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By C. A. Hartnagel

During- the past 10 years the annual production of petroleum in New York has averaged close to 5,000,000 bbl., the total for the period being 49,881,000 bbl. In 6 of the 10 years, the production was slightly in excess of the 5,000,000 mark. The 1944 production of 4,697,000 bbl. represents a 7 per cent decline from the previous year. Of the total 1944 output, the Allegany County district, which includes two small areas of Steuben County, contributcd 3,614,065 bbl., a decline of 5 per cent from 1943, and the contribution of Cattaraugus County, which represents the northern extension of the Bradford pool of Pennsylvania into New York was 1,082,935 bbl., a decline of more than 14 per cent. Since March 1942, the posted price of New York crude oil has remained at $3.00 per bbl. On lug. I, 1944, a Federal subsidy of 75¢ per bbl. was granted to oil producers, thus making the price actually $3.75 per bbl. Since all of the oil produced in New York comes under the designation "stripper well operations," it is entitled to the Federal subsidy. During the last few years there has been little change in the number of wells drilled annually. In the Allegany field, which accounts for three fourths of the oil produced in the state, 1240 wells, including water-intake wells, were drilled during 1944 as compared with 1223 in 1943. There was no marked increase in the number of wells drilled after granting the subsidy of 75¢ per bbl. of oil on Aug. I, the increase being but 14 wells during the last half of the year over the preceding six months. In flooding operations it is not to be expected that even a substantial increase in the price of crude oil will be reflected quickly in an increase of the number of wells drilled or in a marked increase in production of crude oil. In flooded areas, oil is obtained through a program extending over a number of years. This program involves the drilling of the water or input pressure wells, drilling of the oil wells, building up the oil flood to maximum production, and finally the watering out of the well when the amount of oil produced in proportion to the water becomes so small that pumping is no longer profitable. The various operations may extend over a period of 10 years or more, during which time the price of crude may have fluctuated greatly. Although the rate of production can be controlled to a limited extent, it is evident that a flood when once begun must be continued regardless of the price of crude. During the past seven years New York crude has had a price range from $1.68 per bbl. in 1938 to the present price of $3.75 per barrel The field pattern now in general use for wells in a flood project is the "five-spot." Under this arrangement, the lease is divided into squares with a water well at each corner and an oil well in the center. In the all-over pattern of the lease each oil well is acted upon by four water wells and each water well supplies part of the pressure to four oil wells. Spacing between the input water wells and the oil wells usually varies from zoo to 225 ft. or, on an acre basis, there is one oil well and one water well for each 2 1/2 acres. In recent years there has been a tendency to increase

Jan 1, 1945

By H. Herman, M. E. Fine

Kinetics of reversion and reformation of GP I were studied resistometrically in Al-1.7 at. pct Cu. The reversion process is over in roughly 1/2 minute at 205 "C irrespective of the amount of primary aging. After reversion the occurrence of an incubation time before reaging begins has been substantiated. The reaging kinetics is drastically accelerated by plastic deformation to the specimen. An incubation time is observed only if the specimen is aged before reversion. The incubation time and the effect of plastic deformation indicate that nucleation of GP I is heterogeneous. Simple clusters of copper atoms apparently do not act as nuclei for GP I. AFTER quenching aluminum-rich copper from the solid solution range, Guinier-Preston zones of the first kind, GP I, form very rapidly at room temperature. The rate, largely controlled by the concentration of vacancies, is initially most rapid1 (that is, at the time of the first measurement: 1/2 min) and decreases with time. The nucleation is thought to be athermal. If after aging for several days the GP I is dissolved by reversion at 205°C, according to measurement of Young's modulus an incubation period is observed before GP I begins to form on subsequent aging.2 Yet if the reversion is carried out immediately after quenching, both resistivity3 and modulus changes2 show no incubation effect. The zones which form after reversion have the same structure as those which form after the quench.4 Because of entropy considerations and also the short diffusion time, the solid solution after reversion, 2 min at 205°C, is probably more highly clustered than at the original solution treating temperature, 520" to 550°C. It appears most reasonable to associate with nucleation the incubation time observed on reaging after reversion. A simple cluster of copper atoms, many of which are presumed to be present after reversion, is then not a sufficient nucleus for GP I; a GP I nucleus must contain something in addition to a cluster of copper atoms. The purpose of the present note is to give some additional experimental information concerning the incubation time and rates of reaging after reversion. The existence of the incubation time has been verified by measurement of another property, the electrical resistivity. Acceleration of reaging after reversion by plastic deformation has also been investigated. In acl.dition, the kinetics of the reversion process itself was studied. EXPERIMENTAL Electrical resistance was measured by the poten-tiometric four probe method. The 1.7 at. pct Cu alloy was furnished by the Aluminum Co. of America in the form of 1/2 in. rod. The major impurities reported by Alcoa were Fe (0.002 wt pct), Si (0.003 wt pct), and Mg (0.001 wt pct). Specimens for measuremenl of resistance were prepared by rolling to 0.010 in., cutting 2 by 0.2 in. pieces, rolling the middle pclrtions of these to 0.005 in., and splitting the 0.010 in. sections up to the reduced central section to form current and potential leads. Aluminum extension wires insulated with ceramic tubes were spot welded to the leads. The specimen was supported by the lead wires. The whole specimen assembly was annealed at 500" C in an air furnace for more than 12 hr and then aged at room temperature. This was done to assure quick and complete resolution during subsequent solution treatments. These were carried out in Houghton's "430 Temper Salt" at 520'C for 1 hr. Unless otherwise specified, quenching was accomplished by quickly transferring the specimen from a salt pot to 25°C water. Aging was carried out in a 3 liter dewar of distilled water, rotated and stirred. The temperature was controlled to +0.01°C with a thermomercurial regulator in conjunction with a transistorized relay

Jan 1, 1962

By W. P. Evans, R. W. Buenneke

Warren and Averbach's multiple order, Fourier method was applied to solid specimens of SAE 1045 steel. The material was hardened to three hardness levels and specimens of each hardness were shot peened to three intensities. Particle size, root-mem-square strain, mean strain, md macro residual stress were determined for each. Microstrains caused by either hardening or peening varied markedly over microregions. In general, increasing the hardness or peening intensity increased the rms strain and decreased the particle size. Similar effects were observed by varying hardness and peening intensity independently. At a Rockwell hardness of C 50, peening had little effect on line broadening, but both mean strain and macro residual stress increased. Mean strain was independent of column length. Induced macro residual stress by peening was affected most by initial hardness, but not by specific peening intensity. The purpose of this work is to establish the state of residual strain and particle size by X-ray diffraction in hardened and cold-worked plain carbon steel and attempt to relate these X-ray measured parameters to fatigue performance. X-ray line broadening (and its micro implications), along with X-ray residual stress (and its macro implications), may be basic indicators of the inherent fatigue resistance of the material. X-ray line broadening is caused by variable lattice strains and small particle size. Both are a result of plastic deformation which accompanies hardening or cold working processes. Therefore, X-ray line broadening is a good measure of both. warren1 has recently reviewed the Warren and Averbach2,3 Fourier analysis of line broadening. Strain and particle size effects can be separated because broadening due to particle size is independent of order of the diffraction peaks, while broadening due to strain is not. Microstrain is obtained as a root-mean-square strain averaged over discrete distances within the crystals causing diffraction. These distances are quite small, varying from 10 to 10081, and may be interpreted as the gage length over which the strains are averaged. Because of their variable nature, the X-ray line is broadened. The plot of rms strain vs distance (or column length) within the specimen gives a measure of their variability. Small particles also cause X-ray line broadening as already mentioned. A particle is interpreted as a region within a crystal or grain which diffracts X-rays coherently. This region is one of given orientation and may be bounded by a small angle grain boundary, dislocations, a twin boundary, or a stacking fault. The present work covers measurement of X-ray line broadening and macro residual stress on an SAE 1045 steel, quenched and tempered to various hardnesses. Various amounts of cold working were produced by shot peening the surfaces to various Almen intensities. Particle size, root-mean-square strain, and mean strain were calculated from the Fourier coefficients of the X-ray diffraction profiles in a direction normal to the peened surface. No effort was made to separate the various causes of particle size broadening. Macro residual stresses were reported in directions parallel to the peened surface. I) X-RAY METHOD The Fourier coefficients were determined for the 110 and 220 X-ray profiles. They were corrected for instrumental broadening by the method of Stokes,4 using an annealed reference specimen of similar geometry presumed to be free from broadening due to small particles and distortions. The nth Fourier cosine coefficient, A,, is related to a particle size coefficient, Ap, and a distortional coefficient, ADn, by the equation:

Jan 1, 1963

By Rex W. Woods

The clue history of performance of a highly volatile type oil reservoir which is now greater than 80 per cent depleted is presented. The reservoir is at a depth of approximately 8,200 ft and includes an area greater than 7,500 acres. The reservoir has been exploited by 10 wells which to date have yielded about 10,880,000 bbl of stock tank oil by pressure depletion. Reservoir pressure has declined from an original of 5,000 psi to approximately 1,450 psi. Produced gas/oil ratio has increased from 3,200 to 23,000 cu ft/bbl with a corresponriing increase in APl gravity of the stock tank oil from 440 to 620 . Pressure and fluid data are given for different stages of depletion. INTRODUCTION In papers by Sloan,' and Cook, Spencer and Bo-browski,' properties of highly volatile type reservoir oil were discussed in detail and methods were presented for predicting performance of reservoirs containing this type of fluid. The purpose of this paper is to present performance history of a highly volatile type oil reservoir designated as Reservoir A which has been produced by pressure depletion and field separation without processing of gas GEOLOGY The reterence field which includes Reservoir A is a structural feature north of a trend of major folding along a northeast-southwest axis. In the area of development, the structure has the appearance of a dome with formation dip of three to four degrees, but structural relations between the reference field and the axis of major folding to the south have not been determined. No faulting within the field is evident. Oil and gas productive sands have been found at depths of 7,000 ft to 10,000 ft in a columnar section of Mio-Oligocene age. The sand bodies in the section are lenticular and usually continuity of sand is limited to a small area. Sand A which forms Reservoir A at a depth of 8,200 ft, however, has exceptional continuous development in the reference field. Fig. 1 shows an isopachous map of net oil sand for Reservoir A. Net thickness of oil sand at producing wells ranges from 14 to 34 ft with an average of 22 ft. Pinch-out of sand has been shown by drilling in the southwest part of the field, but extent of the reservoir on the northwest and northeast parts of the field is indicated only by thinning of the sand. The vertical oil column between the highest and lowest producing well in the reservoir is 339 ft. No water-oil contact has been found within the reservoir. As interpreted from the isopachous map, the reservoir includes about 8,900 acres with an average net sand thickness of 12 ft. Because of limited data on extent of the reservoir, the isopachous map permits only an approximation of sand volume in the reservoir. DEVELOPMENT AND PRODUCTION Reservoir A was discovered during 1938 and was developed with eight wells to the end of 1942. One well was completed during 1946 and the tenth well in the reservoir was completed during 1951. Three of the original wells and the last completion have produced from Sand A only. Six wells have produced from Sand A through the casing side of dual completions. Initial producing rates of the original wells ranged from 800 to 1,000 BOPD. Production history for the reservoir is shown in Fig. 2. Production of the reservoir was begun during 1940 and in May, 1952, peak production from seven wells was 5,300 BOPD. At the end of March, 1954. cumulative production was 10.880,000

Jan 1, 1956

By J. B. Clark, A. S. Yue

PfANN1 has shown that when a cylinder of molten binary alloy freezes directionally, the solute distribution can be described analytically by cg=k(l-g)k-1 [1] in which Cg is the solute concentration in the solid at the point where a fraction g of the original liquid has frozen and Co is the initial solute concentration. The term k is the effective distribution coefficient of the solute and is defined as the ratio Cx/CL where Cl is the solute concentration in the main body of the liquid. Both the slope and the intercept at -log (1 - g) = 0 of a logarithmic plot of Eq. [I.] provide a measure of k. Under conditions of freezing where diffusion in the solid is negligible and the solute concentration in the liquid is uniform, the effective distribution coefficient k, derived as above, is equal to the equilibrium distribution coefficient taken from the phase diagram. However, under ordinary freezing conditions, even though solid-state diffusion is negligible, the solute rejected from the freezing solid does not have sufficient time to diffuse uniformly throughout the main body of the liquid. A concentration gradient is formed in a boundary layer in front of the advancing solid-liquid interface as pointed out by Rutter and Chalmers.' Thus, under these conditions, the concentration of the freezing liquid in the boundary layer is higher than that predicted from the equilibrium phase diagram and consequently the effective distribution coefficient k, obtained from directional freezing experiments, is larger than the equilibrium distribution coefficient. The symbol k will designate the effective distribution coefficient in the discussion which follows. In this paper, the determination of the effective distribution coefficient is demonstrated for several dilute binary alloys and a polynary magnesium alloy. The effect of freezing rate on the value of the derived k is presented in detail. An example for the calculation of the solidus in a dilute binary solution using the experimentally determined effective distribution coefficient is given. MATERIALS STUDIED Binary magnesium alloys of copper, nickel, and zinc containing approximately 0.10 wt pct solute and a polynary alloy containing approximately 0.10 wt pct each of several elements were selected for study. The spectrographic analyses of these alloys are given in Table I. The analyses are believed accurate to within +5 pct of the stated value. EXPERIMENTAL PROCEDURE Extruded rods of the alloys, 3/8 in. in diam and 11 in. long were used for directional freezing studies. The alloy rods were melted horizontally in a high-purity graphite boat by a Nichrome-wound tube furnace which moved parallel to the length of the rod. The boat was supported inside a Vycor tube suitably connected to provide a protective atmosphere of dry SO2. For an experimental run, the following procedure was used. The alloy rod was cleaned in dilute HNO, and dried. The graphite boat containing the alloy rod was placed within the Vycor tube and the tube connected to the gas train' The 'ystem was purged for 20 min with dry argon and then a flow of dried SO, was maintained for the duration of the run. The movable furnace was positioned and either all or a desired portion of the alloy rod was melted. After attainment of steady-state temperature gradients the molten bar was solidified from one end to the other at a controlled rate by pulling the furnace along the length of the bar at the desired speed. At the conclusion of the run, the directionally frozen alloy rod was analyzed spectrographically at 1 1/4-in. intervals.

Jan 1, 1961

By Robert Lowrie

Nine intermetallic compounds were tested in tension at various temperatures. Seven exhibited extensive plastic deformation at elevated temperatures. Correlations of tensile strength and elongation are attempted with melting (decomposition) temperature, valence electron configurations of the component elements, heat of formation, crystal structure, density, and volume decrease accompanying compound formation. A LTHOUGH intermetallic compounds have been -tX known for many years, the study of their mechanical properties, particularly in tension, is just beginning. The problem has been unattractive because of the well-known, erratic behavior of brittle materials tested in tension. The strong influence of surface or internal flaws as stress raisers in non-ductile materials and the effect of eccentricity of loading in superimposing bending stresses on the state of tension in the specimen are extremely difficult to mitigate and impossible to completely eliminate. Thus, tensile properties determined for brittle materials, such as intermetallic compounds at temperatures low in comparison to their melting points, are at best only general guides to the values to be expected in an ideal test of a perfect specimen of the material. It is, nevertheless, surprising that apparently no attempt was made to follow up the pioneer work of Tammann and Dahl1 in this field. Working with crude apparatus, these investigators succeeded in showing unequivocally that at temperatures sufficiently close to their melting points (from 75" to 400°C for the compounds tested) intermetallic compounds did exhibit plasticity. This was indicated by the appearance of slip lines on the surface of the specimen. No observations of strength were made in these tests, which were of a compressive or indentation type. Rossi2 in 1932 attempted to study the physical and mechanical properties of single crystals of a group of intermetallic compounds. However, he was able to prepare only one material, Cu2Z8,, in the form of large, defect-free, single crystals. Thus, he was able to report only the relative fragility of the compounds at room temperature. He reported one compound, Ag,Zn,, to be somewhat plastic at room temperature and Cu,Si to be friable, the latter in agreement with results reported herein. Although test results are available only in classified literature, it has also been announced that MoSi, possesses some ductility at elevated temperatures." In 1948 and 1949 Savitskii and Savitskii and Baron -ublished their work on the hot extrusion of Mg-Zn, Al-Mg, and Cu-Zn compounds. Under the favorable state of stress existing for this process MgZn, MgZn,, MgZn,, ß (Al-Mg), ? (Al-Mg) and 0 (Cu-Zn) could be reduced by amounts up to 90 pct at elevated temperatures. These authors also report that hardnesses of Mg-Zn compounds decrease from room temperature values of about 300 kg per sq mm to 30 to 50 kg per sq mm at 325°C. They found that alloys consisting solely of one Mg-Zn compound were most resistant to softening on heating, mixtures of a compound and eutectic less resistant, and mixtures of two compounds least resistant. The more rapid softening of mixtures of

Jan 1, 1953

By M. T. Hepworth, W. B. Sample

HYDROGEN solubility and linear contraction measurements were made at constant temperature on an alloy of titanium of constant oxygen-to-titanium molal ratio but variable hydrogen content. A cylindrical specimen of titanium (0.25 by 1.6 in.) containing 0.75 at. pct 0 and less than 0.03 at. pct N was cast from a master button of iodide process titanium which had been alloyed with titanium dioxide. Four vacuum fusion analyses, which were made along the length of the cylinder after the hydrogen solubility studies were made, revealed a variation of oxygen content of less than 0.02 at. pct. The specimen was introduced into a quartz furnace tube, annealed and outgassedat 1050"~ for about 1 hr, and then held at 800" * 0.5" for about 30 hr, during which latter time experimental data were taken. The leak rate to the furnace chamber was not sufficient to contaminate the specimen during the run as determined by leak-rate studies and vacuum fusion analyses for oxygen and nitrogen before and after the runs. The furnace chamber was attached to a modified Sieverts apparatus used to introduce measured quantities of purified hydrogen to the specimen. A quartz pushrod transmitted changes in length of the specimen to a Chevenard dilatometer. The push-rod passed through a vacuum grease seal to the dilatometer which amplified motion of the rod by a factor of 319. During hydrogen addition, the pushrod did not contact the specimen. Measured quantities of hydrogen were added to the specimen and equilibrium hydrogen pressures recorded as a function of hydrogen content. The solubility data, which appear in Fig. 1, agree well with a separate investigation made with a different apparatus. The solubility limit of the hcp a phase appears as an abrupt discontinuity in slope at 3.4 at. pct H. The solubility plot has been extended as a dashed line at this discontinuity in order to emphasize the discontinuity. The hydrogen content at which bcc P appears is not clearly defined. An arrow indicates solubility data were taken upon hydrogen addition. Upon reaching the arbitrary maximum hydrogen content of the run, the quartz pushrod was pressed against the specimen in order to record the change in length with hydrogen removal. A pressure of about 100 g per sq cm was required to overcome the friction of the vacuum seal in order to obtain reproducible linear contraction data. The contraction ratio ~2/1", change in length divided by original length, was set equal to zero for the maximum hydrogen content. The relative contraction of the specimen was observed upon removal of hydrogen in the following manner. The system was opened to the pumps for a few seconds and an unknown quantity of hydrogen was removed. The system was then isolated from the pumps by closing a stopcock and allowed to return to equilibrium. When the temperature returned to 800°C, the pressure stabilized, and contraction ceased, measurements of contraction and pressure were made. The hydrogen content of the specimen was then deduced by measuring the equilibrium PIydrogen pressure and referring to the solubility plot. Linear contraction was then plotted against interpolated values of atomic percent hydrogen. The justification for this procedure is the established reversibility of the hydrogen equilibrium.' Uniaxial compression was assumed to have no effect on hydrogen pressure. The isothermal linear contraction data are plotted on Fig. 1. An arrow indicates data were taken upon removal of hydrogen. The solubility limits of the two phase a i /3 region can be identified by discontinuities ill slope of the dilatometric plot at 9.1 and 3.4 at. pct H, agreeing well with other studies.' Dashed extensions of the plots emphasize the discontinuities. Isothermal studies of expansion made upon hydrogen addition gave curves of much smaller slope and less pronounced discontinuities. A uniaxial compressive stress tends to accentuate volume changes in going from the more open bcc phase to the hcp phase.2 Incomplete data on ex-

Jan 1, 1962

"The Southern Cross mining district was discovered during the early rush of gold seekers over Montana following the discovery of gold in 1861. Placers were worked near the Atlantic Cable mine in 1866, and soon attention was turned to quartz lode mining. High grade ores were discovered in the North Atlantic claim, adjoining the present Southern Cross group. The early metallurgical treat¬ment of these ores was by means of arrastres, a crude form of amalgamating mill, illustrated on the page opposite. This old arrastre located by the roadside on Warm Springs creek, was built by Barker Bros. in 1879. Further discoveries overtaxed the capacity of this plant, and in 1875 Thomas' Stuart employed a contractor named Jeptha J. Corner to convert the old Wilson & Fifer sawmill located at the Big Spring into an up-to-date gold quartz mill. 'For this trans¬formation Corner received the sum of $1,400.00. The illustrations give a good idea of the nature of its construction. Practically no iron was used in the mill, excepting for the stamps, dies and cams and cam shafts. Whether or not the saving attained reached the limits of present day perfection is not known. There being no steam boilers available, the early prospectors believed in the principle of conservation of fire wood, water power was therefore used, generated by a ""direct-connected"" over-shot wheel. Water for power purposes was supplied by the nearby spring. History fails to record the tonnage treated in this relic of early Montana milling practice.The ores of the Southern Cross district have not proved readily amenable to mill treatment, but being largely composed of iron oxides, they are most desirable fluxing ores for smelter operations. The B. A. & P. Ry. extends into the district. Electric power is furnished by the Flint Creek 'station, three miles distant."

Jan 1, 1913

By S. A. Braley

THE first commercial production of bituminous coal in the United States was in 1820, and formation of acid in the areas from which the coal was removed began at that time. Thus it is 130 years since the development of mine acid began. The coal operator has had to deal with the acid water produced in his mines, and his losses from corrosion of pumps and equipment have been tremendous. Other industries and the public have been forced to spend large amounts for their water requirements because of the acid discharge from the mines. There are many contradictions in the literature on this subject probably because of variations in the analytical procedures followed and differences in the methods of calculation and reporting. The opinions previously expressed may be summarized as follows: The production of mine acid has been looked upon as a simple chemical reaction wherein the oxygen of the air has reacted with pyrite to produce ferrous sulphate and free sulphuric acid. This reaction appears in many chemistry texts and generally has not been considered worthy of further study. Since the measurement of hydrogen ion concentration or activity was developed and expressed in terms of pH, indicator and instrumental methods for pH determination have become readily available, making it natural to think of it as a measure of acid content. Special purpose analytical methods applicable to potable waters, sewage effluents, and boiler waters, based in general upon the determination of what may be regarded as impurities, have been applied to more concentrated solutions constituting mine discharges, without reference to the fact that these specialized procedures had been developed to serve as operating guides for water-treatment plants. It has been assumed that the pounds of acid deliv- Table I. Showing pH and Titratable Acid of Varying Concentrations of Ferrous and Ferric Sulphates Ferric Ferrous ion Acldfty Ion Acidity (Fe+++) ppm CaCO3 We++) ppm CaCOa ppm PA equiv. PPm pH equiv. 11.200 1.80 30,000 11,200 3.98 20,000 5,600 2.01 15,000 5,600 4.15 10,000 2,800 2.21 7,500 2,800 4.41 5,000 1.120 2.48 3,000 1,400 4.68 2.500 560 2.60 1,500 140 5.00 250 280 2.65 750 28 5.00 50 112 2.81 300 56 3.07 150 28 3.38 75 ered by a mine was roughly a constant varying with the number of acres mined, and that the concentration of the acid in the drainage was inversely proportional to the volume of flow. Increased flow was thought to result in a dilution of the acid produced. When the Sanitary Water Board of the Commonwealth of Pennsylvania established a fellowship at Mellon Institute, the first approach to the problem was to review some of the chemical reactions involved and their relation to acid production. Since the sulphates of iron were among the principal constituents of coal-mine drainage, the first studies were based upon solutions of chemically pure ferrous and ferric sulphate. These are both neutral salts, that is, the iron and the sulphate are equivalent, but they produce acid reactions in water solution because as salts of strong acids with weak bases, they hydrolyze to form acid solutions. Solutions of each salt, of varying concentrations, were prepared and the pH, titrable acidity and iron and sulphate

Jan 1, 1952

By Jack White

MUFULIRA Copper Mines, Limited, conducted tests on the concentrator in 1942 to determine which type of ball mill, that is, Conical Trunnion overflow or Cylindrical Grate discharge, produced the greater quantity of finished product at the lowest cost. All the data which follows applies to Mufulira ore and to the particular degree of grinding produced with the classifiers installed at Mufulira concentrator. JACK WHITE, Member AIME, is Concentrator Superzntendent, Mufulira Copper Mines, Ltd., Mufulira, Nortltern Rhodesia. Sun Francisco Meeting, February 1949. TP 2729 B. Discussion of this paper (2 copies) may be sent to Transactions AIME before Feb. 28, 1950. Manuscript received Feb. 28, 1949. Test Procedure: The test was carried out using ball mills No. 1 to 9 (conical trunnion overflow) as the standard with which to compare No. 10 (cylindrical grate discharge mill). The conical trunnion overflow ball mills are 10 ft diam by 72 in., and the cylindrical grate discharge mill is a No. 99. Each mill runs in closed circuit with a Dorr type DSFX classifier 8 ft wide by 30 ft long. The feed is considered as being identical to all ten units. The figures for the test were derived as follows. Dry Tons Milled: For No. 10 unit (cylindrical grate discharge mill) this figure was taken from the ball mill weightometer, which was corrected for error, and then for moisture content. The weightorneter was checked twice a week during the test, and the error did not exceed 3 pct at any time. The moisture was obtained from a 24 hr moisture sample taken by the ball mill operator hourly, and placed in a closed bucket. The sample was cut where the conveyor drops the feed into the ball mill chute. The Mill Sampling Department made a daily moisture determination on this sample. To obtain the dry tons on units No. 1 to 9 the No. 10 figure was deducted from the month's dry tons milled figure, which, in turn, was taken from the crusher weightometer tons corrected for weightometer error and moisture. All tons reported in this test are short tons of 2000 lb. Ball Mill Hours: This was taken daily from the Shift Boss reports giving actual running hours for each unit. Screen Analyses: Coarse Heads (Ball Mill Feed): The monthly composite coarse heads screen analysis, done by the Mill Sampling Department, was used for the minus 200 mesh in the feed to the mills. F. X. Classifier Overflow: The ball mill operators took an hourly 24 hr sample of the overflows of units No. 1 to 9. This was a hand sample, but cut with a special cutter, and is believed to be very reliable. On No. 10 unit, an hourly 24 hr sample, and an hourly shift sample were cut in the same way. These five samples were split, filtered, and dried by the Research Department and were then wet screened on a 200 mesh screen. The average of the three shifts samples on No. 10 unit had to check the 24 hr sample within 1.5 pct to be acceptable. A weighted composite was cut each day from both 24 hr samples, and at the end of each month it was screened as follows: Wet screened through 325 mesh, the plus 325 then screened on a rotap for 15 min through 65, 100, 150, 200, and 325. This was done in duplicate. All splitting, drying, and screening of samples was done by one of the Mill Research staff, to insure accuracy. F. X. Classifier Overflow Densities: These were taken from the Shift Boss reports. Densities were taken by the ball mill operator every hour. Circulating Loads: These were taken a number of times during the test both by direct method (weighing a measured portion of classifier rake sand, and deducting moisture) and by calculation using the formula:

Jan 1, 1951

By M. C. Flemings, R. Mehrabian, G. E. Nereo

Analytical expressions derived previously are used to describe quantitatively effects on macrosegregation of some solidification and mold design variables. Al-4.5 pct Cu alloy is used as example. It is shown that abrupt changes in heat transfer rate result in solute-rich or solute-poor "bands". Severe solute-rich bands accowzpany "reheating" that can result, for example, from abrupt formation of an air gap at a mold-metal interface. With planar isotherms, solute-poor regions also result from reduction in cross section through which fluid flow to feed shrinkage takes place. It is suggested that the negative "cone" of segregation often found at the base of large ingots results from this reduction in cross section for feeding. Consideration is given to the positive and negative segregation to be expected in laboratory ingots in association with changes in ingot cross section. Under-riser positive segregation is considered and it is concluded this segregation results when vertical temperature gradient is low in the region of the riser; the segregation is accentuated by the temperature gradient reversal which can occur in inadequately insulated risers ("'hot tops"). Finally it is shown for Al-4.5 pct Cu alloy that the assumption of constant k and p in analytic solutions gives calculated results close to those obtained for the case of ziariable k and 0. A basic "local solute redistribution equation" was derived earlier' for calculation of macrosegregation resulting from flow of solute-rich liquid to feed solidification shrinkage, thermal contraction, and/or other contractions occurring during solidification. This expression relates fraction liquid, g~, to liquid composition, CL, at a given position x, y, z, in a solidifying Eq. [I] is for the general case of three-dimensional heat and fluid flow assuming constant solid (but not necessarily liquid) density during solidification, negligible net solute change from diffusion, and no pore formation. In this paper we first demonstrate application of this equation for calculation of macrosegregation in several examples involving one-dimensional heat and fluid flow. Specifically considered are examples in which segregation results from sudden changes in heat flow conditions. Next, Eq. [I] is used to describe segregation in examples where isotherms remain planar but where fluid flow is no longer one-dimensional. Application of this expression illustrates the type of segregation to be expected in unidirectionally solidified ingots of gradually or abruptly varying cross section. For segregation calculations, A1-4.5 pct Cu alloy is employed with constant k and p Vz = 0.172, 4 = 0.055), eutectic composition (CE = 33 pct Cu). In all examples, fraction eutectic is neglected in velocity calculations; this was previously shown to introduce little error.' A linear distribution of fraction liquid in the liquid-solid zone is assumed. In a concluding section it is shown that the assumption employed of constant k and /3 gives results close to those obtained when the actual (variable) values of k and 0 are employed.

Jan 1, 1969

By Paul Gordon

The distribution coefficient, k, of interest in zone refining is generally defined as the ratio of the solid to the liquid solubilities of one element in another at the normal melting point of the solvent. In practice, distribution coefficients are frequently calculated from solubilities at temperatures well below the melting point of the solvent, e.g., at a eutectic temperature. This is done because of the general lack of accurate data on the liquidus and solidus curves in most phase diagrams. The practice is equivalent to assuming that the liquidus and solidus curves are straight lines in the temperature range between the melting point of the solvent and the temperature at which data for the solubilities are known. It is recognized that the k values so derived may be in serious error; we have found evidence in recent zone-refining operations that a case in point is silicon in aluminum. The phase diagram found in the literature for silicon in aluminum indicates a eutectic on the aluminum-rich side at 12.5 at. pct Si and at 577°C,1 and a solid solubility of silicon in aluminum at this temperature of 1.59 pct.2 It also shows the liquidus and solidus as nearly straight lines from 577°C to the melting point of aluminum (660°C)1,2 The k value obtained from this data is 0.13. This is almost exactly the same as the k value (about 0.14)' obtained in a similar way for copper in aluminum. Yet we have found by mass-spectrograph analyses* of three bars of zone-refined aluminum that copper is efficiently removed from aluminum by zone refining but silicon is not. Two of the three bars of aluminum were zone-refined in our laboratories, the other in the laboratories of AIAG Metals, Inc. The former two bars, designated bars PG2 and PG3, were 30 in. long by 1 in. in diameter during refining; each was processed in a high-purity graphite boat* and kept under refining stage of the process consisted of thirty unidirectional zone traverses at rates of about 1 to 2 in. per hr, with a zone length of 1 to 2 in. At approximately the middle of the refining period a 6-in. piece of the impurity-laden finishing end of the bar* was cut off and replaced with new start- ing material. Following refining, the purest 20-in. section of the bar (obtained by discarding approximately 2 in. of the starting end and 8 in. of the finishing end of the bar) was leveled and then analyzed. The AIAG bar was 16 in. long and about 1.2 in. in diameter; it was purified by eight passes of a 2-in. zone at a rate of 1.6 in. per hr, the bar being contained in a sintered alumina boat lined with loose alumina powder of the highest purity. Data for the silicon and copper contents of the three refined bars are given in Table I. Derived data for the efficiencies of the zone-refining operations are listed in Table 11. It is clear from these two tables that the copper is removed much more efficiently—by a factor of 10 to 50 times—from aluminum during zone refining than is silicon. For example, in bar PG3 the thirty zone passes reduced the copper content from 10 to 0.02 ppm, i.e., by 500 times, whereas the same treatment lowered the silicon content by only a factor of about 16. It seem virtually certain, therefore, that the distribution co efficient, k, for silicon in aluminum is well above that for copper and is very likely not much below unity. This also implies that the solidus line on the aluminum-rich side of the A1-Si phase diagram is very probably appreciably curved near the aluminum melting point since the phase-diagram data indicate such curvature is unlikely in the liquidus.

Jan 1, 1965

By T. A. Read, M. W. Burkart

The crystal geometry of the cubic-tetragonal interface after partial transformation of an indium-thallium alloy single crystal is described and a general theory is presented. The effects of applied stresses on this transformation are interpreted and the latent heat of transformation is obtained from observations of transformation under stress. A DIFFUSIONLESS phase transformation between face-centered cubic and face-centered tetragonal structures has been reported for the indium-thallium system by Bowles, Barrett, and Guttman1, 2 The transformation takes place at approximately 105 "C at 18 atomic pct Tl and 25°C at 23 pct Tl. In their study, Bowles, Barrett, and Guttman used poly-crystalline samples whereas in the present study single crystals were used to eliminate the transformation constraints imposed by adjoining grains. The use of single crystals made possible a comprehensive study of the effect of stress on the transformation. In the course of the work, it was possible to formulate a new method of analyzing dif-fusionless transformations (presented in this paper) which permits calculation of the geometry of the interphase interface from a knowledge of the crystal structures of the initial and final phases. The specimens were prepared from chemically pure thallium and 99.97 pct In which were weighed out to produce 3 to 4 grams of alloy of the desired concentration. The metal was placed in clean fused silica tubing, then melted, degassed and sealed under vacuum. (To obtain single crystals, it was found that both degassing and extreme cleanliness were essential.) Single-crystal specimens were grown by a modified Bridgman technique.8 pecimens were removed from the tube by dissolving the quartz in concentrated hydrofluoric acid which attacks the specimen very slowly. The specimen then was polished mechanically to produce four flat surfaces, electropolished, and annealed at 140°C for 48 hr. The electropolishing solution used was that described by Bowles, Barrett, and Guttman and the polishing was carried out on both the high and low temperature phases of the alloy. The high temperature polishing was done at 110°C with a stainless steel cathode. Visual Observation of the Transformation in Single Crystals A visual study of the transformation was made on specimens which had been electropolished in the high temperature phase. The specimens were supported on the stage of a metallograph by an electrically heated holder which contained an opening for observing the specimen. Visual evidence of transformation was found in the presence of an interface which separated the two phases. The interface plane defines the boundary of the phase undergoing transformation and manifests itself by the sharp change in angle between the surface of the specimen and the incident light at the juncture of the two phases. On slow cooling, well-annealed specimens transformed from the face-centered cubic structure to the face-centered tetragonal structure by the motion of a single plane interface which traversed the specimen from one end to the other. Upon heating, the interface moved back in the reverse direction. The interface could be started, stopped, or reversed at will. A temperature hysteresis of about 31/2oC was observed in the reversal of the interface. Holding an interface stationary caused it to disappear completely in most cases, whereas in other instances the interface became less distinct depending upon its orientation. The interface could be made to reappear by changing the temperature of the specimen. The low temperature tetragonal structure exhibits only the fine markings or subbands reported by Bowles, Barrett, and Guttman and is illustrated in Fig. 1. These subbands are twin-related. Back-reflection Laue patterns show the breakup of the cubic spots into pairs of spots corresponding to the twin orientations of the tetragonal phase.

Jan 1, 1954

By Peter M. Fozzard

The San Bartolomt silver deposit was discovered by a United Nations team of geologists working with a counter- part team of staff of the Ecuadorian Government's General Directorate of Geology and Mines (DGGM). The Phase I project over five areas of operation during which this discovery was made was financed through a United Nations Development Program contribution of $860,000 and an Ecuadorian Government participation of about $680,000 equivalent. Existence of mineralization at San Bartolomé was first recognized in 1966 when a reconnaissance geochemical stream-sediment program was carried out over a 10 500 km2 (4,054 sq mile) area centered around the city of Cuenca in southern Ecuador. Over the course of this project more than 10,000 samples of stream-sediment, soil, and rock materials were collected. Average costs per sample were $10.00, as follows: collection, $5; sample preparation, $1.60; assay work, $3.40. Initially in the program (1965-1966) sediments were collected along all motorable roads and tracks. Routine analyses, originally by colorimetry and later by AAS, were for Cu, Pb, Zn and occasionally As, Ni, and Co. Discovery geochemical samples from the San Bartolomé drainage area were among the first to be taken in 1965. As luck would have it, the road along which this traverse was taken passes only some 100 m (328 ft) downstream from the mineralized suboutcrop. The relevant two streams sampled are of inconsequential size, some 1 m (3.3 ft) in width, with a limited flow volume throughout the year. Original anomalies were recognized through cold-extractable Cu/Zn analyses. The pH of all river waters was also recorded at sample sites. Resampling the discovery sediments when AAS became available showed total extractable values of between 150 ppm-300 ppm Zn, 550 ppm Pb, and 10 ppm Ag. In 1967 the first followup was by rough-and-ready means. Dithizone field-kits (THM) were used to rapidly test soils from the surrounding area. The area has no outcrop. This work allowed the definition of an area of interest of some 2 km (1.2 miles) x 500 m (1640 ft). Six approximately 1 km (0.6 mile) to 1.5 km (0.9 miles) lines spaced at approximate 250 m (820 ft) intervals were established and used for IP surveys and soil sampling at 50 m (164 ft) intervals. Where one of the lines crossed the westernmost geochemical discovery creek a first-priority geophysical anomaly coincided with a major Zn/Pb (and later Ag) soil anomaly. A pit was sunk and encountered mineralized vein material at a depth of 1.5 m (5 ft). This lucky glory hole confirmed the geochemical discovery and prompted systematic followup. Immediately, costeaning of the west bank of the discovery creek, the Quebrada Ocashuaico, was carried out and exposed weathered and leached mineralization. Nearly 100 mineralized veinlets ranging in thickness from 0.5 cm (0.2 in.) to 8 cm (3 in.) were exposed across the 180 m (59 1 ft) costean. Sixty mineralized veinlets were determined over a 90 m (295 ft) wide zone. Sampling delineated minable widths averaging between 0.16 and 0.31 kg/t (5 and 10 oz per st) Ag with associated copper (very sporadic) lead and zinc. Over the period 1968- 1972 a considerable amount of detailed work was completed: detailed IP, EM Turam, magnetic and mise-a-la-masse geophysics, very detailed soil- sampling, trenching, drilling and glory-hole drifting, and cross-cutting. Numerous problems were encountered: the area was found to be a most difficult geoelectrical target; zero outcrop; pyrite (nonargentiferous zones) associated with faulting; mineralized groundwater; extensive clay development; loss of diamond drill-core, and no two-dimensional surface information. As the program developed the complexity of the structure was slowly unravelled, using a degree of good guesswork. Apart from photogeological and ground geological mapping at various scales, the following

Jan 1, 1985

By S. A. Hovanessian

Analytical solutions are obtained for calculating the pressure distribution in rectangular fields due to injection and/or producing wells located anywhere within the field. The field is assumed to be homogeneous with either constant pressure or no-flow boundaries. These solutions are extended to include the calculation of average reservoir pressure and permeability from pressure build-up curves. Numerical examples are given to illustrate the application of equations to practical problems. INTRODUCTION Pressure distribution analyses are of considerable importance in the field of reservoir mechanics. A number of papers dealing with this subject have appeared in the petroleum literature. perrinel in 1956 presented a summary of the methods available for pressure build-up calculations and discussed the applicability of each in some detail. More recently (1958), Hazebroek, et a1,2 discussed a theoretical method for obtaining pressure distribution in a radial field. Also in 1958, Nisle3 gave a theoretical solution of the pressure distribution in a field extending to infinity with a partially penetrating line source at the origin. Mathews, et a1,4 applied the method of images to existing solutions for pressure distribution in radial fields and obtained expressions for calculating pressures in bounded reservoirs. However, a literature survey revealed that a general analytical solution for the pressure distribution in a rectangular field, with injection and/or production wells located anywhere within the field, was not available. Such a solution could be used to approximate the pressure distribution in a field the shape of which is nearly rectangular. Furthermore, it could be applied to pressure calculations pertaining to a single well taken from a system of wells which were drilled in a rectangular pattern. In this case the boundaries of the well drainage area are considered to be the perpendicular bisectors of the lines joining the well and its nearest neighbors. The basic problem considered in this paper consists of a rectangular field with either constant-pressure 01 no-flow boundaries and with either an injection or production well located anywhere within the field. The physical properties of the rock and fluids present are considered to be constant. Analytical expressions are obtained for the pressure distribution within the field during the production or injection periods. These expressions, which are infinite series, can be used to evaluate pressure at any point within the field as a function of time and position. For fields containing more than one well (production and/or injection), the solutions for each well acting independently are superposed. That is, at any point in the field, the pressures due to each injection 01. production well acting alone can be algebraically added to give the pressure resulting from all wells acting simultaneously. Evaluation of the series solutions given in this paper is readily accomplished by means of an electronic digital computer; and, in most cases, sufficient accuracy is obtained by setting the upper limits of summation at 20. These solutions are extended to include the calculation of average reservoir pressure and permeability from build-up data. A number of numerical examples are given to illustrate application of the solutions to actual field problems. ANALYTICAL SOLUTIONS The partial differential equation representing the pressure distribution in a homogeneous rectangular field (see Fig. I.), having a single source or sink of strength (2, can be written*

By D. H. Shaffer, W. F. Harris, W. M. Hickam, M. H. Loeffler

Experiments have been performed on the quantitative addition to niobium of enriched isotopes 018 and 017 at the 0.1 - 40 micro-gram level and their subsequent recovery. A measured quantity of molecular oxygen of known isotopic concentration is added to niobium metal by oxidation. Recovery of the enriched isotopes as carbon monoxide is by the vacuum fusion technique. Quantitative determinations of the enriched isotopes are made in standard volumes at constant temperature using accurately calibrated micromanometers and the mass spectrometer as pressure measuring instruments. THE presence of low concentrations of nonmetallic impurities in metals can often adversely affect the physical properties of the metal. The increase in hardness and the embrittlement of refractory metals due to oxygen is well known. In metallurgical studies dealing with the diffusion rates or the effect of oxygen on the physical properties of refractory metals, it is often necessary to add small quantities of oxygen to the metal and later recover the total quantity present. It is desirable, therefore, to establish the accuracy with which microgram quantities of oxygen can be added to niobium and recovered by vacuum fusion. The successful addition of microgram quantities of oxygen to metals by the usual manometric techniques and the subsequent recovery by vacuum fusion is difficult because of the uncertainty in the accurate determination of the quantity of oxygen originally present in the metal and because of the chance of contamination by atmospheric oxygen. In order to minimize these uncertainties earlier workers have added quantities of O16 at levels much higher than the oxygen concentrations that are of interest.'-3 In order to eliminate the uncertainty associated with the O16 additions to metals at low microgram levels, experiments have been performed on the quantitative addition of oxygen highly enriched in O17 and O18 at the 0.1 to 40 pg level to niobium and the subsequent quantitative recovery of the isotopes by vacuum fusion. Since the natural abundance of O17 is 0.04 pct and of 0" is 0.2 pct this enriched oxygen provides a uniqueness from interference not achieved in earlier work.'-= A measured quantity of molecular oxygen of known isotopic concentration is diffused into the metal. Recovery of the isotopes in the form of carbon monoxide is by vacuum fusion. The total quantity of gas is determined in standard volumes at constant tempera- ture using accurately calibrated Consolidated Electrodynamics micromanometers and the mass spectrometer for pressure measurements. The molecular and isotopic composition is determined mass spectrometrically. APPARATUS A schematic of the oxygen addition apparatus is shown in Fig. 1. Take-offs are provided for the attachment of the isotope container and for sample bulbs which are used to transfer samples to the mass spectrometer. Metal valves are used throughout the system including the sample bulbs in order to achieve a vacuum of 10"6 mm Hg. Evacuation is accomplished with a 3-stage oil-diffusion pump backed by a mechanical pump. A liquid nitrogen trap is used to remove condensables and to prevent oil vapor from entering the system. A micromano-meter is used for pressure measurements. The furnace assembly is shown in Fig. 2. It consists of a quartz tube joined to the apparatus through a 40/W joint with Apiezon W low-pressure wax. The furnace cap, also a 40/W pyrex joint, is provided with a pyrex hook. The sample is suspended from this hook with a platinum wire. The total volume of the furnace section is 435 ml. All volumes were determined by expanding a known volume of gas at a known pressure into the evacuated system and re-measuring the pressure. Both the micromanometer used on the oxygen addition system and the micromanometer used on the mass spectrometer were compared to a precision

Jan 1, 1961

By Pol Duwez, Paul Pietrokowsky

Titanium and vanadium form a complete series of solid solutions at temperatures above 885°C. Below 885°C, vanadium is slightly soluble in a titanium (about 1.5 pct V at 650°C) and a two-phase a plus ß region extends to 18.5 pct V at 650°C. The alloys up to 15.0 pct V transform into a supersaturated a solid solution upon rapid cooling from the ß phase. Above 15 pct V the ß phase may be retained. The temperature at which the ß to a' martensite-type transformation takes place decreases steadily from 850°C for 0.5 pct V to 325°C for 12.7 pct V. IN the transition series of the periodic table, the six elements that have a body-centered cubic structure at all temperatures, namely chromium, vanadium, molybdenum, columbium, tungsten, and tantalum, fulfill the conditions required for the existence of complete series of solid solutions with the high temperature (ß) form of titanium. Up to the present time, complete solubility at temperatures above the a to ß transformation of titanium has been observed in the systems Ti-MO,1,2 Ti-Cb,2 Ti-W,³ and Ti-Ta.³ The two remaining elements, vanadium and chromium, have atomic diameters which are not as near that of titanium as the atomic diameters of the four other elements. Both are smaller than titanium and the difference, expressed in percentage of the titanium atomic diameter, is 12.3 pct for chromium and 8.2 pct for vanadium. On this basis, the least favorable conditions for solid-solution formation are therefore encountered in the Ti-Cr system. The early work on the Ti-Cr system4 revealed that up to about 1100°C the solubility of chromium in ß titanium is limited, and an intermetallic phase exists near the stoichiometric composition TiCr2. It was found later' that a continuous series of solid solutions extends across the diagram at higher temperatures, and TiCr2 forms by solid state reaction. It became apparent therefore that complete solubility would also be present in the Ti-V system. The present investigation confirms this possibility. The iodide-refined titanium used in this investigation was purchased from the New Jersey Zinc Co., New York. According to the manufacturer, a typical analysis of this product is 0.0065 pct Mn, 0.0022 pct Fe, 0.0015 pct Cu, and 0.0042 pct Pb. The Vickers hardness number (10 kg load) of the crystalline bar varies between 55 and 80. The vanadium metal was purchased from the Westinghouse Electric Corp., Lamp Div., Bloomfield, N. J. The purity of this metal is probably above 99 pct V. The oxygen content must have been quite low, since a bar about 1/4 in. square could be cold rolled into a ribbon 0.020 in. thick. To prepare the various alloys on the titanium-rich side of the diagram, the titanium rod was machined into cups 1 cm in diam and about 1.5 cm high. Pieces of vanadium, of the proper weight, were cut from the square bars and placed within the cups prior to melting. On the vanadium-rich end of the diagram, single pieces of the metals, in the proper weight pro-

Jan 1, 1953

By R. L. Smith, I. G. Greenfield

The binary system Ga-Sb has been investigated by thermal, X-ray, and metallo-graphic methods. 'The intermetallic compound GaSb melts at 705.9OC and forms a eutectic with antimony at 11.8 atomic pct Ga. This eutectic melts at 589.8OC. A eutectic appears to be formed at 29.8°C but is too close to the composition of pure gallium to be detected. IN the course of an investigation of the semiconducting properties of the intermetallic compound, GaSb, the phase equilibrium between gallium and antimony has been investigated. Recently, the phase diagram of similar systems, such as In-Sb,' In-AS,' and Bi-As3 have been determined. These diagrams have the same general appearance in that an intermetallic compound is formed at 50 atomic pct and a eutectic is formed on both sides of the intermetallic compound. Jenny,& who has been investigating the semiconducting properties of intermetallic compounds, has concluded from thermal data of several alloys that the phase diagram of the Ga-Sb system resembles those mentioned previously. This paper represents a more detailed study of the Ga-Sb equilibrium. Experimental Procedure The gallium that was used to prepare the alloys was obtained from A. D. Mackay Inc. and the Aluminum Co. of America; the latter reported the purity as 99.95 pct. The antimony was obtained from Bradley Mining Corp. who specified a purity of 99.997 pct. Since the intermetallic compound of GaSb was prepared primarily to be used for further studies of the semiconducting properties, additional purification by a standard zone-melting technique under an atmosphere of hydrogen was performed. Hall-effect measurements on this material indicated an impurity content of less than 3 ppm.5 The antimony also was purified by zone melting and used in conjunction with the compound GaSb to make the necessary alloys for the determinations of the antimony-rich side of the phase diagram. The antimony-rich alloys were chill cast in Vycor tubes which were evacuated to a pressure of less than one micron. Since these alloys expand on freezing, precautions were taken to prevent oxidation of the ingot in the event the tube fractured. To insure homogeneity, the brittle alloys were ground and then placed in the furnace for the thermal-arrest determinations. Since the cost of gallium is high, the experimental procedure was complicated somewhat because of the necessarily limited sizes of the melts. In order to economize, the gallium-rich side of the diagram was determined by using a 35 g ingot of pure gallium initially and adding increasing amounts of antimony in order to obtain additional alloys. The furnace used in the determination of the cooling curves is illustrated in Fig. 1. A 2¼ in. quartz tube, sealed at one end, was fitted with a brass flange which was attached with DeKhotinsky cement. The brass collar was water cooled to prevent the cement from softening. An "0" ring was used to provide a seal between the brass collar and the furnace cover. Nichrome ribbon was wound around a 2 ½ in. asbestos-covered copper core which was used to reduce the thermal gradient in the furnace. The insulation consisted of alternate layers of asbestos and aluminum foil surrounded by sil-o-cel refractory and

Jan 1, 1956

By C. S. Smith, Chih-Chung Wang

TURNBULL and his collaborators1,2 have developed the theory of homogeneous nucleation as applied, inter alia, to solidification of liquid metals. Vonnegut³ and Turnbull4 have shown that if a liquid metal is subdivided into small droplets a vast majority of them will undercool very considerably before solidification, generally to as low as about 0.8 of the freezing temperature on the absolute scale. The nuclei effective at small degrees of supercooling in bulk metal seem to be internal or surface heterogeneities, relatively small in number. If the metal is subdivided, those droplets that happen to contain such nuclei will solidify at a temperature not greatly below the true freezing point, but only a small part of the whole volume will be affected and the majority of the drops will under-cool to the much lower temperature at which homo- geneous nucleation occurs as a result of fluctuations. It occurred to one of the authors that an appropriate subdivision to give effective freedom from random nuclei is produced during the solidification of many alloys that contain a minor amount of a phase of low melting point, and that one might then expect marked undercooling of the distributed phase. Experimental: The alloys selected for initial study were copper with minor amounts of lead and bismuth, and aluminum with tin. In all these alloys, the major component freezes at a temperature not much below that of the pure metal, and there is little further change in constitution on cooling until the lower melting point constituent freezes in an almost pure state. Cooling curves were taken using the controlled heat flow method permitting approximate specific heats to be obtained. Chromel-alumel thermocouples were used, with the standard emf tables, since extreme precision was not needed. The crucible (3/4 in. id, 5/16 in. wall) was made of B & W K-20 insulating brick. It held about 10 cc of the alloy being investigated. The cooling rate was 2.5" to 2.9°C per min under a controlled temperature difference of 20°. Approximate specific heats were computed from the inverse rate curves together with data from a blank run and from a standard run with a copper cylinder of known heat capacity. The alloys for investigation were made from high-purity metals (99.99+pct) and cast into graphite molds. The castings were machined to fit the crucible and to provide a hole for the inner thermocouple. Cooling curves were taken after heating to a temperature about 50" above the melting point of the minor, lower melting-point, constituent. Results The lead phase in an alloy of copper with 5 pct lead did not undercool more than 3" below the melting point of lead (327°C) either as cast or after annealing to produce a new dispersion of the liquid phase. A copper-zinc-lead alloy with 23.75 pct zinc and 5 pct lead undercooled more but showed no thermal effect below 319°C. A cast alloy of copper with 5 pct bismuth undercooled to 249°C (M.P. bismuth 27l °C), but once solidification started it was completed at the same temperature. This was anticipated, since the bismuth forms a nearly continuous phase between the grains of copper, and a solid crystal nucleated anywhere would rapidly* con- sume the entire network of liquid, unless the physical continuity of the liquid were broken through volume changes, inadequate fluidity, or gas evolution. Similar arguments apply in the case of copper-lead alloys, where the lead-rich liquid forms a network along grain edges, though not grain faces. In both cases there would be a few isolated particles

Jan 1, 1951

By G. C. Wallick, J. S. Aronofsky

This paper presents an experimental verification of numerical solutions of the differential equation describing the transient flow of an ideal gas through a porous material including gas slip effects. Several experiments previously proposed by one of the authors are described together with the correlation of the experimental results with the numerical solutions. Excellent agreement is shown between experiment and theory, thus demonstrating the validity of both the basic assumption made in the derivation of the differential equation and of the numerical solutions of the differential equation. INTRODUCTION In a recent paper,' one of the authors has discussed a numerical solution of the differential equation describing the unsteady flow of an ideal gas through a porous material. This paper was primarily concerned with the effect of gas slip on the flow behavior. In steady state measurements, Klinkenberg2 and others have observed that the apparent gas permeability Kn of a porous material may be expressed as a linear function of the reciprocal average pressure 1/P of the form, ka = b + m/P........(1) where the intercept b is a constant for a given porous material and the slope m is a constant for a given porous material-gas combination. Aronofsky1 assumed that Equation (1) could be used to describe transient flow if P was replaced by the average pressure in an infinitesimal volume element. A number of numerical solutions of the resultant differential equation were presented and specific flow experiments were proposed as a means of testing the numerical solutions. The purpose of the present paper is to describe the results of several of these experiments and the correlation of the experimental data with the results of the numerical analysis. Reference should be made to the previous paper' for details of the mathematical and numerical analysis. EXPERIMENTAL PROCEDURE A simplified schematic drawing of the experimental apparatus is shown in Fig. 1. An 8.89 cm diameter limestone core of length L = 14.82 cm was mounted in a conventional rubber sleeve permeameter cell. The external sleeve pressure in this cell was maintained equal to 500 psig during all experimental tests, thus permitting only longitudinal flow through the core. One end of the core, X = L, was connected to an adjustable cavity of volume V as well as a pressure gauge or manometer. The other end of the core, X = 0, was connected to a Nullmatic pressure regulator which was in turn connected to a nitrogen cylinder or vacuum pump. In each experiment, the core and adjacent dead volume were charged with nitrogen to a uniform gas pressure P1. The pressure at X = 0 was then suddenly raised or lowered to a constant pressure P, and the resulting pressure buildup or pressure decline at X — L was recorded as a function of the time. The porosity + and the permeability constants m and b were determined using the transient method which was suggested by the results of the numerical analysis and which was described in the earlier paper.' The following average values for these constants were obtained as a result of 19 separate evaluations: 171 -0.259 2 0.005 md-atm; b = 0.374 5 0.008 md; and F = 0.098 ± 0.005*. It should be noted that in order that transient phenomena will be slow enough to be observed conveniently, it is desirable to use a porous material of very low permeability, e.g., less than I md. Moreover, it is in this low permeability range that the gas slip effects are most significant. Thus, such a low permeability sample is very suitable for use in an experimental verification of the numerical solutions previously described.

Jan 1, 1955