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By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski's method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6'7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6'7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann' suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in 'K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1' values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By R. E. Reed-Hill, W. H. Hartt, W. A. Slippy

An unusual form of double kinking has been observed at the ends of {1121} twins in deformed zirconium. These kinks lie partly outside of the twin and partly inside. While they are undoubtedly closely associated with accommodating the twinning shear into the matrix, they are apparently closely related to other important aspects of twin growth. A mechanism is proposed for {1121} twin growth involving interactions between 1/3 (1120) dislocations in the bend planes and twinning dislocations. It is also shown that boundaries without long range strain fields develop at the tapered ends of the twins. The {1121} twins can, therefore, grow without forming high-energy noncoherent twin boundaries containing large numbers of closely spaced twinning dislocations. NUMEROUS investigators have indicated that slip is often closely associated with deformation twinning. An example is twin accommodation kinking,1-3 where dislocations form bend planes and permit accommodation of a twinning shear within the parent crystal. Another is the incorporation of slip dislocations into twins, as proposed by Sleeswyk and verbraak4 and Ishii and Kiho5 for iron and ß-tin, respectively, and observed in hcp metals by Price.6 In addition, it has been shown that shear discontinuities exist at the points of twin intersections in zinc,7 magnesium,8 titanium,9 ß-tin,10 and bismuth," where the continuity conditions for twin intersections, originally proposed by cahn,12 are not satisfied. A similar situation occurs for zig-zag (1121) twins in zirconium13 and ?-phase silver-aluminum alloys,14 where the twinning shears of the two component twins are not parallel. In all these latter cases additional deformation by slip is believed to accommodate the twinning shear discontinuity. The present paper is concerned with a newly observed aspect of the slip and twinning interrelation, in which two kinks, one inside the twin and the other external to the twin, are formed. These kinks, observed in conjunction with (1121) twinning in zirconium, form to accommodate the twinning shear. A model has been constructed explaining the growth and accommodation of (1121) twins in terms of these kinks. This mechanism may be significant since it is concerned with an important twin mode, which occurs not only in zirconium but also in titanium and hafnium. The practical significance of (1121) twinning has been adequately demonstrated. At 77° K the high ductility of zirconium containing a large number of grains unfavorably oriented for slip is primarily due to (1121) twinning.'5 Also, (1121) twins nucleated at 77°K may grow during further deformation at room temperature. This growth can greatly increase the transverse ductility15 as well as produce large mechanical hysteresis effects.= EXPERIMENTAL PROCEDURE Arc-melted, sponge zirconium plate previously described17 was prestrained 0.65 pct at 77° K by cold-rolling to introduce {1121} twins into the structure. Tensile specimens were cut with axes normal to the plate rolling direction. These specimens were pulled in tension to near the point of failure in an Instron machine at room temperature at a cross-head speed of 2 x10-2 in. per min. This additional deformation caused growth of the twins nucleated by prestrain. Deformed specimens were then prepared for metallo-graphic examination. This included an anodizing treatment18 that made the surfaces sensitive to polarized light, permitting small lattice rotations to be revealed. EXPERIMENTAL RESULTS Nature of the Twin-Kink Band Structure. Fig. 1 is a photomicrograph of a typical specimen after prestrain at 77° K. The structure is characterized primarily by long, narrow, parallel sided (1121) twins which norma1ly traverse the entire grain. Fig. 2 shows several (1121) twins after additional straining at room temperature. These lie near the center of the polarized light photomicrograph and are inclined upward to the right. It is evident that this latter deformation has resulted in appreciable twin growth. The dark regions extending from the ends of these twins are accommodation kinks. The difference in reflected light intensity indicates the

Jan 1, 1969

By C. R. McEwen

This paper presents a technique for calculating the original amount of hydrocarbon in place in a petroleum reservoir, and for determining the constants characterizing the aquifer performance, based on pressure-production data. A method for doing this based on a least-squares line-fitting computationwus proposed by vanEverdingen,Timmerman andMcMahon in 1953. We found that their method would not work when there is error in the reservoir pressure data — even moderate error. The technique presented here appears to give reasonable answers when pressure data are uncertain to the degree expected in reservoir pressure determinations. The major change introduced in the present analysis is to limit the least-squares line-fitting to yield only one constant— the amount of hydrocarbon in place. The water-influx constant is then taken as proportional to the oil (or gas) in place. The constant of proportionality can be computed from estimates of effective compressibility and reservoir water saturation. It is also pointed out that the commonly used least-squares analysis assumes all of the uncertainty to be in the dependent variable. The material balance should be arranged so that this condition is fulfilled if correct inferences are to be made from statistical calculations. Examples are shown of the application of the new technique to gas reservoirs—both hypothetical and real—and to the oil-reservoir example of van Ever-dingen, Timmerman and McMahon. INTRODUCTION The amount of hydrocarbon originally in place in a petroleum resenroir can be estimated by means of the material-balance calculation. Simultaneous observations of pressure and amounts of produced fluids are required, together with the PVT data applicable to the reservoir fluids. If water encroachment is occurring, it is desirable to try to infer the behavior of the aquifer, as well as the original hydrocarbon in place, from the pressure-production data. This imposes additional demands on the method of calculation, and uncertainty in the data can result in large uncertainty in the answer. In addition, if the size of a gas cap is to be established, the whole problem becomes indeterminate, as pointed out by Woods and Muskat.1 Brownscombe and Collins2 simulated a gas reservoir and its aquifer on a reservoir analyzer and derived quantitative information on the effect of uncertainty in pressure and aquifer permeability on computed gas in place. Among the various techniques of estimating the performance of an aquifer, the method of van Ever-dingen and Hurst? based on compressible flow theory, seems to have been the most generally successful (see Ref. 4, for example). In this paper we shall confine ourselves to their representation of the aquifer. In 1953,' van Everdingen, Timmerman and McMahon5 introduced a statistical technique for deriving the amount of oil originally in place and the parameters which describe the aquifer. (We shall refer to this technique as the "VTM method'', as suggested by Mueller.6) Their example reservoir had no gas cap. It has been our experience that the VTM method gives a reasonable answer when the data are very accurate, but that inaccuracy (particularly in pressure) can cause the method to break down. The effect was first observed in gas reservoirs, but has since been seen in oil reservoirs also. In this paper we present another statistical method which has been successful in achieving a reasonable answer where the VTM method has failed. In the new method, one less parameter is derived from material-balance computations. It is assumed that values can be established for effective compressibility in the aquifer and reservoir water saturation independently of the material-balance calculation. The water-influx constant can then be obtained from these data and the quantity of hydrocarbon in place.

By S. A. Mersol, C. T. Lynch, F. W. Vahldiek

The room-temperature Knoop hardness of single -crystal titanium diboride has been determined. Variations in microhardness have been correlated with orientation and structural imperfections in the crystals. Maximum differences in hardness values of 750 kg per sq mm with respect to orientation and 450 kg per sq mm with respect to substructure were found. The effects of etchants, load on indenter, and degvee of cracking of indentation were studied. The average hardness was determined as 2800 kg per sq mm on the as-grown crystals. Annealing increased the average hardness to 3375 kg per sq mm. ThE microhardness of polycrystalline titanium diboride approximating the stoichiometric composition TiB, has been studied by several investigators. The values for the Knoop hardness number range from 2710 kg per sq mm (Khn = 2710 kg per sq mm) to 3400 kg per sq mm.'-4 Samsonov et al.' reported a Vickers hardness number of 3400 kg per sq mm (Vhn = 3400 kg per sq mm) at 120-g loads for a 98 pct Ti + B material of 96 pct theoretical density. Recently Dunegan measured the Vickers hardness and obtained 2060 kg per sq mm with a 10-g load (Vhnlo = 2060 kg per sq mm), 1425 kg per sq mm for Vhnloo, and 1320 kg per sq mm for Vhnlooo. We have obtained a Khnloo = 3000 * 350 kg per sq mm for hot-pressed polycrystalline TiB2 that was 99.1 pct Ti + B and 96.6 pct of theoretical density. The present investigation has been made on single-crystal titanium diboride boules, and is believed to be the first such study on TiB, crystals of known orientation. EXPERIMENTAL The single crystals were prepared by a Verneuil-type process using an electric arc by the Linde Division of Union Carbide Corp. The largest specimens were 6 mm in diameter by 12 mm long. The crystals were of theoretical density (4.50 g per cm3) with a Ti + B content of 99.8 pct. The major impurities present were: 0.03 pct (by weight) 0, 0.06 pct C, 0.01 pct Si, 0.05 pct Fe, 0.01 pct Cr, and 0.01 pct Ni. The crystals were boron-rich, the average boron content being 31.S7 wt pct (stoichiometric value is 31.12 wt pct), and titanium-poor, the average titanium content being 68.2 wt pct (stoichiometric value is 68.88 wt pct). Titanium was determined gravimetrically by cupferron precipitation and boron by titration of H3B03 from a NaOH-fused specimen after removal of titanium with BaC03. The outer edge of the boule accounted for some of the excess boron. An electron-microprobe analysis showed that the titanium content increased from 60.0 wt pct at the edge to 68.5 wt pct at D, ~ 1000 p, where D, = distance from outer edge (see Fig. 5). X-ray measurements indicate that the boules are single crystals with considerable substructure. Upon etching this structure is seen in the form of a Widmanstatten-type rhombohedral line pattern in the basal (c) plane and a parallel "lines" pattern in the prism (a) planes. A typical WidmanstHtten-type pattern is seen in in Fig. 1. Electron microscopy reveals that the lines are less than 1 p across, which does not allow direct electron probe or microfocus X-ray determination of their composition. The identity of the second phase has not been established. It might be a higher boride or a nonstoichiometric TiB2. On annealing above 2200°C the precipitate is dispersed and dissolves in the matrix. The best etchants found were HF/HNO/HO, KF(CN)$NOH/HO (Murakami's Etch), and A large number of other etchants were previously Studied. The acidic etchant produced an acicular or "needles" pattern in the (a) planes which is an etchant effect on the "lines" pattern.

Jan 1, 1965

By Albert Brown, Emil R. Ermert, Fredrick C. Pearson

EARLY in 1946 the Shen-Penn Production CO., a subsidiary of the Philadelphia and Reading Coal and Iron Co., was organized to operate the Shenan-doah Stripping, one of the largest open-pit anthracite mines in the world. This mine is located in the Western Middle Field near Shenandoah, Schuylkill County, Pa., and involves the removal of approximately 60,400,000 cu yd of overburden to permit the recovery of 9,200,000 gross tons of rough cleaned coal from an area 8000 ft long and 2700 ft wide, with a maximum depth of 400 ft. Operations began in August 1946, and within the next few years 31,811,-000 cu yd of overburden and 2,994,000 gross tons of rough cleaned coal had been removed. During the early days of open-pit mining operations, steam was the primary motive power. However, as the size of the equipment increased, so did the problems of fuel, water, labor, and maintenance. Because of its efficiency and convenience, electric power rapidly replaced steam. Later the modern diesel engine was developed, and today practically all stripping equipment is either electric, diesel-electric, or diesel-powered. In locations where electric power is not readily available or where operations are scattered over a large area, diesel power is favored. At Shenandoah operations are highly concentrated in a relatively small area, and this fact, coupled with the availability of ample electric energy, indicated the selection of electric-powered equipment. Since this was a new company, it was necessary to purchase every item, from the smallest tools to stripping shovels. Although the organization period was hampered by the postwar scarcity of materials, an excellent opportunity was afforded to set up a thoroughly modern plant. This paper will describe the power facilities, with particular emphasis on the more unusual features. The substation is a major item in a power distribution system, and a simple arrangement utilizing high quality equipment is an excellent investment. With this in mind, a 3000-kva unit type substation was selected and installed. This unit is made up of three sections, which are assembled simply by bolting together the various sections and connecting the power leads, see Fig. 1. The transformer proper, rated at 3000 kva, is oil-filled and nitrogen-sealed, having a 66,000-v Delta primary and 4160-v Wye secondary with a grounded neutral and 46-ohm ground resistor. The function of this resistor will be described later. Electrical energy is purchased from a public utility and is delivered to the main substation at 66,000 v over one or the other of two incoming lines. These lines terminate on a high voltage switching section on which high voltage fuses and Thyrite lightning arresters are installed. The outgoing feeder switching unit is made up of the following: 1—An auxiliary compartment consisting of potential and current transformers with necessary terminal blocks for connecting to power company metering equipment. 2—Another auxiliary compartment containing a control transformer, battery, and battery charger for the furnishing of power for tripping and reclosing of power circuit breakers. The assemblies in these auxiliary compartments are mounted on carriages that can be rolled in and out with ease. Potential transformers are readily accessible for inspection and fuse replacement. When withdrawn from the operating position they are completely de-energized and grounded. 3—Two feeder breaker compartments, each with a 1200-amp, 5000-v, solenoid-operated magneblast air circuit breaker, voltmeter, ammeter, overcurrent relays, and a ground relay. These power circuit breakers can be quickly and safely withdrawn or repaired. A built-in isolating mechanism is used for lowering the breaker to a transfer truck for repair or inspection or as a means of disconnecting the breaker from the source of power as an added precaution when working on power lines. Thus inspec-

Jan 1, 1953

By C. Kremer Bain

DURING the past several years of diamond drilling in Washington County, Mo., the St. Joseph Lead Co. has discovered a concentration of commercial lead-zinc ore at four different points within an area of 36 square miles. The largest and to date the most promising group of these orebodies is located in the Indian Creek area. It was considered to be of sufficient value to warrant development. The Indian Creek area is in the center of the northern half of Washington County, 11 miles northwest of Potosi, Mo., the county seat. The location is readily accessible from Potosi by car or truck over the all-weather Missouri State Highway No. 114. The topography is one of rolling relief, varying from an elevation of 700 ft above sea level on Mineral Fork and Indian Creek to a maximum of 1176 ft at High Point Tower. It is divided in equal halves between the drainage to Mineral Fork and to Indian Creek. The shaft site at 1060 elevation is on the divide between the two drainage areas. The Indian Creek side is rough and heavily wooded, with only a few cultivated clearings. The slopes to Mineral Fork are more gentle and rounded, with much of the area cleared for farm land. Most of the surface is covered with Potosi and Eminence formations, which show little evidence of any structure. Ore structure was worked out by extensive diamond core drilling, with holes varying in depth from about 700 to 1300 ft. As of Oct. 1, 1950, 218 prospect holes had been drilled within the 36-square mile area. The ore is disseminated galena with considerable accompanying sphalerite in the Bonne Terre forma-tion in the shape of irregular blanket-type deposits. The main controlling structural feature of the outlined mineral zone is a buried pre-Cambrian rhy-olite-porphyry ridge extending partly through the Bonne Terre formation, which laps against the por phyry and also covers it. The mineralized zone parallels and forms an irregular halo around the porphyry ridge and is concentrated in the Bonne Terre formation where the La Motte sandstone is cut out by the porphyry ridge. This is a very common mineral occurrence in the southeastern Missouri lead belt district. The La Motte sandstone, which normally underlies the Bonne Terre formation, is thus cut out entirely. In this area the Bonne Terre is usually about 275 to 320 ft thick, the La Motte varying in thickness from zero up to 400 ft. Commercial concentrations of ore are indicated at several places, the most notable being at the shaft site where an orebody at least 4000 ft long with widths of 500 to 600 ft has been outlined. The total thickness of mineralized rock reaches 150 ft in some holes, although total ore thickness runs from 8 ft to about 60 ft, often in more than one layer. Preliminary Planning Ore reserves as outlined lend themselves to open-stope mining with trackless haulage and mobile loading machines and drilling equipment. This type of equipment has proved to be very efficient during recent years in the company's lead belt operations. After a study of bids for shaft sinking and an estimation of comparative costs, it was decided that the shaft would be sunk by St. Joseph Lead Co. personnel using company equipment. Since the plant site is about 26 miles from the company's nearest lead belt operations, it was necessary to plan a complete surface plant, including mill, shops, office, change room, and warehousing facilities. Immediately following the filing of an application for a certificate of necessity, a headframe was selected for which detailed drawings were already available. The order was placed for fabrication so that it could be delivered and erected in time to serve for sinking the shaft. This eliminated the expense of a temporary headframe. Drilling was started on two churn drill holes near shaft location, and two 1000-gpm deep well pumps

Jan 1, 1954

By A. J. May

THE Star shaft is near the north boundary of the group of mining claims belonging to the Ground Hog Unit of the American Smelting and Refining Co., near Vanadium, N. Mex. The shaft bins and surface plant are served by a siding from the Atchison, Topeka and Santa Fe railroad, and this factor of railroad transportation influenced the choice of site. This paper describes the shaft sinking only, and does not cover the surface plant or other parts of the mine or its equipment. A. J. MAY is Engineer in Charge of Shaft Sinking, Ground Hog Unit, American Smeling and Refining Co, Vanadium, New Mexico. El Paso Meeting, October 1948. TP 2737 A. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Nov. 29, 1948; revision received June 22, 1949. Experience with this shaft seems of interest because of the mechanical mucking, good rate of progress, and the costs obtained at the present level of labor and material costs. The shaft has four compartments, as shown in fig. 1. Equipment: Riddell Mucker: The mucking was done by a clamshell bucket and a Riddell mucker, which, as in other shafts sunk with this machine, consisted of a carriage mounted on axles with double flanged wheels that traveled back and forth on a swinging track, parallel to the long axis of the shaft (fig. 2 to 6). Three air motors were mounted on the carriage; one hoisted the clam, one operated the bucket opening and closing device, and the third moved the carriage along the track. The carriage was designed with guide shoes and could be hoisted to the surface in either skip compartment without trouble (fig. 4). During blasting operations the clam was tied on the rails and the carriage was hoisted up a few sets to protect it from flying rock. No attempt was made to hoist the carriage and clam together lest the clam catch in the timbers. The track on which the carriage operated was built of extra heavy 6 in. pipe with 1x2 in. strap welded on top for rails. A Yzx4 in. angle was welded on the bottom of the 6 in. pipe with a 1 in. round rod welded in the angle for a filler and additional strength. The end or cross pieces of the track which kept the track to gauge, were also made of reinforced, heavy 6 in. pipe and were bolted to the long members on which the carriage traveled (fig. 2 and 3). This section of track was used, instead of heavy railroad rails, for two reasons: (1) this section would bend before it snapped and was much safer for the men in the bottom; and (2) it was a better blasting shield, and protected the timbers better, in fact, only five wall plates were broken by blasting in 1926 ft of shaft, although 150 to 225 lb of 40 pct powder was loaded per round, depending on the ground conditions. The swinging track was supported by four % in. hoisting cables anchored to the end plates. There were also four safety cables fastened two to three sets above the carriage, which would catch the carriage if one of the supporting cables should fail for any reason (fig. 7). Clamshell Buckets: Two clams were used, each of % yard capacity, both manufactured by Blaw-Knox, Nos. 662 and 663. The No. 663 clam was 4 in. wider and 5 in. shorter than the No. 662, but seemed to dig and load more satisfactorily. It was easier to hoist and lower when it came up for repair. It did not turn over as easily, had less spill

Jan 1, 1951

By R. M. Rose, D. P. Ferriss, J. Wulff

Single crystals of tantalum, tungsten, and the binary alloys thereof were grown by electron-beam zone melting and tested in tension between 77° and 373°K. The ductile-to-brittle transition temperature increased sharply with solute concentration, for both tungsten-rich and tantalum-rich alloys; apparently, the maximum transition temperature exists near the 50 pet concentration. Twinning was observed to be a consequence of cleavage-crack propagation. Cleavage occurred on(100)planes, and extensive tearing and "river markings" were present. The onset of brittleness could not be associated with any change in deformation mode, the yield point phenomenon, or the large rise in yield stress with decreasing temperature. Cleavage was observed to initiate at either the specimen surface, or subgrain boundaries. The observation was made that the grain boundaries of Polycrystalline materials are probably even better as nucleation sites for fracture, and are responsible for brittleness at high temperatures and lower solute concentrations than those of the corresponding single crystals. TUNGSTEN and tantalum, the two high-melting neighbors in the third transition period of the periodic table, present striking contrasts. Although both are bee, tungsten has far higher elastic moduli, and the highest ductile-to-brittle transition (DBT) of all the pure metals.' Tantalum, however, is ductile at liquid helium temperatures. Large strain aging and yield point phenomena are observed in tantalum,2,3 but only to a lesser extent in tungsten.4 Tungsten work-hardens at a high rate,5 whereas this effect is negligible in tantalum.' Since the mutual solid solubility of these two metals is complete,7 and no ordering has yet been reported in the binary system, the possibility of depressing tungsten's DBT by tantalum additions was considered. Also, tungsten additions to tantalum could produce hard, high-melting alloys which might be ductile at room temperature. Such alloys offered excellent bases for complex alloy development, particularly with regard to the effect of rhenium on Group VI metals.8"10 In addition, there was the opportunity to examine flow and fracture modes in the vicinity of the DBT, with particular emphasis on the correlation between brittleness and fundamental deformation mechanisms. Myers11 has reported that recrystallized alloys with up to 10 pet W in tantalum are ductile at room temperature, but alloys with 20 pct W could not be swaged at temperatures as high as 500°C. The whole spectrum of Ta-W alloys has been surveyed by Braun, Sedlatschek, and Kiefferl2 using sintered powder compacts. In addition to some physical properties they reported a maximum hardness at about 50 at. pet W, dropping to much lower hardness levels for the pure components. They were able to cold work tantalum-base alloys with as much as 30 pet W and to warm work tungsten-base alloys with up to 20 pet Ta by procedures similar to those used for pure tungsten. EXPERIMENTAL In order to study deformation modes and to keep the impurity concentrations at a minimum, electron-beam zone melting was used to prepare single crystals of high purity. The electron-beam zone melting apparatus is similar to that described by Calverley, Davis, and ever" and incorporates a grid control rectifier to maintain control of emission current. Pure metals were refined by making three zone passes at 4 mm per min up the rod. Alloys were prepared by melting together wire of one constituent on a previously melted rod of the major constituent. Subsequently, two zone passes were made in opposite directions to level the composition after the manner suggested by pfann.14 Purification of the starting materials was accomplished by evaporation of the several impurities, and the degree to which this was accomplished is indicated in the chemical analyses of Table I. The uniformity of composition along a zone levelled rod was within the i 1 pet accuracy of the fluorescent X-ray technique used to determine composition. Crystallographic orientation of the

Jan 1, 1962

By H. Bernstein

Grain coarsening tests were carried out on AI-4.5 pct Cu and AI-4.5 pct Si alloys. The effects of three variables, melt composition, pour temperature, and mold temperature, were determined. It was found that the macrostructure generally coarsened with increased pour and mold temperatures. Coarsening was extreme in the unrefined alloys but was retarded by the active grain refiners like titanium and columbium. The effect of boron was spectacular in suppressing coarsening tendencies. The results of the investigation support the carbide theory of nucleation as opposed to the peritectic theory. A REVIEW of prior work on the subject of grain refinement in the light metals indicated that, for the most part, it had been concerned with the positive effects of addition agents upon structure. This work produced various theories of refinement. Prominent among them were the peritectic theory and the transition element carbide theory. Certain inadequacies in the former theory appeared to be explained satisfactorily by the transition element carbide theory. In order to appraise these theories further, a study was undertaken of the permanence of grain refinement effects when subjected to thermal or chemical variations. It was considered that a study of this kind would be of practical value, since the light metals are exposed to thermal and chemical variations in the normal course of foundry operations. Accordingly, two alloys of commercial importance were selected for this investigation, the A1-Cu and A1-Si alloys. Experimental Procedure and Results Raw Materials: The base alloys, A1-Cu and A1-Si, were prepared from virgin aluminum and hardeners, induction melted, and pigged for remelting. The grain refiners, including titanium, columbium, zirconium, and boron, were added as master alloys. Analyses of the raw materials and base alloys are listed in Table I. Melting and Casting Practice: The metals were melted in clay-graphite crucibles in a Hevi-Duty pit-type resistance furnace, equipped with a Leeds and Northrup Micromax Recorder and Controller. After melt down of the base alloys, the additions were made. For each casting, approximately 80 grams of metal were poured into a preheated graphite mold held in a transite flask. The mold (Fig. 1) weighed 320 grams. To determine the effect of superheat upon structure, a set of melts was heated successively to four temperature levels, 705°, 775°, 845°, and 915°C, and test specimens were cast at each level. Prior to each pour, the furnace temperature was held constant for 20 min. Next, a set of melts was put through a superheat cycle and test specimens were cast at melt temperatures of 705" and 915°C successively. The crucibles then were cooled in air to 705°C as deter-mined by immersion thermocouple and additional test specimens were poured. The cooling interval was approximately 1 min. Another set of melts was furnace cooled with the cover slightly ajar and test specimens cast as before. The interval in this case was 15 to 20 min, varying with the superheat temperature. The mold temperature for all these tests was 400°C. To determine the effect of cooling rate without superheat upon structure, a set of melts was heated to 705°C, and castings were poured at mold temperatures of 205", 400°, and 540°C. An interval of 15 min elapsed between each pour. Mold temperatures were measured by a direct reading millivolt-meter, using a chromel-alumel thermocouple located at midwall thickness of the mold. To demonstrate the phenomenon of chemical coarsening, agents such as chromium and beryllium, which had acted as coarseners in a previous investigation,' were added to the A1-Cu alloy. Test speci-

Jan 1, 1955

By H. M. Myers, J. E. Funk

The two-phase flow of a drilling fluid in a diamond drill bit is investigated by deriving and solving the steady-state continuity and momentum equations. Parameters in this analysis are rotational speed of the bit, local rate of addition of drill solids, non-Newtonian nature of the drilling fluid and drilling rate. The describing equations relate the flow and pressure drop to the design characteristics of the bit. The equations are integrated numerically yielding the flow-rate pressure drop characteristics for the bit, flow distribution in the bit and velocity and static pressure as a function of position in each flow channel of the bit. Results are presented for a particular bit design. This paper shows that under normal drilling conditions certain parameters may be neglected in the hydraulic calculations for a diamond drill bit. Therefore, shortened forms of the equations presented can be used to fit the proper diamond bit to the drilling fluid hydraulic system. INTRODUCTION Like the conventional bit, the diamond drill bit is a key component in the circulating system of a well. The conventional rock bit is fitted to the circulating system by selecting the flow nozzles which provide the system with the proper flow-rate pressure drop relationship. Fluid behavior across the face of the diamond bit must be better understood so the bit can also be fitted to the circulating system. Data from field-operated diamond bits are presently available and do yield some information regarding the flow-rate pressure drop relationship. However, the number of factors affecting this relationship is quite large. Drilling parameters and conditions such as bit penetration rate, bit weight and rotational speed are important. Moreover, flow channels in the bit are part of the cutting head, and introducing drilled solids into the flow channels reduces the flow area, causes additional drag and influences the pressure drop. Many tests would have to be performed if field tests were required to study all parameters which might influence fluid behavior in the bit. A logical approach to this problem is to investigate analytically the fluid behavior in the bit, including parameters that are present under normal drilling operations. This approach, which seems to offer the best method for future studies, is presented in this paper. Following is the general procedure. 1. Equations describing the most general flow channel are written and include the addition of drilling solids (which is related to penetration rate), rotation of the bit, design parameters of the bit and non-Newtonian properties of the fluid. 2. A typical bit is designed and the bit parameters are substituted into the equations. 3. Parameters are assumed (penetration rate, rotational speed of the bit, mud weight, etc.). 4. The describing equations are numerically integrated to obtain the pressure drop across the face of the bit as a function of flow rate. 5. The pressure-drop contribution of each component (friction, acceleration, etc.) is obtained from the numerical solution, and those factors which largely influence the total pressure drop are identified. Classifying the drilling fluid is important in establishing the friction factor relationship since the frictional pressure losses are the main contributors to the total pressure drop. High-density drilling fluid is commonly assumed to be a Bingham plastic. 1-3 Govier4 presented a method for selecting a friction factor in the laminar flow region from the rheology properties of the mud and a modified Reynolds number. Metzner5 presented a criterion for selecting the friction factor in the turbulent flow region. The bit design used in conjunction with the solution of the equations has divergent flow channels. Stall, which is the backflow of fluid in the channels due to eddies that occur on the outer perimeter of the flow stream, can occur in these divergent channels (or diffusers). When stall does occur the static

By Michel Elle, John Chipman

The equilibrium of gaseous H20-H2 mixtures with liquid iron-columbium alloys in the range 0.2 to 2.4 pct Cb shows that the activity coefficient of oxygen is strongly diminished by Cb. The oxide in equilibvium with the melt is identified as CbO2. The equi-librium constant at 1600 deg C is [%Cb][fo. % 0]2 = 2.9 x 10-4 where log fo= —0.14 [%Cb]. The deoxidizing power is comparable to that of vanadium, COLUMBIUM (niobium) is finding increasing use as an alloying element in steel. It forms several stable oxides and is removed from the steel bath by oxidizing slags. The specific oxide formed in steel-making is not known although Sazanov snd Shvarts-man,' in their study of its partition between slag and metal, have assumed this to be Cb2O5 It is the purpose of this study to determine its deoxidation equilibrium at 1600°c, the nature of the oxide formed and the interaction between columbium and oxygen in the melt. The investigation was based on the reaction H2 + O=H2O; Kl=ph2o/(pH2[%O]) [1] in which 0 signifies oxygen dissolved in the liquid Fe-Cb alloy. The method and equipment of recent studies2,3 were utilized. In brief, the molten alloy, contained in a small crucible, is held in a controlled mixture of steam, hydrogen, and argon until equilibrium is reached. It is then cooled quickly in a stream of helium and analyzed for columbium and oxygen, the latter by vacuum fusion.4 The solubility of the oxide in liquid iron is determined by visual observation of scum formation on the surface of the melt. Crucibles of MgO proved unsatisfactory because of partial reduction at the metal interface. Pure A12O3 crucibles were heavily blackened by the melt and could not be used at high concentrations of columbium. Silica crucibles were more satisfactory but these introduced some silicon into the melt thus necessitating an uncertain but small correction for its effect on the activities of the other solutes. In silica it was possible to observe the scum formation when the melt became saturated and there was no apparent reaction between scum and crucible. The procedure for saturated melts was as follows. The alloy charge composed of electrolytic iron and columbium grain was melted and held at constant temperature. The gas ratio H2O:H2 was progressively increased by raising the saturator temperature until a point was reached at which a bright film appeared on the surface and covered it completely. This film could be dissolved by raising the temperature of the melt and it reappeared when the temperature was lowered. Under a partial film covering, utilizing bare areas for temperature measurement, the melt was brought to equilibrium with the atmosphere by holding at temperature for about 1 hr as suggested by Dastur.5 INTERACTION IN THE MELT Several experiments were made without columbium to establish a base in silica crucibles. The results are shown in Table I. Except for one run, they agreed well with Floridis1 comparable results in other crucibles. The value of log K1 is taken from Table I as 0.58. This is slightly larger than Floridis' result, probably because of less elaborate safeguards against thermal diffusion. Results obtained in the Fe-Cb-0 series in which no scum formed are shown in Table 11. The equilibrium ratio Kl is defined as ph2o/(ph2[%O]). It is related to the equilibrium constant K1 as follows:

Jan 1, 1962

By V. M. Dobrynin

Experimental data demonstrate that physical properties of porous rocks change under pressure. In this paper an assumption is made and proved that under pressure the changes of physical properties such as porosity, density, permeability, resistivity and velocity of elastic waves are controlled to a large extent by the pore compressibility of rocks. It is also shown that the pore compressibility of rocks can be determined, within the range of pressures from 0 to 20,000 psi, by knowing the maximum pore compressibility and the magnitude of the pressure. Mathematical equations were developed which permit one to define changes in physical properties of porous rocks under pressure. These equations were verified by experimental data obtained from the study of sandstones. INTRODUCTION In studying the behavior of porous rocks under pressure in the field of petroleum technology, the most interesting aspect is the observation of those properties which characterize the rocks as possible reservoirs — for example, porosity, permeability, resistivity, density and the velocity of elastic waves. The literature dealing with this problem mainly contains data concerning the study of only one or at most two of these parameters, but not of the group as a whole. An attempt is made in this paper to find general equations involving each of these parameters, which will permit the study of the behavior of rocks under pressure. All experimental data used here were obtained from the investigation of consolidated sandstones. EXPERIMENTAL In addition to the use of published experimental data, an experiment was carried out which studied the main physical properties of sandstones under pressure. Two homogeneous quartz sandstones were chosen for this purpose: (1) the Torpedo sandstone from Kansas, and (2) the Medina sandstone from Ohio. The porosity of the Torpedo sandstone was 20.2 per cent, and that of the Medina 8.7 per cent. Permeabilities were 45 md and less than 1 md, respectively. Each sandstone contained about 5 per cent clay minerals, consisting mostly of kaolinite and chlorite, which were distributed quite evenly throughout the samples. One cylindrical sample 2 in. in diameter and 5 in. in length was cut from each sandstone and then saturated in a vacuum with a 3N solution of NaC1. This high concentration was used in order to obtain true formation factors and to decrease the swelling of the clay minerals. The methods of mounting the samples and measuring the changes in porosity and resistivity were practically the same as those described by Fatt and Mann.1,2 Changes of resistivity under pressure were studied for sandstones with 100 per cent water saturation, and for sandstones with the irreducible water saturation. The irreducible saturation was obtained by enclosing the saturated rock samples in relatively fine silicate powder so as to remove the water by capillary action. This procedure is described by Orkin and Kuchinski.3 Changes of permeability with pressure were determined at room temperature using nitrogen as the flowing medium. In studying the effects of pressure, one series of measurements was made using an internal pore pressure Pi equal to the atmospheric pressure, while the overburden pressure Pe ranged from 0 to 20,000 psi. A second series of measurements was used over the same range of overburden pressure, but with an internal pore pressure of 1,800 psi. When the results were compared on the basis of net overburden pressure (Pe — 0.85 Pi ), there was practically no difference for these two sandstones. The origin of the factor 0.85 in the expression for net overburden pressure is given by Brandt,4 Fatt5 and Geertsma.6 The relatively large bulk volumes of the sample (about 15 cu in.) made it possible to observe a

By E. B. Burwell, R. H. Nesbitt

Designed by army engineers, the NX borehole camera provides the most economical method of subsurface exploration so far devised. Continuous cylindrical color photographs now reveal minor flaws in foundation bedrock not always disclosed by borehole samples. A unique projector transforms the photographs into true-to-scale images of three dimensions. ANEW milestone in the progress of photography and subsurface exploration was reached when the Chief of Army Engineers announced the development of the NX borehole camera. In obtaining continuous undistorted cylindrical color pictures of dry or water-filled borings the device surpasses all other cameras designed for photographing interior surfaces of pipes, wells, and conduits. The usefulness of the camera and the unique projector that comes with it are at once apparent. To the geological, mining, and civil engineer alike it signifies the end of guesswork with respect to underground conditions that have eluded identification by conventional core-drilling methods. To the medical profession it may well signal new progress in photo optics which could result in cylindrical color photographs supplementing the X-ray and existing photographic methods used in exploratory surgery. The pilot model of the camera has more than paid for itself as a result of its success in bringing to the surface at two dams information previously obtainable only by costly drilling of mansized boreholes for subsurface on-the-spot examination. Such bores cost as much as $200 per lineal foot as against $10 per ft for the conventional 3-in. or NX exploratory core borings from which the present invention derives its name. The NX camera can now photograph completely the interior surface of these borings. Research and development for the first camera and projection equipment were conducted by Engineering Research Associates, Division of Remington Rand, Inc., under the technical supervision of the Geology and Geophysics Branch, Office of the Chief of Army Engineers in Washington, in accordance with plans and specifications furnished by this branch. Subsequent modifications of the camera-lowering device, transporting equipment, and special field tools were made in the Corps of Engineers' Ohio River Division Laboratories in Cincinnati. The background of this development is interesting. Among the more difficult foundation problems involved in construction of concrete dams are those resulting from bedrock imperfections that escape disclosure by conventional exploration methods. Often these imperfections are of sufficient magnitude to introduce costly changes, especially when their presence is discovered only after foundation excavation is well in progress. Bedrock flaws most frequently camouflaged may be ruptures resulting from the enormous stresses to which rocks have been subjected, or they may be planes or zones of weakness related to chemical alteration and underground erosion. Obviously, detailed information on their location, dimensions, and structure is important, as these factors can affect the stability of a dam and the security of life and property downstream. Their discovery and appraisal entail extensive subsurface exploration. At present the most economical exploratory tool available to geologists and engineers is the small-diameter diamond core drill by means of which cores of the foundation bedrock are recovered for examination and testing. All too often, however, these samples fail to disclose minor foundation flaws that may be of major importance before a structure is completed. As a result, the small-diameter drillings are supplemented generally by more reliable but much more costly shafts, tunnels, or large-diameter calyx drill holes that permit the investigator to examine the foundation rocks in place. It was to reduce the number and cost of these expensive and time-consuming investigations, as well as to obtain more complete information on rock structure from the smaller borings, that the NX borehole camera was developed. That it has been eminently satisfactory in accomplishing that purpose is demonstrated by its success most recently at the Folsom dam, under construction on the American River, 23

Jan 1, 1955

By T. M. Kegley, J. H. Frye, D. L. McElroy, M. L. Picklesimer, E. E. Stansbury

Measurements of rate of growth, thermodymmic quantities, and partitioning of Mn are reported for high-purity eutectoid Fe-C and Fe-C-Mn steels for the auistenite-pearlite reaction. Evaluztion of the cotnstants of a derived-rate equation with these data indicate that Mn additions cause the decrease observed by increasivg the activation energy and apparent activation entropy or the movenment of complexes at the interface. A diffusion-controlled mechanism is not required. Appreciable partitioning of Mn to cementite occurs entirely behind the austenite-pearlite interface for more than 30°C of subcooling. ThE growth of pearlite from austenite has been extensively studied over a period of years. but the rate-controlling step in the process is not known nor is the mechanisrn of the effect of alloying elements understood. A comprehensive review of the subject has been given by Mehl and Hagel. The present study has been concerned with further considerations of the effects of alloying elements on the rate of growth of pearlite. Analytical relatioriships for the rate of growth of pearlite have been considered by Zener.2 Turnbull,3 Machlin,4 Cahn.5 Frye,6 and Frye et a1.7 The derived expressions in each case involve the free energy of the transformation. the interlamellar spacing. and some rate term of the nature of the diffusion coefficient. mobility or frequency of occurrence of some rate-determining step. The treatments. of course. differ in detail. Further consideration is given in the present paper to the equation of Frye, Stansbury. and McElroy which was derived from modified absolute rate theory without in any way specifying the mechanism of the reaction. This equation is r=c ? T ? F exp -?E*/RT [1] where r = rate of growth in mm/sec c = a constant AT = equilibrium transformation temperature minus actual transformation temperature "C ?F = free energy per mol of austenite minus that of pearlite ?E* = activation energy R= gas constant ?F in Eq. [1] is computed from the following: ?F=?H?T/To - ?T' dT' ?T' ?CdT"/T" [2] To To where AH is the enthalpy per mol of austenite minus that of pearlite at the equilibrium temperature, To, and AC is the difference in specific heat between austenite and pearlite per mol. Subsequently, Darken, Fisher, and Galligan8 have reported that a layer of ferrite separates pearlite from austenite at the growing interface (i,e., the advancing face of Fe3C is in contact with ferrite, not austenite) and the ratio of the thickness of this layer to the spacing of the pearlite has not been found to vary with alloy content or transformation temperature. This observation does not require any alteration in the above equation: however, it may require that a different significance be attached to the factor, AT. The AT term appears in Eq. [I] as a consequence of a factor for the amount of growth per complex transformed at the interface.* It is based *This is not the sole reason for expecting such a relationship. See Ref. 7._______________________________________________________ on a l/2 ?T dependence of the interlamellar spacing. Zener2 has developed a theory which leads to Soa 1/?V where So = the pearlite interlamellar spacing. This relation is as consistent with the data on interlamellar spacing as other relationships, although, as pointed out by Mehl and Hagel,1 the data are not sufficiently precise to consider the relationship as confirmed. The work of Darken, Fisher, and Galligan8 requires that the above be written where f = the thickness of ferrite layer between austenite and pearlite. The present paper is concerned with iron-carbon-manganese eutectoid alloys and reports experimental measurements of the following kinds: 1) the effect of

Jan 1, 1961

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By P. Shahinian, M. R. Achter

In a comparison of the creep -rupture properties of nickel in air arid in vacuum there is a reversal in relative strengths with variations in stress. At low stresses the properties are better in air while at high stresses they are better in vacuum. In the early stages of creep in a high stress test the specimen in air nzay have the lower creep rate but the one in vacuum is creeping at a lower rate in the later stages. A mechanism, involving two competing processes in terms of oxidation strengthening and weakening by surface-energy reduction, is proposed to explain these reversals. It had generally been assumed that, relative to their properties in air, the high-temperature strengths of metals would be increased in an inert atmosphere as a result of the elimination of the deteriorating effects of oxidation. However, several recent investigations have shown that the creep strength may be greater in air than in nonoxidizing gases. Pickus and Parker1 found that the creep rate of nickel was lower in air than in hydrogen or nitrogen. Internal oxidation was mentioned by Shepard and Schalliol as a possible cause for the longer creep life of Hastelloy C in air than in vacuum or helium. Sweetland and Parker, who observed lower creep rates for aluminum and copper in air than in helium, discuss the possible applicability of the dislocation-barrier mechanism to explain their results. Surface oxide layers may interfere with the escape of dislocations through the surface or with their generation there. In addition to showing the strengthening in air of low-alloy and stainless steel, and nickel and cobalt-base alloys, shahinian4 presented notch-effect data which indicate the role of stress concentrations; alloys of relatively low ductility were more sensitive to atmosphere strengthening when notched specimens were used. Although Bleakney's copper wires had a lower reduction of area in air than in vacuum, it is difficult to interpret his results in terms of strength changes since the stresses employed were not measured. In contrast to these data showing the strengthening in air, a number of investigations, most at relatively low temperatures, have demonstrated that the environment may cause a decrease in strength. These results are generally explained in terms of the effect of environment on surface energy. In a review of the subject, Benedicks and Harden use the concept of atomic bonding to explain how the adsorption of impurities would decrease the energy of a clean surface. A decrease in surface energy would facilitate the propagation of cracks or extension of the surface. Use of this mechanism is made by sato7 to explain the weakening of steel specimens bent in various liquids, by Potek and Shcheglakovs for the reduction of fracture strength of steel in molten metal, and by Benedicks and Harden for the reduction of strength of a variety of materials in a number of liquids. A similar explanation might be used for the results of Forestier and Clauss. The fracture stress of fine wires pulled in a variety of gases, including air, is lower than in vacuum. They attributed their results to the "tendency" for the gases to condense on the metal surface. That the strength of metals is affected by the type of gas in which the test is conducted has been demonstrated convincingly; the mechanism of the effect, however, is still uncertain. This investigation represents one in a series to explore the influence of variations in alloy composition and test conditions on the atmosphere effect in the expectation that the results would afford an insight into the processes taking place. To determine the effect of specimen composition, the present investigation was conducted

Jan 1, 1960

By Herman Dykstra, Irving Fatt

Relative wetting phase permeabilities calculated from capillary pressure-saturation data are compared with measured relative permeability data. The equation relating relative permeability to capillary pressure-saturation data is derived by assuming that a porous medium is analogous to a bundle of capillary tubes. The equation includes a term to correct for the difference between fluid path length and length of core. Relative oil permeability data in the water-oil-gas system are presented, and it is shown that if the water is considered part of he rock matrix, the relative oil permeability curve is typical of a wetting phase relative permeability curve. Apparatus for measuring two and three-phase relative permeabilities are described. INTRODUCTION The difficulty in measuring relative permeability of cores has made it desirable to have a correlation between relative permeability and some more easily measured property of porous media. Such an easily measured property is the capillary preisure-saturation relation. In the past there has been a tendency to separate the capillary pressure concept from the very complex pore geometry and to consider that the capillary pressure-saturation curve give? only some characteristic distribution of interfacial curvature between two fluids.' Recently, however, it has been realized that if capillary pressure data are to yield information concerning pore size distribution2 and fluid flow in porous media. the pore must be assumed to have a simple shape such as a cylinder or a sphere. Childs and George' showed that relative water permeability could be calculated from the capillary pressure-water saturation curve by assuming that the pores are cylinders in which the fluid flowing obeys Poiseuille's Law, and that the capillary preisure curve indicated the size and number of pores. Purcell5 derived an equation relating the permeability of a porous medium to the capillary pressure curve by assuming the porous medium to he analogous to a bundle of capillary tubes. Gates and Lietz6 calculated relative permeability by an equa-tion derived from Purcell's equation. In this paper an equation is derived giving the relative water permeability as a function of water saturation by as-sulning that the core sample can be represented by a bundle of capillary tubes in which the fluid path length is not the same as the bulk length, and in which the fluid path length varies with saturation. THEORY For a bundle of N capillary tubes the flow through dN tubes will be dQ = qav dN ..........(1) where Q is the total flow rate through all the tubes and q., is the aberage flow rate through the tubes in the interval dN. If the interval dN is made small the average flow rate through a tube in the interval dN is given by Poiseuille's Law, 8 nl where ?P is the pressure drop across the tube of length 1 and radius r, and µ is the viscosity of the fluid. Substituting for qav in Equation (1), dQ =pr4 ? P/8µl dN.........(3) Darcy's Law for linear flow of an incompressible fluid in a porous medium is Q = KA?P/µL...........(4) where K is the permeability and ?P is the pressure drop across a bundle of tubes which has replaced the porous medium of length L and cross-sectional area A. Differentiating Darcy's Law with A, ?P, µ, and L constant, dQ = A?P/µL dK.........(5) Equating (3) and (5) gives dK------------dN.........(6) 8Al If the pores are assumed to be cylinders dV =pr2ldN..........(7) where V is the volume of flowing fluid in the pores. Substituting for dN in Equation (6) gives dK = —dV..........(8) 8AI' By definition the saturation, S, of the core is v v S =V/Vp..........(9) Vv -PAL

Jan 1, 1951

By Bernhard Blumenthal

A melting process was developed by which high purity electrolytic uranium crystals can be converted into sound ingots without serious contamination. Careful preparation of the crystals, melting in a high vacuum, and directional solidification led to a metal of better than 99.993 wt pct purity. The metallographic examination showed a substantially clean metal with only residual amounts of a second phase which responded to heat treatment. The density of high purity uranium is 19.05 g per cu cm. FOR the study of the fundamental properties of uranium and its alloys, a base metal of high purity is needed, and an investigation was started at Argonne several years ago to examine various methods of preparing high purity uranium. Early success was achieved by the fused salt electrolysis process in preparing high purity metal in crystal form,' and the problem became that of melting the crystals into ingots without contamination. The electrolytic crystals contained a few ppm of heavy metals, less than 15 ppm C, and large quantities of potassium and lithium in the form of trapped fused salt electrolyte. On melting in vacuo in magnesia or urania crucibles, the metal picked up considerable quantities of carbon and some iron, copper, and silicon but lost most of the potassium and lithium. It was not metallographically clean, and much research work was necessary to determine the optimum melting conditions for minimum contamination. This work has resulted in the development of a melting procedure by which sound ingots can be prepared with only a limited contamination by carbon. In the section entitled "Melting of the Electrolytic Metal," the equipment and processes that have been developed for melting the electrolytic crystals are described in detail. The "Metallography" section is devoted to the metallography of high purity uranium, and the section "Density of High Purity Uranium" contains the first property measurement on high purity uranium—a density determination. Melting of the Electrolytic Metal Apparatus—Melting and Vacuum Equipment: Uranium may be melted in either resistance or induction-type electric furnaces. Resistance heating was found to be preferable to induction heating for melting down the electrolytic crystals, for several reasons: Although induction heating permits fast heating, this advantage cannot be utilized when crucibles with limited thermal shock resistance are used. Temperature control of induction-heated melts is poor, and the stirring effect increases the rate of contamination of the melt from the crucible, slag, or the furnace atmosphere; liquation and controlled solidification are difficult to carry out. Because of these objections, resistance heating was chosen. A 10 kw Globar resistance furnace of low heat capacity permitted uniform heating of a uranium charge to its melting point in 45 min. The furnace was insulated with a removable aluminum shield so that, after melting and removal of the shield, the furnace could be quickly cooled to room temperature. The furnace was equipped with an apparatus for directional solidification; see Fig. la. The crucible was suspended in the center of the furnace; and when the melting was complete, the crucible was slowly lowered into the cold end of the furnace tube. Solidification took place upward from the bottom; and when the rate of lowering was small, a sound ingot free from sink holes and shrinkage cavities was produced. To remove the large quantities of gas contained in the electrolytic crystals, melting in a high vacuum is mandatory. While, from the standpoint of contamination, melting in a highly purified argon atmosphere appeared feasible, lithium and potassium removal proved less efficient under such conditions. Also, a vacuum-melted ingot has a cleaner surface than one melted in an inert atmosphere. The vacuum system must be of very high pumping speed and leak tight so that a vacuum of less than 2x10-7 mm Hg is attainable when the system is pumped down cold. The system must have a high pumping speed, so that the pressure maximum which may rise to 1x10-4 mm during heating can be quickly reduced

Jan 1, 1956

By H. F. Webster, C. G. Dunn

Rolling md annealing procedures are described for developing the (110) preferred orientation in tantalum for use as a thermionic-emission materinl where electrodes of a uniform high work function are needed. The development of a (110) [001] annealing texture is also reported. A preferential growth process due to low (110) gas-metal surface energy is considered in explanation of the observed growth of (110) grains. ThE growth of (110)-oriented grains in thin strips of rolled zone-refined tantalum, previously discussed briefly,' is reported together with more recent information on the formation of a (110)[001.] annealing texture, i.e., one where the [001] direction of each grain lies close to the rolling direction. The development of tantalum sheet with a (110) preferred orientation (position of [001 ] directions unspecified) is of importance as a thermionic-emission material in thermionic-energy converters. Since therm ionic-emission properties of cesium-coated crystals vary over a wide range depending on (hkl) a2-7 a single (hkl) preferred orientation is more useful than either several preferred orientations or none. Furthermore, the (110) preferred orientation yields the highest thermionic-emission density for a cesium coverage of less than a monolayer.5-7 A consideration of the stability of the grain structure needed at high operating temperatures suggests that the preferred orientation itself should be produced by annealing processes. Information on annealing textures in tantalum, however, is rather limited. Pugh and Hibbard 8 obtained (111)[112] and (lll)[112] components in a 1400°C recrystallization texture in 95 pct cold-rolled foil; these components were enhanced on annealing at 2500°C. Muller9 rolled 99.97 Ta to 90 pct reduction in thickness in the final stage and noted only a slight sharpening of the rolling texture, with some intensification of the (111)[112] component upon annealing at 1200°C. The experimental procedure followed in the present work stemmed from the idea of using possible differences in (hkl) surface energies to provide a small driving force for growth of grains having the lowest (hkl) surface energy.l0* This would mean using high-purity tantalum processed into thin sheet form and annealed at high temperatures either in a noncontaminating atmosphere or in one producing additional sample purification. EXPERIMENTAL Zone-Refined Tantalum. National Research Corp. tantalum in the form of 1/8-in.-diam rod and of 99.98 purity (53 ppm 0, 15 ppm N, and 8 ppm C) was zone-melted four times. The traversing speed was 4 mm per min. Such treatment increased the resistance ratio, R293k/R20K , where R293K is the resistance of the specimen at 20°C and R20K the re-resistance at liquid-hydrogen temperature, from a value of 25 for the initial rod to 175 for the zone-refined rod (the increase in the resistance ratio provides a measure of purification11,12). Part of a zone-refined rod was rolled unidirec-tionally to a strip 0.003 in. thick and 0.28 in. wide. Samples were given anneals in the range 1300" to 2100°C using ac conduction heating in an oil-free vacuum system. Recrystallization to small grains appeared to be complete at 1300°C. Large grains were formed at higher temperatures, but these were not entirely strain-free, some grains showing asterism in Laue X-ray patterns and some displaying a range in orientation. Part of the difficulty was caused by thermal expansion of the tantalum strip as it was held between fixed supports. However, in a different arrangement with the tantalum freely suspended in a tantalum can, high-frequency induction heating in vacuo at about l0-6 Torr produced

Jan 1, 1964

By N. K. Chen, R. Maddin

THE textures of straight-rolled and of cross-rolled molybdenum were first determined with the aid of pole figures by Custers and Riemersma.' These authors have shown that for straight-rolling, the main texture was (100) [0111 with a considerable spread about the rolling direction. After cross-rolling a second texture was obtained in which there was a [111] axis perpendicular to the rolling plane, possessing a rotary symmetry. Recently Semchy-shen and Timmons2 in their study of preferred orientation of arc-cast molybdenum sheet obtained similar pole figures. In these two investigations, polycrystalline materials were used. In the main, the textures of molybdenum in these cases are qualitatively consistent with rolling textures of other body-centered cubic metals, such as iron and Fe-Si alloys." In the present investigation, single crystals of molybdenum were deformed by rolling with respect to specific crystallographic planes and directions. Since the deformation textures of polycrystalline aggregates have been related intimately to the behavior of individual grains,4 a study of possible correlations of final textures with respect to the initial orientations of the single crystals might conceivably lead to a better understanding of the textures. Annealing treatments were carried out after deformation in order to study the recrystallization characteristics as well as the recrystallization texture. Rolling of Single Crystals Single crystals of molybdenum (about 1/8 in. in diarn x 1-in. long), grown by the method previously described,5 were cold-rolled without intermediate anneals. Except for specimens MR-1 and MR-2, which were rolled at random in the preliminary test in order to find a proper rate of reduction, all other specimens were carefully documented as to their respective orientation before deformation by means of X-ray Laue back-reflection methods. A stereo-graphic projection was constructed from which it was possible to determine a particular plane and direction to be considered for rolling. Parallel flat surfaces were then polished metallographically with respect to a reference scratch on the specimen which was mounted in sealing wax. These flat surfaces contained the plane chosen for rolling. After etching, a Laue back-reflection photogram was again made of one of the flat surfaces to determine the exact plane of rolling. The initial orientations of all the specimens (specified by two elements for each crystal, direction of rolling and the pole of the rolling plane) are summarized in Fig. 1. The specimens were mounted in plasticene between two hardened Si-Fe plates. The sandwich was then rolled down, keeping the direction constant in the case of straight-rolling. In cross-rolling (MR-10, MR-11, and MR-12) the sandwich was rotated 90" after each pass so that every first and third pass contained the same rolling direction. Specimens MR-14, MR-15, and MR-16 were compression-rolled following the manner of Barrett." In these cases the direction of the sandwich through the rolls was changed by 3" to 5" for each pass until the specimens were rolled to the desired reduction in thickness. It was found that if extreme care was exercised in rolling, i. e., the amount of deformation per pass was extremely small, the specimens could be rolled to a large reduction in thickness. The rate of reduction used, with a single exception of MR-1. was generally 0.001 in. per 10 passes. Thus, it took about 800 passes to reduce a specimen to a final reduction in thickness of 87 to 98 pct. The results of rolling are shown in Table I. Cold-Rolling Textures The final orientations were determined by the conventional Laue transmission method," using molybdenum radiation, with or without a zirconium filter. Pole figures were plotted from (1101 and (200) reflections in which three degrees of intensity— heavy, medium, and light—were determined visually. Three main types of textures have been observed from the deformed single crystals. These are: 1—a

Jan 1, 1954