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By Mark J. Klein

The creep of 043 was studied over the temperature range 1650" to 3200°F and over the stress range 3000 to 44,000 psi. The steady-state creep rate over this range of stress and temperature can be expressed by the equation where A is a constant, is the stress, and is -0.8 x 103 psi-'. Over a narrow range of stress variations c0 a and for this proportionality n varies from 3 to 30 in accordance with the relation n = aB. Above about 2400° F, H, the apparent activation energy for creep, is 110,000 cal per mole, a value about equal to that estimated for self-diffusion in this alloy. Below 2400°F, H increases with decreasing temperature reaching a value of -125,000 cal per mole at 1700° F. In this temperature region, H appears to be a function of the interstitial concentration of the alloy. MOST of the detailed creep studies of dispersion strengthened metals have been concerned with metals having fcc structures. However, there are a number of important refractory alloys with bcc structures that derive part of their high temperature strength from an interstitial phase and whose creep behavior has not been well defined. This paper describes the creep behavior of the bcc alloy, D43, over the temperature range 1650" to 3200°F (0.4 to 0.7 Thm) and over the stress range 3000 to 44,000 psi. In addition to colum-bium, this alloy contains 10 pct W. 1 pct Zr, and sufficient carbon (-0.1 pct) to form a carbide dispersion throughout the matrix of the alloy. The effects of variations in temperature and stress on the steady-state creep rate of this alloy are presented in this paper. EXPERIMENTAL PROCEDURES Creep tests were made in a vacuum of 106 torr under constant tensile stress conditions using a Full-man-type lever arm.' Creep specimens were machined from 0.020-in. D43 sheet (grain size -5 x l0-4 in.) processed in a duplex condition (solution annealed -2900°F, 40 pct reduction in area, aged 2600°F). The specimens were tested in this condition without further heat treatment. Specimen extensions over 1-in. gage lengths were continuously recorded using a high temperature strain gage extensometer. Differential temperature and stress measurements were used to determine temperature and stress dependencies of the creep rate. Activation energies were calculated from the changes in strain rate induced by abrupt shifts in the temperature during constant stress creep tests. The 100°F temperature shifts used in most of the activation energy determinations required 15 to 90 sec depending upon the temperature at which the shift was made. The dependence of strain rate on stress was determined by measuring the change in strain rate for incremental stress reductions during constant temperature tests. It has been shown that columbium-base alloys such as D43 are susceptible to contamination by gaseous interstitial elements during vacuum heat treatments.' In this regard, it is unlikely that these alloys can be heat treated without some loss or gain of interstitial elements despite the precautions taken to control the heat treating environment. However, several factors suggest that changes in interstitial concentrations of the specimens during testing did not affect the results presented in this paper. First, the dependence of the creep rate on the stress or temperature determined during the course of a single creep test showed no variations with the duration of the test. A variation would be expected if a loss or gain in interstitial concentration during the course of the test affected results. In addition, precautions taken during this investigation to minimize interstitial contamination by wrapping the gage lengths of the specimens with various foils2 (Mo, Ta, W) did not produce a detectable change in the stress and temperature dependencies relative to the unwrapped specimens. The averages of duplicate analyses for carbon and oxygen in several specimens determined before and after creep testing are listed in Table I. The combined nitrogen and hydrogen concentrations which were ordinarily less than 50 ppm did not change in a detectable way with creep testing. The analyses show that only minor changes in carbon concentration occurred during creep testing except for specimen 4. This specimen which was tested at 3100°F lost a significant amount of its carbon concentration to the vacuum environment. Specimen 1 gained 100 ppm of O, while specimens 2, 3, and 4, which were tested at progressively higher temperatures, lost increasing portions of their initial oxygen concentrations during testing. RESULTS AND DISCUSSION The Temperature Dependence of the Creep Rate. The apparent activation energy for creep, H, was de-rived from creep curves similar to that shown in Fig. 1. Steady-state creep was rapidly attained at the beginning of the test and with each change in temperature. This behavior suggests that the alloy rapidly attains a stable structure with each shift in temperature or that the structure is constant throughout the test. Since the dispersion will tend to stabilize the structure, the latter is probably the case. The activation energy was found to be independent of the direction of the temperature shift and the magnitude of the shift (50" or 100°F). Although H was approximately independent of the strain, there was a tendency for it

Jan 1, 1970

By Oliver Bowles

ALTHOUGH Oliver Bowles retired as chief of the nonmetal economics division of the Bureau of Mines last year, that retirement has not lessened his active interest in the field of nonmetallic minerals, in writing, nor in his hobby, cultivation of African violets. Excellent co-ordination of the timing of a professional meeting and a flower show permitted him on at least one occasion to attend technical sessions and take in the African violet exhibition which happily arrived simultaneously in one city. Dr. Bowles celebrated his seventieth birthday on Jan. 10, 1947, and

Jan 1, 1948

By AIME

Generally speaking, the mining industry had a good year in 1948 with most mineral products being produced in record quantities for peacetime standards. The big boys-iron and steel, coal, and petroleum-indicated the industry-wide trend by surpassing 1947 production figures. Although exploration and expansion are being pushed aggressively in all branches of the industry, there is a pronounced trend to engineering and research directed at cutting production costs, improving the product, and finding new markets. These improvement campaigns are making headway; in the bituminous coal industry, 5.43 tons per man employed is the new production record; 83 million tons of iron ore were unloaded at lower Lake ports, breaking another peacetime record; magnesium, due to improvement in manufacturing techniques, now competes on the market with aluminum.

Jan 1, 1949

By Theodore Marvin

USE of airplanes to facilitate mining and petroleum operations has definitely left the "doubting Thomas" stage. As a matter of fact, front pages no longer record the novelty of this efficient arm of the mineral industry. We are now down to the facts basis. The recent aviation issue of Engineering and Mining Journal added - to our fund of knowledge on applications which the A.I.M.E. Aviation Committee is extensively adding to through its world-wide compilation of specific data. Another indication of the advance of flying in our. industries is the addition of regular aviation specialists to the staffs of various mining and petroleum companies, who function in the organization the same as do the metal

Jan 1, 1936

By William E. Hughes, Roderick K. Davey

The objective of this chapter is to review and discuss interpolation techniques commonly in use in the mining Industry today, including simple examples. This chapter will not attempt to compare the relative accuracy of each technique as this subject has adequately been covered by several authors (Knudsen and Kim, 1967; David, 1974; and Barnes, 1979) When appropriate, methods will be compared relative to the results of simple examples and computational ease. The examples presented are based on metallic deposits. The techniques, however, are not restricted to metallic deposits and can generally be applied to nonmetallic ones. The purpose of interpolation, as applied to a mineralized deposit, 1s to extend the knowledge of the grade and geology of localized samples to an estimate of the grade and mineralogy of a larger block of ground or even an entire deposit. The word interpolation means to compute values between given values and is limited to that region between the known values. The distinction between interpolation and extrapolation is important and must be adhered to in the application of these techniques in general, the interpolation must be limited to the area enclosed by verified samples. The methods being discussed can be broadly broken into three categories. ( 1 ) geometrical methods, (2) distance weighting methods, and (3) geostatistical techniques.

Jan 1, 1979

By G. Derge, Ling Yang, G. M. Pound

The specific conductance and its temperature dependence were measured over the entire composition range of the molten Cu2S-CuCI system. At a typical temperature of 1200°C, 10 rnol pet of the ionically conducting CuCl reduced the specific conductance from about 77 ohm-lcm-l for pure Cu2S to about 32 ohm -1cm -1, and 50 mol pet CuCl reduced the conductance to that for pure CuCI—about 5 ohm 1cm1. The nature of electrical conduction in molten Cu2S, FeS, CuCI, and mixtures was studied by measuring the current efficiency of electrolysis at about 1100°C. The Cu2S, FeS, and mattes were found to conduct exclusively by electrons, but addition of 1 5 wt pet CUS to Cu2S produces a small amount of electrolysis. Addition of CuCl to Cu2S suppresses electronic conduction, and ionic conduction reaches almost 100 pet at a CuCl concentration of about 50 mol pet. These facts are interpreted in terms of electron energy level diagrams by analogy to the situation in solids. RESULTS of electrical conductivity studies on molten Cu-FeS mattes as a function of composition and temperature have been reported.' The specific conductances ranged from about 100 ohm-' cm-' for pure Cu2S to 1500 ohm-' cm-1 for pure FeS. This is in sharp contrast with the low specific conductance of molten ionic salts for which the transfer of electricity is by migration of ions in the field. In general, these ionically conducting molten salts, such as NaC1, KC1, CuC1, etc., have a specific conductance of the order of magnitude of 5 ohm-' cm-'. It was concluded on the basis of this evidence that molten FeS and Cu,S exhibit electronic conduction. Pure molten FeS has a small negative temperature coefficient of specific conductance, resembling metallic conduction, while pure molten Cu2S has a small positive temperature coefficient, resembling semi-conduction. The molten Cu2S-FeS mattes follow a roughly additive rule of mixtures, both with respect to specific conductance and temperature coefficient. Savelsberg2 has studied the electrolysis of molten Cu2S and Cu2S + FeS. He concluded that while molten Cu2S is an electronic conductor, there is some ionic conduction in molten Cu2S + FeS3 owing to the formation of the molecular compound 2Cu2S.FeS and its dissociation into Cu1 and FeS2-1 ions. The present work does not verify his results. Chipman, Inouye, and Tomlinson" have studied the specific conductance of molten FeO and report a high specific conductance, about 200 ohm-1 cm-1 of the same order of magnitude as that found for molten mattes, and a positive temperature coefficient. They interpret these results in terms of p-type semiconduction in the ionic liquid by analogy to the situation in solid FeO.1 imnad and Derne' detected appreciable ionization in molten FeO by means of electrolytic cell efficiency measurements. In order to verify the conclusion that electrical conduction in molten Cu2S and mattes is electronic, and to gain further insight into the structure of molten sulfides, the following investigations were carried out in the present work: 1) The specific conductance, s of the molten system Cu2S-CuC1 was measured as a function of temperature over the entire composition range. As discussed later, molten CuCl is an ionic substance. It was thought that if molten Cu2S were simply ionic in nature, addition of small amounts of CuCl might not have a catastrophic effect in lowering the high conductance of the Cu2S. On the other hand, if much electronic conduction occurs, addition of the ionic CuCl should have a large effect in destroying the electronic conduction. 2) The electrolytic cell efficiency of the following molten systems was measured at about 1100°C in specially designed cells: Cu3; Cu2S + FeS, 50:50 by wt; FeS; Cu2S + CuS, 15 wt pet; Cu2S + CuC1, 5.9 to 46.4 mol pet; and CuC1. This gives a direct measure of the fraction of current carried by ions in these melts. Further, the cell efficiency, extrapolated to zero ionic current, is given by cell efficiency = (s leasile + s elexstronic). [1] s lucile for molten CulS would be expected to be no greater than that for molten CuC1, whose s lonle is about 5 ohm-' cm-1, as will be seen in the following. u,.,,.,.,.......for molten Cu,S is of the order of 100 ohm-' cm-'.' Thus, a large increase in cell efficiency from 0 to values of 10 to 100 pet upon addition of CuCl to Cu2S would indicate destruction of the electronic conductance. Conductance Measurements Experimental Procedure—The apparatus and experimental method were the same as those described in detail in connection with the study of electrical conduction in molten Cu,S-FeS mattes.' A four terminal conductivity cell and an ac poten-

Jan 1, 1957

By Robert Bell

THE " Tar-Sands." is the name which has been given to the extensive horizontal deposit of fine Cretaceous sand, blackened by tarry petroleum, which forms the banks of the last or lowest 130 miles of the Athabasca river before it terminates in Athabasca lake. The Cretaceous strata, to which these sands belong, extend northwesterly from Dakota all the way to this lake and for 500 miles beyond it. The Athabasca river forms the uppermost section of the Athabasca-Mackenzie, one of the great rivers of the world. It rises on the Pacific side of the Rocky mountains, westward of Edmonton, and flows north of east to a point called Athabasca. Landing, 100 miles north of Edmonton, where it turns northward and runs about 280 miles before it falls into the west end of Athabasca lake. The section of this river-system which discharges the lake just named into Great Slave lake, is called Slave river, and below the latter lake it becomes the Mackenzie river. Along the section of 280 miles of the Athabasca river above mentioned, the Cretaceous strata consist of bluish-gray and drab-gray marls, on top, from Athabasca Landing to Drowned rapid, 110 miles down stream; then heavily bedded gray sandstones, 225 ft. in greatest thickness, underlying these, form the banks for about 40 miles further. The strata appear to be horizontal, but they really clip very slightly to the southward. At Drowned rapid, we see the first of the tar-sands resting on almost horizontal beds of bluish-gray limestone of Devonian age. In some places the limestone is associated with shaly or marly bands. Notwithstanding the great hiatus between the two series, the horizontal tar-sands lie conformably upon the almost level upper beds of the limestone wherever the two formations are seen together, all along the river, throughout a

Mar 1, 1908

EDITORIAL comments on the anthracite report of the Federal Fact-finding Coal Commission, which became public on July 5, together with an analysis of its more important conclusions, will be found on another page of this issue. In this place, only a few extracts from the report, bearing more directly on technical matters, can be quoted, for lack of space. COST OF MINING Mining cost, as it stands on the books of each mining company, represents the average cost of the total output, all sizes, of anthracite. Egg coal has at least five times the market value of barley, but these' sizes are mined together and their costs can not be separated. Mine costs directly reflect the conditions under which these deposits of coal are recovered. Even within the few counties in which anthracite is found there is a conspicuous range of natural conditions. The distinc-tion between the Northern, Middle, and Southern field, or, as they are also termed, the Wyoming, Lehigh, and Schuykill regions, is primarily geologic and topo-graphic, but the effects of the natural conditions largely control costs. The contrast is great between Some of the level-lying beds of moderate but fairly constant thickness under the broad Wyoming Valley, where mining and underground haulage present relatively simple problems to the engineer, and the steeply pitching or overturned and faulted beds of variable thickness in the Schuykill field, where crushed coal' and treacherous roof multiply the difficulties of mining; and increase the unavoidable waste. Even more direct is the connection between geologic processes and the, differences in the character of the coal as mined, the varying proportions of large and small sizes demanding differences in preparation and resulting in different average prices realized for the product of the mines.

Jan 8, 1923

By Bauer, Alan

In considering blasting it is necessary to consider the drilling and explosives since one is generally concerned with the total cost of muck of a certain size in the pit or through the crusher. To get a current idea of the drilling situation in open pit mines plotted in Fig. 1 are the drilling costs per ton of material vs. hole diameter for rotary drill holes in large limestone, iron ore and taconite operations. The exception is the 2-in. diam hole which was drilled with a percussion drill in limestone.

Jan 1, 1968

By James Aston

INDICATIVE of the practical importance of the achievement of James Aston , recipient of the Robert W. Hunt Medal for 1930, is the following prosaic item from the financial columns of a recent issue of a New York newspaper. "According to private advices from Pittsburgh, production costs of the A. M. Byers Co. for 1929 were reduced about $5 a ton by the use of the Aston process for making wrought iron pipe. A greater saving is anticipated for 1930, when more of the company?s requirements will be produced by the new method."

Jan 1, 1930

By Richard Kunter

INTRODUCTION Additional work has been done on the CIP circuit at Creede, and a brief description of this work is presented in this paper. DREDGE The original dredge for the Bulldog was built by Al Hack, Inc. of Denver. The dredge cutter head is mounted on a boom made of 6-inch diameter pipe which is raised and lowered by a cable-pulley system. Maximum cutting depth is 8 feet. Slurry from the dredge flows through a floating 6-inch diameter pipe supported on 55-gallon drums which runs from the dredge to the shore and then to a trash screen and pumping system. See Figures 1 and 2. The cutter head, suction pump, winches for dredge movement, and all other operations are controlled from a small operations house located toward the rear of the dredge. All of the basic dredge equipment is mounted on a chassis about 8 ft x 16 ft in size. Additional buoyancy was originally provided by sealed 55-gallon drums supported along the sides of the chassis by a small wooden framework. Additional framework and barrels on the front of the chassis on either side of the cutter boom provided additional stability, particularly when digging in hard material. The dredge was quite stable, but two problems were apparent. For one, it could have been sunk by someone from the shore firing a rifle into all of the barrels. In prime deer-hunting and sportsman country

Jan 1, 1983

By Richard H. Olson, Lawrence A. Roe

Talc, when it can be isolated as a pure mineral, has a composition of 63.36% Si02, 31.89% MgO, and 4.75% H20. However, as an industrial commodity, talc rarely approaches theoretical purity. Nevertheless, the impure talc products of commerce find a multitude of uses and few substitutes in many industrial applications. Minerals commonly associated with and sold together in talcose mixtures are tremolite, chlorite, dolomite, mica, and magnesite. Steatite was originally a mineralogical name applied to pure talc. In today's commerce steatite generally refers to the massive variety of talc suitable for electrical insulator manufacture. Block steatite ore can be machined into various shapes. Impure varieties of massive or block talc are still commonly referred to as soapstone. Soft massive talc, suitable for crayon manufacture, has been referred to as French chalk. It has been common practice to discuss talc, soapstone, and pyrophyllite under the same general heading. In the case of soapstone and talc, this is a natural thing since many different types of platy, soft minerals exhibiting a high degree of lubricity (commonly referred to as "slip") have been grouped together and called soapstone or talc. Further, there is a mineralogical relationship of pyrophyllite to montmorillonite and talc to hectorite. Thus, talc and pyrophyllite are sometimes referred to as clay minerals. When finely divided talc or pyrophyllite are combined with water in proportions to make a slurry, the end product does have the appearance of a clay-water mixture. Soapstone for utensils and ornaments was mined by prehistoric Indians on Santa Catalina Island, CA. In the mid-1800s, soapstone from deposits along the western foothills of the Sierra Nevada mountains was used by white settlers for building and ornamental stone and in the linings and foundations of furnaces (Anon. 1956). Previous to 1916, the annual recorded production in California did not exceed 2000 tons. In the period 1912 to 1918, output rose sharply when the Talc City, Western, and Silver Lake mines were put into operation. From 1916 to 1935, the state's annual output of talc was in the range of 9,000 to 20,000 tons. In the mid-1930s, the use of talc in wall tile grew rapidly. In California, the production of talc grew to 63,000 stpy in 1943. The post-war building boom helped California production to grow to 120,000 tons in 1951. In 1968, production was 165,000 tons, 1969 was 145,000 tons, 1970 was 185,000 tons, and 1972 was 155,000 tons. Talc mining in New York state dates to about 1878 when a Colonel Palmer and associates opened the first commercial talc mine on the Nelson Freeman farm near Talcville, New York. In 1893, this operation was sold to the International Pulp Co. which changed its name to the International Talc Co. in 1944. The company was acquired by R.T. Vanderbilt Co., Inc. in 1974. A new talc operation, the Gouverneur Talc Co. owned by the R.T. Vanderbilt Co., began operations near Balmat, NY, in 1948. The initial capacity of the processing plant was 200 stpd (Gillingham, 1950). Subsequent expansions have increased capacity to over 600 stpd. The Vermont talc industry began just after the start of the 20th century. Talc was discovered in the area of the present Johnson, VT, talc mine in 1902. The American Minerals Co. initiated plant operations at Johnson in 1904. The Magnesia Talc Co. opened a plant at Waterbury, VT, in 1913 (Burmeister, 1963; Trauffer, 1964) and acquired American Minerals Co. in 1923. The Waterbury mine has a long history as a producer of talc crayons. The Eastern Magnesia Talc Co. was formed in 1924 by a merger of the Eastern Talc, Co.

Jan 1, 1983

By R. P. Alger, C. A. Doh, M. P. Tixier

The principle, the equipment and field operation of sonic logging are described. The tfio-receiver system produces logs independent of hole size and mud. Field experience is given and forms the basis for the interpretation of the log. The derivaiion of porosity values from measured velocities is discussed, according to the type of formations (hard formations, compacted sands, and unconsolidated formations). The time-average equation proposed by M. R. J. Wyllie, A. R. Gregory and L. W. Gardner is uscd as a basis for the computation of porosity in limestones, cemented sandstones and compacted sands. Variations in the lithologic character of limestones do not seem to change the porosity calibration markedly. The compaction of sands is related to the compaction of shale adjacent to them; and, thus, the shale velocity is used for the establishtnent of empirical relations for the computation of porosity in un-consolidated formations. Various forrnu.las are tentatively presented to account for shale and fluid content. Field experience demonstrates that considerable attenuation of sonic energy takes place in unconsolidated formations, particularly when gas bearing, and in fractrured formations. Unusually large attenuation produces skipped cycles, a feature easily recognized. The application of sonic logging to structura1 studies is featured, showing its possible integration with the dipmeter. Correlation and its application to the irrterpretation of seisrmic surveys are reviewed. The paper is illustrated with field examples. Sonic logging is the recording of the time required for a sound wave to traverse a definite length of formation. Sonic travel-times are inversely proportional to the speed of sound in the various formations. The speed of sound in subsurface formations depends upon the elastic properties of the rock matrix, the porosity of the formations and their fluid content and pressure. Below the "weathered" or low-velocity layer extending from 50 to 100 ft or so below the surface, sound velocities may range from about 6,000 ft/sec in shallow shales to as much as 34,000 ft/sec in dolomites. In hard formations (well cemented and/or compacted), the sonic log reflects the amount of fluid in the formations; hence, it correlates well with their porosity. In unconsolidated formations, which are usually of fairly high porosity, the sonic log gives an approach to porosity determination, when its readings are corrected for lack of compaction, shaliness, and fluid content. In such formations the sonic log may also indicate the presence of gas and may distinguish between oil- and water-bearing beds. Field experience with the sonic log in soft formations is more limited than that in hard formations. As a result, interpretation in soft formations is not as well developed at the present time. In all types of formations the sonic log is of considerable value for correlation and for the more detailed and accurate interpretation of seismic data. EQUIPMENT AND PRINCIPLE FIELD OPERATION The basic features of the sonic log" are a two-receiver system and two available short spacings. The log is recorded on film using a standard field unit. An SP curve is run along with the sonic curve to give a more interpretable log and to establish absclute depth control for comparison with other logs run in the same well. If desired, a gamma-ray curve may be recorded simultaneously with the sonic curve. Fig. 1 shows the sonic-gamma ray combination sonde. The sonic portion consists of a sound transmitter and three receivers mounted 3, 4 and 6 ft from the transmitter. When the first and second receivers are used, a sonic log of I -ft spacing (distance between receivers) is obtainea. Use of the first and third receivers provides a 3-ft spacing. The transmitter emits pulses at the rate of l0/sec. After the transmission of a pulse the first arrival of sound energy at each receiver triggers its response system. The differ-

By H. C. Brassfield, R. E. Fryxell, E. C. Duderstadt, E. A. Aitken, P. K. Conn

Permeation rates of hydrogen through are-cast tungsten were measured at temperatures from 1300" to 2600°C with hydrogen pressure differentials of 1 and 0.1 atm across isothermal membranes. Rates were nearly Proportional to square root of pressure, were inversely ProPortional to membrane thickness, and were temperature-dependent according to the equation: p = permeation coefficient in cu cm (stp)-mm per sq cm-min-atmlr2, R = gas constant in cal per mole-OK, T = absolute temperature in OK. Permeation rates of oxygen through tungsten were deternlined in the range 1965" to 2300°C and at calculated oxygen (02) pressures of 3.3 x 10-4 to 2.2 x at?n using sealed capsules containing Kmown quantities of tungsten oxide. Permeation coefficients obtained in this manner had a temperature dependency in the range of 40 to 45 kcal per mole of permeating species. Permeation coefficients for oxygen were higher than those for hydrogen in the temperature range studied. This is probably the result of oxygen solubility being much greater than hydrogen solubility at these temperatures at a gzven pressure. The purpose of this investigation was to determine experimentally the permeabilities of hydrogen and oxygen through polycrystalline tungsten at temperatures ranging from 1300° to 2600°C. Permeation rates of hydrogen through tungsten have been measured at temperatures up to 925°C,but no previous measurements have been reported for the temperature range covered in this investigation. Some diffusion measurements3&apos;&apos; and solubility measurements3 have been made for hydrogen at temperatures below 2200°C. No previous permeability studies of oxygen through tungsten are known to the authors; however, efforts have been made to determine diffusion rates5-&apos; and solubilities PERMEATION THEQRY Permeation has been defined by ortton" as the overall steady-state flow process from the gas phase on one side of a membrane or wall to the gas phase on the other side and includes the steps of adsorption, solution, diffusion, exsolution, and desorption; in a given temperature range, any of these processes may be rate-controlling. For diatomic gases, which dissociate prior to diffusion, the quantity of gas which permeates through a membrane or wall at a given temperature is directly proportional to the surface area of the membrane, the length of time of permeation, and the difference between the square roots of the pressures on each side of the membrane, and it is inversely proportional to the thickness of the membrane when diffusion-controlled, thus: q = total amount of gas permeating a membrane, p = temperature-de pendent permeation coefficient, A = area of membrane exposed, / = time, p i = gas pressure of high-pressure side, p2 = gas pressure of low-pressure side, d = thickness of membrane. When the surface reactions are not rate-controlling steps and the solution of the gas in the metal follows Henry&apos;s law, the permeation coefficient, P, is equal to the product of diffusivity and solubility. The permeation coefficient is also temperature-dependent according to the equation: Po = permeation constant, Q = activation energy, R = gas constant, T = absolute temperature. MATERIALS The tungsten materials used in this investigation were greater than 99.9 pct pure. The interstitial impurities ranged from < 1 to 50 pprn C, 7 to 35 ppm O, less than 15 pprn N, and undetectable quantities of hydrogen. Previous high-temperature studies of are-cast tungsten have shown that thermal treatment similar to that which the hydrogen permeation cells experienced reduces the carbon content from starting levels of 50 to 60 ppm to about 30 ppm. Metallic impurities were in the low (1 to 50) ppm range. The argon gas used in this investigation contained about 8 ppm N. None of the following gases were

Jan 1, 1968

By J. Szekely, V. Stanek

Steady state heat transfer and fluid flow rates are predicted for the counter-current contacting of gas and solid streams. For a .fixed pressure drop across the bed the convective heat transfer rate is affected by the gas flow rate, which in turn is affected by the temperature distribution in the system. Variations in bed voidage and in particle size were found to change the predicted temperature profiles quite markedly, in particular when the thermal capacities of the gas and solid streams were equal. IN Part I we examined the effect of step and pulse changes in the inlet gas temperature on transients in the flow of gases through fixed packed beds. Here we shall discuss heat flow and fluid flow interactions in the counter-current heat exchange between packed solids and a gas stream. Counter-current heat exchange in packed beds has been extensively studied. In his now classical paper, Furnas&apos; assumed constant property values and developed a simple analytical. expression for the temperature profiles in the gas and in the solid stream. A highly sophisticated analysis of counterflow systems, allowing for transients and interparticle conduction was developed by Amundsen. In preparing a very readable review of this topic Elliott&apos; also presented a number of elegant solutions, including the case involving heat generation. A great deal of work has been done on the application of these concepts to the modelling of the blast furnace. However, in all this previous work the mass flow of the gas was regarded as a quantity independent of the gas-solid heat exchange process. In the following we shall consider counter-current heat exchange between a gas stream and a packed bed of solids, under conditions where the pressure drop across the bed is specified, rather than the mass flow of the gas. FORMULATION Consider a packed bed, extending from y&apos; = 0 to y&apos; = L, in which moving solids and a moving gas are contacted in a counterflow arrangement. Let cold solids, with an initial temperature Tsi and mass flow GA, enter at y&apos; = L, and hot gas with an initial temperature of Tgi and mass flow Gg enter at y&apos; = 0. In contrast to the problems considered in Part I this system has a nontrivial steady state and we shall restrict our attention to the study of the pressure drop flow relationships and the resultant temperature distributions for steady state conditions. Under these conditions the formulation of the problem requires the statement of the following: 1) heat balance on the gas 2) heat balance on the solids 3) the mechanical energy balance equation and in addition the knowledge of the equation of state, and a functional relationship between viscosity and temperature and an expression for the heat transfer coefficient in terms of the other parameters. On neglecting temperature gradients within the solids and for a constant mass flow of the gas, the solution to this problem is well known.&apos;" The expressions for the temperature profiles of the gas and solid streams may be put in the following form: where Tg and T, denote the dimensionless gas and solid temperatures respectively, y is a dimensionless distance, and R is the ratio of the thermal masses. These quantities are defined as follows: For the particular case of equal thermal mass capacities by the gas and the solid, that is R = 1, the Eqs. [1]and[2] simplify to Eqs. (71 and[8], respectively: i.e., the resultant profiles are linear. As for most practical cases , solutions given by Eqs. [7] and [8] will contain only the inlet temperatures as parameters. For a fixed, predetermined value of C;b the above

Jan 1, 1970

By W. S. Hyler, W. L. Bruckart

The powder metallurgy and arc-cast types of wrought molybdenum stock were studied in rotating beam fatigue. Endurance ratios of unnotched specimens after 5x10 cycles were found to be 0.74 and 0.81, respectively. Fatigue notch factors (K,) of 1.36 and 2.05, respectively, were obtained on V-notched specimens having a theoretical stress-concentration factor Kt = 3.1. MOLYBDENUM and its alloys are rapidly gaining importance as engineering materials of construction for high temperature applications. AS a wrought material, molybdenum and its alloys are outstanding above 1800°F. It is necessary, however, with molybdenum to provide elevated temperature oxidation protection. This is currently being studied by a number of investigators. Thus far, there have been no published data on the fatigue behavior of molybdenum either at room temperature or at elevated temperature. The knowledge of fatigue behavior, particularly notched fatigue behavior, becomes increasingly important as the engineering importance of a material increases, especially from the design standpoint. The work described here was directed toward determination of the notched and unnotched rotating beam fatigue characteristics of molybdenum at room temperature. Also, it was desired to learn whether any difference exists between wrought molybdenum of the powder metallurgy and the are-cast types. Fabrication History of Bar Stock For this work, bar stock was procured from Climax Molybdenum Co. (are-cast type) and from Westing-house Electric Corp. (powder metallurgy type). The processing histories of these materials are listed in Table I. The first lot of are-cast molybdenum was deoxidized by aluminum additions. The second lot was deoxidized by carbon." Both lots of the powder Microstructure A microscopic examination of these materials, as received, revealed the powder metallurgy molybdenum to be free of inclusions and to be finely fibered. On the other hand, the are-cast C molybdenum possessed numerous carbide inclusions, and the arc-cast A appeared to have coarse grained fibers. These are shown in Fig. 1. Owing to the large apparent difference in fineness of fiber between the are-cast A and the powder product and are-cast C, a check was made of the recrystallized grain sizes to determine whether these differences persisted. A series of recrystallization anneals revealed mixed grain sizes in both the are-cast A and the powder product. Variations in grain diameter of as much as 50 times were found after full recrystallization at 1200°C for 30 min. There was no distinction between the two. Arc-cast C was not checked. Room Temperature Mechanical Properties Prior to subjecting the materials to fatigue tests, room temperature mechanical properties were determined. These data, together with the tensil: strength of the notched bars, data,togetherare listed in Table tensil: There were no significant differences in the tensile strengths of the two types of molybdenum. However, the powder metallurgy material was generally more ductile and yielded at a somewhat lower stress than the arc-cast material. Tensile strengths of the notched specimens indicated a slightly greater notch strengthening effect in the are-cast C than in the powder product, lot 2. Room Temperature Fatigue Properties Sample Preparation: Specimens were prepared for use in R. R. Moore rotating beam fatigue machines. These specimens had a continuous radius test section with a minimum diameter of 0.260 in. The specimens were prepared by grinding to shape and polishing to produce a smooth unworked surface. Polishing consisted of rotating a disk in the continuous radius section on which were attached, successively, emery belts of 240, 400, and 600 grit. The specimens were slowly rotated during the operation. The belt speed was high, and rotation was such that polishing scratches were longitudinal. Unnotched Fatigue Properties: Unnotched fatigue data were obtained from a number of specimens of each of the four lots of molybdenum. The results of the tests are presented in Fig. 2. From this figure,

Jan 1, 1956

By G. Derge, Ling Yang, John Henderson

Self-diffusion coefficients of aluminum have been measured by the capillary reservoir technique in liquids of the CaO-SiO2-Al2O3 system containirg equimolar portions of CaO and SiO2, in the temperature range 1400o to 1520oC. For the melt containing 6.0 mole pct Al2O3 the results can be expressed by the equation D = [(4.3 * 0.3) x 104] exp [(-85,000 * 17,500)/RT]cm~sec-&apos;; for the melt containing 12.5 mole pct Al2O3, by the equation D = (5.4 i 0.2) exp [(-60,000 * 10,00O)/RT] cm2sec-: A concept of the constitution of these melts has been developed which proposes that the ratios O/(Si +Al) and Al2 O3/CaO determine the dominant species present. In recent years considerable work has been done on the system CaO-SiO2-A12O3 with a view to elucidating the structure of liquids of this system. Conductivity,&apos; electromotive force, 3 density,4 and activity5 measurements have all contributed to an understanding of the problem, but as yet there is no entirely satisfactory theory that can account for all the observed experimental results. In principle, measurements of self-diffusion coefficients should give further information which is not obtainable in other ways. Self-diffusion coefficients for calcium, silicon,6 and oxygen7 have been measured. The present investigation extends the series of self-diffusion coefficient measurements to include aluminum and develops a concept of constitution for liquids of this system which is compatible with all the observed experimental results. EXPERIMENTAL The technique used in the measurement of the self-diffusion coefficient of aluminum was the capillary-reservoir method,8 A126 being incorporated in the melt contained in the capillary and inactive aluminum in the reservoir melt. This method was chosen because it minimizes convection currents&apos; in the diffusion zone. It has the further advantage that the boundary conditions are such that a slight modifica- tion of Anderson and saddington&apos;s8 solution of Fick&apos;s Law yields an equation which requires measurements only of the length and the initial and final average specific activities of the solidified melt within the capillary. where t is the diffusion time, Co is the average specific activity of the melt contained in the capillary at t = O, C is the average specific activity of the melt contained in the capillary at t = t, 1is the length of the capillary, and D is the self-diffusion coefficient. The equation is of somewhat different form than those previously applied to high temperature diffusion studies because the specific activity of the melt in the reservoir was negligible both before and after diffusion. The diffusion apparatus is shown schematically in Fig. 1. It consisted of a silicon carbide resistance furnace containing the inactive melt in a graphite crucible, internal dimensions 7/8 by 4 in., enclosed in a 1 1/4- by 1 1/2- by 30-in. McDanel tube. A 3/8-in. McDanel thermocouple sheath to which graphite radiation shields and a graphite protection tube were affixed, was used to hold the capillaries. By moving this sheath through a rubber seal at the top of the McDanel tube the capillaries could be lowered into or raised out of the melt. Temperature was measured with a Pt-Pt 13 pct Rh thermocouple which was calibrated periodically against a standard couple. The furnace temperature was controlled to ± 5°C through the thermocouple immersed in the melt. Temperature variation over the depth of the melt was less than ± 3°C. The inactive melts were prepared from pure native quartz, assaying better than 99.9 pct SiO2, A.R. grade A12O3 and A.R. grade CaCO,. The same quartz and CaCO3 were used in preparing the active melts, the

Jan 1, 1962

By William Hurst, A. F. van Everdingen

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst&apos; shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.&apos; The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy&apos;s equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949

By R. E. Collins

The existence of fluid migration across fixed boundaries in oil and gas reservoirs has been known for many years. Several techniques have been developed in the past for estimating The rate of migration across fixed boundaries as an aid in planninng field development and in the valuation of oilfied properties. The principal de/errc7nt to the use of these techniques lies in the rather extensive reservoir and field data required for ca1cula1ion.s of fluid migration. For this reason, a new, simplified procedure has been developed which makes possible the calculation of fluid migration with a minimum of field and resrvoir data. This new technique is based on certain. solutions of the differential equations describing flour in the reservoir which assume, for the portion of the reservoir of interest, that the formation can be approximated by a homogeneous rock of uniforrn thickness, that only a Single mobile fluid phase exists, and {hut fluid production at the well is solely a result of expun.rioti of rile resersoir fluds. The results of the, present work are compiled in a set of curves. These curves can he used to calculate both rule and cummulative fluid migration when the abovc assumptions ore ju.r/ifiril. The only data required for such calcu1ations are the production hisrories of all wells in the field, the permeability and porosity of the reservoir., the, compressibility and viscosity of the fluid. and the shape of the reservoir, INTRODUCTION The migration of fluids across fixed boundaries in oil and gas reservoirs has long been recognized as an engineering and economic problem, but no methods for estimating the extent of migration during the development stage of a reservoir have been published. The investigation reported here has been directed toward providing a simple technique for estimating the extent of such migration and has therefore been restricted to the simple case of a homogeneous reservoir of uniform thickncss containing compressible liquids. It is assumed that only a single mobile fluid phase exists and that fluid production at the wells is solely by expansion of the reservoir fluids. Obviously, few, if any. reservoirs conform to these assumptions during their entire productive life. On the other hand, most reservoirs approximate fluid expansion reservoirs during their initial stages of primary production. Consequently, the present work should be applicable during the field development of most reservoirs, regardless of whether or not they ultimately are gas cap, dissolved-gas, or water-drive reservoirs. The mathematical analysis of this problem has been outlined in the Appendix, while the results of the investigation are presented in the following discussion. DISCUSSION OF CALCULATION PROCEDURE SLNGLE Well, Ini-iimite Reservoir The procedure for calculating fluid migrations is based on solutions of the partial differentia1 equations describing the flow of a homogeneous compressible liquid in a homogeneous reservoir of uniform thickness. This differential equation has the form of the well-known diffusion equation. The equation, as applicable to our problem, is where p is fluid density, is porosity, EL is viscosity, c is compressibility,* and k is permeability; .r, y and t are the space coordinates and time. Derivation of this equation is given in the Appendix. The analytical solution of this equation for a single well of negligible radius producing at a constant rate. q, from a reservoir of infinite areal extent for a time, 1. can he readily obtained. From this solution the rate of flow and also the cumulative flow across a straight line segment of length, 1, at a perpendicular distance. 6. from the well can be computed. One end of the line must be on the perpendicular joining the well to the

By A. F. van Everdingen, William Hurst

For several years the authors have felt the need for a source from which reservoir engineers could obtain fundamental theory and data on the flow of fluids through permeable media in the unsteady state. The data on the unsteady state flow are composed of solutions of the equation Two sets of solutions of this equation are developed, namely. for "the constant terminal pressure case" and "the constant terminal rate case." In the constant terminal pressure case the pressure at the terminal boundary is lowered by unity at zero time, kept constant thereafter, and the cumulative amount of fluid flowing across the boundary is computed, as a function of the time. In the constant terminal rate case a unit rate of production is made to flow across the terminal boundary (from time zero onward) and the ensuing pressure drop is computed as a function of the time. Considerable effort has been made to compile complete tables from which curves can be constructed for the constant terminal pressure and constant terminal rate cases, both for finite and infinite reservoirs. These curves can be employed to reproduce the effect of any pressure or rate history encountered in practice. Most of the information is obtained by the help of the Laplace transformations, which proved to be extremely helpful for analyzing the problems encountered in fluid flow. The application of this method simplifies the more tedious mathematical analyses employed in the past. With the help of Laplace transformations some original developments were obtained (and presented) which could not have been easily foreseen by the earlier methods. INTRODUCTION This paper represents a compilation of the work done over the past few years on the flow of fluid in porous media. It concerns itself primarily with the transient conditions prevailing in oil reservoirs during the time they are produced. The study is limited to conditions where the flow of fluid obeys the diffusivity equation. Multiple-phase fluid flow has not been considered. A previous publication by Hurst&apos; shows that when the pressure history of a reservoir is known, this information can be used to calculate the water influx, an essential term in the material balance equation. An example is offered in the literature by Old² in the study of the Jones Sand, Schuler Field, Arkansas. The present paper contains extensive tabulated data (from which work curves can be constructed), which data are derived by a more rigorous treatment of the subject matter than available in an earlier publication.&apos; The application of this information will enable those concerned with the analysis of the behavior of a reservoir to obtain quantitatively correct expressions for the amount of water that has flowed into the reservoirs, thereby satisfying all the terms that appear in the material balance equation. This work is likewise applicable to the flow of fluid to a well whenever the flow conditions are such that the diffusivity equation is obeyed. DIFFUSITY EQUATION The most commonly encountered flow system is radial flow toward the well bore or field. The volume of fluid which flows per unit of time through each unit area of sand is expressed by Darcy&apos;s equation as where K is the permeability, the viscosity and aP/ar the pressure gradient at the radial distance r. A material balance on a concentric element AB, expresses the net fluid traversing the surfaces A and B, which must equal the fluid lost from within the element. Thus, if the density of the fluid is expressed by p, then the weight of fluid per unit time and per unit sand thickness, flowing past Surface A, the surface nearest the well bore, is given as The weight of fluid flowing past Surface B, an infinitesimal distance 6r, removed from Surface A, is expressed as

Jan 1, 1949