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By Victor deWolfe

INTRODUCTION The Henderson Mine, located near Empire, Colorado, utilizes a continuous panel caving system to extract ore as one of the world's major producers of molybdenum. Any mine using a caving-by-gravity technique of mining must rely on closely controlled draw of the caved ore. This control is essential to insure proper caving action, to avoid damaging load concentrations of weight and to minimize the dilution of ore with waste material. Henderson is no exception. Draw control is a major factor in all production planning, from long- range plans to short-range and day-to-day ore scheduling. Draw control is reviewed constantly and administered daily in an effort to optimize production efficiency, ore recovery, and cave management. MINING METHOD The cave at Henderson is massive, moving slowly through large panels that are 244 m (800 ft.) wide by 610 m (2,000 ft.) long. Generally two cave areas are drawn at one time. The areas under active draw vary in size but can be as large as 244 m (800 ft.) by 244 m (800 ft. ) containing 400 draw points. Each draw point contains 45,360 mt (50,000 st) on the average and takes about two and one half years to exhaust. A complete panel is worked for seven to ten years. No pillar exists between panels, but rather a buffer zone of broken ore, or "static face," is left in each panel to be drawn with the adjacent, yet-to-be-caved panel in efforts of minimizing dilution of a working area from an exhausted one. (Figure 1) Production drifts are driven on 24.4 m (80 ft.) centers through the ore body. Between the production drifts are funnel-shaped draw bells on 12.2 m (40 ft.) x 24.4 m (80 ft.) centers to receive ore from the cave. Each bell is accessed by two draw points, one from the production drift on either side, thus forming a 12.2 m (40 ft.) x 12.2 m (40 ft.) draw pattern. Extraction of the ore is by rubber-tired, 3.8 m3 (5 yd3) load-haul-dump equipment. The LHDs then tram the ore a maximum of 49 m (160 ft.) to ore passes. Cave initiation and bell development are done from the undercut drifts which are parallel to and 17 m (55 ft.) directly above the production drifts. Longhole rings are drilled and blasted from the undercut drifts to define the bells and establish the undercut for caving. (Figure 2) DRAW CONTROL Since the cave line at Henderson is constantly advancing, it is necessary to be continually initiating new cave at one end while exhausting it at the opposite end. There must exist, therefore, an angle on the ore-waste contact in the broken rock from initiation to exhaustion. The basic concept of draw control is to keep this angle as smooth and even as possible, particularly at the time of exhaustion. If this is achieved, draw points are exhausted more or less in a line, avoiding pockets of remaining ore surrounded by exhausted areas. These pockets would cause spotty ore extraction at the time of exhaustion, increasing the amount of dilution occurring while introducing the potential for significant weight problems in the production area. To arrive at the desired angle on the ore- waste contact, maximum tonnage percentages are assigned to each row of draw points increasing at 10% or 15% increments (depending on cave size and velocity of draw) working away from the cave line. The available tonnage indicated by these percentages is the maximum allowable tonnage to be extracted from each draw point until the available tonnage percent- age is increased. As the cave moves, these percentages increase for each draw point regularly. However, in general the tonnage drawn from each draw point is kept at about 50% of this allowable maximum in order to maintain adequate available tonnage in the cave to sustain production for seven months if cave initiation were to cease. This available tonnage cushion is a safeguard built into the draw control program at Henderson to accommodate fluctuations in the rate of cave advance. When draw points move past the row of 100% tonnage availability, they are drawn past the desired 50% at the same increments per row until exhausted. (Figure 3) To achieve proper draw control, the number of LHD buckets to be taken from each draw point is assigned daily. The actual buckets taken, which may at times deviate from the

Jan 1, 1981

By H. L. Bilhartz, H. F. Dunlap, C. R. Bailey, Ellis Shuler

Data are presented which indicate that the saturation exponent, n, in the equation, R. = R100S-11, relating core resistivity, I:,. to the resistivity at 100 per cent saturation. R100. and to the saturation, S. may vary appreciably from the value of two which is usually assumed for this exponent when interpret ing well logs. Values ranging from one to two and one-half have been found on (.ore sample investigated to date. Attempts to correlate this saturation exponent with porosity or permeability of the core have not been successful. The saturation exponent is apparently not a function of the interfacial tension between the brine and the displacing fluid. Some evidence is given indicating that the resistance of the core is not a unique function of the saturation but depends upon the manner in which this saturation was achieved. Equipment and technique are discussed for measurement of resistivities in core plugs in which water saturation can be varied. lNTRODUCTION A number of investigations of the resistivity-saturation relationship for un-c~~nsolidated sands and consolidated (.ore samples have been reported in the literature. According to most of these: R. = R¹ººS², where R² = the resistivity of a formation at saturation S, and R¹ºº= the resistivity of the formation at 100 per cent water saturation. Much of this work was (lone on unconsolidated sands desaturated by gas or oil. Hen-clerson and Ynster worked exclusively with dynamic systems, flowing oil or gas through consolidated cores. There is some doubt as to how well this reproduces static reservoir conditions. Jakosky and Hopper³ onsidered also the case of consolidated core plugs, but the oil-water distribution in the emulsions which they used to saturate their cores is almost certainly different from that occurring in reservoirs. Recently Guyod quotes the results of some Russian work which indicates that n may vary from 1.7 to 4.3. No experimental details of this work are available. In connection with electric log interpretation it is important to know the value of the saturation exponent. For example, if in a given reservoir it is found that the resistivity is three time.; the resistivity observed when the reservoir is 100 pel. cent 'saturated with water, this fact would be interpreted as indicating a water saturation of 33 per cent if the saturation exponent were 1 and a water saturation of 6-1 per cent if the saturation exponent were 2.5. EXPERIMENTAL METHOD In the work to be described it was assumed that reservoir conditions are most nearly obtained when core plugs are desaturated by the capillary pressure technique referred to in numerous places in the literature, as for example. in Bruce and Welge's paper.' In this technique the core. saturated 100 per cent with brine, is placed in contact with a ceramic disc permeable to brine but not to the displacing medium for the displacement pressures used. Pres-ure is then applied to the displacing medium and brine forced out of the core through the ceramic disc. Fig. 1 shows the core plug in place in the cell in which resistivity and saturation measurements are made. Fig. 2 shows the schematic electrical diagram wed to make resistivity measurements on the core plug. A four-electrode type circuit is used, employing a Hewlett-Packard model 400A. AC vacnum tube voltmeter. The 60-cycle AC current througli the core is adjusted to 1 milliampere and measured by noting the voltage drop across the calibrated 100-ohm resistor. The vo1tages appearing at probes 1, 2, 3, and 4 are then successively measured. Voltage drops across the top, center, and bottom portions of the core are obtained by sublracting the voltages appearing at successive probes. This technique avoids any polarization or other high contact resistance phenomena which may develop at the current input electrodes. Resistances which may develop between the core and the probes, and which are small compared to the 1-megoam input impedance 01' the vacuum tube voltmeter will (obviously not affect the measurements allpreciably. Any very appreciable resistallces which may develop at any of the probe wires are detected and allowed for by inserting a 1-megohm resistor in series with the voltage measuring probe. If the probe resistance is actually zero, the new voltage measured after insertion of the I-megolim resistor will be approximately one-half of that previously measured. since the input impedance of the vacuum tube voltmeter is itself 1 megohm. If an! appreciable probe resistance has developed, the new voltage is found to be appreciably greater than one-half of the previously measured voltage. Such probe resistance; have been found to develop only occasionally and usually can be traced to poor connections betwern the core

Jan 1, 1949

By G. H. F. Gardner

The velocity and attenuation of elastic waves in sandstones were measured as a function of both pressure and fluid saturation. A large change occurs in these quantities if water is added and the rock is not compressed, but the change is small if the rock is subjected to a large overburden pressure. Measurements were made by vibrating cylindrical samples in both the extensional and torsional modes at frequencies up to 30,000 cycles/sec. Formulas were derived which enable the attenuation of dilatational waves in dry rocks to be deduced from the data. Similar experimental methods were used to investigate the properties of unconsolidated sands. Velocities were found to vary with the 1/4 power of the overburden pressure and attenuations to decrease with the 1/6 power. The effects of grain size, amplitude and fluid saturation were studied. Formulas by which the effects produced by a jacket around the sample may be calculated were derived. The practical application of these results to formation valuation is discussed. INTRODUCTION The attenuation of elastic waves in the earth has been of interest to the seismologist and geophysicist for many years, but only recently to the petroleum engineer. Engineering interest has been brought about by the success of velocity logging devices, for it is possible by modification of these instruments to measure the attenuation of sound waves in addition to their velocity and, hence, deduce the mobility of formation fluids as well as the porosities of the rocks which contain them. The main problem is to decide whether field measurements can be made with sufficient accuracy to be of practical use. This problem can only be solved after we know the magnitude of the attenuations which are typical of the earth at various depths. The logarithmic decrement of a fluid-saturated rock is the sum of a "sloshing" decrement and a "jostling" decrement, the former caused by the mobility of the fluid contained within the rock and the latter by the granular framework of the rock. Sloshing decrements can be calculated' using Biot's theory, but the jostling losses are less well understood. The present paper reports an experimental investigation of jostling losses in consolidated and uncon- solidated sands, particularly with respect to the effect of overburden pressure and fluid saturation. Born' showed that the decrement of a sandstone may increase dramatically when only a few per cent by weight of distilled water is added, and that the additional loss is proportional to the frequency of vibration. His measurements were made with no compressive stress on the framework of the rock. M. Gondouin3 investigated similar phenomena for fluid-saturated plasters but also did not compress the samples. In the present paper it is shown that compression of the framework reduces this effect, so that at depth the jostling decrement of a sandstone may be expected to be almost independent of fluid saturation and frequency. Decrements for many sedimentary rocks have been given by Volarovich,4 but all for the state of zero overburden pressure. Anomalously low velocities have been logged in shallow unconsolidated gas sands. Results of the present investigation confirm that these velocities are not caused by correspondingly high attenuations, because the jostling decrement in a packing of sand grains is small and much less than in a consolidated sandstone at the same depth. Velocities in sands have been measured by Tsareva5 and by Hardin6 as a function of pressure, but the corresponding decrements do not appear to have been measured previously. The widely used "resonant bar method" of measuring velocities and decrements was employed. Comments on variations of this technique have recently been published by McSkimmin.7 The main novelty of the present technique was the application of pressure to the samples. It was found possible to do this by placing the apparatus inside a pressure vessel, provided the conditions leading to large additional losses were avoided. These conditions are discussed below. EXPERIMENTAL TECHNIQUE Cylindrical samples were caused to vibrate in both the extensional and torsional mode of vibration and the amplitude of vibration was measured as a function of frequency in the neighborhood of a resonant frequency. The resonant frequency, fr, is related to the corresponding elastic modulus by the formulas where E and N are Young's modulus and the modulus of rigidity, p is the density of the sample, and A the wavelength of the vibration.

Jan 1, 1965

By F. A. Forward, J. Halpern

A new process for extracting uranium from ores with carbonate solutions is described. Leaching is carried out under oxygen pressure to ensure that all the uranium is converted to the soluble hexavalent state. By this method), alkaline leaching can be used successfully to treat a greater variety of ores, including pitchblende ores, than has been possible in the past. The advantages of carbonate leaching over conventional acid leaching processes are enhanced further by a new method which has been developed for recovering uranium from basic leach solutions. This is achieved by reducing the uranium to the tetravalent state with hydrogen in the presence of a suitable catalyst. A high grade uranium oxide product is precipitated directly from the leach solutions. Vanadium oxide also can be precipitated by this method. The chemistry of the leaching and precipitation reactions are discussed, and laboratory results are presented which illustrate the applicability of the process and describe the variables affecting leaching and precipitation rates, recoveries, and reagent consumption. THE extractive metallurgy of uranium is influenced by a number of special considerations which generally do not arise in connection with the treatment of the more common base metal ores. Perhaps foremost among these is the very low uranium content of most of the ores which are encountered today, usually only a few tenths of one percent. A further difficulty is presented by the fact that the uranium often occurs in such a form that it cannot be concentrated efficiently by gravity or flotation methods. In these and other important respects, there is evident some degree of parallelism between the extractive metallurgy of uranium and that of gold and, as in the latter case, it has generally been found that uranium ores can best be treated directly by selective leaching methods. It is readily evident that this parallel does not extend to the chemical properties of the two metals. Unlike gold, which is easily reduced to metallic form, uranium is highly reactive. It tends to occur as oxides, silicates, or salts. Two ores are of predominant importance as commercial sources of this metal: pitchblende which contains uranium as the oxide, U3O51 and carnotite in which the uranium is present as a complex salt with vanadium, K2O-2UCV3V2O5-3H2O. These ores may vary widely in respect to the nature of their gangue constituents. Some are largely siliceous in composition, while others consist mainly of calcite. Sometimes substantial amounts of pyrite or of organic materials are present and these may lead to specific problems in treating the ore. Further complications may be introduced by the presence of other metal values such as gold, copper, cobalt, or vanadium whose re- covery has to be considered along with that of the uranium, or whose separation from uranium presents particular difficulty. In general, there are two main processes for recovering uranium in common use today.'.2 One of these employs an acid solution such as dilute sulphuric acid to extract the uranium from the ore. A suitable oxidizing agent such as MnO, or NaNO, is sometimes added if the uranium in the ore is in a partially reduced state. The uranium dissolves as a uranyl sulphate salt and can be precipitated subsequently by neutralization or other suitable treatment of the solution. The second process employs an alkaline leaching solution, usually containing sodium carbonate. The uranium, which must be in the hexavalent state, is dissolved as a complex uranyl tricarbonate salt, and then is precipitated either by neutralizing the solution with acid or by adding an excess of sodium hydroxide. The latter method has the advantage of permitting the solutions to be recycled, since the carbonate is not destroyed. This is essential if the process is to be economical, particularly with low grade ores. With each of these processes, there are associated a number of advantages and disadvantages and the choice between using acid or carbonate leaching is generally determined by the nature of the ore to be treated. In the past, more ores appear to have been amenable to acid leaching than to carbonate leaching and the former process correspondingly has found wider application. With most ores, acid leaching has been found to operate fairly efficiently and to yield high recoveries. One of the main disadvantages has been that large amounts of impurities, such as iron and aluminum, sometimes are taken into solution along with the uranium. This may give rise to a high reagent consumption and to difficulties in separating a pure uranium product. Excessive reagent consumption in the acid leach process also may result

Jan 1, 1955

By John C. Sawyer

The mechanism of catastrophic oxidation of chromium and 446 stainless steel is examined. Data are presented to show that accelerated oxidation of these two materials, as caused by lead oxide, can occur in the absence of a liquid layer contrary to presently accepted theory. An alternate theory is proposed in which the rate of accelerated oxidation is a function of the rate at which lead oxide destroys the protective oxide formed on the base metal. An example of the application of the theory is given for the catastrophic oxidation of chromium in the presence of lead oxide. WHEN stainless iron-, nickel-, or cobalt-base alloys are heated in air to moderate temperatures in the presence of certain metallic oxides, oxidation will proceed at an accelerated rate. This phenomenon, often called "catastrophic oxidation", is most pronounced for the stainless steels. With these alloys the condition is so severe that large masses of oxide will form on the surface of the alloy in 1 hr or less at temperatures of 1200o to 1700oF. While a number of oxides are known to cause this effect, PbO, V2O5, and Moo3 are the most familiar, having been the subject of one or more investigations which have appeared in the literature.1-7 In presenting the results of these investigations, many of the authors have offered possible explanations to account for the more rapid rate of oxidation observed; however, the liquid layer theory as proposed by Rathenau and Meijering 2 has been the most commonly accepted mechanism. The liquid layer theory proposes that a low-melting oxide layer is formed on the surface of the alloy as the result of the interaction of the alloy oxide and the contaminating oxide. When the temperature of oxidation is above the melting point of the oxide on the surface, a liquid layer will form and oxidation will proceed at an accelerated rate. At temperatures below the melting point of the surface oxide, oxidation will proceed more slowly in the normal manner. It is argued that the rates of diffusion of oxygen and metal ions through the liquid layer are extremely rapid thereby accounting for the high rate of oxidation. Various experimental data have been presented to show that the temperature at which accelerated oxidation first becomes apparent coincides with the melting point of the eutectic oxide which would be present on the surface. Some exceptions have been observed, e.g., silver will oxidize in the presence of Moo3 at temperatures below the lowest melting eutectic; on the other hand, stainless steel will not be catastrophically oxidized at 1500oF in a molten bath of PbO and SiO2. In reviewing the various theories which have been used to explain catastrophic oxidation, Kubaschewski and Hopkins 8 favor the liquid layer theory, but note that, ".. .as experimental observations are not altogether in agreement with this theory (liquid layer theory), one should consider it a necessary but not a sufficient condition." In contemplating the liquid layer theory, it appears that sufficient evidence has not been presented to establish the theory beyond question. As a means of further clarification, a program of research was undertaken to determine in greater detail the mechanism of accelerated oxidation as caused by lead oxide. The first part of the program deals with a comparison of the oxidation of both AISI 446 stainless steel and chromium metal in the presence of lead oxide, vs the oxidation of these two materials in air alone. These comparisons are made at a number of different temperatures, most of which are below the melting point of the surface oxides. The second part of the program is concerned with a presentation of an alternate theory of accelerated oxidation exemplified by the system Cr-PbO-Air. PROCEDURE AND RESULTS Several experimental methods are commonly used to follow the progress of oxidation. One of these, the weight-gain method, was chosen for this work. This procedure requires that a specimen of the alloy be weighed, oxidized for a given period of time at an elevated temperature, and reweighed—the difference between the two weights being noted. The weight gain of the specimen represents the amount of oxygen acquired from the atmosphere to transform a portion of the specimen to oxide. In those cases where there is a tendency for the specimen or oxide to volatilize at the testing temperature, additional data must be collected so that a correction factor can be determined. This factor must be applied to the weight change in order to ascertain the actual amount of oxidation which has taken place. The specimens used for this work were 1 1/2 in.

Jan 1, 1963

By Irving B. Cadoff, Ernest Levine

The crack formation and propagation in the single -phase Cu-4 pct Ag alloys were studied. The alloys were loaded in mercury to various stress levels, the mercury was removed, and the specimen examined for cracks. Cracks were found to develop below the fracture stress; the frequency of such cracks increased with increasing stress level. Some cracks were nmpropagative. Fracture in mercury was found to occur by the link-up of cracks formed at various stress levels rather than by the growth and propagation of a single crack. If the mercury environment is removed prior to a critical amount of crack formation, then continued loading results in ductile fracture. The appearance of the cracks at selected grain boundaries is related to the relative orientation of the boundaries, as are the propaga-tive characteristics of the crack. The mercury interaction appears to be one of lowering the strength of the metal-metal bonds in the high-stress area of the grain boundary. GRIFFITH'S microcrack theory1 proposed a critical crack size above which a crack in an elastic material grows with decreasing energy at a stress of From his theory it was proposed that the presence of a liquid tends to lower the surface energy of the microcrack faces2 leading to a decrease in the critical crack size necessary for spontaneous fracture propagation. stroh3 proposed that the stress concentration at a grain boundary due to pile-up may initiate a microcrack at the grain boundary. petch4 and Stroh5 evaluated the stress distribution at the head of a pile-up in a polycrystal-line material and deduced that the critical crack size and hence of is dependent on the grain size. Experimental verification of this dependence was found by petch6 for hydrogen embrittlement of steel. Studies in stress-corrosion cracking7 have provided a picture of fracture which shows that initial separations occur in a scattered, independent fashion in regions of high tensile stress. A minimum or threshold stress is necessary to produce a sufficient stress concentration to initiate frac- ture. These separations join up to form a crack. The extension of fracture is largely discontinuous and consists of a joining up of cracks. In recent worka evidence of this scattered crack network was found in a Cu-Ag alloy embrittled by mercury. For the Cu alloy-Hg couple, the crack path has also been found to be dependent on the orientation of adjacent grains, and with the addition of zinc to mercury a reduction in embrittlement along with a change in fracture morphology was found.9 In this present study, a mercury-dewetting method was used to observe crack initiation and fracture morphology when a Cu-4 pct Ag alloy is deformed in mercury and Hg-Zn solutions. PROCEDURE Specimens of Cu-4 pct Ag were prepared as in previous crack-path studies.' The specimens were heated at 770°C for 24 hr and water-quenched Tension tests using a table-model Instron were carried out in mercury and in various concentrations of Hg-Zn. Loading was in steps up to the fracture stress, with the load being removed and the specimen examined for surface cracks at each step. The specimens were dewetted after each load to permit examination of the surface structure and rewetted prior to continued loading. The specimens were wetted by electro polish ing in phosphoric acid, rinsing in alcohol, and then immersing in a pool of mercury. Dewetting was accomplished by flame heating the specimen for 30 sec in a vacuum. Some surface contamination was found, but not enough to obscure crack configurations and grain boundaries. RESULTS Fracture Characteristics in Mercury. Fig. 1 is a stress-strain curve showing the progressive step-wise loading of the specimen. As may be seen from the graph, the first position stopped at a is at a stress 5000 psi below the expected fracture stress of 25,000 psi. Examination of the specimen after removal of mercury showed only one crack. The appearance of this crack at a stress far below the fracture stress of this alloy in mercury did not affect the stress-strain curve in any manner. The specimen was then recoated with mercury and deformation was continued (curve b, Fig. 1) raising the stress by 4000 psi, and the same procedure re~eated. The initial crack was located and appeared as in Fig. 2 (crack lb). In this figure the crack is

Jan 1, 1964

By R. L. Skaggs, D. T. Peterson

The effect of carbon in solid solution on the plastic behavior of thorium was studied by measuring the flow stress of Th-C alloys from 4.2" to 573°K and at several strain rates. Carbon was found to strengthen thorium primarily by increasing the thermally activated component of the flow stress. The strengthening due to carbon was directly proportional to the carbon content and decreased rapidly with increasing temperature up to 423" K. The flow stress also increased with increasing strain rate. The strengthening appears to be due to a strong short-range interaction between carbon atoms and dislocations. A yield point was observed in the Th-C alloys which increased with increasing carbon content. JTREVIOUS study of the mechanical properties of thorium has been confined largely to the measurement of the engineering properties. Work prior to 1956 has been summarized by Milko et al.1 who reported that additions of carbon to thorium sharply increased the room-temperature strength. In addition, the yield strength was observed to decrease rapidly over the temperature range from 25" to 500°C. In 1960, Klieven-eit2 measured the flow stress of thorium containing 400 ppm C. He found that over the temperature range from 78" to 470°K the flow stress was strongly dependent on temperature and rate of deformation. A drop in the load-elongation curve, or a yield point, was observed over most of the above temperature range. Above 470°K, the flow stress was nearly independent of temperature and strain rate. This strong temperature and strain rate dependence of flow stress is not generally observed in fcc metals. It is, in fact, more typical of the behavior reported for bcc metals. Bechtold,3 Wessel,4 and conrad5 have pointed out the striking difference between the commonly studied bcc metals and fcc metals in regard to the effect of temperature and strain rate on the flow stress. Zerwekh and scott6 studied the plastic deformation of thorium reported to contain 12 ppm C. They found that this material did not obey the Cottrell-Stokes law as expected for fcc metals. In addition, they found values of the activation volume smaller by an order of magnitude than expected for an fcc metal. They concluded that thorium was strengthened by a randomly dispersed solute. Thorium differs from many other fcc metals that have been studied extensively in that it shows a relatively high carbon solubility at room temperature. Mickleson and peterson7 report the solubility limit at room temperature to be 3500 ppm C. The lowest value reported is that of Smith and Honeycombe8 who report the limit to be 2000 ppm C at 350°C. The pres- ent investigation was a systematic study of the flow stress and yield point phenomenon of thorium over a broad range of carbon content, temperature, and strain rate. EXPERIMENTAL PROCEDURE The thorium used in this investigation was produced by the reduction of thorium tetrachloride with magnesium as described by Peterson et a1.' Chemical analysis of the original ingot after arc melting and electron beam melting is shown in Table I. Alloys were prepared by arc melting this thorium with high-purity spectrographic graphite. Threaded specimens with a gage length 0.252 in. diam by 1.6 in. long were used for the constant stress or creep measurements. These specimens were machined from rod which had been cold-rolled and swaged to % in. diam. Tensile specimens were prepared by swaging annealed 3/8 -in.-diam rod to 0.102 *0.001 in. The as-swaged wire was cut to lengths of 2 in., annealed, and the center 1-in. gage length elec-tropolished to 0.100 ±0.001 in. The specimens were gripped for a length of 3 in. at each end by a serrated four-jaw collet which was tightened by a tapered compression nut. No slipping occurred in the grips and negligible deformation was observed outside the 1-in. gage length. Both the creep and tensile specimens were annealed at 730°C under a vacuum of 1 x X Torr. The resulting structures consisted of equiaxed recrystallized grains with a grain size of 3200 grains per sq mm for the tensile specimens and 2200 grains per sq mm for the creep specimens. After the specimens were prepared, samples were analyzed for nitrogen, oxygen, and hydrogen. The results of these analyses are given in Table 11.

Jan 1, 1969

By C. R. Bailey, H. F. Dunlap, Ellis Shuler, H. L. Bilhartz

Data are presented which indicate that the saturation exponent, n, in the equation, R. = R100S-11, relating core resistivity, I:,. to the resistivity at 100 per cent saturation. R100. and to the saturation, S. may vary appreciably from the value of two which is usually assumed for this exponent when interpret ing well logs. Values ranging from one to two and one-half have been found on (.ore sample investigated to date. Attempts to correlate this saturation exponent with porosity or permeability of the core have not been successful. The saturation exponent is apparently not a function of the interfacial tension between the brine and the displacing fluid. Some evidence is given indicating that the resistance of the core is not a unique function of the saturation but depends upon the manner in which this saturation was achieved. Equipment and technique are discussed for measurement of resistivities in core plugs in which water saturation can be varied. lNTRODUCTION A number of investigations of the resistivity-saturation relationship for un-c~~nsolidated sands and consolidated (.ore samples have been reported in the literature. According to most of these: R. = R¹ººS², where R² = the resistivity of a formation at saturation S, and R¹ºº= the resistivity of the formation at 100 per cent water saturation. Much of this work was (lone on unconsolidated sands desaturated by gas or oil. Hen-clerson and Ynster worked exclusively with dynamic systems, flowing oil or gas through consolidated cores. There is some doubt as to how well this reproduces static reservoir conditions. Jakosky and Hopper³ onsidered also the case of consolidated core plugs, but the oil-water distribution in the emulsions which they used to saturate their cores is almost certainly different from that occurring in reservoirs. Recently Guyod quotes the results of some Russian work which indicates that n may vary from 1.7 to 4.3. No experimental details of this work are available. In connection with electric log interpretation it is important to know the value of the saturation exponent. For example, if in a given reservoir it is found that the resistivity is three time.; the resistivity observed when the reservoir is 100 pel. cent 'saturated with water, this fact would be interpreted as indicating a water saturation of 33 per cent if the saturation exponent were 1 and a water saturation of 6-1 per cent if the saturation exponent were 2.5. EXPERIMENTAL METHOD In the work to be described it was assumed that reservoir conditions are most nearly obtained when core plugs are desaturated by the capillary pressure technique referred to in numerous places in the literature, as for example. in Bruce and Welge's paper.' In this technique the core. saturated 100 per cent with brine, is placed in contact with a ceramic disc permeable to brine but not to the displacing medium for the displacement pressures used. Pres-ure is then applied to the displacing medium and brine forced out of the core through the ceramic disc. Fig. 1 shows the core plug in place in the cell in which resistivity and saturation measurements are made. Fig. 2 shows the schematic electrical diagram wed to make resistivity measurements on the core plug. A four-electrode type circuit is used, employing a Hewlett-Packard model 400A. AC vacnum tube voltmeter. The 60-cycle AC current througli the core is adjusted to 1 milliampere and measured by noting the voltage drop across the calibrated 100-ohm resistor. The vo1tages appearing at probes 1, 2, 3, and 4 are then successively measured. Voltage drops across the top, center, and bottom portions of the core are obtained by sublracting the voltages appearing at successive probes. This technique avoids any polarization or other high contact resistance phenomena which may develop at the current input electrodes. Resistances which may develop between the core and the probes, and which are small compared to the 1-megoam input impedance 01' the vacuum tube voltmeter will (obviously not affect the measurements allpreciably. Any very appreciable resistallces which may develop at any of the probe wires are detected and allowed for by inserting a 1-megohm resistor in series with the voltage measuring probe. If the probe resistance is actually zero, the new voltage measured after insertion of the I-megolim resistor will be approximately one-half of that previously measured. since the input impedance of the vacuum tube voltmeter is itself 1 megohm. If an! appreciable probe resistance has developed, the new voltage is found to be appreciably greater than one-half of the previously measured voltage. Such probe resistance; have been found to develop only occasionally and usually can be traced to poor connections betwern the core

Jan 1, 1949

By R. H. Schnitzel

Internal-friction peaks have been observed in tungsten single crystals at about 300° and 400°C. The characteristics of these peaks are similar to interstitial peaks observed in other bee metals; therefore, the origin of these peaks appears to he the Snoek mechanism. The interstitial responsible for the peak at about 300°C has not been identified. Carburizing increases the magnitude of the peak at about 400°C; consequently, it appears reasonable to suppose that the specific interstitial associated with this peak is carbon. The activation energies associated with the 300° and 400°Cpeaks are about 35,000 and 45,000 cal per mole, respectively. INTERNAL - friction peaks resulting from the stress-induced diffusion of interstitials (Snoek relaxation peaks) have been frequently observed in bee metals.1-5 Attempts to detect Snoek relaxation peaks in tungsten have, however, not been fruitful.' Failure to find Snoek peaks in sintered tungsten can perhaps be attributed to one or more of the following difficulties: a) the relatively low purity of the sintered tungsten; b) the lack of extensive metallurgical knowledge about tungsten-interstitial alloys, such as suitable interstitial dosing and quenching procedures; and c) the inconsistency of some of the interstitial analyses of tungsten, which reflects itself in one's inability to be sure of the nature of the specimens. This present investigation did not overcome all of these difficulties for successful tungsten internal-friction measurements. Some of these difficulties still persist and new difficulties were encountered during the course of this investigation. Nevertheless, the use of electron-beam tungsten single crystals having somewhat greater purity levels than sintered tungsten combined with appropriate carburizing and quenching procedures permitted a reasonable attempt to be made. As a consequence, internal-friction peaks were observed in these tungsten single crystals at about 300° and 400°C. These peaks were found to be unstable, since they annealed rapidly away during a sequence of internal-friction measurements. Hence, it was necessary to construct an apparatus having a faster heating rate to study some of the details of these peaks. From the behavior of these peaks as well as our knowledge of similar peaks in other bee metals, one can reasonably conclude that these peaks are caused by residual interstitial impurities within these crystals. Further investigation of these peaks after the application of various metallurgical treatments lent credence to this supposition. EXPERIMENTAL TECHNIQUE The internal friction of tungsten single crystals was measured using two different pieces of apparatus both of which are of essentially the same conventional design, namely the KE type of torsion pendulum. The important difference between these two types of apparatus was in the attainable heating rate and method of protection of the specimen from atmospheric contamination. The apparatus designated "number 1" was enclosed in a vacuum chamber which was heated by an externally mounted furnace. It had a slow rate of heating which was estimated to be about 4°C per min from room temperature to about 350°C and then about 1°C per min to 600°C. The internal friction of tantalum was measured with this apparatus and the established Snoek peaks were found.' These tantalum peaks in the temperature range from room temperature to 400° C served as a check for the apparatus. The apparatus designated "number 2" having a faster heating rate than number 1 was not elaborate. It consisted of a mounted nickel tube to which split heating elements were attached. Argon was used as the protective atmosphere. The measured heating rate was about 12° to 15°C per min whereas the cooling rate was somewhat slower at about 10° C per min because of the increased difficulty encountered in stabilizing the temperature. No surface oxidation of the specimen was noted after any test. This apparatus was also checked with the known peaks of tantalum.1 The preparation of the single-crystal specimens for internal-friction measurements consisted of centerless grinding the crystals from an approximate 0.200 in. diameter to 0.030 to 0.040 in. in diameter, and then electropolishing them to about 0.020 in. in diameter. Single crystals processed in this manner are designated as being in the virgin condition. Since the length of crystal varied from 3 to 9 in., the test frequency varied from about 1 to 2 cps. The frequencies of measurement, axial orientations, and chemical analyses for the various crystals are listed in Table I. The controlled addition of carbon into tungsten is a difficult problem. Attempts to find the critical conditions necessary for an equilibrium treatment were not fruitful. Therefore, a simple nonequi-librium method was used. The addition of carbon to these crystals consisted of appropriately combining three treatments—carburizing to achieve a case, annealing to partially dissolve the carbon into the

Jan 1, 1965

By Allan E. Martin, Harold M. Feder, Irving Johnson

The cadmium-uranium system was studied by thermal, metallographic, X-7-ay and sampling techniques; special emphasis was placed on the establishment of the liquidus lines, The single inter metallic phase, identified as the compound UCd11 melts peritectically at 473°C to form a-umnium and melt containing 2.5 wt pct uranium. The cadmium-rich eutectic (0.07 wt pct uranium) freezes at 320.6°C. Solid solubilities in uraizium and cadmium appear to be negligible. Between 473°C and 600°C the liquidus line is retograde. NO publication relating to the cadmium-uranium phase diagram was found in the literature. The establishment of this diagram was of considerable interest to us because of a possible application of the system to the pyrometallurgical reprocessing of nuclear fuels. Analysis of liquid samples, metallographic examination, thermal analysis, and X-ray diffraction analysis were used to establish the phase diagram from about 300° to 670°C. Particular emphasis was placed on the establishment of the liquidus lines. The same system was concurrently studied in this laboratory by the galvanic cell method.' Both studies benefited from a continual interchange of information. MATERIALS AND EXPERIMENTAL PROCEDURES Stick cadmium (99.95 pct Cd, American Smelting and Refining Co.) contained 140 ppm lead as the major impurity. Reactor grade uranium (99.9 pct U, National Lead Co.) was most often used in the form of 20-meshspheres. This form was particularly suitable because it does not oxidize as readily as finer powder. The liquidus lines were determined by chemical analysis of filtered samples of the saturated melts. The liquid sampling technique is described elsewhere2 alumina crucibles (Morganite Triangle RR), tantalum stirring rods, tantalum thermocouple protecthecadmiumtion tubes, Vycor or Pyrex sampling tubes, and grades 60 or 80 porous graphite filters were used. Uranium dissolves in liquid cadmium rather slowly. In order to achieve saturation of the melts it was necessary to modify the procedure of Ref. 2 by the use of more vigorous stirring and longer holding periods (at least 3 hr) at each sampling temperature. The samples were analyzed for uranium by spectro-photometry (dibenzoyl methane method) or by polar- ography. The analyses are estimated to be accurate to 2 pct. Thermal analysis was performed on alloys contained in Morganite alumina crucibles in helium atmospheres. Standard techniques were employed; heating and cooling rates were about 1°C per min. For the determination of the peritectic temperature, Cd-10 pct U charges were first held for at least 50 hr at temperatures in the range 435° to 460°C to form substantial amounts of the intermediate phase. For the determination of the effect of cadmium on the a-p transformation temperature of uranium, charges of Cd-25 pct U (-140+100 mesh uranium spheres) were first held near the transformation temperature, with stirring, to promote solution of cadmium in the solid uranium. The holding times and temperatures for these treatments were 18 hr at 680°C for the cooling run and 28 hr at 630°C for the heating run. Alloy specimens for X-ray diffraction and metallographic examination of the intermediate phase were prepared in sealed, helium-filled Vycor or Pyrex tubes. Ingots from solubility runs and thermal analysis experiments also were examined metallographically. Crystals of the intermediate phase were recovered from certain cadmium-rich alloys by selective dissolution of the matrix in 20 pct ammonium nitrate solution at room temperature. Temperatures were measured with calibrated Pt/Pt-10 pct Rh thermocouples to an estimated accuracy of 0.3°C. However, the depression of the freezing point of cadmium at the eutectic is estimated to be accurate to 0.05°C because a special calibration of the thermocouple was made in place in the equipment with pure cadmium just prior to the measurement. EXPERIMENTAL RESULTS The results of this study were used to construct the cadmium-uranium phase diagram shown in Fig. 1. This diagram is relatively simple; it is characterized by a single intermediate phase, 6 (UCd11), which decomposes peritectically, and which forms a eutectic system with cadmium. The solid solubilities in the terminal phases appear to be negligible. An unusual feature of the diagram is the retrograde slope of the liquidus line above the peritectic temperature. The Liquidus Lines. The liquidus lines above and below the peritectic temperature are based on three separate solubility experiments. The data are shown in Fig. 1 and are given in Table I. It is apparent from the figure that the solubility data obtained by the approach to saturation from higher temperatures fall on substantially the same lines as those obtained

Jan 1, 1962

By N. J. Grant, C. C. Wang

The Ti-Cr-O ternary system has been studied in detail near the titanium-rich corner within the limits of 10 wt pct 0, and 20 wt pct Cr. Studies were extended, but not in detail, to the region beyond 25 wt pct 0, (50 atomic pct) and 62 wt pct Cr (60 atomic pct). Four isothermal sections at 1400°, 1200°, 1000°, and 800°C are presented as well as two vertical sections at 1 and 2 wt pct 02. DURING the last decade much interest has been shown in the development of high strength titanium alloys for high temperature and corrosion resistant applications. Extensive research is being carried out at present, as the current literature indicates, in order to study the properties of titanium and to develop improved alloys. Two of the important alloying elements in commercial titanium alloys are chromium and oxygen and it would be desirable to know their combined influence upon titanium. For this purpose the present work was carried out to investigate the titanium-rich corner of the ternary system TiICr-0. The binary systems Ti-Cr and Ti-0 have been published recently. The Ti-Cr system was studied by several investigators " and their results are in close agreement. The eutectoid decomposition of the B phase has been shown to be extremely sluggish. TiCr, was the only intermetallic compound found in this binary system and was formed at 1350°C by a transformation from the p phase. TiCr? was established as the cubic C 15 (MgCu,) type of structure with 24 atoms per unit cell and was designated as the y phase. This terminology will be adopted in the present work. There was disagreement about the actual composition of this compound among the several investigators, although it is evident from their data that the compound probably has a solubility range of about 2 to 3 pct and is in the vicinity of 65 pct Cr. It has been indicated recently that a high temperature modification of this y phase (TiCr,) existed at a temperature above 1300°C." ' This high temperature modification was identified as a hexagonal C 14 (MgZn,) type of structure with 12 atoms per unit cell. The exact transformation temperature from the high temperature phase to the low temperature phase has not been established. A considerable hysteresis was observed and, due to the sluggishness of this transformation, the high temperature phase often co-existed with the low temperature phase at temperatures below 1300°C. A preliminary study of several Ti-0 compounds and the Ti-0 system had been carried out by Ehr-1ich."-"' The most complete binary Ti-0 system was the one reported recently by Bumps, Kessler, and Hansen." The first intermediate phase found in the system was the 8 phase which formed by a peritec-toid reaction of the phases a and Ti0 at temperatures below 925 °C. This reaction is extremely sluggish. The structure of this 8 phase was tentatively identified by these authors as being tetragonal and the lattice constants were found as c,, - 6.645A, a,, = 5.333A and c/a = 1.246A. Experimental Procedure The raw materials used for this investigation were TiO,, electrolytic chromium, iodide titanium, and sponge titanium. The TiO, was in the form of powder of chemically pure grade (99.8 pct pure). The chemical analysis of the electrolytic chromium was: 0, 0.50 pct; Fe, 0.07; Cu, N, and C, 0.01; and Pb, 0.001. The oxygen in the chromium was calculated as part of the final oxygen content of the alloys. The alloys were prepared by the cold crucible method using a tungsten arc. The entire system was evacuated and flushed with purified helium three times and then filled with helium. Each alloy was melted, turned over, and remelted at least four times to insure homogeneity. The total melting time was generally from 6 to 10 min. A master alloy of 25 pct 0,-75 pct Ti was prepared to facilitate alloying by melting compacts of TiOl powder with either iodide or sponge titanium, yielding the compound TiO. It was found necessary to bake the TiO, powder compact at about 150°C to remove adsorbed moisture. This was done to prevent the disintegration and spattering of the compact when the arc was struck. TiO, powder dissolved quite readily into the melt and no other trouble was encountered.

Jan 1, 1955

By E. S. Bartlett, D. N. Williams

QUANTITATIVE values for the oxidation rate of unalloyed molybdenum in air at temperatures above the melting point (1460°F) of the characteristic oxide are contained in the literature as a result of previous investigations. Lustman' reported values corresponding to 0.36 in. penetration per day (IPD) at 1500 and 1600°F in still air, noting essentially no variation in rate with temperature. Jones, Spretnak, and Speiser' reported values corresponding to 0.14 and 0.13 IPD at 1500 and 1800°F, respectively, in still air, attributing the decreased oxidation rate at higher temperatures to a lesser accumulation of the corrosive molten oxide on the surface at the higher temperature as a result of increased volatilization rate. Harwood3 ecently summarized work in the field, presenting generalized data corresponding to 0.48 to 0.96 IPD at 1800°F and 0.55 to 0.83 IPD at 1700°F in slowly flowing air. In a recent program at Battelle, it became desirable to know more about the characteristic oxidation behavior of molybdenum under varying conditions of temperature and atmosphere. Using oxidation-test apparatus designed for dynamic, continuous recording of weight change during testing,' values for the oxidation rate of molybdenum were obtained at temperatures from 1400 to 2150°F. In addition the effect of air flow on the oxidation rate was studied briefly at temperatures of 1600, 1800, and 2000°F. Exhaust of the contaminated atmosphere from the oxidation chamber was effected by an impeller pump attached to a 3/16-in.-diam opening in the oxidation chamber. The volumetric exhaust rate (cubic feet per hour) was normally maintained slightly in excess of the input rate to avoid condensation of MOO,,' on the sample suspension rod. The entering atmosphere was preheated prior to admission to the oxidation chamber by a 1 1/2-in.-diam cup packed with shredded asbestos. The experimental data are presented in Table I. Comparing conditions 2 and 3 (taking into account the temperature difference) and conditions 8 and 9. shows that in the absence of forced exhaust an atmosphere of moving air results in greater oxidation rate than a stagnant atmosphere. The use of forced exhaust, as shown by comparing conditions 3 and 4 and conditions 14 and 15: resulted in an even greater increase in oxidation rate. By virtue of the size of the atmosphere input and exhaust openings, it was calculated that the exhaust velocity was about 60 times that of the input velocity for essentially equal volumetric flow rates. Because of the proximity (about 3/4 in.) of the exhaust port to the specimen, it is logical to assume that cleansing of the atmosphere immediately surrounding the specimen was accomplished much more efficiently by the exhaust flow than by the input flow at a constant-volumetric flow rate. Also, it can be seen by comparing conditions 4 through 7 and conditions 11 through 13 that increasing the rate of atmosphere flow (by increasing input velocity with a proportional increase in exhaust velocity) above some optimum value has little, if any, further effect on the oxidation rate. These results suggest that there is a maximum oxidation rate for molydenum at a given temperature which is obtained when conditions are maintained such that the partial pressure of MOO3 in the atmosphere surrounding the specimen is at a low value. By controlling the partial pressure of MOO, surrounding the sample, it is possible to control the rate of volatilization of MOO:, from the surface. This, in turn, affects the rate of oxidation, since the thickness of the MOO3 layer determines the amount of oxygen which will be able to reach the reaction surface.' When the liquid oxide layer is less than some critical thickness, i.e., when the volatilization rate is high, enough oxygen is transported to the active surface to permit oxidation to proceed at the maximum rate allowed by the kinetics of the oxidation reaction. However, if the volatilization of MOO,, is suppressed, the thickness of the layer of MOO3 on the surface increases, and the diffusion of oxygen through the oxide layer becomes the rate-controlling step in the oxidation process. The lack of agreement between the present results and those of previous investigators is presumed to be due to differences in removal of the oxidation product (Moo,) from the immediate vicinity of the sample. By comparing conditions 1, 5, 10, 12 and 14, it is seen that when forced exhaust was used the oxidation rate of molybdenum increased with increasing temperature. A rapid increase was observed between 1400 and 1600°F, attributable to the effects

Jan 1, 1959

By N. C. J. Ros

The paper deals with pressure gradients occurring in flowing and gas-lift wells, a knowledge of which can be applied to the determination of optimum flow-string dimensions and to the design of gas-lift installations. The study is based on a pressure-balance equation for the pressure gradient. It appears that a pressure-gradient correlation of general validity must essentially consist of two parts-—one part being a correlation for liquid hold-up and the other part being one for wall friction. Dimensional analysis indicates that both liquid hold-up and wall friction are related to nine dimensionless groups. It is shown that in the field of interest only four groups are really important. On the basis of these four groups a restricted experimental program could be selected that nevertheless covered practically all conditions encountered in oil wells. This experimental program has been carried out in a laboratory installation. Three essentially different flow regimes were found. The pressure gradients in these regious are presented in the form of a set of correlations. Comparison of these correlations with a few available oilfield data showed excellent agreement. INTRODUCTION Prediction of the pressure drop in the flow string of a well is a widely known problem in oilfield practice. Accurate data on the pressure gradient of a simultaneous flow of gas and liquid in a vertical pipe are especially useful for the determination of optimum flow-string dimensions. It is well known that with moderate gas and liquid flows such a vertical string acts as a "negative restriction". The pressure drop decreases (1) when the throughput through a given pipe increases, and (2) when at a given throughput the cross-sectional area is decreased. The reason is that, with increasing velocities, the flow becomes more agitated so that the gas slips relatively more slowly through the liquid. With the resulting increase in gas content in the string, the static head decreases. When the area becomes very small, however, the high velocities entail great wall friction, which causes an increase in pressure drop. For a given flow, therefore, minimal pressure drop is obtained by using a certain cross section. This means that, in principle, each well can be provided with an optimum flow string for minimum pressure drop and, hence, maximum possible production rate. The procedure for the selection of the optimum string has been discussed by Gilbert.' A necessary tool in the procedure, however, is accurate knowledge of the pressure gradient to be expected for various values of the governing variables. Another application of pressure-gradient data lies in the field of gas-lift practice: they provide a means of determining the optimum gas-injection rate, optimum injection pressure and optimum injection depth. Much work has already been done in the study of the pressure gradient of vertical gas-liquid flow. Poett-mann and Carpenter2 presented a pressure-gradient correlation based on measurements in wells. This correlation has been found to provide accurate predictions in high-pressure wells and in high-production wells for flow through both tubing and annuli.2-5 However, when their method is checked on low pressure-low production wells or on wells with viscous crudes, serious discrepancies are found. As we shall see in the next section, this is due to the fact that their correlation factor, representing all irreversible energy losses, is given as a function of only one correlation group. Some important variables, such as gas-liquid ratio and liquid viscosity, are not incorporated in this group so that their specific effects are not accounted for. To study also the mechanism of vertical gas-liquid flow outside the ranges covered by the Poettmann-Carpenter publication and extensions, a laboratory investigation has been carried out. This study is founded on a pressure-gradient equation that is based on a pressure balance. To reduce the number of test runs required, a dimensional analysis has been carried out, followed by a selection of relevant dimensionless groups. These groups guided a subsequent experimental study, and with their aid the experimental program could be minimized while still covering the majority of the situations encountered in oilfield practice. In this paper the choice of a formula for the pressure gradient is discussed first. This is followed by a brief description of the experimental setup. Subsequently, the dimensional analysis is discussed and the relevant dimensionless groups are selected, resulting in the experimental program required. The general relationships of pressure gradient and liquid hold-up are then described; various flow patterns and a certain flow instability (so-called "heading") are discussed and a set of correlations is presented which shows a good agreement with the measurements and a few available field

By D. Y. F. Lai, R. J. Borg

Tracer diffusion of Fe59 has been measured in the a-stabilized Fe-1.8 at. pet V alloy from 700° to 1500°C. The activation energies are obtained in both the presence and absence of magnetic order. Furthermore, it is established that diffusion in the alloy is identical to that in pure iron and consequently the values of Do and Q accurately represent the temperature dependence for self-diffusion. The purpose of this investigation is to obtain an accurate estimate of the temperature dependence for self-diffusion in bee iron in both the presence and absence of magnetic order, and, in so doing, to establish the temperature range of the magnetic effect.&apos;" As the temperature interval suitable for diffusion measurements is severely limited in both bee phases of pure iron because of the intervening fee ? phase, the experiments were performed on an a-stabilized alloy containing 1.8 at. pet V. This alloy is bee over the entire range from room temperature to the melting point. Although there have been several independent investigations of self-diffusion of iron in a, iron,1, 3-6 there still exists considerable disagreement regarding the values of Do and Q for the paramagnetic region. The two systematic studies of diffusion in 6 iron6, 7 previously reported are also only in fair agreement; but in view of the extremely small temperature range available for diffusion studies, i.e., 1390o to 1535oC, this is not surprising. It is comparatively easy to obtain accurate values of Do and Q for the a-stabilized alloy inasmuch as measurements can be made over the entire temperature range -700o to 1500°C. However, in order to assume that these same values apply to pure iron requires careful comparison of the data in the a, and 6 regions in both the alloy and pure iron. We have made several measurements in the appropriate temperature ranges and are unable to establish any systematic difference between the diffusion coefficients of iron in pure iron and in the alloy. We therefore conclude that the values obtained for the alloy are truly applicable to pure iron; the complete evidence favoring this conclusion will be discussed later in this paper. EXPERIMENTAL The experimental methods will be given here only in barest detail since they have been thoroughly de- scribed elsewhere.l, 7 The alloy was prepared by induction melting and chill casting under argon. Diffusion samples were machined from the ingot and annealed in hydrogen for several days at 900°C to give an average grain diameter of 1 to 2 mm. The penetration profiles of the tracer were established by a sectioning technique, the residual activity being counted after the removal of each section. The tracer used is Fe59 which emits two high-energy ? rays of 1.098 and 1.289 Mev, respectively; these were detected by a ? scintillation counter equipped with a pulse-height analyzer. For the measurements in the temperature range -700o to 1130°C the samples were vapor-plated with Fe59, encapsulated in quartz under vacuo, and annealed in resistance-heated furnaces which are controlled to ±1°C. The specimens diffused at higher temperatures are prepared as edge-welded couples, the two halves being separated by a thin washer of the alloy to prevent sintering. The diffusion anneal is then carried out by inductive heating under a dynamic vacuum. The temperature is monitored pyrometrically. RESULTS The diffusion coefficients are obtained from the penetration profiles in the usual way using the error-function complement relationship. The results over the entire temperature range are shown in Fig. 1. In the linear region, 900o < t > 1500°C the least mean squares (lms) values of the diffusion coefficients are given by D = 1.39 exp[-(56.5 ± 1) x 103/Rt] cm2/sec [l] The average departure of the measured diffusion coefficients from the values given by Eq. [1]In order to determine whether or not the slope is truly constant over the entire range from 900" to 1500°C, the data are arbitrarily divided into two groups, the first containing values between -900" and 1133°C and the second between -1133o and 1500°C. The lms values for the two groups are given by Eqs. [2] and [3]: D = 0.519 exp[-55.7 x 103 /RT](900° to 1133°C) cm2/sec [2] D = 1.45 exp[-56.7x103/RT] (1133° to 1500=C) cm2/sec [3] Thus, there is no significant difference between the high- and low-temperature segments of the linear region. This not only assures us of the consistency of the values obtained by induction heating as compared to those obtained from the resistance-heated

Jan 1, 1965

By H. D. Hodges, J. K. Godbey

In order to better understand the fracturing process, bottom-hole pressures were measured during a number of typical fracturing operations. A recently developed system was used that allows simultaneous surface recording of both the bottom-hole and wellhead pressures on the same chart. The results from six fracruring treatments are summarized on the basis of the pressure data obtained. Al-though no complete analysis is attempted, the value of accurate pressure measurements is emphasized. Important characteristics of the bottom-hole pressure record do not appear at the wellhead because of the damping effect of the fluid-filled column. In four of the six treatments described, the formations apparently fractured during the initial surge of pressure with only crude oil in the well. The properties of the fluids used during the treatments are given and the fluid friction losses are obtained directly from the pressure records. This technique is also shown to be adequate for determining when various fluids, used during the process, enter the formation. INTRODUCTION Hydraulic fracturing for the purpose of increasing well productivity is now accepted in many areas as a regular completion and workover practice. Numerous articles have appeared in the literature discussing the various techniques and theories of hydraulic fracturing&apos;. In general, three basic types of formation fractures are recognized today. These are the horizontal fracture, the vertical fracture, and fractures along natural planes of weakness in the formation&apos;. Any one or all three of these fracture types may be present in a fracturing operation. However, with only the wellhead pressure record as a guide, it is difficult at best to determine if the formation actually fractured, and is almost impossible to determine the type of fracture induced. These difficulties arise in part because the wellhead pressure record, especially when fracturing through tubing, does not accurately reflect the pressure variations occurring at the formation. Several factors contribute to this effect and preclude the possibility of using the wellhead pressure as a basis for accurately calculating the bottom-hole pressure. These factors are: 1. The compressibilities of the fluids which damp the pressure variations. 2. The changes in the densities of the fluids or apparent densities of the sand-laden fluids. 3. The flowing friction of the various fluids and mixtures, which is dependent on the flow rates and the condition of the tubing, casing, or wellbore. 4. The non-Newtonian characteristics of a sand-oil mixture and its dependence upon the fluid properties, the concentration of sand, and the mesh size used. 5. The unknown and variable temperatures throughout the fluid column. Because of these reasons it was determined that in order to obtain a more accurate knowledge of the nature of fracturing, the bottom-hole pressure must be measured along with the pressure at the surface during a fracturing treatment. Even with accurate pressure data, a reliable estimate of the nature of fracturing is still dependent upon knowledge of the tectonic conditions. However, the hydraulic pressure on the formation is basic to any approach to a complete analysis. In order to accomplish this objective a system was developed to record the wellhead and bottom-hole pressures simultaneously at the surface. By recording both pressures on a dual pen strip-chart recorder, it was possible to greatly expand the time scale so that rapid pressure variations would be faithfully recorded. By such simultaneous recording, time discrepancies inherent in separate records are eliminated, thus overcoming one of the most difficult problems associated with bottom-hole recording systems. This paper illustrates the results obtained by using this system during six typical fracturing operations. All of these tests were taken in wells that were treated through tubing. By a direct comparison of the wellhead and bottom-hole pressures, the importance of obtaining complete pressure information during a fracturing treatment is emphasized. THE INSTRUMENTATION AND PROCEDURES The bottom-hole pressure measuring instrument consisted of a pressure-sensing element, a telemetering section, and a lead-filled weight or sinker bar. The pressure-sensing element used was an isoelastic Amerada pressure-gauge element. By using an isoelastic element, no temperature compensation was necessary in the tests described, since the temperature was believed to be well below the maximum temperature limit of 270°F. The rotary output shaft of this helical Bourdon tube element was coupled to a precision miniature potentiometer. The rotation of the pressure-gauge shaft thus changed the resistance presented by the potentiometer

By Tuncel M. Yegulalp, Malcolm T. Wane

In general, many problems relating to the exploitation of mineral deposits are probabilistic in nature. This derives from the fact that the geologic universe is inherently random. Probability theory and statistics have been found useful for forecasting the behavior of natural events that occur in the geologic universe. The objective of this paper is to illustrate the application of the theory of extremes to this fore-casting problem. For example, it is customary for design purposes to determine the rupture strength of geologic materials. The theory of extremes is exceedingly useful in describing that portion of the frequency distribution of rupture strength which contains the least strengths. Parameters describing the distribution of the least strengths are more important to the designer of mining excavations than parameters describing the total distribution. The basic principles of the theory of extremes will be detailed and illustrated. Any person required to work in the laboratory of nature is aware that uncertainty is a salient feature of all mining enterprises. A mining engineer required to plan the most efficient, practicable, profitable, and safe mine finds himself face to face with numerous ill-understood and often unquantifiable states of nature. Basic information necessary for adequate planning is often lacking or derived from incomplete tests on samples or experience of doubtful validity. The planning procedure usually takes the form of determining a feasible layout with the intent of determining an optimal layout when and if the necessary details and information become available. The crux of the entire procedure is the choosing of numbers to put into the operational and structural models which encompass the plan. Many times these numbers must be assigned qualitatively from past experiences and are called the "most probable ones." At other times, load records, performance records and material tests provide a basis for extrapolation. In any event, the numbers are chosen from a distribution or set of all numbers. Since each number in the distribution represents a possible state, the choice of any particular value is based upon a decision rule. To illustrate, consider the design of an underground structure or the design of a rock slope. The initial step is the formulation of the various possible structural actions which result from the geometry of the layout. For a given structural model various intensities of behavior are possible depending upon the load, deformation, and material characteristic spec-trums, respectively. Of particular interest to mining people is the failure behavior or condition, i.e., when there is a complete collapse of structural resistance by either structural instability or fracture. A necessary feature of the analysis is the "rupture strength" of the material. Information on the rupture strength is derived from testing either in situ or in the laboratory and the usual outcome is a variation in the test results. The methodology used to overcome this variation is to construct a frequency distribution of rupture strengths, and then determine a measure of central tendency and variability. The main idea involved is that the central tendency number will be used in the failure calculations and the measure of dispersion will be used to estimate the probability of failure. In particular if the distribution of rupture strength is normal, the mean rupture strength is the central tendency number and the standard deviation of the rupture strength is the measure of variability. Suppose the mean value of rupture strength is 1000 psi and the standard deviation is 200 psi. Insertion of 1000 psi into the failure calculation produces results that are unsafe, hence a common decision rule is to reduce the mean value by a "factor of ignorance" so that the failure calculation will produce a "safe result." If two is chosen as a factor of ignorance, this means the value inserted in the calculation is 500 psi or 2.5 times the standard deviation. The next step is to determine the percentage chance that failure will occur from a design created on this basis. Tables on the normal distribution function show that this percentage chance is 0.621% or approximately 7 times out of 1000. In practice, however, the situation is more complicated than represented by the foregoing illustration. The laboratory or field testing program usually constitutes a pathetically small sample of the geologic universe of interest and not enough testing is carried out to determine the exact form of the distribution of the test results. The normal, Cauchy and Student&apos;s T distributions are strikingly similar, and it becomes a matter of mathematical convenience to assume the normal law for phenomena which follow other laws.

Jan 1, 1969

By Shiou-Chuan Sun, R. F. Wesner, J. D. Morgan

0. C. Ralston and F. Fraas—Dr. Sun and associates have presented an interesting paper not all of which is comprehended by us. The data assembled measure the deflections of particles in an electrostatic field as a function of a number of independent variables and some dependent variables that are not sharply differentiated. These data are all based on a Johnson type machine of definite, well-described geometry, something not often done in electrostatic separation literature. One new fact brought out by this technique is the effect of coal dust on admixed pyrite and quartz. The effects are opposite in character, as should be expected and we do not agree with the authors that these effects are negligible. Fraas&apos; also used a multiple cell "distribution analyzer" and gives in fig. 5 of his paper a straight line plot with no humps or curves. This is not necessarily at variance with Sun&apos;s results because Fraas used a larger gap between electrodes and had no evidence of particles adhering to or dropping off the charged electrode. The section of Sun&apos;s paper on effect of surface conductivity contains a speculation that the dielectric constant "represents more or less the electrical conductance of the bulk body instead of the surface of the mineral particles." A simple picture of the meaning of the dielectric constant is that it is the specific inductive capacity of a dielectric when used as the dielectric between the plates of a condenser. It is at once evident that the above speculation confuses capacity with conductance—two definitely independent variables. We ask the authors to state in what group or subdivision their garnet belongs; what method and units were used in calculating the data of col. A, table I and their meaning; what was the temperature of the carrier roll and, finally, has any effort been made to investigate the effects of particle shape on distribution in the electrostatic field? S. B. Hudson—I have read this article with great interest. We have been engaged in research work on the principles of electrostatic separation in this laboratory for some time now, and our findings agree with those of the authors in many respects. The article shows evidence of careful and valuable research in the field of electrostatic separation. A "distribution analyser," very similar to that described in an earlier article by one of the authors," was incorporated in an inclined plate-type electrostatic separator designed and built in the Melbourne University laboratory in 1948 for investigation purposes.22 The actual splitting edges were machined from y! in. per-spex, and the paper hoppers were supported on linen thread immediately below the perspex dividers. These dividers fitted into machined slots in a framework to give accurate Yz-in. spacings. The hoppers (staggered) fed directly into a rack of test tubes, which is supported on a vertical pantograph arrangement. The rack was positioned with guides on the horizontal pantograph stand, and this ensured positive alignment when replacing the rack after making weighings. In later work, when much heavier feed rates were used, of the order of 30 to 40 Ib per in. per hr a rack fitted with rectangular metal containers and similarly aligned was used. Some work was done here on comparing the distributions of minerals when passed separately and when passed as a mixture, and it was found that there was quite an appreciable difference in the two results.= However, in our separator the particles do not pass down the plate in a single layer, and this difference is probably caused by collisions of one mineral particles with the other mineral particles. In most of the investigational work here, the change of the center point of the distribution is measured to establish the effect of a variable, such as voltage. Two minerals (zircon and rutile) have been studied rather exhaustively, and it was found that their distributions are very nearly normal. Owing to the sharpness of the distribution curves, the usual method of obtaining the mean or median was inaccurate, and was not used; instead the mean (also the median), calculated on the assumption of a normal distribution, was used to locate the center point of each distribution and proved satisfactory. The effect of polarity becomes very apparent in the plate-type separator where frictional charges play a very important part when using highly resistive minerals such as zircon. With rutile, a comparatively conductive mineral, polarity of the electrode has little effect. On the other hand, the magnitude of the voltage has a far greater effect on conductive than on resistive minerals. Shiou-Chuan Sun (authors&apos; reply)—Thanks are extended to Drs. Ralston and Fraas for their keen interest in this paper. Their questions concerning coal dust,

Jan 1, 1951

By Shiou-Chuan Sun, R. F. Wesner, J. D. Morgan

0. C. Ralston and F. Fraas—Dr. Sun and associates have presented an interesting paper not all of which is comprehended by us. The data assembled measure the deflections of particles in an electrostatic field as a function of a number of independent variables and some dependent variables that are not sharply differentiated. These data are all based on a Johnson type machine of definite, well-described geometry, something not often done in electrostatic separation literature. One new fact brought out by this technique is the effect of coal dust on admixed pyrite and quartz. The effects are opposite in character, as should be expected and we do not agree with the authors that these effects are negligible. Fraas&apos; also used a multiple cell "distribution analyzer" and gives in fig. 5 of his paper a straight line plot with no humps or curves. This is not necessarily at variance with Sun&apos;s results because Fraas used a larger gap between electrodes and had no evidence of particles adhering to or dropping off the charged electrode. The section of Sun&apos;s paper on effect of surface conductivity contains a speculation that the dielectric constant "represents more or less the electrical conductance of the bulk body instead of the surface of the mineral particles." A simple picture of the meaning of the dielectric constant is that it is the specific inductive capacity of a dielectric when used as the dielectric between the plates of a condenser. It is at once evident that the above speculation confuses capacity with conductance—two definitely independent variables. We ask the authors to state in what group or subdivision their garnet belongs; what method and units were used in calculating the data of col. A, table I and their meaning; what was the temperature of the carrier roll and, finally, has any effort been made to investigate the effects of particle shape on distribution in the electrostatic field? S. B. Hudson—I have read this article with great interest. We have been engaged in research work on the principles of electrostatic separation in this laboratory for some time now, and our findings agree with those of the authors in many respects. The article shows evidence of careful and valuable research in the field of electrostatic separation. A "distribution analyser," very similar to that described in an earlier article by one of the authors," was incorporated in an inclined plate-type electrostatic separator designed and built in the Melbourne University laboratory in 1948 for investigation purposes.22 The actual splitting edges were machined from y! in. per-spex, and the paper hoppers were supported on linen thread immediately below the perspex dividers. These dividers fitted into machined slots in a framework to give accurate Yz-in. spacings. The hoppers (staggered) fed directly into a rack of test tubes, which is supported on a vertical pantograph arrangement. The rack was positioned with guides on the horizontal pantograph stand, and this ensured positive alignment when replacing the rack after making weighings. In later work, when much heavier feed rates were used, of the order of 30 to 40 Ib per in. per hr a rack fitted with rectangular metal containers and similarly aligned was used. Some work was done here on comparing the distributions of minerals when passed separately and when passed as a mixture, and it was found that there was quite an appreciable difference in the two results.= However, in our separator the particles do not pass down the plate in a single layer, and this difference is probably caused by collisions of one mineral particles with the other mineral particles. In most of the investigational work here, the change of the center point of the distribution is measured to establish the effect of a variable, such as voltage. Two minerals (zircon and rutile) have been studied rather exhaustively, and it was found that their distributions are very nearly normal. Owing to the sharpness of the distribution curves, the usual method of obtaining the mean or median was inaccurate, and was not used; instead the mean (also the median), calculated on the assumption of a normal distribution, was used to locate the center point of each distribution and proved satisfactory. The effect of polarity becomes very apparent in the plate-type separator where frictional charges play a very important part when using highly resistive minerals such as zircon. With rutile, a comparatively conductive mineral, polarity of the electrode has little effect. On the other hand, the magnitude of the voltage has a far greater effect on conductive than on resistive minerals. Shiou-Chuan Sun (authors&apos; reply)—Thanks are extended to Drs. Ralston and Fraas for their keen interest in this paper. Their questions concerning coal dust,

Jan 1, 1951

By H. M. Zoerb

Based on the belief that operating details are a definite contributing factor to major economies, this paper traces the development of crushing cavity design in Symons cone crushers to attain maximum liner utilization. Wear rates are analyzed and compared in this presentation and drawings illustrate succeeding design changes. IN these times of rising labor and material costs, it has become more and more necessary that attention be paid to some operating details which, in their obscurity, may he the key to major economies. Liner wear in crushing cavities of secondary and tertiary crushers can become an appreciable cost item when the material to be crushed is hard and abrasive. This item of cost not only includes the value of the crushing members, but also more intangible costs such as labor and lost production due to more frequent replacement. The variables which are encountered in ores and minerals to be reduced; the design of plant and machine application; the sizes, shape, and fineness, characteristics of the crushed product; the moisture; hardness; friability; and abrasiveness of the material to be crushed are all influencing factors which must be taken into consideration in the selection of a crusher, and particularly in the design of crushing cavity and liners to be used in a crusher. Through a research program undertaken in cooperation with many operators of Symons cone crushers a new approach to crusher cavity design was made, resulting in the development of liners for specific operations which showed: 1—maximum utilization, as high as 70 to 80 pct of original weight of metal, and 2— maximum capacity of unit during the greater portion of its life. It has been found that liners so designed for a given operation will show added economies in power consumption, maintenance, and general wear and tear on the crushing unit. Initial work in the so-called tailoring of crushing cavitles was begun on the tertiary or fine crushing units where as a rule reduction ratios were low, varying from 3 to 6. Parallel or sizing zones in the lower portion of the crushing cavity were too long, resulting in a tendency to pack. It was found that very little additional crushing was done in the parallel zone after the initial impact in that zone and that a relatively small amount of&apos; additional crushing was done by attrition, which required very careful feed control. A small amount of over-feeding would result in packing which not only consumed power but caused unnecessary liner wear as well. The illustrations which follow in this discussion will show only contours of crushing cavities, and for purposes of simplification the cavities will be considered only in their closed position. The first step, therefore. was to reduce the sizing zone to a minimum. This was done by removing the lower portion of the liner as shown in Fig. 1. The result of the change was a saving of 15 to 20 pct in liner cost, less power consumption, with no change in capacity. This change in design, while an improvement, did not go far enough. As wear took place, the change in the liner was not uniform throughout its entire length, resulting in a restriction of the feed opening and thereby loss of capacity. Furthermore, progressive wear of the liner had the effect of lengthening the parallel zone until finally the entire crushing cavity was all parallel zone, see Fig. 2. It is obvious from the reduced feed opening of the worn liner that the ability of the machine to receive material is lessened considerably. Furthermore, the long parallel zone with its worn, irregular profile did not operate at its highest efficiency. The first attempt to overcome this difficulty was carried out on a 5 1/2-ft crusher installed in a plant producing roofing granules. The material being crushed was a very hard graywacke and the crusher was closed-circuited with a screen having .232-in. slotted openings. A radical change in contour was developed, as illustrated in Fig. 3. Equal wear lines on both concave and mantle are designated 1, 2, 3, etc. The method of development of this contour is as follows: Since adjustment for wear is vertical, corresponding intersections of wear lines and vertical lines developed concave and mantle contours which maintained equal but lengthening wear surfaces in the parallel zone. The ideal contour, of course, is one in which the length of the parallel zone remains constant, but because of present foundry practice and heat treating characteristics this is impossible.

Jan 1, 1954

By Reaves. M. J.

The title of my talk, "What Happened to the Uranium Boom?" is old news. Certainly it is for this group. All of us that make our living in uranium know that the boom of the last half of the 1970&apos;s is over. U.S. production has been exceeding consumption by more than two to one. Mines and mills are closing and yellowcake prices have been dropping for over 20 months. The gloomy outlook for the industry in the near term has been well documented by soothsayers of various descriptions, your daily newspapers, and in the Nuexco Monthly Reports. I&apos;d like to attempt to describe the next upturn in the market (speculate, really) based upon the clues we&apos;re seeing now. In order to do that, I&apos;d first like to go over briefly, some of the market factors that contributed to the recent price drop and resultant production cutbacks, and then hypothesize on the way these factors are changing and will change. Market prices are greatly affected (maybe even entirely determined) by buyer perceptions. This is particularly true with uranium, because of the long lead times associated with nuclear plant construction and also with conventional mine/mill development. Before the price rise (say, 1975) utility uranium buyers believed that: 1) U.S. producers would have difficulty expanding to meet U.S. demand. 2) Australian and Canadian production was essential to avoid shortages in the early 1980&apos;s. 3) Uranlum prices would continue to rise as demand exceeded supply. 4) Enrichment capacity would become inadequate. It was thought necessary, therefore, to build enriched inventory in the early 1980&apos;s for use in the late 1980&apos;s. Artificially accelerated expansion of the uranium producer industry was necessary to accommodate anticipated enrichment demand. Current perceptions are largely the opposite. These are the beliefs that were held most of this year and late last year as prices dropped. 1) U.S. production is far in excess of domestic need. Contraction of the U.S. production lndustry is necessary. 2) Canadian and Australian supply is optional and not essential. Producers in those countries are expanding mainly by displacing higher cost production and not because they fill a void, 3) Prices may be essentially stable for some time. 4) Enriched uranium is in excess supply. That is 1981. 1982 is shaping up to look like this: 1) Prices will have bottomed out. (That is not Nuexco&apos;s opinion necessarily, by the way, but it is my opinion.) 2) There will still be substantial utility inventories, but fewer spot sales. 3) Canadian and perhaps Australian sellers will have made substantial sales in the U.S. and will be aggressively seeking more. 4) U.S. production will have been dramatically curtailed. U.S. utilities that wish to con- tract long term will have difficulty in finding domestic sellers. Concern will develop about the availability of U.S. production capability. Virtually all long term con- tracts signed will be with non-U.S. sellers. 5) An awareness will begin to develop among U.S. buyers that we are approaching a period of dependence upon foreign uranium (which will be true). The history of the uranium market has been one of dramatic changes and overreaction to those changes. The rapid price rise of a few years ago generated excess U.S. production capacity and the rapid price drop of the last two years will almost certainly result in too little capacity. It will soon be difficult for U.S. buyers to buy domestic material except on the spot market. The question is, "will they care?" The lack of demand, of course, is the underlying reason for the current poor health of the uranium industry. In 1972, 1973 and 1974 collectively, there were 105 nuclear reactors ordered in the U.S. That ordering rate was expected to continue and accelerate throughout this century. In 1975, 1976, 1977, 1978, 1979, and 1980 altogether, there were 56 more reactors cancelled than ordered. The net growth of our only customer since 1974 has been a negative 56. TO put this in perspective, if these 56 reactors were operating now it would more than double present U.S. uranium consumption. Underlying lack of demand is something that is simply not going to change in this decade. Time is going to be required. The NRC indicates that the maximum feasible number of new reactors that can be licensed each year is six. That would increase uranium consumption by only 10% per year. New reactors, if ordered tomorrow, would not generate new uranium demand until after 1990. Even so, United States&apos; consumption of uranium will rise from the 1980 level of 18 million pounds per year, to

Jan 1, 1982