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By W. G. Pfann

The simultaneous segregation of two solutes during the directional solidification of an ingot is treated mathematically on the basis of simplifying assumptions. Expressions are derived for the difference in concentration of two solutes, and for the location and concentration gradient of a pn barrier formed in a semiconductor by the segregation of a donor and an acceptor. THE problem of normal segregation of a single solute during the freezing of an alloy has been treated mathematically by a number of investigators. Gulliver' showed that coring increases the quantity of eutectic above that to be expected at equilibrium, for a system having limited solid solubility and, on the basis of simplifying assumptions, calculated the fraction of eutectic to be expected. Scheuer2 expressed composition of solid solution in terms of a distribution coefficient and the fraction solidified and compared experiment with calculation for the systems A1-Cu, Al-Zn, Cu-Sn, Cu-Zn. Hayes and Chipman,3 in a detailed study of segregation in a low carbon, rimming steel ingot, calculated distribution coefficients for a number of solutes in iron, compared calculated and experimental segregation curves, and discussed the effects of process variables such as rate of solidification and stirring. In the present paper a mathematical analysis is made of the simultaneous segregation of two solutes during the orderly freezing of a solid solution system, with particular emphasis on the difference in solute concentrations. Although the analysis is quite general and can be applied to the segregation of minor elements in alloys, it is directed in particular at the solidification of a semiconductor containing a donor and an acceptor. Normal segregation has unique aspects in a semiconductor, because of the ways in which donors and acceptors affect the electrical properties. The difference between two solute concentrations becomes of importance, as does also the gradient of the difference where the difference goes through zero, this being the concentration gradient of excess carriers at a pn barrier. A primary object of this paper is to extend the mathematical treatment of segregation to include these newer aspects which are of particular significance for semiconductors. One property of interest is the electrical conduc- tivity, which arises from the presence of donors 'or acceptors in solid solution. The conductivity may be either n-type or p-type depending on whether donors or acceptors, respectively, are in atomic excess. For both germanium and silicon, elements of Group V of the Periodic System, such as P, As, and Sb, are donors and elements of Group 111, as B, Al, In, and Ga, are acceptors.4-6 If a donor or acceptor is present alone in solid solution, the conductivity is proportional to its concentration." If both a donor and an acceptor are present, then the conductivity is proportional to the difference in their atomic concentrations. If the donor and acceptor segregate at different rates then a pn barrier in certain circumstances may form at some point in the ingot. Accordingly, equations are derived and illustrated which express the effect of segregation on: 1—the concentration of a single solute with a discussion of the assumptions; 2—the difference between two solute concentrations and means for minimizing its variation in an ingot; and 3—the location and concentration gradient of a pn barrier. The analysis is applicable to processes in which the entire charge is melted and then progressively frozen from one end. The method in which an ingot is solidified in a crucible7 and that in which a solidifying rod is pulled from the melt8 both fall into this category. Segregation of One Solute If a cylinder of molten alloy is caused to freeze slowly from one end, a normal segregation of solutes will usually occur, producing a lengthwise concentration gradient in the ingot. Depending on whether a solute raises or lowers the melting point of the solvent, it will become concentrated in the first or last regions, respectively, to freeze. If it is assumed that freezing is such that there is no diffusion of solute in the solid, complete diffusion in the liquid, and that k, the distribution coefficient, defined as the ratio of solute concentration in the just-freezing solid to that in the liquid, is constant, then the

Jan 1, 1953

By W. A. Hockings, M. E. Volin, A. L. Mular

Batch grinding tests at short times were made in a laboratory rod mill with 10 x 14 mesh quartzite in corn syrup-water mixtures of varying viscosity. The weight fraction broken and size modulus were found to be independent of viscosity up to 20 cp, but at higher viscosities breakage of the feed decreased while the size modulus increased. The mechanisms of the effect of viscosity are discussed on the basis of particle dynamics. The effect of viscosity of the suspending medium on grinding has not been accorded much attention, although both wet and dry grinding are used in bene-ficiation processes and the viscosities of water and air differ greatly. schweyerl investigated the rates of grinding of quartzite in a pebble mill with air, water and glycerol as the suspending media and found the rate in terms of new surface developed per thousand revolutions of the mill to be constant and dependent on viscosity up to 20,000 rev, but to decrease and become independent of viscosity for longer grinding times. Based on considerations of the drag forces exerted on suspended particles and on the grinding media under turbulent and laminar flow conditions, viscosity can be expected to inhibit the rate of grinding in a given system as it changes the flow conditions from turbulent to laminar. The objective of this study was to determine the effect of viscosity of the suspending fluid in the batch grinding of a homogeneous feed of uniform size for short residence times, a region of more practical interest than the long times investigated by Schweyer. In actual grinding operations, the viscosity of the fluid does not change, but the consistency (apparent viscosity) of the pulp increases with additions of fines. In this study the consistency of the pulp was not measured because it was thought that the grinding times were too short to alter the apparent viscosity appreciably.* *Minus 200 mesh quartz at 65% solids has an apparent viscosity of about 25 cp as measured by a simple consistometer. Personal communication from D. F. Kelsall to A. L. Mular. For the purposes of this study, the effect of viscosity on grinding can be shown sufficiently well on the basis of the cumulative weight fraction finer than the feed size at any time, and the size modulus, ku, of the finer than feed sizes. The parameter, ku, is obtained from a form of the Gaudin-Schuhmann equation. METHOD AND MATERIAL The grinding tests were accomplished in a laboratory rod mill 10-1/2 in. long and 8 in. bore with a 20-lb rod charge consisting of two 1-in., eight 3/4-in., eight 1/2-in., and eight 1/4-in. diam rods. The mill speed was 43.2 rpm. Charges of 400 g 10 x 14 mesh Wisconsin quartzite** were ground for times of 60, **Courtesy of Minnesota Mining and Mfg. Co. 120, 180 and 240 sec in 500 cc of fluid made up of corn syrup and water in measured proportions. The temperature of the pulp was measured immediately upon completion of grinding, and the size distribution of the quartzite was determined by a wash-wet-dry screening technique. Corn syrup was chosen because of its high viscosity and ideal viscous behavior, and also because its density is not greatly different from that of water. The viscosity of each fluid mixture was measured with an Ostwald viscometer at 25 C. and a correction was made for the temperature of the pulp according to tabulated values for sucrose solutions. The density differences were so small that they probably did not significantly affect breakage. RESULTS AND DISCUSSION The conditions of the grinding tests, computed viscosities, weight fractions finer than the feed size and values of a and ku are listed in Table I. The values of a and ku were taken from the linear portions of the log-log plots of cumulative weight fraction finer vs size for the various grinding times. The plots for tests in fluids of average viscosity 8.6 cp are shown in Fig. 1. In general all of the sets of curves were linear throughout most of the size

Jan 1, 1965

By T. H. Alden

A correlation has been found in rock-salt structure single crystals between the latent hardening, measured by the direct stress activation of oblique slip systems, and the stress-strain behavior in simple compression. Materials with high latent hardening, like LiF, strain-harden at a low rate (Stage I) even when severely constrained. KCl, in contrast, shows low latent hardening and a tendency to strain-harden at a high rate (Stage 11). This correlation suggests that oblique slip is essential for Stage II hardening of these materials. THE role of secondary slip in the strain hardening of metal single crystals is a topic of lively controversy. On the one hand are theories in which secondary dislocations participate directly in Stage II hardening in the fcc metals, for example through the production of sessile dislocations,1 forest intersections, or jog formation. Much of the experimental evidence on which these theories are based has been reviewed by Clarebrough and Hargreaves.~ On the other hand, a recent theory5 denies that secondary slip has an essential role in Stage II hardening or in the transition from Stage I to Stage 11. In the latter view, Stage I is not terminated by an increase in the activity of secondary systems but by the exhaustion of undeformed material.6 The experiments reported in this paper will not resolve this controversy since the materials being studied are cubic ionic crystals rather than metals. However, the results do show in an unusual way a direct connection between "secondary" (nonortho-gonal or oblique) slip and strain hardening in these materials. Specifically, a correlation has been found between two independently measured properties, first the latent hardening of oblique (110)(1i0) slip systems as measured by direct stress activation of these systems, and second the stress-strain behavior at small strains. From prior work, it was known that in most cubi-cally oriented rock-salt structure crystals, two orthogonal slip systems operate and exclude the other equally stressed pair, oblique to the first pair.7'8 This observation apparently indicates that a significant interference exists between slip on oblique (110) planes and a relatively small interference between orthogonal (110) planes. The present experiments were begun with the intent of obtaining a quantitative measure of this difference by means of a study of latent hardening in these crystals. I) EXPERIMENTAL METHODS The experiments were basically of two types, first the determination of stress-strain curves by compression along a single (100) axis, and second the measurement of latent hardening by compressive prestrain along one cube axis followed by the determination of the yield stress in a second (latent) cube direction. All tests were done at room temperature in an Instron machine by compression between lapped, parallel steel faces. Three specimen shapes were used. For long crystals (nominal dimensions, 1/8 in. square by 1/2 in. long) the ends were lubricated with an oil-graphite mixture. Superior results with short crystals (about 1/8 in. cube) were obtained using 0.003-in. teflon film.' Thin crystals (1/4 in. square by 3/32 in.) were used for latent-hardening measurements and similar results were obtained with either lubricant. Test specimens were cleaved from Harshaw single crystals which had been irradiated to a dose of lo8 roentgen using a cobalt-60 source. The irradiation raises the yield stress and tends to prevent plastic deformation during sample preparation.10 Prior to testing, the irradiation hardening was removed by an anneal at 400°C. Ideal compression specimens have flat, parallel faces. In short specimens particularly, satisfactory results demand a close approximation to this ideal. In the present work, cleaved surfaces were often used directly as compression faces. The degree of success using this method depends on two factors: 1) the smoothness of cleavage faces, and 2) the extent to which the crystal is deformed or crushed by the chisel during the cutting of a long crystal into short pieces. Unfortunately, only one material of those studied, LiF, was completely satisfactory. NaF, NaC1, KC1, and KBr behaved less well so that

Jan 1, 1964

By L. R. Plitt, E. O. Lilge

Tests carried out with both kaolin and silica slurries show that flocculants of the polyacrylamide type can be used to improve the thickening performance of hydrocyclones. This thickening improvement demonstrates that contrary to previously held theories, flocs can be formed which are capable of resisting the shear forces in a hydrocyclone. For the 1.25-in.-diam cyclone used, optimum thickening occurs when the flocculant solution is injected into the slurry stream at or near the feed inlet. Hydrocyclones offer many distinct advantages over gravity thickeners. These advantages include simplicity, low initial and operating costs, small space requirements, and flexibility of operation. In spite of these advantages hydrocyclones have not been widely used as thickeners. The main reason for their lack of application is that hydrocyclones are unable to efficiently remove semicolloidal particles (less than 5 microns) from the suspending solution. In gravity thickeners, the fine particles can be induced to form particle aggregates, or flocs, which have the settling characteristics of large particles. In the hydrocyclone, however, it was always assumed that the existence of shear would prevent the formation of flocs.1-3 Thus, if no floc structure is retained, the thickening hydrocyclone must be designed so that its separation size is below the size of the smallest particle to be recovered. To obtain a very small separation size requires the formation of very high centrifugal forces, which necessitates the use of small-diameter cyclones. Small hydrocyclones have, in turn, very low throughput capacities which render them impractical for many industrial thickening applications. Thus, if the effects of flocculation cannot be utilized, the usefulness of hydrocyclones as thickeners remains limited to pulps which contain no very fine particles. It is well established that most substances acquire a surface electric charge when brought into contact with an aqueous medium. The repulsive interactions between similarly charged particles act to prevent flocculation. One method of flocculating a dispersion is to neutralize the repulsive surface charges by the addition of an electrolyte. The reduction of the electrostatic surface charge (Zeta potential) then permits the universal van der Waals attractive forces to operate between the atoms of the various particles and form particle aggregates. The lime additions used by thickener operators promotes flocculation by this mechanism. A second method of flocculating a dispersion is by the addition of long-chain macromolecules. In this case flocculation is brought about by a bridging mechanism in which the molecules are adsorbed with part of their length on two or more particles, thus forming a molecular bridge between the particles.4,5 The molecules also form bridges between themselves when a single particle is bonded to several polymer molecules. The type of bonding between the flocculant molecule and the particle may be hydrogen bonding, chemical bonding, or electrolytic attraction.6 The flour and glue which are used as thickener additives are believed to promote flocculation in this manner. In the past decade synthetic long-chain polymers with extremely high flocculating capabilities have been developed. The flocs formed by these new polymeric flocculants are larger and more shear-resistant than those formed by the presence of electrolytes.7 The advent of these flocculants raises the question: Are the flocs formed by these synthetic polymers stable enough to resist the liquid shearing forces in a hydrocyclone? The investigations reported in this paper were carried out in order to provide some answers to this question. EXPERIMENTAL WORK For the bulk of the test work a 5% slurry of commercially available kaolin with an average particle size of 5 microns was used. An initial evaluation of the available flocculants was carried out to determine which flocculant formed the most shear-resistant flocs. A combination of the techniques used by Healy7 and Booth8 was used for this purpose. This initial study revealed that the neutral high-molecular weight polyacrylamides produced the most shear-resistant flocs. One of these flocculants, Separan MGL*, was selected and then used for all the hydrocyclone tests. The flocculant was dissolved in water and added to the hydrocyclone as a dilute solution.

Jan 1, 1968

By Michael Hoch, Walter C. Wyder

The Cr-Ni system was investigated between 900" and 1400°C and 45 to 100 wt pct Cr. The Cr-Fe system was studied between 1200" and 1385°C and 70 to 100 wt pct Cr. Powdered alloy compacts were produced from high-purity chromium, nickel, and iron poulders. The compacts were sintered in an argon atmosphere and then machined into small, 0.030-in. diam cylindrical specimens. These were then heated by induction in the high-temperature X-ray diJfractwn camem under a helium atmosphere and irradiated with copper Ka radiation. From the results of the high-temperature X-ray diffraction patterns it can be concluded that chromium exists only in the bcc form, and that no eutectoid reaction occurs in the Cr-Ni system in the temperature interval 900" to 1400°C. The X-ray diffraction patterns are in agreement with the Cr-Ni phase diagram of Bechtoldt and Vacher, and Williams. It is possible that chromium undergoes one or more allotropic transformations between room temperature and its melting point. Most of the evidence was gathered from the study of the chromium-rich ends of the Cr-Ni and Cr-Fe binary systems. All the investigations rely heavily on indirect methods: thermal analysis, electrical resistivity, and micro-graphic inspection of quenched samples. In the present work the chromium-rich side of the Cr-Ni and Cr-Fe binary systems is studied, using high-temperature X-ray diffraction techniques. Thus the coexistent structures can be observed directly at temperature. PREVIOUS INVESTIGATIONS ~ansenl shows two possible Cr-Ni phase diagrams 1) a simple eutectic [Liquid =a-Cr(bcc) + y-Ni(fcc)], 2) a eutectic [Liquid+ P-Cr(fcc) + y-Ni(fcc)] and euctectoid [p-Cr(fcc) ==a-Cr(bcc) + yNi(fcc)]. The latter is based on the work of Grant and co-workers.2 Stein and rant'" placed the eutectoid composition at 1215°C and 68 wt pct Cr; their diagram is shown in Fig. l. Similarly, Sully3 also discusses the two proposed diagrams. Price and Grant,4 working on an isothermal section of the Cr-Ni- Fe ternary diagram at 1300°C, made no mention of a ß-chromium phase (fcc). The ß-chromium structure was also reported by Misencik 5 in the Cr-Nb(Cb) system. Williams 6 studied the Cr-Ni system using precipitation techniques. His work included the chromium and nickel solvus lines below 1250°C. He reported no ß structure nor any eutectoid reaction. The solvus lines which he produced were very similar to those of Jette, et al 7 below 1000°C. He concluded that Grant and coworkers2 had misinterpreted their data, and that effects which they had reported were actually due to the rapid and extensive precipitation of the nickel-rich phase. Bechtoldt and vacher8 used sintered powdered alloy compacts in an attempt to find the ß phase. They used metallographic and room-temperature X-ray diffraction techniques and also failed to detect the fcc chromium phase. They attributed the low slope of the chromium solvus at approximately 1150°C as the probable cause of the abundant precipitation obtained. They also stated that the precipitation was the probable cause for the abrupt discontinuities in the thermal analysis and electrical resistivity data which led to the conclusion that a eutectoid reaction existed. Fig. 1 also shows their diagram. Grigor'ev and coworkers9 investigated the polymorphic changes of chromium in the Cr-Ni phase diagram. Using standard microstructural and thermal analysis techniques, they published a phase diagram which contained five polymorphic forms of pure chromium and four eutectoid reactions. They stated that the room-temperature bcc chromium transformed to a fcc structure at 930°C, to bcc at 1300°C, to hcp at 1650oC, and then finally to bcc at 1830°C. The eutectoid reactions were placed at 850°, 960o, 1140°, and 1220°C. Also to be noted was the fact that the uppermost phase, the bcc above 1830°C, was different from the upper phase of Grant and coworkers,2 the fcc above 1840°C. Their eutectoid reactions, temperatures and compositions fall

Jan 1, 1963

By F. W. Archibald

The American Smelting and Refining Co. has standardized its copper converting practice to attain a maximum unit blister production with a minimum of refractory consumption by careful location of the tuyeres and by applying magnetite coatings on the hard-burned magnesite brick linings. THE American Smelting and Refining Co. operates four primary copper smelters in the United States with a total of 17 Peirce-Smith type converters; 15 of them are 13 ft in diameter by 30 ft long, and two are smaller. Some details of operations vary with locale; however, fundamentals of design, operation, and maintenance are common to all plants. All converter shells are l-in. thick except for one new converter with riding rings on the ends which has a shell thickness of 1 1/2 in. More tuyeres can be installed with rings on the ends and hence more air can be used. Welded construction is replacing riveted. Minor shell repairs are made after each campaign. Principal causes of complete shell replacement are warpage and cracking resulting from localized over-heating. A 13x30 ft shell is being replaced after 34 years of operation and a total production of approximately 750,000 tons of blister. Converters are driven by 80 hp DC motors through company-designed worm gear reducers. Rotation is 0.38 rpm which permits the skimmer to spot the converter quite accurately for skimming slag. At three of the plants, protection against unscheduled air or power failures is afforded by the installation of emergency drives, consisting of auxiliary air motors or storage batteries. In order to avoid excessive splash out of the converters, the converter mouths are located as far back on the shells as existing flue facilities will permit. At one plant, the back of the mouth is only 13" to the rear of the vertical center line of the converter,. whereas it is 28" at another plant. Newly-lined mouth areas vary from 36 to 44 sq ft with effective operating areas about 25 pct less. It is important to keep the converter mouths as clean as possible. Dirty mouths create back pressures in the converters and as a consequence the tuyere air volumes are reduced. Mouths are generally cleaned by bumping with an empty ladle. Small mouth-cleaning rams have been used but unless extreme care is exercised the brickwork may be damaged. After considerable experimentation, the plants standardized tuyere elevations at 4 to 4% in. below horizontal center line at the shell with a downward pitch of about 13/16 in. per ft of length. Tuyeres are spaced at 6 in. centers except at the riding rings where there are no tuyeres. With this tuyere location, several of the plants now freeze magnetite slag in the bottoms, fronts, and backs up to the bottom of the tuyeres to control the internal shape of the converter. This has the effect of improving the agitation and mixing so that there is a marked increase in converting speed besides affording protection to the brick lining. Currently, the trend is to increase tuyere diameters from 1% to 2 in. to increase the air flow. At present, all converters are hand-punched but one converter is being equipped with a set of mechanical tuyere punchers. Rods for punching are % in. hexagonal smelter bar upset to ll/s in. and rods for cleaning tuyeres are upset to about 1% in., or larger, depending upon the tuyere diameter. Two of the plants use pneumatic reamers for cleaning the tuyeres between charges to minimize disturbing the coating on the inside of the refractory lining. Most of the puncher's platforms are pneumatically or hydraulically mounted so that a convenient punching position can be maintained regardless of tuyere position. For normal operations, tuyere air pressures vary from 15 to 13.5 psi, although some cycles such as magnetiting require pressures down to 8 psi. Air requirements vary from an average of 25,000 cfm on the newer installations down to 12,000 cfm on the older ones. Converter hoods are designed to protect the punchers from sparks, splash or hood accretions as well as to prevent the escape of objectionable

Jan 1, 1955

By J. R. Hauber, N. R. Borch

A study uras made on the creep behavior of cast and extruded SR grade beryllium. It is shown that, for stresses below about 1000 psi in the temperature range 760" to 85o° c, the creep behatior is nearly exactly described by the Nabarro-Herring mechanism. The activation energy is apparently that for self-diffusion, 42 2 kcal per mole, below 1000 psi, but it rises to 88.6' kcal per mole at higher stresses. The slress exponent is 4.5 at the higher stresses. Tertiary creep in this material is clearly related to void formation apparently caused by grain boundary sliding. BERYLLIUM is becoming an increasingly important technological material. A search of the literature has revealed a lack of fundamental studies on the creep of beryllium. This investigation was therefore undertaken to gain insight into the creep behavior of this material. EXPERIMENTAL PROCEDURE Tensile creep samples were prepared from cast and extruded SR grade beryllium. The vendor's chemical analysis of the beryllium tested is shown in Table I. The test specimens were machined as shown in Fig. 1 from i -in.-diam rods. The machined creep specimens were annealed to remove surface damage and to establish a variation in grain size. The heat treatments and their resulting grain diameters are shown in Table 11. The average grain diameters were determined by the intercept method. True average grain diameters were estimated by multiplying the measured average grain diameters by 1.5.' The creep tests were performed at temperatures from 700" to 850°C in a vacuum of 105 Torr or better in a tantalum-element resistance furnace. Loads were applied by an Instron testing machine such that the stress was held constant to within 20 psi. The test temperature was measured by thermocouples on the sample. With one exception the deviation from the desired test temperature was 2"C, and in that case the deviation was 4"C. Elongations were measured by an extensometer within the vacuum chamber which was fastened to the creep specimens at the grooves in the grip ends, as shown in Fig. 1. The precision of measurement of elongation was 1 X loe4 in. The creep tests were begun only after thermal equilibrium had been established in the sample and the extensometer to insure that there was no strain rate component due to transient thermal effects. Two kinds of creep experiments were performed. First, at constant grain size, the effects of varying stress and temperature were studied. In the second set of experiments, the temperature was held constant and the grain size was varied. The activation energy for creep was determined by varying the temperature at constant stress, as described by orn, during the first set of experiments. The variable grain size experiments revealed that creep at low stress apparently occurred by the abarro-errin' mechanism. In all of the creep tests, the stress was held constant only until sufficient strain had occurred to accurately determine the creep rate. The stress was then raised to a new value and the new creep rate determined. This process was reported until tertiary creep occurred. In this manner several data points were obtained from each specimen. The assumption was made that the structure was not changing appreciably between the incremental stress levels. This was verified by reducing stresses to previously tested levels and comparing the creep rates with the creep rates obtained at the lower strains. The re-producibility was within experimental error over strains on the order of 1 pct. EXPERIMENTAL RESULTS A typical series of creep tests is shown in Fig. 2. Primary creep was not observed in any test. Transient creep, which we define as creep rates that are nonlinear with time, was not observed for any change in stress except where tertiary creep occurred. The absence of both primary and transient creep has been previously reported for hot-pressed powder beryllium.= The data for the creep behavior at constant grain size are summarized in Fig. 3. The data show two distinctly different stress dependencies. At stresses below about 1000 psi, in the equation:

Jan 1, 1969

By Gerald G. Griswold, James O. Greenslade, Cherie Tilley, Richard Reseigh

INTRODUCTION The Harrison Western Corporation, a leading Denver based mine contracting and engineering concern, is presently engaged in sinking two 1,006 m (3,300 ft) shafts for the Phillips Uranium Corporation at their Nose Rock Project, approximately 13 miles northeast of the small community of Crownpoint in McKinley County, New Mexico. The Nose Rock Project is the first attempt by the Phillips Uranium Corporation to tap the deep uranium reserves in what has become known as the Grants Mineral Belt. (See Figure 1) Project Description Phillips Uranium Corporation's plan for the large 2700 metric ton per day (2950 tons/day) mining facility calls for a series of deep access and ventilation shafts ranging from 4.27 m (14 ft) to 5.49 m (18 ft) in diameter to approximate depths of 1,006 m (3,300 ft). The initial pair of shafts consists of one production shaft and one ventilation shaft separated by a distance of 91 m (300 ft). The interbedded layers of sedimentary sandstones and shales to be penetrated by the shafts contain several major water producing aquifers, the deepest being the mineralized zone called the Westwater Canyon Member of the Morrison Formation. A series of temporary and permanent water pumping stations is planned. Generally, the temporary stations are located above major aquifers to facilitate water removal while sinking through the aquifer and the permanent stations constitute what, in the final mode, will be the mine dewatering system. In addition, Phillips Uranium Corporation has In- stalled and is maintaining a system of depressurization wells that temporarily pump the major aquifers and considerably reduce the water inflows during shaft construction. The major aquifers are also chemically grouted prior to sinking. Site work for the project was initiated in the fall of 1976. Full scale shaft sinking commenced in November of 1977 on the 4.88 m (16 ft) diameter ventilation shaft and on the 5.49 m (18 ft) production shaft by another contractor. Harrison Western Corporation began work on the project on November 4, 1979 wlth the production shaft at a depth of 633 m (2,076 ft) and the ventilation shaft at a depth of 474 m (1,554 ft). This paper will address only the portion of shaft sinking completed by Harrison Western. Geology and Hydrology The Nose Rock Project is located on the Chaco Slope in the southern extreme of the San Juan Basin in northwest New Mexico. The southern San Juan Basin is generally bound by the Defiance Uplift to the west, the Zuni Uplift to the south and the Nacimiento Uplift to the east. The Grants Mineral Belt occupies most of the southern portion of the San Juan Basin and this project is located on the northern extreme of the Grants Mineral Belt. The San Juan Basin is comprised of sedimentary rock of continental, marginal-marine and marine origin, that dip northward from the Zuni Uplift and Chaco Slope into the interior of the San Juan Basin. (See Figure 2) Major Formations The major geologic formations to be penetrated range from mudstone and shales to siltstones and sandstones. The sandstones are highly productive aquifers which, under static conditions, would flow artesian. Water temperatures in the aquifers are high and therefore are a force to be dealt with. Temperatures range from 18ºC (65OF) in the upper aquifers to 48ºC (118º'F) in the lower. The mudstones are generally bentonitlc. (See Figure 2) GALLUP SANDSTONE: The Gallup Sandstone is the first major regressive wedge in the San Juan Basin of the Cretaceous era and at this project is about 35 m (115 ft) thick. It is medium grained and prior to depressurization carried a hydrostatic water pressure of over 72.5 kg per cm2 (1,031 psi) which 1s artesian. Compressive strength ranges from 334.7 kg per cm2 (4,760 psi) to 421.8 kg per cm2 (6,000 psi). Water temperature is approximately 30°C (86°F).

Jan 1, 1982

By Dick Whittington, W. R. Taylor

GENERAL In mid-1974, a representative of ARCO Petroleum Company walked into our Austin offices and asked for a permit for ARCO's first Clay West Mine site. This was the first in situ uranium mining permit issued in the United States. That initial permit, issued in January 1975, was for three acres. The four years since have been characterized by growth and change. Today there are 16 permits approved for approximately 1,540 production acres issued to five companies at eight sites in four counties. There are approximately seven additional permit applications being processed or on the verge of being submitted for an estimated 2,000 additional acres of production. As a rough gauge of the financial scope of this activity, at the typical 40 production wells per acre and an estimated $2,000/well, operators hale installed or committed $122 million for production wells. This does not account for the exploration and development wells installed to delineate the ore or the cost of processing facilities for extracting the uranium. HISTORY OF URANIUM MINING IN TEXAS Information I have concerning early in situ uranium mining activities is "sketchy" but the apparent first on-site test of in situ uranium mining was conducted between 1967 and 1971 at the Dueterstat site, north of Yorktown in Gonzales County, by City Service. Others ran tests at the Bruni site in Webb County and the Burns and Clay West sites in Live Oak County in the mid-70's. During this period, Texas Water Quality Board personnel in the central and district offices maintained a general surveillance of these various test activities. Regulation of in situ uranium mining was formalized with the issuance of a permit in January 1975 with the advent of ARCO's initial production scale (3 acre) effort in the Clay West area at the Moser mine site. Since 1975, the accelerating rate of mining and exploration activity is noticeable. There were 16 exploratory rigs operating early in 1977. This year, the rig count is averaging 46--a 287% increase. HISTORY OF LEGISLATION Paralleling this mining activity was state and federal legislation which subjected in situ mining to environmental regulation. The following is a brief chronology of the legislation that is directly or indirectly related to uranium mining. As most of you know, disposal wells are an integral part of most in situ uranium mines operating in Texas. They are used both during production and during aquifer restoration following production. The wells are regulated by the Texas Injection Well Act, enacted in 1961 by the Texas Legislature. In 1967, the Water Quality Act established the Texas Water Quality Board, and provided for the regulation of water quality by the so-called permit system. In 1969, the Solid Waste Act was enacted by the Texas Legislature. The legislation provides for control of wastes from manufacturing, mining, and agriculture. This Act regulated uranium surface mining activities until 1975 when the Texas Surface and Mining Reclamation Act placed responsibility with the Railroad Commission for uranium open-pit mining and surface mining of coal and lignite. In 1972, the Federal Water Pollution Control Act (Public Law 92-500) was passed. This legislation forms the legal base for the NPDES (National Pollutant Discharge Elimination System) and the subsequent point source effluent guidelines and standards. The November 6, 1975 issue of the Federal Register published interim final rules for Best Practical Treatment levels for effluent discharges from ore mining and dressing operations. Litigation was immediately initiated by eleven companies against these proposed rules, and they are currently being reconsidered for reissuance in 1979. In 1974, the Federal Safe Drinking Water Act (Public Law 93-523) was enacted. A part of this legislation is the Underground Injection Congrol Program. The regulations implementing this program have undergone various public hearings and it is expected that they will be published in the Federal Register before the end of 1978. In 1975, the Texas Surface Mining and Reclamation Act (Senate Bill 55), providing for the Railroad Commission's authority to require reclamation of surface mines, was passed. In 1977, an amendment to Senate Bill 55 was introduced that proposed to place regulation of in situ mining of coal, lignite, and

Jan 1, 1979

By W. S. Row

This mine is operated at 4000 to 4500 tons daily through a single shaft, with one rock hoist and one senice hoist. Latest shaft construction is concrete with wooden dividers. Economics of drifters and air-leg drills are compared, as well as costs of shrinkage and sub-level stoping. Economy of large haulage equipment and underground crushing is shown. THE property of Kerr-Addison Gold Mines is located in the Larder Lake district of Ontario about 3 miles from the Quebec boundary on the highway between Kirkland Lake and Noranda. It is roughly 320 miles due north of Toronto and 365 miles north of Buffalo, N. Y. The property was staked in 1906 and after several development efforts finally came into continuous production at 500 tons per day in 1937. In 1939 the daily tonnage -was increased to 1200 and in 1941 to 2100 tons. At the end of the war, because of the shortage of labor, tonnage was down to 1100 tons per day, rising to 2200 in February 1947. A further plant expansion inaugurated in 1946 was completed by December 1948, bringing the capacity of the mine and mill to a production rate of 4000 tons per day. Current production, with 880 men employed, is 4400 tons per day. Changes in mining methods and equipment, required by the recently completed expansion program, have yielded interesting comparative results, some of which are described in this paper. Hoisting of ore and waste from the mine, as well as all service facilities for handling men and supplies underground, are provided for in a single vertical five-compartment shaft. Ore and waste are hoisted in 12½-ton skips in balance by a 14-ft diam hoist with drums 115 in. wide, grooved for 2?-in. wire ropes. This hoist, with a total rope pull of 85,000 lb, was designed to operate at a speed of 2600 ft per min to a depth of 4000 ft, hoisting 15 tons of ore in each skip. It is amplidyne-controlled and powered with dual drive dc motors of 2250-hp each, through flexible couplings to two pinion shafts, one on each side of the main gear. Each motor has a peak load rating of 4500-hp at point of greatest duty. Direct current power to the hoist motors is supplied from a motor generator set consisting of a 5000-hp synchronous motor driving two 1750-kw dc generators. The loading pockets used so far are at depths of 1500 and 2725 ft respectively. Consequently the present hoisting speed is 2000 ft per min and the skips capacity only 12½ tons. Now that the shaft has been deepened the new pockets at 3934 ft will be increasingly used so that the speed and the skip size will be increased up to original specifications as required. Some difficulty in meeting the required hoisting cycle is expected because of the shape of the skips. As now in use the cross-sectional dimensions of the inside of the skip are 4 ft 6 in. x 3 ft 8 in. To hold 121/2 tons, therefore, they are 14 ft 10 in. deep. Since the skips are the conventional overturning or Kim-berley type, considerable hoisting time is lost in retardation in entering the headframe dump and in acceleration when leaving. It is expected that to obtain the specified tonnage from this hoist when the skip size is increased to 15 tons it may be necessary to resort to bottom dump skips. This type of skip could reduce considerably the present excessive acceleration and retardation times. Analyses of the skip-hoisting operation are made monthly, and every effort is made to reduce controllable delays. For a nine-month period in 1951 such an analysis shows that the hoist was in operation 92.5 pct of the available time, which was allotted as shown in Table I. Overall hoisting costs, cage and skip, for the year 1951, averaged $0.168 per ton of ore milled. The mine is serviced entirely by means of a single cage, capacity 35 men or 15,700 lb, operating in con-

Jan 1, 1954

By J. F. Smith, J. E. Davison

A value for the enthalpy of formation of z2 of -3.14 i 0.21 kcal per g-atom has been measured by the technique of acid solution calorimetry. This result is in quite good agreement with two earlier determinations by tin solution calorimetry and by direct reaction caloriinetry, and averaging of values determined from the three independent calorimetric techniques gives enhanced precision and accuracy with AHh8 (CaMgZ) = - 3.15 i 0.05 kcal per g-atom. For comparison with experimental data, values for the enthalpies of formation of CaMgz, SrMgz, and BaMgz of -9.8, -7.9, and -2.8 kcal per g-atom were estimated from a calculation based on the LVigizer-Seitz approximation as modified by Raimes for polyvalent elements. While complete quantitative accord between these calculated talues and available experimental data is lacking, nonetheless numerical accord is better than might be expected and, more importantly, parallel numerical trends are observed between experimental and calculated vnlues. WITHIN the past decade the enthalpy of formation of CaMg, has been determined a) from measurement of magnesium vapor pressures over binary Ca-Mg alloys,' b) by solution calorimetry with liquid tin as the solvent,' c) from measurement of hydrogen vapor pressures over ternary alloys of calcium, magnesium, and hydrogen,3 and d) by direct reaction alorimetr. The value from tin solution calorimetry is the most precise and is probably the most reliable, and this value is within the quoted uncertainties of the other three experimental results. The overall agreement among the four independent investigations is quite good, particularly so when the diversity of techniques is noted. On the basis of this agreement, CaMgz was chosen as a test material to evaluate the operation of a newly constructed apparatus for the determination of enthalpies of formation of intermetallic phases by acid solution calorimetry. This was believed to be a severe test because of the high chemical reactivity of both calcium and magnesium which reactivity presumably accounts for the fact that an early determination5 of the enthalpies of formation of Ca-Mg alloys by acid solution calorimetry yielded values significantly more negative than the four recent determinations. EXPERIMENTAL APPARATUS AND MATERIALS Experimental Apparatus. The enthalpy of formation of CaMg, was determined by measuring the difference between the heat evolved when dissolving the metallic compound and the heat evolved when dissolving equivalent amounts of unreacted metallic elements in hydro- chloric acid. This was done differentially with an apparatus consisting of twin calorimeters which were constructed to be as nearly identical as possible. The advantage of differential calorimetry is that systematic errors arising from the individual calorimeter design tend to cancel. A schematic representation of the apparatus is shown in Fig. 1. A dead air space around both calorimeters was provided by a large, thermally insulated jacket. Each calorimeter consisted of a 2-liter Dewar flask which was completely enclosed in a copper container. Each Dewar contained 1600 g of 2.5hr HCl to act as the solvent, and thermal effects resulting from solvent evaporation were minimized by covering the acid with 50 g of mineral oil. There was no detectable reaction between the acid and the mineral oil. Equivalent amounts of mechanical energy were added to the calorimeters through twin stirring rods which were driven at the same rpm by a single motor with the intent of the stirring being to maintain thermal equilibrium throughout the solvent. To calibrate the heat capacities of the calorimeters, known amounts of electrical energy could be added by passing measured voltages and currents for known times through submerged heaters, approximately 20 ohms, which were wound noninductively from Manganin wire. A 6-v storage battery was used as a power source, and a dummy heater was used as an exercise circuit to allow the battery to stabilize at a constant electromotive force before energizing one or the other of the calorimetric heaters. A type K-2 potentiometer was used to measure the potential drop across an energized heater while the current was determined from the potential drop across an external standard resistor. Times of energization were measured with an electric timer, and the electrical energy supplied to a heater

Jan 1, 1969

By D. L. Sikarskie, B. Paul

A theory is presented for the static penetration of a single rigid wedge into brittle material. The material considered is one which exhibits both crushing and chipping phases in the penetration process. If the wedge angle and three parameters are specified, the theory predicts forces and associated penetrations during both the crushing and chipping phases. For certain ranges of the parameters agreement with the limited experimental data available is promising, except for the initial phase of the penetration process where refinements on the proposed theory are required. The theory also predicts that for certain values of the wedge angle and other known parameters, the chipping process does not occur and penetration is due entirely to crushing. When viewed in detail, the drilling of rock by percussive means involves, among other things, system dynamics, actuating forces, dynamic stress levels and the actual penetration mechanism of the bit into rock. If rock drills are to be significantly improved, a thorough understanding of the entire system would be highly desirable. In this paper, one aspect of the system, namely the mechanism of penetration of the bit, will be studied in detail. It has been found1 that for the velocities encountered in percussive drilling (of the order of 20 fps) a static analysis adequately describes the penetration process, at least for some rocks. Hence, we will only be concerned with describing analytically the static penetration of a single wedge shaped tool. It will further be assumed that the wedge is long enough to permit a two-dimensional analysis. Numerous authors have studied the static penetration of a wedge into rock. The following papers give some of this work and provide additional references to other work. Cheatham2,3 has assumed the rock to behave plastically and has obtained force-penetration equations for both Coulomb-Mohr and parabolic yield criteria. Evans and Murrell4 have studied the penetration of two types of coal and have found equations relating the penetration characteristic (P/dSc) to wedge angle for the various strength coals tested. race' attempted to find a correlation between hardness as determined by indenting the material and other mechanical properties and concluded that the results of such a test are generally inconclusive. His paper however contains a very extensive bibliography on the indenting of many different materials. Gnirk6 also has a fairly complete literature review on the static penetration of rock, of which he makes use in his indexing studies. A wide range of behavior is found in the wedge penetration of different rocks under different external conditions. For example, a rock that is essentially elastic-brittle at standard pressure may become elastic-plastic at a high confining pressure.7 It has also been observed4. " that some rocks will merely be crushed and indented by a wedge, whereas others will crack and form chips, furthermore the existence or non-existence of chips depends in great measure on the geometry of the indentor, type of rock and the depth of penetration. Hence, to attempt a theory which embraces all possible behavior is not practical at present. We, therefore, confine our attention to predicting the force-penetration characteristic and volume removal behavior for a type of rock which exhibits both crushing and chipping phases in the penetration process. Such behavior is characteristic of the harder rocks such as granites and represents a more difficult problem than the behavior of softer rocks such as coal and certain sandstones. In this preliminary study an attempt will be made to describe only the essential features of this complex penetration process. A qualitative description of these essential features is obtained with the aid of Fig. 1.1, where a wedge of vertex angle 28 is shown at some intermediate stage of the penetration process. As the wedge advances, the rock is fragmented (i.e. crushed) in some local region surrounding the wedge, the shape of this region being unknown. Simultaneous with the fragmentation in this local region, essentially elastic stresses are assumed to be building up in the surrounding rock. When a certain penetration level, di+1, is reached, the stresses along some surface are sufficient to cause failure and a chip is thus formed. The process now repeats, i.e., a crushing phase followed by the formation of a chip.

Jan 1, 1965

By D. Turnbull, J. H. Hollomon

THERE is a large body of evidence'" indicating that solidification during the liquid-solid transition is usually induced by heterogeneities present in the liquid. By dispersing liquid metals into small droplets, the impurities responsible for catalyzing solidification are isolated within a small number of these droplets. The effect of the foreign body therefore is restricted to a single drop by this technique. Thus upon cooling below the melting temperature, solidification is initiated by homogeneous nucleation in the majority of the droplets that do not contain impurities. In the case of solidification of liquid metals, the activation energy for nucleation is so great that its rate changes by orders of magnitude for a change in temperature of only several degrees centigrade.' Effectively homogeneous nucleation occurs at a critical temperature upon continuous cooling. Thus by microscopic observation of single particles during cooling, a temperature at which the rate of homogeneous nucleation becomes sensible can be determined.3 since at the temperatures at which nucleation occurs in the absence of impurities the rate of crystal growth is extremely rapid, the temperature at which the entire particle solidifies is very nearly the temperature at which the nucleation of the solidification occurs. Thus for liquids that freeze at high temperatures the onset of nucleation can be established by simply observing the temperature at which the marked heat evolution and increase in brightness of the particle occur. For liquids that freeze at lower temperatures the onset of nucleation can be determined by a rumpling and change in shape of the particle resulting from its solidification. The microscopic technique for observing the solidification of small particles has already been described." In earlier papers the nucleation of solidification of pure metals 5,6 and of alloy systems7 showing complete liquid and solid solubility have been described. In the present paper, the observations are extended to a simple eutectic system (Pb-Sn) where the possibility of the formation of two solid phases exists. Metals for the investigation were obtained from the American Smelting and Refining Co. in the form of pure lead and pure tin, 99.8 and 99.9 pct purity, respectively. An ingot of each of the pure metals was made into shot by heating the metals at a temperature about 50 °C in excess of the melting point and pouring the liquid slowly into a container of water at 15°C. Samples of the shotted pure metals were weighed out to make alloys containing 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, and 90 atomic pct Pb. Samples of each alloy were then melted in separate beakers. Each melt was poured through a pyrex funnel into a cylindrical mold (% in. ID). The casting solidified in 10 to 20 sec. The inside of the mold as well as the funnel through which the metal was poured were coated with graphite to eliminate adherence of the metal. Analyses were performed on some of the compositions and are given in Table I. The compositions also were checked for these samples and for those that were not analyzed by determining the spread between the liquidus and the solidus upon melting the small metal particles. These measurements agreed as well with the nominal compositions as the analyses listed above. Results The results of the supercooling experiments for the several alloys are summarized in Table II and plotted on the constitution diagram in Fig. 1. Data for the pure lead and pure tin were taken from earlier investigations. The values for the maximum supercooling of the several alloys are the average of several determinations on a number of drops of each alloy. The maximum value in any determination was within about 2 pct of the average. For the alloys containing from 20 to 60 atomic pct Sn, inclusive, two marked changes of the surface structure were observed upon cooling. At the higher temperature, after the first appearance of the solid phase it continued to grow slowly at a constant temperature and then stopped. At the lower temperature the alteration of surface structure was abrupt. For the alloys containing from 70 to 95 atomic pct Sn, inclusive, an abrupt change in surface structure was observed at a single critical temperature.

Jan 1, 1952

By Y. Kondo, S. Yamazaki, Z. Asaki

Thermal deco7nposition of Pyrite particles in a fluidized bed with inert gas stream was studied. Assuming that heat transfer from the surroundings to the fluidized particles controls the overall decomposition rate, rate equations for the batch process and for the continuous process were derived. In the batch experiment, a linear rate equation satisfies the experimental results and the overall heat transfer coefficient calculated from the rate constant agrees fairly well with that obtained by Leva.l1 For the continuous process, two rate equations were derived, one on the assumption of complete mixing of particles and another on the upward piston flow of particles in a fluidized bed. The former holds for a bed containing a higher fraction of decomposed pyrite realized at lower feeding rates. The latter can be applied for a bed at higher feeding rates. Thus, segregation of particles in the fluidized bed was indicated at higher feeding rates. Bed temperatures also correspond to these conditions. ThERMAL decomposition of pyrite may be represented by Eq. [I]. The pressure of diatomic sulfur gas reaches 1 atm at about 690°C. The thermodynamics,' kinetics,2'3 composition, and properties3-5 of decomposed products of such a reaction have been studied. Pyrite is a very common sul-fide mineral and is often accompanied with other sul-fides. It is of basic interest in nonferrous metallurgy to clarify the behavior of pyrite in the pyrometallur-gical processes of sulfide minerals of metals such as copper, lead, zinc, nickel, and so forth. Interest in this reaction increased recently because of possible elimination of arsenic from pyrite in processing highly purified iron oxide pellets. Producing elemental sulfur from pyrite, instead of sulfuric acid, also aroused interest in this reaction. It is indicated that the thermal decomposition of solid particles, such as calcium carbonate, proceeds through three major sequential steps: heat transfer, interfacial chemical reaction, and mass transfer.637 It is known that the decomposed product of pyrite is very porous2, 3 and the diatomic sulfur gas evolved can easily escape through this layer of decomposed product. It depends upon the circumstances, therefore, whether the heat transfer to the interface within particles or the chemical reaction at the interface determines the overall decomposition rate. The enthalpy change in the decomposition of pyrite is about 33 kcal per mole FeS2 which is comparable to that of calcium carbonate. The decomposition of calcium car- bonate becomes more and more dependent on the rate of transport of heat when reaction temperature increases, such as occurs in a fluidized bed.6'7 It is reasonable to presume, therefore, that the thermal decomposition of pyrite, an endothermic process, carried out in a fluidized bed may be analyzed according to the heat transfer controlling model. This work intends, first, to propose a mathematical model that determines the overall rate in a fluidized bed for the decomposition process and, second, to investigate a few characteristics of the fluidized bed based upon the experimental results obtained. KINETICS OF THERMAL DECOMPOSITION IN A FLUIDIZED BED It is intended in this section to obtain rate equations for thermal decomposition of pyrite in a fluidized bed by assuming that the overall rate is determined by heat transfer from the surroundings to the particles. Both batch and continuous processes are considered. 1) Batch Process. To obtain the rate equation in the batch process, the following two additional assumptions are made. First, the temperature of preheated inert gas, tg, blown into the fluidized bed is assumed to be the same as the temperature of the fluidized bed, tf. Thus, no heat exchange occurs between the gas and particles in the bed and only the heat transfer from the reactor wall kept at tw to the particles is to be considered. Second, the decomposition is assumed to start at the outer surface of the particles and to proceed toward the center. At any given time during decomposition, undecomposed pyrite remains in the tori at a temperature: td. The decomposed shell is composed of FeS1+x whose outer surface is at tp Diatomic sulfur gas evolving at the interface is heated to tf during its escape through the decomposed shell. This is illustrated in Fig. 1. With the above-mentioned assumptions of heat transfer, we have:

Jan 1, 1969

By J. E. Warren, J. H. Hartsock

Because of the extensive utilization of hydraulic fracturing for the stimulation of low-productivity wells, the two related problems of fracture design and evaluation have become economically significant and, as a consequence, helve motivated this investigation. The producing characteristics of horizontally fractured wells were studied to determine the fracture configuration that should be employed as the basis for the design of the treatment and to develop a method that can be used to establish the degree to which the design objectives have been achieved. The equations which describe the steady-state flow of a single-phase fluid into, and through. a finite-capacity fracture were solved numerically for an idealized reservoir-fracture model. The numerical results were used to obtain an apparent skin effect for each combination of the parameters considered. Based on the computed results, subject to the limitcitions implied by the assumptions that were made, the following general conclusions were drawn. 1. For a radius of drainage at least four times us large as the radius of the fracture, an apparent skin effect that is independent of the radius of drainage can be calculated. 2. The productivity of the hydraulically fractured system, relative to that of the unfructured well, can be determined from the apparent skin effect and can be used to establish design objectives. 3. In the evaluation of a fracture job, it is not Possible to determine both the radius of the fracture and its flow capacity uniquely from the apparent skin effect; an independent determination of one of the quantities is necessary. lNTRODUCTION Although hydraulic fracturing has been employed as a method for stimulating the productivity of literally hundreds of thousands of wells during the past 10 years, it is only in the last few years that improvements in fracture design1-6 and fracturing technique' have combined to increase the probability of obtaining a successful treatment to such an extent that the mechanics of the method may be considered to be standardized. From an economic point of view, however, two related questions must be satisfactorily answered before hydraulic fracturing can be used in the most profitable manner. The two questions are the following. I. For a particular well in a given formation, what are the optimum design specifications for the fracture treatment? 2. Have the design objectives been achieved by the fracture treatment? The significance of these questions has been recoguized, and some attempts to obtain answers have been made. Howard, et al,8 endeavored to determine the optimum treatment, based on maximizing profits, for any given formation; unfortunately, this work was based on a crude method for approximating the productivity of a well. Carter and Tracy9 utilized the same approximation to study the effect of fracturing on the behavior of a well producing by virtue of a solution-gas drive. Electrolytic models were used by van Poollen10 to investigate the variation in productivity due to fracturing; however, only a limited number of results were presented. Later, from the same model results, van Poollen, et al,11 attempted to justify an approximate expression for determining the productivity of a fractured well. It is quite apparent that there is a definite lack of the practical information necessary for specifying the optimum fracture configuration to be considered for design purposes. The only detailed attempt to develop a procedure for evaluating the result of a given fracture treatment appears to be that of van Dam and Horner.12 These authors described a technique for analyzing pressure build-down data, obtained immediately after fracturing, to determine the final fracture volume, the final fracture porosity, the fracture area, the fracture thickness and the in situ fluid loss of the fracturing fluid. While this approach should be useful whenever acceptable pressure measurements are available, it does not yield a value for the flow capacity of the fracture. Since the problems of fracture design and evaluation are inversely related, it should be sufficient to study the effect of the fracture configuration on the performance of a well. The primary objective of this investigation is to evolve a technique for computing the desired solutions. The secondary objective is to analyze these computed results in order to prescribe a method for evaluating fracture treatments. Because this study is exploratory in nature, its scope

By Margaret V. Doyle, R. W. Powers

INTERNAL friction measurements, carried out as functions of temperature, have been used extensively to obtain data on the mobility of interstitial impurities in the Group V metals, vanadium, colum-bium, and tantalum. For a given frequency of vibration, the internal friction peaks at a temperature which depends principally on the particular metal and interstitial impurity. Relaxation times and corresponding activation energies are determined from a knowledge of such peak temperatures for various vibration frequencies. These experimentally determined relaxation times are related to the average jump frequencies of the interstitial impurity atoms using the model of Snoek1 and can be related to macroscopic diffusion coefficients as shown by Polder.2 In these Group V elements, the impurity whose diffusion rate has been the hardest to pin down by the internal friction technique has been carbon. The experimental difficulties associated with carbon in these metals were not evident in the earliest investigation carried out by Ke on tantalum.3 The carbon peak was thought to occur near 140°C at 1 cps on the basis of the enhancement of the height of this peak measured on specimens which had been coated with colloidal carbon and heated in vacuo at 1200°C. Presumably on the basis of similar evidence, Wert identified a peak also near 140°C at 1 cps in columbium with the diffusion of carbon in that element." Later, the difficulties of admitting carbon into these metals without simultaneously introducing oxygen were pointed out by Ang and Wert- nd by Marx, Baker, and Sivertsen.6 The latter suggested that the peaks attributed to carbon in tantalum and columbium might arise from the presence of traces of oxygen, adventitiously absorbed during the carburization. Such suspicion was confirmed, at least in tantalum, when it was found possible to prepare C-Ta specimens without contamination by oxygen. Specimens sci prepared, aitnough high in carbon content, gave no evidence of a damping peak near 140°C.7 Recently, the authors were able to Show that carbon diffuses in tantalum at a rate only slightly slower than that for nitrogen.8 At 1 cps, the carbon peak lies at 34g °C, only a few degrees above the nitrogen peak at 341 °C. However, the two could be distinguished by a different stability with respect to aging at 400 °C and by a different dependence of peak height on solute concentration. On the basis of this experience with tantalum, it appeared worthwhile to search also for a carbon peak in columbium in the vicinity of the nitrogen peak." In this report, the location of the carbon peak in columbium is made known and its position relative to the nitrogen peak is compared with the authors' previous findings in tantalum. In addition, a second source of internal friction seen only in specimens of very high purity is discussed. Columbium was obtained from the Fansteel Metallurgical Corp. as either 30 or 40 mil diam stock. The manufacturer gives the following analysis as typical of this material: 99.4 pct minimum Cb, 0.10 pct maximum C, 0.5 pct Ta, 0.04 pct Ti, 0.02 pct maximum Si, and 0.01 pct maximum Fe. Wires 13 in. long were degassed near 2200°C for 4 to 16 hr in an ultimate vacuum better than 2.10" mm Hg in an apparatus described previously.8 This treatment reduced the oxygen and nitrogen damping peaks observed in the as-received material to less than 0.0001 in Q-1 above background. The latter value varied somewhat from specimen to specimen in the range 0.0004 to 0.0008, depending chiefly on the wire diameter and the frequency of vibration. The high temperature evacuation left the specimen in a rather soft condition, the Vhn being reduced to 40 from a value near 121 in the as-received conGi~iur~. The gram size was about the diameter of the specimen. After outgassing, specimens were loaded with carbon by absorption of such hydracarbons as methane or ethylene. Carbon was also added to a few speclrnens by heating them at

Jan 1, 1958

By R. L. Perrine

A stability theory is developed for miscible liquid-liquid displacement within a porous medium. In the usual case considered, a high-density high-viscosity "oil" is displaced downdip by a low-density low-viscosity "solvent'! Perturbation methods are used to find the conditions under which the spreading mechanism changes from the stable dispersion process to unstable viscous fingering. We find that instability is conditional, that there is a dependence on the shape of a disturbance leading to a"diameter" effect and that very difficult experimental scaling problems may result. A useful consequence is the definition of a minimum "slug size" for stable miscible displacement. This should make possible optimum use of the solvent process for oil recovery. The results may apply to many situations in which one fluid displaces another of somewhat different fluid properties within a porous medium. INTRODUCTION The process of miscible liquid-liquid displacement looked very favorable when it first received serious consideration as a means to increase petroleum recovery. Some early laboratory results were interpreted to mean that only a small "slug" of solvent was needed, perhaps 2 to 3 per cent of a hydrocarbon pore volume. This "slug" could recover the oil in an entire reservoir provided the fluids remained miscible.1,2 Only a slow growth of the "mixing zone", or gradual transition from oil to solvent, should occur. This would follow naturally from mixing by a dispersion mechanism such as that described by Scheidegger.3 And, indeed, laboratory cores have shown this kind of behavior provided solvent viscosity was at least as great as that of the oi1.2,4-6 The same kind of behavior has also been observed with solvent viscosity lower than that of the oil after the distance traversed became large. Not all laboratory results have been this favorable, however.7-9 Mixing zone growth may become proportional to the distance traveled rather than the square root of this quantity. Such behavior accompanies high rates in short systems of large diameter, provided the viscosity ratio is adverse. If this more rapid spreading were to persist in a reservoir, the solvent requirement for miscible "slug" displacement could exceed 30 per cent of a pore volume. There is considerable economic importance in the difference between 3 and 30 per cent solvent. A 1ogical conclusion is that two different kinds of flow behavior are possible, with each kind leading to a different result. One kind gives efficient displacement, the other does not. In the efficient case, the solvent bank spreads out only by the mechanism we have termed dispersion. Under these conditions, displacement is as near piston-like as possible. In the second kind of flow, found only with adverse viscosity ratios, viscous fingering occurs. That is, permeability variations cause a small finger of low-viscosity solvent-rich fluid to move ahead of its average position within the mixing zone. This creates a path of low resistance to flow, and an even greater amount of solvent-rich fluid follows. Thus, the process is autocatalytic. Once started, the fingering mechanism rapidly becomes dominant. The question to be answered is this. Under what conditions will each of these two different kinds of flow occur? In particular, what conditions denote the transition from dispersion to viscous fingering as the solvent spreading mechanism? The answer may tell us whether or not the desirable, near piston-like miscible displacement process is practical. An answer to this problem can be obtained from theory by the use of perturbation methods. The procedure is as follows. We first formulate a mathematical representation of the system. Then a small disturbance (or perturbation) in solvent concentration profile is introduced and observed to see what happens. Unstable flow is indicated when a small disturbance will grow larger. This will lead to eventual viscous fingering. If on the other hand the disturbance dies out, the displacement is stable. In this latter case, with dispersion as the spreading mechanism, near piston-like displacement is possible. Thus, this paper presents the development of a stability theory for miscible liquid-liquid displace-

By R. L. Mauger, P. E. Damon, B. J. Giletti

This report includes the lead isotopic dating of a suite of galenas from Arizona and an application of the K-Ar method to the dating of a Laramide porphyry copper deposit, the Silver Bell Mining District. The lead isotopic data supports prior age assignments based upon geologic inference. The Silver Bell study illustrates the necessity of correlative geologic and petrographic investigations for the interpretation of the results of potassium-argon dating. LEAD ISOTOPIC DATING OF GALENAS FROM ARIZONA ORE DEPOSITS A group of galenas from Arizona ore deposits have been analyzed for lead isotope ratios. The results were used to calculate model ages by the. method of Russell, Stanton and Farquhar,l6 in which the age is calculated directly from the Pb206/Pb207 ratio. The use of Pb206/Pb207 ratios eliminates the errors inherent in measuring the abundance of Pb204. The Holmes-Houtermanns model is the other model commonly used for calculating model ages. Both models assume that any lead sample is composed of primeval and radiogenic components and the calculated age is the time at which the lead was extracted from its source area. Using the Holmes-Houtermanns model, a lead is ordinary if its isotopic ratios lie on an isochron. The growth curve that passes through the experimental point determines the U/Pb ratio in the source area. The RSF model assumes the source area for conformable leads is the mantle, that this has a uniform U/Pb ratio, and thus all ordinary leads must lie on a single growth curve, having a mantle U/Pb ratio. The definition of an ordinary lead differs between the models, and differences in age arise mainly from the assumptions made to evaluate parameters in the model equations. These assumptions depend on the hypothesis chosen to explain ore genesis. In the RSF Model, the Pb206/Pb207 ratio is derived as a function of time. The equation contains three undetermined parameters which are evaluated by assuming three known points lie on the curve. These are the following: 1) Primeval lead from the Canyon Diablo and Henbury meteorites, 2) Modern conformable leads which lie on Patterson's zero isochron, 3) Lead from the Bathurst, New Brunswick base metal deposits. The Bathurst deposits are postulated to be examples of "conformable base metal deposits", as proposed by Stanton.l9 A conformable deposit has a particular genetic history and, as a result, the orebody conforms to stratigraphic layering in the host rock. The metals are brought to the surface in volcanic rocks which originated in the mantle. Weathering products of these rocks, including sulfur and metals, accumulate in areas undergoing sedimentation. The formation of sulfide ion in the sediments by the action of sulfate reducing bacteria causes fixation of iron as pyrite. If the pyrite becomes concentrated in favorable stratigraphic horizons, any base metal deposit eventually formed by replacement of pyrite will have a strata bound character. Compaction and expulsion of pore water from the sediments at depth result in upward mobility of solutions containing soluble base metal chlorides. The strata with high pyrite content act as chemical traps for the base metal ions and replacement occurs. An important result of this general evolutionary model is that, if complete separation of lead and parent isotopes occurred during accumulation of the sediments, any ore deposit formed solely of metals derived from those sedimentary rocks will contain "conformable" lead. This would be true even if the actual ore deposit were formed at a later date by some epigenetic process. In this case, mineralization would be controlled by local conditions, and need not conform to stratigraphic layering. Also, any ore deposit containing lead derived from a mantle or mantle-like source, even though not conformable in Stanton's sense, will fall on the curve for conformable ores and thus give a meaningful model age. Model ages for Arizona galena deposits are listed in Table 1. Fig. 1 is a location map. Jerome-Humbolt District: Galenas from the United Verde mine at Jerome and the Iron King mine at Humbolt give model ages of 1750 m.y. and 1640 m.y. respectively. Both deposits are massive sulfide bodies in a host rock of older Precambrian

Jan 1, 1965

By R. H. Edsal, G. Horvay

The transient one-dimensional heat-conduction equation is solved for two semi-infinite media, at different initial temperatures, brought into (poor) thermal contact. It is shown that the two interface temperatures gradually approach the well-known, instantaneously assumed, common interface temperature of the case of zero contact resistance. The present analysis, with slight modifications, may be used in fair approximation also for the class of problems involving a change of phase. One particular application of the boundary value problem solved in this paper concerns the determination of the temerature distribution in metal castings and molds.P This problem has been treated extensively by analytical methods (see e.g., the literature listed in Refs. 1 to 4) by electrical analogs (see e.g., Refs. 11 to 14) and also by experimental methods (see the literature listed in Refs. 4, 5), but prior to the work of Pellini and Ruddle the experimental results were rather unreliable. Immediate motivation for the work described in this paper was to better understand the results of Pellini,' which are typified by the curves of Fig. 1. Pellini cast 20-in. high, 7-in. sq steel ingots into cast-iron molds of various thicknesses. He measured the temperatures at mid-height, at a number of stations in the casting and the mold, and obtained the cooling curves shown in Fig. 1. The most conspicuous thing about Fig. 1 is the large temperature discontinuity at the interface between casting and mold, due presumably to the shrinking away of the casting from the wall and the attendant creation of an airgap, as the casting cools. Such a contact resistance slows down the anticipated freezing rate; an analytical prediction of this is of much interest in foundry practice. The determination of the effect of contact resistance in the presence of a change of phase will be dealt with, by an approximate method, in a separate paper.' In the present paper the much simpler problem is considered in which there is contact resistance but no change of phase. This problem frequently arises in the analysis of aircraft structures.+ It can initial temperature, and may be regarded as semi-infinite. We suppose the thermal properties in the two media to be time, temperature, and space independent; there are no sources or sinks within the media. In Fig. 2(a) we illustrate, schematically, the case of no contact resistance. The semi-infinite media "0" and "2:' initially at temperatures 8 (- m) and 8(+ -), respectively, are brought into contact at time t =0. A common interface temperature 8,i = is instantaneously established, and thereafter remains constant. Temperature curves are drawn for three instants of time. When there is contact resistance between the two media, the temperature equalization occurs as sketched in Fig. 2(b). Fig. 2(c) illustrates a temperature curve, using the dimension-less notation Barber-Weiner-Boley6 have stated the equations [23a, b] given below, which govern the heat transfer in the two media, and solved them for a rather complicated special case. In their example both media "O" and "2" are finite, are insulated at their far ends, and there is steady heat input into medium 2. In Eq. [27] we give the general solution of the most important special case, where the two media are semi-infinite and there are no sources or sinks. In this case the results may be stated in simple closed form. In Fig. 3, to be discussed in the next section, we illustrate the variation of the interface temperature when steel at 2760" is brought into contact with iron at 100". This example, if we disregard the effect of the heat of fusion, is comparable to Pellini's experimental results, Fig. 1. (Unfortunately, however, experimental determination of the interface temperatures was difficult to carry out, and hence Fig. 1 is not very accurate near the interface.) In Figs. 4 and 5 of the following section, we similarly compare Pellini's sandcasting tests with analytical results for the case where steel at 2760" is brought into contact with sand at 100". It will be pointed out that, insofar as the interface temperatures are concerned, heat of fusion has a minor effect, and so the present approximation, with small modifications, may be

Jan 1, 1961

By P. J. Spencer, J. N. Pratt

The vapor pressure of manganese over liquid Mn-Sn alloys has been determined by a high-temperature torsion-effusion technique. Alloys containing from 8 to 100 at. pct Mn were investigated in the temperature range jrom 1280" to 1580" and the measured pressure values were used to calculate the partial and integral thermodynamic properties of the liquid alloys. The activities show small negative departures from ideality while the integral heats and excess entropies of mixing are asymmetric inform, changing from positive to negative with increasing manganese content. The possible contribution of various factors to the observed thermodynamic properties is discussed. COMPARATIVELY few thermodynamic data are available for manganese alloy systems.' Therefore, as part of a continuing program of studies of the thermodynamic properties of transition metal alloys, measurements have been made on various binary alloys involving this element. In recent publications,2~3 investigations of liquid Mn-Cu alloys and of the Mn-Au system in both solid and liquid states have been reported. For the first-mentioned system the work suggested that magnetic interactions may be responsible for the observed form of the thermodynamic properties, while in the second the influence of the electrochemical factor appears to be dominant. The present paper describes a similar study of liquid Mn-Sn alloys. Again the thermodynamic properties have been obtained from vapor pressure measurements made by use of a high-temperature torsion-effusion technique.4 A detailed description of the apparatus and of the experimental procedures used in alloy preparation and pressure measurement may be found elsewhere.2'4 EXPERIMENTAL RESULTS Sixteen alloys, ranging in composition from 8 to 100 at. pct Mn, were prepared from spectroscopically standardized manganese of 99.99 pct purity and tin of 99.999 pct purity, both supplied by Johnson-Matthey and Co., Ltd. One-gram samples of the alloys were obtained by carefully weighing appropriate amounts of the pure components into an effusion cell; this was then suspended in the apparatus and the metals melted together in situ by heating under vacuum to approximately 1550°K. After allowing sufficient time for a homogeneous liquid alloy to be formed, vapor pressure measurements were commenced. These were determined as rapidly as possible at a series of steady temperatures within the range of interest. The duration of experimental runs on individual samples was kept sufficiently short to ensure insignificant varia- tion of alloy composition during investigation. After completing pressure measurements, the alloys were rapidly cooled and their compositions checked by weighing or chemical analysis. All experiments were conducted using effusion cells machined entirely from boron nitride. Measurements were made using a variety of cells with orifice areas ranging from 0.0032 to 0.0075 sq cm and lengths of the order of 0.04 cm; the usual effusion correction factors for orifice geometry and molecular distribution were calculated using Freeman and Searcy's equation5 and had values between 0.6 and 0.75 for the orifices employed here. The vapor pressures of manganese over the alloys were measured at approximately 20°K intervals in the temperature range 1280" to 1580°K. In view of the close approximation of the measured pressures to Clausius-Clapeyron behavior in the experimental temperature range, the data for each alloy have been expressed by equations of the form: logp(atm) =-A/T + B A least-squares computer treatment was applied to the vapor pressure values in order to obtain the coefficients A and B with their associated error. The resulting equations are listed in Table I, together with the equation for pure solid manganese obtained from a previous study.4 To minimize the effect of possible apparatus calibration errors, the activities and partial free energies of manganese in the alloys were calculated by initial reference to the latter equation, obtained from identical torsion-effusion measurements. The immediately resulting thermodynamic quantities, based on a solid manganese reference state, were then converted to refer to the more appropriate supercooled pure liquid manganese standard; tabulated values of the free energies of solid and liquid manganese from Hultgren et al.' were used for this purpose. Partial entropies of solution of manganese were calculated from the temperature coefficients of the free energies and partial heats from the Gibbs-Helmholtz relationship.

Jan 1, 1969