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By D. J. Freeh, W. E. Horst, R. C. Kellner

This paper is concerned with the description of grinding characteristics in a batch grinding system. A mathematical model was developed and used for simulating the system on an analog computer. A general equation describing the change of selected size fractions with respect to time is presented. The empirical verification of the model is discussed. In order to understand the performance of a grinding system, it would be desirable to have a mathematical description of the system's behavior. The development of a mathematical model to describe the performance of a batch dry-grinding operation was investigated. This is the first step toward reaching the objective of a practical mathematical description of a grinding system that could be employed for process control and optimization of a simple or complex grinding circuit. Although this article is concerned only with batch grinding performance, experimental work is being conducted to extend the model to continuous grinding systems. BASIC PROCESS CONSIDERATIONS In a paper dealing with the probability theory of wet ball milling, Roberts1 correlated the rate of change of oversize material, C, with energy input, E, as follows where the energy input is expressed in power/unit mass and k is a constant for each particle size. Experimental grinding studies were made by Bowdish2 to extend the previous work of Roberts. The work of Bowdish also showed that the rate of breaking of oversize particles in a ball mill is proportional to the concentration of oversize particles present. He further demonstrated that breaking of oversize particles is proportional to the surface area of the balls used for grinding. Rate equations were presented and it was concluded that grinding could be considered as a first order phenomenon according to the rate equation [2] di which is in accordance with Eq. 1. In Eq. 2, the effect of ball area is included in the constant k,. Other rate equations were reported to show the effect of a change in ball area and removal of fines during grinding. Correlation studies made by Arbiter and BhranY indicate a first-order rate equation for quartz; however, their data showed less than first-order rates existed for some of the other materials evaluated. More recently Kelsall4 has shown that the rate of breakage of any narrow size range of quartz could be described by a first-order rate equation. Several other investigators5-7 have described grinding behavior in terms of rate equations or kinetics. In general, the rate equations have been described for each particle size; however, the interactions between sizes and the overall relationships that exist have not been considered, at least not in the form of solving a group of simultaneous differential equations. Extensive work has been conducted by various investigators using a probabilistic approach which has expanded stein's' earlier work. Selection and breakage matrices are incorporated in the probabilistic model as contrasted with the deterministic method presented here. A batch grinding operation may be considered as an unsteady-state process from the standpoint that the conditions within the mill are a function of time. Therefore, a plot of mass fraction of the i-th size versus time would give a set of curves as shown in Fig. 1. In these curves X , represents the mass fraction of large size material, X2 intermediate size, and X3 small size material. An examination of these curves shows a strong similarity to the curves that would be obtained from a chemical reaction of the type9 A?B?C, [3] where A would be comparable to the largest size material being broken to an intermediate size, 3, and

Jan 1, 1968

By C. Gatlin, C. E. Nemir

A common cure of lost circulation is the introduction of granular bridging agents into the mud system. Many materials, such as ground nut shells, are used for this purpose. If the trouble causing void (fracture, fissure, vug, etc.) is not too large, the granular agent forms a "bridge" across or within the opening. Successively smaller particles in the mud stream then accumulate on and/or within this bridge until normal filtration is finally established. The efficiency of many bridging agents has been studied in the laboratory using various slot testers.',' Many investigators have remarked that a granular bridging material should have the proper particle size distribution. With the exception of the broad range specified in the patent of Goins and Nash,3 here is apparently no definition as to what this distribution should be. A bridge may be initiated when several particles of lost circulation material lodge against each other in a fracture or other void. Smaller particles then may bridge the openings between the larger, previously bridged particles. This process continues until the voids become quite small and the problem becomes one of filtration. It would seem logical that an optimum particle size distribution exists, i.e., one containing the proper quantity of properly sized material to fill the successively smaller voids of the bridge. The filtration characteristics of drilling fluids may be subject to a similar analysis. It has been clearly demonstrated by many workers that the filtration behavior of various muds can be altered by particle size control.'.' Slusser, et al, divided filtration into three periods and showed that particle sizes affecting a given period did not necessarily affect other portions of the filtration curve. An analagous problem is the proper sizing of gravel, liner slots and screen sizes in various sand-exclusion problems. Here the situation is reversed in that a proper "void" size, rather than the size of the bridging agent, is sought. The classic work of Coberly 9 forms the quantitative basis for most sand-exclusion processes. It is interesting to note that, in general, Coberly's work has been overlooked by most drilling-mud researchers. Other investigators have made various studies of the effect of particle size distribution .on drilling-mud properties. As a part of their studies, Fancher and Oliphant reported 30-minute filtration loss of a variety of mixtures of particle sizes.'' Gates and Bowie noted an effect of particle size distribution on filtration, as well as on other physical properties.' MAXIMUM DENSITY THEORY A maximum density mixture has been mentioned as the possible solution for both lost circulation and mud filtration problems. Furnas 12 derived mathematically a method for obtaining maximum density of beds of packed solids, having either a given number of component sizes or a continuous gradation of sizes. This work was verified experimentally by Anderegg.13 or mixtures having a continuous grading of sizes, the interval between sizes is taken as successive screen sizes of interval 2 The ratio of the quantity of each size and the next smaller size is given by the equation Fig. I, number of size intervals of ratio 2 taken from Furnas' paper, gives the value of n + 1 for any given values of + and K, where K is the ratio of the diameter of the smallest particles to the diameter of the largest particles. Measurement by weight assumes, of course, constant density for all particle sizes. Choosing the quantity of the smallest particle size as a unit weight, the required weights of the successively larger interials are then r1 r2 r3 . ®1,2,3. Thus, the grading curve of a maximum density mixture represents a geometric pro gression of ratio r.

By T. M Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953

By R. W. Heckel, H. W. Paxton

The growth of grain boundary films and Widmanstiitten plates of proeutectoid cementite in hypereutectoid steels ulas considered quantitatively in three plain carbon steels and one "pure" iron-carbon alloy. Growth was found to take place at a slower rate than would be predicted on the basis of a model invoking rate control by long range diffusion of carbon. The films in the pure alloy grew faster than those in the plain carbon steels. A possible explanation is suggested. In 1904, Nernsst' and Brunner2 postulated that ionic crystals growing in supersaturated aqueous solutions grew at rates determined by diffusion through the solution to the growing crystal interface. The gradient down which the diffusion took place was assumed to be fixed by the supersaturated bulk solution concentration, the concentration dt the crystal surface and some arbitrary distance. The flux of material to the crystal was described as Flux where D is the diffusion coefficient, A the crystal surface area, Ci the bulk solution concentration, Co the saturated solution concentration, and 6 the thickness of the diffusion zone. It is obvious that the expression is an adaptation of F+ick's3 first law of diffusion (steady state). This was the initial formulation of what will be defined here as "diffusion controlled growth," i.e., growth limited by the long range diffusion of a component either to or from the advancing interface assuming both phases at the interface to be in equilibrium. This idea of equilibrium interface concentration implies an infinite reaction rate at the interface. Volmer, Zener,' and 11schner6 have derived expressions for the diffusion controlled growth of spherical precipitates in metallic systems. These analyses agree that the growth in a given direction should be parabolic with time. Brown and Hawkes7 observed that graphite, formed both from the decomposition of cementite and from the decomposition of eutectoid austenite in cast irons, grew according to a parabolic relationship and, therefore, concluded that the laws of diffusion controlled growth, as defined above, were obeyed. They, among others, failed to consider, however, that parabolic growth is a necessary, but not sufficient, condition for diffusion controlled growth. Mehl and Dube"' have pointed out that equilibrium may not be realized because the concentration at the interface cannot change instantaneously from that of the bulk to the saturation value. Furthermore, they propose that an equilibrium solute concentration in the parent phase adjacent to the precipitate would remove the thermodynamic activity gradient across the interface and, thus, stop the growth process. Frisch" has also emphasized the importance of interface concentrations that vary throughout the growth of a new phase. The variation in activity across an interface, as discussed by Onol' and Cahn and Hilliard,12 is of fundamental importance to this question. Ham13 considered the data of Turnbull14 on the growth of barium sulfate in aqueous solutions. He concluded that the data could be analyzed in terms of a radiation-type boundary condition. Flux across interface = K (c, - C,) [21 where C, is the concentration in the solution at the interface, Co the saturated solution concentration, and K the proportionality constant. The edgewise growth of Widmanstlitten plates, frequently referred to as the rate of lengthening, was first considered by Zener.'' Basing a mathematical analysis on steady-state (constant velocity) growth he concluded that where G is the growth rate, D the solute diffusivity, Ci the concentration in the bulk, Co the equilibrium interface concentration, C, the concentration in the precipitate, a a constant, Y the radius of curvature of the edge of the plate, and rC the critical radius, i.e., the radius which would increase the activity of solute at the interface at equilibrium under the influence of capillarity to that of the bulk. Zener1'

Jan 1, 1961

By T. M. Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the 'active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. dC Thus----— kc [1] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of un-floatable mineral. Hence the first order equation is It has been proposed by various workers1-' that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris- as discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1953

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

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

Jan 1, 1964

By D. F. Gibbons

THIS investigation was undertaken in order to gain further information on the mechanism of plastic deformation of iron at temperatures between room temperature and 77.2°K, and also to contribute to our understanding of the low temperature brittleness phenomenon that occurs in both the tensile and impact tests. It was decided to study as pure an iron as possible and to use the tensile test in order to simplify the problem as much as possible. Two series of iron were used throughout the investigation: iron A, obtained from the National Research Corp. and supplied as gas-free, high purity iron; and iron B, obtained from Fast' and produced by melting iron under purified hydrogen. Typical analyses of samples of both irons, after fabrication, are given in Table I. The main difference in composition of these irons is in their nickel and oxygen contents. Nickel has a very large solid solubility in iron. However, oxygen has an extremely small solid solubility. An attempt was made to reduce the oxygen content still further by remelting under purified hydrogen. This was successful in reducing the oxygen content to -0.0006 pct. However, no results on tests of this iron are included, since difficulty was encountered in fabricating the ingot. Wire specimens 1 mm in diameter were used for the investigation. The wires were produced from the ingots, as supplied, by cold rolling and swaging, with intermediate vacuum anneals at 700°C. Care was taken to reduce preferred orientation in the wires to a minimum by keeping the percentage of reduction in area between anneals of 30 to 40 pct. X-ray transmission photographs showed no indication of preferred orientation. The final grain size of iron A was 20 to 24 grains per linear mm and of iron B, 16 to 18 grains per linear mm. All specimens were tested in the decarburized and denitrided condition unless otherwise stated. The procedure was to pass hydrogen, saturated with water vapor at 26oC, over the specimens at 730°C for 2 hr. The specimens were quenched in iced water and then annealed in a vacuum of - 5x10-6 mm Hg for one day at 560°C to remove hydrogen. Higher temperatures were used for the vacuum anneal but this temperature was found to be quite satisfactory in removing hydrogen. The specimens were slow-cooled after the vacuum anneal. Where it is stated that the specimens were carburized, the specimens were given an identical decarburizing treatment and then carburized by passing hydrogen, saturated with pure n-heptane vapor at 0°C, over the specimens at 730°C. The specimens were then homogenized at 730°C for 2 hr in dry hydrogen. After the carburizing treatment the specimens were given the same vacuum anneal as for the decarburized specimens. The carbon content was determined from the maximum value of the internal friction carbon peak.2 Apparatus Fig. 1 shows a diagram of the tensile apparatus, with half the cooling coil removed. The cooling coil enabled temperatures from 200" to 77.2oK to be obtained. The apparatus was designed to fit a standard Tinius Olsen Universal tensile machine. The apparatus consisted of the rigid plate A which carried two carefully machined hooks H. These hooks attached the plate firmly to the moving crosshead of the tensile machine. The lower grip B was rigidly suspended from the plate A by three stainless steel rods. The upper grip C was joined to the upper grip of the tensile machine by the stainless steel rod E. The lower part of the apparatus was surrounded by a Dewar vessel, which was made a sliding fit inside the brass collar D. The specimen was held in a clamp which fitted into the grip, forming a ball and socket joint (see inset a). This was to attain as nearly pure

Jan 1, 1954

By Forrest F. Craig

Both early and more recent1 laboratory measurements of gas-oil relative permeabilities were made by subjecting oil-saturated cores to external gas drives. In these runs it was generally assumed that the flowing gas/oil ratio was constant at every point throughout the core. Using this assumption, the resulting equation for the gas-oil relative permeability ratio becomes A where Q is the flow rate at the producing end of the system. This relative permeability was then specified for the average saturation of the core. The assumption and resulting equation fail to recognize that in an external drive, the oil flow rate varies from zero at the injection end to a maximum at the producing end. The assumption also fails to consider the existence of a saturation gradient during an external drive. This saturation gradient is due solely to non-steady-state flow. Some authors2,3,4 have used this erroneous method of calculating relative permeability ratios from external drives. Other authors5,6,7 have used relative permeability ratios in calculating expected field performance by external drive, using Equation (1) and making the incorrect assumption that the saturation is uniform within the driven portion of the reservoir. To find the correct relation between the relative permeability. ratio at the average saturation and the produced gas/oil ratio, the insertion in Equation (1) of a factor, F, to adjust it for oil velocity gradient has been considered. The equation then takes the form Assuming that the oil velocity is directly proportional to the distance from the injection point leads to the conclusion that, for a linear system, the average oil velocity is one-half that at the producing end. Thus, the average gas/oil ratio is twice the produced gas/oil ratio, and Equation (2) is transformed into However, here again the existence of a saturation gradient is not recognized. The produced gas/oil ratio is related to the relative permeability ratio at the saturation of the outlet end of the system. It can be shown quite readily that, if the true log k,/k, saturation relationship is linear over small ranges of saturation, then d log kjko Where aaxv and u2 are the average and outlet saturations, respectively. Examination of Equation (3) shows that the factor F cannot have a single value over the whole saturation range. Another method of dealing with external drives is that of Buckley and Leverett.' Their method, which assumes no gas expansion and outlet end effects, considers fully the saturation gradient present due solely to the displacement mechanism during an external drive, and applies Equation (1) to each point along this gradient. The calculation of production history using relative permeability ratio is straightforward. However, the calculation of relative permeability ratios from production history by this method is impractical. In a recent paper, Welge,1 using an approach similar to that of Buckley and Leverett, presents a simplified method for determining the saturation at the producing end of the system. At thi; saturation, the relative permeability ratio calculated by Equation (1) applies exactly, after breakthrough of the stabilizej front. By this method, relative permeability ratios or production history may be calculated with equal ease. Use of this method as a laboratory tool in determination of relative permeability ratios by external drive requires the knowledge of the total injected fluid volume; in addition to the average saturation and producing ratio. As a preliminary test of this method of calculation, laborntory external gas drives were run on a 3% in. diameter, 11 in. long sample of Nellie Bly consolidated sandstone. This core sample had a permeability of 824 md and a porosity of 28.1 per cent. The driving fluid was air. Three different oils were used, having viscosities of 1.4, 9.8, and 125 cp, respectively. The runs were made under identical pressure differentials,

Jan 1, 1952

By Wayne L. Worrell

Thermodynamic data for the stable carbides and oxides of chromium, molybdenum, and tungsten have been critically eualuuted and are used to determine the stable condensed phases at 1 atm total pressure in each metal-carbon-oxygen system. Pourbaix-Ellingham diagrams have been constructed and are used to estimate the minimum temperatures neces.see)*y to oblain these metals by corbolhermic redlrction under reduced pressures. USING recently reported data for the carbides and oxides of chromium, molybdenum, and tungsten, the stable phases in the Group VI metal-carbon-oxygen systems at specific temperatures and pressures can be determined. The thermodynamically stable regions in each metal-carbon-oxygen system can be completely pictured using a Pourbaix-Ellingham diagram in which the two coordinates are oxygen potential (-RT In Po2) and temperature. Worrell and chipman' have described and constructed such diagrams for the metal-carbon-oxygen systems of vanadium, columbium, and tantalum. Downing2 has used similar diagrams to provide a description of the reactions in submerged arc furnaces. One of the examples which he cited was the Cr-C-O system; however, an improved diagram is presented in this paper using recently obtained data for the carbides of chromium. Although some of the oxides and carbides of the Group VI metals exist over slight ranges of composition,3 all solid phases are represented as stoi-chiometric compounds in the subsequent diagrams. Any error introduced into the calculated equilibria by neglecting the compositional variation of these phases is less than the uncertainty in the thermodynamic data. In a Pourbaix-Ellingham diagram for a three-component system, the phase rule requires that at equilibrium four condensed phases specify a point, three condensed phases determine a line, and two condensed phases define an area. To obtain a well-defined area at high oxygen potentials and teniperatures, the initial carbon to oxygen mole ratio is specified to be more than sufficient to reduce the oxide but not enough to convert all the metal to carbide. Thus, the lowest regions in the subse- quent Pourbaix-Ellingham diagrams represent areas in which the metal and its carbide are the stable condensed phases. Cr-C-O SYSTEM A) Thermodynamic Data. To simplify the subsequent calculations, all thermodynamic data are presented in the form of linear Gibbs-energy-of-formation* equations which were derived for the temperature range 505° to 2000°K and are reasonably accurate over the entire temperature ranges of the diagrams. The thermodynamic data for the compounds occurring in the Cr-C-O system are summarized in Table I. Several volatile chromium oxides have been reported,4 but their influence is negligible in the Cr-C-O system. Thermodynamic data for CO and CO2 were taken from the compilation of Coughlin.5 The only solid chromium oxide sufficiently stable to exist below 1800°K in the Cr-C-O system is Cr2Os.11 The Gibbs-energy-of-formation equation for Cr2O3 was obtained by revising the data tabulated in Coughlin,5 using the heat of formation of ah' and the high-temperature thermal data for chromium.7 In 1953 Richardson8 re-evaluated the original work of Kelley and coworkers,9 who measured the thermodynamic properties of the chromium carbides. However, the high-temperature equilibrium results of Boericke9 yield values for ?G°f of Cr2O3 which are 2 kcal more positive than the accepted data. His results for the chromium carbides are based on the same questionable equilibria. Gleiser10 recently determined the Gibbs energy of formation of Cr3C2 and the equation in Table I was calculated from her data and the thermal data of Kelley and coworkers.9 Thermodynamic data for the Cr7C3 and Cr23C6 carbides were obtained by combining the Cr3C2 data

Jan 1, 1965

By S. Weinig, E. S. Machlin

IN a previous study of the grain boundary stress relaxation phenomenon,' the authors had arrived at the conclusion that two successive steps were involved in the complete relaxation of stress at a grain boundary. These two steps were grain boundary migration and grain boundary slip. It was further suggested that the slower of these two processes is rate controlling. In an attempt to ascertain the validity of the above, a study of grain growth kinetics on the same alloys used for the previous study was undertaken. Separate wire specimens, 0.030 in. diam, in the same as-deformed state (99 pct reduction in area) as in the previous investigation were heated to the various temperatures for a sequence of times. The compositions used and the temperatures of testing are summarized in Table I. A statistical determination of grain size was then made on each specimen, using the average length of traverse between boundaries as a measure of the grain size. Examples of typical results obtained are shown in Figs. '1 and 2. The grain growth law D = ktn was found to fit most of the data. Using this relation, values of the grain growth exponent n were calculated and the inter -esting dependence of n on solute content shown in Figs. 3 and 4 was then obtained. Also, it was found that the constant K which was obtained from extrapolation is roughly independent of solute content. (K is uncertain to within ±25 pct.) An estimate of the activation energy for grain growth was made using the technique of Burke? This method utilizes the plot of the reciprocal of time necessary for the grain size to increase from a definite starting size Do, to a final size D, for each isothermal heat treatment. The slope of this curve corresponds to the heat of activation for the process. In Fig. 5 the rate of grain growth is plotted against the reciprocal of absolute temperature. The activation energies were obtained from these curves and are summarized in Fig. 6. Discussion It is interesting to note that the same saturation in the variability with concentration has been found for the grain growth exponent n in this research as was found in the previous researches on both grain boundary stress relaxationa and internal friction of dislocation origin." The significant feature is that saturation in the variation of these properties has been found to occur at about the same level of solute concentration, namely, between 0.1 and 0.5 atomic pct. The only characteristic common to these different quantities is that solute adsorption at grain boundaries and dislocation can take place and affect these values in a similar fashion. Thus, it is concluded that the grain growth exponent n depends upon solute adsorption at the grain boundaries. It appears, therefore, that theoretical considerations leading to the contrary conclusions5,6 have not treated the real process by which solute atoms exert their effect on grain growth. Prior to the analysis of the observed activation energies, certain of the aspects of the aforementioned grain boundary stress relaxation investigation will be briefly reviewed. It was found that with the addition of solute atoms the grain boundary stress relaxation peak (internal friction vs temperature) decreased in intensity. Simultaneously a second peak was observed which increased with increasing solute atoms. Both of these peaks were shown to be the result of grain boundary stress relaxation. They have been termed, respectively, poire peak and solute peak. It was suggested that the solute peak was dependent upon grain boundary migration, whereas the pure peak was a manifestation of grain boundry slip. Activation energies for both peaks were obtained as a function of Solute content. The value of the activation energy in the temperature range corresponding to the solute peak was

Jan 1, 1958

By T. M. Morris

THE rate of flotation of solid particles determines the percentage recovery of these particles which can be obtained during a given time interval. It is an established fact that the recovery is greatest in the fine sand size range and falls off on either side of this size range. It is also a fact that the history of the development of concentrating devices has been marked by a desire to recover the small particles: tables were developed to treat material too fine to recover in jigs; flotation recovers material too fine to be recovered on tables. As our ores become more complex and require finer grinding, a greater proportion is in the slow-floating size range. It is therefore of economic importance that the effect of size of particle upon rate of flotation be studied. Many studies have been made along this line. The present investigation attempts to quantify the rate of flotation by means of a rate equation, and then compares the effect of size upon the rate of flotation. It was found that the flotation rate constant increases with increase in diameter of particle in the size range smaller than the optimum size particle. The flotation rate constant decreases with an increase in diameter of particle in the size range coarser than the optimum size particle. This suggested two different actions taking place, and these are discussed. Suggestions for further work in order to improve the flotation rate of both fine and coarse particles are made. The usual method of expressing rate is to plot cumulative percent recovery vs time. If we knew the equation of this kind of curve we could replot it as a straight line, and the slope of the line would be an index of the magnitude of the flotation rate. It is easier to compare straight lines than curves. The basis used for obtaining the equation of the recovery vs time curve is the law of mass action. This law states that the "rate of a chemical reaction is proportional to the `active masses' of the reacting substances present at any given time." This, of course, implies a constant temperature. We can modify this for our use by using the term flotation reaction instead of chemical reaction and the term floatable particle instead of active masses. [ ] where C denotes concentration of particles, t denotes time, k denotes a proportionality constant. If the exponent of C is 1, then we have a first order rate reaction. If the exponent of C is 2, then we have a second order rate reaction. For a first order rate reaction, we obtain, after integration, [ ] where k is again a proportionality constant and has the dimension of the reciprocal of time. C, is the original concentration or weight or percentage of floatable particles. C, is the concentration or weight or percentage of floatable particles remaining in the flotation cell after time t. If all particles of the mineral to be floated were capable of floating we could take C, as 100 and C, would be 100 - R, where R is the cumulative percentage recovery of mineral at time t. But it is not usual for all of the particles to be capable of floating, because of surface oxidation, etc. Therefore, we must introduce a factor x which is the percentage of unfloatable mineral. Hence the first order equation is [ ] It has been proposed by various workers1-3 that this equation describes the flotation rate. More recently N. Arbiter4 states that a second order rate equation fits the recovery vs time curve more closely than does a first order rate equation. Morris' has discussed the evidence presented for this statement. It has been concluded that the first

Jan 1, 1952

By O. J. C. Runnals

The intermetallic compounds NpAl2, NpAl3, and NpAl have been prepared, and examined by X-ray diffraction methods. The compounds are isostructural with the corresponding U-Al compounds. NpAl3 is face-centered cubic with a = 7.785A and has the MgCu2 structure. NpAl is simple cubic with a = 4.2624 and has the AuCU3 structure. NpAl4 is body-centered orthorhombic with a = 4.428, b = 6.268, and c = 13.71A. The published description for the atomic positions in UAl, applies also to NpAl4 THE U-Al system has been examined by Gordon and Kaufmann.1 They identified the following intermetallic compounds: UAI2, UAl3, and a third, tentatively identified as UAl5. A structure analysis of the latter compound by Borie2 proved that the formula UAl4 was more consistent with the X-ray data. The crystal structures of UAl2 and UA have been reported by Rundle and Wilson.3 UAl2 was found to be isostructural with MgCu. The atomic positions in the simple cubic UA1, cell were found similar to those in the AuCu3 structure. Three analogous compounds exist in the binary system Np-Al. X-ray data for the compounds NpAl2, NpAl3, and NpAl4 are reported below. The neptunium used in the investigation was supplied through the courtesy of the Argonne National Laboratory as neptunium (V) nitrate. It was stated to have a radioactive content of 99.25 pct Np237. The impurity limits had been established by a spectrographic analysis given in Table I. Any titanium, boron, or bismuth impurity should be effectively removed during the fluorination of NpO2 to NpF4, and sodium, lithium, magnesium or strontium during the alloying procedure. The oxalate ignition technique, described by Westrum for the preparation of finely-divided reactive PuO2, was used.The neptunium (V) nitrate solution, containing 100 mg Np, was evaporated to dryness on oxalic acid crystals. The resulting oxalate was calcined to NpO, by heating in platinum at 650°C for 2 hr. An equimolar mixture of anhydrous hydrogen fluoride and purified hydrogen was passed over the NpO2 for 2 hr at 500°C. According to Fried and Davidson" the above fluorination conditions should produce the purple-black fluoride, NpF3 However, the light-green product showed only NpF4 lines on an X-ray diffraction pattern and contained only an estimated 5 pct of finely dispersed black NpF3 particles on microscopic examination. NpAl3: An intimate mixture of 50 mg of neptunium fluoride and aluminum powder (99.99 pct pure, —28 to $60 mesh) was heated to 900°C in a BeO crucible in vacuum by a tungsten coil for 2 hr, to allow the following reaction to proceed: NPF4 + 7Al + NpAl, + 4AlF. [1] The formation and sublimation of aluminum mono-fluoride in this system was verified from an X-ray diffraction analysis of the sublimate. The diffraction pattern was similar to one obtained in the aluminum reduction of UF4 to UF3,6 showing both Al and AlF3 lines. The resulting alloy was sintered at 1100°C for 1 hr. A powdered specimen of the crystalline product was sealed in a thin-walled quartz capillary for X-ray examination. The photograph was taken on a 14.32 cm General Electric powder diffraction camera, using filtered copper radiation. The films were calibrated in terms of a NaCl standard pattern. The wavelengths used in the calculations were 1.5418A for Cu K and 1.5405A for Cu K The powder diffraction pattern showed that NpAl is simple cubic with a = 4.262 % 0.005A, and is isostructural with UA13 where a = 4.27A1 or a =

Jan 1, 1954

By W. R. Hibbard

It has been proposed1 on the basis of slip and flow that the ideal deformation texture of drawn wire for face-centered cubic metals is a (111) direction parallel to the wire axis. Under these considerations, an intermediate [loo] texture is permissible but should eventually change to the stable [Ill] orientation. This theory does not explain why copper and its alloys containing up to about 30 pct nickel, 5 pct zinc and 1 pct aluminum were found to have a double [Ill], [100] texture, while alloys with at least 8 pct zinc and 2 pct aluminum developed essentially a single [Ill] texture.1,2 It does suggest, however, that the [loo] component of the former alloys should disappear with additional deformation.3 Some evidence exists to support this suggestion. Howald4 reported that annealed copper wire previously drawn 93.8 pct and 98.5 pct developed a single [Ill] texture. Since, in wire, the drawn and annealed textures are similar, these wires probably had a single [Ill] deformation texture before annealing. In addition, although cold rolled polycrystalline copper and 80-20 brass were found to form different types of pole figures,5,6 single crystals of these metals when rolled from the stable (110) [112] orientation were found to produce essentially the same polo figure.7.8 It may be, therefore, that while the addition of solute elements changes the path by which the final texture is obtained, the final texture is not changed. Experimental Results The wires remaining from the previous investigation1 already drawn about 50 pct reduction in diameter were further drawn to 86 pct and then to 96.4 pct total reduction in diameter. The textures were determined after these stages by transmission X ray photograms taken with a copper K-alpha beam rotated 0 degrees toward the wire axis. It was found that the ratio of the [111].] and [100] intensities of the double texture in copper and its alloys containing 0.94 pct aluminum, 30.70 pct nickel, 2.61 pct zinc and 4.99 pct zinc increased from about 3:l for the 50 pct reduction to about 9:l for the 86 pct reduction. After 96.4 pct reduction, these wires exhibited essentially a single [lll] texture. Summary Thus, the drawn wire deformation texture of copper and its alpha solid solution alloys containing aluminum, nickel or zinc is essentially a single [Ill] texture as predicted by theoretical considerations of slip and flow.' For copper and its alloys containing up to about 1 pct aluminum, 5 pct zinc and at least 30 pct nickel, an intermediate [loo] component is found after about 50 pct reduction in diameter, but disappears after about 95 pct reduction in diameter. For alpha solid solution alloys containing at least about 2 pct aluminum and 8 pct zinc the single [Ill] texture is developed considerably more easily and is found after about 50 pct reduction in diameter. No explanation of this compositional effect is apparent. Similar work is contemplated for cold rolled and cold compressed alloys. References 1. w. R. Hibbard, Jr. and M. K. Yen: Trans. AIME 175, 126. Metals Tech., Feb. 1948, TP 2334. 2. W. R. Hibbard, Jr. and D. E. Trout, 11: Trans. AIME 185, 620. Jnl. of Melals, Sept. 1949, TN 18. 3. W. R. Hibbard. Jr.: Disc. of R. M. Brick's paper on Deformation Textures, ASM Symp. on Cold Working of Metals, Oct. 1948. 4. T. S. Howald: Disc. of Ref. 1. Trans. AIME, 175, 126. Melals Tech. Aug. 1948, TP 2449. 5. R. M. Brick, D. L. Martin and R. P. Angier: Trans. ASM (1943) 31, 675. 6. 0. Dahl and F. Pawlek: Zlsch. Melall. (1936) 28, 266. 7. C. S. Barrett and F. W. Steadman: Trans. AIME (1942) 147, 57. 8. J. E. Burke and C. S. Barrett: Trans. AIME 175, 106. Melals Tech., Feb. 1948. TP 2327.

Jan 1, 1950

By P. T. Carter, A. B. Murad, H. B. Bell

The distribution of manganese and oxygen between molten iron and FeO-MnO-SiO2 slags not saturated with SiO2 has been determined and used to calculate activities of MnO and SiO2 in MnO-SiO2 slags. These were found to be intermediate between the corresponding activities in FeO-SiO2 and CaO-SiO2 slags. THE equilibrium constant for the reaction between molten iron containing manganese and slags containing FeO and MnO, namely: FeO(slag) + Mn = MnO (slag) + Fe(1iquid) is most conveniently represented by: (MnO) Kmn== (FeOHMn] [Fe] is omitted, since for dilute solutions of manganese in iron, afe is approximately constant. When activities are used for (MnO), (FeO) and [Mn], Kmn is a true equilibrium constant and will apply to all types of slags, but when weight percentages are used, the values obtained for Kmn for different slags vary considerably. The equilibrium between iron containing manganese and relatively pure FeO-MnO slags has been investigated by several workers;1-4 the most recent investigation reported is that of Chipman, Gero, and Winkler.4 Their results, corresponding to slags containing up to 4 pct SiO2, were represented by the equation: 6440 log KMn = +2.95 In this case both slag and metal may be assumed to be ideal solutions, therefore the values of Kmn so derived represent the true constant for the manganese reaction. As the molecular weights of MnO and FeO are almost equal, weight concentration of these oxides may also be used in the above expression. Acidic oxides such as SiO2 and P2O5 affect the activities of FeO and MnO differently, so that when total concentrations by weight of FeO and MnO are used in the above expression for Kmn the values obtained are no longer constant. These will be denoted by K'mn. Körber and Oelsen5 investigated the manganese reaction using silica-saturated iron-manganese-silicate slags and found: 7940 logK'mn =3.172 This corresponds to Kmn values much higher than those obtained for pure oxide slags. The results of Körber and Oelsen, and Chipman, Gero, and Winkler are summarized in Table I. In the present investigation it was decided to study the manganese reaction using iron-manganese-silicate slags not saturated with silica, and which fell mainly between the orthosilicate join 2FeO . SiO2 - 2MnO.SiO2 and the FeO-MnO side of the ternary system FeO-MnO-SiO2. It has been shown" that the phases present in solidified slags of this part of the diagram are (FeO, MnO) and (2Fe0.Si02, 2Mn0-SiO,) solid solutions. Such an investigation would be of interest in deoxidation and also gives information on activities in liquid slags. This equilibrium has not as yet been investigated successfully. Hilty and Crafts7 attempted to examine this reaction in a rotating crucible furnace, but were unable to obtain suitable slag samples. In the present investigation one series of experiments was carried out in a rotating crucible furnace, because the success of Taylor and Chipman8 with such a furnace in their study of oxygen distribution between molten iron and (CaO, MgO) — FeO-Si0, slags suggested that it would minimize contamination of the slag by the crucible material. A second series was carried out using a wire-wound resistance furnace. Rotating Crucible Furnace Experiments In all cases the metallic charge consisted of 800 to 1000 g Armco iron containing 0.02 pct C, 0.03 pct Mn, and traces of Si. Manganese and silicon additions consisted of electrolytic manganese (99.9 pct)

Jan 1, 1953

By L. Burris, C. H. Stockman, I. G. Dillion

Zone melting is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Equations are presented which 1—predict the concentration profiles after successive passes of the zone and 2—give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing in the last zone length. These equations were solved numerically using an electronic computer, and the concentration profiles are presented as a function of the solute distribution coefficient and the ratio of molten zone to total bar length. ZONE MELTING is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Separation occurs if the solid freezing from a solution at any moment has a composition different from that of the liquid from which it is freezing. Solutes which lower the freezing point will tend to remain in solution and will be moved in the direction of zone travel. Solutes which raise the freezing point will preferentially freeze out, and they will be moved in a direction opposite to that of zone travel. After repeated unidirectional passage of a molten zone through a bar of material, impurities will be concentrated in the ends of the bar. A limiting concentration gradient will be reached in the bar after a large number of passes of the molten zone. Both the magnitude of this limiting concentration gradient and the rate of movement of solute in any pass depend on the zone length and on the equilibrium concentrations of solute in the liquid and solid phases. The basic theory of zone melting was thoroughly covered by Pfann.1 The purpose of this paper is to extend the theory of zone melting by presenting 1—equations which relate the concentration profiles in successive passes of the zone and 2—equations which give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing* in the last zone length concentration of a given solute in the solid to the concentration of the same solute in the liquid. Analytical methods for determining the concentration profiles after any pass have been developed by Lord2 and Reiss. The method developed by Lord does not take into account normal freezing in the last zone and also becomes very complicated when the number of passes becomes large. The method developed by Reiss enables the direct calculation of the complete concentration profiles (including that in the last zone) after any pass for values of k close to unity (0.9 < k < 1.1). Both methods are useful and provide valuable insight into the zone melting process. The equations given in this article are based on the same assumptions used by Pfann. These are: 1—uniform composition in the liquid, 2—negligible diffusion in the solid, 3—constant distribution coefficient, 4—constant length of the liquid zone (except at the ends), and 5—solubility of the solute in the melt is not exceeded at any point. Equations for Concentrations in Successive Passes For a melted zone of length 1 at the left-hand end of a bar of uniform unit cross-section, the amount of solute in the liquid is J0Cn-1(x) dx [1] where the subscript is the number of the pass. Cn-1(x) represents the concentration (expressed as weight per unit volume) obtained in the previous

Jan 1, 1956

By Herbert H. Kellogg

Graphs representing the standard free-energy of formation as a function of temperature for 21 fluorides are presented, along with estimated values for the standard free-energy of formation of 20 atedadditional fluorides. A few of the many possible uses of these data in metallurgical calculations are discussed, including the fluorination of oxides, sulphides, metallurgicaland chlorides, and the reduction of metal fluorides. RECENT papers which have presented free-energy data for oxides, sulphides, chlorides, carbonates, sulphates, and silicates in the form of free energy vs. temperature plots,1-5 have found important uses in teaching and metallurgical development work. This method of presentation of thermo-dynamic data serves to make available in readily usable form thermodynamic constants which are scattered throughout the literature, and to show by graphical means the stability relations which exist between the compounds of a given type. It is certainly desirable to have these free-energy-temperature diagrams for as many types of compounds as are of present or potential use in metallurgical processes. Thus, even though there are but few uses of metallic fluorides in extractive metallurgy today, the potential uses of fluorine processes are of great importance and serve as the principal justification of this paper. Recent developments in the production of fluoro-carbons have resulted in vastly improved methods for the production and handling of fluorine and corrosive fluorides, with consequent reduction in costs.".&apos; The extractive metallurgist should no longer overlook possible fluorine processes when development of a new process for a relatively high unit-price metal is being considered. In a previous paperv he author outlined in some detail the importance and use of free-energy data in metallurgical calculations and also discussed the properties of a standard free-energy vs. temperature diagram. The same method of presentation is adopted in this paper, and the reader is referred to the earlier work for explanations of the use of free-energy data. Thermodynamic Data This paper presents standard free-energy vs. temperature diagrams, Figs. 1 and 2, for those fluorides for which the major thermodynamic constants are known. In the calculations of the standard free-energy of formation (AGO), values of the enthalpy of formation at 298°K (?Ho,) were taken from "Selected Values of Thermodynamic Constants"8 most of the values of standard entropy at 298°K (S°298) were taken from "Selected Values"," but in a few cases the values given by Kelley9 ere preferred; data for the Phase changes came from "selected Values" and several of Kellley&apos;s publics- tions;0-12 and most of the specific-heat data were taken from Kelley.l0 The appendix gives a detailed list of the sources of the data. As explained in an earlier paper,6 he accuracy of some of the standard free-energy relationships is not high. An error of +1 kcal at 1000°C is expected in most of the curves of Figs. 1 and 2. The error may be as high as +3 kcal in some of the curves. Rather than attempt to estimate the reliability of each curve, the source of the data used is reported in the appendix, and the reader may compare these data with newer values as they become available. Figs. 1 and 2 fail to show values for the fluorides of many important metals. In most cases this is because the entropy of the metallic fluoride is unknown. For preliminary calculations it is often useful to have available the best estimate of an unknown datum, rather than no information at all. With this in mind, Table I lists estimated standard free-energy values for a number of important metallic fluorides not included in Figs. 1 and 2. The values reported in Table I were, calculated by Brewer et al.13 and are based on estimated entropy values. The estimated uncertainty of the values for each fluoride were calculated from the uncertainty values given by Brewer1&apos; for ?H°, and the entropy function.

Jan 1, 1952

By Strathmore R. B. Cooke

On the basis of experiments con- ducted on quartz using a bubble pick-up method, it was shown in an earlier paper1 that this mineral will preferentially adsorb hydrogen, calcium, or sodium ions, depending on the relative concentrations of those ions in the solution in which the quartz is immersed. For quartz particles ranging in size from 0.2 to 1 mm, it was demonstrated that the concentration of calcium in solution (assumed present as ions) necessary to completely activate quartz for flotation is given by the expression: In this expression, ionic concentrations are in mols per liter. It was further shown that the pick-up method is apparently more sensitive to changes in reagent concentration than the standard captive-bubble method, and that induction times are apparently much reduced. Since completing these earlier tests, a new type of cell has been constructed; this is shown in Fig 1 and 2. In Fig 1, A is a ground joint, B is a ceutral tube reaching to within a few millimeters of the bottom of the cell, and C is a stopper which may be removed for re- agent addition, and serves the further purpose of excluding carbon dioxide from the air during the test. The entire cell is constructed of Pyrex glass, and does not give the trouble experienced with the earlier cell, in which activating ions were released from the glass at high pH values. The only critical factor in the construction of the cell is the clearance between the central tube and

Jan 1, 1949

By L. L. Melton, D. L. Lord, B. W. Hulsey

A mathematical model d1.20p/4L = A(8v)8 derived from the Blasius equation is proposed to be applicable to turbulent flow through straight cylindrical pipe for time-independent fluids which produce a diameter family of straight parallel lines on a log (dp/4L) vs log (8v/d) plot or stress-flow diagram. Such a correlation should permit scale-up with data taken from one pipe diameter for Newtonian, inelastic non-Newtonian and viscoelastic fluids, such as dilute polymer fracturing fluids, which produce considerable frictional pressure reductions. The Newtonian diameter exponent value 1.20 is shown to be empirically valid for turbulent non-Newtonian flow by application of numerical analysis methods. Multiple regression analysis is applied to a logarithmic linearization of the proposed model. An improved data fit results from further linearization achieved by taking linear terms from a generalized Taylor&apos;s series expansion about the multiple regression coefficients. Extensive experimental data obtained in five pipe diameters with water, sodium carboxymethyl-celIulose solutions, guar gum solutions, bentonite clay suspensions and calcium carbonate slurries are presented. Except for calcium carbonate slurries, which were investigated rather than time-dependent cement slurries, the fluids studied contain drilling or fracturing fluid additives. The behavior exhibited by these fluids is considered typical of most fluids encountered in drilling, cementing and fracturing operations. INTRODUCTION Considerable difficulties have been encountered in predicting turbulent flow pressure drops produced by non-Newtonian fluids flowing through straight cylindrical pipe. Correlations previously presented require extensive experimental data which represent several pipe diameters and a wide flow rate range to estimate the necessary scale-up parameters.l-7 One must implement either elaborate experimental apparatus or spend considerable time and effort to gather these data. Presented here is a correlation method which should minimize the experimental effort and data analysis normally required by utilizing flow data taken with only one pipe diameter. Turbulent flow data (up-stream and down-stream pressure and volumetric flow rates) were collected for five pipe diameters through operation of a small pipeline system having an electronic data acquisition and digitizing system. A mathematical model derived from the Blasius equation was utilized to describe the functional relationship between pressure drop and the two independent variables, diameter and average flow velocity. A correlation, which should produce a valid single-pipe scale-up, resulted from a computer-implemented statistical and numerical data analysis for several time-independent non-Newtonian fluids.

By W. R. Ingalls

DUPING the last two years, and especially during the last six months, a number of important articles upon the new methods for the desulphurization of galena have been published in the technical periodicals, particularly in the Engineering and Mining Journal and in Metallurgie. I proposed for these methods the type-name of "lime-roasting" of galena as a convenient metallurgical classification,&apos; and this term has found some acceptance. The articles referred to have shown the great practical importance of these new processes, and the general recognition of their metallurgical and commercial value which has already been accorded to them. It is my present purpose to review broadly the changes developed by them in the metallurgy of lead, in which connection it is necessary to refer briefly to the previous state of the art. The elimination of the sulphur-content of galena has been always the most troublesome part of the smelting-process, being both costly in the operation and wasteful of silver and lead. Previous to the introduction of the Huntington-Heberlein process at Pertusola, Italy, it was effected by a variety of methods. In the treatment of non-argentiferous galena concentrate, the smelting was done by the roast-reduction method (roasting in reverberatory furnace and smelting in blast-furnace); the roast-reaction method, applied in reverberatory furnaces; and the roast-reaction method, applied in Scotch hearths 2 Precipitation-smelting, simple, had practically gone out of use, although its reactions enter into the modern blast-furnace practice, as do also those of the roast-reaction method.

Sep 1, 1906

By Paul Gemmill

Production was first recorded from the Pioche district in 1864, and it has continued to show an inherent ability to take on new life after periods of depression in the metal markets. Production from replacement leadsilver- zinc sulfide ore bodies in limestones of Cambrian age now accounts for several times the gross value of silver production from rich fissures in Lower Cambrian Quartzite. Aggregate production of some 6 million tons represents a gross value over $100-million. Future output is expected mostly to be from limestone replacement deposits of which the most productive are "channels" of ore up to several hundred feet wide and several thousand feet long with thicknesses from a few feet up to 50 feet. Such channels are restricted to the lowermost limestone bed of the district, about 250 feet above the basement quartzite. The "blotter-like" characteristic of this highly productive Jimesto~e bed in absorbing mineralization is believed to be, at least in part, due to lithology, including free carbon in the bed, which has created a unique set of conditions for delicately balanced mineralizing solutions that rejected any tendency to replace siliceous wall rock and were properly constituted for replacement of Limestone. All recognizable orogenic history is considered to be related to the Basin and Range faulting that created the mountain ranges. The faults developed after mid-Tertiary time and after widespread extrusives that are themselves involved in the faulting. Flat faults, formerly believed to be part of regional thrust faulting, are now interpreted as gravity slide faulting that can be shown to be large in magnitude and not simply local landslides. Large slide faults generally have concealed the great magnitude of mountain-bordering faults. Mineralization that accounts for ore is later than the faulting. Most faults are pre-mineral since they influence the shape of ore bodies, and some clearly have been offset by fault fissures containing ore. Post-mineral movement probably has been an important component of some large, initially pre-mineral faults. A single period of mineralization was begun by the introduction of large quantities of ironmanganese carbonate, and, in places, carbonate manganese with minor values in sulfides. Closely following the carbonate invasion, massive sulfides were brought in, usually replacing part of the carbonate body though in some places the massive sulfides replaced limestone that was not previously mineralized. Manganese mineralization is not a "halo" but leaks of manganese to higher formations and to the surface are the most significant exploration guides. The Pioche district is expected to be long lived with technological developments in ore treatment being important to the exploitation of low-grade manganiferous ores, while aggressive exploration is expected to find important quantities of bedded lead-silver-zinc ores of the massive sulfide type.

Jan 1, 1968