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By Jens P. Nielsen, W. H. Justice

This paper describes an improved acidizing technique which has been applied in acidizing gas wells in the La Gloria Field. Wells acidized in this manner exhibited a much greater increase in deliverahility than wells acidized in the conventional manner. The acid is injected into the well in small slugs separated by a small volume of high pressure gas. The acid and gas are displaced from the tuhing by high pressure gas to reduce the hydrostatic head on the well when the acid is recovered from the well. The well is opened for production as soon as the acid and gas are displaced. This procedure permits a very rapid recovery of the acid which results in large increases in the deliverability of the gas wells. It has been found advantageous in the acidization of gas injection wells to inject the high pressure gas directly after the acid without backflowing the acid out of the well. This practice has made it possible to inject the gas in the injection wells of this field with a much lower pressure differential. This reduces the horsepower required to inject the gas and also decrease:, the number of injection wells required per reservoir. INTRODUCTION The results obtained by acidizing gas wells ill the La Gloria Field have varied considerably in the past. For this reason. a planned study of the acidizing procedure was undertaken in order to obtain more consistent results. The Frio Sands of the La Gloria Field are rather permeable and it was not necessary to acidize many of the wells when they were originally completed. At the completion of an eight-year cycling program in several of the gas reservoirs, it became necessary to recomplete many wells in other reservoirs. It was found that the opan Flow potential of the wells recompleted in different sands was not as large as wells that were originally completted in that reservoir. A study of the drilling records of several of these wells indicated that the sands had originally been subjected to considerable hydrostatic drilling fluid overload while the well was being drilled to the deeper sands of the field. It is indicated that during this eight-year period, the drilling mud and water that were lost into the formation when the well was being drilled had formed a relatively impermeable Eone around the well bore. This impermeable zone around the well bore made it very difficult to obtain high deliverability wells when the original wells are recompleted in other zones. Muskat' has shown that in uniformly permeable and porous formations a zone of partial plugging one ft in radius around the well would drastically decrease the productivity of the well. The analysis for this problem shows that the production capacity of a well is very sensitive to the value of the permeability of the zone immediately surrounding the well bore. This is to be expected in view of the highly localized character of the pressure drop in a radial flow system about the well center. The reduction of the deliverability is not proportional to the thickness of the mud-affected zone as the major portion of the reduction in deliverahility IS caused hy the

Jan 1, 1952

By L. Himmel, R. F. Mehl, C. E. Birchenall

The rates of self-diffusion of iron in artifically prepared wustites of various compositions have been determined using the decrease in surface activity technique. Similar measurements are reported for artificial magnetites of nearly stoichiometric composition and for natural hematite single crystals. These data, together with appropriate thermodynamic data derived from the present study or from the literature, are used to calculate the rates of oxidation of iron and its oxides, taking as a basis the theoretical rate equations developed by Wagner. The calculations are compared with experimental rate constant data for these same reactions and are shown to provide essential confirmation for the Wagner theory. For the most part, the results are also consistent with the previously proposed transport mechanisms in the oxides of iron. WHEN a metal is exposed to an oxidizing atmosphere at elevated temperatures, a superficial oxide layer is formed which then thickens according to some characteristic rate law. Provided that the oxide layer is dense and continuous and does not present any paths for gaseous diffusion, continued growth must inevitably involve the migration of the reactants—either the metal or oxygen or both—through the lattice of the solid oxide. This is true whether the reaction rate is controlled by the diffusion process itself or by a slow step in a reaction at one of the interfaces. If the overall rate is limited by diffusion, and if the concentrations or thermodynamic activities of the reactants at the boundaries of the oxide layer are independent of time, the familiar parabolic rate law is observed. Under these conditions, Wagner1 has shown that the rate constant may be expressed in terms of the mobilities of the reacting components and the appropriate concentration or activity gradients which are established across the growing oxide layer. In presenting the phenomenological basis for the theory, Wagner has emphasized the role played by lattice defects in diffusion processes in oxides. The essential validity of this theory has been confirmed by experiment for a number of simple systems including the growth of Cu2O on copper.'-' One of the objectives of the present study has been to extend the Wagner approach to the more complex process of the oxidation of iron and its oxides, and particularly to wustite, which is normally the major constituent of the oxide scales formed on iron at temperatures above approximately 570°C. For this purpose the rates of self-diffusion of iron in w?stite, magnetite, and hematite have been measured by tracer techniques and the necessary thermodynamic data have been obtained from equilibrium studies involving the oxides and their atmospheres. These data have subsequently been used to test the underlying assumptions of the Wagner theory as well as the detailed mechanism of the scaling of iron previously proposed by Davies, Simnad, and Birchenall.5 Lengthy treatments of diffusion and conduction phenomena in ionic crystals have been published." * The latest, by Jost,8 also summarizes much of the existing experimental data. In general, however, the oxides of iron have not been considered specifically and hence a brief review of the available

Jan 1, 1954

By Howard R. Keil

Reactor at Carlton mill successfully calcines pyrite-telluride flotation concentrate for cyanidation. CARLTON mill in the Cripple Creek district, 45 miles southwest of Colorado Springs, Colo., has been in operation for approximately three years, treating the custom sulpho-telluride ores formerly handled by the Golden Cycle mill in Colorado Springs. At the new mill the pyrite-telluride flotation concentrates have been roasted, prior to cyani-dation, in a Dorrco FluoSolids reactor, which has proved capable of yielding calcine readily amenable to cyanidation. Incoming ores are crushed at Carlton to % in. and sampled in 30 to 75-ton lots before the individual lots are mixed in the fine ore bin. The composite ore then goes to the grinding circuit. Classifier overflow from the grinding circuit is treated by flotation to produce a concentrate containing approximately 85 pct of the values in 5 pct of the weight. The flotation concentrate goes to the FluoSolids reactor prior to cyanidation. Cyanide solution values are recovered by zinc dust precipitation. Flotation tailings are thickened and cyanided, the values from this part of the circuit being recovered from solution by activated carbon. Gold values in the flotation concentrates consist of a small amount of finely divided metallic gold; the tellurides, sylvanite and calaverite; and gold very intimately associated with the pyrite. The metallic gold and a part of the telluride values can be extracted from the concentrates by cyaniding without roasting. However, extraction on the tellurides by this method is not satisfactory, and the pyrite values are so intimately associated with the pyrite that very fine grinding and cyanidation for a prolonged period under ideal laboratory conditions does not yield good recovery. Upon roasting, the tellurides are oxidized to very finely divided metallic gold which is readily soluble in cyanide. The pyrite is oxidized mainly to a porous iron oxide which allows cyanide solution to penetrate to gold particles and take them into solution. Feeding the Reactor Flotation concentrates move by gravity to a thickener. Thickener underflow is discharged at approximately 60 pct solids, by means of a diaphragm pump, into a storage and blending agitator. From here the concentrates are pumped to a disc filter. The filter cake, at 84 to 88 pct solids, drops directly into a repulper where it is repulped into a slurry of 78 to 80 pct solids. The repulped filter cake flows into a 6x6-ft slurry agitator from which it is fed directly into the reactor by the Moyno pump. The Moyno pump has eliminated a large number of difficulties that were first encountered in feeding a wet concentrate to the reactor. On the original installation in Canada a screw feeder was used to introduce the filter cake directly into the reactor. Since the reactor is under a slight positive pressure it was necessary to have a suitable seal to prevent gas escaping from the reactor at this point. When the concentrates produced in flotation were coarse or granular they could be readily fed to the reactor but when fine-textured, clayey concentrates were produced a great deal of trouble was encountered.

Jan 1, 1955

By J. H. Rushton, L. H. Mahony

Principles of fluid motion and turbulence which have been found to be of use in mixing and agitation problems are discussed, as well as suggested applications in extractive-metallurgy processes. Various types of impellers are described, together with other conditions that affect flow pattern and turbulence. The choice of equipment for particular requirements is considered, and equations for power input are given. Modern heavy-duty mixing and agitation equipment can take an increasingly important part in such extractive-metallurgy processes as solids handling, crystallizing and leaching, chemical operations, and flotation. Application of mixing and fluid-mechanics principles to extraction methods can lead to greater process rates and a resultant saving in time and money. MIXERS are being applied with increasing frequency to problems in the metallurgical industries. The increase represents in part the modernization of mechanical equipment used through the application of unitized drives, modern electric motors and speed reducers, and recently developed materials of construction. Some applications have resulted from process changes and the use of techniques for operations similar to those that have been demonstrated and proven in the chemical industry. Still more applications are being developed through the use of fluid-dynamics principles not previously recognized as applicable to these operations. It is the purpose of this paper to describe those principles of fluid motion and turbulence which have been found to be of use in mixing and agitation problems, and to suggest applications for them in the extractive-metallurgy processes. Modern mixing equipment has been designed to provide the fluid motion consistent with that best suited to different operations.' When properly applied, these more efficient fluid-handling mixers result in lower process-production costs. Metallurgical operations usually involve large amounts of solids. The characteristics of the ore control the process and only enough liquid is added to provide sufficient fluidity for handling and processing. The reactive part of the ore, the mineral value to be extracted, is likely to be low in percentage, and the quantity of reagent required is similarly low, but excessive dilution makes additional reagent necessary and therefore is undesirable. Thus, the primary problems in minerals processing are to handle as high a concentration of solids as possible and to distribute reagents uniformly. These pulps, or slurries, are in a range of solids concentration where hindered settling rates apply, and care must be taken to agitate and mix sufficiently to maintain suspension and flow throughout the equipment. Such slurries have high densities which are the weighted average of the components and viscosities that are spoken of as "effective viscosities" but are difficult to evaluate. It is convenient to separate metallurgical operations involving mixers and agitators into three categories: solids handling, mechanical or physical operations, and chemical operations. In each of these categories fluid motion is required to maintain suspension, to distribute surface-active agents, to blend components and reactants, and to induce high rates of chemical reaction. After a discussion of some basic principles of mixing and agitation, examples of application to the three categories will follow. Fluid Motion The fundamental problems of mixing and agitation of liquids have to do with the mechanics of fluid streams and the means by which they are

Jan 1, 1955

By Augustus Locke

Jan 1, 1923

By Augustus Locke

Jan 1, 1923

By N. H. van Lingen

A laboratory stud], has been made to determine what factors affect the penetration rate of roller bits, diamond bits and drag bits in rock drilling with clay /water muds. The rather simple relations that exist when pressures in and around the borehole are equal become more conzplicated when under down-hole conditions the penetration rate is hampered by the existence of a pressure differential between the mud at the hole bottom and the pore liquid at cutting depth. Expressions that have been derived for both the penetration rate and the magnitude of the pressure differential in permeable rock together fully account for operating, rock, mud and bit variables. In impermeable rock a similar pressure differential is caused by the bit action itself. In all cases, the pressure difierential and the reduction in penetration rate increase with the effectiveness of the plastering at the bottom of the hole by mud particles. Where bits are employed whose action is largely that of crushing, however, the plastering may become even more effective owing to the addition of rock particles rubbed into the pores of the rock. With roller bits, a plastically hehaving layer may be formed, which causes a further reduction in penetration. In the case of bits whose action is chiefly scraping, moreover, penetration may be arrested by the bit's becoming balled-up. The various adverse effects are reduced by thorough scavenging of the hole bottom. This paper shows how with jet bits the efficiency of such scavenging may he improved by suitable choice of the position of the nozzles. INTRODUCTION The reduction in a bit's penetration rate with increasing depth of hole has been the subject of many investigations. Various investigators ',' have independently reached the conclusion that this reduction occurs not so much because the rock-breaking process becomes more difficult as it does because the lifting of the rock fragments is impaired by a fluid pressure differential holding the fragments down. When such a pressure differential can be avoided, as in air drilling and to a smaller extent in water drilling, penetration rates remain high. Although the range of applicability of these techniques is being extended, most oil wells still have to be drilled with mud. In this paper we present the results of laboratory experiments carried out to determine what factors govern the hold down effect encountered in mud drilling. In the course of this investigation, the well known importance of bottom scavenging came more and more into prominence. Not only may it reduce the magnitude of the hold-down forces, but also it appeared to be a means of preventing the accumulation of a plastic mass of cuttings and mud on the hole bottom and bit which may cause penetration to cease almost completely. So that the effects of fluid pressures may be more readily understood, the factors that govern penetration rate in the absence of these pressures will first be discussed. The effect of down-hole pressures will then be assessed for the case of permeable rock where fluid pressures are well defined, and it will be demonstrated how rock strengthening due to confining can be accounted for. Subsequently, fluid pressures in less-permeable rock will be examined; we will show that in impermeable rock it is the bit action that governs fluid-pressure distribution and hold-down. In the case of poor scavenging and/or high bit load. cutting cake manifests itself. The effect, like various others. appears to depend on the type of bit used. From the very beginning, therefore, we shall base our discussion on the three main types of bits used in rotary oil-well drilling— roller bits, diamond bits and drag bits. Since space is limited, it will be impossible to make more than a passing reference to many aspects of the problem. Moreover. certain relations that are not of primary irnportance to our argument will unavoidably have to be stated in a somewhat dogmatic fashion, and the experimental data on which these are based necessarily must be omitted. EQUIPMENT The drilling experiments were performed on three machines, of which one has been designed for the realistic simulation of down-hole pressure conditions. HIGH-PRESSURES MACHINE In this machine (diagramed in Fig. 1) the mud, pore and confining pressures can all be adjusted independently. The foil-covered rock sample contained in the inner pressure vessel is confined by oil that is pressurized by means of a hand pump. The pore space of the watersaturated sample is connected to an arrangement which keeps the pressure in the pore space constant regardless of the rate of filtrate flow through the sample.

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

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

By GUY C. RIDDELL, Donald M. Liddell

THE electronic arts today constitute the outstanding development in the field of rare metals, if not indeed in the arena of scientific progress at large. The year 1930 may become known as the year in which the electronic tube took hold of the wheels of industry; it is the year in which the tube's emancipation from the art of communication was proclaimed. The little tube which made a $500,000,000 industry out of a vacuum has now been applied to mining, manufacturing, transportation, chemistry, and other industries. Not many appreciate the extensive utility that e1ectroni.t tubes have already found in transportation, where they control the speed and security of express trains, as well as operate traffic lights on important highways-in the case of the Detroit-Windsor bridge counting the traffic and instantly turning the reports into the superintendent's office some distance away. In an Ohio steel mill, ten-ton ingnts 'rash back and forth through the rolls, reversed by their own shadows. The vacuum tube also starts, stops, and levels, fast passenger elevators.

Jan 1, 1931

By C. Dean Starr

The physical basis of the equation correlating electrical conductizlity and temperature coefficient of resistance of solid solution alloys has been inzlestzgated and the nature of the constants evaluated. It is shaun that the same form of correlation is valid irrespective of the magnitude of the temperature coefficient. However, the effect of therma1 expansion and change in resistivity with temberature nust be considered when the magnitude of the temperature coefficient of resistance is near zero. In a comprehensive literature survey conducted at the Armour Research Foundation in 1950, it was found that a linear relationship exists between the electrical conductivity, K, and the temperature coefficient of resistance, a, for solid solution alloys. This was expressed by the equation where B, a constant, depends on the solvent metal but not the solute. A continuing investigation by Hansen, Johnston, and Parks showed this equation was generally appropriate for Cu, Ag, Au, Pd, Pt, and Co base binary solid solution alloys as well as for many ternary alloys of copper over a range of conductivities and temperature coefficient of resistances from 0.02 to 0.60 reciprocal pohm cm and-0.00015to0.004Q per 0 per "C respectively. Eq. [I] was not always valid for alloys that exhibited a change in state (magnetic to nonmagnetic) or for alloys that had a temperature coefficient of resistance near or below zero. For example, in nickel alloys, a simple linear curve as predicted by Eq. [l] was not obtained when the conductivity was plotted against the temperature coefficient of resistance. Hansen suggested that deviations observed were caused by transitions from a ferromagnetic to a nonmagnetic state. Subsequent and more extensive data by ronin on Ni-Mn alloys confirmed Hansen's postulate. While both states independently showed a linear relationship between K and a, the value of B was different for the two states. In some copper and gold base alloys, as well as the platinum and palladium alloys investigated by Hansen, the conductivity did not extrapolate to zero at zero a as demanded by Eq. [I]. This deviation can be readily corrected by simply adding a constant to Eq. [I.] whence Eq. [2] shows the K decreases as a decreases but that K has a positive value when a = 0 which is observed for commercial solid solution alloys as well as the experimental alloys tested by Hansen. While other methods of correlation of electrical properties have been made such as the one by Starr and Wang3 who found a linear relationship between resistivity and temperature coefficient of resistance for Ni-Cr-Al-Cu alloys, the data, in general, can also be correlated by a form of Eq. [2]. Thus, Hansen's empirical equation has considerable merit. The objective of this paper is to determine the physical basis for this equation and to examine the region near zero a in more detail. ELECTRICAL CONDUCTIVITY VS TEMPERATURE COEFFICIENT OF FU3SISTANCE The resistance of a metal or alloy is defined as

Jan 1, 1963

By J. A. Clum, R. W. Heins, T. D. Tiemann

The use of Na-montmorillonite clay binders (Western Bentonite) in the pelletizing of iron ore concentrates is well established as is the idea that alternative binders must be found. 1-6 This note summarizes work done7 in evaluating a Wisconsin montmorillonite clay binder. The clay occurs in irregualr beds overlying the Prairie du Chien Dolomite and the St. Peters Sandstone near Hersey, St. Croix County.

Jan 1, 1978

By J. H. Wright

Longhole sublevel stopes excavate ore with which the production geologist has only remote contact; therefore, predicting grade and tonnage from such a stope can be a problem. However, the longholes themselves yield data that can be used to improve those predictions. Here, a radial distribution method of weighting sample data is discussed, which is useful in forecasting grade and tonnage from certain longhole sublevel stopes.

Jan 1, 1985

By Charles F. Johnson

A pulse technique is described for the measurement of bar velocity. A low frequency sine wave pulse is used which allows the wave-length to become much larger than the lateral dimensions of the test specimen. The low frequency pulse method has been tested and compared with the resonant frequency method and the results show that both methods give, on the average, equivalent velocities.

Jan 1, 1971

By J. S. Blakemore, E. O. Hall

SERRATED yielding, commonly called the Portevin-Le Chatelier effect, is known to occur in a wide range of alloys where the moving dislocations are considered to be locked by the diffusion of solute atoms to them. From the work of Cottrell,1 an approximate relationship between strain rate, E, dislocation density, p , and solute diffusion coefficient, D, giving rise to serrated yielding is: e =Dp

Jan 1, 1969

By Edwin A. Zink, Gerald P. Zink, John E. Wolgamott

Recent advances in high-pressure water technology can be effectively employed in underground mining. The new equipment is based on standard industrial water cleaning hardware and is compatible with conventional mining techniques. Three viable applications are addressed: rock drilling, hole notching, and rock bolting. Highlights of test results are presented that were obtained in several underground mines during the last two years of development work.

Jan 1, 1982

By Richard E. Chism

The dry methods of assaying mercury-ores and other combinations of mercury all rest upon the volatility of this metal as a beginning. After the separation of the mercury in the form of vapor from the matrix upon which the assay is performed, the mercurial vapors are either condensed upon cold surfaces or received upon a gold plate into which the mercury is absorbed.

Jan 1, 1899

By James Tucker MacKeni~ie

BORN in Florida, educated in Ten¬nessee, employed all his life in the iron industry of Alabama, J. T. MacKenzie is truly of the South. In courtesy, hospitality, as well as in accent of speech, he is true to the tradition of the South. His alma neater, the University of the South, has given him the honorary degree of Doctor of Science for his achievements in metallurgy. He has been active in many technical societies; has received the Whiting Medal of the American Foundrymen's Association for his work in the advancement of gray iron metallurgy, and is chairman of the gray iron division of the A.F.A.; was instrumental in initiating the Alloys of Iron Research of the Engineering Foundation and has served as a member of its Alloys of Iron Committee since the Committee's organization.

Jan 1, 1938

By E. M. Furness, A. S. Henderson

ORIGINALLY the Babbitt experimental plant grinding circuit consisted of one rod mill 10 ½ ft diam by 12 ft long in open circuit followed by two ball mills 10 ½ ft diam* 12 ft long in parallel circuit. Shortly after operations commenced it was apparent that the rod mill could not function satisfactorily at the required 125 gross tons of ore per hr. Attempts to operate at this rate produced: 1) excessive tramp material over rod mill trommel screen which could not be handled in this open circuit and 2) excess build-up of coarse ore in the ball mill circuits because of inadequate rod mill grinding. Since Reserve Mining Co. ore must be ground to 85 pct -325 mesh to produce a satisfactory iron concentrate, an efficient and controlled grinding circuit is highly important. The first step in trying to resolve this grinding problem was to determine which unit of the circuit was actually in trouble and to what extent. A series of tests conducted at a lower tonnage rate of rod mill feed indicated that one ball mill could grind satisfactorily at rates up to 70 gross tons of rod mill feed per hr.

Jan 12, 1957

By Ulf S. Landergren

Diffusion coefficients and marker movements have been determined in brass using welded couples. Three different concentration ranges were employed at 750°C, while a fourth concentration range was measured at 500°, 600°, 700°, and 800°C. Marker displacements toward and porosity development in the high zinc side of the couple were observed in all cases. The results were interpreted as favoring a vacancy diffusion mechanism. IN the large amount of diffusion literature which has accumulated during the past half century, very few experimental data have been presented on body-centered-cubic metallic phases. The impressive combination of experimental and theoretical studies which has given the vacancy mechanism a fairly secure position as the preferred mechanism for most face-centered-cubic metals has no counterpart for body-centered-cubic phases, although the theoretical picture seems to be in a better state than the experimental work. The attempts to select diffusion mechanisms by the theoretical calculation of the activation energy for the various conceivable unit diffusion processes and the energy of formation of the type of lattice defect required have been based on models of two kinds. The first kind utilizes potential functions fitted for certain properties of pure crystalline copper; the second kind is fitted for sodium. The latter is an example of an open metal in which the metallic ion is small compared with interatomic distance,&apos; while the former is characteristic of the larger class of metals in which the ions have diameters about as large as the interatomic distance. brass should resemble copper in this fundamental property. It should be evident that results on the mechanism of diffusion obtained for one of these classes need not necessarily apply to the other. Huntington and Seitz, using a model of the copper type, showed that the activation energies to be expected for interstitial migration or a two-atom direct interchange were much higher than that for vacancy diffusion. Zener pointed out that a four-atom ring rotation would involve an activation energy considerably lower than the two unlikely mechanisms although still higher than the vacancy mechanism in the face-centered-cubic structure. Furthermore, he argued, the four-atom rotation would be relatively easier in a body-centered-cubic lattice and might be competitive with the vacancy mechanism. Paneth showed that a body-centered-cubic crystal-like sodium could form interstitial defects of special type, called a crowdion, by crowding an extra atom into < 111 > directions where the defects would affect a line of about eight atoms. The defect was constrained to move along the defining line. Unlike the face-centered-cubic case, therefore, the theoretical calculations for the body-centered-cubic mechanism do not provide a very clear-cut answer, and the absence of adequate experimental studies is the more serious. This investigation was undertaken for the purpose of obtaining useful information on diffusion in body-centered-cubic phases. brass was chosen for several reasons: 1—the phase field is sufficiently wide at high temperatures to permit the use of diffusion couples with adequate concentration ranges for satisfactory chemical analysis, 2-—thermodynamic activity data are available for the calculation of mobilities from diffusion coefficients, 3—the phase is as close to the theoretical model of the copper -type on which the calculations have been done as any body-centered-cubic metallic phase is likely to be. Measurements of the movements (if found) of inert markers during the diffusion process would indicate that a vacancy or Or mechanism played a major role in diffusion in brass. If no marker movement should be found, a ring mechanism would be indicated but not assured. Experimental Procedure The alloys used in these experiments, listed in Table I with analyses, were supplied by the Naval Research Laboratory. They were from ingots of 3x3 in. cross-section, heated to 760°C, reduced under a

Jan 1, 1957

By A. A. Rauth

In this paper, the author derives a series of formulas from basic principles and illustrates the application of these formulas to practical grinding charge problems. The paper establishes the nearly proportional relationship of mill power to charge level and shows how this relationship can be used to advantage in the design, manufacture and operation of grinding mills. The procedures outlined offer a rapid means of anticipating the power requirements for a given charge or determining makeup charges for a given power reading. The theories which have been developed concerning the dynamics of grinding have been motivated largely by the desire to derive workable formulas for the accurate determination of grinding mill power. This accurate determination has always been handicapped by the large number of variables to be considered, some of which are mill diameter, length, speed, liner design, grinding charge and material density, volumetric mill loading, internal friction, and charge size and gradation. In efforts to determine mill power, attempts have been made to utilize torque concepts. The formulas derived consider the grinding mass as a rigid body and utilize factors that are based on empirical data so that the movement of the charge within the mill is compensated for. These formulas are of principal interest to the mill designer since he is charged with the responsibility of analyzing all of the variables and from them predicting a mill size and a motor size which are compatible both with each other and with the grinding job for which they were intended. The mill operator, on the other hand, has an entirely different problem. The mill dimensions are already established and so is the driving motor. The operator&apos;s main concern is to obtain maximum performance from the mill he already has. For him, the many variables which perplex the mill designer are fixed values. Mill diameter, length and speed are set and, to a large extent, so are the conditions inside the mill from which the torque formula advocates derive their empirical data. It is conceivable that if the major mill dimensions which affect power demand are held constant, and if the variables influencing empirical factors are held fairly constant, as they are in an operating mill, then the only major variable remaining which affects power is the level of the charge itself. Under this condition.

Jan 1, 1970