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The performance of a two-horizon depletion-type reservoir produced through combination wells is analyzed. By introducing some simplifying approximations, it has been possible to obtain formulas which are easy to handle. Only ordinary differential equations are used, and the development of the analysis can be followed without difficulty by the non-specialist. A rigorous analysis has been made of this problem. It has been found that the approximations introduced in the simplified analysis are fully justified and that errors seldom will be more than 2 per cent. The report shows the effect of the rate of withdrawal upon the relative depletion of the two horizons. Numerical examples are given. INTRODUCTION In its simplest form an oil reservoir consists of a continuous, homogeneous body of porous and permeable rock, enclosed at the top and the bottom by impermeable material. The flow of fluid through such a reservoir has been the subject of numerous papers, and the mathematical analysis of well performance, pressure build-up, etc., has reached a high degree of refinement. One of the basic assump tions introduced into these analyses is the homogeneity of the reservoir. In non-homogeneous reservoirs, these computations still can be carried out satisfactorily, provided small irregularities in the physical properties of the rock are distributed in a random fashion. The flow equations are derived as solutions of the continuity equation, and their solutions are dependent upon the assumption of many constant factors in the reservoir: permeability to oil, compressibility of the reservoir fluid, viscosity saturation, etc. When these axe assumed to be constant, the continuity equation can be solved rigorously. When these assumptions do not hold and corrections are introduced, it becomes very difficult and often impossible to solve analytically. The present analysis is concerned with production from a two-layer depletion-type reservoir in which the layers have different permeabilities. Instead of using the continuity equation, results were derived from some simple physical ideas. In a single-layer reservoir in which the oil is at a pressure above the bubble point, the rate of production often has been assumed to be directly proportional to the pressure drawdown. In the simplified analysis it has also been assumed that the drop in average reservoir pressure is directly proportional with the cumulative withdrawal. These considerations in the past have been the basis of the analysis of reservoir performance and have been applied to a variety of problems, often with marked success. In the problem under investigation these relationships are shown to be compatible with the equation of continuity, but the approach has the advantage of leading to ordinary differential equations in which changes in constants can be introduced without making the analytical solution impossible. It has the additional advantage that it can be understood more readily by the large group of engineers who are not reservoir specialists. For that reason, detailed steps in the mathematical developments have been shown in full. SCOPE OF ANALYSIS The analysis in this paper has been applied to a two-layer depletion-type reservoir in which both horizons are produced simultaneously in the same well. Because of the difference in permeability, it is obvious that the depletion of the two zones will proceed at different rates. For various problems it may be of interest to know the degree of depletion of the two zones at any arbitrary time and to in-

By C. A. Bruch, W. E. McHugh, R. W. Hockenbury

Commercially pure molybdenum specimens were irradiated in the Materials Testing Reactor for an estimated exposure of 1.9 to 5.9x10 20 thermal nvt. Prior to irradiation, the material was ductile in the tension test; whereas after irradiation, it was brittle. The results of tension tests conducted at various temperatures revealed that the transition temperature for this material had been increased from —30' to +70°C as a result of the radiation exposure. From metallographic studies, it is concluded that the embrittlement is due to submicroscopic changes which raise the flow stress-temperature curve of the material. PRIOR to ten years ago, the bombardment of metals with high speed heavy particles such as protons, deuterons, a particles, and neutrons was primarily of academic interest. These particles existed in extremely small numbers in a few laboratories and only under very special conditions. With the introduction of the nuclear power reactors, these particles are now available in enormous quantities and it has become important from a practical standpoint to learn how well metals withstand severe reactor radiations. The principal radiations of concern in reactors are neutrons and y rays, since the heavier charged particles exist only in limited regions of reactors. Seitz,' in a theoretical approach, has shown that all of these high energy particles, except y rays, have enough energy to knock atoms from lattice sites and that these knocked-on atoms have enough energy to cause additional displacements of neighboring atoms. The result of this process would be a lattice containing many imperfections in the form of interstitial atoms and vacancies. Hence, it would be expected that the properties of metals can be changed by reactor radiations, and such has been found to be the case. Only a limited amount of data have been published in the open literature,2,3 and these data have been for relatively low integrated-neutron-flux exposures. In general, one effect of reactor radiations on the mechanical properties of metals has been to increase strength and decrease ductility. It is now possible to irradiate specimens in the Materials Testing reactor at much higher fluxes and to higher integrated exposures than previously possible.' The data which are being presented here describe the effects of a relatively high exposure on some mechanical properties of molybdenum. Experimental Procedures Material: The molybdenum used in this investigation was obtained from the Climax Molybdenum Co. The two heats from which the material originated were melted under a vacuum of 5 to 30 microns and cast in 7 in. diam water-cooled copper molds. One ingot contained 0.061 pct C and the other 0.066 pct. Both ingots were hot worked by extrusion and rolling into % in. diam rods, after which they were annealed and straightened. The rods were subsequently heated to 1100°C in a hydrogen atmosphere and swaged to ½ in. diam rods at the Research Laboratory of the General Electric Co. The resulting material had an average hardness of 264 VPN, or 99.2 Rb, and had an average of 5000 grains per sq ml in the transverse section, Test Specimens: Substandard-size tensile specimens were prepared according to the specifications shown in Fig. 1. These specimens were used also for hardness measurements. The metallographic specimens were small disks which were polished, etched, and photographed at X1000 prior to irradiation. The field studied was

Jan 1, 1956

By T. J. Whalen, S. M. Kaufman

Surface-tension measurements for liquid Fe-C-Co and Fe-C-Ni alloys were performed by the sesszle-drop technique at 1350o and 1425°C. Cobalt was shown to he more effective than nickel in lowering the surface tension of Fe-C alloys A minimum value for surface tension of 1640 dynes per cm was found in the Fe-C-Co system at a concentration of 1.5 pet C and 12pet Co. Analysis of these measurements in terms of adsorption and desorption behavior indicated that cobalt and nickel lower surface tension in Fe-C alloys by replacing carbon at the liquid-vapor interface. Comparison of results to date for Fe-C liquid alloys has shown that most substitutional-type elements having about the same atomic diameter as iron also have relatively the same influence on surface tension when present in dilute amounts. It has been shown previously that surface-adsorption behavior in liquid Fe-C ternary alloys is related to the manner in which the ternary addition affects the activity of carbon in the bulk solution.' Certain ternary additions, such as chromium, tending to decrease carbon activity cause adsorption of carbon and chromium to the liquid-vapor interface. Additions, such as silicon, increase the carbon activity, resulting in a desorption of carbon and an adsorption of silicon. Both cases were shown to cause a decrease in surface tension due to adsorption. It is the object of this paper, as part of the writers' continuing interest in the effect of alloying additions on the surface tension of Fe-C alloys, to present and discuss surface-tension data on solutions in the ternary systems Fe-C-Co and Fe-C-Ni. Available activity measurements for these systems in the solid state indicate a strong increase in carbon activity when either nickel or cobalt is added to Fe-C alloys.2, 3 EXPERIMENTAL PROCEDURE The alloy compositions used are shown in Table I. These alloys were prepared by vacuum melting in stabilized zirconia crucibles and then vacuum casting into cold-steel molds. The nominal analyses for the alloys used in this investigation are given in Table I. Surface tensions and densities were measured by the sessile-drop method4,5 in conjunction with the tables of Bashforth and bdams.' Specimens were prepared by slicing 1/4-in. cubes from the center of the vacuum-cast ingots and grinding the edges of these cubes until their shapes approximated spheres with flat bottoms. Proper handling techniques, including an acetone rinse immediately before use, assured minimum contamination from sources extraneous to the actual melting. For each experimental run a sample was placed on a BeO plaque and positioned and leveled inside a vacuum induction heating apparatus. The sample and plaque arrangement sat inside a molybdenum tube which acted as the susceptor. Diagrams of this apparatus may be found in the literature.= After heating to temperatures just above the liquidus at pressures of the order of 10-4 to 10- 5 mm Hg, photographs of the drop profile were made using its natural thermal radiation as a light source. Some measurements were made with partial pressures (-1 cm Hg) of a mixture of H2 and He gases. The H2-He atmospheres proved to be necessary at higher nickel contents to retard excessive vaporization losses. Chemical analysis for carbon and the ternary addition was performed for each alloy sample after completion of the experimental run.

Jan 1, 1964

By V. Patarini, M. Salkind

BECAUSE of its high strength and stiffness coupled with low density, continuous boron filament is showing great promise as a potential reinforcement for both metals and nonmetals. Of primary consideration for structural applications is the fatigue behavior of boron fiber composites. Composite fatigue behavior is dependent upon three factors: 1) fiber fatigue behavior, 2) matrix fatigue behavior, and 3) the effect of the interface and fiber ends. The purpose of this note is to describe the behavior of boron filament in rotating beam fatigue. The filament, described by Talley' and Galasso, Salkind, Kuehl, and Patarini,' was made by the hydrogen reduction of boron trichloride on a hot tungsten filament. Testing was performed using a commercial rotating beam wire fatigue tester* described by Votta.~ One end of the test sample is held in a chuck in a synchronous motor. The sample is bent around in a "U" shape, and the other end inserted into a carbide bushing. The maximum strain occurs at the bottom of the "U" where the radius of curvature is a minimum. The strain is adjusted by adjusting the length of the specimen and the location of the bushing. Samples were rotated at 3600 rpm and an automatic shutoff device used to determine the number of cycles to failure. The measurements were accurate to the nearest 360 cycles. The fatigue behavior is summarized in Fig. 1 for fifty-one samples of 4.8 x 10"3 in. diam fibers and ten samples of 3.2 X 10"3 in. diam fiber. The two sample groups represent two different filament production runs and two different nominal size groups. Both groups exhibited nominal tensile strengths of 400,000 psi. No significant difference in the fatigue behavior of the two sample groups is apparent. The scatter in the data is not unexpected for a brittle filament which exhibits a tensile strength distribution with a standard deviation of 10 to 15 pct. Because the test procedure provides a known outer fiber strain in the sample, the maximum stress was calculated assuming a Young's modulus of 58 x 10' psi. This value was selected as being representative of several nominal fiber sizes.2 All of the samples which failed exhibited sudden, catastrophic fracture, and no permanent deformation. One sample was stopped after 1.66 x lo8 cycles at *200,000 psi. The fiber exhibited no apparent damage or deformation. It is apparent that the fatigue resistance of boron filament is quite good. It can therefore be speculated that the fatigue behavior of boron fiber composites would be controlled by the "weaker links", namely matrix fatigue resistance and interface behavior. In fact, preliminary investigations have revealed that this is true for boron-reinforced aluminum? It should be noted that the data presented herein may not necessarily reflect the tensile fatigue behavior of boron filament. It is well-known that boron filament has a radial residual stress pattern with the outer surface in ~om~ression.~ Because of this fact, tensile failure is normally nucleated in the interior of the filament.5 Since the data presented herein is for a rotating beam test in which only the outer surface of the fiber is stressed to the maximum value, it would be incorrect to assume that the failure mechanism and fatigue behavior would be the same if the fiber were tested in tensile fatigue. The fact that many of the data are well above the nominal 400,000 psi tensile strength would tend to support this argument. The authors would like to express their appreciation to the United Aircraft Research Laboratories for supporting this investigation and for permission to publish the results. A portion of this effort was supported by the Air Force Materials Laboratory under contract AF33(615)-2125.

Jan 1, 1968

By B. N. Webber

During World War II the Pocos de Caldas bauxite deposits of Minas Gerais in Brazil yielded some 60,000 tons. Since then they have maintained a small but almost continuous production. Known for many years, the deposits have been reconnoitered by a number of geologists,1-4 but no dimensional study has been possible because there have not been enough exposures to show clearly the depth, bedrock, and habit of occurrence. The deposits are somewhat unorthodox in their occurrence mainly on steep slopes of mountainous terrain. Although the parent rocks are a sequence of alkalic intrusions that bauxitize readily under the proper conditions, bauxitization has not been the dominant weathering process in the area. It is limited to certain localities where important volumes of bauxite have formed by laterization of several rock types, each yielding a distinctive type of bauxite. Bauxitization may be observed in several stages and in both direct and indirect cycles of formation. The deposits are unique in being of demonstrably recent age, so that the conditions under which the bauxite formed are essentially those of the present time. The bauxitization sequence is postulated in Fig. 1. Pocos de Caldas district is situated at approximately 21" 50' south latitude and 46" 30' west longitude in southwestern Minas Gerais, near its boundary with the state of Sao Paulo. It lies within the Eastern Plateau physiographic province of Brazil, occupying a prominent highland area that rises some 2000 ft above the surrounding country. The central portion of the Pocos de Caldas highland is characterized by gently undulating topography, with generally sluggish drainage, and is surrounded by a rim of hills rising above 1000 ft above it. In cross section the highland resembles a truncated cone with a depressed central area. The rim has been sculptured into a more prominent and abrupt topographic pattern than the central area, and streams that are of low to moderate gradient in the central plateau plunge over the rim in a spectacular series of cascades and falls. GEOLOGIC SETTING The Pocos de Caldas highland owes its physiographic expression mainly to the differential erosion of a complex intrusion of alkalic rocks into gneiss and sandstone. Erosion was guided somewhat by faulting. The highland is almost circular, and its limits, except in one locality, coincide with the periphery of the intrusion. The alkalic intrusions largely control its shape and extent, aided by some subsidence through faulting of the central portion. The mountainous rim of chilled phase, the later intrusions, and the indurated intruded rocks have resisted erosion more effectively than the central portion of the intrusion, which is composed of more coarsely crystalline alkalic rocks that form a central basin in the highland. Gneiss and sandstone are found coincident in elevation with the topographically highest intrusions. BAUXITE TYPES Most of the bauxite, which varies in physical type, is on the top and steep slopes of the northern rim. The only alumina mineral is gibbsite, definitely crystalline but iron-stained unless of secondary origin. Clay particles occurring with the bauxite are kaolinite. Some types of bauxite are an index to their origin. There are four general physical types of bauxite or bauxite laterite: 1) Surface Rubble: This partly nodular and partly fragmented type, usually less than 3 ft thick, results from surface weathering of massive bauxite or may form by superficial enrichment of nodular bauxite with a clay matrix when the interstitial clay is removed by surface runoff.

Jan 1, 1960

By R. B. Basham, C. W. Macune

Very small anomalies in oil well temperatures are detected and measured by recording the difference in temperature existing between two thermally sensitive elements which are Spaced several feet apart on a small diameter carrier and lowered into the bore hole. The elements operate in a balanced electrical circuit, sending only a reference signal to the surface as long as normal gradient temperatures are encountered. When either element enters a temperature disturbance, the circuit is unbalanced and produces large recorder deflections for minute anomalies. The system is highly sensitive to small changes in thermal gradients caused by gas or fluid movements and to the boundaries between beds of different thermal conductivities. Typical logs show successful applications of the process to locating gas and water leaks in casing, gas entry. and gas-oil contact. INTRODUCTION Temperature measurements in oil wells have been made for many years in the search for additional sub-surface data. It has been generally agreed that many conditions in the bore hole cause temperature anomalies which, if located and measured, could yield useful information. But it has been recognized also that many of the irregularities, such as those produced by small water and gas leaks in casing, might be very small and therefore difficult to detect with certainty.' Although tem-perature measurements have been made which show anomalies of less than one degree deviation from normal gradient temperatures, the results are usually uncertain and unconvincing. The general practice, therefore. has been to apply temperature surveys only to well conditions known to produce appreciable disturbances, such as large gas movements and cement hydration. The recent demand for additional data has focused attention on the problem of making dependable temperature measurements in the many instances when anomalies are small but none the less significant. It was for the purpose of detecting these minute irregularities in bore hole temperature that the program described in the following text was undertaken. It is emphasized that this presentation is not offered as a complete study, for the process is still partially experimental. But it is believed that the results obtained thus far will be of interest to the industry and will indicate some of the system's potential usefulness. DIFFERENTIAL MEASUREMENT The chief value of differential measurement lies in the fact that a difference between two factors can be measured with a scale of values best suited to that difference, a scale that might be cumbersome or impractical if applied to the factors themselves. When it is known that all factors will be nearly equal in value, and therefore the differences consistently small, it is possible to select a scale which will permit very accurate measurement of the differences. This advantage is in contrast to the difficulty of measuring small increments of a single variable, where the increment must be measured by a large scale which is suitable for measuring the entire factor. Gradient temperatures are usually measured under this latter condition where temperature measuring apparatus must have a scale extending over the range of expected temperatures, say 50' to 25O°F, and it becomes almost impossible to detect small irregularities of less than one degree. The use of large strip chart recorders and divided multiple ranges tend to amplify the small anomaly and make it more pronounced. But the instability of instruments, both

Jan 1, 1952

By C. A. Bruch, J. F. Duffey

On the basis of metallographic and cooling-rate studies of 15 U-Zr alloys, a new version of the 6 phase region of the U-Zr phase diagram is proposed. IN several published diagrams of U-Zr alloy system:' there is good agreement that at elevated temperatures complete solid solubility exists between y uranium and ß zirconium. Similarly, there is reasonably good agreement concerning the uranium-rich and zirconium-rich ends of the diagram. However, there is no agreement concerning the nature of the diagram at intermediate compositions and at temperatures below about 650°C. The early work of Saller et al.8 hows an intermediate phase, 6. In a later diagram by Saller and Rough' shown in Fig. 1, the d phase field is drawn with dotted lines, indicating doubt that this phase exists. The diagram of Summers-Smith2 does not show the d phase. More recently Holden and Seymour' have shown that in the composition range 40 to 60 wt pet Zr, the high-temperature ? phase, which is body-cen-tered-cubic, transforms to an ordered structure, 8. They found that the order-disorder transformation occurs between 595° and 610°C, and presented a diagram based on the study of four different alloy compositions. Most recently Saller et a1.5 presented a new diagram which differs with respect to the composition limits of the 8 field from the others proposed by these authors. The purpose of the present investigation was to determine the boundaries of the d phase field. Experimental Procedures and Results Alloys—Buttons, weighing 80 g of 15 different alloy compositions were prepared by arc melting Mal-linckrodt uranium and iodide-process zirconium in a water-cooled crucible. A controlled atmosphere of argon and helium was maintained in the furnace. Prior to making each button, a sacrificial button of zirconium was melted to increase the purity of the furnace atmosphere. Each alloy was then melted six times to improve its homogeneity. Subsequently the alloy buttons were jacketed in copper and hot rolled to slabs at 775°C. From these slabs, specimens were machined for chemical, thermal, and metallographic analyses, Table I gives both the estimated chemical composition of the alloys, and the values which were obtained by analysis. The oxygen contents varied from 0.013 to 0.032 pet, nitrogen from 0.0014 to 0.014 pet, and carbon from 0.0013 to 0.011 pet. The purity of the alloys ranged from 99.947 to 99.975 pet. Thermal Analysis—The specimens for thermal analysis were blocks 11/4 x 1/4 x % in. The bead of a calibrated thermocouple was placed between two of these blocks and molybdenum wire was wrapped around the assembly. Each assembly was sealed in a quartz capsule having an argon atmosphere. The capsule was placed inside a refractory crucible which was heated in a furnace. Using a method described by Smith,' the emf of a differential thermocouple, with junctions inside and outside of the refractory crucible, was used to activate the

Jan 1, 1959

By T. C. King

AT the new Graham-Central Mill of Eagle-Picher, near Galena, Ill., material is simultaneously dewatered and introduced into the ball-mill scoop boxes by the use of variable-speed, 24-in. spiral classifiers. This arrangement has proved satisfactory in that the moisture content of the wet feed is reduced, thus allowing maintenance of density within the mills, and a constant feed at any desired rate to the mills is provided. In this mill the primary feed is wet crushed to minus ½ in. and preconcentrated by jigs to produce a bulk lead-zinc-iron concentrate and a waste tailing. The jig concentrate is then dewatered by a conventional dewatering classifier and stored in, bins ahead of the ball mills. Even though this material is well dewatered, the discharge at the bin bottom is sloppy because of the gradual drainage of the water from the surface of the particles. Conventional belt feeders with vertical cutoff gates are unsatisfactory because of the flushing characteristic of the wet sand.

Jan 1, 1950

By R. A. Morse, C. R. Holmgren

The production of oil by water flooding can be substantially increased by the maintenance of free gas saturation in the reservoir during the flooding operation. This effect is accomplished by the alteration of oil relative permeability characteristics and the occupation by gas of pore space that would otherwise be filled with residual oil. The amount of reduction In residual oil can be calculated from appropriate water-oil relative permeability characteristics. This paper presents experimental data in support of the foregoing conclusions and an example of the calculations. The microscopic pore saturation concepts of the mechanism are discussed. A method of practical application to field floods is presented together with discussion of certain limitations. INTRODUCTION The presence of free gas has been reported by a number of investigators to significantly affect the oil recovery which can be obtained from sandstone flow systems by water flooding.1,2,3,4,5 The effect of gas, noted in every instance, has been to cause lower residual oil saturations than could be obtained by water flooding the same systems in the absence of free gas. The degree of improvement in recovery has been observed to vary widely, depending on the systems used and the conditions of the tests. The increased oil recovery obtained because of the presence of gas during a water flood has been variously attributed to changes in physical characteristics of the oil, selective plugging action of the gas, inclusion of oil mist in the free gas phase, and the additional sweeping or driving action of the free gas. All but the first of these suggestions imply changes in the displacement mechanism. The change in viscosity and inter-facial tension of the oil phase, within the pressure range used for all the experimental work, is certainly not sufficient to account for the differences in residual oil saturation noted dess there is a drastic change in the displacement process. One other effect which logically seems capable of causing differences in residual oil saturation of the magnitude noted in the experimental work is that of simple replacement. In a water-wet system containing oil, water, and gas, it is to be expected that the gas will exist inside the oil. This is the position of minimum free surface energy, since the gas-oil interfacial tension will be less than the gas-water interfacial tension. There is no apparent reason to expect that the existence of free gas within the oil phase should alter the saturation at which the non-wetting phase (now oil and gas) should become discontinuous and hence trapped so as to be unrecoverable by direct displacement by water. If this is the situation, then trapping of a certain percentage of gas saturation during water flood should result, at infinite water-oil ratio, in a like reduction of oil saturation below that attainable by flooding in the absence of free gas. It is visualized that the gas will exist as bubbles inside the discontinuous residual oil as illustrated in Fig. 1, with the size of the oil bubbles being substantially unchanged due to the presence of the gas. As a practical matter, it can be anticipated that the presence of a free gas saturation inside the oil phase will reduce the relative permeability to oil which will exist at any particular water saturation. This reduction will be caused by two factors — -the addition of the gas-oil interface, and the reduction of area available for oil flow in the pores containing gas. This reduction in oil permeability at any particular water saturation will result in water breakthrough at a lower water satu-

Jan 1, 1951

By P. P. Reichert, L. S. Gournay, N. T. Burdine

An investigation of equivalent pore entry radii in typical samples of petroleum reservoir rock and the pore volume associated with each value of pore entry radius has been made. Theoretical discussions together with experimental procedures for obtaining pore entry radii and the distribution of pore volume with pore entry radii are presented. Experimental results on a number of core samples, along with typical distribution curves, are shown. Data on the per cent of the pore volume filled by mercury at a pressure of 1500 psi are included. The results of re-runs of samples, made possible by regenerative apparatus, show the repeatability of the data and indicate the amount of physical change in the samples by mercury penetration. Theoretical equations for calculating permeability from pore size distribution data were derived and the results of such calculations are compared with measured gas permeability data. The effect of the shape, surface area, and weight of the sample on the pore size distribution of reservoir rocks was investigated experimentally. Mercury capillary pressure curves are compared with those obtained by the porous diaphragm method using pas to displace water. Standard core analysis techniques, in general, lead to quantities which are statistical averages of the varying properties of the samples under examination. Although such statistical information has real value in predicting the gross performance of porous bodies. it fails to provide fundamental information concerning the properties of the porous medium itself or any processes which may be occurring in it. For example, a gas permeability measurement on a core sample is an indirect way of determining an average pore radius for that particular sample. Since there are many combinations of pore radii that will give the same radius. and, hence, the same permeability, no information is obtained on the pore size distribution. Furthermore, similar values in permeability do not imply similarity in other properties of a porous medium. For instance, it is possible to have two core samples with identical permeability which would have different residual oil contents at the end of an air-oil drive, or even different amounts of interstitial water. It has been recognized for some time by the petroleum industry that a determination of pore size distribution for porous reservoir rocks offered promise of increased understanding of fundamental flow processes in the porous matrix. and therefore of petroleum res- ervoir performance in general. There have recently been published several methods for determination of pore size distribution in porous materials. A report is given here of the modifications in equipment and technique required to adapt one of these methods to measurements on petroleum reservoir core samples. Although only a few correlations or applications of the method are available for presentation at this time, the technique is brought to the attention of the industry so that the opinions and experience of others with this or similar techniques may be exchanged. It seems possible that the method will have wide application in the future. METHOD There are three general methods which may be employed to measure the pore size distribution in naturally occurring rock formations. One method1 is based on experimentally determined adsorption isotherms for calculating the surface area of the porous medium. Knowing the surface area and the pore volume, a rough estimate of the pore radius can be made. Since this method depends on the thickness and uniformity of the adsorbed layer, the validity of the results would be highly questionable. A second method utilizes capillary pressure data obtained by static dis-

Jan 1, 1950

By J. Skrove, C. R. Boardman

In situ permeability of the rock outside the Hardhat chimney was determined by pressurization of long holes with air. Experimental data indicated a remarkable difference between fracture permeability of the rock near the chimney and that at a considerable distance. Although permeable fault zones were known to exist in the granite stock, the measurements of background permeability were quite low, on the order of tenths to several millidarcies. The observed difference is about two or three orders of magnitude above this background in the region 125 to 215 ft radially from the shot point, or 80 to 165 ft radially from the vertical axis of the chimney. The presence of a collapsed drift immediately beyond this region precluded measurements which could have defined the maximum extent of the zone of high permeabilily. INTRODUCTION Previous exploration has revealed that contained nu-clear explosions create cavities which generally collapse, resulting in rubble-filled chimneys and annular fractured zones. These geometries have been shown to result in complex flow regimes which should increase the production rate from hydrocarbon reservoirs.' Empirical scaling equations have been developed for estimatina chimney radii and heights for a variet; of rock media.' The exten; of the annular fractured zone has been documented and associated permeability changes have been observed qualitatively for several explosions. This study was begun to establish the nature and magnitude of the permeability of the latter region. It is anticipated that results will be useful in estimating permeability changes and consequent production stimulation which might ensue from a contained explosion in a hydrocarbon reservoir. The post-shot environment of the Hardhat event (a 5-kt contained nuclear explosion in granitic rock) was c'hosen for the experimental measurements. The Hardhat device was detonated at a depth of 939 ft, and subsequent exploration revealed a chimney of broken rock with a radius of 65 to 70 ft and a height above shot point of 281 ft.' BeFore the explosion, the Hardhat medium was highly jointed and fractured (Fig. I). Jt was expected that differential rock motion along these and other weaknesses induced during cavity growth and collapse would significantly alter the permeability of the rock mass. EXPERIMENTAL METHOD Initially, three 2-in. diameter holes (Nos. 10, 12 and 19) were drilled about 25 ft outward through the walls of the 500-ft level drift (elevation 4,253 ft, Fig. 2). One was drilled near the chimney and two holes, one vertical and the other horizontal, were drilled near the shaft. Order-of-magnitude differences in permeability obtained by pressurization measurements indicated further: investigation was warranted. A series of 3-in. diameter holes was then drilled with water as a coolant into the walls and roof of the drift (Fig. 2). An 11-in. long packer was set from 1 to 8 Et inside each hole and air was injected at measured Row rates. Hole pressures were monitored at the collar. Permeability was low enough in the holes near the access shaft that pressure could be maintained long enough to obtain good pressure decay rates. In the vicinity of the chimney, however, permeability was so high that this was not possible and air was injected under steady-state conditions. About one year later, these same holes were retested to

Jan 1, 1967

By E. C. Smith

THE CHAIRMAN.-Mr. Earle Smith- has kindly offered to make some remarks in connection with segregation in the product, Mr. Smith: E. C. SMITH,* Cleveland, Ohio-I will start this off by a story of the code days of the American Iron and Steel Institute. In those days, Republic did not have a big strip mill, and the question came up of the check analysis of rimmed steel. I suggested that they let me be the chairman of the Committee on Accumulating the Information on the Variation of the Composition of the Ingots of Rimmed Steel. Somebody wanted to know why I wanted to be the chairman. I said, "We don't make any of the big ingots of rimmed steel, and no matter who makes them they are so bad that you don't dare publish the information. So if I collect it and hide it you can't charge me with having done anything that really disrupted the commercial situation. So, everybody furnished me with a rather complete story as to the horrible variations in big rimmed ingots. I took it out to my house and put it away, and it is still there. Now, segregation in the big ingot is no longer an "-academic-matter-as far as II am concerned. ¬I am in a situation like that of the German who was told in 1936 about the coming war. He said: "Until it is your throat that is going to be cut, you don't pay any attention to what is happening to the other man." That is the way with the problem that we have in front of us. Recently I have been told that the comptroller was questioning the payment for certain articles of stamped steel that had been made from rimmed steel, because upon check analysis of the rimmed steel it had been determined that these stamped articles were not within the compositions that were included in the specification, and therefore he as the comptroller had no alternative. It was not meeting the specification; therefore, no payment. So I would say to all of you: You can very seriously consider this matter of segregation now and on into the future on the basis of the fact that it is actually going to cost your companies, which are making these products, money unless there is some new idea about the infallibility of quantitative chemists who analyze some of these products or lawyers who read specifications. I don't know which man is going to be the major factor in the future. If the National Bureau of Standards could in some way show the specification writers the variation between good chemists analyzing for what they expect to be umpire results, the writers would certainly realize that some of the specifications to which we have calmly signed our names as being O.K. are well, as one man said to me, they might be filled by the devil, and they, certainly could be filled by the Lord, but they could not be filled by mankind. I would like to inject two or three things into a segregation study which I want you to think about, because I would be a little surprised if there is very much discussion of them. In the first place, we generally make steel in the United States in the basic open hearth, and I do not think there has been nearly enough consideration given to segregation within the bath before it moves into the ladle. I am sure that any of the people who handled the 9400 series of the NE series when it contained the 0.60 per cent silicon have more respect than they had previously for the segregation that is within the ladle; that is, before the metal reaches the ingot mold, the frozen ingots and the segregation in them. Another point to which I think we ought to give serious consideration is the segregation of iron oxide in the ingot-iron type of material, where the distinction between that and the steel segregation is that it is actually segregating iron oxide. Normally we are segregating some form of carbon or sulphur, or something like. that, with the stamping steel industry now coming down into the ranges of chemistry, where the segregation of iron oxide will be just

Jan 1, 1944

By W. F. Kieschnick, and W. J. McGuire&apos, Eugene Harrison

This paper concerns the induction and extension of fractures into rock formations as involved in drilling, completing, and production stimulating operations on wells. Conclusions concerning formation breakdown are derived from (I) a review and extension of published analyses relating to mechanical theories of rock stress and the state of stress in the earth's crust and (2) a correlation of field data from fracturing operations. Conclusions concerning the mechanics of fracture extension, which indicate the relationship between fracture dimensions and rock properties, depth, and volume of injected fluid, are tentative and largely establish limits of relationships. These conclusions are derived from stress calculations, limited field data, and laboratory experimental studies. The experimental work involves the study of the stresses at the fracture boundaries and the geometry of pressurized fractures by means of photo-elastic modeling methods. Results of this investigation indicate that a large majority of pressure induced wellbore fractures are vertical, particularly in deeper wells; and variations in the pressures necessary to create and extend fractures can be explained largely on a basis of established rock properties. It is also shown that variations due to tectonic forces should usually be expected to be slight. Other results indicate that during that extension of fractures rather large fracture volumes are temporarily created by the parting of the formation. The purpose of this paper is to present the results of calculations and laboratory experiments concerning the mechanics of fracture induction and extension with a view to broadening existing knowledge relating to these phenomena. It is believed that continued progress in developing knowledge of this type is important to the further development of techniques for drilling and completing wells. When a wellbore is subjected to sufficiently high pressure, fracturing of the formation surrounding the well occurs. This phenomenon is a common cause of lost circulation during drilling operations, is a deliberately planned factor in most squeeze cementing operations, and is the controlling factor in many productivity stimulation operations. The exploitation of formation fracturing in recent years has been particularly impressive in sand-viscous fluid well stimulation treatments which were first introduced to the industry by the Stanolind research group1,2,3 several years ago. The borehole fracturing phenomenon has been analyzed mathematically by application of the principles defining the elastic and inelastic behavior of thick-walled cylinders of homogeneous, isotropic, and impermeable material.1,5,6 This basic argument is re-presented in this paper along with new considerations which strengthen it. In addition to these arguments relating to fracture induction some calculations and experimental results relating to the mechanics of fracture extension are presented. Since the nature of the pressure induced fracture at distances from the well is of great importance in considerations of well stimulation procedures there appears to be a need for an integrated approach which deals with the mechanics of fracture extension as well as with wellbore rupture.

Jan 1, 1955

By J. J. Gilman

RECENT experiments have shown that the mar-tensite reaction in a standard tool steel is influenced by the history of the reacting austenite. The martensite reaction proceeds to a given extent at a higher temperature in austenite formed from an annealed spheroidal structure than it does in austenite formed from tempered martensite: that is to say, a prequench lowers the temperature range of the martensite reaction in this steel. Furthermore, a prequench alters the appearance of the martensite as compared to martensite formed from "virgin" austenite. The steel used for this work was a manganese nondeforming tool steel of the following composition: C, 0.85 pct; Mn, 1.43; Si, 0.23; Ni, 0.12; Cr, 0.59; and W, 0.59. A piece from a rolled bar was forged to Vz in. sq and annealed to a spheroidal structure. Disks 1/8 in. thick were used in the experiments. Several sets of the specimens were prepared and austenitized in lead at 1475°F. Three sets were held at 1475°F for 15 min, quenched in water, and immediately reheated to 1475°F. After this quench the three sets were held for 5 min, 30 min, and 3 hr, respectively, at 1475°F and then the individual specimens in each set were quenched in molten baths to 325", 300°, and 275ºF, respectively, and held for 15 sec. Immediately after the quenching treatments? the specimens were tempered at 600°F for 30 sec to darken the martensite and then were quenched in water. The holding times were short enough to avoid isothermal transformation. Three other sets of specimens were given the same final quenching treatments as the first three, but they were austenitized at 1475°F for 20 min, 35 min, and 3 hr and 15 min, respectively, without an intermediate water quench. The two individual specimens from each set were quenched together in order to eliminate quenching errors. Several experiments were run in this way but only the six sets referred to are described in detail because they all yielded essentially the same results. By means of the stated heat treatments the martensite reaction was investigated for: 1—austenite formed from an annealed structure, and 2— austenite formed from tempered martensite. The martensite reactions of the two types of austenite differed significantly. This is shown by Figs. 1 and 2. Comparison of the photographs on the left in Figs. 1 and 2 with those on the right shows that less martensite was formed by a quench to a given temperature from prequenched austenite than from austenite formed from an annealed structure, that is, the prequench suppressed the martensite reaction. The effect was observed for specimens austenitized 20 min, 35 min, and 3 hr and 15 min. A comparison of Figs. 1 and 2 shows that the martensite reactions in both sets of specimens occurred at lower temperatures with increased austenitization time. This was caused by the increased dissolution of residual carbides with time at 1475°F. However, the difference in amount of martensite formed in prequenched austenite as compared to virgin austenite was approximately the same for all three austenitization times. One further observation should be noted. The needles of the martensite formed from virgin austenite are somewhat longer on the average and show less of a tendency to cluster than those of martensite formed from prequenched austenite. This causes the martensite on the right in Figs. 1 and 2 to have a more acicular appearance than the martensite on the left. Since the sets of specimens used in this work were austenitized for identical total lengths of time and the effect of a prequench on the martensite reaction existed for specimens held at the austenitizing tem-

Jan 1, 1953

By Orville R. Lyons

CENTRIFUGAL force has been utilized for the dewatering of fine coal for over 50 years by means of machines commonly called centrifugal dryers. In any centrifuge the coal and water are subjected to a spinning action which usually inctedtocreases in intensity as the coal progresses through the machine. This spinning action, or the centrifugal force that it induces, tears water away from coal particles and produces a dewatered coal. The effectiveness of the dewatering action for any particular machine is governed by the size-consist of the coal and the centrifugal force imparted to the water on the coal. Four makes of centrifuge are currently being used to dewater fine bituminous coal in the United States. These include the vertical, basket-screen C.M.I. (Centrifugal and Mechanical Industries) Carpenter, Reineveld, and the horizontal solid-bowl Bird. The C.M.I. and Reineveld centrifuges are similar in construction and are variations of the Elmore centrifuge, varying principally in the slope of the basket, operating speed, size of perforations in the basket, and diameter of the basket. The same operating description suffices for both. These centrifuges are made up of two rotating elements, an outside conical screen frame and an inside solid cone which carries spiral pusher blades. The screen frame is supported by a hollow shaft, and the solid cone by a spindle shaft passing through the hollow shaft. Both the screen frame and the solid cone rotate at high speeds; the solid cone, with its scraping flights, rotating somewhat more slowly than the screen. The wet coal enters the machine at the top, falls on the cone, and is thrown against the screen by centrifugal force. The coal slides down the screen until it meets the upper end of the flights, where it is moved slowly along the flights until discharged at the bottom. The elfluent passes through the sieve basket or screen and discharges into a launder. The Carpenter centrifuge consists of a conical rotating element with a vertical axis, built up of three rows of perforated stainless-steel plates or stainless-steel wedge-wire or round-wire sections cut and rolled to conform to the surface of the cone. Wet material is delivered to a conical hopper inside the centrifuge casing and is distributed in a thin, even layer over the inner surface of the cone by a disk mounted on the rotor shaft. Impacting of the coal against the screen and the centrifugal force exerted as the material moves downwards creates a dewatering effect. The moisture is forced through the coal bed and then through the perforated plates of the basket, collecting in a circular trough built into the centrifuge. The effluent is conducted from the trough through the centrifuge casing by outlet pipes. The dewatered coal is discharged over the inside bottom edge of the rotor. The Bird centrifuge consists of a tank or truncated conical shell, which is revolved at the desired speed by means of a drive sheave. A screw conveyor rotates inside the cone or bowl at a slightly lower speed in the same direction of rotation. The feed entrance, in the center of the large end of the truncated cone, is high enough to allow formation of a pool of slurry. Adjustable effluent-discharge ports are located in the large end of the bowl so the level of the liquid can be regulated. The solids are moved forward by the screw conveyor as fast as deposited and carried above the level of the pool for an interval before leaving the bowl. In the past these four makes of centrifuge could be compared only by indirect means. The author published a rough comparison method in 1949' but

Jan 1, 1952

By P. R. PaeIay, A. Slibar

Using three-dimensional, stress-deformation rate equations for a Bingham plastic, an approximate solution for the laminar flow of drilling mud between the drill pipe and casing is given for the case when the velocity gradients due to axial flow are large compared to velocity gradients due to rotation. INTRODUCTION The fact that drilling mud can be treated, to a first approximation, as a Bingham plastic has been established by several investigators12,3,4,5. A Bingham plastic is a material that is rigid until a certain combination of stresses exceeds a critical value. When the stresses are sufficiently high to initiate flow, the reduced stresses have a constant ratio to the corresponding deformation rates at each point. Prediction of pressure and torque requirements to produce the desired flow of the material have been made by analytical solutions due to Bingham6, Reiner7, and Buckingham8. One part of the present means of calculation that requires clarification is the flow between the drill pipe and casing. Present methods treat the flow resulting from the rotation of the drill pipe separate from the flow produced by the axial pressure gradient. Since the non-linear behavior of a Bingham plastic implies that solutions cannot be superposed, the present analytical investigation was undertaken to obtain a solution to the problem of combined axial and tangential flow. Equations have been proposed for the three-dimensional flow of a Bingham plastic9,10,11 and it has been shown that the proposed equations lead to the usual solutions from the one-dimensional theory". Applying these equations to the flow between two concentric cylinders the problem of axial flow only13 and tangential flow only12 have been solved. In addition to the separate problems of axial and tangential flow between concentric cylinders, the authors have determined the relationship between external torque on the inside cylinder and axial pressure gradient necessary to initiate flow". The solution given in Ref. 14 points out the complexity of the present problem. The problem considered here is the case of simultaneous axial and tangential flow. The axial flow, necessary to keep the drill bit free of removed material, results from the axial pressure gradient. Tangential flow is present since the drill pipe rotates in the hole. The solution given here is valid when the shear stresses in the drilling mud due to rotation are small compared to the shear stresses resulting from the axial flow. This case for laminar flow can be encountered in oilfield drilling. STRESS-DEFORMATION RATE EQUATIONS A detailed derivation of the equations governing the behavior of a Bingham plastic is given in Ref. 10. This section briefly outlines the physical reasoning leading to this three-dimensional formulation of the stress-deforma-tion rate law. Experiments on a certain class of materials have demonstrated the following properties: (1) when a certain combination of the stresses is below a critical value no deformation of the material occurs, (2) to a first approximation this combination of stresses is independent of the hydrostatic pressure (negative average normal stress), (3) if flow occurs the ratio of the reduced stress to the corresponding deformation rate is constant at each point of the flowing material, and (4) incom-pressibility. For the one dimensional case of shear deformation, Bingham6 formulated the governing equation as dxx, = 0 for sxx < to and µdxx = s xx = to for sxx to , . where dxx is the shear deformation rate, sxx the shear stress, to the critical shear stress, and p the slope of the sxx vs dxx curve for dxx > 0. Fig. 1 shows the behavior for pure shear between two parallel plates. Taking into account the physical properties given above and assuming the critical combination of stresses to be measured by the octahedral shear stress, the fol-lowing three-dimensional equations have been proposed.

Jan 1, 1958

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and &apos;n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By R. A. Morse, C. R. Holmgren

The production of oil by water flooding can be substantially increased by the maintenance of free gas saturation in the reservoir during the flooding operation. This effect is accomplished by the alteration of oil relative permeability characteristics and the occupation by gas of pore space that would otherwise be filled with residual oil. The amount of reduction In residual oil can be calculated from appropriate water-oil relative permeability characteristics. This paper presents experimental data in support of the foregoing conclusions and an example of the calculations. The microscopic pore saturation concepts of the mechanism are discussed. A method of practical application to field floods is presented together with discussion of certain limitations. INTRODUCTION The presence of free gas has been reported by a number of investigators to significantly affect the oil recovery which can be obtained from sandstone flow systems by water flooding.1,2,3,4,5 The effect of gas, noted in every instance, has been to cause lower residual oil saturations than could be obtained by water flooding the same systems in the absence of free gas. The degree of improvement in recovery has been observed to vary widely, depending on the systems used and the conditions of the tests. The increased oil recovery obtained because of the presence of gas during a water flood has been variously attributed to changes in physical characteristics of the oil, selective plugging action of the gas, inclusion of oil mist in the free gas phase, and the additional sweeping or driving action of the free gas. All but the first of these suggestions imply changes in the displacement mechanism. The change in viscosity and inter-facial tension of the oil phase, within the pressure range used for all the experimental work, is certainly not sufficient to account for the differences in residual oil saturation noted dess there is a drastic change in the displacement process. One other effect which logically seems capable of causing differences in residual oil saturation of the magnitude noted in the experimental work is that of simple replacement. In a water-wet system containing oil, water, and gas, it is to be expected that the gas will exist inside the oil. This is the position of minimum free surface energy, since the gas-oil interfacial tension will be less than the gas-water interfacial tension. There is no apparent reason to expect that the existence of free gas within the oil phase should alter the saturation at which the non-wetting phase (now oil and gas) should become discontinuous and hence trapped so as to be unrecoverable by direct displacement by water. If this is the situation, then trapping of a certain percentage of gas saturation during water flood should result, at infinite water-oil ratio, in a like reduction of oil saturation below that attainable by flooding in the absence of free gas. It is visualized that the gas will exist as bubbles inside the discontinuous residual oil as illustrated in Fig. 1, with the size of the oil bubbles being substantially unchanged due to the presence of the gas. As a practical matter, it can be anticipated that the presence of a free gas saturation inside the oil phase will reduce the relative permeability to oil which will exist at any particular water saturation. This reduction will be caused by two factors — -the addition of the gas-oil interface, and the reduction of area available for oil flow in the pores containing gas. This reduction in oil permeability at any particular water saturation will result in water breakthrough at a lower water satu-

Jan 1, 1951

By Michael Hoch, Walter C. Wyder

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

Jan 1, 1963

By A. Berghezan, E. Bull Simonsen

A simple and general method is described for melting and zone refining refractory metals by induction heating on a specially shaped water-cooled copper crucible. The crucible is the essential part of the apparatus and is placed horizontally. It consists of either a copper plate, or a flattened tube, or of several parallel small diameter tubes all water cooled. The charge lies on the crucible, or whenever possible, is suspended above it. This assembly goes into a transparent quartz tube and the whole is passed through the coil of a radio frequency generator. Vaarious atmospheres can be used. No contamination is detected from the copper crucible. purification is obtained both by selective evaporation of impurities and by zone refining. METHODS of melting and refining relatively large ingots of all reactive and refractory metals as well as some semiconductor materials have been developed in this laboratory during the past several years using induction heating and cold crucibles. These methods are simple and permit the use of a variety of starting materials in preparing ingots of suitable shapes. Among these methods, two are of particular interest. One deals only with the problem of melting without contamination. In this method the induction coil has a specially designed shape and acts simultaneously as heating element and crucible. The second goes one step further, being designed for both melting and further purification of the refractory metals. The aim of this paper is to describe the second method which is of more general interest and of greater applicability to metallurgical problems. A) THE PRINCIPLE OF THE MELTING AND PURIFICATION METHOD As originally proposed by one of us1 the method consists of heating a charge of any refractory metal or semiconductor material to the melting point on a water-cooled copper crucible by passing both the charge and the crucible through the induction coil of a radiofrequency generator. Although both are subjected to the same induction field, one achieves the melting of a refractory metal on a copper crucible even when the refractory metal has a melting point of more than 2000°C above that of the crucible. This seemingly "odd" method works effectively for the following reasons. Because of its high electrical and thermal conductivity as compared with the material being melted, copper can be used as the crucible and kept at a low temperature while the material is heated by induction to its melting point. With water Silver and other highly conducting materials can also be used. If a nonconducting material is contemplated, e.g. SiO or a high polymer, a very thin wall should provide efficient cooling. cooling through ducts in the crucible its temperature can be kept between 40" to 70°C; thus its electrical resistivity is kept low, while the resistivity of the charge increases rapidly as its temperature is increased. B) APPARATUS The crucible is the essential part of the apparatus. It has been designed in various shapes depending on the atmosphere used, whether vacuum or an inert gas or hydrogen. In all crucible designs an effort was made to reduce its volume to "nothing but the cooling water" in order to avoid shielding the ingot from the induction field. In practice it is either a

Jan 1, 1962