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By S. A. Falconer

This paper deals with the practical application of the Dutch State Mines cyclone separator for fine-coal cleaning. The more important operating variables are discussed, and results of a number of continuous-scale tests on various fine coals with a 6-in. cyclone separator are given. Descriptions of the Cyanamid Pilot Plant and the 50 tph Cyclone Separator Plant at the Emma Washery in Holland are included. TODAY, as never before, the coal producers of this country are faced with the necessity for obtaining maximum yield of marketable coal of all sizes down to and including the finest. Particular interest is being displayed in a more effective means of recovering the finer sizes which in the past so often have been discarded to waste or treated by inadequate equipment. The reasons for this interest are easily understood. Rising mining costs have resulted in the increased use of mechanized equipment underground for full seam mining. This, in turn, means more refuse in the run-of-mine and also more fines in the feed going to the cleaning plant. Stringent antistream pollution laws now make it necessary at least to impound the fines, and usually it is a paying proposition to recover the coal from these fines before sending them to the storage area. Finally, the market and price of the finer sizes has increased, but at the same time specifications have tightened and the demand is for higher grade products. During the past four years a great deal of publicity has been given to this new process and apparatus for treating fine sizes of ores as well as coal. Excellent discussions of the apparatus itself and the theoretical aspects of the basic operating principles involved in its operation have been presented by M. G. Driessen,1-3 M. R. Geer and H. F. Yancey,4,5 J. W. Hyer6 and more recently by D. A. Dahlstrom8 as well as others.7,9-11 In view of this, it has been decided to include in the present paper only a brief description of the cyclone separator and its operating principles. This paper deals primarily with some of the more practical commercial aspects of the process and equipment required for its operation; the variables in the operation of the cyclone, their effect and means for control; and the results obtained with a 6-in. semicommercial size separator on a variety of fine coals, bituminous and anthracite, using finely ground magnetite for the separating medium solids. A description is included of the commercial-size cyclone separator pilot plant installed by the Dutch State Mines at its Emma mine in Holland, where finely ground slate is utilized as medium solids. Field of Application: The Dutch State Mines cyclone separator operates most efficiently on ores and coal in the size range of % in. to about 48 mesh. On some types of feed, effective separation can be made on sizes as small as 100 mesh, but up to the present, this may be considered exceptional. Depending upon the type of medium used, the specific gravities of separation can be varied within wide limits, up to as high as 2.70, if magnetite is used as medium. Early Development: The development of the Dutch State Mines cyclone as a separator, or cleaner, was the outgrowth of early experimental work by Dries-sen' and others in Holland, just prior to World War 11, in the course of which was discovered the effectiveness of the cyclone in reclaiming and thickening the dense medium used in the "Loess" process of

Jan 1, 1951

By B. D. Smith, K. H. Coats

Experiments in which calcium chloride displaced sodium chloride from four cores showed the extent of asymmetry in the resulting effluent concentration profiles. These results provided a check on how validly the mixing process is modeled by a differential (i.e., not finite-stage) capacitance mathematical model. The effluent concentration profile from two consolidated cores exhibited considerable asymmetry, while two unconsolidated cores yielded nearly symmetrical profiles. All runs resulted in breakthrough of the 50 per cent concentration significantly before one pore volume was injected. In addition, velocity appreciably affected the effluent concentration profile from a Torpedo sandstone core. The differential capacitance model matched the data significantly better than a simple diffusion model. The capacitance model allows determination of the amount of dead-end pore space in a porous matrix and the effect of velocity on the rate of diffusion into this space. An experimental program yielding insight into the physical validity of the capacitance effect is described. INTRODUCTION Axial dispersion — the mixing accompanying the flow of miscible fluids through porous media — has been the subject of many relativeiy recent studiesl-13 and a comprehensive review of the topic has been given by Perkins and Johnston.14 This dispersion is of practical interest in studies of the miscible displacement process, fixed-bed chemical reactors, and the adsorption of solutes from a flowing stream onto the surface of a porous medium. In the latter case, the effect of dispersion must be considered when adsorption parameters are determined from the nature of concentration profiles. In general, early studies of dispersion assumed applicability of a simple diffusion equation and were concerned with correlation of the experimentallv determined "effective" diffusion coefficient with system properties over a large range of the latter. Recent have been concerned with the deviations between the asymmetrical effluent concentration profiles observed and the symmetrical ones predicted by the diffusion model. In the present study, effluent concentration profiles were obtained from consolidated and unconsolidated cores. These profiles were compared with those predicted by a differential (i.e., not finite-stage) capacitance model. Solutions to the simple diffusion model, for three sets of boundary conditions, were compared with one another and with the experimental profiles. SUMMARY OF PREVIOUS WORK The reader is referred to Perkins and johnston14 for an extensive review of studies of dispersion in porous media. Many investigators have employed the simple diffusion model characterized by Eq. 1 below: The dispersion coefficient D for unconsolidated systems is correlated by u is interstitial velocity and dp is particle diameter. Since heterogeneity of the sand pack affects the mixing, this equation is also expressed as where a is proportional to the degree of heterogeneity and is about 3.5 for random packs of unconsolidated sand.l4 Eq. 3 holds for 2 For a Do homogeneous (regular) type of packing, should be 1 or less.6 Aris and Amundson6 and Carberry and Bretton consider o to be the number of particle lengths per mixing cell in the finite-stage model. Data from consolidated cores indicate dp to be about 0.36 cm for outcrop rocks, Torpedo sandstone having a reported value of 0.17 cm.15 For v /Do less than about 2, the effect of molecular diffusion must be considered and the total dispersion coeffi-

Jan 1, 1965

By R. J. Towner

Tensile properties of Aluminum Powder Metallurgy (APM) products at 600°, 800°, and 1000°F were lowered by cold reductions of as little as 10 or 20 pct. The detrimental effect of cold work on yield strength at elevated temperatures increased with temperature. Heating cold-worked products at 850° to 1150°F removed the structural effects of cold work through the process of recovery and restored, at least partially, the strength at 600°F to the level of hot-worked material. Material containing 5 pct A1203 was recrystallized by cold reductions of 97 pct or more followed by annealing at 1100°F. Recrystallization lowered sharply the strength at room temperature, but raised the strength at 600°and 800°F relative to that of the cold-worked state The high strength of Aluminum Powder Metallurgy (APM) products at elevated temperatures'-4 is well-known. In this paper, some conditions of processing that can affect this important characteristic are presented. The following nomenclature will be used to identify different alloys: All of the above alloys are of the aluminum-aluminum oxide type made from milled powders of commercially pure aluminum with the exception of M486, which is fabricated from atomized A1-Fe alloy powder. The products made from milled powders are hardened by a dispersion of aluminum oxide par- ticles in the aluminum matrix, while the intermetal-lic compound FeAL is the dispersion hardening agent in M 486.' The process used for making all APM products involves the application of heat and pressure to form a compact from powder which is fabricated into an extrusion, sheet, strip, or wire by standard techniques. Probably the most common cold-worked APM product is sheet. Cremens, Bryan, and rant' determined the room-temperature tensile properties and the 600°F stress-rupture properties of XAPOOl and XAPOO3 sheet and reported that there was little difference between the as-extruded, cold-worked, and annealed at 1200°F conditions. On the other hand, Emmons6" found that the tensile and stress-rupture properties of XAPOOl and XAPOO3 sheet at 600" and 800°F were lower than those of extrusions. The tensile properties of XAPOO3 sheet were also determined at elevated temperatures by Doyle' and ~ayward.' According to Friske" and Kendal et a1.," cold working by swaging, rolling, and tube drawing reduced the tensile and creep-rupture strength of XAP 001 Recrystallized aluminum powder metallurgy products are rare because the dispersion in the aluminum matrix is usually too fine, uniform, and concentrated to permit recrystallization. However, Lenel12 was able to recrystallize wires made from aluminum powders containing about 1.75 and 3.0 pct oxide and found that the tensile properties at room temperature remained higher than those of annealed commercially pure aluminum because of the dispersed oxide particles. Westerman and Lenel13 found the kinetics of recrystallization of the powder products were very different from those of cold-drawn commercially pure aluminum wire. The alloy containing 3.0 pct oxide recrystallized to a very coarse grain size was more creep-resistant at 400" to 600°C (752" to 1112°F) than in the as-extruded, fine-grained condition, according to Ansell and weertman.14 Ansell and aenel" further studied creep at 500" to 620°C (932" to 1148°F) of recrystallized 1.75 pct oxide wire and confirmed the creep model of Ansell and Weertman. The present work is being reported for the fulfillment of the following objectives: 1) to show the effect of cold work on tensile properties at elevated temperatures;

Jan 1, 1964

By F. C. Schora, H. P. Meissner

Both a graphical and an analytical technique are presented for calculating stream compositions and temperatures in adiabatic staged systems in which solids travel countercurrently to a gas stream. Such a system might be a tower containing several plates, on each of which the descending solid is fluidized by the rising gas stream. Examples are presented in which chemical reactions occur, including the oxidation of SO, by a solid catalyst and the gaseous reduction of iron oxides. COUNTERCURRENT staged processes involving reactions between solid and gas streams are becoming more common. These operations are generally carried out in a series of beds of fluidized solids, with each bed or "plate" acting as a stage. Fig. 1 is a schematic diagram of such a series of stages located in a column, down through which a solids stream moves from stage to stage counter to a rising gas stream. Typical reactions carried out in such systems are the dehydration of aluminum trihydrate, the calcining of limestone, and the gaseous reduction of iron oxides. Calculation of the performance of these counter-current systems rapidly becomes more complex with increases in the number of stages and in the number of chemical reactions occurring. Calcula-tional procedures for isothermal operations of such systems have been described.4 Actual tower operations, however, are generally adiabatic, and in consequence far from isothermal. The object here is to present both graphical and analytical techniques applicable to such adiabatic towers operating continuously and in steady state. In this introductory discussion, the graphical techniques presented are of the McCabe-Thiele type, rather than of the Pon-chon type. In all the examples presented, it will be assumed that both thermal and chemical equilibrium are attained in each bed. The assumption that the gas and solid streams leaving each bed are at the same temperature as the bed is in accordance with the familiar behavior of actual fluidized solid systems. Chemical equilibrium, on the other hand, is not necessarily attained in any given stage between these two streams, even with deep beds, since reaction rates may be slow. In the last section of this paper, discussion is presented of methods suitable for use when chemical equilibrium is not attained. The adiabatic tower in Fig. 1 has "n" stages numbered from 1 to n, starting with the bottom stage as number 1. In analyzing this tower's performance, it is important to express gas flow rates in terms of a key component or element which remains completely within the gas stream throughout the tower. Similarly, solid flow is best expressed in terms of a key compound or element which remains within the solid phase throughout the tower. Thus, in burning limestone with a hot flue gas, the gas flow might be expressed as G, the pound mols of nitrogen flowing through the tower per unit time, while solid flow might be expressed as S, the pound atoms of calcium in all forms in the solid stream per unit of time. Defined in this way, both G and S are constant throughout the tower. The enthalpy of the gas and solid streams are now best expressed in terms of these key components. That is, the gas stream enthalpy H is expressed as Btu in the total gas per mol of the key component in the gas. Similarly, the solids stream enthalpy h is expressed as Btu in the total solid stream per pound mol (or pound atom) of the key component in this stream.

Jan 1, 1962

By W. R. Foster, J. M. McMillen, A. S. Odeh

The complete equations of average linear momentum balance for a single-phase fluid in an incompreisible, homogeneous, porous medium are derived. The derivation begins with Euler's equation of motion for a continuum and uses an integral transform recently developed by Slattery. 7 For steady flow of a compressible, Newtonian fluid, the usual equations of motion result. For transient flow, the space-time description of the pressure is determined in the lowest approximation by the telegrapher's equation. From the analysis a new phenomenological coefficient results which connects the viscous traction to the deriv ative of the linear momentum density. The magnitude of this coefficient determines the velocity of sound through the pore structure in this approximation to the pressure field. INTRODUCTION The modification of Darcy's law of momentum balance for steady, single-phase flow through porous media has been discussed for many years. The first modification was suggested by Forcheimerl who added terms of higher order in the velocity. These can be expected to appear because the underlying microscopic equations of momentum balance are themselves nonlinear in the point velocity field. The Reynolds tensor pvv, which represents the convective flux of momentum density, appears in the momentum balance equation. Only in rectilinear flow (parallel stream lines) does the divergence of this tensor vanish. Since the steady flow stream lines in most porous media are not parallel, nonlinear dependence of the pressure gradient on the velocity should naturally appear. This nonlinearity has nothing to do with turbulence in the ordinary sense of random fluctuations in the pressure and velocity fields. It arises simply because the stream lines converge and diverge, even for steady flows. Klinkenberg2 demonstrated that the permeability coefficient in Darcy's law depends on the absolute pressure or, alternatively, on the density field. However, because he neglected inertial terms of the Forcheimer type, his correction coefficient could not be represented by a constant but tended toward a constant as the velocity decreased. Forcheimer's and Klinkenberg's modifications can be combined in a rigorous way to account for both inertia and slip during steady flow. This will be shown in a future paper. The transient change of pressure in porous media has been described by the diffusion equation.3 This form results from eliminating the velocity and density fields from a combination of the equations of motion in the form of Darcy's law, the continuity equation and an equation of state. Fatt4 suggested that the cause of deviations from the prediction of the diffusion equation for pressure transients lies not in the choice of Darcy's law as the equation of motion but on the existence of dead-end pores which might invalidate the averaged equation of continuity. On the other hand, Oroveanu and Pascal5 noted chat the time derivative of the momentum density must be included in the equations of motion since this measures the local rate of change of momentum density. Their differential equation for pressure is the telegrapher's equation (neglecting gravity). However, their form of this equation predicts that the speed of pressure propagation through the pore structure is the same as that through the bulk fluid. M. K. Hubbert6 attempted a derivation of Darcy's law by volume averaging the Navier-Stokes equations. Since these equations represent momentum balance at a point within an open set of points containing the fluid itself, Hubbert's volume averaging cannot lead to tenns involving transfer of momentum between the fluid and the walls of the pores. Once these viscous tractions are lost by choosing a control volume containing only fluid, they cannot

By R. D. Satterley

THE Sherwood mine is an iron-ore mine owned and operated by the Inland Steel Co. in the Iron River district of the Menominee Range in Michigan. The property consists of an 80-acre tract in the village of Mineral Hills, about a mile north of the city of Iron River. The ore mined is a reddish brown, nonbessemer hematite and limonite. The ore bodies lie in a large syncline having an east-west strike and are associated with a rock structure that is folded in a complex manner. The two 40-acre tracts run north and south and the shaft is at about the center of the north forty. The shaft is 1286 ft. deep, with the principal operating level at a depth of 1000 ft. from surface. A new level at a depth of 1200 ft. is in process of development. The ore body at the 1000 ft. level is east and west at approximately the line between the north and south forties and at this elevation is from 50 to 250 ft. wide and extends above the level at varying heights of from 50 to 250 feet. The 1000-ft. haulage drift extends south from the shaft, through the east-west ore body to the slates on the south side of the body. The ore body was intercepted in the drifting at about 800 ft. from the shaft and was about 200 ft. wide at that point. A crosscut was extended to the east and west property lines along the south boundary of the ore body. This east-west ore body is laid out in areas 80 ft. wide for stoping with pillars 40 ft. wide. With this plan a stope is approximately 80 by 200 ft. and has a pillar on both sides that is approximately 40 by 200 ft. The ore has a height of from 50 to 250 ft. above the elevation of the level, therefore the height of the stopes varies in accordance with the height of the ore body at each location. From the crosscut, two main raises, each 6 by 7 ft., are put up into each 80 ft. stope area (Fig. I). One of the main raises serves as a manway and the other as an ore raise, through which the ore is transferred from the stope to the tramming equipment. The original layout was for scraping of the ore from under the stopes into the ore raises. The ore raise is put halfway (east and west) along the 80-ft. stope area and usually is in iron formation. The manway and ore raise are on approximately 15-ft- centers. These main raises are put up to a height of from 22 to 30 ft. above the level floor, then from the top of the ore raise a scraper drift (8 X 8 ft.) is driven across the width of the ore body, which is in the neighborhood of 200 ft. From the scraper drift, mill raises are put up at 12 ½ -ft. centers, staggered on opposite sides of the drift, and these are extended 23 ft. above the elevation of the scraper-drift floor. The sublevel connecting the top of these mill raises is called a mill "sub." Other sublevels are developed parallel to the scraper and mill subs at 25-ft. vertical intervals above the mill sub. The mill sub and the other subs above the mill sub are known as sublevels or dog drifts, and are 4 ft. wide and 6 ft. high. These dog drifts

Jan 1, 1945

By Tell Ertl

The term oil shale is defined. Foreign oil-shale developments are outlined briefly. The richest and most extensive oil-shale deposits in the United States lie in western Colorado. The Bureau of Mines is opening two adjacent areas for underground mining. in western Colorado. From the first area the oil shale is mined selectively as required by the retorting plant. The second area is being developed as a unit of a full scale oil-shale mine to ascertain the most practical methods of mining oil shale and to determine costs. In both of these mining areas, research will be carried on to develop new and improved practices for mining oil shale. Introduction Oil shale is a sedimentary rock containing a solid mineraloid of indefinite composition known as kerogen. On heating oil shale, the kerogen undergoes thermal decomposition and some of the vapor products of the decomposition can be condensed as shale oil. Oil from shale can be a major source of liquid fuels since extensive deposits of oil shale are known to exist throughout the world. The United States considers the establishment of an oil-shale industry only when doubt exists of the adequacy of the domestic supply of crude petroleum. On the other hand, oil shale is not strange to foreign oil men. The industry is an old one in other parts of the world. The French industry has been in existence since 1838, the Scottish since 1859, the Australian since 1860, the Estonian and Swedish The since World War 1, and the Manchurian industry since 1929. The most highly exploited oil-shale deposits are the Carboniferous shales of Scotland. About 20 seams ranging from 4 to I2 ft in thickness are worked. The yield during recent years in scotland has been 18 to 25 gal of shale oil per ton, from 3&"30'000 tons per year' The French and Swedish oil-shale deposits are of lower grade than the Scottish. The Estonian oil-shale deposits are 7 ft thick, and the oil yield averages 50 gal per ton. Over 1,000,-ooo tons are mined each year, half of which is used directly as fuel to substitute for coal and the other half is used for the production of oil. Immense deposits of oil shale that will yield 10 to 15 gal per ton exist in Germany. Because of the impending loss of the Rumanian and Polish oil fields and the bombing of synthetic liquid fuel plants, the Nazis in 1943 started a large-scale oil-shale program in Germany. By V-E Day, it is said, oil-shale production had reached the rate of 2500 tons per day and rapid expansion of the industry was imminent. Australian oil shale, known as torbanite, occurs in beds 2 to 6 ft thick. It is of a very high grade and on retorting yields 80 to 160 gal per ton. The oil-shale industry of Manchuria was the largest in the world during the past decade. The well-known Fushun coal deposit in Manchuria has an overburden of 500 million tons of oil shale about 450 ft thick that will yield 10 to 15 gal of shale oil per ton. The oil shale is

Jan 1, 1949

By P. Shahinian, R. L. Stegman, M. R. Achter

Creep strength has been determined as a function of oxygen pressure for nickel at 510" and 600°C. Creep-rupture life drops from its highest value at the ultimate vacuum of 10-7 torr to a high pressure plateau of nearly constant life which, at 600°C, commences at torr. This behavior is described in terms of a model that relates surface gas adsorption and the generation of fresh crack surfaces. In a calculation based a this model the predicted pressure beyond which the creep strength should not decrease further has been found to agree well with the observed value. The introduction of oxygen during creep in vacuum was found to cause a prompt rise of the creep rate. The magnitude of the environmental effect was much less than generally observed in fatigue and this is attributed to the diffarent crack morphologies in creep and fatigue. GASEOUS environments are known to affect creep resistance adversely1-5 but the effects have received less attention than the much larger ones in fatigue. At low temperatures it has been shown for nickel that the creep rates are faster and the rupture lives are shorter in air than in vacuum and that these environmental effects can be correlated with faster crack growth rates in the reactive environment.' In support of a mechanism of gas adsorption at the crack tip to explain the above effects, a calculation based on kinetic gas theory showed that surface coverage by gas was not as rapid as the exposure of fresh metal at the crack tip in the ultimate vacuum but was in air.7 In fatigue a number of investigations have demonstrated that the reduction of life with gas pressure usually follows a step curve with most of the reduction occurring in a transition range at intermediate pressures and little or no change at high and low pressure.8 There have been no studies, however, in which creep strength has been determined as a function of reactive gas pressure to see whether similar effects would be found. This investigation was undertaken to study the kinetics of the environmental effect in the creep of nickel. EXPERIMENTAL PROCEDURES The environmental creep apparatus was constructed to minimize many of the experimental conditions which can cause scatter in data. Dead weight loading is employed and weights are contained within the environmental chamber to eliminate bellows and the necessity for compensation for gas pressure changes. Elongation over the specimen gage length is recorded from a Riehle Model DV Controlled Environment Extensometer which provides readout to 2.5 x 10- in. Temperature is monitored and controlled from a thermocouple at- tached to the specimen gage length to +0.5oC or better. The freon trapped oil diffusion pump vacuum system included an auxiliary liquid nitrogen trap and, with a wide range variable conductance leak valve, pressures from the ultimate vacuum of 10"7 to l03 torr of any desired gas are obtainable. Pressure is measured by means of a hot filament ionization gage below 10"3 torr and a NRC Model 530 Alphatron Vacuum Gauge above 10-3 torr. The oxygen, which was leaked into the environmental chamber, was an Aviator's Grade of 99.5 pct purity with a dew point of -80°F. Analysis of the nominal 99.8 pct Ni showed the following percentages of major impurities: 0.02 C, 4.01 Mn, 0.005 Si, 0.01 Cu, 0.02 Fe, and 0.034 Mg. Cylindrical specimens were machined with a 0.180

Jan 1, 1970

By W. L. Prehn, Adele Chambers, R. L. Slobod

The centrifuge has been found to be an extremely useful tool for determining capillary pressure curves and for establishing connate water and residual oil in small core plugs. The use of the centrifuge for determining the properties of small core plugs has been discussed in the literature,',' but practically no experimental evidence has been presented justifying the use of this method in preference to other methods (mainly disc method) now in use. Data have been accumulated and are now presented demonstrating the advantages of the centrifugal method, some of which are: (1) rapid establishment of equilibrium, (2) excellent precision yielding very reproducible results, (3) availability of high pressure differences between phases, (4) simple operational procedure, and (5) ability to establish connate water, residual oil, or to obtain complete capillary pressure curve in one day or less. A commercially available centrifuge capable of speeds up to 3,800 rpm, and a high speed attachment providing a maximum rate of rotation of 18,000 rpm were used in this work in conjunction with core holding tubes designed specifically for this application. In view of the outstanding advantages associated with the use of the centrifuge the conclusion has been drawn that this method should be used in place of the more tedious, slower, and less reliable disc method for determining capillary pressure curves and for establishing connate water and residual oil in small core plugs. INTRODUCTION The need for accurate values of connate water, residual oil, and capillary pressure curves in reservoir engineering has been recognized for many years, and the extent of the effort devoted toward solving these problems is reflected in the large number of papers3-" which have appeared in the literature during the past decade. Most of the methods discussed in the recent literature employ a porous disc as a semi-permeable membrane to separate two immiscible phases and make pos-ible the application of an explicit difference in pressure between two phases in the core. Thus, in the determination of the capillary pressure curve the wetting phase (water) is displaced by the non-wetting phase (air or oil). Several investigators1,2 have used centrifugal forces to develop pressure differences between phases. As a result of the first work' in this field the conclusion was reached that "the more rapid centrifugal method for measuring irreducible saturation may have equal value, (compared to use of discs) but more work is required to establish this point." This work was followed in 1945 by a more detailed study2 in which the concepts of this experimental work were more clearly enunciated. A method for calculating saturation for any given speed of rotation based on the observed volume of water displaced was developed and a wider application of the method was suggested. The absence of any subsequent pertinent literature on this subject is interpreted as indicating that no additional work has been completed to substantiate or deny the earlier claims and suggestions of promise contained in the original papers on this subject. One purpose of this report is to provide evidence designed to establish the practical value of centrifugal methods in determining core properties such as connate water and capillary pressure curves. It is also our purpose to suggest a broadening of the scope of this tool to include determinations of residual oil by gas or water drives. THEORY AND PRACTICE IN USE OF CENTRIFUGE Hassler and Brunner2 have clearly presented the basic concepts involved in the use of the centrifuge by relating the performance of a small core in a field of high acceleration to the

Jan 1, 1951

By R. L. Slobod, W. L. Prehn, Adele Chambers

The centrifuge has been found to be an extremely useful tool for determining capillary pressure curves and for establishing connate water and residual oil in small core plugs. The use of the centrifuge for determining the properties of small core plugs has been discussed in the literature,',' but practically no experimental evidence has been presented justifying the use of this method in preference to other methods (mainly disc method) now in use. Data have been accumulated and are now presented demonstrating the advantages of the centrifugal method, some of which are: (1) rapid establishment of equilibrium, (2) excellent precision yielding very reproducible results, (3) availability of high pressure differences between phases, (4) simple operational procedure, and (5) ability to establish connate water, residual oil, or to obtain complete capillary pressure curve in one day or less. A commercially available centrifuge capable of speeds up to 3,800 rpm, and a high speed attachment providing a maximum rate of rotation of 18,000 rpm were used in this work in conjunction with core holding tubes designed specifically for this application. In view of the outstanding advantages associated with the use of the centrifuge the conclusion has been drawn that this method should be used in place of the more tedious, slower, and less reliable disc method for determining capillary pressure curves and for establishing connate water and residual oil in small core plugs. INTRODUCTION The need for accurate values of connate water, residual oil, and capillary pressure curves in reservoir engineering has been recognized for many years, and the extent of the effort devoted toward solving these problems is reflected in the large number of papers3-" which have appeared in the literature during the past decade. Most of the methods discussed in the recent literature employ a porous disc as a semi-permeable membrane to separate two immiscible phases and make pos-ible the application of an explicit difference in pressure between two phases in the core. Thus, in the determination of the capillary pressure curve the wetting phase (water) is displaced by the non-wetting phase (air or oil). Several investigators1,2 have used centrifugal forces to develop pressure differences between phases. As a result of the first work' in this field the conclusion was reached that "the more rapid centrifugal method for measuring irreducible saturation may have equal value, (compared to use of discs) but more work is required to establish this point." This work was followed in 1945 by a more detailed study2 in which the concepts of this experimental work were more clearly enunciated. A method for calculating saturation for any given speed of rotation based on the observed volume of water displaced was developed and a wider application of the method was suggested. The absence of any subsequent pertinent literature on this subject is interpreted as indicating that no additional work has been completed to substantiate or deny the earlier claims and suggestions of promise contained in the original papers on this subject. One purpose of this report is to provide evidence designed to establish the practical value of centrifugal methods in determining core properties such as connate water and capillary pressure curves. It is also our purpose to suggest a broadening of the scope of this tool to include determinations of residual oil by gas or water drives. THEORY AND PRACTICE IN USE OF CENTRIFUGE Hassler and Brunner2 have clearly presented the basic concepts involved in the use of the centrifuge by relating the performance of a small core in a field of high acceleration to the

Jan 1, 1951

By N. K. Chen, R. Maddin

Single crystals of molybdenum were extended at temperatures from 1300° to 2500°C. It was found that with increasing temperatures, the yield becomes more pronounced and the number of slip bands for equal amounts of elongation decreases. Slip at high temperatures fragments the structure. OTHER than the investigations on sodium and potassium by Andrade and Tsien,&apos; the researches of Steijn and Brick&apos; on a iron single crystals at low temperatures are about the only studies of the influence of temperature on glide of body-centered cubic single crystals. The effect of test temperature on glide has been rather widely investigated with hexagonal crystals" and less widely with face-centered cubic crystals. ~~ a result of these studies it can be said that, in general, the onset of plastic flow as measured by the initial rate of strain hardening becomes more abrupt with increasing temperature, and the value of the yield decreases with increasing temperature. Strain hardening, however, is markedly affected by changes in temperature except at very low and very high temperatures where the strain hardening rate becames constant. In the present investigation it is shown that temperature affects the glide of molybdenum single crystals in much the same manner as crystals of other classes, it., for comparable strains the number of slip bands decreases with increasing temperature; shear along the slip bands increases with increasing temperature; the yield becomes more pronounced with increasing temperature of test; and the strain hardening approaches a constant at very high temperatures. In addition, it is shown that, in agreement with the work of Tsien and Chow, Qlip occurs on (110) planes in <Ill> directions. It is further shown that slip at high temperatures fragments the structure into either irregular sized cells or bent atomic planes which are roughly aligned in crystallographic directions. Experimental Procedure Single crystals 3 mm in diameter by about 25 mm long were prepared using the technique previously described.&apos; The furnace in which the crystals were grown served as the extension apparatus for the tension tests. It consisted of a 4 in. water-cooled brass tube 20 in. long which was continuously evacuated at the bottom. Two water-cooled copper electrodes held the specimen by means of spherical collets secured in place in the electrodes by set screws. These electrodes served also to transmit power and stress to the specimen. The lower electrode was clamped to a stand, while the upper electrode was fastened to one side of a lever arm flexibly supported at the top through a slightly offset pinion. A metal bellows operating elastically was attached to the upper electrode to affect a vacuum seal and allow freedom of motion. The level of the arm was adjusted by rotating a graduated nut. Rotation of the electrode was prevented by a key fitted into a groove. After the specimen was mounted and the vacuum secured, the lever arm was adjusted so that the bellows was at its relaxed position. This insured that the total weight of the specimen, the upper electrode, and the downpull of the vacuum were balanced by the horizontal beam. Since the specimen was heated by its own resistance, expansion of the specimen proceeded freely by this arrangement. During the time of heating the specimen, the beam was maintained in a horizontal position by turning the nut at the top. By graduating the lever arm and using a known dead weight on the lever arm to supply a tensile stress, the graduated nut could be read to 0.0001 in. extension. Since

Jan 1, 1955

By Harry M. Mikami

Chromite is the only ore mineral of metallic chromium and chromium compounds and chemicals. Because of this fact, chromite and chrome ore are used synonymously in trade literature. In commercial market quotations, chrome ore is the term commonly used. Chromite per se, because of properties imparted by its chromium content, is used in refractories and in special purpose molding sands for metal casting. There are many other minerals containing some, generally minor, amounts of chromium, but none are commercial sources of the element (Thayer, 1956). Chromium and chromite have many diverse uses that, directly and indirectly, critically affect vast segments of our modern industrial system. Most important are probably the metallurgical applications wherein chromium is a component of heat-, abrasion-, corrosion-and oxidation-resistant and high-strength alloys of many types. Stainless steels are the largest volume category of chrome-bearing alloys. Chromium chemicals are used in leather tanning, in pigments, dyes and mordants, printing, chemical process industries, photography, pharmaceuticals, metal plating, pure chromium metal production, and for many other purposes. Chromite is a necessary constituent in basic refractories indispensable for the production of steel, copper, cement, and glass. Under present conditions, the US and North America, with the possible exception of Cuba, have no commercial ore reserves. There are chromite deposits, as will be described, but they would be used only under highly abnormal conditions if all outside sources were cut off for an extended period. All chromite used in the US is imported from the eastern hemisphere in which are contained the principal world reserves. The main suppliers in 1980 were the Republic of South Africa (43%), the USSR (21% ), the Philippines (12%), Albania (11 %), Turkey (8%), and others (5%). The strategic nature of chromite is obvious. End Uses-Grades and Specifications As noted before, the three principal uses for chromite are metallurgical, refractories, and chemical with a fourth minor use as foundry molding sand. For metallurgical applications chrome ore is first reduced in electric carbon arc furnaces to various types of ferrochromium alloys. There are high, medium, and low carbon ferrochromiums with carbon ranging from 0.01 up to 10%. Chromium itself ranges from 50 to 73 %. Ferrosilicon chromium and ferrochromium-silicon grades have chromium from 33 to 67% and silicon from 3 to about 48%. Since iron is reduced with chromium, the Cr:Fe ratio of the ore will determine the ultimate grade of the ferrochromium whereas carbon and silicon can be controlled during processing. MgO, A12O3, CaO, and excess SiO2, are removed in slag. A small amount of pure chromium metal is prepared by alumino-thermic and electrolytic processes from essentially iron-free chrome components that have been made via the chemical route. The higher grades of ferrochromium with chromium in the 66 to 73% range can only be made from ores with not only high chromium content, but low iron, i.e., high Cr:Fe ratio. These ores, conventionally termed metallurgical grade, have Cr2O3 contents of 45 to 56% with Cr: Fe ratios of 2.5 to 4.3. A standard composition is generally 48% Cr2O3 and 3:1 Cr:Fe ratio. Very high grade ores are often blended with lower grades even with the high iron chemical grade. For some ferrochromiums, additions of high alumina refractory grade are used as slag conditioners to facilitate smelting while still contributing chromium values. A lower grade ferrochromium, the high carbon charge chrome, has become the predominant grade in use today for making chromium-bearing steel alloys. This

Jan 1, 1983

By R. E. Fryxell, E. C. Duderstadt, P. K. Conn

Permeation rates for nitrogen through are-cast tungsten were measured in the temperature range 1800° to 2600°C at nitrogen pressure differentials of 1.0 and 0.1 atm. Gas chromatography was used to measure the quantities of nitrogen which permeated through 0.26-and 0.53-mm-thick membranes. Permeation rates were proportional to the difference between the square roots of the nitrogen pressure on each side of the membrane and inversely proportional to membrane thickness, indicating that atomic nitrogen was the difjusing species and that diffusion was the rate-limiting step of the process. Permeation coefficients calculated from the rates may be represented by the equation: where P is expressed in the units cu cm (stP)-mm per 1/2 sq cm-min-atm"&apos; and 70.0 * 0.8 is the activation energy in kcal per mole of permeating species. In a previous paper&apos; permeation rates were reported for hydrogen and for oxygen through tungsten. The permeation cells used for the hydrogen measurements were suitable for measuring nitrogen permeation under similar conditions, so the study was extended to include nitrogen. Permeation rates of nitrogen through the polycrys-talline arc-cast tungsten membranes were measured in the temperature range 1800" to 2600°C using two membrane thicknesses and two nitrogen pressure differentials. Permeation coefficients were calculated and the activation energy of the process determined. THEORY For diatomic gases which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at an elevated temperature where bulk diffusion is the rate-limiting step of the process is given by the equation: where: q = total amount of gas permeating a membrane, P = temperature-dependent permeation coefficient, A = area of membrane, t = time, p1 = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, and d = thickness of membrane. When bulk diffusion is the rate-controlling step, and the solubility of the gas obeys Henry&apos;s law, a further relationship is that, for any given temperature and pressure, the permeation is the product of diffusivity and the amount in solution. The permeation coefficient, P, is temperature-dependent according to the equation: where: Po = permeation constant, Q = activation energy, R = gas constant, and T = absolute temperature. EXPERIMENTAL PROCEDURES Cell Design and Experimental Apparatus. Two of the permeation cells used for the previous measurements of hydrogen permeation are shown in Fig. 1. Each consisted of a cylindrical chamber divided into two parts by a permeation membrane fabricated from high-purity (>99.9 pct W) wrought tungsten sheet made from vacuum arc-cast tungsten. The membrane in one cell was 0.26 mm thick and the other was 0.53 mm. The fabrication of these cells was described previously.&apos; The permeation cells were mounted vertically in a high-temperature tungsten resistance furnace and the membranes and the center portions heated to test temperatures. Temperatures were measured by sighting an optical pyrometer on the edge of the membrane through a small hole in a tungsten plate which was fastened to the side of the cell. This arrangement provided an approximate black-body condition and eliminated the need for emittance corrections. Appropriate corrections were made for the quartz window through which the temperatures were measured. Argon gas flowed through the 10-liter volume of the furnace at the rate of 4.7 liters per min. An impurity

Jan 1, 1969

By J. A. Snyder, W. L. Finlay

G. Edmunds—Solid solubility is considered to be of either the interstitial or the substitutional type. Is it possible, in a binary alloy as the simplest case, that some of the solute atoms are present in the normal lattice sites (substitutionally or filling lattice vacancies) while simultaneously others are in interstitial positionss One might even ask whether a distribution of the two types may be the normal situation. H. M. Meyer—Metastable states of interstitial atoms occupying vacant lattice sites possibly occur as well as of substitutional atoms squeezed in between regular matrix positions. However (as we know since Hume-Rothery), the solute atoms choose between the two kinds of solutions; consequently, every solute will be unequivocally either substitutional or interstitial in the equilibrium state of the solid solution. M. Balicki—In view of the fact that the authors apparently correlate the analysis of the alloys at the ingot stage with the properties exhibited at the testing stage, I would like to ask whether this is a fully justifiable procedure. In other words, how good are their determinations of solute concentration for correlating them with the mechanical properties. The answer to this question may explain some of the divergencies. Assuming good enough homogenization of the samples and exact determination of mechanical properties the position of the plotted experimental points will depend solely upon the accuracy of composition determination. If this is not accurate, say due to loss or pickup of elements during processing from the ingot to the testing stage, or due to a systematic error in the method employed for obtaining solute concentration data, the points will deviate from their true position and may align themselves along a different curve than the one expected. H. V. Kinsey—We have been studying the creep-rupture properties of titanium-base alloys at 1000°F. In the course of this work, anomalies in behavior of the alloys that would suggest that the material under test was becoming stronger as the test progressed have been observed. If this was so, the most likely explanation that we could think of was that the test bars were absorbing oxygen and nitrogen from the air during the test and were thereby becoming strengthened. In an attempt to determine the strengthening effect of absorbed oxygen and nitrogen the following experiment was conducted. A length of cold-rolled titanium was supplied by the E. I. du Pont Co. Two test bars, having a 1/4 in. diam gauge length, were prepared from this material. One bar was tested in the as-received condition. The second bar was heated in air at 1550°F for 100 hr and subsequently air cooled prior to testing. A testing temperature of 1000°F was employed. The results of these tests are tabulated in table 11. In the author&apos;s opinion, is it reasonable to assume that the bar that was exposed to air at 1550°F for 100 hr was stronger because it absorbed oxygen and nitrogen from the air during this heat treatment? W. L. Finlay (authors&apos; reply)—Direct experimental evidence for or against Mr. Edmunds&apos; interesting suggestion will probably never be available. It seems possible, however, that mixed interstitial-substitutional solid solution might well occur with interstitial elements. The less likely possibility of interstitial solution of a normally substitutional element like copper in aluminum was recently discussed at length by the

Jan 1, 1951

By D. R. Parrish, W. E. Lamoreaux, W. W. Owens

Several methods are now being used by the industry for determining the gas-oil flow characteristics of reservoir rock samples. Most of the laboratory experirnerltal rlzethods can be classified either as steady-state, unsteady-state, or Hassler-type tests. Although the validity of the results obtained by any specific method is not questiorzed, in general, the complexity of these methods leaves much to be desired. This investigation dealt primarily with the development of a simplified unsteady-state (gas drive) laboratory test method for measuring kg/ko re1ationships of small core samples. A procedure for selecting uniform and representative sandstone rock samples was developetl since it was observed that the reliability of the test resu1ts was dependent upon having a sample which was uniform in porosity and permeability. The importance of factors known to influence the results of this type test, such as oil viscosity, gas expansion, and pressure differential were eva/uated. The method of calculating the test results was found to give valid data over a wide range of gas expansion. The limits of pressure differential and oil viscosity which would insure reliable results were defined. In cornparisorz with other presently used testing methods, the gar drive method requires considerably less apparatus, is less time consuming, and is more readily adaptable to a routine type core test. INTRODUCTION The detcrmination of the gas-oil flow characteristics of reservoir rocks has been given concentrated study by the oil industry for the past decade. Both analytical and experimental methods have been considered. The analytical methods have generally relied on a simplified characterization of porous materials in order that the fundamental laws of fluid flow and capillarity could be utilized. More direct experimental methods have been proposed by numerous production research laboratories with the primary goal being a simple and inexpensive, yet reliable method for measuring the gas-oil flow characteristics of reservoir rock samples. The experimental methods which have been reported in the literature generally can be grouped into one of the following classifications: 1. Steady state1,2,3,4 in which a fixed ratio of flowing fluids is forced through the test sample until equilibrium conditions of saturation and pressure gradient are established. 2. Hassler or stationary liquid method5,6,7 in which a uniform liquid saturation is attained, usually through capillary desaturation, then gas or oil is flowed through the sample at a pressure drop insufficient to disturb the pre-established saturation. :. Non-steady state method1,8,9,10 In which only the gas phase is injected into the sample, causing displacement of the oil phase and resulting in a system of continually changing average saturation and saturation gradient. The steady-state and Hassler methods have been most popular because, no doubt, of the simplicity of the actual relative permeability calculations. The problems involved in these methods were limited to apparatus design and measurement techniques. In the steady-state method, for instance, a constant flowing fluid ratio is established which, at equilibrium, results in an essentially uniform saturation over the entire length of the test sample. Therefore, the basic flow characteristics could be obtained by correlating the average saturation of the test sample with the kg/ko determined at various flowing gas-oil ratios.

Jan 1, 1957

By Fritz Wald, Martin Weinstein, Herbert E. Bates

ONE of the methods for preparing a fiber-reinforced composite is that of directional solidification of a eutectic melt. Its major drawback lies in the fact that the matrix in this case is a pure constituent (or a terminal solid solution of fixed concentration) and the ratio of fiber to matrix volume is fixed. Only very few, if any, pure metal matrices possess technically useful properties, and the necessity for alloying is the inevitable consequence of this fact. Nevertheless, structures similar to binary eutectic ones can be obtained in higher-order systems by pseudoeutectic reactions of a type where crystallites and a solid-solution matrix are simultaneously precipitated from a liquid.1"3 Trials to solidify such alloys directionally—the matrix consisting of a solid solution of chromium, nickel, and silicon and the reinforcing phase being Cr3C2— will be reported elsewhere.4 This note describes constitutional studies carried out primarily to determine -the position of the pseudoeutectic and further to insure that no undesirable reactions between the reinforcing phase and components of the matrix occur in the solid state at elevated temperatures. In the investigation it was specifically desired to reinforce a matrix which is as close as possible to the 80/20 Nichrome composition with Cr3C2 to insure good oxidation resistance and improve the strength at high temperatures. No konstitutional information on the quaternary C-Cr-Ni-Si svstem in the range of interest was found in the literature. Nevertheless, the two most important ternaries c-cr-Ni5 and have been completely investigated. On C-Cr-Si some investigations have been conducted,7"9 and C-Ni-Si was studied with a few alloys in the course of the present investination 9 Eight alloys were prepared to investigate the changes in the constitution of the ternary C-Cr3Ce-yNi eutectic5 with silicon contents up to 10 wt pct. Five alloys were made with varying chromium and carbon contents around compositions containing -60 to 70 wt pct Ni and 5 to 6 wt pct Si. The latter alloys were designed to locate the y(Ni-Cr-Si-C)-Cr3C2 pseudoeutectic reaction and to determine the maximum chromium content in solid solution compatible with a two-phase equilibrium between y and Cr3C2 only. The alloys were prepared from electrolyte nickel, semiconductor-grade silicon, high-purity chromium (99.999 pct pellets), and semiconductor-grade graphite. They were melted inductively in high-purity alumina crucibles under flowing argon. Twenty-gram charges were prepared and investigated by optical microscopy (including hot-stage investigations), X-ray powder methods, and electronmicroprobe analysis. The alloys were studied in the as-cast condition and also after a homogenization annealing treatment of 48 days at 900°C in evacuated quartz ampoules. The structures of all alloys based on the ternary eutectic plus silicon in the as-cast state consisted generally of an inhomogeneous solid solution and at least two other phases. Annealing of the alloys showed that the solid solution was homogenized but that an incomplete solid-state reaction had taken place in all alloys with silicon contents over 5 wt pct. This reaction is clearly visible in Fig. 1 around the large Cr3C2 crystals (gray areas). Below this concentration, the alloys consisted of a homogeneous matrix and precipitates of Cr3C2 plus graphite, Fig. 2. The Cr3C2 was entirely unreacted here. From these observations and subsequent X-ray and microprobe investigations, it was deduced that the

Jan 1, 1969

By S. R. Goodman, Hsun Hu, R. S. Cline

The quenching technique has been used to study phase relations in the composition area 2FeO.SiO2-FeO-SiO2-MnO.Si02-ZMnO.SiO2 of the system iron oxide-manganese oxide-silica under strongly reducing conditions such as exist in a gas mixture consisting of equul parts of carbon dioxide and hydrogen. Liquidus and solidus temperatures of most mixtures in the composition area studied are in the range of 1173° to 1345°C. EQUILIBRIUM relations existing among the oxides of iron, manganese, and silicon are of particular interest in two areas of steelmaking: slags and ingot inclusions. Mixtures of these oxides represent about 90 pct of the slag in the acid steelmaking process, and so dominate the chemistry of the whole refining process. These constituents also play an important role in the early slags existing at the time of the "lime boil" in the basic open hearth process. If these slags are liquid, they "wet" the lumps of lime rising from the bottom of the bath, and react with them. A liquid slag rich in CaO is then formed at the very beginning of the refining. Because the temperature is still low, all conditions for a good dephosphoriza-tion are fulfilled at this stage of the operation. Metal deoxidized with ferromanganese or silico-manganese is likely to contain, as inclusions, phases made up from among the oxides of iron, manganese, and silicon. A knowledge of stability relations existing among the phases present in this system, therefore, enables one to predict the hardness of the inclusions encountered. Moreover, because the shape of the inclusions in steel has a profound influence on the physical properties of the metal, it is important to establish whether or not the oxidic material is present as liquid or crystalline phases during heating and rolling of the steel (-1150 to 1350°C). A knowledge of melting relations in synthetic mixtures of iron oxide, manganese oxide, and silica will give a clue to these problems. Methods for determining such relations and the results obtained are described iln this paper. I) PREVIOUS WORK A number cf previous studies have dealt with the three "binary"* systems bounding the system iron oxide-mangar,.ese oxide-silica. The system iron oxide-silica was studied by Bowen and shairerl in 1932. Their data were obtained by equilibration of mixtures in contact with metallic iron. Phase relations for the system iron oxide-silica ill atmospheres of different oxygen pressures car1 be derived from data on the system FeO-Fe2O3-SiO2 as determined by Muan.2 The diagram shown iri Fig. l is a section of this system in an atmosphere of CO2 and H2 in ratio 1:l. The system manganese oxide-silica has also been the subject of several investigations. Most of the early studies suffered from a lack of proper control of the atmosphere under which the equilibrations were carried mt. Phase diagrams for the system at two well defined levels of oxygen pressures have been determined recently. Glasser3 determined stability relations in an atmosphere consisting of carbon dioxide and hydrogen in ratio 5:1, diagram Fig. 2, and Muan4 studied phase relations in the system in air.

Jan 1, 1962

By M. A. Dayananda, R. E. Grace, P. F. Kirsch

Ternary diffusion experiments were carried out at 750°C with vapor-solid diffusion couples in single-phase copper-rich Cu-Zn-Sn alloys. The Philibert-Guy method was used to calculate intrinsic diffusion coefficients at compositions corresponding to the plane of inert markers imbedded in the diffusion couples. Inter diffusion coefficients were determined at common composition points of intersecting diffusion paths. Intevdiffusion coefficients were also obtained at compositions corresponding to maxima in the tin concentration pvofiles Relations between the interdiffusion coefficients and the expansion of vapor-solid diffusion couples are described in detail. Such relations permit the calculation of constant interdiffusion coefficients in binary couples from expansion data directly. In ternary couples expansion data provide an additional constraint on the interdiffusion coefficzents. ThE phenomenological analysis of diffusion in ternary solid solutions has been developed extensively, and various approaches taken in the determination of diffusion coefficients have been reviewed recently by Guy et al.&apos; Finite,&apos; semi-infinite,3 and infinite4 diffusion couples have been used in studies of ternary diffusion, but most of the work has been done with infinite diffusion couples. Semi-infinite diffusion couples3 (vapor-solid couples) have been used to determine both intrinsic and interdiffusion coefficients in the Cu-Zn-Mn system, in which two diffusing species, zinc and manganese, were supplied from the vapor phase. If only one component has a sufficiently high vapor pressure to be supplied from a vapor source, vapor-solid diffusion couples may still be used. In this case the boundary conditions at the gas/solid interface may be governed by partial equilibria rather than by virtually complete equilibrium between the phases. In the present work diffusion measurements were carried out at 750°C with vapor-solid couples of Cu-Zn-Sn alloys. Only zinc was transported between the vapor source and the diffusion disks, because the vapor pressures of both copper and tin are at least 108 lower than that of zinc. Both intrinsic and interdiffusion measurements were made at several compositions. A secondary objective was to relate expansion of the diffusion couples with the interdiffusion process. Such measurements for binary couples yield average values of the interdiffusion coefficients over composition increments. In ternary diffusion couples ex- pansion data provide an additional constraint on the interdiffusion coefficients. COMPOSITION-DEPENDENT INTRINSIC AND INTERDIFFUSION COEFFICIENTS As shown by Philibert and GUy5 the determination of intrinsic diffusion coefficients in a ternary system requires two independent diffusion couples containing marker planes with identical composition. In the case of vapor-solid couples such a requirement torresponds to two couples set up with the same vapor source exposed to two diffusion disks of different composition. Inert markers placed initially on the disk surfaces become imbedded during diffusion. If the pair of couples exhibits appreciable marker burial with marker planes of virtually the same composition, the intrinsic diffusion coefficient may be evaluated at the composition of the marker planes. Fig. 1 is a schematic diagram of the concentration of of a Cu-Zn-Sn ternary vapor-solid couple after diffusion of zinc from a vapor source into a binary Cu-Sn alloy. The areas, Ai correspond to the cumulative intrinsic fluxes of the three diffusing species across the marker plane:5 where Ji is the intrinsic flux of component i, t is the diffusion time, and D3i are the intrinsic diffusion coefficients. For the determination of interdiffusion coefficients a pair of diffusion couples with intersecting diffusion paths is needed. At the composition point of intersection (C1, C2) the coefficients are evaluated from the equation:3

Jan 1, 1969

By W. A. Backofen, B. B. Hundy

THE pole figure interpretation in a recent paper&apos; on the torsion texture of copper was questioned in discussion,2 nd a simpler alternative interpretation was proposed. In the hope of reaching a positive decision in favor of one or the other, further studies were undertaken with 70-30 brass and Armco iron. This additional work has not answered all the questions about torsion textures, but the new pole figures do offer support for the original interpretation and show that the texture is more complicated than the alternative suggests. From the previous paper,&apos; the appropriate method of describing the texture in a twisted bar is known to be a pole figure plotted on a plane tangent to the surface of the bar. The axes of the pole figure are chosen to coincide with directions in the tangent plane which are parallel and at right angles to the bar axis (the longitudinal direction, L.D., and the transverse direction, T.D.), for these directions define symmetry axes of the texture. Therefore any ideal orientation that might be selected to represent the texture gives the crystallographic plane parallel to the tangent plane and the crystallographic direction parallel to the axis of the torsion specimen. A unique texture was assumed in the original interpretation, and the four ideal orientations, (112) [111], (111) [112], (110) [001], and (112) [131], were used in its description. Of the four orientations, the first three provide possible slip directions along the direction labeled T.D. in the pole figure, which is one of maximum shear stress in a specimen being twisted. The alternative, however, simply considered the texture to be made up of two components, one a [Ill] alignment along the specimen axis with a random orientation about the axis as in the wire texture, and the other a superimposed orientation (110) [0011. Experimental evidence for this simpler interpretation was derived from two observations: 1—twisting did not alter the orientation of a single-crystal torsion specimen of a brass in which an octahedral plane was perpendicular (and a [Ill] direction parallel) to the axis, and 2—deformation bands with approximately the (110) [001] orientation were seen to develop in the crystal during the test. The new pole figures were obtained with a brass and an iron torsion specimen of 3/4 and 1 in. gage length diameter, respectively. After annealing, polishing, and twisting, seven rods, about 0.030 in. in diameter and with different orientations, were prepared from material near the surface of each specimen; these were required for the method of constructing pole figures by using a Geiger counter as developed by Norton.5 Since the shear strain gradient in plastic torsion is linear, it was readily computed that the material supplying the brass rods had been subjected to a shear strain of about 3.2, and that supplying the iron rods had received a shear strain of about 2. All details concerning specimen design, testing procedure, rod preparation, and use of the Norton technique can be found in ref. 1. Only this procedure was followed in working out the (111) and (100) pole figures for brass, Figs. 1 and 2. However, X-ray photograms were also involved in the construction of the (110) pole figure for Armco iron, Fig. 3. The photograms were made according to the conventional transmission diffraction technique using a small sheet taken parallel to the specimen surface and etched to a thickness of about 0.0025 in. They were especially important in locating the boundaries

Jan 1, 1954

By J. G. Richardson, K. H. Coats

During the initial growth of a gas bubble in an aquifer storage reservoir the injected gas tends to override the water. The resulting low displacement efficiency and high rate of gas travel down-structure make it difficult to maintain water-free production. This paper illustrates the use of two-dimensional, two-phase calculations to simulate this gas-water displacement. Calculations were performed for a stratified aquifer and for several homogeneous sands differing in permeability, porosity and thickness. Results are discussed and compared with performance predictions obtained from the simpler Buckley-Leuerett and Dietz formulas. This comparison indicates the necessity for the two-dimensional calculations in realistically simulating the gravity override of the water by injected gas. INTRODUCTION In recent years natural gas has been stored near markets in aquifers where insufficient storage capacity is available in depleted fields. Operators of these aquifer storage reservoirs have encountered technical problems relating to the gas-water displacement accompanying initial growth of the gas bubble. Injected gas tends to override the water, with a resultant low displacement efficiency and high rate of gas travel down-structure toward spill points. Low displacement efficiency makes if difficult to sustain water-free gas production. Sometimes the fingering of gas down-structure may be so pronounced that the injection rate must be severely curtailed, which excessively lengthens the time required for bubble growth. This paper is concerned with estimating — for given aquifer characteristics and fluid properties — the displacement efficiency, rate of gas movement down-structure and rate of gravity drainage of water behind the gas front. Several published articles relate to simulative capability necessary to handle this problem. The Dietz formula1 and Buckley-Leverett2 method have some applicability to the problem; Woods and comer3 reported one-dimensional, radial calculations which accounted for the two-phase flow of gas and water. Most recent research directed toward understanding aquifer behavior in relation to gas storage has concentrated on single-phase flow in aquifer.4 Douglas, Peaceman and Rachford5 presented a method for calculating multidimensional two-phase flow in reservoirs; their method has been applied in work reported by Nielsen and Tek,6 Blair and peaceman7 and Goddin.8 Refs. 5 and 7 show comparisons between experimental data and calculations similar to those employed here. One purpose of this paper is to illustrate the use of two-dimensional, two-phase flow calculations in simulating the difficult problem of water displacement by gas in a vertical cross-section. The pronounced fluid density and viscosity differences combine with the disparity in horizontal and vertical dimensions of the cross-section to pose one of the more difficult problems in reservoir simulation. The calculations described account for capillary and gravity forces, relative permeability and reservoir heterogeneity. An example reservoir is described and calculated results are presented for a variety of injection rates and values of permeability, reservoir thickness and dip angle. A second purpose is to compare the two-dimensional calculations with results obtained from the Buckley-Leverett and Dietz formulas. For this reason most calculations were performed for a simplified example reservoir to which the latter techniques might reasonably be applied. However, the computer program employed applies equally well to cases involving arbitrary spatial variations of permeability, porosity, reservoir thickness and dip angle.