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By B. H. Caudle, A. B. Dyes

In a recent publication' it was shown that wells with a free surface in a homogeneous gravity-drainage reservoir have a hyperbolic decline with index n '. This paper reports efforts to extend this theory to practical field cases. As a first step in making the extension, a large number of lease production curves from gravity-drainage fields in the stripper stage were fitted with the general hyperbolic decline equation, q/q, = 1/(1 + y) y and n in each case being determined by statistical methods. It was found that this equation is reliable for decline curve extrapolation for periods up to at least 25 years. The resrilts obtained were disturbing in the sense that values for the index, n, were often smaller than one, which fact leads to the prediction that a well would produce all infinite amount of oil in infinite time. A theoretical investigation based on the results of the previous paper provides a suitable explanation for these low values of n. It suggests that these are obtained if production occurs from two or more layers of diflerent permeabilitv and thicktress or two lnyers having different skin effects. It is predicted that as the more permeable layers are exhausted, the index of decline, n, will rise from a value smaller than 2, to n = 2. A practical method is given for fitting the general hyperbolic decline Eq. 6 to production decline data. When this method is used, the index of decline observed in gravity-drainage reservoirs in the stripper stage when wing only data over early years 01 decline usually agrees quite closely with that determined using data over 25 years or more. This indicates that the hyperbolic decline equation is reliable for predicting behavior of such reservoirs. A method is also suggested for taking into account any changes in the value of the index INTRODUCTION As a result of both experimental work with models and theoretical deductions, it was recently concluded' that wells having a free surface in a homogeneous reservoir producing by pure gravity drainage should have a hyperbolic decline with n = 2. The present report details efforts to extend this work on ideal homogeneous reservoirs to actual field cases. It should be remembered that both the previous work and the present extension are based on the assumption that the reservoir is at very low pressure, and hence, nearly all the potential available for driving fluid to the well is the gravity head. Attempts to apply conclusions of this study to reservoirs which have considerable pressures supplementing the gravity drive may lead to difficulty. WELLS WITH NO FREE SURFACE In a dipping gravity-drainage reservoir such as that shown in Fig. 1, some of the down-dip wells have no free surface. The previous study' showed that the up-dip wells, which have a free surface, should follow Eq. 1. The following approximate analysis, of a type which was justified experimentally for up-dip wells in the work just mentioned, leads to results for the down-dip wells.

By G. W. Riley, D. E. Pickett

HINDERED SETTLING CONCENTRATION In the free settling of mineral particles in a liquid, the falling particles are at a distance from each other so that no particle is affected by its neighbor. In hindered settling, the concentration of particles is sufficiently high so that each particle is affected by its proximity to other particles in the suspension. Richards and Locke86 have described the hindered settling phenomenon as the condition “.. where particles of mixed sizes, shapes and densities in a crowded mass, yet free to move along themselves, are sorted in a rising current of water, the velocity of which is much less than the free-falling velocity of the particles but yet fast enough so the particles are in motion." This is the condition normally encountered in mineral con¬centration processes. The well known Newton equation for free settling of coarse (ap proximately +10-mesh, 1/16-in. or -- 2000-µm) spherical particles is:87 where v," is free settling velocity, cm/sec; p' is density of the fluid; p is density of the particle, g/cm3; d is particle diameter, cm; g is acceleration due to gravity, cm/sec2; and Q is coefficient of resistance, dimensionless, ~0.4. For the settling of fine spheres in water (approximately 150 mesh or 100 µm) the equation of Stokes pertains:87 where µ is viscosity of the fluid in poises and the other symbols have the same meaning as those in Eq. 1. For particles whose size lies between about 10 mesh (--2000 µm) and 150 mesh (100 µm), their settling velocity can be determined from experimental data. These data are available in convenient form in the text by Taggart88 based on the original work of Richards. Alternatively, a Reynolds number-coefficient of resistance plot may be used to determine the settling rate of such particles.87 The settling rate of spherical particles under hindered settling conditions can also be calculated from Eqs. I and 2 by replacing p', the density of the fluid, by p" the apparent density of the suspen¬sion. The concentration of particles in the fluid thus imparts an appar¬ent density to the composite fluid or suspension greater than that of the liquid alone, resulting in a buoyant effect on the larger particles. Particle shape affects the settling rate of both coarse and fine particles. The general effect is to reduce their settling velocities and the effect is greater for coarse particles and for those settling under hindered settling conditions than for fine particles or free settling ones. For two particles of differing densities but settling at the same velocity under Newtonian conditions, the ratio of their diameters from Eq. 1, called the free settling ratio is: where L signifies the lighter particle and H, the heavier particle. Under Stokesian conditions the exponent would be 0.5. For hindered settling conditions the fluid density p' is replaced by the apparent density of the suspension, p", to obtain a generalized equation for the hindered settling ratio: assuming both particles settle in approximately the same regime. The free settling ratio as given by Eq. 3 has been called by Taggart88 the "concentration criterion" and is used to predict the effectiveness of any gravity concentration process (see Introduction to this section). Based on Eqs. 3 and 4, if two particles of densities pH and p,, settle at the same velocity, the diameter of the lighter particle will be larger than that of the heavier particle. For example, in the case of galena (pH = 7.5) and quartz (pL = 2.65) settling in water (p =1.0) under free settling, Newtonian conditions 3.9. Thus, a quartz particle nearly four times as large as a galena particle will settle at the same velocity. Any quartz particle just slightly less than four times the diameter of the largest galena particle may be separated from it. Under hindered settling, Newtonian condi¬tions in a suspension where p" = 1.65, dL/dH = 5.85 or any quartz particle just slightly less than about six times the largest galena particle may be separated from it. Reference to Eq. 4 indicates that a superior separation between two minerals of differing densities is favored by: (1) coarse particles settling under Newtonian conditions, (2) a large difference in (pa - PL), and (3) separation under hindered settling conditions where p" is high. Of course, there are practical limits to increasing p" excessively because at very high percent solids suspen¬sion fluidity would be lost and the hindered settling separation process defeated. Examples of hindered settling separators are the Dorrco-Fahren¬wald sizer,89 the Rheolaveur box 90 the Spitzkasten,89 and the Willoughby washer.91 These devices make a mineral separation on the basis of both specific gravity and size and all of them are essentially obsolete except for the Dorrco-Fahrenwald sizer and similar devices which still find application for the removal of coarse particles from a much finer particle assemblage and for preconcentration ahead of shaking tables. However, nearly all gravity concentration processes (jigs, tables, flowing film concentrators, heavy media separators) and many sizing devices (sizing classifiers, clarifiers, thickeners, hydrosepa¬rators) make use of the hindered settling phenomenon during the separation of particles. JIGGING Introduction In jigging, a mixture of ore particles, supported on a perforated plate or screen in a layer or "bed" with a depth many times the thickness of the largest particle, is subjected to an alternating rising and falling (pulsating) flow of fluid with the objective of causing all

Jan 1, 1985

By S. Nikolic, O. O. Kehinde-Philllps, O. T. Djamgouz, D. H. Rousell

"A bulk mining method is employed at the Lockerby mine resulting in the formation of large muck-piles. If these muckpiles remain in the stopes for some time they may agglomerate to the extent that the muck cannot be removed by a scooptram. A laboratory investigation was undertaken with sulphide material from the mine in order to detemine the time that oxidation begins and the flowability of the material as a f unction of several factors. The laboratory results are applied to the conditions in the muck-piles.The time of the beginning of oxidation of the material decreases as the sulphide composition, water content and availability of air increases. Oxidation is retarded by the addition of a copper sulphate solution instead of water. The unconfined yield force (strength} of the material increases with an increase in the sulphide composition, water content and time. The material ceases to be free-flowing before there is visible evidence of oxidation and this suggests that oxidation actually begins earlier and that agglomeration is also due to the capillary action of water.Broken ore should be removed from the stope prior to the time a muck-pile ceases to be free -flowing-perhaps as early as two days f or high-grade ore and 5 days f or low-grade ore. In order to control dust, 1.4 weight per cent of a 5 per cent solution of copper sulphate should be added 10 the muck-pile rather than water. This inhibits oxidation and increases the time that a muck-pile remains free-flowing."

Jan 1, 1984

By J. A. Brown, F. P. Kerr, M. A. Archer

Extensive testwork on Global Atomic’s Dasa Project in Niger has been conducted at SGS Minerals laboratory in Lakefield, Ontario. Much of this testwork has focused on a two-stage counter-current leach as a means of improving leach efficiency and decreasing reagent consumption. The ore contains uranium mineralization requiring relatively high sulphuric acid concentrations during leaching to achieve acceptably high extractions. Excess free acidity in the leach solution may be utilized by recycling the high acid solution and contacting it with fresh ground ore. The resulting pregnant leach solution (PLS), now higher in uranium concentration and depleted in free acid, is forwarded on to uranium recovery by solvent extraction. The first stage residue proceeds to the second stage leach where fresh acid and oxidant are provided to leach the remaining uranium. This paper presents the results of the testwork conducted on both a Master Composite and Variability samples.

Jan 1, 2020

By B. Nowak

For sources with an iron-to-vanadium ratio of far above 1, it is proposed to leach in acid and to oxidize under autoclave conditions. During this oxidation process, it is experimentally shown that divalent iron contained in this solution will be oxidized to trivalent iron, whereas free acid contained will be consumed by this reaction. In case no acid is present or already fully consumed, a solid consisting of ferric compounds and an iron-vanadium-co-precipitate will form that can be filtered from the solution. If choosing the right reaction conditions, this filter cake has an iron-to-vanadium ratio of close to 1, whereas the liquid remainder is almost vanadium free. This precipitate, identified as FeVO4, 1.1 H2O, can be processed by conventional technologies such as caustic leaching, or probably salt roasting or reduction with aluminum, yielding common marketable products.

By Wilson Blake

The Bureau of Mines used a mathematical model based on the finite element method of stress analysis to calculate stresses and displacements surrounding an open pit mine in a gravity-loaded rock mass. Comparison of the finite element solution for a semicircular notch in a gravity-loaded plate with the theoretical solution for a semicircular notch in a plate under uniform compression parallel to the free boundary demonstrates the inapplicability of the latter method to openings at the free surface of a gravity-loaded medium. High stress concentrations are formed at irregularities along the boundary of an open pit in a gravity-loaded continuous competent rock; however, for this type of rock the magnitudes of the stresses are too low to be considered a major factor in open pit slope stability. High stress magnitudes will occur if, in addition to the gravity stress field, a large horizontal stress field exists.

Jan 1, 1967

By Batric Pesic

Recovery of gold from refractory ores was studied by pressure oxidation as the method of ore pretreatment followed by bromination of oxidized residues. Three different ores were examined, Au-Ag, Au-Ag-Te, and Au-silver free ore. Pyrite was the major host mineral for gold in these ores. The effect of pressure oxidation parameters (temperature, pressure of oxygen, time, and pulp density) on subsequent bromination under standard conditions was examined. Bromination of residues produced under standard pressure oxidation conditions was examined as a function of: temperature, bromine and sodium bromide concentration, and time. Recovery of gold on activated carbon, from the pulp after bromination, was studied too. Recovery of gold from silver containing ores was lower (87-91%) than the recovery of gold from silver free gold ore (97%). In each studied case, the presence of activated carbon in the pulp further increased the recovery of gold.

Jan 1, 1992

By Terry L. Muldoon

The Bureau of Mines conducted an investigation to quantify microphone response variations that could result when the microphone is worn by a worker, as with a personal noise dosimeter, and to suggest an optimum placement and orientation of the microphone for noise exposure measurements. Previous studies have shown no significant variations in a diffuse field. This investigation, therefore, was conducted in the free-field conditions of an anechoic chamber using an anthropometric dummy as a subject, and broad band noise as the acoustic stimulus. This investigation established that, in a free field, the wearer's body does significantly affect microphone response; the response variations are a function of azimuth, and location and orientation of the microphone. Results suggest that locating the microphone on top of the subject's shoulder, oriented parallel to the body axis, should yield data comparable to that obtained using a sound-level meter.

Jan 1, 1973

By M. R. Yenchek

The U.S. Bureau of Mines designed and constructed sensitive and coordination-free ground-fault relays (GFR's) for use on mine power systems. First, a list of GFR attributes for mine ac utilization applications was compiled. These practical guidelines specified design, construction, transient immunity, reliability, and operating criteria. The time-current characteristics of the ac and dc units, subsequently fabricated, were designed to be below the human electrocution threshold. The significant and highly variable capacitance of high-voltage distribution cables was found to preclude the sensing of ground currents in the milliampere range. However, the coordination-free system developed for high-voltage distribution should enhance safety by significantly decreasing response time to ground faults. Implementation of the sensitive GFR technology in the mining industry has the potential to eliminate the majority of injuries and nearly all the deaths resulting from contact with energized components.

Jan 1, 1990

By Wilbur I. Duvall

This report presents experimental data on crater formation in four rock types. From an analysis of these data a general theory of rock breakage by explosives is deduced. This theory accounts for most of the rock breakage and other phenomena that occur when a concentrated charge is detonated in a drill hole near a free surface. From instrumented crater tests and high-speed motion pictures of the explosions, various experimental checks on the deduced theory of rock breakage are made. The general mechanism of rock breakage by explosives as described in this report is outlined briefly below. The detonation of the explosive charge creates a high gas pressure in the charge hole, which in turn generates a compressive strain pulse in the surrounding rock. This compressive strain pulse travels outward in all directions from the charge hole. Near the charge hole the amplitude of this strain pulse is sufficient to cause crushing of the rock. However, as the strain pulse travels outward its amplitude decays rapidly until no further crushing of the rock is possible. The compressive strain pulse continues to travel outward until it is reflected by a free surface. Upon reflection the compressive strain pulse becomes a tensile strain pulse. As the strength of rock in tension is much less than in compression, the reflected tensile strain pulse is able to break the rock in tension, progressing from the free surface back toward the shot point. In other words, the rock is pulled apart, not pushed apart.

Jan 1, 1957

By Masaru Kato

The plated gold being used by the electronics industry can be broadly classified into two categories: soft gold and hard gold. Soft gold is used for circuit metallization and for bonding semiconductor chips, while hard gold is indispensable as the contact material on electrical connectors, electromechanical relays, and printed circuit boards. The traditional baths from which to plate soft gold as well as hard gold contain the cyanide complex, [Au(CN)2]-, as the source of gold, which liberates free cyanide ions during the plating. The free cyanide is not only highly toxic but also attacks photoresists used to delineate circuit patterns and bonding pads. For these reasons, non-cyanide baths are in use to plate soft gold, whereas hard gold can be plated only from cyanide baths at present. In this presentation, the current status of both electrolytic and electroless non-cyanide processes for plating soft gold will be reviewed.

Oct 1, 2003

By W. B. Hall, Joy D. Lewis

Mine-run ore is received at Vitro in gondola cars and fed directly to a Cedar Rapids impact crusher. Following screening, the undersize travels through a recently installed three-stage sampling plant where successive cuts are executed by conventional Geary-Jennings type cutters to produce a final sample of 1 lb per ton of raw ore fed. Crushed ore is transported to one of three storage silos or to stockpile, depending upon grade and type of amen- ability. This permits the blending of a mill feed with some degree of consistency. Final grinding is accomplished in one of two closed circuit ball mill-classifier systems allowing simultaneous processing of two basic types of ores. High acid consumers may be leached separately in the required environment. Part of the free acid remaining can then be utilized by an ore stream entering later whose component ores require much less free acid for leaching.

Jan 11, 1958

By Robert C. Emmett, Donald A. Dahlstrom

FOR many years gravitational classification has been employed as a basic tool in beneficiation of minerals and coal. While improvements have been made to increase efficiency and fields of application, the basic flow pattern has remained relatively unchanged in most gravitational classifiers. Feed slurry is introduced into a settling pool wherein the coarser solids settle against either an upward or horizontal fluid current, or a combination of both, and are withdrawn in a concentrated underflow stream. The finer solids below the classification point possess too low a settling velocity and thus are primarily swept out through a weir overflow by the bulk of the fluid. Because of its simplicity, efficiency, and low power and maintenance costs, gravitational classification finds a wide acceptance for separations in the range of 20 to 325 mesh. Two factors resulting from the basic flow pattern employed in gravitational classification present difficult problems for certain installations. If classification at 60 to 200 mesh of separation is desired, capacity in terms of gallons of overflow per minute per square foot of settling pool area must be low to allow required solids to settle to the underflow. If a thousand or more gal per min of feed slurry must be handled, either a very large classifier or a number of smaller units must be employed, taking up floor space and head room. Examples of this are the large classifiers, wetting tanks, or settling tanks used in the coal industry for recovery of process water from fine solids. Units as large as 50 or 60 ft in diam and 60 ft high, requiring substantial amounts of steel, are not uncommon. A second factor is the lack of self-regulation in gravitational classification. As overflow rate increases, mesh of separation increases correspond-ingly. This normally heightens difficulties of bene-ficiation. If a fine mesh of separation is required at varying feed rates, the problem is more than doubled in complexity. One of the primary advantages of gravitational classification is low power requirement. Gravity feeds or very low pressure heads are employed. However, fluid energy is still present in the inlet stream and provision must be made to dissipate it properly to obtain uniform upward or horizontal currents. Rather than waste this energy, it would be desirable to utilize it to secure a greater degree of self-regulation and simultaneously increase classification capacity per square foot of area. A free vortex could be realized by a tangential entry of feed, resulting in generation of centrifugal force to complement force of gravity in its action. With greater force it should be possible to gain finer separation at any overflow rate per square foot of settling pool area as compared with conventional gravitational classification. Furthermore, as feed rate increases, centrifugal force will also increase and at least partially offset faster currents sweeping solid particles to the overflow. A more stable classification point should result. The liquid-solid cyclone is the most common application of a free vortex in the beneficiation field.' Many previous papers have emphasized uniformity of flow pattern within the cyclone which is largely responsible for the sharp classification that can be obtained.'-4 If a free vortex can be maintained in a non-pressurized vessel with a free surface it may be possible to realize a third advantage of sharper classification. This open-top cyclone would then achieve a minimum energy loss comparable to that with conventional classifiers, and a mesh of separation coarser than 150 mesh, extending the range of application of the free vortex. This is not presently possible with ordinary cyclones. To test the applicability of the free vortex to gravitational classification, a 30-in. diameter open-top cyclone was constructed at Northwestern University. The cylindrical section was 30 in. high and the conical section included an angle of 60". The feed nozzle was a standard 4-in. pipe entering tan-gentially, with centerline 17 1/2 in. below the top of the cyclone. The conical section was flanged near

Jan 1, 1954

By J. C. Fisher

Nucleation theory is applied to martensite nucleation in substitutional iron alloys. Composition fluctuations are neglected, and a steady rate of nucleation is predicted for any composition and temperature. The maximum rate of nucleation (as a function of temperature) is shown to be measurable only for on extremely narrow composition range, being too great or too small outside this range. A number of experimental observations, including completely isothermal transformation in some alloys and composition-dependence of M. temperature in others, are compared with the calculated behavior. IN a previous report,¹ nucleation theory was applied to the formation of isothermal martensite in an Fe-Ni-Mn alloy. The experimental observations of Cech and Hollomon² were accounted for quantitatively. It now is of interest to examine the predictions of nucleation theory with respect to martensite transformation in substitutional iron alloys of other compositions. Since Fe-Ni alloys have received considerable attention, both as to their transformation kinetics and their free energies, they will be treated in detail, although the results apply with equal validity to other substitutional alloys. In substitutional alloys, where composition fluctuations can be neglected in volumes of critical nuclear size, the rate of nucleation of martensite in subcooled austenite is¹ n - Nv exp (—W*/kT) [I] where the free energy of formation of the critical size nucleus is W* = 8192 p (?² s³) [2] In the expressions for n and W*, the symbols have the following meanings: N is the number of atoms per unit volume; v, the atomic vibration frequency; 8, a function of the elastic constants of austenite and the shear angle of martensite; , the austenite/mar-tensite inter facial free energy; and ?fc is the free energy change per unit volume accompanying the transformation. Jones and Pumphrey² have determined the austenite to martensite free energy change as a function of nickel content and temperature for Fe-Ni alloys. Their expression is ?F = 2500 C + 1.25 (1 —C)?FFc cal per mol [3] where C is the atom fraction of nickel, and ?Ffe is the free energy change per unit volume for pure iron as tabulated by Zener4 (or, equivalently, Fisher"). From Eqs. 1 to 3, it is possible to calculate isothermal nucleation rates as a function of temperature and composition for Fe-Ni alloys. The only unknown parameter is (?² s³). The best value of this parameter for Fe-Ni alloys, determined from M. temperatures in a manner to be described shortly, is (?² s³)= 9.92 (10)21 cgs units [4] Taking this value of (?² s³), C-curves for isothermal nucleation were calculated for Fe-Ni alloys of several compositions, and are plotted in Fig. 1. It is evident from Fig. 1 that completely isothermal nucleation of martensite in Fe-Ni alloys can be observed experimentally for only a very narrow range of compositions. Cech and Hollomon find that a nucleation rate of about 10' nuclei per cc per sec is as fast as they can follow dilatometrically, and a rate of about 10-1 nucleus per cc per sec is about the slowest that can be measured conveniently. If the nucleation rate is to lie between the limits 10-1 10 the nickel content of an Fe-Ni alloy must fall in the atomic fraction range 0.299 5 C 5 0.302. Nickel contents lower than 0.299 correspond to nucleation rates too great to follow, and those higher than 0.302 to nucleation rates too slow to measure in a reasonable time.* In view of the narrow corn- position range in which successful isothermal measurements can be made, it is not surprising that only one substitutional alloy has been described' that comes close to being in the proper range.

Jan 1, 1954

By Boxun Lu, Juan Wei, Kun Chen, Wanlin Wang, Lejun Zhou

"Slag system is an indispensable part during the continuous casting process, and playing various important roles like absorbing inclusions, modifying heat transfer rate, preventing oxidation of molten steel, etc. to ensure the smooth process and excellent slab quality. However most slags contains more than 8% fluorides which tend to introduce a series of environmental and health problems. This study involves the research of the removal of fluorine through the chemical composition optimization. Through the studies of CCT, DHTT, XRD and SEM, it has been successfully founded that the crystalline phase of Ca11Si4B2O22 discovered in this study shows very similar crystallization property as Cuspidine (Ca4Si2O7F2), which is the most important crystalline phase in the current fluorine bearing slags. Moreover, the optimized free/low fluorine slag shows the opportunity to replace conventional high-fluorine mold slag for casting medium carbon steels that is regarded as the bottleneck of green slag development for continuous casting.IntroductionMold flux has been widely used in continuous casting to control heat transfer, lubricate the strand, absorb inclusions, provide insulation and prevent oxidation of the molten steel[1-3]. It usually contains fluorides, like CaF2, NaF etc., which are used to control the viscosity and solidification temperature of mold fluxes [4-5]. However, the presence of fluoride leads to corrosion of equipment, serious environmental pollution (toxic volatiles and water pollution), and high processing cost of cooling water[6-7]. Therefore, the study of low or free fluorine mold flux is of interest and attracts worldwide attention.S. Y. Choi et al. [4] used B2O3 as a substitute for cuspidine in steel B2PB2) however, B2O3 content was extremely high (up to 30 w%). Other studies have investigated F-free mold flux by adding or optimizing components as MgO, Li2O, B2O3 et al[8-11]. However, most of these focused on the melting and viscosity issues or for low or ultra-low carbon steels, where crystallization tendency is not significantly strong. Very few studies regarding to the development of low/free Fluorine mold flux for casting medium carbon (MC) steels have been conducted, due to the difficulty of the crystallization and heat transfer control without the formation of cuspidine."

Jan 1, 2014

By Lester Guttman

THE connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermo-dynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that called by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulae for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß-brass; 2. a- brass; 3. AuCu3; 4. AuCu. When the temperature is so high that no long-range order exists, these formulae reduce to the same form for all lattice types, namely: [ ] Here the symbols have the following meanings: [F-Helmholtz free energy E-energy S-entropy k-the gas constant per molecule z-coordination number, (e.g. 12 in. a-brass). N-total number of atoms c-atomic fraction of A] VAA, VBB, VAB-energy per bond of the corresponding bonds log means log, throughout The superscript 0 denotes the thermo- dynamic function in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition [ ] The free energy may also be written in terms of µA and µB, the chemical potentials or partial free energies per atom:

Jan 1, 1948

By P. P. Gregory

Natural petroleum gas occurring in the oil-bearing reservoirs is found to exist either as free gas associated with the oil and/or in solution in the oil. In some virgin fields practically no free gas is encountered under the reservoir conditions of pressure and temperature, although in other fields a considerable section of the "pay" horizon is occupied by free gas. In other words, a given oil field may or may not have a gas cap before the exploitation takes place. However, when the reservoir pressure is reduced to a point below the critical saturation pressure by withdrawals of fluids from the producing formation, the gas dissolved in the oil inevitably begins to come out of solution and becomes free gas. Under the controlled methods of production and drilling, a portion of this gas is produced with the oil to the surface and a portion of it remains within the reservoir to accumulate at higher structural levels toward which it migrates by virtue of its low specific gravity. The rate of growth of a gas cap in a given structure depends primarily upon the rate of decline in the reservoir pressure. If the rate of pressure decline is rapid, the gas cap likewise will grow rapidly. On the other hand, shrinkage in the gas-cap area was noted in some fields in which reservoir pressures wereincreasing. Determination of Gas-oil Contact and Thickness of Gas Cap The gas-oil contact can be conveniently located in the process of drilling a well and by electrical logging. However, very little can be found in the petroleum literature concerning methods of predetermining gas-oil contacts in producing reservoirs. Therefore, the writer feels justified in describing briefly a simple, workable, and inexpensive method of determining gas-oil contacts and outlining the limits of gas-cap areas in a field where such knowledge may be essential for efficient production and development operations. The method involves the determination of the following data: (I) Structural data, such as the depth or elevation of the top' of "pay" horizon; (2) reservoir pressures; (3) tubing and casing pressures at the well head; (4) static oil-pressure gradient; (5) static gas-pressure gradient. These data can be secured with a minimum of expense, inasmuch as the

Jan 1, 1938

By Jerry R. Johanson

Introduction Many solids processes that look feasible on paper or even in pilot studies become disasters in full scale. Changes in solids flow characteristics from pilot scale to full scale be- cause of larger solids contact pressures, thermal shocks, or unforeseen temperature excursions often cause full-scale solids flow problems not encountered in the laboratory or pilot studies. Fortunately, proper applications of solids flow principals and solids flow properties measurement at full scale conditions can anticipate the problems and thus provide an accurate basis for full-scale design or existing plant modifications. Solids flow properties The basic solids flow property definitions are given in Table 1 (Johanson, 1966, 1976, 1978, 1985). In this section, the author will discuss each property and its potential for creating full-scale pilot plants. Unconfined yield strength The unconfined yield strength of a bulk solid determines the tendency for cohesive hangups of the solids in the process and is effected by the time at rest, chemical reactions, temperature, liquid content, solids size consist, and phase changes of solids or fluids involved in the process. One of the common mistakes is to consider the solids condition only at the beginning and the end of the process. For example, consider the direct reduction of iron ore. The feed solids are free-flowing, hard lump ore or pellets. The end result is a hard, free-flowing reduced sponge iron lump or pellet. One might conclude that the process involves free-flowing lumps. This conclusion may seem reasonable based on laboratory studies oreven pilot plant studies where solids contact pressures are very low. Unfortunately, during the reduction reactions at high temperatures, the rock or pellets soften and, with solids contact pressures associated with the full-scale plant, may fuse together, thus providing a possible solids hangup in the moving bed reactor not evident in the low pressure pilot scale. Fig. 1 shows some typical unconfined yield strength measurements for pellets as a function of solids contact pressure at various times at rest. Note at low consolidation pressures, generally associated with laboratory or pilot plant studies, the pellets show no strength unless held at rest for an extended time. This will produce a very free-flowing condition in pilot plants that will not exist in the full size reactor.

Jan 1, 1990

By J. P. Nielsen

When two grains in a polycrystalline specimen meet at a point in the course of grain-boundary movements, and the new boundary created at the point is one of relatively low specific free energy, a nonequilibrium boundary condition occurs. The nonequilibrium is enhanced if the other grain boundaries involved at the point of meeting are relatively high in specific free energy. The nonequilibrium results in a correction by growth of the complex grain (two subgrains) to a large size, sufficient in many cases for it to become a self-propagating unit, i.e., a recrystallization grain. This mechanism, herein called "geometrical coalescence," is proposed as a logical origin for recrystallization nuclei, particularly for secondary recrystallization. RECENT publications1-' indicate that considerable progress has been made toward a complete understanding of the three microstructural processes in metals: recovery, recrystallization, and grain growth. However, a major problem persists, namely, the origin of recrystallization nuclei. It is generally accepted that once a recrystallization nucleus, a secondary recrystallization nucleus particularly, has reached a certain size, it will continue to grow at the expense of its neighbors, simply as a consequence of grain-boundary free-energy considerations. What has remained obscure, however, is the mechanism whereby such a nucleus comes into being and grows to the self-propagating size. Recrystallization Nucleation in a Two-Dimensional Grain-Boundary System In the left portion of Fig. 1 is shown schematically the meeting of grains 1 and 4 on disappearance of boundary 2-3, i.e., the boundary that existed between grains 2 and 3, as might happen in the course of normal grain-boundary migration. If, by chance —and the probability is not necessarily small— grains 1 and 4 are close together in their mutual orientations, or in some other special way mutually oriented so that the new common boundary has relatively a very low specific free energy (hereinafter referred to by s), then the grain boundary arrangement as depicted in the figure is highly unstable. This is particularly so if boundaries 1-3, 3-4, 4-2, and 2-1 are high in their s values. Assuming, for the sake of argument, that boundary 1-4 has a s equal to zero, and the s's of all the other boundaries present are equal to each other and constant, then the boundary arrangement on the right in Fig. 1 will be

Jan 1, 1955

By J. Gurland

The strength variation ofWC-Co alloys with composition and particle spacing falls into two ranges. 1) Above a critical value of the mean free path, the strength follows a dispersion hardening relation; it is proportional to the volume fraction of WC and in-versely proportional to the particle size. 2) Below a critical value of the mean free path, the strength variation is based upon the Griffith criterion of fracture and is controlled by the case of crack propagation. The maximum strength is attained when the structure and load just satisfy the critical conditions for spontaneous crack propagation. THE relation between the strength and the structure of cemented carbides is of interest not only for its own sake but also for its contribution to the understanding of composite materials in general. The cemented carbides are essentially aggregates of a brittle carbide constituent and a ductile binder phase and, at certain structures of intermediate composition, the composite alloys attain strengths far higher than those of the separate constituents in bulk. It is this variation of strength with structure which will be discussed. The experimental procedures of sample preparation, mechanical testing, and quantitative metallo-graphic analysis have been described in Ref. 1. The reported strengths are the maximum fiber-stresses in bending calculated on the basis of completely elastic behavior. The plastic contribution to the over-all deformation is small and was neglected in the calculations (the elongation at fracture of the most ductile alloy, 50 pct WC-50 pct Co, is less than 0.5 pct).2 The pertinent structural parameters are: f, the volume fraction of tungsten carbide; p, the mean free path through the binder phase; the contiguity C, defined as the average fraction of surface area shared by a particle of wc with all neighboring particles of the same phase; and d, the average equivalent spherical diameter of the WC particles. The strength variation of WC-Co alloys with composition and particle spacing is shown in Fig. 1 and Table I, which are based partly on previously published data' and partly on new experimental work which extends the range to higher values of the mean free path. Each data point represents the average of five samples. For a given composition, the transverse rupture strength reaches a maximum

Jan 1, 1963