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By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2'3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By E. B. Hunt

Paraffin deposition has been studied in the laboratory under conditions simulating deposition in well tubing. A theoretical analysis has been made of the cooling of the oil and the precipitation of paraffin from the oil as it flows up the well tubing and through surface flowlines. It is proposed that paraffin deposits are initiated by the precipitation of paraffin directly on or adjacent to the pipe wall and grow by diffusion of paraffin from solution to the deposit. This mechanism is consistent with laboratory and field observations, and has proved useful in the design and interpretation of laboratory paraffin-deposition tests. Tests have been made of the effect of plastic pipe coatings and chemical additives on paraffin deposition. INTRODUCTION Paraffin deposits which form in well tubing and surface flowlines interfere with production and must be removed. Over the years much progress has been made in developing and improving methods of removing these deposits after they form. Much less progress has been made in developing methods of preventing or inhibiting the formation of paraffin deposits. This is due, it is believed, to the lack of knowledge of the mechanism of paraffin deposition, the absence of satisfactory laboratory testing methods and the difficulties in evaluating the results of field tests of preventive treatments. The present investigation was undertaken to elucidate the mechanism of paraffin deposition and to develop suitable laboratory tests for studying the inhibition of paraffin deposition in well tubing and surface flowlines. Current theories on the mechanism of paraffin deposition have been evolved from field observations, from laboratory studies of various factors which might be involved in paraffin deposition, and from laboratory paraffin-deposition tests.1-9 Paraffin deposits have been formed in the laboratory by immersing a cold finger into a hot wax-oil solution and by flowing hot wax-oil solutions through cooled pipe or over cooled plates. These laboratory conditions differ in important features from field conditions, and the observed deposition behavior is not entirely field-like." Thus, there is reason to question the field applicability of the results of these tests. The present investigation was undertaken to determine how to perform and interpret laboratory paraffin-deposition tests to obtain information on the inhibition of deposition in the field. The paraffin problem in the broadest sense encompasses the formation of any predominantly organic deposit in well tubing, surface flowlines and other equipment in contact with crude oil or gas. The present investigation was limited to paraffin deposition involving the precipitation of paraffin wax from solution by cooling and its concentration in a deposit on a cooled surface. This probably excludes its applicability to those problems arising from asphaltic-base crudes, but not those arising from paraffin-or mixed-base crudes. This also excludes its applicability to emulsion and congealing oil problems which are often included as part of the paraffin problem. The phenomenon of cooling appears to be the controlling factor in paraffin deposition involving the precipitation of paraffin wax and its concentration in the deposit. Deposits of this type are usually found in the field only where cooling occurs. Early in this laboratory investigation, it was not found possible to form deposits under constant temperature conditions from a wax-oil slurry, either by steady flow through pipe or by gas-lift up a pipe. Thus, the investigation was limited to situations involving cooling. THEORY The relationships involved in establishing the temperature profiles in an oil stream as it flows up well tubing with a linear (geothermal) pipe-wall temperature distribution or through surface flowlines with essentially constant pipe-wall temperature are presented in the Appendix. The relationship between radial distance in the pipe and the rate of cooling of the oil is then combined with a relationship between cloud point and rate of cooling to develop the pattern of formation of a wax cloud in the oil. The following discussion of paraffin deposition under various laboratory and field conditions is based upon this development which is presented in the Appendix. PARAFFIN DEPOSITION IN SURFACE FLOWLINES The average temperature of the oil coming out of a well is somewhat higher than the ground temperature. Thus, the oil continues to cool on its trip through the surface flowline, and wax deposition can occur. The temperature distributions calculated from Eq. A-4 are given in Fig. 1. As can be seen, almost all the cooling occurs in the first 500 ft from the wellhead. In addition, the radial temperature gradient near the wall decreases rapidly with distance and becomes very small after a few hundred feet. Thus, growth of a paraffin deposit would be expected to decrease rapidly with distance from the wellhead and become negligible after a few hundred feet, since growth is dependent on concentration gradient. Wax precipitation and diffusion of wax to the already

By Benny J. Nelson

AS a part of the fundamental research program of Aluminum Research Laboratories, some data were obtained on the ternary system Mg-Al-Mn. As very little information on the magnesium corner of this diagram has heretofore been published, it seems desirable to make available the values found for the liquidus and solidus surfaces of this system. Procedure The settling procedure was used for the determination of the liquidus compositions. Metallo-graphic examination of quenched samples, and stress-rupture upon incipient melting, were used for the solidus determinations. The settling procedure has been described in a previous paper.' Briefly, this method involved saturating the alloy with manganese at a temperature substantially above that at which the sohbility was to be determined, then cooling the melt to the latter temperature, and holding it at that temperature for a substantial period of time. Samples for analysis .were carefully ladled from the upper portion of the melt at hourly intervals during the holding period. After the ladling of each sample, the melt was stirred to redistribute some of the manganese that had already settled, because it appeared that when the latter particles of manganese again settled, they aided in carrying down more of the manganese and thus hastened the attainment of equilibrium. The melts were prepared and held in a No. 8 Tercod crucible holding approximately 4 lb of metal. The manganese was added either in the form of a prealloyed ingot (Dow M) containing about 1.5 pct Mn or by the use of a flux (Dow 250) containing manganese chloride. In calculating the flux additions, it was assumed that the manganese introduced would be equal to 22 pct of the total weight of the flux. Temperatures were measured with an iron-constantan thermocouple enclosed in a seamless steel tube, the lower end of which was welded shut. This protection tube also served as a stirring rod. The samples ladled from the upper portions of the melts at the various intervals were analyzed for aluminum, manganese, and iron. When making the alloys which were to be used for the determination of the solidus, 2½ in. diam tilt mold ingots were cast, scalped to 2.0 in. in diam, and extruded into ? in. diam wire. The principal impurities in the melts for this investigation were iron and silicon; their total not exceeding 0.03 pct. Portions of the wire, approximately 2 in. in length, were enclosed in stainless steel capsules for protection from the atmosphere. Bundles of these capsules, with a dummy capsule containing an iron-constantan thermocouple, were heated inside a large steel block (acting as a heat reservoir) in a closed circulating-air type electric furnace. At ap- propriate times, the capsules were removed and quenched in water. The wires were examined metallographically to determine the temperature of initial melting. Short times at temperature were used at the beginning for wire specimens of all alloys to obtain quickly the approximate temperatures at which melting could be first observed. When approximate solidus temperatures had thus been determined, equilibrium heating was attempted. This equilibrium heating consisted of an 8 or 16 hr period at a temperature, about 50 °F below the lowest temperature at which melting occurred when short heating cycles were used, followed by further heating for 1 hr periods at consecutive 10" higher temperatures. The theory for the method of stress-rupture at incipient melting has been well covereda and its limitations are recognized. Thus, if the interfacial tensions are such that the first minute quantity of liquid is "bunched up" at the grain boundary junctions instead of spreading out along the grain boundaries,³ temperatures higher than the solidus are required before melting will be manifested by rupture of the specimen. This point will be elaborated later. Specimens of the wires with a reduced section (approximately 1/16 in. diam) were suspended vertically in a tubular furnace. The setup used is shown in Fig. 1. The clamp holding the specimen was made from alumel thermocouple wire and the thermocouple was thus completed across the specimen by attaching a chrome1 wire to its lower end. Temperatures were read from a Speedomax recorder used in conjunction with a calibrated thermocouple. The small weight attached to the specimen and a vibrator attached to the furnace tube, to aid in distributing the molten constituent along the grain boundaries, were used to bring about rupture at a temperature closely approximating the solidus. The specimens were heated at a rate of about 5°C per min. The rupture of the specimens was indicated both by sound and by the action of the recorder. An argon atmosphere containing a small amount of SO² was used for protection of the specimen. The assembly was taken out of the furnace immediately following rupture and the specimen removed. Some of the broken specimens were examined metallographically and will be referred to later. Results and Discussion Fig. 2 shows a set of typical time-composition curves for liquid samples of the Mg-Al-Mn alloys used for the settling tests. The data as presented

Jan 1, 1952

By L. D. Hall, D. R. Mash

The paper presents the results of experiments on the anelastic. behavior of gold, as manifested by grain boundary relaxation. Two grain boundary internal friction peaks are found for 99.9998 pct Au. It is found that the peaks are associated with primary and secondary recrystallization. However, the existence of two discrete peaks cannot be explained on the basis of grain size and shape alone. It is suggested that grain boundary stability, as determined by orientation, plays a role in the observed effects. EVIDENCE for the viscous behavior of grain boundaries in metals has been presented in recent years by several investigators, based upon studies of various anelastic effects, especially internal friction. KG1 has contributed greatly to this field, having put forward a coherent body of evidence for stress relaxation by the viscous intercrystalline flow mechanism. In this connection, he has made extensive use of pure aluminum (99.991 pct) as the test material, although he has also studied other metals and alloys, including pure iron (Puron).² Rotherham, Smith, and Greenough³ have studied the internal friction of pure tin, interpreting their results in a manner similar to that of KG. In view of the importance of such studies in shedding light upon the fundamental structure and behavior of the grain boundaries in pure metals, it appears that the use of a very pure test material which is inert to its environment should provide useful information on anelastic properties and the source of such behavior in pure metals. The present work was carried out on spectrograph-ically pure, 99.9998 pct Au, free of all impurities except for a trace of silver, estimated to be present to the extent of about 0.0002 pct. The term "pure gold" will hereafter refer to this very pure material. Gold of commercial purity, 99.98 pct, was also studied to observe the effects of small amounts of impurities. A pure gold "single crystal" specimen was also tested for comparison. The variation of the internal friction and rigidity modulus as a function of temperature was determined by means of a torsion pendulum apparatus employing extremely low stress amplitudes and a frequency of vibration of the order of 1 cycle per sec. A 12 in. length of 0.031 in. (20 gage) gold wire formed the suspension element. The apparatus was similar to that described by Ke.l The test procedure and the basic requirements to be met for obtaining useful experimental data by this method have been given elsewhere.1,2 It should be made clear that in all of the experiments to be described, the internal friction and rigidity were independent of the amplitude of torsional vibration. The semilog plot of amplitude of vibration vs ordinal number of vibration was a straight line. This was carefully verified for each internal friction measurement. The linear variation shows that the internal friction was independent of stress; i.e., that the specimens were not being cold-worked during testing. The reproducibility of the internal friction curves, which were obtained by cyclic heating and cooling, indicates that the gold was unaffected by its environment during the tests. The measure of internal friction adopted in the present study is the conventional "logarithmic decrement," defined as follows: log. dec. = l/n In A0/An [I] where n is the number of cycles or vibrations; A,, the initial amplitude of vibration; and An, the amplitude after the nth cycle. When the logarithmic decrement is small, the shear modulus, G, of the wire is proportional to the square of the frequency of vibration provided the length and radius of the wire are kept constant. A plot of frequency squared vs temperature gives the following ratio:' This expresses the fraction of the stress which has not been relaxed at a given temperature. Gr and Gv are the relaxed and unrelaxed moduli, respectively. The frequency of vibration in the polycrys-talline specimen is fp, and the frequency of vibration of a single crystal is f8. This latter quantity is obtained simply by extrapolating the linear, low temperature portion of the curve of frequency squared vs temperature for the polycrystalline specimens. The theory of viscous grain boundary stress relaxation as demonstrated by the anelastic behavior of metals has been discussed in detail by Zener4 and need not be reproduced here. Experimental Results Initial measurements of the internal friction of pure gold were carried out on specimens which had been drawn with no intermediate annealing, resulting in a material which had undergone approximately 99 pct reduction of area in final processing. Annealing was then carried out at successively higher temperatures starting at 400°F for 1 hr and proceeding in this manner to as high as 1600°F in 100°F intervals. After each annealing treatment an internal friction and rigidity vs temperature curve was obtained over the range from room temperature to the particular annealing temperature. The resulting internal friction curves did not exhibit well defined maxima (peaks), but rather several fairly flat

Jan 1, 1954

By L. F. Bryant, J. P. Hirth, R. Speiser

The surface, gain boundary, and twin boundary energies, as well as the surface diffusion coefficient, of cobalt were determined from tests at 1354°C in pure hydrogen. A value of 1970 ergs per sq cm was calculated for the surface energy, using the zero creep method. It was possible to measure the creep strains at room temperature because the phase transformation was accompanied by negligible irreversible strain and no kinking. Established techniques based on interference microscopy were used to obtain values for the other three properties. The gain boundary and twin boundary energies were 650 ad 12.7 ergs per sq cm, respectively, while a value of 2.75 x l0 sq cm per sec was determined for the surface dufusion coefficient. In the course of a general study of cobalt and cobalt-base alloys, information was required about the surface energy of cobalt. Hence, the present program was undertaken to measure the interfacial free energy, or, briefly, the surface energy, of the solid-vapor interface of cobalt. The microcreep method was selected for this measurement because other surface properties could also be determined from the accompanying thermal grooving at grain boundaries and twin boundaries. A brief summary of the methods for determining the various surface properties follows. At very high temperatures and under applied stresses too small to initiate slip, small-diameter wires will change in length by the process of diffu-sional creep described by Herring.1 The wires acquire the familiar bamboo structure and increase or decrease in length in direct proportion to the net force on the specimen. For a specimen experiencing a zero creep rate, the applied load, wo, necessary to offset the effects of the surface energy, y,, and grain boundary energy, y b, is given by the relation: where r is the wire radius and n is the number of grains per unit length of wire. The first results obtained from wire specimens were reported by Udin, Shaler, and Wulff.' udin3 later corrected these results for the effect of grain boundary energy. The grain boundary energy is determined from measurements of the dihedral angle 8 of the groove which develops by thermal etching at the grain boundary-free surface junction. For an equilibrium configuration: Measurements of the angle 8 can be made on the creep specimens4'5 or on sheet material, as was done in this investigation by a method employing interference microscopy.= If the vapor pressure is low, the rate at which grain boundary grooves widen is determined primarily by surface diffusion and, to a lesser extent, by bulk diffusion. The surface diffusion coefficient, D,, is obtained from interferometric measurements of the groove width as a function of the annealing time, t. As predicted by Mullins~ and verified by experiment, the distance, w,, between the maxima of the humps formed on either side of the grain boundary increases in proportion to if grooving proceeds by surface diffusion alone. For this case: where fl is the atomic volume and n is the number of atoms per square centimeter of surface. When volume diffusion also contributes to the widening, the surface diffusion contribution can be extracted from the data by the method described by Mullins and shewmon.8 Where a pair of twin boundaries intersects a free surface, a groove with an included angle of A + B (using the groove figure and notations of Robertson and shewmong) forms by thermal etching at one twin boundary-free surface junction. If the "torque terms", i.e., the terms in the Herring10 equations describing the orientation dependence of the surface energy, are sufficiently large, an "inverted groove" with an included angle of 360 deg-A'-B' develops at the other intersection. The angles A + B and A' + B' are measured interferometrically. When the angle, , between the twinning plane and the macroscopic surface plane is near 90 deg, the twin boundary energy is calculated from the relation: 1) EXPERIMENTAL TECHNIQUES Five-mil-diam wire containing 56 parts per million impurities was used for making ten creep specimens. These specimens had about 15 mm gage lengths with appended loops of wire and carried loads (the specimen weight below the midpoint of the gage length) ranging from 3.7 to 149.8 mg. The wires were hung inside a can made from 99.6 pct pure cobalt sheet. Beneath the wires were placed small specimens of 20-mil-thick, 99.9982 pct pure cobalt sheet from which the relative twin boundary and grain boundary energies and the surface diffusion coefficient were measured. All the specimens were annealed at a temperature of 1354" i 3°C which is 92 pct of the absolute melting point of cobalt. The furnace atmosphere was 99.9 pct pure hydrogen that was purified further by a Deoxo catalytic unit, magnesium perchlorate, and a liquid-nitrogen cold trap. As a precautionary measure the gas was then passed through titanium alloy turnings which were heated to 280" to 420°C and replaced after every test period. The hydrogen was maintained at a

Jan 1, 1969

By Che-Yu Li, J. L. Gregg, W. F. Brehm

Oriented, oxygen-doped niobium bicrystals were tested in liquid lithium. The grain boundaries were attacked preferentially. The depth of the penetrated zone varies as (time)2. The penetration was aniso-tropic, had a high activation energy, and increased with the increased oxygen doping level. A possible model was proposed to account for the experimental observations. 1 HE grain boundary penetration of a metallic system by liquid metal has been studied by several investigators. Their results are summarized by Bishop.' Most of these works show that the penetration by liquid metal corresponds to the phenomenon of liquid metal wetting. In the case of a grain boundary, wetting will occur when twice the solid-liquid interfacial tension is smaller than the grain boundary tension resulting in the replacement of the grain boundary by two new solid-liquid interfaces. Other possibilities exist; for example, the atoms of the liquid metal may diffuse into the grain boundary region due to chemical potential gradient. The gradient can be produced by impurity segregation or simply be due to the increase in solubility in the grain boundary region. The penetrated grain boundary in these cases may remain solid at the test temperature. The Nb-Li system has been of considerable interest because of its possible technological applications. For fundamental interest it provides a possibility of studying the grain boundary penetration process which is not controlled by the wetting mechanism. The pure niobium is not attacked by the liquid lithium, but if niobium containing more than 300 to 500 ppm oxygen by weight is exposed to liquid lithium, corrosion occurs at the solid-liquid interface and preferentially at grain boundaries. Previous investigators2-' have proposed that this preferential corrosion at grain boundaries is caused by oxygen segregation there, with subsequent inward diffusion of lithium to form a Li-Nb-0 compound. These investigators also found that the corrosion could be retarded by adding 1 pct Zr to the niobium to precipitate the oxygen as ZrO2 upon proper heat treatment. However, there are no quantitative data on the kinetics of the grain boundary penetration process to test the validity of the proposed corrosion mechanism. In this work an investigation of this penetration process in oriented bicrystals was made as a function of the oxygen doping level in the bulk niobium and the grain boundary orientation. A possible model for the penetration process based on the experimental results was proposed. EXPERIMENTS Oriented niobium bicrystals were grown by arc-zone melting oriented single-crystal seeds.7 These bicrystals contained simple tilt boundary. The [001] directions in the two grains were tilted about a common [110]. The bicrystals were 31/2 in. long and 5 by 4 in. in cross section with the straight, symmetric, planar grain boundary longitudinally bisecting the crystal rod. The bicrystals were doped with oxygen by anodically depositing a layer of Nb2O on the surface in a 70 pct HNO solution at 100 v, using a stainless-steel cathode. The specimens were homogenized by annealing in evacuated quartz tubes at 127 5°C. Oxygen content of the niobium was measured from microhardness values, after DiStefano and Litmman.' Supplementary checks were made with vacuum-fusion analysis.7 Individual test specimens cut from the doped bi-crystal rods, about by by % in. in size, were tested inside double jacket sealed capsules. The inner jacket was niobium, the outer was stainless steel. The niobium inner jacket eliminated the problem of dissimilar-metal mass transfer.' The lithium (99.8 pct pure, obtained from Lithium Corp. of America) was handled only in a purified argon atmosphere in a Blickman stainless-steel glove box. After introduction of lithium, the capsules were sealed by welding. Further detailed experimental procedures are given in Ref. 7. The capsules were heat-treated in vertical Marshall resistance furnaces. Temperatures were controlled to When heating above 1100°C, it was necessary to seal the furnace work tube and flow argon through to prevent failure of the stainless-steel outer jacket of the capsule. Tests were made on 6" 2", 16" 2, and 33" i2" bicrystals at oxygen levels up to 2600 ppm by weight in the 6' and 16" crystals and with 1300 ppm oxygen in the 33' crystals. The oxygen levels were controlled to 100 ppm. Most of the quantitative data were obtained from 16" bicrystals between 800" and 1050°C. The capsules were quenched into water after the test and cut open with a water-cooled abrasive wheel. The capsules were then submerged in water, which dissolved the lithium and freed the specimen. Measurement of the depth of the penetrated zone in the grain boundary was done either on metallographically prepared surfaces or directly on the grain boundary plane after the specimen was fractured in tension in the grain boundary plane. The depth of penetration measured by both methods agreed well. Further details describing these techniques have been reported elsewhere.'p7

Jan 1, 1969

By F. S. Young, K. E. Gray

Drilling tests with a 11/4-in. diameter roller bit were performed on Berea and Bandera sandstones and Leuders limestone using water and two conventional drilling muds as circulating fluids to evaluate the influence of dynamic filtration on penetration rate. The muds possessed widely differing API fluid-loss properties. Mud filtrate was constrained to flow beneath the bit; no filtrate flowed radially through the borehole wall. Rock pore pressure at three different locations ahead of the bit, cumulative filtrate volume, borehole pressure and bit location were monitored during drilling. The rock samples, cored in three orientations with respect to bedding planes, possessed a wide range of liquid permeabilities. and were drilled at borehole-to-formation pressure differentials of 0, 250, 500 and 1,000 psig. The effect on penetration rate of API fluid loss, borehole pressure and rock permeability was studied. Rock permeability damage and pore pressure gradients beneath the bit were evaluated. The importance of borehole-to-formation pressure differential was illustrated for each drilling fluid and rock permeability combination. Penetration rates decreased with increased borehole pressure and reduced fluid loss. The observed penetration rate reduction due to changing fluid Ioss was attributed to decreased filtrate flow and improved mud cake plastering hy the low fluid-loss mud. The reduction in filtrate flow could not be related to spurt-loss phenomena. Rock permeability influences penetration rate through particle invasion ahead of the hit, which damage leads to high pressure gradients. Penetration rate variance with sample orientation was evident for water-drZled samples but less obvious for mud-drilled rocks. Permeability damage beneath the bit ranged from 1 to 3 cm. Maximum damage occurred in the first 0.1 cm. Pressure gradients varied with API fluid 10.s.s and could be correlated with penetration rate. The pressure gradient was found to influence penetration rare in rocks of all permeabilities tested. INTRODUCTION Early microbit and small-scale drilling experiments proved to be invaluable contributions to understanding the mechanics of drilling at depth. For example, the effect of borehole-to-pore pressure differential on drilling rate was demonstrated conclusively by Murray and Cunningham', Eckel' and others .' However, the effects of various drilling fluid properties on drilling rate, particularly filtration, have not been studied extensively on a laboratory basis. Microbit correlations of penetration rate with different viscosity and API fluid-loss muds led EckelV o conclude that viscosity and density. more than API fluid loss, were the most important fluid properties in controlling drill bit penetration rates. Ferguson and Klotz6 studied filtration beneath the bit and stated that the maximum amount of filtrate which could conceivably flow beneath a drilling bit could be described by a potential function associated with flow from a moving disc source. and be characterized by a depth-of-filtrate invasion. Invasion depth is a function of penetration rate, formation porosity and permeability, flooding efficiency, pressure difference between borehole and formation and borehole radius, assuming that no filtrate flows through the borehole walls. Electric analog and experimental measurements were obtained, assuming no plugging of the formation pores. Theoretically, filtrate invasion was predicted to extend from 1- to 15-hole radii beneath the cutting surface; experimental results indicated that the extent of invasion was only Y2 in. Comparing these data with results of core-plugging experiments by Norwak and Krueger' led Ferguson and Klotz to state that the drilling operation apparently contributes to higher filtration rates than are observed in nondrilling core filtration tests in which the core face is jetted and scraped. Glenn and Slusser: in describing a linear filtering system in which a rotating bit continuously scraped mud cake from the surface but did not penetrate Alundum cores, stated that mud-solids invasion and permeability damage of the cores were most severe in the first 2 to 3 cm. The filtrate flow rate through the core was found to stabilize after sufficient time had elapsed for the formation of an internal mud cake whose effective permeability was estimated to be 50 to 300 times as high as that of bulk filter cake. Krueger and Vogel reported core permeability damage depths up to 12 in. during a 5-day exposure period in which filter cake buildup was prevented. Havenaar pointed out that the discrepancy between reported and calculated values of filtrate volume obtained in the experiments of Ferguson and Klotz was due, among other things, to failure of the reported API fluid loss to truly represent filtration beneath the bit. Williams," Pro-koplz and others"" have shown that dynamic filtration tests (where a flow of fluid parallel to the filter surface continually erodes the deposited filter cake until a dynamic equilibrium between wall-shearing forces and normally directed compaction forces is attained) yield higher filtration rates than do static tests. Cunningham and Goinss reported results of drilling tests in impermeable shales. They found that by reducing

By J. D. Defilippi, E. M. Gilbert, K. G. Brickner

FCC chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Transformation to martensite is considered to be responsible for this behavior in some metastable Cr-Mn-N steels. However, very stable Cr-Mn-N steels also exhibit a ductile-to-brittle transition. The results of this study indicate that deformation faulting is the probable cause of the brittle behavior of stable Cr-Mn-N steels. Deformation faulting accounts for the ductile behavior of these steels in a tension test at -320°F and brittle behavior in an impact test at -320°F. Deformation faulting also accounts for the toPological features observed on the fracture surfaces of impact specimens of these steels. FACE- centered- cubic chromium-manganese-nitrogen (Cr-Mn-N) steels differ from most other fcc materials in that these steels undergo a ductile-to-brittle transition. Many Cr-Mn-N steels transform to martensite during deformation,l-5 and several investigatorsl-3 have suggested that the brittle behavior of these steels is caused by martensite formation. However, very stable Cr-Mn-N steels also exhibit brittle behavior. Schaller and Zackeyl reported that a very stable Cr-Mn-N steel (less than 3 pct martensite formed at -320°F) exhibited a transition temperature higher than that for steels in which large volume fractions of martensite formed during testing. The explanation given by Schaller and Zackey for this observation was that in the very stable steel the martensite, because of its higher interstitial content, was more brittle than that formed in their other steels. This explanation was questioned by Tisinai and samans4 and Baldwin.6 Moreover, because the toughness of stainless martensite at cryogenic temperatures is generally very low, this explanation does not account for Thompson's7 observation that small additions of nickel (1 to 3 pct) greatly improve the toughness of high nitrogen (0.35 pct) Cr-Mn-N steels. The present paper summarizes the results of an investigation of the low-temperature brittleness in very stable Cr-Mn-N steels. The importance of the mode of deformation on the toughness of these steels is discussed. Table I. Compositions of the Steels Invertigated, Pet Steel C Mn P S Si Ni Cr N - A 0.09 14.70 0.018 0.011 0.47 0.22 18.40 0.54 B 0.12 14.90 0.001 0.008 0.48 0.14 17.80 0.38 C 0.12 14.95 0.004 0.005 0.62 3.95 18.43 0.38 MATERIALS AND EXPERIMENTAL WORK The compositions of the steels investigated are shown in Table I. Steels A and B had compositions within the limits of a proprietary Cr-Mn-N stainless steel,* whereas Steel C was similar in composition to the proprietary steel except for its 3.95 pct Ni content. All steels were hot-rolled to 1/2-in. thick plate. The plates were subsequently annealed for 1 hr at 2000°F and water-quenched. Standard longitudinal and transverse Charpy V-notch impact specimens were machined from the annealed plates. Duplicate longitudinal and transverse impact specimens were tested at 212", 80°, 32", 0°, -100°,-160°,-200°,-256", and -320°F. Longitudinal tension-test specimens were also machined from the plates and tested at a crosshead speed of 0.05 in. per min at the aforementioned temperatures. The fractured impact and tension-test specimens of all three steels were examined to determine whether martensite had formed during testing. Magnetic, X-ray, electron-diffraction, and electron-microscopy techniques were used to detect the presence of martensite in the highly deformed areas of these specimens. Metallographic examination of highly deformed areas of impact and tension-test specimens revealed the presence of dark-etching bands, such as those shown in Fig. 1. These bands were observed only in deformed samples and were thought to be associated with the low-temperature brittleness of the Cr-Mn-N steels. Accordingly, a sample 1 in. wide by 3 in. long was cut from the 1/2-in.-thick plate of Steel C. This sample was surface-ground to a in. and then cold-rolled 60 pct at -320°F. Thin foils were prepared from the cold-rolled sample and examined in a JEM electron microscope. Brightfield, dark-field, and selected-area diffraction techniques were used to determine the cause of the dark-etching bands. Fractographic experiments were also performed. Impact specimens Of Steels A, B, and C were broken at -320oF, and the fracture surfaces of these specimens were immediately shadowed with carbon. The carbon replicas were examined in a Siemens electron microscope, and attempts were made to correlate the topological features of the fracture surfaces with the deformation mechanisms that could be occurring during an impact test of these steels.

Jan 1, 1970

By R. D. Schoone, J. T. Michalak

Recovery, recrystallization, and texture development of a cold-rolled aluminum-killed steel have been studied during simulated box annealing. Two different initial conditions existed prior to cold rolling: 1) essentially all of the nitrogen in solid solution and 2) most of the nitrogen precipitated as AlN. The combined effect of nitrogen and aluminum in solid solution before annealing was to inhibit recovery and sub-grain growth at temperatures above about 1000°F and to raise the recrystallization temperature range on continuous heating at 40°F per hr from 1000"-1050°F to 1065"-1085°F. For the material with nitrogen and aluminum initially in solution there was an inhibition in the nucleation of the (001) [110] texture component and an enhancement of the (111) [110] texture component. The differences in annealing behavior mzd texture development are attributed to preprecipitation clustering of aluminum and nitrogen at subboundary sites developed by prior cold working. THE annealing of cold-worked aluminum-killed steels has been the subject of numerous investigations.'-'2 These studies have been concerned with kinetics of recrystallization, with microstructure and texture development, and with the individual and combined effects of composition, thermal history prior to cold rolling, and heating rates during subsequent annealing. It has been shown that the inhibition of recrystallization, and the development of the pancake-shaped grain and recrystallization texture characteristic of aluminum-killed steels, can be associated with the precipitation of A1N particles during a recrystallization anneal involving heating rates in the range 20" to 80°F per hr. If the AIN is precipitated before cold rolling or if more rapid heating rates are employed, the cold-rolled steels recrystallize more rapidly to an equiaxed grain structure and texture comparable to that of rimmed low-carbon steel. The retardation of recrystallization, the development of the elongated grain structure, and the pronounced (111) texture have been attributed to: 1) precipitation of A1N at prior cold-worked grain boundaries to form a mechanical barrier to grain boundary migration;' 2) precipitation on the boundaries of the growing recrystal-lizing grains as well as on cold-worked grain boundaries;'" and 3) preprecipitation clustering or precipitation on subboundaries to retard recovery, nucleation, and growth. The present study was undertaken to study in more detail recrystallization and texture development during commercial box annealing of cold-rolled aluminum-killed steels. Comparison of the annealing be- havior after cold rolling, for two different conditions prior to cold rolling, was made in an attempt to define more clearly the role of aluminum and nitrogen in forming the recrystallization texture. A) MATERIAL AND PROCEDURE The material used in this investigation was a commercial low-carbon aluminum-killed steel which was hot-rolled with a finishing temperature of about 1565"F, then coiled at about 1020°F. The composition, in wt pct, was: 0.050 C, 0.30 Mn, 0.007 P, 0.019 Si, 0.03 Cu, 0.02 Ni, 0.02 Cr, 0.045 Al, and 0.004 N. Two 4.5 by 13 by 0.078 in. sections were cut from the center section of a hot-rolled panel and one of these was reheated to provide two different conditions prior to cold rolling: low AlN: as commercially hot-rolled, with aluminum and nitrogen in solid solution; and high AlN: as commercially hot-rolled, then reheated at 1300°F for 3.5 hr to precipitate most of the nitrogen as AlN. ~etallc&a~hic examination indicated that the reheating did not change grain size nor carbide distribution (some spheroidization of pearlite was noted). Texture analysis at half-thickness level showed that both sections had the same substantially random as-hot-rolled texture. The results of check chemical analysis of each sample are given in Table I. Both sections were cold-reduced 65 pct on a laboratory rolling mill to a final thickness of 0.027 in. Cold rolling, in one direction only, was in the direction of the prior hot rolling. Specimens 1.0 by 1.25 in. were cut from the cold-rolled sheets and given a simulated box anneal in an atmosphere of 2 pct HZ-98 pct He. Specimens were heated at a constant rate of 40°F per hr from room temperature to various temperatures in the range 750" to 1300°F and cooled immediately by withdrawal to the water-cooled end of a tube furnace. The temperature in the 6-in. uniform hot zone of the furnace was controlled within 3"F. Selection of the individual specimens was made to give a random distribution of annealing temperatures with respect to location in the cold-rolled sheet. At least two specimens of each condition were annealed to the same temperature and smaller specimens for light microscopy, transmission electron microscopy, and X-ray studies were prepared from each of these. Rolling-plane sections for each of these studies were taken at half thickness. Light microscopy and transmission electron micro-

Jan 1, 1969

By M. T. Simnad, G. Derge, I. George

Measurements of current efficiency on iron-silicate slags in iron crucibles showed that conduction is about 10 pct ionic in slags with less than 10 pct silica and about 90 pct ionic in slags with more than 34 pct silica, increasing linearly in the intermediate range. The balance of the conduction is electronic in character. Silicate ions are discharged at the anode with the evolution of gaseous oxygen. Transport experiments show that the ionic current is carried almost entirely by ferrous ions, which may be assigned a transport number of one. THERE has been increased evidence in recent years that the constitution of liquid-oxide systems (slags) is ionic.1-3 The principal studies designed to establish the structure of liquid slags have been by electrochemical methods', " and conductivity measurements1,6,7 which also have indicated the presence of semiconduction in several silicate systems1,4-0 and in pure iron oxide.' It is well known that many slag-forming metallic oxides have an ionic lattice type in the solid state, and their properties are determined to a large extent by the lattice defects and ion sizes. As Richardson8 as pointed out, the detailed models of liquid slags cannot be found on thermodynamic data only but "must rest on a proper foundation of compatible structural and thermodynamic knowledge, combined by statistical mechanics." A careful thermodynamic study of the iron-silicate slags has been carried out by Schuhmann with Ensio9 and with Michal.10 They obtained experimental data relating equilibrium CO2: CO ratios to slag composition and made thermodynamic calculations of the activities of FeO and SiO, and of the partial molal heats of solution of FeO and SiO2 in the slags. It was found that the activity-composition relationships deviate considerably from those to be expected from an ideal binary solution of FeO and SiO2. However, the partial molal heat of solution of FeO into the slags was estimated to be zero. Their experimental results were correlated with the constitution diagram for FeO-SiO2 of Bowen and Schairer,11 with the results of Darken and Gurry" on the Fe-O system, and with the work of Darken"' on the Fe-Si-O system. All these studies were found to be consistent with one another. The variation of the mechanism of conduction with composition in the liquid iron-oxide-silica system in the range from pure iron oxide to silica saturation (42 pct SiO2) in iron crucibles was reported in a preliminary note." The current efficiency, or conformance to Faraday's law, showed some ionic conductance at all compositions, the proportion increasing with the concentration of silica. The current-efficiency experiments since have been extended. Furthermore, transport-number measurements have been completed in silica-saturated iron silicates to determine the nature of the conducting ions. Experimental Current Efficiency in Liquid Iron Oxide and Iron Silicates using Iron Anodes: This study was carried out by passing direct current through slags in the range from pure iron oxide to iron oxide saturated with silica (42 pct silica), using pure iron rods as anodes and the iron container as the cathode. A copper coulometer was included in the circuit to indicate the quantity of current passed during electrolysis. Assuming that the cation involved is Fe-+, the theoretical quantity of iron lost from the anode according to Faraday's law may be calculated and when compared with the actual loss observed, gives an indication of the extent to which Faraday's law has been obeyed. It also gives an indication of the presence and extent of ionic conduction in the melt. Preparation of the Slags: About 100 g of chemically pure Fe,O, powder is placed in an iron pot which is heated by induction until the contents liquefy. In this way, FeO is produced according to the reaction Fe2O3 + Fe = 3 FeO. More Fe2O3 or SiO, powder is added and, when a sufficient quantity of molten slag is obtained, the induction unit is turned off, the pot withdrawn, and the molten slag poured on to an iron plate. Homogenization and Electrolysis of the Slag: Apparatus—After considerable development, the setup illustrated in Fig. 1 proved to be quite satisfactory. A is an Armco iron cylinder, 1 in. ID and 1/8 in. wall, consisting of three sections placed one on top of the other. The bottom section is a pot about 5 in. long with a small hole drilled in its bottom to allow withdrawal of gases during evacuation of the apparatus. The middle section is 6 in. long and consists of a pot which serves as the slag container, while the top section is a hollow-cylinder continuation of the slag-container pot. The height of this latter section is about 5 in., giving an overall length of approximately 16 in. The iron cylinder is constructed in this way for ease of fabrication, the individual sections becoming welded together after the

Jan 1, 1955

By J. P. Sheehan, W. R. Hibbard, M. Baeyertz

This paper deals with molybdenum modifications of 5140 steel that have the same hardenability but a better tolerance for phosphorus than the AISI-SAE 5140 grade. Lack of toughness in steels with higher than normal phosphorus contents is well known to metallurgists. This problem is troublesome even within normal phosphorus ranges, if the heat treatment or the design of the part or the service is critical. Under such unfavorable conditions and also in the case of phosphorus contents toward the upper side of the commercial range, the use of molybdenum to replace a part of the chromium in 5140 steel provides a factor of safety. The toughness of steel is variously exhibited in different mechanical tests; broadly the term is applied to the capacity of the steel to deform prior to fracture. Defined in this way, toughness is considered to be an inherent quality that depends upon the composition and structure of the steel, and also upon its temperature during deformation and fracture in the test. In the present state of our knowledge, the type of mechanical test needs to be included in any discussion of toughness, because the revelation of this quality in steel depends on the stress state and rate of stressing imposed by the test. In comparing the toughness of one steel with another by laboratory testing, it has long been customary to use notched tests that impose severe constmint to deformation, and then to test over a range of temperatures to obtain the so-called transition. At temperatures above the transition, the steel fails after considerable deformation and absorption of energy. Below the transition, less energy is absorbed as the steel fails largely by cleavage. The transition range itself is characterized by a more or less abrupt change in energy absorption and type of fracture. The conventional V-notch Charpy impact test has been used exclusively in the work covered by this report. For the steels under study, rather sharp transitions are obtained with this test, at testing temperatures that are easily obtained in the laboratory. The position of the transition on the testing temperature scale provides a rather sensitive index of the toughness of the steel, when the steels under study are similar in character as they are in this work. Turning to the metallurgical reasons for the greater toughness of one steel as compared to another, the authors propose to limit the discussion to the small field under study. Only one structural state is considered, tempered martensite of a hardness of about 28 Rockwell C or 269 Brinell. The study deals first with the loss of toughness in AISI-SAE 5140 steel caused by increasing the phosphorus content from about 0.020 to 0.040 pct. A second part of the work deals with counteracting this loss in toughness by replacing a part of the chromium by molybdenum. A series of molybdenum modifications was studied, in each of which the chromium was reduced sufficiently to duplicate the hardenability of 5140 steel. Phosphorus affects the toughness of steel in two ways. An inherent lack of toughness of phosphorus-bearing ferrite as compared to low phosphorus ferrite has often been noted. Jolivet and Vidall have shown that phosphorus has the same effect in tempered martensite in chromium steels. The other well known effect of phosphorus is to make steel susceptible to temper embrittlement. Temper brittleness is a loss in toughness brought about by tempering steel within a limited temperature interval somewhat below the A1 temperature. In most of the standard AISI-SAE alloy steels, this temperature interval is approximately 850-1100°F. Either of these types of loss in toughness is easily followed by the shift in the transition temperature obtained with the notched-bar impact test. The data to be presented show the beneficial effect of substituting molybdenum for a part of the chromium in 5140 steel with either moderate (0.020 pct) or high (0.040 pct) phosphorus contents. Both the inherent lack of toughness of phosphorus-bearing steel and temper brittleness are counteracted by this use of molybdenum. The work of Jolivet and Vidal mentioned above shows the detrimental effect of phosphorus on the toughness of tempered martensite in the absence of temper embrittlement, as well as the temper brittleness caused by phosphorus. They used two steels, essentially 0.25 pct C-1.4 pct Cr, with 0.044 and 0.013 pct P, respectively. The nonembrittled state was obtained by quenching in oil from 1610°F, then tempering for one hour at 1200°F and quenching in water. In this state the transition temperature range of the low phosphorus steel in the notched-bar impact test was below that of the steel with 0.044 pct P. An additional treatment of 24 hr at 975°F (that is, in the embrittling range) caused both steels to lose toughness, but the high phosphorus steel showed the greater embrittlement. Recently Hollomon2 has published a comprehensive survey and bibliography of the literature on temper brittleness, to which the reader is re-

Jan 1, 1950

By J. F. Peters

The term solution loss is discussed and defined. Examples are given showing that solution loss may either have a favorable or unfavorable effect on blast furnace performance. A theory is advanced explaining the contradictions encountered during earlier studies of the problem. MANY papers have been written and numerous theories advanced concerning the chemical reactions in the iron blast furnace. Richards, discussing the utilization of fuel in the blast furnace, said: "All the carbon burnt in the furnace should be first oxidized at the tuyeres to CO and all the reduction of oxides above the tuyeres should be caused by CO, which thus becomes CO,. This dictum is not Gruner's own words, but expresses their sense, and from the point of view of the present discussion, it is the correct principle upon which to obtain the maximum generation of heat in the furnace from a given weight of fuel." Richards also said the cubic feet of wind per pound of coke does not express how efficiently a furnace is running, but it will be shown later where Howland paid much attention to this figure. Richards pointed out a shortcoming of Grun-er's discussion in that Richards claimed there is not enough CO generated in a good working blast furnace to possibly combine with the oxygen of the ore, so some of it must be reduced by solid carbon. Mathesius2 made two important contributions. First, he wrote the direct and indirect reduction equations showing the heats of formation in each case and stressed that the indirect reduction reaction produces heat while direct reduction absorbs heat. Secondly, he substantiated Richards' conclusion that there may be a deficiency of CO gas and that some direct reduction is required, but he pointed out that "direct reduction in the hearth has often been confused with direct reduction in the stack, which more correctly should be termed 'premature combustion'." Then he said that "as this carbon is consumed partly by economical (direct reduction in the hearth) and partly by wasteful reactions in ever varying proportions, it is evident that the relation of this total carbon gasified above the tuyeres to the fuel consumption of a furnace cannot possibly have a direct bearing on the economy of furnace operation. The premature combustion of carbon (CO2+C?2CO) must therefore in all cases be considered a detrimental reaction." Johnson3 discussed this whole problem. Through experience Johnson found that when departure from Gruner's ideal working is considerable, the fuel economy is poor, and when the quantity of blast goes up, the fuel economy goes up in the same proportion. Johnson said that the wind per pound of coke is a measure of fuel economy, which will be shown to be wrong. Howland4 established the fact from operating data that there was no relationship between the coke consumption of a furnace and the percentage of coke burned at the tuyeres. But some of his calculations have led to questionable conclusions, such as "it is practically impossible to obtain low coke consumption unless we keep our wind low." Howland made an important contribution when, in his concluding paragraphs, he reached certain negative decisions as to why one coke works better than another. He said the reason one coke works better than another in a blast furnace is not because: 1—there is any difference in the percentage gasified at the tuyeres, or 2—there is any difference of wind required per pound of coke. Korevaar5 propounded a new theory on combustion which disagrees with Gruner because "as far as we can see, this is sufficient proof for the invalidity of Gruner's ideal, for if it was valid, the Low coke consumption should always be accompanied by a higher percentage of carbon burned at the tuyeres. This not being the case, we must deliberately give up our belief in Gruner's ideal." The part in italics will be proved to be wrong. Martin" contended that there was not enough reducing capacity in the blast furnace unless solution loss occurs. He came to a series of conclusions, such as: 1—The greatest efficiency of the blast furnace may not be attained when the reduction is performed entirely by carbon monoxide as demanded by Gruner's definition of the ideally perfect working of the blast furnace. 2—The so-called solution loss reactions, which should more properly be termed direct reduction reactions, promote furnace efficiency. 3—In modern blast furnace practice, the carbon consumption of the process is determined primarily by the carbon needed for reduction purposes, any thermal deficiency created by the reduction process being balanced in practice by the use of blast heat. From a practical standpoint further discussion of the theory of chemical reactions is of little moment. There is however one phase of the general theory of chemical reactions which is very important and that is the combustion of coke in the blast furnace. The purpose of this paper is to show that the reaction

Jan 1, 1955

By J. E. Ryan

TRONA, Calif., is a miniature urban community of some 3500 people, located on the northwest shore of dry Searles Lake in the extreme northwest corner of San Bernardino County, approximately 186 miles north and east of Los Angeles. Since it is situated on the Mojave Desert, a typically desert climate prevails with wide variations in temperature between day and night, extreme daytime summer heat, and cool to cold winters. Rainfall averages somewhat less than 4 in. per year, and dust storms are common. The rate of evaporation, .however, is great, amounting to 6 to 9 ft of water per year. The extremely low humidity makes the summer heat of 110°F tolerable with only a mild, temporary discomfort. Nature of Deposit During the periods when Searles Basin was flooded, the waters that passed through Indian Wells Valley spread out to form a broad, shallow lake providing, in effect, a settling basin for suspended sediment. The drainage into the deeper and more isolated Searles Basin thus was clarified to a great degree before concentration began. Today, the elevation of the dry surface of Searles Lake is 1618 ft, and the salt deposit measures 5x7 miles. At the eastern and northeastern margins of the main playa zone and just at the foot of the alluvial slope of sand and coarser wash from the Slate Range mountains, a rim of crusted salts rises a few feet above the level of the flat. The deposit is a saline efflorescence composed of salts that were presumably brought up with rising ground waters to be deposited at the surface by solar evaporation. This deposit consists chiefly of trona, and it is after this Trona Reef that the town Trona was named. Strip mining operations have been conducted in the past at infrequent intervals for the recovery of crude trona salts. The main focal point of interest in Searles Lake from a commercial standpoint is the main salt body located almost centrally in the basin. The exposed portion of this porous saline deposit covers approximately 12 sq miles and averages 71 ft deep. Its interstitial voids, which constitute 50 pct of the total volume, are permeated with a brine, which is in equilibrium with the soluble salt deposits. The brine is the raw material for the operations of the American Potash and Chemical Corp. plant at Trona, shown in Fig. 1. The soluble salt deposits are of interest for their potential values in future technologic development. The brine, which is stratified according to slight differences in density, stands usually within 6 in. of the surface of this exposed, firm, salt body. The surface is usually dry and will support the weight of heavy mobile units and drilling equipment. Occasionally, however, surface waters from the higher watersheds encroach upon the main salt body during infrequent periods of precipitation on the surrounding mountains. This water dissolves surface salt, becomes a dilute brine, and has been observed to stand as high as 18 in. above the salt surface when undisturbed. Windstorms will shift the water back and forth across the lake surface. The exposed salt body is surrounded by additional submerged areas of commercial soluble salt deposits covering some 20 sq miles, hidden from view by marginal playa mud. These vary in depth up to as much as 30 ft. Thus, the outline of exposed and submerged salt deposits of commercial value is estimated to cover a total area of 32 sq miles, which is roughly circular but slightly elongated from northwest to southeast. It has been estimated that each square mile contains about 100 million tons% f alkali salts. The results of drill borings in the past 15 years have brought to light the interesting fact that the main salt body lies superimposed on an impervious mud deposit from 10 to 15 ft thick containing relatively little soluble salt. Under this deposit lies a second soluble salt body 35 ft deep. The lower salt body is interspersed with numerous insoluble mud lenses and its composition is considerably different from that of the primary, or main salt deposit. Recent drill borings have not penetrated beyond 300 ft. They have, however, revealed that underlying the lower salt body, the mud sediments carry deposited minerals of trona, nahcolite, mirabilite and much less soluble carbonates or sulphates of calcium and/ or magnesium. This structure is shown in Fig. 2. Current Lake Survey Program Several hundred holes have been drilled in the deposit. However, to carry out a thorough and carefully correlated study of the composition of the soluble salts and other minerals in the dry lake basin, a drilling program was inaugurated recently and is now nearing completion. In this survey, pattern drill holes are sunk at regular lh-mile intervals to a depth of approximately 150 ft. Drilling equipment consists of a No. 51 C. P.

Jan 1, 1952

By Thomas R. Smith

This paper covers oil shale resources in those countries that border the Pacific Rim. The major known resources around the Pacific Rim occur in the Western United States, Australia, the People's Republic of China, (PRC) and the Thailand/Burma region. The location of these deposits is shown in Figure 1. In 1965, the U.S. Geological Survey estimated world oil shale deposits of over 4 quadrillion tons having a potential oil yield of over 2 quadrillion barrels. If all this were extracted, it could meet the world's entire energy needs far into the future. However, the Survey also estimated the spent shale waste could cover all of the surface of the world to a depth of about 10 feet. Thus, for this and many other technical and economic reasons, it does not appear to be feasible to develop a large portion of the world's oil shale resources in this century; nor will shale in itself solve our energy problems. Nevertheless, shale oil and other ' synthetic fuels are expected to play an important role in new energy supplies in the longer term. WHAT IS OIL SHALE OR SHALE OIL? The term "oil shale" is sometimes a misnomer, in that the rock is often more of a limestone or siltstone than a shale. The common link between resources termed “oil shale" is that they all contain an insoluble substance cal led kerogen (which is from the Greek words for waxmaking). Kerogen is a form of organic carbon derived from a variety of plants ranging from algae to higher plants. When heated sufficiently, the kerogen generates hydrocarbons called shale oil, a form of synthetic crude oil that in most cases is lower in hydrogen content than conventional crude oil. The amount of oil in oil shale is relatively small --roughly 10 percent (by weight) in the richer shales. To upgrade this synthetic oil to usable products, additional processing is necessary. This brief sketch gives an idea of what this different, but significant, form of hydrocarbon is like. ENVIRONMENTS OF DEPOSITION Most oil shale deposits fall into three environments of sediment deposition: 1ake (called lacustrine), sea (marine) and river (fluvial-deltaic). In each case, the deposition of oil shales took place in quiet water environments where plant life, particularly algal plants, could flourish and, after dying, be deposited in unoxygenated water where the kerogen precursors would be safe from destruction by oxidation. The oil shales that were deposited in large lake basins (lacustrine) have attracted the most attention for development over the years. They often have multiple seams, deposited in a cyclic nature with extensive areal distribution and rapid vertical changes in kerogen content. Grades are moderate to high, ranging from 80 to 200 liters per tonne. Rundle in Australia and the Piceance Creek Basin in Colorado are examples of this type. Both deposits represent large volumes of oil shale in small areas which could provide the large volume of feedstock needed for future commercial operations. The stratigraphic sections of these two deposits feature thick oil shale seams with average grades of 80 - 125 liters/tonne conducive to both open pit, and underground operations. However, the rock strength of the Rundle shale is not sufficient to - support underground mining. On the other hand, the Colorado deposits, being more carbonate in nature, are sufficiently strong to support either type of mining depending on the overburden to ore ratio. These latter types of deposits will likely provide the first target for development of a commercial industry. The marine type is characterized by extensive areal distribution with relatively thin seams. The grades are generally low to moderate, ranging from 50 to 120 liters per tonne. The marine oil shales are common worldwide, and their attractiveness for mining is dependent on the overburden to ore ratio. Because of their widespread areal distribution, their in situ resources can be quite large. The Toolebuc Formation in Central , Queensland, Australia is a good example of this type of deposit being 7-10 meters thick over an extensive area. The Julia Creek deposit with its favorable overburden-to-ore ratio is being studied for possible development. In a fluvial-deltaic environment, there are many small lakes or bogs associated with rivers in which a very pure type of oil shale called torbanite could form. Torbanites are very high grade containing up to 75 percent hydrocarbons. The known occurrences are generally small lenticular deposits associated with coal seams. Even with the high grades, it is not likely that any of the known deposits would warrant commercial development because of their small size. The torbanite deposits in New South Wales, Australia were processed prior to World War I1 near the town of Glen Davis. However, today's known resources of this type are not large enough to warrant a commercial plant.

Jan 1, 1982

By T. S. Lovering

GEOCHEMICAL prospecting extends the age-old method of searching out lodes with a gold pan and rationalizes the prospector's hunch that certain plants are associated with ore. It uses sensitive but cheap and rapid analytical methods to find the diagnostic chemical variations related to hidden mineral deposits. Exploration geologists can gain tremendous assistance from this new tool, although its optimum use is not simple. To bring out the geochemical pattern that reveals the presence of a hidden ore deposit with a minimum number of samples requires a combination of shrewdness, chemical knowledge, and exploration geology. The use of sensitive analytical methods for prospecting had its start in the 1930's in northern Europe, where Scandinavian and Russian geologists had some success in these early efforts. Very little geochemical prospecting was carried on in the United States at this time, and no sustained interest was manifest until the close of World War 11, when geochemical investigations were started by the Mineral Deposits Branch of the U. S. Geological Survey. The purpose of these investigations was to apply geochemical principles and techniques to surface exploration for mineral deposits. Both the research on analytical methods and the routine trace analyses for field investigations were at first conducted by a single group, but it later became apparent that the trace analyses could be done by men of less experience than that required for successful research on methods. For the past several years there have been two groups of chemists, and although their functions overlap, three of the chemists are chiefly concerned with research, while four to six other men make the trace analyses for field projects. The chemical investigations, as well as the field projects of the Geochemical Exploration Section, concern only those phases of the subject that are appropriate to a government organization; every effort is made to help private industry, but not to compete with it, in finding orebodies. The chief aim of the Section, therefore, is to develop new analytical techniques and publish the results promptly, to carry out field investigations of the fundamental principles of geochemical dispersion, and to field test promising- techniques under controlled conditions. Some routine geochemical exploration work is carried on in connection with DMEA loans, and in district studies where the project chief wishes geochemical information on certain areas for his report. It should be emphasized, however, that geologists of the Geochemical Exploration Section are primarily concerned with fundamental principles underlying the distribution, migration, and concentration of elements in the earth's crust. To facilitate the use of geochemical methods the USGS has published much information on its methods of analysis and has provided opportunities from time to time for qualified professional personnel to study these methods, to work in the USGS laboratory, or to attend demonstrations of the analytical techniques at the Denver Federal Center. Typical of the research carried on are the problems now being investigated: 1) Development of rapid and sensitive analytical methods suitable to the determination of traces of metals and other minor elements in various materials, such as rock, soils, plants, and water. At the present time attention is being concentrated on U, Bi, Cr, and Hg, and satisfactory rapid trace analytical methods are virtually perfected for U and Bi. Good methods are also available for: Cu, Zn, Pb, Ni, Co, As, Sb, W, Mo, Ag, Nb, Ge, V, Ti, Fe, Mn, S, and P. 2) The relation of geochemical anomalies in plant materials to the geochemical distribution of elements in soils surrounding the plant. 3) A study of the dispersion halos in transported sedimentary cover such as glacial drift and alluvium over known orebodies. 4) A study of the behavior of ore metals in the weathering cycle. 5) A study of the behavior of the ore metals during magmatic differentiation. This requires a study of the distribution of minor metals in fresh igneous rocks and their component minerals in a well established differentiation series and in adjacent country rock. 6) A study of the dispersion of metals in primary halos in the wall rock surrounding orebodies. 7) Regional and local studies of the metal content of surface and groundwater in mineralized and barren areas. Many field projects of the Mineral Deposits Branch also require the services of USGS chemists during their investigation of the geochemical environment of ore deposits. From the work that has been done certain general principles have emerged. Concentrations of an element that are above the general or background value of barren material are called positive geochemical anomalies or simply an anomaly, whereas values less than background are called negative anomalies. The anomalies most commonly investigated in geochemical prospecting are those formed at the earth's surface by agents of weathering, erosion, or surficial transportation, but more and more attention is being given to primary anomalies found

Jan 1, 1956

By T. M. Allen, W. H. White

THE Greenwood-Grand Forks area of southern central British Columbia, known as the Boundary District, has a long history of mining exploration and production. At the turn of the century this was the premier copper mining camp in the British Empire, its total production amounting to some 20 million tons. Most of this ore came from the great Granby mines at Phoenix, but the Motherlode mine at Deadwood camp, 6 miles to the west, and several mines in Summit camp, 5 miles north of Phoenix, made important contributions. The large deposits were exhausted in 1918 and the district since has seen only desultory exploration and salvage operations. The orebodies are mineralized skarn zones in limestone members of a thick series of Upper Paleozoic sedimentary and volcanic strata. Chalcopyrite is the primary ore-mineral. Copper carbonates and silicates occur sparingly in outcrops, but the oxidized zone generally is very shallow. Much of the surface is mantled by glacial drift which in most places ranges in thickness from 2 to 15 ft. In some of the hanging valleys, however, the glacial drift may be as much as 100 ft thick and may assume drumlin-like forms. In 1951 an ambitious program aimed at the discovery of new orebodies and important extensions of abandoned deposits was launched by Attwood Copper Mines, Ltd. In this district so thoroughly searched by an earlier generation of prospectors, any orebody which had remained undiscovered must have little or no surface indication. Consequently, in addition to the basic detailed geological work, the program of exploration included magnetometer and self-potential surveys. Geological bets and geophysical anomalies were tested further, prior to diamond drilling, by a study of copper distribution in tree twigs and/or in the soil. The soil sampling and analytical methods used and some of the results seem of sufficient importance to warrant this paper. The authors had done some plant sampling in this and other districts, using the dithizone neutral-color-end-point method (Warren and Delavault, 1948, 1949; White, 1950),1-3 but they were unfamiliar with its soil application. Finally, after much experimenting in the field, they adopted the methods described here. These methods are not entirely original or defensible on theoretical grounds, but under field conditions of rapid sampling and analysis the results are reliable enough to be of use. Fig. 1, which shows the results of duplicate analyses of duplicate soil samples taken at 50-ft intervals across an anomalous zone, indicates the relative dependability both of the sampling and analytical methods. Sampling and Analytical Equipment A 2-ft piece of 1-in. solid drill steel, one end sharpened to a broad, conical point. The steel is marked at 1 ft from the point. A 2-ft piece of ½-in. black iron pipe, one end filed to a bevelled cutting edge. The pipe is marked at 1 ft 3 in. from the cutting end. A 3-lb hammer. A plastic or rubberized sheet about 18 in. square. Moisture-proof assay pulp envelopes. A 10-mesh seive made from window screen with the paint burnt off. A small assay spatula. A pan balance sensitive to 10 mg. Two ignition trays about 4 in. square, made of sheet iron turned up along the edges. A Coleman two-burner gasoline stove. An asbestos board about 5x8 in., used as a hot plate on the gasoline stove. A circular aluminum rack to hold 8 test tubes while refluxing (design of Almond and Morris). Pyrex Glassware Large refluxing test tubes, 25x200 mm, marked at 40 ml volume. Breakers, 20 ml. Pipettes, 1, 5, and 10-ml capacity. Graduate, 50 ml. Shaking cylinders, 100 ml, glass stoppers. Burette, 25 or 50-ml capacity, with holder. Chemical Supplies 1 N sulphuric acid. Hydroxylamine hydrochloride, solid crystals. Fisher Alkacid test paper. Copper standard solution. Dithizone standard solution 60 mg per liter. Water reasonably free of metals. Soil Sampling Method: The problem of how to take a soil sample is extremely crucial. The method outlined below, adopted after a number of tests, has the advantages of uniform pattern, uniform depth, and uniform size of sample. The area to be tested was marked off by chain and compass lines 100 ft apart, normal to the strike of possible ore deposits. Numbered stakes were set at 50-ft intervals along these lines and a soil sample was taken at each stake in the following manner. The drill steel was driven into the ground normal to the slope of the surface to the marked depth of 1 ft, moved slightly from side to side, then carefully withdrawn. The iron pipe was inserted to the bottom of this hole, tapped down to the marked depth of 1 ft 3 in. and withdrawn; the 3-in. soil plug in the

Jan 1, 1955

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By H. I. Aaronson, W. L. Winterbottom, G. M. Pound

On the basis of a statistical thermodynamic treatment of the data of smithz2 on the activity of carbon in austenite, a Darken and smith23 deduced that the interaction energy, wy, between carbon atoms occupying nearest-neighboring interstitial sites is repulsive. Aaronson, Domian, and pound 24 (ADP) have applied two different statistical thermodynamic analyses to the same data. One analysis, a composite of the treatments of Darken and Smith,23 Speiser and Spret-nak," and Kaufman, Radcliffe, and Cohen,26 primarily takes account of the positional entropic effects of wy in dilute solutions. The other, due to Lacher 27 and Fowler and Guggenheim," is also applicable to more concentrated solid solutions. The equations which both analyses produce for a,, can be rearranged so that, when In a,, is plotted against the appropriate function of the carbon content of the austenite, the plot will have a slope of unity when the correct value of wy is employed. Since no other constant need be simultaneously evaluated in order to make this determination, ascertaining the most probable value of wy from Smith's data on the bases of these analyses was an elementary problem in least-squares statistics. ADP demonstrated that the wy's obtained from both analyses vary with temperature in a statistically significant manner. McLellan, Gerrard, Horowitz, and sprague 29 (MGHS), on the other hand, have recently made a new statistical thermodynamic study of a,, and have concluded from this study that wy is independent of temperature. The equation which they derived for a,, is: where 0 = ratio of the mole fraction of carbon atoms to that of iron atoms, z = number of sites from which occupancy is excluded by the presence of a carbon atom and the repulsive character of its interaction with nearest-neighboring carbon atoms (z = zb in Ref. 24), and x = a geometric parameter taking account of overlapping of the exclusion shells of nearby carbon atoms. z is 1 when wy = 0 and 13 when wy = Q. For a given value of z there is a definite value of X . In the absence of an equation connecting z and X, MGHS computed geometrically the value of x at several integral values of z; x increases from 0.47 to 8.67 as z is increased from 2 to 5. MGHS fitted Eq. [I] to the a,, data of Ellis, Davidson, and Bodsworth30 at 925° and 1050°C and to the data of smithz2 at 1000°C. Confining z to integral values in the range 4 to 6, and also somewhat restricting AG, the values of z, X, and AG were sought which would minimize the average root mean square percent deviation, D, of the calculated a,, values from those obtained experimentally. Finding that D was almost always smallest when z = 5, they concluded that z is independent of temperature. Since:23, 26 where R = gas constant and T = absolute temperature, and w,, was considered to be similarly invariant, this statement cannot be strictly true. The temperature range employed, however, was small and the interval between the values of z tested was sufficiently large so that the results could still be consistent with a constant The statistical treatment of the a,, data applied by MGHS is clearly quite approximate. Since more than three values of a,, are available at each temperature, z, and X, and AG have actually been over deter mined, rather than underdetermined as their treatment implies. In order to make more complete and exact use of the a,, data, we shall employ the Legendre Method of Least Squares, as described by Whittaker and Robinson. This technique permits conversion of the overdetermined system of equations produced by the substitution into Eq. [I] of the available pairs of a,, and 0 data at a given temperature into an even determined system. Solution of the latter system yields the most probable value of each of the three constants. This procedure will allow a statistically rigorous test to be made of the conclusion drawn by MGHS in respect of the temperature dependence of In order to obtain linear iiequations of conditions" from Eq. [I], the exact values of the three unknown constants are replaced by G/RT = =/RT + y, where z, i, and aG are estimated values of the constants. This allows the conditional equations to be written in the form:'l where fi -f6, i, =/RT) = the right-hand side of Eq. [I] for a given pair of ayi and values. When applied to Eq. [I], these relationships become: The i equations of condition are reduced to three "normal equations" in the manner discussed by Whittaker and Robinson. The normal equations are then solved for a, ß, and y. Both of these operations are most conveniently performed by means of the computer technique of Winterbottom and Gjostein.32 This technique was used iteratively until the value of 0 (the most sensitive of the three correction factors) became 10.01. (Until they became small, a, 8, and y

Jan 1, 1969

By E. V. Potter

For a nurnber of years, it has been known that manganese made by electro-deposition under certain conditions is ductile while under other conditions it is very brittle. The ductile metal is gamma manganese normally stable only between 1100 and 1138°C1; the brittle metal is alpha manganese, stable up to 727OC. The ductile metal is not stable, but gradually changes to the brittle form; the time required to complete the transfornlation is about 20 days at room temperature. Other observations have indicated that the transformation is completed in 10 to 15 min. at about 125°C, while at — 10°C, no appreciable change occurs in 9 months. The properties of gainma and alpha Illanganese in the pure state are ordinarilj difficult to determine because the gamma structure cannot be retained by normal quenching procedures and alpha manganese is so brittle, it is difficult to obtain specimens free from flaws. In a recent investigation2 some properties of gamma and alpha manganese were determined by studying the ductile electrolytic metal and determining the changes in its properties as it transformed to the brittle alpha form. These investigations provided an excellent opportunity for following the progress of the transition and studying its mechanism. The results of a series of such investigations are reported in this paper. Procedure Various properties of manganese were determined starting with the metal in the original ductile gamma form and following the subsequent changes in its properties as the metal transformed to the brittle alpha form. These observations were made at various temperatures, the data providing information regartling the mechanism of the transformation as well as the effect of temperature 011 the transition rate. Structure and resistivity values gave the most significant results, so this paper is concerned primarily with them. The structure was studied microscopically as well as by X ray diffraction. The resistivity was determined on strips of the metal by measuring the potential drop across a given length of the specimen. Current was passed through the specimen by wires soldered to its ends, and the potential connections were made by wires looped around the specimen near its center. The current was determined by the potential drop across a standard resistor connected in series with the specimen, the potential drop being measured on a potentiometer. In the temperature range from room temperature to 100°C an ordinary drying oven was used to heat the specimen. This was entirely satisfactory except at 100°C, where the time required to heat the specimen was long compared to the transition time, making the initial section of the resistivity curve unsatisfactory. To overcome this limitation, at 100°C and higher a thermostatically controlled oil bath was used to heat the specimens. The block on which the specimen was mountetl was plunged into the hot oil at the start of each test. The heating time was thereby reduced from 5 min. to about 6 sec, and dependable resistivity values could be obtained through 160°C. At this point the whole transition, including the warm-up time for the specimen, required only about 20 sec and it was not considered worth while trying to extend the temperature range further. Aside from the heating problem, the problem of making a sufficient number of accurate resistivity determinations became more and more difficult as the temperature was raised. Using the manually operated potentiometer, 100°C was about as far as it was possible to go. At this temperature and above, a self-balancing photoelectric recording potentiometer was used. Its response was quite rapid, and it proved to be entirely satisfactory all the way through 160°C, where the tests were stopped because of the specimen heating problem rather than any limitation of the potentiometer recorder. The metal used in these tests was prepared at the Salt Lake City laboratory of the Bureau of Mines. The method of preparation is discussed in a paper by Schlain and Prater.3 The sheets were about 2 3/8 by 5 3/16 in. and varied from 10 to 16 mils in thickness. They could be cut readily into pieces suitable for the various tests. X ray and microstructure determinations were made on pieces about 1/8 to 1/4 in. wide and about 1 in. long, while resistivity measurements were made on strips as long as possible and about 55 in. wide. The thickness of each sheet was not uniform over all its surface. This had no bearing on the X ray and microstructure determinations, but sections as nearly uniform and free from flaws as possible were chosen for the resistivity determinations. The gamma manganese was electro-deposited at 30°C, the time of deposition ranging from 5 to 12 hr for each sheet. Whenever possible, the tests were started directly after the metal was stripped from the cathode; otherwise the sheet was placed immediately

Jan 1, 1950

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951