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By D. R. Shreve, L. W. Welch

An analysis for predicting the behavior of reservoirs exploited by a combined gas drive and gravity draintrge mechanism is presented. The method allows the prediction of gas-oil ratio, oil production rate, and cumlulative oil recovery for high relief pools in which pressure is maintained either by gas injection in the crest of the structure or by a combined gas and water injection program. The reservoir is represented by a model of communicating vertical prisms, with production or injection at the upper or lower boundaries of each prism. The theory of macroscopic gravitational segregation of two fluids within a reservoir is discussed in detail for all ranges of saturation. A description of an application of the analysis to a typical field problem is also presented. INTRODUCTION The importance of gravity drainage as a producing mechanism has become more evident during recent years. However, many of the reservoir engineering methods which have been used in the past for predicting the behavior of reservoirs producing by this mechanism have required such drastic, simplifying assumptions that the calculated performance in some cases does not resemble the actual pool behavior. The mechanism of fluid displacement in porous media has been described by Buckley and Leverett,1 and a simplified "one zone" method based on this development has been used by engineers to evaluate the performance of gravity drainage pools. Welge2 has modi- fied this approach so that the calculation time has been markedly decreased. In addition, many other authors3-9 have analyzed various phases of the gravity drainage producing mechanism during the past several years. In a high relief reservoir in which gravity may affect the recovery mechanism, there are two main types of exploitation programs which can be employed: 1. Reservoir pressure is maintained by injecting gas into the upper portions of the reservoir. In this case gas is not released from solution and, if dynamic pressure drops are small compared to the total pressure of the system, the gas and oil may be considered to be immiscible and to have constant fluid characteristics. 2. Reservoir pressure is not maintained and a "natural depletion" mechanism prevails. The term "natural depletion" can be used to describe the production history of a reservoir in which a gradual decline of average pressure and the associated release of solution gas continue throughout the producing life. In this mechanism gas is released throughout the reservoir and there is a continuous change in the characteristics of both the gas and the oil phases. It is the purpose of this paper to present the results of mathematical developments by which a method has been devised for evaluating the performance of reservoirs which are depleted by the first type of exploitation program discussed above. It should be mentioned that, although throughout the analysis gas and oil represent the two fluids existing in the reservoir, the method is equally applicable to gravity drainage in water-oil systems. STATEMENT OF PROBLEM In reservoirs of pronounced structural relief, where the closure of the oil section is great or the angle of

Jan 1, 1957

By L. W. Bahney

Frequently in using a thermo-electric pyrorneter for measuring the temperature of a furnace, a hole is drilled at the back or side of the furnace, through which is introduced the tube containing the thermo-couple. At times the couple is left almost where it drops, for the reason that it soon becomes too hot to be handled easily, and the space at the back or side of the furnace may be so small and uncomfortably hot that an easy and accurate adjustment is nearly impossible. In order to overcome this clumsy and unscientific method of using the thermo-electric pyrorneter, I designed an adjustable stand, to hold the clay or quartz tube inclosing the platinum and platinum-rhodium leads that constitute the couple of the Le Chate-lier thermo-electric pyrometer. This stand also allows an easy and rapid adjustment of position to varying heights and angles, as may be desired for special reading, This stand is illustrated in Fig. 1. The couple in the tube might be of better service if the tube were held a little higher above the charge in a roasting-dish, changing the height and angle if desired. The stand, made of 1.5-in. water-pipe and mounted on casters, is heavy enough so it cannot be tipped over easily. It is adjusted to any position, and has a universal clamp which holds the clay or quartz protecting-tube. To avoid disturbing the wires of the couple at the cold junction each time the tube is moved, the cooling-bottle sets in a wire basket so placed that it moves forward or back with the couple. To overcome the necessity of leveling and adjusting a galvanometer at each furnace, a switch-board is used to connect

Jan 1, 1910

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homogeneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity p1 and a lower layer, extending to infinity, of resistivity pz. It has been shown by Lancaster-Jones2 that the apparent resistivity obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the formhere pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 — p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between pa/p1, h/a and k. Such a set of curves for the case when p1 > p2 is given in Fig. 1. When pl is less than pz it is more convenient to use conductivity instead of resistivity. Hence, if oa = the apparent conductivity = lip, and a1 = the conductivity of the upper layer = l/pl, it follows that GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula

Jan 1, 1940

By G. F. Tagg

In an earlier paper1, the author described a method of interpreting earth-resistivity curves, based on the theoretical investigation of a single horizontal underlying stratum. If the four-electrode system of Wenner is employed, the resistivity in a homogeneous soil is given by the formula where a is the electrode separation and R is the resistance of the earth between the two inner electrodes. If the earth is not perfectly homogeneous, the application of this formula gives an apparent specific resistance varying with the electrode separation. In the special case of the single horizontal underlying stratum, there is a surface layer of thickness h and resistivity p1 and a lower layer, extending to infinity, of resistivity pz. It has been shown by Lancaster-Jones2 that the apparent resistivity obtained by an application of equation 1 is related to the true resistivities, the depth h and the electrode separation a by an expression of the formhere pa is the apparent resistivity and F is a function (actually an infinite series), of the ratio h/a, and a reflection coefficient k = (p2 — p1)/(p2 + p1). For given values of h/a and k, the right-hand side of equation 2 can be calculated, and curves drawn showing the relationship between pa/p1, h/a and k. Such a set of curves for the case when p1 > p2 is given in Fig. 1. When pl is less than pz it is more convenient to use conductivity instead of resistivity. Hence, if oa = the apparent conductivity = lip, and a1 = the conductivity of the upper layer = l/pl, it follows that GeophyGical prospecting by earth-resistivity methods is frequently applied to investigation of structural problems in geology. Fig. 1 indicates a scheme of the general arrangement used in these methods of measurements. The battery (or generator) E is connected with two "current electrodes" I1 and I2. The current of intensity J, supplied by this battery, passes through the earth between these elcc- trodes. A potential difference U will be measured between two other electrodes V1 and Vz, called "potential electrodes." According to the configuration of electrodes (Fig. I), the resistivity of a homogeneous soil results from the formula

Jan 1, 1940

By R. H. Oliver

The purposes, types, preparation, and testing of flocculants are discussed. A flocculation compendium is included, indicating choice of flocculant for a given set of conditions. An economic evaluation of the process is presented. Solid-liquid separation is a major expense in most mineral processing flowsheets today. Proper use of flocculation can often lower the overall cost of a solid-liquid separation by reducing the size of sedimentation or filtration equipment. PURPOSE OF FLOCCULATION When is use of a flocculant justified in terms of overall process economy? 1) when it results in process improvement, such as producing a clear liquor for electrolysis, precipitation, ion exchange, or solvent extraction; 2) when it results in satisfying requirements of pollution abatement ordinances; 3) when it results in increased recovery of values that would otherwise be lost; or 4) when it results in considerable savings in capital expenditure due to use of smaller equipment. When can the use of a flocculant adversely effect overall process economy? 1) when it results in increased filter cake moisture, 2) when it results in decreased filtration rates, 3) when it results in considerable bulking of sedimentation underflow, 4) when it contaminates either the supernatant or sludge, or 5) when the cost of using the flocculant is greater than the savings due to its use. First step in consideration of flocculants for a given application is establishment of desired goals in terms of increased clarity of effluent, increased recovery of solids, or decreased size of equipment. The most economical solution to a solid-liquid separation problem is that combination of equipment and flocculant costs which meets the established goals at the lowest total annual expenditure. This economic decision can be made only after technical data has been obtained as outlined in next four sections. TYPES OF FLOCCULATION Flocculation is a process wherein individual particles are united into more or less tightly bound agglomerates or flocs, thereby increasing effective particle size of solids suspended in a liquid. Degree of flocculation of a suspension of finely divided solids in a liquid is controlled by a combination of probability of collision between particles and probability of adhesion after the collision has occurred.' Probability of collision can be increased commercially through use of a paddle-type flocculator, combination flocculator, and clarifier or flocculating-type feedwell. Probability of adhesion usually can be increased by addition of a reagent known as a flocculant. Reagents act as flocculants through one or a combination of three possible mechanisms. The first is electrolytic neutralization of inter molecular repulsive force due to Zeta potential. This neutralization enables Van der Waal's cohesive force to hold the particles together after they collide.' The second is the precipitation, within a definite pH range, of voluminous metallic hydroxide flocs which entrap fine particles. This process is known as coagulation.14 Third is the bridging of two or more particles by either natural or synthetic long-chain, high-molecular-weight organic polymers. This bridging is accomplished by adsorption of two particles at different sites on the same molecule or by bonding of two molecules, each adsorbed to a different particle. Considerable effort has been expended in explaining the action of these polyelec-trolytes and detailed accounts are available in the literature. CHOICE OF FLOCCULANTS It is impossible, at the present time, to specify the optimum type or amount of flocculant for a given application from a knowledge of the material to be treated. The standard procedure is to choose reagents or combination of reagents most likely to be effective on the slurry; then test them.' The accompanying Flocculation Compendium (Table I) contains details of all currently available reagents sold as flocculants and it should be used when selecting the group of reagents for tests. This selection can be based on information listed in columns 4 and 5. Column 4 presents industries in which each floc-

Jan 1, 1961

By H. D. Strain

Potash is a generic term used to describe a number of compounds containing the element potassium (K), which is one of the three major plant nutrients. Potash content of these compounds is commonly expressed as percentage potassium oxide (K20), and the market value of the products is usually dependent on contained K20. Most of the potash produced (approximately 95%) is used in agriculture as fertilizer. Potash products today are shipped by producing countries all over the world to meet the need for increased food production. WORLD POTASH RESERVES Apparent world potash reserves are shown in Table 15.2B.1 and total some 96 billion mt of recoverable potassium oxide. The Canadian reserves account for approximately one-half the known world reserves. The reserves shown represent the potassium oxide content of a variety of potash-bearing ores. The major ore is sylvinite (a mechanical mixture of KC1 and NaCl) from which KC1 or sylvite is recovered (63.2% K20 equivalent). Other ores, such as langbeinite (potassium, magnesium sulfate-22.7% K20) and carnallite (potassuim magnesuim chloride-17.0% K20) are also mined in various parts of the world, mainly for the potassium content. Theoretically, potassium is available in almost unlimited qualities from brines and saline waters. To date, the cost of recovery from salt brines has been greater than the costs by mining operations, but new technology could make brines and seawater an increasingly important source. POTASH PRODUCTION Potash production dates back to the 1860s in Germany, which was the only recorded producing country until 1912. By 1912 Germany was producing approximately 1 million tpy of K2O equivalent. Production began in France in 1913 and in the United States in 1915. World potash production and consumption are shown in Table 15.2B.2 for the years 1950-51 through 1967-68. In 1967 and 1968 the major potash-pro¬ducing countries in order of importance were those listed in Table 15.2B.3. By 1972 Canadian production had outstripped U.S. production. WORLD CONSUMPTION World consumption of potash for the years 1950-51 through 1967-68 is shown in Table 15.2B.2. Table 15.2B.4 shows total world consumption of potassium materials in 1967-68 by country. More than 70% of the world's potash is

Jan 1, 1976

By R. L. Templin

THE modulus of elasticity is defined as the ratio of stress within the proportional limit to corresponding strain. This property, as thus defined, is a constant for each kind of material; and in tension or compression is usually designated by the symbol E. The modulus of elasticity serves as an index of the stiffness of a material or a measure of its ability to resist change of shape under stresses not higher than the proportional limit. In view of the frequency with which the modulus of elasticity is used in engineering calculations, it is surprising to note the uncertainty that exists as to authentic values, and the marked lack of published information relating to the variation of the constant E within individual alloy systems. A value of 10,000,000 lb. per sq. in. has been quoted as representative of aluminum and its alloys. This value has been found to be approximately correct for pure aluminum and aluminum alloys in which the total percentage of the alloying elements is low, but seriously in error in the case of alloys that contain relatively large amounts of the alloying elements.

Jan 1, 1930

By David R. Mitchell, B. M. Bird

DENSE-MEDIA processes utilize the familiar laboratory float-and-sink procedure on a commercial scale. Just as wood chips float on water and sand sinks, so coal floats and refuse sinks when placed in a medium intermediate in specific gravity between the coal and refuse. Liquids intermediate in specific gravity between coal and refuse used in commercial plants are of four types: (1) organic liquids of high specific gravity-halogenated hydrocarbons; (2) dissolved salts in water; (3) pseudo liquids obtained by suspending solids, such as sand or magnetite, in water, and, (4) fluidizing a mass of sand or other solids by air currents. Those most widely used for cleaning coal are solutions of calcium chloride in water and a suspended sand or magnetite pseudo liquid. Laboratory float-and-sink testing is an intermittent operation during which every opportunity is given for particles lighter than the medium to float and particles heavier to sink. Commercial processes are continuous; vertical and horizontal currents of the separating medium occur as either part of the process or unavoidedly produced by the introduction of feed and withdrawal of products, 'so that the exact separation of the laboratory technique is not duplicated by commercial processes. However, separations close to the theoretical are obtained in commercial machines by careful technical control of the process. Most machines in commercial installations are crowded to get as much out of the equipment as possible, so that careful technical control is necessary is get the recoveries and grade of product desired. Sizes usually cleaned are plus ¼ in. or plus 1/8 -in. in the United States and plus 1/16-in. in Great Britain. Coal as small as 1 mm. has been cleaned in some experimental installations. The separation of coal from refuse in sizes finer than about 1/8-in. is made difficult by viscosity effects and hence at the present time cleaning is confined to the coarser sizes. Technical advances in the art of cleaning coal by dense-media processes is progressing rapidly and it is likely that equipment, media, and procedures will be developed to clean sizes down to 0.5 mm. efficiently and at low cost.

Jan 1, 1950

By J. B. Chatelain, M. F. Dufour

FLUID jet mills, employing a compressible fluid to grind materials to the subsieve range, was developed in the early 1930's, and the subsequent acceptance of these units was the result of their ability to pulverize solids that, because of physical properties, could not be processed by other attrition methods, such as ball, pebble, and hammer mills. Also, the fluid energy pulverizer is the only grinding device that will discharge continuously a 5-micron or smaller product. Simultaneous ultra-fine grinding and classification is the widest application of this unit. Jet mills may be used to advantage to reduce particle size of solids suspended in liquids, for coating one material with another, and effecting chemical reactions and changes in physical characteristics other than a reduction in size. Materials that can be processed by this grinding method include nonmetallic and metallic minerals, ores, metals, pigments, insecticides, fungicides, pharmaceuticals, plastics, dyes, and numerous other organic and inorganic products. Grinding principles utilized in the fluid mills available on the market are basically the same, the major difference being in the shape of the, grinding and classification chamber. Grinding in fluid jet pulverizers is accomplished by collisions between particles of the material being ground with the energy being supplied by compressed fluids entering the grinding chamber at high velocities. The "Micronizer" is a fluid energy mill employing a relatively flat cylindrical grinding chamber. Fig. 1 shows general construction details. The mill shown is equipped with a venturi type feeder using a compressed fluid to inject the feed into the grinding chamber. The energy consumed in forcing the feed into the grinding chamber against the mill pressure is, in some cases, as much as 40 pct of the total required for processing. Recent improvements, using a compression screw feeder as shown in Fig. 2, can reduce this to 1 or 2 pct of the total energy requirements. Grinding Grinding, as carried out in the. Micronizer involves the action of gaseous jets emerging from nozzles located in the peripheral wall of the grinding chamber. The axes, of the jets are tangential to a circle of smaller diameter than the grinding chamber as is shown in Fig. 1, and the gases entering the chamber maintain a high rotational velocity. The feed introduced into the mill is accelerated by the rotating gases and is thrown to the outside where a portion, coming in the zone of action of a nozzle, is further accelerated tangentially and inward. Violent collisions occur between the particles so accelerated and other particles circulating at a slower rate in a thin band near the periphery. It is estimated over 90 pct of the reduction in Micronizers occur as a result of impact within a fraction of an inch of the orifice. Observations also indicate that size reduction is independent of any interaction with the walls of the

Jan 1, 1952

By P. E. Baker

A paper by A. S. Odeh' expounds a capillary-flow theory which purportedly provides a mechanism whereby relative permeability depends on oil-water viscosity ratio and may be greater than unity for high viscosity ratios. Core-measurement results are presented to support the theoretical development. This paper presents arguments to indicate that (1) the theoretical treatment is basically incorrect, (2) data reported are insufficient to support the conclusions and (3) literature cited does not support the theory or the conclusions. PROPOSED MECHANISM The essence of Odeh's theory is that oil flows as a filament along the central portion of a straight, uniform capillary of radius r filling the tube to a radius ri. Surrounding the filament of oil is an annulus of water in which exists vortex motion but no net flow. The water is described as being in "microscopic but not macroscopic" motion. The oil filament is aided in its flow by moving upon the water vortexes as if on roller bearings. This process is presented as a steady-state flow condition. The first objection to the existence of vortexes in the presumed water layer is that the theory provides no mechanism whereby they can be established. This fact was mentioned by C. F. Weinaug in a discussion published with Odeh's paper. The capillary contains no irregularities or obstructions, and the water is not presumed to be in turbulent flow. Apparently, cylindrical symmetry is assumed; therefore, the supposed vortexes must be toroidal, the line of zero velocity being a circle concentric with and in a plane perpendicular to the axis of the capillary. This is a rather difficult picture to accept. The author referred to Yuster's statement' that he had observed the "spinning in place" of otherwise immobile water. Yuster's article does not describe the conditions under which this motion was observed or the means used to observe it. However, the article does make clear that the observed motion was not in a straight, uniform capillary but, rather, apparently oc-cured in some kind of dead-ended pore space. Obvious- ly, such a report cannot be considered as support for Odeh's concept of two-phase capillary flow.

By Roscoe C. Clark, Henry F. Coffer, J. J. Reynolds

A cement slurry lightweight additive has been adapted in the Conoco laboratories for use in oil well cements. This additive makes possible the use of air to lighten oil well cement slurries. Specifically, the additive consists of small clay bubbles of air having sufficient strength to resist crushing by bottom hole pressures. Clay bubble cement slurry weights can be safely reduced to 10 Ibs/gal. In addition, the clay bubbles tend to act as lost circulation materials and to provide a cement texture which should produce good perforating characteristics. Clay bubble cement is relatively impermeable. INTRODUCTION In many areas in Oklahoma, Texas, Wyoming, and California, difficulties are experienced during casing cementing operations with lost returns caused by the high density of the cement slurries. Wells in these areas are ordinarily drilled with 9 to 11 lbs/gal. drilling mud while neat cement slurries may range in densities from 14.5 to 17 lbs/gal. In these areas, cement slurry weights are at present being successfully reduced to around 12 lbs/gal. (under bottom-hole conditions) by the use of additives in the cement. Since the use of additives will decrease the strength which the cement will develop, the amount of additives which can be used must be based on the minimum cement strength which is acceptable; and thus the maximum slurry weight can be reduced. At present, the minimum tensile strength generally acceptable is 50 lbs/sq in. cured for 24 hours under bottom-hole temperature. This figure is based on laboratory tests1 and on a large number of cement jobs which have been conducted using cement which will not develop more than 50 psi tensile strength in 24 hours under bottom-hole conditions. Two additives are now in use for decreasing cement slurry weights. These are expanded perlite and/or bentonite. The density of both of these materials is greater than that of the cement slurry; however, large quantities of water may be added with these materials without producing a slurry which will settle out of suspension. It is these large quantities of water which contribute to the reduction in the slurry weight. The minimum slurry weight at present obtainable with expanded perlite and/or bentonite is approximately 12 lbs/gal. using a standard Portland cement slurry. In many areas, this weight reduction is insufficient; and returns are still lost during casing cementing operations. In many cases, the pay formation itself is fractured; and a considerable quantity of this cement is lost to the pay zone. It is therefore believed that if cement slurry weights can be reduced to as low as 10 lbs/gal., two advantages will accrue: 1. The lighter densities (10 to 12 lbs/gal.) should mitigate or eliminate lost returns during casing cementing operations. 2. Cement slurries above 12 Ibs/gal. (the present minimum limit ) should develop considerably more strength than is now being obtained. A tensile strength of 100 psi is desirable.' It is the object of this paper to describe a cement slurry having a weight of 10 lbs/gal. and capable of

Jan 1, 1955

By F. X. Tartaron

This article is a continuation of a previous paper by the writer in which Kick's Law was stated to be a part of comminution theory. ln the present paper, a broadening of ideas is attempted in order to state a general theory. The word "general" is employed because the new theory includes all previous laws and generalizations which are considered to be essentially correct. These ideas are combined into a coherent whole and the general theory can be expressed by the equation In the author's previous paper on comminution, ' the equations developed were based on Charles' equation of exponents a-n +1 = 0. 2 This paper is divided into two parts, designated as First Approach and Second Approach. In the First Approach, the equations of the previous paper are utilized, with Charles' equation of exponents being necessary. In the Second Approach, a separate and independent method is used to derive the same conclusions as in the First Approach, but without the use of Charles' equation of exponents. Holmes accepts the theoretical foundation of Kick's Law as sound but denies that the law as such operates in comminution. His idea is that Kick's Law requires homogenous matter whereas the presence of cracks, flaws and cleavage planes, which predominate in the coarser particles, makes matter unhomogene-ous. This explains why there is no experimental evidence to support Kick's Law. However, since the basis of the law is theoretically sound, all experimental evidence must be viewed as emanating from it. This requires modification of current comminution equations to fit this concept. Holmes makes the modification by changing the constant exponent n in the general energy equation used by Charles (E = - JCdx/xn) to a variable exponent r. The writer asserts that Kick's Law operates in comminution without modification but it does not

Jan 1, 1963

By Ellis Clark

The mining town of Pribram is situated in Central Bohemia, on the western slope of the Heiliger Berg. 30 miles southwest from Prague. Birkenberg, the village ill which most of the shafts and ore-dressing establishments are situated, is built on a mountain of the same name. It is about a mile from Pribram, is 1700 feet above the sea, and is surrounded by graywacke rocks of Silurian origin, which arc intersectd by greenstone dikes, and in the southerly, southeasterly, arid southwesterly direction are bounded by granite. The graywacke formations consist on one side of graywacke sandstone and quartzite, and on the other of graywacke slate. These last are separated from the first in the immediate vicinity of the mines by a graywacke seam converted into clay. For many years this so-called clay seam (lettenkluft) was considered as a boundary of the ore deposits in both zones of graywacke. The graywacke formation L divided according to its harduess, structure, texture, and color, into fine, coarse, compact, slaty, whitish-gray, reddish-gray, and black graywacke. The miner divides the formation into four divisions. The first or lowest division, which is in contact with the granite, consists of a fine-grained dirty gray slate; the -second is a very fine to a very coarse schist, white to reddish-gray in color, and rich in quartz, but containing little mica; the third consists of a slate with a confused cleavage, which has a dirty gray, dark gray, and very often black color and is often graphitic in its composition; the fourth consists of a fine to coarse-grained graywacke schist, of a grayish-white or reddish-gray color, and rich in quartz. The cleavage in all four divisions strikes from northeast to southwest, and the dip is sometimes northwesterly, sometimes southerly, and often vertical. All four zones are cut through by a great number of diorite arid greenstone dikes and chimneys. The thickness of these dikes, which are of

Jan 1, 1881

By W. B. Mather

The object of this paper is to record and interpret data collected during the examination of over 250 barite deposits in the Central Mineral District of Missouri. In the course of this study, the origin of the deposits, which the author believes to be hydrothermal, has been given particular attention. Economic barite deposits occur in two main areas in Missouri: (I) in the Washington County District of Southeast Missouri, from which over 90 pct of the state's production is derived; and (2) in the Central Mineral District, which includes portions of 15 counties in Central Missouri (Fig I). Barite in the smaller Washington County District is mined from widespread low grade, relatively shallow residual deposits, whereas in the Central District, it is mined

Jan 1, 1948

By W. B. Mather

The object of this paper is to record and interpret data collected during the examination of over 250 barite deposits in the Central Mineral District of Missouri. In the course of this study, the origin of the deposits, which the author believes to be hydrothermal, has been given particular attention. Economic barite deposits occur in two main areas in Missouri: (I) in the Washington County District of Southeast Missouri, from which over 90 pct of the state's production is derived; and (2) in the Central Mineral District, which includes portions of 15 counties in Central Missouri (Fig I). Barite in the smaller Washington County District is mined from widespread low grade, relatively shallow residual deposits, whereas in the Central District, it is mined

Jan 1, 1948

By W. B. Mather

THE object of this paper is to record and interpret data collected during the examination of over 250 barite deposits in the Central Mineral District of Missouri. [ ] In the course of this study, the origin of the deposits, which the author believes to be hydrothermal, has been given particular attention. Economic barite deposits occur in two main areas in Missouri: (I) in the Washington County District of Southeast Missouri, from which over go pct of the state's production is derived; and (2) in the Central Mineral District, which includes portions of 15 counties in Central Missouri (Fig I). Barite in the smaller Washington County District is mined from widespread low grade, relatively shallow residual deposits, whereas in the Central District, it is mined

Jan 1, 1947

By C. W. Allen, B. D. Cullity

The proportional limit of iron crystals in torsion is governed by the resolved shear stress in the most highly stressed slip systems, averaged around the specimen circumference, and does not obey a critical resolved shear stress law. Crystals of most orientations exhibit a stage of easy plastic deformation, akin to easy glide in tensile or shear specimens. Transient deformation, similar to that which occurs in single crystals of other materials, is also observed. THE torsional deformation of single crystals of magnesium (hcp) and aluminum (fcc) has been described recently by Choi et al.,&apos; especially with respect to the criterion for the orientation dependence of the onset of plastic flow in these materials. The purpose of this paper is to present results of torsion tests of iron single crystals and thus to extend this yield criterion to a bcc metal. In addition to considering the variation of proportional limit with crystal orientation, this paper also briefly treats work hardening, transient deformation, and the mechanism of plastic flow in iron. The effects of the method of surface polishing and the chemical purity of the iron have been investigated. STRESS DISTRIBUTION It is convenient to express the stress at any point of a cylindrical crystal stressed in torsion in terms of t0, which is the shear stress acting at the surface on a plane normal to the axis of the cylinder and in a direction tangential to the cylinder. This stress is given by To = 2T/pr3 [1] where T is the applied torque and r the specimen radius. The shear stress t, resolved in any chosen slip system is given in terms of 7, by1 Ts/TO = sin 0, cos d sin (0, -) + cos , sin d sin d - ) [2] where 0 and d are the angles between the specimen axis and the slip plane normal and slip direction, respectively; h is the angular circumferential position on the specimen at which t, is being determined, measured from an arbitrary reference plane which includes the axis;o and d are the angular coordinates of the projections of the slip plane normal and slip direction on a transverse section with respect to this same reference plane. Slip in iron occurs in a <1ll> direction on the {ll0}, (1121, and (123) planes, which together comprise 48 slip systems. A complete evaluation of the stress distribution in an iron crystal stressed in torsion would therefore require a calculation of Ts/T0 as a function of for 48 different slip systems. Fortunately Gough,&apos;who studied the behavior of iron crystals in alternating torsion, was able to simplify this problem considerably. He showed that it was sufficient to consider a kind of average slip plane for each slip direction, namely the mathematical plane of maximum resolved shear stress containing the slip direction considered. This simplifying approximation is possible because, for each slip direction, the active slip plane or planes lie very near this mathematical plane of maximum shear stress. Vogel and rick&apos; have critically reviewed the early work of Taylor and Elam,13 Taylor,14 and Fahrenhorst and schmid8 from which the identification of the above crystallographic planes as slip planes in the bcc lattice largely stems. While their criticism is clearly justified, their own results do little to clarify the issue. The role of cross slip (screw dislocations changing glide planes) is evidently so important in this case, as Read3 has suggested, that methods for deducing slip systems from observations of gross slip traces are inadequate, such traces commonly arising from complex dislocation motion. Thus the treatment given here involving the plane of maximum resolved shear stress seems a logical simplification especially in view of Gough&apos;s2 study of a iron. There is, however, an assumption built into the subsequent treatment the comparative validity of which is difficult to assess, namely, that slip in all slip systems in iron may be characterized by a common critical resolved shear stress. The shear stress 7, resolved in a slip direction defined by d andd, and on the plane of maximum shear stress containing this direction, is found by first maximizing 7s/70 with respect to either Oo or 4,. The slip plane coordinates are then eliminated by using the relation between 0, ,o and d, d, namely,

Jan 1, 1963

By K. V. S. Sastry

INTRODUCTION Flotation is by far the most important unit operation of mineral processing. Most of the common base metals are produced from flotation concentrates of metal sulfides. Flotation is proving to be a valuable process for producing non-metallic minerals such as ceramic oxides, silicates, clays and phosphate fertilizers. All these fltation separations are carried out on materials which are predominantly in the 10 to 100 micronssize range. The present practice of flotation circuits for the production of large tonnages of metallic and non-metallic mineral concentrates is fairly well understood, developed, and standardized. Two kinds of problems are encountered (1, 2) with fine particles smaller than 10 microns. First is the interference of the fine particles with the flotation of the coarser particles and the second is the poor flotation behavior of fine particles. In general, these problems are handled either by eliminating, minimizing, or ignoring the fines in the flotation circuit feed. In recent years, however, a considerable number of experimental and theoretical studies have been carried out to understand the flotation behavior of fine particulates. This literature is summarized in four review papers (2-5). Application of the conventional flotation techniques for the separation of mineral fines is known to be uneconomical, and to present several scientific and technological problems (1-5). The objective of this presentation is to examine the flotation behavior of fine particles in terms of their physical-chemical properties and to review the potential techniques of fine particle flotation. Specific reference to the problem areas and research needs will also be included in the discussion.

Jan 1, 1979

By A. F. Giamei, E. J. Freise

A discussion of the various factors affecting the accuracy of volume fraction determination by the direct comparison X-ray diffraction method is presented. To minimize errors introduced by nonrandomization effects such as preferred orientation and large grain size, as well as errors introduced by statistical effects, an iterative mathematical analysis is introduced. This analysis is applied to all observable diffractio~ spectra from a given specimen by means of computer techniques and is statistically superior to the standard direct comparison technique which utilizes only one or tm sets of intensity spectra. The computer program also presents a graphical interpretation of- the results which enables the investigator to visualize and readily assess the scatter in volume fraction estimates caused by deviations from randomness. Finally, the iterative analysis is applied to experimental data collected from a series of plain carbon steels in both the as-received and spheroidized conditions to determine the volume fraction of cemen-tite present in each case. The results show markedly good agreement with chemical analyses for all spheroidized specimens. In theory, quantitative X-ray diffraction is a power-ful analytical technique for precise determination of the volume fractions of various phases present in a multiphase poly crystalline aggregate. There are two generally used methods; both utilize the fact that the intensity of a diffraction line of a particular phase is a function of volume fraction of that phase present in the aggregate. The more common method is the so-called internal standard technique where a known amount of standard substance is mixed with the aggregate containing the unknown. The resulting ratio of the intensity of a particular diffraction line of the unknown to the intensity of a diffraction line from the standard is used to find the weight fraction of unknown material by reference to the intensity data obtained from a previously prepared set of standards containing the same amount of standard material. The details of this technique are outlined in standard works on X-ray diffraction.&apos; The disadvantages of the technique are that it requires the use of powder specimens and that the powder mixture must be homogeneous near the surface to the maximum effective beam depth. The alternative technique is the direct comparison method in which the ratio of the intensity of a diffraction line of a phase in the aggregate to the intensity of a second-phase diffraction line yields the ratio of the volume fractions of each phase present. This method has been applied most extensively to the determination of the percentage of retained austenite in martensitic steels and to determining the amounts of hcp and fcc allotropic modifications in pure cobalt5 and the amounts of hexagonal and rhombohedra1 modifications in graphite.8 This method is applicable to bulk as well as powder aggregates and is the technique which will be considered in the following text. It is the purpose of the present communication to show that by combining the results of X-ray diffrac-tometry with the use of high-speed digital computers the results of the direct comparison quantitative X-ray analysis technique can be optimized by using all of the data available on a diffraction pattern. THEORETICAL DISCUSSION In optimizing any quantitative X-ray diffraction experiment, the problem of accuracy vs time to collect and analyze the experimental data arises. For any method to be practical, it is required that both experimental and analytical procedures are reasonably short. In most of the previous work performed by the direct comparison method, intensity data from only one or two sets of peaks were used to calculate the volume fraction of phases present in the aggregate. Consequently, rather long-time experimental measurements are required to assure that the intensity data are sufficiently accurate to justify the use of one or two sets of data. By using computer techniques to analyze the experimental data it becomes feasible to use all of the available data on a diffraction pattern. By so doing, the time spent in measuring any one diffraction maxima can be appreciably reduced. Although this results in poor counting statistics for any one maxima, the number of data points available for analysis is greatly increased. Based on the above discussion, it will be assumed that a continuous scanning counter-diffractometer technique will be used to collect intensity data from a two-phase mixture. The integrated intensity of the ith diffraction line from the a phase in the aggregate is given by:&apos;" where is the volume fraction of the a phase, The various quantities in Eq. [la] are angular independent while those in [lb] depend on the hkl spectrum of a particular phase. The meaning of the individual quantities in Eqs. [la] and [lb] are given in Appendix 1. It is convenient at this point to outline briefly the factors which will affect the measured intensity of any one hkl spectrum. a) Extinction effects arise from two independent experimental conditions. Primary extinction arises from a high degree of crystal perfection and results in spectra having lower intensity than predicted by Eq. [I]. Any treatment, such as powdering, which reduces

Jan 1, 1968

By Kenneth A. Gutschick, Robert S. Boynton

Lime has become a general and loosely used term to denote almost any kind of calcareous material or finely divided form of limestone or dolomite, as well as burned forms of lime. However, according to Webster, lime is only calcined limestone (known as quicklime, unslaked lime, or calcium oxide). It also embraces the secondary product of quicklime, i.e., hydrated lime or slaked lime (calcium hydroxide). There are two basic types of limestone used for lime manufacture-high calcium and high magnesium (dolomitic). The dolomitic quicklimes and hydrated limes correspond to their "high calcium" counterparts. The only difference is that the dolomitic types are a combination of the elements calcium and magnesium, in varying percents, whereas high calicum limes contain less than 5% MgO down to 1/2%. In either case a pure form of limestone of at least 97% combined carbonate content is needed to make salable lime, barring a few exceptions. The calcination of both types is diagrammed chemically as follows: [ ] In the foregoing reversible reactions the limestone is burned (calcined) in lime kilns, with the carbon dioxide content of the stone expelled as a gas. The weight loss during calcination of pure high calcium limestone is 44%; with equimolecular dolomitic limestone, the weight loss is 48%. Since lime has a strong affinity for CO_, particularly if moisture is present, it will readily revert to its original carbonate form. This occurs when quicklime "air-slakes" and adsorbs CO.. from the air. Thus, quicklime is perishable and should be stored in dry, water-tight areas. Depending upon the type of kiln used and the physical structure of the stone, the size of the quicklime may range from sandlike granules to 8 in. lumps. However, pebble sizes ranging from 1/4 in. to 2 in. are the most common. Screened quicklime fines are also com¬pressed (pelletized) into 1 in. pellets. For some purposes ground or pulverized forms of quicklime are used, ranging from No. 10 mesh to dust. Generally a pebble of quicklime is about the same size as the pebble of limestone before calcination (perhaps shrinking slightly). A more stable form of lime is hydrated lime. This is obtained by adding water to quicklime, slaking it into a dry, fine, subsieve size white powder. Because its affinity for moisture has been satisfied, it is not vulnerable to further moisture like quicklime. However, it has the same strong affinity for CO_. The following reversible chemical reactions illustrate how hydrated lime when heated (or dehydrated) can revert to the original oxide form:

Jan 1, 1975