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By N. O. Gray, John Henderson

Hydrogen-reduction data for naturally occurring single crystals and Prepared polycrystals of dense hematite have been presented. Results cover the temperature range 400o to 1000oC, for particles from ten sources, ranging in size from 0.07 to 10 mm and in shape from spheres to cylinders, cubes, and thin slabs. A consistent pattern of behavior has been demonstrated for single crystals and the reduction mechanism shown to be temperature-dependent. Below 579oC reduction is a simple topochemical process but at higher temperatuves it is complex and occurs in two distinct stages. Prepared particles from these laboratories behave in a similar manner to the single crystals. Data from two investigators showing topochernical reduction of Prepared particles above 575°C are inconsistent with that for other dense hematites. It is concluded that topochenzical reaction should not be used as a model for generalized rate expressions for dense hematites. SINCE 1958, McKewan1-6 has brought to prominence a simple concept of dense hematite reduction. This model is that oxygen is lost from a hematite particle undergoing reduction only from an oxide-iron interface that recedes in such a way that the oxide remaining retains the original shape of the particle, i.e., reduction occurs topochemically. An adjunct to this concept is that any intermediate oxides in the transition from hematite to iron only form thin layers so that oxygen cannot be lost from the particle without movement of the oxide-iron interface. Further, the rate of oxygen loss from the particle is said to be proportional to the area of the receding interface so that the iron layer grows linearly with time and the over-all reduction process can be described by the equation where ro and do are the initial particle radius and density, respectively, R is the fraction of the original oxygen lost, i.e., the fractional reduction, at time t, and K is the rate constant. The idea of an underlying simplicity in hematite reduction is attractive because it gives a tractable basis from which general theories of hematite reduction can be developed and it has received wide support,7-14 based mainly on the large amount of data13 that can be fitted to Eq. [I]. However, despite the fact that this equation has been derived for dense materials, the bulk of the data that have been used to test it13 have been for materials of only about 90 pct of theoretical density (5.26 g cm-3) or less, so that its generality for dense hematites has not been demonstrated. In any case, as will be seen, adherence of reduction data to Eq. [1] does not necessarily imply that reaction occurs topochemically. In this work only data for hematites approaching theoretical density are considered and it will be shown that in only one study besides McKewan's is topochemical behavior observed over the whole range of temperature investigated. For the majority of materials a linear rate of interface advance is observed to complete reduction only when wustite is not a stable intermediate phase in the transition of hematite to iron, i.e., at temperatures below about 575°C. Above this temperature, reduction is an exceedingly complex series of reactions that takes place in two distinct stages and it is only in the first stage that reaction in any way resembles a topochemical process. This means then that, far from representing general behavior as has commonly been supposed, topochemical reaction for dense hematites is only a particular behavior that may be observed under some circumstances. EXPERIMENTAL Hydrogen-reduction data have been collected and cross-checked in these laboratories by three techniques, weight loss, collection of water evolved in the reduction reactions, and direct metallographic examination. Details of these techniques are discussed elsewhere," where it is shown that results obtained by the three methods are in close agreement. The weight-loss method, by which most of the results were obtained, consisted of hanging the sample in a platinum mesh basket from an Ainsworth Model AV-AU-1 vacuum recording balance inside a vertical l 1/4-in.-ID alumina tube furnace. Dry deoxidized hydrogen was flowed downwards through the tube at 2 to 4 liters min-1 (stp). Single crystals from two sources and artificial oxides from three sources have been examined. The single crystals were from hematite deposits at Yampi Sound, Western Australia, and Brazil, the latter being obtained from Gregory, Bottley and Co., London, U.K. The "Yampi Blue" crystals were hand-picked from washed, magnetically concentrated, sized fractions, -200 mesh BSS (mean diameter ca 0.07 mm) and —36 + 44 mesh BSS (mean diameter ca 0.4 mm) while 10-mm cubes were cut from the Brazilian crystals with a diamond saw. The starting materials for the prepared particles were hematites designated, respectively, "Specpure Iron Oxide", Laboratory No. S639 from Johnson Matthey & Co. Ltd., London, U.K., "Calcined Ferric Oxide" from B.D.H. Laboratory Chemicals Division, Poole, U.K., and "Pigment Grade Oxide", EPR-50, from C. K. Williams & Co., Easton, Pa., U.S.A. Approximately spherical particles were prepared from the artificial oxides by rolling the material, moistened if necessary, in a glass jar, and cylindrical compacts approximately 10 mm in diam and of approximately equal height were pressed in a steel die at 200 psi. These spheres and cylinders were subsequently fired in oxygen for 20 to 100 hr at 1370°C. The

Jan 1, 1967

By D. G. Russell

Two techniques have been developed with which the applicability of pressure build-up analyses can be extended to include pressure data which previously have been considered virtually unusable. One of the interpretation methods makes possible the analysis of pressure build-up performance during the wellbore fill-up or after production period which occurs soon after a well is closed in. The other technique is an extension of a method for analyzing pressure build-up performance during the late-time portion of the pressure build-up which occurs after boundary eflects first begin to alter the shape of a conventional pressure build-up curve. With both of these methods it is possible to obtain estitnates of the kh product, the skin factor and the reservoir pressure. In addition, with the late-time analysis technique it is possible to obtain an estimate of the contributory drainage volume of the well being tested. This means that in some cases a check on reservoir limit test and (or) material-balance calculations can now be obtained from pressure build-ups. Both methods are slightly more time-consuming than conventional pressure build-up analysis methods because trial-and-error plots of pressure data must be made. The late-time method for analysis of pressure build-ups is in principle applicable to the late-time portion of a two-rate flow test or a pressure drawdown test. The interpretation formulas and procedures for these types of tests are also outlined. In these cases, as with pressure build-ups, it is significant that an estimate of the contributory pore volume is also obtained. On the basis of limited experience with the new techniques, it appears that satisfactory estimates of the kh product, skin factor, reservoir pressure and, for late-time analysis, contributory drainage volume can be obtained. INTRODUCTION The analysis of bottom-hole pressure build-up behavior in closed-in wells has been a a subject of interest in petroleum engineering circles for many years. In fact, few other subjects have received as much attention as pressure buildup analysis methods have. The cause for this interest is essentially twofold in nature. First, the pressure behavior of a well can normally be measured with a reasonably high degree of accuracy so that good data for analysis can be obtained. Secondly, over a fairly wide range of operating conditions, valuable information as to the quality of the reservoir rock and completion efficiency of the well can be obtained at a nominal cost. In recent years, numerous papers have been prepared on the effects of various operating conditions and reservoir heterogeneities on pressure buildup behavior. Very little work has been done, however, on extension of pressure build-up analysis methods to those pressure data which are not amenable to analysis by the present methods. The theory upon which the analysis of shut-in bottom-hole pressure build-up data is based is derived from the solution of the radial flow equation for a slightly compressible fluid for constant-rate conditions. It requires that the well be closed in for a sufficient period of time to obtain a clearly defined linear portion on the plot of observed bottom-hole pressure vs log (t + ?t)/ ?t (where At is shut-in time, and t is producing time to the instant of shut-in). From the slope of the plot and other normally obtainable data, the formation permeability, the well damage or skin factor, and the reservoir pressure at infinite shut-in time (if the reservoir were infinite) can be estimated. The successful application of this procedure depends on being able to recognize the straight-line section on the basic pressure build-up plot. The presently used pressure build-up interpretation theory also assumes that a well is closed in at the sand face and that no production into the well occurs after shut-in. In practice, of course, the well is closed in at the surface, and inflow into the well continues until the well fills sufficiently to transmit the effect of closing-in to the formation. This adjustment period is commonly referred to as the "afterproduction" or "fill-up" portion of the pressure build-up. During the period that the well fill-up effect is most pronounced, the basic pressure build-up plot is nonlinear. At later shut-in times after the effects of a drainage boundary have been felt at the well, deviation from the straight-line behavior of the pressure build-up plot also results. In many cases either of these effects or a combination of both can make the straight-line portion on the pressure build-up plot difficult to recognize. Obviously, an extension of pressure build-up analysis methods to include the afterproduction period and the period in which boundary effects are being felt would be desirable and might render valuable pressure data which for years have been considered virtually unusable. The principal reference of note concerning pressure buildup analysis during the afterproduction period is a paper by Gladfelter, Tracy and Wilsey.1 In the approach of these authors it is necessary to measure the rate of influx into the well during the afterproduction period. This is done through sonic measurements or through measurement of tubing-head and casing-head pressures simultaneously with

Jan 1, 1967

By J. W. Givens, P. B. Crawford

A potentiometric model study has been made of the effect of vertical fractures existing in the matrix of the reservoir on the flooding or cycling performance. Fractures can have unusual flow characteristics. Fluid entering one side of a fracture can emerge on either the same or opposite side of the fracture, depending on the particular streamline. Fracture orientation has a great influence on the sweep efficiency. However, sustained fluid injection may still permit large areas to be swept. INTRODUCTION One can find considerable information available in the literature on the effect of fractures originating at the wellbore on sweep efficiencies of water-flooding or gas cycling programs.1-5 However, there arc few, if any, quantitative data reported in the literature on the effect of vertical or horizontal fractures existing out in the reservoir matrix on secondary recovery performance. Several papers have been presented on the effect of vertical and horizontal fractures on the productivity or conductivity of waterflood and gas injection patterns, but in all cases the fractures initiated at the well and simulated commercial fractures.6,7 It is believed that natural fractures may exist out in the reservoir matrix and would effect the displacement performance. The purpose of this report was to study the effect of a few isolated vertical fractures existing out in the reservoir matrix on the performance of waterflood or gas injection patterns. DESCRIPTION AND EQUIPMENT Since the potentiometric model was described by Lee8 it has been widely used to study numerous types of fluid displacement problems. The potentio- metric model can be used for fluid displacement studies when the following assumptions are valid: (a) steady-state conditions exist; (b) the mobilicy ratio is one; and (c) the capillary and gravitational effects can be neglected. Five-spot and direct line drive square patterns were studied using a copper strip of the desired length and orientation to simulate a vertical fracture in the reservoir matrix. The 20 x 20-in. model was considered to represent only one element of an infinite array of similar patterns. DISCUSSION AND RESULTS FIVE-SPOT PATTERN — ONE FRACTURE BETWEEN INJECTION AND PRODUCING WELLS Fig. 1 shows a quadrant of a five-spot pattem with the vertical fracture existing out in the matrix along a line connecting the injection and producing wells. Length of the fracture was equal to 35.4 per cent of the distance between injection and producing wells. In this particular pattern it is noted that fluid breaks through from the injection well to the producing well when the dimensionless time is equivalent to 26.9. Dimensionless time is defined as volume of fluid injected divided by the volume of displaceable fluid in the pattem expressed as a per cent. The cross-hatched areas of this

Jan 1, 1967

By M. Garfinkle

LITERATURE data1'3 have suggested that the resolved shear stress necessary to initiate slip in a particular slip system in tungsten single crystals is strongly dependent on the tensile orientation of the crystals. This orientation dependence is contrary to the critical resolved shear stress criterion. Because the Schmid factors for slip on particular {110}( I l l), {112}(Ill), or {123}(111) slip systems in a (100) oriented tungsten crystal are virtually identical to the respective Schmid factors for a (110) oriented crystal, slip should initiate on the same system in both orientations, independent of the values of the critical resolved shear stresses. Thus, it would be expected that, for a critical resolved shear stress model to hold, the proportional-limit stress for these two orientations must be similar. The expectation of similar proportional -limit stresses has not been borne out by reported experimental observations. Rose et nl.' reported that the proportional-limit stress for crystals near the (110) orientation was 92,000 psi, approximately three times that of (100) oriented crystals (31,000 psi). Garlick and probst2 reported greater than a fourfold difference. Most recently, Beardmore and ~ull~ examined tungsten crystals with orientations along the edge of the standard stereographic triangle and showed a gradual increase in proportional-limit stress from 28,000 psi for the (100) orientation to 93,000 psi for the (110) orientation. Again, the difference was more than threefold. As has been emphasized by these investigators, the apparent gross variation of proportional-limit stress with orientation precludes any meaningful analysis of slip mechanics using a simple critical resolved shear stress relation. The purpose of the present communication is to report that, by use of refined strain-measuring techniques, the proportional-limit stresses for the (100) and (110) orientations are quite similar. Obviously, to determine accurately the value of the proportional-limit stress, which is by definition the stress at which nonlinear stress-strain behavior first occurs, the method of measuring strain must be capable of high accuracy. The investigators cited used as the measured elongation the crosshead displacement of the tensile machine. This method, however, introduces extraneous strain contributions from the load train. Because these extraneous contributions are considerable in the initial portions of loading (as has been well-documented in the literature) the proportional-limit stress measurement, dependent on the deviation of a line from linearity, can be significantly affected. During the course of a recent study, room-temperature strain was measured directly on several (100)-and (110)-oriented tensile specimens axially oriented within 5 deg of the desired direction. Each specimen was fitted with two foil strain gages mounted on opposite sides of the 0.08-in.-diam reduced section. The tensile specimens were loaded at a crosshead speed of 0.01 in. per min on an Instron Universal Testing Machine. Strain was monitored through an external bridge circuit in which the specimen strain gages comprised two arms. The bridge output was recorded against the applied load. A strain of 2 x 10"" could be readily detected by this method. Some specimens were subjected to conventional loading while the load for others was cycled between zero and continually increasing values until the first deviation from linearity was observed. The results of these methods were similar, and the stress at which nonlinear behavior occurred was considered the proportional-limit stress. The proportional-limit stresses measured in this study are approximately 5000 and 6500 psi for the ( 100) - and ( 110) -oriented crystals, respectively, a range of values almost a magnitude less than those reported previously. Representative curves are presented in Fig. 1. Because of the nature of the measurements made, the point of departure of a line from linearity is often debatable. While the load-strain curve for the (100) -oriented crystals made a relatively abrupt deviation from linearity, the curve for the (110) -oriented crystal was more gradual, so that the actual point of tangency may be at a lower load than reported. Thus, the difference in values for the proportional-

Jan 1, 1967

By R. A. Guereco

Accurate measurements of physical dimensions of a section of stainless steel capillary tubing are presented and used to develop two final working equations for an absolute gas viscosimeter. The effects of pressure and temperature on these dimensions are considered. The internal surface finish and nonuniformity of the capillary bore are discussed, as well as entrance, kinetic energy, gas slippage, and gas compressibility correction factors.

Jan 1, 1967

By S. E. Wolfe

The presence of helical ribs in smooth-bore round pipe results in the transport of granular solid particles m water at a much lower velocity than required to transport the same solids in a smooth pipe. The helical motion imparted to the flowing mixture effectively returns settled solid particles to the main stream. The flow may be stopped and restarted without difficulty. Due to the lower velocity required for satisfactory transport large power savings are realized. Also: due to lower velocity, the wear on the pipe walls is much reduced. For satisfactory performance, the ribs should have a high angle relative to the long axis of the pipe and the lineal spacing between adjacent ribs should be modest.

Jan 1, 1967

By Ronald R. Hartman

I can recall a time 10 or 12 years ago when I spent a pleasant Sunday afternoon driving to Jim Thorpe, Pennsylvania to see a carnotite deposit that had recently been discovered. The announcement of the discovery stated that it was in the Pottsville conglomerate in a road cut along the highway. To my surprise, the highway was lined with cars and every weekend prospector for 100 miles had come to see the ?big uranium deposit of the east?. I literally had to stand in line to make a measurement with the scintillation counter I had with me. The thought at first occurred to me that this is evidence of how thoroughly the surface of the United States must have been prospected, more likely, perhaps it points out quite the opposite. A lot of time and energy was being spent in tracing the footsteps of others and a lot of time was spent looking for the obvious occurrences. The point is, that in the early days a tremendous amount of uranium exploration was carried out but few systematic surveys were made. Thorium anomalies were usually discounted after cursory surface field checks. Conversely, in airborne surveys - anomalies due to elevation changes or thin over- burden on hilltops were often investigated more thoroughly than smaller indications on hillsides and valleys. An adequate supply of uranium was nevertheless found due to the ingenuity and persistence of the geological profession and the public in general. This ?adequate? supply, like so many estimates for raw materials turned out to be far too low.

Jan 1, 1967

Jan 1, 1967

By R. E. Hook, R. L. McGaughey, A. M. Adair

The initial yielding characteristics of a vacuum-melted iron have been measured as a function of thertnal history after slow cooling or quenching from a 700°C recrystallizntion anneal. A thermal history favoring the segregation of interstitials to grairz boundaries results in a material having high values of upper and lower yield stress and long, irregutar Luders' plateaus, wheueas specimens treated to minimize grain boundary segregation have significantly lower values of these yielding characteristics. The struc- ture of typical grain boundary areas as revealed by electron transmission microscopy is consistent with these findings. The grain boundaries in iron are considered to be principally responsible for the release of dislocations during macroscopic yielding and it is suggested that strong locking results when a substantial amount of grain boundary segregution is present; it follows that weak locking results from a more random distribution of interstitials to grown in dislocations. RECENT years have seen an increased emphasis placed on a more quantitative study of the influence of grain boundaries on the yield behavior of bcc metals. The earlier picturk of dislocation pileups at grain boundaries building up a sufficient stress concentration to unlock dislocations in neighboring grains1

Jan 1, 1967

By J. F. Breedis

The stabilization of austenite in Fe-Ni alloys against martensitic transformation after reversion has been attributed' to the lattice imperfections remaining from previous transformation. More recently, however, such stabilization has been associatedzy3 with compositional changes which occur in martensite during slow heating. Dislocation arrangements in deformed austenitic stainless steels strongly influence transformation to martensite on quenching.4 Therefore, it is of interest to observe the transformation behavior of stainless steel after reversion, especially since previous studies have been confined to Fe-Ni alloys. The transformation-product morphology also differs in the two iron-alloy systems;6 plate martensite forms in the latter while stainless steel transforms to lath-type martensite. Samples of Fe-16 wt pct Cr-12 wt pct Ni (maximum C + N = 0.005 wt pct, 0 = 0.02 wt pct), prepared by vacuum melting and casting from high-purity components, were annealed at 900°C for 24 hr, after cold rolling to produce a 40-p grain diameter. The M, temperature of this alloy is -80°C and samples are fully austenitic after annealing. The amount of martensite present after quenching, annealing, and requenching was determined magnetically, to within 0.01 wt pct, using a vibrating specimen magnetometer. Nearly 14 pct of martensite forms during the initial quench in 1 min at -196°C. Two-min and 2-hr anneals were done in air and in evacuated quartz capsules, respectively. All specimens were electro-polished before making the magnetic measurements.

Jan 1, 1967

Jan 1, 1967

Copper waste dump leaching is growing in importance because of the.large tonnages (up to 250,000 ton/day) of low grade waste rock available from open cut mining of copper deposits and proof that controlled leaching of copper from such dumps can be profitable.Overburden or waste rock, ranging in size from large boulders to fines, is dumped as cheaply as possible on sloping sites. Copper is leached from the dumps by applying up to 12,000 gal/min of leach solution (a combination of spent solution from cementation and make-up water) to the top of the dumps by various techniques.Efliuent from the dumps is sent to a cementation plant for copper recovery.Factors which may be controlled, either directly or indirectly, to give a controlled copper content in the dump efliuent (usually 1-2 g/l.) are the cycle of operations (i.e. the alternate wetting and drying periods), thevolume of solution applied to the dump, pH, Fe2+ and Fe3+ content or redox potential, oxygen content, bacteria and their necessary nutrients, and temperature.Dissolution of oxide copper minerals appears to be mainly a function of acid concentration. Copper sulphide minerals need oxidation for dissolution to occur and this is accomplished by a combination of oxygen,ferric ion, and bacteria. Oxidation of pyrite, oxidation of Fe2+ to Fe3 +, and hydrolysis of Fe3+ are of some importance in leaching practice. The presence of gangue carbonate minerals is detrimental.Physical factors connected with penetration of solution into large rocks are important and the treatment of an individual dump usually extends over a period of many years. Recovery of copper from solution is usually achieved by cementation with iron (usually in the form of crumpled cans) but the use of sponge iron is becoming more important. Iron consumption varies from 1 to 4 lbiron per pound of copper. Preconcentration of the copper in the efliuent solution by solvent extraction followed by electrolysis may become a useful method.Application of dump leaching techniques to metals other than copper depends on finding an economic method of recovering the metal from solution...

Jan 1, 1967

By Robert D. Pehlke, Robert G. Blossey

The solubility of nitrogen in liquid cobalt and a number of dilute cobalt alloys Was measured in the temperature range 1550" to 1700°C at nitrogen pressures to 1 atm. At 1600°C and 1 atm nitrogen pressure, the solubility in pure cobalt is 0.0047 wt pct [3.8 cu cm (stp) per 100 g Co]. The standard free- energy change for the solution reaction 1/2 N,(g) = gout pct in Co) is iF - 10,000 + 5.24 T cal per g atom N. The alloying elements Cv, Cu, Mo, Nb, Tu, W, and V increase the nitrogen solubility, while Al, Fe, Ni, and Si decrease the nitrogen solubility. THE solubility of nitrogen in cobalt was studied previously by Sieverts, Busch and Dodd,2 and Schenck, Frohberg, and Graf.3 Sieverts investigated the solution below the melting point of cobalt, and Busch and Dodd worked with the liquid metal; however, neither study found any solubility for nitrogen in cobalt. Schenck et al, reported a solubility of 0.005 wt pct N in cobalt at 1600°C. Seagle et al. 4 reported residual nitrogen in cobalt after electron-beam melting, although no reasons were ventured for the presence of this interstitial impurity. This investigation was undertaken to clarify these inconsistencies, and to provide additional data on atomic interactions in dilute metallic solution. EXPERIMENTAL PROCEDURE This study was well-suited to the Sieverts' method, which has not changed significantly since its introduction by Sieverts. 5 The apparatus was of the same design as that described by Humbert and Elliott, 6 with a reaction bulb similar to that reported by Weinstein and Elliott. 7 The buret was not water-jacketed, but the measured gas volumes were corrected for small changes in room temperature. The melt temperature was measured by a disappear ing-filament optical pyrometer sighted through a prism onto the melt surface. Temperature calibration was made based on a measurement of the melting point of pure cobalt taken as 1495°C. The difference between the reciprocal of the observed and the true temperatures was assumed to be a constant, neglecting the changes in emissivity with small additions of alloying elements. The total error in gas-volume measurement caused by accuracy limitations in reading the mercury level in the buret, variation in ambient temperature, and variation in melt temperature was about 0.5 cu cm. This represents approximately 10 pct of the total solubility, and is a larger relative error than in previous studies6-' because of the small nitrogen solubilities encountered in the present investigation. The source and purity of the materials used are listed in Table IA. Recrystallized alumina crucibles were used throughout the investigation. Examination of the crucibles after solidification of the melts showed no reaction or penetration. Alloying of the cobalt melt was accomplished with the dropping technique described by Humbert. 6 The investigation was started using cobalt from African Metals Corp. in shot form, but this material was not of sufficient purity and did not yield consistent solubility results. Sherritt Gordon Mines Ltd. cobalt was then used throughout the investigation. In experiments involving alloying elements which could react with oxygen dissolved in the melt, the cobalt was further refined by annealing at 1400°C in a dry-hydrogen atmosphere. This treatment, described by Woolley and Pehlke, 8 markedly reduced the oxygen content. The oxygen and nitrogen analyses of the cobalt used in this study are presented in Table IB. RESULTS Hot Volume. The hot volume was measured prior to each run and was 50 to 55 cu cm (stp) at 1600°C. It increased linearly with increasing pressure and decreasing melt temperature. Pure Cobalt. Measurements of the solubility of nitrogen in pure cobalt and the temperature coefficient of solubility are summarized in Table 11. At 1600°C and 1 atm nitrogen pressure, the solubility was found

Jan 1, 1967

By J. A. Herbst, G. E. Agar

The effect of fluid viscosity on the classification of solids in a liquid-solid cyclone was investigated. The separation size was found to be proportional to Additionally, it was found that the prediction of flow rate through a cyclone is dependent on a Reynolds criterion. Above a critical value, the flow can be predicted by a simple equation, whereas, below this value a variable orifice coefficient must be introduced. INTRODUCTION The solid-liquid cyclone is widely used as a device for classification, thickening, and heavy media separations. The more important variables and how they affect the performance of a cyclone are known and have been the subject of several investigations.' In general, these studies have paid little attention to the viscosity and those which have, introduced it through Stokes settling considerations. Systems which contain appreciable amounts of swelling clays exhibit viscosities much greater than water, and in these systems the viscosity term becomes important in determining the separation size. The work described here was done to determine in a Newtonian system the dependence of separation size on viscosity. BACKGROUND The separation size for a cyclone classifier has been related to the parameters of the cyclone by an equation of the form: where a is probably between 1.3 and 1.5, ß is between 0.50 and 0.57, and 6 has a theoretical value of 0.5. where y has a value between 1.8 and 2.0. Although these relationships are empirical, equations that differ only in the exponents have been derived from theoretical considerations. Those interested in the origin of these equations are referred to some of the original work.6,7 MATERIALS AND PROCEDURE The laboratory apparatus used in this study is pictured diagramatically in Fig. 1. Feed slurry was pumped from an agitated 15-gallon plastic tank by a centrifugal pump driven by 3/4 hp motor. The static pressure of the feedstream and thus the pressure drop through the cyclone was measured on a gage located as close to inlet of the cyclone as possible. When samples were not being taken, overflow and

Jan 1, 1967

By W. O. Philbrook, R. H. Spitzer, F. S. Manning

A generalized mathematical model has been developed to describe the kinetics of gas-solid reactions with special attention given to the hydrogen reduction oj dense spheres of hematite. This reduction process must pvoceed through a sequence of transport and chemical .reaction steps acting in series. Under typical experimental conditions, none oj the individual transport and reaction resistances may be neglected in the development of a physically significant model. A linear vate of thickening oj the product layer, usually taken as evidence of interface-controlled .reuction, may be observed even though transport resistances play a dominant role in the over-all kinetics. The temperature and pressure dependencies of all terms have been carefully evaluated in order to .make fill use oj arailable expe-inzental data in evaluation oj the model. FOR obvious technological reasons, the kinetics of reduction of iron oxides has become the subject of intensive experimental and theoretical investigation during recent years. Continuing efforts to construct mathematical models to describe the kinetics of reaction between a gas stream and a granular bed of solid particles have demonstrated the necessity of a thorough understanding of the reaction kinetics of a single particle within the system as a prerequisite to the construction of physically significant models of complex, reacting systems. This paper presents a critical examination of the transport and chemical-reaction processes involved in single-particle oxide reduction and develops the mathematical expressions necessary to evaluate their importance. Comparison of theoretical predictions with experimental results contributes important new understanding of the complex nature of this process. The reduction process has been studied under a wide range of experimental variables, and it is not surprising that apparent conflicts in observation and interpretation appear in the literature. The interested reader is referred to the reviews of Themelis and auvin"? and Manning and philbrook3 for a description of much of this work. The course of reaction commonly has been followed by measuring the oxygen weight loss from the particle as a function of time. A number of authors have suc- cessfully correlated their data in terms of a model which assumes that the reduction process is controlled by the rate of reaction at a single, sharply defined, advancing interface. According to this model, the interface will advance linearly with time. A mathematical model for gaseous reduction in a packed bed developed by the present authors in an earlier paper4 recognized that reduction must proceed through the series hematite (Fe203), magnetite (Fe30,), wiistite (Fe,O), and finally metallic iron. The reduction scheme permitted a stepwise topochemical reduction of the individual particles to metal or to the lowest oxide thermodynamically possible for the local gas composition in the bed. The limiting situations of theoretically dense and very porous oxide structures were considered. On the basis of available experimental evidence, the simplifying assumption was made in each case that all product layers would thicken linearly with time. A generalized single-particle model has now been developed to determine the significance of transport resistances in the product layers and in the gas film surrounding the particle. The analysis shows that the interplay of transport and chemical resistances is such that an apparently linearly advancing interface may be observed despite the fact that the reaction may be under significant transport control. Attention thus far has been focused on the development of a model for the topochemical behavior of dense spheres of hematite in atmospheres capable of reducing them completely to metal. The formation of successive product layers of iron, Fe,O, and Fe304 is assumed to follow the mechanism originally described by dstrijm.' All oxygen removal from the core occurs at the iron/Fe,O interface, intermediate oxide layers being propagated by sol id-state diffusion without change in the oxygen density of the core. Since fractional reduction is operationally defined in terms of oxygen weight loss, the kinetics of the over-all reduction of FeZ03 to iron is properly studied in terms of the gas-solid reaction occurring at the iron-wiistite interface. The fractional reduction of a partially reduced oxide sphere is given by: here refers to the radial position of the iron/Fe,O interface. This model is not universally applicable because, as explained in the earlier paper,4 a consideration of porous particles or of dense particles in atmospheres not capable of reducing wiistite must allow for the possibility of gaseous reduction at interfaces other than the one between iron and Fe,O. However, evidence that certain hematite specimens actually do follow the dense-pellet mechanism developed here is provided by the data of cewan' and of Bogdandy and

Jan 1, 1967

By J. H. Anderson, G. A. Parks, B. K. Jindal

Both temperature and humidity are important variables in electrical separations. By independent control of temperature and water vapor pressure, it is shown that charge depends primarily upon relative humidity, not on temperature or water pressure alone. All the effects of temperature changes other than modification of humidity are apparently small. However, humidity control can be achieved through manipulation of the more tractable variable, temperature. Both temperature and humidity are important variables in electrical separations. Some of their effects have been described in general by Fraas1,2 and by Ralston.3 The influence of temperature and humidity may be considered a problem in industrial separations because humidity, especially, is not normally controlled, hence leads to unpredicted quality control problems. The problem is significant whether the separation is based on conductivity differences or on contact electrification. There is no doubt that water adsorbs from humid atmospheres onto mineral surfaces resulting in conductivity changes.'-8 An empirical relationship between conductivity and humidity is1.4-6,8 where a and b are constants peculiar to the substrate, and s and h are the conductivity and relative humidity respectively. Some authors have taken advantage of differences in a and b among minerals to make or propose electrodynamic separations in which h is the key control variable. Fraasl,2 reported that the charge developed on quartz and feldspar through contact with aluminum is sensitive to humidity, as illustrated schematically in Fig. 1. Lawver9 found that the charge developed by quartz on contact with several materials was tem-

Jan 1, 1967

By V. Leroy, A. G. Guy

Serious disagreements are often found between experimentally determined intrinsic diffusion coefficients and those calculated employing the usual form of the vacancy theory. In the new theory it is proposed that the total intrinsic flux, Ji, of component i, is the sum of a part, f, due to the usual random exclzanges of component i with the vacancies, and a second part, Ji, due to exchanges with the uacancies composing the net vacancy flux. The present treatment, while less powerful than that of Manning, has the advantage of easy uisualization and of facilitating the application of the vacancy-flux effect to complex systems. IT is becoming increasingly evident that there are serious deficiencies in the version of the vacancy theory of diffusion that has been widely used for the past 20 years. One type of evidence is the frequent lack of agreement between intrinsic diffusion coefficients and tracer diffusion coefficients, even taking account of the thermodynamic factor. A second kind of evidence is the observation of a Kirkendall shift larger than theoretically possible, that is, larger than can be accounted for without assigning a negative value to one of the two intrinsic diffusion coefficient.'- The thermodynamic factor could conceivably make both coefficients negative, but not just one. It is clear that a cause of these anomalies, apart from any inadequacy of the usual vacancy theory, might lie in an oversimplified treatment of the data. Adequate experimental techniques, including the use of moderate pressure during the diffusion anneal, are now available to insure that porosity, lateral expansion, and so forth, can be kept negligibly small in most cases. The effect of differences in atomic volume can be of major importance, and it is essential that one of the available methods4 be used to account for this factor. In the present treatment this is accomplished by the consistent use of moles per cubic centimeter as the unit of concentration. Of the various possible inadequacies of the vacancy theory, attention will be given here only to effects of the net vacancy flux. annin' has previously considered this question, beginning with an analysis of atomic jumping of tracer atoms. When he added the effect of a concentration gradient, new terms arose that could be associated with the flow of vacancies. The present treatment uses quite a different approach. The usual vacancy flux, J,, is introduced explicitly, and a simple analysis predicts major changes in the intrinsic diffusion coefficients from this cause. The usual assumptions are made that only a vacancy mechanism is operative, that the formation of voids can be neglected, and that changes in the partial molal volumes, vl and v2, are negligible. The significant diffusion coefficients for the present topic are Dl and D,, the intrinsic coefficients, which enter in the equations, where the flux Ji, moles per sq cm per sec, is that crossing the Kirkendall interface. The concentration, ci, is in units of moles per cu cm, and the concentration gradient, aci/ax, is evaluated at the Kirkendall interface. It will be recalled' that the calculation of Dl and D2 involves the measurement of areas on the diffusion curve with respect to the positions of the Kirkendall and Matano interfaces. In the case of the anomalies mentioned earlier, the Kirkendall shift is too large to be accounted for by the diiferetzce in fluxes (J2 -J1), given by Eqs. [I] and [2]. The logical inference is that the flux of the solvent atoms, J1, is actually in the same direction as the flux of the solute atoms, Jz. In terms of Eq. [I] this requires that Dl have a negative value. However, it would be somewhat misleading to state that the solvent atoms are diffusing up their own concentration gradient. The explanation that will be advanced here pictures competing processes producing the net flux of solvent atoms: 1) diffusion of the solvent atoms down their own gradient by random exchanges with vacancies; and 2) diffusion of solvent atoms in the opposite direction by exchanges with the net vacancy flux. ACTION OF THE NET VACANCY FLUX Theories of vacancy diffusion can be formulated with varying degrees of refinement, and the present theory has purposely been kept as simple as appeared adequate to explain the phenomenon in question. In particular the following aspects have been neglected: 1) the gradient of vacancy concentration in comparison to the gradient of the atomic species; 2) departure of vacancy concentration from the local equilibrium value; 3) variation of the jump frequency, LO, with the specific surroundings of the atom-vacancy pair being considered; 4) correlation effects. These and other refinements can be considered once the essential mechanism has been established. The essential idea of the present analysis is to calculate the total intrinsic flux, Ji, of component i as the sum, JlJ?±j{ [3] where J; is attributable to the usual random atomic jumping, and J{ is a contribution arising from the net vacancy flux, J,. The latter quantity, of course,

Jan 1, 1967

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By O. M. McRae. Discussion by R. W. Jones

R. W. Jones (Senior Exploration Geologist, Standard Oil Co. of California, Box 250, Seattle, Wash.) -Mr. McRae6 and his colleagues are to be congratulated for providing a more coherent structural synthesis of the complex structure in the Courtland-Gleeson area, Cochise County, Arizona, than the "gigantic thrust breccia" concept of Gilluly. 4 However, a few problems of interpretation remain. It is the intent of this note to point out some of these problems, and, drawing on my own work in the area as well as the work of McRae6 and Gilluly, 4 to suggest some interpretations which differ from those previously published. GRAVITY SLIDES In an unpublished manuscript (Jones5) I previously argued that most of the complex structures in the Courtland-Gleeson area can be most reasonably interpreted in terms of gravity sliding caused by uplift and eastward tilting of Jurassic intrusives and associated Paleozoic rocks. Although the field work and drill hole data described by McRae6 provided excellent documentation for two important gravity slides, McRae6 interpreted the basic structure in the Courtland-Gleeson area in terms of major eastward directed thrusting. I continue to disbelieve the

Jan 1, 1967

By D. A. Elgillani, S. Atak, D. A. Rice, M. C. Fuerstenau, R. B. Bhappu

Quartz and feldspar cannot be floated with sulfonate at any pH; spodumene floats over a narrow acid pH range, while beryl responds moderately over a broad pH range. After wet-grinding in a steel mill, beryl, quartz, and spodumene float well with sulfonate below about pH 7, whereas the improvement in the response of feldspar is not so marked. A mechanism by which iron can be adsorbed on these minerals is presented. Also, the responses of leached, natural, and wet-ground beryl to amine, sulfonate, and oleate flotation are shown and related to the measured zero-points-of-charge of these materials. Earlier work with leached beryl showed that good flotation could be obtained with alkyl aryl sulfonate over a rather wide pH range using a Fagergren flotation cell.' When a similar response was observed with leached quartz, it was decided that unintentional activation was being obtained from the metallic components of the Fagergren cell. To obviate this difficulty, a microflotation cell was designed, and an experimental technique was devised. These have been described elsewhere. Experiments conducted with the small cell showed that leached quartz could not be floated at any pH with any sulfonate addition,3 which is in agreement with the observations of Kraeber and Boppel.4 Similarly, it was also found that leached beryl responded to sulfonate flotation only over a narrow pH range rather than the broad range reported earlier.1 This early work,1 however, revealed the important effect that wet-grinding in a steel mill has on the flotation response of certain silicates. That is, it was found that quartz and especially beryl floated well over an unusually wide pH range after wet-grinding in a steel mill. Microcline, however, floated poorly below pH 4, even though wet-ground under the same conditions. The work of Eigeles6 on adsorption of oleic acid on leached quartz and iron-contaminated quartz at constant pH is in agreement with these flotation data. Other research has shown that ferric iron, added as a salt to the system, functions as an activator in the narrow pH range in which Fe +++ iron hydrolyzes to its hydroxy complexes.3,5 These phenomena indicate that iron functions differently in flotation systems depending on its method of introduction. The object of this paper is to determine the mechanism by which iron is adsorbed on certain minerals, the mechanism of collector adsorption after iron abstraction, and the role that Fe++ and Fe+++ assume in the selective separation of these minerals. EXPERIMENTAL MATERIALS AND METHODS Sodium alkyl aryl sulfonate, mol wt 450,7 pure potassium oleate, and pure dodecylamine were used as collectors. All other chemicals were reagent grade in quality, i.e., n-amyl alcohol as frother; HC1, H2SO4, and KOH for pH adjustment; and ferric chloride as activator. Conductivity water, made by passing distilled water through an ion exchange column, was used in the experimental work. All minerals used in the investigation were hand-picked specimens. Sample Preparation: Each of the minerals was crushed through 8 mesh, and the product was divided into two groups, one to be ground dry and the other wet. Dry grinding was accomplished with an alumina mortar and pestle. The product was dry-screened to 48 x 150 mesh, cleaned magnetically, deslimed in conductivity water, and dried. Preparation of the samples by wet-grinding involved grinding a 200-g charge of the mineral (-8 mesh) at 60% solids with natural water in a mild steel rod mill for four minutes. This charge was then wet-screened immediately with natural water to 48 x 150 mesh, dried, and cleaned magnetically. Some experiments were also conducted with leached beryl and quartz. These products were prepared by leaching the sized sample (48 x 150 mesh) with concentrated HC1 with a percolation technique until no iron could be detected in the leach liquor. Following this step, the sample was rinsed with conductivity

Jan 1, 1967