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By Malcolm T. Hepworth

RECENT interest in thermoelectric devices has been directed toward studies of the properties of thermoelectric materials of semiconducting solid compounds with little attention given to ionic and semiconducting liquids such as aqueous solutions, fused salts, and mattes. One type of thermoelectric system is the thermocell: a nonisothermal galvanic cell with two identical electrodes at different temperatures connected by an electrolyte bridge. An electromotive force, v, is generated which is a function of the electrode reactions and the properties of the electrolyte according to the Eastman' equation: where S* is the entropy change of the system arising from the electrode reactions and by heat transferred by ion migration and by thermal conduction. The quantity nF is the product of equivalents passed and Faraday's constant. A value of S* of 23.06 cal per "C is equivalent to 1 mv-Faraday per "C. The symbol, a, is used for dV/dT in analog to the See-beck coefficient of solid-state thermoelements. de Bethune2 has calculated the temperature coefficients of the electromotive force of a large number of nonisothermal aqueous cells from measurements on the nonisothermal temperature coefficients of the standard hydrogen electrode, combined with data on the isothermal temperature coefficients of half-cells tabulated in the literature. Values of these coefficients (a) in de Bethune's compilation ranged up to 3 mv per C. In particular he reported a value of +2.059 mv per "C at 25'C for the cell: Fe (aqueous, unit activity) (aqueous, unit activity) written for the hot-electrode reaction. The positive sign indicates that the hot electrode is positive (an "n-type thermocell"). In analog to a solid-state p-n system, it would be possible to couple two thermocells together to form a system in which the figure of merit could be calculated by adding the temperature coefficients according to the relationship described by offee:' where a is the Seebeck coefficient in volts per "C, p is the specific resistivity in ohm-cm, and K is the thermal conductivity in watts per cm "C. Even though ionic systems have rather high electrical resistivities compared with semiconducting and metallic systems, it was felt that a preliminary study of one ionic system should be made to establish some basis for evaluating the possibility of a p-n thermocell for energy conversion. Accordingly the Fe", Fe"' system was studied as a possible component for a p-n system. A glass system was constructed consisting of two vertical water-jacketed tubes connected by a horizontal tube, Fig. 1. Platinum-black electrodes 1 cm by 1 cm in dimension were inserted in each vertical tube with thermometers to register the electrode-compartment temperatures. The temperature of the electrode compartments was controlled by circulating water from thermostatted baths around the electrode compartments. The electromotive force of the cell was then read by a potentiometer for zero current as a function of the temperature of the hotter electrode. Current output of the cell for varying external loads was also measured. The cell resistance was measured by means of a bridge circuit with 10,000 cps signal and oscilloscope. Resistance measurements were converted to specific resistivity by calibrating the cell with a solution of known conductivity.

Jan 1, 1965

By F. W. Schaller

TETRAGONALITY is an important aspect of the models of transformation, strengthening, and tempering of ferrous martensite. When the c/a

Jan 1, 1963

By R. G. Turner, M. G. Hubbard, A. E. Dukler

Gas phase hydrocarbons produced from underground reservoirs will, in many instances, have liquid phase material associated with them, the presence of which can affect the flowing characteristics of the well. Liquids can come from condensation of hydrocarbon gas (condensate) or from interstitial water in the reservoir matrix. In either case, the higher density liquid phase, being essentially discontinuous, must be transported to the surface by the gas. In the event the gas phase does not provide sufficient transport energy to lift the liquids out of the well, the liquids will accumulate in the wellbore. The accumulation of the liquid will impose an additional back pressure on the formation that can significantly affect the production capacity of the well. In low pressure wells the liquid may completely kill the well; and in the higher pressure wells there can occur a variable degree of slugging or churning of the liquids, which can affect calculations used in routine well tests. Specifically, the calculated bottom-hole pressures used in multirate backpressure tests will be erroneous if the well is not removing liquids on a continuous basis, and gas:liquid ratios observed during such a test may not be correct. Several authors1,3,8,14 have suggested methods to determine if the flow rate of a well is sufficient to remove liquid phase material. Vitter14 and Duggan' proposed that wellhead velocities observed in the field would be adequate for keeping wells unloaded. Jones8 and Dukler3 presented analytical treatments resulting in equations for calculating, from physical properties, the minimum necessary flow rate. An analysis of these studies indicates the existence of two proposed physical models for the removal of gas well liquids: (1) liquid film movement along the walls of the pipe and (2) liquid droplets entrained in the high velocity gas core. Although there probably is a continuous exchange of liquid between the gas core and the film, they will be treated separately for the purposes of this study. The development and comparison of these separate models with experimental data will permit the determination of which, if either, is the controlling mechanism for the removal of liquids from gas wells. The Continuous Film Model Liquid phase accumulation on the walls of a conduit during two-phase gas/liquid flow is inevitable due to the impingement of entrained liquid drops and the condensation of vapors. The movement of the liquid on the wall is therefore of interest in the analysis of liquid removal from gas wells. If the annular liquid film must be moved upward along the walls in order to keep a gas well from loading up, then the minimum gas flow rate necessary to accomplish this is of primary interest. The analysis technique used follows Dukler2 and Hewitt5 and involves describing the profile of the velocity of a liquid film moving upward on the inside of a tube. The minimum rate of gas flow required to move the film upward is then calculated.

Jan 1, 1970

By J. P. Neumann, L. Raymond

At temperatures near 1000°C, only the (112) (111) slip systems are operatire in tungsten. Therefore, the substructure introduced into the billet upon rleforming a single crystal by rolling at 1000 "C can be controlled by proper selection 01. processing ral'iubles. Using a reduction of 10 pct pel- pass, the (001)[110] and the (110)[001] crystals will deform by duplex slip rip to a 50 pet reduction in thickuess. These rolled single-crystal sheels are characlerized by anisotropic hardening, retention of ductility with warm working, lattice bending which is related to the conlacl (angle, and macroscopic dimensional changecs in the length bid not the width of the billet. When several slip systems become operative, a greater degree of work hardening is itztvoducetl into the crystal. This rolling- condition is characlerized by isotropic hardening, loss of ductilily with warm working, complex lattice distortions, and macro-scopic dimensional changes in both the length rind Width of the billel. IN tungsten, the {1 10}(111) slip systems are operative below room temperature,' while above 700°C only the {112{ (111) slip systems are observed.2,3 In the transition region, i.e., room temperature. both systems appear. It is the purpose of this investigation to show that tungsten single crystals deformed by rolling at a temperature where only one slip system is operative generate dislocation substructure which depends on the crystal orientation. For a specific crystal orientation. the resulting dislocation substructure can be further influenced by modifying the rolling procedure. Crystals oriented for multiple slip display less substructural sensi- tivity to modifications in processing techniques than do single crystals oriented for duplex slip. Under simple slip modes of deformation, very little work hardening is introduced into a rolled single-crystal sheet. Mechanical properties such as room-temperature strength. ductility, and hardness are used to confirm the existence of the different work-hardened conditions generated within the crystal by modified warm-rolling techniques. EXPERIMENTAL PROCEDURE Material. Single-crystal billets of four different crystal orientations. grown by the Arc-Verneuil technique. were ground to a size of 0.25 by 0.375 by 3 in. In terms of their rolling plane and rolling direction, the billets had the following orientations: (1101 [001 ] (110) [110] (001) [110] (001) [100] The actual orientation of all crystals was within 5 deg of the ideal orientations. The typical impurity content of the crystals is given in Table I. Polishing and Etching. Polishing was done elec-trolytically in a 20 g per liter aqueous solution of NaOH at approximately 10 v. It was established by the Laue back-reflection X-ray technique that the surface damage due to grinding and cutting operations with a diamond wheel did not exceed 0.001 in. Therefore after each cutting or grinding operation at least 0.002 in. was removed electrolytically from the surface in order to eliminate surface effects. By lowering the voltage to 3 v, subgrain boundaries and individual dislocations are identified in agreement with Berlec 4 where the etch-pit traces on a cubic plane form a square. The etching time was about 5 sec at room temperature. Rolling. Rolling was carried out on a Loma 2-high mill (Model 600). The peripheral velocity of the 6-in.-diameter rolls was 500 in. per min, with the surface temperature of the rolls about 400° to 450° C The billets were heated before each pass for 30 min in argon to 1000 C. Oxidation of the crystals during rolling in air resulted in a thin layer of greenish-yellow WO 3 This oxide was removed after each pass by immersing the crystals for a few minutes in a boiling NaOH solution. Prior to the initial rolling pass, a surface layer of 0.001 in. was removed by polishing. The crystals were then annealed in vacuum (10-4 torr) at 2400 C for 30 min. All crystals were rolled in the same direction; i.e., the same end was always introduced into the rolls. The rolling program was conducted in

Jan 1, 1965

By H. J. Modi, D. W. Fuerstenau

pH effectively regulates the flotation of corundum through its control of the surface charge. Since collector ions function as counter ions in the double layer, the collector must be anionic when corundum is positively charged and cationic when it is negatively charged. Even a long-chained xanthate will float positively charged corundum. Association of the hydrocarbon chains of the adsorbed collector ions gives rise to increased adsorption and increased rate of flotation. Because of this phenomenon, neutral organic molecules aid flotation although the unionized collector cannot promote flotation independently. Na2SO4 was found to depress the flotation of corundum with animic collectors through ionic competition whereas the same salt activates corundum for flotation with cationic collectors. A close connection between ion association, electrokinetic behavior, and floatability is suggested. As part of the increasing interest in the physical chemistry of flotation, strong experimental evidence has been obtained which indicates that organic ions are adsorbed as counter ions by non-metallic oxide minerals mainly because of the electrical forces which exist at interfaces(1-3). Thus flotation of such minerals without activation should then be appreciable only when the mineral and the collector are oppositely charged. Since only limited work has been reported on the effect of surface charge upon flotation behavior(3) this general hypothesis on the flotation of insoluble oxide minerals has not been tested thoroughly. Investigating the flotation of a mineral for which extensive electrokinetic data exist yields a way to test this hypothesis more extensively. The electrokinetic behavior of corundum in solutions containing both organic and inorganic electrolytes has been studied quite thoroughly' Electro-kinetic measurements have shown that in the case of corundum, simply by controlling pH the solid surface can be charged either positively or negatively. For this reason corundum was chosen for study. The object of this paper is to present a study of the flotation of corundum and to explain the results in the light of our knowledge of adsorption mechanisms gained from streaming potential investigations. This paper is concerned mainly with the effect of surface charge on flotation with anionic and cationic collectors, but in addition such flotation phenomena as collector hydrolysis, Van der Waals attraction between hydrocarbon chains, ionic competition, and activation are discussed. While the present paper is confined to a reporting of the data obtained and some of the more immediate conclusions, it will be seen that the results, in combination with those on other systems, do promise a

Jan 1, 1961

By Douglas D. Donald

The New Jersey Zinc Co. successfully holed through a 2 1/2-mile haulage tunnel connecting its new Ivanhoe shaft with the Van Mater Shaft at Austinville, Va. This 8x 10-ft cross-section tunnel was driven from both ends and met at a point approximately a mile from one shaft and a mile and a half from the other. In order to make certain that the faces met accurately on line and grade it was necessary to refine conventional mine surveying practices. The mines that are serviced by these shafts are located in the southwestern part of Virginia approximately midway between Roanoke and Bristol at the west foot of the Blue Ridge. While the presence of lead-zinc sulfide ores has been known in this area for more than 200 years, it was in 1902 that New Jersey Zinc Co. acquired the Austinville property, which has been in constant operation since that time. About ten years ago the company undertook an extensive diamond drilling program at Ivanhoe several miles to the southwest. This program was successful in locating sufficient ore to justify the purchase of a number of the properties in this area and plans were made to develop the new orebodies. The discovery of this ore as well as substantial addi- tional reserves at Austinville resulted in a decision by the company to increase its daily milling capacity to 3000 tons, of which about 1000 tons would be supplied from the Ivanhoe mine. After careful consideration of all possible methods of transporting this volume of ore from Ivanhoe to the mill, it became evident that diesel locomotive haulage through a 2½-mile tunnel between the two mines would best suit prevailing conditions. Since the lowest operating level, known as the 1100 level, of each mine would be at approximately the same elevation, it was obvious that such a tunnel should be driven on this level. Not only would this tunnel facilitate feeding Ivanhoe ore into the underground crusher and skip loading installation at Austinville, but it would also open up a known orebody 5000 ft southwest of the Van Mater shaft. In addition it would provide a valuable diamond drilling base from which a large and a potentially favorable but untested block of ground might be explored. In order to hasten the completion of the tunnel, it was felt that it should be driven from both ends. ENGINEERING CONTROL PROCEDURES It was vital that the tunnel junction be made accurately on line and grade; thus it was felt that engineering control of an unusually high degree of reliability was required to prevent an accumulation

Jan 1, 1959

By E. B. Brauer, W. Hurst, J. D. Clark

Because of drilling, completion, and workover practices, the permeability around a wellbore generally is different from the permeability of the formation. The zone with the altered permeability is called "skin" and its effect on the pressure or flow behavior of the well is called "skin effect". Hawkinsl has shown that the radius and the permeability of this zone are related to the skin by: If the permeability in the skin zone is less than that of the formation, the skin is positive; if it is more than that of the formation, the skin is negative. If the two permeabilities are equal, s is zero; that is, there is no skin. Van Everdingen2 and Hurst3 have given mathematical solutions to the case of a zone of reduced permeability around the wellbore. This skin effect is illustrated in Fig. 1. They treat the positive skin as a zone of reduced permeability of infinitesimal thickness around the wellbore. When applied to a well with negative skin, however, their solutions lead to the calculated flowing well pressure which is smaller than the formation pressure, i.e., an injection situation. This is a physical contradiction. In this paper, it is shown that this mathematical difficulty can be overcome by assuming an effective wellbore radius larger than the actual wellbore. Existing solutions2"4 are modified to include the effect of an enlarged wellbore radius, and thus enable the engineer to deal with negative as well as positive skins. Theoretical Development Van Everdingen and Hurst,4 through the use of Laplace transformation, obtained the following expression for transient fluid influx into a wellbore: The values for QtD, reported extensively by van Everdingen and Hurst,4 are obtained from the following integral:

Jan 1, 1970

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Jan 1, 1938

By R. E. Ray, J. W. Stevenson, J. A. Berry

Conventional concrete block plastered with a cementitious coating is the most common material used in the construction of permanent stoppings to direct airflow in underground mines in the US. All mines experience various degrees of strata convergence depending on depth of overburden, geological conditions, and type of roof support employed. Strata convergence will cause cracks and joint openings in masonry stoppings, resulting insignificant air leakage losses. Where strata convergence is severe, complete structural failure of the stopping can ultimately occur. Reconstruction of damaged or destroyed stoppings adds expensive overhead to mining operations, and even greater expenses are incurred from the additional fan horsepower required to overcome leakage losses. Ideally, a stopping should maintain high resistance to airflow while yielding to strata convergence. By properly incorporating a polyisocyanurate rigid foam material within the masonry block structure, stopping service life can be increased in mines experiencing strata convergence problems such as floor heave, roof loading, and lateral rib movement.

Jan 1, 1986

By E. Northcott, I. M. LeBaron

Before describing the electrostatic processing of feldspar, it might be well to review some of the basic definitions and terminology of feldspars. The feldspar minerals constitute a group of alumino-silicates of potassium, sodium, and calcium. Barium feldspar sometimes occurs naturally but is very rare. Hardness varies between 6 and 6.5 and specific gravity between 2.5 and 2.8. Color is generally white or pale shades of red, yellow, or green. The approximate chemical composition of the principal feldspars is given in Table I. The albite (sodium aluminum silicate) and an-

Jan 1, 1959

By L. D. Jaffe

IN previous metallographic work on titanium and its alloys, difficulty has been encountered in distinguishing spheroidal particles of titanium hydride, dispersed in a-titanium, from other phases that may be present, such as p-titanium. This problem is common in examination of commercial unalloyed titanium.' In the course of an investigation of the Ti-H phase diagram, it was noted that titanium hydride, dispersed in a matrix of a-titanium, showed strong optical anisotropy when examined under polarized light. With sensitive tint illumination, particles of the hydride, when the stage is rotated, changed from bright yellow to bright blue in color. Since P-titanium is cubic, it showed no color change on rotation, remaining dark gray or blue-gray. Although a-titanium is hexagonal, it showed only a minor color change, going from pale pinkish-blue to pale purplish-blue. These colors could be modified somewhat by adjustment of the illumination. They were observed in specimens mechanically polished, both without etching and after etching with hydrofluoric acid-nitric acid mixtures in either water or glycerine. The strong color change of the hydride seems to offer a simple method for its metallographic identification. Optical anisotropy of titanium hydride is inconsistent with its accepted face-centered-cubic structure.' Samples of iodide titanium containing 6 to 40 atomic pct deuterium were prepared for diffraction studies. After deuterating and slow cooling' the samples were held 21 % hr at 400 °C, water quenched, held 61 hr at 100°C and quenched, then held 64% hr at 255 C and quenched. Debye ex-posures with MoKa X-rays and 1.111A neutrons were made at room temperature of samples as-deuterated and after the 100" and 255°C treatments. Table I shows the lines observed, in addition to those attributable to a-titanium. These data show that the hydride phase was not cubic, but probably tetragonal. The titanium atoms appeared to form a body-centered-tetragonal lattice complex, two titanium atoms per cell, with approximate dimensions: a = 3.12A, c = 4.18A, and c/a =1.34A. This is equivalent to a face-centered-tetragonal complex, four titanium atoms per cell, with approximate dimensions: a = 4.42A, c = 4.18A, and c/a - 0.946A. The presence of the 2.98 and 1.81A neutron lines indicates that the true Bravais lattice is not identical with this lattice complex, but may be primitive tetragonal with dimensions some multiple of those of the complex. The relative intensities of the hydride and a-titanium X-ray lines as functions of overall composition indicated that the hydride, presumably in equilibrium with the a at 100" to 255"C, contained more than 62 atomic pct H. Acknowledgments The experimental work covered in this report was done at Brookhaven National Laboratory, through the courtesy of D. Gurinsky. The cooperation of J. Sadofsky, 0. Kammerer, A. McReynolds, and A. Cendrowski is gratefully acknowledged.

Jan 1, 1957

By Sherwin F. Kelly

GEOPHYSICS may be considered a vice (albeit, I submit, a comparatively harmless one) whose career is aptly described by Pope's lines: Vice is a monster of so frightful mien, As to be hated needs but to be seen; Yet too oft, familiar with her face, We first endure, then pity, then embrace. Although there may be some that have not yet succeeded in emancipating themselves from the first stage of horrified contemplation, geophysicists may be duly thankful that there are mining men and geologists that have arrived at a state of apparently irretrievable damnation.

Jan 1, 1936

By Robert B. Kistler, Ward C. Smith

The borate industry is one of the few sectors of the mining and mineral-processing industry which the United States still dominates. Since about 1927, the United States has supplied over half of the world's total boron and borate raw materials, and many of the chemical derivatives as well. Chiefly responsible for this record are companies producing sodium borates from two large deposits in southern California, at Boron (Kramer) and Searles Lake. The sodium borates, or products derived from borax and borax-containing brines, are the preferred borates for industry because they are soluble in water and combine readily with most other chemicals. Calcium borates (or sodium-free compounds) are required for certain end uses, but in general, nonsodium borates are used only where borax is not avail- able. During the past hundred years, the use of boron compounds throughout the world has risen from a few tons per year to the equivalent of about a million tons of B2O3. Leadership in supplying borates has shifted from country to country and from region to region during this period, generally as the result of the development of newly discovered deposits that were better in quality, more accessible, or more economically exploitable than previous sources (Table 1). Primary Products and End Uses The principal borate products offered by primary producers in the United States are listed in Table 2. In general, these products are utilized worldwide by almost all consumers, regardless of the original source of the primary borates. In the United States, the primary borates all originate in southern California. Colemanite is produced as crude or processed crude ore from the Death Valley area and is utilized by the fiber glass and ceramic industries without further treatment. Production from Searles Lake, Calif., is from brines that are processed in chemical plants where borax and other compounds are recovered and the principal borate products are produced. At Boron, Calif., the world's leading producer is mining a deposit of mineral borax and operating a chemical refinery. The mineral borax is mined together with included clay, and refined borax or "lo-mol" is one of the refinery products. The mineral and the chemical compound are identical, Na2B4O7- lOH2O. In addition to ship- ping all major refined borate products from Boron, the company ships semiprocessed ore concentrates to treatment plants elsewhere.

Jan 1, 1975

By C. J. Beevers

Tlze influence of zirconium hydride precipitate mprphology on the fructure of Zr-H alloys tested at strain rates of 10- sec at 20° and - 196°C and at strain rates of -500 sec.-1 at 20°C has been inves-tigated. The critical stage in the embrittlement of these alloys was the fracture of the zirconium hyhide precipitates to form large interval cracks at a stress of 25,000 10 137,000 psi. In specimens con-temping up to 100 ppm H the preciptates existed as isolafed platelets in the zirconium matrix and their fracture as enhanced by low temperature (—196°C) and high strain rate (-500 set-f) loading. These resl~lts lead to the conclusion that the rate of strain hardening of the zirconium metal controls the frac-tzrm of the hydride platelets. Increased hydrogen contents of 500 to 2000 ppm resulted in an increase in the 1)volume fraction and size of precipitates and crlso led to crack propogation in the hydride at both 20 and —196C at the low strain rates (10'* sec-'). Quenching led to refinerment of hydride precipitate size and reduced the degree of embrittlement at — 196°C; this effect is attributed to the absence of fracture of the fine precipitates. The formation of zirconium hydride precipitates has been shown to be the cause of hydrogen embrittlement of zirconium.' Several investigators'-" have studied the problem in broad outline, demonstrating that impact-loading conditions, testing temperatures below room temperature, and increasing hydrogen content produce increased brittleness. For example, Muehlenkamp and schwope2 showed that the transition temperature for notched impact tests was raised from 150" to 350°C on increasing the hydrogen content from 45 to 490 ppm. The degree of embrittlement is also controlled by the morphology of the zirconium hydride precipitates. The solubility of hydrogen in zirconium decreases from 600 ppm at 550°C to 10 ppm at 20"C,~ so that the form of the zirconium hydride precipitates (ZrH2) can be modified by varying the cooling rate through the Zr-aZr + ZrH2 phase boundary.= Forscher showed that quenching a specimen containing 35 ppm H from above 315°C resulted in a reduction in area of 70 pct at -196"C, whereas slowly cooling from above 315°C resulted in a ductility of half this value. The role of the hydride precipitate in the fracture process has been examined by Young and schwartz6 and more recently by westlake.' From metallo-graphic observations on slowly cooled Zr-H alloys they have suggested that cracks are nucleated in the hydride precipitates by the interactions of twins in the zirconium metal with the hydride. The experiments reported in this paper show that crack propagation in the zirconium hydride precipitates is the critical stage in the embrittlement of Zr-H alloys. The factors influencing fracture of the hydride precipitates and crack propagation in the zirconium metal will be related to the problem of embrittlement. EXPERIMENTAL TECHNIQUES The zirconium used in these experiments was produced from an ingot of vacuum arc-melted iodide zirconium forged down to 1 in. diameter at 800' to 850°C. The 1-in.-diameter bar was surface-machined and cold-swaged to 0.375 in. diameter. After a vacuum anneal at 800°C for 1 hr the hardness was 60 to 70 Vdh. The total impurity content was approxi-

Jan 1, 1965

A record $18.7 billion worth of metals, non- metals and fuels was produced in the U.S. during 1962, according to a year-end estimate from the USBM. The 1962 total value, based on preliminary statistics compiled by the Bureau, was nearly $600 million more than in 1961. Most minerals gained both in value and volume of production during 1962 according to information collected by the Bureau. All mineral fuels except anthracite showed increases. Among nonmetallic minerals- other than fuels-gains exceeded losses by two to one. Metal production held steady as gains and losses balanced.

Jan 2, 1963

By J. B. Clark

In 1933, R. paris1 published a phase diagram for the entire Mg-Ca-Zn system. He reported the existence of a ternary intermetallic phase, Mg5Zn5Ca2, which formed a quasi-binary with the magnesium solid solution. Since then, no extensive work has been reported on the system. Recently however, indications of the existence of a second ternary in-termetallic phase in equilibrium with the magnesium solid solution led to a reinvestigation of the solid phase equilibria involving the magnesium solid solution. The 335°C (635°F) isothermal section was chosen for study. Metallography and powder X-ray diffraction were selected as the best mutually corroborating methods for determining the solid phase constitution. Seventy-six alloys were prepared from singly sublimed (99.95 pct) magnesium, electrolytic (99.95 pct) zinc and USP calcium. The analyses of some of the alloys are shown in Fig. 1. The alloys were melted in a graphite crucible under a chloride flu and chill cast in a split graphite mold. Dif-fusion couples (see Fig. 2) were prepared by casting molten Mg-20 wt pct Zn alloy around a cylinder of Mg-30 wt pct Ca alloy. The alloy samples and the diffusion couples were sealed under argon in Pyrex vials and annealed in a furnace capable of controlling within 1/2°C of 335°C. At the conclusion of the anneal, the alloy samples were quenched in ice water and the diffusion couples were air cooled. Procedures standard for magnesium alloys were used for metallographic examination. Powder X-ray diffraction patterns were taken on a G. E. camera with a 14.32 cm dim using nickel-filtered copper radiation. The redetermined 335°C (635°) section of the Mg-Ca-Zn phase diagram is shown in Fig. 1. TWO ternary intermetallic phases, designated w and

Jan 1, 1962

By E. P. Abrahamson II

The effect of transition elements which form binary solid solution upon the recrystallization temperature of zirconium has been investigated. All additions raised the recrystallization temperature. A correlation is obtained between the logarithm of the rate of change of recrystallization temperature with atomic percent solute and the free atom ground state electron configuration of the solute element. ThE work of Abrahamson, et al., on dilute binary solid-solution alloys indicated a correlation between the free-atom ground state electron configuration of the solute and either the brittle-ductile transition or recrystallization temperature. These studies were carried out on bcc base materials. The implication is that the outer s and d electrons of the solute are the prime determinant of the absolute rate of change of recrystallization or transition temperature. Furthermore, the limit of linearity has been shown to be a function of solute electron configuration for recrystallization in iron and vanadium. To date no Complete systematic recrystallization study of dilute binary zirconium base alloys has been made. It is the purpose of this study to note whether the change in solvent structure from bcc to hcp will influence the correlation. It was also desired to learn more of the role of the electron configuration of the solvent on recrystallization temperature. PROCEDURE All alloys were made using 99.87 pct Zr with 0.01 Cr, 0.04 Fe, 0.006 Hf, 0.003 Mg, 0.003 Mn, 0.003 N, and 0.080 0 (132 BHN). The solute elements were 99.9 pct pure. According to the published binary phase diagrams6 and metallographic examinations at X750, all alloys used were solid solutions. The alloys were arc melted and remelted six times in the form of cubic 200-g buttons under an argon atmosphere. They were then hot pressed at 950°C to 0.450 in., upset pressed to 0.350 in., and annealed at 800°C for 1 hr. The specimens were then Blanchard ground to 0.250 in., removing 0.050 in. from each side. The grain size of the material at this stage was found to be 8000 100 grains per sq mm. The specimens were then cold rolled to 0.130 in. and cold pressed to 0.125 in., yielding 50 1 pct cold work. All alloys were then chemically analyzed for the principal addition. The interstitial contents remained at the values of the starting material when checked on random alloy specimens. The rolled sheet was cut into 6.75 by 0.25-in. lengths and heat treated in a gradient furnace for 1 hr. The gradient was 250o to 900°C over the 6-in. length, recorded continuously by six thermocouples resting on each specimen. Control was 3oC, accomplished at the hot end. The recrystallization temperature was determined metallographically using polarized light. The criterion chosen was the point on the specimen showing the first recrystallized grain at a constant magnification, X200. Specimens were repeated, and the agreement was found to be 3°C. RESULTS Three different pure zirconium specimens were tested, and the recrystallization temperature was

Jan 1, 1962

By J. C. Martin

Stmplified equations are developed for the flow of fluids in gas drive reservoirs in which the effects of gravity can be neglected. The results show that the pressure distribution is governed by a nonlinear heat flow type of equation, and the saturation distributions are related to the pressure by the same equations QS those developed by Muskat for the average pressure and saturations in gas drive reservoirs. Unrler certain conditions the equation for the pressure can be approximated by the linear form of the heat flow equatlon. This equation tk analogous to the equation for the pressure in single-phase compressible flow The analysis reveals that the equation for the pressure in n~ultiphase flows can be obtained directly from the equation for the pressure in slngle-phase flows by simply replacing the single-phase compressibility by the total compressibility and the single-phase mobility by the sum of the mobilities of all the fluids present. Perrine's method of pressure buildup analysis for multiphme flows is based on these same substitutions. Thus, the development presented in this paper constitutes a theoretical justification for Perrine's method of pressure buildup analysis. One of the most difficult problems associated with the production of oil is the determination of the flow of the fluids within the reservoirs. One purpose of this paper is to present the development of simplified equations for the flow in gas drive reservoirs. The other purpose is to present some of the needed theoretical foundation for the methods currently being used in the analysis of multiphase pressure buildup data. The analysis presented in this paper makes use of a partial linearization of the equations governing multiphase flows. It is felt that the process of linearizing or partially linearizing the nonlinear equations of multiphase flows can lead to useful results since this process has proved extremely valuable in the study of other fields of science and engineering where nonlinear equations are encountered. Pressure buildup data of shut-in wells have been used for many years to estimate the static reservoir pressure. These data have also been used in studying the aver- age permeability both away from and close to the well-bores. The majority of the buildup data are obtained from wells producing two or three fluids. As yet the theoretical foundations for the methods of buildup analysis used in connection with rnultiphase buildup data have not been established. A number of methods of analysis of pressure buildup data have been developed." Most of these methods apply only to single-phase flows, and almost all of the theoretical analysis is confined to single-phase flows. Perrine' developed a method of analysis for rnultiphase flows from the method for single-phase flows of Miller, Dyes, and Hutchinson.' He did this by simply replacing the single-phase compressibility by the multiphase compressibility and replacing the single-phase mobility by the sum of the mobilities of the fluids in the rnultiphase flows. Obviously, such a procedure lacks a certain amount of theoretical justification, and such practices can lead to erroneous results. Fortunately, Perrine's results have a theoretical justification, and this justification is presented in the following discussion. It is assumed that gravitational effects and the cornpressibility of the rock can be neglected. Under these assumptions the equations governing the simultaneous flow of gas, oil and water in porous media areo* The preceding equations can be expanded into the following expressions.

By Dogan E. Gücer

In the following note, with the help of a new parameter of strain hardening, the attention is drawn to the close relationship between the relative performances of steels under plastic range cycling and their strain hardening characteristics. If a cantilever beam of rectangular cross section is tested with the arrangement shown in Fig. 1 in reversed bending between constant deflection limits at the lever head, the longitudinal strain-deflection hysteresis shown in Fig. 2 is obtained. There is no lateral strain due to constraint at the rectangular test section.' If the absolute value of strain undergone between a maximum state of tension and maximum state of compression is called A, it will be seen that A decreases with cycling rapidly due to the strain hardening in the test section and the ensuing change in the bent beam profile. It will also be seen that A reaches an approximately stable value around 10th cycle. If we call the first cycle strain range, A,, and that of 10th cycle, A,,, then is an index of the strain hardening capacity at a particular deflection level. A plot of n vs ? is reproduced in Fig. 3 for two ASTM steels: A-302 and A-201. A-302 is a low alloy structural steel, A-201 a low-carbon steel. The specimens were first normalized at 1650°F for 75 min then grooved with a milling cutter; and the notches were ground to 50G finish. The final operation before testing was a stress relief at 1150°F for 75 min. The behavior of the two steels changes around ?1 = 0.8 pct or A,, = A, -n = 0.7. If these curves are compared with the endurance life curves given in Fig. 4, it will be seen that the relative performance of the two steels also change around A,, =. 0.70 pct. The steel with lower strain hardening capacity (7) at a certain strain level shows a longer endurance life, irrespective of their strength levels. Since the exponent governs strain hardening at lower strain levels than the Modulus, the relative values of both parameters also coincide with the change in n values and the relative performances of the two steels at different strain levels. These two observations indicate to the close relationship be-

Jan 1, 1962

By T. C. M. Pillay, John Chipman

The Si-0 equilibrium in liquid iron was investigated in some detail by Gokcen and Chipman1 who reported equilibrium constants of the following reactions: In each case the thermodynamic equilibrium constant K was obtained by extrapolating K' to infinite dilution. Their results on reaction [I] were consistent with those of earlier observers, and there seems to be little doubt as to the approximate validity of the equilibrium product determined. On the other hand, the results on reactions [2] and [3] indicated unusual curvilinear relationships between the activity coefficients of silicon and of oxygen and the silicon concentration. Since a linear relation is observed in all other similar instances, it was concluded that some source of error had affected the gas-metal equilibrium relationships. Recently the authors undertook a restudy of these equilibria with the view especially to establishing the equilibrium constant of reaction [2]. Their experiments, however, were discontinued before a tbroughly satisfactory answer had been obtained and consequently have remained unpublished until the present time. Quite recently Matoba, Gunji, and Kuwana2 published the results of a very thorough study of these equilibria. It is the purpose of the present note to Compare these three sets of experimental data, a comparison which leads to Confirmation of the results of Matoba and coworkers. The experimental arrangements described by Dutilloy and Chipman were employed. A controlled mixture of Hz, H,0, and argon was led into the induction furnace over the surface of the Fe-Si melt contained in a silica crucible. On account of the slow approach to equilibrium, runs were continued for at least 8 hr and, in some cases, as much as 12 hr. Samples were taken by means of silica tubes at the start and during the final 4-hr period of each run. Out of twelve runs only seven appeared to have approached equilibrium with sufficient certainty to be reported here. The results of these experiments, all at 1600°c, are shown by the triangles in Fig. 1. Equilibrium was approached from both oxidizing and reducing conditions and the direction of approach is indicated by the shape of the triangle. Attempts to extend the study to higher silicon concentrations were unsuccessful on account of the transfer of silica from the metal bath to the upper portions of the crucible by means of a silicon-monoxide mechanism. Matoba, Gunji, and Kuwana used similar methods and approached equilibrium from both sides. Their results at three temperatures are shown by the solid lines of Fig. 1. A line corresponding to 1600 deg is interpolated from their equations and is shown by the dotted line. The results of Gokcen and Chipman at 1600 deg in the range 0.02 to 2.0 pct Si are also shown. At concentrations up to about 0.6 pct Si, these investigators approached equilibrium from both directions, and their results in this range appear to be trustworthy. Above 1 pct Si, however, all of their experiments involved oxidation only, as shown by a decrease in the silicon content of the bath. It now seems certain that they failed to reach equilibrium at these higher silicon concentrations and that the curvilinear relation shown by their results is incorrect. It is evident that their results in the lower silicon range are in good agreement with those of Matoba and coworkers. In fact, a straight line drawn through their results would parallel the dotted line and would differ from it by only 0.05 in log K. The new data also lie close to that line. It may thus be concluded that the three sets of data are in good agreement and that the equations proposed by Matoba and coworkers for reaction [2] are satisfactory . They take the limiting value of log K', at 0 pct Si as log K ,. The slope of each line gives the value

Jan 1, 1962