Search Documents

By D. L. Albright, G. A. Colligan

An investigation has been conducted to determine the nature of the crystallographic substructure of nickel and a 1.0 wt pct Ag-Ni alloy which had been undercooled 105°C prior to solidification. A rotating back-reflection X-ray technique and modified Weissmann diffractometer were used to orient single-crystal sections from these poly-crystalline ingots and to determine the substruc-tural features of these single crystals, The sub-grain size in the pure nickel ingot is 0.5 mm diam while the silver-doped nickel subgrain size is only 0.1 mm diam. The misorientation between adjacent subgrains is approximately 1 deg of arc in both ingots, and the spread of orientation of sub-grains about the mean orientation of the crystal is 5 deg of arc in both ingots. The addition of silver results in a stable impurity substructure which is preserved during isothermal solidification and subsequent cooling to room temperature. In the absence of silver the initial impurity substructure is destroyed by dislocation interactions which produce a secondary substructure which grows to a size five times larger than the initial substructure. THE process of undercooling a metal entails cooling of the molten sample below the equilibrium freezing point without the occurrence of solidification, i.e., by exercising proper constraint over the experimental variables contributing to nucleation in the melt. The current work of walker1 and Colligan Metal reports undercooling large continuous samples of nickel by imposing appropriate restrictions upon the parameters of solidification. The silver-nickel equilibrium diagram3 reveals the presence of a monotectic reaction at 1435°C. At this temperature the maximum solid solubility of silver in nickel is approximately 3 wt pct, but this solubility decreases with decreasing temperature and the solute is rejected as a silver-rich liquid phase at temperatures below 1435°C. Thus, the 1.0 wt pct solute should be held in solution during undercooling and solidification and subsequently precipitate as a silver-rich liquid phase at grain and subgrain boundaries following solidification during cooling below 1435. This assumes no solute segregation sufficient to cause the monotectic reaction. One would expect this second phase to inhibit grain and subgrain growth by retarding dislocation motion after solidification is complete. The effectiveness of silver addition in growth retardation of high-angle grain boundaries has been demonstrated by Colligan and suprenantS4 The principal [l00] dendrite growth directions in a 2 wt pct Ag-Ni alloy undercooled 53 all radiated from the nucleation site. A similar pure nickel ingot undercooled 59°C exhibited a random orientation of [l00] dendrite directions with respect to the nucleation site. Since undoped nickel ingots do not retain any evidence of the casting or solidification texture and silver-doped ingots do retain this texture, it is reasonable to assume that considerable grain growth has taken place in the pure nickel. These particular experiments were performed in order to reveal the differences, if any, in the features of the crystallographic substructure of undoped undercooled nickel and silver-doped undercooled nickel. 1) EXPERIMENTAL PROCEDURE Data are reported on selected specimens from two massive (approximately 260 g) undercooled ingots of nickel. One ingot consisted of electrolytic nickel and the other of this same material with 1.0 wt pct addition of high-purity silver. Powder patterns were taken of both the as-received and as-solidified materials; in all cases the reflections recorded were attributable to the individual elements nickel and/or silver. Fig. 1 is a. schematic diagram of the apparatus employed for the undercooling experiments. The equipment consists in part of a fused silica crucible for containing the charge. A fused silica tube encloses the system, which is covered by a brass cap to permit partial sealing of the inert atmosphere. This cap contains a hole through which a Pt-Pt 13 pct Rh thermocouple is inserted for temperature measurement. The charge is inductively heated under a purified argon atmosphere.

Jan 1, 1963

By R. I. Jaffee, E. S. Bartlett, D. N. Williams

The oxidation resistance and fabricability of molybdenum powder-metallurgy alloys containing up to 20 wt pct nickel in the form of a fine dispersion were studied. The effects of dispersion distribution and of amount and type (pure nickel or nickel compounds) of additive were considered. A definite improvement in oxidation resistance was observed, but the amount of improvement fell far short of requirements for an oxidation-resistant alloy. Fabricability by hot-rolling was limited. INVESTIGATIONS at Ohio State university1 and Battelle Memorial institute2 have indicated that the attainment of a truly oxidation-resistant molybdenum-base alloy for high-temperature service, with the coincident retention of high-temperature strength and toughness, will be a difficult, if not impossible, feat. Among the most promising alloy systems studied was the molybdenum-nickel system shown in Fig. 1. Alloys in this system show good oxidation resistance at temperatures well above the normal melting point of molybdenum trioxide because of the regenerative formation of protective nickel-molyb-date (NiMoO4) on the surface of the alloy during exposure at high temperatures. Unfortunately, the required alloy content to obtain oxidation resistant molybdenum-nickel alloys far exceeds the limits of the narrow terminal solid-solution boundary, and closely approaches the peri-tectic composition involving the brittle intermetal-lic compound, MoNi. Because of the peritectic reaction, fusion alloys are characteristically brittle, since the MoNi phase, being the last to form, tends to occur as a continuous grain-boundary network around each molybdenum grain. An added problem with this system is that the protective nickel-molybdate layer formed at high temperatures is unstable, undergoing one or more allotropic modifications upon cooling. The volume changes associated with this modification during cooling are such as to cause violent expulsion of the protective molybdate coating from the surface of the piece. This is, of course, quite detrimental in material exposed to cyclic temperature during service. The research reported here resulted from an attempt to overcome the aforementioned problems associated with the molybdenum-nickel alloys primarily by controlling the amount, size, and location of the MoNi phase. By using powder-metallurgy techniques of alloy preparation and sintering the blended molybdenum-nickel powder mixtures at a temperature below the peritectic reaction temperature, molybdenum-nickel alloys with a randomly dispersed MoNi phase were produced. MATERIALS The molybdenum powder used in the preparation of alloys for this study was commercial hydrogen reduced, minus 325-mesh (Tyler) material. Master alloys, by which nickel was added, consisted of elemental carbonyl nickel powder (12 average particle size), an alloy of 50 wt pct Ni-50 wt pct Cr, and compounds of MoNi, Ni,Si, and Ni2B. The nickel-chromium powder was prepared by filing a vacuum-arc-melted ingot, separating impurities magnetically, and screening to minus 200-mesh. The MoNi powder was prepared by pulverizing a hydrogen-sintered powder-metallurgy compact to minus 325-mesh material. Further sizing of this powder for study of effects of dispersion distribution was accomplished by air classification of the minus 325-mesh powder. The Ni2Si and Ni2B powders were prepared by crushing vacuum-sintered powder-metallurgy compacts to minus 200-mesh material. EXPERIMENTAL PROCEDURE Specimen Preparation—The general procedure followed in the preparation of alloys for testing is described as follows: 1) Blending. Either hand-blending of the powders in a ceramic mortar and pestle for X 1/2 or mechanical blending was used. Hand-blending seemed preferable for optimum homogeneity. 2) Compacting. Most of the blended powders were pressed to green compacts at pressures of 15 tons per sq in. in a single-action die, although some were pressed at 80 tons per sq in. A 1 X 11/4 X 1/4-in. green compact was the standard size for oxidation test material, and 7 X 1/2 X 1/4-in. compacts were used for fabricability test specimens. 3) Sintering. All green compacts were sinteredat

Jan 1, 1959

By J. R. Low, D. F. Stein

Single crystals of iron have been grown from three different lots of Ferrovac "E" of somewhat different chemical composition by the strain anneal technique. Using a technique to seed the crystal similar to Dunn's for silicon-iron, it has been possible to orient the crystals grown in both direction and plane of growth. Crystals having the plane of the strip oriented (100) , (110), (111), (112), (123), and (491) have been grown. The growth directions used have been [100], [110], 45 deg from a [110}, and various others of no specific crystal orientation. The usual dimensions of the crystals were 8 by 1 by 0.08 in. Attempts to grow crystals were about 90 pct successful. METHODS of growing single crystals of high purity iron have been reported in the literature.1-4 However, each of these methods was not completely reliable when used on materials having slightly different chemical composition and in some instances a small number of successes were obtained using identical materials. Except for the method used by S. Dohi and T. Yamoshita,1 it has not been possible to reorient single crystals of high purity iron to give any desired orientation. The method to be described has made it possible to grow single crystals from three different lots of material having different compositions, and to orient the crystals with respect to growth direction and surface. STARTING MATERIAL The material used during this investigation was a vacuum melted high purity iron marketed by the Vacuum Metals Corporation designated Ferrovac "E." Three lots of Ferrovac "E" having the following composition were used with equal success: The compositions listed are those of the as-received material; and they may have been modified before the growth of single crystals. Analysis of heat B just before growth and after growth revealed that the heat treatment prior to growth did not change the carbon content, but the oxygen content was changed from 0.0092 pct to 0.0034 pct and the nitrogen content from 0.0003 pct to 0.0001 pct. After growth of the single crystals, the carbon had dropped to 0.001 pct. None of the heat treatments would be expected to change any of the other impurities very markedly. Heat C would be expected to have a metallic impurity content similar to heats A and B. PROCEDURE Ferrovac "E" iron which had been obtained in bar form having a diameter of about 1 in. was rolled into strip for growing single crystals. By passing the 1-in. bar through a cold rolling mill several times, it was reduced to a strip 0.15 in. thick. The strips obtained were then cut into suitable lengths for heat treating (about 9 in. long), annealed at 925°C for 2 hr in dry hydrogen and water quenched. It was then necessary to bake the strip at 200°C for 24 hr in air in order to prevent cracking during further rolling operations. While it was possible to cold roll the 1-in. bar directly to the desired 0.080-in. strip, the intermediate anneal was used because the strip so obtained produced better single crystals. The strip obtained by rolling the 1 -in. bar directly to 0.080-in. strip produced single crystals having a large number of occluded grains. Experiments showed that the optimum reduction in area by rolling prior to the growth of single crystals was about 50 pct. Attempts to grow single crystals from material that had been reduced less than 40 pct were unsuccessful presumably because the matrix did not possess the critical amount of texture necessary for growth. The strip obtained after the rolling operations had very irregular edges which were ground to give a strip with uniform dimensions. The strip was then annealed at 825°C for 3 hr in hydrogen and furnace cooled. Fig. 1 illustrates the grain size obtained. A temperature of 940°C was used for the annealing temperature on one group of strips

Jan 1, 1962

By W. A. Young

Polynomial functions of temperature were obtained for the specific heats, thermal diffusivities, and thermal conductivities of zirconium hydrides containing 4 at. pct U. Three hydrides (H/Zr atom ratios of 1.58, 1.65, and 1.70) were studied over the range a" to 900°C and a fourth (H/Zr = 1.81) was studied over the range 0° to 760°C. The specific heats were determined from enthalpy measurements which were obtained using a unique drop calorimeter specifically designed for use with materials in which high temperature phase transitions and/or high dissociation pressures occur. Thermal diffusivities were measured by the flash method using a pulsed laser. The thermal conductiuities were obtained as the product of specific heat, thermal diffusivity, and density. The specific heats agree, within 10 pct, with values derived using a theoretical model in which the hydrogen and zirconium atoms are treated as Einstein and Debye oscillators, respectively. RELIABLE values of the thermophysical properties of the fuel are required to predict the operating temperatures and temperature response of SNAP nuclear reactors. Among the most important of these properties are the thermal conductivity, specific heat, and thermal diffusivity. A considerable number of investigations1-4 have been made of these properties for the Zr-H and Zr-H-U systems.* However, little of the drides, however, this direct method cannot yield meaningful results, since the hydrogen will redistribute under the influence of the thermal gradient, thus forming a concentration gradient; hence, one has a spectrum of compositions, rather than a homogenous alloy. Although the "average" composition of the material may be identical to the initial uniform concentration, the directly measured value of conductivity will be dependent on the thickness of the specimen, due to the highly sensitive dependence of transport properties on hydrogen content. This dependence is strikingly illustrated by the work of Bickel,5 who found that the electrical conduction of zirconium hydrides ranges from primarily hole conduction to primarily electronic conduction, depending upon the hydrogen content. Fortunately, the direct measurement of thermal conductivity is unnecessary, since it can be expressed as the product of the specific heat, thermal diffusivity, and density, all of which can be directly measured with considerable accuracy. EXPERIMENTAL Specimen Preparation. The combined fuel-moderator material used in SNAP reactors is a hydrided zirconium-uranium alloy containing -10 wt pct U. The alloy used in this work was representative of that used in nuclear reactors except that normal uranium was substituted for the enriched uranium required for reactor usage. It was produced by a triple-arc-melt and double-extrusion process. All specimens were prepared from a single cylindrical extrusion which contained 10.30 pet U, 89,35 pct Zr, and 0.35 pct impurities, The specimens for each composition were hydrided simultaneously with ultrapure hydrogen (10 ppm total impurities) using standard fuel production techniques which routinely yield homogeneous, crack-free fuel with negligible increases in the impurity levels. The hydrogen content of each specimen was determined from its weight gain and the density was measured by liquid displacement, Chemical analyses yielded hydrogen concentrations which agreed with the weight gain data within ±0.02 in H/Zr atom ratio) the concentrations of all other elements agreed almost exactly with the initial values after adjustment for the added hydrogen. The specimens used for the determination of specific heat were centerless ground to 2.00 cm diam after hydriding. A thin slice was carefully removed From each end for metallographic examination. In every case, this examination revealed a uniform structure as evidenced by the appearance and distribution of the two phases present in the fuel at the hydrogen concentrations used. TWO specimens (H/Zr = 1.600 and 1.632) appeared to be entirely 6 phase with equi-axed grains; the specimen with H/Zr = 1.756 showed

Jan 1, 1970

By R. E. Cook

This paper presents results of a study to determine to what extent errors in estimated free gas saturation affect the results of static pressure calculations from build-up curves in two-phase systems. Use is made of the method of pressure build-up curve analysis developed by Miller, Dyes and Hutchinson1 , with modifications for two-phase flow advanced by Perrine2. Cornhined fluid compressibility of gas-oil mixtures is included, with special attention given to the discontinuity that occurs in fluid compressibility at the saturation pressure and its effect on static pressure calculations from build-up curves. The sensitivity of static pressure calculations to errors in gas saturation is considered over wide ranges of formation and fluid properties and reservoir pressure conditions. It is concluded from this study that for analyses of two-phase pressure build-up curves (I) the use of under-saturated crude compressibility data, even when producing GOR's are at or near solution values, will result in very significant negative errors in calculated static pressrrre, and (2) except for large values of buildup curve .slope and/or very low crude gravities, rather large errors in calculated gas saturation can he tolerated without .significant effect on calculated static pressures. The conc1usions arc qualified as referring only to the effects of gas saturation and excludc possible errors in the nuumerous other factors that enter into the ancllysis of pressure build-up curves. INTRODUCTION As part of the analysis of basic data for several major Eocene reservoirs in the Bolivar Coastal field (Western Venezuela), it was necessary to analyze a large number of pressure build-up curves for oil permeability and static reservoir pressure. From performance data it became apparent that gravity segregation is very active in these reservoirs. As a result of this performance it was recognized that the free gas saturation within the oil leg of the reservoirs would be small but would be subject to certain errors in calculation due to the inaccuracy of relative permeability data in the low gas saturation region. Since all of the various methods of build-up curve analysis were originally derived for sin- gle-phase, constant compressibility systems, and since the presence of a small but rather indeterminate gas saturation would greatly affect the reservoir fluid compressibility, a study was undertaken to investigate the effect of gas saturation on the results of two-phase pressure build-up analyses. TWO-PHASE BUILD-UP CURVE ANALYSIS The method of analysis used in this investigation is basically that originally developed by Miller, Dyes and Hutchinson1, with modifications for two-phase flow advanced by Perrine2. Miller, et al, showed that the original equation for single-phase permeability away from the well bore, held for two-phase flow except that the calculated permeability is the effective permeability to oil away from the wellbore. This finding was acknowledged by Per-rine, who also presented the equation for effective gas permeability* as Since Eqs. 1 and 2 contain no terms influenced by fluid compressibility, no distinct problem should develop in calculating permeability from two-phase build-up curves. In regard to the calculation of static reservoir pressure from build-up curves in single-phase systems, the modified Miller, et al, method as presented by Perrine is briefly as follows. 1. From build-up curve data, PVT data for the reservoir fluid and the well spacing and sand thickness, calculate the climensionless shut-in time corresponding to the highest value of actual shut-in time (t, hrs) on the straight-line portion of a semi-log build-up curve. Dimenrsionless shut-in time is related to actual shut-in time by the relation, t- 0.000264 kt 2. From a graph of dimension less shut-in time vs dimensionless pressure difference (Fig. 1 1 ) find the value of dimensionless pressure difference corresponding to the value of 7 calculated under (1) above. Dimen-

By W. A. Backofen, D. H. Avery, W. F. Hosford

Sheets of the magnesium alloys AZ31B, HK31A, and ZE10A in several different tempers were tested in tension and determinations were made of the ratio of width-to-thickness strain. A marked increase in the ratio with tensile straining and a dependence upon alloy and test direction are rationalized in terms of a balance between the amounts of basal and prism-plane slip. All such variations are related, in turn, to the prevailing crystallographic texture. Fracture appearance is explained on the basis of anisotropy in plastic flow, and implications for developing texture -hardening effects in these alloys are discussed. ThE crystallographic texture or preferred orientation of a given material is determined by details of processing history. Such texture is known to influence many aspects of material behavior, in particular both the yielding and strain-hardening characteristics which are of special interest in the present work. Traditionally, the resulting plastic anisotropy has not been regarded as especially desirable. Earing in drawn sheet is perhaps the most common example of an unwanted effect of texture. However, it has also been recognized that suitable textures may be usefully employed to improve drawability,1,2 as a specific example, and generally to control yielding resistance under combined-stress loading.374 Texture would seem to be a detail of structure not yet exploited to nearly the fullest extent. A convenient basis for characterizing anisotropy in plastic behavior is the ratio of width-to-thickness strains obtained in a tension test;5&apos;6 the parameter is frequently labeled "R" and its value is revealing with respect to the nature of the prevailing texture. R gives a useful measure of a material&apos;s "thinning resistance". For an isotropic material, R = 1. With R > 1 the increased through-thickness strength in a sheet means greater resistance to yielding under biaxial tension, or "texture hardening";3&apos;4 if R < 1 the result may be a "texture softening" under the same loading conditions.4 Most R data relate to steel sheets for deep-drawing applications. Values for steel and other materials of cubic structures are not often much greater than 1 and nearly constant with strain in testing.1,2,7,8 To explore the implications of plastic anisotropy further, it was felt that experiments with much more strongly textured materials would be useful, and this led to the choice of magnesium alloys. The "ideal" sheet texture for magnesium contains the (0001) plane in the rolling plane, which ought to lead to R values approaching infinity. However, departures from the ideal texture, the possibility of slip in non-close-packed directions, and deformation by twinning would all be expected to introduce some range of R. Accordingly, studies on these materials were undertaken. EXPERIMENTAL Alloys in sheet form, Table I, were selected to obtain a variation in crystallographic texture, in the expectation that this would be reflected in differences in plastic anisotropy. Pole figures constructed by the Schulz surface-reflection technique9 were provided with the experimental materials by the Dow Metal Products Co. Profiles of pole density along great circles through the rolling (0 deg) and transverse (90 deg) directions were prepared from the pole figures and are collected in Figs. 1 and 2; considerable departure from the "ideal" (0001) alignment in the rolling plane is evident, with the largest angular spread in both directions being found in the ZEl0 alloy. Results of tensile tests on full-thickness specimens of 6-in. gage length by 1/2-in. width are given in Fig. 3 as engineering stress-strain curves* in rolling and transverse directions. All tests but one were made at a constant drive rate of 0.02 in. per min, and the final values of percent elongation at fracture, over the initial 6-in. gage length, are noted at the ends of the curves; one test on ZE10A-

Jan 1, 1965

By W. A. Tiller, S. O’Hara

Grain refinement in stirred melts has previously been shown to arise from dendrite segmentation. The present work discusses experiments capable of distinguishing between remelting and mechanical effects which result from fluid motion. Nucleation of still un-dercooled Sn-1 pct Pb melts with a single-crystal seed shows that the grain size of the resulting ingots decreases as the undercooling at nucleation increases up to about 1Z0C, then increases again for larger undercoolings. Pure melts exhibit little refinement as a result of nucleation at any undercooling up to 12°C. The presence of fluid motion gives rise to grain multiplication in pure melts, but the magnitude of this effect is partly obscured by solid-state pain growth. The results indicate that two grain-multiplication pvocesses can operate, one which involves dendrite remelt ing, and another associated with fluid motion. Small ingot experiments indicated that an equiaxed transition can be caused by fluid motion. THE presence of forced convection during recales-cence of undercooled Sn-1.3 pct Pb melts has been shown to give rise to extensive grain refinement during solidification of small ingots of this alloy.&apos;&apos;2 In Ref. 2, this refining was shown to result entirely from dendrite fragmentation and not from any nucleation mechanism. The purpose of the present work is to establish what processes lead to dendrite segmentation. Experiments were therefore carried out to determine the resulting structure of both pure tin and Sn-1 pct Pb melts, nucleated at various undercoolings by single-crystal seeds in the absence of forced or natural convection. By comparing the information obtained from these experiments with the results of Refs. 1 and 2, the effects of fluid motion on the ingot structure, and the details of the segmentation mechanisms, should become clear. The results of these experiments should also be helpful in understanding the solidification structures of larger ingots since natural convection, which is known to play an important role in determining ingot structure13 differs only in degree from the fluid-motion effects studied here. I) EXPERIMENTAL PROCEDURE The apparatus shown in Fig. 1 was constructed to permit controlled nucleation of stirred or unstirred supercooled melts using a seed oriented in the tin dendrite growth direction. Because the melts, in all cases, were capable of larger supercoolings than the one used in each experiment, the structure observed always resulted from a single nucleation event at the surface. The sequential procedure was as follows: Tin was melted under purified hydrogen and the oxide removed at a temperature of 450°C . Electromagnetic stirring was then used to clear the surface completely and during this time the guide tube was lowered underneath the melt surface. A pointed Czochralski-like crystal was then propagated from a specially prepared tin dendrite seed4 inside the guide tube while the temperature of the bulk melt was held just above the melting point, ensuring a perfectly clean seed which was epitaxial with the original dendrite. The dendrite and epitaxial seed, still in the guide tube, were withdrawn from the melt which, in turn, was undercooled to 2C° below the temperature at which the nucleation experiment was to be performed. The melt was held there for several minutes, both in stirred and in still-melt experiments. The temperature was next raised to the required value and the melt nucleated by the carrot seed inside the guide tube, the heater power being shut off just after nucleation. In experiments where quenching after nucleation was required, a high-density graphite crucible was used, but otherwise the procedure was as described above. The temperature gradient in the melt before nucleation was kept below 1C° per cm by carrying the experiment out just below the center of the heater shown in Fig. 1.

Jan 1, 1968

By Forrest F. Craig

Both early and more recent1 laboratory measurements of gas-oil relative permeabilities were made by subjecting oil-saturated cores to external gas drives. In these runs it was generally assumed that the flowing gas/oil ratio was constant at every point throughout the core. Using this assumption, the resulting equation for the gas-oil relative permeability ratio becomes A where Q is the flow rate at the producing end of the system. This relative permeability was then specified for the average saturation of the core. The assumption and resulting equation fail to recognize that in an external drive, the oil flow rate varies from zero at the injection end to a maximum at the producing end. The assumption also fails to consider the existence of a saturation gradient during an external drive. This saturation gradient is due solely to non-steady-state flow. Some authors2,3,4 have used this erroneous method of calculating relative permeability ratios from external drives. Other authors5,6,7 have used relative permeability ratios in calculating expected field performance by external drive, using Equation (1) and making the incorrect assumption that the saturation is uniform within the driven portion of the reservoir. To find the correct relation between the relative permeability. ratio at the average saturation and the produced gas/oil ratio, the insertion in Equation (1) of a factor, F, to adjust it for oil velocity gradient has been considered. The equation then takes the form Assuming that the oil velocity is directly proportional to the distance from the injection point leads to the conclusion that, for a linear system, the average oil velocity is one-half that at the producing end. Thus, the average gas/oil ratio is twice the produced gas/oil ratio, and Equation (2) is transformed into However, here again the existence of a saturation gradient is not recognized. The produced gas/oil ratio is related to the relative permeability ratio at the saturation of the outlet end of the system. It can be shown quite readily that, if the true log k,/k, saturation relationship is linear over small ranges of saturation, then d log kjko Where aaxv and u2 are the average and outlet saturations, respectively. Examination of Equation (3) shows that the factor F cannot have a single value over the whole saturation range. Another method of dealing with external drives is that of Buckley and Leverett.&apos; Their method, which assumes no gas expansion and outlet end effects, considers fully the saturation gradient present due solely to the displacement mechanism during an external drive, and applies Equation (1) to each point along this gradient. The calculation of production history using relative permeability ratio is straightforward. However, the calculation of relative permeability ratios from production history by this method is impractical. In a recent paper, Welge,1 using an approach similar to that of Buckley and Leverett, presents a simplified method for determining the saturation at the producing end of the system. At thi; saturation, the relative permeability ratio calculated by Equation (1) applies exactly, after breakthrough of the stabilizej front. By this method, relative permeability ratios or production history may be calculated with equal ease. Use of this method as a laboratory tool in determination of relative permeability ratios by external drive requires the knowledge of the total injected fluid volume; in addition to the average saturation and producing ratio. As a preliminary test of this method of calculation, laborntory external gas drives were run on a 3% in. diameter, 11 in. long sample of Nellie Bly consolidated sandstone. This core sample had a permeability of 824 md and a porosity of 28.1 per cent. The driving fluid was air. Three different oils were used, having viscosities of 1.4, 9.8, and 125 cp, respectively. The runs were made under identical pressure differentials,

Jan 1, 1952

By R. I. Jaffee, C. M. Craighead, G. A. Lenning

THERE has been considerable discussion among A metallurgists and others interested in the development of titanium alloys as to the nature of the fine line markings which appear in the microstruc-tures of unalloyed titanium and a titanium alloys. These markings have been variously called x phase, etching pits, and twins. Figs. 1 to 3 show typical examples of the line markings as they appear, respectively, in high purity iodide titanium, commercial purity titanium rod, and a high purity a alloy containing 0.2 pct N. The commercial purity titanium sample, shown in Fig. 2, contains both line markings and some spheroidal retained-ß phase. The ß phase seen in this micrograph should not be confused with the line marking, since it originates from the iron present as an impurity in the sponge metal. It will be noted that the line markings seem to have a definite orientation pattern with respect to the grains and in titanium noticeably resemble the precipitation occurring in artificially aged high purity Al-Cu alloys. This similarity led to the hypothesis that the line markings observed in titanium and a titanium alloys resulted from precipitation of some unknown phase. With the work of Hägg1 and McQuillan2 as background, there was little reason to suspect hydrogen of being responsible for the line markings. Hagg reported that up to 33 atomic pct H was soluble in a titanium, and McQuillan reported an a solubility of up to 8 atomic pct. Furthermore, McQuillan examined metallographically a 5.1 atomic pct H alloy quenched from 300°C and stated that the structure appeared to be a single-phase a solid solution. Line markings have been observed frequently and were first noted by Jaffee and Campbell3 in 1949. They did not observe them in vacuum-annealed titanium and a Ti-O and Ti-N alloys, but did observe them in Ti-H alloys containing 0.25, 0.5, and 1 atomic pct H. They stated that it was doubtful that the markings were a second phase based on hydrogen, because 1 atomic pct was far from the accepted solid solubility of hydrogen in titanium. Finlay, Resketo, and Vordahl,4 in 1950, concluded that the markings were a true second phase as a result of observations on their etching characteristics. Anderson5 Commenting on these markings in titanium was inclined to associate them with hydrogen, but was loath to call them titanium hydride, because of the reported high solubility of hydrogen. Work at Battelle Memorial Institute for the Navy Bureau of Aeronautics," done concurrently with the work described in this paper, provided information on the experiment converse to that described by Jaffee and Campbell in 1949. This work showed that the amount of line markings in unalloyed titanium could be decreased by vacuum annealing at elevated temperature. It was suggested that this was the result of removal of hydrogen; previously, the data of Jaffee and Campbell9 howed that the markings appeared when hydrogen was added. Recent work at Battelle for the Ordnance Corps, Department of the Army, which is described here, now establishes the identity of the markings as a titanium hydride phase. A sample of high-purity titanium rod 1/4 in. diam, 0.009±0.001 wt pct H (0.43 atomic pct), Fig. 1, was resistance heated in a 0.05 micron vacuum for 41/2 hr at 1500°C. During the early states of heating, the pressure increased to 150 microns, indicating that gases were being evolved. After cooling in vacuum, the iodide titanium rod was analyzed for hydrogen. Vacuum-fusion analysis showed 0.0006 ±0.0003 wt pct H (0.03 atomic pct) to be present.* Metallographic examination of the vacuum-annealed rod showed only a transformed ß structure. There was no evidence of fine line markings, Fig. 4. A section of this vacuum-annealed rod was cold rolled to 0.040 in. thick sheet and annealed for 1 hr

Jan 1, 1953

By John Chipman

THE equilibrium between titanium in liquid iron and titanium oxides has been studied by Hadley and Derge.&apos; They have shown that a minimum occurs in the oxygen content of the metal between 0.1 and 1.0 pct Ti, but its exact level was not fixed. The oxide phase in this minimum range was principally TiO, containing some iron oxide. On the other hand, for concentrations above 5 pct Ti the oxide phase was TiO and the oxygen content of the metal increased rapidly with increasing titanium content. From their observations and the free energy of Ti0 and TiOz reported by Kelley and ah,&apos; it is possible to derive approximate values for the activity coefficients of titanium and oxygen in liquid iron-titanium alloys and the conditions for equilibrium in steel deoxidation. Neglecting possible departures from the stoichio-metric composition, the condition of equilibrium with Ti0 may be expressed as follows: TiO= Ti_ + C) log K = log NTl + log [% O] + log yTi + log fQ Here as a matter of convenience the titanium concentration is expressed in mol fraction while that of oxygen is in weight percent. The activity coefficients are yTi and fo. The value of log fo approaches zero as the concentration of titanium approaches zero, while that of log yTi approaches a limiting value of In Fig. 1 the sum of log NTi + log [% 0] is plotted for mol fractions of titanium between 0.05 and 0.50. The smooth extrapolation gives a value of —4.15 which corresponds to log K — log y:i . We therefore have the equation: According to the data of Kelley and Mah,&apos; the free energy of formation of Ti0 at 1900°K is -82,400 cal. The free energy of solution of half a mol of oxygen in iron, taking 1 pct 0 as the standard state, is -29,300 cal. From these we write: From these equations the activity coefficient of titanium at infinite dilution in iron is found to have a value of 0.011 or log y°. = -1.96. This is only an approximate value but is certainly better than the estimated 0.05 in Basic Open Hearth Steelmaking To obtain approximate values for the activity coefficient at intermediate concentrations, it is as- sumed that log yTi(l is constant and equal to -1.96. This corresponds to a value of E;: = 3 In yTi/aNTi = 9.0 which is not unreasonable We now have the value for the activity of titanium and the percentage of oxygen in equilibrium with TiO. It is therefore a simple matter to calculate the activity coefficient of oxygen which is shown in Fig. 2. The effect of titanium is rather large, being comparable to that of vanadium, but not so large as has been reported for aluminum. The slope of the line at low concentrations corresponds to E: = aln yo/ aNTi=-0.37. At concentrations below 1 pct Ti the deoxidation constant and oxygen content for equilibrium with TiO, can be calculated from the foregoing data and the free energy of formation of TiO,, which according to Kelley and Mah is -144,600 cal at 1900°K. The free energy of solution of oxygen has been given; that of Ti to form a dilute solution with 1 pct Ti as the standard state is RT ln (0.5585 y:i/47.9) = -34,800 cal. From these data we find (for concentrations in wt pct): TiO, = Ti + 2 -0; hFTgO0= + 51,200 cal log if =-5.89 The interaction coefficients, concentrations being expressed as wt pct, are e;: = alogfTi/a[% Ti] = +0.048 and e:&apos; = a logfo,/a[ojTi] = -0.187. The calculation gives the following results which, in view of the impurity of the oxide phase, must be regarded as approximate:

Jan 1, 1961

By J. M. Smith, G. P. Willhite, J. S. Dranoff

Heat transfer rates were measured in sandstones with flow of gases perpendicular to the direction of energy transfer. Effective thermal conductivities ker ranged from 0.7 to 1.7 Btu/(br)(ft)(°F). The contribution of the solid phase appeared to be the most important in these consolidated materials, although the thermal conductivity of the gas had some effect. The velocity of the gas through the pores of the sandstones had no influence upon ker up to values of 168 lb/(br) (sq ft) in agreement with data obtained for unconsolidated beds of glass beads. The present results indicated that gas mixing, and hence heat transfer by convection in the pores, is less for perpendicular transfer of energy than when fluid flow and energy transfer are in the same direction. HEAT TRANSFER PERPENDICULAR TO FLUID FLOW IN POROUS ROCKS Heat transfer in porous media with pore sizes in the micron range depends upon the fluid in the pores and the geometry of the solid phase. The best characterized system is a bed of solid spherical particles. Heat transfer in this system has been studied extensive1y (Ref. 8 summarizes the literature up to 1959) when the pores contain stagnant fluid. When the fluid is in motion the directions of flow and energy transfer have an effect on the heat transfer rates, as demonstrated by comparing the work of Willhite, et al l3 for perpendicular flow and that of Kunii and Smith9 for parallel flow of energy and fluid. For perpendicular flow, no increase in effective thermal conductivity ke was noted up to mass velocities G of 77 lb/(hr) (sq ft). In contrast, for parallel flow ke, increased with G in the same range of flow rates. These higher values of ke in the direction of flow also have been observed3,4,10 in beds of larger particles, 0.1- to 0.5-in. diameter. For beds of consolidated materials, such as porous rocks, data are not available for these compar- isons, although Adivarahan1 reported results for the parallel case. Hence the primary objective of this work was to measure ke values for perpendicular flow of fluid and energy in porous rocks. Of interest also was the variation in effective conductivity with fluid velocity. APPARATUS AND PROCEDURE In the experimental method, a constant heat flux was applied to the inner surface of an annular section of the porous rock. By cooling the outer wall, a temperature gradient through the annular sample was established and measured with thermocouples placed within the sample at various radial positions, and at three elevations (A,B.C). The location of the 2-in. O.D., 3.75-in. long sample in the apparatus is shown in Fig. 1. Fluid entered the bottom (1) of the 3-in. I.D. (approximate) steel shell, flowed upwards through the sample and out at the top (3). pressure taps (2,4) were used to check the permeability of the sample. The energy flowed radially from the centrally-located electric heater through the sample and was absorbed in the water-cooled jacket. The samples studied were naturally occurring sandstones from different locations with the properties given in Table 1. These materials are identical with those used by Adivarahan 1 for the parallel flow of energy and fluid. Prior to use they were refluxed with toluene to remove hydrocarbons and leached with distilled water to remove soluble salts. Each sample was visually examined and discarded if large nonhomogeneities, such as cracks or stone particles, were noted. Eight copper-constantan thermocouples were inserted in holes drilled radially into the sample with

By C. R. Simcoe, T. J. Koppenaal

The effect of direct and alternating currents on the quench aging behavior in an Al-4 pct Cu alloy has been investigated by use of resistivity measurements. The reaction rate increases with direct current density in the investigated range of 1000 to 3000 amps per sq cm. Alternating current of a specific frequency is observed to decrease the reaction rate by a factor of about two. ErDMANN-JESNITZER et al.,1,2 investigated the effect of direct and alternating current on the quench and strain aging behavior of low-carbon iron. In both cases they observed that direct current accelerates the aging reaction and that an alternating current can completely inhibit the aging process. The purpose of the present research was to investigate these phenomena in the quench aging behavior of an Al-4 pct Cu alloy and to determine the correlation, if any, between the increase in the observed reaction rate and possible heating effects accompanying the aging with direct current. EXPERIMENTAL PROCEDURE The aluminum-base alloy used in this investigation contained 3.98 wt pct Cu (1.72 at. pct) with impurities of 0.003 pct Si, 0.002 pct Fe, and 0.001 pct Mg. The alloy was rolled into a ribbon about 0.36 mm thick and 3.7 mm wide. The ribbon was split end from end with the ends being used as electrical contacts and the central unsplit section, about 5.3 cm in length, serving as the specimen. Solution treatment was accomplished by quenching from a salt bath at 520° ± 2°C into water at 25° ±0.5°C; the specimen was immediately transferred to a liquid nitrogen bath. All aging was done at 75° ± 0.2°C in a rapidly stirred ethylene glycol bath. Resistivity measurements were made by the double potentio-metric method employing a standard resistor; for purposes of convenience, the resistance measurements were made at 77°K. The transfer of the specimen from the aging bath to a liquid nitrogen dewar was accomplished in less than 1 sec. The aging kinteics were studied with the specimen being aged under the influence of direct current, alternating current, and without any type of current. The amount of heating caused by direct currents was investigated by soldering a thermocouple on the specimen surface and measuring the temperature change after applying various current densities. The temperature was observed to increase (from 75°C, the aging temperature) about 0.8°, 3.0°, and 8.5°C with direct currents of 1000, 2000, and 3000 amp per sq cm, respectively. When employing alternating current, the circuit was monitored with an oscilloscope and adjustments made to produce a normal sine-wave pattern. RESULTS Prior investigations3&apos;4 in the aging characteristics of A1-4 wt pct Cu have shown that the resistivity initially increases, reaches a maximum, and then decreases to values significantly lower than the as-quenched resistivity. This type of behavior is seen in Fig. 1 which shows the resistivity at 77°K as a function of aging time at 75°C observed in this investigation. At this aging temperature, the resistivity maximum is seen to occur in about 1 to 1-1/2 min and it further decreases to the as-quenched value in about 24 min. The behavior observed with the application of direct currents of 1000, 2000, and 3000 amp per sq cm during aging is shown in Fig. 2. With increasing current densities, (+) ?pmax decreases and the rate of the aging process increases. The time necessary to reach the as-quenched resistivity value decreases from 24 min for aging without current to about 16, 10, and 7 min for aging with 1000, 2000, and 3000 amp per sq cm direct current, respectively. Fig. 3 shows the results obtained when two changes were made during the aging with 2000 amp per sq cm

Jan 1, 1963

By N. J. Grant, B. C. Giessen, Paul Predecki

ALLOYS of gold, silver, and aluminum with elements of the groups BII, BIII, BIV, and BV were prepared by a rapid quenching technique (splat) and were examined by X-ray diffraction. Five new intermediate phases were found and will be described briefly herein. For the gold and silver systems, the concentration ranges having an electron/atom ratio e/a of 1.4 to 1.5 ("3/2 Hume-Rothery phases") were studied primarily. Master alloys were prepared from high-purity metals (99.9+ pct or better) by melting either in evacuated fused silica capsules or by nonconsum-able-electrode arc melting in an argon atmosphere. Small pieces, 20 to 50 mg, of each alloy were blast-atomized to form a splat, by a technique similar to that described by Duwez and Willens.1 The technique used for this study is described in detail in Ref. 2; it utilizes a resistance-heated graphite crucible with a small hole at the bottom, directed toward a metal substrate or quenching plate. The prepared alloy rests over the fine hole, through which it is expelled by an explosion shock wave in the form of fine droplets (1 to 50 µ) of molten metal onto a copper or silver substrate, which is maintained at about -190°C. The resulting very high cooling rates (see Ref. 2 for quantitative measurements) can prevent the process of nuclea-tion and growth in many instances, resulting in the formation of metastable phases. The splat particles were transferred to a GE-XRD5 diffractometer and maintained at -190°C, where they were examined with CuKa radiation. The samples were then allowed to warm to room temperature or were heated to higher temperatures until the equilibrium structures formed. Of fifteen alloy systems considered, nonequi-librium structures were encountered in six; these are described below and summarized in Table I. In the system Au-Sb a metastable £ phase (A3 type, hcp, a = 2.898 + 0.002A; c = 4.731 * 0.004A; c/a = 1.633) was found in the concentration range Au + 13 to 15 at. pct Sb. This phase is isomorphous with the stable phases in the systems Au-Cd, Au-In, and Au-Sn, all at an average e/a ratio of 1.4 to 1.5. The concentration range of one-phase metastable was deduced from the small amounts of supersaturated gold solid-solution phase present in the splat product. It was found that ? could also be retained by splatting onto a substrate held at room temperature: however, decomposed into the equilibrium phases Au + AuSb2 after heating to 200°C for 1/2 hr, or on holding the powdered splatted alloy at 20°C for several months. Calorimetric measurements will be made in an attempt to decide the question whether ? is metastable at all temperatures or whether it is a stable phase at low temperatures. There is evidence that another phase, possibly also close-packed but with a different stacking sequence, can be obtained by rapid quenching of alloys with a different antimony content. Klement, Willens, and Duwez3 reported the existence of an amorphous phase on quenching Au-Si alloys (25 at. pct Si) to - 196°C. They found that on heating to room temperature another phase of unknown crystal structure was formed. This was confirmed (see Table I); however, the new crystalline phase, designated as ?, could also be formed simply by rapid quenching to room temperature, and even was found to exist already in the as-cast Au + 20 at. pct Si alloy. It was found that ? decomposed into Au + Si on the specimen surface at room temperature. This behavior, and the question whether or not there is an equilibrium-temperature region for ?, have not yet been resolved. It is probable that ? (Au + 20 to 21 at. pct Si) is cubic of the -brass type (D81-3) with a = 9.60, + 0.01A and N = 52 atoms per cell [compare 6 (CU-Sn)4]. Except for two very weak lines, the powder pattern of about thirty lines could be indexed on this basis; however, a determination of the atom positions has not yet been attempted. For Au-Ge the C phase was observed at about 21 at. pct Ge as reported by Luo et at.5 Lattice parameters a = 2.876A, c = 4.73,A, c/a = 1.64 were found. In the Au-Pb system, formation of a ? phase was not observed, but in the lead-rich region at 75 at. pct Pb, broad peaks belonging to an amorphous phase were found. The maximum diffracted intensity occurred at 28 = 32.4 deg which is about 1 deg larger than the position of the (111) line of lead (Cuka). For Ag-Pb, an amorphous phase analogous to the one found in the Au-Pb system was observed; this metastable phase exists probably at about 75 at. pct Pb. Since no lead-rich alloys were tested, all alloys consisted of silver + amorphous phase at -190°C. In A1-Ge alloys, line-rich and complex powder patterns were obtained at about 30 at. pct Ge; they bear similarities to those of aluminum and germanium, but are of lower symmetry; the existence of more than one intermediate phase is possible. The authors are grateful to the Kennecott Copper Corp. for Fellowship support, and ARPA (Contract

Jan 1, 1965

By P. Pietrokowsky

RECENTLY a comprehensive investigation of the various sigma binary alloys was published by Duwez and Baen.1 It was shown that the following conditions are necessary for the formation of the sigma phase: (1) the difference in atomic diameters of the two alloying metals must not be more than about 8 pct; (2) of the two elements which form sigma, one must exhibit a body-centered cubic structure while the second metal must be face-centered cubic, at least in one of its allotropic forms. In addition, a tetragonal unit cell was proposed and powder patterns of six sigma phases were indexed for d spacings greater than 1.640 kx. Since the indexing, based on tetragonal symmetry, led to only fair agreement, the possibility of sigma being orthorhombic was investigated. Various methods for indexing orthorhombic powder patterns are de- scribed in the literature.&apos; The method used in this investigation was a graphical examination of the differences in values of sin&apos; 9 for the adjacent lines of the powder diffraction pattern. This method led to a complete indexing of the Cr-Co (60-40) pattern. Because of the strong similarity between the various sigma alloys, it was then possible to assign indexes to the patterns of Fe-Cr (50-50), Fe-Cr-Mo (30-30-40), Fe-V (50-50), Co-V (50-50), and Ni-V (50-50). The values of sin&apos; 9 and indexes of the six sigma alloys, together with visually estimated intensities, are presented in table 1. In general, the similitude between the six patterns is quite good. For spacings greater than 1.75 kx a few differences are noticeable. In the Ni-V pattern, no (320) exists and the two strong lines (030) and (031) are separated by only two lines of lower intensity, unlike any of the other sigma patterns. However, very little is known about the Ni-V phase diagram and it is possible that the equal atomic percentage composition in this system lies in a two-phase region. At lower spacings there is a close analogy between the patterns. The planes

Jan 1, 1951

By J. B. Newkirk, R. W. Hendricks, R. Baro

STUDIES of the kinetics of precipitation in binary alkali halide systems are of interest from a theoretical point of view, because of the possibility of controlling diffusion rates by additions of aliovalent impurities. This note reports some preliminary results of a study of the kinetics of precipitation of AgCl from supersaturated solid solutions of AgCl in NaCl containing trace amounts of divalent cation impurities. In their study of the system NaC1- AgC1, Stokes and Li1 derived the phase diagram containing a mis-cibility gap with a broad maximum at approximately 170°C. They found that single crystals quenched from above the miscibility gap and aged at various temperatures within the two-phase region gradually turned light blue, then cloudy white, and finally opaque. The rate of transformation depended markedly on the aging temperature. The light-blue color in the early stages of aging was interpreted to be the result of Rayleigh scattering from precipitated particles less than 0.1 µ in diameter. These qualitative observations have been confirmed by us. However, a more precise tool was needed in order to quantitatively follow the growth kinetics of the precipitate particles. Because of the suspected small size of the precipitate particles and for other reasons, small-angle X-ray scattering was thought to be a suitable technique for this study. Small-angle X-ray intensities scattered from powder specimens were recorded on a General Electric XRD-5 diffractometer using the four-slit geometry described by Neynaber, Brammer, and Beeman.2 The slits were 0.08 mm wide by 10.00 mm high. It was found that, with very careful alignment, meaningful data could be obtained to within 3 min from the middle of the direct beam. Chromium radiation (?Ka = 2.29Å) was used in order to spread the scattered intensity to a relatively high angle, as indicated by Eq. [1]. A specimen containing 21.0 at. pet AgCl was prepared by melting analytic reagent-grade AgCl and NaCl under a chlorine atmosphere in a vycor cap-

Jan 1, 1964

By E. P. Klier, Volker Weiss, George Sachs

IT has been shown that the isothermal transformation of austenite in a special steel can be modified by isothermal holding in the high subcritical transformation range.&apos; Since this treatment potentially leads to increased hardenability, limited testing has been completed to determine if the stabilization effects observed with this treatment can be used to advantage in the heat-treating of 4340 steel. As an index of the effects of the several austenitizing treatments on the hardenability of the steel, Jominy-type hardenability tests were completed for specimens 2.5 in. in diameter and 8 in. long. Since the steel studied is to be used at strength levels where notch sensitivity is of major concern, notch sensitivity after selected austenitizing treatments has been evaluated by notch tensile tests for several specimen sizes. The steel composition and the austenitizing treatments are given in Table I. The test specimens are presented in Fig. 1. The hardenability data are given in Fig. 2 and the notch tensile properties are presented in Fig. 3. The hardenability of the steel investigated when determined by use of the standard Jominy test specimen2 as high and remained essentially unchanged for the different austenitizing treatments. For the larger test specimen, as has been shown by other investigations," the characteristic hardenability indexes are changed and it becomes possible to isolate austenitizing treatments which promote maximum hardenability. The stepped austenitizing treatment promotes higher hardenability as is indicated in Fig. 2. The evaluation of notch sensitivity for very high strength steels is best accomplished by means of the notch tensile test. The experimental conditions of the test, however, modify the notch strengths measured, and in the present experimentation an effort was made to achieve a limiting notch condition by fixing the notch root radius at 0.001 in. while the specimen diameter was allowed to increase from 0.3 to 1.1 in.* For this root radius the notch strength, 0.3-in.-diam specimen, and this trend differs from that for the larger specimens. At the highest tempering temperatures the 1.1-ip.-diam specimens yield comparable results for the austenitizing treatments compared. However, as the tempering temperature is progressively lowered below 800°F, em-

Jan 1, 1958

By M. E. Fine

IN the apparatus for measuring internal friction shown in fig. 1, a modification of that described by Kê,1,2 the parasitic energy loss or background is equivalent to a Q-1 of approximately 4x10-5. This low value of background was obtained by using a jeweler&apos;s collet of appropriate size for the upper support, eliminating lateral motion without immersing the bob in oil, and designing the bob to reduce air resistance. The pendulum is supported on the frame through a snug fitting, sliding rotary joint (fig. I-B). A slight twist of the top imparts essentially pure torsional motion to the pendulum. No evidence of energy loss in the sliding joint has been observed. In the bob (E) steel balls are used in the torsion arm, and the bottom is filled with lead giving a total weight of 94 g. A lighter bob may be used for small diameter specimens. Another bob was a solid disc with provision for adding discs to change the frequency. The oscillating image of the filament is recorded on a revolving drum camera (fig. 1-3) driven by a synchronous motor. This allows use of frequencies higher than can be measured visually on a glass scale. Samples varying in diameter from 0.020 to 0.075 in. have been measured, the frequencies have ranged from 1 to 12 cps, and the maximum strain varied from 0.5 to 10x10-5. With appropriate modification the sample may be placed in a thermostat. The apparatus may also be used to measure the shear modulus. In the examples of measurement given in table I the internal friction of Permendur and the 46.8 Ni-Fe alloy are due, for the most part, to magneto-mechanical hysteresis8 (elastic hysteresis accompanying stress-induced magnetostriction) which depends on strain amplitude and increases with annealing. The internal friction of most materials decreases with annealing. References IT. S. K6: Physics Review (1947) 71, 533. 2 T. S. Kê: Transactions AIME (1948) 176, 448; Metals Technology (June 1948) TP 23703. 3 R. Becker and W. Döring: Ferromagnetismus. 365 (1939). J. Springer.

Jan 1, 1951

By Geoffrey Purcell

For anyone contemplating flotation research with only a very limited amount of mineral available for testing, the choice of suitable experimental equipment is by no means obvious. Hallimond&apos;s original and delightfully simple cell1 has been modified by subsequent investigators2to give quantitative and reproducible results on small samples. However, the modifications have necessarily compromised its simplicity, and the services of a skilled glass blower are required to duplicate the cell. Vacuum flotation tests3 at best qualitative and may, under certain conditions4, be quite impracticable. A hundred years ago, Thoreau observed that "our life is frittered away by detail," and his advice was to "simplify, simplify," The success of the simple cell described below, which was developed by the author and differs somewhat from Hallimond&apos;s original, suggests that Thoreau&apos;s advice still has merit a century later. CELL CONSTRUCTION The cell [Fig. 1 (a) and 1 (b)] consists essentially of a 25-ml pipet from which has been cut the con- stricted top. The length cut off is not critical since this merely determines the final volume of the cell. Cell volume may be varied in this way from 20 to 50 cc. A pyrex extension tube, equal in diameter and approximately half the length of the cut pipet, is attached to the top of the pipet by means of 2 ½ in. of close-fitting tygon tubing. When assembled, the two pyrex tubes should be spaced about ½ in. apart. Another length of tygon tubing is added to the extension piece for sealing purposes. A ¾ -in. disc of porous material (teflon cloth is ideal), secured in place over the pipet tip with another piece of shaped tygon tubing, completes the cell assembly. Tygon tubing may be shaped by pushing it over the pipet tip or some similar form and heating carefully over a low flame. For flotation [Fig. 1 (c) 1, the pyrex extension tube is rotated approximately 70º from the vertical and held in position by a wire hook and eye. Floated material, after reaching the free surface, falls and rests on this inclined plane. The barrier formed by the bent tygon tubing ensures that floated material does not slide back and return to the vertical portion of the cell.

Jan 11, 1965

By Richards R. Vandervoot

T HE creep behavior of many polycrystalline metals at moderate stresses can be described by the empirical relationship: where Em is the minimum creep rate, A is a constant, a is the applied stress, E is the average elastic modulus at the test temperature, and D is the self-diffusion coefficient.&apos; This equation is generally applicable for strain rates of less than around 10-5 per sec and temperatures greater than about one-half the melting point in absolute units. Under these conditions atomic mobility plays an important role in the deformation process, and steady-state creep occurs when a dynamic equilibrium is reached between the generation and recovery of dislocation substructure. Although several theoretical mechanisms have been proposed to explain the creep of polycrystalline solids,2"4 the dislocation climb model2 is in accord with most experimental observations. The majority of creep data used to develop Eq. [1] came from metals with either the fcc or hcp crystal structures. However, on the basis of results for a and 7 iron as well as those for a and a thallium, Sherby concluded that the high-temperature deformation behavior of close-packed metals and bcc metals is probably the same.&apos; The greater creep resistance of fcc and hcp metals and alloys on a relative temperature scale was attributed to lower diffusivities in the close-packed structures. To further compare the creep properties of fcc, hcp, and bcc metals, creep data for all six bcc refractory metals were analyzed according to Eq. [I]. The results are shown in Fig. 1. The sources of information for the quantities used to prepare this figure are listed in Table I, except for high-temperature elastic moduli. The latter data were obtained from Refs. 28 and 29. The dashed lines in the figure represent the range and breadth of data analyzed by Sherby for fcc and hcp metals. In general, the deformation behavior of all of the refractory metals, ex- cept possibly that of tungsten, can be represented by Eq. [1]. This correlation is strong evidence of the similarity that exists between creep of pure close-packed metals and creep of pure bcc metals. At (Em/D) < 108, the results of Flagella and Tarr on tungsten (W-1 in Fig. 1) agree with the five-power stress law, while those of Green (W-5 in Fig. 1) show a seven-power stress dependence. Where (Em/D) > 108, the stress exponents for other data on tungsten were in the range 10 to 15. It is possible that the creep rate dependence on stress in this region is not a power law but exponential (i.e., Em - eßo). However, it was not feasible to differentiate between these two cases because of the steep slope and scatter in the data. Note the inflection point in the curve for the data of Flagella and Tarr (W-1 in Fig. 1). The slope of the line changes from 5 to around 10 at Em/D = 108. The breakdown of the fifty-power stress law at high stresses is not uncommon in other metals, and this phenomenon may result from nonequilibrium conditions in the material such as excess lattice vacancies produced by rapid straining.30 The mechanical strength of a polycrystalline metal is related to its microstructure. Attempts to establish the influence of grain size on the creep rate of metals and alloys have led to a wide variety of results. For example, the following effects have been observed: creep rate decreases as grain size increases;31&apos;32 creep rate decreases as grain size decreases;&apos;,33 creep rate is a minimum at some critical grain size and increases with either an increase or decrease in

Jan 1, 1969

By David Cornell

Back pressure test data on natural gas wells are short time test data of unsteady state nature. Performance curves from which unsteady state effects have been eliminated, called stabilized performance curves, are necessary for understanding the behavior of gas wells and for scheduling gas fields for periods up to 20 years. A calculation procedure has been developed whereby three day, seven day, 30 day, or other duration stabilized performance curves may be calculated from back pressure test data. Such curves are essential for correct gas deliverability calculations and gas field scheduling. I NTRODUCTION The manner in which a back pressure test is made will affect the slope of the back pressure curve because the radius of drainage changes with the length of time that the well is allowed to flow. The reciprocal of the slope of the back pressure curve is defined as n in Equation 1 and varies from 0.5 to 1.0. If the flow is viscous and the radius of drainage constant, n will have a value of 1.0. Because of turbulence in the formation near the wellbore, the pressure drop is usually greater than the viscous flow pressure drop and the exponent n is frequently less than 1.0. In addition, since the radius of drainage moves away from the well-bore during the test, the gas flows a greater and greater distance as the test proceeds, with a resulting increased pressure drop at the high flow rates, and, again, n for the test tends to be less than 1.O. The effect of the changes in the radius of drainage may be calculated and the results used in preparing stabilized performance curves for fixed values of the radius of drainage. Such curves can be made for a defi- nite time period, such as three day, seven day, or 30 day stabilized performance curves. These cukes will show the effect of turbulence near the wellbore and can be used to predict the performance of the gas well at any flow rate or for any production period. In order to discuss the importance of the radius of drainage quantitatively, it should be defined. Muskat" defines the radius of drainage as follows: "... the radius of drainage gives the distance from the well to which the approximately steady state condition has been established ... it being assumed that no gas is removed from any point until the radius of drainage has passed that uoint." An eauivalent definition of the radius of drainage is that radius at which the extrapolated portion of the steady state portion of the pressure gradient gives a pressure equal to the shut-in reservoir pressure. This definition is also implied in the back pressure equation. The radius of drainage is, then, the distance into the reservoir from which the gas appears to originate at any time. It is, however, only a useful concept and does not actually exist. Fig. 1 illustrates the definition of the radius of drainage. At the end of each flow period the radius of drainage may depend on three factors: (1) the duration of each flow period; (2) the rate of gas production; and (3) the rate and duration of the previous flow periods. In general, back pressure tests are conducted with various lengths of production time and at various flow rates. Each individual back pressure test, therefore, requires an individual analysis. The calculations of the change in the radius of drainage have been made, however, for the case of equal flow periods for all four production rates and several sets of increasing flow rates. Fig. 2 illustrates the results of such calculations made by the method of Cornell and Katz2 for the case of 8, = 50,000 and the flow rate increasing in the ratio 1.0:2.0:3.0:4.0 for each flow period. The increase in the radius of drainage during the test is apparent.

Jan 1, 1956