chlorine gas before casting. The alloy was cast in the form of a sheet ingot in a cold iron tilting mold (approximately 200 by 165 by 40 mm.) and into small chill-cast slabs for chemical analysis (75 by 40 by 5 mm.). The chemical analyses were made upon drillings from the analysis slabs. The analytical methods were those described in "Chemical Analysis of Aluminum," published by the Aluminum Company of America. The composition of the alloy was found to be: magnesium 10.30, silicon 0.013, iron 0.008 and copper 0.005 per cent. In order to insure homogeneity the alloy was given two intermediate anneals at 430' C. for a total time of 36 hr. The ingot was hot-rolled

Jan 1, 1937

B. R. Coil (Electrical Installations at the Miami Mine are Cheaper with Flexible Cable, P. 356) was born in Higginsville, Mo., and attended McKinley High School and Missouri School of Mines. He received a B.S. in mining engineering. Mr. Coil has worked for the Braden Copper Co., Rancagua, Chile as junior engineer and foreman. He was employed by Miami Copper Co. as a jigger boss, shift boss, development engineer and mine foreman. He worked as mine superintendent and general superintendent of the Castle Dome Copper Company, Inc. Mr. Coil may be reached at Box 100, Miami, Ariz. He is an AIME Member. Mr. C. R. Ross was co-author with Mr. Coil in the preparation of this paper. His paper covers the present installation of electrical equipment in block caving stopes along with background data. In this paper he has given one solution to wiring problems in heavy stopes.

Jan 1, 1952

By Robert U. Richards

THE spitzlutte, as described by Rittinger, is an instrument by which sand is sorted in a continual upward-flowing stream of water. Its usual form is that of a pointed box, placed with the point downward, the box receiving its feed of sand and water on one side and discharging its tailings on the other. The sorted product or concentration is discharged at the bottom, at the apex of the box, through which it falls against an upward current -of water, which current serves to effect the sorting and separation. To make this exposure to the quicksand condition still more effective, an inverted dam is placed across the spitzlutte, which forces the sand in its passage from the feed side to the discharge to pass down into the more active portion of the upward-flowing current of water. In the form adopted for small tests in the mining laboratory of the Massachusetts Institute of Technology (see accompanying sketch) the feed is through a central funnel instead of being at the side, and the apex of this funnel, extending down nearly to, the apex of the cone, takes the place of the inverted dam in the large spitzlutte. To keep the experiment perfectly under control a bulb or bottle is attached by a rubber connecting-tube to receive the concentrations, and between this bottle and the apex of the spitzlutte is placed -1 glass tube of conical form, with a side tube for the admission of water. By regulating the admission of water through this tube the concentration may be allowed to go down into the bulb as fast or as slowly as the richness of the ore seems to demand. This spitzlutte may be used on products that have been previously sized to take out the heavy mineral. As, an example of this a test was made upon a' sample of ore where the galena, blende, and quartz were much mixed up, but separated fairly when crushed. The sample of ore was from Newburyport, and assayed 16.50 per cent. lead.. After sizing through a series of sieves the ore yielded concentrations and tailings to the spitzlutte as follows

Jan 1, 1881

By F. B. Richards

For the last five years the furnace-men drawing their oresupply from the Lake Superior districts have had to solve the problem of using the very fine Mesabi ores as part of their oremixture. It is not my purpope to dwell on the early experiences and the progressive development in the use of these ores up to this time, but to lay before the members of the Institute one prominent feature concerning them, namely, the frequent and sometimes very disastrous slips (?) or explosions (?) occurring at furnaces where these ores are used. The Transactions of the Institute contain very little on this subject. Mr. F. E. Bachman, in his discussion of Mr. 0. 0. Laudig's paper (Trans., xxvi., 1061), advances a theory as to the cause of these occurrences; but this is the only reference to the subject in the Transactions up to this time, so far as I can recall. Probably all the furnace-men running the harddriven coke-furnaces in the central West have had more or less experience with this trouble; and I believe the majority of

Jan 1, 1899

By J. L. Humphrey

The origin of roof bolting is obscure, but is believed to have begun some 40 years ago in the mines of St. Joseph Lead Co. in southern Missouri. It was not until after World War II, and more particularly after 1949, as a result of the concentrated effort of the USBM, that roof bolting attracted widespread interest. It is estimated that at the end of 1954, 26 pct of all bituminous coal mining in the U. S. was being done under roof bolts. Those mines alone use nearly 2,000,000 roof bolts per month, according to USBM statistics. Uses in metal mines are increasing rapidly, as confidence and knowledge grow. The application has found equal success in other fields, such as tunneling work for dam and waterway construction and right of way maintenance on highways and railroads.

May 1, 1956

By Thomas M. Drown

The following description of an attempt to separate bituminous coal from its slaty and mineral admixtures without the aid of jigging, was suggested by the successful use of dense solutions (such as the double iodide of mercury and potassium and cadmium borotungstate) in the separation of the mineral components of igneous rocks.* In the case of coal it is essential that we have a solution of a specific gravity greater than the coal, and less than the mineral or slate associated with it. Further, in order that such a solution should be practically admissible, it must be cheap and readily obtainable. Calcium chloride fulfils all these conditions, although it is not intended to be affirmed, in the absence of actual trial, that its use on a large scale would be economically successful. The records of experiments on several samples of bituminous coal

Jan 1, 1885

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before breakage, which appears as heat An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories the romnnred. THE present status of the theory of comminution is extremely unsatisfactory. The amount of various ores and rock products crushed and ground annually approaches the staggering sum of perhaps one half billion tons. Yet the basic concepts underlying an operation of such magnitude are unknown, and actual knowledge of what takes place in comminution is almost entirely empirical. The responsibility for this situation cannot be charged to apathy or lack of appreciation of the importance of the problem. Many attempts have been made to evolve a workable hypothesis, but none has been completely successful. General Considerations In order to break rock, it must be subjected to a stress which strains the rock beyond its critical breaking point. The stress imparts energy to the rock, most of which is released in the form of heat when the stress and resulting strain are removed. If the strain induced exceeds the critical strain, the energy is released by breaking; if the induced strain does not reach the critical point, the energy is released with removal of the stress as energy of resilience. Rock is a brittle material and it is assumed that it breaks approximately at its yield point, so that no permanent deformation results from strains below the critical. When rock is broken the total energy input is accounted for by the heat liberated, and by the surface energy of the new surface produced. A small and probably negligible amount is released as noise. Rock is commonly broken under compression and the applied stress is ordinarily compressive. However, for breakage to occur, it is only necessary that the induced strain exceed the critical value, and this strain may represent the resultant of compressive, shearing, and tensile forces. The stress-strain diagram of rocks under compression, and the modulus of elasticity as determined therefrom, should be fundamental considerations in the development of any theories of rock breakage. Crushing in jaw or gyratory crushers results primarily from a squeezing action, and reduction in a hammer mill is the result of impact. The action in rod and ball mills is a combination of impacting, squeezing, and wearing away by attrition, or rubbing. In ordinary crushing and grinding, the forces are applied at protruding points and are not distributed evenly throughout the rock. This is one of the features of comminution which theoretical considerations have not covered adequately. Another feature is the effect of impact velocities, which may greatly influence the total energy required for breakage. Impact velocities may vary from 1 or 2 fps in crushers to 10 or 20 fps for ball mills, and as high as 100 or more for hammer mills. However, according to the findings of geophysicists, the velocity of sound and of compression waves in stone is many times greater; the primary longitudinal compression waves travel at perhaps 15,000 fps, and the secondary transverse waves, which may reach the surface and cause cracks to form thereon, travel at perhaps 5000 fps. When a crack tip forms, the total surrounding stresses are concentrated in this tip, which rapidly extends throughout the rock particle.1 It would seem that the energy required to deform the rock beyond its critical strain, resulting in the formation of a crack tip, represents practically all of the energy required. Most of the primary crack tips presumably form on the surface. A simple method of designating feed and product size is necessary for the evaluation of crushing and grinding results. Taggart's suggestion2 that the 80 pet passing size be used has been found very practical. In this paper, the square opening screen size which 80 pct of the feed passes is designated as the feed size F, and the size which 80 pct of the product passes, or the product size, is designated as P. The reduction ratio at the 80 pet passing size, or F/P is designated as n. The feed and prod-

Jan 1, 1951

By Fred C. Bond, Jen-Tung Wang

Comminution energy is principally energy of deformation before breakage, which appears as heat An empirical equation is presented which covers the entire comminution range. The new strain-energy theory considers comminution from the known principles of mechanics and the reduction ratio. Energy requirements according to the different theories the romnnred. THE present status of the theory of comminution is extremely unsatisfactory. The amount of various ores and rock products crushed and ground annually approaches the staggering sum of perhaps one half billion tons. Yet the basic concepts underlying an operation of such magnitude are unknown, and actual knowledge of what takes place in comminution is almost entirely empirical. The responsibility for this situation cannot be charged to apathy or lack of appreciation of the importance of the problem. Many attempts have been made to evolve a workable hypothesis, but none has been completely successful. General Considerations In order to break rock, it must be subjected to a stress which strains the rock beyond its critical breaking point. The stress imparts energy to the rock, most of which is released in the form of heat when the stress and resulting strain are removed. If the strain induced exceeds the critical strain, the energy is released by breaking; if the induced strain does not reach the critical point, the energy is released with removal of the stress as energy of resilience. Rock is a brittle material and it is assumed that it breaks approximately at its yield point, so that no permanent deformation results from strains below the critical. When rock is broken the total energy input is accounted for by the heat liberated, and by the surface energy of the new surface produced. A small and probably negligible amount is released as noise. Rock is commonly broken under compression and the applied stress is ordinarily compressive. However, for breakage to occur, it is only necessary that the induced strain exceed the critical value, and this strain may represent the resultant of compressive, shearing, and tensile forces. The stress-strain diagram of rocks under compression, and the modulus of elasticity as determined therefrom, should be fundamental considerations in the development of any theories of rock breakage. Crushing in jaw or gyratory crushers results primarily from a squeezing action, and reduction in a hammer mill is the result of impact. The action in rod and ball mills is a combination of impacting, squeezing, and wearing away by attrition, or rubbing. In ordinary crushing and grinding, the forces are applied at protruding points and are not distributed evenly throughout the rock. This is one of the features of comminution which theoretical considerations have not covered adequately. Another feature is the effect of impact velocities, which may greatly influence the total energy required for breakage. Impact velocities may vary from 1 or 2 fps in crushers to 10 or 20 fps for ball mills, and as high as 100 or more for hammer mills. However, according to the findings of geophysicists, the velocity of sound and of compression waves in stone is many times greater; the primary longitudinal compression waves travel at perhaps 15,000 fps, and the secondary transverse waves, which may reach the surface and cause cracks to form thereon, travel at perhaps 5000 fps. When a crack tip forms, the total surrounding stresses are concentrated in this tip, which rapidly extends throughout the rock particle.1 It would seem that the energy required to deform the rock beyond its critical strain, resulting in the formation of a crack tip, represents practically all of the energy required. Most of the primary crack tips presumably form on the surface. A simple method of designating feed and product size is necessary for the evaluation of crushing and grinding results. Taggart's suggestion2 that the 80 pet passing size be used has been found very practical. In this paper, the square opening screen size which 80 pct of the feed passes is designated as the feed size F, and the size which 80 pct of the product passes, or the product size, is designated as P. The reduction ratio at the 80 pet passing size, or F/P is designated as n. The feed and prod-

Jan 1, 1951

By Clarence Zener

Theoretical considerations by one of the authors have ledl to the prediction that the dynamic internal friction of annealed metals has a broad maximum at a certain grain size. This prediction they have verified2 for alpha brass. In the present paper the theory is extended to include the precise manner in which the internal friction varies with grain size on either side of the maximum. New experimental data are presented to test this extended theory. The physical basis for the type of internal friction that is being investigated lies in the interplay between stress and temperature. Just as local fluctuations in temperature give rise to local fluctuations in stress, so likewise fluctuations in stress give rise to fluctuations in temperature. But temperature gradients give rise to necessarily irreversible thermal currents, and hence to internal friction. The theory for this type of internal friction has been developed quantitatively,³ and has been experimentally verified,4,5 for the particularly simple case of the transverse thermal currents accompanying transverse vibrations. Of more fundamental importance are the intercrystalline thermal currents accompanying all types of vibration. The variation in stress across grain boundaries arises from the elastic anisotropy and at least partial random orientation of the individual crystallites. An exact quantitative treatment of the internal friction due to these thermal currents is of course out of the question. However, much information can be obtained from general arguments.1,6 Thus when the frequency of vibration f is low, or when the grain size d is small, adjacent grains remain nearly in thermal equilibrium, and vibration proceeds isothermally with little internal friction. Again, when the frequency is high, or the grain size large, the heat flow per cycle is small, the vibration proceeds adiabatically with little internal friction. The internal friction will become a maximum in the transition region. The degree of adiabatic-

Jan 1, 1940

By Clarence Zener

Theoretical considerations by one of the authors have ledl to the prediction that the dynamic internal friction of annealed metals has a broad maximum at a certain grain size. This prediction they have verified2 for alpha brass. In the present paper the theory is extended to include the precise manner in which the internal friction varies with grain size on either side of the maximum. New experimental data are presented to test this extended theory. The physical basis for the type of internal friction that is being investigated lies in the interplay between stress and temperature. Just as local fluctuations in temperature give rise to local fluctuations in stress, so likewise fluctuations in stress give rise to fluctuations in temperature. But temperature gradients give rise to necessarily irreversible thermal currents, and hence to internal friction. The theory for this type of internal friction has been developed quantitatively,³ and has been experimentally verified,4,5 for the particularly simple case of the transverse thermal currents accompanying transverse vibrations. Of more fundamental importance are the intercrystalline thermal currents accompanying all types of vibration. The variation in stress across grain boundaries arises from the elastic anisotropy and at least partial random orientation of the individual crystallites. An exact quantitative treatment of the internal friction due to these thermal currents is of course out of the question. However, much information can be obtained from general arguments.1,6 Thus when the frequency of vibration f is low, or when the grain size d is small, adjacent grains remain nearly in thermal equilibrium, and vibration proceeds isothermally with little internal friction. Again, when the frequency is high, or the grain size large, the heat flow per cycle is small, the vibration proceeds adiabatically with little internal friction. The internal friction will become a maximum in the transition region. The degree of adiabatic-

Jan 1, 1940

By Wendell S. Williams

Single crystals of TIC doped with boron at high temperat~ires develop second-phase inclusions. The inclusions are in the form of lamellae lying parallel to {l 11 } planes of the Tic matrix and can be vevealed by etching [100] cleavage faces of the boron-doped Tic crystals. measurements of the critical resolved shear stress. t, of TIC crystals containing such inclusions showed that the ropid drop in t wilh increasing temperatu.ve found for pure Tic was greatly reduced. At 1600°C, the inclusion containing crystals had a value of t five limes that of pure Tic. The hardening effect also was found to inhibit hot pressing of TiC powders containing boron impurity. Thermochemical and crys-tallographic arguments suggest that the inclusions are TiB2. The boron content of the hardened carbide is a few tenths of 1 pct. TITANIUM carbide is noted for its high room-temperature hardness. However, measurements of the critical resolved shear stress, T, of single crystals of Tic at high temperatures have shown that t decreases exponentially with increasing temperature.' This temperature dependence of t is attributed to thermally activated dislocation mobility limited by a large Peierls stress.' In turn, this large Peierls stress is believed to be a consequence of strong co-valent and ionic binding in Tic. The rapid drop in 7 with increasing temperature, characteristic of pure Tic, is lessened by the introduction of second-phase inclusions. Exposure of Tic to boron at high temperatures produces such inclusions. A report of the influence of boron on t in Tic is presented, followed by a discussion of the nature and formation of boron-containing inclusions in Tic which are believed to be responsible for the hardening effect. I) CRITICAL RESOLVED SHEAR STRESS OF BORON-DOPED Tic CRYSTALS Tic single crystal boules grown by Union Carbide Corp., Linde Division, were doped with boron by placing them in a carbon crucible packed with boron powder and heating in a vacuum furnace to 2000°C for 1 hr. Samples 1 by 1 by 3 mm were cleaved from these doped boules. High-temperature compression tests' were made on these samples to determine the critical resolved shear stress as a function of temperature . The rapid drop in critical resolved shear stress found for pure Tic crystals' did not occur: tests indicated that the boron-doped crystals at 1600°C had values of T equal to those of pure Tic crystals heated to only 1100°C, Fig. 1. No difference in the shape of the individual stress-strain curves was produced by the boron doping, but the stress scale was multiplied by a large factor. The hardening effect of boron in Tic probably extends to temperatures lower than those used in the present work (1100°C minimum). At room temperature, however, the influence of boron is difficult to determine because the stress required for gross plastic flow in pure Tic is SO high that in practice fracture cccurs first. Microhardness is the only test that can give an indication of the yield stress in Tic at room temperature. such measurements were made5 on boron-doped Tic; the matrix had a hardness value

Jan 1, 1967

By Sir Nathaniel Barnaby

We must not conceal from ourselves that, against the perils arising from perforation of the shells or hulls of ships, we are greatly worse off in these days of steel and iron than we were when our ships were built of oak, teak and pine. Apart from the greater

Jan 1, 1891