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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 D. Havlena, A. S. Odeh

The use of the straight-line method of solving the material balance equation is illustrated by means of six field cases. Also, the application of statistical criteria to arrive at the most probable answer is shown. The theory underlying the straight-line method of solution and the applicability of the statistical criteria was presented in a previous paper.' The field cases include saturated and undersaturated oil reservoirs with and without water drive. The aquifers discussed are: limited radial, infinite radial, very small aquifer and infinite linear. The field cases also include a gas reservoir producing under water drive. INTRODUCTION In a previous paper,' the authors presented the theory underlying the solution of the material balance as an equation of a straight line. The appropriate equations for various material balance cases as well as the methods of analysis and interpretation with comments and discussion were also included. To illustrate the various theoretical cases treated previously, five field cases are analyzed in this paper by employing the straight-line method of solving the material balance equation (MBE) and one example previously published is referred to. The use of statistical criteria to arrive at the most probable answer is also shown. All the field examples presented, except Case 2, are excerpts from complete reservoir studies. To illustrate the method, only sections specifically dealing with the material balance principles are included. Additional geologic information and basic data are reported to better acquire an understanding of the cases and thus to better follow the reasoning that suggested the successful application of the straight-line method of solving the MBE. The six cases are: (1) saturated reservoir, small gas cap, limited aquifer; (2) saturated reservoir, very small gas cap, infinite aquifer; (3) undersaturated-saturated reservoir, very small aquifer; (4) highly undersaturated reservoir, no water drive; (5) high undersaturated one-well reservoir, limited aquifer; and (6) gas reservoir, infinite linear aquifer. THE D4 SAND, GUICO FIELD, VENEZUELA The D, sand, which was discovered in 1943, is presently in a depleted state. Since its discovery it has produced under water drive, gas-cap-gas expansion, and solution gas drive. In Nov., 1947, water injection was initiated to arrest further pressure decline. When discovered, the D, sand was a saturated reservoir with a gas cap /oil zone volume ratio m estimated volu-metrically at 0.0731, an average permeability of 500 md, a porosity value of 25 per cent, and an oil viscosity at reservoir conditions of 0.3 cp. The volumetrically determined stock-tank oil initially in place was 23.1 million bbl. The volumetrically weighted physical data and production data available until Nov., 1953 are reported in Table 1. In Ref. 1, the effects on the straight-line plot of various values of ro/r for a constant ?to, or of various dimen-sionless times for a constant r8/r10 were theorized and were illustrated in Fig. 3A of that reference. In this field case, the previously theoretically predicted effects are established. Thus, the MBE calculations using Eq. 3c of Ref. 1 were performed for various r6/r10 and dimension-less time values. Eq. 3c of Ref. 1 is:

Jan 1, 1965

By J. Lyden

In the Picher field, structure made openings for the circulation of the mineralizing solutions by flexing, shearing, and fracturing the sedimentary beds. This structure is used with the spatial and genetic relationship of the ore minerals, sphalerite and galena, and the gangue minerals, dolomite and jasperoid, in prospecting for ore bodies. THE Picher Mining Field, fig. 1, which lies between Baxter Springs, Kansas, and Commerce, Okla., is the most intensely mineralized and the largest zinc-lead ore producing area in the Tri-State District of Missouri, Kansas, and Oklahoma. It has a vast lateral extent of underground workings that is unequaled for the observation of the geology of zinc-lead ore bodies in sedimentary horizons; and thousands of churn drill holes in the unmined areas supplement the underground observations with useful data for the interpretation of the geology. This paper is confined to the ore deposits of the Picher mining field. The reader is referred to the bibliography for the general geology of the Tri-State district which has been ably covered by many geologists. The writer was co-author of several publications on the Tri-State district.'-" This paper is necessarily a repetition of parts of those publications but contains a few changes and additions on the deposition of the minerals. The parts of this paper concerning mineralization maps and pipe slump-structures are not covered in the above publications. Geology The geology of the Picher mining field is similar to that of the entire Tri-State district because the sedimentary horizons that are found here are found throughout the district, and the ore bodies in the respective horizons have similar characteristics. The beds that contain the ore bodies in the Picher field are illustrated and described in fig. 2. The five unconformities found in the mines of the Picher field are indicated on the geologic section, fig. 2. The unconformity shown at the base of Meramec (B bed) is relatively unimportant since B bed was mostly eroded from the area of the Picher field before the Chester beds were deposited. B bed has been observed in the cuttings from only a few churn drill holes. The Pennsylvanian (Cherokee shale) formation is the top horizon found in the Picher mining field. It has been eroded from the southeastern part of the field, but because of the regional dip of the sedimentary beds to the west, it attains thicknesses of 100 ft to 200 ft along the west edge of the field. It is 200 ft to 300 ft thick in the Miami trough. It was deposited on the Boone limestone surface, which contained relatively few shallow erosion channels and very few depressions. Subsequent to the deposition of the shale, solution of limestone from underlying limestone horizons by circulating solutions caused the overlying beds, including the Cherokee shale, to slump into the larger openings formed by the solution and removal of the limestone. Chert The origin of the chert in the Tri-State district has been a controversial subject among geologists. Tarr7 advocated a syngenetic origin for the chert, postulating that it formed from colloidal silica deposited in the Mississippian seas. Leith, Dake and Leighton' argued in favor of silicification of erosion

Jan 1, 1951

By J. Lyden

In the Picher field, structure made openings for the circulation of the mineralizing solutions by flexing, shearing, and fracturing the sedimentary beds. This structure is used with the spatial and genetic relationship of the ore minerals, sphalerite and galena, and the gangue minerals, dolomite and jasperoid, in prospecting for ore bodies. THE Picher Mining Field, fig. 1, which lies between Baxter Springs, Kansas, and Commerce, Okla., is the most intensely mineralized and the largest zinc-lead ore producing area in the Tri-State District of Missouri, Kansas, and Oklahoma. It has a vast lateral extent of underground workings that is unequaled for the observation of the geology of zinc-lead ore bodies in sedimentary horizons; and thousands of churn drill holes in the unmined areas supplement the underground observations with useful data for the interpretation of the geology. This paper is confined to the ore deposits of the Picher mining field. The reader is referred to the bibliography for the general geology of the Tri-State district which has been ably covered by many geologists. The writer was co-author of several publications on the Tri-State district.'-" This paper is necessarily a repetition of parts of those publications but contains a few changes and additions on the deposition of the minerals. The parts of this paper concerning mineralization maps and pipe slump-structures are not covered in the above publications. Geology The geology of the Picher mining field is similar to that of the entire Tri-State district because the sedimentary horizons that are found here are found throughout the district, and the ore bodies in the respective horizons have similar characteristics. The beds that contain the ore bodies in the Picher field are illustrated and described in fig. 2. The five unconformities found in the mines of the Picher field are indicated on the geologic section, fig. 2. The unconformity shown at the base of Meramec (B bed) is relatively unimportant since B bed was mostly eroded from the area of the Picher field before the Chester beds were deposited. B bed has been observed in the cuttings from only a few churn drill holes. The Pennsylvanian (Cherokee shale) formation is the top horizon found in the Picher mining field. It has been eroded from the southeastern part of the field, but because of the regional dip of the sedimentary beds to the west, it attains thicknesses of 100 ft to 200 ft along the west edge of the field. It is 200 ft to 300 ft thick in the Miami trough. It was deposited on the Boone limestone surface, which contained relatively few shallow erosion channels and very few depressions. Subsequent to the deposition of the shale, solution of limestone from underlying limestone horizons by circulating solutions caused the overlying beds, including the Cherokee shale, to slump into the larger openings formed by the solution and removal of the limestone. Chert The origin of the chert in the Tri-State district has been a controversial subject among geologists. Tarr7 advocated a syngenetic origin for the chert, postulating that it formed from colloidal silica deposited in the Mississippian seas. Leith, Dake and Leighton' argued in favor of silicification of erosion

Jan 1, 1951

INTRODUCTION TO MINERAL INVENTORY The first explanations to be made must answer the questions: What is a mineral inventory, and how is a mineral inventory different from an ore reserve? The term mineral inventory is a relatively new designation-born of the computer age and grown to common usage with the development of computer techniques for extending drill-hole sample values to regularly gridded data blocks representing in situ mineral values. The term has been generally accepted by geologists and engineers because it has a precise meaning which avoids many of the ambiguities of ore reserve. A mineral inventory is an estimated inventory of mineral in place and is usually achieved by dividing the deposit into regularly spaced gridded blocks to which are assigned estimated values using various extension techniques. A mineral inventory makes no presumptions about the mineability of the blocks or their cutoff grade. Such parameters are implied with the use of the term ore reserve. Ore has a specific definition (see Chapter 1) and ore reserve must reflect that definition and thus has economic and mining constraints. An ore reserve will be different under different economic and mining conditions and is subject to reclassification by many factors. The term mineral inventory avoids all such ambiguities. A mineral inventory estimate may be good or poor according to how much is known about the deposit, how extensively it has been sampled, and what techniques have been employed to assign estimated grade to the blocks. Such an inventory, however, does not change with time, economic conditions, or mining technology, but only with new and better data and methods. Thus, the mineral inventory is an excellent designation for describing mineral value distribution within a deposit's geological setting. The techniques for assigning values and tonnage to mineral blocks or panels are the subjects of this chapter. Whether a summation of the blocks be called a mineral inventory or mineral reserve is not important. Many conventional methods for computing reserves of minerals refer to the methods in terms of ore reserve calculations. OBJECTIVES OF MINERAL INVENTORY OR RESERVES Mineral inventories are computed for the purpose of determining the quantity, the quality or value, and the spatial distribution of potentially economic minerals within the earth. Such computations are made at all stages in the life of a mineral extraction process, from the early exploration phase to the final year in the life of a mine. To quote Popoff (1966, p. 2), "They are the most responsible and irreplaceable tasks in the valuation of a mineral deposit. Efficiency in extraction and productiveness is impossible without accurate reserve computations." The accuracy of estimate required for each of the three parameters of quantity, value, and location is dependent upon the objective for which the reserve estimate is being made. Again quoting Popoff (1966, p. 2): Reserves are computed to determine the extent of exploration and development; distribution of values; annual output; probable and possible productive life of the mine; method of extraction and plan design; improvements in extraction, treatment, and processing; and requirements for capital, equipment, labor, power, and materials. Such computations are used to assist development

Jan 1, 1980

By J. R. Johanson

With the continuing development of automatic operations, it is important that reliable discharge rates through hoppers and bins be obtained for bulk solids. In most applications a feeder is used to control the feed rate. The selection of this feeder size is usually based on the rated ability of the feeder to move material without regard to the capability of the material to flow through the opening in the hopper onto the feeder. The dis charge rate through a given hopper opening may vary from zero to a theoretical maximum depending on the flow properties of the material. This paper presents an equation for the maximum discharge rate for a bulk material as a function of the hopper shape, the opening size and the flow properties of the material. Discharge-rate tests on various materials indicate good agreement with calculated values for opening sizes from a fraction of an inch to several feet. As part of a program to develop improved design criteria for bulk storage and handling facilities, a specific study of the methods involved in calculating the rate of discharge of bulk solids from hoppers and bins has been made. This study is closely related to earlier work done on the prevention of flow problems through the choice of proper design geometry of hoppers and bins1. The present paper is an extension of this earlier work, and therefore many of the concepts previously derived and explained will be used without explanation. Two types of flow will be considered: plane-strain flow in a wedge-shaped hopper and axial-symmetry flow in a conical hopper. The literature contains many studies on discharge rate for regular-shaped dry particles2*3 such as glass beads, lead shot and coarse dry sand. However, the work is empirical in nature, and it is difficult to extrapolate the given information to apply to moist, sticky materials typical of many industries. Some studies4 have shown a decrease in discharge rate with an increased moisture content of the material. However, no attempt was made to correlate the discharge rate with moisture. The method of calculating discharge rate presented in this paper was derived analytically from the basic knowledge of the flow of frictional, cohesive, granular solids, The equation includes the effect of material cohesion (stickiness), hopper configuration, opening size and bulk density of the material. THEORETICAL WORK The basic assumptions made in deriving the discharge rate equation are as follows: 1) The material is a frictional, cohesive, granular solid. 2) The flow is considered continuous and without significant density change. 3) The material at the hopper opening forms a continuously failing arch that is in dynamic equilibrium. 4) The strength of the material in the arch, which must be overcome for the arch to fail, is caused by the pressure in the flowing mass near the hopper opening. 5) This pressure at the hopper opening can be calculated5. If we consider the dynamic equilibrium of an arch of uniform thickness such as that shown in Fig. 1,

Jan 1, 1965

By T. P. Papazoglou, N. A. D. Parlee, W. C. Phelps

HE high vapor pressures of metals such as lead, calcium, lithium, bismuth, and magnesium at steel-making temperatures present experimental problems which have thus far rendered it almost impossible to obtain really reliable data for their solubilities in liquid iron. Many investigators have attempted to equilibrate liquid iron in the same crucible with the undissolved liquid phase of such volatile metals. The published results,l-6 although useful, are often questionable on the grounds of not being obtained under true equilibrium conditions. Such information is not always of practical value in any case since the equilibrium vapor pressure is often several atmospheres and steel is not currently made at these pressures. Solubility measurements at lower partial pressures (< 1 atm) appeared to be more practical and easier to make. These data could be used to calculate solubilities at other pressures where Henry&apos;s Law is obeyed, and to estimate solubilities under other conditions of temperature and pressure with useful accuracy. This note outlines the development of a general technique for the measurement of solubilities in systems of this kind. The method involves equilibration of the high-boiling metal at known temperatures with the vapors of a low-boiling metal at known partial pressures. Analyses of quenched samples provide vapor pressure-solubility data and make calculations of alloy thermodynamics possible. The principle involved is similar to the closed-system diffusion-transport method which is difficult to apply with most high-melting liquid metals like iron, due to closure problems. A two-zone horizontal (molybdenum wire element) tube furnace, Fig. 1, provides two constant-temperature zones in a reaction tuve (3/4 in. ID by 1 in. OD by 36 in.). A high-boiling metal sample, 9, introduced in the higher-temperature zone, is maintained at temperature T1, and a volatile metal sample, 7, in the lower-temperature zone, is held at T2. A stream of argon with 10 pct hydrogen is passed via flowmeters, 1, and mixing-drying towers, 2 and 3. through the reaction tube at a favorable flowrate and acts as a carrier gas which entrains vapor from the volatile liquid metal at a specific constant partial pressure. The gas mixture passes through a system of constrictions, 6 and 8, to the higher-temperature zone, establishes intimate contact with the high-boiling liquid sample, 9, and exits through a small condenser tube. The entire system is at (nearly) atmospheric pressure and the volume of carrier gas passed is measured with a wet gas meter. When the high-boiling sample attains equilibrium with the vapor phase, both samples are removed and quenched. Analysis of the high-boiling sample for solute content reveals its solubility for the low-boiling metal at a vapor pressure calculated from carrier-gas volume and either a) weight loss of volatile metal or 6) weight gain of high-boiling sample plus condenser (which collects the undissolved vapors). To test the capabilities of the method, liquid silver at 1403&apos;C was equilibrated with lead vapor at various partial pressures. The relatively simple Pb-Ag system was particularly suitable for uncovering experimental problems and providing the first step toward investigations with more volatile metals and more difficult combinations.

Jan 1, 1965

Jan 1, 1971

By D. J. Carney, R. L. Stephenson

A sampling technique has been developed for procuring a sample of sinter representative of the entire depth of the sintering bed. The sampling method involves the use of an open-bottom metal basket that rides on the grate of the sintering machine and when removed contains a sample of the sintered product. Additional data have been obtained to indicate that the tumbler test is a suitable means of measuring sinter strength. IN the last few years additional sintering facilities have been installed in both the Pittsburgh and the Chicago district of the United States Steel Co. Since the construction of these sintering plants made possible the use of higher percentages of flue-dust sinter in our blast-furnace burdens, it became important to study means of controlling the quality of sinter to obtain optimum results in the blast furnace. For controlling an operating process, it is necessary first to establish standards by which the quality of the product can be judged. For sinter, it appeared that an important property was its strength or its resistance to degradation during transportation and charging into the furnace. Consequently work was undertaken to establish a standard for sinter strength that could be used both for controlling sintering-plant operations and for correlating sinter quality with blast-furnace performance. The first problem in setting up a standard was that of procuring a sample that would be representative of the sinter made under any particular set of conditions at the sintering plant. Since the United States Steel Co. sintering plants discharge the finished sinter either into a large pit or onto a rotary cooler, the sinter becomes inseparably mixed with material sintered 2 hr before or 2 hr afterwards. For this reason the exact identity of the sinter is lost. A sample selected as the cooler is discharged, or as the sinter is removed from the pit, cannot be said to be truly representative of the sinter made at any specific time. Sampling The first attempt to procure a sample that would be representative of a specific sinter mix and of specific operating conditions was made by stopping the Dwight Lloyd sintering machine and removing an entire pallet full of sinter. This method, however, proved very difficult to perform and interfered considerably with the operation of the plant. To overcome this difficulty, a sampling method was devised by technologists at South Works enabling them to secure, without interrupting the sintering operation, a sample of about 1 cu ft of sinter, representative of sinter for the full depth of the sintering bed. The South Works method involves the use of a steel-frame-work basket. A typical basket is shown in Fig. 1. The basket has been used both with and without crossbars along the bottom. As long as the crossbars are in the same direction as the grate bars on the sintering machine they do not interfere with the sintering process. The basket is set on an empty grate of the Dwight Lloyd sintering machine before it passes under the swinging feed spout, see Fig. 2. When the basket is removed after it has travelled the length of the sintering machine, it contains the sample. Just before the basket is removed, the sinter is scored and chipped to facilitate removal of the sample from the sinter bed. A view of the basket after its removal is shown in Fig. 3. Although the sampling method was originally designed for use on a Dwight Lloyd sintering machine, it can also be used on the Greenawalt type of machine. When used on the Greenawalt-type machine, the basket is placed on the sintering grate before the charging car passes over it, and finally it is removed just before the pan is dumped. Testing After a method of obtaining a representative sample of sinter had been developed, the next step was to select a method of measuring its strength. The irregular shape and size of the sinter pieces precluded the use of a simple compression test for determining strength; consequently, the shatter test and tumbler test were investigated. To perform the shatter test, a sample of sinter, approximately 5 lb, is dropped from a hinged-bottom box at a height of 3 ft onto a steel plate. The broken sinter is sieve-analyzed after a specified number of drops. The tumbler test is performed with the use of a standard ASTM coke-tumbling drum. The drum is 3 ft in diam and is equipped with two lifter bars diametrically opposite one another on the inner periphery of the drum. The drum is rotated at a speed of 24 rpm for 200 revolutions, and after tumbling the sample is sieve-analyzed. To express as single numbers the results of sieve analyses after shattering or tumbling, the method suggested by R. E. Powers1 was employed. This method involved plotting the size of the sieve openings on a logarithmic scale and the cumulative per cent larger than each sieve on a probability scale as described by J. B. Austin.&apos; By interpolating from the plotted data, which in most cases approximated

Jan 1, 1954

By A. H. Daane, J. F. Haefling

BECAUSE of the wide use of platinum in industry and research, the physical properties of this metal, including its vapor pressure, have been studied in some detail.&apos; The other members of the palladium-platinum group of metals have not been studied as extensively, and only qualitative information is available on the vapor pressure of palladium. Data given in literature by Vines1 and Brewer2 on the vapor pressure of palladium are based on the qualitative observations by Holborn and Austin3 and Crookes4 on the rate of volatilization of palladium filaments in various atmospheres. The general observation that palladium is the most volatile metal of the palladium-platinum metal group was corroborated by Bell, Love and Normand who studied the separation of isotopes of the platinum-group metals by a mass spectrometric method. We have measured the vapor pressure of palladium using the Knudsen effusion technique. In this work, the effusion vessel was suspended from a quartz-fiber microbalance into an induction furnace, and the amount of vapor effusing from the vessel was determined by direct weighing of the vessel during the measured heating times. This technique has been described in a report from this laboratory." The vapor pressure of palladium was calculated from these measurements using the equation P...... = 17.14 -W- (77m)&apos;u [1] a t where ? is the weight loss in grams of vapor of molecular weight m from a vessel having an orifice of a sq cm, during t sec. The derivation of this equation from kinetic theory has been described in a previous report from this laboratory: as well as in texts discussing the kinetic theory of gases.%" Test Vessel—In the search for a suitable material for the effusion vessel, it was found that tantalum reacted with palladium metal to form intermetallic compounds, and graphite was readily dissolved in palladium metal to form what appeared to be a liquid phase at a temperature several hundred degrees below the melting point of palladium. On cooling, the graphite gathered into spherical balls in the palladium, with crystals extending radially from the center of these balls, some of which were a millimeter or more in diameter. However, palladium metal vapor did not attack the graphite vessel, so graphite could be used where it did not contact condensed palladium. Tungsten did not appear to react with palladium vapor or molten palladium at its melting point, but it was not convenient to use a tungsten-vapor pressure vessel because of the difficulty of fabricating this metal. Since the vapor-pressure range to be studied (10 2 to 10 &apos; mm) did not appear to extend above the melting point of palladium, a combination of tungsten and graphite served to provide a very satisfactory effusion vessel. The lower half of the graphite vessel was lined with some strips of tungsten foil and the sample of palladium consisting of a coil of sheet was placed in the tungsten liner; in this way, no contamination of the palladium by carbon occurred. Procedure After outgassing at 1500C, the tungsten-lined graphite effusion vessel was loaded with 300 mg of

Jan 1, 1959

By Asheim, Harald A.

Parameter estimates affect both the optimum field development decisions and the economic result. A general methodology for assessment of the effects of parameter uncertainty in offshore development decision situations is proposed, and used to analyze aspects of the initial development situation for the Statfjord field.

Jan 1, 1982

By V. Pasupathi, R. E. Hummel, J. W. Koger

Specimens of P1 brass were plastically deformed at room temperature to various degrees of deformation and subsequently cooled in order to transform them to low-temperature martensite. Deformation shifts Ms. A, , and the temperature of minimum resistivity to lower temperatures, and also decreases the temperature coefficient of electrical resistivity. These properties change rapidly up to about 15 pct reduction but vary very little with higher deformation. The possible relationships between martensite formed by deformation and the M, temperature of low-temperature martensite are discussed. Evidence is given that deformation martensite delays the formation of low-temperature martensite. BETA&apos; brass undergoes at least two different types of martensitic transformations. One of these transformations (B1- B2) was first observed by Kaminski and ~urdjumov&apos; and occurs when 81 brass with a zinc content between 38 and 42 wt pct (quenched from the single-phase region) is cooled below room temperature. Jollev and Hull&apos; determined the structure of 0" from X-ray and electron-diffraction data as ortho-rhombic. Kunze came to the conclusion that the super-lattice cell of 0" is one-sided face-centered triclinic (pseudomonoclinic). The second martensitic transformation (B1-A1) occurs when the specimens are deformed at or somewhat above room temperature. This type of martensite will be called deformation martensite. Horn-bogen, Segmuller, and Wassermann4 determined the structure of deformation martensite to be bct. (An intermediate phase, az, occurs before the final phase appears.) At deformations higher than 70 pct, a, transforms into a.4 A critical temperature Md exists above which no transformation occurs during deformation and is estimated to be around 400°C in P1 brass.5 This martensite has elastic properties.6 When the sample is stressed, martensitic plates appear; when the stress is released, the plates disappear. The present paper studies the effect of deformation martensite on the formation of low-temperature martensite. The experiments involved samples of 8, brass which were plastically deformed by various amounts and were subsequently cooled below the transformation temperature. EXPERIMENTAL PROCEDURE The 13 brass investigated was made from 99.999 pct pure copper and 99.9999 pct pure zinc and contained 38.8 wt pct Zn. The specimens, consisting of foils 0.1 mm in thickness, were heat-treated at 8&apos;70°C for 15 min in an argon atmosphere and then quenched into ice water. They were then deformed by cold rolling and subsequently cooled at a rate of 1°C per min. The martensitic transformation that occurred during cooling was followed by electrical resistivity measurements. The resistance measurement technique and its accuracy have been described in a previous paper. Because the transformation 81 —-8" occurs below room temperature, the samples were placed in a cryo-stat which contained isopentane as a cooling medium. The isopentane was cooled by liquid nitrogen pumped under pressure through a 15-ft coil of copper tubing which was immersed in the isopentane. The nitrogen flow was regulated by a temperature controller using two thermistors in the cooling medium. The cryogenic liquid could be heated with an immersion heater. The useful temperature range with this device was from +25° to approximately -155~C. EXPERIMENTAL RESULTS Resistivity Measurements. The following abbreviations are used in this paper to label the characteristic temperatures during the martensitic transformation. M, is the starting point of the martensitic transformation and is defined as that temperature where the resistivity vs temperature curve on cooling first deviates from a straight line. Mf is the temperature at which the martensitic transformation is completed. On reheating, the transformation from martensite to the parent phase starts at a temperature A, and ceases at a temperature Af. Fig. 1 presents five different resistivity vs temperature curves corresponding to the transformation of brass from Dl to 8" after different degrees of reduction in thickness. The following observations can be made from these curves. 1) With increasing degree of deformation the Ms temperature is shifted to lower temperatures. This shift ranges up to 35°C compared to the undeformed state. This is also indicated in Fig. 2, where AM, (the shift of Ms, compared to the undeformed state) is plotted vs the degree of deformation. AM, increases rapidly until a reduction of about 15 pct is reached. With higher deformations, no additional increase in AM, was found. 2) With increasing degree of deformation the temperature of minimum resistivity (M) is also shifted to lower temperatures. The shift, attains a maximum of about 61°C compared to the undeformed state. In Fig. 3, AM is plotted as a function of deformation. It can be seen that, as in 1 above, AM increases rapidly and no further shift of M occurs for deformations greater than 15 pct. 3) The temperature coefficient of resistivity, is given by the slopes (dp/dT) of the linear portions of

Jan 1, 1969

By Douglas J. Robinson

A pilot scale process has been developed to separate mercury, tin, silver, and copper from dental amalgam scrap. Laboratory research led to a process which was operated in 55 gallon drum sized reactors to treat 2000 Tr oz charges of scrap per day. This paper discusses the development work, presents a flowsheet and gives an indication of the equipment necessary to carry out the process on a commercial scale.

Jan 1, 1984

By R. A. Deju, R. B. Bhappu

Further information on the surface characteristics of the silicate minerals was obtained by experimentally correlating the oxygen-silicon ratio of the silicates with their electrokinetic properties. Specifically, the behavior of the minerals in an electric field was investigated using zero point of charge as a parameter. A modified electrophoresis cell was used for the determination of electrophoretic mobilities. It was shown that there is an increase in the zero point of charge with increasing oxygen-silicon ratio in the silicates. Finally, a chemical interpretation was presented to describe the surface phenomena observed in the experiments. In recent years great interest in surface chemistry has produced a number of methods to study the surfaces of minerals and to observe the phenomena occurring at their interfaces. One such method is discussed in this paper. A rather complete review of the surface characteristics of the oxide minerals has been undertaken by parks,&apos; but, a similar study has not been made for the silicate minerals. Two previous papers by the authors2&apos;3 attempted to remedy this situation. In these papers it was demonstrated that the reaction between the silicate mineral particles and acidic water involves mainly an exchange of metal ions for hydrogen ions on the surface of the solid, leading to an increase in pH of the aqueous phase. Also, the degree of reaction was found to depend on the oxygen-silicon ratio of the silicate structure, being least for the quartz and greatest for the olivines. A hypothesis was then set forth explaining that upon the fracturing of a silicate mineral, the oxygen-metal bond (which is almost entirely ionic in character) will break more easily than the stronger oxygen-silicon bond. This results in the exposure of unsatisfied oxygen sites on one hand and active, exchangeable cations on the other. These active sites on the fractured surfaces are then available for reaction with the hydrogen ions in acidified aqueous solution. Thus, an increase in degree of adsorption of hydrogen ions occurs as the oxygen-silicon ratio increases due to the presence of a larger number of active sites on such minerals. A correlation between oxygen-silicon ratio and electrokinetic properties will be further pursued in this paper from both the theoretical and experimental points of view. Efforts will then be made to present a chemical interpretation of surface phenomena observed in the experiments. It is believed that this study may supply pertinent information on the behavior of silicate minerals in froth flotation systems. ELECTROKINETIC STUDIES Equipment: In a previous paper,2 Deju and Bhappu described a simple method for determing the zero point of charge using a potential across a cata-phoresis cell and observing particle movement by means of a Rayoscope* optical system. This setup is simple in design and operation and extremely reliable. With care, reproducible results within 1.5% accuracy may be obtained. A new setup has been developed, based partly on the design by Zeta-Meter Corp.4 and partly on previous cells used at the New Mexico Bureau of Mines. This new, modified cell is shown in Fig. 1. Although

Jan 1, 1967

By Robert Lowrie

Nine intermetallic compounds were tested in tension at various temperatures. Seven exhibited extensive plastic deformation at elevated temperatures. Correlations of tensile strength and elongation are attempted with melting (decomposition) temperature, valence electron configurations of the component elements, heat of formation, crystal structure, density, and volume decrease accompanying compound formation. A LTHOUGH intermetallic compounds have been -tX known for many years, the study of their mechanical properties, particularly in tension, is just beginning. The problem has been unattractive because of the well-known, erratic behavior of brittle materials tested in tension. The strong influence of surface or internal flaws as stress raisers in non-ductile materials and the effect of eccentricity of loading in superimposing bending stresses on the state of tension in the specimen are extremely difficult to mitigate and impossible to completely eliminate. Thus, tensile properties determined for brittle materials, such as intermetallic compounds at temperatures low in comparison to their melting points, are at best only general guides to the values to be expected in an ideal test of a perfect specimen of the material. It is, nevertheless, surprising that apparently no attempt was made to follow up the pioneer work of Tammann and Dahl1 in this field. Working with crude apparatus, these investigators succeeded in showing unequivocally that at temperatures sufficiently close to their melting points (from 75" to 400°C for the compounds tested) intermetallic compounds did exhibit plasticity. This was indicated by the appearance of slip lines on the surface of the specimen. No observations of strength were made in these tests, which were of a compressive or indentation type. Rossi2 in 1932 attempted to study the physical and mechanical properties of single crystals of a group of intermetallic compounds. However, he was able to prepare only one material, Cu2Z8,, in the form of large, defect-free, single crystals. Thus, he was able to report only the relative fragility of the compounds at room temperature. He reported one compound, Ag,Zn,, to be somewhat plastic at room temperature and Cu,Si to be friable, the latter in agreement with results reported herein. Although test results are available only in classified literature, it has also been announced that MoSi, possesses some ductility at elevated temperatures." In 1948 and 1949 Savitskii and Savitskii and Baron -ublished their work on the hot extrusion of Mg-Zn, Al-Mg, and Cu-Zn compounds. Under the favorable state of stress existing for this process MgZn, MgZn,, MgZn,, ß (Al-Mg), ? (Al-Mg) and 0 (Cu-Zn) could be reduced by amounts up to 90 pct at elevated temperatures. These authors also report that hardnesses of Mg-Zn compounds decrease from room temperature values of about 300 kg per sq mm to 30 to 50 kg per sq mm at 325°C. They found that alloys consisting solely of one Mg-Zn compound were most resistant to softening on heating, mixtures of a compound and eutectic less resistant, and mixtures of two compounds least resistant. The more rapid softening of mixtures of

Jan 1, 1953

By J. B. Newkirk

Results of a Debye-Scherrer X-ray investigation are given which show that the order-disorder transformation is a first-order or heterogeneous reaction in Cu-AU alloys with compositions near CuAu. Evidence was found for conventional tie-line segregation across a usual type of two-phase field separating the ordered and disordered fields in the Cu-Au equilibrium phase diagram. The horizontal and vertical widths of the two-phase fields are about 3 atomic pct and 20°C, respectively, at 43 and 54 atomic pct Au. No evidence for the existence of an ordered structure based on a stoichiometric composition of Cu3Au2 could be found. ALTHOUGH the modern theories relating the de-Agree of order of binary alloys to temperature and composition have met with considerable success, the nature of the transformation from the disordered state to the ordered state and vice versa has never been well understood. It has been assumed by some&apos; that this is a second-order transformation, that is, a homogeneous change of state. Others2 hold that the transformation is first-order and that the effects characteristic of heterogeneous phase transformation apply. Since this subject is discussed in detail in a recent paper,&apos; the arguments will not be repeated here. The present paper summarizes an experiment which was designed to distinguish between these two viewpoints for the case of Cu-Au alloys near the composition CuAu. The Cu-Au system is an important one because it furnishes prototype alloys, the behavior of which has formed the basis of much of the present-day order-disorder theory. It has recently been shown- hat in alloys near Cu3Au there is a temperature range within which the ordered and disordered states coexist in equilibrium and are distinguishable as separate phases. Therefore, the transformation must be first-order for these alloys. A similar demonstration for alloys near CuAu, however, has been lacking. Experimental Method Essentially the experiment consisted of equilibrating Cu-Au samples at various temperatures, quenching them in water to retain the high temperature states, and then examining them at room temperature for the coexistence of the ordered and disordered structures. The thermal gradient method of heat treatment- as used because it was important that all temperatures over the transformation range should be represented in the test. Briefly, this method consisted of holding a wire of the desired composition, sealed under vacuum in Pyrex, in a known temperature gradient for a long enough time to allow each part of the wire to assume the crystal structure characteristic of the temperature at which it was held. The temperature gradient was produced by inserting into an ordinary wire-wound cylindrical laboratory furnace, an 18 in. length of 1/8 in. ID ceramic tube which was heavily wrapped with asbestos. The furnace power was controlled by a Tag-liabue Celectray controller and a chromel-alumel thermocouple with the junction located on the heating elements. During the equilibrating treatment the widest variation of temperature within the gradient tube was approximately 4°C at the highest temperature. The temperature at various places within the tube was determined, before inserting

Jan 1, 1954

By E. H. Edwards, J. Washburn

Zinc crystals were deformed in simple shear and it was found that anisotropic strain hardening occurred in which the inactive slip systems were hardened more than the active system. The formation of dislocation barriers by dislocation interaction was discussed as a possible explanation of the hardening of the latent systems. STRAIN hardening which accompanies slip in a metal crystal is not limited to the slip systems actively contributing to the plastic strain. There is also a strengthening of the latent slip systems which are crystallographically equivalent to the active system. In the case of aluminum deformed in tension, Taylor and Elam1 found that plastic flow on one set of octahedral planes caused either the same or a slightly greater hardening on an inactive set. Similar results have been obtained for crystals of a brass2 and of Cu-A1 solid solutions.3 Experiments by Rohm and Kochendorfer4 indicated that the hardening of the active system exceeded the hardening of any latent system for aluminum crystals deformed in shear. On the other hand, strain hardening in zinc and cadmium crystals tested in simple shear at —196°C was recently found to be greater in the latent than in the active slip direction." When the strain direction was shifted during testing to a direction 60" from the original, a higher stress was required for glide to continue than would have been needed for flow to proceed in the original direction. The relation between the hardening of active and latent systems must be complex, depending upon the relative orientations of the systems and upon the experimental techniques used to deform the crystal. A detailed knowledge of the hardening produced in latent systems would be valuable in choosing between possible dislocation models of the strain-hardening process. The experimental data now available are incomplete and even contradictory. The present study was undertaken to provide quantitative information regarding the relative amount of hardening of active and latent systems for a particularly simple case. Zinc crystals were deformed in simple shear along one of the three crystallographically equivalent directions [250], [1210], and [1120] in the slip plane, and the relative hardening produced in each of these directions was compared. Experimental Procedure and Results The single crystals of 99.99 pct purity zinc used in this investigation were grown from the melt in the form of 1 in. diam spheres. Shear specimens were acid-machined from the crystals by a method which has been described previously. The gage section of the test specimen was a cylinder having a height of 1/8 in. and a cross-sectional area of approximately 1/3 sq in. All specimens were machined with the axis of this cylindrical gage section aligned with the [0001] axis of the crystal. An innovation in the design of the shearing apparatus for these tests was the provision for a rapid shift in the direction of the applied stress from one slip direction to any other slip direction lying in the same slip plane. Fig. 1 shows a section through the specimen and shearing apparatus, and Fig. 2 is a

Jan 1, 1955

By Homer N. Mead

This report develops equations for decline curve analysis based upon the premise that the rate of change of the reciprocal of decline for succeeding time intervals is constant when the reservoir is produced under a fixed set of conditions. A method is shown for predicting maximum production rate against cumulative production for any reservoir. A method is also presented for predicting future production rate by an analysis of past production performance after decline has been esrahlished. INTRODUCTION No significant contribution to the analysis of decline curves by the loss-ratio method has been made since J. J. Arps paper1. The concept of loss-ratio that was developed by Arps and his contemporaries has been redefined in another way and the concept of instantaneous loss-ratio at time zero has been added. In the mathematical developmerit by Arps, production rate was related as a continuous function with time and his equatlons were developed on that basis. In this paper, production is considered to be a series of segments for equal time intervals and equations have been developed based upon these finite differences. It is realized that decline curve analysis is not the answer to all predictions of reservoir behavior. However, as production must decline from an initial maximum rate to zero in any reservoir, if such decline can be expressed as an infinite series, this series should accurately predict production. Decline curve analysis should be considered a valuable tool that may be used in conjunction with predictions of future recoveries by other methods. Various uses of the decline curve method will be discussed in this paper. Equations predicting production rate at any time and cumulative production by exponential and hyperbolic decline will be developed. Characteristic values of b related to various types of drive will be discussed. After that a hypothetical reservoir will be studied and ultimate recovery by natural depletion and pressure maintenance compared, then actual field examples will be shown and discussed. The rate-cumulative curve introduced by H. N. Marshs in 1928 is an important one for use in estimating future production rate and ultimate recovery. This graphical method is the one that is used in conjunction with the equations to be developed for predicting production behavior. EXPONENTIAL DECLINE In exponential decline each succeeding production rate per unit of time is a constant percentage of the production rate just before it. Since (1 — r) is the common ratio, where r is the constant decline rate, this condition may be expressed as a geometrical progression; thus Pn = P (1 - r)n-1 . ......(1) Where r is less than unity, r Since P1 (1 - r)n = Pn+1 P1 - Pn+1 C =P1-Pn+1/r........(2) LOSS-RATIO In this paper the calculation for loss-ratio has been changed from the method presented by Johnson and Bollens2. The first loss-ratio to be calculated is a,; it is the initial production per unit of time after decline has set in divided by the difference between the initial and the second production rate. This loss-ratio is for the first time interval. After b (which is the constant change

Jan 1, 1957

By R. P. Thomas

Secondary fertilizer minerals are the mineral materials used to supply directly and indirectly the secondary and trace plant food nutrient needs of a fertilizer. Since few soils contain sufficient availability of all plant nutrients for their proper growth, man has prepared mixtures of plant food materials to correct these nutrient deficiencies. These mixtures or fertilizers, when added correctly to a soil, make it possible for abundant and economic crop growth. Many kinds of materials are used as sources of these needed nutrients. They come from natural and synthetic materials and minerals including many beneficiated byproduct compounds. A fertilizer consists largely of carriers of one or more of the three major plant foods, namely nitrogen (N), phosphorus-phosphorus pentoxide (P2O5) and potassium-potash (K2O). Many other nutrients are just as essential for plant growth as the three major plant foods. In fact, the efficient use of fertilizers today depends upon an adequate supply of all these other nutrients. Since these additional materials are usually removed from the soil by plants and supplied in fertilizer in less quantities than the major nutrients, they are called secondary and minor nutrients. In the early days these special nutrients were contained as impurities in the primary nutrient carriers. Today, fertilizers are made primarily from concentrated and synthetic materials which carry very few of these other essential nutrients. Consequently, many secondary and trace nutrient carriers, as salts, byproduct compounds and even minerals have to be added to fertilizers. Secondary Nutrient Carriers The secondary plant foods in fertilizer are next to the major nutrients in abundance. They are calcium, magnesium, sulfur, chlorine, silicon and sodium. Although many of these elements are added to a fertilizer as part of the major nutrient carriers, they are also added in special carriers. The large tonnage of these secondary nutrient carriers used in fertilizers represents only a small percentage of the total production of these materials. A fertilizer producer thinks in terms of materials which supply nutrients instead of minerals. Therefore, these materials will be discussed by elements. CALCIUM Soils need calcium to supply the nutrient needs of plants and maintain the desired physical and biological conditions in the soil. The available calcium is usually 40 to 80 pct of the exchangeable bases. (These bases are ones which can be displaced by other cations and determined quantitatively. They are then expressed as milliequivalents per hundred grams of soil-me.) Direct applications of lime materials such as burnt, ground or hydrated limes are the important sources of calcium for the soil. Most crops, especially legumes, have a high requirement for calcium. The average farmer does not use enough lime to maintain the proper level of available calcium. Hence, it is necessary for many fertilizers to contain soluble calcium materials for efficient use of the major nutrients. The following major nutrient carriers supply some calcium: calcium nitrate, ammonium nitrate mixtures and cyanamid, and many of the phosphates. Both synthetic and natural gypsum are used in fertilizer production. Some crops such as peanuts require a large amount of soluble calcium. Gypsum is the important supplier of this soluble calcium. It is not applied with the fertilizer

Jan 1, 1960

By Edwin B. Wilson, Charles F. Cockrell

The application of evolutionary operation is proposed for the cleaning of coal by the heavy media process. Analysis of the data given suggests some benefits that may not be immediately appreciated unless evolutionary operation is applied. For example, while it may seem obvious to increase specific gravity when the ash and sulfur content of the clean coal is lower than that allowed, evolutionary operation may show that an increase in feed rate or an increase in both feed rate and specific gravity would be a more profitable alternative. In addition, by using evolutionary operation, up-to-date knowledge of the effect of change of feed rate or specific gravity on yield and product quality is available. This information facilitates confidence about decisions made in regard to the day-to-day operation of these units. A number of other applications in the minerals industry are proposed. An application of evolutionary operation in a related field is also given where a large number of variables were required to be optimized.

Jan 1, 1969